Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,102,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 102, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 102);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 102 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.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: | \(581.406281043\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + \cdots + 14\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | multiple of \( 2^{119}\cdot 3^{56}\cdot 5^{14}\cdot 7^{7}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2} \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.42719e13\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.38447e15 | 1.49754 | 0.748768 | − | 0.662832i | \(-0.230646\pi\) | ||||
0.748768 | + | 0.662832i | \(0.230646\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.15040e30 | 1.24262 | ||||||||
\(5\) | −7.99157e34 | −0.402390 | −0.201195 | − | 0.979551i | \(-0.564482\pi\) | ||||
−0.201195 | + | 0.979551i | \(0.564482\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.14769e42 | 0.661516 | 0.330758 | − | 0.943716i | \(-0.392696\pi\) | ||||
0.330758 | + | 0.943716i | \(0.392696\pi\) | |||||||
\(8\) | 1.46670e45 | 0.363326 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.90557e50 | −0.602594 | ||||||||
\(11\) | −6.08310e52 | −1.56241 | −0.781204 | − | 0.624276i | \(-0.785394\pi\) | ||||
−0.781204 | + | 0.624276i | \(0.785394\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.09809e56 | −1.16865 | −0.584326 | − | 0.811519i | \(-0.698641\pi\) | ||||
−0.584326 | + | 0.811519i | \(0.698641\pi\) | |||||||
\(14\) | 7.50557e57 | 0.990644 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.48993e60 | −0.698522 | ||||||||
\(17\) | 1.97536e62 | 1.43872 | 0.719358 | − | 0.694640i | \(-0.244436\pi\) | ||||
0.719358 | + | 0.694640i | \(0.244436\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.54133e64 | −0.672982 | −0.336491 | − | 0.941687i | \(-0.609240\pi\) | ||||
−0.336491 | + | 0.941687i | \(0.609240\pi\) | |||||||
\(20\) | −2.51767e65 | −0.500016 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.45050e68 | −2.33976 | ||||||||
\(23\) | 6.11246e68 | 1.04462 | 0.522312 | − | 0.852754i | \(-0.325070\pi\) | ||||
0.522312 | + | 0.852754i | \(0.325070\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.30565e70 | −0.838082 | ||||||||
\(26\) | −5.00284e71 | −1.75010 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.91648e72 | 0.822010 | ||||||||
\(29\) | −7.52088e73 | −1.05967 | −0.529834 | − | 0.848101i | \(-0.677746\pi\) | ||||
−0.529834 | + | 0.848101i | \(0.677746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.26748e75 | −0.615428 | −0.307714 | − | 0.951479i | \(-0.599564\pi\) | ||||
−0.307714 | + | 0.951479i | \(0.599564\pi\) | |||||||
\(32\) | −1.44246e76 | −1.40939 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.71018e77 | 2.15453 | ||||||||
\(35\) | −2.51550e77 | −0.266187 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.84306e79 | 1.17856 | 0.589281 | − | 0.807928i | \(-0.299411\pi\) | ||||
0.589281 | + | 0.807928i | \(0.299411\pi\) | |||||||
\(38\) | −6.05972e79 | −1.00781 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.17212e80 | −0.146199 | ||||||||
\(41\) | 3.79846e81 | 1.36152 | 0.680758 | − | 0.732508i | \(-0.261650\pi\) | ||||
0.680758 | + | 0.732508i | \(0.261650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.82567e82 | −0.590563 | −0.295282 | − | 0.955410i | \(-0.595413\pi\) | ||||
−0.295282 | + | 0.955410i | \(0.595413\pi\) | |||||||
\(44\) | −1.91642e83 | −1.94147 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.45750e84 | 1.56436 | ||||||||
\(47\) | 1.21503e84 | 0.440196 | 0.220098 | − | 0.975478i | \(-0.429362\pi\) | ||||
0.220098 | + | 0.975478i | \(0.429362\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.27334e85 | −0.562397 | ||||||||
\(50\) | −7.88223e85 | −1.25506 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.60984e86 | −1.45219 | ||||||||
\(53\) | −1.92092e87 | −1.61279 | −0.806393 | − | 0.591380i | \(-0.798584\pi\) | ||||
−0.806393 | + | 0.591380i | \(0.798584\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.86136e87 | 0.628697 | ||||||||
\(56\) | 4.61670e87 | 0.240346 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.79333e89 | −1.58689 | ||||||||
\(59\) | 9.03706e88 | 0.337288 | 0.168644 | − | 0.985677i | \(-0.446061\pi\) | ||||
0.168644 | + | 0.985677i | \(0.446061\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.82351e89 | −0.680942 | −0.340471 | − | 0.940255i | \(-0.610586\pi\) | ||||
−0.340471 | + | 0.940255i | \(0.610586\pi\) | |||||||
\(62\) | −3.02228e90 | −0.921625 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.30118e91 | −1.41209 | ||||||||
\(65\) | 1.67671e91 | 0.470254 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.68394e92 | 1.02223 | 0.511116 | − | 0.859512i | \(-0.329232\pi\) | ||||
0.511116 | + | 0.859512i | \(0.329232\pi\) | |||||||
\(68\) | 6.22317e92 | 1.78777 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.99813e92 | −0.398625 | ||||||||
\(71\) | −2.66050e92 | −0.0863806 | −0.0431903 | − | 0.999067i | \(-0.513752\pi\) | ||||
−0.0431903 | + | 0.999067i | \(0.513752\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.19661e94 | −0.955316 | −0.477658 | − | 0.878546i | \(-0.658514\pi\) | ||||
−0.477658 | + | 0.878546i | \(0.658514\pi\) | |||||||
\(74\) | 4.39473e94 | 1.76494 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.00620e94 | −0.836258 | ||||||||
\(77\) | −1.91477e95 | −1.03356 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.68984e95 | 1.28482 | 0.642412 | − | 0.766360i | \(-0.277934\pi\) | ||||
0.642412 | + | 0.766360i | \(0.277934\pi\) | |||||||
\(80\) | 3.58816e95 | 0.281078 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.05733e96 | 2.03892 | ||||||||
\(83\) | 2.05551e96 | 0.250885 | 0.125443 | − | 0.992101i | \(-0.459965\pi\) | ||||
0.125443 | + | 0.992101i | \(0.459965\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.57862e97 | −0.578925 | ||||||||
\(86\) | −4.35327e97 | −0.884390 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.92207e97 | −0.567663 | ||||||||
\(89\) | 4.58460e98 | 1.64857 | 0.824283 | − | 0.566178i | \(-0.191579\pi\) | ||||
0.824283 | + | 0.566178i | \(0.191579\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.60413e98 | −0.773082 | ||||||||
\(92\) | 1.92567e99 | 1.29807 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.89721e99 | 0.659210 | ||||||||
\(95\) | 2.03092e99 | 0.270801 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.41618e99 | −0.438432 | −0.219216 | − | 0.975676i | \(-0.570350\pi\) | ||||
−0.219216 | + | 0.975676i | \(0.570350\pi\) | |||||||
\(98\) | −3.03625e100 | −0.842210 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.04141e101 | −1.04141 | ||||||||
\(101\) | 1.91765e101 | 1.16022 | 0.580110 | − | 0.814538i | \(-0.303009\pi\) | ||||
0.580110 | + | 0.814538i | \(0.303009\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.30544e101 | 1.19245 | 0.596227 | − | 0.802816i | \(-0.296666\pi\) | ||||
0.596227 | + | 0.802816i | \(0.296666\pi\) | |||||||
\(104\) | −3.07727e101 | −0.424601 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.58037e102 | −2.41521 | ||||||||
\(107\) | 2.09657e102 | 0.688064 | 0.344032 | − | 0.938958i | \(-0.388207\pi\) | ||||
0.344032 | + | 0.938958i | \(0.388207\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.37901e101 | 0.0177636 | 0.00888179 | − | 0.999961i | \(-0.497173\pi\) | ||||
0.00888179 | + | 0.999961i | \(0.497173\pi\) | |||||||
\(110\) | 1.15918e103 | 0.941497 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.41329e103 | −0.462083 | ||||||||
\(113\) | −4.37593e102 | −0.0913290 | −0.0456645 | − | 0.998957i | \(-0.514541\pi\) | ||||
−0.0456645 | + | 0.998957i | \(0.514541\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.88482e103 | −0.420346 | ||||||||
\(116\) | −2.36938e104 | −1.31676 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.15486e104 | 0.505101 | ||||||||
\(119\) | 6.21780e104 | 0.951733 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.18454e105 | 1.44112 | ||||||||
\(122\) | −2.34239e105 | −1.01973 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.99309e105 | −0.764740 | ||||||||
\(125\) | 5.79386e105 | 0.739626 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.11318e106 | −1.21018 | −0.605088 | − | 0.796159i | \(-0.706862\pi\) | ||||
−0.605088 | + | 0.796159i | \(0.706862\pi\) | |||||||
\(128\) | −1.83002e106 | −0.705265 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.99806e106 | 0.704222 | ||||||||
\(131\) | −1.48036e107 | −1.77079 | −0.885393 | − | 0.464842i | \(-0.846111\pi\) | ||||
−0.885393 | + | 0.464842i | \(0.846111\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.99929e106 | −0.445188 | ||||||||
\(134\) | 4.01531e107 | 1.53083 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.89725e107 | 0.522722 | ||||||||
\(137\) | 1.25472e108 | 1.56372 | 0.781859 | − | 0.623455i | \(-0.214272\pi\) | ||||
0.781859 | + | 0.623455i | \(0.214272\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.05964e108 | −0.635199 | −0.317599 | − | 0.948225i | \(-0.602877\pi\) | ||||
−0.317599 | + | 0.948225i | \(0.602877\pi\) | |||||||
\(140\) | −7.92483e107 | −0.330769 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.34388e107 | −0.129358 | ||||||||
\(143\) | 1.27629e109 | 1.82591 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.01037e108 | 0.426400 | ||||||||
\(146\) | −2.85327e109 | −1.43062 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.80639e109 | 1.46450 | ||||||||
\(149\) | 8.73079e109 | 1.56728 | 0.783641 | − | 0.621214i | \(-0.213360\pi\) | ||||
0.783641 | + | 0.621214i | \(0.213360\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.82348e110 | 1.66942 | 0.834708 | − | 0.550693i | \(-0.185637\pi\) | ||||
0.834708 | + | 0.550693i | \(0.185637\pi\) | |||||||
\(152\) | −3.72735e109 | −0.244512 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.56571e110 | −1.54779 | ||||||||
\(155\) | 1.01292e110 | 0.247642 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.49484e110 | 0.831067 | 0.415533 | − | 0.909578i | \(-0.363595\pi\) | ||||
0.415533 | + | 0.909578i | \(0.363595\pi\) | |||||||
\(158\) | 2.07207e111 | 1.92407 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.15275e111 | 0.567124 | ||||||||
\(161\) | 1.92401e111 | 0.691036 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.38327e111 | −0.458880 | −0.229440 | − | 0.973323i | \(-0.573689\pi\) | ||||
−0.229440 | + | 0.973323i | \(0.573689\pi\) | |||||||
\(164\) | 1.19667e112 | 1.69184 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.90130e111 | 0.375710 | ||||||||
\(167\) | −1.51500e112 | −0.857491 | −0.428746 | − | 0.903425i | \(-0.641044\pi\) | ||||
−0.428746 | + | 0.903425i | \(0.641044\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.17885e112 | 0.365747 | ||||||||
\(170\) | −3.76418e112 | −0.866961 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.75162e112 | −0.733843 | ||||||||
\(173\) | −8.48260e110 | −0.00807609 | −0.00403804 | − | 0.999992i | \(-0.501285\pi\) | ||||
−0.00403804 | + | 0.999992i | \(0.501285\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.04052e113 | −0.554405 | ||||||||
\(176\) | 2.73127e113 | 1.09138 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.09319e114 | 2.46879 | ||||||||
\(179\) | −7.70832e113 | −1.31184 | −0.655921 | − | 0.754829i | \(-0.727720\pi\) | ||||
−0.655921 | + | 0.754829i | \(0.727720\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.10499e113 | −0.884121 | −0.442060 | − | 0.896985i | \(-0.645752\pi\) | ||||
−0.442060 | + | 0.896985i | \(0.645752\pi\) | |||||||
\(182\) | −1.57474e114 | −1.15772 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.96512e113 | 0.379539 | ||||||||
\(185\) | −1.47290e114 | −0.474242 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.20163e115 | −2.24786 | ||||||||
\(188\) | 3.82785e114 | 0.546995 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.84267e114 | 0.405535 | ||||||||
\(191\) | −1.29493e115 | −0.831879 | −0.415939 | − | 0.909392i | \(-0.636547\pi\) | ||||
−0.415939 | + | 0.909392i | \(0.636547\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.90903e115 | 1.10434 | 0.552171 | − | 0.833731i | \(-0.313799\pi\) | ||||
0.552171 | + | 0.833731i | \(0.313799\pi\) | |||||||
\(194\) | −2.24526e115 | −0.656568 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.01154e115 | −0.698843 | ||||||||
\(197\) | −1.44395e115 | −0.194539 | −0.0972697 | − | 0.995258i | \(-0.531011\pi\) | ||||
−0.0972697 | + | 0.995258i | \(0.531011\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.20582e116 | 0.975440 | 0.487720 | − | 0.873000i | \(-0.337829\pi\) | ||||
0.487720 | + | 0.873000i | \(0.337829\pi\) | |||||||
\(200\) | −4.84839e115 | −0.304497 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.57259e116 | 1.73747 | ||||||||
\(203\) | −2.36734e116 | −0.700987 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.03557e116 | −0.547861 | ||||||||
\(206\) | 1.26507e117 | 1.78574 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.42028e116 | 0.816329 | ||||||||
\(209\) | 1.54591e117 | 1.05147 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.28579e116 | −0.138158 | −0.0690789 | − | 0.997611i | \(-0.522006\pi\) | ||||
−0.0690789 | + | 0.997611i | \(0.522006\pi\) | |||||||
\(212\) | −6.05166e117 | −2.00407 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.99922e117 | 1.03040 | ||||||||
\(215\) | 1.45900e117 | 0.237637 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.98964e117 | −0.407115 | ||||||||
\(218\) | 3.28822e116 | 0.0266016 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.53152e118 | 0.781229 | ||||||||
\(221\) | −4.14448e118 | −1.68136 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.08484e117 | −0.182362 | −0.0911810 | − | 0.995834i | \(-0.529064\pi\) | ||||
−0.0911810 | + | 0.995834i | \(0.529064\pi\) | |||||||
\(224\) | −4.54042e118 | −0.932333 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.04343e118 | −0.136769 | ||||||||
\(227\) | 7.11138e118 | 0.745844 | 0.372922 | − | 0.927863i | \(-0.378356\pi\) | ||||
0.372922 | + | 0.927863i | \(0.378356\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.22725e118 | −0.486722 | −0.243361 | − | 0.969936i | \(-0.578250\pi\) | ||||
−0.243361 | + | 0.969936i | \(0.578250\pi\) | |||||||
\(230\) | −1.16477e119 | −0.629484 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.10309e119 | −0.385005 | ||||||||
\(233\) | −1.44195e119 | −0.405020 | −0.202510 | − | 0.979280i | \(-0.564910\pi\) | ||||
−0.202510 | + | 0.979280i | \(0.564910\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.71003e118 | −0.177131 | ||||||||
\(236\) | 2.84704e119 | 0.419119 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.48262e120 | 1.42526 | ||||||||
\(239\) | 7.34680e119 | 0.571484 | 0.285742 | − | 0.958307i | \(-0.407760\pi\) | ||||
0.285742 | + | 0.958307i | \(0.407760\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.91398e120 | −0.977411 | −0.488706 | − | 0.872449i | \(-0.662531\pi\) | ||||
−0.488706 | + | 0.872449i | \(0.662531\pi\) | |||||||
\(242\) | 5.20899e120 | 2.15813 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.09480e120 | −0.846149 | ||||||||
\(245\) | 1.01760e120 | 0.226303 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.33193e120 | 0.786482 | ||||||||
\(248\) | −1.85902e120 | −0.223601 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.38153e121 | 1.10762 | ||||||||
\(251\) | 1.31699e121 | 0.863098 | 0.431549 | − | 0.902089i | \(-0.357967\pi\) | ||||
0.431549 | + | 0.902089i | \(0.357967\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.71827e121 | −1.63213 | ||||||||
\(254\) | −5.03881e121 | −1.81228 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.47055e121 | 0.355928 | ||||||||
\(257\) | 3.41822e121 | 0.679480 | 0.339740 | − | 0.940519i | \(-0.389661\pi\) | ||||
0.339740 | + | 0.940519i | \(0.389661\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.80137e121 | 0.779638 | ||||||||
\(260\) | 5.28230e121 | 0.584345 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.52987e122 | −2.65182 | ||||||||
\(263\) | −4.70322e121 | −0.291494 | −0.145747 | − | 0.989322i | \(-0.546559\pi\) | ||||
−0.145747 | + | 0.989322i | \(0.546559\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.53511e122 | 0.648969 | ||||||||
\(266\) | −1.90741e122 | −0.666686 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.30509e122 | 1.27024 | ||||||||
\(269\) | −3.47750e121 | −0.0689886 | −0.0344943 | − | 0.999405i | \(-0.510982\pi\) | ||||
−0.0344943 | + | 0.999405i | \(0.510982\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.93405e122 | 1.21927 | 0.609634 | − | 0.792683i | \(-0.291317\pi\) | ||||
0.609634 | + | 0.792683i | \(0.291317\pi\) | |||||||
\(272\) | −8.86921e122 | −1.00497 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.99185e123 | 2.34173 | ||||||||
\(275\) | 2.01086e123 | 1.30943 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.61374e123 | −1.18042 | −0.590208 | − | 0.807252i | \(-0.700954\pi\) | ||||
−0.590208 | + | 0.807252i | \(0.700954\pi\) | |||||||
\(278\) | −2.52667e123 | −0.951233 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.68947e122 | −0.0967127 | ||||||||
\(281\) | 7.67814e123 | 1.68108 | 0.840538 | − | 0.541753i | \(-0.182239\pi\) | ||||
0.840538 | + | 0.541753i | \(0.182239\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.67598e123 | −0.562546 | −0.281273 | − | 0.959628i | \(-0.590757\pi\) | ||||
−0.281273 | + | 0.959628i | \(0.590757\pi\) | |||||||
\(284\) | −8.38165e122 | −0.107338 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.04328e124 | 2.73437 | ||||||||
\(287\) | 1.19564e124 | 0.900665 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.01690e124 | 1.06990 | ||||||||
\(290\) | 1.43316e124 | 0.638549 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.76980e124 | −1.18709 | ||||||||
\(293\) | −1.82743e124 | −0.484201 | −0.242100 | − | 0.970251i | \(-0.577836\pi\) | ||||
−0.242100 | + | 0.970251i | \(0.577836\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.22204e123 | −0.135721 | ||||||||
\(296\) | 2.70321e124 | 0.428202 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.08183e125 | 2.34706 | ||||||||
\(299\) | −1.28245e125 | −1.22080 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.74665e124 | −0.390667 | ||||||||
\(302\) | 4.34803e125 | 2.50001 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.14104e125 | 0.470093 | ||||||||
\(305\) | 7.85053e124 | 0.274004 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.99534e125 | 1.25336 | 0.626681 | − | 0.779276i | \(-0.284413\pi\) | ||||
0.626681 | + | 0.779276i | \(0.284413\pi\) | |||||||
\(308\) | −6.03230e125 | −1.28431 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.41528e125 | 0.370853 | ||||||||
\(311\) | 1.21415e126 | 1.58443 | 0.792215 | − | 0.610243i | \(-0.208928\pi\) | ||||
0.792215 | + | 0.610243i | \(0.208928\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.93941e125 | 0.466322 | 0.233161 | − | 0.972438i | \(-0.425093\pi\) | ||||
0.233161 | + | 0.972438i | \(0.425093\pi\) | |||||||
\(314\) | 1.54868e126 | 1.24455 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.73765e126 | 1.59654 | ||||||||
\(317\) | 3.07972e126 | 1.53115 | 0.765576 | − | 0.643346i | \(-0.222454\pi\) | ||||
0.765576 | + | 0.643346i | \(0.222454\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.57503e126 | 1.65563 | ||||||||
\(320\) | 1.83900e126 | 0.568210 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.58775e126 | 1.03485 | ||||||||
\(323\) | −5.02002e126 | −0.968230 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.93556e126 | 0.979427 | ||||||||
\(326\) | −5.68283e126 | −0.687189 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.57119e126 | 0.494674 | ||||||||
\(329\) | 3.82454e126 | 0.291197 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.91257e127 | 1.63291 | 0.816456 | − | 0.577407i | \(-0.195936\pi\) | ||||
0.816456 | + | 0.577407i | \(0.195936\pi\) | |||||||
\(332\) | 6.47568e126 | 0.311754 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.61247e127 | −1.28412 | ||||||||
\(335\) | −1.34573e127 | −0.411336 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.69384e127 | 1.74114 | 0.870568 | − | 0.492047i | \(-0.163751\pi\) | ||||
0.870568 | + | 0.492047i | \(0.163751\pi\) | |||||||
\(338\) | 2.81094e127 | 0.547720 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.97329e127 | −0.719381 | ||||||||
\(341\) | 7.71024e127 | 0.961549 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.11349e128 | −1.03355 | ||||||||
\(344\) | −2.67771e127 | −0.214567 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.02265e126 | −0.0120942 | ||||||||
\(347\) | −5.05616e127 | −0.261326 | −0.130663 | − | 0.991427i | \(-0.541711\pi\) | ||||
−0.130663 | + | 0.991427i | \(0.541711\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.51214e128 | −1.35796 | −0.678981 | − | 0.734156i | \(-0.737578\pi\) | ||||
−0.678981 | + | 0.734156i | \(0.737578\pi\) | |||||||
\(350\) | −2.48108e128 | −0.830241 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.77464e128 | 2.20204 | ||||||||
\(353\) | 5.20749e127 | 0.113242 | 0.0566208 | − | 0.998396i | \(-0.481967\pi\) | ||||
0.0566208 | + | 0.998396i | \(0.481967\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.12616e127 | 0.0347587 | ||||||||
\(356\) | 1.44433e129 | 2.04853 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.83803e129 | −1.96453 | ||||||||
\(359\) | −1.83400e128 | −0.170267 | −0.0851336 | − | 0.996370i | \(-0.527132\pi\) | ||||
−0.0851336 | + | 0.996370i | \(0.527132\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.80148e128 | −0.547095 | ||||||||
\(362\) | −2.17106e129 | −1.32400 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.08057e129 | −0.960643 | ||||||||
\(365\) | 9.56277e128 | 0.384409 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.13701e129 | −0.651884 | −0.325942 | − | 0.945390i | \(-0.605681\pi\) | ||||
−0.325942 | + | 0.945390i | \(0.605681\pi\) | |||||||
\(368\) | −2.74445e129 | −0.729693 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.51208e129 | −0.710194 | ||||||||
\(371\) | −6.04644e129 | −1.06688 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.00257e129 | −0.807311 | −0.403656 | − | 0.914911i | \(-0.632261\pi\) | ||||
−0.403656 | + | 0.914911i | \(0.632261\pi\) | |||||||
\(374\) | −2.86525e130 | −3.36625 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.78209e129 | 0.159935 | ||||||||
\(377\) | 1.57795e130 | 1.23838 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.67101e129 | 0.100392 | 0.0501959 | − | 0.998739i | \(-0.484015\pi\) | ||||
0.0501959 | + | 0.998739i | \(0.484015\pi\) | |||||||
\(380\) | 6.39822e129 | 0.336502 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.08772e130 | −1.24577 | ||||||||
\(383\) | −4.14692e130 | −1.46618 | −0.733091 | − | 0.680131i | \(-0.761923\pi\) | ||||
−0.733091 | + | 0.680131i | \(0.761923\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.53020e130 | 0.415893 | ||||||||
\(386\) | 6.93649e130 | 1.65379 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.96648e130 | −0.544802 | ||||||||
\(389\) | 6.92348e130 | 1.11653 | 0.558264 | − | 0.829663i | \(-0.311468\pi\) | ||||
0.558264 | + | 0.829663i | \(0.311468\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.20743e131 | 1.50292 | ||||||||
\(392\) | −1.86761e130 | −0.204333 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.44306e130 | −0.291330 | ||||||||
\(395\) | −6.94455e130 | −0.517000 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.86213e130 | −0.511231 | −0.255616 | − | 0.966778i | \(-0.582278\pi\) | ||||
−0.255616 | + | 0.966778i | \(0.582278\pi\) | |||||||
\(398\) | 2.87523e131 | 1.46076 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.48421e131 | 0.585419 | ||||||||
\(401\) | 6.21084e129 | 0.0215953 | 0.0107977 | − | 0.999942i | \(-0.496563\pi\) | ||||
0.0107977 | + | 0.999942i | \(0.496563\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.65930e131 | 0.719221 | ||||||||
\(404\) | 6.04138e131 | 1.44171 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.64485e131 | −1.04975 | ||||||||
\(407\) | −1.12115e132 | −1.84140 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.03956e132 | 1.33297 | 0.666487 | − | 0.745517i | \(-0.267797\pi\) | ||||
0.666487 | + | 0.745517i | \(0.267797\pi\) | |||||||
\(410\) | −7.23823e131 | −0.820441 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.67143e132 | 1.48176 | ||||||||
\(413\) | 2.84458e131 | 0.223121 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.64267e131 | −0.100954 | ||||||||
\(416\) | 3.02642e132 | 1.64708 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.68619e132 | 1.57462 | ||||||||
\(419\) | 1.38531e132 | 0.524491 | 0.262246 | − | 0.965001i | \(-0.415537\pi\) | ||||
0.262246 | + | 0.965001i | \(0.415537\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.31976e132 | 0.392869 | 0.196435 | − | 0.980517i | \(-0.437064\pi\) | ||||
0.196435 | + | 0.980517i | \(0.437064\pi\) | |||||||
\(422\) | −7.83486e131 | −0.206896 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.81740e132 | −0.585967 | ||||||||
\(425\) | −6.52984e132 | −1.20576 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.09213e132 | −0.450454 | ||||||||
\(428\) | 6.60505e132 | 0.855000 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.47895e132 | 0.355870 | ||||||||
\(431\) | 1.47645e133 | 1.34313 | 0.671564 | − | 0.740946i | \(-0.265623\pi\) | ||||
0.671564 | + | 0.740946i | \(0.265623\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.39695e133 | 1.72592 | 0.862958 | − | 0.505276i | \(-0.168609\pi\) | ||||
0.862958 | + | 0.505276i | \(0.168609\pi\) | |||||||
\(434\) | −9.51319e132 | −0.609670 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.34445e131 | 0.0220733 | ||||||||
\(437\) | −1.55337e133 | −0.703013 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.80750e133 | −0.649563 | −0.324781 | − | 0.945789i | \(-0.605291\pi\) | ||||
−0.324781 | + | 0.945789i | \(0.605291\pi\) | |||||||
\(440\) | 7.13014e132 | 0.228422 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.88239e133 | −2.51789 | ||||||||
\(443\) | −5.76910e133 | −1.31135 | −0.655677 | − | 0.755041i | \(-0.727617\pi\) | ||||
−0.655677 | + | 0.755041i | \(0.727617\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.66382e133 | −0.663366 | ||||||||
\(446\) | −1.68936e133 | −0.273094 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.24339e133 | −0.934119 | ||||||||
\(449\) | 1.99115e133 | 0.229437 | 0.114718 | − | 0.993398i | \(-0.463403\pi\) | ||||
0.114718 | + | 0.993398i | \(0.463403\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.31064e134 | −2.12724 | ||||||||
\(452\) | −1.37859e133 | −0.113487 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.69569e134 | 1.11693 | ||||||||
\(455\) | 5.27774e133 | 0.311080 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.63995e133 | 0.171921 | 0.0859603 | − | 0.996299i | \(-0.472604\pi\) | ||||
0.0859603 | + | 0.996299i | \(0.472604\pi\) | |||||||
\(458\) | −1.72332e134 | −0.728884 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.53891e134 | −0.522329 | ||||||||
\(461\) | −7.99190e133 | −0.243082 | −0.121541 | − | 0.992586i | \(-0.538784\pi\) | ||||
−0.121541 | + | 0.992586i | \(0.538784\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.09340e134 | 0.756129 | 0.378064 | − | 0.925779i | \(-0.376590\pi\) | ||||
0.378064 | + | 0.925779i | \(0.376590\pi\) | |||||||
\(464\) | 3.37682e134 | 0.740202 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.43829e134 | −0.606532 | ||||||||
\(467\) | −6.56173e134 | −1.03876 | −0.519381 | − | 0.854543i | \(-0.673837\pi\) | ||||
−0.519381 | + | 0.854543i | \(0.673837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.30051e134 | 0.676222 | ||||||||
\(470\) | −2.31533e134 | −0.265259 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.32546e134 | 0.122545 | ||||||||
\(473\) | 1.11058e135 | 0.922701 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.40074e134 | 0.564014 | ||||||||
\(476\) | 1.95886e135 | 1.18264 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.75182e135 | 0.855819 | ||||||||
\(479\) | 7.37311e134 | 0.324121 | 0.162061 | − | 0.986781i | \(-0.448186\pi\) | ||||
0.162061 | + | 0.986781i | \(0.448186\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.86691e135 | −1.37733 | ||||||||
\(482\) | −4.56384e135 | −1.46371 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.88220e135 | 1.79076 | ||||||||
\(485\) | 7.52501e134 | 0.176421 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.08383e135 | 1.15868 | 0.579341 | − | 0.815085i | \(-0.303310\pi\) | ||||
0.579341 | + | 0.815085i | \(0.303310\pi\) | |||||||
\(488\) | −1.44081e135 | −0.247404 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.42644e135 | 0.338897 | ||||||||
\(491\) | 4.22617e135 | 0.532514 | 0.266257 | − | 0.963902i | \(-0.414213\pi\) | ||||
0.266257 | + | 0.963902i | \(0.414213\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.48564e136 | −1.52456 | ||||||||
\(494\) | 1.27138e136 | 1.17778 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.69091e135 | 0.429890 | ||||||||
\(497\) | −8.37441e134 | −0.0571422 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.79965e136 | 1.00256 | 0.501279 | − | 0.865286i | \(-0.332863\pi\) | ||||
0.501279 | + | 0.865286i | \(0.332863\pi\) | |||||||
\(500\) | 1.82530e136 | 0.919071 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.14033e136 | 1.29252 | ||||||||
\(503\) | 3.61622e136 | 1.34608 | 0.673041 | − | 0.739605i | \(-0.264988\pi\) | ||||
0.673041 | + | 0.739605i | \(0.264988\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.53251e136 | −0.466861 | ||||||||
\(506\) | −8.86611e136 | −2.44417 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.65737e136 | −1.50378 | ||||||||
\(509\) | 3.70155e135 | 0.0757069 | 0.0378535 | − | 0.999283i | \(-0.487948\pi\) | ||||
0.0378535 | + | 0.999283i | \(0.487948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.76654e136 | −0.631957 | ||||||||
\(512\) | 8.14614e136 | 1.23828 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.15064e136 | 1.01755 | ||||||||
\(515\) | −4.23989e136 | −0.479832 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.39117e136 | −0.687766 | ||||||||
\(518\) | 1.38332e137 | 1.16754 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.45922e136 | 0.170855 | ||||||||
\(521\) | −1.29061e137 | −0.813746 | −0.406873 | − | 0.913485i | \(-0.633381\pi\) | ||||
−0.406873 | + | 0.913485i | \(0.633381\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.43042e137 | −0.743240 | −0.371620 | − | 0.928385i | \(-0.621198\pi\) | ||||
−0.371620 | + | 0.928385i | \(0.621198\pi\) | |||||||
\(524\) | −4.66373e137 | −2.20041 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.12147e137 | −0.436523 | ||||||||
\(527\) | −2.50373e137 | −0.885425 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.12389e136 | 0.0912399 | ||||||||
\(530\) | 3.66044e137 | 0.971855 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.52010e137 | −0.553198 | ||||||||
\(533\) | −7.96952e137 | −1.59114 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.67549e137 | −0.276870 | ||||||||
\(536\) | 2.46983e137 | 0.371403 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.29201e136 | −0.103313 | ||||||||
\(539\) | 7.74587e137 | 0.878693 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.27854e136 | 0.0402563 | 0.0201282 | − | 0.999797i | \(-0.493593\pi\) | ||||
0.0201282 | + | 0.999797i | \(0.493593\pi\) | |||||||
\(542\) | 2.13030e138 | 1.82590 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.84938e138 | −2.02771 | ||||||||
\(545\) | −1.10205e136 | −0.00714789 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.81194e138 | 1.51582 | 0.757908 | − | 0.652361i | \(-0.226221\pi\) | ||||
0.757908 | + | 0.652361i | \(0.226221\pi\) | |||||||
\(548\) | 3.95288e138 | 1.94310 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.79484e138 | 1.96091 | ||||||||
\(551\) | 1.91130e138 | 0.713137 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.73529e138 | 0.849931 | ||||||||
\(554\) | −6.23240e138 | −1.76771 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.33828e138 | −0.789308 | ||||||||
\(557\) | 4.55257e138 | 0.983036 | 0.491518 | − | 0.870867i | \(-0.336442\pi\) | ||||
0.491518 | + | 0.870867i | \(0.336442\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.83043e138 | 0.690163 | ||||||||
\(560\) | 1.12944e138 | 0.185938 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.83083e139 | 2.51747 | ||||||||
\(563\) | 1.09186e139 | 1.37243 | 0.686217 | − | 0.727397i | \(-0.259270\pi\) | ||||
0.686217 | + | 0.727397i | \(0.259270\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.49705e137 | 0.0367499 | ||||||||
\(566\) | −8.76527e138 | −0.842433 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.90215e137 | −0.0313843 | ||||||||
\(569\) | −1.38183e139 | −1.01692 | −0.508460 | − | 0.861086i | \(-0.669785\pi\) | ||||
−0.508460 | + | 0.861086i | \(0.669785\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.25037e139 | −0.770750 | −0.385375 | − | 0.922760i | \(-0.625928\pi\) | ||||
−0.385375 | + | 0.922760i | \(0.625928\pi\) | |||||||
\(572\) | 4.02083e139 | 2.26891 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.85096e139 | 1.34878 | ||||||||
\(575\) | −2.02057e139 | −0.875481 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.89173e139 | −1.77862 | −0.889312 | − | 0.457301i | \(-0.848816\pi\) | ||||
−0.889312 | + | 0.457301i | \(0.848816\pi\) | |||||||
\(578\) | 4.80925e139 | 1.60222 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.89351e139 | 0.529851 | ||||||||
\(581\) | 6.47009e138 | 0.165965 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.16851e140 | 2.51983 | ||||||||
\(584\) | −1.75506e139 | −0.347091 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.35745e139 | −0.725109 | ||||||||
\(587\) | 3.73373e139 | 0.570057 | 0.285029 | − | 0.958519i | \(-0.407997\pi\) | ||||
0.285029 | + | 0.958519i | \(0.407997\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.22109e139 | 0.414172 | ||||||||
\(590\) | −1.72207e139 | −0.203248 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.27521e139 | −0.823252 | ||||||||
\(593\) | 8.44292e139 | 0.771313 | 0.385656 | − | 0.922642i | \(-0.373975\pi\) | ||||
0.385656 | + | 0.922642i | \(0.373975\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.96900e139 | −0.382968 | ||||||||
\(596\) | 2.75055e140 | 1.94753 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.05797e140 | −1.82820 | ||||||||
\(599\) | 1.37418e140 | 0.755074 | 0.377537 | − | 0.925995i | \(-0.376771\pi\) | ||||
0.377537 | + | 0.925995i | \(0.376771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.04647e140 | −0.950264 | −0.475132 | − | 0.879914i | \(-0.657600\pi\) | ||||
−0.475132 | + | 0.879914i | \(0.657600\pi\) | |||||||
\(602\) | −1.37027e140 | −0.585038 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.74469e140 | 2.07444 | ||||||||
\(605\) | −1.74580e140 | −0.579892 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.81132e140 | −0.509292 | −0.254646 | − | 0.967034i | \(-0.581959\pi\) | ||||
−0.254646 | + | 0.967034i | \(0.581959\pi\) | |||||||
\(608\) | 3.66577e140 | 0.948493 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.87194e140 | 0.410331 | ||||||||
\(611\) | −2.54925e140 | −0.514436 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.22003e139 | −0.0893139 | −0.0446570 | − | 0.999002i | \(-0.514219\pi\) | ||||
−0.0446570 | + | 0.999002i | \(0.514219\pi\) | |||||||
\(614\) | 1.19112e141 | 1.87696 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.80839e140 | −0.375518 | ||||||||
\(617\) | −4.53230e140 | −0.558365 | −0.279182 | − | 0.960238i | \(-0.590063\pi\) | ||||
−0.279182 | + | 0.960238i | \(0.590063\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.58319e140 | 0.479502 | 0.239751 | − | 0.970834i | \(-0.422934\pi\) | ||||
0.239751 | + | 0.970834i | \(0.422934\pi\) | |||||||
\(620\) | 3.19111e140 | 0.307724 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.89511e141 | 2.37274 | ||||||||
\(623\) | 1.44309e141 | 1.09055 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.40829e140 | 0.540464 | ||||||||
\(626\) | 1.17779e141 | 0.698334 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.04614e141 | 1.03270 | ||||||||
\(629\) | 3.64070e141 | 1.69562 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.90514e140 | 0.0755866 | 0.0377933 | − | 0.999286i | \(-0.487967\pi\) | ||||
0.0377933 | + | 0.999286i | \(0.487967\pi\) | |||||||
\(632\) | 1.27454e141 | 0.466809 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.34350e141 | 2.29296 | ||||||||
\(635\) | 1.68876e141 | 0.486962 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.67159e141 | 0.657246 | ||||||||
\(638\) | 1.09090e142 | 2.47937 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.46247e141 | 0.283792 | ||||||||
\(641\) | 2.72348e141 | 0.488421 | 0.244210 | − | 0.969722i | \(-0.421471\pi\) | ||||
0.244210 | + | 0.969722i | \(0.421471\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.31375e141 | 0.814230 | 0.407115 | − | 0.913377i | \(-0.366535\pi\) | ||||
0.407115 | + | 0.913377i | \(0.366535\pi\) | |||||||
\(644\) | 6.06141e141 | 0.858691 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.19701e142 | −1.44996 | ||||||||
\(647\) | −6.34797e140 | −0.0711162 | −0.0355581 | − | 0.999368i | \(-0.511321\pi\) | ||||
−0.0355581 | + | 0.999368i | \(0.511321\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.49734e141 | −0.526981 | ||||||||
\(650\) | 1.65377e142 | 1.46673 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.50826e141 | −0.570211 | ||||||||
\(653\) | −1.11233e142 | −0.781837 | −0.390919 | − | 0.920425i | \(-0.627843\pi\) | ||||
−0.390919 | + | 0.920425i | \(0.627843\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.18304e142 | 0.712547 | ||||||||
\(656\) | −1.70548e142 | −0.951050 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.11951e141 | 0.436078 | ||||||||
\(659\) | −2.40144e142 | −1.06355 | −0.531776 | − | 0.846885i | \(-0.678475\pi\) | ||||
−0.531776 | + | 0.846885i | \(0.678475\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.18550e142 | 0.830571 | 0.415285 | − | 0.909691i | \(-0.363682\pi\) | ||||
0.415285 | + | 0.909691i | \(0.363682\pi\) | |||||||
\(662\) | 6.94494e142 | 2.44535 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.01481e141 | 0.0911531 | ||||||||
\(665\) | 6.39269e141 | 0.179139 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.59711e142 | −1.10695 | ||||||||
\(668\) | −4.77285e142 | −1.06553 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.20886e142 | −0.615990 | ||||||||
\(671\) | 5.97574e142 | 1.06391 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.76621e142 | −0.576958 | −0.288479 | − | 0.957486i | \(-0.593150\pi\) | ||||
−0.288479 | + | 0.957486i | \(0.593150\pi\) | |||||||
\(674\) | 1.83457e143 | 2.60742 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.71387e142 | 0.454483 | ||||||||
\(677\) | −9.42279e142 | −1.07017 | −0.535084 | − | 0.844799i | \(-0.679720\pi\) | ||||
−0.535084 | + | 0.844799i | \(0.679720\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.96392e142 | −0.290030 | ||||||||
\(680\) | −2.31536e142 | −0.210338 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.83848e143 | 1.43995 | ||||||||
\(683\) | −1.77484e143 | −1.29096 | −0.645481 | − | 0.763777i | \(-0.723343\pi\) | ||||
−0.645481 | + | 0.763777i | \(0.723343\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.00272e143 | −0.629225 | ||||||||
\(686\) | −2.65508e143 | −1.54778 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.19715e142 | 0.412522 | ||||||||
\(689\) | 4.03026e143 | 1.88479 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.13672e143 | −0.863190 | −0.431595 | − | 0.902068i | \(-0.642049\pi\) | ||||
−0.431595 | + | 0.902068i | \(0.642049\pi\) | |||||||
\(692\) | −2.67236e141 | −0.0100355 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.20563e143 | −0.391345 | ||||||||
\(695\) | 8.46817e142 | 0.255598 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.50332e143 | 1.95884 | ||||||||
\(698\) | −8.37459e143 | −2.03360 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.27804e143 | −0.688912 | ||||||||
\(701\) | 1.00021e143 | 0.195582 | 0.0977912 | − | 0.995207i | \(-0.468822\pi\) | ||||
0.0977912 | + | 0.995207i | \(0.468822\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.68382e143 | −0.793151 | ||||||||
\(704\) | 1.39983e144 | 2.20626 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.24171e143 | 0.169583 | ||||||||
\(707\) | 6.03617e143 | 0.767504 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.19635e144 | 1.31893 | 0.659466 | − | 0.751735i | \(-0.270783\pi\) | ||||
0.659466 | + | 0.751735i | \(0.270783\pi\) | |||||||
\(710\) | 5.06976e142 | 0.0520524 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.72422e143 | 0.598966 | ||||||||
\(713\) | −7.74744e143 | −0.642891 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.01996e144 | −0.734728 | ||||||||
\(716\) | −2.42843e144 | −1.63012 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.37313e143 | −0.254981 | ||||||||
\(719\) | −6.63155e143 | −0.360418 | −0.180209 | − | 0.983628i | \(-0.557677\pi\) | ||||
−0.180209 | + | 0.983628i | \(0.557677\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.66999e144 | 0.788828 | ||||||||
\(722\) | −1.86024e144 | −0.819295 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.86844e144 | −1.09862 | ||||||||
\(725\) | 2.48614e144 | 0.888089 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.70060e144 | 0.839407 | 0.419704 | − | 0.907661i | \(-0.362134\pi\) | ||||
0.419704 | + | 0.907661i | \(0.362134\pi\) | |||||||
\(728\) | −9.68626e143 | −0.280880 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.28022e144 | 0.575667 | ||||||||
\(731\) | −3.60636e144 | −0.849653 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.92252e144 | −1.62597 | −0.812985 | − | 0.582284i | \(-0.802159\pi\) | ||||
−0.812985 | + | 0.582284i | \(0.802159\pi\) | |||||||
\(734\) | −5.09564e144 | −0.976220 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.81699e144 | −1.47228 | ||||||||
\(737\) | −1.02436e145 | −1.59714 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.09564e144 | 0.556900 | 0.278450 | − | 0.960451i | \(-0.410179\pi\) | ||||
0.278450 | + | 0.960451i | \(0.410179\pi\) | |||||||
\(740\) | −4.64022e144 | −0.589300 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.44176e145 | −1.59770 | ||||||||
\(743\) | −1.16041e145 | −1.20136 | −0.600682 | − | 0.799488i | \(-0.705104\pi\) | ||||
−0.600682 | + | 0.799488i | \(0.705104\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.97728e144 | −0.630658 | ||||||||
\(746\) | −1.43130e145 | −1.20898 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.78562e145 | −2.79323 | ||||||||
\(749\) | 6.59935e144 | 0.455166 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.16350e144 | 0.0701371 | 0.0350686 | − | 0.999385i | \(-0.488835\pi\) | ||||
0.0350686 | + | 0.999385i | \(0.488835\pi\) | |||||||
\(752\) | −5.45541e144 | −0.307487 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.76258e145 | 1.85452 | ||||||||
\(755\) | −1.45725e145 | −0.671756 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.51960e144 | −0.222621 | −0.111310 | − | 0.993786i | \(-0.535505\pi\) | ||||
−0.111310 | + | 0.993786i | \(0.535505\pi\) | |||||||
\(758\) | 3.98447e144 | 0.150340 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.97874e144 | 0.0983890 | ||||||||
\(761\) | 5.40410e145 | 1.67031 | 0.835157 | − | 0.550011i | \(-0.185377\pi\) | ||||
0.835157 | + | 0.550011i | \(0.185377\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.34070e143 | 0.0117509 | ||||||||
\(764\) | −4.07954e145 | −1.03371 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.88822e145 | −2.19566 | ||||||||
\(767\) | −1.89606e145 | −0.394172 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.96750e145 | 0.540891 | 0.270446 | − | 0.962735i | \(-0.412829\pi\) | ||||
0.270446 | + | 0.962735i | \(0.412829\pi\) | |||||||
\(770\) | 3.64872e145 | 0.622815 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.16461e145 | 1.37227 | ||||||||
\(773\) | −9.98016e144 | −0.139982 | −0.0699911 | − | 0.997548i | \(-0.522297\pi\) | ||||
−0.0699911 | + | 0.997548i | \(0.522297\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.18986e145 | 0.515779 | ||||||||
\(776\) | −1.38107e145 | −0.159294 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.65089e146 | 1.67204 | ||||||||
\(779\) | −9.65313e145 | −0.916276 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.61841e145 | 0.134962 | ||||||||
\(782\) | 2.87908e146 | 2.25067 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.71721e145 | 0.392847 | ||||||||
\(785\) | −5.19040e145 | −0.334413 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.20626e146 | −0.683465 | −0.341732 | − | 0.939797i | \(-0.611014\pi\) | ||||
−0.341732 | + | 0.939797i | \(0.611014\pi\) | |||||||
\(788\) | −4.54902e145 | −0.241738 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.65591e146 | −0.774227 | ||||||||
\(791\) | −1.37740e145 | −0.0604156 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.06106e146 | 0.795784 | ||||||||
\(794\) | −2.11315e146 | −0.765587 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.79881e146 | 1.21210 | ||||||||
\(797\) | −2.00327e146 | −0.599921 | −0.299961 | − | 0.953952i | \(-0.596974\pi\) | ||||
−0.299961 | + | 0.953952i | \(0.596974\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.40012e146 | 0.633317 | ||||||||
\(800\) | 4.76828e146 | 1.18118 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.48096e145 | 0.0323398 | ||||||||
\(803\) | 7.27908e146 | 1.49259 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.53759e146 | −0.278066 | ||||||||
\(806\) | 6.34102e146 | 1.07706 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.81262e146 | 0.421538 | ||||||||
\(809\) | −2.46422e145 | −0.0346960 | −0.0173480 | − | 0.999850i | \(-0.505522\pi\) | ||||
−0.0173480 | + | 0.999850i | \(0.505522\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.96232e146 | −0.616781 | −0.308391 | − | 0.951260i | \(-0.599790\pi\) | ||||
−0.308391 | + | 0.951260i | \(0.599790\pi\) | |||||||
\(812\) | −7.45807e146 | −0.871058 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.67336e147 | −2.75756 | ||||||||
\(815\) | 1.90461e146 | 0.184649 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.63963e146 | 0.397438 | ||||||||
\(818\) | 2.47880e147 | 1.99618 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.56327e146 | −0.680780 | ||||||||
\(821\) | 2.07513e147 | 1.38904 | 0.694522 | − | 0.719472i | \(-0.255616\pi\) | ||||
0.694522 | + | 0.719472i | \(0.255616\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.08912e147 | 1.23672 | 0.618361 | − | 0.785894i | \(-0.287797\pi\) | ||||
0.618361 | + | 0.785894i | \(0.287797\pi\) | |||||||
\(824\) | 7.78148e146 | 0.433249 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.78283e146 | 0.334132 | ||||||||
\(827\) | −3.48507e147 | −1.61504 | −0.807521 | − | 0.589839i | \(-0.799191\pi\) | ||||
−0.807521 | + | 0.589839i | \(0.799191\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.30518e147 | −1.35579 | −0.677894 | − | 0.735160i | \(-0.737107\pi\) | ||||
−0.677894 | + | 0.735160i | \(0.737107\pi\) | |||||||
\(830\) | −3.91691e146 | −0.151182 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.82809e147 | 1.65024 | ||||||||
\(833\) | −2.51530e147 | −0.809129 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.21072e147 | 0.345046 | ||||||||
\(836\) | 4.87025e147 | 1.30658 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.30323e147 | 0.785445 | ||||||||
\(839\) | −4.20113e147 | −0.940561 | −0.470281 | − | 0.882517i | \(-0.655847\pi\) | ||||
−0.470281 | + | 0.882517i | \(0.655847\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.19065e146 | 0.122896 | ||||||||
\(842\) | 3.14692e147 | 0.588336 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.03516e147 | −0.171677 | ||||||||
\(845\) | −9.42090e146 | −0.147173 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.87626e147 | 0.953323 | ||||||||
\(848\) | 8.62477e147 | 1.12657 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.55702e148 | −1.80567 | ||||||||
\(851\) | 1.12656e148 | 1.23115 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.14274e148 | 1.10923 | 0.554614 | − | 0.832108i | \(-0.312866\pi\) | ||||
0.554614 | + | 0.832108i | \(0.312866\pi\) | |||||||
\(854\) | −7.37310e147 | −0.674571 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.07504e147 | 0.249991 | ||||||||
\(857\) | 1.25430e148 | 0.961328 | 0.480664 | − | 0.876905i | \(-0.340396\pi\) | ||||
0.480664 | + | 0.876905i | \(0.340396\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.03083e148 | 1.38362 | 0.691812 | − | 0.722078i | \(-0.256813\pi\) | ||||
0.691812 | + | 0.722078i | \(0.256813\pi\) | |||||||
\(860\) | 4.59645e147 | 0.295291 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.52056e148 | 2.01138 | ||||||||
\(863\) | −8.95017e147 | −0.482266 | −0.241133 | − | 0.970492i | \(-0.577519\pi\) | ||||
−0.241133 | + | 0.970492i | \(0.577519\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.77894e145 | 0.00324974 | ||||||||
\(866\) | 5.71545e148 | 2.58462 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.25690e148 | −0.505888 | ||||||||
\(869\) | −5.28612e148 | −2.00742 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.53306e148 | −1.19463 | ||||||||
\(872\) | 2.02260e146 | 0.00645397 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.70398e148 | −1.05279 | ||||||||
\(875\) | 1.82372e148 | 0.489274 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.88741e148 | 0.690285 | 0.345142 | − | 0.938550i | \(-0.387831\pi\) | ||||
0.345142 | + | 0.938550i | \(0.387831\pi\) | |||||||
\(878\) | −4.30994e148 | −0.972744 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.18271e148 | −0.439159 | ||||||||
\(881\) | −6.06187e148 | −1.15166 | −0.575828 | − | 0.817571i | \(-0.695320\pi\) | ||||
−0.575828 | + | 0.817571i | \(0.695320\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.10147e148 | −0.186619 | −0.0933097 | − | 0.995637i | \(-0.529745\pi\) | ||||
−0.0933097 | + | 0.995637i | \(0.529745\pi\) | |||||||
\(884\) | −1.30568e149 | −2.08928 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.37563e149 | −1.96380 | ||||||||
\(887\) | 4.72512e148 | 0.637192 | 0.318596 | − | 0.947891i | \(-0.396789\pi\) | ||||
0.318596 | + | 0.947891i | \(0.396789\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.65162e148 | −0.800550 | ||||||||
\(890\) | −8.73627e148 | −0.993415 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.23201e148 | −0.226606 | ||||||||
\(893\) | −3.08779e148 | −0.296244 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.16016e148 | 0.527872 | ||||||||
\(896\) | −5.76033e148 | −0.466544 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.74784e148 | 0.343590 | ||||||||
\(899\) | 9.53260e148 | 0.652149 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.79449e149 | −2.32034 | ||||||||
\(902\) | −5.50966e149 | −3.18563 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.41816e147 | −0.0331822 | ||||||||
\(905\) | 7.27632e148 | 0.355761 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.12427e149 | 0.491703 | 0.245852 | − | 0.969307i | \(-0.420932\pi\) | ||||
0.245852 | + | 0.969307i | \(0.420932\pi\) | |||||||
\(908\) | 2.24037e149 | 0.926797 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.25846e149 | 0.465854 | ||||||||
\(911\) | −4.17428e148 | −0.146185 | −0.0730926 | − | 0.997325i | \(-0.523287\pi\) | ||||
−0.0730926 | + | 0.997325i | \(0.523287\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.25039e149 | −0.391985 | ||||||||
\(914\) | 8.67937e148 | 0.257457 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.27688e149 | −0.604809 | ||||||||
\(917\) | −4.65970e149 | −1.17140 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.30867e149 | 1.87111 | 0.935553 | − | 0.353186i | \(-0.114902\pi\) | ||||
0.935553 | + | 0.353186i | \(0.114902\pi\) | |||||||
\(920\) | −7.16454e148 | −0.152723 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.90564e149 | −0.364024 | ||||||||
\(923\) | 5.58197e148 | 0.100949 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.09252e149 | −0.987732 | ||||||||
\(926\) | 7.37612e149 | 1.13233 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.08486e150 | 1.49348 | ||||||||
\(929\) | −7.17354e149 | −0.935277 | −0.467638 | − | 0.883920i | \(-0.654895\pi\) | ||||
−0.467638 | + | 0.883920i | \(0.654895\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.23597e149 | 0.378483 | ||||||||
\(932\) | −4.54272e149 | −0.503284 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.56463e150 | −1.55558 | ||||||||
\(935\) | 9.60291e149 | 0.904517 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.12560e150 | −0.951774 | −0.475887 | − | 0.879507i | \(-0.657873\pi\) | ||||
−0.475887 | + | 0.879507i | \(0.657873\pi\) | |||||||
\(938\) | 1.26389e150 | 1.01267 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.05905e149 | −0.220105 | ||||||||
\(941\) | −8.61109e149 | −0.587195 | −0.293597 | − | 0.955929i | \(-0.594853\pi\) | ||||
−0.293597 | + | 0.955929i | \(0.594853\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.32179e150 | 1.42227 | ||||||||
\(944\) | −4.05758e149 | −0.235603 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.64814e150 | 1.38178 | ||||||||
\(947\) | 1.36513e150 | 0.675307 | 0.337654 | − | 0.941270i | \(-0.390367\pi\) | ||||
0.337654 | + | 0.941270i | \(0.390367\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.51059e150 | 1.11643 | ||||||||
\(950\) | 2.00313e150 | 0.844632 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.11963e149 | 0.345789 | ||||||||
\(953\) | −4.18075e149 | −0.150336 | −0.0751680 | − | 0.997171i | \(-0.523949\pi\) | ||||
−0.0751680 | + | 0.997171i | \(0.523949\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.03485e150 | 0.334740 | ||||||||
\(956\) | 2.31454e150 | 0.710135 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.75810e150 | 0.485383 | ||||||||
\(959\) | 3.94947e150 | 1.03442 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.63510e150 | −0.621249 | ||||||||
\(962\) | −9.22054e150 | −2.06260 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.02982e150 | −1.21455 | ||||||||
\(965\) | −2.32477e150 | −0.444376 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.04342e150 | −0.179648 | −0.0898238 | − | 0.995958i | \(-0.528630\pi\) | ||||
−0.0898238 | + | 0.995958i | \(0.528630\pi\) | |||||||
\(968\) | 3.20407e150 | 0.523595 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.79432e150 | 0.264196 | ||||||||
\(971\) | 3.53326e150 | 0.493861 | 0.246930 | − | 0.969033i | \(-0.420578\pi\) | ||||
0.246930 | + | 0.969033i | \(0.420578\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.33540e150 | −0.420194 | ||||||||
\(974\) | 1.45067e151 | 1.73517 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.41068e150 | 0.475653 | ||||||||
\(977\) | 1.53694e151 | 1.57392 | 0.786960 | − | 0.617004i | \(-0.211654\pi\) | ||||
0.786960 | + | 0.617004i | \(0.211654\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.78886e151 | −2.57573 | ||||||||
\(980\) | 3.20585e150 | 0.281207 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.00772e151 | 0.797460 | ||||||||
\(983\) | −9.55031e150 | −0.717901 | −0.358951 | − | 0.933357i | \(-0.616865\pi\) | ||||
−0.358951 | + | 0.933357i | \(0.616865\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.15394e150 | 0.0782807 | ||||||||
\(986\) | −3.54247e151 | −2.28309 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.67977e151 | 0.977294 | ||||||||
\(989\) | −1.11594e151 | −0.616917 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.87889e150 | −0.293478 | −0.146739 | − | 0.989175i | \(-0.546878\pi\) | ||||
−0.146739 | + | 0.989175i | \(0.546878\pi\) | |||||||
\(992\) | 1.82830e151 | 0.867376 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.99685e150 | −0.0855725 | ||||||||
\(995\) | −9.63637e150 | −0.392507 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.59519e150 | −0.132317 | −0.0661586 | − | 0.997809i | \(-0.521074\pi\) | ||||
−0.0661586 | + | 0.997809i | \(0.521074\pi\) | |||||||
\(998\) | 4.29120e151 | 1.50137 | ||||||||
\(999\) | 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 | 9.102.a.b.1.7 | 8 | ||
3.2 | odd | 2 | 1.102.a.a.1.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.102.a.a.1.2 | ✓ | 8 | 3.2 | odd | 2 | ||
9.102.a.b.1.7 | 8 | 1.1 | even | 1 | trivial |