Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,20,Mod(1,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.1");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.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: | \(36.6106714490\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1453}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 363 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7}\cdot 3\cdot 5 \) |
Twist minimal: | no (minimal twist has level 8) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(19.5591\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −22637.5 | −0.664013 | −0.332007 | − | 0.943277i | \(-0.607726\pi\) | ||||
−0.332007 | + | 0.943277i | \(0.607726\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −996804. | −0.228242 | −0.114121 | − | 0.993467i | \(-0.536405\pi\) | ||||
−0.114121 | + | 0.993467i | \(0.536405\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.24780e7 | 0.678852 | 0.339426 | − | 0.940633i | \(-0.389767\pi\) | ||||
0.339426 | + | 0.940633i | \(0.389767\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.49805e8 | −0.559087 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.59555e9 | −0.587634 | −0.293817 | − | 0.955862i | \(-0.594926\pi\) | ||||
−0.293817 | + | 0.955862i | \(0.594926\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.68575e9 | −0.201013 | −0.100507 | − | 0.994936i | \(-0.532046\pi\) | ||||
−0.100507 | + | 0.994936i | \(0.532046\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.25652e10 | 0.151555 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.70499e11 | −1.37130 | −0.685652 | − | 0.727930i | \(-0.740483\pi\) | ||||
−0.685652 | + | 0.727930i | \(0.740483\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.03766e11 | 0.429249 | 0.214625 | − | 0.976697i | \(-0.431147\pi\) | ||||
0.214625 | + | 0.976697i | \(0.431147\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.64072e12 | −0.450767 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.41235e13 | 1.63503 | 0.817517 | − | 0.575904i | \(-0.195350\pi\) | ||||
0.817517 | + | 0.575904i | \(0.195350\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.80799e13 | −0.947906 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.10207e13 | 1.03525 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.75566e13 | 0.224729 | 0.112365 | − | 0.993667i | \(-0.464158\pi\) | ||||
0.112365 | + | 0.993667i | \(0.464158\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.97149e13 | −0.541506 | −0.270753 | − | 0.962649i | \(-0.587273\pi\) | ||||
−0.270753 | + | 0.962649i | \(0.587273\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.04032e14 | 0.390197 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.22464e13 | −0.154942 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.12013e15 | 1.41694 | 0.708469 | − | 0.705742i | \(-0.249386\pi\) | ||||
0.708469 | + | 0.705742i | \(0.249386\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.73986e14 | 0.133475 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00183e15 | 1.43199 | 0.715995 | − | 0.698106i | \(-0.245974\pi\) | ||||
0.715995 | + | 0.698106i | \(0.245974\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.41815e15 | 1.03715 | 0.518574 | − | 0.855033i | \(-0.326463\pi\) | ||||
0.518574 | + | 0.855033i | \(0.326463\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.47728e14 | 0.127607 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.14830e16 | 1.49667 | 0.748336 | − | 0.663320i | \(-0.230853\pi\) | ||||
0.748336 | + | 0.663320i | \(0.230853\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.14583e15 | −0.539160 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.51784e16 | 0.910563 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.49535e16 | 1.03875 | 0.519374 | − | 0.854547i | \(-0.326165\pi\) | ||||
0.519374 | + | 0.854547i | \(0.326165\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.58086e15 | 0.134122 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.36678e16 | −0.285027 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.22986e15 | −0.108652 | −0.0543258 | − | 0.998523i | \(-0.517301\pi\) | ||||
−0.0543258 | + | 0.998523i | \(0.517301\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.29766e17 | 1.42078 | 0.710391 | − | 0.703808i | \(-0.248518\pi\) | ||||
0.710391 | + | 0.703808i | \(0.248518\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.70966e16 | −0.379537 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.66119e15 | 0.0458796 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.74592e17 | −1.23304 | −0.616520 | − | 0.787340i | \(-0.711458\pi\) | ||||
−0.616520 | + | 0.787340i | \(0.711458\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.19720e17 | −1.08568 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.56270e17 | −0.404504 | −0.202252 | − | 0.979334i | \(-0.564826\pi\) | ||||
−0.202252 | + | 0.979334i | \(0.564826\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.21165e17 | −1.63254 | −0.816269 | − | 0.577672i | \(-0.803961\pi\) | ||||
−0.816269 | + | 0.577672i | \(0.803961\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.09283e17 | 0.629422 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.33076e17 | −0.398916 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.09830e17 | −0.196974 | −0.0984871 | − | 0.995138i | \(-0.531400\pi\) | ||||
−0.0984871 | + | 0.995138i | \(0.531400\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.73363e17 | −0.128336 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.15127e17 | −0.185030 | −0.0925152 | − | 0.995711i | \(-0.529491\pi\) | ||||
−0.0925152 | + | 0.995711i | \(0.529491\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.68357e17 | 0.312989 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.97438e17 | −0.149223 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.78627e18 | 0.842981 | 0.421491 | − | 0.906833i | \(-0.361507\pi\) | ||||
0.421491 | + | 0.906833i | \(0.361507\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.57048e17 | −0.136458 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.80455e18 | 0.359567 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.01837e17 | −0.0979725 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.58373e18 | 1.01286 | 0.506432 | − | 0.862280i | \(-0.330964\pi\) | ||||
0.506432 | + | 0.862280i | \(0.330964\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.98621e18 | 0.328538 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.62374e18 | −0.329689 | −0.164845 | − | 0.986320i | \(-0.552712\pi\) | ||||
−0.164845 | + | 0.986320i | \(0.552712\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.07112e19 | 1.56405 | 0.782026 | − | 0.623246i | \(-0.214186\pi\) | ||||
0.782026 | + | 0.623246i | \(0.214186\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.63548e18 | 0.102884 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.42775e19 | 1.27661 | 0.638305 | − | 0.769784i | \(-0.279636\pi\) | ||||
0.638305 | + | 0.769784i | \(0.279636\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.19033e19 | −0.524946 | −0.262473 | − | 0.964939i | \(-0.584538\pi\) | ||||
−0.262473 | + | 0.964939i | \(0.584538\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.53569e19 | −0.940866 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.65952e18 | −0.0832833 | −0.0416417 | − | 0.999133i | \(-0.513259\pi\) | ||||
−0.0416417 | + | 0.999133i | \(0.513259\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.40783e19 | −0.373183 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.99424e18 | 0.112384 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.85965e19 | −0.930912 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00400e19 | −0.654687 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.79540e19 | −0.950860 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.70346e19 | 0.444593 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.57941e19 | −0.679284 | −0.339642 | − | 0.940555i | \(-0.610306\pi\) | ||||
−0.339642 | + | 0.940555i | \(0.610306\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.73784e19 | −0.688680 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.73472e19 | 0.287198 | 0.143599 | − | 0.989636i | \(-0.454132\pi\) | ||||
0.143599 | + | 0.989636i | \(0.454132\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.37598e19 | 0.291397 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.08896e19 | −0.236288 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.14142e18 | −0.0157863 | −0.00789315 | − | 0.999969i | \(-0.502512\pi\) | ||||
−0.00789315 | + | 0.999969i | \(0.502512\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.82616e20 | 1.67542 | 0.837709 | − | 0.546117i | \(-0.183895\pi\) | ||||
0.837709 | + | 0.546117i | \(0.183895\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.59947e20 | −0.993809 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.53202e19 | 0.118122 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.75005e19 | −0.0512926 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.39126e20 | 0.358009 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.27921e20 | 0.742163 | 0.371081 | − | 0.928600i | \(-0.378987\pi\) | ||||
0.371081 | + | 0.928600i | \(0.378987\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.20975e20 | −0.241220 | −0.120610 | − | 0.992700i | \(-0.538485\pi\) | ||||
−0.120610 | + | 0.992700i | \(0.538485\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.35694e20 | 0.766677 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.94601e19 | 0.123594 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.68747e20 | 0.783199 | 0.391599 | − | 0.920136i | \(-0.371922\pi\) | ||||
0.391599 | + | 0.920136i | \(0.371922\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.64884e20 | −0.689742 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.02364e21 | 1.10995 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.77617e21 | 1.71279 | 0.856393 | − | 0.516325i | \(-0.172700\pi\) | ||||
0.856393 | + | 0.516325i | \(0.172700\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.03699e20 | −0.0890591 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.55998e21 | −1.19485 | −0.597424 | − | 0.801926i | \(-0.703809\pi\) | ||||
−0.597424 | + | 0.801926i | \(0.703809\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.40285e21 | −0.959594 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.92330e20 | −0.239987 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.55034e21 | −0.849159 | −0.424580 | − | 0.905391i | \(-0.639578\pi\) | ||||
−0.424580 | + | 0.905391i | \(0.639578\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.31039e21 | −0.643488 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.63666e20 | 0.0721461 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.89048e21 | 1.14516 | 0.572579 | − | 0.819849i | \(-0.305943\pi\) | ||||
0.572579 | + | 0.819849i | \(0.305943\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.15105e21 | −1.83633 | −0.918163 | − | 0.396204i | \(-0.870327\pi\) | ||||
−0.918163 | + | 0.396204i | \(0.870327\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.93758e21 | −0.943418 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.11655e21 | −0.323404 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.08131e21 | 0.805824 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.97310e21 | 0.702784 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.17061e21 | −1.53369 | −0.766847 | − | 0.641830i | \(-0.778176\pi\) | ||||
−0.766847 | + | 0.641830i | \(0.778176\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.25664e21 | −0.630921 | −0.315461 | − | 0.948939i | \(-0.602159\pi\) | ||||
−0.315461 | + | 0.948939i | \(0.602159\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.73430e20 | −0.0304646 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.19004e22 | 1.89729 | 0.948643 | − | 0.316349i | \(-0.102457\pi\) | ||||
0.948643 | + | 0.316349i | \(0.102457\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.18989e21 | 0.317188 | 0.158594 | − | 0.987344i | \(-0.449304\pi\) | ||||
0.158594 | + | 0.987344i | \(0.449304\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.21607e21 | 0.818754 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.27247e21 | 0.152558 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.99224e21 | −0.326840 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.17750e21 | −0.914126 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.77464e21 | −0.252241 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.32425e22 | 1.93019 | 0.965096 | − | 0.261898i | \(-0.0843484\pi\) | ||||
0.965096 | + | 0.261898i | \(0.0843484\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.53757e21 | 0.268596 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.40723e21 | −0.236720 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.77758e21 | −0.367602 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.85891e22 | 1.08403 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.15329e21 | 0.275650 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.36614e21 | 0.165286 | 0.0826429 | − | 0.996579i | \(-0.473664\pi\) | ||||
0.0826429 | + | 0.996579i | \(0.473664\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.17484e22 | 0.529961 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.44209e21 | 0.142750 | 0.0713751 | − | 0.997450i | \(-0.477261\pi\) | ||||
0.0713751 | + | 0.997450i | \(0.477261\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.04661e22 | −1.16246 | −0.581232 | − | 0.813738i | \(-0.697429\pi\) | ||||
−0.581232 | + | 0.813738i | \(0.697429\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.54002e21 | 0.264886 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.01497e22 | 0.328527 | 0.164264 | − | 0.986416i | \(-0.447475\pi\) | ||||
0.164264 | + | 0.986416i | \(0.447475\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.14463e22 | −0.341603 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.75002e21 | 0.130793 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.94716e22 | −1.51192 | −0.755961 | − | 0.654616i | \(-0.772830\pi\) | ||||
−0.755961 | + | 0.654616i | \(0.772830\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.71172e21 | −0.157642 | −0.0788210 | − | 0.996889i | \(-0.525116\pi\) | ||||
−0.0788210 | + | 0.996889i | \(0.525116\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.37522e22 | −0.950037 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.12619e21 | 0.123059 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.64040e21 | −0.0862847 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.13368e21 | 0.122863 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.83985e22 | −1.09181 | −0.545904 | − | 0.837848i | \(-0.683814\pi\) | ||||
−0.545904 | + | 0.837848i | \(0.683814\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.49051e22 | −0.960802 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.51299e22 | −0.207828 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.76051e22 | −0.479603 | −0.239801 | − | 0.970822i | \(-0.577082\pi\) | ||||
−0.239801 | + | 0.970822i | \(0.577082\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.11846e22 | 0.961892 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.14084e22 | −0.125643 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.77095e23 | 1.81396 | 0.906980 | − | 0.421173i | \(-0.138382\pi\) | ||||
0.906980 | + | 0.421173i | \(0.138382\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.48737e22 | −0.237086 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.30742e22 | −0.559751 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.19248e23 | 0.985837 | 0.492919 | − | 0.870075i | \(-0.335930\pi\) | ||||
0.492919 | + | 0.870075i | \(0.335930\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.67879e22 | 0.668730 | 0.334365 | − | 0.942444i | \(-0.391478\pi\) | ||||
0.334365 | + | 0.942444i | \(0.391478\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.26102e22 | 0.0906100 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.30869e22 | 0.557021 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.99312e21 | 0.0500217 | 0.0250109 | − | 0.999687i | \(-0.492038\pi\) | ||||
0.0250109 | + | 0.999687i | \(0.492038\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.17991e22 | 0.302749 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.90889e22 | 0.268085 | 0.134043 | − | 0.990976i | \(-0.457204\pi\) | ||||
0.134043 | + | 0.990976i | \(0.457204\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.70773e23 | −1.38240 | −0.691201 | − | 0.722662i | \(-0.742918\pi\) | ||||
−0.691201 | + | 0.722662i | \(0.742918\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.36241e22 | 0.0650550 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.17567e23 | 0.972109 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.10497e23 | 0.880473 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.71677e23 | −0.672555 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.47805e23 | 0.909635 | 0.454818 | − | 0.890585i | \(-0.349704\pi\) | ||||
0.454818 | + | 0.890585i | \(0.349704\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.20676e21 | 0.0247988 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.88512e23 | −0.608350 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.08549e23 | −0.328664 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.47741e23 | 0.704070 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.20325e22 | 0.218918 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.29351e23 | −0.324281 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.71564e23 | −0.639820 | −0.319910 | − | 0.947448i | \(-0.603653\pi\) | ||||
−0.319910 | + | 0.947448i | \(0.603653\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.68850e23 | −1.03855 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.17401e23 | 0.869620 | 0.434810 | − | 0.900522i | \(-0.356816\pi\) | ||||
0.434810 | + | 0.900522i | \(0.356816\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.21476e23 | −0.434166 | −0.217083 | − | 0.976153i | \(-0.569654\pi\) | ||||
−0.217083 | + | 0.976153i | \(0.569654\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.69461e22 | 0.0866261 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.33402e23 | −1.44808 | −0.724038 | − | 0.689760i | \(-0.757716\pi\) | ||||
−0.724038 | + | 0.689760i | \(0.757716\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.06823e22 | −0.132059 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.49582e23 | −0.847686 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.04825e23 | −0.588631 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.38957e23 | 0.190542 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.69460e23 | 0.348571 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.32267e23 | 1.01602 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.25972e24 | −1.45181 | −0.725904 | − | 0.687796i | \(-0.758578\pi\) | ||||
−0.725904 | + | 0.687796i | \(0.758578\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.27864e23 | −0.792191 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.73714e23 | 0.281431 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.60548e23 | 0.836163 | 0.418082 | − | 0.908409i | \(-0.362703\pi\) | ||||
0.418082 | + | 0.908409i | \(0.362703\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.02049e22 | 0.0553012 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.66333e23 | 0.318207 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.27161e24 | −1.04486 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.18698e23 | 0.247798 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.55690e24 | 1.88184 | 0.940922 | − | 0.338623i | \(-0.109961\pi\) | ||||
0.940922 | + | 0.338623i | \(0.109961\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.73272e24 | 1.20750 | 0.603751 | − | 0.797173i | \(-0.293672\pi\) | ||||
0.603751 | + | 0.797173i | \(0.293672\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.15275e23 | −0.208100 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.44110e23 | 0.465348 | 0.232674 | − | 0.972555i | \(-0.425253\pi\) | ||||
0.232674 | + | 0.972555i | \(0.425253\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.55771e23 | 0.0923246 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.10010e24 | 0.618138 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.67777e24 | 0.893995 | 0.446997 | − | 0.894535i | \(-0.352493\pi\) | ||||
0.446997 | + | 0.894535i | \(0.352493\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.61389e24 | −0.815745 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.06407e23 | 0.434720 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.18541e23 | 0.372613 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.06458e24 | −0.460096 | −0.230048 | − | 0.973179i | \(-0.573888\pi\) | ||||
−0.230048 | + | 0.973179i | \(0.573888\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.95060e24 | −0.800606 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.80858e24 | 0.705156 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.55316e24 | −1.31638 | −0.658189 | − | 0.752853i | \(-0.728677\pi\) | ||||
−0.658189 | + | 0.752853i | \(0.728677\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.38372e23 | −0.295216 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.34936e23 | −0.0451736 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.96331e24 | 0.943418 | 0.471709 | − | 0.881754i | \(-0.343637\pi\) | ||||
0.471709 | + | 0.881754i | \(0.343637\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.48941e24 | 0.451054 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.14872e22 | −0.0119544 | −0.00597718 | − | 0.999982i | \(-0.501903\pi\) | ||||
−0.00597718 | + | 0.999982i | \(0.501903\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.32012e23 | 0.0910493 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.22113e24 | −0.579855 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.32009e24 | 0.328158 | 0.164079 | − | 0.986447i | \(-0.447535\pi\) | ||||
0.164079 | + | 0.986447i | \(0.447535\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.46978e24 | −2.24213 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.45448e23 | −0.190703 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.09159e23 | 0.0449577 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.49987e24 | −0.512162 | −0.256081 | − | 0.966655i | \(-0.582431\pi\) | ||||
−0.256081 | + | 0.966655i | \(0.582431\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.90612e23 | −0.193491 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.22882e24 | 0.973939 | 0.486970 | − | 0.873419i | \(-0.338102\pi\) | ||||
0.486970 | + | 0.873419i | \(0.338102\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.12669e23 | 0.108850 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.72809e23 | 0.0292916 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.14760e24 | −0.832641 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.59253e24 | −0.554663 | −0.277331 | − | 0.960774i | \(-0.589450\pi\) | ||||
−0.277331 | + | 0.960774i | \(0.589450\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.11139e22 | 0.0104823 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.24006e23 | −0.0737583 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.14120e23 | 0.0422317 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.66148e24 | −1.11250 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.64100e24 | 0.937815 | 0.468907 | − | 0.883247i | \(-0.344648\pi\) | ||||
0.468907 | + | 0.883247i | \(0.344648\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.63037e24 | −0.777782 | −0.388891 | − | 0.921284i | \(-0.627142\pi\) | ||||
−0.388891 | + | 0.921284i | \(0.627142\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.46172e24 | −0.836769 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.21225e25 | 1.29987 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.40518e24 | 0.964500 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.99562e23 | −0.0784347 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.83021e24 | 0.828776 | 0.414388 | − | 0.910100i | \(-0.363996\pi\) | ||||
0.414388 | + | 0.910100i | \(0.363996\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.89602e24 | −0.170298 | −0.0851488 | − | 0.996368i | \(-0.527137\pi\) | ||||
−0.0851488 | + | 0.996368i | \(0.527137\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.96168e23 | 0.0340590 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.52727e24 | 0.701837 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.03577e25 | 1.60441 | 0.802206 | − | 0.597047i | \(-0.203660\pi\) | ||||
0.802206 | + | 0.597047i | \(0.203660\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.99359e24 | 0.301437 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.63050e24 | 0.696327 | 0.348164 | − | 0.937434i | \(-0.386805\pi\) | ||||
0.348164 | + | 0.937434i | \(0.386805\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.77736e24 | −0.192403 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.42330e24 | −0.492806 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.24366e25 | 1.42764 | 0.713818 | − | 0.700331i | \(-0.246964\pi\) | ||||
0.713818 | + | 0.700331i | \(0.246964\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.37951e25 | −0.841485 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.73856e24 | 0.160173 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.55268e23 | 0.0311454 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.43601e25 | −0.772597 | −0.386299 | − | 0.922374i | \(-0.626247\pi\) | ||||
−0.386299 | + | 0.922374i | \(0.626247\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.75043e25 | −1.41965 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.20527e25 | 1.58747 | 0.793736 | − | 0.608262i | \(-0.208133\pi\) | ||||
0.793736 | + | 0.608262i | \(0.208133\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.99392e24 | −0.237368 | −0.118684 | − | 0.992932i | \(-0.537868\pi\) | ||||
−0.118684 | + | 0.992932i | \(0.537868\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.79878e24 | −0.0820682 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.24714e24 | 0.361238 | 0.180619 | − | 0.983553i | \(-0.442190\pi\) | ||||
0.180619 | + | 0.983553i | \(0.442190\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.99019e25 | −0.837051 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.28750e25 | −0.520054 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.57083e25 | −0.609463 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.09160e25 | −0.406888 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.62149e25 | −0.580750 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.71323e25 | 0.933899 | 0.466950 | − | 0.884284i | \(-0.345353\pi\) | ||||
0.466950 | + | 0.884284i | \(0.345353\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.60902e24 | −0.284823 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.31727e25 | −0.737019 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.55949e24 | −0.231178 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.00346e25 | 1.47145 | 0.735725 | − | 0.677281i | \(-0.236842\pi\) | ||||
0.735725 | + | 0.677281i | \(0.236842\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.02081e25 | −1.13731 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.80743e25 | −1.03600 | −0.517998 | − | 0.855382i | \(-0.673323\pi\) | ||||
−0.517998 | + | 0.855382i | \(0.673323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.17717e25 | −0.308172 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.97667e24 | −0.0749861 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.13262e25 | −0.274598 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.94991e25 | −0.455049 | −0.227525 | − | 0.973772i | \(-0.573063\pi\) | ||||
−0.227525 | + | 0.973772i | \(0.573063\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.53141e25 | 0.793394 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.11673e25 | 0.890546 | 0.445273 | − | 0.895395i | \(-0.353107\pi\) | ||||
0.445273 | + | 0.895395i | \(0.353107\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.61216e24 | 0.0752488 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.17570e25 | 0.637183 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.45581e24 | 0.124776 | 0.0623881 | − | 0.998052i | \(-0.480128\pi\) | ||||
0.0623881 | + | 0.998052i | \(0.480128\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.95164e25 | −1.10825 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.47669e25 | 0.444382 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.06450e25 | −0.356982 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.27708e25 | −0.879495 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.50958e25 | 0.563853 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.61781e25 | 1.17997 | 0.589986 | − | 0.807413i | \(-0.299133\pi\) | ||||
0.589986 | + | 0.807413i | \(0.299133\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.54461e25 | −1.12686 | −0.563431 | − | 0.826163i | \(-0.690519\pi\) | ||||
−0.563431 | + | 0.826163i | \(0.690519\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.96640e25 | 0.427284 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.34488e25 | 0.742569 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.24857e26 | 1.67334 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.69800e24 | 0.0607456 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.30713e25 | −0.287849 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.41999e25 | −0.291376 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.54332e25 | −0.760400 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.82435e25 | 0.316829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.27935e26 | 1.38553 | 0.692763 | − | 0.721165i | \(-0.256393\pi\) | ||||
0.692763 | + | 0.721165i | \(0.256393\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.16607e26 | 1.21934 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.18652e25 | 0.119814 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.03216e26 | 1.00662 | 0.503310 | − | 0.864106i | \(-0.332115\pi\) | ||||
0.503310 | + | 0.864106i | \(0.332115\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.43225e25 | −0.794340 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.06001e25 | 0.0964649 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.52080e25 | −0.133716 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.52759e25 | 0.214745 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.15924e26 | −0.951811 | −0.475905 | − | 0.879497i | \(-0.657880\pi\) | ||||
−0.475905 | + | 0.879497i | \(0.657880\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.62710e25 | −0.208480 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.97532e25 | −0.535078 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.69128e25 | 0.496226 | 0.248113 | − | 0.968731i | \(-0.420190\pi\) | ||||
0.248113 | + | 0.968731i | \(0.420190\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.65102e24 | 0.0190087 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.25650e25 | −0.0871210 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.98116e26 | −1.32847 | −0.664236 | − | 0.747523i | \(-0.731243\pi\) | ||||
−0.664236 | + | 0.747523i | \(0.731243\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.67644e26 | −1.73586 | −0.867930 | − | 0.496687i | \(-0.834550\pi\) | ||||
−0.867930 | + | 0.496687i | \(0.834550\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.62325e26 | 1.01839 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.55350e26 | −1.54986 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.86979e25 | −0.109805 | −0.0549027 | − | 0.998492i | \(-0.517485\pi\) | ||||
−0.0549027 | + | 0.998492i | \(0.517485\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.37222e25 | 0.418940 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.28398e25 | −0.125608 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.14675e26 | −0.610403 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.97828e24 | −0.0256507 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.83068e26 | 0.913167 | 0.456583 | − | 0.889681i | \(-0.349073\pi\) | ||||
0.456583 | + | 0.889681i | \(0.349073\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.81291e25 | −0.232441 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.69396e26 | −1.25982 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.12500e25 | 0.413250 | 0.206625 | − | 0.978420i | \(-0.433752\pi\) | ||||
0.206625 | + | 0.978420i | \(0.433752\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.84412e25 | 0.212473 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.95735e25 | −0.210617 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.37311e26 | −0.976705 | −0.488353 | − | 0.872646i | \(-0.662402\pi\) | ||||
−0.488353 | + | 0.872646i | \(0.662402\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.29560e26 | 0.915355 | 0.457677 | − | 0.889118i | \(-0.348681\pi\) | ||||
0.457677 | + | 0.889118i | \(0.348681\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.78431e26 | 0.689376 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.99121e25 | 0.149427 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.10962e26 | 0.402608 | 0.201304 | − | 0.979529i | \(-0.435482\pi\) | ||||
0.201304 | + | 0.979529i | \(0.435482\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.88055e25 | −0.101300 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.82556e25 | −0.300851 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.27027e25 | −0.0419779 | −0.0209890 | − | 0.999780i | \(-0.506681\pi\) | ||||
−0.0209890 | + | 0.999780i | \(0.506681\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.77368e25 | 0.217026 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.22914e26 | −1.31384 | −0.656921 | − | 0.753960i | \(-0.728141\pi\) | ||||
−0.656921 | + | 0.753960i | \(0.728141\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.49720e26 | 1.65608 | 0.828039 | − | 0.560671i | \(-0.189457\pi\) | ||||
0.828039 | + | 0.560671i | \(0.189457\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.79354e26 | 1.69268 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.01943e26 | 0.572259 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.07930e26 | 0.846431 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.28108e25 | 0.167492 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.51045e26 | −1.94305 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.83709e25 | −0.0712187 | −0.0356093 | − | 0.999366i | \(-0.511337\pi\) | ||||
−0.0356093 | + | 0.999366i | \(0.511337\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.26153e26 | −1.28167 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.55838e25 | 0.155041 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.72353e25 | 0.108378 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.01545e26 | 0.226153 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.77075e26 | 1.89620 | 0.948102 | − | 0.317965i | \(-0.102999\pi\) | ||||
0.948102 | + | 0.317965i | \(0.102999\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.19589e26 | 0.880683 | 0.440341 | − | 0.897830i | \(-0.354857\pi\) | ||||
0.440341 | + | 0.897830i | \(0.354857\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.71311e25 | 0.157185 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.89932e26 | −0.771611 | −0.385805 | − | 0.922580i | \(-0.626076\pi\) | ||||
−0.385805 | + | 0.922580i | \(0.626076\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.32252e25 | 0.0638473 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.30790e26 | 0.244093 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.24023e26 | 0.949895 | 0.474947 | − | 0.880014i | \(-0.342467\pi\) | ||||
0.474947 | + | 0.880014i | \(0.342467\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.72279e25 | −0.0655505 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.33597e26 | 0.912730 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.67459e26 | −1.27539 | −0.637696 | − | 0.770288i | \(-0.720112\pi\) | ||||
−0.637696 | + | 0.770288i | \(0.720112\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.32790e26 | −0.214413 | −0.107206 | − | 0.994237i | \(-0.534191\pi\) | ||||
−0.107206 | + | 0.994237i | \(0.534191\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.16658e26 | −0.183035 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.36199e25 | −0.0665088 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.47960e26 | 0.367440 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.62010e25 | −0.109752 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.96346e26 | −0.834899 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.37509e26 | −0.459349 | −0.229674 | − | 0.973268i | \(-0.573766\pi\) | ||||
−0.229674 | + | 0.973268i | \(0.573766\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.41648e26 | −0.981323 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.12451e27 | −1.44667 | −0.723336 | − | 0.690496i | \(-0.757392\pi\) | ||||
−0.723336 | + | 0.690496i | \(0.757392\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.49654e26 | 0.687585 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.79203e25 | −0.0947880 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.05871e26 | −0.835081 | −0.417540 | − | 0.908658i | \(-0.637108\pi\) | ||||
−0.417540 | + | 0.908658i | \(0.637108\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.13138e24 | 0.00360309 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.89676e26 | 0.771891 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.91786e26 | −0.208802 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.70572e25 | 0.0498408 | 0.0249204 | − | 0.999689i | \(-0.492067\pi\) | ||||
0.0249204 | + | 0.999689i | \(0.492067\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.16435e26 | 0.223029 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.81394e26 | −0.382400 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.01273e27 | −1.96369 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.29764e26 | −0.218147 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.38593e25 | 0.0497668 | 0.0248834 | − | 0.999690i | \(-0.492079\pi\) | ||||
0.0248834 | + | 0.999690i | \(0.492079\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.76295e26 | 0.608220 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.59116e26 | 0.226829 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.62642e26 | −0.223810 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.80682e26 | −0.232849 | −0.116425 | − | 0.993200i | \(-0.537143\pi\) | ||||
−0.116425 | + | 0.993200i | \(0.537143\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.36348e26 | 0.110126 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.12585e27 | −0.885381 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.52074e25 | −0.0269604 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.34629e27 | 1.00394 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.82032e27 | 1.32198 | 0.660988 | − | 0.750397i | \(-0.270138\pi\) | ||||
0.660988 | + | 0.750397i | \(0.270138\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.50111e27 | 1.06176 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.51937e26 | 0.104676 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.17421e26 | −0.213022 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.47227e27 | 0.962522 | 0.481261 | − | 0.876577i | \(-0.340179\pi\) | ||||
0.481261 | + | 0.876577i | \(0.340179\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.19193e27 | 0.759173 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.29187e27 | −1.42224 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.23845e27 | 1.35350 | 0.676751 | − | 0.736212i | \(-0.263387\pi\) | ||||
0.676751 | + | 0.736212i | \(0.263387\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.38682e26 | −0.0817127 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.26190e27 | 0.724576 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.64717e26 | −0.260056 | −0.130028 | − | 0.991510i | \(-0.541507\pi\) | ||||
−0.130028 | + | 0.991510i | \(0.541507\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.05047e26 | 0.0572942 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.63164e26 | −0.299393 | −0.149696 | − | 0.988732i | \(-0.547830\pi\) | ||||
−0.149696 | + | 0.988732i | \(0.547830\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.26873e26 | −0.169392 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.04771e26 | 0.103448 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.75959e27 | 0.866629 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.04104e26 | 0.290090 | 0.145045 | − | 0.989425i | \(-0.453667\pi\) | ||||
0.145045 | + | 0.989425i | \(0.453667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.54837e27 | 0.724975 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.20588e26 | 0.0550564 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.91726e27 | −1.74410 | −0.872051 | − | 0.489415i | \(-0.837211\pi\) | ||||
−0.872051 | + | 0.489415i | \(0.837211\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.46929e27 | 0.637985 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.21509e27 | −1.36157 | −0.680783 | − | 0.732486i | \(-0.738360\pi\) | ||||
−0.680783 | + | 0.732486i | \(0.738360\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.62725e26 | −0.356360 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.34301e26 | −0.174988 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.55669e25 | 0.0218404 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.87198e27 | 1.48468 | 0.742339 | − | 0.670024i | \(-0.233716\pi\) | ||||
0.742339 | + | 0.670024i | \(0.233716\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.51285e26 | 0.318463 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.22257e27 | −0.811240 | −0.405620 | − | 0.914042i | \(-0.632944\pi\) | ||||
−0.405620 | + | 0.914042i | \(0.632944\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.44123e27 | 0.513297 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.83782e27 | −0.638709 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.81240e27 | 0.614680 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.18148e26 | 0.237700 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.20184e26 | 0.232652 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.66929e26 | −0.178759 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.32013e27 | −1.02187 | −0.510934 | − | 0.859620i | \(-0.670700\pi\) | ||||
−0.510934 | + | 0.859620i | \(0.670700\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.00900e27 | −1.20449 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.92757e26 | −0.0565370 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.97349e26 | −0.285596 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.63079e26 | 0.157428 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.80480e27 | 1.03867 | 0.519335 | − | 0.854571i | \(-0.326180\pi\) | ||||
0.519335 | + | 0.854571i | \(0.326180\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.69936e27 | −2.05239 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.81053e27 | −0.471300 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.77370e27 | 0.959334 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.02037e27 | −0.253336 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.69948e27 | −0.654609 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.75938e26 | −0.160102 | −0.0800508 | − | 0.996791i | \(-0.525508\pi\) | ||||
−0.0800508 | + | 0.996791i | \(0.525508\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.86888e27 | −0.432398 | −0.216199 | − | 0.976349i | \(-0.569366\pi\) | ||||
−0.216199 | + | 0.976349i | \(0.569366\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.96466e27 | −0.444045 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.77050e27 | −0.390929 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.06376e27 | 0.445195 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.61973e26 | 0.0762919 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.78616e27 | 0.367841 | 0.183921 | − | 0.982941i | \(-0.441121\pi\) | ||||
0.183921 | + | 0.982941i | \(0.441121\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.84426e27 | −0.974831 | −0.487415 | − | 0.873170i | \(-0.662060\pi\) | ||||
−0.487415 | + | 0.873170i | \(0.662060\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.88088e27 | −0.369870 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.46068e26 | −0.143376 | −0.0716879 | − | 0.997427i | \(-0.522839\pi\) | ||||
−0.0716879 | + | 0.997427i | \(0.522839\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.45101e27 | 1.77505 | 0.887524 | − | 0.460761i | \(-0.152424\pi\) | ||||
0.887524 | + | 0.460761i | \(0.152424\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.80944e26 | −0.0332151 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.12077e27 | 0.739352 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.55499e27 | 0.272714 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.26996e27 | −0.560596 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.87983e27 | 1.48822 | 0.744108 | − | 0.668059i | \(-0.232875\pi\) | ||||
0.744108 | + | 0.668059i | \(0.232875\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.79503e27 | −0.949497 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.11125e27 | −0.178012 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.39837e27 | 0.219019 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.90202e27 | −0.444435 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.12963e27 | 0.917934 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.58201e28 | 2.31674 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.81716e26 | −0.126274 | −0.0631369 | − | 0.998005i | \(-0.520110\pi\) | ||||
−0.0631369 | + | 0.998005i | \(0.520110\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.91076e26 | 0.0547751 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.68989e26 | −0.0231495 | −0.0115747 | − | 0.999933i | \(-0.503684\pi\) | ||||
−0.0115747 | + | 0.999933i | \(0.503684\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.45204e28 | 1.94556 | 0.972779 | − | 0.231735i | \(-0.0744403\pi\) | ||||
0.972779 | + | 0.231735i | \(0.0744403\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.92517e27 | −0.645493 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.45753e27 | −0.186860 | −0.0934299 | − | 0.995626i | \(-0.529783\pi\) | ||||
−0.0934299 | + | 0.995626i | \(0.529783\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.54539e27 | 0.193813 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.76512e27 | −0.584645 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.64282e26 | 0.115749 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.11044e27 | 0.247857 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.92794e27 | −0.566279 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.68420e27 | 0.301813 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.44834e27 | 0.929555 | 0.464777 | − | 0.885428i | \(-0.346134\pi\) | ||||
0.464777 | + | 0.885428i | \(0.346134\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.60968e27 | −0.604010 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.79803e26 | 0.0400209 | 0.0200105 | − | 0.999800i | \(-0.493630\pi\) | ||||
0.0200105 | + | 0.999800i | \(0.493630\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.64147e27 | −0.169280 | −0.0846400 | − | 0.996412i | \(-0.526974\pi\) | ||||
−0.0846400 | + | 0.996412i | \(0.526974\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.63143e26 | −0.0164667 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.53135e28 | −1.51286 | −0.756432 | − | 0.654072i | \(-0.773059\pi\) | ||||
−0.756432 | + | 0.654072i | \(0.773059\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.76863e27 | −0.461133 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.96696e26 | 0.0754144 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.93306e27 | 0.642445 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.88124e27 | −0.261373 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.45729e27 | 0.218237 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.39952e27 | −0.121692 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.67313e28 | −1.42444 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.60823e27 | −0.467511 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.13459e27 | 0.419126 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.27504e28 | −1.81853 | −0.909265 | − | 0.416218i | \(-0.863355\pi\) | ||||
−0.909265 | + | 0.416218i | \(0.863355\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.35473e27 | 0.184325 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.90023e28 | 1.45674 | 0.728369 | − | 0.685185i | \(-0.240279\pi\) | ||||
0.728369 | + | 0.685185i | \(0.240279\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.44818e27 | 0.108730 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.92819e27 | 0.215327 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.70685e27 | 0.194965 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.01793e27 | −0.495122 | −0.247561 | − | 0.968872i | \(-0.579629\pi\) | ||||
−0.247561 | + | 0.968872i | \(0.579629\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.14753e27 | 0.424849 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.20106e27 | 0.0813106 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.02518e28 | −1.34312 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.34582e28 | −0.874441 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.04079e28 | 0.662545 | 0.331273 | − | 0.943535i | \(-0.392522\pi\) | ||||
0.331273 | + | 0.943535i | \(0.392522\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.71064e27 | −0.231434 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.44891e27 | −0.577439 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.07146e27 | −0.183923 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.36290e28 | −1.38650 | −0.693249 | − | 0.720698i | \(-0.743821\pi\) | ||||
−0.693249 | + | 0.720698i | \(0.743821\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.01366e27 | 0.288292 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.44433e27 | −0.250441 | −0.125220 | − | 0.992129i | \(-0.539964\pi\) | ||||
−0.125220 | + | 0.992129i | \(0.539964\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.23963e28 | 2.34135 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.96360e27 | −0.160405 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.77081e28 | −0.939390 | −0.469695 | − | 0.882829i | \(-0.655636\pi\) | ||||
−0.469695 | + | 0.882829i | \(0.655636\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.31127e27 | 0.328162 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.88661e28 | 0.961542 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.35882e27 | 0.217764 | 0.108882 | − | 0.994055i | \(-0.465273\pi\) | ||||
0.108882 | + | 0.994055i | \(0.465273\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.14769e27 | 0.350053 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.82645e27 | 0.0876886 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.27684e26 | −0.0107166 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.53162e28 | −0.706771 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.57756e28 | −0.713735 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.24623e27 | 0.144003 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.37579e27 | 0.320817 | 0.160408 | − | 0.987051i | \(-0.448719\pi\) | ||||
0.160408 | + | 0.987051i | \(0.448719\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.16422e27 | 0.390859 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.32649e28 | 0.554780 | 0.277390 | − | 0.960757i | \(-0.410531\pi\) | ||||
0.277390 | + | 0.960757i | \(0.410531\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.77313e28 | 1.13736 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.14565e27 | −0.126522 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.57429e28 | 0.620991 | 0.310496 | − | 0.950575i | \(-0.399505\pi\) | ||||
0.310496 | + | 0.950575i | \(0.399505\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.28044e28 | −0.495364 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.73480e27 | 0.293490 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.23838e27 | 0.0833059 | 0.0416529 | − | 0.999132i | \(-0.486738\pi\) | ||||
0.0416529 | + | 0.999132i | \(0.486738\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.18624e28 | −0.433040 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.88404e28 | −0.674649 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.82761e28 | 1.69577 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.72873e27 | 0.0940288 | 0.0470144 | − | 0.998894i | \(-0.485029\pi\) | ||||
0.0470144 | + | 0.998894i | \(0.485029\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.85170e28 | 0.964019 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.18289e27 | −0.0723956 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.56740e28 | 0.510008 | 0.255004 | − | 0.966940i | \(-0.417923\pi\) | ||||
0.255004 | + | 0.966940i | \(0.417923\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.59484e28 | 1.46689 |
(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 | 16.20.a.e.1.1 | 2 | ||
4.3 | odd | 2 | 8.20.a.a.1.2 | ✓ | 2 | ||
8.3 | odd | 2 | 64.20.a.k.1.1 | 2 | |||
8.5 | even | 2 | 64.20.a.j.1.2 | 2 | |||
12.11 | even | 2 | 72.20.a.a.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.20.a.a.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
16.20.a.e.1.1 | 2 | 1.1 | even | 1 | trivial | ||
64.20.a.j.1.2 | 2 | 8.5 | even | 2 | |||
64.20.a.k.1.1 | 2 | 8.3 | odd | 2 | |||
72.20.a.a.1.2 | 2 | 12.11 | even | 2 |