Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [387,8,Mod(1,387)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(387, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("387.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 387 = 3^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 387.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(120.893004862\) |
Analytic rank: | \(1\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 3 x^{12} - 1279 x^{11} + 3765 x^{10} + 598742 x^{9} - 1518614 x^{8} - 124677082 x^{7} + 193428526 x^{6} + 11160446785 x^{5} + \cdots + 1551032970660 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-16.1540\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 387.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 15.1540 | 1.33944 | 0.669720 | − | 0.742614i | \(-0.266414\pi\) | ||||
0.669720 | + | 0.742614i | \(0.266414\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 101.645 | 0.794098 | ||||||||
\(5\) | −210.950 | −0.754717 | −0.377359 | − | 0.926067i | \(-0.623168\pi\) | ||||
−0.377359 | + | 0.926067i | \(0.623168\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1100.87 | 1.21309 | 0.606543 | − | 0.795051i | \(-0.292556\pi\) | ||||
0.606543 | + | 0.795051i | \(0.292556\pi\) | |||||||
\(8\) | −399.390 | −0.275793 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3196.74 | −1.01090 | ||||||||
\(11\) | 3136.09 | 0.710419 | 0.355209 | − | 0.934787i | \(-0.384410\pi\) | ||||
0.355209 | + | 0.934787i | \(0.384410\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5743.36 | −0.725044 | −0.362522 | − | 0.931975i | \(-0.618084\pi\) | ||||
−0.362522 | + | 0.931975i | \(0.618084\pi\) | |||||||
\(14\) | 16682.6 | 1.62486 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19062.9 | −1.16351 | ||||||||
\(17\) | −27231.5 | −1.34431 | −0.672155 | − | 0.740410i | \(-0.734631\pi\) | ||||
−0.672155 | + | 0.740410i | \(0.734631\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 54685.6 | 1.82909 | 0.914545 | − | 0.404484i | \(-0.132549\pi\) | ||||
0.914545 | + | 0.404484i | \(0.132549\pi\) | |||||||
\(20\) | −21441.9 | −0.599320 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 47524.4 | 0.951563 | ||||||||
\(23\) | −12024.9 | −0.206079 | −0.103040 | − | 0.994677i | \(-0.532857\pi\) | ||||
−0.103040 | + | 0.994677i | \(0.532857\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −33625.2 | −0.430402 | ||||||||
\(26\) | −87035.1 | −0.971153 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 111897. | 0.963310 | ||||||||
\(29\) | −132127. | −1.00600 | −0.503001 | − | 0.864286i | \(-0.667771\pi\) | ||||
−0.503001 | + | 0.864286i | \(0.667771\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 281517. | 1.69722 | 0.848612 | − | 0.529016i | \(-0.177439\pi\) | ||||
0.848612 | + | 0.529016i | \(0.177439\pi\) | |||||||
\(32\) | −237758. | −1.28265 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −412666. | −1.80062 | ||||||||
\(35\) | −232228. | −0.915537 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −214511. | −0.696215 | −0.348107 | − | 0.937455i | \(-0.613176\pi\) | ||||
−0.348107 | + | 0.937455i | \(0.613176\pi\) | |||||||
\(38\) | 828707. | 2.44996 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 84251.4 | 0.208145 | ||||||||
\(41\) | −302212. | −0.684808 | −0.342404 | − | 0.939553i | \(-0.611241\pi\) | ||||
−0.342404 | + | 0.939553i | \(0.611241\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −79507.0 | −0.152499 | ||||||||
\(44\) | 318767. | 0.564142 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −182226. | −0.276030 | ||||||||
\(47\) | −235041. | −0.330218 | −0.165109 | − | 0.986275i | \(-0.552798\pi\) | ||||
−0.165109 | + | 0.986275i | \(0.552798\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 388365. | 0.471578 | ||||||||
\(50\) | −509557. | −0.576498 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −583782. | −0.575757 | ||||||||
\(53\) | −55032.5 | −0.0507754 | −0.0253877 | − | 0.999678i | \(-0.508082\pi\) | ||||
−0.0253877 | + | 0.999678i | \(0.508082\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −661558. | −0.536165 | ||||||||
\(56\) | −439676. | −0.334560 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.00226e6 | −1.34748 | ||||||||
\(59\) | −150144. | −0.0951754 | −0.0475877 | − | 0.998867i | \(-0.515153\pi\) | ||||
−0.0475877 | + | 0.998867i | \(0.515153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.65598e6 | −0.934113 | −0.467057 | − | 0.884227i | \(-0.654686\pi\) | ||||
−0.467057 | + | 0.884227i | \(0.654686\pi\) | |||||||
\(62\) | 4.26612e6 | 2.27333 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.16294e6 | −0.554531 | ||||||||
\(65\) | 1.21156e6 | 0.547203 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.76796e6 | 0.718144 | 0.359072 | − | 0.933310i | \(-0.383093\pi\) | ||||
0.359072 | + | 0.933310i | \(0.383093\pi\) | |||||||
\(68\) | −2.76793e6 | −1.06752 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.51919e6 | −1.22631 | ||||||||
\(71\) | −3.57159e6 | −1.18429 | −0.592144 | − | 0.805832i | \(-0.701718\pi\) | ||||
−0.592144 | + | 0.805832i | \(0.701718\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −430044. | −0.129385 | −0.0646923 | − | 0.997905i | \(-0.520607\pi\) | ||||
−0.0646923 | + | 0.997905i | \(0.520607\pi\) | |||||||
\(74\) | −3.25070e6 | −0.932538 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.55849e6 | 1.45248 | ||||||||
\(77\) | 3.45242e6 | 0.861799 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.44014e6 | −1.69780 | −0.848900 | − | 0.528554i | \(-0.822734\pi\) | ||||
−0.848900 | + | 0.528554i | \(0.822734\pi\) | |||||||
\(80\) | 4.02131e6 | 0.878118 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.57974e6 | −0.917259 | ||||||||
\(83\) | −5.50388e6 | −1.05656 | −0.528282 | − | 0.849069i | \(-0.677163\pi\) | ||||
−0.528282 | + | 0.849069i | \(0.677163\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.74447e6 | 1.01457 | ||||||||
\(86\) | −1.20485e6 | −0.204263 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.25252e6 | −0.195928 | ||||||||
\(89\) | 3.53700e6 | 0.531826 | 0.265913 | − | 0.963997i | \(-0.414327\pi\) | ||||
0.265913 | + | 0.963997i | \(0.414327\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.32268e6 | −0.879541 | ||||||||
\(92\) | −1.22227e6 | −0.163647 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.56182e6 | −0.442308 | ||||||||
\(95\) | −1.15359e7 | −1.38045 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.08749e6 | −0.232233 | −0.116117 | − | 0.993236i | \(-0.537045\pi\) | ||||
−0.116117 | + | 0.993236i | \(0.537045\pi\) | |||||||
\(98\) | 5.88530e6 | 0.631651 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.41782e6 | −0.341782 | ||||||||
\(101\) | −1.59947e7 | −1.54473 | −0.772364 | − | 0.635180i | \(-0.780926\pi\) | ||||
−0.772364 | + | 0.635180i | \(0.780926\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.14391e7 | −1.03148 | −0.515739 | − | 0.856746i | \(-0.672483\pi\) | ||||
−0.515739 | + | 0.856746i | \(0.672483\pi\) | |||||||
\(104\) | 2.29384e6 | 0.199962 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −833964. | −0.0680106 | ||||||||
\(107\) | −5.13105e6 | −0.404914 | −0.202457 | − | 0.979291i | \(-0.564893\pi\) | ||||
−0.202457 | + | 0.979291i | \(0.564893\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.10496e7 | −1.55687 | −0.778433 | − | 0.627727i | \(-0.783985\pi\) | ||||
−0.778433 | + | 0.627727i | \(0.783985\pi\) | |||||||
\(110\) | −1.00253e7 | −0.718161 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.09857e7 | −1.41143 | ||||||||
\(113\) | 1.44050e7 | 0.939156 | 0.469578 | − | 0.882891i | \(-0.344406\pi\) | ||||
0.469578 | + | 0.882891i | \(0.344406\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.53665e6 | 0.155531 | ||||||||
\(116\) | −1.34300e7 | −0.798865 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.27528e6 | −0.127482 | ||||||||
\(119\) | −2.99782e7 | −1.63077 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.65210e6 | −0.495306 | ||||||||
\(122\) | −2.50947e7 | −1.25119 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.86147e7 | 1.34776 | ||||||||
\(125\) | 2.35737e7 | 1.07955 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.66397e7 | −1.15403 | −0.577014 | − | 0.816734i | \(-0.695782\pi\) | ||||
−0.577014 | + | 0.816734i | \(0.695782\pi\) | |||||||
\(128\) | 1.28098e7 | 0.539893 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.83600e7 | 0.732946 | ||||||||
\(131\) | 1.53052e7 | 0.594825 | 0.297413 | − | 0.954749i | \(-0.403876\pi\) | ||||
0.297413 | + | 0.954749i | \(0.403876\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.02015e7 | 2.21884 | ||||||||
\(134\) | 2.67918e7 | 0.961911 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.08760e7 | 0.370751 | ||||||||
\(137\) | 2.88018e7 | 0.956968 | 0.478484 | − | 0.878096i | \(-0.341186\pi\) | ||||
0.478484 | + | 0.878096i | \(0.341186\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.41973e7 | 0.764213 | 0.382106 | − | 0.924118i | \(-0.375199\pi\) | ||||
0.382106 | + | 0.924118i | \(0.375199\pi\) | |||||||
\(140\) | −2.36047e7 | −0.727026 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.41240e7 | −1.58628 | ||||||||
\(143\) | −1.80117e7 | −0.515085 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.78722e7 | 0.759247 | ||||||||
\(146\) | −6.51690e6 | −0.173303 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.18039e7 | −0.552863 | ||||||||
\(149\) | −1.88108e7 | −0.465859 | −0.232929 | − | 0.972494i | \(-0.574831\pi\) | ||||
−0.232929 | + | 0.972494i | \(0.574831\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.28673e7 | −1.24959 | −0.624796 | − | 0.780788i | \(-0.714818\pi\) | ||||
−0.624796 | + | 0.780788i | \(0.714818\pi\) | |||||||
\(152\) | −2.18409e7 | −0.504450 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.23181e7 | 1.15433 | ||||||||
\(155\) | −5.93860e7 | −1.28092 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.80087e7 | −1.19631 | −0.598156 | − | 0.801380i | \(-0.704100\pi\) | ||||
−0.598156 | + | 0.801380i | \(0.704100\pi\) | |||||||
\(158\) | −1.12748e8 | −2.27410 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.01549e7 | 0.968040 | ||||||||
\(161\) | −1.32378e7 | −0.249992 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.85826e7 | 1.78297 | 0.891484 | − | 0.453051i | \(-0.149665\pi\) | ||||
0.891484 | + | 0.453051i | \(0.149665\pi\) | |||||||
\(164\) | −3.07183e7 | −0.543805 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.34059e7 | −1.41520 | ||||||||
\(167\) | −3.30309e7 | −0.548798 | −0.274399 | − | 0.961616i | \(-0.588479\pi\) | ||||
−0.274399 | + | 0.961616i | \(0.588479\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.97623e7 | −0.474311 | ||||||||
\(170\) | 8.70519e7 | 1.35896 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.08146e6 | −0.121099 | ||||||||
\(173\) | 9.21797e7 | 1.35355 | 0.676774 | − | 0.736191i | \(-0.263377\pi\) | ||||
0.676774 | + | 0.736191i | \(0.263377\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.70168e7 | −0.522115 | ||||||||
\(176\) | −5.97829e7 | −0.826576 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.35998e7 | 0.712349 | ||||||||
\(179\) | −8.22086e7 | −1.07135 | −0.535675 | − | 0.844424i | \(-0.679943\pi\) | ||||
−0.535675 | + | 0.844424i | \(0.679943\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.53246e7 | −0.568144 | −0.284072 | − | 0.958803i | \(-0.591686\pi\) | ||||
−0.284072 | + | 0.958803i | \(0.591686\pi\) | |||||||
\(182\) | −9.58141e7 | −1.17809 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.80263e6 | 0.0568351 | ||||||||
\(185\) | 4.52510e7 | 0.525445 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.54003e7 | −0.955023 | ||||||||
\(188\) | −2.38907e7 | −0.262226 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.74816e8 | −1.84902 | ||||||||
\(191\) | 1.21596e8 | 1.26270 | 0.631352 | − | 0.775496i | \(-0.282500\pi\) | ||||
0.631352 | + | 0.775496i | \(0.282500\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.40361e8 | 1.40538 | 0.702691 | − | 0.711495i | \(-0.251981\pi\) | ||||
0.702691 | + | 0.711495i | \(0.251981\pi\) | |||||||
\(194\) | −3.16339e7 | −0.311062 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.94752e7 | 0.374480 | ||||||||
\(197\) | 5.68563e7 | 0.529842 | 0.264921 | − | 0.964270i | \(-0.414654\pi\) | ||||
0.264921 | + | 0.964270i | \(0.414654\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.29464e7 | 0.296361 | 0.148181 | − | 0.988960i | \(-0.452658\pi\) | ||||
0.148181 | + | 0.988960i | \(0.452658\pi\) | |||||||
\(200\) | 1.34296e7 | 0.118702 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.42385e8 | −2.06907 | ||||||||
\(203\) | −1.45454e8 | −1.22037 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.37517e7 | 0.516836 | ||||||||
\(206\) | −1.73348e8 | −1.38160 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.09485e8 | 0.843593 | ||||||||
\(209\) | 1.71499e8 | 1.29942 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.35087e8 | −1.72282 | −0.861411 | − | 0.507908i | \(-0.830419\pi\) | ||||
−0.861411 | + | 0.507908i | \(0.830419\pi\) | |||||||
\(212\) | −5.59375e6 | −0.0403207 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.77561e7 | −0.542358 | ||||||||
\(215\) | 1.67720e7 | 0.115093 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.09913e8 | 2.05888 | ||||||||
\(218\) | −3.18986e8 | −2.08533 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.72438e7 | −0.425768 | ||||||||
\(221\) | 1.56400e8 | 0.974685 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.86931e7 | 0.414807 | 0.207404 | − | 0.978255i | \(-0.433499\pi\) | ||||
0.207404 | + | 0.978255i | \(0.433499\pi\) | |||||||
\(224\) | −2.61739e8 | −1.55597 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.18293e8 | 1.25794 | ||||||||
\(227\) | 3.33942e8 | 1.89487 | 0.947436 | − | 0.319945i | \(-0.103664\pi\) | ||||
0.947436 | + | 0.319945i | \(0.103664\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.08822e8 | 1.69935 | 0.849677 | − | 0.527303i | \(-0.176797\pi\) | ||||
0.849677 | + | 0.527303i | \(0.176797\pi\) | |||||||
\(230\) | 3.84405e7 | 0.208325 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.27703e7 | 0.277448 | ||||||||
\(233\) | −1.57739e8 | −0.816947 | −0.408473 | − | 0.912770i | \(-0.633939\pi\) | ||||
−0.408473 | + | 0.912770i | \(0.633939\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.95819e7 | 0.249221 | ||||||||
\(236\) | −1.52613e7 | −0.0755787 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.54291e8 | −2.18431 | ||||||||
\(239\) | 1.84694e8 | 0.875105 | 0.437553 | − | 0.899193i | \(-0.355845\pi\) | ||||
0.437553 | + | 0.899193i | \(0.355845\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.79565e7 | 0.220692 | 0.110346 | − | 0.993893i | \(-0.464804\pi\) | ||||
0.110346 | + | 0.993893i | \(0.464804\pi\) | |||||||
\(242\) | −1.46268e8 | −0.663432 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.68321e8 | −0.741778 | ||||||||
\(245\) | −8.19256e7 | −0.355908 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.14079e8 | −1.32617 | ||||||||
\(248\) | −1.12435e8 | −0.468082 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.57236e8 | 1.44599 | ||||||||
\(251\) | 4.64988e8 | 1.85602 | 0.928012 | − | 0.372550i | \(-0.121517\pi\) | ||||
0.928012 | + | 0.372550i | \(0.121517\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.77112e7 | −0.146402 | ||||||||
\(254\) | −4.03699e8 | −1.54575 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.42976e8 | 1.27768 | ||||||||
\(257\) | −2.59186e8 | −0.952456 | −0.476228 | − | 0.879322i | \(-0.657996\pi\) | ||||
−0.476228 | + | 0.879322i | \(0.657996\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.36148e8 | −0.844569 | ||||||||
\(260\) | 1.23149e8 | 0.434533 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.31935e8 | 0.796732 | ||||||||
\(263\) | 2.19827e8 | 0.745137 | 0.372569 | − | 0.928005i | \(-0.378477\pi\) | ||||
0.372569 | + | 0.928005i | \(0.378477\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.16091e7 | 0.0383211 | ||||||||
\(266\) | 9.12296e8 | 2.97201 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.79704e8 | 0.570277 | ||||||||
\(269\) | −5.19950e8 | −1.62865 | −0.814327 | − | 0.580407i | \(-0.802893\pi\) | ||||
−0.814327 | + | 0.580407i | \(0.802893\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.80890e8 | 0.857323 | 0.428661 | − | 0.903465i | \(-0.358985\pi\) | ||||
0.428661 | + | 0.903465i | \(0.358985\pi\) | |||||||
\(272\) | 5.19110e8 | 1.56411 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.36463e8 | 1.28180 | ||||||||
\(275\) | −1.05452e8 | −0.305766 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.46843e8 | 0.697818 | 0.348909 | − | 0.937157i | \(-0.386552\pi\) | ||||
0.348909 | + | 0.937157i | \(0.386552\pi\) | |||||||
\(278\) | 3.66686e8 | 1.02362 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9.27495e7 | 0.252498 | ||||||||
\(281\) | −1.74389e8 | −0.468863 | −0.234432 | − | 0.972133i | \(-0.575323\pi\) | ||||
−0.234432 | + | 0.972133i | \(0.575323\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.30249e8 | −1.39068 | −0.695341 | − | 0.718680i | \(-0.744746\pi\) | ||||
−0.695341 | + | 0.718680i | \(0.744746\pi\) | |||||||
\(284\) | −3.63033e8 | −0.940441 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.72950e8 | −0.689925 | ||||||||
\(287\) | −3.32696e8 | −0.830731 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.31214e8 | 0.807172 | ||||||||
\(290\) | 4.22376e8 | 1.01697 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.37116e7 | −0.102744 | ||||||||
\(293\) | −2.11533e8 | −0.491294 | −0.245647 | − | 0.969359i | \(-0.579000\pi\) | ||||
−0.245647 | + | 0.969359i | \(0.579000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.16728e7 | 0.0718305 | ||||||||
\(296\) | 8.56736e7 | 0.192011 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.85059e8 | −0.623990 | ||||||||
\(299\) | 6.90633e7 | 0.149416 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.75266e7 | −0.184994 | ||||||||
\(302\) | −8.01153e8 | −1.67375 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.04246e9 | −2.12816 | ||||||||
\(305\) | 3.49328e8 | 0.704991 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.83496e8 | −0.756444 | −0.378222 | − | 0.925715i | \(-0.623464\pi\) | ||||
−0.378222 | + | 0.925715i | \(0.623464\pi\) | |||||||
\(308\) | 3.50920e8 | 0.684353 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.99937e8 | −1.71572 | ||||||||
\(311\) | −2.71805e8 | −0.512386 | −0.256193 | − | 0.966626i | \(-0.582468\pi\) | ||||
−0.256193 | + | 0.966626i | \(0.582468\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.82814e8 | 0.521309 | 0.260655 | − | 0.965432i | \(-0.416062\pi\) | ||||
0.260655 | + | 0.965432i | \(0.416062\pi\) | |||||||
\(314\) | −8.79065e8 | −1.60239 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.56250e8 | −1.34822 | ||||||||
\(317\) | −1.50905e8 | −0.266070 | −0.133035 | − | 0.991111i | \(-0.542472\pi\) | ||||
−0.133035 | + | 0.991111i | \(0.542472\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.14363e8 | −0.714683 | ||||||||
\(320\) | 2.45321e8 | 0.418514 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.00606e8 | −0.334849 | ||||||||
\(323\) | −1.48917e9 | −2.45887 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.93122e8 | 0.312061 | ||||||||
\(326\) | 1.49392e9 | 2.38818 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.20701e8 | 0.188865 | ||||||||
\(329\) | −2.58749e8 | −0.400583 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.82795e8 | 0.731754 | 0.365877 | − | 0.930663i | \(-0.380769\pi\) | ||||
0.365877 | + | 0.930663i | \(0.380769\pi\) | |||||||
\(332\) | −5.59439e8 | −0.839015 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.00551e8 | −0.735082 | ||||||||
\(335\) | −3.72952e8 | −0.541996 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.19140e8 | −0.738891 | −0.369445 | − | 0.929252i | \(-0.620452\pi\) | ||||
−0.369445 | + | 0.929252i | \(0.620452\pi\) | |||||||
\(338\) | −4.51019e8 | −0.635311 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.83895e8 | 0.805672 | ||||||||
\(341\) | 8.82863e8 | 1.20574 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.79073e8 | −0.641021 | ||||||||
\(344\) | 3.17543e7 | 0.0420580 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.39689e9 | 1.81300 | ||||||||
\(347\) | −2.17439e8 | −0.279373 | −0.139686 | − | 0.990196i | \(-0.544609\pi\) | ||||
−0.139686 | + | 0.990196i | \(0.544609\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.23345e8 | −0.155322 | −0.0776609 | − | 0.996980i | \(-0.524745\pi\) | ||||
−0.0776609 | + | 0.996980i | \(0.524745\pi\) | |||||||
\(350\) | −5.60954e8 | −0.699341 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.45629e8 | −0.911221 | ||||||||
\(353\) | −3.57356e8 | −0.432404 | −0.216202 | − | 0.976349i | \(-0.569367\pi\) | ||||
−0.216202 | + | 0.976349i | \(0.569367\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.53426e8 | 0.893802 | ||||||||
\(356\) | 3.59517e8 | 0.422322 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.24579e9 | −1.43501 | ||||||||
\(359\) | 2.89591e8 | 0.330335 | 0.165168 | − | 0.986266i | \(-0.447184\pi\) | ||||
0.165168 | + | 0.986266i | \(0.447184\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.09664e9 | 2.34557 | ||||||||
\(362\) | −6.86850e8 | −0.760995 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.42666e8 | −0.698442 | ||||||||
\(365\) | 9.07177e7 | 0.0976488 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.92000e8 | −0.941963 | −0.470981 | − | 0.882143i | \(-0.656100\pi\) | ||||
−0.470981 | + | 0.882143i | \(0.656100\pi\) | |||||||
\(368\) | 2.29229e8 | 0.239774 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.85735e8 | 0.703802 | ||||||||
\(371\) | −6.05834e7 | −0.0615950 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.71138e9 | 1.70752 | 0.853761 | − | 0.520665i | \(-0.174316\pi\) | ||||
0.853761 | + | 0.520665i | \(0.174316\pi\) | |||||||
\(374\) | −1.29416e9 | −1.27920 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.38732e7 | 0.0910718 | ||||||||
\(377\) | 7.58854e8 | 0.729396 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.74180e7 | 0.0447410 | 0.0223705 | − | 0.999750i | \(-0.492879\pi\) | ||||
0.0223705 | + | 0.999750i | \(0.492879\pi\) | |||||||
\(380\) | −1.17256e9 | −1.09621 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.84267e9 | 1.69132 | ||||||||
\(383\) | 3.02938e8 | 0.275523 | 0.137761 | − | 0.990465i | \(-0.456009\pi\) | ||||
0.137761 | + | 0.990465i | \(0.456009\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.28287e8 | −0.650414 | ||||||||
\(386\) | 2.12703e9 | 1.88243 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.12182e8 | −0.184416 | ||||||||
\(389\) | −2.48110e8 | −0.213708 | −0.106854 | − | 0.994275i | \(-0.534078\pi\) | ||||
−0.106854 | + | 0.994275i | \(0.534078\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.27455e8 | 0.277034 | ||||||||
\(392\) | −1.55109e8 | −0.130058 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.61601e8 | 0.709691 | ||||||||
\(395\) | 1.56950e9 | 1.28136 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.17389e9 | −0.941589 | −0.470794 | − | 0.882243i | \(-0.656033\pi\) | ||||
−0.470794 | + | 0.882243i | \(0.656033\pi\) | |||||||
\(398\) | 4.99270e8 | 0.396958 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.40993e8 | 0.500776 | ||||||||
\(401\) | 4.69179e8 | 0.363357 | 0.181679 | − | 0.983358i | \(-0.441847\pi\) | ||||
0.181679 | + | 0.983358i | \(0.441847\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.61686e9 | −1.23056 | ||||||||
\(404\) | −1.62578e9 | −1.22667 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.20422e9 | −1.63461 | ||||||||
\(407\) | −6.72726e8 | −0.494604 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.36052e9 | −1.70599 | −0.852995 | − | 0.521918i | \(-0.825217\pi\) | ||||
−0.852995 | + | 0.521918i | \(0.825217\pi\) | |||||||
\(410\) | 9.66094e8 | 0.692271 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.16272e9 | −0.819096 | ||||||||
\(413\) | −1.65288e8 | −0.115456 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.16104e9 | 0.797406 | ||||||||
\(416\) | 1.36553e9 | 0.929981 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.59890e9 | 1.74049 | ||||||||
\(419\) | 2.55941e9 | 1.69977 | 0.849886 | − | 0.526967i | \(-0.176671\pi\) | ||||
0.849886 | + | 0.526967i | \(0.176671\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.64111e7 | −0.0237819 | −0.0118909 | − | 0.999929i | \(-0.503785\pi\) | ||||
−0.0118909 | + | 0.999929i | \(0.503785\pi\) | |||||||
\(422\) | −3.56252e9 | −2.30762 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.19794e7 | 0.0140035 | ||||||||
\(425\) | 9.15662e8 | 0.578594 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.82301e9 | −1.13316 | ||||||||
\(428\) | −5.21543e8 | −0.321542 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.54163e8 | 0.154160 | ||||||||
\(431\) | 1.88575e9 | 1.13452 | 0.567262 | − | 0.823538i | \(-0.308003\pi\) | ||||
0.567262 | + | 0.823538i | \(0.308003\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.74195e8 | −0.280705 | −0.140352 | − | 0.990102i | \(-0.544824\pi\) | ||||
−0.140352 | + | 0.990102i | \(0.544824\pi\) | |||||||
\(434\) | 4.69643e9 | 2.75774 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.13958e9 | −1.23631 | ||||||||
\(437\) | −6.57588e8 | −0.376937 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.83494e9 | 1.03513 | 0.517565 | − | 0.855644i | \(-0.326838\pi\) | ||||
0.517565 | + | 0.855644i | \(0.326838\pi\) | |||||||
\(440\) | 2.64220e8 | 0.147870 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.37009e9 | 1.30553 | ||||||||
\(443\) | −2.78161e9 | −1.52014 | −0.760070 | − | 0.649841i | \(-0.774836\pi\) | ||||
−0.760070 | + | 0.649841i | \(0.774836\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.46129e8 | −0.401378 | ||||||||
\(446\) | 1.04098e9 | 0.555609 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.28024e9 | −0.672694 | ||||||||
\(449\) | 2.43689e9 | 1.27050 | 0.635250 | − | 0.772307i | \(-0.280897\pi\) | ||||
0.635250 | + | 0.772307i | \(0.280897\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.47766e8 | −0.486500 | ||||||||
\(452\) | 1.46419e9 | 0.745782 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.06056e9 | 2.53807 | ||||||||
\(455\) | 1.33377e9 | 0.663805 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.65375e9 | 1.79074 | 0.895369 | − | 0.445324i | \(-0.146912\pi\) | ||||
0.895369 | + | 0.445324i | \(0.146912\pi\) | |||||||
\(458\) | 4.67990e9 | 2.27618 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.57837e8 | 0.123507 | ||||||||
\(461\) | 1.07049e9 | 0.508897 | 0.254449 | − | 0.967086i | \(-0.418106\pi\) | ||||
0.254449 | + | 0.967086i | \(0.418106\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.98983e9 | 1.86819 | 0.934095 | − | 0.357025i | \(-0.116209\pi\) | ||||
0.934095 | + | 0.357025i | \(0.116209\pi\) | |||||||
\(464\) | 2.51872e9 | 1.17049 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.39038e9 | −1.09425 | ||||||||
\(467\) | 3.19032e9 | 1.44952 | 0.724762 | − | 0.688999i | \(-0.241950\pi\) | ||||
0.724762 | + | 0.688999i | \(0.241950\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.94629e9 | 0.871171 | ||||||||
\(470\) | 7.51365e8 | 0.333817 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.99659e7 | 0.0262487 | ||||||||
\(473\) | −2.49341e8 | −0.108338 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.83881e9 | −0.787244 | ||||||||
\(476\) | −3.04712e9 | −1.29499 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.79886e9 | 1.17215 | ||||||||
\(479\) | 2.57106e9 | 1.06890 | 0.534450 | − | 0.845200i | \(-0.320519\pi\) | ||||
0.534450 | + | 0.845200i | \(0.320519\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.23201e9 | 0.504787 | ||||||||
\(482\) | 7.26734e8 | 0.295604 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.81084e8 | −0.393321 | ||||||||
\(485\) | 4.40356e8 | 0.175270 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.60295e9 | 1.02121 | 0.510604 | − | 0.859816i | \(-0.329422\pi\) | ||||
0.510604 | + | 0.859816i | \(0.329422\pi\) | |||||||
\(488\) | 6.61381e8 | 0.257622 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.24150e9 | −0.476718 | ||||||||
\(491\) | −1.12697e9 | −0.429662 | −0.214831 | − | 0.976651i | \(-0.568920\pi\) | ||||
−0.214831 | + | 0.976651i | \(0.568920\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.59801e9 | 1.35238 | ||||||||
\(494\) | −4.75956e9 | −1.77633 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.36653e9 | −1.97473 | ||||||||
\(497\) | −3.93184e9 | −1.43664 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.16790e9 | −1.50164 | −0.750820 | − | 0.660507i | \(-0.770341\pi\) | ||||
−0.750820 | + | 0.660507i | \(0.770341\pi\) | |||||||
\(500\) | 2.39614e9 | 0.857268 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.04644e9 | 2.48603 | ||||||||
\(503\) | −4.24704e9 | −1.48799 | −0.743993 | − | 0.668187i | \(-0.767070\pi\) | ||||
−0.743993 | + | 0.668187i | \(0.767070\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.37409e9 | 1.16583 | ||||||||
\(506\) | −5.71476e8 | −0.196097 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.70778e9 | −0.916412 | ||||||||
\(509\) | −4.51429e9 | −1.51732 | −0.758661 | − | 0.651486i | \(-0.774146\pi\) | ||||
−0.758661 | + | 0.651486i | \(0.774146\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.73421e8 | −0.156955 | ||||||||
\(512\) | 3.55781e9 | 1.17149 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.92771e9 | −1.27576 | ||||||||
\(515\) | 2.41307e9 | 0.778475 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.37110e8 | −0.234593 | ||||||||
\(518\) | −3.57859e9 | −1.13125 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.83886e8 | −0.150915 | ||||||||
\(521\) | 1.82834e9 | 0.566402 | 0.283201 | − | 0.959061i | \(-0.408604\pi\) | ||||
0.283201 | + | 0.959061i | \(0.408604\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.74437e8 | −0.267284 | −0.133642 | − | 0.991030i | \(-0.542667\pi\) | ||||
−0.133642 | + | 0.991030i | \(0.542667\pi\) | |||||||
\(524\) | 1.55569e9 | 0.472350 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.33127e9 | 0.998066 | ||||||||
\(527\) | −7.66612e9 | −2.28160 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.26023e9 | −0.957531 | ||||||||
\(530\) | 1.75924e8 | 0.0513288 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.11916e9 | 1.76198 | ||||||||
\(533\) | 1.73572e9 | 0.496516 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.08239e9 | 0.305596 | ||||||||
\(536\) | −7.06108e8 | −0.198059 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.87934e9 | −2.18148 | ||||||||
\(539\) | 1.21795e9 | 0.335018 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.52769e9 | 1.22938 | 0.614690 | − | 0.788769i | \(-0.289281\pi\) | ||||
0.614690 | + | 0.788769i | \(0.289281\pi\) | |||||||
\(542\) | 4.25662e9 | 1.14833 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.47448e9 | 1.72429 | ||||||||
\(545\) | 4.44041e9 | 1.17499 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.38403e9 | 0.622811 | 0.311406 | − | 0.950277i | \(-0.399200\pi\) | ||||
0.311406 | + | 0.950277i | \(0.399200\pi\) | |||||||
\(548\) | 2.92755e9 | 0.759927 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.59802e9 | −0.409555 | ||||||||
\(551\) | −7.22545e9 | −1.84007 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.19061e9 | −2.05958 | ||||||||
\(554\) | 3.74067e9 | 0.934685 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.45952e9 | 0.606860 | ||||||||
\(557\) | 2.04626e9 | 0.501727 | 0.250864 | − | 0.968022i | \(-0.419285\pi\) | ||||
0.250864 | + | 0.968022i | \(0.419285\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.56638e8 | 0.110568 | ||||||||
\(560\) | 4.42693e9 | 1.06523 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.64269e9 | −0.628014 | ||||||||
\(563\) | −3.85093e9 | −0.909465 | −0.454733 | − | 0.890628i | \(-0.650265\pi\) | ||||
−0.454733 | + | 0.890628i | \(0.650265\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.03873e9 | −0.708797 | ||||||||
\(566\) | −8.03541e9 | −1.86273 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.42646e9 | 0.326618 | ||||||||
\(569\) | 1.30991e9 | 0.298091 | 0.149045 | − | 0.988830i | \(-0.452380\pi\) | ||||
0.149045 | + | 0.988830i | \(0.452380\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.44368e9 | 0.774098 | 0.387049 | − | 0.922059i | \(-0.373494\pi\) | ||||
0.387049 | + | 0.922059i | \(0.373494\pi\) | |||||||
\(572\) | −1.83079e9 | −0.409028 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.04168e9 | −1.11271 | ||||||||
\(575\) | 4.04339e8 | 0.0886969 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.53520e9 | 0.549411 | 0.274706 | − | 0.961528i | \(-0.411420\pi\) | ||||
0.274706 | + | 0.961528i | \(0.411420\pi\) | |||||||
\(578\) | 5.01922e9 | 1.08116 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.83306e9 | 0.602917 | ||||||||
\(581\) | −6.05904e9 | −1.28170 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.72587e8 | −0.0360718 | ||||||||
\(584\) | 1.71755e8 | 0.0356833 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.20558e9 | −0.658059 | ||||||||
\(587\) | 7.98017e9 | 1.62847 | 0.814233 | − | 0.580539i | \(-0.197158\pi\) | ||||
0.814233 | + | 0.580539i | \(0.197158\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.53949e10 | 3.10437 | ||||||||
\(590\) | 4.79970e8 | 0.0962127 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.08920e9 | 0.810050 | ||||||||
\(593\) | −4.65675e8 | −0.0917047 | −0.0458523 | − | 0.998948i | \(-0.514600\pi\) | ||||
−0.0458523 | + | 0.998948i | \(0.514600\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.32390e9 | 1.23077 | ||||||||
\(596\) | −1.91201e9 | −0.369938 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.04659e9 | 0.200134 | ||||||||
\(599\) | −6.41918e9 | −1.22035 | −0.610177 | − | 0.792265i | \(-0.708902\pi\) | ||||
−0.610177 | + | 0.792265i | \(0.708902\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.93318e9 | −1.11488 | −0.557438 | − | 0.830219i | \(-0.688216\pi\) | ||||
−0.557438 | + | 0.830219i | \(0.688216\pi\) | |||||||
\(602\) | −1.32638e9 | −0.247788 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.37368e9 | −0.992299 | ||||||||
\(605\) | 2.03611e9 | 0.373816 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.51996e9 | −1.54624 | −0.773121 | − | 0.634259i | \(-0.781305\pi\) | ||||
−0.773121 | + | 0.634259i | \(0.781305\pi\) | |||||||
\(608\) | −1.30019e10 | −2.34609 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.29373e9 | 0.944293 | ||||||||
\(611\) | 1.34993e9 | 0.239423 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.16503e9 | 0.905652 | 0.452826 | − | 0.891599i | \(-0.350416\pi\) | ||||
0.452826 | + | 0.891599i | \(0.350416\pi\) | |||||||
\(614\) | −5.81152e9 | −1.01321 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.37886e9 | −0.237678 | ||||||||
\(617\) | 2.47374e9 | 0.423991 | 0.211995 | − | 0.977271i | \(-0.432004\pi\) | ||||
0.211995 | + | 0.977271i | \(0.432004\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.19636e9 | −0.880607 | −0.440304 | − | 0.897849i | \(-0.645129\pi\) | ||||
−0.440304 | + | 0.897849i | \(0.645129\pi\) | |||||||
\(620\) | −6.03627e9 | −1.01718 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.11895e9 | −0.686309 | ||||||||
\(623\) | 3.89376e9 | 0.645151 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.34590e9 | −0.384352 | ||||||||
\(626\) | 4.28577e9 | 0.698263 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.89627e9 | −0.949989 | ||||||||
\(629\) | 5.84144e9 | 0.935929 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.50866e9 | 0.714405 | 0.357203 | − | 0.934027i | \(-0.383731\pi\) | ||||
0.357203 | + | 0.934027i | \(0.383731\pi\) | |||||||
\(632\) | 2.97152e9 | 0.468241 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.28681e9 | −0.356384 | ||||||||
\(635\) | 5.61964e9 | 0.870965 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.23052e9 | −0.341915 | ||||||||
\(638\) | −6.27926e9 | −0.957274 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.70223e9 | −0.407466 | ||||||||
\(641\) | 7.93187e8 | 0.118952 | 0.0594761 | − | 0.998230i | \(-0.481057\pi\) | ||||
0.0594761 | + | 0.998230i | \(0.481057\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.11969e10 | −1.66095 | −0.830477 | − | 0.557053i | \(-0.811932\pi\) | ||||
−0.830477 | + | 0.557053i | \(0.811932\pi\) | |||||||
\(644\) | −1.34555e9 | −0.198518 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.25669e10 | −3.29350 | ||||||||
\(647\) | −1.19259e10 | −1.73111 | −0.865554 | − | 0.500815i | \(-0.833034\pi\) | ||||
−0.865554 | + | 0.500815i | \(0.833034\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.70864e8 | −0.0676144 | ||||||||
\(650\) | 2.92657e9 | 0.417986 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.00204e10 | 1.41585 | ||||||||
\(653\) | 2.22608e9 | 0.312857 | 0.156428 | − | 0.987689i | \(-0.450002\pi\) | ||||
0.156428 | + | 0.987689i | \(0.450002\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.22863e9 | −0.448925 | ||||||||
\(656\) | 5.76104e9 | 0.796778 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.92109e9 | −0.536557 | ||||||||
\(659\) | 8.32960e7 | 0.0113377 | 0.00566885 | − | 0.999984i | \(-0.498196\pi\) | ||||
0.00566885 | + | 0.999984i | \(0.498196\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.64097e9 | 0.894389 | 0.447194 | − | 0.894437i | \(-0.352423\pi\) | ||||
0.447194 | + | 0.894437i | \(0.352423\pi\) | |||||||
\(662\) | 7.31629e9 | 0.980140 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.19820e9 | 0.291392 | ||||||||
\(665\) | −1.26995e10 | −1.67460 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.58881e9 | 0.207316 | ||||||||
\(668\) | −3.35741e9 | −0.435800 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.65172e9 | −0.725970 | ||||||||
\(671\) | −5.19329e9 | −0.663612 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.72281e9 | 0.470780 | 0.235390 | − | 0.971901i | \(-0.424363\pi\) | ||||
0.235390 | + | 0.971901i | \(0.424363\pi\) | |||||||
\(674\) | −7.86707e9 | −0.989699 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.02518e9 | −0.376649 | ||||||||
\(677\) | −1.49598e10 | −1.85296 | −0.926480 | − | 0.376343i | \(-0.877181\pi\) | ||||
−0.926480 | + | 0.376343i | \(0.877181\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.29805e9 | −0.281719 | ||||||||
\(680\) | −2.29429e9 | −0.279812 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.33789e10 | 1.61501 | ||||||||
\(683\) | −6.36282e9 | −0.764148 | −0.382074 | − | 0.924132i | \(-0.624790\pi\) | ||||
−0.382074 | + | 0.924132i | \(0.624790\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.07573e9 | −0.722240 | ||||||||
\(686\) | −7.25989e9 | −0.858609 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.51563e9 | 0.177433 | ||||||||
\(689\) | 3.16071e8 | 0.0368144 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.18625e10 | 1.36774 | 0.683870 | − | 0.729604i | \(-0.260296\pi\) | ||||
0.683870 | + | 0.729604i | \(0.260296\pi\) | |||||||
\(692\) | 9.36957e9 | 1.07485 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.29507e9 | −0.374203 | ||||||||
\(695\) | −5.10441e9 | −0.576764 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.22969e9 | 0.920595 | ||||||||
\(698\) | −1.86917e9 | −0.208044 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.76256e9 | −0.414611 | ||||||||
\(701\) | −8.69584e9 | −0.953451 | −0.476725 | − | 0.879052i | \(-0.658176\pi\) | ||||
−0.476725 | + | 0.879052i | \(0.658176\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.17306e10 | −1.27344 | ||||||||
\(704\) | −3.64707e9 | −0.393949 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.41539e9 | −0.579179 | ||||||||
\(707\) | −1.76081e10 | −1.87389 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.50844e9 | −0.685828 | −0.342914 | − | 0.939367i | \(-0.611414\pi\) | ||||
−0.342914 | + | 0.939367i | \(0.611414\pi\) | |||||||
\(710\) | 1.14174e10 | 1.19719 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.41264e9 | −0.146674 | ||||||||
\(713\) | −3.38521e9 | −0.349762 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.79957e9 | 0.388743 | ||||||||
\(716\) | −8.35606e9 | −0.850758 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.38847e9 | 0.442464 | ||||||||
\(719\) | 3.90453e9 | 0.391757 | 0.195879 | − | 0.980628i | \(-0.437244\pi\) | ||||
0.195879 | + | 0.980628i | \(0.437244\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.25929e10 | −1.25127 | ||||||||
\(722\) | 3.17725e10 | 3.14175 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.60700e9 | −0.451163 | ||||||||
\(725\) | 4.44280e9 | 0.432986 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.72837e10 | −1.66827 | −0.834133 | − | 0.551563i | \(-0.814032\pi\) | ||||
−0.834133 | + | 0.551563i | \(0.814032\pi\) | |||||||
\(728\) | 2.52522e9 | 0.242571 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.37474e9 | 0.130795 | ||||||||
\(731\) | 2.16509e9 | 0.205005 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.26113e9 | 0.774775 | 0.387387 | − | 0.921917i | \(-0.373378\pi\) | ||||
0.387387 | + | 0.921917i | \(0.373378\pi\) | |||||||
\(734\) | −1.35174e10 | −1.26170 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.85901e9 | 0.264328 | ||||||||
\(737\) | 5.54450e9 | 0.510183 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.43474e9 | 0.586510 | 0.293255 | − | 0.956034i | \(-0.405261\pi\) | ||||
0.293255 | + | 0.956034i | \(0.405261\pi\) | |||||||
\(740\) | 4.59952e9 | 0.417255 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.18083e8 | −0.0825027 | ||||||||
\(743\) | −9.72354e9 | −0.869689 | −0.434844 | − | 0.900506i | \(-0.643197\pi\) | ||||
−0.434844 | + | 0.900506i | \(0.643197\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.96813e9 | 0.351592 | ||||||||
\(746\) | 2.59344e10 | 2.28712 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.68048e9 | −0.758383 | ||||||||
\(749\) | −5.64860e9 | −0.491196 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.14363e10 | −0.985252 | −0.492626 | − | 0.870241i | \(-0.663963\pi\) | ||||
−0.492626 | + | 0.870241i | \(0.663963\pi\) | |||||||
\(752\) | 4.48056e9 | 0.384211 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.14997e10 | 0.976982 | ||||||||
\(755\) | 1.11524e10 | 0.943088 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.15016e9 | −0.599073 | −0.299537 | − | 0.954085i | \(-0.596832\pi\) | ||||
−0.299537 | + | 0.954085i | \(0.596832\pi\) | |||||||
\(758\) | 7.18573e8 | 0.0599278 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.60733e9 | 0.380717 | ||||||||
\(761\) | −3.88824e9 | −0.319821 | −0.159910 | − | 0.987132i | \(-0.551121\pi\) | ||||
−0.159910 | + | 0.987132i | \(0.551121\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.31728e10 | −1.88861 | ||||||||
\(764\) | 1.23596e10 | 1.00271 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.59073e9 | 0.369046 | ||||||||
\(767\) | 8.62330e8 | 0.0690064 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.58580e10 | −1.25750 | −0.628748 | − | 0.777609i | \(-0.716432\pi\) | ||||
−0.628748 | + | 0.777609i | \(0.716432\pi\) | |||||||
\(770\) | −1.10365e10 | −0.871191 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.42669e10 | 1.11601 | ||||||||
\(773\) | 6.91144e9 | 0.538196 | 0.269098 | − | 0.963113i | \(-0.413274\pi\) | ||||
0.269098 | + | 0.963113i | \(0.413274\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.46606e9 | −0.730488 | ||||||||
\(776\) | 8.33725e8 | 0.0640482 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.75987e9 | −0.286249 | ||||||||
\(779\) | −1.65267e10 | −1.25258 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.12008e10 | −0.841340 | ||||||||
\(782\) | 4.96227e9 | 0.371071 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.40336e9 | −0.548684 | ||||||||
\(785\) | 1.22369e10 | 0.902877 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.31218e9 | −0.607860 | −0.303930 | − | 0.952694i | \(-0.598299\pi\) | ||||
−0.303930 | + | 0.952694i | \(0.598299\pi\) | |||||||
\(788\) | 5.77913e9 | 0.420747 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.37842e10 | 1.71630 | ||||||||
\(791\) | 1.58580e10 | 1.13928 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.51087e9 | 0.677274 | ||||||||
\(794\) | −1.77892e10 | −1.26120 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.34882e9 | 0.235340 | ||||||||
\(797\) | −2.22972e10 | −1.56008 | −0.780038 | − | 0.625733i | \(-0.784800\pi\) | ||||
−0.780038 | + | 0.625733i | \(0.784800\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.40051e9 | 0.443916 | ||||||||
\(800\) | 7.99464e9 | 0.552057 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.10996e9 | 0.486695 | ||||||||
\(803\) | −1.34866e9 | −0.0919172 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.79251e9 | 0.188673 | ||||||||
\(806\) | −2.45019e10 | −1.64826 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.38814e9 | 0.426025 | ||||||||
\(809\) | −1.32718e10 | −0.881275 | −0.440638 | − | 0.897685i | \(-0.645248\pi\) | ||||
−0.440638 | + | 0.897685i | \(0.645248\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.23818e9 | 0.279002 | 0.139501 | − | 0.990222i | \(-0.455450\pi\) | ||||
0.139501 | + | 0.990222i | \(0.455450\pi\) | |||||||
\(812\) | −1.47847e10 | −0.969092 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.01945e10 | −0.662492 | ||||||||
\(815\) | −2.07960e10 | −1.34564 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.34789e9 | −0.278934 | ||||||||
\(818\) | −3.57714e10 | −2.28507 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.48001e9 | 0.410419 | ||||||||
\(821\) | 1.61244e10 | 1.01691 | 0.508455 | − | 0.861089i | \(-0.330217\pi\) | ||||
0.508455 | + | 0.861089i | \(0.330217\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.67540e9 | −0.104766 | −0.0523829 | − | 0.998627i | \(-0.516682\pi\) | ||||
−0.0523829 | + | 0.998627i | \(0.516682\pi\) | |||||||
\(824\) | 4.56865e9 | 0.284474 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.50478e9 | −0.154646 | ||||||||
\(827\) | 2.26903e10 | 1.39499 | 0.697496 | − | 0.716588i | \(-0.254297\pi\) | ||||
0.697496 | + | 0.716588i | \(0.254297\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.14017e10 | −1.30469 | −0.652345 | − | 0.757922i | \(-0.726215\pi\) | ||||
−0.652345 | + | 0.757922i | \(0.726215\pi\) | |||||||
\(830\) | 1.75945e10 | 1.06808 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.67916e9 | 0.402059 | ||||||||
\(833\) | −1.05758e10 | −0.633948 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.96786e9 | 0.414187 | ||||||||
\(836\) | 1.74319e10 | 1.03187 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.87854e10 | 2.27674 | ||||||||
\(839\) | −3.21757e10 | −1.88088 | −0.940439 | − | 0.339962i | \(-0.889586\pi\) | ||||
−0.940439 | + | 0.339962i | \(0.889586\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.07698e8 | 0.0120406 | ||||||||
\(842\) | −5.51774e8 | −0.0318544 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.38953e10 | −1.36809 | ||||||||
\(845\) | 6.27835e9 | 0.357970 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.06257e10 | −0.600848 | ||||||||
\(848\) | 1.04908e9 | 0.0590775 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.38760e10 | 0.774992 | ||||||||
\(851\) | 2.57947e9 | 0.143475 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.66660e9 | −0.478109 | −0.239055 | − | 0.971006i | \(-0.576838\pi\) | ||||
−0.239055 | + | 0.971006i | \(0.576838\pi\) | |||||||
\(854\) | −2.76259e10 | −1.51780 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.04929e9 | 0.111672 | ||||||||
\(857\) | −4.64158e9 | −0.251903 | −0.125951 | − | 0.992036i | \(-0.540198\pi\) | ||||
−0.125951 | + | 0.992036i | \(0.540198\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.96063e10 | 1.05541 | 0.527703 | − | 0.849429i | \(-0.323053\pi\) | ||||
0.527703 | + | 0.849429i | \(0.323053\pi\) | |||||||
\(860\) | 1.70478e9 | 0.0913954 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.85767e10 | 1.51963 | ||||||||
\(863\) | −2.94733e10 | −1.56096 | −0.780478 | − | 0.625183i | \(-0.785024\pi\) | ||||
−0.780478 | + | 0.625183i | \(0.785024\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.94453e10 | −1.02155 | ||||||||
\(866\) | −7.18597e9 | −0.375987 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.15010e10 | 1.63495 | ||||||||
\(869\) | −2.33330e10 | −1.20615 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.01541e10 | −0.520686 | ||||||||
\(872\) | 8.40702e9 | 0.429372 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.96511e9 | −0.504885 | ||||||||
\(875\) | 2.59515e10 | 1.30959 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.55789e9 | −0.128051 | −0.0640256 | − | 0.997948i | \(-0.520394\pi\) | ||||
−0.0640256 | + | 0.997948i | \(0.520394\pi\) | |||||||
\(878\) | 2.78067e10 | 1.38650 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.26112e10 | 0.623831 | ||||||||
\(881\) | 2.66718e10 | 1.31412 | 0.657062 | − | 0.753837i | \(-0.271799\pi\) | ||||
0.657062 | + | 0.753837i | \(0.271799\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.99020e9 | −0.243924 | −0.121962 | − | 0.992535i | \(-0.538919\pi\) | ||||
−0.121962 | + | 0.992535i | \(0.538919\pi\) | |||||||
\(884\) | 1.58972e10 | 0.773996 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.21527e10 | −2.03614 | ||||||||
\(887\) | 2.25283e10 | 1.08392 | 0.541959 | − | 0.840405i | \(-0.317683\pi\) | ||||
0.541959 | + | 0.840405i | \(0.317683\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.93268e10 | −1.39994 | ||||||||
\(890\) | −1.13069e10 | −0.537622 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.98228e9 | 0.329398 | ||||||||
\(893\) | −1.28534e10 | −0.603999 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.73419e10 | 0.808567 | ||||||||
\(896\) | 1.41019e10 | 0.654937 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.69288e10 | 1.70176 | ||||||||
\(899\) | −3.71960e10 | −1.70741 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.49861e9 | 0.0682579 | ||||||||
\(902\) | −1.43625e10 | −0.651638 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.75321e9 | −0.259012 | ||||||||
\(905\) | 9.56121e9 | 0.428788 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.20475e10 | 0.981145 | 0.490573 | − | 0.871400i | \(-0.336788\pi\) | ||||
0.490573 | + | 0.871400i | \(0.336788\pi\) | |||||||
\(908\) | 3.39434e10 | 1.50472 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.02120e10 | 0.889127 | ||||||||
\(911\) | −4.20990e9 | −0.184484 | −0.0922418 | − | 0.995737i | \(-0.529403\pi\) | ||||
−0.0922418 | + | 0.995737i | \(0.529403\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.72607e10 | −0.750602 | ||||||||
\(914\) | 5.53690e10 | 2.39859 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.13901e10 | 1.34945 | ||||||||
\(917\) | 1.68490e10 | 0.721574 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.55285e10 | −0.659972 | −0.329986 | − | 0.943986i | \(-0.607044\pi\) | ||||
−0.329986 | + | 0.943986i | \(0.607044\pi\) | |||||||
\(920\) | −1.01311e9 | −0.0428944 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.62223e10 | 0.681637 | ||||||||
\(923\) | 2.05129e10 | 0.858661 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.21296e9 | 0.299652 | ||||||||
\(926\) | 6.04620e10 | 2.50233 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.14142e10 | 1.29035 | ||||||||
\(929\) | 2.69496e10 | 1.10280 | 0.551401 | − | 0.834240i | \(-0.314093\pi\) | ||||
0.551401 | + | 0.834240i | \(0.314093\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.12380e10 | 0.862560 | ||||||||
\(932\) | −1.60333e10 | −0.648736 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.83462e10 | 1.94155 | ||||||||
\(935\) | 1.80152e10 | 0.720772 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.04584e10 | −0.415315 | −0.207657 | − | 0.978202i | \(-0.566584\pi\) | ||||
−0.207657 | + | 0.978202i | \(0.566584\pi\) | |||||||
\(938\) | 2.94942e10 | 1.16688 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.03973e9 | 0.197906 | ||||||||
\(941\) | −2.29124e10 | −0.896412 | −0.448206 | − | 0.893930i | \(-0.647937\pi\) | ||||
−0.448206 | + | 0.893930i | \(0.647937\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.63407e9 | 0.141125 | ||||||||
\(944\) | 2.86217e9 | 0.110737 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.77852e9 | −0.145112 | ||||||||
\(947\) | 2.22008e10 | 0.849460 | 0.424730 | − | 0.905320i | \(-0.360369\pi\) | ||||
0.424730 | + | 0.905320i | \(0.360369\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.46990e9 | 0.0938096 | ||||||||
\(950\) | −2.78654e10 | −1.05447 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.19730e10 | 0.449753 | ||||||||
\(953\) | −1.45448e10 | −0.544357 | −0.272178 | − | 0.962247i | \(-0.587744\pi\) | ||||
−0.272178 | + | 0.962247i | \(0.587744\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.56506e10 | −0.952985 | ||||||||
\(956\) | 1.87732e10 | 0.694920 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.89619e10 | 1.43173 | ||||||||
\(959\) | 3.17069e10 | 1.16088 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.17393e10 | 1.88057 | ||||||||
\(962\) | 1.86700e10 | 0.676131 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.87452e9 | 0.175252 | ||||||||
\(965\) | −2.96090e10 | −1.06067 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.60488e10 | −1.63767 | −0.818833 | − | 0.574032i | \(-0.805379\pi\) | ||||
−0.818833 | + | 0.574032i | \(0.805379\pi\) | |||||||
\(968\) | 3.85496e9 | 0.136602 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.67317e9 | 0.234764 | ||||||||
\(971\) | −2.30696e10 | −0.808671 | −0.404335 | − | 0.914611i | \(-0.632497\pi\) | ||||
−0.404335 | + | 0.914611i | \(0.632497\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.66380e10 | 0.927056 | ||||||||
\(974\) | 3.94451e10 | 1.36785 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.15677e10 | 1.08685 | ||||||||
\(977\) | −5.54001e10 | −1.90055 | −0.950276 | − | 0.311408i | \(-0.899199\pi\) | ||||
−0.950276 | + | 0.311408i | \(0.899199\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.10923e10 | 0.377819 | ||||||||
\(980\) | −8.32729e9 | −0.282626 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.70781e10 | −0.575506 | ||||||||
\(983\) | 3.63783e10 | 1.22153 | 0.610766 | − | 0.791811i | \(-0.290861\pi\) | ||||
0.610766 | + | 0.791811i | \(0.290861\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.19938e10 | −0.399881 | ||||||||
\(986\) | 5.45244e10 | 1.81143 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.19244e10 | −1.05311 | ||||||||
\(989\) | 9.56063e8 | 0.0314268 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.33718e9 | 0.0436446 | 0.0218223 | − | 0.999762i | \(-0.493053\pi\) | ||||
0.0218223 | + | 0.999762i | \(0.493053\pi\) | |||||||
\(992\) | −6.69328e10 | −2.17695 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.95833e10 | −1.92430 | ||||||||
\(995\) | −6.95003e9 | −0.223669 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.40234e10 | 0.767718 | 0.383859 | − | 0.923392i | \(-0.374595\pi\) | ||||
0.383859 | + | 0.923392i | \(0.374595\pi\) | |||||||
\(998\) | −6.31605e10 | −2.01135 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 387.8.a.d.1.11 | 13 | ||
3.2 | odd | 2 | 43.8.a.b.1.3 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.8.a.b.1.3 | ✓ | 13 | 3.2 | odd | 2 | ||
387.8.a.d.1.11 | 13 | 1.1 | even | 1 | trivial |