Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,88,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 88, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 88);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 88 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(95.8667262922\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2 x^{3} + \cdots + 13\!\cdots\!68 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{45}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 17\cdot 29 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.03541e17\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.79609e12 | −0.707107 | ||||||||
\(3\) | −8.65990e20 | −1.52313 | −0.761567 | − | 0.648086i | \(-0.775570\pi\) | ||||
−0.761567 | + | 0.648086i | \(0.775570\pi\) | |||||||
\(4\) | 7.73713e25 | 0.500000 | ||||||||
\(5\) | −4.55634e30 | −1.79234 | −0.896172 | − | 0.443708i | \(-0.853663\pi\) | ||||
−0.896172 | + | 0.443708i | \(0.853663\pi\) | |||||||
\(6\) | 7.61733e33 | 1.07702 | ||||||||
\(7\) | 8.09122e36 | 1.40039 | 0.700196 | − | 0.713951i | \(-0.253096\pi\) | ||||
0.700196 | + | 0.713951i | \(0.253096\pi\) | |||||||
\(8\) | −6.80565e38 | −0.353553 | ||||||||
\(9\) | 4.26681e41 | 1.31994 | ||||||||
\(10\) | 4.00780e43 | 1.26738 | ||||||||
\(11\) | 2.92903e45 | 1.46603 | 0.733013 | − | 0.680214i | \(-0.238113\pi\) | ||||
0.733013 | + | 0.680214i | \(0.238113\pi\) | |||||||
\(12\) | −6.70027e46 | −0.761567 | ||||||||
\(13\) | 3.57915e48 | 1.25096 | 0.625481 | − | 0.780239i | \(-0.284903\pi\) | ||||
0.625481 | + | 0.780239i | \(0.284903\pi\) | |||||||
\(14\) | −7.11711e49 | −0.990226 | ||||||||
\(15\) | 3.94575e51 | 2.72998 | ||||||||
\(16\) | 5.98631e51 | 0.250000 | ||||||||
\(17\) | 1.14630e53 | 0.342586 | 0.171293 | − | 0.985220i | \(-0.445206\pi\) | ||||
0.171293 | + | 0.985220i | \(0.445206\pi\) | |||||||
\(18\) | −3.75313e54 | −0.933338 | ||||||||
\(19\) | 4.19816e54 | 0.0993750 | 0.0496875 | − | 0.998765i | \(-0.484177\pi\) | ||||
0.0496875 | + | 0.998765i | \(0.484177\pi\) | |||||||
\(20\) | −3.52530e56 | −0.896172 | ||||||||
\(21\) | −7.00692e57 | −2.13298 | ||||||||
\(22\) | −2.57640e58 | −1.03664 | ||||||||
\(23\) | 1.69882e59 | 0.988523 | 0.494261 | − | 0.869313i | \(-0.335439\pi\) | ||||
0.494261 | + | 0.869313i | \(0.335439\pi\) | |||||||
\(24\) | 5.89362e59 | 0.538510 | ||||||||
\(25\) | 1.42979e61 | 2.21249 | ||||||||
\(26\) | −3.14825e61 | −0.884564 | ||||||||
\(27\) | −8.95634e61 | −0.487312 | ||||||||
\(28\) | 6.26028e62 | 0.700196 | ||||||||
\(29\) | −1.43497e63 | −0.348764 | −0.174382 | − | 0.984678i | \(-0.555793\pi\) | ||||
−0.174382 | + | 0.984678i | \(0.555793\pi\) | |||||||
\(30\) | −3.47072e64 | −1.93039 | ||||||||
\(31\) | 7.01020e64 | 0.936476 | 0.468238 | − | 0.883602i | \(-0.344889\pi\) | ||||
0.468238 | + | 0.883602i | \(0.344889\pi\) | |||||||
\(32\) | −5.26561e64 | −0.176777 | ||||||||
\(33\) | −2.53651e66 | −2.23296 | ||||||||
\(34\) | −1.00829e66 | −0.242245 | ||||||||
\(35\) | −3.68664e67 | −2.50998 | ||||||||
\(36\) | 3.30128e67 | 0.659970 | ||||||||
\(37\) | 1.12712e67 | 0.0684220 | 0.0342110 | − | 0.999415i | \(-0.489108\pi\) | ||||
0.0342110 | + | 0.999415i | \(0.489108\pi\) | |||||||
\(38\) | −3.69274e67 | −0.0702688 | ||||||||
\(39\) | −3.09951e69 | −1.90538 | ||||||||
\(40\) | 3.10089e69 | 0.633689 | ||||||||
\(41\) | 2.21344e70 | 1.54515 | 0.772573 | − | 0.634926i | \(-0.218969\pi\) | ||||
0.772573 | + | 0.634926i | \(0.218969\pi\) | |||||||
\(42\) | 6.16335e70 | 1.50825 | ||||||||
\(43\) | −2.09683e70 | −0.184368 | −0.0921839 | − | 0.995742i | \(-0.529385\pi\) | ||||
−0.0921839 | + | 0.995742i | \(0.529385\pi\) | |||||||
\(44\) | 2.26623e71 | 0.733013 | ||||||||
\(45\) | −1.94410e72 | −2.36579 | ||||||||
\(46\) | −1.49430e72 | −0.698991 | ||||||||
\(47\) | −3.31913e72 | −0.609211 | −0.304605 | − | 0.952479i | \(-0.598525\pi\) | ||||
−0.304605 | + | 0.952479i | \(0.598525\pi\) | |||||||
\(48\) | −5.18409e72 | −0.380784 | ||||||||
\(49\) | 3.20846e73 | 0.961095 | ||||||||
\(50\) | −1.25766e74 | −1.56447 | ||||||||
\(51\) | −9.92683e73 | −0.521804 | ||||||||
\(52\) | 2.76923e74 | 0.625481 | ||||||||
\(53\) | 4.44080e74 | 0.437987 | 0.218994 | − | 0.975726i | \(-0.429723\pi\) | ||||
0.218994 | + | 0.975726i | \(0.429723\pi\) | |||||||
\(54\) | 7.87808e74 | 0.344581 | ||||||||
\(55\) | −1.33457e76 | −2.62762 | ||||||||
\(56\) | −5.50660e75 | −0.495113 | ||||||||
\(57\) | −3.63557e75 | −0.151362 | ||||||||
\(58\) | 1.26222e76 | 0.246613 | ||||||||
\(59\) | −3.55044e76 | −0.329776 | −0.164888 | − | 0.986312i | \(-0.552726\pi\) | ||||
−0.164888 | + | 0.986312i | \(0.552726\pi\) | |||||||
\(60\) | 3.05287e77 | 1.36499 | ||||||||
\(61\) | 4.48709e77 | 0.977501 | 0.488751 | − | 0.872423i | \(-0.337453\pi\) | ||||
0.488751 | + | 0.872423i | \(0.337453\pi\) | |||||||
\(62\) | −6.16624e77 | −0.662189 | ||||||||
\(63\) | 3.45237e78 | 1.84843 | ||||||||
\(64\) | 4.63168e77 | 0.125000 | ||||||||
\(65\) | −1.63078e79 | −2.24215 | ||||||||
\(66\) | 2.23114e79 | 1.57894 | ||||||||
\(67\) | −3.23091e79 | −1.18870 | −0.594348 | − | 0.804208i | \(-0.702590\pi\) | ||||
−0.594348 | + | 0.804208i | \(0.702590\pi\) | |||||||
\(68\) | 8.86905e78 | 0.171293 | ||||||||
\(69\) | −1.47116e80 | −1.50565 | ||||||||
\(70\) | 3.24280e80 | 1.77482 | ||||||||
\(71\) | −5.50387e79 | −0.162529 | −0.0812643 | − | 0.996693i | \(-0.525896\pi\) | ||||
−0.0812643 | + | 0.996693i | \(0.525896\pi\) | |||||||
\(72\) | −2.90384e80 | −0.466669 | ||||||||
\(73\) | 1.31003e81 | 1.15541 | 0.577704 | − | 0.816246i | \(-0.303949\pi\) | ||||
0.577704 | + | 0.816246i | \(0.303949\pi\) | |||||||
\(74\) | −9.91427e79 | −0.0483817 | ||||||||
\(75\) | −1.23818e82 | −3.36993 | ||||||||
\(76\) | 3.24817e80 | 0.0496875 | ||||||||
\(77\) | 2.36994e82 | 2.05301 | ||||||||
\(78\) | 2.72636e82 | 1.34731 | ||||||||
\(79\) | 3.68237e82 | 1.04556 | 0.522781 | − | 0.852467i | \(-0.324895\pi\) | ||||
0.522781 | + | 0.852467i | \(0.324895\pi\) | |||||||
\(80\) | −2.72757e82 | −0.448086 | ||||||||
\(81\) | −6.03670e82 | −0.577699 | ||||||||
\(82\) | −1.94696e83 | −1.09258 | ||||||||
\(83\) | 4.18874e83 | 1.38735 | 0.693675 | − | 0.720288i | \(-0.255990\pi\) | ||||
0.693675 | + | 0.720288i | \(0.255990\pi\) | |||||||
\(84\) | −5.42134e83 | −1.06649 | ||||||||
\(85\) | −5.22293e83 | −0.614031 | ||||||||
\(86\) | 1.84439e83 | 0.130368 | ||||||||
\(87\) | 1.24267e84 | 0.531214 | ||||||||
\(88\) | −1.99339e84 | −0.518319 | ||||||||
\(89\) | 3.62485e83 | 0.0576534 | 0.0288267 | − | 0.999584i | \(-0.490823\pi\) | ||||
0.0288267 | + | 0.999584i | \(0.490823\pi\) | |||||||
\(90\) | 1.71005e85 | 1.67286 | ||||||||
\(91\) | 2.89597e85 | 1.75184 | ||||||||
\(92\) | 1.31440e85 | 0.494261 | ||||||||
\(93\) | −6.07076e85 | −1.42638 | ||||||||
\(94\) | 2.91954e85 | 0.430777 | ||||||||
\(95\) | −1.91283e85 | −0.178114 | ||||||||
\(96\) | 4.55997e85 | 0.269255 | ||||||||
\(97\) | 3.64891e86 | 1.37275 | 0.686377 | − | 0.727246i | \(-0.259200\pi\) | ||||
0.686377 | + | 0.727246i | \(0.259200\pi\) | |||||||
\(98\) | −2.82219e86 | −0.679597 | ||||||||
\(99\) | 1.24976e87 | 1.93507 | ||||||||
\(100\) | 1.10625e87 | 1.10625 | ||||||||
\(101\) | −3.42457e86 | −0.222140 | −0.111070 | − | 0.993813i | \(-0.535428\pi\) | ||||
−0.111070 | + | 0.993813i | \(0.535428\pi\) | |||||||
\(102\) | 8.73173e86 | 0.368971 | ||||||||
\(103\) | 2.85691e86 | 0.0789729 | 0.0394864 | − | 0.999220i | \(-0.487428\pi\) | ||||
0.0394864 | + | 0.999220i | \(0.487428\pi\) | |||||||
\(104\) | −2.43584e87 | −0.442282 | ||||||||
\(105\) | 3.19259e88 | 3.82304 | ||||||||
\(106\) | −3.90617e87 | −0.309704 | ||||||||
\(107\) | 1.13039e88 | 0.595710 | 0.297855 | − | 0.954611i | \(-0.403729\pi\) | ||||
0.297855 | + | 0.954611i | \(0.403729\pi\) | |||||||
\(108\) | −6.92963e87 | −0.243656 | ||||||||
\(109\) | 5.13968e88 | 1.21027 | 0.605136 | − | 0.796122i | \(-0.293119\pi\) | ||||
0.605136 | + | 0.796122i | \(0.293119\pi\) | |||||||
\(110\) | 1.17390e89 | 1.85801 | ||||||||
\(111\) | −9.76076e87 | −0.104216 | ||||||||
\(112\) | 4.84366e88 | 0.350098 | ||||||||
\(113\) | −2.13560e89 | −1.04859 | −0.524297 | − | 0.851536i | \(-0.675672\pi\) | ||||
−0.524297 | + | 0.851536i | \(0.675672\pi\) | |||||||
\(114\) | 3.19788e88 | 0.107029 | ||||||||
\(115\) | −7.74041e89 | −1.77177 | ||||||||
\(116\) | −1.11026e89 | −0.174382 | ||||||||
\(117\) | 1.52716e90 | 1.65119 | ||||||||
\(118\) | 3.12300e89 | 0.233187 | ||||||||
\(119\) | 9.27495e89 | 0.479754 | ||||||||
\(120\) | −2.68534e90 | −0.965194 | ||||||||
\(121\) | 4.58746e90 | 1.14923 | ||||||||
\(122\) | −3.94689e90 | −0.691198 | ||||||||
\(123\) | −1.91681e91 | −2.35347 | ||||||||
\(124\) | 5.42388e90 | 0.468238 | ||||||||
\(125\) | −3.57015e91 | −2.17320 | ||||||||
\(126\) | −3.03674e91 | −1.30704 | ||||||||
\(127\) | 9.51041e90 | 0.290227 | 0.145113 | − | 0.989415i | \(-0.453645\pi\) | ||||
0.145113 | + | 0.989415i | \(0.453645\pi\) | |||||||
\(128\) | −4.07407e90 | −0.0883883 | ||||||||
\(129\) | 1.81583e91 | 0.280817 | ||||||||
\(130\) | 1.43445e92 | 1.58544 | ||||||||
\(131\) | −1.57599e92 | −1.24811 | −0.624054 | − | 0.781381i | \(-0.714515\pi\) | ||||
−0.624054 | + | 0.781381i | \(0.714515\pi\) | |||||||
\(132\) | −1.96253e92 | −1.11648 | ||||||||
\(133\) | 3.39682e91 | 0.139164 | ||||||||
\(134\) | 2.84194e92 | 0.840536 | ||||||||
\(135\) | 4.08081e92 | 0.873430 | ||||||||
\(136\) | −7.80130e91 | −0.121122 | ||||||||
\(137\) | 3.50582e92 | 0.395772 | 0.197886 | − | 0.980225i | \(-0.436592\pi\) | ||||
0.197886 | + | 0.980225i | \(0.436592\pi\) | |||||||
\(138\) | 1.29405e93 | 1.06466 | ||||||||
\(139\) | 4.17926e92 | 0.251163 | 0.125582 | − | 0.992083i | \(-0.459920\pi\) | ||||
0.125582 | + | 0.992083i | \(0.459920\pi\) | |||||||
\(140\) | −2.85240e93 | −1.25499 | ||||||||
\(141\) | 2.87433e93 | 0.927910 | ||||||||
\(142\) | 4.84126e92 | 0.114925 | ||||||||
\(143\) | 1.04834e94 | 1.83394 | ||||||||
\(144\) | 2.55425e93 | 0.329985 | ||||||||
\(145\) | 6.53824e93 | 0.625104 | ||||||||
\(146\) | −1.15231e94 | −0.816997 | ||||||||
\(147\) | −2.77849e94 | −1.46388 | ||||||||
\(148\) | 8.72068e92 | 0.0342110 | ||||||||
\(149\) | −3.99336e94 | −1.16879 | −0.584394 | − | 0.811470i | \(-0.698668\pi\) | ||||
−0.584394 | + | 0.811470i | \(0.698668\pi\) | |||||||
\(150\) | 1.08912e95 | 2.38290 | ||||||||
\(151\) | 3.15860e93 | 0.0517604 | 0.0258802 | − | 0.999665i | \(-0.491761\pi\) | ||||
0.0258802 | + | 0.999665i | \(0.491761\pi\) | |||||||
\(152\) | −2.85712e93 | −0.0351344 | ||||||||
\(153\) | 4.89104e94 | 0.452193 | ||||||||
\(154\) | −2.08462e95 | −1.45170 | ||||||||
\(155\) | −3.19409e95 | −1.67849 | ||||||||
\(156\) | −2.39813e95 | −0.952692 | ||||||||
\(157\) | −8.27405e94 | −0.248934 | −0.124467 | − | 0.992224i | \(-0.539722\pi\) | ||||
−0.124467 | + | 0.992224i | \(0.539722\pi\) | |||||||
\(158\) | −3.23905e95 | −0.739323 | ||||||||
\(159\) | −3.84569e95 | −0.667113 | ||||||||
\(160\) | 2.39919e95 | 0.316844 | ||||||||
\(161\) | 1.37455e96 | 1.38432 | ||||||||
\(162\) | 5.30994e95 | 0.408495 | ||||||||
\(163\) | −2.58181e96 | −1.51972 | −0.759859 | − | 0.650087i | \(-0.774732\pi\) | ||||
−0.759859 | + | 0.650087i | \(0.774732\pi\) | |||||||
\(164\) | 1.71256e96 | 0.772573 | ||||||||
\(165\) | 1.15572e97 | 4.00222 | ||||||||
\(166\) | −3.68445e96 | −0.981005 | ||||||||
\(167\) | −9.25583e96 | −1.89779 | −0.948897 | − | 0.315587i | \(-0.897799\pi\) | ||||
−0.948897 | + | 0.315587i | \(0.897799\pi\) | |||||||
\(168\) | 4.76866e96 | 0.754124 | ||||||||
\(169\) | 4.62432e96 | 0.564906 | ||||||||
\(170\) | 4.59413e96 | 0.434186 | ||||||||
\(171\) | 1.79128e96 | 0.131169 | ||||||||
\(172\) | −1.62234e96 | −0.0921839 | ||||||||
\(173\) | −3.50847e97 | −1.54922 | −0.774609 | − | 0.632440i | \(-0.782054\pi\) | ||||
−0.774609 | + | 0.632440i | \(0.782054\pi\) | |||||||
\(174\) | −1.09307e97 | −0.375625 | ||||||||
\(175\) | 1.15688e98 | 3.09836 | ||||||||
\(176\) | 1.75341e97 | 0.366507 | ||||||||
\(177\) | 3.07464e97 | 0.502294 | ||||||||
\(178\) | −3.18846e96 | −0.0407671 | ||||||||
\(179\) | −1.83037e98 | −1.83414 | −0.917070 | − | 0.398727i | \(-0.869452\pi\) | ||||
−0.917070 | + | 0.398727i | \(0.869452\pi\) | |||||||
\(180\) | −1.50418e98 | −1.18289 | ||||||||
\(181\) | 1.94555e98 | 1.20233 | 0.601166 | − | 0.799124i | \(-0.294703\pi\) | ||||
0.601166 | + | 0.799124i | \(0.294703\pi\) | |||||||
\(182\) | −2.54732e98 | −1.23874 | ||||||||
\(183\) | −3.88578e98 | −1.48887 | ||||||||
\(184\) | −1.15616e98 | −0.349496 | ||||||||
\(185\) | −5.13555e97 | −0.122636 | ||||||||
\(186\) | 5.33990e98 | 1.00860 | ||||||||
\(187\) | 3.35754e98 | 0.502240 | ||||||||
\(188\) | −2.56805e98 | −0.304605 | ||||||||
\(189\) | −7.24677e98 | −0.682427 | ||||||||
\(190\) | 1.68254e98 | 0.125946 | ||||||||
\(191\) | −1.16015e99 | −0.691137 | −0.345569 | − | 0.938393i | \(-0.612314\pi\) | ||||
−0.345569 | + | 0.938393i | \(0.612314\pi\) | |||||||
\(192\) | −4.01099e98 | −0.190392 | ||||||||
\(193\) | 1.79323e99 | 0.679037 | 0.339518 | − | 0.940599i | \(-0.389736\pi\) | ||||
0.339518 | + | 0.940599i | \(0.389736\pi\) | |||||||
\(194\) | −3.20961e99 | −0.970683 | ||||||||
\(195\) | 1.41224e100 | 3.41510 | ||||||||
\(196\) | 2.48242e99 | 0.480548 | ||||||||
\(197\) | 8.15218e98 | 0.126472 | 0.0632358 | − | 0.997999i | \(-0.479858\pi\) | ||||
0.0632358 | + | 0.997999i | \(0.479858\pi\) | |||||||
\(198\) | −1.09930e100 | −1.36830 | ||||||||
\(199\) | 1.47457e100 | 1.47420 | 0.737100 | − | 0.675784i | \(-0.236195\pi\) | ||||
0.737100 | + | 0.675784i | \(0.236195\pi\) | |||||||
\(200\) | −9.73065e99 | −0.782235 | ||||||||
\(201\) | 2.79794e100 | 1.81055 | ||||||||
\(202\) | 3.01229e99 | 0.157077 | ||||||||
\(203\) | −1.16107e100 | −0.488406 | ||||||||
\(204\) | −7.68051e99 | −0.260902 | ||||||||
\(205\) | −1.00852e101 | −2.76943 | ||||||||
\(206\) | −2.51297e99 | −0.0558422 | ||||||||
\(207\) | 7.24855e100 | 1.30479 | ||||||||
\(208\) | 2.14259e100 | 0.312741 | ||||||||
\(209\) | 1.22965e100 | 0.145686 | ||||||||
\(210\) | −2.80823e101 | −2.70330 | ||||||||
\(211\) | 9.00286e100 | 0.704845 | 0.352422 | − | 0.935841i | \(-0.385358\pi\) | ||||
0.352422 | + | 0.935841i | \(0.385358\pi\) | |||||||
\(212\) | 3.43591e100 | 0.218994 | ||||||||
\(213\) | 4.76630e100 | 0.247553 | ||||||||
\(214\) | −9.94304e100 | −0.421231 | ||||||||
\(215\) | 9.55387e100 | 0.330450 | ||||||||
\(216\) | 6.09537e100 | 0.172291 | ||||||||
\(217\) | 5.67211e101 | 1.31143 | ||||||||
\(218\) | −4.52091e101 | −0.855792 | ||||||||
\(219\) | −1.13447e102 | −1.75984 | ||||||||
\(220\) | −1.03257e102 | −1.31381 | ||||||||
\(221\) | 4.10277e101 | 0.428562 | ||||||||
\(222\) | 8.58566e100 | 0.0736918 | ||||||||
\(223\) | 1.72978e102 | 1.22104 | 0.610518 | − | 0.792003i | \(-0.290961\pi\) | ||||
0.610518 | + | 0.792003i | \(0.290961\pi\) | |||||||
\(224\) | −4.26053e101 | −0.247557 | ||||||||
\(225\) | 6.10064e102 | 2.92036 | ||||||||
\(226\) | 1.87849e102 | 0.741468 | ||||||||
\(227\) | 4.25570e102 | 1.38627 | 0.693133 | − | 0.720810i | \(-0.256230\pi\) | ||||
0.693133 | + | 0.720810i | \(0.256230\pi\) | |||||||
\(228\) | −2.81288e101 | −0.0756808 | ||||||||
\(229\) | −6.53591e102 | −1.45366 | −0.726830 | − | 0.686818i | \(-0.759007\pi\) | ||||
−0.726830 | + | 0.686818i | \(0.759007\pi\) | |||||||
\(230\) | 6.80854e102 | 1.25283 | ||||||||
\(231\) | −2.05235e103 | −3.12701 | ||||||||
\(232\) | 9.76593e101 | 0.123307 | ||||||||
\(233\) | 1.13778e103 | 1.19145 | 0.595723 | − | 0.803190i | \(-0.296866\pi\) | ||||
0.595723 | + | 0.803190i | \(0.296866\pi\) | |||||||
\(234\) | −1.34330e103 | −1.16757 | ||||||||
\(235\) | 1.51231e103 | 1.09191 | ||||||||
\(236\) | −2.74702e102 | −0.164888 | ||||||||
\(237\) | −3.18890e103 | −1.59253 | ||||||||
\(238\) | −8.15833e102 | −0.339237 | ||||||||
\(239\) | −6.02602e102 | −0.208796 | −0.104398 | − | 0.994536i | \(-0.533292\pi\) | ||||
−0.104398 | + | 0.994536i | \(0.533292\pi\) | |||||||
\(240\) | 2.36205e103 | 0.682495 | ||||||||
\(241\) | −4.45946e103 | −1.07533 | −0.537663 | − | 0.843160i | \(-0.680693\pi\) | ||||
−0.537663 | + | 0.843160i | \(0.680693\pi\) | |||||||
\(242\) | −4.03517e103 | −0.812631 | ||||||||
\(243\) | 8.12293e103 | 1.36722 | ||||||||
\(244\) | 3.47172e103 | 0.488751 | ||||||||
\(245\) | −1.46188e104 | −1.72261 | ||||||||
\(246\) | 1.68605e104 | 1.66415 | ||||||||
\(247\) | 1.50258e103 | 0.124314 | ||||||||
\(248\) | −4.77090e103 | −0.331094 | ||||||||
\(249\) | −3.62741e104 | −2.11312 | ||||||||
\(250\) | 3.14033e104 | 1.53669 | ||||||||
\(251\) | 9.77624e103 | 0.402129 | 0.201064 | − | 0.979578i | \(-0.435560\pi\) | ||||
0.201064 | + | 0.979578i | \(0.435560\pi\) | |||||||
\(252\) | 2.67114e104 | 0.924216 | ||||||||
\(253\) | 4.97590e104 | 1.44920 | ||||||||
\(254\) | −8.36544e103 | −0.205221 | ||||||||
\(255\) | 4.52300e104 | 0.935253 | ||||||||
\(256\) | 3.58359e103 | 0.0625000 | ||||||||
\(257\) | −8.02362e104 | −1.18108 | −0.590540 | − | 0.807008i | \(-0.701085\pi\) | ||||
−0.590540 | + | 0.807008i | \(0.701085\pi\) | |||||||
\(258\) | −1.59722e104 | −0.198568 | ||||||||
\(259\) | 9.11979e103 | 0.0958176 | ||||||||
\(260\) | −1.26176e105 | −1.12108 | ||||||||
\(261\) | −6.12277e104 | −0.460347 | ||||||||
\(262\) | 1.38626e105 | 0.882545 | ||||||||
\(263\) | 6.81082e104 | 0.367387 | 0.183694 | − | 0.982984i | \(-0.441195\pi\) | ||||
0.183694 | + | 0.982984i | \(0.441195\pi\) | |||||||
\(264\) | 1.72626e105 | 0.789469 | ||||||||
\(265\) | −2.02338e105 | −0.785023 | ||||||||
\(266\) | −2.98788e104 | −0.0984038 | ||||||||
\(267\) | −3.13909e104 | −0.0878140 | ||||||||
\(268\) | −2.49980e105 | −0.594348 | ||||||||
\(269\) | 5.61863e105 | 1.13607 | 0.568036 | − | 0.823004i | \(-0.307703\pi\) | ||||
0.568036 | + | 0.823004i | \(0.307703\pi\) | |||||||
\(270\) | −3.58952e105 | −0.617608 | ||||||||
\(271\) | −1.30826e106 | −1.91659 | −0.958293 | − | 0.285787i | \(-0.907745\pi\) | ||||
−0.958293 | + | 0.285787i | \(0.907745\pi\) | |||||||
\(272\) | 6.86210e104 | 0.0856465 | ||||||||
\(273\) | −2.50788e106 | −2.66828 | ||||||||
\(274\) | −3.08375e105 | −0.279853 | ||||||||
\(275\) | 4.18790e106 | 3.24357 | ||||||||
\(276\) | −1.13826e106 | −0.752827 | ||||||||
\(277\) | 9.10031e105 | 0.514264 | 0.257132 | − | 0.966376i | \(-0.417222\pi\) | ||||
0.257132 | + | 0.966376i | \(0.417222\pi\) | |||||||
\(278\) | −3.67612e105 | −0.177599 | ||||||||
\(279\) | 2.99112e106 | 1.23609 | ||||||||
\(280\) | 2.50900e106 | 0.887412 | ||||||||
\(281\) | 5.37779e105 | 0.162884 | 0.0814421 | − | 0.996678i | \(-0.474047\pi\) | ||||
0.0814421 | + | 0.996678i | \(0.474047\pi\) | |||||||
\(282\) | −2.52829e106 | −0.656132 | ||||||||
\(283\) | 7.69995e106 | 1.71308 | 0.856540 | − | 0.516080i | \(-0.172609\pi\) | ||||
0.856540 | + | 0.516080i | \(0.172609\pi\) | |||||||
\(284\) | −4.25841e105 | −0.0812643 | ||||||||
\(285\) | 1.65649e106 | 0.271292 | ||||||||
\(286\) | −9.22133e106 | −1.29679 | ||||||||
\(287\) | 1.79094e107 | 2.16381 | ||||||||
\(288\) | −2.24674e106 | −0.233335 | ||||||||
\(289\) | −9.88183e106 | −0.882635 | ||||||||
\(290\) | −5.75109e106 | −0.442016 | ||||||||
\(291\) | −3.15992e107 | −2.09089 | ||||||||
\(292\) | 1.01358e107 | 0.577704 | ||||||||
\(293\) | −3.33111e107 | −1.63624 | −0.818120 | − | 0.575047i | \(-0.804984\pi\) | ||||
−0.818120 | + | 0.575047i | \(0.804984\pi\) | |||||||
\(294\) | 2.44399e107 | 1.03512 | ||||||||
\(295\) | 1.61770e107 | 0.591072 | ||||||||
\(296\) | −7.67079e105 | −0.0241908 | ||||||||
\(297\) | −2.62334e107 | −0.714412 | ||||||||
\(298\) | 3.51260e107 | 0.826458 | ||||||||
\(299\) | 6.08034e107 | 1.23660 | ||||||||
\(300\) | −9.57999e107 | −1.68496 | ||||||||
\(301\) | −1.69659e107 | −0.258187 | ||||||||
\(302\) | −2.77834e106 | −0.0366001 | ||||||||
\(303\) | 2.96565e107 | 0.338349 | ||||||||
\(304\) | 2.51315e106 | 0.0248438 | ||||||||
\(305\) | −2.04447e108 | −1.75202 | ||||||||
\(306\) | −4.30220e107 | −0.319749 | ||||||||
\(307\) | 3.69472e107 | 0.238266 | 0.119133 | − | 0.992878i | \(-0.461988\pi\) | ||||
0.119133 | + | 0.992878i | \(0.461988\pi\) | |||||||
\(308\) | 1.83365e108 | 1.02651 | ||||||||
\(309\) | −2.47406e107 | −0.120286 | ||||||||
\(310\) | 2.80955e108 | 1.18687 | ||||||||
\(311\) | 1.47704e108 | 0.542395 | 0.271197 | − | 0.962524i | \(-0.412580\pi\) | ||||
0.271197 | + | 0.962524i | \(0.412580\pi\) | |||||||
\(312\) | 2.10942e108 | 0.673655 | ||||||||
\(313\) | 6.95025e108 | 1.93118 | 0.965588 | − | 0.260077i | \(-0.0837480\pi\) | ||||
0.965588 | + | 0.260077i | \(0.0837480\pi\) | |||||||
\(314\) | 7.27793e107 | 0.176023 | ||||||||
\(315\) | −1.57302e109 | −3.31302 | ||||||||
\(316\) | 2.84910e108 | 0.522781 | ||||||||
\(317\) | 7.54268e108 | 1.20628 | 0.603140 | − | 0.797636i | \(-0.293916\pi\) | ||||
0.603140 | + | 0.797636i | \(0.293916\pi\) | |||||||
\(318\) | 3.38271e108 | 0.471720 | ||||||||
\(319\) | −4.20308e108 | −0.511297 | ||||||||
\(320\) | −2.11035e108 | −0.224043 | ||||||||
\(321\) | −9.78909e108 | −0.907347 | ||||||||
\(322\) | −1.20907e109 | −0.978861 | ||||||||
\(323\) | 4.81234e107 | 0.0340445 | ||||||||
\(324\) | −4.67067e108 | −0.288849 | ||||||||
\(325\) | 5.11744e109 | 2.76775 | ||||||||
\(326\) | 2.27098e109 | 1.07460 | ||||||||
\(327\) | −4.45091e109 | −1.84341 | ||||||||
\(328\) | −1.50639e109 | −0.546292 | ||||||||
\(329\) | −2.68558e109 | −0.853133 | ||||||||
\(330\) | −1.01658e110 | −2.83000 | ||||||||
\(331\) | −2.84136e109 | −0.693439 | −0.346720 | − | 0.937969i | \(-0.612704\pi\) | ||||
−0.346720 | + | 0.937969i | \(0.612704\pi\) | |||||||
\(332\) | 3.24088e109 | 0.693675 | ||||||||
\(333\) | 4.80922e108 | 0.0903130 | ||||||||
\(334\) | 8.14151e109 | 1.34194 | ||||||||
\(335\) | 1.47211e110 | 2.13055 | ||||||||
\(336\) | −4.19456e109 | −0.533246 | ||||||||
\(337\) | −1.31735e110 | −1.47164 | −0.735819 | − | 0.677179i | \(-0.763202\pi\) | ||||
−0.735819 | + | 0.677179i | \(0.763202\pi\) | |||||||
\(338\) | −4.06760e109 | −0.399449 | ||||||||
\(339\) | 1.84941e110 | 1.59715 | ||||||||
\(340\) | −4.04104e109 | −0.307016 | ||||||||
\(341\) | 2.05331e110 | 1.37290 | ||||||||
\(342\) | −1.57562e109 | −0.0927506 | ||||||||
\(343\) | −1.05086e109 | −0.0544815 | ||||||||
\(344\) | 1.42703e109 | 0.0651839 | ||||||||
\(345\) | 6.70312e110 | 2.69865 | ||||||||
\(346\) | 3.08609e110 | 1.09546 | ||||||||
\(347\) | −5.97459e110 | −1.87058 | −0.935289 | − | 0.353884i | \(-0.884861\pi\) | ||||
−0.935289 | + | 0.353884i | \(0.884861\pi\) | |||||||
\(348\) | 9.61472e109 | 0.265607 | ||||||||
\(349\) | −5.68870e110 | −1.38710 | −0.693548 | − | 0.720410i | \(-0.743954\pi\) | ||||
−0.693548 | + | 0.720410i | \(0.743954\pi\) | |||||||
\(350\) | −1.01760e111 | −2.19087 | ||||||||
\(351\) | −3.20561e110 | −0.609608 | ||||||||
\(352\) | −1.54231e110 | −0.259159 | ||||||||
\(353\) | 9.43721e110 | 1.40166 | 0.700832 | − | 0.713327i | \(-0.252812\pi\) | ||||
0.700832 | + | 0.713327i | \(0.252812\pi\) | |||||||
\(354\) | −2.70448e110 | −0.355175 | ||||||||
\(355\) | 2.50775e110 | 0.291307 | ||||||||
\(356\) | 2.80459e109 | 0.0288267 | ||||||||
\(357\) | −8.03202e110 | −0.730730 | ||||||||
\(358\) | 1.61001e111 | 1.29693 | ||||||||
\(359\) | 8.72474e110 | 0.622507 | 0.311253 | − | 0.950327i | \(-0.399251\pi\) | ||||
0.311253 | + | 0.950327i | \(0.399251\pi\) | |||||||
\(360\) | 1.32309e111 | 0.836431 | ||||||||
\(361\) | −1.76707e111 | −0.990125 | ||||||||
\(362\) | −1.71132e111 | −0.850177 | ||||||||
\(363\) | −3.97269e111 | −1.75044 | ||||||||
\(364\) | 2.24065e111 | 0.875918 | ||||||||
\(365\) | −5.96892e111 | −2.07089 | ||||||||
\(366\) | 3.41797e111 | 1.05279 | ||||||||
\(367\) | −2.12057e111 | −0.580068 | −0.290034 | − | 0.957016i | \(-0.593667\pi\) | ||||
−0.290034 | + | 0.957016i | \(0.593667\pi\) | |||||||
\(368\) | 1.01697e111 | 0.247131 | ||||||||
\(369\) | 9.44432e111 | 2.03950 | ||||||||
\(370\) | 4.51728e110 | 0.0867166 | ||||||||
\(371\) | 3.59315e111 | 0.613353 | ||||||||
\(372\) | −4.69703e111 | −0.713190 | ||||||||
\(373\) | −6.35036e111 | −0.857954 | −0.428977 | − | 0.903315i | \(-0.641126\pi\) | ||||
−0.428977 | + | 0.903315i | \(0.641126\pi\) | |||||||
\(374\) | −2.95332e111 | −0.355137 | ||||||||
\(375\) | 3.09171e112 | 3.31008 | ||||||||
\(376\) | 2.25888e111 | 0.215389 | ||||||||
\(377\) | −5.13599e111 | −0.436290 | ||||||||
\(378\) | 6.37433e111 | 0.482549 | ||||||||
\(379\) | −6.49105e111 | −0.438035 | −0.219018 | − | 0.975721i | \(-0.570285\pi\) | ||||
−0.219018 | + | 0.975721i | \(0.570285\pi\) | |||||||
\(380\) | −1.47998e111 | −0.0890571 | ||||||||
\(381\) | −8.23592e111 | −0.442054 | ||||||||
\(382\) | 1.02048e112 | 0.488708 | ||||||||
\(383\) | 3.64877e112 | 1.55955 | 0.779777 | − | 0.626058i | \(-0.215333\pi\) | ||||
0.779777 | + | 0.626058i | \(0.215333\pi\) | |||||||
\(384\) | 3.52811e111 | 0.134627 | ||||||||
\(385\) | −1.07983e113 | −3.67970 | ||||||||
\(386\) | −1.57734e112 | −0.480151 | ||||||||
\(387\) | −8.94677e111 | −0.243354 | ||||||||
\(388\) | 2.82321e112 | 0.686377 | ||||||||
\(389\) | 2.98278e112 | 0.648356 | 0.324178 | − | 0.945996i | \(-0.394912\pi\) | ||||
0.324178 | + | 0.945996i | \(0.394912\pi\) | |||||||
\(390\) | −1.24222e113 | −2.41484 | ||||||||
\(391\) | 1.94735e112 | 0.338654 | ||||||||
\(392\) | −2.18356e112 | −0.339799 | ||||||||
\(393\) | 1.36479e113 | 1.90104 | ||||||||
\(394\) | −7.17074e111 | −0.0894290 | ||||||||
\(395\) | −1.67782e113 | −1.87400 | ||||||||
\(396\) | 9.66956e112 | 0.967533 | ||||||||
\(397\) | 1.58119e113 | 1.41774 | 0.708869 | − | 0.705340i | \(-0.249206\pi\) | ||||
0.708869 | + | 0.705340i | \(0.249206\pi\) | |||||||
\(398\) | −1.29704e113 | −1.04242 | ||||||||
\(399\) | −2.94162e112 | −0.211965 | ||||||||
\(400\) | 8.55917e112 | 0.553123 | ||||||||
\(401\) | −1.43347e112 | −0.0831014 | −0.0415507 | − | 0.999136i | \(-0.513230\pi\) | ||||
−0.0415507 | + | 0.999136i | \(0.513230\pi\) | |||||||
\(402\) | −2.46109e113 | −1.28025 | ||||||||
\(403\) | 2.50906e113 | 1.17150 | ||||||||
\(404\) | −2.64964e112 | −0.111070 | ||||||||
\(405\) | 2.75053e113 | 1.03543 | ||||||||
\(406\) | 1.02129e113 | 0.345355 | ||||||||
\(407\) | 3.30137e112 | 0.100308 | ||||||||
\(408\) | 6.75585e112 | 0.184486 | ||||||||
\(409\) | 3.85069e113 | 0.945310 | 0.472655 | − | 0.881247i | \(-0.343296\pi\) | ||||
0.472655 | + | 0.881247i | \(0.343296\pi\) | |||||||
\(410\) | 8.87102e113 | 1.95828 | ||||||||
\(411\) | −3.03600e113 | −0.602814 | ||||||||
\(412\) | 2.21043e112 | 0.0394864 | ||||||||
\(413\) | −2.87274e113 | −0.461816 | ||||||||
\(414\) | −6.37589e113 | −0.922626 | ||||||||
\(415\) | −1.90853e114 | −2.48661 | ||||||||
\(416\) | −1.88464e113 | −0.221141 | ||||||||
\(417\) | −3.61920e113 | −0.382555 | ||||||||
\(418\) | −1.08161e113 | −0.103016 | ||||||||
\(419\) | −3.83071e113 | −0.328828 | −0.164414 | − | 0.986391i | \(-0.552573\pi\) | ||||
−0.164414 | + | 0.986391i | \(0.552573\pi\) | |||||||
\(420\) | 2.47015e114 | 1.91152 | ||||||||
\(421\) | 4.69775e113 | 0.327808 | 0.163904 | − | 0.986476i | \(-0.447591\pi\) | ||||
0.163904 | + | 0.986476i | \(0.447591\pi\) | |||||||
\(422\) | −7.91900e113 | −0.498401 | ||||||||
\(423\) | −1.41621e114 | −0.804122 | ||||||||
\(424\) | −3.02225e113 | −0.154852 | ||||||||
\(425\) | 1.63897e114 | 0.757969 | ||||||||
\(426\) | −4.19248e113 | −0.175046 | ||||||||
\(427\) | 3.63061e114 | 1.36888 | ||||||||
\(428\) | 8.74599e113 | 0.297855 | ||||||||
\(429\) | −9.07855e114 | −2.79334 | ||||||||
\(430\) | −8.40367e113 | −0.233664 | ||||||||
\(431\) | 2.61807e114 | 0.657990 | 0.328995 | − | 0.944332i | \(-0.393290\pi\) | ||||
0.328995 | + | 0.944332i | \(0.393290\pi\) | |||||||
\(432\) | −5.36154e113 | −0.121828 | ||||||||
\(433\) | 3.19596e114 | 0.656715 | 0.328358 | − | 0.944553i | \(-0.393505\pi\) | ||||
0.328358 | + | 0.944553i | \(0.393505\pi\) | |||||||
\(434\) | −4.98924e114 | −0.927323 | ||||||||
\(435\) | −5.66205e114 | −0.952118 | ||||||||
\(436\) | 3.97663e114 | 0.605136 | ||||||||
\(437\) | 7.13192e113 | 0.0982345 | ||||||||
\(438\) | 9.97890e114 | 1.24440 | ||||||||
\(439\) | 1.78415e114 | 0.201476 | 0.100738 | − | 0.994913i | \(-0.467880\pi\) | ||||
0.100738 | + | 0.994913i | \(0.467880\pi\) | |||||||
\(440\) | 9.08258e114 | 0.929005 | ||||||||
\(441\) | 1.36899e115 | 1.26859 | ||||||||
\(442\) | −3.60884e114 | −0.303039 | ||||||||
\(443\) | 7.51654e114 | 0.572079 | 0.286040 | − | 0.958218i | \(-0.407661\pi\) | ||||
0.286040 | + | 0.958218i | \(0.407661\pi\) | |||||||
\(444\) | −7.55203e113 | −0.0521080 | ||||||||
\(445\) | −1.65161e114 | −0.103335 | ||||||||
\(446\) | −1.52153e115 | −0.863402 | ||||||||
\(447\) | 3.45821e115 | 1.78022 | ||||||||
\(448\) | 3.74760e114 | 0.175049 | ||||||||
\(449\) | −3.51489e115 | −1.49003 | −0.745016 | − | 0.667046i | \(-0.767558\pi\) | ||||
−0.745016 | + | 0.667046i | \(0.767558\pi\) | |||||||
\(450\) | −5.36618e115 | −2.06501 | ||||||||
\(451\) | 6.48322e115 | 2.26522 | ||||||||
\(452\) | −1.65234e115 | −0.524297 | ||||||||
\(453\) | −2.73532e114 | −0.0788381 | ||||||||
\(454\) | −3.74336e115 | −0.980238 | ||||||||
\(455\) | −1.31950e116 | −3.13989 | ||||||||
\(456\) | 2.47424e114 | 0.0535144 | ||||||||
\(457\) | 2.79083e115 | 0.548755 | 0.274378 | − | 0.961622i | \(-0.411528\pi\) | ||||
0.274378 | + | 0.961622i | \(0.411528\pi\) | |||||||
\(458\) | 5.74905e115 | 1.02789 | ||||||||
\(459\) | −1.02666e115 | −0.166946 | ||||||||
\(460\) | −5.98885e115 | −0.885886 | ||||||||
\(461\) | −1.12627e116 | −1.51584 | −0.757918 | − | 0.652349i | \(-0.773783\pi\) | ||||
−0.757918 | + | 0.652349i | \(0.773783\pi\) | |||||||
\(462\) | 1.80526e116 | 2.21113 | ||||||||
\(463\) | 7.18872e115 | 0.801454 | 0.400727 | − | 0.916198i | \(-0.368758\pi\) | ||||
0.400727 | + | 0.916198i | \(0.368758\pi\) | |||||||
\(464\) | −8.59021e114 | −0.0871909 | ||||||||
\(465\) | 2.76605e116 | 2.55656 | ||||||||
\(466\) | −1.00080e116 | −0.842479 | ||||||||
\(467\) | −4.19475e115 | −0.321678 | −0.160839 | − | 0.986981i | \(-0.551420\pi\) | ||||
−0.160839 | + | 0.986981i | \(0.551420\pi\) | |||||||
\(468\) | 1.18158e116 | 0.825597 | ||||||||
\(469\) | −2.61420e116 | −1.66464 | ||||||||
\(470\) | −1.33024e116 | −0.772100 | ||||||||
\(471\) | 7.16525e115 | 0.379159 | ||||||||
\(472\) | 2.41630e115 | 0.116593 | ||||||||
\(473\) | −6.14167e115 | −0.270288 | ||||||||
\(474\) | 2.80499e116 | 1.12609 | ||||||||
\(475\) | 6.00249e115 | 0.219867 | ||||||||
\(476\) | 7.17615e115 | 0.239877 | ||||||||
\(477\) | 1.89481e116 | 0.578117 | ||||||||
\(478\) | 5.30055e115 | 0.147641 | ||||||||
\(479\) | 5.34212e116 | 1.35869 | 0.679343 | − | 0.733821i | \(-0.262265\pi\) | ||||
0.679343 | + | 0.733821i | \(0.262265\pi\) | |||||||
\(480\) | −2.07768e116 | −0.482597 | ||||||||
\(481\) | 4.03414e115 | 0.0855934 | ||||||||
\(482\) | 3.92258e116 | 0.760371 | ||||||||
\(483\) | −1.19035e117 | −2.10850 | ||||||||
\(484\) | 3.54937e116 | 0.574617 | ||||||||
\(485\) | −1.66257e117 | −2.46045 | ||||||||
\(486\) | −7.14500e116 | −0.966774 | ||||||||
\(487\) | −1.85775e116 | −0.229868 | −0.114934 | − | 0.993373i | \(-0.536666\pi\) | ||||
−0.114934 | + | 0.993373i | \(0.536666\pi\) | |||||||
\(488\) | −3.05376e116 | −0.345599 | ||||||||
\(489\) | 2.23582e117 | 2.31474 | ||||||||
\(490\) | 1.28589e117 | 1.21807 | ||||||||
\(491\) | 7.39691e116 | 0.641217 | 0.320609 | − | 0.947212i | \(-0.396113\pi\) | ||||
0.320609 | + | 0.947212i | \(0.396113\pi\) | |||||||
\(492\) | −1.48306e117 | −1.17673 | ||||||||
\(493\) | −1.64491e116 | −0.119482 | ||||||||
\(494\) | −1.32169e116 | −0.0879036 | ||||||||
\(495\) | −5.69434e117 | −3.46830 | ||||||||
\(496\) | 4.19652e116 | 0.234119 | ||||||||
\(497\) | −4.45330e116 | −0.227604 | ||||||||
\(498\) | 3.19070e117 | 1.49420 | ||||||||
\(499\) | 6.47026e115 | 0.0277682 | 0.0138841 | − | 0.999904i | \(-0.495580\pi\) | ||||
0.0138841 | + | 0.999904i | \(0.495580\pi\) | |||||||
\(500\) | −2.76227e117 | −1.08660 | ||||||||
\(501\) | 8.01546e117 | 2.89060 | ||||||||
\(502\) | −8.59927e116 | −0.284348 | ||||||||
\(503\) | 4.31145e117 | 1.30742 | 0.653711 | − | 0.756744i | \(-0.273211\pi\) | ||||
0.653711 | + | 0.756744i | \(0.273211\pi\) | |||||||
\(504\) | −2.34956e117 | −0.653519 | ||||||||
\(505\) | 1.56035e117 | 0.398151 | ||||||||
\(506\) | −4.37684e117 | −1.02474 | ||||||||
\(507\) | −4.00462e117 | −0.860429 | ||||||||
\(508\) | 7.35832e116 | 0.145113 | ||||||||
\(509\) | 3.40293e117 | 0.616069 | 0.308035 | − | 0.951375i | \(-0.400329\pi\) | ||||
0.308035 | + | 0.951375i | \(0.400329\pi\) | |||||||
\(510\) | −3.97847e117 | −0.661323 | ||||||||
\(511\) | 1.05997e118 | 1.61802 | ||||||||
\(512\) | −3.15216e116 | −0.0441942 | ||||||||
\(513\) | −3.76001e116 | −0.0484266 | ||||||||
\(514\) | 7.05765e117 | 0.835150 | ||||||||
\(515\) | −1.30171e117 | −0.141546 | ||||||||
\(516\) | 1.40493e117 | 0.140409 | ||||||||
\(517\) | −9.72183e117 | −0.893119 | ||||||||
\(518\) | −8.02186e116 | −0.0677533 | ||||||||
\(519\) | 3.03830e118 | 2.35967 | ||||||||
\(520\) | 1.10985e118 | 0.792721 | ||||||||
\(521\) | −2.19738e118 | −1.44366 | −0.721828 | − | 0.692072i | \(-0.756698\pi\) | ||||
−0.721828 | + | 0.692072i | \(0.756698\pi\) | |||||||
\(522\) | 5.38564e117 | 0.325515 | ||||||||
\(523\) | −6.55512e116 | −0.0364550 | −0.0182275 | − | 0.999834i | \(-0.505802\pi\) | ||||
−0.0182275 | + | 0.999834i | \(0.505802\pi\) | |||||||
\(524\) | −1.21936e118 | −0.624054 | ||||||||
\(525\) | −1.00184e119 | −4.71922 | ||||||||
\(526\) | −5.99086e117 | −0.259782 | ||||||||
\(527\) | 8.03578e117 | 0.320824 | ||||||||
\(528\) | −1.51843e118 | −0.558239 | ||||||||
\(529\) | −6.74035e116 | −0.0228224 | ||||||||
\(530\) | 1.77979e118 | 0.555095 | ||||||||
\(531\) | −1.51490e118 | −0.435285 | ||||||||
\(532\) | 2.62817e117 | 0.0695820 | ||||||||
\(533\) | 7.92223e118 | 1.93292 | ||||||||
\(534\) | 2.76117e117 | 0.0620939 | ||||||||
\(535\) | −5.15046e118 | −1.06772 | ||||||||
\(536\) | 2.19884e118 | 0.420268 | ||||||||
\(537\) | 1.58508e119 | 2.79364 | ||||||||
\(538\) | −4.94220e118 | −0.803325 | ||||||||
\(539\) | 9.39766e118 | 1.40899 | ||||||||
\(540\) | 3.15738e118 | 0.436715 | ||||||||
\(541\) | −6.90077e118 | −0.880676 | −0.440338 | − | 0.897832i | \(-0.645141\pi\) | ||||
−0.440338 | + | 0.897832i | \(0.645141\pi\) | |||||||
\(542\) | 1.15075e119 | 1.35523 | ||||||||
\(543\) | −1.68483e119 | −1.83131 | ||||||||
\(544\) | −6.03596e117 | −0.0605612 | ||||||||
\(545\) | −2.34181e119 | −2.16922 | ||||||||
\(546\) | 2.20596e119 | 1.88676 | ||||||||
\(547\) | −2.85000e117 | −0.0225111 | −0.0112556 | − | 0.999937i | \(-0.503583\pi\) | ||||
−0.0112556 | + | 0.999937i | \(0.503583\pi\) | |||||||
\(548\) | 2.71250e118 | 0.197886 | ||||||||
\(549\) | 1.91456e119 | 1.29024 | ||||||||
\(550\) | −3.68371e119 | −2.29355 | ||||||||
\(551\) | −6.02425e117 | −0.0346584 | ||||||||
\(552\) | 1.00122e119 | 0.532329 | ||||||||
\(553\) | 2.97949e119 | 1.46419 | ||||||||
\(554\) | −8.00471e118 | −0.363640 | ||||||||
\(555\) | 4.44734e118 | 0.186791 | ||||||||
\(556\) | 3.23355e118 | 0.125582 | ||||||||
\(557\) | 2.61775e118 | 0.0940214 | 0.0470107 | − | 0.998894i | \(-0.485031\pi\) | ||||
0.0470107 | + | 0.998894i | \(0.485031\pi\) | |||||||
\(558\) | −2.63102e119 | −0.874049 | ||||||||
\(559\) | −7.50487e118 | −0.230637 | ||||||||
\(560\) | −2.20694e119 | −0.627495 | ||||||||
\(561\) | −2.90760e119 | −0.764979 | ||||||||
\(562\) | −4.73035e118 | −0.115176 | ||||||||
\(563\) | −5.74342e118 | −0.129436 | −0.0647181 | − | 0.997904i | \(-0.520615\pi\) | ||||
−0.0647181 | + | 0.997904i | \(0.520615\pi\) | |||||||
\(564\) | 2.22391e119 | 0.463955 | ||||||||
\(565\) | 9.73052e119 | 1.87944 | ||||||||
\(566\) | −6.77294e119 | −1.21133 | ||||||||
\(567\) | −4.88443e119 | −0.809004 | ||||||||
\(568\) | 3.74574e118 | 0.0574626 | ||||||||
\(569\) | −1.05774e120 | −1.50313 | −0.751566 | − | 0.659657i | \(-0.770701\pi\) | ||||
−0.751566 | + | 0.659657i | \(0.770701\pi\) | |||||||
\(570\) | −1.45706e119 | −0.191832 | ||||||||
\(571\) | −3.49608e119 | −0.426492 | −0.213246 | − | 0.976999i | \(-0.568404\pi\) | ||||
−0.213246 | + | 0.976999i | \(0.568404\pi\) | |||||||
\(572\) | 8.11116e119 | 0.916972 | ||||||||
\(573\) | 1.00468e120 | 1.05270 | ||||||||
\(574\) | −1.57533e120 | −1.53004 | ||||||||
\(575\) | 2.42896e120 | 2.18710 | ||||||||
\(576\) | 1.97625e119 | 0.164992 | ||||||||
\(577\) | −7.07886e119 | −0.548044 | −0.274022 | − | 0.961723i | \(-0.588354\pi\) | ||||
−0.274022 | + | 0.961723i | \(0.588354\pi\) | |||||||
\(578\) | 8.69215e119 | 0.624117 | ||||||||
\(579\) | −1.55292e120 | −1.03426 | ||||||||
\(580\) | 5.05872e119 | 0.312552 | ||||||||
\(581\) | 3.38920e120 | 1.94283 | ||||||||
\(582\) | 2.77949e120 | 1.47848 | ||||||||
\(583\) | 1.30072e120 | 0.642101 | ||||||||
\(584\) | −8.91557e119 | −0.408498 | ||||||||
\(585\) | −6.95824e120 | −2.95951 | ||||||||
\(586\) | 2.93007e120 | 1.15700 | ||||||||
\(587\) | 7.32347e119 | 0.268509 | 0.134255 | − | 0.990947i | \(-0.457136\pi\) | ||||
0.134255 | + | 0.990947i | \(0.457136\pi\) | |||||||
\(588\) | −2.14975e120 | −0.731939 | ||||||||
\(589\) | 2.94299e119 | 0.0930624 | ||||||||
\(590\) | −1.42294e120 | −0.417951 | ||||||||
\(591\) | −7.05971e119 | −0.192633 | ||||||||
\(592\) | 6.74730e118 | 0.0171055 | ||||||||
\(593\) | 8.21847e120 | 1.93603 | 0.968014 | − | 0.250896i | \(-0.0807253\pi\) | ||||
0.968014 | + | 0.250896i | \(0.0807253\pi\) | |||||||
\(594\) | 2.30751e120 | 0.505165 | ||||||||
\(595\) | −4.22598e120 | −0.859884 | ||||||||
\(596\) | −3.08971e120 | −0.584394 | ||||||||
\(597\) | −1.27696e121 | −2.24541 | ||||||||
\(598\) | −5.34832e120 | −0.874412 | ||||||||
\(599\) | 7.76478e120 | 1.18049 | 0.590245 | − | 0.807224i | \(-0.299031\pi\) | ||||
0.590245 | + | 0.807224i | \(0.299031\pi\) | |||||||
\(600\) | 8.42665e120 | 1.19145 | ||||||||
\(601\) | 1.84325e120 | 0.242406 | 0.121203 | − | 0.992628i | \(-0.461325\pi\) | ||||
0.121203 | + | 0.992628i | \(0.461325\pi\) | |||||||
\(602\) | 1.49234e120 | 0.182566 | ||||||||
\(603\) | −1.37857e121 | −1.56901 | ||||||||
\(604\) | 2.44385e119 | 0.0258802 | ||||||||
\(605\) | −2.09020e121 | −2.05982 | ||||||||
\(606\) | −2.60861e120 | −0.239249 | ||||||||
\(607\) | −5.51306e120 | −0.470635 | −0.235318 | − | 0.971919i | \(-0.575613\pi\) | ||||
−0.235318 | + | 0.971919i | \(0.575613\pi\) | |||||||
\(608\) | −2.21059e119 | −0.0175672 | ||||||||
\(609\) | 1.00548e121 | 0.743908 | ||||||||
\(610\) | 1.79834e121 | 1.23886 | ||||||||
\(611\) | −1.18797e121 | −0.762100 | ||||||||
\(612\) | 3.78426e120 | 0.226096 | ||||||||
\(613\) | 1.87741e121 | 1.04479 | 0.522395 | − | 0.852703i | \(-0.325039\pi\) | ||||
0.522395 | + | 0.852703i | \(0.325039\pi\) | |||||||
\(614\) | −3.24991e120 | −0.168480 | ||||||||
\(615\) | 8.73366e121 | 4.21822 | ||||||||
\(616\) | −1.61290e121 | −0.725849 | ||||||||
\(617\) | −9.23457e120 | −0.387268 | −0.193634 | − | 0.981074i | \(-0.562027\pi\) | ||||
−0.193634 | + | 0.981074i | \(0.562027\pi\) | |||||||
\(618\) | 2.17621e120 | 0.0850553 | ||||||||
\(619\) | 1.40132e121 | 0.510498 | 0.255249 | − | 0.966875i | \(-0.417843\pi\) | ||||
0.255249 | + | 0.966875i | \(0.417843\pi\) | |||||||
\(620\) | −2.47131e121 | −0.839243 | ||||||||
\(621\) | −1.52152e121 | −0.481719 | ||||||||
\(622\) | −1.29922e121 | −0.383531 | ||||||||
\(623\) | 2.93295e120 | 0.0807374 | ||||||||
\(624\) | −1.85546e121 | −0.476346 | ||||||||
\(625\) | 7.02701e121 | 1.68263 | ||||||||
\(626\) | −6.11350e121 | −1.36555 | ||||||||
\(627\) | −1.06487e121 | −0.221900 | ||||||||
\(628\) | −6.40174e120 | −0.124467 | ||||||||
\(629\) | 1.29202e120 | 0.0234404 | ||||||||
\(630\) | 1.38364e122 | 2.34266 | ||||||||
\(631\) | −1.14147e122 | −1.80380 | −0.901898 | − | 0.431949i | \(-0.857826\pi\) | ||||
−0.901898 | + | 0.431949i | \(0.857826\pi\) | |||||||
\(632\) | −2.50609e121 | −0.369662 | ||||||||
\(633\) | −7.79639e121 | −1.07357 | ||||||||
\(634\) | −6.63461e121 | −0.852968 | ||||||||
\(635\) | −4.33327e121 | −0.520186 | ||||||||
\(636\) | −2.97546e121 | −0.333557 | ||||||||
\(637\) | 1.14835e122 | 1.20229 | ||||||||
\(638\) | 3.69707e121 | 0.361542 | ||||||||
\(639\) | −2.34840e121 | −0.214528 | ||||||||
\(640\) | 1.85629e121 | 0.158422 | ||||||||
\(641\) | 9.70612e121 | 0.773965 | 0.386983 | − | 0.922087i | \(-0.373517\pi\) | ||||
0.386983 | + | 0.922087i | \(0.373517\pi\) | |||||||
\(642\) | 8.61058e121 | 0.641591 | ||||||||
\(643\) | −1.41822e122 | −0.987570 | −0.493785 | − | 0.869584i | \(-0.664387\pi\) | ||||
−0.493785 | + | 0.869584i | \(0.664387\pi\) | |||||||
\(644\) | 1.06351e122 | 0.692159 | ||||||||
\(645\) | −8.27356e121 | −0.503320 | ||||||||
\(646\) | −4.23298e120 | −0.0240731 | ||||||||
\(647\) | 1.71225e122 | 0.910400 | 0.455200 | − | 0.890389i | \(-0.349568\pi\) | ||||
0.455200 | + | 0.890389i | \(0.349568\pi\) | |||||||
\(648\) | 4.10837e121 | 0.204247 | ||||||||
\(649\) | −1.03993e122 | −0.483461 | ||||||||
\(650\) | −4.50134e122 | −1.95709 | ||||||||
\(651\) | −4.91199e122 | −1.99749 | ||||||||
\(652\) | −1.99758e122 | −0.759859 | ||||||||
\(653\) | −2.47769e122 | −0.881704 | −0.440852 | − | 0.897580i | \(-0.645324\pi\) | ||||
−0.440852 | + | 0.897580i | \(0.645324\pi\) | |||||||
\(654\) | 3.91506e122 | 1.30349 | ||||||||
\(655\) | 7.18075e122 | 2.23704 | ||||||||
\(656\) | 1.32503e122 | 0.386286 | ||||||||
\(657\) | 5.58963e122 | 1.52507 | ||||||||
\(658\) | 2.36226e122 | 0.603256 | ||||||||
\(659\) | −1.48578e122 | −0.355172 | −0.177586 | − | 0.984105i | \(-0.556829\pi\) | ||||
−0.177586 | + | 0.984105i | \(0.556829\pi\) | |||||||
\(660\) | 8.94196e122 | 2.00111 | ||||||||
\(661\) | 4.76145e122 | 0.997645 | 0.498823 | − | 0.866704i | \(-0.333766\pi\) | ||||
0.498823 | + | 0.866704i | \(0.333766\pi\) | |||||||
\(662\) | 2.49929e122 | 0.490335 | ||||||||
\(663\) | −3.55296e122 | −0.652758 | ||||||||
\(664\) | −2.85071e122 | −0.490503 | ||||||||
\(665\) | −1.54771e122 | −0.249430 | ||||||||
\(666\) | −4.23023e121 | −0.0638609 | ||||||||
\(667\) | −2.43777e122 | −0.344761 | ||||||||
\(668\) | −7.16135e122 | −0.948897 | ||||||||
\(669\) | −1.49797e123 | −1.85980 | ||||||||
\(670\) | −1.29488e123 | −1.50653 | ||||||||
\(671\) | 1.31428e123 | 1.43304 | ||||||||
\(672\) | 3.68957e122 | 0.377062 | ||||||||
\(673\) | 1.03092e122 | 0.0987573 | 0.0493787 | − | 0.998780i | \(-0.484276\pi\) | ||||
0.0493787 | + | 0.998780i | \(0.484276\pi\) | |||||||
\(674\) | 1.15875e123 | 1.04060 | ||||||||
\(675\) | −1.28057e123 | −1.07817 | ||||||||
\(676\) | 3.57790e122 | 0.282453 | ||||||||
\(677\) | −1.52310e123 | −1.12752 | −0.563758 | − | 0.825940i | \(-0.690645\pi\) | ||||
−0.563758 | + | 0.825940i | \(0.690645\pi\) | |||||||
\(678\) | −1.62676e123 | −1.12936 | ||||||||
\(679\) | 2.95241e123 | 1.92239 | ||||||||
\(680\) | 3.55454e122 | 0.217093 | ||||||||
\(681\) | −3.68540e123 | −2.11147 | ||||||||
\(682\) | −1.80611e123 | −0.970786 | ||||||||
\(683\) | 3.13567e123 | 1.58136 | 0.790678 | − | 0.612232i | \(-0.209728\pi\) | ||||
0.790678 | + | 0.612232i | \(0.209728\pi\) | |||||||
\(684\) | 1.38593e122 | 0.0655845 | ||||||||
\(685\) | −1.59737e123 | −0.709359 | ||||||||
\(686\) | 9.24344e121 | 0.0385243 | ||||||||
\(687\) | 5.66004e123 | 2.21412 | ||||||||
\(688\) | −1.25523e122 | −0.0460920 | ||||||||
\(689\) | 1.58943e123 | 0.547905 | ||||||||
\(690\) | −5.89613e123 | −1.90823 | ||||||||
\(691\) | −3.79375e123 | −1.15285 | −0.576427 | − | 0.817149i | \(-0.695553\pi\) | ||||
−0.576427 | + | 0.817149i | \(0.695553\pi\) | |||||||
\(692\) | −2.71455e123 | −0.774609 | ||||||||
\(693\) | 1.01121e124 | 2.70985 | ||||||||
\(694\) | 5.25531e123 | 1.32270 | ||||||||
\(695\) | −1.90421e123 | −0.450170 | ||||||||
\(696\) | −8.45720e122 | −0.187813 | ||||||||
\(697\) | 2.53726e123 | 0.529345 | ||||||||
\(698\) | 5.00383e123 | 0.980825 | ||||||||
\(699\) | −9.85303e123 | −1.81473 | ||||||||
\(700\) | 8.95089e123 | 1.54918 | ||||||||
\(701\) | 5.95337e123 | 0.968342 | 0.484171 | − | 0.874973i | \(-0.339121\pi\) | ||||
0.484171 | + | 0.874973i | \(0.339121\pi\) | |||||||
\(702\) | 2.81968e123 | 0.431058 | ||||||||
\(703\) | 4.73184e121 | 0.00679944 | ||||||||
\(704\) | 1.35663e123 | 0.183253 | ||||||||
\(705\) | −1.30965e124 | −1.66313 | ||||||||
\(706\) | −8.30106e123 | −0.991126 | ||||||||
\(707\) | −2.77090e123 | −0.311083 | ||||||||
\(708\) | 2.37889e123 | 0.251147 | ||||||||
\(709\) | −4.61148e123 | −0.457857 | −0.228928 | − | 0.973443i | \(-0.573522\pi\) | ||||
−0.228928 | + | 0.973443i | \(0.573522\pi\) | |||||||
\(710\) | −2.20584e123 | −0.205985 | ||||||||
\(711\) | 1.57120e124 | 1.38008 | ||||||||
\(712\) | −2.46695e122 | −0.0203836 | ||||||||
\(713\) | 1.19091e124 | 0.925728 | ||||||||
\(714\) | 7.06504e123 | 0.516704 | ||||||||
\(715\) | −4.77661e124 | −3.28706 | ||||||||
\(716\) | −1.41618e124 | −0.917070 | ||||||||
\(717\) | 5.21848e123 | 0.318024 | ||||||||
\(718\) | −7.67436e123 | −0.440179 | ||||||||
\(719\) | −1.03961e124 | −0.561257 | −0.280628 | − | 0.959816i | \(-0.590543\pi\) | ||||
−0.280628 | + | 0.959816i | \(0.590543\pi\) | |||||||
\(720\) | −1.16380e124 | −0.591446 | ||||||||
\(721\) | 2.31159e123 | 0.110593 | ||||||||
\(722\) | 1.55433e124 | 0.700124 | ||||||||
\(723\) | 3.86184e124 | 1.63787 | ||||||||
\(724\) | 1.50530e124 | 0.601166 | ||||||||
\(725\) | −2.05171e124 | −0.771638 | ||||||||
\(726\) | 3.49442e124 | 1.23775 | ||||||||
\(727\) | 4.12807e123 | 0.137721 | 0.0688605 | − | 0.997626i | \(-0.478064\pi\) | ||||
0.0688605 | + | 0.997626i | \(0.478064\pi\) | |||||||
\(728\) | −1.97090e124 | −0.619368 | ||||||||
\(729\) | −5.08297e124 | −1.50477 | ||||||||
\(730\) | 5.25032e124 | 1.46434 | ||||||||
\(731\) | −2.40359e123 | −0.0631618 | ||||||||
\(732\) | −3.00648e124 | −0.744433 | ||||||||
\(733\) | −8.86059e123 | −0.206747 | −0.103374 | − | 0.994643i | \(-0.532964\pi\) | ||||
−0.103374 | + | 0.994643i | \(0.532964\pi\) | |||||||
\(734\) | 1.86528e124 | 0.410170 | ||||||||
\(735\) | 1.26598e125 | 2.62377 | ||||||||
\(736\) | −8.94534e123 | −0.174748 | ||||||||
\(737\) | −9.46343e124 | −1.74266 | ||||||||
\(738\) | −8.30731e124 | −1.44214 | ||||||||
\(739\) | 3.39289e124 | 0.555311 | 0.277656 | − | 0.960681i | \(-0.410443\pi\) | ||||
0.277656 | + | 0.960681i | \(0.410443\pi\) | |||||||
\(740\) | −3.97344e123 | −0.0613179 | ||||||||
\(741\) | −1.30122e124 | −0.189348 | ||||||||
\(742\) | −3.16057e124 | −0.433706 | ||||||||
\(743\) | 2.33957e124 | 0.302776 | 0.151388 | − | 0.988474i | \(-0.451626\pi\) | ||||
0.151388 | + | 0.988474i | \(0.451626\pi\) | |||||||
\(744\) | 4.13155e124 | 0.504301 | ||||||||
\(745\) | 1.81951e125 | 2.09487 | ||||||||
\(746\) | 5.58583e124 | 0.606665 | ||||||||
\(747\) | 1.78726e125 | 1.83122 | ||||||||
\(748\) | 2.59777e124 | 0.251120 | ||||||||
\(749\) | 9.14626e124 | 0.834227 | ||||||||
\(750\) | −2.71950e125 | −2.34058 | ||||||||
\(751\) | −1.22902e125 | −0.998208 | −0.499104 | − | 0.866542i | \(-0.666337\pi\) | ||||
−0.499104 | + | 0.866542i | \(0.666337\pi\) | |||||||
\(752\) | −1.98694e124 | −0.152303 | ||||||||
\(753\) | −8.46613e124 | −0.612496 | ||||||||
\(754\) | 4.51767e124 | 0.308504 | ||||||||
\(755\) | −1.43917e124 | −0.0927724 | ||||||||
\(756\) | −5.60692e124 | −0.341213 | ||||||||
\(757\) | −1.63786e125 | −0.941035 | −0.470518 | − | 0.882391i | \(-0.655933\pi\) | ||||
−0.470518 | + | 0.882391i | \(0.655933\pi\) | |||||||
\(758\) | 5.70959e124 | 0.309738 | ||||||||
\(759\) | −4.30908e125 | −2.20733 | ||||||||
\(760\) | 1.30180e124 | 0.0629729 | ||||||||
\(761\) | −1.79055e125 | −0.818001 | −0.409001 | − | 0.912534i | \(-0.634123\pi\) | ||||
−0.409001 | + | 0.912534i | \(0.634123\pi\) | |||||||
\(762\) | 7.24439e124 | 0.312580 | ||||||||
\(763\) | 4.15863e125 | 1.69486 | ||||||||
\(764\) | −8.97626e124 | −0.345569 | ||||||||
\(765\) | −2.22852e125 | −0.810484 | ||||||||
\(766\) | −3.20949e125 | −1.10277 | ||||||||
\(767\) | −1.27075e125 | −0.412537 | ||||||||
\(768\) | −3.10335e124 | −0.0951959 | ||||||||
\(769\) | −7.38198e124 | −0.213982 | −0.106991 | − | 0.994260i | \(-0.534122\pi\) | ||||
−0.106991 | + | 0.994260i | \(0.534122\pi\) | |||||||
\(770\) | 9.49826e125 | 2.60194 | ||||||||
\(771\) | 6.94838e125 | 1.79895 | ||||||||
\(772\) | 1.38744e125 | 0.339518 | ||||||||
\(773\) | −7.15284e125 | −1.65451 | −0.827257 | − | 0.561824i | \(-0.810100\pi\) | ||||
−0.827257 | + | 0.561824i | \(0.810100\pi\) | |||||||
\(774\) | 7.86966e124 | 0.172078 | ||||||||
\(775\) | 1.00231e126 | 2.07195 | ||||||||
\(776\) | −2.48332e125 | −0.485342 | ||||||||
\(777\) | −7.89765e124 | −0.145943 | ||||||||
\(778\) | −2.62368e125 | −0.458457 | ||||||||
\(779\) | 9.29236e124 | 0.153549 | ||||||||
\(780\) | 1.09267e126 | 1.70755 | ||||||||
\(781\) | −1.61210e125 | −0.238271 | ||||||||
\(782\) | −1.71291e125 | −0.239465 | ||||||||
\(783\) | 1.28521e125 | 0.169957 | ||||||||
\(784\) | 1.92068e125 | 0.240274 | ||||||||
\(785\) | 3.76994e125 | 0.446174 | ||||||||
\(786\) | −1.20048e126 | −1.34424 | ||||||||
\(787\) | −9.03009e125 | −0.956734 | −0.478367 | − | 0.878160i | \(-0.658771\pi\) | ||||
−0.478367 | + | 0.878160i | \(0.658771\pi\) | |||||||
\(788\) | 6.30745e124 | 0.0632358 | ||||||||
\(789\) | −5.89810e125 | −0.559581 | ||||||||
\(790\) | 1.47582e126 | 1.32512 | ||||||||
\(791\) | −1.72796e126 | −1.46844 | ||||||||
\(792\) | −8.50543e125 | −0.684149 | ||||||||
\(793\) | 1.60600e126 | 1.22282 | ||||||||
\(794\) | −1.39083e126 | −1.00249 | ||||||||
\(795\) | 1.75223e126 | 1.19570 | ||||||||
\(796\) | 1.14089e126 | 0.737100 | ||||||||
\(797\) | −1.66930e126 | −1.02117 | −0.510584 | − | 0.859828i | \(-0.670571\pi\) | ||||
−0.510584 | + | 0.859828i | \(0.670571\pi\) | |||||||
\(798\) | 2.58747e125 | 0.149882 | ||||||||
\(799\) | −3.80471e125 | −0.208707 | ||||||||
\(800\) | −7.52873e125 | −0.391117 | ||||||||
\(801\) | 1.54666e125 | 0.0760991 | ||||||||
\(802\) | 1.26089e125 | 0.0587615 | ||||||||
\(803\) | 3.83710e126 | 1.69386 | ||||||||
\(804\) | 2.16480e126 | 0.905273 | ||||||||
\(805\) | −6.26294e126 | −2.48117 | ||||||||
\(806\) | −2.20699e126 | −0.828373 | ||||||||
\(807\) | −4.86568e126 | −1.73039 | ||||||||
\(808\) | 2.33064e125 | 0.0785384 | ||||||||
\(809\) | −1.36471e126 | −0.435794 | −0.217897 | − | 0.975972i | \(-0.569920\pi\) | ||||
−0.217897 | + | 0.975972i | \(0.569920\pi\) | |||||||
\(810\) | −2.41939e126 | −0.732162 | ||||||||
\(811\) | −2.64389e126 | −0.758292 | −0.379146 | − | 0.925337i | \(-0.623782\pi\) | ||||
−0.379146 | + | 0.925337i | \(0.623782\pi\) | |||||||
\(812\) | −8.98334e125 | −0.244203 | ||||||||
\(813\) | 1.13294e127 | 2.91922 | ||||||||
\(814\) | −2.90392e125 | −0.0709288 | ||||||||
\(815\) | 1.17636e127 | 2.72386 | ||||||||
\(816\) | −5.94251e125 | −0.130451 | ||||||||
\(817\) | −8.80282e124 | −0.0183216 | ||||||||
\(818\) | −3.38710e126 | −0.668435 | ||||||||
\(819\) | 1.23566e127 | 2.31232 | ||||||||
\(820\) | −7.80303e126 | −1.38472 | ||||||||
\(821\) | 5.96183e126 | 1.00335 | 0.501675 | − | 0.865056i | \(-0.332717\pi\) | ||||
0.501675 | + | 0.865056i | \(0.332717\pi\) | |||||||
\(822\) | 2.67050e126 | 0.426254 | ||||||||
\(823\) | 1.04559e127 | 1.58296 | 0.791481 | − | 0.611194i | \(-0.209310\pi\) | ||||
0.791481 | + | 0.611194i | \(0.209310\pi\) | |||||||
\(824\) | −1.94431e125 | −0.0279211 | ||||||||
\(825\) | −3.62668e127 | −4.94040 | ||||||||
\(826\) | 2.52689e126 | 0.326553 | ||||||||
\(827\) | −3.82531e126 | −0.469005 | −0.234502 | − | 0.972116i | \(-0.575346\pi\) | ||||
−0.234502 | + | 0.972116i | \(0.575346\pi\) | |||||||
\(828\) | 5.60829e126 | 0.652395 | ||||||||
\(829\) | −9.99951e126 | −1.10371 | −0.551857 | − | 0.833939i | \(-0.686081\pi\) | ||||
−0.551857 | + | 0.833939i | \(0.686081\pi\) | |||||||
\(830\) | 1.67876e127 | 1.75830 | ||||||||
\(831\) | −7.88078e126 | −0.783293 | ||||||||
\(832\) | 1.65775e126 | 0.156370 | ||||||||
\(833\) | 3.67785e126 | 0.329258 | ||||||||
\(834\) | 3.18348e126 | 0.270507 | ||||||||
\(835\) | 4.21727e127 | 3.40150 | ||||||||
\(836\) | 9.51398e125 | 0.0728432 | ||||||||
\(837\) | −6.27857e126 | −0.456356 | ||||||||
\(838\) | 3.36953e126 | 0.232517 | ||||||||
\(839\) | −2.44629e127 | −1.60274 | −0.801368 | − | 0.598171i | \(-0.795894\pi\) | ||||
−0.801368 | + | 0.598171i | \(0.795894\pi\) | |||||||
\(840\) | −2.17277e127 | −1.35165 | ||||||||
\(841\) | −1.48696e127 | −0.878364 | ||||||||
\(842\) | −4.13219e126 | −0.231795 | ||||||||
\(843\) | −4.65711e126 | −0.248094 | ||||||||
\(844\) | 6.96562e126 | 0.352422 | ||||||||
\(845\) | −2.10700e127 | −1.01251 | ||||||||
\(846\) | 1.24571e127 | 0.568600 | ||||||||
\(847\) | 3.71181e127 | 1.60938 | ||||||||
\(848\) | 2.65840e126 | 0.109497 | ||||||||
\(849\) | −6.66808e127 | −2.60925 | ||||||||
\(850\) | −1.44165e127 | −0.535965 | ||||||||
\(851\) | 1.91478e126 | 0.0676367 | ||||||||
\(852\) | 3.68774e126 | 0.123777 | ||||||||
\(853\) | 2.77724e127 | 0.885791 | 0.442895 | − | 0.896573i | \(-0.353951\pi\) | ||||
0.442895 | + | 0.896573i | \(0.353951\pi\) | |||||||
\(854\) | −3.19352e127 | −0.967947 | ||||||||
\(855\) | −8.16166e126 | −0.235100 | ||||||||
\(856\) | −7.69306e126 | −0.210615 | ||||||||
\(857\) | 1.00314e127 | 0.261034 | 0.130517 | − | 0.991446i | \(-0.458336\pi\) | ||||
0.130517 | + | 0.991446i | \(0.458336\pi\) | |||||||
\(858\) | 7.98558e127 | 1.97519 | ||||||||
\(859\) | 5.66901e127 | 1.33292 | 0.666461 | − | 0.745540i | \(-0.267808\pi\) | ||||
0.666461 | + | 0.745540i | \(0.267808\pi\) | |||||||
\(860\) | 7.39195e126 | 0.165225 | ||||||||
\(861\) | −1.55094e128 | −3.29577 | ||||||||
\(862\) | −2.30287e127 | −0.465269 | ||||||||
\(863\) | 4.04829e127 | 0.777682 | 0.388841 | − | 0.921305i | \(-0.372876\pi\) | ||||
0.388841 | + | 0.921305i | \(0.372876\pi\) | |||||||
\(864\) | 4.71606e126 | 0.0861453 | ||||||||
\(865\) | 1.59858e128 | 2.77673 | ||||||||
\(866\) | −2.81119e127 | −0.464368 | ||||||||
\(867\) | 8.55757e127 | 1.34437 | ||||||||
\(868\) | 4.38858e127 | 0.655717 | ||||||||
\(869\) | 1.07858e128 | 1.53282 | ||||||||
\(870\) | 4.98039e127 | 0.673249 | ||||||||
\(871\) | −1.15639e128 | −1.48701 | ||||||||
\(872\) | −3.49788e127 | −0.427896 | ||||||||
\(873\) | 1.55692e128 | 1.81195 | ||||||||
\(874\) | −6.27331e126 | −0.0694623 | ||||||||
\(875\) | −2.88869e128 | −3.04334 | ||||||||
\(876\) | −8.77753e127 | −0.879921 | ||||||||
\(877\) | −8.92776e127 | −0.851648 | −0.425824 | − | 0.904806i | \(-0.640016\pi\) | ||||
−0.425824 | + | 0.904806i | \(0.640016\pi\) | |||||||
\(878\) | −1.56935e127 | −0.142465 | ||||||||
\(879\) | 2.88471e128 | 2.49222 | ||||||||
\(880\) | −7.98912e127 | −0.656906 | ||||||||
\(881\) | −1.86268e128 | −1.45776 | −0.728882 | − | 0.684639i | \(-0.759960\pi\) | ||||
−0.728882 | + | 0.684639i | \(0.759960\pi\) | |||||||
\(882\) | −1.20417e128 | −0.897027 | ||||||||
\(883\) | −6.21741e127 | −0.440879 | −0.220439 | − | 0.975401i | \(-0.570749\pi\) | ||||
−0.220439 | + | 0.975401i | \(0.570749\pi\) | |||||||
\(884\) | 3.17437e127 | 0.214281 | ||||||||
\(885\) | −1.40091e128 | −0.900282 | ||||||||
\(886\) | −6.61162e127 | −0.404521 | ||||||||
\(887\) | 2.08936e128 | 1.21713 | 0.608563 | − | 0.793505i | \(-0.291746\pi\) | ||||
0.608563 | + | 0.793505i | \(0.291746\pi\) | |||||||
\(888\) | 6.64283e126 | 0.0368459 | ||||||||
\(889\) | 7.69508e127 | 0.406431 | ||||||||
\(890\) | 1.45277e127 | 0.0730687 | ||||||||
\(891\) | −1.76817e128 | −0.846921 | ||||||||
\(892\) | 1.33835e128 | 0.610518 | ||||||||
\(893\) | −1.39342e127 | −0.0605404 | ||||||||
\(894\) | −3.04187e128 | −1.25881 | ||||||||
\(895\) | 8.33980e128 | 3.28741 | ||||||||
\(896\) | −3.29642e127 | −0.123778 | ||||||||
\(897\) | −5.26551e128 | −1.88352 | ||||||||
\(898\) | 3.09173e128 | 1.05361 | ||||||||
\(899\) | −1.00595e128 | −0.326609 | ||||||||
\(900\) | 4.72015e128 | 1.46018 | ||||||||
\(901\) | 5.09048e127 | 0.150048 | ||||||||
\(902\) | −5.70270e128 | −1.60176 | ||||||||
\(903\) | 1.46923e128 | 0.393254 | ||||||||
\(904\) | 1.45341e128 | 0.370734 | ||||||||
\(905\) | −8.86459e128 | −2.15499 | ||||||||
\(906\) | 2.40601e127 | 0.0557469 | ||||||||
\(907\) | −5.88338e128 | −1.29930 | −0.649650 | − | 0.760233i | \(-0.725085\pi\) | ||||
−0.649650 | + | 0.760233i | \(0.725085\pi\) | |||||||
\(908\) | 3.29269e128 | 0.693133 | ||||||||
\(909\) | −1.46120e128 | −0.293212 | ||||||||
\(910\) | 1.16065e129 | 2.22024 | ||||||||
\(911\) | 9.72924e126 | 0.0177431 | 0.00887155 | − | 0.999961i | \(-0.497176\pi\) | ||||
0.00887155 | + | 0.999961i | \(0.497176\pi\) | |||||||
\(912\) | −2.17636e127 | −0.0378404 | ||||||||
\(913\) | 1.22689e129 | 2.03389 | ||||||||
\(914\) | −2.45484e128 | −0.388029 | ||||||||
\(915\) | 1.77049e129 | 2.66856 | ||||||||
\(916\) | −5.05692e128 | −0.726830 | ||||||||
\(917\) | −1.27517e129 | −1.74784 | ||||||||
\(918\) | 9.03063e127 | 0.118049 | ||||||||
\(919\) | −3.66875e128 | −0.457397 | −0.228699 | − | 0.973497i | \(-0.573447\pi\) | ||||
−0.228699 | + | 0.973497i | \(0.573447\pi\) | |||||||
\(920\) | 5.26785e128 | 0.626416 | ||||||||
\(921\) | −3.19959e128 | −0.362912 | ||||||||
\(922\) | 9.90678e128 | 1.07186 | ||||||||
\(923\) | −1.96992e128 | −0.203317 | ||||||||
\(924\) | −1.58793e129 | −1.56351 | ||||||||
\(925\) | 1.61155e128 | 0.151383 | ||||||||
\(926\) | −6.32327e128 | −0.566713 | ||||||||
\(927\) | 1.21899e128 | 0.104239 | ||||||||
\(928\) | 7.55602e127 | 0.0616533 | ||||||||
\(929\) | 1.32535e129 | 1.03192 | 0.515961 | − | 0.856612i | \(-0.327435\pi\) | ||||
0.515961 | + | 0.856612i | \(0.327435\pi\) | |||||||
\(930\) | −2.43304e129 | −1.80776 | ||||||||
\(931\) | 1.34696e128 | 0.0955089 | ||||||||
\(932\) | 8.80311e128 | 0.595723 | ||||||||
\(933\) | −1.27910e129 | −0.826140 | ||||||||
\(934\) | 3.68974e128 | 0.227461 | ||||||||
\(935\) | −1.52981e129 | −0.900186 | ||||||||
\(936\) | −1.03933e129 | −0.583786 | ||||||||
\(937\) | 3.47257e128 | 0.186200 | 0.0930998 | − | 0.995657i | \(-0.470322\pi\) | ||||
0.0930998 | + | 0.995657i | \(0.470322\pi\) | |||||||
\(938\) | 2.29948e129 | 1.17708 | ||||||||
\(939\) | −6.01885e129 | −2.94144 | ||||||||
\(940\) | 1.17009e129 | 0.545957 | ||||||||
\(941\) | 2.67043e128 | 0.118969 | 0.0594843 | − | 0.998229i | \(-0.481054\pi\) | ||||
0.0594843 | + | 0.998229i | \(0.481054\pi\) | |||||||
\(942\) | −6.30262e128 | −0.268106 | ||||||||
\(943\) | 3.76023e129 | 1.52741 | ||||||||
\(944\) | −2.12540e128 | −0.0824440 | ||||||||
\(945\) | 3.30188e129 | 1.22314 | ||||||||
\(946\) | 5.40227e128 | 0.191123 | ||||||||
\(947\) | −3.26641e127 | −0.0110369 | −0.00551845 | − | 0.999985i | \(-0.501757\pi\) | ||||
−0.00551845 | + | 0.999985i | \(0.501757\pi\) | |||||||
\(948\) | −2.46729e129 | −0.796265 | ||||||||
\(949\) | 4.68878e129 | 1.44537 | ||||||||
\(950\) | −5.27985e128 | −0.155469 | ||||||||
\(951\) | −6.53189e129 | −1.83733 | ||||||||
\(952\) | −6.31220e128 | −0.169619 | ||||||||
\(953\) | 5.18763e129 | 1.33176 | 0.665882 | − | 0.746057i | \(-0.268055\pi\) | ||||
0.665882 | + | 0.746057i | \(0.268055\pi\) | |||||||
\(954\) | −1.66669e129 | −0.408790 | ||||||||
\(955\) | 5.28606e129 | 1.23875 | ||||||||
\(956\) | −4.66241e128 | −0.104398 | ||||||||
\(957\) | 3.63983e129 | 0.778774 | ||||||||
\(958\) | −4.69898e129 | −0.960736 | ||||||||
\(959\) | 2.83664e129 | 0.554235 | ||||||||
\(960\) | 1.82755e129 | 0.341248 | ||||||||
\(961\) | −6.89312e128 | −0.123012 | ||||||||
\(962\) | −3.54847e128 | −0.0605236 | ||||||||
\(963\) | 4.82317e129 | 0.786302 | ||||||||
\(964\) | −3.45034e129 | −0.537663 | ||||||||
\(965\) | −8.17057e129 | −1.21707 | ||||||||
\(966\) | 1.04704e130 | 1.49094 | ||||||||
\(967\) | 2.49187e129 | 0.339214 | 0.169607 | − | 0.985512i | \(-0.445750\pi\) | ||||
0.169607 | + | 0.985512i | \(0.445750\pi\) | |||||||
\(968\) | −3.12206e129 | −0.406315 | ||||||||
\(969\) | −4.16744e128 | −0.0518543 | ||||||||
\(970\) | 1.46241e130 | 1.73980 | ||||||||
\(971\) | −1.61081e129 | −0.183235 | −0.0916173 | − | 0.995794i | \(-0.529204\pi\) | ||||
−0.0916173 | + | 0.995794i | \(0.529204\pi\) | |||||||
\(972\) | 6.28481e129 | 0.683612 | ||||||||
\(973\) | 3.38153e129 | 0.351727 | ||||||||
\(974\) | 1.63409e129 | 0.162541 | ||||||||
\(975\) | −4.43165e130 | −4.21565 | ||||||||
\(976\) | 2.68611e129 | 0.244375 | ||||||||
\(977\) | −1.68757e130 | −1.46841 | −0.734207 | − | 0.678925i | \(-0.762446\pi\) | ||||
−0.734207 | + | 0.678925i | \(0.762446\pi\) | |||||||
\(978\) | −1.96665e130 | −1.63677 | ||||||||
\(979\) | 1.06173e129 | 0.0845215 | ||||||||
\(980\) | −1.13108e130 | −0.861306 | ||||||||
\(981\) | 2.19300e130 | 1.59749 | ||||||||
\(982\) | −6.50639e129 | −0.453409 | ||||||||
\(983\) | −2.56799e130 | −1.71205 | −0.856023 | − | 0.516938i | \(-0.827072\pi\) | ||||
−0.856023 | + | 0.516938i | \(0.827072\pi\) | |||||||
\(984\) | 1.30452e130 | 0.832076 | ||||||||
\(985\) | −3.71441e129 | −0.226681 | ||||||||
\(986\) | 1.44688e129 | 0.0844862 | ||||||||
\(987\) | 2.32569e130 | 1.29944 | ||||||||
\(988\) | 1.16257e129 | 0.0621572 | ||||||||
\(989\) | −3.56214e129 | −0.182252 | ||||||||
\(990\) | 5.00879e130 | 2.45246 | ||||||||
\(991\) | 2.46716e130 | 1.15609 | 0.578047 | − | 0.816003i | \(-0.303815\pi\) | ||||
0.578047 | + | 0.816003i | \(0.303815\pi\) | |||||||
\(992\) | −3.69130e129 | −0.165547 | ||||||||
\(993\) | 2.46059e130 | 1.05620 | ||||||||
\(994\) | 3.91717e129 | 0.160940 | ||||||||
\(995\) | −6.71864e130 | −2.64227 | ||||||||
\(996\) | −2.80657e130 | −1.05656 | ||||||||
\(997\) | 5.35925e130 | 1.93137 | 0.965683 | − | 0.259723i | \(-0.0836311\pi\) | ||||
0.965683 | + | 0.259723i | \(0.0836311\pi\) | |||||||
\(998\) | −5.69130e128 | −0.0196351 | ||||||||
\(999\) | −1.00949e129 | −0.0333428 |
(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 | 2.88.a.b.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.88.a.b.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial |