GeographicLib  2.0
GeodesicExact.cpp
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1 /**
2  * \file GeodesicExact.cpp
3  * \brief Implementation for GeographicLib::GeodesicExact class
4  *
5  * Copyright (c) Charles Karney (2012-2022) <charles@karney.com> and licensed
6  * under the MIT/X11 License. For more information, see
7  * https://geographiclib.sourceforge.io/
8  *
9  * This is a reformulation of the geodesic problem. The notation is as
10  * follows:
11  * - at a general point (no suffix or 1 or 2 as suffix)
12  * - phi = latitude
13  * - beta = latitude on auxiliary sphere
14  * - omega = longitude on auxiliary sphere
15  * - lambda = longitude
16  * - alpha = azimuth of great circle
17  * - sigma = arc length along great circle
18  * - s = distance
19  * - tau = scaled distance (= sigma at multiples of pi/2)
20  * - at northwards equator crossing
21  * - beta = phi = 0
22  * - omega = lambda = 0
23  * - alpha = alpha0
24  * - sigma = s = 0
25  * - a 12 suffix means a difference, e.g., s12 = s2 - s1.
26  * - s and c prefixes mean sin and cos
27  **********************************************************************/
28 
31 
32 #if defined(_MSC_VER)
33 // Squelch warnings about potentially uninitialized local variables and
34 // constant conditional expressions
35 # pragma warning (disable: 4701 4127)
36 #endif
37 
38 namespace GeographicLib {
39 
40  using namespace std;
41 
43  : maxit2_(maxit1_ + Math::digits() + 10)
44  // Underflow guard. We require
45  // tiny_ * epsilon() > 0
46  // tiny_ + epsilon() == epsilon()
47  , tiny_(sqrt(numeric_limits<real>::min()))
48  , tol0_(numeric_limits<real>::epsilon())
49  // Increase multiplier in defn of tol1_ from 100 to 200 to fix inverse
50  // case 52.784459512564 0 -52.784459512563990912 179.634407464943777557
51  // which otherwise failed for Visual Studio 10 (Release and Debug)
52  , tol1_(200 * tol0_)
53  , tol2_(sqrt(tol0_))
54  , tolb_(tol0_ * tol2_) // Check on bisection interval
55  , xthresh_(1000 * tol2_)
56  , _a(a)
57  , _f(f)
58  , _f1(1 - _f)
59  , _e2(_f * (2 - _f))
60  , _ep2(_e2 / Math::sq(_f1)) // e2 / (1 - e2)
61  , _n(_f / ( 2 - _f))
62  , _b(_a * _f1)
63  // The Geodesic class substitutes atanh(sqrt(e2)) for asinh(sqrt(ep2)) in
64  // the definition of _c2. The latter is more accurate for very oblate
65  // ellipsoids (which the Geodesic class does not attempt to handle). Of
66  // course, the area calculation in GeodesicExact is still based on a
67  // series and so only holds for moderately oblate (or prolate)
68  // ellipsoids.
69  , _c2((Math::sq(_a) + Math::sq(_b) *
70  (_f == 0 ? 1 :
71  (_f > 0 ? asinh(sqrt(_ep2)) : atan(sqrt(-_e2))) /
72  sqrt(fabs(_e2))))/2) // authalic radius squared
73  // The sig12 threshold for "really short". Using the auxiliary sphere
74  // solution with dnm computed at (bet1 + bet2) / 2, the relative error in
75  // the azimuth consistency check is sig12^2 * abs(f) * min(1, 1-f/2) / 2.
76  // (Error measured for 1/100 < b/a < 100 and abs(f) >= 1/1000. For a
77  // given f and sig12, the max error occurs for lines near the pole. If
78  // the old rule for computing dnm = (dn1 + dn2)/2 is used, then the error
79  // increases by a factor of 2.) Setting this equal to epsilon gives
80  // sig12 = etol2. Here 0.1 is a safety factor (error decreased by 100)
81  // and max(0.001, abs(f)) stops etol2 getting too large in the nearly
82  // spherical case.
83  , _etol2(real(0.1) * tol2_ /
84  sqrt( fmax(real(0.001), fabs(_f)) * fmin(real(1), 1 - _f/2) / 2 ))
85  {
86  if (!(isfinite(_a) && _a > 0))
87  throw GeographicErr("Equatorial radius is not positive");
88  if (!(isfinite(_b) && _b > 0))
89  throw GeographicErr("Polar semi-axis is not positive");
90  C4coeff();
91  }
92 
94  static const GeodesicExact wgs84(Constants::WGS84_a(),
96  return wgs84;
97  }
98 
99  Math::real GeodesicExact::CosSeries(real sinx, real cosx,
100  const real c[], int n) {
101  // Evaluate
102  // y = sum(c[i] * cos((2*i+1) * x), i, 0, n-1)
103  // using Clenshaw summation.
104  // Approx operation count = (n + 5) mult and (2 * n + 2) add
105  c += n ; // Point to one beyond last element
106  real
107  ar = 2 * (cosx - sinx) * (cosx + sinx), // 2 * cos(2 * x)
108  y0 = n & 1 ? *--c : 0, y1 = 0; // accumulators for sum
109  // Now n is even
110  n /= 2;
111  while (n--) {
112  // Unroll loop x 2, so accumulators return to their original role
113  y1 = ar * y0 - y1 + *--c;
114  y0 = ar * y1 - y0 + *--c;
115  }
116  return cosx * (y0 - y1); // cos(x) * (y0 - y1)
117  }
118 
119  GeodesicLineExact GeodesicExact::Line(real lat1, real lon1, real azi1,
120  unsigned caps) const {
121  return GeodesicLineExact(*this, lat1, lon1, azi1, caps);
122  }
123 
124  Math::real GeodesicExact::GenDirect(real lat1, real lon1, real azi1,
125  bool arcmode, real s12_a12,
126  unsigned outmask,
127  real& lat2, real& lon2, real& azi2,
128  real& s12, real& m12,
129  real& M12, real& M21,
130  real& S12) const {
131  // Automatically supply DISTANCE_IN if necessary
132  if (!arcmode) outmask |= DISTANCE_IN;
133  return GeodesicLineExact(*this, lat1, lon1, azi1, outmask)
134  . // Note the dot!
135  GenPosition(arcmode, s12_a12, outmask,
136  lat2, lon2, azi2, s12, m12, M12, M21, S12);
137  }
138 
140  real azi1,
141  bool arcmode, real s12_a12,
142  unsigned caps) const {
143  azi1 = Math::AngNormalize(azi1);
144  real salp1, calp1;
145  // Guard against underflow in salp0. Also -0 is converted to +0.
146  Math::sincosd(Math::AngRound(azi1), salp1, calp1);
147  // Automatically supply DISTANCE_IN if necessary
148  if (!arcmode) caps |= DISTANCE_IN;
149  return GeodesicLineExact(*this, lat1, lon1, azi1, salp1, calp1,
150  caps, arcmode, s12_a12);
151  }
152 
154  real azi1, real s12,
155  unsigned caps) const {
156  return GenDirectLine(lat1, lon1, azi1, false, s12, caps);
157  }
158 
160  real azi1, real a12,
161  unsigned caps) const {
162  return GenDirectLine(lat1, lon1, azi1, true, a12, caps);
163  }
164 
165  Math::real GeodesicExact::GenInverse(real lat1, real lon1,
166  real lat2, real lon2,
167  unsigned outmask, real& s12,
168  real& salp1, real& calp1,
169  real& salp2, real& calp2,
170  real& m12, real& M12, real& M21,
171  real& S12) const {
172  // Compute longitude difference (AngDiff does this carefully). Result is
173  // in [-180, 180] but -180 is only for west-going geodesics. 180 is for
174  // east-going and meridional geodesics.
175  using std::isnan; // Needed for Centos 7, ubuntu 14
176  real lon12s, lon12 = Math::AngDiff(lon1, lon2, lon12s);
177  // Make longitude difference positive.
178  int lonsign = signbit(lon12) ? -1 : 1;
179  lon12 *= lonsign; lon12s *= lonsign;
180  real
181  lam12 = lon12 * Math::degree(),
182  slam12, clam12;
183  // Calculate sincos of lon12 + error (this applies AngRound internally).
184  Math::sincosde(lon12, lon12s, slam12, clam12);
185  // the supplementary longitude difference
186  lon12s = (Math::hd - lon12) - lon12s;
187 
188  // If really close to the equator, treat as on equator.
189  lat1 = Math::AngRound(Math::LatFix(lat1));
190  lat2 = Math::AngRound(Math::LatFix(lat2));
191  // Swap points so that point with higher (abs) latitude is point 1
192  // If one latitude is a nan, then it becomes lat1.
193  int swapp = fabs(lat1) < fabs(lat2) || isnan(lat2) ? -1 : 1;
194  if (swapp < 0) {
195  lonsign *= -1;
196  swap(lat1, lat2);
197  }
198  // Make lat1 <= -0
199  int latsign = signbit(lat1) ? 1 : -1;
200  lat1 *= latsign;
201  lat2 *= latsign;
202  // Now we have
203  //
204  // 0 <= lon12 <= 180
205  // -90 <= lat1 <= -0
206  // lat1 <= lat2 <= -lat1
207  //
208  // longsign, swapp, latsign register the transformation to bring the
209  // coordinates to this canonical form. In all cases, 1 means no change was
210  // made. We make these transformations so that there are few cases to
211  // check, e.g., on verifying quadrants in atan2. In addition, this
212  // enforces some symmetries in the results returned.
213 
214  real sbet1, cbet1, sbet2, cbet2, s12x, m12x;
215  // Initialize for the meridian. No longitude calculation is done in this
216  // case to let the parameter default to 0.
217  EllipticFunction E(-_ep2);
218 
219  Math::sincosd(lat1, sbet1, cbet1); sbet1 *= _f1;
220  // Ensure cbet1 = +epsilon at poles; doing the fix on beta means that sig12
221  // will be <= 2*tiny for two points at the same pole.
222  Math::norm(sbet1, cbet1); cbet1 = fmax(tiny_, cbet1);
223 
224  Math::sincosd(lat2, sbet2, cbet2); sbet2 *= _f1;
225  // Ensure cbet2 = +epsilon at poles
226  Math::norm(sbet2, cbet2); cbet2 = fmax(tiny_, cbet2);
227 
228  // If cbet1 < -sbet1, then cbet2 - cbet1 is a sensitive measure of the
229  // |bet1| - |bet2|. Alternatively (cbet1 >= -sbet1), abs(sbet2) + sbet1 is
230  // a better measure. This logic is used in assigning calp2 in Lambda12.
231  // Sometimes these quantities vanish and in that case we force bet2 = +/-
232  // bet1 exactly. An example where is is necessary is the inverse problem
233  // 48.522876735459 0 -48.52287673545898293 179.599720456223079643
234  // which failed with Visual Studio 10 (Release and Debug)
235 
236  if (cbet1 < -sbet1) {
237  if (cbet2 == cbet1)
238  sbet2 = copysign(sbet1, sbet2);
239  } else {
240  if (fabs(sbet2) == -sbet1)
241  cbet2 = cbet1;
242  }
243 
244  real
245  dn1 = (_f >= 0 ? sqrt(1 + _ep2 * Math::sq(sbet1)) :
246  sqrt(1 - _e2 * Math::sq(cbet1)) / _f1),
247  dn2 = (_f >= 0 ? sqrt(1 + _ep2 * Math::sq(sbet2)) :
248  sqrt(1 - _e2 * Math::sq(cbet2)) / _f1);
249 
250  real a12, sig12;
251 
252  bool meridian = lat1 == -Math::qd || slam12 == 0;
253 
254  if (meridian) {
255 
256  // Endpoints are on a single full meridian, so the geodesic might lie on
257  // a meridian.
258 
259  calp1 = clam12; salp1 = slam12; // Head to the target longitude
260  calp2 = 1; salp2 = 0; // At the target we're heading north
261 
262  real
263  // tan(bet) = tan(sig) * cos(alp)
264  ssig1 = sbet1, csig1 = calp1 * cbet1,
265  ssig2 = sbet2, csig2 = calp2 * cbet2;
266 
267  // sig12 = sig2 - sig1
268  sig12 = atan2(fmax(real(0), csig1 * ssig2 - ssig1 * csig2),
269  csig1 * csig2 + ssig1 * ssig2);
270  {
271  real dummy;
272  Lengths(E, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2,
273  cbet1, cbet2, outmask | REDUCEDLENGTH,
274  s12x, m12x, dummy, M12, M21);
275  }
276  // Add the check for sig12 since zero length geodesics might yield m12 <
277  // 0. Test case was
278  //
279  // echo 20.001 0 20.001 0 | GeodSolve -i
280  //
281  // In fact, we will have sig12 > pi/2 for meridional geodesic which is
282  // not a shortest path.
283  if (sig12 < 1 || m12x >= 0) {
284  // Need at least 2, to handle 90 0 90 180
285  if (sig12 < 3 * tiny_ ||
286  // Prevent negative s12 or m12 for short lines
287  (sig12 < tol0_ && (s12x < 0 || m12x < 0)))
288  sig12 = m12x = s12x = 0;
289  m12x *= _b;
290  s12x *= _b;
291  a12 = sig12 / Math::degree();
292  } else
293  // m12 < 0, i.e., prolate and too close to anti-podal
294  meridian = false;
295  }
296 
297  // somg12 == 2 marks that it needs to be calculated
298  real omg12 = 0, somg12 = 2, comg12 = 0;
299  if (!meridian &&
300  sbet1 == 0 && // and sbet2 == 0
301  (_f <= 0 || lon12s >= _f * Math::hd)) {
302 
303  // Geodesic runs along equator
304  calp1 = calp2 = 0; salp1 = salp2 = 1;
305  s12x = _a * lam12;
306  sig12 = omg12 = lam12 / _f1;
307  m12x = _b * sin(sig12);
308  if (outmask & GEODESICSCALE)
309  M12 = M21 = cos(sig12);
310  a12 = lon12 / _f1;
311 
312  } else if (!meridian) {
313 
314  // Now point1 and point2 belong within a hemisphere bounded by a
315  // meridian and geodesic is neither meridional or equatorial.
316 
317  // Figure a starting point for Newton's method
318  real dnm;
319  sig12 = InverseStart(E, sbet1, cbet1, dn1, sbet2, cbet2, dn2,
320  lam12, slam12, clam12,
321  salp1, calp1, salp2, calp2, dnm);
322 
323  if (sig12 >= 0) {
324  // Short lines (InverseStart sets salp2, calp2, dnm)
325  s12x = sig12 * _b * dnm;
326  m12x = Math::sq(dnm) * _b * sin(sig12 / dnm);
327  if (outmask & GEODESICSCALE)
328  M12 = M21 = cos(sig12 / dnm);
329  a12 = sig12 / Math::degree();
330  omg12 = lam12 / (_f1 * dnm);
331  } else {
332 
333  // Newton's method. This is a straightforward solution of f(alp1) =
334  // lambda12(alp1) - lam12 = 0 with one wrinkle. f(alp) has exactly one
335  // root in the interval (0, pi) and its derivative is positive at the
336  // root. Thus f(alp) is positive for alp > alp1 and negative for alp <
337  // alp1. During the course of the iteration, a range (alp1a, alp1b) is
338  // maintained which brackets the root and with each evaluation of
339  // f(alp) the range is shrunk, if possible. Newton's method is
340  // restarted whenever the derivative of f is negative (because the new
341  // value of alp1 is then further from the solution) or if the new
342  // estimate of alp1 lies outside (0,pi); in this case, the new starting
343  // guess is taken to be (alp1a + alp1b) / 2.
344  //
345  // initial values to suppress warnings (if loop is executed 0 times)
346  real ssig1 = 0, csig1 = 0, ssig2 = 0, csig2 = 0, domg12 = 0;
347  unsigned numit = 0;
348  // Bracketing range
349  real salp1a = tiny_, calp1a = 1, salp1b = tiny_, calp1b = -1;
350  for (bool tripn = false, tripb = false;
351  numit < maxit2_ || GEOGRAPHICLIB_PANIC;
352  ++numit) {
353  // 1/4 meridian = 10e6 m and random input. max err is estimated max
354  // error in nm (checking solution of inverse problem by direct
355  // solution). iter is mean and sd of number of iterations
356  //
357  // max iter
358  // log2(b/a) err mean sd
359  // -7 387 5.33 3.68
360  // -6 345 5.19 3.43
361  // -5 269 5.00 3.05
362  // -4 210 4.76 2.44
363  // -3 115 4.55 1.87
364  // -2 69 4.35 1.38
365  // -1 36 4.05 1.03
366  // 0 15 0.01 0.13
367  // 1 25 5.10 1.53
368  // 2 96 5.61 2.09
369  // 3 318 6.02 2.74
370  // 4 985 6.24 3.22
371  // 5 2352 6.32 3.44
372  // 6 6008 6.30 3.45
373  // 7 19024 6.19 3.30
374  real dv;
375  real v = Lambda12(sbet1, cbet1, dn1, sbet2, cbet2, dn2, salp1, calp1,
376  slam12, clam12,
377  salp2, calp2, sig12, ssig1, csig1, ssig2, csig2,
378  E, domg12, numit < maxit1_, dv);
379  // Reversed test to allow escape with NaNs
380  if (tripb || !(fabs(v) >= (tripn ? 8 : 1) * tol0_)) break;
381  // Update bracketing values
382  if (v > 0 && (numit > maxit1_ || calp1/salp1 > calp1b/salp1b))
383  { salp1b = salp1; calp1b = calp1; }
384  else if (v < 0 && (numit > maxit1_ || calp1/salp1 < calp1a/salp1a))
385  { salp1a = salp1; calp1a = calp1; }
386  if (numit < maxit1_ && dv > 0) {
387  real
388  dalp1 = -v/dv;
389  real
390  sdalp1 = sin(dalp1), cdalp1 = cos(dalp1),
391  nsalp1 = salp1 * cdalp1 + calp1 * sdalp1;
392  if (nsalp1 > 0 && fabs(dalp1) < Math::pi()) {
393  calp1 = calp1 * cdalp1 - salp1 * sdalp1;
394  salp1 = nsalp1;
395  Math::norm(salp1, calp1);
396  // In some regimes we don't get quadratic convergence because
397  // slope -> 0. So use convergence conditions based on epsilon
398  // instead of sqrt(epsilon).
399  tripn = fabs(v) <= 16 * tol0_;
400  continue;
401  }
402  }
403  // Either dv was not positive or updated value was outside legal
404  // range. Use the midpoint of the bracket as the next estimate.
405  // This mechanism is not needed for the WGS84 ellipsoid, but it does
406  // catch problems with more eccentric ellipsoids. Its efficacy is
407  // such for the WGS84 test set with the starting guess set to alp1 =
408  // 90deg:
409  // the WGS84 test set: mean = 5.21, sd = 3.93, max = 24
410  // WGS84 and random input: mean = 4.74, sd = 0.99
411  salp1 = (salp1a + salp1b)/2;
412  calp1 = (calp1a + calp1b)/2;
413  Math::norm(salp1, calp1);
414  tripn = false;
415  tripb = (fabs(salp1a - salp1) + (calp1a - calp1) < tolb_ ||
416  fabs(salp1 - salp1b) + (calp1 - calp1b) < tolb_);
417  }
418  {
419  real dummy;
420  Lengths(E, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2,
421  cbet1, cbet2, outmask, s12x, m12x, dummy, M12, M21);
422  }
423  m12x *= _b;
424  s12x *= _b;
425  a12 = sig12 / Math::degree();
426  if (outmask & AREA) {
427  // omg12 = lam12 - domg12
428  real sdomg12 = sin(domg12), cdomg12 = cos(domg12);
429  somg12 = slam12 * cdomg12 - clam12 * sdomg12;
430  comg12 = clam12 * cdomg12 + slam12 * sdomg12;
431  }
432  }
433  }
434 
435  if (outmask & DISTANCE)
436  s12 = real(0) + s12x; // Convert -0 to 0
437 
438  if (outmask & REDUCEDLENGTH)
439  m12 = real(0) + m12x; // Convert -0 to 0
440 
441  if (outmask & AREA) {
442  real
443  // From Lambda12: sin(alp1) * cos(bet1) = sin(alp0)
444  salp0 = salp1 * cbet1,
445  calp0 = hypot(calp1, salp1 * sbet1); // calp0 > 0
446  real alp12;
447  if (calp0 != 0 && salp0 != 0) {
448  real
449  // From Lambda12: tan(bet) = tan(sig) * cos(alp)
450  ssig1 = sbet1, csig1 = calp1 * cbet1,
451  ssig2 = sbet2, csig2 = calp2 * cbet2,
452  k2 = Math::sq(calp0) * _ep2,
453  eps = k2 / (2 * (1 + sqrt(1 + k2)) + k2),
454  // Multiplier = a^2 * e^2 * cos(alpha0) * sin(alpha0).
455  A4 = Math::sq(_a) * calp0 * salp0 * _e2;
456  Math::norm(ssig1, csig1);
457  Math::norm(ssig2, csig2);
458  real C4a[nC4_];
459  C4f(eps, C4a);
460  real
461  B41 = CosSeries(ssig1, csig1, C4a, nC4_),
462  B42 = CosSeries(ssig2, csig2, C4a, nC4_);
463  S12 = A4 * (B42 - B41);
464  } else
465  // Avoid problems with indeterminate sig1, sig2 on equator
466  S12 = 0;
467 
468  if (!meridian && somg12 == 2) {
469  somg12 = sin(omg12); comg12 = cos(omg12);
470  }
471 
472  if (!meridian &&
473  // omg12 < 3/4 * pi
474  comg12 > -real(0.7071) && // Long difference not too big
475  sbet2 - sbet1 < real(1.75)) { // Lat difference not too big
476  // Use tan(Gamma/2) = tan(omg12/2)
477  // * (tan(bet1/2)+tan(bet2/2))/(1+tan(bet1/2)*tan(bet2/2))
478  // with tan(x/2) = sin(x)/(1+cos(x))
479  real domg12 = 1 + comg12, dbet1 = 1 + cbet1, dbet2 = 1 + cbet2;
480  alp12 = 2 * atan2( somg12 * ( sbet1 * dbet2 + sbet2 * dbet1 ),
481  domg12 * ( sbet1 * sbet2 + dbet1 * dbet2 ) );
482  } else {
483  // alp12 = alp2 - alp1, used in atan2 so no need to normalize
484  real
485  salp12 = salp2 * calp1 - calp2 * salp1,
486  calp12 = calp2 * calp1 + salp2 * salp1;
487  // The right thing appears to happen if alp1 = +/-180 and alp2 = 0, viz
488  // salp12 = -0 and alp12 = -180. However this depends on the sign
489  // being attached to 0 correctly. The following ensures the correct
490  // behavior.
491  if (salp12 == 0 && calp12 < 0) {
492  salp12 = tiny_ * calp1;
493  calp12 = -1;
494  }
495  alp12 = atan2(salp12, calp12);
496  }
497  S12 += _c2 * alp12;
498  S12 *= swapp * lonsign * latsign;
499  // Convert -0 to 0
500  S12 += 0;
501  }
502 
503  // Convert calp, salp to azimuth accounting for lonsign, swapp, latsign.
504  if (swapp < 0) {
505  swap(salp1, salp2);
506  swap(calp1, calp2);
507  if (outmask & GEODESICSCALE)
508  swap(M12, M21);
509  }
510 
511  salp1 *= swapp * lonsign; calp1 *= swapp * latsign;
512  salp2 *= swapp * lonsign; calp2 *= swapp * latsign;
513 
514  // Returned value in [0, 180]
515  return a12;
516  }
517 
518  Math::real GeodesicExact::GenInverse(real lat1, real lon1,
519  real lat2, real lon2,
520  unsigned outmask,
521  real& s12, real& azi1, real& azi2,
522  real& m12, real& M12, real& M21,
523  real& S12) const {
524  outmask &= OUT_MASK;
525  real salp1, calp1, salp2, calp2,
526  a12 = GenInverse(lat1, lon1, lat2, lon2,
527  outmask, s12, salp1, calp1, salp2, calp2,
528  m12, M12, M21, S12);
529  if (outmask & AZIMUTH) {
530  azi1 = Math::atan2d(salp1, calp1);
531  azi2 = Math::atan2d(salp2, calp2);
532  }
533  return a12;
534  }
535 
537  real lat2, real lon2,
538  unsigned caps) const {
539  real t, salp1, calp1, salp2, calp2,
540  a12 = GenInverse(lat1, lon1, lat2, lon2,
541  // No need to specify AZIMUTH here
542  0u, t, salp1, calp1, salp2, calp2,
543  t, t, t, t),
544  azi1 = Math::atan2d(salp1, calp1);
545  // Ensure that a12 can be converted to a distance
546  if (caps & (OUT_MASK & DISTANCE_IN)) caps |= DISTANCE;
547  return GeodesicLineExact(*this, lat1, lon1, azi1, salp1, calp1, caps,
548  true, a12);
549  }
550 
551  void GeodesicExact::Lengths(const EllipticFunction& E,
552  real sig12,
553  real ssig1, real csig1, real dn1,
554  real ssig2, real csig2, real dn2,
555  real cbet1, real cbet2, unsigned outmask,
556  real& s12b, real& m12b, real& m0,
557  real& M12, real& M21) const {
558  // Return m12b = (reduced length)/_b; also calculate s12b = distance/_b,
559  // and m0 = coefficient of secular term in expression for reduced length.
560 
561  outmask &= OUT_ALL;
562  // outmask & DISTANCE: set s12b
563  // outmask & REDUCEDLENGTH: set m12b & m0
564  // outmask & GEODESICSCALE: set M12 & M21
565 
566  // It's OK to have repeated dummy arguments,
567  // e.g., s12b = m0 = M12 = M21 = dummy
568 
569  if (outmask & DISTANCE)
570  // Missing a factor of _b
571  s12b = E.E() / (Math::pi() / 2) *
572  (sig12 + (E.deltaE(ssig2, csig2, dn2) - E.deltaE(ssig1, csig1, dn1)));
573  if (outmask & (REDUCEDLENGTH | GEODESICSCALE)) {
574  real
575  m0x = - E.k2() * E.D() / (Math::pi() / 2),
576  J12 = m0x *
577  (sig12 + (E.deltaD(ssig2, csig2, dn2) - E.deltaD(ssig1, csig1, dn1)));
578  if (outmask & REDUCEDLENGTH) {
579  m0 = m0x;
580  // Missing a factor of _b. Add parens around (csig1 * ssig2) and
581  // (ssig1 * csig2) to ensure accurate cancellation in the case of
582  // coincident points.
583  m12b = dn2 * (csig1 * ssig2) - dn1 * (ssig1 * csig2) -
584  csig1 * csig2 * J12;
585  }
586  if (outmask & GEODESICSCALE) {
587  real csig12 = csig1 * csig2 + ssig1 * ssig2;
588  real t = _ep2 * (cbet1 - cbet2) * (cbet1 + cbet2) / (dn1 + dn2);
589  M12 = csig12 + (t * ssig2 - csig2 * J12) * ssig1 / dn1;
590  M21 = csig12 - (t * ssig1 - csig1 * J12) * ssig2 / dn2;
591  }
592  }
593  }
594 
595  Math::real GeodesicExact::Astroid(real x, real y) {
596  // Solve k^4+2*k^3-(x^2+y^2-1)*k^2-2*y^2*k-y^2 = 0 for positive root k.
597  // This solution is adapted from Geocentric::Reverse.
598  real k;
599  real
600  p = Math::sq(x),
601  q = Math::sq(y),
602  r = (p + q - 1) / 6;
603  if ( !(q == 0 && r <= 0) ) {
604  real
605  // Avoid possible division by zero when r = 0 by multiplying equations
606  // for s and t by r^3 and r, resp.
607  S = p * q / 4, // S = r^3 * s
608  r2 = Math::sq(r),
609  r3 = r * r2,
610  // The discriminant of the quadratic equation for T3. This is zero on
611  // the evolute curve p^(1/3)+q^(1/3) = 1
612  disc = S * (S + 2 * r3);
613  real u = r;
614  if (disc >= 0) {
615  real T3 = S + r3;
616  // Pick the sign on the sqrt to maximize abs(T3). This minimizes loss
617  // of precision due to cancellation. The result is unchanged because
618  // of the way the T is used in definition of u.
619  T3 += T3 < 0 ? -sqrt(disc) : sqrt(disc); // T3 = (r * t)^3
620  // N.B. cbrt always returns the real root. cbrt(-8) = -2.
621  real T = cbrt(T3); // T = r * t
622  // T can be zero; but then r2 / T -> 0.
623  u += T + (T != 0 ? r2 / T : 0);
624  } else {
625  // T is complex, but the way u is defined the result is real.
626  real ang = atan2(sqrt(-disc), -(S + r3));
627  // There are three possible cube roots. We choose the root which
628  // avoids cancellation. Note that disc < 0 implies that r < 0.
629  u += 2 * r * cos(ang / 3);
630  }
631  real
632  v = sqrt(Math::sq(u) + q), // guaranteed positive
633  // Avoid loss of accuracy when u < 0.
634  uv = u < 0 ? q / (v - u) : u + v, // u+v, guaranteed positive
635  w = (uv - q) / (2 * v); // positive?
636  // Rearrange expression for k to avoid loss of accuracy due to
637  // subtraction. Division by 0 not possible because uv > 0, w >= 0.
638  k = uv / (sqrt(uv + Math::sq(w)) + w); // guaranteed positive
639  } else { // q == 0 && r <= 0
640  // y = 0 with |x| <= 1. Handle this case directly.
641  // for y small, positive root is k = abs(y)/sqrt(1-x^2)
642  k = 0;
643  }
644  return k;
645  }
646 
647  Math::real GeodesicExact::InverseStart(EllipticFunction& E,
648  real sbet1, real cbet1, real dn1,
649  real sbet2, real cbet2, real dn2,
650  real lam12, real slam12, real clam12,
651  real& salp1, real& calp1,
652  // Only updated if return val >= 0
653  real& salp2, real& calp2,
654  // Only updated for short lines
655  real& dnm) const {
656  // Return a starting point for Newton's method in salp1 and calp1 (function
657  // value is -1). If Newton's method doesn't need to be used, return also
658  // salp2 and calp2 and function value is sig12.
659  real
660  sig12 = -1, // Return value
661  // bet12 = bet2 - bet1 in [0, pi); bet12a = bet2 + bet1 in (-pi, 0]
662  sbet12 = sbet2 * cbet1 - cbet2 * sbet1,
663  cbet12 = cbet2 * cbet1 + sbet2 * sbet1;
664  real sbet12a = sbet2 * cbet1 + cbet2 * sbet1;
665  bool shortline = cbet12 >= 0 && sbet12 < real(0.5) &&
666  cbet2 * lam12 < real(0.5);
667  real somg12, comg12;
668  if (shortline) {
669  real sbetm2 = Math::sq(sbet1 + sbet2);
670  // sin((bet1+bet2)/2)^2
671  // = (sbet1 + sbet2)^2 / ((sbet1 + sbet2)^2 + (cbet1 + cbet2)^2)
672  sbetm2 /= sbetm2 + Math::sq(cbet1 + cbet2);
673  dnm = sqrt(1 + _ep2 * sbetm2);
674  real omg12 = lam12 / (_f1 * dnm);
675  somg12 = sin(omg12); comg12 = cos(omg12);
676  } else {
677  somg12 = slam12; comg12 = clam12;
678  }
679 
680  salp1 = cbet2 * somg12;
681  calp1 = comg12 >= 0 ?
682  sbet12 + cbet2 * sbet1 * Math::sq(somg12) / (1 + comg12) :
683  sbet12a - cbet2 * sbet1 * Math::sq(somg12) / (1 - comg12);
684 
685  real
686  ssig12 = hypot(salp1, calp1),
687  csig12 = sbet1 * sbet2 + cbet1 * cbet2 * comg12;
688 
689  if (shortline && ssig12 < _etol2) {
690  // really short lines
691  salp2 = cbet1 * somg12;
692  calp2 = sbet12 - cbet1 * sbet2 *
693  (comg12 >= 0 ? Math::sq(somg12) / (1 + comg12) : 1 - comg12);
694  Math::norm(salp2, calp2);
695  // Set return value
696  sig12 = atan2(ssig12, csig12);
697  } else if (fabs(_n) > real(0.1) || // Skip astroid calc if too eccentric
698  csig12 >= 0 ||
699  ssig12 >= 6 * fabs(_n) * Math::pi() * Math::sq(cbet1)) {
700  // Nothing to do, zeroth order spherical approximation is OK
701  } else {
702  // Scale lam12 and bet2 to x, y coordinate system where antipodal point
703  // is at origin and singular point is at y = 0, x = -1.
704  real x, y, lamscale, betscale;
705  real lam12x = atan2(-slam12, -clam12); // lam12 - pi
706  if (_f >= 0) { // In fact f == 0 does not get here
707  // x = dlong, y = dlat
708  {
709  real k2 = Math::sq(sbet1) * _ep2;
710  E.Reset(-k2, -_ep2, 1 + k2, 1 + _ep2);
711  lamscale = _e2/_f1 * cbet1 * 2 * E.H();
712  }
713  betscale = lamscale * cbet1;
714 
715  x = lam12x / lamscale;
716  y = sbet12a / betscale;
717  } else { // _f < 0
718  // x = dlat, y = dlong
719  real
720  cbet12a = cbet2 * cbet1 - sbet2 * sbet1,
721  bet12a = atan2(sbet12a, cbet12a);
722  real m12b, m0, dummy;
723  // In the case of lon12 = 180, this repeats a calculation made in
724  // Inverse.
725  Lengths(E, Math::pi() + bet12a,
726  sbet1, -cbet1, dn1, sbet2, cbet2, dn2,
727  cbet1, cbet2, REDUCEDLENGTH, dummy, m12b, m0, dummy, dummy);
728  x = -1 + m12b / (cbet1 * cbet2 * m0 * Math::pi());
729  betscale = x < -real(0.01) ? sbet12a / x :
730  -_f * Math::sq(cbet1) * Math::pi();
731  lamscale = betscale / cbet1;
732  y = lam12x / lamscale;
733  }
734 
735  if (y > -tol1_ && x > -1 - xthresh_) {
736  // strip near cut
737  // Need real(x) here to cast away the volatility of x for min/max
738  if (_f >= 0) {
739  salp1 = fmin(real(1), -x); calp1 = - sqrt(1 - Math::sq(salp1));
740  } else {
741  calp1 = fmax(real(x > -tol1_ ? 0 : -1), x);
742  salp1 = sqrt(1 - Math::sq(calp1));
743  }
744  } else {
745  // Estimate alp1, by solving the astroid problem.
746  //
747  // Could estimate alpha1 = theta + pi/2, directly, i.e.,
748  // calp1 = y/k; salp1 = -x/(1+k); for _f >= 0
749  // calp1 = x/(1+k); salp1 = -y/k; for _f < 0 (need to check)
750  //
751  // However, it's better to estimate omg12 from astroid and use
752  // spherical formula to compute alp1. This reduces the mean number of
753  // Newton iterations for astroid cases from 2.24 (min 0, max 6) to 2.12
754  // (min 0 max 5). The changes in the number of iterations are as
755  // follows:
756  //
757  // change percent
758  // 1 5
759  // 0 78
760  // -1 16
761  // -2 0.6
762  // -3 0.04
763  // -4 0.002
764  //
765  // The histogram of iterations is (m = number of iterations estimating
766  // alp1 directly, n = number of iterations estimating via omg12, total
767  // number of trials = 148605):
768  //
769  // iter m n
770  // 0 148 186
771  // 1 13046 13845
772  // 2 93315 102225
773  // 3 36189 32341
774  // 4 5396 7
775  // 5 455 1
776  // 6 56 0
777  //
778  // Because omg12 is near pi, estimate work with omg12a = pi - omg12
779  real k = Astroid(x, y);
780  real
781  omg12a = lamscale * ( _f >= 0 ? -x * k/(1 + k) : -y * (1 + k)/k );
782  somg12 = sin(omg12a); comg12 = -cos(omg12a);
783  // Update spherical estimate of alp1 using omg12 instead of lam12
784  salp1 = cbet2 * somg12;
785  calp1 = sbet12a - cbet2 * sbet1 * Math::sq(somg12) / (1 - comg12);
786  }
787  }
788  // Sanity check on starting guess. Backwards check allows NaN through.
789  if (!(salp1 <= 0))
790  Math::norm(salp1, calp1);
791  else {
792  salp1 = 1; calp1 = 0;
793  }
794  return sig12;
795  }
796 
797  Math::real GeodesicExact::Lambda12(real sbet1, real cbet1, real dn1,
798  real sbet2, real cbet2, real dn2,
799  real salp1, real calp1,
800  real slam120, real clam120,
801  real& salp2, real& calp2,
802  real& sig12,
803  real& ssig1, real& csig1,
804  real& ssig2, real& csig2,
805  EllipticFunction& E,
806  real& domg12,
807  bool diffp, real& dlam12) const
808  {
809 
810  if (sbet1 == 0 && calp1 == 0)
811  // Break degeneracy of equatorial line. This case has already been
812  // handled.
813  calp1 = -tiny_;
814 
815  real
816  // sin(alp1) * cos(bet1) = sin(alp0)
817  salp0 = salp1 * cbet1,
818  calp0 = hypot(calp1, salp1 * sbet1); // calp0 > 0
819 
820  real somg1, comg1, somg2, comg2, somg12, comg12, cchi1, cchi2, lam12;
821  // tan(bet1) = tan(sig1) * cos(alp1)
822  // tan(omg1) = sin(alp0) * tan(sig1) = tan(omg1)=tan(alp1)*sin(bet1)
823  ssig1 = sbet1; somg1 = salp0 * sbet1;
824  csig1 = comg1 = calp1 * cbet1;
825  // Without normalization we have schi1 = somg1.
826  cchi1 = _f1 * dn1 * comg1;
827  Math::norm(ssig1, csig1);
828  // Math::norm(somg1, comg1); -- don't need to normalize!
829  // Math::norm(schi1, cchi1); -- don't need to normalize!
830 
831  // Enforce symmetries in the case abs(bet2) = -bet1. Need to be careful
832  // about this case, since this can yield singularities in the Newton
833  // iteration.
834  // sin(alp2) * cos(bet2) = sin(alp0)
835  salp2 = cbet2 != cbet1 ? salp0 / cbet2 : salp1;
836  // calp2 = sqrt(1 - sq(salp2))
837  // = sqrt(sq(calp0) - sq(sbet2)) / cbet2
838  // and subst for calp0 and rearrange to give (choose positive sqrt
839  // to give alp2 in [0, pi/2]).
840  calp2 = cbet2 != cbet1 || fabs(sbet2) != -sbet1 ?
841  sqrt(Math::sq(calp1 * cbet1) +
842  (cbet1 < -sbet1 ?
843  (cbet2 - cbet1) * (cbet1 + cbet2) :
844  (sbet1 - sbet2) * (sbet1 + sbet2))) / cbet2 :
845  fabs(calp1);
846  // tan(bet2) = tan(sig2) * cos(alp2)
847  // tan(omg2) = sin(alp0) * tan(sig2).
848  ssig2 = sbet2; somg2 = salp0 * sbet2;
849  csig2 = comg2 = calp2 * cbet2;
850  // Without normalization we have schi2 = somg2.
851  cchi2 = _f1 * dn2 * comg2;
852  Math::norm(ssig2, csig2);
853  // Math::norm(somg2, comg2); -- don't need to normalize!
854  // Math::norm(schi2, cchi2); -- don't need to normalize!
855 
856  // sig12 = sig2 - sig1, limit to [0, pi]
857  sig12 = atan2(fmax(real(0), csig1 * ssig2 - ssig1 * csig2),
858  csig1 * csig2 + ssig1 * ssig2);
859 
860  // omg12 = omg2 - omg1, limit to [0, pi]
861  somg12 = fmax(real(0), comg1 * somg2 - somg1 * comg2);
862  comg12 = comg1 * comg2 + somg1 * somg2;
863  real k2 = Math::sq(calp0) * _ep2;
864  E.Reset(-k2, -_ep2, 1 + k2, 1 + _ep2);
865  // chi12 = chi2 - chi1, limit to [0, pi]
866  real
867  schi12 = fmax(real(0), cchi1 * somg2 - somg1 * cchi2),
868  cchi12 = cchi1 * cchi2 + somg1 * somg2;
869  // eta = chi12 - lam120
870  real eta = atan2(schi12 * clam120 - cchi12 * slam120,
871  cchi12 * clam120 + schi12 * slam120);
872  real deta12 = -_e2/_f1 * salp0 * E.H() / (Math::pi() / 2) *
873  (sig12 + (E.deltaH(ssig2, csig2, dn2) - E.deltaH(ssig1, csig1, dn1)));
874  lam12 = eta + deta12;
875  // domg12 = deta12 + chi12 - omg12
876  domg12 = deta12 + atan2(schi12 * comg12 - cchi12 * somg12,
877  cchi12 * comg12 + schi12 * somg12);
878  if (diffp) {
879  if (calp2 == 0)
880  dlam12 = - 2 * _f1 * dn1 / sbet1;
881  else {
882  real dummy;
883  Lengths(E, sig12, ssig1, csig1, dn1, ssig2, csig2, dn2,
884  cbet1, cbet2, REDUCEDLENGTH,
885  dummy, dlam12, dummy, dummy, dummy);
886  dlam12 *= _f1 / (calp2 * cbet2);
887  }
888  }
889 
890  return lam12;
891  }
892 
893  void GeodesicExact::C4f(real eps, real c[]) const {
894  // Evaluate C4 coeffs
895  // Elements c[0] thru c[nC4_ - 1] are set
896  real mult = 1;
897  int o = 0;
898  for (int l = 0; l < nC4_; ++l) { // l is index of C4[l]
899  int m = nC4_ - l - 1; // order of polynomial in eps
900  c[l] = mult * Math::polyval(m, _cC4x + o, eps);
901  o += m + 1;
902  mult *= eps;
903  }
904  // Post condition: o == nC4x_
905  if (!(o == nC4x_))
906  throw GeographicErr("C4 misalignment");
907  }
908 
909  // If the coefficient is greater or equal to 2^63, express it as a pair [a,
910  // b] which is combined with a*2^52 + b. The largest coefficient is
911  // 831281402884796906843926125 = 0x2af9eaf25d149c52a73ee6d
912  // = 184581550685 * 2^52 + 0x149c52a73ee6d which is less than 2^90. Both a
913  // and b are less that 2^52 and so are exactly representable by doubles; then
914  // the computation of the full double coefficient involves only a single
915  // rounding operation. (Actually integers up to and including 2^53 can be
916  // represented exactly as doubles. Limiting b to 52 bits allows it to be
917  // represented in 13 digits in hex.)
918 
919  // If the coefficient is less than 2^63, cast it to real if it isn't exactly
920  // representable as a float. Thus 121722048 = 1901907*2^6 and 1901907 < 2^24
921  // so the cast is not needed; 21708121824 = 678378807*2^5 and 678378807 >=
922  // 2^24 so the cast is needed.
923 
924  void GeodesicExact::C4coeff() {
925  // Generated by Maxima on 2017-05-27 10:17:57-04:00
926 #if GEOGRAPHICLIB_GEODESICEXACT_ORDER == 30
927  static const real coeff[] = {
928  // C4[0], coeff of eps^29, polynomial in n of order 0
929  3361,real(109067695),
930  // C4[0], coeff of eps^28, polynomial in n of order 1
931  real(121722048),real(30168404),real(0x269c465a0c9LL),
932  // C4[0], coeff of eps^27, polynomial in n of order 2
933  real(21708121824LL),-real(10786479696LL),real(8048130587LL),
934  real(0xbfa33c13e963LL),
935  // C4[0], coeff of eps^26, polynomial in n of order 3
936  real(0x738319564e0LL),-real(0x4c2475635c0LL),real(0x25d0be52da0LL),
937  real(643173496654LL),real(0xa0f21774b90225LL),
938  // C4[0], coeff of eps^25, polynomial in n of order 4
939  real(0x7a99ea0a52f40LL),-real(0x5a5f53e2c3b50LL),real(0x3b83d2c0c8da0LL),
940  -real(0x1d8a81cb5cc70LL),real(0x1605bd50459c1LL),
941  real(0x6fb2ae4757107d03LL),
942  // C4[0], coeff of eps^24, polynomial in n of order 5
943  real(0x2507d929b7f89580LL),-real(0x1ce7bf02c3715a00LL),
944  real(0x15463c23456c8680LL),-real(0xdfecff0050dfd00LL),
945  real(0x6f141ba97196780LL),real(0x1b71ab9c78b8b48LL),
946  reale(1520879,0x957266bcf90f9LL),
947  // C4[0], coeff of eps^23, polynomial in n of order 6
948  reale(5214,0xb54b8c26f5620LL),-reale(4202,0x4ae5f5bcbf950LL),
949  reale(3272,0xab988a50dfac0LL),-reale(2404,0x84ae60c9e7b30LL),
950  real(0x62be65b26227b760LL),-real(0x30f2645200be8b10LL),
951  real(0x2472ebc3f09ad327LL),reale(9429453,0x6b5ee3606e93bLL),
952  // C4[0], coeff of eps^22, polynomial in n of order 7
953  reale(213221,0x21fe88963f0e0LL),-reale(174746,0x12fe03af82e40LL),
954  reale(140344,0xd3dfad978d4a0LL),-reale(109009,0x13ee03d15f180LL),
955  reale(79932,0x9fff01479b460LL),-reale(52447,0x53ea945b584c0LL),
956  reale(25976,0xa5a6ee990f820LL),reale(6403,0x87dc4a069efc6LL),
957  reale(273454149,0x29bfc1ec86bafLL),
958  // C4[0], coeff of eps^21, polynomial in n of order 8
959  reale(1513769,0x9572babb99080LL),-reale(1247902,0x66609b16e1250LL),
960  reale(1017692,0x228016ac84e60LL),-reale(814136,0x86ec313455df0LL),
961  reale(630421,0xa88f591713840LL),-reale(461205,0x487f023b60f90LL),
962  reale(302134,0x36942691aea20LL),-reale(149503,0x5a1d9af94cb30LL),
963  reale(111169,0xb14ab93d4ba6dLL),reale(1367270745,0xd0bec99ea1a6bLL),
964  // C4[0], coeff of eps^20, polynomial in n of order 9
965  reale(2196138,0xe1b60fe1808c0LL),-reale(1802572,0x3b4b1c2a34200LL),
966  reale(1475191,0x47b8ccbe8340LL),-reale(1196055,0x2e2a401c46980LL),
967  reale(952413,0x117e9e1fb75c0LL),-reale(734856,0x2e19f1e7be100LL),
968  reale(536171,0x8daa599335040LL),-reale(350594,0xa58d466a3880LL),
969  reale(173293,0x7b19cdc9682c0LL),reale(42591,0xb005bdeb82d74LL),
970  reale(1367270745,0xd0bec99ea1a6bLL),
971  // C4[0], coeff of eps^19, polynomial in n of order 10
972  reale(9954363,0x5ecc5371ca720LL),-reale(8035921,0x7cc90565e0670LL),
973  reale(6522783,0x32e1ec30d1a80LL),-reale(5291286,0x4172ef2beb090LL),
974  reale(4260231,0x65c388ed45de0LL),-reale(3373847,0x4da61e8c704b0LL),
975  reale(2592185,0xcd194d02dbd40LL),-reale(1885401,0xa08c9a20ef6d0LL),
976  reale(1230164,0x4c527bc6a84a0LL),-reale(607279,0x24d6e51bd7af0LL),
977  reale(450701,0xae98337b7d081LL),reale(4101812237LL,0x723c5cdbe4f41LL),
978  // C4[0], coeff of eps^18, polynomial in n of order 11
979  reale(16160603,0x85a3ec5761ce0LL),-reale(12587219,0x97b7f7c505ac0LL),
980  reale(9979192,0xa0e43863a93a0LL),-reale(7988280,0xcfaf566027f00LL),
981  reale(6410314,0xbffc30c12660LL),-reale(5117692,0xfd9318db4c340LL),
982  reale(4026292,0x94c482b815d20LL),-reale(3077917,0x9c480ad851f80LL),
983  reale(2230377,0x99db799d8bfe0LL),-reale(1451530,0xb0005d9658bc0LL),
984  reale(715485,0xdbe6a2ef6d6a0LL),reale(175141,0x3547b8669b9beLL),
985  reale(4101812237LL,0x723c5cdbe4f41LL),
986  // C4[0], coeff of eps^17, polynomial in n of order 12
987  reale(30091817,0x8745c27487540LL),-reale(21716256,0x7a4bb1495e170LL),
988  reale(16366670,0xd4e8bc19a0660LL),-reale(12670374,0x9eda0f5df2ed0LL),
989  reale(9963727,0x5ae4f6d3c8380LL),-reale(7887824,0x191034733ae30LL),
990  reale(6231873,0x96448488ef0a0LL),-reale(4863678,0x67c3c74b1b90LL),
991  reale(3695513,0x2e7ae0f4851c0LL),-reale(2665992,0xe6864878c32f0LL),
992  reale(1729741,0xf881cba41aae0LL),-reale(851104,0x888fd5b7ab050LL),
993  reale(629987,0x9ea5a19626943LL),reale(4101812237LL,0x723c5cdbe4f41LL),
994  // C4[0], coeff of eps^16, polynomial in n of order 13
995  reale(79181861,0x46beef62ca900LL),-reale(45969492,0x85a19d8425400LL),
996  reale(30736937,0x10d9a95bb4f00LL),-reale(22084618,0xaf3a6659fa600LL),
997  reale(16548053,0x58583f22e9500LL),-reale(12711232,0x3d7f1b1be3800LL),
998  reale(9889259,0xbbf5d84b2bb00LL),-reale(7711253,0x36b17889dca00LL),
999  reale(5958759,0x73d1ebe040100LL),-reale(4493987,0xfa374abbe1c00LL),
1000  reale(3224517,0x29027e04ea700LL),-reale(2084431,0x8d77e42beee00LL),
1001  reale(1023433,0xbf113370eed00LL),reale(249103,0x93cdbdabe0fb0LL),
1002  reale(4101812237LL,0x723c5cdbe4f41LL),
1003  // C4[0], coeff of eps^15, polynomial in n of order 14
1004  reale(100415733,0x1c7e0d98777e0LL),-reale(220472579,0x196c2a7ff77f0LL),
1005  reale(81497972,0xcf48e14d7b2c0LL),-reale(47157604,0xb4c79beff0c90LL),
1006  reale(31400333,0x3ade51fc905a0LL),-reale(22437640,0x62c8445afeb30LL),
1007  reale(16688020,0xb49b2cc64ec80LL),-reale(12687475,0x35a524f08d7d0LL),
1008  reale(9727302,0xc96eb1166e360LL),-reale(7422875,0x3574dc9ff9670LL),
1009  reale(5546536,0x3897621326640LL),-reale(3953280,0x7a61d237aeb10LL),
1010  reale(2544043,0x942757fc8f120LL),-reale(1245848,0x5f59e2e2499b0LL),
1011  reale(918672,0xb7e149f3f515dLL),reale(4101812237LL,0x723c5cdbe4f41LL),
1012  // C4[0], coeff of eps^14, polynomial in n of order 15
1013  -reale(410150575,0x33edeefdadd60LL),reale(389451478,0x4a8eb37cf8e40LL),
1014  reale(102537774,0xdf54e754057e0LL),-reale(228145792,0x9928ef6984980LL),
1015  reale(84014235,0x8c476a1354120LL),-reale(48417903,0x9486b64af140LL),
1016  reale(32072368,0xac5157de0d660LL),-reale(22757026,0x6fd3c1d71f100LL),
1017  reale(16760216,0x75de552320fa0LL),-reale(12564203,0xce657c7ead0c0LL),
1018  reale(9433140,0xee7b325fde4e0LL),-reale(6966096,0xc0a9d97231880LL),
1019  reale(4923714,0x7fe1a8c934e20LL),-reale(3150864,0xcacdc5bf45040LL),
1020  reale(1538058,0xc6e75548f4360LL),reale(371250,0x9b28ca926da22LL),
1021  reale(4101812237LL,0x723c5cdbe4f41LL),
1022  // C4[0], coeff of eps^13, polynomial in n of order 16
1023  reale(10071346,0xbead2787bab00LL),reale(77935892,0xc8037e807a610LL),
1024  -reale(424974584,0x95c58aa2abc60LL),reale(405632040,0xf37804095de30LL),
1025  reale(104709205,0x2c34dddf07040LL),-reale(236671973,0xc06ad427a5bb0LL),
1026  reale(86756233,0x36f6256b264e0LL),-reale(49748360,0xa42ca4c379390LL),
1027  reale(32735340,0x1aa6eba145580LL),-reale(23012513,0x41e6e60af5570LL),
1028  reale(16722020,0xa0e65eb557620LL),-reale(12285046,0x712c138942d50LL),
1029  reale(8933912,0x44131ea6cfac0LL),-reale(6247309,0xac4879043a730LL),
1030  reale(3969671,0x8774cc7c1760LL),-reale(1929932,0x2a739696c4f10LL),
1031  reale(1414943,0x9f9bcb791811fLL),reale(4101812237LL,0x723c5cdbe4f41LL),
1032  // C4[0], coeff of eps^12, polynomial in n of order 17
1033  reale(1301009,0x7885767b34dc0LL),reale(3139452,0x6299dbe8eac00LL),
1034  reale(10399899,0xe9c2f692aa40LL),reale(80694987,0xafcfc919b1e80LL),
1035  -reale(441529449,0x34f14f083e140LL),reale(423985433,0x2e9be95704100LL),
1036  reale(106892519,0x9a909730adb40LL),-reale(246219322,0x3cc21ecefbc80LL),
1037  reale(89751674,0x8e9ea1f760fc0LL),-reale(51139306,0x4d1fa35b2aa00LL),
1038  reale(33357165,0x391836578ec40LL),-reale(23152852,0x670df382e5780LL),
1039  reale(16502135,0xfb453b1baa0c0LL),-reale(11755175,0x732a395d89500LL),
1040  reale(8105218,0xa64658fb65d40LL),-reale(5103238,0xc9c658d3f3280LL),
1041  reale(2468214,0x7d6aacb2351c0LL),reale(588064,0xecbdce72e5104LL),
1042  reale(4101812237LL,0x723c5cdbe4f41LL),
1043  // C4[0], coeff of eps^11, polynomial in n of order 18
1044  reale(365173,0x141eb92882aa0LL),reale(660579,0x721db1cc80890LL),
1045  reale(1339643,0x6f3cff39e7d00LL),reale(3240370,0xc29100e665970LL),
1046  reale(10762711,0xac38fa6376f60LL),reale(83769430,0x6edf90fa38050LL),
1047  -reale(460180081,0xa7a2c15d05240LL),reale(445039582,0xb96af8d66e930LL),
1048  reale(109020126,0x840edc5d1e420LL),-reale(257005247,0x2ec795996fff0LL),
1049  reale(93028106,0x54adfb574be80LL),-reale(52565819,0x1d828e2b6cf10LL),
1050  reale(33879206,0x109475f98e8e0LL),-reale(23088279,0x158dbde3c1830LL),
1051  reale(15975944,0x7a6ca24c70f40LL),-reale(10806612,0x3c0d699b76f50LL),
1052  reale(6721635,0xd5a36326ddda0LL),-reale(3228909,0xe44dc20d06870LL),
1053  reale(2345355,0x81bdf10588059LL),reale(4101812237LL,0x723c5cdbe4f41LL),
1054  // C4[0], coeff of eps^10, polynomial in n of order 19
1055  reale(142358,0x43f28ef2bce60LL),reale(224104,0xc49bf70fb8540LL),
1056  reale(374789,0x29edb81ed2220LL),reale(679606,0x56dce126b3a00LL),
1057  reale(1381751,0x3315a15e701e0LL),reale(3351469,0xe4cb186e3aec0LL),
1058  reale(11166107,0x295c18ed1d5a0LL),reale(87224183,0xbf27e3cc5cb80LL),
1059  -reale(481408924,0xf800e4fbbfaa0LL),reale(469519077,0x9e18ca33e7840LL),
1060  reale(110970854,0x606788cedf920LL),-reale(269315695,0x90dadb20d6300LL),
1061  reale(96606791,0x8c213171618e0LL),-reale(53972000,0xd509f5454de40LL),
1062  reale(34191407,0x9021dc5d4cca0LL),-reale(22654105,0x9f8b9187f1180LL),
1063  reale(14912791,0x946e9b2907c60LL),-reale(9121084,0x6067cd3f714c0LL),
1064  reale(4341360,0x73b562399020LL),reale(1011849,0x75de66a5bdb46LL),
1065  reale(4101812237LL,0x723c5cdbe4f41LL),
1066  // C4[0], coeff of eps^9, polynomial in n of order 20
1067  reale(66631,0x784cbdfb1b2c0LL),reale(96606,0x3419bb8e05f90LL),
1068  reale(145459,0xb79bffbfb42e0LL),reale(229589,0x824d22506cd30LL),
1069  reale(385010,0x35e34fd0f4f00LL),reale(700134,0x4df5413db48d0LL),
1070  reale(1427794,0x581b23c083b20LL),reale(3474469,0x224df4c0f7670LL),
1071  reale(11618119,0x6c8cba4306b40LL),reale(91144571,0x713d14f45fa10LL),
1072  -reale(505869523,0xd3d937aa3bca0LL),reale(498449385,0x686859af477b0LL),
1073  reale(112524504,0x2ca5b0e042780LL),-reale(283533725,0xba4eec11a6cb0LL),
1074  reale(100487121,0xc424152de7ba0LL),-reale(55236514,0x8c4dd4ee50f10LL),
1075  reale(34077723,0x322bbe9b9a3c0LL),-reale(21528502,0x2ca44d130cb70LL),
1076  reale(12851809,0x7f1d30d5603e0LL),-reale(6038295,0xecbfc0da7fdd0LL),
1077  reale(4313665,0xa0fbedf62e95bLL),reale(4101812237LL,0x723c5cdbe4f41LL),
1078  // C4[0], coeff of eps^8, polynomial in n of order 21
1079  reale(34939,0x4781a8598a880LL),reale(47986,0x870a153a0ba00LL),
1080  reale(67643,0xf93c5a3d5fb80LL),reale(98366,0xdef5527b5d100LL),
1081  reale(148567,0x565e4f7b51e80LL),reale(235242,0x766e64b79c800LL),
1082  reale(395796,0x5614c84bc3180LL),reale(722239,0xc9f1a6fcbf00LL),
1083  reale(1478257,0xd3352c2795480LL),reale(3611438,0xfdbc40cced600LL),
1084  reale(12129091,0x5ec9e3d72a780LL),reale(95645231,0xe79e249b02d00LL),
1085  -reale(534473300,0x6333290e9b580LL),reale(533336700,0xd7635e240e400LL),
1086  reale(113268651,0x31e09daaa5d80LL),-reale(300181610,0x6cd38634ee500LL),
1087  reale(104606327,0x6a6e0bd3d0080LL),-reale(56090968,0xcfc000b8f0e00LL),
1088  reale(33084425,0x428f85e945380LL),-reale(19025074,0x3fea5ea1f7700LL),
1089  reale(8768855,0x59c11511e7680LL),reale(1959911,0x57aea52b92dd8LL),
1090  reale(4101812237LL,0x723c5cdbe4f41LL),
1091  // C4[0], coeff of eps^7, polynomial in n of order 22
1092  reale(19712,0xac93bc6991f60LL),reale(26064,0x47e63bb6f7b10LL),
1093  reale(35129,0x85349dd791940LL),reale(48412,0xcf2b50a5e4170LL),
1094  reale(68486,0xf23457a2e7b20LL),reale(99959,0x1aee9379bdd0LL),
1095  reale(151547,0xc976e86422100LL),reale(240911,0x67a8290f88c30LL),
1096  reale(407002,0x79f859786e6e0LL),reale(745880,0xf6e3b80f24890LL),
1097  reale(1533569,0xcfffb4a9fa8c0LL),reale(3764807,0xab1a08cbd8ef0LL),
1098  reale(12712489,0x4098eb8542a0LL),reale(100884327,0x9a754746dfb50LL),
1099  -reale(568536969,0xbcc82f5b36f80LL),reale(576497219,0x10ca042b229b0LL),
1100  reale(112392819,0xaecaa4a6c6e60LL),-reale(319979712,0xfe05e4aae49f0LL),
1101  reale(108728942,0x9b1cd9ac3b840LL),-reale(55904982,0xfebe8a174c390LL),
1102  reale(30158727,0xd0df7149f4a20LL),-reale(13482566,0x2ca2af46da730LL),
1103  reale(9304222,0x6328f1d67a7f5LL),reale(4101812237LL,0x723c5cdbe4f41LL),
1104  // C4[0], coeff of eps^6, polynomial in n of order 23
1105  reale(11639,0x4298ebe4bc020LL),reale(14966,0xe9089607c0a40LL),
1106  reale(19534,0x1996a62965260LL),reale(25928,0xdcaffa7bfcb80LL),
1107  reale(35089,0x59fa64f7d88a0LL),reale(48563,0x32ed377221cc0LL),
1108  reale(69004,0xe5c9403173ae0LL),reale(101181,0xf483b00105600LL),
1109  reale(154143,0xf39432e434120LL),reale(246274,0xfc90899a3cf40LL),
1110  reale(418255,0xdad9486cf7360LL),reale(770731,0xbf0321b55e080LL),
1111  reale(1593877,0xd61fe95ba9a0LL),reale(3937200,0x3820413b3e1c0LL),
1112  reale(13385919,0xf48ca237dbbe0LL),reale(107086956,0x9d1b10f932b00LL),
1113  -reale(610048075,0x6c1b2715a7de0LL),reale(631706048,0xcac1d46451440LL),
1114  reale(108187733,0xaf9fd1440d460LL),-reale(343908890,0x37b3c0b50a80LL),
1115  reale(112109635,0x3a73d439f8aa0LL),-reale(53028119,0x15d1799f5d940LL),
1116  reale(22454404,0x49a70d2177ce0LL),reale(4553016,0x22f700960daaaLL),
1117  reale(4101812237LL,0x723c5cdbe4f41LL),
1118  // C4[0], coeff of eps^5, polynomial in n of order 24
1119  reale(7030,0x634f92bbfec80LL),reale(8852,0x183ea9c784b10LL),
1120  reale(11280,0x864427e0ea420LL),reale(14569,0x4ed71f4155e30LL),
1121  reale(19103,0x13b2c1ad2ffc0LL),reale(25480,0x35983eb20bf50LL),
1122  reale(34659,0x18ad59c5f9360LL),reale(48227,0x95f2c0574270LL),
1123  reale(68917,0x8c5b3ac32f300LL),reale(101660,0x272f49f96bb90LL),
1124  reale(155850,0xbc628b339b2a0LL),reale(250657,0x122490d07feb0LL),
1125  reale(428675,0x21f5a97506640LL),reale(795748,0x8d9dd2ee8dfd0LL),
1126  reale(1658420,0x22b44d2c5a1e0LL),reale(4130702,0x814b60cb632f0LL),
1127  reale(14171990,0xb8691b29bf980LL),reale(114585240,0x7599d8275cc10LL),
1128  -reale(662180135,0x55c1167b3fee0LL),reale(705602404,0xf6219ee07f30LL),
1129  reale(96655880,0xe42cfbbc64cc0LL),-reale(373149978,0xd8d5a94d3dfb0LL),
1130  reale(112272021,0x704341a757060LL),-reale(42251989,0xbf5a94cca7c90LL),
1131  reale(26498553,0xea37274059c77LL),reale(4101812237LL,0x723c5cdbe4f41LL),
1132  // C4[0], coeff of eps^4, polynomial in n of order 25
1133  reale(4244,0x3972351df5940LL),reale(5257,0xaa8f87b5d5600LL),
1134  reale(6578,0xed6cb3b3fa2c0LL),reale(8324,0xb4008d853180LL),
1135  reale(10662,0x703b07259b440LL),reale(13846,0x8f2f6ca125d00LL),
1136  reale(18261,0x3a455b4269dc0LL),reale(24508,0x5045fb81ae880LL),
1137  reale(33557,0x1b3e945f36f40LL),reale(47022,0x9499ec44e400LL),
1138  reale(67699,0x7a940285938c0LL),reale(100662,0x403646e1e5f80LL),
1139  reale(155637,0xf20897fb50a40LL),reale(252593,0x7106d86756b00LL),
1140  reale(436178,0xe720d891ff3c0LL),reale(818051,0x1d79595b01680LL),
1141  reale(1723706,0xc365c92e70540LL),reale(4344105,0xb055b91247200LL),
1142  reale(15096896,0xe96c54f834ec0LL),reale(123888911,0x435c586708d80LL),
1143  -reale(730395130,0x8d07d85ee1fc0LL),reale(811137162,0xd7ccf03d27900LL),
1144  reale(66848989,0xdd39a234bc9c0LL),-reale(407950245,0xd67367b7fbb80LL),
1145  reale(99073631,0x21cb91dfe1b40LL),reale(14205410,0x589c3f44ce7acLL),
1146  reale(4101812237LL,0x723c5cdbe4f41LL),
1147  // C4[0], coeff of eps^3, polynomial in n of order 26
1148  reale(2481,0x8d2c27b46b620LL),reale(3034,0xe44720f3fdf90LL),
1149  reale(3743,0xf82fc54a92780LL),reale(4662,0xb922ac44f6b70LL),
1150  reale(5867,0xae02c805f08e0LL),reale(7469,0x40a687e9b4d50LL),
1151  reale(9629,0xbb2099bca6640LL),reale(12592,0xa0727e14e5130LL),
1152  reale(16731,0xdc4cfea134ba0LL),reale(22636,0xbf84f9dc44310LL),
1153  reale(31263,0xfe99294d5c500LL),reale(44220,0x78f2e666feef0LL),
1154  reale(64313,0xe77c1f84fde60LL),reale(96684,0x43c9282e120d0LL),
1155  reale(151281,0x84eb0984fa3c0LL),reale(248729,0xa2c4a502aa4b0LL),
1156  reale(435615,0xd80deb212120LL),reale(829647,0x194fc60e84690LL),
1157  reale(1777619,0x17dfea7bc6280LL),reale(4562307,0x417bb8824d270LL),
1158  reale(16175470,0xd3a7db47373e0LL),reale(135804489,0xbb999e2601450LL),
1159  -reale(825156505,0xa8162cc9f9ec0LL),reale(977623624,0xd8c5ee7f4d830LL),
1160  -reale(20397512,0x4ab8f862cc960LL),-reale(435632583,0xf2b7943e115f0LL),
1161  reale(143237887,0xa8277df5ccab1LL),reale(4101812237LL,0x723c5cdbe4f41LL),
1162  // C4[0], coeff of eps^2, polynomial in n of order 27
1163  real(0x52cac993243497e0LL),real(0x6437dfaee57b9d40LL),
1164  real(0x7a3f9cad4d2f48a0LL),reale(2405,0xee01eec3f2b00LL),
1165  reale(2986,0x65a22988df560LL),reale(3743,0xe8ba104bd58c0LL),
1166  reale(4745,0x82561551e620LL),reale(6086,0xa7581d3ddee80LL),
1167  reale(7912,0x8561dfdd262e0LL),reale(10440,0x7aa2aab74b440LL),
1168  reale(14008,0x9b1a2c148b3a0LL),reale(19155,0xcd3b8407d7200LL),
1169  reale(26767,0x9792b4f9c2060LL),reale(38350,0xb50c17257efc0LL),
1170  reale(56574,0xaf828f4edf120LL),reale(86399,0xb1bc40483f580LL),
1171  reale(137581,0x7d29442656de0LL),reale(230687,0xc9059cc5d4b40LL),
1172  reale(413025,0xcba5d91bbdea0LL),reale(806439,0xbad85d457b900LL),
1173  reale(1777226,0xdb254a1088b60LL),reale(4709200,0x187f6563b06c0LL),
1174  reale(17312174,0x4c53d944cbc20LL),reale(151524377,0x682a2ddefc80LL),
1175  -reale(970338799,0x73aba5c04720LL),reale(1287957204,0xb756685e76240LL),
1176  -reale(416692036,0xd1e73fe253660LL),-reale(78129756,0xe75b5bfa6fa32LL),
1177  reale(4101812237LL,0x723c5cdbe4f41LL),
1178  // C4[0], coeff of eps^1, polynomial in n of order 28
1179  real(0xb4c355cd41c92c0LL),real(0xd8fea3a41cc7830LL),
1180  real(0x1064f0c6b9a6ad20LL),real(0x13f7a88902ef1b10LL),
1181  real(0x1884a414973fcb80LL),real(0x1e5fa2ae5243d7f0LL),
1182  real(0x25fe0bb384ddd9e0LL),real(0x3006f6e3e0e25ad0LL),
1183  real(0x3d6c2c13c34ec440LL),real(0x4f91f34825bd4fb0LL),
1184  real(0x688ffb74f98676a0LL),reale(2233,0xdec33bb086290LL),
1185  reale(3036,0xe53843c2cdd00LL),reale(4213,0xb13e1137e3f70LL),
1186  reale(5984,0xaa1cca8abe360LL),reale(8732,0xb9880d6c69250LL),
1187  reale(13152,0x1eadcfcfd75c0LL),reale(20566,0x4e1752c3c0730LL),
1188  reale(33653,0xf4262a5798020LL),reale(58247,0x3a420e3524a10LL),
1189  reale(108257,0x7934f39e3ee80LL),reale(221025,0xaccc1c0dc06f0LL),
1190  reale(514222,0xffbb852faace0LL),reale(1456965,0x29e8a4070e9d0LL),
1191  reale(5827860,0xa7a2901c3a740LL),reale(56821641,0x6270fd1339eb0LL),
1192  -reale(416692036,0xd1e73fe253660LL),reale(625038055,0x3adadfd37d190LL),
1193  -reale(273454149,0x29bfc1ec86bafLL),reale(1367270745,0xd0bec99ea1a6bLL),
1194  // C4[0], coeff of eps^0, polynomial in n of order 29
1195  reale(42171,0xbca3d5a569b4LL),reale(46862,0xd0a41cdef9cf0LL),
1196  reale(52277,0xa2d5316ac1b2cLL),reale(58560,0x6f94d669a7a28LL),
1197  reale(65892,0x788629d238da4LL),reale(74502,0x6b99bdf690d60LL),
1198  reale(84681,0x87b277eadbb1cLL),reale(96804,0x8c76c6701c898LL),
1199  reale(111359,0x1427f62cd3d94LL),reale(128987,0x59921e2221dd0LL),
1200  reale(150546,0xaa0136eb20f0cLL),reale(177198,0x7742592373f08LL),
1201  reale(210542,0x4360b9bd64984LL),reale(252821,0x8a8c09196de40LL),
1202  reale(307248,0x66986780ae6fcLL),reale(378530,0x79d0ac77ed78LL),
1203  reale(473750,0x5114d83948174LL),reale(603901,0x80acdb5cb5eb0LL),
1204  reale(786661,0x2afc1dbf812ecLL),reale(1051686,0xda8ab314e3e8LL),
1205  reale(1451326,0xc0ede2017b564LL),reale(2083956,0x5d3b51a63af20LL),
1206  reale(3149615,0xde5c8fc3f62dcLL),reale(5099378,0x12ae3e18b3258LL),
1207  reale(9106032,0x45ee012c1b554LL),reale(18940547,0x20d0545bbdf90LL),
1208  reale(52086504,0x9a3ce7fc4a6ccLL),reale(312519027,0x9d6d6fe9be8c8LL),
1209  -reale(1093816596,0xa6ff07b21aebcLL),
1210  reale(2734541491LL,0xa17d933d434d6LL),
1211  reale(4101812237LL,0x723c5cdbe4f41LL),
1212  // C4[1], coeff of eps^29, polynomial in n of order 0
1213  917561,real(273868982145LL),
1214  // C4[1], coeff of eps^28, polynomial in n of order 1
1215  -real(125915776),real(90505212),real(0x73d4d30e25bLL),
1216  // C4[1], coeff of eps^27, polynomial in n of order 2
1217  -real(0x2f7e4f2fca0LL),real(0x161b06db8f0LL),real(379339642199LL),
1218  real(0x145a25f15d59339LL),
1219  // C4[1], coeff of eps^26, polynomial in n of order 3
1220  -real(0x780f9f651c0LL),real(0x49cd6538080LL),-real(0x275396e6f40LL),
1221  real(0x1c1406225eaLL),real(0x1e2d6465e2b066fLL),
1222  // C4[1], coeff of eps^25, polynomial in n of order 4
1223  -real(0x226e68a74f6c2c0LL),real(0x178fbd94c6e4130LL),
1224  -real(0x10bafa7048ffb60LL),real(0x7b204e43552d10LL),
1225  real(0x1ebd785c76c649LL),reale(369943,0xaebaf6655156dLL),
1226  // C4[1], coeff of eps^24, polynomial in n of order 5
1227  -real(0x26adfa4c2bcf8500LL),real(0x1be7e116f09bc400LL),
1228  -real(0x1641521374362300LL),real(0xd7dd4a2b1831200LL),
1229  -real(0x7449d087ac65100LL),real(0x525502d56a2a1d8LL),
1230  reale(4562638,0xc0573436eb2ebLL),
1231  // C4[1], coeff of eps^23, polynomial in n of order 6
1232  -reale(27299,0x1e7fae46f2ae0LL),reale(20250,0xb050f61211530LL),
1233  -reale(17170,0x1ccacfb407b40LL),reale(11560,0x5557506ac7a50LL),
1234  -reale(8300,0x1ee1dfec0f3a0LL),reale(3760,0xc5da39149a170LL),
1235  real(0x3aaaad07e2dbe15fLL),reale(141441801,0x4a8f52a67aa75LL),
1236  // C4[1], coeff of eps^22, polynomial in n of order 7
1237  -reale(223720,0xada70de871dc0LL),reale(168212,0x95f7a36b8e780LL),
1238  -reale(147708,0x4639d71413140LL),reale(104570,0x398040c96dd00LL),
1239  -reale(84304,0x27ca2fe2f28c0LL),reale(50205,0xd862a9f308280LL),
1240  -reale(27426,0xbe7e08935dc40LL),reale(19210,0x9794de13dcf52LL),
1241  reale(820362447,0x7d3f45c59430dLL),
1242  // C4[1], coeff of eps^21, polynomial in n of order 8
1243  -reale(1591044,0x45108afb80980LL),reale(1200725,0xfaaefe8d2aff0LL),
1244  -reale(1074110,0x244b18cc1fd20LL),reale(779463,0x6e55e2794e4d0LL),
1245  -reale(667443,0x7f273db50d4c0LL),reale(440073,0xbd38cdf5ffbb0LL),
1246  -reale(320490,0xb0902bc064460LL),reale(142410,0x1eb038cc00090LL),
1247  reale(35531,0x5cce3f7afbb81LL),reale(4101812237LL,0x723c5cdbe4f41LL),
1248  // C4[1], coeff of eps^20, polynomial in n of order 9
1249  -reale(6932123,0xff59c6bb56f80LL),reale(5207764,0x9d4c81592dc00LL),
1250  -reale(4682178,0xdef9cf054a880LL),reale(3431350,0xdcd7f0ab97d00LL),
1251  -reale(3036244,0xeb9781cfe3980LL),reale(2097463,0x35c6f48ae00LL),
1252  -reale(1714507,0xab45478b85280LL),reale(997568,0xe75b4df283f00LL),
1253  -reale(555001,0x356f72a492380LL),reale(383325,0x3033ad4799914LL),
1254  reale(12305436712LL,0x56b51693aedc3LL),
1255  // C4[1], coeff of eps^19, polynomial in n of order 10
1256  -reale(10475274,0x80e3f984eb560LL),reale(7761418,0x6cb2d37d31d50LL),
1257  -reale(6912729,0x2574b8548f80LL),reale(5061056,0xbff13b9f8e7b0LL),
1258  -reale(4542234,0x9c8561f8559a0LL),reale(3202970,0x45874de1c0010LL),
1259  -reale(2776395,0x2331e9957c0LL),reale(1780809,0x24244086de270LL),
1260  -reale(1321308,0xb7d4404aacde0LL),reale(572110,0xf0d923e3d0ad0LL),
1261  reale(142666,0x15ad08c690505LL),reale(12305436712LL,0x56b51693aedc3LL),
1262  // C4[1], coeff of eps^18, polynomial in n of order 11
1263  -reale(16991539,0x3bfa3a952a5c0LL),reale(12232630,0xc216625651e80LL),
1264  -reale(10582386,0xca84c044c7740LL),reale(7659664,0x22fef68736200LL),
1265  -reale(6852368,0xbf4b993050cc0LL),reale(4854746,0x78ae9dfa88580LL),
1266  -reale(4332124,0x5850c11d91e40LL),reale(2896859,0x8330e6242d100LL),
1267  -reale(2410777,0x3c4e4b27563c0LL),reale(1359574,0x6f5bc7e308c80LL),
1268  -reale(775169,0xf705a84369540LL),reale(525423,0x9fd72933d2d3aLL),
1269  reale(12305436712LL,0x56b51693aedc3LL),
1270  // C4[1], coeff of eps^17, polynomial in n of order 12
1271  -reale(31605635,0x9b2a6245129c0LL),reale(21349095,0xec111ef51efd0LL),
1272  -reale(17343382,0xc6b59d854f620LL),reale(12224940,0xad54b9902f0LL),
1273  -reale(10665275,0xcb2c9d1586680LL),reale(7495419,0x2bbe593f97c10LL),
1274  -reale(6731026,0x5bd11498926e0LL),reale(4567553,0xbb95797dfef30LL),
1275  -reale(4019270,0xe17fb3dce340LL),reale(2483542,0x18261977df050LL),
1276  -reale(1889445,0x252a3b83f47a0LL),reale(789608,0x3727b34041370LL),
1277  reale(196748,0x5030b26b63d7fLL),reale(12305436712LL,0x56b51693aedc3LL),
1278  // C4[1], coeff of eps^16, polynomial in n of order 13
1279  -reale(83651327,0x7df35b769ce00LL),reale(46183264,0x6a662d0fec800LL),
1280  -reale(32523895,0xbf44a3e60200LL),reale(21575930,0xbd1dba7599c00LL),
1281  -reale(17706525,0xdbcb8c6749600LL),reale(12151631,0x7c587583d3000LL),
1282  -reale(10707728,0xa79806e6f4a00LL),reale(7245171,0x8aa6d7e27c400LL),
1283  -reale(6517082,0x9ff2c462fde00LL),reale(4168671,0x7a21919979800LL),
1284  -reale(3551918,0x26047c5101200LL),reale(1918361,0x786d4fd8aec00LL),
1285  -reale(1131511,0x7e7a26769a600LL),reale(747310,0xbb693903a2f10LL),
1286  reale(12305436712LL,0x56b51693aedc3LL),
1287  // C4[1], coeff of eps^15, polynomial in n of order 14
1288  -reale(63372442,0x2cb5338504ea0LL),reale(236021120,0xed659df2db350LL),
1289  -reale(86667901,0x5273be9be40LL),reale(47209611,0xc1161d91d1e30LL),
1290  -reale(33537857,0x3d1f3cdba35e0LL),reale(21739691,0xd5c3b2c9df710LL),
1291  -reale(18074666,0x2123c601d8980LL),reale(11984705,0x3d2e52a8729f0LL),
1292  -reale(10682808,0x1cfcfab158d20LL),reale(6875060,0xeec2e9924a2d0LL),
1293  -reale(6158904,0xf3892aedc14c0LL),reale(3612073,0x775a08e9d4db0LL),
1294  -reale(2844696,0x4fdad4b74f460LL),reale(1130419,0xe52285ff91690LL),
1295  reale(281319,0xf8ed6ce679421LL),reale(12305436712LL,0x56b51693aedc3LL),
1296  // C4[1], coeff of eps^14, polynomial in n of order 15
1297  reale(377918798,0xab0ca9f0672c0LL),-reale(418618018,0x8099eba53f80LL),
1298  -reale(60854873,0x3eafa33f453c0LL),reale(245263030,0xf5560cf897d00LL),
1299  -reale(90083330,0xb4182a1e90640LL),reale(48226005,0xa87e22e4ae980LL),
1300  -reale(34666917,0x2b03feac26cc0LL),reale(21804113,0xa9bac4593e00LL),
1301  -reale(18434597,0x75e58711b4f40LL),reale(11683388,0x18da60c9eb280LL),
1302  -reale(10544255,0x717858fde75c0LL),reale(6335167,0xce8110cc57f00LL),
1303  -reale(5568830,0x1a6ca9ba6a840LL),reale(2826076,0xf4ab3cac7db80LL),
1304  -reale(1750284,0x2ff80145eaec0LL),reale(1113751,0xd17a5fb748e66LL),
1305  reale(12305436712LL,0x56b51693aedc3LL),
1306  // C4[1], coeff of eps^13, polynomial in n of order 16
1307  -reale(7676111,0x5b2a6c5f6c100LL),-reale(64415807,0x4cf1fd08a9430LL),
1308  reale(389009273,0x614b445047d20LL),-reale(437396877,0xd309fa5941090LL),
1309  -reale(57368388,0x6af986a1a0c0LL),reale(255600151,0x61702d3245910LL),
1310  -reale(94005962,0x2924b0b2256a0LL),reale(49188288,0xa4967a4d0acb0LL),
1311  -reale(35935634,0xccf0586b2e080LL),reale(21713831,0x3869a07cfee50LL),
1312  -reale(18759173,0xcf3c8197a7a60LL),reale(11187408,0x277eed08021f0LL),
1313  -reale(10209411,0xbc33094486040LL),reale(5549613,0x5f33e35304b90LL),
1314  -reale(4590963,0x90f6e6e49ce20LL),reale(1692490,0x5de933ef26f30LL),
1315  reale(420297,0x50d0b3d8c1d9bLL),reale(12305436712LL,0x56b51693aedc3LL),
1316  // C4[1], coeff of eps^12, polynomial in n of order 17
1317  -reale(852919,0x6a82cfa963080LL),-reale(2188759,0x20ca5d762f800LL),
1318  -reale(7786929,0x3421dcca91f80LL),-reale(65787035,0x1d560be049100LL),
1319  reale(401061675,0x8c48395cfc980LL),-reale(458713135,0x22175c326fa00LL),
1320  -reale(52544362,0x54a9b8a28c580LL),reale(267237346,0x9f71e62ba7d00LL),
1321  -reale(98592445,0x567d144d01c80LL),reale(50019657,0x7efcd81e48400LL),
1322  -reale(37374118,0xabf7952238b80LL),reale(21383288,0xfc61768bbcb00LL),
1323  -reale(18992011,0x5234632e06280LL),reale(10406178,0xe1fef86250200LL),
1324  -reale(9523344,0xe57e66503f180LL),reale(4398013,0x8a16c0de4d900LL),
1325  -reale(2932033,0xa738784cb8880LL),reale(1764194,0xc6396b58af30cLL),
1326  reale(12305436712LL,0x56b51693aedc3LL),
1327  // C4[1], coeff of eps^11, polynomial in n of order 18
1328  -reale(210362,0x76b369d3025e0LL),-reale(399459,0x1eaf9acef0ab0LL),
1329  -reale(856141,0xe229f972ba700LL),-reale(2206922,0xef935c87bb50LL),
1330  -reale(7896496,0x6b0bc697c0820LL),-reale(67217074,0x2cc6331df1df0LL),
1331  reale(414202467,0x2b5605d0252c0LL),-reale(483149583,0xa02db175d690LL),
1332  -reale(45836711,0xc18042256fa60LL),reale(280420397,0xa9af8baa076d0LL),
1333  -reale(104078404,0x7a91f5b525380LL),reale(50585814,0x9d940e3bb2630LL),
1334  -reale(39015494,0x6a69555b81ca0LL),reale(20678727,0x5f0f1f3a9390LL),
1335  -reale(19012332,0x416957968b9c0LL),reale(9200947,0xc21b589061af0LL),
1336  -reale(8178296,0xad1e8ab768ee0LL),reale(2676456,0xd6956da2a1850LL),
1337  reale(661843,0xede00571b821dLL),reale(12305436712LL,0x56b51693aedc3LL),
1338  // C4[1], coeff of eps^10, polynomial in n of order 19
1339  -reale(73282,0x88acf774cdcc0LL),-reale(119856,0xfafc4232d6980LL),
1340  -reale(209310,0xc95dad3d9d040LL),-reale(398728,0xc3246fdb30c00LL),
1341  -reale(857927,0x8ca89fdf097c0LL),-reale(2222415,0x7f22a8f79ee80LL),
1342  -reale(8002412,0xa401cae100b40LL),-reale(68698832,0xcf05dd2d1e900LL),
1343  reale(428572510,0x4af905b8fd40LL),-reale(511480829,0xaa7af93dad380LL),
1344  -reale(36412636,0xa51695c145640LL),reale(295430858,0x62539c3ab7a00LL),
1345  -reale(110834541,0xf7ac6a286ddc0LL),reale(50648730,0xf42d6a1912780LL),
1346  -reale(40882711,0xc825af61d7140LL),reale(19389515,0xc578a6be65d00LL),
1347  -reale(18548541,0x30b0433e6e8c0LL),reale(7353872,0xa4f0c77ab4280LL),
1348  -reale(5517208,0xc642445621c40LL),reale(3035548,0x619b33f1391d2LL),
1349  reale(12305436712LL,0x56b51693aedc3LL),
1350  // C4[1], coeff of eps^9, polynomial in n of order 20
1351  -reale(31116,0x5ced59f2a6a40LL),-reale(46466,0x39ef1648a3c30LL),
1352  -reale(72339,0x13bec712995a0LL),-reale(118591,0xe96704ee23c10LL),
1353  -reale(207681,0xf3272ddf69500LL),-reale(396975,0x5586a3fda15f0LL),
1354  -reale(857776,0x96a9e394d3460LL),-reale(2234014,0x9c760527155d0LL),
1355  -reale(8101033,0x1f3b77f93fc0LL),-reale(70217181,0xc7476a97287b0LL),
1356  reale(444320933,0x84d59896b7ce0LL),-reale(544755366,0x60ab42e093790LL),
1357  -reale(22958170,0x5fc77e584ca80LL),reale(312550991,0xea91e4bc80e90LL),
1358  -reale(119474190,0x655c7a979e1e0LL),reale(49778595,0x69cfb591beb0LL),
1359  -reale(42938053,0xad555dfab9540LL),reale(17185991,0x9567a8e814cd0LL),
1360  -reale(16947236,0xc941a0517b0a0LL),reale(4507394,0xb6bfddcb2cf0LL),
1361  reale(1103154,0xee71952935057LL),reale(12305436712LL,0x56b51693aedc3LL),
1362  // C4[1], coeff of eps^8, polynomial in n of order 21
1363  -reale(15013,0x669ca85dbff00LL),-reale(21081,0x7f4d799198400LL),
1364  -reale(30470,0xbdb587d74d900LL),-reale(45587,0xe4badb51b1a00LL),
1365  -reale(71124,0x646ea35b6300LL),-reale(116891,0x8adb62aa4d000LL),
1366  -reale(205315,0x1aa2ab2ec7d00LL),-reale(393884,0x4b8d8eda78600LL),
1367  -reale(855000,0x2faa553050700LL),-reale(2239966,0xb31164c141c00LL),
1368  -reale(8186764,0x97347e701e100LL),-reale(71742883,0x7f111739b7200LL),
1369  reale(461586973,0x9a516d5401500LL),-reale(584418823,0xe1245bd6e6800LL),
1370  -reale(3315305,0x14110f9c0500LL),reale(331936814,0x28269ca022200LL),
1371  -reale(131069117,0x7ee7ad0730f00LL),reale(47184778,0x227a729454c00LL),
1372  -reale(44897669,0x9cd1b2a1e900LL),reale(13574545,0xcd96a182a3600LL),
1373  -reale(12485695,0x45db16a057300LL),reale(5879734,0x70bef82b8988LL),
1374  reale(12305436712LL,0x56b51693aedc3LL),
1375  // C4[1], coeff of eps^7, polynomial in n of order 22
1376  -reale(7900,0x638c66d8a8320LL),-reale(10613,0xf2ac3092c9cb0LL),
1377  -reale(14565,0xe107ae27501c0LL),-reale(20489,0xead89ce414d0LL),
1378  -reale(29670,0x849ce08edf860LL),-reale(44482,0xeb1f022729ef0LL),
1379  -reale(69562,0xbdfcfee35b00LL),-reale(114632,0x975e8fa16f10LL),
1380  -reale(201989,0x9411d71111da0LL),-reale(389021,0x33d7ff034b930LL),
1381  -reale(848628,0xc0285ec233440LL),-reale(2237713,0xb97d9ca55b150LL),
1382  -reale(8250880,0x9132887d792e0LL),-reale(73221392,0xf1ffe05c8b70LL),
1383  reale(480452831,0x383b5471fd280LL),-reale(632496874,0xca3591eba7b90LL),
1384  reale(26233104,0x13df159bb07e0LL),reale(353203487,0x101c2c33c4a50LL),
1385  -reale(147596513,0x7a337ff05e6c0LL),reale(41406718,0x88562e0e69230LL),
1386  -reale(45513246,0x22b5bfcbced60LL),reale(7934370,0xa8c8e9d8c2810LL),
1387  reale(1869414,0xdc5c61854a479LL),reale(12305436712LL,0x56b51693aedc3LL),
1388  // C4[1], coeff of eps^6, polynomial in n of order 23
1389  -reale(4406,0xf939ae5c97c40LL),-reale(5729,0xf863eba5bf80LL),
1390  -reale(7570,0xa927e082c4c0LL),-reale(10189,0xdc3d2b5930900LL),
1391  -reale(14011,0xfd72406188940LL),-reale(19751,0x4ee9330f94280LL),
1392  -reale(28665,0xa6c18d00fb1c0LL),-reale(43078,0xe8ed052a45400LL),
1393  -reale(67543,0xd4150add2640LL),-reale(111634,0xb28e55bb02580LL),
1394  -reale(197389,0xccdd68505cec0LL),-reale(381765,0x22e00b9b89f00LL),
1395  -reale(837258,0xa000eefe9340LL),-reale(2223425,0xd3d15b309a880LL),
1396  -reale(8279438,0xc28db224c5bc0LL),-reale(74551261,0xb7816e54f2a00LL),
1397  reale(500824278,0x3891b999befc0LL),-reale(691847154,0x918a2dd450b80LL),
1398  reale(72461747,0xa045596356740LL),reale(374046829,0x41b777218cb00LL),
1399  -reale(172833056,0x62b9485f4dd40LL),reale(29915148,0x80284d25e7180LL),
1400  -reale(39423763,0x40d338467c5c0LL),reale(13659048,0x68e501c228ffeLL),
1401  reale(12305436712LL,0x56b51693aedc3LL),
1402  // C4[1], coeff of eps^5, polynomial in n of order 24
1403  -reale(2545,0x1363104362d80LL),-reale(3226,0xe67b1424a4830LL),
1404  -reale(4144,0x8c711302fa660LL),-reale(5400,0xc1bfe2853af90LL),
1405  -reale(7153,0xb2c26c1682b40LL),-reale(9653,0x9e8ef4e7cf0f0LL),
1406  -reale(13308,0xeb09aee491820LL),-reale(18810,0x561040fe22850LL),
1407  -reale(27375,0xc35e0fb3fc900LL),-reale(41260,0x7d7f41fc271b0LL),
1408  -reale(64893,0xc7a96414399e0LL),-reale(107622,0xe02e2157de910LL),
1409  -reale(191035,0x6ce8a0a1be6c0LL),-reale(371181,0x96988a373aa70LL),
1410  -reale(818768,0xa91a46aa60ba0LL),-reale(2191167,0x9fde37effd1d0LL),
1411  -reale(8249435,0xe27cdc35b6480LL),-reale(75540143,0x55cc77d97b30LL),
1412  reale(522119910,0xf5aa540a8b2a0LL),-reale(766397212,0x64559a510c290LL),
1413  reale(148547296,0x8152775e2ddc0LL),reale(385247751,0x81b301a133c10LL),
1414  -reale(213402544,0x90fce845e3f20LL),reale(10198756,0x255c7c31664b0LL),
1415  reale(1365904,0xd74a19c69db33LL),reale(12305436712LL,0x56b51693aedc3LL),
1416  // C4[1], coeff of eps^4, polynomial in n of order 25
1417  -real(0x5cd20bbc3c672180LL),-real(0x73720b2d98187c00LL),
1418  -reale(2321,0xc4eb857568680LL),-reale(2952,0xb2617088c8f00LL),
1419  -reale(3804,0x417bd8fa2e380LL),-reale(4973,0x5ec86f601d200LL),
1420  -reale(6609,0x998272f30a880LL),-reale(8950,0x197c7ab46b500LL),
1421  -reale(12382,0xcc481e2a44580LL),-reale(17565,0x5f7861969a800LL),
1422  -reale(25660,0x4a6f330e22a80LL),-reale(38825,0xe447100991b00LL),
1423  -reale(61313,0x47573aa0ec780LL),-reale(102123,0xa55bb6037e00LL),
1424  -reale(182121,0xfb4d0590e8c80LL),-reale(355742,0x340be91b74100LL),
1425  -reale(789743,0xf318e4285e980LL),-reale(2131260,0x2c59b0f82d400LL),
1426  -reale(8121193,0x3f9cc7c594e80LL),-reale(75808472,0x814742dd4a700LL),
1427  reale(542406027,0xe15955752d480LL),-reale(860719085,0xb088c959b2a00LL),
1428  reale(281794203,0x6d691a09a0f80LL),reale(349671639,0x4a19c69db3300LL),
1429  -reale(268081590,0x1f35e51280d80LL),reale(42616231,0x9d4bdce6b704LL),
1430  reale(12305436712LL,0x56b51693aedc3LL),
1431  // C4[1], coeff of eps^3, polynomial in n of order 26
1432  -real(0x34f88b61ee2c2e60LL),-real(0x40e8b73250ad02b0LL),
1433  -real(0x50402824a1190680LL),-real(0x643133a56bf6de50LL),
1434  -real(0x7e70b50d7e53aea0LL),-reale(2583,0x89ee9103c6bf0LL),
1435  -reale(3343,0x2d56b6f20aac0LL),-reale(4390,0x9150bee746f90LL),
1436  -reale(5862,0xecb9ee1767ee0LL),-reale(7978,0x9b4551158ad30LL),
1437  -reale(11096,0x13774a5e7af00LL),-reale(15825,0x3f23db737e8d0LL),
1438  -reale(23248,0xf45a340cbf20LL),-reale(35380,0xaf4478627e670LL),
1439  -reale(56209,0x8a81f32e3340LL),-reale(94205,0x2f98ae2576a10LL),
1440  -reale(169093,0xeae4ad4ee8f60LL),-reale(332577,0xf0ed8664037b0LL),
1441  -reale(743995,0x906300fb45780LL),-reale(2026493,0x9c6e844791350LL),
1442  -reale(7821602,0x7531c16940fa0LL),-reale(74557824,0x1ed43b2e7c0f0LL),
1443  reale(555703654,0x34418f385c440LL),-reale(974709694,0x84f4a67130490LL),
1444  reale(527421389,0x42f7f1faaa020LL),reale(94702735,0xa411a5cab5dd0LL),
1445  -reale(117194635,0x5b0909f7a774bLL),
1446  reale(12305436712LL,0x56b51693aedc3LL),
1447  // C4[1], coeff of eps^2, polynomial in n of order 27
1448  -real(0x1bd57a8f504dd3c0LL),-real(0x21b6ff10b9172180LL),
1449  -real(0x292825cda3a88940LL),-real(0x32aacbfadedfca00LL),
1450  -real(0x3ef38a62fa0322c0LL),-real(0x4f013a1cfd80d280LL),
1451  -real(0x64414a4729c69840LL),-reale(2060,0x90ead26a03300LL),
1452  -reale(2683,0x237c6d92be1c0LL),-reale(3547,0x3d9a05c33e380LL),
1453  -reale(4770,0x6ec9da59bf740LL),-reale(6541,0x1657e411dc00LL),
1454  -reale(9170,0x1a8b4944fd0c0LL),-reale(13190,0xb069410801480LL),
1455  -reale(19554,0x9e393a3b06640LL),-reale(30047,0xba30505448500LL),
1456  -reale(48224,0x707d4f4f6afc0LL),-reale(81689,0xf05ca40b52580LL),
1457  -reale(148265,0xab90de58ba540LL),-reale(294962,0x64373b047ee00LL),
1458  -reale(667587,0xc0c688fa83ec0LL),-reale(1840377,0xc842d822d680LL),
1459  -reale(7199121,0xfc41489b57440LL),-reale(69934327,0xdb9ec152bd700LL),
1460  reale(541991040,0xe60e5a413c240LL),-reale(1060670639,0x2d9274118e780LL),
1461  reale(833384073,0xa3ce7fc4a6cc0LL),-reale(234389270,0xb61213ef4ee96LL),
1462  reale(12305436712LL,0x56b51693aedc3LL),
1463  // C4[1], coeff of eps^1, polynomial in n of order 28
1464  -real(0xb4c355cd41c92c0LL),-real(0xd8fea3a41cc7830LL),
1465  -real(0x1064f0c6b9a6ad20LL),-real(0x13f7a88902ef1b10LL),
1466  -real(0x1884a414973fcb80LL),-real(0x1e5fa2ae5243d7f0LL),
1467  -real(0x25fe0bb384ddd9e0LL),-real(0x3006f6e3e0e25ad0LL),
1468  -real(0x3d6c2c13c34ec440LL),-real(0x4f91f34825bd4fb0LL),
1469  -real(0x688ffb74f98676a0LL),-reale(2233,0xdec33bb086290LL),
1470  -reale(3036,0xe53843c2cdd00LL),-reale(4213,0xb13e1137e3f70LL),
1471  -reale(5984,0xaa1cca8abe360LL),-reale(8732,0xb9880d6c69250LL),
1472  -reale(13152,0x1eadcfcfd75c0LL),-reale(20566,0x4e1752c3c0730LL),
1473  -reale(33653,0xf4262a5798020LL),-reale(58247,0x3a420e3524a10LL),
1474  -reale(108257,0x7934f39e3ee80LL),-reale(221025,0xaccc1c0dc06f0LL),
1475  -reale(514222,0xffbb852faace0LL),-reale(1456965,0x29e8a4070e9d0LL),
1476  -reale(5827860,0xa7a2901c3a740LL),-reale(56821641,0x6270fd1339eb0LL),
1477  reale(416692036,0xd1e73fe253660LL),-reale(625038055,0x3adadfd37d190LL),
1478  reale(273454149,0x29bfc1ec86bafLL),
1479  reale(12305436712LL,0x56b51693aedc3LL),
1480  // C4[2], coeff of eps^29, polynomial in n of order 0
1481  185528,real(30429886905LL),
1482  // C4[2], coeff of eps^28, polynomial in n of order 1
1483  real(17366491968LL),real(4404238552LL),real(0x74e318fa9c07fLL),
1484  // C4[2], coeff of eps^27, polynomial in n of order 2
1485  real(412763643136LL),-real(248137794944LL),real(164642704408LL),
1486  real(0x4d882f0532d9e9LL),
1487  // C4[2], coeff of eps^26, polynomial in n of order 3
1488  real(0x11462b92d913a0LL),-real(0xdd4620ebadc40LL),
1489  real(0x5974730e46be0LL),real(0x16bcec57851ccLL),
1490  reale(33547,0x1cf91962af003LL),
1491  // C4[2], coeff of eps^25, polynomial in n of order 4
1492  real(0xc83679b433c00LL),-real(0xb29b6d58dfb00LL),real(0x5f4e3bdd4de00LL),
1493  -real(0x3affd9960e900LL),real(0x2665fb625f490LL),
1494  reale(15809,0x8f200ee7e2a7dLL),
1495  // C4[2], coeff of eps^24, polynomial in n of order 5
1496  real(0x67b92a8524a18e80LL),-real(0x609d7d3ca356ae00LL),
1497  real(0x39db180d1b52d580LL),-real(0x2fa1e9183dec9700LL),
1498  real(0x1294d8f2627edc80LL),real(0x4bc94ddbc9bad70LL),
1499  reale(22813193,0xc1b4051297e97LL),
1500  // C4[2], coeff of eps^23, polynomial in n of order 6
1501  reale(24830,0x3d0fb879bb600LL),-reale(23212,0xa100635ccdb00LL),
1502  reale(14957,0x147cd156ba400LL),-reale(13653,0x51ea4b9c89d00LL),
1503  reale(7024,0x2535370909200LL),-reale(4511,0x3af63b60c9f00LL),
1504  reale(2865,0xf50f5adcce1f0LL),reale(235736335,0x7c44346acc6c3LL),
1505  // C4[2], coeff of eps^22, polynomial in n of order 7
1506  reale(1046092,0x25a6222f26060LL),-reale(949436,0x14a3a722f1840LL),
1507  reale(652845,0xb96689ab42720LL),-reale(615919,0x6f1345ab50580LL),
1508  reale(356624,0x982d38f2a9de0LL),-reale(303839,0x22c37d5c832c0LL),
1509  reale(113262,0x286189b57e4a0LL),reale(28978,0x12ae8b059bc84LL),
1510  reale(6836353729LL,0x13b9f01928417LL),
1511  // C4[2], coeff of eps^21, polynomial in n of order 8
1512  reale(4643688,0x71b79cbf7cc00LL),-reale(3959056,0x83e38a4f9d180LL),
1513  reale(2926140,0x6f81ce5fc3900LL),-reale(2722736,0xdd03df5282c80LL),
1514  reale(1710940,0xc70403130e600LL),-reale(1602990,0x9ebb76967a780LL),
1515  reale(787738,0x6bf60987b1300LL),-reale(530212,0xcde2a88ab0280LL),
1516  reale(326645,0xab9033855e368LL),reale(20509061187LL,0x3b2dd04b78c45LL),
1517  // C4[2], coeff of eps^20, polynomial in n of order 9
1518  reale(2366152,0x4fc26559c91c0LL),-reale(1830925,0x4d73259824200LL),
1519  reale(1477489,0x62c9a90a52a40LL),-reale(1299560,0xe7bf798235180LL),
1520  reale(885946,0x5cb0a99f5e2c0LL),-reale(843740,0x47153eb842100LL),
1521  reale(469359,0x79db9d7cfb40LL),-reale(417111,0x1a4c5e2477080LL),
1522  reale(146559,0x51b0aa3dcb3c0LL),reale(37677,0x6dd5ee66abd48LL),
1523  reale(6836353729LL,0x13b9f01928417LL),
1524  // C4[2], coeff of eps^19, polynomial in n of order 10
1525  reale(11390177,0xa8f910291300LL),-reale(7729638,0x6f23cf47c2480LL),
1526  reale(6929266,0x5fb765e065c00LL),-reale(5514735,0x5eb0876136380LL),
1527  reale(4148166,0x27d6c40aa500LL),-reale(3788609,0xfef33001c8280LL),
1528  reale(2322601,0x1de03c2bc2e00LL),-reale(2237878,0x77b7642b94180LL),
1529  reale(1037457,0x571c66f013700LL),-reale(742165,0x8c39e6d5b6080LL),
1530  reale(439349,0xf7cfa6e796fc8LL),reale(20509061187LL,0x3b2dd04b78c45LL),
1531  // C4[2], coeff of eps^18, polynomial in n of order 11
1532  reale(19643005,0x3eb0d373a0e0LL),-reale(11359402,0x98e8f09139c0LL),
1533  reale(11381255,0xacc1b03fd73a0LL),-reale(7834592,0x92741bdd3b00LL),
1534  reale(6664656,0xa317edb25b660LL),-reale(5516050,0x3ff87cc43bc40LL),
1535  reale(3774293,0xd5e83edc68920LL),-reale(3594547,0xbec9f61701d80LL),
1536  reale(1908400,0x61c5f793c0be0LL),-reale(1786093,0xfaf3f7a19bec0LL),
1537  reale(579905,0x9d50696085ea0LL),reale(150042,0xa9efa9004c604LL),
1538  reale(20509061187LL,0x3b2dd04b78c45LL),
1539  // C4[2], coeff of eps^17, polynomial in n of order 12
1540  reale(38321815,0x1e48683dc9800LL),-reale(18616913,0x727791f8dfa00LL),
1541  reale(20113440,0xb841223d75400LL),-reale(11495937,0x9838f29931e00LL),
1542  reale(11261630,0x21fd3747b1000LL),-reale(7960716,0x75135ee9c200LL),
1543  reale(6275150,0xa8a2fa972cc00LL),-reale(5471565,0x945df446e600LL),
1544  reale(3293426,0x6eab44c698800LL),-reale(3257897,0x559df659f8a00LL),
1545  reale(1401057,0x756ea738a4400LL),-reale(1086629,0xf49cb94a8ae00LL),
1546  reale(610116,0x479bdc6c290e0LL),reale(20509061187LL,0x3b2dd04b78c45LL),
1547  // C4[2], coeff of eps^16, polynomial in n of order 13
1548  reale(102781113,0x98fe5a9192500LL),-reale(40336104,0xccc089a851400LL),
1549  reale(40165652,0x6e617f3b73300LL),-reale(18616625,0x95536d5576600LL),
1550  reale(20514709,0xd39b96f5ec100LL),-reale(11691503,0x7c1154bb0b800LL),
1551  reale(10980290,0x40d1adbe6cf00LL),-reale(8104717,0x4a433bfb60a00LL),
1552  reale(5726151,0xc3b2b2965d00LL),-reale(5331323,0xa4559d80c5c00LL),
1553  reale(2689333,0x7cf2f82446b00LL),-reale(2678624,0x7904ff2b8ae00LL),
1554  reale(779755,0xfacbca777f900LL),reale(203539,0xb4670b88476e0LL),
1555  reale(20509061187LL,0x3b2dd04b78c45LL),
1556  // C4[2], coeff of eps^15, polynomial in n of order 14
1557  -reale(23295494,0x8be82e34e6400LL),-reale(256522224,0x1264f586eb600LL),
1558  reale(109420782,0x9692235ce1800LL),-reale(40005401,0x76f47ac799a00LL),
1559  reale(42210732,0x9175627089400LL),-reale(18637789,0x360d04338fe00LL),
1560  reale(20777547,0x32d7f69c1000LL),-reale(11978808,0x3c6fce691e200LL),
1561  reale(10467739,0x890cbd2438c00LL),-reale(8246695,0x5d95a89294600LL),
1562  reale(4981450,0x2e83f5dba0800LL),-reale(4997884,0x48d2490e42a00LL),
1563  reale(1949724,0xd6b9d613a8400LL),-reale(1687002,0x42840cd678e00LL),
1564  reale(881316,0x5154c853b06e0LL),reale(20509061187LL,0x3b2dd04b78c45LL),
1565  // C4[2], coeff of eps^14, polynomial in n of order 15
1566  -reale(315852553,0x127aa1fb9560LL),reale(452067016,0x32f06289dc340LL),
1567  -reale(36389203,0xc905d2dd0bc20LL),-reale(265701999,0x414c3c9652f80LL),
1568  reale(117462481,0xb44ff33f8ed20LL),-reale(39375172,0xb9e521c5c6240LL),
1569  reale(44443567,0x98c20ae94660LL),-reale(18737379,0x9088d09ce7500LL),
1570  reale(20789662,0x74772cb6e2fa0LL),-reale(12399165,0xc39cbc16e07c0LL),
1571  reale(9634015,0x48be8ec7788e0LL),-reale(8326007,0x8f1246dddba80LL),
1572  reale(4012687,0x8a9763f933220LL),-reale(4283805,0xe15bd5742d40LL),
1573  reale(1064918,0x3e0322e890b60LL),reale(281445,0x189dacfa2913cLL),
1574  reale(20509061187LL,0x3b2dd04b78c45LL),
1575  // C4[2], coeff of eps^13, polynomial in n of order 16
1576  reale(4607575,0xc9d7900c88800LL),reale(44527228,0x61b96ac1eb380LL),
1577  -reale(320302478,0xa276d3450e900LL),reale(471382647,0x4d0623cc86a80LL),
1578  -reale(52535715,0x404f1a5b09a00LL),-reale(275262322,0xf3348bb543e80LL),
1579  reale(127364360,0xbf0504ec13500LL),-reale(38376532,0x74833ebc78780LL),
1580  reale(46801690,0x6a3245e5c4400LL),-reale(19021914,0x3bda110f1b080LL),
1581  reale(20372666,0xf7fc04d85300LL),-reale(12992077,0x825700022f980LL),
1582  reale(8374681,0xba502a56d2200LL),-reale(8187369,0x8d48a8bba280LL),
1583  reale(2818780,0x7113503f27100LL),-reale(2834494,0xf2038f04beb80LL),
1584  reale(1337917,0xc906f381aecf8LL),reale(20509061187LL,0x3b2dd04b78c45LL),
1585  // C4[2], coeff of eps^12, polynomial in n of order 17
1586  reale(388658,0x19c7c6f8ea2c0LL),reale(1117971,0xaadcbdb38ac00LL),
1587  reale(4519560,0xaee28ee393540LL),reale(44278119,0xe09b9f50af680LL),
1588  -reale(324493551,0x5c00bae29840LL),reale(492697628,0x7d1cc3fd18100LL),
1589  -reale(72657626,0xb42806bf185c0LL),-reale(284925253,0x57cc84a557480LL),
1590  reale(139770748,0x33e950dc3acc0LL),-reale(36961790,0xef70c005baa00LL),
1591  reale(49119876,0xa052562f03f40LL),-reale(19681131,0xbaa50226adf80LL),
1592  reale(19252422,0xc3af9265b71c0LL),-reale(13755373,0x2f0960c0cd500LL),
1593  reale(6600104,0x6565773f88440LL),-reale(7462805,0xbfb982e534a80LL),
1594  reale(1452711,0x6b2cd84feb6c0LL),reale(390635,0x965de9321fbe8LL),
1595  reale(20509061187LL,0x3b2dd04b78c45LL),
1596  // C4[2], coeff of eps^11, polynomial in n of order 18
1597  reale(73868,0xf53613318fd00LL),reale(155158,0x6bea1fc037e80LL),
1598  reale(370865,0xe686995a3a800LL),reale(1077531,0xb6b00d00e5180LL),
1599  reale(4409046,0x1d5f244685300LL),reale(43860006,0xf94485a638480LL),
1600  -reale(328226208,0x254b380304200LL),reale(516242826,0x48cfde1d3d780LL),
1601  -reale(98028430,0xc7227901d5700LL),-reale(294125055,0xf41dd5cbff580LL),
1602  reale(155591277,0xc58331ae9d400LL),-reale(35168366,0x6c3820d072280LL),
1603  reale(51023141,0xfcae9f00dff00LL),-reale(21033813,0x6b0840ce0ef80LL),
1604  reale(17035669,0xa0ab037f7ea00LL),-reale(14520825,0x209891efc9c80LL),
1605  reale(4321952,0xda1143d705500LL),-reale(5322397,0x9ed9b44796980LL),
1606  reale(2165443,0xa5af00ad58358LL),reale(20509061187LL,0x3b2dd04b78c45LL),
1607  // C4[2], coeff of eps^10, polynomial in n of order 19
1608  reale(19809,0x63304b335a660LL),reale(35566,0xcb4164f348e40LL),
1609  reale(68577,0xe86c972757e20LL),reale(145245,0xbc9cc7446e200LL),
1610  reale(350489,0x7e29a3d4285e0LL),reale(1029750,0x45087f82835c0LL),
1611  reale(4270842,0x2203011585da0LL),reale(43220702,0xa65b618eca980LL),
1612  -reale(331199124,0xa89ccd5235aa0LL),reale(542217711,0x200e3727c5d40LL),
1613  -reale(130429686,0x3b8b1d50d02e0LL),-reale(301749371,0x2c4d836f88f00LL),
1614  reale(176097282,0x8ddfe73d104e0LL),-reale(33280999,0x8c12e2a85fb40LL),
1615  reale(51717673,0x23cc103525ca0LL),-reale(23558374,0x76fe0e70fc780LL),
1616  reale(13250268,0x69c1c450ca460LL),-reale(14595460,0xd8a80a3d5d3c0LL),
1617  reale(1848614,0x7d3564e37c20LL),reale(506231,0x2a6100a6a6db4LL),
1618  reale(20509061187LL,0x3b2dd04b78c45LL),
1619  // C4[2], coeff of eps^9, polynomial in n of order 20
1620  reale(6397,0xfcd62c9faa400LL),reale(10440,0x3fc8ff8e75700LL),
1621  reale(17841,0xb7bede1dba00LL),reale(32272,0x7935213063d00LL),
1622  reale(62742,0x8933a9bfd5000LL),reale(134128,0x223daf23d6300LL),
1623  reale(327129,0xfca43cca0e600LL),reale(973230,0x31dda9e44900LL),
1624  reale(4098328,0x3528b970ffc00LL),reale(42289297,0xe5d54d5326f00LL),
1625  -reale(332951092,0xecfda756dee00LL),reale(570709002,0x2878cf4ff5500LL),
1626  -reale(172380399,0x5788b53115800LL),-reale(305626020,0x9c65fcc7d8500LL),
1627  reale(202987914,0xbd0aab0ad3e00LL),-reale(32233434,0x3f0406dec9f00LL),
1628  reale(49604551,0xc747777555400LL),-reale(27757216,0x323bffb167900LL),
1629  reale(7652705,0x1c15203ae6a00LL),-reale(11782806,0x2b7827f239300LL),
1630  reale(3811565,0x362856b8e6d30LL),reale(20509061187LL,0x3b2dd04b78c45LL),
1631  // C4[2], coeff of eps^8, polynomial in n of order 21
1632  reale(2297,0xe5959dcaf9680LL),reale(3515,0xaf44e93439a00LL),
1633  reale(5557,0xf844363205d80LL),reale(9134,0x3148872cf3100LL),
1634  reale(15730,0x1f27208afe480LL),reale(28695,0xbe2e993314800LL),
1635  reale(56314,0x2c7b05479ab80LL),reale(121661,0x287926e675f00LL),
1636  reale(300328,0xfc8a376113280LL),reale(906274,0xf1fb199eef600LL),
1637  reale(3883000,0x5f528c391f980LL),reale(40968060,0xe6e08c5558d00LL),
1638  -reale(332763533,0x8282a4a507f80LL),reale(601507851,0xf6ba284c8a400LL),
1639  -reale(227453313,0x642fd223ab880LL),-reale(301473974,0xbe5976c5a4500LL),
1640  reale(238209921,0x57c5b91e6ce80LL),-reale(34582562,0x41ecac4f5ae00LL),
1641  reale(41696071,0xee870caef9580LL),-reale(33183269,0xa456f79c1700LL),
1642  reale(1407347,0x27b05f0931c80LL),reale(329283,0x26010fabff570LL),
1643  reale(20509061187LL,0x3b2dd04b78c45LL),
1644  // C4[2], coeff of eps^7, polynomial in n of order 22
1645  real(0x367dbe5da7953e00LL),real(0x4f9a921ac6fb1900LL),
1646  real(0x773454548df74400LL),reale(2938,0xbc18faed4af00LL),
1647  reale(4681,0x407a350a64a00LL),reale(7756,0xa0ed83ee90500LL),
1648  reale(13477,0x2fbfd87edd000LL),reale(24826,0x9ea174e739b00LL),
1649  reale(49249,0xd3391f1d95600LL),reale(107696,0xcac2013cff100LL),
1650  reale(269571,0xe064d3a745c00LL),reale(826840,0x70825da398700LL),
1651  reale(3613882,0x7ef0aa40a6200LL),reale(39120270,0xc5673698bdd00LL),
1652  -reale(329492011,0x53f65ac991800LL),reale(633695353,0xfeb5c44027300LL),
1653  -reale(300630213,0xecf09fbea9200LL),-reale(280700646,0xcee0a2073700LL),
1654  reale(282664342,0x7b726e8a17400LL),-reale(46720160,0x11dfe8c55a100LL),
1655  reale(23527957,0x90f427ad67a00LL),-reale(33848503,0x5eac35f0d4b00LL),
1656  reale(7456233,0x7c1f0b332cab0LL),reale(20509061187LL,0x3b2dd04b78c45LL),
1657  // C4[2], coeff of eps^6, polynomial in n of order 23
1658  real(0x14f52a063dc5fc20LL),real(0x1d93a1e9ceb48740LL),
1659  real(0x2a911c303b723a60LL),real(0x3ea26bba66a54980LL),
1660  real(0x5e84fad71b3608a0LL),reale(2349,0x85d3117e94bc0LL),
1661  reale(3776,0x1c9d51cf2c6e0LL),reale(6317,0x5193932d16e00LL),
1662  reale(11091,0xc7716ff97d520LL),reale(20667,0xe33c2c4a29040LL),
1663  reale(41523,0x1a30a42ae9360LL),reale(92100,0xbd0a1f1419280LL),
1664  reale(234309,0x70b77706661a0LL),reale(732507,0x72fafb4df54c0LL),
1665  reale(3276808,0xe462aef209fe0LL),reale(36551902,0x4c4d10a4b700LL),
1666  -reale(321265885,0x720bf168351e0LL),reale(664675522,0x65892c55e9940LL),
1667  -reale(398339257,0x2b82ef41c13a0LL),-reale(225754486,0xf240500d62480LL),
1668  reale(330356701,0xbb7252695baa0LL),-reale(82401980,0x37f104ae0a240LL),
1669  -reale(4970822,0x52bf5cccc8720LL),-reale(3278171,0x9e4b710fe0e14LL),
1670  reale(20509061187LL,0x3b2dd04b78c45LL),
1671  // C4[2], coeff of eps^5, polynomial in n of order 24
1672  real(0x7d5242068d47400LL),real(0xac3832c9e621080LL),
1673  real(0xf0840d5e59cf500LL),real(0x155fabefd3362980LL),
1674  real(0x1f01ffac4c30b600LL),real(0x2e0489bbd6aca280LL),
1675  real(0x461560bdbc05f700LL),real(0x6df6210d29c3bb80LL),
1676  reale(2857,0xf2e1b87d2f800LL),reale(4836,0xd8d8f4249b480LL),
1677  reale(8600,0x17271d36df900LL),reale(16248,0x163bc1ffccd80LL),
1678  reale(33146,0xc23750bad3a00LL),reale(74792,0x260310eab4680LL),
1679  reale(194024,0xef2cdae46fb00LL),reale(620545,0xfcf47db535f80LL),
1680  reale(2853712,0x7228ad7b17c00LL),reale(32984640,0x1c4ce82435880LL),
1681  -reale(304937768,0x83ef272fd0300LL),reale(687819348,0xf9e0f9c397180LL),
1682  -reale(526420007,0xa1ce2482e4200LL),-reale(101220737,0xb065c6f7c1580LL),
1683  reale(344186593,0xf79ee4a13ff00LL),-reale(151524377,0x682a2ddefc80LL),
1684  reale(15298134,0x380aba4a19708LL),reale(20509061187LL,0x3b2dd04b78c45LL),
1685  // C4[2], coeff of eps^4, polynomial in n of order 25
1686  real(0x2b077c634ede840LL),real(0x39e80232e455600LL),
1687  real(0x4f004399e9803c0LL),real(0x6d6a8dd96e7d980LL),
1688  real(0x9a16639c690ff40LL),real(0xdd0eb6a29ee1d00LL),
1689  real(0x143ca2e567649ac0LL),real(0x1e583a687f6ce080LL),
1690  real(0x2ebb5ae27bca9640LL),real(0x4a366ef6d0a8e400LL),
1691  real(0x7a244f6987aeb1c0LL),reale(3355,0xff6a995ee780LL),
1692  reale(6059,0x95d9afc38ad40LL),reale(11647,0x91c4ac30bab00LL),
1693  reale(24220,0xbe377a4d448c0LL),reale(55835,0xd9394a033ee80LL),
1694  reale(148417,0x27a782b394440LL),reale(488256,0xe5126fdac7200LL),
1695  reale(2322515,0xb040a0735fc0LL),reale(28019858,0x3d9464fe1f580LL),
1696  -reale(275064197,0x290d46715a4c0LL),reale(686424553,0x6984a82213900LL),
1697  -reale(677745912,0x9f6fb36960940LL),reale(151524377,0x682a2ddefc80LL),
1698  reale(169007958,0xfd6a53329f240LL),-reale(85232462,0x13a97b9cd6e08LL),
1699  reale(20509061187LL,0x3b2dd04b78c45LL),
1700  // C4[2], coeff of eps^3, polynomial in n of order 26
1701  real(0xc4c78b5f73e700LL),real(0x1046756e5efb980LL),
1702  real(0x15cbc98d9fba400LL),real(0x1d9279681ffce80LL),
1703  real(0x28b2f34344c6100LL),real(0x38e6214caec8380LL),
1704  real(0x50f0f0d0c655e00LL),real(0x7563dc0de2d1880LL),
1705  real(0xadfad5eb325db00LL),real(0x1083ab8775a8cd80LL),
1706  real(0x19c9d8efc1ad1800LL),real(0x29945e7f0056e280LL),
1707  real(0x4594bf2102ba5500LL),real(0x79a9d12705de9780LL),
1708  reale(3587,0xb2b264e0cd200LL),reale(7053,0x1d58043372c80LL),
1709  reale(15040,0x44c8073c3cf00LL),reale(35667,0x702872e47e180LL),
1710  reale(97902,0x6929355be8c00LL),reale(334186,0x1d1de4e87f680LL),
1711  reale(1659947,0xed2beccfc4900LL),reale(21110207,0x53559189eab80LL),
1712  -reale(222144335,0x8c70c0703ba00LL),reale(617753229,0x694fabb034080LL),
1713  -reale(769277606,0x6fd24e8e23d00LL),reale(454573131,0x1387e899cf580LL),
1714  -reale(104173009,0x3479cff894d98LL),
1715  reale(20509061187LL,0x3b2dd04b78c45LL),
1716  // C4[2], coeff of eps^2, polynomial in n of order 27
1717  real(0x24546bc28a93e0LL),real(0x2f6c4d745b8e40LL),
1718  real(0x3e90f252c210a0LL),real(0x5380c389acd700LL),
1719  real(0x70da9adde57d60LL),real(0x9aa08aca5a9fc0LL),
1720  real(0xd7127fe199fa20LL),real(0x130248120008880LL),
1721  real(0x1b6103e1c56a6e0LL),real(0x283fa247b6e3140LL),
1722  real(0x3c89da46fe8a3a0LL),real(0x5d71643158b3a00LL),
1723  real(0x948b363af771060LL),real(0xf445a32263b42c0LL),
1724  real(0x1a1d56e9fe070d20LL),real(0x2ecb290f0241eb80LL),
1725  real(0x58a5da95527fb9e0LL),reale(2876,0x680343126d440LL),
1726  reale(6354,0x3e35c062e36a0LL),reale(15689,0x7d2910c199d00LL),
1727  reale(45107,0x47d6102c9a360LL),reale(162386,0x35cf6d6d5e5c0LL),
1728  reale(857038,0x54e3334f72020LL),reale(11655721,0x4f45203874e80LL),
1729  -reale(131126864,0xbbc9aa7b23320LL),reale(378810942,0x9046972ad7740LL),
1730  -reale(416692036,0xd1e73fe253660LL),reale(156259513,0xceb6b7f4df464LL),
1731  reale(20509061187LL,0x3b2dd04b78c45LL),
1732  // C4[3], coeff of eps^29, polynomial in n of order 0
1733  594728,real(456448303575LL),
1734  // C4[3], coeff of eps^28, polynomial in n of order 1
1735  -real(3245452288LL),real(1965206256),real(0x17609e98859b3LL),
1736  // C4[3], coeff of eps^27, polynomial in n of order 2
1737  -real(0x15f49b7dd3600LL),real(0x7876e24c6900LL),real(0x1f5dd75c0b28LL),
1738  reale(4837,0x68f14547adebLL),
1739  // C4[3], coeff of eps^26, polynomial in n of order 3
1740  -real(0x33418e8004000LL),real(0x17b00d59dc000LL),
1741  -real(0x11669ade1c000LL),real(0xa37322475bc0LL),
1742  reale(6709,0x6c31d1e089667LL),
1743  // C4[3], coeff of eps^25, polynomial in n of order 4
1744  -real(0xc3e38d2fc36800LL),real(0x6a604d6faf7a00LL),
1745  -real(0x650b3de948f400LL),real(0x20a6596010be00LL),
1746  real(0x88f534a1fae70LL),reale(275086,0x53fa9cf60167fLL),
1747  // C4[3], coeff of eps^24, polynomial in n of order 5
1748  -real(0xdd5f9d233a5800LL),real(0x8b724926c9e000LL),
1749  -real(0x8af41510346800LL),real(0x3d05686ce77000LL),
1750  -real(0x2f9901c72df800LL),real(0x1ae74f29ea4ce0LL),
1751  reale(223345,0xf3eec944ed143LL),
1752  // C4[3], coeff of eps^23, polynomial in n of order 6
1753  -reale(81630,0xcf55ff9c68c00LL),reale(60811,0x59dd5ef6a6e00LL),
1754  -reale(57592,0x6457f059a8800LL),reale(30387,0x2572e53b9c200LL),
1755  -reale(30167,0xe11b4690d8400LL),reale(9044,0xd72699d03d600LL),
1756  reale(2392,0x21f43a8f7f830LL),reale(990092609,0x9eb428d5a933LL),
1757  // C4[3], coeff of eps^22, polynomial in n of order 7
1758  -reale(3070961,0xf14af9164000LL),reale(2767073,0x4d2d51bbc4000LL),
1759  -reale(2322170,0xf623e90f3c000LL),reale(1476552,0x4ed8bf53f8000LL),
1760  -reale(1490469,0x7e13eaba44000LL),reale(616004,0x8b84c9ea6c000LL),
1761  -reale(517487,0xf3178ed39c000LL),reale(279040,0x23dc4dd774ec0LL),
1762  reale(28712685662LL,0x1fa68a0342ac7LL),
1763  // C4[3], coeff of eps^21, polynomial in n of order 8
1764  -reale(3998482,0x374a7520d6800LL),reale(4351696,0x89a9dbf785900LL),
1765  -reale(3077852,0x4b8dc9fbd6e00LL),reale(2436308,0x9b47462d3fb00LL),
1766  -reale(2230379,0xda399323b400LL),reale(1147885,0x7a5199072bd00LL),
1767  -reale(1196012,0x91bb473d37a00LL),reale(325643,0x5e75ef9e35f00LL),
1768  reale(87110,0x728c765d95698LL),reale(28712685662LL,0x1fa68a0342ac7LL),
1769  // C4[3], coeff of eps^20, polynomial in n of order 9
1770  -reale(5536106,0x41a6dc97e5400LL),reale(6819318,0x7020ae33aa000LL),
1771  -reale(3996497,0x7d04a5d65ec00LL),reale(4026336,0x4a526eb153800LL),
1772  -reale(3081046,0x922df73cac400LL),reale(2027203,0x8c3cc70035000LL),
1773  -reale(2046086,0x4cc9bc51b5c00LL),reale(787253,0x8fa9057e6800LL),
1774  -reale(725367,0x21dd9ffc63400LL),reale(368582,0x69a43eb914890LL),
1775  reale(28712685662LL,0x1fa68a0342ac7LL),
1776  // C4[3], coeff of eps^19, polynomial in n of order 10
1777  -reale(8942538,0x3b8622ae62a00LL),reale(10481872,0x1e7c948175300LL),
1778  -reale(5381394,0x830498d800800LL),reale(6645195,0x535f47efddd00LL),
1779  -reale(4043713,0x9ba9cf138e600LL),reale(3563786,0x6253b3df24700LL),
1780  -reale(3045580,0xe2f1f7a110400LL),reale(1548984,0x4828fbf665100LL),
1781  -reale(1694435,0x63dcfc138a200LL),reale(406057,0xe76a74dc3bb00LL),
1782  reale(110280,0xa64ca1bbeb438LL),reale(28712685662LL,0x1fa68a0342ac7LL),
1783  // C4[3], coeff of eps^18, polynomial in n of order 11
1784  -reale(18204995,0x3f490d6ed8000LL),reale(15367333,0xa666c37198000LL),
1785  -reale(8424707,0xb9613a5da8000LL),reale(10765521,3190860555LL<<17),
1786  -reale(5300295,0xd300940f58000LL),reale(6273886,0xba1b2aa228000LL),
1787  -reale(4137511,0x6a32b5bc28000LL),reale(2951915,0x3ffeb65fb0000LL),
1788  -reale(2898950,0x38c8743c58000LL),reale(1027617,0x2c3889c5b8000LL),
1789  -reale(1062542,0x7c8a4a4828000LL),reale(500325,0x147f19cd83980LL),
1790  reale(28712685662LL,0x1fa68a0342ac7LL),
1791  // C4[3], coeff of eps^17, polynomial in n of order 12
1792  -reale(46659673,0x7940546261000LL),reale(20576887,0xb72d09f420c00LL),
1793  -reale(17371112,0xc460beb873800LL),reale(16552256,0x8d133b2d84400LL),
1794  -reale(7883306,0x3c181b1016000LL),reale(10867815,0x95ba8c80bfc00LL),
1795  -reale(5343012,0x31a34980f8800LL),reale(5640245,0x12558783a3400LL),
1796  -reale(4241979,0x47a64b12cb000LL),reale(2204426,0xf7d60f21fec00LL),
1797  -reale(2506924,0x6e46ed413d800LL),reale(503732,0xa322eb69a2400LL),
1798  reale(139663,0x777cb98300b20LL),reale(28712685662LL,0x1fa68a0342ac7LL),
1799  // C4[3], coeff of eps^16, polynomial in n of order 13
1800  -reale(156865464,0x9b4a437ced000LL),reale(26751997,0x84cabd1d8c000LL),
1801  -reale(47510066,0xf418e3e50b000LL),reale(22667291,0xeea5410a3a000LL),
1802  -reale(16175537,0xc4ceea20b9000LL),reale(17818506,0xfb6c54d608000LL),
1803  -reale(7402653,0x2459922697000LL),reale(10650742,0xeb52d29456000LL),
1804  -reale(5558253,0xfdda6aad45000LL),reale(4690304,0xc3737ed884000LL),
1805  -reale(4248624,0xb4bb4dab63000LL),reale(1382140,0xc755b095f2000LL),
1806  -reale(1646389,0x4c787b5791000LL),reale(701746,0xdc0286e009640LL),
1807  reale(28712685662LL,0x1fa68a0342ac7LL),
1808  // C4[3], coeff of eps^15, polynomial in n of order 14
1809  reale(158569992,0x763cf17d39800LL),reale(242045827,0xf358b9d531400LL),
1810  -reale(171801710,0xfbdaa54751000LL),reale(26564510,0xe59a1e6b54c00LL),
1811  -reale(47715397,0x8fdbdb93bb800LL),reale(25503418,0x124aa89300400LL),
1812  -reale(14593564,0x65519680b6000LL),reale(19028249,0x27fd86c303c00LL),
1813  -reale(7127523,0x40a42052f0800LL),reale(9926805,0x1876eddc2f400LL),
1814  -reale(5956098,0xfb7e2f3f1b000LL),reale(3422018,0xde3cf0f552c00LL),
1815  -reale(3909386,0x4ce6da2de5800LL),reale(606166,0xec68c0e73e400LL),
1816  reale(172919,0x9ad62b665b520LL),reale(28712685662LL,0x1fa68a0342ac7LL),
1817  // C4[3], coeff of eps^14, polynomial in n of order 15
1818  reale(234628808,0x48818da828000LL),-reale(452308383,0x26baa88038000LL),
1819  reale(184630907,0xde7b734758000LL),reale(240946965,0x4db221ae90000LL),
1820  -reale(189474421,0xed4c1e36d8000LL),reale(27214973,0x55324802d8000LL),
1821  -reale(46882338,0xe5fcdfdca8000LL),reale(29262846,2319362995LL<<17),
1822  -reale(12682237,0x3cee53d458000LL),reale(19904432,0x70537f02e8000LL),
1823  -reale(7274198,0xbf917ba828000LL),reale(8480909,0x438c3da230000LL),
1824  -reale(6415713,0xc95c9b8258000LL),reale(1960896,0x685dc04df8000LL),
1825  -reale(2745254,0xf883406d28000LL),reale(1023946,0x4eef421f04580LL),
1826  reale(28712685662LL,0x1fa68a0342ac7LL),
1827  // C4[3], coeff of eps^13, polynomial in n of order 16
1828  -reale(2272755,0x57fd708a77000LL),-reale(26091168,0x1366cec7d9d00LL),
1829  reale(231976719,0xafe6927fcde00LL),-reale(464894868,0x24c5c39795700LL),
1830  reale(215184123,0xaf8273d716c00LL),reale(236438336,0xab29f0bfd4f00LL),
1831  -reale(210344218,0x367ffa8b78600LL),reale(29454299,0x2f129bee9500LL),
1832  -reale(44460297,0xf9cfdfb8bb800LL),reale(34058265,0xda8305b9abb00LL),
1833  -reale(10677799,0x93543d448ea00LL),reale(19950418,0xbb16c712a0100LL),
1834  -reale(8097327,0xc3857f1ecdc00LL),reale(6164437,0x8a1d8a85ca700LL),
1835  -reale(6487914,0xa92c56ec54e00LL),reale(653539,0x4a58f163aed00LL),
1836  reale(193289,0xc4fa7fb371708LL),reale(28712685662LL,0x1fa68a0342ac7LL),
1837  // C4[3], coeff of eps^12, polynomial in n of order 17
1838  -reale(136365,0x73a1fcfe6ac00LL),-reale(450638,0xd074750f34000LL),
1839  -reale(2128024,0x54e7feac4d400LL),-reale(24952088,0x92a9c1fc91800LL),
1840  reale(228113259,0x85d44607e4400LL),-reale(477191195,0x7e69e50f07000LL),
1841  reale(251096618,0x1896eb4cd1c00LL),reale(226763725,0xac7cda7d93800LL),
1842  -reale(234776156,0x14cc4b0edcc00LL),reale(34557325,0x4230b4bd66000LL),
1843  -reale(39741101,0x3a85821c7f400LL),reale(39764072,0x42dd69fc98800LL),
1844  -reale(9161206,0x9c1a792d6dc00LL),reale(18380268,0xf302f56753000LL),
1845  -reale(9708385,0x581708d300400LL),reale(3148914,0x8380fab1bd800LL),
1846  -reale(5050904,0x8a565e3e8ec00LL),reale(1566765,0x6fd98617e9df0LL),
1847  reale(28712685662LL,0x1fa68a0342ac7LL),
1848  // C4[3], coeff of eps^11, polynomial in n of order 18
1849  -reale(18810,0x4977f6cdda600LL),-reale(44617,0xf507aa2256700LL),
1850  -reale(121680,0x26c8d0378b000LL),-reale(408670,0xadcc6d8f87900LL),
1851  -reale(1967116,0xd731d207dba00LL),-reale(23614778,0x5c1a1fadbeb00LL),
1852  reale(222693980,0x695506ba87c00LL),-reale(488598159,0xe2ab67bc47d00LL),
1853  reale(293333811,0x10f016a3f3200LL),reale(209273530,0x4db1c2b811100LL),
1854  -reale(262769616,0x9b49f60945800LL),reale(44647130,0x3acb33bfff00LL),
1855  -reale(31983858,0x227f1389ce200LL),reale(45626356,0x9e16c6ccb8d00LL),
1856  -reale(9276161,0xf8fb16a652c00LL),reale(14205372,0x289c377eefb00LL),
1857  -reale(11490116,0xc948e407f600LL),reale(414830,0x163387d5d8900LL),
1858  reale(117690,0xc756ec17c4aa8LL),reale(28712685662LL,0x1fa68a0342ac7LL),
1859  // C4[3], coeff of eps^10, polynomial in n of order 19
1860  -reale(3667,0x8ba48fb7ec000LL),-reale(7355,0xde5d961edc000LL),
1861  -reale(15963,0x138d280434000LL),-reale(38393,53315683LL<<17),
1862  -reale(106358,0x1cca460dcc000LL),-reale(363723,0x77fed5aee4000LL),
1863  -reale(1788619,0xb46088e414000LL),-reale(22045766,0x7d53064fc8000LL),
1864  reale(215267089,0x7c4e47994000LL),-reale(498143540,0xc077eb386c000LL),
1865  reale(342855614,0x4b25e0bbcc000LL),reale(179961617,0x7ca6ea4dd0000LL),
1866  -reale(293329289,0xb4e43f9ccc000LL),reale(63137066,0xbcee02f98c000LL),
1867  -reale(20920174,0xdceb909f94000LL),reale(49479848,0x7088e98168000LL),
1868  -reale(12768344,0x1ee1d8cbec000LL),reale(6948560,0xd8f6969c04000LL),
1869  -reale(10643749,0x466c677134000LL),reale(2529930,0x161dcdf222440LL),
1870  reale(28712685662LL,0x1fa68a0342ac7LL),
1871  // C4[3], coeff of eps^9, polynomial in n of order 20
1872  -real(0x354d49acec3dd800LL),-real(0x606a7d34c50a0200LL),
1873  -reale(2939,0xdc47a7c209c00LL),-reale(5971,0x671f2d9dad600LL),
1874  -reale(13140,0xcdf9f327fe000LL),-reale(32101,0x6baea5bb9ea00LL),
1875  -reale(90511,0x408ba9a232400LL),-reale(315893,0xc97e5e852be00LL),
1876  -reale(1591343,0xfce30d8d1e800LL),-reale(20207205,0x8b4272e60d200LL),
1877  reale(205238828,0x21c1cf60c5400LL),-reale(504251582,0xb2b181bcfa600LL),
1878  reale(400330413,0xa384192d01000LL),reale(132810886,0x4094526254600LL),
1879  -reale(323039224,0xd5680dd0e3400LL),reale(95085342,0xbfbbc74d27200LL),
1880  -reale(8279837,0x6ce790195f800LL),reale(46514941,0x8e0e73ffc5e00LL),
1881  -reale(20732718,0x38ef4b2eebc00LL),-reale(922541,0xf2a1d94487600LL),
1882  -reale(491669,0x5bd07d195db30LL),reale(28712685662LL,0x1fa68a0342ac7LL),
1883  // C4[3], coeff of eps^8, polynomial in n of order 21
1884  -real(0xd828cefda55a800LL),-real(0x16c6eac98e7b6000LL),
1885  -real(0x27e1e798049c9800LL),-real(0x490330552dbbf000LL),
1886  -reale(2255,0x88ea2b8740800LL),-reale(4647,0x88c66c31f8000LL),
1887  -reale(10390,0xd13f35560f800LL),-reale(25836,0xfcd55e2db1000LL),
1888  -reale(74324,0xc0bfff0e86800LL),-reale(265480,0xf5ce67923a000LL),
1889  -reale(1374647,0xa0b10ca8f5800LL),-reale(18058373,0x723761b2e3000LL),
1890  reale(191831943,0xc85920c253800LL),-reale(504361484,0x6e935002fc000LL),
1891  reale(465423127,0xbaa71ebb04800LL),reale(59036306,0xf120275a2b000LL),
1892  -reale(342905949,0x5a93131732800LL),reale(146354899,0x9f9c2b8142000LL),
1893  -reale(1641748,0x1e8ba62ca1800LL),reale(28969072,0x51c8dabef9000LL),
1894  -reale(27136540,0x3d9359d98800LL),reale(4249105,0xd55e5a0325120LL),
1895  reale(28712685662LL,0x1fa68a0342ac7LL),
1896  // C4[3], coeff of eps^7, polynomial in n of order 22
1897  -real(0x38123cee860f400LL),-real(0x59d375c04e8be00LL),
1898  -real(0x942bf86bd4c1800LL),-real(0xfcbda8858afb200LL),
1899  -real(0x1c02af2dc3443c00LL),-real(0x33fc822f8d2b6600LL),
1900  -real(0x65e35fc07de4e000LL),-reale(3414,0xc7eb297eb5a00LL),
1901  -reale(7775,0x1c0e884298400LL),-reale(19731,0x6a31912ef0e00LL),
1902  -reale(58089,0x9471e600da800LL),-reale(213111,0x15a6331c60200LL),
1903  -reale(1139019,0x77ee6ce2ccc00LL),-reale(15560104,0x33d66a0afb600LL),
1904  reale(174045800,0x2f0a20e9d9000LL),-reale(494300177,0xd9e4761bbaa00LL),
1905  reale(535087920,0xe9f8f195ec00LL),-reale(53102016,0x93f6bbbe95e00LL),
1906  -reale(331738553,0x77bff637f3800LL),reale(216985631,0x987f3afb7ae00LL),
1907  -reale(21074121,0x8043eaffd5c00LL),-reale(4185955,0xa3ff769180600LL),
1908  -reale(4713710,0xd2e19a34f30b0LL),reale(28712685662LL,0x1fa68a0342ac7LL),
1909  // C4[3], coeff of eps^6, polynomial in n of order 23
1910  -real(0xe0ca252d14c000LL),-real(0x15a70af15f24000LL),
1911  -real(0x222b3f817554000LL),-real(0x375f97b48cd8000LL),
1912  -real(0x5c7b9631f8ac000LL),-real(0x9fe2527c7fcc000LL),
1913  -real(0x11face3d5ef34000LL),-real(0x21e77d8dabde0000LL),
1914  -real(0x439dcbf7fdccc000LL),-reale(2310,0x1731d0ccf4000LL),
1915  -reale(5373,0x35ee2c1554000LL),-reale(13965,0xf39edc32e8000LL),
1916  -reale(42247,0xa0aa0b1cac000LL),-reale(159930,0xa2319a759c000LL),
1917  -reale(887131,0xc123fa86b4000LL),-reale(12685735,0x6243721af0000LL),
1918  reale(150650948,0x968da6a8b4000LL),-reale(467294064,0x1610ada8c4000LL),
1919  reale(599544322,0x5feb9b1dac000LL),-reale(214883240,0x150075a4f8000LL),
1920  -reale(244806233,0x53bd4b2bac000LL),reale(272520146,0x88b0e96a94000LL),
1921  -reale(87760725,0x27ae1fc734000LL),reale(5827860,0xa7a2901c3a740LL),
1922  reale(28712685662LL,0x1fa68a0342ac7LL),
1923  // C4[3], coeff of eps^5, polynomial in n of order 24
1924  -real(0x32b69e04189800LL),-real(0x4bd39320660300LL),
1925  -real(0x73a508e7ef1600LL),-real(0xb44a7ec206b900LL),
1926  -real(0x1200d9d52c6d400LL),-real(0x1d916a5ad4bcf00LL),
1927  -real(0x321a3f994641200LL),-real(0x57fce6d660f8500LL),
1928  -real(0xa10c564a22b1000LL),-real(0x1356fa3ebba41b00LL),
1929  -real(0x275fd13435900e00LL),-real(0x5604e2d76283d100LL),
1930  -reale(3283,0xdf8f52c874c00LL),-reale(8783,0x8ddc09700e700LL),
1931  -reale(27451,0x143e179f50a00LL),-reale(107903,0xe48c7d6f59d00LL),
1932  -reale(625732,0xe2abef41d8800LL),-reale(9446536,0xacc19c0743300LL),
1933  reale(120325828,0x5507fb0eafa00LL),-reale(412649247,0xc3fe82376e900LL),
1934  reale(633089704,0xd19d26ed03c00LL),-reale(418090362,0x84d33548fff00LL),
1935  -reale(13712613,0x4e3334f720200LL),reale(163180098,0x55c7c31664b00LL),
1936  -reale(61921019,0x751f3b2bed108LL),
1937  reale(28712685662LL,0x1fa68a0342ac7LL),
1938  // C4[3], coeff of eps^4, polynomial in n of order 25
1939  -real(0x30fab48eb2c00LL),-real(0x4779db0cde000LL),
1940  -real(0x6a1a5308c1400LL),-real(0xa07c7893bf800LL),
1941  -real(0xf7d15b087bc00LL),-real(0x1878e181999000LL),
1942  -real(0x27ab652bf7a400LL),-real(0x422ed0b6682800LL),
1943  -real(0x721448fff54c00LL),-real(0xcc1e5699294000LL),
1944  -real(0x17d5829db9a3400LL),-real(0x2ed74923dde5800LL),
1945  -real(0x61c84aba5ffdc00LL),-real(0xdbaa1b53c88f000LL),
1946  -real(0x21cc8beefe3fc400LL),-real(0x5da8efb832aa8800LL),
1947  -reale(4876,0x5d83861736c00LL),-reale(20082,0x8bb9af0c4a000LL),
1948  -reale(123005,0x97d1502b45400LL),-reale(1983151,0x65e045fd8b800LL),
1949  reale(27425226,0x9c6669ee40400LL),-reale(105081920,0xe8c662ae85000LL),
1950  reale(191976586,0x46cce583c1c00LL),-reale(186491540,0xf45203874e800LL),
1951  reale(93245770,0x7a2901c3a7400LL),-reale(18940547,0x20d0545bbdf90LL),
1952  reale(9570895220LL,0xb53783566b8edLL),
1953  // C4[3], coeff of eps^3, polynomial in n of order 26
1954  -real(0x10330cb256200LL),-real(0x172cb16211100LL),
1955  -real(0x21a8187537800LL),-real(0x31b06260f1f00LL),
1956  -real(0x4ab014ab28e00LL),-real(0x7280309c9cd00LL),
1957  -real(0xb366eef7be400LL),-real(0x11ff8a58b05b00LL),
1958  -real(0x1dae666558ba00LL),-real(0x327547ac4a0900LL),
1959  -real(0x58c9207d125000LL),-real(0xa2826b77361700LL),
1960  -real(0x137557a5841e600LL),-real(0x275355b4b1bc500LL),
1961  -real(0x54b37d85300bc00LL),-real(0xc517d06239a5300LL),
1962  -real(0x1f8f2f623d981200LL),-real(0x5b85a3034c390100LL),
1963  -reale(5020,0xa2ee6bc312800LL),-reale(21965,0x48d3177570f00LL),
1964  -reale(144343,0x4c469a2853e00LL),-reale(2526007,0xb6d389c1bbd00LL),
1965  reale(38395317,0x415c2de726c00LL),-reale(163180098,0x55c7c31664b00LL),
1966  reale(326360196,0xab8f862cc9600LL),-reale(303048754,0xd0545bbdf900LL),
1967  reale(104173009,0x3479cff894d98LL),
1968  reale(28712685662LL,0x1fa68a0342ac7LL),
1969  // C4[4], coeff of eps^29, polynomial in n of order 0
1970  4519424,real(0x13ed3512585LL),
1971  // C4[4], coeff of eps^28, polynomial in n of order 1
1972  real(322327509504LL),real(86419033792LL),real(0x12e7203d54087bdLL),
1973  // C4[4], coeff of eps^27, polynomial in n of order 2
1974  real(0xdf868e997000LL),-real(0xc54488fde800LL),real(0x67996a8dfb80LL),
1975  reale(6219,0x86ed0fee71e5LL),
1976  // C4[4], coeff of eps^26, polynomial in n of order 3
1977  real(0x1e30d5f17398800LL),-real(0x20335f44c005000LL),
1978  real(0x8656a9da59d800LL),real(0x246f3281df3200LL),
1979  reale(1871928,0xea4bbbb5bea41LL),
1980  // C4[4], coeff of eps^25, polynomial in n of order 4
1981  real(0x640278dc982000LL),-real(0x64de2b5e388800LL),
1982  real(0x266cf1cb211000LL),-real(0x24af02897bd800LL),
1983  real(0x125236c4932c80LL),reale(225070,0xa1cd0c0f186c5LL),
1984  // C4[4], coeff of eps^24, polynomial in n of order 5
1985  real(0x183393315f62f400LL),-real(0x147c8a635ba4f000LL),
1986  real(0xaadb07a361e2c00LL),-real(0xbd0a07cdca37800LL),
1987  real(0x2c490db64a86400LL),real(0xc3000bbe3e2580LL),
1988  reale(8327613,0x62a2be2e87a79LL),
1989  // C4[4], coeff of eps^23, polynomial in n of order 6
1990  reale(7399,0xe4703b1ceb000LL),-reale(4925,0x718bf750ef800LL),
1991  reale(3656,0xc01290e152000LL),-reale(3594,0x9ae0aefbbc800LL),
1992  real(0x5080258211e79000LL),-real(0x5458466826cf9800LL),
1993  real(0x27a09e95cf36b080LL),reale(97921247,0xc3bd6c206251LL),
1994  // C4[4], coeff of eps^22, polynomial in n of order 7
1995  reale(4319137,0xe5044c1364800LL),-reale(2259378,0xc043aee633000LL),
1996  reale(2431286,0xcceb783bf5800LL),-reale(1865690,0x884902c9a2000LL),
1997  reale(996566,0x94ae3b7946800LL),-reale(1135368,0x2cb1c30811000LL),
1998  reale(231629,0x92b25177d7800LL),reale(64961,0x89605803fda00LL),
1999  reale(36916310137LL,0x41f43bb0c949LL),
2000  // C4[4], coeff of eps^21, polynomial in n of order 8
2001  reale(6174501,0x53f34a829c000LL),-reale(2885765,0xddf01a0f35800LL),
2002  reale(4089976,0x588848e445000LL),-reale(2309244,0x73683320c8800LL),
2003  reale(1950621,0xac1b944ace000LL),-reale(1810054,0xa24c07eb4b800LL),
2004  reale(609590,0x74daa18497000LL),-reale(712107,0x16cff78e5e800LL),
2005  reale(310317,0x16957f6a36b80LL),reale(36916310137LL,0x41f43bb0c949LL),
2006  // C4[4], coeff of eps^20, polynomial in n of order 9
2007  reale(7763095,0xd98a0c3214600LL),-reale(4551997,0xf65d38a54d000LL),
2008  reale(6348004,0x7dcc619ba1a00LL),-reale(2777846,0x11091dc381c00LL),
2009  reale(3645151,0x5af876afd6e00LL),-reale(2403756,0x12692c3266800LL),
2010  reale(1377366,0xde24866584200LL),-reale(1585712,0xf2192bea6b400LL),
2011  reale(268682,0xb0f056b079600LL),reale(77255,0xca5a822ebf740LL),
2012  reale(36916310137LL,0x41f43bb0c949LL),
2013  // C4[4], coeff of eps^19, polynomial in n of order 10
2014  reale(8073134,0x8bff962f2e000LL),-reale(9331256,0xe8e10405e1000LL),
2015  reale(8608510,0x42ad0321d8000LL),-reale(3959617,0x4c778c1e2f000LL),
2016  reale(6283090,0x55033b3d82000LL),-reale(2832307,0xbbdb17809d000LL),
2017  reale(2955095,0x929c8347ec000LL),-reale(2459067,0xd43d49c36b000LL),
2018  reale(787004,0x9cc4866d6000LL),-reale(1039103,0x6b1983acd9000LL),
2019  reale(412222,0xf695367aa1b00LL),reale(36916310137LL,0x41f43bb0c949LL),
2020  // C4[4], coeff of eps^18, polynomial in n of order 11
2021  reale(8586281,0xffd2991fd000LL),-reale(20926106,0xdd733d721a000LL),
2022  reale(9282973,0x193483c94f000LL),-reale(8121077,0x9b55004148000LL),
2023  reale(9430655,0x90c0e29221000LL),-reale(3512067,0x80c2ac76000LL),
2024  reale(5840995,0x1886eb4173000LL),-reale(3061324,0xab1a78b4a4000LL),
2025  reale(2049544,0x4067911445000LL),-reale(2292525,0x617c054ad2000LL),
2026  reale(297833,0x966e637f97000LL),reale(88539,0x9a2e50b8c6400LL),
2027  reale(36916310137LL,0x41f43bb0c949LL),
2028  // C4[4], coeff of eps^17, polynomial in n of order 12
2029  reale(32196457,0xd679f8ae1c000LL),-reale(40594018,0x37167c5ef5000LL),
2030  reale(8052650,0x2eda271162000LL),-reale(20325613,0xcd34eeff17000LL),
2031  reale(11030346,0x5827875768000LL),-reale(6662972,0x9685f0fc59000LL),
2032  reale(10015916,0xfa65faac6e000LL),-reale(3377057,0x1ef6021e7b000LL),
2033  reale(4892320,0x94cb79bcb4000LL),-reale(3369439,0x93437f1d3d000LL),
2034  reale(1068721,0xdee482d47a000LL),-reale(1596884,0xcb3e26805f000LL),
2035  reale(562334,0xcf5270735f500LL),reale(36916310137LL,0x41f43bb0c949LL),
2036  // C4[4], coeff of eps^16, polynomial in n of order 13
2037  reale(239019678,0x7928c61a8b800LL),-reale(41200119,0x147c0b11e000LL),
2038  reale(27063572,0xac3757be98800LL),-reale(45155983,0xc412cf1f79000LL),
2039  reale(8354845,0xf8b6ea7445800LL),-reale(18750027,0x4e7377c014000LL),
2040  reale(13292220,0xfed958edd2800LL),-reale(5165101,0x26aa3105af000LL),
2041  reale(10025000,0x43fec217f800LL),-reale(3715677,0xed5a4430a000LL),
2042  reale(3405288,0xc16fe1018c800LL),-reale(3440521,0x6cb0e4f2e5000LL),
2043  reale(291108,0x30be23439800LL),reale(90314,0xe93f4121c6900LL),
2044  reale(36916310137LL,0x41f43bb0c949LL),
2045  // C4[4], coeff of eps^15, polynomial in n of order 14
2046  -reale(301344600,0x1f7a69f35a000LL),-reale(137666269,0x81776c9d9b000LL),
2047  reale(257500426,0xa27a71193c000LL),-reale(52745704,0xa8e59f44d000LL),
2048  reale(20527629,0x3707e00852000LL),-reale(49389175,0x1679a6a55f000LL),
2049  reale(10057417,0xa546ce8428000LL),-reale(15960633,0x79a78f6a91000LL),
2050  reale(15828795,0x3b7a7e96fe000LL),-reale(4041479,0x5385608da3000LL),
2051  reale(9015452,0x8a056dcb14000LL),-reale(4531739,0xb18fd7c855000LL),
2052  reale(1608583,0x5c81da4aaa000LL),-reale(2620079,0xb9c03a2467000LL),
2053  reale(790676,0xf12036cb88d00LL),reale(36916310137LL,0x41f43bb0c949LL),
2054  // C4[4], coeff of eps^14, polynomial in n of order 15
2055  -reale(152316078,0x9ee9710b1f000LL),reale(396132268,0xf6300698d2000LL),
2056  -reale(331944543,0x2a26efc8bd000LL),-reale(111967823,0x409ccb544c000LL),
2057  reale(276102802,0x8592b62d25000LL),-reale(69409637,0x2e4659b6a000LL),
2058  reale(12806364,0xaa4a38387000LL),-reale(52382533,0xaa3aad6588000LL),
2059  reale(13858261,0x7d9fda6f69000LL),-reale(11925525,0x17f68feba6000LL),
2060  reale(17994828,0x2633a57dcb000LL),-reale(3926621,0x9c334da6c4000LL),
2061  reale(6610729,0xa84ec063ad000LL),-reale(5341800,0xcfe0c57fe2000LL),
2062  reale(171304,0xc92dc0ce0f000LL),reale(53498,0x8a12fdd94c400LL),
2063  reale(36916310137LL,0x41f43bb0c949LL),
2064  // C4[4], coeff of eps^13, polynomial in n of order 16
2065  reale(945329,0x3e694a5630000LL),reale(13046260,0xd11553dc81000LL),
2066  -reale(145063327,0x6c5bbd04f6000LL),reale(395288944,0x9758cc3483000LL),
2067  -reale(364989750,0x4da45c465c000LL),-reale(77659847,0x7f601a5fdb000LL),
2068  reale(293261136,0xdb46a6c9be000LL),-reale(92956699,0x68d702f4d9000LL),
2069  reale(4748491,0xd717292318000LL),-reale(52641236,0xde7217eeb7000LL),
2070  reale(20401071,0xa831b35d72000LL),-reale(7165143,0xe2daef21b5000LL),
2071  reale(18530179,0x70f1fa908c000LL),-reale(5449998,0x995f61f213000LL),
2072  reale(2985284,0xf423c13426000LL),-reale(4674955,0x4c99b17411000LL),
2073  reale(1148405,0xaa811667d8300LL),reale(36916310137LL,0x41f43bb0c949LL),
2074  // C4[4], coeff of eps^12, polynomial in n of order 17
2075  reale(39064,0xc457745427a00LL),reale(149707,0xe179ab818a000LL),
2076  reale(834482,0xb3de3faf4c600LL),reale(11844090,0x43801d34c0c00LL),
2077  -reale(136492367,0x606ac4f4b6e00LL),reale(391413380,0x8b1b355567800LL),
2078  -reale(399991879,0xf56c51d232200LL),-reale(32313943,0x670cb1cd91c00LL),
2079  reale(306137820,0x47c0d4df8aa00LL),-reale(125355715,0x12c37db13b000LL),
2080  -reale(1549012,0x61de67b1d0a00LL),-reale(48002827,0x1ef791fca4400LL),
2081  reale(29707099,0x80264b6e6c200LL),-reale(3304868,0xd90dacdedd800LL),
2082  reale(15595740,0x1c41b85df0e00LL),-reale(8339676,0x731c5b6cf6c00LL),
2083  -reale(264319,0x3253133a92600LL),-reale(128183,0x1fd72f4c70540LL),
2084  reale(36916310137LL,0x41f43bb0c949LL),
2085  // C4[4], coeff of eps^11, polynomial in n of order 18
2086  reale(3796,0xb8b80a685d000LL),reale(10243,0xe5415b1644800LL),
2087  reale(32134,0x75fe9c2f28000LL),reale(125896,0x13cc0b67cb800LL),
2088  reale(720062,0x2eb5ef2cf3000LL),reale(10542664,0x8e7784ebe2800LL),
2089  -reale(126401502,0xa942d02d22000LL),reale(383396973,0xa914c081a9800LL),
2090  -reale(435856143,0x9e18e4ddf7000LL),reale(26921352,0xa17bcee040800LL),
2091  reale(309790567,0x432113bb94000LL),-reale(168177156,0xf5a6b5d938800LL),
2092  -reale(1732899,0x7848d10f61000LL),-reale(36033193,0x6ff05a93a1800LL),
2093  reale(39850986,0x4a7ce5d24a000LL),-reale(3520516,0x12d4d9afda800LL),
2094  reale(7904559,0x47211641b5000LL),-reale(9293198,0x11e52b76c3800LL),
2095  reale(1712350,0xd1c47193d5a80LL),reale(36916310137LL,0x41f43bb0c949LL),
2096  // C4[4], coeff of eps^10, polynomial in n of order 19
2097  real(0x20b0c3dbe662b800LL),real(0x49a4ee6b654d5000LL),
2098  reale(2895,0xbb9a481b3e800LL),reale(7963,0xd6290c9168000LL),
2099  reale(25525,0x742091bd91800LL),reale(102493,0xec03f49fb000LL),
2100  reale(603292,0x6fe940faa4800LL),reale(9144553,0x3f081030e000LL),
2101  -reale(114581171,0x9502f66408800LL),reale(369767644,0x159b783921000LL),
2102  -reale(470438620,0x42537ac0f5800LL),reale(102998223,0x33db2118b4000LL),
2103  reale(295924658,0xfd504b0d5d800LL),-reale(220875824,0xd68590c9b9000LL),
2104  reale(12088406,0x3b87c77470800LL),-reale(15966308,0xf7cc70b9a6000LL),
2105  reale(44660638,0xbb68d3ddc3800LL),-reale(11155854,0x316b572a93000LL),
2106  -reale(1400757,0x91d7719929800LL),-reale(909990,0x5b4dcbdcd9200LL),
2107  reale(36916310137LL,0x41f43bb0c949LL),
2108  // C4[4], coeff of eps^9, polynomial in n of order 20
2109  real(0x55091490e3fe000LL),real(0xab3101736f26800LL),
2110  real(0x16d77945c4e3b000LL),real(0x345d2a91137d7800LL),
2111  reale(2099,0xc55d2c398000LL),reale(5898,0x424192198800LL),
2112  reale(19366,0xa6f5f449f5000LL),reale(79943,0x847cdfac49800LL),
2113  reale(486014,0x6a1dc16732000LL),reale(7659629,0x94cc8fca800LL),
2114  -reale(100839015,0x651046eed1000LL),reale(348607247,0x22ddc22bfb800LL),
2115  -reale(499815073,0x4df2756234000LL),reale(197958555,0x77a0b2f8bc800LL),
2116  reale(251323198,0x2663cfb2e9000LL),-reale(276534810,0xe292670a12800LL),
2117  reale(51555588,0x6a67a23666000LL),reale(5587968,0x5e92831b6e800LL),
2118  reale(32523682,0xed2ae23e23000LL),-reale(21111776,0x46401336e0800LL),
2119  reale(2489921,0xe3c1e337a6d80LL),reale(36916310137LL,0x41f43bb0c949LL),
2120  // C4[4], coeff of eps^8, polynomial in n of order 21
2121  real(0xeb8379f6b27c00LL),real(0x1b6c4de1f1d7000LL),
2122  real(0x355a1dadc956400LL),real(0x6d308de46411800LL),
2123  real(0xed54313f63d4c00LL),real(0x22ae87428a2ac000LL),
2124  real(0x58ce5dd980bc3400LL),reale(4090,0xd3c824bc46800LL),
2125  reale(13806,0x44b4a8a441c00LL),reale(58809,0x7ab991df81000LL),
2126  reale(370898,0xe410033e70400LL),reale(6109620,0x6402b9f6fb800LL),
2127  -reale(85053139,0x4bf446ca91400LL),reale(317515928,0x1b63894556000LL),
2128  -reale(517123103,0xa7a388b5a2c00LL),reale(310296682,0xe98bc80130800LL),
2129  reale(156996715,0xaa3cf3c05bc00LL),-reale(312601560,0xdd28200ed5000LL),
2130  reale(125126811,0xf01e02788a400LL),reale(4091818,0xb5091207e5800LL),
2131  -reale(866059,0xc9a79cf1f7400LL),-reale(4943757,0xf4721fe538b80LL),
2132  reale(36916310137LL,0x41f43bb0c949LL),
2133  // C4[4], coeff of eps^7, polynomial in n of order 22
2134  real(0x2814d49c0c5000LL),real(0x468b0d3a3db800LL),
2135  real(0x80724d98876000LL),real(0xf31dbc49b20800LL),
2136  real(0x1e12cb4a6a67000LL),real(0x3eb5a58b5455800LL),
2137  real(0x8b1eef20fbf8000LL),real(0x14cb29a266eda800LL),
2138  real(0x36974c82ca289000LL),reale(2585,0xefae20720f800LL),
2139  reale(9007,0x1d6baf437a000LL),reale(39779,0x24ec74fd54800LL),
2140  reale(261696,0x442f64f42b000LL),reale(4534975,0xa5b17f809800LL),
2141  -reale(67279179,0x4d9bf05604000LL),reale(273758534,0xd27122c18e800LL),
2142  -reale(510920394,0x40d515b3000LL),reale(428723861,0x53ee2b6143800LL),
2143  -reale(7330129,0x37be948582000LL),-reale(275708250,0xae16364977800LL),
2144  reale(204390109,0xe684af0fef000LL),-reale(52540960,0x7463315742800LL),
2145  reale(2056891,0xfeee14beab380LL),reale(36916310137LL,0x41f43bb0c949LL),
2146  // C4[4], coeff of eps^6, polynomial in n of order 23
2147  real(0x628e4f4bb7800LL),real(0xa60e374943000LL),real(0x11fae77940e800LL),
2148  real(0x2022ddc061a000LL),real(0x3b7f2e2d7a5800LL),
2149  real(0x72aa26ca9f1000LL),real(0xe77392a11fc800LL),
2150  real(0x1ed1e51d0348000LL),real(0x460248a5fa93800LL),
2151  real(0xabd9e84dc89f000LL),real(0x1d078c2cd5cea800LL),
2152  real(0x58c9fda5cf076000LL),reale(5134,0xa77137081800LL),
2153  reale(23653,0x63d76094d000LL),reale(163469,0x772f4630d8800LL),
2154  reale(3004667,0x8d384291a4000LL),-reale(47956830,0xd53f134a90800LL),
2155  reale(214953528,0xfe0a5a4ffb000LL),-reale(463620631,0xbff95a7639800LL),
2156  reale(519033396,0x411553aad2000LL),-reale(237300381,0xd565fafaa2800LL),
2157  -reale(84296486,0x10fabff57000LL),reale(142611178,0x607af3a3b4800LL),
2158  -reale(46622885,0x3d1480e1d3a00LL),reale(36916310137LL,0x41f43bb0c949LL),
2159  // C4[4], coeff of eps^5, polynomial in n of order 24
2160  real(0xc0b5b2cac000LL),real(0x139ac5d2ed800LL),real(0x20abe97223000LL),
2161  real(0x37e2f8cba0800LL),real(0x6269b1d1ba000LL),real(0xb3074a8a43800LL),
2162  real(0x151de1e3911000LL),real(0x298e5ccaa76800LL),
2163  real(0x55d208375c8000LL),real(0xbb7ea958fd9800LL),
2164  real(0x1b5e1854857f000LL),real(0x4547c4b8360c800LL),
2165  real(0xc1cdc899e5d6000LL),real(0x2682d6f5e00af800LL),
2166  reale(2326,0xf44888e46d000LL),reale(11275,0x7d4afe8b62800LL),
2167  reale(82638,0x859516eee4000LL),reale(1628359,0xc1653179c5800LL),
2168  -reale(28286265,0xc31f9b1d25000LL),reale(141205400,0x2bb5164778800LL),
2169  -reale(353352393,0x632221a20e000LL),reale(504046796,0x730ece181b800LL),
2170  -reale(416863444,0x7c7b16f237000LL),reale(186491540,0xf45203874e800LL),
2171  -reale(34967163,0xedcf60a95eb80LL),reale(36916310137LL,0x41f43bb0c949LL),
2172  // C4[4], coeff of eps^4, polynomial in n of order 25
2173  real(0xe07098dae00LL),real(0x16338b625000LL),real(0x23dda179f200LL),
2174  real(0x3b41a69cf400LL),real(0x645a89a6b600LL),real(0xaeabe0e09800LL),
2175  real(0x1397028dcfa00LL),real(0x246014e923c00LL),real(0x4633de275be00LL),
2176  real(0x8d95c8a56e000LL),real(0x12c670f9ba0200LL),
2177  real(0x2a433484738400LL),real(0x6608a70542c600LL),
2178  real(0x10c10ac322d2800LL),real(0x30ddb4b92590a00LL),
2179  real(0xa2e30513d28cc00LL),real(0x289386109855ce00LL),
2180  reale(3347,0x17499d2cb7000LL),reale(26358,0x5763b5c021200LL),
2181  reale(564821,0x99c65b39a1400LL),-reale(10825747,0x58af29d092a00LL),
2182  reale(60624185,0x23d4ea299b800LL),-reale(172778927,0xa61ece902e600LL),
2183  reale(279737311,0x6e7b054af5c00LL),-reale(233114426,0x3166846922200LL),
2184  reale(75762188,0x8341516ef7e40LL),reale(36916310137LL,0x41f43bb0c949LL),
2185  // C4[5], coeff of eps^29, polynomial in n of order 0
2186  3108352,real(0x4338129a0b3LL),
2187  // C4[5], coeff of eps^28, polynomial in n of order 1
2188  -real(4961047LL<<17),real(304969986048LL),real(0x171a7cbcbc0a5e7LL),
2189  // C4[5], coeff of eps^27, polynomial in n of order 2
2190  -real(0xb7a8cf8589000LL),real(0x25cdf8a9f5800LL),real(0xaa8ee05df480LL),
2191  reale(53207,0x4825dfa147919LL),
2192  // C4[5], coeff of eps^26, polynomial in n of order 3
2193  -real(0x4519d2e6066000LL),real(0x17b1d503134000LL),
2194  -real(0x1b53dc2d3c2000LL),real(0xc104a529c3b00LL),
2195  reale(207992,0x1a086a30a3679LL),
2196  // C4[5], coeff of eps^25, polynomial in n of order 4
2197  -real(0xe48436400f9e000LL),real(0x825cbe3b5113800LL),
2198  -real(0x9657faac8f9f000LL),real(0x1ac735d19d16800LL),
2199  real(0x7b639e59c13780LL),reale(8527676,0x2b5901ca2b961LL),
2200  // C4[5], coeff of eps^24, polynomial in n of order 5
2201  -real(0x13b86e0d5c5dc000LL),real(0x135f9b0385fb0000LL),
2202  -real(0x10df1064c3304000LL),real(0x58b0ae17a818000LL),
2203  -real(0x70d05036b8ec000LL),real(0x2e5299a0b610e00LL),
2204  reale(10178194,0x2338af8e3405bLL),
2205  // C4[5], coeff of eps^23, polynomial in n of order 6
2206  -reale(126383,0x5f6b81564f000LL),reale(192332,0x2215a4d90d800LL),
2207  -reale(113392,0x893928fcaa000LL),reale(71665,0x3fb557978e800LL),
2208  -reale(81791,0xa6f9503f45000LL),reale(12036,0x1a6fad5adf800LL),
2209  reale(3561,0x9aef6f2cefa80LL),reale(3470764200LL,0xea81d86b4b937LL),
2210  // C4[5], coeff of eps^22, polynomial in n of order 7
2211  -reale(191647,0x188f775ada000LL),reale(308186,0x45ee8f2434000LL),
2212  -reale(124928,0xd21a49314e000LL),reale(153616,0xaed0e35eb8000LL),
2213  -reale(118466,0xc4b6a2a9a2000LL),reale(38029,0x77ad4b77bc000LL),
2214  -reale(53612,0x41f60b8316000LL),reale(20169,0xecfa5f7fa8900LL),
2215  reale(3470764200LL,0xea81d86b4b937LL),
2216  // C4[5], coeff of eps^21, polynomial in n of order 8
2217  -reale(5169843,0xc81db86efc000LL),reale(5341939,0xe957aa505800LL),
2218  -reale(2049228,0x2e9753666d000LL),reale(3734678,0xdcd2e44998800LL),
2219  -reale(1762099,0xebebc251fe000LL),reale(1337844,0xa441c7cbb800LL),
2220  -reale(1455577,0x7e18adc04f000LL),reale(163809,0xd9aab3cbce800LL),
2221  reale(50215,0x8f7a6f7ead780LL),reale(45119934611LL,0xe897fd72d67cbLL),
2222  // C4[5], coeff of eps^20, polynomial in n of order 9
2223  -reale(11201228,0x9af12fea90000LL),reale(5330620,7096189457LL<<19),
2224  -reale(4084126,0xa473ecba70000LL),reale(5776338,0xc1238f4360000LL),
2225  -reale(1850318,0x7e36514750000LL),reale(3091001,2788978033LL<<18),
2226  -reale(1978996,0x9854b5b30000LL),reale(651396,0xde4e2e0920000LL),
2227  -reale(1009381,0x5e1878c010000LL),reale(341219,0x67868049b6800LL),
2228  reale(45119934611LL,0xe897fd72d67cbLL),
2229  // C4[5], coeff of eps^19, polynomial in n of order 10
2230  -reale(19364139,0xf3aad6c27e000LL),reale(3661269,0x231a8ee911000LL),
2231  -reale(10171658,0x9bc1444518000LL),reale(6650152,0x1449aa44ff000LL),
2232  -reale(2982446,0xb2f133d6b2000LL),reale(5796709,0x225c7b8fcd000LL),
2233  -reale(2004712,0xb33d0f538c000LL),reale(2087887,0x2718a4e53b000LL),
2234  -reale(2041244,0xb9c4a8d7e6000LL),reale(150337,0x64e8ec0109000LL),
2235  reale(48205,0x4eea8f2f13300LL),reale(45119934611LL,0xe897fd72d67cbLL),
2236  // C4[5], coeff of eps^18, polynomial in n of order 11
2237  -reale(17821498,0x43ce2fe394000LL),reale(8113989,0x34042cf6f8000LL),
2238  -reale(21055211,0x1d823792dc000LL),reale(4458324,0xaba1762760000LL),
2239  -reale(8384573,0x54084121e4000LL),reale(8079221,0xcbb99849c8000LL),
2240  -reale(2172398,0x503335ed2c000LL),reale(5129813,0x3b8a4c21b0000LL),
2241  -reale(2481567,0xadec795134000LL),reale(934125,9279934035LL<<15),
2242  -reale(1531704,0x9cc504aa7c000LL),reale(453383,0xd34e451346a00LL),
2243  reale(45119934611LL,0xe897fd72d67cbLL),
2244  // C4[5], coeff of eps^17, polynomial in n of order 12
2245  reale(4095301,0x789aeb9e64000LL),reale(49542396,0x46ab457e8d000LL),
2246  -reale(24303219,0x1ccf0dd62000LL),reale(4679495,0x21a30e03df000LL),
2247  -reale(21666597,0xecbbb1868000LL),reale(6429258,0x6611bb6911000LL),
2248  -reale(5963806,0x7f45fe6c6e000LL),reale(9141324,0xab5773fc63000LL),
2249  -reale(2043796,0x5ca6f33334000LL),reale(3626747,0xd85dd12c15000LL),
2250  -reale(2919955,0xba0fdf867a000LL),reale(85758,0x333e03c667000LL),
2251  reale(28339,0x9119c9ad54d00LL),reale(45119934611LL,0xe897fd72d67cbLL),
2252  // C4[5], coeff of eps^16, polynomial in n of order 13
2253  -reale(273240474,0x43c43c74c8000LL),reale(133674826,0x952bfc30e0000LL),
2254  reale(7048142,0x68e4684408000LL),reale(44883009,0xdb6a70b90000LL),
2255  -reale(32370151,0x153b9e91a8000LL),reale(2006331,0xa0ac245340000LL),
2256  -reale(20459012,0x9d1a27ed8000LL),reale(9634139,0x6e1e5ebef0000LL),
2257  -reale(3415127,0x8d101d0c88000LL),reale(9090639,8214448173LL<<17),
2258  -reale(2849328,0xea461fc3b8000LL),reale(1554483,7516134885LL<<16),
2259  -reale(2460922,0x6540542d68000LL),reale(615586,0x6f27f96118400LL),
2260  reale(45119934611LL,0xe897fd72d67cbLL),
2261  // C4[5], coeff of eps^15, polynomial in n of order 14
2262  reale(385255297,0xc522d651da000LL),-reale(58599463,0x810289e63d000LL),
2263  -reale(271784816,0x96bdc01bbc000LL),reale(164665597,0xfc4f4e3665000LL),
2264  reale(6169937,0xa7ea1cfd2e000LL),reale(36278794,0xf1d4bf77a7000LL),
2265  -reale(41327996,0x5935502f28000LL),reale(1406713,0xae66a659c9000LL),
2266  -reale(16753028,0x6b0d0fac7e000LL),reale(13550589,0x7d5a3390b000LL),
2267  -reale(1765295,0x851b6e8694000LL),reale(7142364,0xca525091ad000LL),
2268  -reale(4183412,0x818c59892a000LL),-reale(96164,0xa4307ac011000LL),
2269  -reale(44020,0x281c2d0515b00LL),reale(45119934611LL,0xe897fd72d67cbLL),
2270  // C4[5], coeff of eps^14, polynomial in n of order 15
2271  reale(85300002,0xc7e70a9f1c000LL),-reale(294351273,0xafb8edef98000LL),
2272  reale(403760509,0xda2cbc2e94000LL),-reale(107444454,0x9ae8f34870000LL),
2273  -reale(261509454,0x4bda846b4000LL),reale(200593259,0xcaf344c1b8000LL),
2274  -reale(1492598,0x1c0b3e713c000LL),reale(23203659,0x98196f9e60000LL),
2275  -reale(49434335,0xf8209c0184000LL),reale(4620325,0x4eb0e8bd08000LL),
2276  -reale(10475101,0x343acca80c000LL),reale(16597245,8542632147LL<<16),
2277  -reale(2356576,0x3bbee61554000LL),reale(3249396,0x1edbdd7e58000LL),
2278  -reale(4240477,0x930e83f9dc000LL),reale(851256,0x2b979a0197a00LL),
2279  reale(45119934611LL,0xe897fd72d67cbLL),
2280  // C4[5], coeff of eps^13, polynomial in n of order 16
2281  -reale(334885,0xc6bdc7fcb0000LL),-reale(5563880,0xa3a405a9f1000LL),
2282  reale(77196254,0x955c2ca786000LL),-reale(280592470,0x60fd2cd013000LL),
2283  reale(419465490,0x135ebd637c000LL),-reale(164134806,0xd03e535795000LL),
2284  -reale(238238642,0xf95f61c30e000LL),reale(239782224,0x6d53e5d49000LL),
2285  -reale(20068072,0x4afa414658000LL),reale(6399560,0x53e56b4c47000LL),
2286  -reale(53380994,0xb54d3160a2000LL),reale(13179100,0x7f23319325000LL),
2287  -reale(3190623,0x71f1454c2c000LL),reale(15946535,0x7112262fa3000LL),
2288  -reale(5597132,0xd891768336000LL),-reale(517466,0x3872db407f000LL),
2289  -reale(280398,0x37b65ce5ca500LL),reale(45119934611LL,0xe897fd72d67cbLL),
2290  // C4[5], coeff of eps^12, polynomial in n of order 17
2291  -reale(9362,0x69735ac9d0000LL),-reale(41698,3327447843LL<<20),
2292  -reale(274851,0x56e2bdf830000LL),-reale(4724425,0xa83b5c01a0000LL),
2293  reale(68370240,0x5baadc4870000LL),-reale(262946254,0xff686b9240000LL),
2294  reale(430395020,0x66a0aab610000LL),-reale(228360148,0x64a23696e0000LL),
2295  -reale(196492193,0xc6f6cbf150000LL),reale(277855749,243039325LL<<19),
2296  -reale(54565881,0x3f0390efb0000LL),-reale(10430670,3478671393LL<<17),
2297  -reale(48232829,0x9769bd8710000LL),reale(26504611,0xd8be140f40000LL),
2298  reale(733724,0x9fb250690000LL),reale(8992810,0x9e09f3a6a0000LL),
2299  -reale(7946224,0xca1f6288d0000LL),reale(1176502,0x79934ee544800LL),
2300  reale(45119934611LL,0xe897fd72d67cbLL),
2301  // C4[5], coeff of eps^11, polynomial in n of order 18
2302  -real(0x274a66713f785000LL),-real(0x78cbe0a9df914800LL),
2303  -reale(6986,0x5cd0ed6f68000LL),-reale(31980,0xbaca6835fb800LL),
2304  -reale(217574,0x7dc41d384b000LL),-reale(3882916,0x2edd7dacd2800LL),
2305  reale(58859398,0xdc7c0f67f2000LL),-reale(240755855,0x78dc5ddf79800LL),
2306  reale(433769587,0x318800cb6f000LL),-reale(298315443,0xab75c9fd0800LL),
2307  -reale(129660149,0x66ef2473b4000LL),reale(305615878,0x94b6a51048800LL),
2308  -reale(109156237,0x593300db57000LL),-reale(18007247,0x43b21e10e800LL),
2309  -reale(29424146,0x61ad17715a000LL),reale(38156138,0xf0096c8a4a800LL),
2310  -reale(4683041,0xee399b1b9d000LL),-reale(1149725,0xbf46657f8c800LL),
2311  -reale(1106736,0x8c2ceac93e180LL),reale(45119934611LL,0xe897fd72d67cbLL),
2312  // C4[5], coeff of eps^10, polynomial in n of order 19
2313  -real(0x3bd4906e474e000LL),-real(0x97941b80ce3c000LL),
2314  -real(0x1a66716bc5afa000LL),-real(0x532298a0bc3e0000LL),
2315  -reale(4939,0xda9250746000LL),-reale(23308,0x7863f72384000LL),
2316  -reale(164254,0x558c90eef2000LL),-reale(3056120,0xcef6e5fe8000LL),
2317  reale(48766418,0xafc6204b42000LL),-reale(213414260,0xdc9b1ebcc000LL),
2318  reale(425806905,0x15318e0496000LL),-reale(369415923,0x757d6c39f0000LL),
2319  -reale(31178847,0x2c748765b6000LL),reale(306118804,0x213b4942ec000LL),
2320  -reale(181898310,0x263b289662000LL),reale(568685,0x4686791808000LL),
2321  -reale(309548,0x34bb55302e000LL),reale(32975540,0x34fcc4d2a4000LL),
2322  -reale(16246779,0x8dca2dd5da000LL),reale(1477949,0xdae92a7065f00LL),
2323  reale(45119934611LL,0xe897fd72d67cbLL),
2324  // C4[5], coeff of eps^9, polynomial in n of order 20
2325  -real(0x69d018a3b9e000LL),-real(0xed437c3919a800LL),
2326  -real(0x237e48279feb000LL),-real(0x5bea2151a0b3800LL),
2327  -real(0x10666acb6ec18000LL),-real(0x350c7e1643d3c800LL),
2328  -reale(3247,0xe2be74bf45000LL),-reale(15860,0x268da19a55800LL),
2329  -reale(116263,0x5e4790b892000LL),-reale(2266502,0x8314b6fb1e800LL),
2330  reale(38294967,0xecf46ee8e1000LL),-reale(180538484,0x555f9ed2b7800LL),
2331  reale(401643505,0x9c33fda5f4000LL),-reale(432258273,0xf8da98e440800LL),
2332  reale(101814780,0x5dd5e11f87000LL),reale(252370005,0x80f91f9d26800LL),
2333  -reale(252307179,0x99e21a8986000LL),reale(63455824,0x191a53ee5d800LL),
2334  reale(12621880,0x95e41abad000LL),reale(2033357,0xc3307b9c44800LL),
2335  -reale(4727243,0x20838a8bae80LL),reale(45119934611LL,0xe897fd72d67cbLL),
2336  // C4[5], coeff of eps^8, polynomial in n of order 21
2337  -real(0xc09a6adbf4000LL),-real(0x18cab6e3030000LL),
2338  -real(0x359d0ace62c000LL),-real(0x7ab7d9cc438000LL),
2339  -real(0x12c67ab580a4000LL),-real(856171152199LL<<18),
2340  -real(0x9233f1c13ddc000LL),-real(0x1e779de654b48000LL),
2341  -real(0x789f22a00b054000LL),-reale(9796,7021023797LL<<16),
2342  -reale(75089,0xae07706a8c000LL),-reale(1543001,0x638fcd4c58000LL),
2343  reale(27798321,0x1e96e700fc000LL),-reale(142306959,0xd3ad6eb8e0000LL),
2344  reale(355697955,0xce7f78ffc4000LL),-reale(469861249,0x5989105b68000LL),
2345  reale(259457720,0x1370b4ff4c000LL),reale(112194489,0x36d40ed990000LL),
2346  -reale(260872269,0xf8005192ec000LL),reale(151422395,0x58f7b5f388000LL),
2347  -reale(32332898,0xbdc6e34964000LL),reale(433029,0xe4d3ce78fba00LL),
2348  reale(45119934611LL,0xe897fd72d67cbLL),
2349  // C4[5], coeff of eps^7, polynomial in n of order 22
2350  -real(0x1441fa2f35000LL),-real(0x272c726527800LL),
2351  -real(0x4ebdd7b856000LL),-real(0xa564301b74800LL),
2352  -real(0x16d6333bd37000LL),-real(0x3580dec1951800LL),
2353  -real(0x865ae53c178000LL),-real(0x16ec61d7f65e800LL),
2354  -real(0x455fa2e228b9000LL),-real(0xef77f4cbfa3b800LL),
2355  -real(0x3d9c6e708569a000LL),-reale(5230,0x8a511fbc88800LL),
2356  -reale(42196,0xcfdba8cebb000LL),-reale(920786,0xf57a80c4e5800LL),
2357  reale(17837247,0x2fc56aab44000LL),-reale(100064916,0x5e72032af2800LL),
2358  reale(283253574,0xc37962f3c3000LL),-reale(455567530,0xe21e28364f800LL),
2359  reale(400948026,0xf028b16722000LL),-reale(118913774,0x549816fe9c800LL),
2360  -reale(112010399,0x36034a3e3f000LL),reale(121825743,0x78c43cf486800LL),
2361  -reale(36338425,0x426e19287b880LL),
2362  reale(45119934611LL,0xe897fd72d67cbLL),
2363  // C4[5], coeff of eps^6, polynomial in n of order 23
2364  -real(0x1b5badebe000LL),-real(0x326332ca4000LL),-real(0x5fd1bd93a000LL),
2365  -real(0xbcd8e5378000LL),-real(0x1837bef256000LL),
2366  -real(0x3404424ccc000LL),-real(0x75bf8cd1d2000LL),
2367  -real(38025986691LL<<17),-real(0x2dc96f11f6e000LL),
2368  -real(0x811a6e895f4000LL),-real(0x195036bc82ea000LL),
2369  -real(0x5af70d135548000LL),-real(0x187d57cdaa406000LL),
2370  -reale(2189,0x32d399c61c000LL),-reale(18742,0x385cb42a82000LL),
2371  -reale(438375,0xd6a8872030000LL),reale(9224813,0x89f7eb41e2000LL),
2372  -reale(57288808,0xfdc8999b44000LL),reale(184899999,0x331692f966000LL),
2373  -reale(357870966,0x3154fb6f18000LL),reale(431875147,0x7929b7544a000LL),
2374  -reale(318710001,0xe0f19bd36c000LL),reale(131641087,0xbb852faace000LL),
2375  -reale(23311442,0x9e8a4070e9d00LL),
2376  reale(45119934611LL,0xe897fd72d67cbLL),
2377  // C4[5], coeff of eps^5, polynomial in n of order 24
2378  -real(92116035LL<<14),-real(0x26e7bc2d800LL),-real(0x46d3779b000LL),
2379  -real(0x84e1d0c0800LL),-real(0x101cbc30a000LL),-real(0x2073376e3800LL),
2380  -real(0x442adb8b9000LL),-real(0x963884ff6800LL),-real(0x15dbd71e08000LL),
2381  -real(0x363ebc6d59800LL),-real(0x9122bbd857000LL),
2382  -real(0x1a90a4ab06c800LL),-real(0x56f0a68cd06000LL),
2383  -real(0x147a29992a8f800LL),-real(0x5d1402e6c175000LL),
2384  -real(0x228e263277d22800LL),-reale(5078,0x584c613b04000LL),
2385  -reale(128863,0x92233985800LL),reale(2982258,0xd360aa0ed000LL),
2386  -reale(20710125,0x5bbe664118800LL),reale(76213261,0x519df32cfe000LL),
2387  -reale(171479837,0xf7a363253b800LL),reale(241341994,0x2d1ed763cf000LL),
2388  -reale(186491540,0xf45203874e800LL),reale(58278606,0x8c59a11a48880LL),
2389  reale(45119934611LL,0xe897fd72d67cbLL),
2390  // C4[6], coeff of eps^29, polynomial in n of order 0
2391  139264,real(63626127165LL),
2392  // C4[6], coeff of eps^28, polynomial in n of order 1
2393  real(247833LL<<16),real(4782743552LL),real(0x219ae3fb400f15LL),
2394  // C4[6], coeff of eps^27, polynomial in n of order 2
2395  real(420150473LL<<18),-real(0x876551ce0000LL),real(0x350bfa156000LL),
2396  reale(4837,0x68f14547adebLL),
2397  // C4[6], coeff of eps^26, polynomial in n of order 3
2398  real(0x297e6b0e9e1000LL),-real(0x2e90de909aa000LL),
2399  real(0x6148b0a84b000LL),real(0x1d77336bca600LL),
2400  reale(207992,0x1a086a30a3679LL),
2401  // C4[6], coeff of eps^25, polynomial in n of order 4
2402  real(0x10bc6a9e4ee30000LL),-real(0xc179e3d40c9c000LL),
2403  real(0x3edf483df118000LL),-real(0x5c91fff78634000LL),
2404  real(0x216fdab58654400LL),reale(10078162,0xbedd8dc0620e7LL),
2405  // C4[6], coeff of eps^24, polynomial in n of order 5
2406  reale(17715,0xdb1cfba26000LL),-reale(7689,0x9976d7f948000LL),
2407  reale(6474,0xb1047d5d4a000LL),-reale(6855,0xa6eeabbaa4000LL),
2408  real(0x2ac3e335ea26e000LL),real(0xd6d2e7c22e28400LL),
2409  reale(372892021,0x96057cce2c163LL),
2410  // C4[6], coeff of eps^23, polynomial in n of order 6
2411  reale(279883,0xa92c150938000LL),-reale(86797,0xd10c69f53c000LL),
2412  reale(160072,0xfd9d58a4d0000LL),-reale(96731,0xc2b3d16724000LL),
2413  reale(32938,0x46d62be868000LL),-reale(52162,0xc27e2d9b0c000LL),
2414  reale(17103,0x67a9fde667c00LL),reale(4101812237LL,0x723c5cdbe4f41LL),
2415  // C4[6], coeff of eps^22, polynomial in n of order 7
2416  reale(293467,0x7db7c77729000LL),-reale(146628,0x46fd92fe6000LL),
2417  reale(282074,0xcdca0f3f8b000LL),-reale(92435,0x174eb2c344000LL),
2418  reale(105774,0xf5edeb18ed000LL),-reale(100726,0x78839052a2000LL),
2419  reale(6619,0xde4489894f000LL),reale(2174,0xdeb0a21cf2e00LL),
2420  reale(4101812237LL,0x723c5cdbe4f41LL),
2421  // C4[6], coeff of eps^21, polynomial in n of order 8
2422  reale(183603,8337878185LL<<19),-reale(387951,0x8934978f10000LL),
2423  reale(363243,0x9b8677d760000LL),-reale(100927,0x6adc79e30000LL),
2424  reale(246790,7131746729LL<<18),-reale(115867,0xce56197550000LL),
2425  reale(45470,0x976a005d20000LL),-reale(74789,0x6bec0ac470000LL),
2426  reale(21823,0x7d1eb3d72b000LL),reale(4101812237LL,0x723c5cdbe4f41LL),
2427  // C4[6], coeff of eps^20, polynomial in n of order 9
2428  reale(2390210,0x71ea4526d8000LL),-reale(11473167,6397281565LL<<18),
2429  reale(3566140,0xe9fdb6daa8000LL),-reale(3459649,0xbdbfad5d70000LL),
2430  reale(5328875,0xe507b89678000LL),-reale(1202839,0xbeff1963a0000LL),
2431  reale(2208040,0x527339ea48000LL),-reale(1770989,0xb71cae09d0000LL),
2432  reale(48626,0x557ebf6618000LL),reale(16670,0x4a1716aa8d000LL),
2433  reale(53323559086LL,0xcd10b72aa064dLL),
2434  // C4[6], coeff of eps^19, polynomial in n of order 10
2435  reale(16170911,0xf66942f9a0000LL),-reale(15946100,0x87937e1ff0000LL),
2436  reale(1191966,5683381737LL<<19),-reale(10381645,0x67a9610710000LL),
2437  reale(5401104,0xec5f94af60000LL),-reale(1916345,0x9f2b7d6630000LL),
2438  reale(5166787,7293640425LL<<18),-reale(1681428,0xa094a5ad50000LL),
2439  reale(912008,0xad6a83a520000LL),-reale(1452992,0x3f13404c70000LL),
2440  reale(367621,0xca46f4fdbb000LL),reale(53323559086LL,0xcd10b72aa064dLL),
2441  // C4[6], coeff of eps^18, polynomial in n of order 11
2442  reale(51879505,0x1c6021da42000LL),-reale(3388727,0x452f2e2244000LL),
2443  reale(10993546,0x58785d1036000LL),-reale(19450323,0x2862de39d0000LL),
2444  reale(1456775,0xebc764482a000LL),-reale(7922511,0x8d8f4f815c000LL),
2445  reale(7390372,0xfe1ce59e1e000LL),-reale(1065019,0x2a2a06ce8000LL),
2446  reale(3871757,0x7ef447ee12000LL),-reale(2395461,0x8df44bf074000LL),
2447  -reale(40351,0xb597a7abfa000LL),-reale(17707,0xeba2dcf1c1400LL),
2448  reale(53323559086LL,0xcd10b72aa064dLL),
2449  // C4[6], coeff of eps^17, polynomial in n of order 12
2450  reale(18941665,0xd940803e20000LL),-reale(2462456,0xc647b5b638000LL),
2451  reale(55543449,0x9a9f25d270000LL),-reale(10182797,0xdffcb19ee8000LL),
2452  reale(4836527,0xb44e233ec0000LL),-reale(21402374,0x58dcab98000LL),
2453  reale(3817083,0xbef1c88b10000LL),-reale(4459099,0x992120d448000LL),
2454  reale(8502561,0xac3fb5bf60000LL),-reale(1525489,0x80b8b610f8000LL),
2455  reale(1649611,0x4cebe6e3b0000LL),-reale(2280763,0x4f507e59a8000LL),
2456  reale(482782,0x1ffc428c24800LL),reale(53323559086LL,0xcd10b72aa064dLL),
2457  // C4[6], coeff of eps^16, polynomial in n of order 13
2458  reale(169672066,0xfc4e53058c000LL),-reale(255936417,0xcd4166f930000LL),
2459  reale(43044311,0x58bada2414000LL),reale(10984552,0x79ecf34458000LL),
2460  reale(54615551,0xb3c2ab069c000LL),-reale(20672829,0x547b9ae620000LL),
2461  -reale(762958,0xc96d76adc000LL),-reale(20252510,0xad74c43098000LL),
2462  reale(8266131,0x9541dc37ac000LL),-reale(1263055,0x9458475310000LL),
2463  reale(7416125,0xebded0d634000LL),-reale(3121438,0x16f54c0588000LL),
2464  -reale(225538,0xf843322744000LL),-reale(111163,0x41ef8785bb800LL),
2465  reale(53323559086LL,0xcd10b72aa064dLL),
2466  // C4[6], coeff of eps^15, polynomial in n of order 14
2467  -reale(371272727,0xe93844d330000LL),reale(258600199,0x3ab9b44ef8000LL),
2468  reale(127447726,0xd7dad2fc20000LL),-reale(278220404,0x7730102b8000LL),
2469  reale(77869881,0xad9b189b70000LL),reale(21813766,0xb09d2ff98000LL),
2470  reale(46644312,9197745227LL<<18),-reale(33841430,0x25b28aa218000LL),
2471  -reale(3096455,0x6fa54a95f0000LL),-reale(14807144,0xa86ee6dfc8000LL),
2472  reale(13281582,0xf66e06a960000LL),-reale(452377,0x35cd9cb178000LL),
2473  reale(3621811,0x85d91d8b0000LL),-reale(3791781,0x3a80710f28000LL),
2474  reale(636887,0x5f8cc1d1bc800LL),reale(53323559086LL,0xcd10b72aa064dLL),
2475  // C4[6], coeff of eps^14, polynomial in n of order 15
2476  -reale(40751652,0x879256f716000LL),reale(182461023,0x62c00442f4000LL),
2477  -reale(366891419,0xe235688602000LL),reale(303920923,0x2a6218fe88000LL),
2478  reale(70640959,0xa70aa30512000LL),-reale(290919308,0xf0cc1f4de4000LL),
2479  reale(124435738,0x116d522626000LL),reale(24575054,0x49539549b0000LL),
2480  reale(29829722,0x6d4c4f193a000LL),-reale(46205497,0xcd680acebc000LL),
2481  reale(1253661,0x8798d15a4e000LL),-reale(5829398,0x329c172b28000LL),
2482  reale(15178042,0x87d0f72562000LL),-reale(3413258,0x604057df94000LL),
2483  -reale(544537,0x1343d1098a000LL),-reale(371792,0x5ec0380ab3400LL),
2484  reale(53323559086LL,0xcd10b72aa064dLL),
2485  // C4[6], coeff of eps^13, polynomial in n of order 16
2486  reale(100946,21976965LL<<20),reale(2010862,0x3c46708bb0000LL),
2487  -reale(34502092,0x6e09dbf3a0000LL),reale(163298206,0x527fb2e110000LL),
2488  -reale(355839921,948516465LL<<18),reale(347383598,0x3243b82e70000LL),
2489  -reale(2611762,0xae3f6124e0000LL),-reale(286060486,421499843LL<<16),
2490  reale(181022396,2339564421LL<<19),reale(11053843,0x8ea9e8f130000LL),
2491  reale(5354229,0xc704cb69e0000LL),-reale(50862137,0xf12aeaf970000LL),
2492  reale(14064844,5665935493LL<<18),reale(1748678,0x2e869553f0000LL),
2493  reale(9719088,0x671cfc38a0000LL),-reale(6714197,0x76aa8fd6b0000LL),
2494  reale(816805,0x9ce5b98e4f000LL),reale(53323559086LL,0xcd10b72aa064dLL),
2495  // C4[6], coeff of eps^12, polynomial in n of order 17
2496  real(0x75cff722d22b8000LL),reale(9742,5260669319LL<<19),
2497  reale(75734,0x79163f0448000LL),reale(1568684,0xd935dd4310000LL),
2498  -reale(28213944,0x88db35f228000LL),reale(141802366,0xe4716652a0000LL),
2499  -reale(336424367,0x7aaa4f7098000LL),reale(384795625,0xe2aff0230000LL),
2500  -reale(92516926,0xbd45322708000LL),-reale(252728877,4730701433LL<<18),
2501  reale(239978666,0xfd893c3a88000LL),-reale(28528394,5445461995LL<<16),
2502  -reale(18370370,0x5cd8a4fbe8000LL),-reale(38961300,0x78b7628f20000LL),
2503  reale(30014507,0xb37b1485a8000LL),-reale(654615,0xa96a2bf90000LL),
2504  -reale(667571,0x85c41bf0c8000LL),-reale(1181523,0x1c81baa857000LL),
2505  reale(53323559086LL,0xcd10b72aa064dLL),
2506  // C4[6], coeff of eps^11, polynomial in n of order 18
2507  real(0x55d873de6520000LL),real(0x12c7cfeef6810000LL),
2508  real(0x4e200e3f1e1LL<<20),reale(6671,0xd2467fb9f0000LL),
2509  reale(53806,3275978471LL<<17),reale(1163348,0xd1cfb7f3d0000LL),
2510  -reale(22032298,0xf3cc53d740000LL),reale(118198962,4397370971LL<<16),
2511  -reale(306929389,0x72efa76b60000LL),reale(409945031,0xba4df5f90000LL),
2512  -reale(195574008,5584443935LL<<19),-reale(178055138,0x4cd4f3ce90000LL),
2513  reale(282861404,0xd715020c60000LL),-reale(99637722,0xf11193d4b0000LL),
2514  -reale(20986520,0xfb661347c0000LL),-reale(8771627,7018708525LL<<16),
2515  reale(31360164,0xdb2c51c420000LL),-reale(12477955,8590832271LL<<16),
2516  reale(873590,0xbe0d3e9693000LL),reale(53323559086LL,0xcd10b72aa064dLL),
2517  // C4[6], coeff of eps^10, polynomial in n of order 19
2518  real(0x5808512b12b000LL),real(0xfaa729276e2000LL),
2519  real(0x3175560e4519000LL),real(0xb21b680b3a90000LL),
2520  real(0x2fcbc5fe71407000LL),reale(4229,0xf0de326e3e000LL),
2521  reale(35532,0x38e22907f5000LL),reale(805604,0x42db4fa3ec000LL),
2522  -reale(16150031,0xfe4d67d51d000LL),reale(93034137,0xf6628ead9a000LL),
2523  -reale(265995225,0x398943192f000LL),reale(414315266,0x970145dd48000LL),
2524  -reale(301204836,0xc549c7ba41000LL),-reale(51738066,0x4e1063bb0a000LL),
2525  reale(275650719,0x10481031ad000LL),-reale(187610845,0x85f00095c000LL),
2526  reale(25230256,0x4ada23b49b000LL),reale(13917204,0x3da6dc4452000LL),
2527  reale(4066715,0x8660f73889000LL),-reale(4361677,0xea98323d07e00LL),
2528  reale(53323559086LL,0xcd10b72aa064dLL),
2529  // C4[6], coeff of eps^9, polynomial in n of order 20
2530  real(0x65fa8c6bf0000LL),real(0xfe88642ae4000LL),real(0x2aa82304e58000LL),
2531  real(0x7ca8bddcccc000LL),real(434853972467LL<<18),
2532  real(0x5e16320d44b4000LL),real(0x1a2859bf40b28000LL),
2533  reale(2409,0x1b825da69c000LL),reale(21179,0xabe6860d90000LL),
2534  reale(506292,0x5b6e5f0684000LL),-reale(10810252,0xeee1886808000LL),
2535  reale(67327238,0xa18a80786c000LL),-reale(213364581,0xe79aac41a0000LL),
2536  reale(387619687,0x51e3ba1054000LL),-reale(387180015,0xd550406b38000LL),
2537  reale(121695298,0x2400c6e23c000LL),reale(172879787,0x9e57682f30000LL),
2538  -reale(230507460,0xb74e70fddc000LL),reale(112381926,0x4eee70a198000LL),
2539  -reale(20283371,0x42949e7bf4000LL),-reale(288686,0x988d3450a7c00LL),
2540  reale(53323559086LL,0xcd10b72aa064dLL),
2541  // C4[6], coeff of eps^8, polynomial in n of order 21
2542  real(0x72e86a7de000LL),real(8772831327LL<<15),real(0x273ffc1812000LL),
2543  real(0x64635c5cac000LL),real(0x11473cdd246000LL),
2544  real(0x33fd816c260000LL),real(0xae6e2137a7a000LL),
2545  real(0x29ff10928814000LL),real(0xc26a115cf4ae000LL),
2546  real(0x492994f20c1c8000LL),reale(10833,0x80f3c9e4e2000LL),
2547  reale(274842,0xd406a2037c000LL),-reale(6296293,0xca802ed0ea000LL),
2548  reale(42731189,0xb6f3d1e130000LL),-reale(151191524,0x41a7e788b6000LL),
2549  reale(320575109,0xae49526ee4000LL),-reale(416345568,0xb8c8445e82000LL),
2550  reale(298319523,0xb52957c098000LL),-reale(42956565,0x78799bae4e000LL),
2551  -reale(119892798,0x70342c95b4000LL),reale(103927174,0x8691916be6000LL),
2552  -reale(29157346,0x2fb5a3d22ec00LL),
2553  reale(53323559086LL,0xcd10b72aa064dLL),
2554  // C4[6], coeff of eps^7, polynomial in n of order 22
2555  real(74709635LL<<15),real(0x4ba47734000LL),real(0xa7b994d0000LL),
2556  real(0x1869c5c6c000LL),real(0x3c23e3d88000LL),real(0x9e1c8b7a4000LL),
2557  real(1882100649LL<<18),real(0x573ad5a4dc000LL),real(0x12f915ab6f8000LL),
2558  real(0x4c1f4084014000LL),real(0x170ced7cbfb0000LL),
2559  real(0x921b89aca54c000LL),real(0x599b4a7922068000LL),
2560  reale(38914,0x1efa73f084000LL),-reale(964915,0x51a6da0ae0000LL),
2561  reale(7200274,0x92a23dbc000LL),-reale(28652022,0x356dea628000LL),
2562  reale(70837833,0x39cdeca8f4000LL),-reale(114872161,0xfcdf3a9570000LL),
2563  reale(122704354,0xd9bfe74e2c000LL),-reale(83141739,0x9edadabcb8000LL),
2564  reale(32332898,0xbdc6e34964000LL),-reale(5485045,0x527ae1fc73400LL),
2565  reale(17774519695LL,0x99b03d0e3576fLL),
2566  // C4[6], coeff of eps^6, polynomial in n of order 23
2567  real(257316433920LL),real(517719121920LL),real(0xfb6e649000LL),
2568  real(0x221f7064000LL),real(0x4d84a37f000LL),real(0xb958155a000LL),
2569  real(0x1d5dd0db5000LL),real(0x4faa5a050000LL),real(0xea04686eb000LL),
2570  real(0x2f40e3db46000LL),real(0xab8623d121000LL),real(0x2d147c4903c000LL),
2571  real(0xe63ae874e57000LL),real(0x60cd21bcc932000LL),
2572  real(0x3f869e23e408d000LL),reale(29814,0xcc97221028000LL),
2573  -reale(808726,0x6d837bf63d000LL),reale(6700876,0x1daf27af1e000LL),
2574  -reale(30153942,0x8594329407000LL),reale(86154121,0x7da76bf014000LL),
2575  -reale(165128732,0xdb80e436d1000LL),reale(210163841,0xd18cc55d0a000LL),
2576  -reale(153581269,0x570b79c9b000LL),reale(46622885,0x3d1480e1d3a00LL),
2577  reale(53323559086LL,0xcd10b72aa064dLL),
2578  // C4[7], coeff of eps^29, polynomial in n of order 0
2579  real(13087612928LL),real(0x90e6983c364f3dLL),
2580  // C4[7], coeff of eps^28, polynomial in n of order 1
2581  -real(161707LL<<21),real(7239297LL<<14),real(0xcf8f801ee602cdLL),
2582  // C4[7], coeff of eps^27, polynomial in n of order 2
2583  -real(3500022825LL<<20),real(630513507LL<<19),real(0x6038c37fa000LL),
2584  reale(72555,0x626230f3330c5LL),
2585  // C4[7], coeff of eps^26, polynomial in n of order 3
2586  -real(92252949633LL<<21),real(16187170389LL<<22),
2587  -real(51975912235LL<<21),real(0x7c00d0f2b78000LL),
2588  reale(3119881,0x867e38d993117LL),
2589  // C4[7], coeff of eps^25, polynomial in n of order 4
2590  -real(0x64d0a86bae7c0000LL),real(0x7c07ce24c65f0000LL),
2591  -real(0x739ece76489e0000LL),real(0x6e7bce15f550000LL),
2592  real(0x24fc420030b8400LL),reale(127915142,0x8a371ad88dcafLL),
2593  // C4[7], coeff of eps^24, polynomial in n of order 5
2594  -reale(5990,0xbd2326cc40000LL),reale(14992,4018200301LL<<20),
2595  -reale(6873,8929851351LL<<18),reale(2782,8051012645LL<<19),
2596  -reale(4583,0xc89924b340000LL),real(0x52aed30dcf988800LL),
2597  reale(430260024,0xe82db7640b7c1LL),
2598  // C4[7], coeff of eps^23, polynomial in n of order 6
2599  -reale(169326,4206873009LL<<17),reale(261065,0x25b4e353d0000LL),
2600  -reale(59142,0xf0c50992c0000LL),reale(111182,4597550539LL<<16),
2601  -reale(88869,504433083LL<<17),reale(2313,0xe34bfe3f90000LL),
2602  real(0x32dc48b9e1d23400LL),reale(4732860273LL,0xf9f6e14c7e54bLL),
2603  // C4[7], coeff of eps^22, polynomial in n of order 7
2604  -reale(467157,1100000847LL<<20),reale(258178,755278933LL<<21),
2605  -reale(91474,559664221LL<<20),reale(248285,171426119LL<<22),
2606  -reale(82821,231309675LL<<20),reale(44668,65972935LL<<21),
2607  -reale(71456,2669582201LL<<20),reale(18220,0x9846e079d4000LL),
2608  reale(4732860273LL,0xf9f6e14c7e54bLL),
2609  // C4[7], coeff of eps^21, polynomial in n of order 8
2610  -reale(10858183,1145150433LL<<21),reale(1155453,0xa514064740000LL),
2611  -reale(4408275,1110140307LL<<19),reale(4494002,0xa8330ec1c0000LL),
2612  -reale(693747,3759921697LL<<20),reale(2336198,8880970129LL<<18),
2613  -reale(1499288,4981657777LL<<19),-reale(18466,6402610053LL<<18),
2614  -reale(7818,0x6ee4879b83000LL),reale(61527183561LL,0xb18970e26a4cfLL),
2615  // C4[7], coeff of eps^20, polynomial in n of order 9
2616  -reale(7907170,4058896835LL<<20),reale(1601483,335338375LL<<23),
2617  -reale(11238504,3427529005LL<<20),reale(2745284,1787777405LL<<21),
2618  -reale(2325455,2252860775LL<<20),reale(4939939,712213223LL<<22),
2619  -reale(1021126,555773201LL<<20),reale(952760,1631005375LL<<21),
2620  -reale(1365312,965324491LL<<20),reale(299618,0x2f589c3f22000LL),
2621  reale(61527183561LL,0xb18970e26a4cfLL),
2622  // C4[7], coeff of eps^19, polynomial in n of order 10
2623  reale(5811147,7891888051LL<<19),reale(19155879,6260648859LL<<18),
2624  -reale(13234724,832589145LL<<21),-reale(473729,0xaccee67ac0000LL),
2625  -reale(9690431,2460044795LL<<19),reale(5218195,5282091375LL<<18),
2626  -reale(699193,3313511321LL<<20),reale(4032431,0xb01d955a40000LL),
2627  -reale(1901524,5999844905LL<<19),-reale(111197,715304509LL<<18),
2628  -reale(51622,0xdda253af9f000LL),reale(61527183561LL,0xb18970e26a4cfLL),
2629  // C4[7], coeff of eps^18, polynomial in n of order 11
2630  -reale(34477536,1085877825LL<<20),reale(44845230,817114545LL<<21),
2631  reale(4606432,1572161669LL<<20),reale(12496576,210421693LL<<23),
2632  -reale(18271471,1543698101LL<<20),-reale(128700,742574025LL<<21),
2633  -reale(6139017,689151983LL<<20),reale(7385046,100502461LL<<22),
2634  -reale(590509,2783893289LL<<20),reale(1800602,699157181LL<<21),
2635  -reale(2092277,3566080099LL<<20),reale(381025,0x99466ecd7c000LL),
2636  reale(61527183561LL,0xb18970e26a4cfLL),
2637  // C4[7], coeff of eps^17, polynomial in n of order 12
2638  -reale(152644671,981125379LL<<19),-reale(24136152,0xd3514f38e0000LL),
2639  -reale(16909786,8097141141LL<<18),reale(53988238,0xc115854860000LL),
2640  -reale(2192558,3293732289LL<<20),reale(3853073,2819007469LL<<17),
2641  -reale(20689919,5309095411LL<<18),reale(3514368,0xf1b4463ee0000LL),
2642  -reale(1814216,3975618817LL<<19),reale(7354899,0xbd88356420000LL),
2643  -reale(2207882,191252177LL<<18),-reale(269543,3717910997LL<<17),
2644  -reale(156646,0x7bcb3b3a6a800LL),reale(61527183561LL,0xb18970e26a4cfLL),
2645  // C4[7], coeff of eps^16, polynomial in n of order 13
2646  reale(52565396,753292423LL<<19),reale(252855342,568744119LL<<21),
2647  -reale(197183211,7281644191LL<<19),-reale(6678358,3552459447LL<<20),
2648  reale(4519131,7283469291LL<<19),reale(56648760,112164189LL<<22),
2649  -reale(15289276,2020707835LL<<19),-reale(3713103,1403767329LL<<20),
2650  -reale(17880720,7304289905LL<<19),reale(9494998,1497636157LL<<21),
2651  reale(492167,2907561065LL<<19),reale(3952538,4294903605LL<<20),
2652  -reale(3358139,5130468237LL<<19),reale(480004,0x1e727719e9000LL),
2653  reale(61527183561LL,0xb18970e26a4cfLL),
2654  // C4[7], coeff of eps^15, polynomial in n of order 14
2655  reale(279617399,0xd9972cba40000LL),-reale(353187715,0x687b832220000LL),
2656  reale(118965967,4456434973LL<<19),reale(220096359,3595022681LL<<17),
2657  -reale(240814657,8170991797LL<<18),reale(28075084,0xec7a345460000LL),
2658  reale(24758769,1818605983LL<<20),reale(48013974,0xb5345431a0000LL),
2659  -reale(32373431,0xc7bac8f4c0000LL),-reale(5075135,8642954025LL<<17),
2660  -reale(9094832,6469786017LL<<19),reale(13639028,3685620545LL<<17),
2661  -reale(1773068,1431802737LL<<18),-reale(460476,0x51ab5a8ea0000LL),
2662  -reale(423738,0x5d98934922800LL),reale(61527183561LL,0xb18970e26a4cfLL),
2663  // C4[7], coeff of eps^14, polynomial in n of order 15
2664  reale(16417106,2408387839LL<<20),-reale(93245803,1562234793LL<<21),
2665  reale(256985456,250552029LL<<20),-reale(365861944,857240429LL<<22),
2666  reale(190902238,1499270843LL<<20),reale(163412998,1423242741LL<<21),
2667  -reale(274443985,2668181351LL<<20),reale(82958237,163620913LL<<23),
2668  reale(33859016,1729347703LL<<20),reale(25275487,1495319443LL<<21),
2669  -reale(45844273,3794232747LL<<20),reale(4490176,231613489LL<<22),
2670  reale(1010900,690735667LL<<20),reale(10013483,1036831025LL<<21),
2671  -reale(5637707,2068106223LL<<20),reale(570308,0x8f0afe45ec000LL),
2672  reale(61527183561LL,0xb18970e26a4cfLL),
2673  // C4[7], coeff of eps^13, polynomial in n of order 16
2674  -reale(25657,393048869LL<<22),-reale(608651,0xacbc40d5c0000LL),
2675  reale(12764052,2144856077LL<<19),-reale(76823449,3121867141LL<<18),
2676  reale(228672619,4131243473LL<<20),-reale(367062288,0xf756dca4c0000LL),
2677  reale(263470997,8569317111LL<<19),reale(78573490,0xffb10f8fc0000LL),
2678  -reale(283548774,1794660389LL<<21),reale(154702622,9227087281LL<<18),
2679  reale(16937276,1939608161LL<<19),-reale(6432822,7897704317LL<<18),
2680  -reale(43016670,946798949LL<<20),reale(22087851,0xaa7600dd40000LL),
2681  reale(1665577,8523064651LL<<19),-reale(163221,0xe0acad2e40000LL),
2682  -reale(1189371,0x766c2260a3000LL),reale(61527183561LL,0xb18970e26a4cfLL),
2683  // C4[7], coeff of eps^12, polynomial in n of order 17
2684  -real(0x13bc5107d5fLL<<20),-real(506650109317LL<<24),
2685  -reale(17217,2185571073LL<<20),-reale(426469,557216187LL<<21),
2686  reale(9411503,1140836685LL<<20),-reale(60299258,66945391LL<<22),
2687  reale(194753933,1835852139LL<<20),-reale(352928157,2046106529LL<<21),
2688  reale(328231147,2405007161LL<<20),-reale(34561926,360605189LL<<23),
2689  -reale(248371006,3915897705LL<<20),reale(226668375,1401273273LL<<21),
2690  -reale(40114392,2920598683LL<<20),-reale(25898188,1028871717LL<<22),
2691  -reale(16043876,2538787453LL<<20),reale(28698456,1825641427LL<<21),
2692  -reale(9602688,2437057327LL<<20),reale(502063,0xa52218333a000LL),
2693  reale(61527183561LL,0xb18970e26a4cfLL),
2694  // C4[7], coeff of eps^11, polynomial in n of order 18
2695  -real(81880241733LL<<19),-real(651169421489LL<<18),
2696  -real(194261131981LL<<22),-real(0x4616f301f1bc0000LL),
2697  -reale(10659,7786635659LL<<19),-reale(276843,0xf150eaf340000LL),
2698  reale(6459374,425055961LL<<20),-reale(44283297,2370521611LL<<18),
2699  reale(156003403,8328479919LL<<19),-reale(319848045,0xab86b09a40000LL),
2700  reale(372382116,1407449139LL<<21),-reale(166870261,0xbaeb2e09c0000LL),
2701  -reale(148815577,7753476247LL<<19),reale(260443738,1330203003LL<<18),
2702  -reale(131653575,428167437LL<<20),reale(2775725,691412797LL<<18),
2703  reale(12306214,6299226531LL<<19),reale(5355345,9401097695LL<<18),
2704  -reale(3966302,0xcbc08bfb17000LL),reale(61527183561LL,0xb18970e26a4cfLL),
2705  // C4[7], coeff of eps^10, polynomial in n of order 19
2706  -real(1704454843LL<<20),-real(2722537665LL<<21),-real(19434970697LL<<20),
2707  -real(4989045369LL<<24),-real(394962411735LL<<20),
2708  -real(0x128b33efecfLL<<21),-reale(5903,789230693LL<<20),
2709  -reale(161527,569013611LL<<22),reale(4006338,1271698701LL<<20),
2710  -reale(29564239,1312346333LL<<21),reale(114267945,2347153791LL<<20),
2711  -reale(265827046,63320697LL<<23),reale(379233361,4202669809LL<<20),
2712  -reale(292689947,1148927723LL<<21),reale(19915451,3747715939LL<<20),
2713  reale(197711494,385979271LL<<22),-reale(197401730,911113003LL<<20),
2714  reale(83971818,387288839LL<<21),-reale(12852829,1345691321LL<<20),
2715  -reale(602476,0x5fc28370ac000LL),reale(61527183561LL,0xb18970e26a4cfLL),
2716  // C4[7], coeff of eps^9, polynomial in n of order 20
2717  -real(304621785LL<<18),-real(0xc9814e4b0000LL),-real(5069418237LL<<17),
2718  -real(0x7c4fe70d90000LL),-real(7691534469LL<<20),
2719  -real(0x7a02179d470000LL),-real(0x274586580a60000LL),
2720  -real(0x10907db87bd50000LL),-reale(2773,9732262223LL<<18),
2721  -reale(80424,78339267LL<<16),reale(2134032,0xd8c3d9bae0000LL),
2722  -reale(17066460,0x8709888510000LL),reale(72842964,6932239995LL<<19),
2723  -reale(192914141,0x448548ebf0000LL),reale(332328916,0xa61d5e5020000LL),
2724  -reale(364348462,0x260e7984d0000LL),reale(215166704,0xfd6630ec0000LL),
2725  reale(5301792,6304582341LL<<16),-reale(118567350,0x6a550b6aa0000LL),
2726  reale(89166503,0x5c73fd2370000LL),-reale(23960987,0x75c7f62663400LL),
2727  reale(61527183561LL,0xb18970e26a4cfLL),
2728  // C4[7], coeff of eps^8, polynomial in n of order 21
2729  -real(11869221LL<<18),-real(7450235LL<<20),-real(79397539LL<<18),
2730  -real(113271327LL<<19),-real(700448177LL<<18),-real(148973407LL<<22),
2731  -real(9118660335LL<<18),-real(20216702289LL<<19),
2732  -real(0xcadd965ff40000LL),-real(386512744317LL<<20),
2733  -real(0xf93c68aca7bLL<<18),-reale(30847,5279995331LL<<19),
2734  reale(882325,8584251383LL<<18),-reale(7706931,2116826591LL<<21),
2735  reale(36580048,2730390969LL<<18),-reale(110604386,3847062005LL<<19),
2736  reale(227103584,0x9e98f54ac0000LL),-reale(323034443,1752619391LL<<20),
2737  reale(314251676,0xb5ebcf2b40000LL),-reale(199218854,3061725287LL<<19),
2738  reale(73903768,9476063903LL<<18),-reale(12124837,0x72a953b85800LL),
2739  reale(61527183561LL,0xb18970e26a4cfLL),
2740  // C4[7], coeff of eps^7, polynomial in n of order 22
2741  -real(575575LL<<17),-real(2681133LL<<16),-real(1637545LL<<18),
2742  -real(16890107LL<<16),-real(23159565LL<<17),-real(0x8210e690000LL),
2743  -real(27276821LL<<20),-real(0x5bebf1b70000LL),-real(3075032387LL<<17),
2744  -real(0x6a5f183250000LL),-real(40477467135LL<<18),
2745  -real(0x11b5c31caf30000LL),-real(0xd14cd352ff20000LL),
2746  -reale(6969,0xb17d189610000LL),reale(216834,7757873387LL<<19),
2747  -reale(2087035,0xf153506af0000LL),reale(11091105,0x4b9d7f7a20000LL),
2748  -reale(38290720,0xa99fbe31d0000LL),reale(91897729,0x9718fbaac0000LL),
2749  -reale(156643857,0x418d7e6eb0000LL),reale(184759421,0x6102c9a360000LL),
2750  -reale(129331594,0xf71b8d2590000LL),reale(38395317,0x415c2de726c00LL),
2751  reale(61527183561LL,0xb18970e26a4cfLL),
2752  // C4[8], coeff of eps^29, polynomial in n of order 0
2753  real(7241<<16),real(0x112c657acf71bLL),
2754  // C4[8], coeff of eps^28, polynomial in n of order 1
2755  real(1165359LL<<20),real(3168035LL<<17),real(0x21ffb4a731cf423fLL),
2756  // C4[8], coeff of eps^27, polynomial in n of order 2
2757  real(41827383LL<<21),-real(137865429LL<<20),real(631109843LL<<16),
2758  reale(4837,0x68f14547adebLL),
2759  // C4[8], coeff of eps^26, polynomial in n of order 3
2760  real(54350489115LL<<22),-real(21656377197LL<<23),real(1080358617LL<<22),
2761  real(0x5c4a2579a0000LL),reale(3535865,0xba8f0d3ad9e09LL),
2762  // C4[8], coeff of eps^25, polynomial in n of order 4
2763  reale(4480,63845967LL<<22),-real(0x5f0bc8cec07LL<<20),
2764  real(0x198015cca1fLL<<21),-real(0x51d1e6f78cdLL<<20),
2765  real(0x14fb331d33f30000LL),reale(144970494,0xe0e91e6ce4f71LL),
2766  // C4[8], coeff of eps^24, polynomial in n of order 5
2767  reale(226427,7535956641LL<<17),-reale(36730,6647829291LL<<19),
2768  reale(116830,5936429895LL<<17),-reale(76966,613785099LL<<18),
2769  -real(0x2a948e8d73a60000LL),-real(0x116572b5168a4000LL),
2770  reale(5363908310LL,0x81b165bd17b55LL),
2771  // C4[8], coeff of eps^23, polynomial in n of order 6
2772  reale(151394,3866446399LL<<20),-reale(105723,1435687723LL<<19),
2773  reale(240417,2090106533LL<<21),-reale(54672,3991575693LL<<19),
2774  reale(46185,3230210197LL<<20),-reale(67790,4028416911LL<<19),
2775  reale(15270,0xa469197488000LL),reale(5363908310LL,0x81b165bd17b55LL),
2776  // C4[8], coeff of eps^22, polynomial in n of order 7
2777  -reale(105618,1394014919LL<<21),-reale(5351753,377020849LL<<22),
2778  reale(3446650,1690522763LL<<21),-reale(453181,286167171LL<<23),
2779  reale(2431204,1637447437LL<<21),-reale(1239333,63204475LL<<22),
2780  -reale(60030,1665832481LL<<21),-reale(26716,0x6a2a5d69d0000LL),
2781  reale(69730808036LL,0x96022a9a34351LL),
2782  // C4[8], coeff of eps^21, polynomial in n of order 8
2783  reale(4362900,465328075LL<<22),-reale(10560212,802403079LL<<19),
2784  reale(656010,2976408017LL<<20),-reale(3068612,8162681445LL<<19),
2785  reale(4482659,1990068235LL<<21),-reale(516359,5969201251LL<<19),
2786  reale(1022585,502576667LL<<20),-reale(1273161,3447687361LL<<19),
2787  reale(245310,0x45a78ad538000LL),reale(69730808036LL,0x96022a9a34351LL),
2788  // C4[8], coeff of eps^20, polynomial in n of order 9
2789  reale(23624906,1629010283LL<<19),-reale(5851601,324958949LL<<22),
2790  reale(255419,6850290885LL<<19),-reale(10559838,1365338319LL<<20),
2791  reale(3058631,5351542623LL<<19),-reale(782822,266312293LL<<21),
2792  reale(4071490,3032871865LL<<19),-reale(1457911,2387656005LL<<20),
2793  -reale(144540,929274797LL<<19),-reale(76349,0x2c1c25d590000LL),
2794  reale(69730808036LL,0x96022a9a34351LL),
2795  // C4[8], coeff of eps^19, polynomial in n of order 10
2796  reale(23056909,2395766741LL<<20),reale(8427619,3212023717LL<<19),
2797  reale(19522568,367619617LL<<22),-reale(12637641,5752438869LL<<19),
2798  -reale(1859539,2126155853LL<<20),-reale(7720368,2358643951LL<<19),
2799  reale(5969641,447801057LL<<21),-reale(4464,2860310889LL<<19),
2800  reale(1954609,2968726289LL<<20),-reale(1904959,7710818563LL<<19),
2801  reale(302310,0x7de136fc28000LL),reale(69730808036LL,0x96022a9a34351LL),
2802  // C4[8], coeff of eps^18, polynomial in n of order 11
2803  -reale(34760584,1377594673LL<<21),-reale(45089279,700199389LL<<22),
2804  reale(38964787,642296389LL<<21),reale(8377867,242649263LL<<24),
2805  reale(10805340,270655563LL<<21),-reale(18348308,77894251LL<<22),
2806  -reale(8504,712824639LL<<21),-reale(2874058,104939633LL<<23),
2807  reale(7002991,271121287LL<<21),-reale(1456031,497148985LL<<22),
2808  -reale(262921,1640850307LL<<21),-reale(186713,0x66184da2b0000LL),
2809  reale(69730808036LL,0x96022a9a34351LL),
2810  // C4[8], coeff of eps^17, polynomial in n of order 12
2811  reale(266733950,1060079417LL<<21),-reale(92315127,311764467LL<<19),
2812  -reale(39784767,2743383633LL<<20),-reale(24124714,5368290721LL<<19),
2813  reale(52035773,16490707LL<<22),-reale(214469,3779317103LL<<19),
2814  -reale(32744,3406796695LL<<20),-reale(19012957,4710528797LL<<19),
2815  reale(5897141,767669011LL<<21),reale(758445,547828629LL<<19),
2816  reale(4185368,186448291LL<<20),-reale(2955613,5547446041LL<<19),
2817  reale(363691,0xed908404b8000LL),reale(69730808036LL,0x96022a9a34351LL),
2818  // C4[8], coeff of eps^16, polynomial in n of order 13
2819  -reale(254507630,0xe2b8b6bb40000LL),-reale(58148124,1471923579LL<<20),
2820  reale(270522720,3187458133LL<<18),-reale(149985652,7726894061LL<<19),
2821  -reale(27328603,0x99e6e9ea40000LL),reale(4011861,407374679LL<<21),
2822  reale(54943982,0xaf3dd22640000LL),-reale(17478454,3922351195LL<<19),
2823  -reale(6848089,0x9bbe86d940000LL),-reale(11885922,3297252137LL<<20),
2824  reale(11706960,678889437LL<<18),-reale(595378,2432546249LL<<19),
2825  -reale(329167,0xe066968840000LL),-reale(450081,0x595d162958000LL),
2826  reale(69730808036LL,0x96022a9a34351LL),
2827  // C4[8], coeff of eps^15, polynomial in n of order 14
2828  -reale(166710239,3480741959LL<<20),reale(313421255,2329933911LL<<19),
2829  -reale(299209385,1287661491LL<<21),reale(24383199,5307535921LL<<19),
2830  reale(248029318,3243559867LL<<20),-reale(210032461,8189928917LL<<19),
2831  reale(10907073,960500783LL<<22),reale(29948106,2038678405LL<<19),
2832  reale(40306034,2725271357LL<<20),-reale(36745958,6196825729LL<<19),
2833  -reale(1934460,123839633LL<<21),-reale(492518,4761069735LL<<19),
2834  reale(9949315,1255380799LL<<20),-reale(4720329,388065197LL<<19),
2835  reale(398374,0x9081f25c18000LL),reale(69730808036LL,0x96022a9a34351LL),
2836  // C4[8], coeff of eps^14, polynomial in n of order 15
2837  -reale(5499415,942753073LL<<21),reale(38811064,349279653LL<<22),
2838  -reale(140017234,1709558915LL<<21),reale(290760665,163783697LL<<23),
2839  -reale(332595868,714890693LL<<21),reale(118902683,730607999LL<<22),
2840  reale(189429058,237701737LL<<21),-reale(256456610,243945477LL<<24),
2841  reale(78365400,1246868327LL<<21),reale(35514427,78282137LL<<22),
2842  reale(8045132,96899221LL<<21),-reale(42695880,422981029LL<<23),
2843  reale(15212575,506177875LL<<21),reale(2863173,903918451LL<<22),
2844  reale(284029,1922203905LL<<21),-reale(1161079,0x6c18f2ad70000LL),
2845  reale(69730808036LL,0x96022a9a34351LL),
2846  // C4[8], coeff of eps^13, polynomial in n of order 16
2847  reale(5407,439728533LL<<23),reale(151556,693836399LL<<19),
2848  -reale(3836797,3870271773LL<<20),reale(28742693,8016450573LL<<19),
2849  -reale(111747677,1508361473LL<<21),reale(256964119,236840267LL<<19),
2850  -reale(347691811,711701031LL<<20),reale(216072654,2622689769LL<<19),
2851  reale(88295276,790755477LL<<22),-reale(263658780,5516898905LL<<19),
2852  reale(163753678,37603151LL<<20),-reale(1803857,6339257275LL<<19),
2853  -reale(22560155,108468139LL<<21),-reale(21197875,3801517693LL<<19),
2854  reale(25658955,3111371333LL<<20),-reale(7416706,6937931487LL<<19),
2855  reale(268690,0x9ce0757848000LL),reale(69730808036LL,0x96022a9a34351LL),
2856  // C4[8], coeff of eps^12, polynomial in n of order 17
2857  real(369814360487LL<<19),real(159053188703LL<<23),
2858  reale(3152,1136779065LL<<19),reale(92558,2295771257LL<<20),
2859  -reale(2473330,1734833909LL<<19),reale(19757571,360351901LL<<21),
2860  -reale(83162616,6619531363LL<<19),reale(212413714,2066066043LL<<20),
2861  -reale(337117487,5524436113LL<<19),reale(299293348,697772127LL<<22),
2862  -reale(51076102,4535292671LL<<19),-reale(200831521,1217539203LL<<20),
2863  reale(227963885,2651839699LL<<19),-reale(87452614,163103009LL<<21),
2864  -reale(9664164,7186873499LL<<19),reale(9739937,3920029055LL<<20),
2865  reale(6101400,4999938359LL<<19),-reale(3588081,0x84422b3e50000LL),
2866  reale(69730808036LL,0x96022a9a34351LL),
2867  // C4[8], coeff of eps^11, polynomial in n of order 18
2868  real(3576016431LL<<20),real(32208729499LL<<19),real(10983028711LL<<23),
2869  real(0x9286be006280000LL),real(0x65e9f47db41LL<<20),
2870  reale(50386,4528870031LL<<19),-reale(1428014,1685009291LL<<21),
2871  reale(12227031,6176103481LL<<19),-reale(56007028,2392678701LL<<20),
2872  reale(159476659,5817614083LL<<19),-reale(295263705,809939737LL<<22),
2873  reale(344605761,6427356205LL<<19),-reale(202719833,951923227LL<<20),
2874  -reale(50658828,5629491977LL<<19),reale(201884255,1512264231LL<<21),
2875  -reale(166564947,5368120671LL<<19),reale(63259557,2614639991LL<<20),
2876  -reale(8140125,1990873493LL<<19),-reale(722971,0xa61c9dba68000LL),
2877  reale(69730808036LL,0x96022a9a34351LL),
2878  // C4[8], coeff of eps^10, polynomial in n of order 19
2879  real(45596577LL<<21),real(81531441LL<<22),real(656187675LL<<21),
2880  real(191463201LL<<25),real(17391213765LL<<21),real(65094511967LL<<22),
2881  real(0x16272ee843fLL<<21),reale(23168,382193603LL<<23),
2882  -reale(700305,441535191LL<<21),reale(6465118,134564813LL<<22),
2883  -reale(32414063,913166045LL<<21),reale(103314135,145041825LL<<24),
2884  -reale(222332965,1267927603LL<<21),reale(326070132,55789563LL<<22),
2885  -reale(309964302,1355885369LL<<21),reale(149975409,308317249LL<<23),
2886  reale(35633361,576916401LL<<21),-reale(113104897,1027785623LL<<22),
2887  reale(77116975,1889590315LL<<21),-reale(20082545,0xcd53c80110000LL),
2888  reale(69730808036LL,0x96022a9a34351LL),
2889  // C4[8], coeff of eps^9, polynomial in n of order 20
2890  real(1123785LL<<21),real(13838643LL<<19),real(23159565LL<<20),
2891  real(171251217LL<<19),real(44667189LL<<23),real(3472549135LL<<19),
2892  real(10302054723LL<<20),real(162001999341LL<<19),
2893  real(500351698399LL<<21),reale(8102,6578411627LL<<19),
2894  -reale(262912,1458939143LL<<20),reale(2634746,8016047177LL<<19),
2895  -reale(14551212,731365323LL<<22),reale(52133305,8561410375LL<<19),
2896  -reale(129964645,2819080401LL<<20),reale(232230181,2215647013LL<<19),
2897  -reale(298362920,1016411147LL<<21),reale(269480987,8039357859LL<<19),
2898  -reale(161945649,1493828379LL<<20),reale(57837731,7816254593LL<<19),
2899  -reale(9237971,9476063903LL<<15),reale(69730808036LL,0x96022a9a34351LL),
2900  // C4[8], coeff of eps^8, polynomial in n of order 21
2901  real(292383LL<<17),real(202215LL<<19),real(2386137LL<<17),
2902  real(3789747LL<<18),real(26247507LL<<17),real(6294651LL<<21),
2903  real(437764365LL<<17),real(1112245757LL<<18),real(0x67551030e0000LL),
2904  real(28804895217LL<<19),real(0x2c0f1d988820000LL),
2905  real(0x66a336663d1c0000LL),-reale(57641,8501165381LL<<17),
2906  reale(631918,3696102011LL<<20),-reale(3870503,720372107LL<<17),
2907  reale(15639991,0xcc8b836440000LL),-reale(44892569,0xd7d7de220000LL),
2908  reale(94682509,2360318459LL<<19),-reale(147486216,0x5ecdb08ae0000LL),
2909  reale(163873573,0xbeaba7b6c0000LL),-reale(110855652,0xd3ce78fba0000LL),
2910  reale(32332898,0xbdc6e34964000LL),reale(69730808036LL,0x96022a9a34351LL),
2911  // C4[9], coeff of eps^29, polynomial in n of order 0
2912  real(16847<<16),real(0x3d2e2985830503LL),
2913  // C4[9], coeff of eps^28, polynomial in n of order 1
2914  -real(207753LL<<23),real(1712087LL<<18),real(0x438da32e1600335LL),
2915  // C4[9], coeff of eps^27, polynomial in n of order 2
2916  -real(3127493161LL<<21),-real(38277317LL<<20),-real(0xe4960490000LL),
2917  reale(161925,0x30e683ffe0741LL),
2918  // C4[9], coeff of eps^26, polynomial in n of order 3
2919  -real(9299582409LL<<22),real(3656674463LL<<23),-real(10918261107LL<<22),
2920  real(80278491423LL<<17),reale(1317283,0x4f8aa089603a9LL),
2921  // C4[9], coeff of eps^25, polynomial in n of order 4
2922  -real(711479186953LL<<22),reale(3279,1361598081LL<<20),
2923  -real(0x3749d192179LL<<21),-real(309897952117LL<<20),
2924  -real(0x1f18264b9990000LL),reale(162025847,0x379b22013c233LL),
2925  // C4[9], coeff of eps^24, polynomial in n of order 5
2926  -reale(133856,15001023LL<<25),reale(223946,23087107LL<<27),
2927  -reale(32028,12079289LL<<25),reale(48931,2142027LL<<26),
2928  -reale(63933,112742755LL<<25),reale(12842,2153614949LL<<20),
2929  reale(5994956347LL,0x96bea2db115fLL),
2930  // C4[9], coeff of eps^23, polynomial in n of order 6
2931  -reale(5988742,4056322469LL<<20),reale(2349145,7648181561LL<<19),
2932  -reale(426462,344885543LL<<21),reale(2475174,940948911LL<<19),
2933  -reale(999559,3441325239LL<<20),-reale(83146,4971496059LL<<19),
2934  -reale(41198,0x4f02423cb8000LL),reale(77934432511LL,0x7a7ae451fe1d3LL),
2935  // C4[9], coeff of eps^22, polynomial in n of order 7
2936  -reale(8631189,1052889985LL<<21),-reale(629492,634245703LL<<22),
2937  -reale(3874477,505696163LL<<21),reale(3866974,513650043LL<<23),
2938  -reale(159710,1408881461LL<<21),reale(1100061,714281683LL<<22),
2939  -reale(1180171,586380503LL<<21),reale(201643,0x9fcf910730000LL),
2940  reale(77934432511LL,0x7a7ae451fe1d3LL),
2941  // C4[9], coeff of eps^21, polynomial in n of order 8
2942  reale(341632,721850923LL<<22),reale(2597220,4632100393LL<<19),
2943  -reale(10372056,1528523471LL<<20),reale(1205419,4719051179LL<<19),
2944  -reale(1145316,921601685LL<<21),reale(3990959,6117017869LL<<19),
2945  -reale(1073059,3486842565LL<<20),-reale(153111,7776387185LL<<19),
2946  -reale(94130,0x280827bb28000LL),reale(77934432511LL,0x7a7ae451fe1d3LL),
2947  // C4[9], coeff of eps^20, polynomial in n of order 9
2948  reale(3783713,134627971LL<<22),reale(23115315,66415493LL<<25),
2949  -reale(6392067,518305043LL<<22),-reale(1733013,275013225LL<<23),
2950  -reale(8816564,833972409LL<<22),reale(4468878,247379557LL<<24),
2951  reale(300534,553592433LL<<22),reale(2085027,317816093LL<<23),
2952  -reale(1725044,456624309LL<<22),reale(240877,0x8d28f00d60000LL),
2953  reale(77934432511LL,0x7a7ae451fe1d3LL),
2954  // C4[9], coeff of eps^19, polynomial in n of order 10
2955  -reale(58776429,1067354331LL<<20),reale(18829393,7579267909LL<<19),
2956  reale(10681211,592856305LL<<22),reale(16946593,1116323851LL<<19),
2957  -reale(14277877,2775669533LL<<20),-reale(2149268,8027942223LL<<19),
2958  -reale(4056423,828321103LL<<21),reale(6443828,4480734455LL<<19),
2959  -reale(857619,751312863LL<<20),-reale(227988,4599783267LL<<19),
2960  -reale(205805,0x3340b739f8000LL),reale(77934432511LL,0x7a7ae451fe1d3LL),
2961  // C4[9], coeff of eps^18, polynomial in n of order 11
2962  -reale(8326980,196156635LL<<21),-reale(34821146,552451591LL<<22),
2963  -reale(46791029,557069513LL<<21),reale(38334852,177025053LL<<24),
2964  reale(8937287,838991609LL<<21),reale(5317827,1033371567LL<<22),
2965  -reale(18378967,400717301LL<<21),reale(2844411,12754877LL<<23),
2966  reale(593018,1659418637LL<<21),reale(4310821,76308389LL<<22),
2967  -reale(2591282,1217948513LL<<21),reale(276451,0x9f1a0fb950000LL),
2968  reale(77934432511LL,0x7a7ae451fe1d3LL),
2969  // C4[9], coeff of eps^17, polynomial in n of order 12
2970  -reale(182057178,279202431LL<<21),reale(246730983,7282837989LL<<19),
2971  -reale(61609386,3656132889LL<<20),-reale(45340440,795982425LL<<19),
2972  -reale(20534253,134894613LL<<22),reale(51951312,243959241LL<<19),
2973  -reale(4823611,581671439LL<<20),-reale(5624597,8387045493LL<<19),
2974  -reale(13789372,989768405LL<<21),reale(9667615,6509295661LL<<19),
2975  reale(215496,1395596667LL<<20),-reale(184969,6596889361LL<<19),
2976  -reale(459826,0xaf07be5d28000LL),reale(77934432511LL,0x7a7ae451fe1d3LL),
2977  // C4[9], coeff of eps^16, polynomial in n of order 13
2978  reale(316814308,524172905LL<<23),-reale(186563878,63588247LL<<25),
2979  -reale(110274143,526845649LL<<23),reale(263023219,83035351LL<<24),
2980  -reale(130904637,509865531LL<<23),-reale(30397924,20206077LL<<26),
2981  reale(13683269,123318603LL<<23),reale(48158450,141529345LL<<24),
2982  -reale(26437768,420249375LL<<23),-reale(5662772,129791197LL<<25),
2983  -reale(2185901,350246489LL<<23),reale(9629298,177188459LL<<24),
2984  -reale(3949112,493038403LL<<23),reale(276643,3634960421LL<<18),
2985  reale(77934432511LL,0x7a7ae451fe1d3LL),
2986  // C4[9], coeff of eps^15, polynomial in n of order 14
2987  reale(78761274,365004673LL<<20),-reale(201515576,8484307809LL<<19),
2988  reale(313194006,1602645493LL<<21),-reale(252751914,5568714583LL<<19),
2989  -reale(13191170,2167441005LL<<20),reale(241719441,7606152787LL<<19),
2990  -reale(201822768,404840345LL<<22),reale(21302083,5136432093LL<<19),
2991  reale(37050656,1255073061LL<<20),reale(20598069,641077127LL<<19),
2992  -reale(39565379,1270355289LL<<21),reale(9630032,7047419793LL<<19),
2993  reale(3352897,1867330359LL<<20),reale(651457,7128437307LL<<19),
2994  -reale(1114108,0x7475455348000LL),reale(77934432511LL,0x7a7ae451fe1d3LL),
2995  // C4[9], coeff of eps^14, polynomial in n of order 15
2996  reale(1503684,1762694997LL<<21),-reale(12945810,457623793LL<<22),
2997  reale(59109631,1997027375LL<<21),-reale(165337541,436423661LL<<23),
2998  reale(292248408,1310925625LL<<21),-reale(302358268,80333091LL<<22),
2999  reale(101329883,1625451155LL<<21),reale(168206436,256940945LL<<24),
3000  -reale(245462494,1698275235LL<<21),reale(106772813,575322475LL<<22),
3001  reale(20184277,1515722423LL<<21),-reale(15841583,115367503LL<<23),
3002  -reale(24343366,297803839LL<<21),reale(22619454,642864953LL<<22),
3003  -reale(5751128,1751200357LL<<21),reale(119914,0x778fad9290000LL),
3004  reale(77934432511LL,0x7a7ae451fe1d3LL),
3005  // C4[9], coeff of eps^13, polynomial in n of order 16
3006  -real(494538685723LL<<23),-reale(30244,7532247025LL<<19),
3007  reale(913230,2357276371LL<<20),-reale(8356271,5886749331LL<<19),
3008  reale(41054740,50726383LL<<21),-reale(125953300,8377060373LL<<19),
3009  reale(252781900,3961145001LL<<20),-reale(323011393,7392450487LL<<19),
3010  reale(214671336,735258085LL<<22),reale(38642307,2838366023LL<<19),
3011  -reale(221064383,2701482241LL<<20),reale(190191489,7753766309LL<<19),
3012  -reale(54203341,2021364059LL<<21),-reale(15936650,4639479773LL<<19),
3013  reale(7069294,1728459477LL<<20),reale(6475976,7904740225LL<<19),
3014  -reale(3243677,0x65d7af1058000LL),reale(77934432511LL,0x7a7ae451fe1d3LL),
3015  // C4[9], coeff of eps^12, polynomial in n of order 17
3016  -real(4941153649LL<<22),-real(2434362319LL<<26),
3017  -real(480183190319LL<<22),-reale(15428,422153761LL<<23),
3018  reale(492912,506448323LL<<22),-reale(4815395,177795021LL<<24),
3019  reale(25573504,64498885LL<<22),-reale(86374812,63633203LL<<23),
3020  reale(196725482,856584503LL<<22),-reale(303474922,105041487LL<<25),
3021  reale(296000607,1045914233LL<<22),-reale(124541003,470657541LL<<23),
3022  -reale(96946363,592229397LL<<22),reale(194787320,217061649LL<<24),
3023  -reale(139624521,484247315LL<<22),reale(48044895,435975913LL<<23),
3024  -reale(5082038,276187937LL<<22),-reale(749748,0x6069872020000LL),
3025  reale(77934432511LL,0x7a7ae451fe1d3LL),
3026  // C4[9], coeff of eps^11, polynomial in n of order 18
3027  -real(231323121LL<<20),-real(2351460757LL<<19),-real(912558841LL<<23),
3028  -real(0xdfda7610580000LL),-real(777314384543LL<<20),
3029  -reale(6590,3852961377LL<<19),reale(223861,17176789LL<<21),
3030  -reale(2346980,3623268951LL<<19),reale(13542533,3871010099LL<<20),
3031  -reale(50565862,7643343277LL<<19),reale(130735502,766383623LL<<22),
3032  -reale(239800507,7719641123LL<<19),reale(308448660,3395101317LL<<20),
3033  -reale(258446712,3844536697LL<<19),reale(99709743,227483207LL<<21),
3034  reale(54337873,5199140497LL<<19),-reale(105984135,215955881LL<<20),
3035  reale(67263140,627338299LL<<19),-reale(17110329,0x5fa94e648000LL),
3036  reale(77934432511LL,0x7a7ae451fe1d3LL),
3037  // C4[9], coeff of eps^10, polynomial in n of order 19
3038  -real(538707LL<<21),-real(1075491LL<<22),-real(9728097LL<<21),
3039  -real(3213907LL<<25),-real(333357375LL<<21),-real(1438804621LL<<22),
3040  -real(39246385997LL<<21),-real(379094211993LL<<23),
3041  reale(25645,1674653973LL<<21),-reale(290249,472854199LL<<22),
3042  reale(1830100,1274307463LL<<21),-reale(7588281,99130323LL<<24),
3043  reale(22282256,82312105LL<<21),-reale(48025833,432719649LL<<22),
3044  reale(76964476,1304326427LL<<21),-reale(91125940,162742323LL<<23),
3045  reale(77471536,1478654845LL<<21),-reale(44556474,1023100235LL<<22),
3046  reale(15423395,377918063LL<<21),-reale(2409905,0x7f0a0dc2b0000LL),
3047  reale(25978144170LL,0x7e28f6c5ff5f1LL),
3048  // C4[9], coeff of eps^9, polynomial in n of order 20
3049  -real(16575LL<<21),-real(226005LL<<19),-real(421083LL<<20),
3050  -real(3487431LL<<19),-real(1025715LL<<23),-real(90604825LL<<19),
3051  -real(308056405LL<<20),-real(5606626571LL<<19),-real(20270111449LL<<21),
3052  -real(0x30ab7cf8dddLL<<19),reale(15220,1707177905LL<<20),
3053  -reale(187210,7636838095LL<<19),reale(1297995,534056013LL<<22),
3054  -reale(6003229,1506461473LL<<19),reale(20010763,3942424887LL<<20),
3055  -reale(50026909,6827222547LL<<19),reale(95435950,2132760845LL<<21),
3056  -reale(138382128,8075045605LL<<19),reale(146522254,737992253LL<<20),
3057  -reale(96396219,7300467927LL<<19),reale(27713913,0x34f39e3ee8000LL),
3058  reale(77934432511LL,0x7a7ae451fe1d3LL),
3059  // C4[10], coeff of eps^29, polynomial in n of order 0
3060  real(14059LL<<19),real(0x168a4531304537LL),
3061  // C4[10], coeff of eps^28, polynomial in n of order 1
3062  -real(1004279LL<<22),-real(3373361LL<<19),reale(3807,0xdf0925caacfb9LL),
3063  // C4[10], coeff of eps^27, polynomial in n of order 2
3064  real(78580619LL<<24),-real(212705597LL<<23),real(705875469LL<<19),
3065  reale(59656,0xa639fabc960fdLL),
3066  // C4[10], coeff of eps^26, polynomial in n of order 3
3067  real(927832218729LL<<21),-real(204500125453LL<<22),
3068  -real(29157611613LL<<21),-real(0x66c4e2e4040000LL),
3069  reale(23087123,0x49a60b16d9e77LL),
3070  // C4[10], coeff of eps^25, polynomial in n of order 4
3071  real(26024288967LL<<27),-real(7678900515LL<<25),real(13514191015LL<<26),
3072  -real(31097026337LL<<25),real(89826688809LL<<21),
3073  reale(25583028,0x820b055e82c23LL),
3074  // C4[10], coeff of eps^24, polynomial in n of order 5
3075  reale(1328855,126349401LL<<24),-reale(550962,13774891LL<<26),
3076  reale(2464835,125518543LL<<24),-reale(784466,25625323LL<<25),
3077  -reale(93184,68528187LL<<24),-reale(52198,1190112709LL<<21),
3078  reale(86138056986LL,0x5ef39e09c8055LL),
3079  // C4[10], coeff of eps^23, polynomial in n of order 6
3080  -reale(1114607,27405733LL<<26),-reale(4563722,53821803LL<<25),
3081  reale(3169393,348585LL<<27),reale(68182,92955763LL<<25),
3082  reale(1172595,45755337LL<<26),-reale(1088988,13585007LL<<25),
3083  reale(166307,46143431LL<<21),reale(86138056986LL,0x5ef39e09c8055LL),
3084  // C4[10], coeff of eps^22, polynomial in n of order 7
3085  reale(5480278,504127481LL<<20),-reale(9293162,155326547LL<<21),
3086  -reale(197247,3072475525LL<<20),-reale(1644302,932629169LL<<22),
3087  reale(3811061,3287215741LL<<20),-reale(747954,323686257LL<<21),
3088  -reale(145848,3935467265LL<<20),-reale(106662,0xb8d6e5aaa0000LL),
3089  reale(86138056986LL,0x5ef39e09c8055LL),
3090  // C4[10], coeff of eps^21, polynomial in n of order 8
3091  reale(22796753,23076841LL<<25),-reale(927290,180149865LL<<22),
3092  -reale(369606,74581989LL<<23),-reale(9303996,552920075LL<<22),
3093  reale(3036817,71115369LL<<24),reale(396000,898162707LL<<22),
3094  reale(2181010,484753161LL<<23),-reale(1556188,389640079LL<<22),
3095  reale(192540,3401040927LL<<18),reale(86138056986LL,0x5ef39e09c8055LL),
3096  // C4[10], coeff of eps^20, polynomial in n of order 9
3097  reale(862955,1266777839LL<<21),reale(7027949,96012647LL<<24),
3098  reale(20762590,1932890753LL<<21),-reale(9559408,1057130891LL<<22),
3099  -reale(3064719,1040728173LL<<21),-reale(5129237,23711641LL<<23),
3100  reale(5760893,1279205669LL<<21),-reale(394463,240514009LL<<22),
3101  -reale(178786,1942994377LL<<21),-reale(217080,8651652815LL<<18),
3102  reale(86138056986LL,0x5ef39e09c8055LL),
3103  // C4[10], coeff of eps^19, polynomial in n of order 10
3104  -reale(10913096,468931943LL<<23),-reale(57356320,139563275LL<<22),
3105  reale(21632622,17971173LL<<25),reale(12352870,1067519707LL<<22),
3106  reale(10546968,197307279LL<<23),-reale(16476123,321986815LL<<22),
3107  reale(466396,220388453LL<<24),reale(183297,876676071LL<<22),
3108  reale(4340035,31265157LL<<23),-reale(2266775,500956659LL<<22),
3109  reale(210337,0xe1ea7a84c0000LL),reale(86138056986LL,0x5ef39e09c8055LL),
3110  // C4[10], coeff of eps^18, polynomial in n of order 11
3111  reale(183220667,2590575043LL<<20),reale(3573393,1902991101LL<<21),
3112  -reale(38433982,657724943LL<<20),-reale(39892891,403988263LL<<23),
3113  reale(42677900,967722655LL<<20),reale(4292702,1711217099LL<<21),
3114  -reale(2792039,799969587LL<<20),-reale(14767346,746757159LL<<22),
3115  reale(7703673,1133060475LL<<20),reale(747527,637790873LL<<21),
3116  -reale(45502,3704918615LL<<20),-reale(458872,0xc21d355260000LL),
3117  reale(86138056986LL,0x5ef39e09c8055LL),
3118  // C4[10], coeff of eps^17, polynomial in n of order 12
3119  -reale(61780842,49135749LL<<25),-reale(196091506,391376453LL<<23),
3120  reale(232013693,187926637LL<<24),-reale(59475550,301219495LL<<23),
3121  -reale(46331600,62864215LL<<26),-reale(5439903,151048009LL<<23),
3122  reale(49627120,102515675LL<<24),-reale(16690048,509576107LL<<23),
3123  -reale(7354945,21733079LL<<25),-reale(3769052,366616397LL<<23),
3124  reale(9145462,214930505LL<<24),-reale(3305318,371590575LL<<23),
3125  reale(189374,6271289399LL<<19),reale(86138056986LL,0x5ef39e09c8055LL),
3126  // C4[10], coeff of eps^16, polynomial in n of order 13
3127  -reale(246951312,552772347LL<<22),reale(295555190,29721595LL<<24),
3128  -reale(151972143,664869293LL<<22),-reale(114414430,423169395LL<<23),
3129  reale(248915402,492058657LL<<22),-reale(140322148,99500631LL<<25),
3130  -reale(15757705,299151505LL<<22),reale(29401843,368167099LL<<23),
3131  reale(29725213,39057725LL<<22),-reale(34936824,2445655LL<<24),
3132  reale(5290998,483472011LL<<22),reale(3412892,270211305LL<<23),
3133  reale(939828,308185177LL<<22),-reale(1058440,2262901433LL<<19),
3134  reale(86138056986LL,0x5ef39e09c8055LL),
3135  // C4[10], coeff of eps^15, polynomial in n of order 14
3136  -reale(29237793,21929809LL<<24),reale(96597143,85827693LL<<23),
3137  -reale(210653294,75090197LL<<25),reale(297719766,264531499LL<<23),
3138  -reale(232859751,332419LL<<24),reale(779198,466262825LL<<23),
3139  reale(210565738,49075321LL<<26),-reale(210231291,35636249LL<<23),
3140  reale(60435795,147172683LL<<24),reale(30790678,95503589LL<<23),
3141  -reale(8341137,27440903LL<<25),-reale(25891285,147600733LL<<23),
3142  reale(19770912,119140889LL<<24),-reale(4475853,348372575LL<<23),
3143  reale(24304,4909664935LL<<19),reale(86138056986LL,0x5ef39e09c8055LL),
3144  // C4[10], coeff of eps^14, polynomial in n of order 15
3145  -reale(326980,1465789373LL<<20),reale(3379554,1566468779LL<<21),
3146  -reale(19029758,226591575LL<<20),reale(68313947,940737655LL<<22),
3147  -reale(165836985,3033756273LL<<20),reale(273579872,472941105LL<<21),
3148  -reale(286670501,2169744907LL<<20),reale(131674848,489609853LL<<23),
3149  reale(102478771,1504412891LL<<20),-reale(220713363,225877065LL<<21),
3150  reale(153302553,1201451329LL<<20),-reale(29968476,1046042243LL<<22),
3151  -reale(18498599,2914872793LL<<20),reale(4637884,270502717LL<<21),
3152  reale(6604171,2668065421LL<<20),-reale(2936921,0x8973648be0000LL),
3153  reale(86138056986LL,0x5ef39e09c8055LL),
3154  // C4[10], coeff of eps^13, polynomial in n of order 16
3155  real(8181919521LL<<26),reale(4651,463423847LL<<22),
3156  -reale(165627,528682553LL<<23),reale(1821092,755660373LL<<22),
3157  -reale(11021646,91392285LL<<24),reale(43145010,992272131LL<<22),
3158  -reale(116748177,310953403LL<<23),reale(223068773,47271409LL<<22),
3159  -reale(294932999,99296991LL<<25),reale(242263024,286305695LL<<22),
3160  -reale(60276785,30271037LL<<23),-reale(125363778,717272947LL<<22),
3161  reale(182026841,37372833LL<<24),-reale(116787755,417593029LL<<22),
3162  reale(36759949,346012225LL<<23),-reale(3061422,962217431LL<<22),
3163  -reale(731281,0xaaf6b13240000LL),reale(86138056986LL,0x5ef39e09c8055LL),
3164  // C4[10], coeff of eps^12, polynomial in n of order 17
3165  real(777809483LL<<21),real(436668683LL<<25),real(99139014933LL<<21),
3166  real(0x1cfc4bfd58dLL<<22),-reale(70023,1623299233LL<<21),
3167  reale(822756,446933025LL<<23),-reale(5376526,2111656919LL<<21),
3168  reale(23042396,297910775LL<<22),-reale(69630161,297782669LL<<21),
3169  reale(153266731,112309515LL<<24),-reale(247130955,1577554627LL<<21),
3170  reale(284460705,580739169LL<<22),-reale(212091093,1801700473LL<<21),
3171  reale(61297082,319619083LL<<23),reale(65462218,2096893009LL<<21),
3172  -reale(98426842,1047683893LL<<22),reale(59152561,1235484315LL<<21),
3173  -reale(14780753,0xb5d74354c0000LL),
3174  reale(86138056986LL,0x5ef39e09c8055LL),
3175  // C4[10], coeff of eps^11, polynomial in n of order 18
3176  real(1233981LL<<23),real(14104237LL<<22),real(6201077LL<<26),
3177  real(933195507LL<<22),real(6966040851LL<<23),real(592370721657LL<<22),
3178  -reale(22184,189431713LL<<24),reale(279989,474035391LL<<22),
3179  -reale(1985627,52832535LL<<23),reale(9357698,635528005LL<<22),
3180  -reale(31645438,92987147LL<<25),reale(79909927,996806539LL<<22),
3181  -reale(153562851,494252097LL<<23),reale(225351987,543734289LL<<22),
3182  -reale(249473559,252214923LL<<24),reale(201676475,478217047LL<<22),
3183  -reale(111804841,353712747LL<<23),reale(37701632,700509149LL<<22),
3184  -reale(5783773,3281237837LL<<18),reale(86138056986LL,0x5ef39e09c8055LL),
3185  // C4[10], coeff of eps^10, polynomial in n of order 19
3186  real(57057LL<<20),real(126819LL<<21),real(1284843LL<<20),
3187  real(478667LL<<24),real(56414325LL<<20),real(279062861LL<<21),
3188  real(8810413183LL<<20),real(99625441377LL<<22),
3189  -reale(3997,1800115191LL<<20),reale(54510,559965495LL<<21),
3190  -reale(421909,1796318189LL<<20),reale(2196607,410595787LL<<23),
3191  -reale(8328804,1896277603LL<<20),reale(24012916,1506461473LL<<21),
3192  -reale(53875133,2685050457LL<<20),reale(94820235,193579723LL<<22),
3193  -reale(129680615,3269639887LL<<20),reale(131955714,608596747LL<<21),
3194  -reale(84828673,2009615045LL<<20),reale(24099054,0xf664899ae0000LL),
3195  reale(86138056986LL,0x5ef39e09c8055LL),
3196  // C4[11], coeff of eps^29, polynomial in n of order 0
3197  -real(255169LL<<19),real(0xbdc79d6e266b55fLL),
3198  // C4[11], coeff of eps^28, polynomial in n of order 1
3199  -real(535829LL<<26),real(6461547LL<<20),real(0x56e2cdab4666fea1LL),
3200  // C4[11], coeff of eps^27, polynomial in n of order 2
3201  -real(54075943LL<<25),-real(11012147LL<<24),-real(184884229LL<<19),
3202  reale(65338,0x3c271ece8bf8fLL),
3203  // C4[11], coeff of eps^26, polynomial in n of order 3
3204  -real(29189823LL<<30),real(157366885LL<<32),-real(637753597LL<<30),
3205  real(13332470307LL<<23),reale(19666808,0xb9ff38da93b23LL),
3206  // C4[11], coeff of eps^25, polynomial in n of order 4
3207  -reale(768828,16543417LL<<28),reale(2405043,41201001LL<<26),
3208  -reale(595679,17511625LL<<27),-reale(94147,42169149LL<<26),
3209  -reale(60455,661597895LL<<21),reale(94341681461LL,0x436c57c191ed7LL),
3210  // C4[11], coeff of eps^24, polynomial in n of order 5
3211  -reale(5042070,2793567LL<<28),reale(2454743,3154771LL<<30),
3212  reale(191058,8757223LL<<28),reale(1233521,5992667LL<<29),
3213  -reale(1001395,9125891LL<<28),reale(137539,51052897LL<<22),
3214  reale(94341681461LL,0x436c57c191ed7LL),
3215  // C4[11], coeff of eps^23, polynomial in n of order 6
3216  -reale(7620321,6390387LL<<27),-reale(1118882,49853273LL<<26),
3217  -reale(2175696,13938625LL<<28),reale(3557797,45648113LL<<26),
3218  -reale(479218,13589073LL<<27),-reale(128928,23280229LL<<26),
3219  -reale(115227,1709406351LL<<21),reale(94341681461LL,0x436c57c191ed7LL),
3220  // C4[11], coeff of eps^22, polynomial in n of order 7
3221  reale(3030693,3978133LL<<30),reale(1618004,874507LL<<32),
3222  -reale(9217736,134985LL<<30),reale(1767041,97063LL<<33),
3223  reale(345531,3069873LL<<30),reale(2240563,263433LL<<32),
3224  -reale(1400217,895853LL<<30),reale(154222,296573467LL<<23),
3225  reale(94341681461LL,0x436c57c191ed7LL),
3226  // C4[11], coeff of eps^21, polynomial in n of order 8
3227  reale(304504,49998275LL<<26),reale(21950325,110791689LL<<23),
3228  -reale(5005332,65785063LL<<24),-reale(3038456,102319349LL<<23),
3229  -reale(5977063,34913149LL<<25),reale(5022754,485487661LL<<23),
3230  -reale(45293,7681997LL<<24),-reale(123970,179449809LL<<23),
3231  -reale(222792,7672407751LL<<18),reale(94341681461LL,0x436c57c191ed7LL),
3232  // C4[11], coeff of eps^20, polynomial in n of order 9
3233  -reale(56432361,120691497LL<<25),reale(6246807,9955417LL<<28),
3234  reale(11410351,83254233LL<<25),reale(14692579,49664915LL<<26),
3235  -reale(13833928,124401461LL<<25),-reale(1245123,9835207LL<<27),
3236  -reale(339985,114545011LL<<25),reale(4291293,22713457LL<<26),
3237  -reale(1980685,98627585LL<<25),reale(159775,7030690975LL<<19),
3238  reale(94341681461LL,0x436c57c191ed7LL),
3239  // C4[11], coeff of eps^19, polynomial in n of order 10
3240  reale(40826627,234278683LL<<24),-reale(19124677,161584861LL<<23),
3241  -reale(51024100,50981393LL<<26),reale(30646271,384869645LL<<23),
3242  reale(9815197,6859997LL<<24),reale(639236,244693975LL<<23),
3243  -reale(14951689,12090449LL<<25),reale(5916250,151054657LL<<23),
3244  reale(1073676,226322463LL<<24),reale(80953,380993803LL<<23),
3245  -reale(451111,0xff79096c0000LL),reale(94341681461LL,0x436c57c191ed7LL),
3246  // C4[11], coeff of eps^18, polynomial in n of order 11
3247  -reale(233788807,3535193LL<<28),reale(177892093,3762413LL<<30),
3248  -reale(5486729,8981851LL<<28),-reale(45008759,222901LL<<32),
3249  -reale(22295157,5977845LL<<28),reale(46499690,3347131LL<<30),
3250  -reale(8381947,991351LL<<28),-reale(7636513,1723229LL<<31),
3251  -reale(5108235,6476849LL<<28),reale(8568922,940153LL<<30),
3252  -reale(2769555,11314291LL<<28),reale(126172,1159668425LL<<21),
3253  reale(94341681461LL,0x436c57c191ed7LL),
3254  // C4[11], coeff of eps^17, polynomial in n of order 12
3255  reale(246666787,23370677LL<<26),-reale(50685638,204720607LL<<24),
3256  -reale(179803952,51059789LL<<25),reale(226753224,100010811LL<<24),
3257  -reale(83690537,703961LL<<27),-reale(36110826,15584139LL<<24),
3258  reale(17880019,26951173LL<<25),reale(35367319,73259919LL<<24),
3259  -reale(29730133,51577369LL<<26),reale(2029349,105583177LL<<24),
3260  reale(3224077,120316375LL<<25),reale(1158582,83501667LL<<24),
3261  -reale(999784,6146420159LL<<19),reale(94341681461LL,0x436c57c191ed7LL),
3262  // C4[11], coeff of eps^16, polynomial in n of order 13
3263  reale(135472555,2919565LL<<26),-reale(240891001,9823619LL<<28),
3264  reale(277187915,48314475LL<<26),-reale(153860890,22130685LL<<27),
3265  -reale(78071452,50966567LL<<26),reale(224257271,6520287LL<<29),
3266  -reale(168898235,23643785LL<<26),reale(25365615,30758325LL<<27),
3267  reale(33991594,22223845LL<<26),-reale(1325267,13358465LL<<28),
3268  -reale(26274549,1352253LL<<26),reale(17195323,12709799LL<<27),
3269  -reale(3493469,55138895LL<<26),-reale(37171,2996514251LL<<20),
3270  reale(94341681461LL,0x436c57c191ed7LL),
3271  // C4[11], coeff of eps^15, polynomial in n of order 14
3272  reale(8369149,65829073LL<<25),-reale(34468304,77612041LL<<24),
3273  reale(98238486,50466661LL<<26),-reale(197855127,257258223LL<<24),
3274  reale(275634083,126808451LL<<25),-reale(237329411,109823349LL<<24),
3275  reale(57709083,378039LL<<27),reale(144028485,10992165LL<<24),
3276  -reale(208082193,86131531LL<<25),reale(120116321,182851999LL<<24),
3277  -reale(12733337,27687817LL<<26),-reale(18886416,178008391LL<<24),
3278  reale(2557866,23705959LL<<25),reale(6572718,173475635LL<<24),
3279  -reale(2666354,4022017967LL<<19),reale(94341681461LL,0x436c57c191ed7LL),
3280  // C4[11], coeff of eps^14, polynomial in n of order 15
3281  reale(54399,8224347LL<<28),-reale(665621,1410497LL<<30),
3282  reale(4527846,10561865LL<<28),-reale(20181039,1593975LL<<31),
3283  reale(63299017,4532479LL<<28),-reale(144047710,3737571LL<<30),
3284  reale(238046961,3527085LL<<28),-reale(274611219,485845LL<<32),
3285  reale(189061064,3080067LL<<28),-reale(9459768,127989LL<<30),
3286  -reale(141083601,3627343LL<<28),reale(166868825,1278147LL<<31),
3287  -reale(97711641,16702617LL<<28),reale(28303864,4120681LL<<30),
3288  -reale(1707991,14300715LL<<28),-reale(691965,964491519LL<<21),
3289  reale(94341681461LL,0x436c57c191ed7LL),
3290  // C4[11], coeff of eps^13, polynomial in n of order 16
3291  -real(394848061LL<<27),-real(277855615551LL<<23),
3292  reale(21507,221049445LL<<24),-reale(280152,15918397LL<<23),
3293  reale(2046623,76965257LL<<25),-reale(9908745,30179611LL<<23),
3294  reale(34287090,9035647LL<<24),-reale(88042794,304571673LL<<23),
3295  reale(170266683,41403331LL<<26),-reale(246546803,514564215LL<<23),
3296  reale(257558635,22204697LL<<24),-reale(171596509,74164853LL<<23),
3297  reale(32098211,100286083LL<<25),reale(71621283,185724333LL<<23),
3298  -reale(91026815,208301517LL<<24),reale(52421624,501338287LL<<23),
3299  -reale(12919309,7987587551LL<<18),reale(94341681461LL,0x436c57c191ed7LL),
3300  // C4[11], coeff of eps^12, polynomial in n of order 17
3301  -real(2506701LL<<25),-real(1595211LL<<29),-real(414133331LL<<25),
3302  -real(9611154693LL<<26),reale(6318,129560535LL<<25),
3303  -reale(88018,7994433LL<<27),reale(693686,99032081LL<<25),
3304  -reale(3663195,37640223LL<<26),reale(14022738,83451835LL<<25),
3305  -reale(40598902,6803915LL<<28),reale(90961965,119128629LL<<25),
3306  -reale(159220781,788729LL<<26),reale(217217490,112380639LL<<25),
3307  -reale(227284915,26366059LL<<27),reale(176075660,9208089LL<<25),
3308  -reale(94610548,45670931LL<<26),reale(31201351,21556291LL<<25),
3309  -reale(4712704,700509149LL<<19),reale(94341681461LL,0x436c57c191ed7LL),
3310  // C4[11], coeff of eps^11, polynomial in n of order 18
3311  -real(13041LL<<24),-real(166957LL<<23),-real(82777LL<<27),
3312  -real(14154867LL<<23),-real(121102751LL<<24),-real(11919970777LL<<23),
3313  real(140288886837LL<<25),-reale(15649,252654239LL<<23),
3314  reale(133731,225409843LL<<24),-reale(773734,115698949LL<<23),
3315  reale(3285982,23309223LL<<26),-reale(10716783,181102411LL<<23),
3316  reale(27557442,232845957LL<<24),-reale(56645854,420384689LL<<23),
3317  reale(93299054,125728615LL<<25),-reale(121534295,132369527LL<<23),
3318  reale(119605179,120525655LL<<24),-reale(75403265,163638237LL<<23),
3319  reale(21207168,6304582341LL<<18),reale(94341681461LL,0x436c57c191ed7LL),
3320  // C4[12], coeff of eps^29, polynomial in n of order 0
3321  real(2113LL<<23),real(0x495846bc80a035LL),
3322  // C4[12], coeff of eps^28, polynomial in n of order 1
3323  -real(5059597LL<<25),-real(23775299LL<<22),
3324  reale(61953,0x75e619a89ce07LL),
3325  // C4[12], coeff of eps^27, polynomial in n of order 2
3326  real(30823201LL<<29),-real(55301563LL<<28),real(131431881LL<<24),
3327  reale(497138,0xbe8dd4238d2e7LL),
3328  // C4[12], coeff of eps^26, polynomial in n of order 3
3329  real(8059635627LL<<28),-real(757042391LL<<29),-real(311216327LL<<28),
3330  -real(7273579LL<<33),reale(21376966,0x1d2a1f8b6ccdLL),
3331  // C4[12], coeff of eps^25, polynomial in n of order 4
3332  reale(590308,751003LL<<30),reale(77521,16047653LL<<28),
3333  reale(426657,125003LL<<29),-reale(306166,5244457LL<<28),
3334  reale(37995,207060411LL<<24),reale(34181768645LL,0x62a1b07dc9473LL),
3335  // C4[12], coeff of eps^24, polynomial in n of order 5
3336  -reale(1599658,2394579LL<<27),-reale(2671318,5123391LL<<29),
3337  reale(3256460,16377243LL<<27),-reale(261261,3982303LL<<28),
3338  -reale(106562,1204279LL<<27),-reale(120793,1029973LL<<24),
3339  reale(102545305936LL,0x27e511795bd59LL),
3340  // C4[12], coeff of eps^23, polynomial in n of order 6
3341  reale(1248773,4542469LL<<29),-reale(2889741,9813249LL<<28),
3342  reale(234885,3135591LL<<30),reale(66922,9908313LL<<28),
3343  reale(755418,635863LL<<29),-reale(419245,13200621LL<<28),
3344  reale(41213,192739239LL<<24),reale(34181768645LL,0x62a1b07dc9473LL),
3345  // C4[12], coeff of eps^22, polynomial in n of order 7
3346  reale(20885911,4938503LL<<28),-reale(1107830,1234733LL<<29),
3347  -reale(2370377,3771643LL<<28),-reale(6561451,624527LL<<30),
3348  reale(4279851,10797315LL<<28),reale(210660,3761905LL<<29),
3349  -reale(68724,2033407LL<<28),-reale(224555,1152577LL<<29),
3350  reale(102545305936LL,0x27e511795bd59LL),
3351  // C4[12], coeff of eps^21, polynomial in n of order 8
3352  -reale(5562062,38325LL<<31),reale(7741765,4470897LL<<28),
3353  reale(17399328,6149297LL<<29),-reale(10890962,10744893LL<<28),
3354  -reale(2368414,446197LL<<30),-reale(891562,9146315LL<<28),
3355  reale(4183586,393403LL<<29),-reale(1730085,6072185LL<<28),
3356  reale(120797,18742483LL<<24),reale(102545305936LL,0x27e511795bd59LL),
3357  // C4[12], coeff of eps^20, polynomial in n of order 9
3358  reale(3332722,179104103LL<<24),-reale(54245156,21887465LL<<27),
3359  reale(18428910,34326153LL<<24),reale(12293411,106053413LL<<25),
3360  reale(4024929,78680811LL<<24),-reale(14528270,1262953LL<<26),
3361  reale(4350569,36952333LL<<24),reale(1251271,92345015LL<<25),
3362  reale(191236,5049199LL<<24),-reale(439124,1983321823LL<<21),
3363  reale(102545305936LL,0x27e511795bd59LL),
3364  // C4[12], coeff of eps^19, polynomial in n of order 10
3365  reale(117817828,9756529LL<<27),reale(29304818,21859033LL<<26),
3366  -reale(33857646,3348243LL<<29),-reale(34756825,30241097LL<<26),
3367  reale(40576649,11012471LL<<27),-reale(1809964,37385419LL<<26),
3368  -reale(7014724,9945043LL<<28),-reale(6163099,62399597LL<<26),
3369  reale(7950550,2557949LL<<27),-reale(2323999,3159279LL<<26),
3370  reale(80031,1030811061LL<<22),reale(102545305936LL,0x27e511795bd59LL),
3371  // C4[12], coeff of eps^18, polynomial in n of order 11
3372  reale(37677439,43610729LL<<26),-reale(212417438,31724009LL<<27),
3373  reale(188774384,60946099LL<<26),-reale(37276694,6182933LL<<29),
3374  -reale(44097735,31570179LL<<26),reale(5696664,10497345LL<<27),
3375  reale(38054298,7154503LL<<26),-reale(24525159,12952085LL<<28),
3376  -reale(350073,57822319LL<<26),reale(2901654,18012267LL<<27),
3377  reale(1319354,63457243LL<<26),-reale(941373,59576227LL<<26),
3378  reale(102545305936LL,0x27e511795bd59LL),
3379  // C4[12], coeff of eps^17, polynomial in n of order 12
3380  -reale(253394431,1462439LL<<28),reale(237669216,409221LL<<26),
3381  -reale(76296320,28335185LL<<27),-reale(133872864,17217849LL<<26),
3382  reale(218174046,2622387LL<<29),-reale(127998192,57914967LL<<26),
3383  reale(363472,30718057LL<<27),reale(32681168,4189163LL<<26),
3384  reale(4677048,16088179LL<<28),-reale(25857930,7142835LL<<26),
3385  reale(14914891,9312419LL<<27),-reale(2731797,52301425LL<<26),
3386  -reale(76352,726189181LL<<22),reale(102545305936LL,0x27e511795bd59LL),
3387  // C4[12], coeff of eps^16, polynomial in n of order 13
3388  -reale(53643409,97684423LL<<25),reale(127408278,3174879LL<<27),
3389  -reale(219370358,126672641LL<<25),reale(262176902,49024297LL<<26),
3390  -reale(182579118,132254331LL<<25),-reale(3956056,15289739LL<<28),
3391  reale(167880537,57011019LL<<25),-reale(188895775,46555265LL<<26),
3392  reale(91621970,25449425LL<<25),-reale(762367,26232331LL<<27),
3393  -reale(18049661,12932969LL<<25),reale(839158,10679509LL<<26),
3394  reale(6440415,29973277LL<<25),-reale(2428550,982597961LL<<22),
3395  reale(102545305936LL,0x27e511795bd59LL),
3396  // C4[12], coeff of eps^15, polynomial in n of order 14
3397  -reale(1786573,13634499LL<<27),reale(8939902,21088027LL<<26),
3398  -reale(31907799,6174271LL<<28),reale(84216248,4944333LL<<26),
3399  -reale(166330228,11364729LL<<27),reale(242706491,8863071LL<<26),
3400  -reale(246937724,7698133LL<<29),reale(139651898,50060433LL<<26),
3401  reale(29493809,19297617LL<<27),-reale(148014628,18656733LL<<26),
3402  reale(151165884,622571LL<<28),-reale(81883041,55488299LL<<26),
3403  reale(21903841,15379355LL<<27),-reale(792996,14574745LL<<26),
3404  -reale(644309,457907141LL<<22),reale(102545305936LL,0x27e511795bd59LL),
3405  // C4[12], coeff of eps^14, polynomial in n of order 15
3406  -reale(6504,28793619LL<<26),reale(93075,33271365LL<<27),
3407  -reale(752118,6462873LL<<26),reale(4061558,11832697LL<<28),
3408  -reale(15840997,35193887LL<<26),reale(46482714,19239327LL<<27),
3409  -reale(104709924,13039269LL<<26),reale(181860520,7828435LL<<29),
3410  -reale(240159499,36173099LL<<26),reale(229992094,10037497LL<<27),
3411  -reale(136854274,43911089LL<<26),reale(9990763,2550227LL<<28),
3412  reale(74520212,5689801LL<<26),-reale(84057599,709549LL<<27),
3413  reale(46786776,54603587LL<<26),-reale(11406945,39298831LL<<26),
3414  reale(102545305936LL,0x27e511795bd59LL),
3415  // C4[12], coeff of eps^13, polynomial in n of order 16
3416  real(1030055LL<<30),real(829418525LL<<26),-real(19924010015LL<<27),
3417  reale(9050,10804695LL<<26),-reale(78488,9283787LL<<28),
3418  reale(459151,22444081LL<<26),-reale(1962716,17985613LL<<27),
3419  reale(6408338,7820523LL<<26),-reale(16395176,1626457LL<<29),
3420  reale(33311385,35536325LL<<26),-reale(53946341,7054843LL<<27),
3421  reale(69201696,61410431LL<<26),-reale(69012103,3773337LL<<28),
3422  reale(51544754,7834329LL<<26),-reale(26961871,12889641LL<<27),
3423  reale(8722958,26104467LL<<26),-reale(1300056,320360129LL<<22),
3424  reale(34181768645LL,0x62a1b07dc9473LL),
3425  // C4[12], coeff of eps^12, polynomial in n of order 17
3426  real(127075LL<<24),real(91195LL<<28),real(26902525LL<<24),
3427  real(715607165LL<<25),-real(73094160425LL<<24),
3428  reale(4440,35913265LL<<26),-reale(41519,978831LL<<24),
3429  reale(264211,112928967LL<<25),-reale(1241795,175695285LL<<24),
3430  reale(4515620,18853435LL<<27),-reale(13069247,261014043LL<<24),
3431  reale(30619380,129358865LL<<25),-reale(58537051,226171969LL<<24),
3432  reale(91194564,65482939LL<<26),-reale(113993206,58979239LL<<24),
3433  reale(109036979,115740763LL<<25),-reale(67602927,138149837LL<<24),
3434  reale(18850816,700509149LL<<21),reale(102545305936LL,0x27e511795bd59LL),
3435  // C4[13], coeff of eps^29, polynomial in n of order 0
3436  -real(634219LL<<23),reale(3193,0x402148867236bLL),
3437  // C4[13], coeff of eps^28, polynomial in n of order 1
3438  -real(400561LL<<32),real(1739049LL<<27),reale(66909,0xbcc54ee94d445LL),
3439  // C4[13], coeff of eps^27, polynomial in n of order 2
3440  -real(6387996953LL<<29),-real(3461245957LL<<28),-real(49206438547LL<<24),
3441  reale(286172946,0xcc6f5fc7e64c9LL),
3442  // C4[13], coeff of eps^26, polynomial in n of order 3
3443  real(7296571113LL<<30),reale(10661,1488313LL<<31),
3444  -reale(6836,2507629LL<<30),real(103233906747LL<<25),
3445  reale(900397808,0x384bb07b32421LL),
3446  // C4[13], coeff of eps^25, polynomial in n of order 4
3447  -reale(1030602,1434287LL<<30),reale(976249,6303335LL<<28),
3448  -reale(29214,7243007LL<<29),-reale(27193,4360723LL<<28),
3449  -reale(41363,170006437LL<<24),reale(36916310137LL,0x41f43bb0c949LL),
3450  // C4[13], coeff of eps^24, polynomial in n of order 5
3451  -reale(2597630,109963LL<<31),-reale(46366,88065LL<<33),
3452  real(835763379LL<<31),reale(754229,667751LL<<32),
3453  -reale(376195,1000319LL<<31),reale(33027,62908623LL<<26),
3454  reale(36916310137LL,0x41f43bb0c949LL),
3455  // C4[13], coeff of eps^23, polynomial in n of order 6
3456  reale(1907767,7512493LL<<29),-reale(1322539,10099505LL<<28),
3457  -reale(6889396,2784065LL<<30),reale(3566231,12064393LL<<28),
3458  reale(392016,1668111LL<<29),-reale(16024,9677725LL<<28),
3459  -reale(223530,46890859LL<<24),reale(110748930411LL,0xc5dcb3125bdbLL),
3460  // C4[13], coeff of eps^22, polynomial in n of order 7
3461  reale(2768819,1533979LL<<30),reale(18682895,1051157LL<<31),
3462  -reale(7962826,2061455LL<<30),-reale(3008388,501585LL<<32),
3463  -reale(1419492,411945LL<<30),reale(4033867,1208903LL<<31),
3464  -reale(1511425,98131LL<<30),reale(90538,115806565LL<<25),
3465  reale(110748930411LL,0xc5dcb3125bdbLL),
3466  // C4[13], coeff of eps^21, polynomial in n of order 8
3467  -reale(51332124,214119LL<<31),reale(7579765,3153587LL<<28),
3468  reale(12475441,1655707LL<<29),reale(7005177,5256105LL<<28),
3469  -reale(13679833,119207LL<<30),reale(3016909,4530623LL<<28),
3470  reale(1323928,2024201LL<<29),reale(284896,6925237LL<<28),
3471  -reale(424636,138679005LL<<24),reale(110748930411LL,0xc5dcb3125bdbLL),
3472  // C4[13], coeff of eps^20, polynomial in n of order 9
3473  reale(47250711,14679LL<<32),-reale(18472981,62575LL<<35),
3474  -reale(42459575,893863LL<<32),reale(33307537,106651LL<<33),
3475  reale(3060800,842635LL<<32),-reale(5867540,102671LL<<34),
3476  -reale(6941741,849331LL<<32),reale(7324844,423881LL<<33),
3477  -reale(1953157,771073LL<<32),reale(46148,28524089LL<<27),
3478  reale(110748930411LL,0xc5dcb3125bdbLL),
3479  // C4[13], coeff of eps^19, polynomial in n of order 10
3480  -reale(218954922,27801141LL<<27),reale(144947317,36456347LL<<26),
3481  -reale(2491117,129025LL<<29),-reale(43746541,53566187LL<<26),
3482  -reale(5414513,33128531LL<<27),reale(38475112,39418671LL<<26),
3483  -reale(19653214,3660993LL<<28),-reale(2031714,8235735LL<<26),
3484  reale(2517568,31068687LL<<27),reale(1433299,8158787LL<<26),
3485  -reale(884985,911850811LL<<22),reale(110748930411LL,0xc5dcb3125bdbLL),
3486  // C4[13], coeff of eps^18, polynomial in n of order 11
3487  reale(186784429,10521821LL<<28),-reale(7066121,6171767LL<<29),
3488  -reale(168709085,159265LL<<28),reale(199772613,1997709LL<<31),
3489  -reale(91000398,5796399LL<<28),-reale(16385586,3500385LL<<29),
3490  reale(28845005,1198547LL<<28),reale(9523912,3994797LL<<30),
3491  -reale(24921512,7172347LL<<28),reale(12920997,2065141LL<<29),
3492  -reale(2137442,11262329LL<<28),-reale(100773,90157665LL<<23),
3493  reale(110748930411LL,0xc5dcb3125bdbLL),
3494  // C4[13], coeff of eps^17, polynomial in n of order 12
3495  reale(153014747,10291963LL<<28),-reale(229746959,27043849LL<<26),
3496  reale(237324258,14238909LL<<27),-reale(127910449,9268979LL<<26),
3497  -reale(52661288,2811671LL<<29),reale(178449477,48064707LL<<26),
3498  -reale(166899831,11458293LL<<27),reale(67870692,24951769LL<<26),
3499  reale(7326612,206249LL<<28),-reale(16569622,39442673LL<<26),
3500  -reale(550002,21806887LL<<27),reale(6246699,62490405LL<<26),
3501  -reale(2219585,747027389LL<<22),reale(110748930411LL,0xc5dcb3125bdbLL),
3502  // C4[13], coeff of eps^16, polynomial in n of order 13
3503  reale(15145062,3114639LL<<29),-reale(45473383,71569LL<<31),
3504  reale(104280194,4043033LL<<29),-reale(182691434,3191599LL<<30),
3505  reale(238813543,4302931LL<<29),-reale(215430056,686779LL<<32),
3506  reale(95643898,4170781LL<<29),reale(58502156,871831LL<<30),
3507  -reale(149008930,6169513LL<<29),reale(135928257,1117477LL<<31),
3508  -reale(68778720,227103LL<<29),reale(17013972,3743517LL<<30),
3509  -reale(171458,5381733LL<<29),-reale(594747,43724235LL<<24),
3510  reale(110748930411LL,0xc5dcb3125bdbLL),
3511  // C4[13], coeff of eps^15, polynomial in n of order 14
3512  reale(268265,12727175LL<<27),-reale(1599130,17232215LL<<26),
3513  reale(6942204,4883571LL<<28),-reale(22914299,20494129LL<<26),
3514  reale(58880733,8011269LL<<27),-reale(118985431,7979051LL<<26),
3515  reale(188592645,4054545LL<<29),-reale(229762161,35295621LL<<26),
3516  reale(203148724,31300867LL<<27),-reale(107385077,53637247LL<<26),
3517  -reale(6680614,2406191LL<<28),reale(75281884,8527271LL<<26),
3518  -reale(77627899,32310399LL<<27),reale(42028799,34263981LL<<26),
3519  -reale(10160264,35032709LL<<22),reale(110748930411LL,0xc5dcb3125bdbLL),
3520  // C4[13], coeff of eps^14, polynomial in n of order 15
3521  real(8350913025LL<<28),-reale(8241,2495877LL<<29),
3522  reale(78008,13111987LL<<28),-reale(500800,4045265LL<<30),
3523  reale(2364509,9424021LL<<28),-reale(8593646,4773407LL<<29),
3524  reale(24709323,11418567LL<<28),-reale(57114100,2066875LL<<31),
3525  reale(106928260,4889705LL<<28),-reale(162113251,5033977LL<<29),
3526  reale(197269922,8596123LL<<28),-reale(188736396,4070811LL<<30),
3527  reale(136566807,16720509LL<<28),-reale(69783667,938643LL<<29),
3528  reale(22203894,1359919LL<<28),-reale(3271109,212531129LL<<23),
3529  reale(110748930411LL,0xc5dcb3125bdbLL),
3530  // C4[13], coeff of eps^13, polynomial in n of order 16
3531  -real(94185LL<<30),-real(86179275LL<<26),real(2372802705LL<<27),
3532  -real(83726038305LL<<26),reale(12668,1555717LL<<28),
3533  -reale(87922,39994007LL<<26),reale(452934,19637187LL<<27),
3534  -reale(1815855,62281965LL<<26),reale(5835571,1574167LL<<29),
3535  -reale(15318374,24668899LL<<26),reale(33211265,14617205LL<<27),
3536  -reale(59722012,27257657LL<<26),reale(88729847,57943LL<<28),
3537  -reale(107054489,21433519LL<<26),reale(99917523,12239271LL<<27),
3538  -reale(61060708,48513541LL<<26),reale(16900731,943456205LL<<22),
3539  reale(110748930411LL,0xc5dcb3125bdbLL),
3540  // C4[14], coeff of eps^29, polynomial in n of order 0
3541  real(41LL<<28),real(0x3fbc634a12a6b1LL),
3542  // C4[14], coeff of eps^28, polynomial in n of order 1
3543  -real(6907093LL<<31),-real(59887787LL<<28),
3544  reale(5739014,0x909af11944e4bLL),
3545  // C4[14], coeff of eps^27, polynomial in n of order 2
3546  reale(3432,499601LL<<33),-real(2083199471LL<<32),real(3406572267LL<<28),
3547  reale(307370942,0xdb94118adae9fLL),
3548  // C4[14], coeff of eps^26, polynomial in n of order 3
3549  reale(287986,4314073LL<<29),reale(5344,3636147LL<<30),
3550  -reale(6205,2906637LL<<29),-reale(13964,12467885LL<<26),
3551  reale(13216950542LL,0xe1def252c54b5LL),
3552  // C4[14], coeff of eps^25, polynomial in n of order 4
3553  -reale(258061,515595LL<<33),-reale(74790,1657665LL<<31),
3554  reale(745027,493173LL<<32),-reale(337382,84843LL<<31),
3555  reale(26418,5099583LL<<27),reale(39650851628LL,0xa59cd6f84fe1fLL),
3556  // C4[14], coeff of eps^24, polynomial in n of order 5
3557  -reale(100052,3082133LL<<30),-reale(6991386,428305LL<<32),
3558  reale(2902871,3549453LL<<30),reale(514674,1320943LL<<31),
3559  reale(32543,4070319LL<<30),-reale(220557,2292103LL<<27),
3560  reale(118952554885LL,0xf0d684e8efa5dLL),
3561  // C4[14], coeff of eps^23, polynomial in n of order 6
3562  reale(6249633,975799LL<<32),-reale(1750517,1286063LL<<31),
3563  -reale(1090661,209219LL<<33),-reale(631632,1802089LL<<31),
3564  reale(1285387,761149LL<<32),-reale(440347,2020899LL<<31),
3565  reale(22303,14762615LL<<27),reale(39650851628LL,0xa59cd6f84fe1fLL),
3566  // C4[14], coeff of eps^22, polynomial in n of order 7
3567  -reale(1155507,7367607LL<<29),reale(11090657,3295693LL<<30),
3568  reale(9416360,3921899LL<<29),-reale(12562252,1614097LL<<31),
3569  reale(1905484,7990669LL<<29),reale(1324142,2135535LL<<30),
3570  reale(362851,6226223LL<<29),-reale(408795,45924241LL<<26),
3571  reale(118952554885LL,0xf0d684e8efa5dLL),
3572  // C4[14], coeff of eps^21, polynomial in n of order 8
3573  -reale(2556392,83451LL<<35),-reale(45924405,628445LL<<32),
3574  reale(25722566,76303LL<<33),reale(6427311,738073LL<<32),
3575  -reale(4460754,79355LL<<34),-reale(7474566,842481LL<<32),
3576  reale(6714086,421381LL<<33),-reale(1643964,835835LL<<32),
3577  reale(21175,2825543LL<<28),reale(118952554885LL,0xf0d684e8efa5dLL),
3578  // C4[14], coeff of eps^20, polynomial in n of order 9
3579  reale(101794762,1213867LL<<31),reale(21384252,53331LL<<34),
3580  -reale(38294895,814203LL<<31),-reale(14666563,397319LL<<32),
3581  reale(37283642,1395551LL<<31),-reale(15279397,125869LL<<33),
3582  -reale(3174330,433863LL<<31),reale(2115734,458067LL<<32),
3583  reale(1510128,1624339LL<<31),-reale(831539,10478291LL<<28),
3584  reale(118952554885LL,0xf0d684e8efa5dLL),
3585  // C4[14], coeff of eps^19, polynomial in n of order 10
3586  reale(50295468,469581LL<<33),-reale(186185623,531407LL<<32),
3587  reale(174713425,41641LL<<35),-reale(59412258,3489LL<<32),
3588  -reale(26728127,294149LL<<33),reale(23787374,31373LL<<32),
3589  reale(13262792,54953LL<<34),-reale(23669724,520005LL<<32),
3590  reale(11190603,172969LL<<33),-reale(1670792,243479LL<<32),
3591  -reale(115324,7271069LL<<28),reale(118952554885LL,0xf0d684e8efa5dLL),
3592  // C4[14], coeff of eps^18, polynomial in n of order 11
3593  -reale(229751836,26450113LL<<27),reale(205122059,12799441LL<<28),
3594  -reale(76881886,7573243LL<<27),-reale(89213757,3943587LL<<30),
3595  reale(179505441,31406283LL<<27),-reale(144430080,11541225LL<<28),
3596  reale(48475411,26026641LL<<27),reale(12591449,3614557LL<<29),
3597  -reale(14798010,26226089LL<<27),-reale(1654995,15989667LL<<28),
3598  reale(6017860,18394141LL<<27),-reale(2035659,55899187LL<<24),
3599  reale(118952554885LL,0xf0d684e8efa5dLL),
3600  // C4[14], coeff of eps^17, polynomial in n of order 12
3601  -reale(60003627,419631LL<<31),reale(122260158,890121LL<<29),
3602  -reale(193015194,2586489LL<<30),reale(228332901,6912147LL<<29),
3603  -reale(182676146,109669LL<<32),reale(57596630,2823965LL<<29),
3604  reale(79437172,3055697LL<<30),-reale(146103578,5035353LL<<29),
3605  reale(121669517,1691035LL<<31),-reale(57926620,1249999LL<<29),
3606  reale(13245099,2677787LL<<30),reale(250593,3348667LL<<29),
3607  -reale(546524,56364575LL<<25),reale(118952554885LL,0xf0d684e8efa5dLL),
3608  // C4[14], coeff of eps^16, polynomial in n of order 13
3609  -reale(2910026,15317989LL<<28),reale(10671028,169493LL<<30),
3610  -reale(30788418,3245427LL<<28),reale(70862414,261923LL<<29),
3611  -reale(130581700,1010945LL<<28),reale(191189814,642567LL<<31),
3612  -reale(216782974,13106831LL<<28),reale(177827671,7710997LL<<29),
3613  -reale(82572754,6587933LL<<28),-reale(19188450,2518521LL<<30),
3614  reale(74652545,11169877LL<<28),-reale(71762036,443641LL<<29),
3615  reale(37978089,1743047LL<<28),-reale(9119456,66783679LL<<25),
3616  reale(118952554885LL,0xf0d684e8efa5dLL),
3617  // C4[14], coeff of eps^15, polynomial in n of order 14
3618  -reale(25313,471763LL<<30),reale(176943,4508751LL<<29),
3619  -reale(914488,1483519LL<<31),reale(3661023,8037561LL<<29),
3620  -reale(11683077,3602217LL<<30),reale(30253421,7276067LL<<29),
3621  -reale(64215578,725077LL<<32),reale(112133608,2030221LL<<29),
3622  -reale(160624032,1744767LL<<30),reale(186713478,2165751LL<<29),
3623  -reale(172286017,2016853LL<<31),reale(121247637,6964321LL<<29),
3624  -reale(60696359,459733LL<<30),reale(19031909,1781195LL<<29),
3625  -reale(2775486,102023215LL<<25),reale(118952554885LL,0xf0d684e8efa5dLL),
3626  // C4[14], coeff of eps^14, polynomial in n of order 15
3627  -real(614557125LL<<27),real(5831464275LL<<28),
3628  -reale(3808,17097199LL<<27),reale(28626,5026047LL<<29),
3629  -reale(160361,32462873LL<<27),reale(702411,15495849LL<<28),
3630  -reale(2480054,13665347LL<<27),reale(7201343,703573LL<<30),
3631  -reale(17420896,11395693LL<<27),reale(35365729,6899711LL<<28),
3632  -reale(60346284,10497687LL<<27),reale(86059048,7827541LL<<29),
3633  -reale(100689087,8447169LL<<27),reale(91987561,3237205LL<<28),
3634  -reale(55509735,6799595LL<<27),reale(15265177,48513541LL<<24),
3635  reale(118952554885LL,0xf0d684e8efa5dLL),
3636  // C4[15], coeff of eps^29, polynomial in n of order 0
3637  -real(204761LL<<28),reale(20426,0xaa7b82b97d24fLL),
3638  // C4[15], coeff of eps^28, polynomial in n of order 1
3639  -real(34699LL<<42),real(26415501LL<<29),reale(6134808,0xac3bb24726559LL),
3640  // C4[15], coeff of eps^27, polynomial in n of order 2
3641  reale(16894,439LL<<40),-reale(3396,5539LL<<38),
3642  -reale(13997,7293149LL<<28),reale(14128464373LL,0x6d08ce11dbba7LL),
3643  // C4[15], coeff of eps^26, polynomial in n of order 3
3644  -reale(50643,63489LL<<36),reale(243167,8553LL<<37),
3645  -reale(100839,3467LL<<36),reale(7018,548741LL<<30),
3646  reale(14128464373LL,0x6d08ce11dbba7LL),
3647  // C4[15], coeff of eps^25, polynomial in n of order 4
3648  -reale(6907413,21379LL<<36),reale(2301071,198931LL<<34),
3649  reale(591806,32973LL<<35),reale(76262,38289LL<<34),
3650  -reale(216244,23833777LL<<27),reale(127156179360LL,0xd54f3ea0b98dfLL),
3651  // C4[15], coeff of eps^24, polynomial in n of order 5
3652  -reale(2869395,52521LL<<36),-reale(3255913,8819LL<<38),
3653  -reale(2304160,33823LL<<36),reale(3661540,28261LL<<37),
3654  -reale(1155441,18213LL<<36),reale(48366,13607837LL<<28),
3655  reale(127156179360LL,0xd54f3ea0b98dfLL),
3656  // C4[15], coeff of eps^23, polynomial in n of order 6
3657  reale(8754539,110435LL<<35),reale(11218727,249609LL<<34),
3658  -reale(11298141,31087LL<<36),reale(996220,194783LL<<34),
3659  reale(1275763,41633LL<<35),reale(426630,95573LL<<34),
3660  -reale(392368,19533817LL<<27),reale(127156179360LL,0xd54f3ea0b98dfLL),
3661  // C4[15], coeff of eps^22, polynomial in n of order 7
3662  -reale(46020147,1607LL<<36),reale(18483914,31121LL<<37),
3663  reale(8546239,40923LL<<36),-reale(2972379,4277LL<<38),
3664  -reale(7799822,49315LL<<36),reale(6131851,9051LL<<37),
3665  -reale(1385578,60289LL<<36),reale(2743,3362879LL<<30),
3666  reale(127156179360LL,0xd54f3ea0b98dfLL),
3667  // C4[15], coeff of eps^21, polynomial in n of order 8
3668  reale(36025526,1303LL<<40),-reale(30131090,26093LL<<37),
3669  -reale(21835156,15459LL<<38),reale(35026415,31673LL<<37),
3670  -reale(11464406,5705LL<<39),-reale(3907909,12145LL<<37),
3671  reale(1722090,1439LL<<38),reale(1557916,18869LL<<37),
3672  -reale(781446,6381283LL<<28),reale(127156179360LL,0xd54f3ea0b98dfLL),
3673  // C4[15], coeff of eps^20, polynomial in n of order 9
3674  -reale(190262221,2387LL<<40),reale(146996287,1227LL<<41),
3675  -reale(33573688,3541LL<<40),-reale(32294922,2067LL<<39),
3676  reale(18331180,2115LL<<40),reale(16022794,2331LL<<40),
3677  -reale(22246846,3383LL<<40),reale(9695242,4143LL<<39),
3678  -reale(1302304,2671LL<<40),-reale(123235,5577019LL<<29),
3679  reale(127156179360LL,0xd54f3ea0b98dfLL),
3680  // C4[15], coeff of eps^19, polynomial in n of order 10
3681  reale(169057636,9637LL<<37),-reale(31515275,17095LL<<36),
3682  -reale(115123722,7359LL<<39),reale(174060780,58071LL<<36),
3683  -reale(122862790,20125LL<<37),reale(32880337,12981LL<<36),
3684  reale(15824026,705LL<<38),-reale(12943852,57005LL<<36),
3685  -reale(2522257,22495LL<<37),reale(5771316,18225LL<<36),
3686  -reale(1873338,7714415LL<<28),reale(127156179360LL,0xd54f3ea0b98dfLL),
3687  // C4[15], coeff of eps^18, polynomial in n of order 11
3688  reale(137352006,26079LL<<36),-reale(197705648,26891LL<<37),
3689  reale(213128803,51077LL<<36),-reale(150461460,3135LL<<39),
3690  reale(25445949,34251LL<<36),reale(93962136,11667LL<<37),
3691  -reale(140732252,24207LL<<36),reale(108614245,6273LL<<38),
3692  -reale(48923563,62665LL<<36),reale(10316934,1969LL<<37),
3693  reale(535285,33757LL<<36),-reale(501186,3348667LL<<30),
3694  reale(127156179360LL,0xd54f3ea0b98dfLL),
3695  // C4[15], coeff of eps^17, polynomial in n of order 12
3696  reale(15155809,205049LL<<34),-reale(39104030,957115LL<<32),
3697  reale(81967212,139599LL<<33),-reale(139468172,993913LL<<32),
3698  reale(190415844,61587LL<<35),-reale(202311488,967447LL<<32),
3699  reale(154439958,403401LL<<33),-reale(61783996,889045LL<<32),
3700  -reale(28504911,66989LL<<34),reale(73132006,1030157LL<<32),
3701  -reale(66442314,293949LL<<33),reale(34502754,346959LL<<32),
3702  -reale(8240730,128798053LL<<25),reale(127156179360LL,0xd54f3ea0b98dfLL),
3703  // C4[15], coeff of eps^16, polynomial in n of order 13
3704  reale(114172,142577LL<<34),-reale(499141,33119LL<<36),
3705  reale(1750098,174183LL<<34),-reale(5016097,114721LL<<35),
3706  reale(11893006,66221LL<<34),-reale(23470909,19093LL<<37),
3707  reale(38591591,188131LL<<34),-reale(52613301,65223LL<<35),
3708  reale(58753809,139305LL<<34),-reale(52512562,23925LL<<36),
3709  reale(36059714,158111LL<<34),-reale(17726185,93229LL<<35),
3710  reale(5486676,138853LL<<34),-reale(792996,14574745LL<<26),
3711  reale(42385393120LL,0x471a6a35932f5LL),
3712  // C4[15], coeff of eps^15, polynomial in n of order 14
3713  real(592706205LL<<33),-reale(9147,839013LL<<32),
3714  reale(55355,240865LL<<34),-reale(262940,644275LL<<32),
3715  reale(1011310,29095LL<<33),-reale(3215965,1023905LL<<32),
3716  reale(8575909,35467LL<<35),-reale(19352216,329839LL<<32),
3717  reale(37124659,455473LL<<33),-reale(60529336,778589LL<<32),
3718  reale(83288367,93771LL<<34),-reale(94856196,165035LL<<32),
3719  reale(85043486,110139LL<<33),-reale(50751757,943257LL<<32),
3720  reale(13877433,107462891LL<<25),reale(127156179360LL,0xd54f3ea0b98dfLL),
3721  // C4[16], coeff of eps^29, polynomial in n of order 0
3722  real(553LL<<31),real(0x292ecb9a960d27d1LL),
3723  // C4[16], coeff of eps^28, polynomial in n of order 1
3724  -real(61453LL<<36),-real(4754645LL<<34),
3725  reale(19591808,0x57955a5f17535LL),
3726  // C4[16], coeff of eps^27, polynomial in n of order 2
3727  reale(33770,14237LL<<36),-reale(12917,115767LL<<35),
3728  real(1665987897LL<<31),reale(2148568314LL,0xda506166fe05fLL),
3729  // C4[16], coeff of eps^26, polynomial in n of order 3
3730  reale(1765351,9719LL<<36),reale(634098,16193LL<<37),
3731  reale(114937,5021LL<<36),-reale(211035,902511LL<<32),
3732  reale(135359803835LL,0xb9c7f85883761LL),
3733  // C4[16], coeff of eps^25, polynomial in n of order 4
3734  -reale(3041817,11535LL<<37),-reale(2643315,63657LL<<35),
3735  reale(3458443,225LL<<36),-reale(1011407,29251LL<<35),
3736  reale(33755,354965LL<<31),reale(135359803835LL,0xb9c7f85883761LL),
3737  // C4[16], coeff of eps^24, polynomial in n of order 5
3738  reale(12443946,111847LL<<35),-reale(9978547,23661LL<<37),
3739  reale(264818,24689LL<<35),reale(1196082,9587LL<<36),
3740  reale(477961,17339LL<<35),-reale(375862,243659LL<<32),
3741  reale(135359803835LL,0xb9c7f85883761LL),
3742  // C4[16], coeff of eps^23, polynomial in n of order 6
3743  reale(11971225,59849LL<<36),reale(9677599,56595LL<<35),
3744  -reale(1515717,2317LL<<37),-reale(7956047,112667LL<<35),
3745  reale(5585704,62147LL<<36),-reale(1169086,64041LL<<35),
3746  -reale(10840,1435009LL<<31),reale(135359803835LL,0xb9c7f85883761LL),
3747  // C4[16], coeff of eps^22, polynomial in n of order 7
3748  -reale(20905609,47207LL<<36),-reale(27003899,18815LL<<37),
3749  reale(32128586,62715LL<<36),-reale(8207156,6437LL<<38),
3750  -reale(4335741,20931LL<<36),reale(1351161,14763LL<<37),
3751  reale(1583200,44703LL<<36),-reale(734819,355141LL<<32),
3752  reale(135359803835LL,0xb9c7f85883761LL),
3753  // C4[16], coeff of eps^21, polynomial in n of order 8
3754  reale(119271221,13241LL<<38),-reale(13185134,117885LL<<35),
3755  -reale(34424757,12741LL<<36),reale(12971898,62105LL<<35),
3756  reale(17958221,23929LL<<37),-reale(20751983,45233LL<<35),
3757  reale(8405753,5609LL<<36),-reale(1009805,84123LL<<35),
3758  -reale(126669,998091LL<<31),reale(135359803835LL,0xb9c7f85883761LL),
3759  // C4[16], coeff of eps^20, polynomial in n of order 9
3760  reale(7281953,46177LL<<36),-reale(132136826,3687LL<<39),
3761  reale(164419146,28463LL<<36),-reale(102943145,13301LL<<37),
3762  reale(20499773,15997LL<<36),reale(17609391,14489LL<<38),
3763  -reale(11127728,9397LL<<36),-reale(3194109,31911LL<<37),
3764  reale(5518515,63129LL<<36),-reale(1729623,95963LL<<34),
3765  reale(135359803835LL,0xb9c7f85883761LL),
3766  // C4[16], coeff of eps^19, polynomial in n of order 10
3767  -reale(197461925,11965LL<<36),reale(194820269,1667LL<<35),
3768  -reale(119937281,937LL<<38),-reale(1213288,24915LL<<35),
3769  reale(103481944,52469LL<<36),-reale(133891976,7945LL<<35),
3770  reale(96822293,18071LL<<37),-reale(41434588,121951LL<<35),
3771  reale(8025452,27431LL<<36),reale(724406,126187LL<<35),
3772  -reale(459367,1295029LL<<31),reale(135359803835LL,0xb9c7f85883761LL),
3773  // C4[16], coeff of eps^18, polynomial in n of order 11
3774  -reale(47525285,62545LL<<36),reale(91887649,22453LL<<37),
3775  -reale(145781941,19979LL<<36),reale(186991182,8001LL<<39),
3776  -reale(187151585,35749LL<<36),reale(133148350,20179LL<<37),
3777  -reale(44425461,13151LL<<36),-reale(35371425,9983LL<<38),
3778  reale(71056997,38023LL<<36),-reale(61631567,21647LL<<37),
3779  reale(31499493,50637LL<<36),-reale(7491423,758351LL<<32),
3780  reale(135359803835LL,0xb9c7f85883761LL),
3781  // C4[16], coeff of eps^17, polynomial in n of order 12
3782  -reale(2259631,24697LL<<37),reale(7098981,78723LL<<35),
3783  -reale(18582556,8879LL<<36),reale(40852668,12369LL<<35),
3784  -reale(75692831,12691LL<<38),reale(118080654,84927LL<<35),
3785  -reale(154130872,52073LL<<36),reale(166118829,74381LL<<35),
3786  -reale(144327913,2259LL<<37),reale(96964720,98683LL<<35),
3787  -reale(46899246,18595LL<<36),reale(14349769,50505LL<<35),
3788  -reale(2057503,1465135LL<<31),reale(135359803835LL,0xb9c7f85883761LL),
3789  // C4[16], coeff of eps^16, polynomial in n of order 13
3790  -reale(18695,264305LL<<33),reale(95700,8265LL<<35),
3791  -reale(398136,419847LL<<33),reale(1375381,177071LL<<34),
3792  -reale(4004787,429789LL<<33),reale(9930000,13635LL<<36),
3793  -reale(21101250,231795LL<<33),reale(38532718,52073LL<<34),
3794  -reale(60367925,93257LL<<33),reale(80490566,118467LL<<35),
3795  -reale(89511061,246751LL<<33),reale(78923731,162339LL<<34),
3796  -reale(46636750,263349LL<<33),reale(12687939,1991833LL<<30),
3797  reale(135359803835LL,0xb9c7f85883761LL),
3798  // C4[17], coeff of eps^29, polynomial in n of order 0
3799  -real(280331LL<<31),reale(154847,0x4e6e7be138cdbLL),
3800  // C4[17], coeff of eps^28, polynomial in n of order 1
3801  -real(82431LL<<38),real(142069LL<<33),reale(989485,0x4511e2f2b39a3LL),
3802  // C4[17], coeff of eps^27, polynomial in n of order 2
3803  reale(30957,2723LL<<36),reale(7080,38071LL<<35),
3804  -reale(9773,1986585LL<<31),reale(6836353729LL,0x13b9f01928417LL),
3805  // C4[17], coeff of eps^26, polynomial in n of order 3
3806  -reale(138771,28785LL<<37),reale(154910,14439LL<<38),
3807  -reale(42193,29611LL<<37),real(1108797915LL<<32),
3808  reale(6836353729LL,0x13b9f01928417LL),
3809  // C4[17], coeff of eps^25, polynomial in n of order 4
3810  -reale(1238256,21701LL<<37),-reale(44811,81027LL<<35),
3811  reale(156785,14859LL<<36),reale(74079,77407LL<<35),
3812  -reale(51372,1082481LL<<31),reale(20509061187LL,0x3b2dd04b78c45LL),
3813  // C4[17], coeff of eps^24, polynomial in n of order 5
3814  reale(10057115,7495LL<<39),-reale(158283,1579LL<<41),
3815  -reale(7978477,2703LL<<39),reale(5079175,3021LL<<40),
3816  -reale(987192,2101LL<<39),-reale(20806,242401LL<<34),
3817  reale(143563428310LL,0x9e40b2104d5e3LL),
3818  // C4[17], coeff of eps^23, polynomial in n of order 6
3819  -reale(30405369,16203LL<<36),reale(28904813,10839LL<<35),
3820  -reale(5472666,28841LL<<37),-reale(4538327,21695LL<<35),
3821  reale(1010309,2151LL<<36),reale(1591197,61387LL<<35),
3822  -reale(691600,842821LL<<31),reale(143563428310LL,0x9e40b2104d5e3LL),
3823  // C4[17], coeff of eps^22, polynomial in n of order 7
3824  reale(2360974,20517LL<<37),-reale(34168343,7885LL<<38),
3825  reale(7988557,399LL<<37),reale(19220645,2761LL<<39),
3826  -reale(19251394,21847LL<<37),reale(7294617,7633LL<<38),
3827  -reale(776533,25709LL<<37),-reale(127091,628387LL<<32),
3828  reale(143563428310LL,0x9e40b2104d5e3LL),
3829  // C4[17], coeff of eps^21, polynomial in n of order 8
3830  -reale(141970389,5875LL<<38),reale(152285106,31LL<<35),
3831  -reale(85013706,54665LL<<36),reale(10784519,74157LL<<35),
3832  reale(18376223,22989LL<<37),-reale(9415616,123045LL<<35),
3833  -reale(3707065,39939LL<<36),reale(5266887,19945LL<<35),
3834  -reale(1601936,974407LL<<31),reale(143563428310LL,0x9e40b2104d5e3LL),
3835  // C4[17], coeff of eps^20, polynomial in n of order 9
3836  reale(174732199,7199LL<<38),-reale(91781661,1783LL<<41),
3837  -reale(22947906,1007LL<<38),reale(109147441,451LL<<39),
3838  -reale(126268040,11085LL<<38),reale(86262862,2409LL<<40),
3839  -reale(35185382,1435LL<<38),reale(6220582,7041LL<<39),
3840  reale(846498,391LL<<38),-reale(421214,84365LL<<33),
3841  reale(143563428310LL,0x9e40b2104d5e3LL),
3842  // C4[17], coeff of eps^19, polynomial in n of order 10
3843  reale(100447726,5039LL<<36),-reale(149758021,121873LL<<35),
3844  reale(181554380,1939LL<<38),-reale(171878757,123903LL<<35),
3845  reale(113962110,29289LL<<36),-reale(29967290,80205LL<<35),
3846  -reale(40353928,13613LL<<37),reale(68655180,86853LL<<35),
3847  -reale(57285125,57949LL<<36),reale(28886745,8439LL<<35),
3848  -reale(6846764,2025561LL<<31),reale(143563428310LL,0x9e40b2104d5e3LL),
3849  // C4[17], coeff of eps^18, polynomial in n of order 11
3850  reale(9163438,32371LL<<37),-reale(22188557,9937LL<<38),
3851  reale(45681407,15569LL<<37),-reale(80085759,21LL<<40),
3852  reale(119267529,32127LL<<37),-reale(149784698,12951LL<<38),
3853  reale(156408668,30941LL<<37),-reale(132494258,5045LL<<39),
3854  reale(87286969,10059LL<<37),-reale(41608633,10397LL<<38),
3855  reale(12599797,16681LL<<37),-reale(1793721,181577LL<<32),
3856  reale(143563428310LL,0x9e40b2104d5e3LL),
3857  // C4[17], coeff of eps^17, polynomial in n of order 12
3858  reale(152058,3531LL<<37),-reale(566838,109449LL<<35),
3859  reale(1788421,65069LL<<36),-reale(4828739,49907LL<<35),
3860  reale(11241509,10969LL<<38),-reale(22666304,107837LL<<35),
3861  reale(39633653,283LL<<36),-reale(59939783,113319LL<<35),
3862  reale(77715030,3737LL<<37),-reale(84609105,47985LL<<35),
3863  reale(73498818,52617LL<<36),-reale(43049308,20443LL<<35),
3864  reale(11659187,1311925LL<<31),reale(143563428310LL,0x9e40b2104d5e3LL),
3865  // C4[18], coeff of eps^29, polynomial in n of order 0
3866  real(35LL<<34),real(0x29845c2bcb5c10d7LL),
3867  // C4[18], coeff of eps^28, polynomial in n of order 1
3868  reale(3628,18373LL<<37),-reale(4063,232509LL<<34),
3869  reale(3097286791LL,0x8a812bfedbe75LL),
3870  // C4[18], coeff of eps^27, polynomial in n of order 2
3871  reale(435730,613LL<<39),-reale(110987,3811LL<<38),real(489021323LL<<34),
3872  reale(21681007540LL,0xc98833f803533LL),
3873  // C4[18], coeff of eps^26, polynomial in n of order 3
3874  -reale(762945,31179LL<<36),reale(988791,87LL<<37),
3875  reale(550009,38375LL<<36),-reale(343815,323189LL<<33),
3876  reale(151767052785LL,0x82b96bc817465LL),
3877  // C4[18], coeff of eps^25, polynomial in n of order 4
3878  reale(1063744,27LL<<41),-reale(7897635,7767LL<<39),
3879  reale(4613149,699LL<<40),-reale(833936,93LL<<39),
3880  -reale(28054,94387LL<<35),reale(151767052785LL,0x82b96bc817465LL),
3881  // C4[18], coeff of eps^24, polynomial in n of order 5
3882  reale(25578507,4379LL<<38),-reale(3209600,1553LL<<40),
3883  -reale(4577572,5923LL<<38),reale(702466,1583LL<<39),
3884  reale(1586031,287LL<<38),-reale(651636,122639LL<<35),
3885  reale(151767052785LL,0x82b96bc817465LL),
3886  // C4[18], coeff of eps^23, polynomial in n of order 6
3887  -reale(32324739,1815LL<<40),reale(3520775,1207LL<<39),
3888  reale(19946468,259LL<<41),-reale(17787966,4575LL<<39),
3889  reale(6336978,3235LL<<40),-reale(589727,5685LL<<39),
3890  -reale(125505,20667LL<<35),reale(151767052785LL,0x82b96bc817465LL),
3891  // C4[18], coeff of eps^22, polynomial in n of order 7
3892  reale(138884729,22203LL<<36),-reale(69168625,14473LL<<37),
3893  reale(3249237,4577LL<<36),reale(18436830,10301LL<<38),
3894  -reale(7840055,31609LL<<36),-reale(4091705,30595LL<<37),
3895  reale(5021146,27565LL<<36),-reale(1488082,115687LL<<33),
3896  reale(151767052785LL,0x82b96bc817465LL),
3897  // C4[18], coeff of eps^21, polynomial in n of order 8
3898  -reale(66334778,1299LL<<41),-reale(40377625,16285LL<<38),
3899  reale(111882749,4839LL<<39),-reale(118325119,4711LL<<38),
3900  reale(76858390,3693LL<<40),-reale(29952902,3569LL<<38),
3901  reale(4790818,4941LL<<39),reale(921311,4421LL<<38),
3902  -reale(386621,181821LL<<34),reale(151767052785LL,0x82b96bc817465LL),
3903  // C4[18], coeff of eps^20, polynomial in n of order 9
3904  -reale(151679112,16629LL<<37),reale(174648786,1667LL<<40),
3905  -reale(156892091,15835LL<<37),reale(96799837,4169LL<<38),
3906  -reale(17949188,6721LL<<37),-reale(43885384,7293LL<<39),
3907  reale(66080580,25305LL<<37),-reale(53357084,1853LL<<38),
3908  reale(26599572,17011LL<<37),-reale(6287689,169979LL<<34),
3909  reale(151767052785LL,0x82b96bc817465LL),
3910  // C4[18], coeff of eps^19, polynomial in n of order 10
3911  -reale(8594193,5169LL<<39),reale(16702080,5475LL<<38),
3912  -reale(27882498,1245LL<<41),reale(39843622,14413LL<<38),
3913  -reale(48340851,951LL<<39),reale(49066184,11639LL<<38),
3914  -reale(40627946,3165LL<<40),reale(26296855,15713LL<<38),
3915  -reale(12371894,1597LL<<39),reale(3711568,4235LL<<38),
3916  -reale(524991,147555LL<<34),reale(50589017595LL,0x2b9323ed5d177LL),
3917  // C4[18], coeff of eps^18, polynomial in n of order 11
3918  -reale(768539,29011LL<<36),reale(2243105,18035LL<<37),
3919  -reale(5671852,39713LL<<36),reale(12494515,7255LL<<39),
3920  -reale(24051943,5231LL<<36),reale(40468348,22085LL<<37),
3921  -reale(59307062,46653LL<<36),reale(74994737,5975LL<<38),
3922  -reale(80108014,59787LL<<36),reale(68664012,25623LL<<37),
3923  -reale(39899358,51033LL<<36),reale(10762327,20443LL<<33),
3924  reale(151767052785LL,0x82b96bc817465LL),
3925  // C4[19], coeff of eps^29, polynomial in n of order 0
3926  -real(69697LL<<34),reale(220556,0x6c98ea537e51fLL),
3927  // C4[19], coeff of eps^28, polynomial in n of order 1
3928  -real(1238839LL<<41),real(675087LL<<35),
3929  reale(141943813,0x222cc7846d81LL),
3930  // C4[19], coeff of eps^27, polynomial in n of order 2
3931  reale(876102,3999LL<<40),reale(573743,1451LL<<39),
3932  -reale(328615,14973LL<<34),reale(159970677260LL,0x6732257fe12e7LL),
3933  // C4[19], coeff of eps^26, polynomial in n of order 3
3934  -reale(7739083,17LL<<46),reale(4186838,53LL<<45),-reale(704448,1LL<<46),
3935  -reale(33249,11241LL<<37),reale(159970677260LL,0x6732257fe12e7LL),
3936  // C4[19], coeff of eps^25, polynomial in n of order 4
3937  -reale(1360864,133LL<<42),-reale(4500609,2667LL<<40),
3938  reale(427896,299LL<<41),reale(1570943,1191LL<<40),
3939  -reale(614728,45789LL<<35),reale(159970677260LL,0x6732257fe12e7LL),
3940  // C4[19], coeff of eps^24, polynomial in n of order 5
3941  -reale(379105,631LL<<42),reale(20252634,139LL<<44),
3942  -reale(16388211,705LL<<42),reale(5510947,339LL<<43),
3943  -reale(439601,699LL<<42),-reale(122601,56745LL<<36),
3944  reale(159970677260LL,0x6732257fe12e7LL),
3945  // C4[19], coeff of eps^23, polynomial in n of order 6
3946  -reale(55355388,567LL<<41),-reale(2520461,2117LL<<40),
3947  reale(18017708,147LL<<42),-reale(6413373,771LL<<40),
3948  -reale(4373212,61LL<<41),reale(4784182,2079LL<<40),
3949  -reale(1386197,54485LL<<35),reale(159970677260LL,0x6732257fe12e7LL),
3950  // C4[19], coeff of eps^22, polynomial in n of order 7
3951  -reale(54112477,29LL<<46),reale(112419812,35LL<<45),
3952  -reale(110372726,9LL<<46),reale(68510282,53LL<<46),
3953  -reale(25556330,19LL<<46),reale(3652507,1LL<<45),reale(962676,17LL<<46),
3954  -reale(355362,30093LL<<37),reale(159970677260LL,0x6732257fe12e7LL),
3955  // C4[19], coeff of eps^21, polynomial in n of order 8
3956  reale(166723371,209LL<<42),-reale(142457721,7469LL<<39),
3957  reale(81530379,2787LL<<40),-reale(7977897,3383LL<<39),
3958  -reale(46298043,1775LL<<41),reale(63437092,799LL<<39),
3959  -reale(49803454,3807LL<<40),reale(24585849,2581LL<<39),
3960  -reale(5799325,105875LL<<34),reale(159970677260LL,0x6732257fe12e7LL),
3961  // C4[19], coeff of eps^20, polynomial in n of order 9
3962  reale(54095236,1729LL<<41),-reale(86448328,33LL<<44),
3963  reale(119042325,527LL<<41),-reale(140012701,875LL<<42),
3964  reale(138519104,1133LL<<41),-reale(112357061,257LL<<43),
3965  reale(71568963,1275LL<<41),-reale(33272498,441LL<<42),
3966  reale(9897515,729LL<<41),-reale(1391838,12705LL<<35),
3967  reale(159970677260LL,0x6732257fe12e7LL),
3968  // C4[19], coeff of eps^19, polynomial in n of order 10
3969  reale(2731650,3225LL<<40),-reale(6520331,5423LL<<39),
3970  reale(13678206,885LL<<42),-reale(25266687,5569LL<<39),
3971  reale(41073925,3215LL<<40),-reale(58519302,7091LL<<39),
3972  reale(72351138,181LL<<41),-reale(75968694,8133LL<<39),
3973  reale(64333849,3333LL<<40),-reale(37115682,4791LL<<39),
3974  reale(9974839,182105LL<<34),reale(159970677260LL,0x6732257fe12e7LL),
3975  // C4[20], coeff of eps^29, polynomial in n of order 0
3976  real(1LL<<39),reale(386445,0x44b61aebc827LL),
3977  // C4[20], coeff of eps^28, polynomial in n of order 1
3978  reale(3670,3431LL<<40),-real(63923791LL<<37),
3979  reale(1044560880,0x57ec63f8653c9LL),
3980  // C4[20], coeff of eps^27, polynomial in n of order 2
3981  reale(165149,453LL<<43),-reale(25858,471LL<<42),-real(26276299LL<<38),
3982  reale(7311926162LL,0x6776bbcac4a7fLL),
3983  // C4[20], coeff of eps^26, polynomial in n of order 3
3984  -reale(4343033,595LL<<42),reale(185313,303LL<<43),
3985  reale(1548473,271LL<<42),-reale(580654,777LL<<40),
3986  reale(168174301735LL,0x4baadf37ab169LL),
3987  // C4[20], coeff of eps^25, polynomial in n of order 4
3988  reale(20236427,149LL<<44),-reale(15067334,133LL<<42),
3989  reale(4797544,165LL<<43),-reale(318599,375LL<<42),
3990  -reale(118861,3875LL<<38),reale(168174301735LL,0x4baadf37ab169LL),
3991  // C4[20], coeff of eps^24, polynomial in n of order 5
3992  -reale(6870833,1979LL<<41),reale(17282399,281LL<<43),
3993  -reale(5135975,189LL<<41),-reale(4572111,263LL<<42),
3994  reale(4557653,1537LL<<41),-reale(1294702,4061LL<<38),
3995  reale(168174301735LL,0x4baadf37ab169LL),
3996  // C4[20], coeff of eps^23, polynomial in n of order 6
3997  reale(111332564,131LL<<43),-reale(102611836,439LL<<42),
3998  reale(61113705,49LL<<44),-reale(21849131,865LL<<42),
3999  reale(2742318,257LL<<43),reale(980372,533LL<<42),
4000  -reale(327159,8391LL<<38),reale(168174301735LL,0x4baadf37ab169LL),
4001  // C4[20], coeff of eps^22, polynomial in n of order 7
4002  -reale(128743521,979LL<<42),reale(67998970,481LL<<43),
4003  reale(279122,855LL<<42),-reale(47847734,245LL<<44),
4004  reale(60794248,257LL<<42),-reale(46583621,181LL<<43),
4005  reale(22803394,43LL<<42),-reale(5369928,2229LL<<40),
4006  reale(168174301735LL,0x4baadf37ab169LL),
4007  // C4[20], coeff of eps^21, polynomial in n of order 8
4008  -reale(88564699,121LL<<45),reale(117949702,533LL<<42),
4009  -reale(134881895,27LL<<43),reale(130376590,239LL<<42),
4010  -reale(103788735,57LL<<44),reale(65154071,233LL<<42),
4011  -reale(29963298,393LL<<43),reale(8844588,195LL<<42),
4012  -reale(1237189,6873LL<<38),reale(168174301735LL,0x4baadf37ab169LL),
4013  // C4[20], coeff of eps^20, polynomial in n of order 9
4014  -reale(7362630,999LL<<40),reale(14785858,137LL<<43),
4015  -reale(26321377,9LL<<40),reale(41483460,1083LL<<41),
4016  -reale(57615917,1643LL<<40),reale(69797568,521LL<<42),
4017  -reale(72155594,1933LL<<40),reale(60438019,617LL<<41),
4018  -reale(34641303,3055LL<<40),reale(9278920,21175LL<<37),
4019  reale(168174301735LL,0x4baadf37ab169LL),
4020  // C4[21], coeff of eps^29, polynomial in n of order 0
4021  -real(2017699LL<<39),reale(144690669,0x92d5d14b2b5b9LL),
4022  // C4[21], coeff of eps^28, polynomial in n of order 1
4023  -reale(21806,31LL<<47),-real(1751493LL<<42),
4024  reale(7668605487LL,0x6644548ff9f4dLL),
4025  // C4[21], coeff of eps^27, polynomial in n of order 2
4026  -real(610053LL<<43),reale(66113,223LL<<42),-reale(23877,14131LL<<38),
4027  reale(7668605487LL,0x6644548ff9f4dLL),
4028  // C4[21], coeff of eps^26, polynomial in n of order 3
4029  -reale(601427,223LL<<44),reale(181759,65LL<<45),-reale(9602,5LL<<44),
4030  -reale(4983,2721LL<<39),reale(7668605487LL,0x6644548ff9f4dLL),
4031  // C4[21], coeff of eps^25, polynomial in n of order 4
4032  reale(16348405,227LL<<44),-reale(4001511,795LL<<42),
4033  -reale(4705038,397LL<<43),reale(4342393,855LL<<42),
4034  -reale(1212256,1051LL<<38),reale(176377926210LL,0x302398ef74febLL),
4035  // C4[21], coeff of eps^24, polynomial in n of order 5
4036  -reale(95167920,19LL<<45),reale(54565817,7LL<<47),
4037  -reale(18712410,5LL<<45),reale(2011897,15LL<<46),reale(981374,25LL<<45),
4038  -reale(301721,597LL<<40),reale(176377926210LL,0x302398ef74febLL),
4039  // C4[21], coeff of eps^23, polynomial in n of order 6
4040  reale(56043535,133LL<<43),reale(7101303,759LL<<42),
4041  -reale(48732132,249LL<<44),reale(58197907,161LL<<42),
4042  -reale(43660867,425LL<<43),reale(21217809,619LL<<42),
4043  -reale(4990122,11039LL<<38),reale(176377926210LL,0x302398ef74febLL),
4044  // C4[21], coeff of eps^22, polynomial in n of order 7
4045  reale(38792824,189LL<<44),-reale(43241527,125LL<<45),
4046  reale(40920531,151LL<<44),-reale(32022608,39LL<<46),
4047  reale(19836099,97LL<<44),-reale(9032168,63LL<<45),
4048  reale(2647359,187LL<<44),-reale(368524,4161LL<<39),
4049  reale(58792642070LL,0x100bdda526ff9LL),
4050  // C4[21], coeff of eps^21, polynomial in n of order 8
4051  reale(15813930,121LL<<45),-reale(27228018,205LL<<42),
4052  reale(41726053,443LL<<43),-reale(56628215,983LL<<42),
4053  reale(67341662,57LL<<44),-reale(68636694,193LL<<42),
4054  reale(56918234,105LL<<43),-reale(32430156,715LL<<42),
4055  reale(8660325,15343LL<<38),reale(176377926210LL,0x302398ef74febLL),
4056  // C4[22], coeff of eps^29, polynomial in n of order 0
4057  -real(229LL<<43),reale(2018939,0x935060fc493cdLL),
4058  // C4[22], coeff of eps^28, polynomial in n of order 1
4059  reale(64733,61LL<<46),-reale(22613,493LL<<43),
4060  reale(8025284812LL,0x6511ed552f41bLL),
4061  // C4[22], coeff of eps^27, polynomial in n of order 2
4062  reale(158513,3LL<<48),-reale(6162,29LL<<47),-reale(4786,487LL<<43),
4063  reale(8025284812LL,0x6511ed552f41bLL),
4064  // C4[22], coeff of eps^26, polynomial in n of order 3
4065  -reale(130438,301LL<<43),-reale(208062,47LL<<44),reale(179942,497LL<<43),
4066  -reale(49466,167LL<<40),reale(8025284812LL,0x6511ed552f41bLL),
4067  // C4[22], coeff of eps^25, polynomial in n of order 4
4068  reale(2120438,3LL<<47),-reale(697803,39LL<<45),reale(61914,3LL<<46),
4069  reale(42203,115LL<<45),-reale(12120,543LL<<41),
4070  reale(8025284812LL,0x6511ed552f41bLL),
4071  // C4[22], coeff of eps^24, polynomial in n of order 5
4072  reale(12722577,33LL<<44),-reale(49104495,51LL<<46),
4073  reale(55677556,71LL<<44),-reale(41002422,115LL<<45),
4074  reale(19800840,109LL<<44),-reale(4652345,837LL<<41),
4075  reale(184581550685LL,0x149c52a73ee6dLL),
4076  // C4[22], coeff of eps^23, polynomial in n of order 6
4077  -reale(124610244,57LL<<46),reale(115654934,113LL<<45),
4078  -reale(89096506,19LL<<47),reale(54518354,119LL<<45),
4079  -reale(24598996,19LL<<46),reale(7163443,125LL<<45),
4080  -reale(992759,1841LL<<41),reale(184581550685LL,0x149c52a73ee6dLL),
4081  // C4[22], coeff of eps^22, polynomial in n of order 7
4082  -reale(27999005,155LL<<43),reale(41827085,121LL<<44),
4083  -reale(55581037,1LL<<43),reale(64987058,83LL<<45),
4084  -reale(65383321,103LL<<43),reale(53725829,211LL<<44),
4085  -reale(30444636,461LL<<43),reale(8107539,715LL<<40),
4086  reale(184581550685LL,0x149c52a73ee6dLL),
4087  // C4[23], coeff of eps^29, polynomial in n of order 0
4088  -reale(4289,21LL<<43),reale(1676392827,0x7a5fe79ee0e95LL),
4089  // C4[23], coeff of eps^28, polynomial in n of order 1
4090  -real(1351LL<<51),-real(234789LL<<44),
4091  reale(1676392827,0x7a5fe79ee0e95LL),
4092  // C4[23], coeff of eps^27, polynomial in n of order 2
4093  -reale(209744,1LL<<50),reale(171585,3LL<<49),-reale(46526,469LL<<43),
4094  reale(8381964137LL,0x63df861a648e9LL),
4095  // C4[23], coeff of eps^26, polynomial in n of order 3
4096  -reale(599194,1LL<<51),reale(41297,0),reale(41388,1LL<<51),
4097  -reale(11218,97LL<<45),reale(8381964137LL,0x63df861a648e9LL),
4098  // C4[23], coeff of eps^25, polynomial in n of order 4
4099  -reale(2134087,7LL<<49),reale(2315275,31LL<<47),-reale(1677358,15LL<<48),
4100  reale(805613,21LL<<47),-reale(189149,1213LL<<41),
4101  reale(8381964137LL,0x63df861a648e9LL),
4102  // C4[23], coeff of eps^24, polynomial in n of order 5
4103  reale(4740508,1LL<<49),-reale(3599518,1LL<<51),reale(2177844,7LL<<49),
4104  -reale(974429,1LL<<50),reale(282071,5LL<<49),-reale(38931,779LL<<42),
4105  reale(8381964137LL,0x63df861a648e9LL),
4106  // C4[23], coeff of eps^23, polynomial in n of order 6
4107  reale(1817763,3LL<<48),-reale(2369306,23LL<<47),reale(2727592,1LL<<49),
4108  -reale(2711734,1LL<<47),reale(2209561,1LL<<48),-reale(1245816,11LL<<47),
4109  reale(330919,1979LL<<41),reale(8381964137LL,0x63df861a648e9LL),
4110  // C4[24], coeff of eps^29, polynomial in n of order 0
4111  -real(1439LL<<46),reale(44813556,0x37a4fd885dffdLL),
4112  // C4[24], coeff of eps^28, polynomial in n of order 1
4113  reale(32742,3LL<<50),-reale(8770,21LL<<47),
4114  reale(1747728692,0x7a229fc651f8bLL),
4115  // C4[24], coeff of eps^27, polynomial in n of order 2
4116  reale(4928,1LL<<51),reale(8067,1LL<<50),-reale(2080,43LL<<46),
4117  reale(1747728692,0x7a229fc651f8bLL),
4118  // C4[24], coeff of eps^26, polynomial in n of order 3
4119  reale(2214330,0),-reale(1581120,0),reale(755790,0),
4120  -reale(177363,7LL<<47),reale(8738643462LL,0x62ad1edf99db7LL),
4121  // C4[24], coeff of eps^25, polynomial in n of order 4
4122  -reale(1116955,0),reale(668788,3LL<<50),-reale(296917,1LL<<51),
4123  reale(85476,1LL<<50),-reale(11752,63LL<<46),
4124  reale(2912881154LL,0x20e45f9fddf3dLL),
4125  // C4[24], coeff of eps^24, polynomial in n of order 5
4126  -reale(2320992,3LL<<48),reale(2634056,1LL<<50),-reale(2590155,5LL<<48),
4127  reale(2094168,1LL<<49),-reale(1175298,7LL<<48),reale(311454,11LL<<45),
4128  reale(8738643462LL,0x62ad1edf99db7LL),
4129  // C4[25], coeff of eps^29, polynomial in n of order 0
4130  -real(3707LL<<46),reale(12720731,0x2bd144a4925efLL),
4131  // C4[25], coeff of eps^28, polynomial in n of order 1
4132  real(301LL<<53),-real(2379LL<<48),reale(139928042,0xe1fdf3124a145LL),
4133  // C4[25], coeff of eps^27, polynomial in n of order 2
4134  -reale(298603,1LL<<51),reale(142145,1LL<<50),-reale(33346,63LL<<46),
4135  reale(1819064557,0x79e557edc3081LL),
4136  // C4[25], coeff of eps^26, polynomial in n of order 3
4137  reale(370617,0),-reale(163358,0),reale(46787,0),-reale(6410,23LL<<47),
4138  reale(1819064557,0x79e557edc3081LL),
4139  // C4[25], coeff of eps^25, polynomial in n of order 4
4140  reale(508963,0),-reale(495426,3LL<<50),reale(397689,1LL<<51),
4141  -reale(222238,1LL<<50),reale(58764,59LL<<46),
4142  reale(1819064557,0x79e557edc3081LL),
4143  // C4[26], coeff of eps^29, polynomial in n of order 0
4144  -real(1LL<<49),reale(131359,0xe834f81ee20c1LL),
4145  // C4[26], coeff of eps^28, polynomial in n of order 1
4146  reale(10305,0),-reale(2417,1LL<<49),reale(145415417,0x1d0ced8b7a293LL),
4147  // C4[26], coeff of eps^27, polynomial in n of order 2
4148  -reale(11556,0),reale(3294,0),-real(3599LL<<49),
4149  reale(145415417,0x1d0ced8b7a293LL),
4150  // C4[26], coeff of eps^26, polynomial in n of order 3
4151  -reale(36490,1LL<<51),reale(29097,0),-reale(16195,1LL<<51),
4152  reale(4273,13LL<<48),reale(145415417,0x1d0ced8b7a293LL),
4153  // C4[27], coeff of eps^29, polynomial in n of order 0
4154  -real(2029LL<<49),reale(16766976,0xd0e6a80084b19LL),
4155  // C4[27], coeff of eps^28, polynomial in n of order 1
4156  real(7LL<<56),-real(61LL<<50),reale(5588992,0x45a238002c3b3LL),
4157  // C4[27], coeff of eps^27, polynomial in n of order 2
4158  reale(3080,0),-real(427LL<<54),real(3599LL<<49),
4159  reale(16766976,0xd0e6a80084b19LL),
4160  // C4[28], coeff of eps^29, polynomial in n of order 0
4161  -real(1LL<<53),reale(827461,0x318a62b8e0a5bLL),
4162  // C4[28], coeff of eps^28, polynomial in n of order 1
4163  -real(29LL<<55),real(61LL<<52),reale(2482383,0x949f282aa1f11LL),
4164  // C4[29], coeff of eps^29, polynomial in n of order 0
4165  real(1LL<<53),reale(88602,0xec373d36a45dfLL),
4166  }; // count = 5425
4167 #else
4168 #error "Bad value for GEOGRAPHICLIB_GEODESICEXACT_ORDER"
4169 #endif
4170  static_assert(sizeof(coeff) / sizeof(real) ==
4171  (nC4_ * (nC4_ + 1) * (nC4_ + 5)) / 6,
4172  "Coefficient array size mismatch in C4coeff");
4173  int o = 0, k = 0;
4174  for (int l = 0; l < nC4_; ++l) { // l is index of C4[l]
4175  for (int j = nC4_ - 1; j >= l; --j) { // coeff of eps^j
4176  int m = nC4_ - j - 1; // order of polynomial in n
4177  _cC4x[k++] = Math::polyval(m, coeff + o, _n) / coeff[o + m + 1];
4178  o += m + 2;
4179  }
4180  }
4181  // Post condition: o == sizeof(coeff) / sizeof(real) && k == nC4x_
4182  if (!(o == sizeof(coeff) / sizeof(real) && k == nC4x_))
4183  throw GeographicErr("C4 misalignment");
4184  }
4185 
4186 } // namespace GeographicLib
GeographicLib::Math::real real
Definition: GeodSolve.cpp:31
Header for GeographicLib::GeodesicExact class.
Header for GeographicLib::GeodesicLineExact class.
#define GEOGRAPHICLIB_PANIC
Definition: Math.hpp:61
Elliptic integrals and functions.
Math::real deltaE(real sn, real cn, real dn) const
Math::real deltaD(real sn, real cn, real dn) const
Exact geodesic calculations.
GeodesicLineExact InverseLine(real lat1, real lon1, real lat2, real lon2, unsigned caps=ALL) const
GeodesicLineExact GenDirectLine(real lat1, real lon1, real azi1, bool arcmode, real s12_a12, unsigned caps=ALL) const
GeodesicLineExact DirectLine(real lat1, real lon1, real azi1, real s12, unsigned caps=ALL) const
Math::real GenDirect(real lat1, real lon1, real azi1, bool arcmode, real s12_a12, unsigned outmask, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21, real &S12) const
GeodesicLineExact Line(real lat1, real lon1, real azi1, unsigned caps=ALL) const
static const GeodesicExact & WGS84()
GeodesicLineExact ArcDirectLine(real lat1, real lon1, real azi1, real a12, unsigned caps=ALL) const
Exception handling for GeographicLib.
Definition: Constants.hpp:316
Mathematical functions needed by GeographicLib.
Definition: Math.hpp:76
static T degree()
Definition: Math.hpp:200
static T LatFix(T x)
Definition: Math.hpp:299
static void sincosd(T x, T &sinx, T &cosx)
Definition: Math.cpp:106
static T atan2d(T y, T x)
Definition: Math.cpp:183
static void norm(T &x, T &y)
Definition: Math.hpp:222
static T AngRound(T x)
Definition: Math.cpp:97
static T sq(T x)
Definition: Math.hpp:212
static T AngNormalize(T x)
Definition: Math.cpp:71
static void sincosde(T x, T t, T &sinx, T &cosx)
Definition: Math.cpp:126
static T pi()
Definition: Math.hpp:190
static T polyval(int N, const T p[], T x)
Definition: Math.hpp:270
static T AngDiff(T x, T y, T &e)
Definition: Math.cpp:82
@ hd
degrees per half turn
Definition: Math.hpp:144
@ qd
degrees per quarter turn
Definition: Math.hpp:141
Namespace for GeographicLib.
Definition: Accumulator.cpp:12
void swap(GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &a, GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &b)