Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,26,Mod(49,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.49");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(197.998389976\) |
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: |
\( x^{4} - 47675x^{2} + 568250244 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{6}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 10) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(154.395 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.49 |
Dual form | 50.26.b.d.49.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).
\(n\) | \(27\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4096.00i | − 0.707107i | ||||||||
\(3\) | − 715531.i | − 0.777344i | −0.921376 | − | 0.388672i | \(-0.872934\pi\) | ||||
0.921376 | − | 0.388672i | \(-0.127066\pi\) | |||||||
\(4\) | −1.67772e7 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.93082e9 | −0.549665 | ||||||||
\(7\) | 6.40133e10i | 1.74801i | 0.485914 | + | 0.874007i | \(0.338487\pi\) | ||||
−0.485914 | + | 0.874007i | \(0.661513\pi\) | |||||||
\(8\) | 6.87195e10i | 0.353553i | ||||||||
\(9\) | 3.35303e11 | 0.395737 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.40584e13 | 1.35060 | 0.675301 | − | 0.737542i | \(-0.264014\pi\) | ||||
0.675301 | + | 0.737542i | \(0.264014\pi\) | |||||||
\(12\) | 1.20046e13i | 0.388672i | ||||||||
\(13\) | 1.57637e13i | 0.187658i | 0.995588 | + | 0.0938289i | \(0.0299107\pi\) | ||||
−0.995588 | + | 0.0938289i | \(0.970089\pi\) | |||||||
\(14\) | 2.62199e14 | 1.23603 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | 1.00698e15i | 0.419187i | 0.977789 | + | 0.209593i | \(0.0672140\pi\) | ||||
−0.977789 | + | 0.209593i | \(0.932786\pi\) | |||||||
\(18\) | − 1.37340e15i | − 0.279828i | ||||||||
\(19\) | 8.66632e15 | 0.898286 | 0.449143 | − | 0.893460i | \(-0.351729\pi\) | ||||
0.449143 | + | 0.893460i | \(0.351729\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.58035e16 | 1.35881 | ||||||||
\(22\) | − 5.75832e16i | − 0.955020i | ||||||||
\(23\) | 1.43338e17i | 1.36384i | 0.731426 | + | 0.681921i | \(0.238855\pi\) | ||||
−0.731426 | + | 0.681921i | \(0.761145\pi\) | |||||||
\(24\) | 4.91709e16 | 0.274832 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.45682e16 | 0.132694 | ||||||||
\(27\) | − 8.46182e17i | − 1.08497i | ||||||||
\(28\) | − 1.07397e18i | − 0.874007i | ||||||||
\(29\) | 3.60779e17 | 0.189351 | 0.0946753 | − | 0.995508i | \(-0.469819\pi\) | ||||
0.0946753 | + | 0.995508i | \(0.469819\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.72952e17 | 0.199053 | 0.0995266 | − | 0.995035i | \(-0.468267\pi\) | ||||
0.0995266 | + | 0.995035i | \(0.468267\pi\) | |||||||
\(32\) | − 1.15292e18i | − 0.176777i | ||||||||
\(33\) | − 1.00592e19i | − 1.04988i | ||||||||
\(34\) | 4.12457e18 | 0.296410 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.62546e18 | −0.197868 | ||||||||
\(37\) | − 7.37033e19i | − 1.84063i | −0.391183 | − | 0.920313i | \(-0.627934\pi\) | ||||
0.391183 | − | 0.920313i | \(-0.372066\pi\) | |||||||
\(38\) | − 3.54972e19i | − 0.635184i | ||||||||
\(39\) | 1.12794e19 | 0.145875 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.57824e19 | −0.455315 | −0.227657 | − | 0.973741i | \(-0.573107\pi\) | ||||
−0.227657 | + | 0.973741i | \(0.573107\pi\) | |||||||
\(42\) | − 1.87611e20i | − 0.960822i | ||||||||
\(43\) | 4.50969e20i | 1.72104i | 0.509418 | + | 0.860519i | \(0.329861\pi\) | ||||
−0.509418 | + | 0.860519i | \(0.670139\pi\) | |||||||
\(44\) | −2.35861e20 | −0.675301 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.87113e20 | 0.964382 | ||||||||
\(47\) | 5.55700e20i | 0.697617i | 0.937194 | + | 0.348809i | \(0.113414\pi\) | ||||
−0.937194 | + | 0.348809i | \(0.886586\pi\) | |||||||
\(48\) | − 2.01404e20i | − 0.194336i | ||||||||
\(49\) | −2.75664e21 | −2.05555 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.20523e20 | 0.325852 | ||||||||
\(52\) | − 2.64471e20i | − 0.0938289i | ||||||||
\(53\) | 4.75642e21i | 1.32994i | 0.746871 | + | 0.664969i | \(0.231555\pi\) | ||||
−0.746871 | + | 0.664969i | \(0.768445\pi\) | |||||||
\(54\) | −3.46596e21 | −0.767188 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.39896e21 | −0.618016 | ||||||||
\(57\) | − 6.20102e21i | − 0.698277i | ||||||||
\(58\) | − 1.47775e21i | − 0.133891i | ||||||||
\(59\) | 1.95774e22 | 1.43253 | 0.716265 | − | 0.697828i | \(-0.245850\pi\) | ||||
0.716265 | + | 0.697828i | \(0.245850\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.95892e21 | −0.142728 | −0.0713641 | − | 0.997450i | \(-0.522735\pi\) | ||||
−0.0713641 | + | 0.997450i | \(0.522735\pi\) | |||||||
\(62\) | − 3.57561e21i | − 0.140752i | ||||||||
\(63\) | 2.14639e22i | 0.691753i | ||||||||
\(64\) | −4.72237e21 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.12026e22 | −0.742379 | ||||||||
\(67\) | − 4.26809e22i | − 0.637234i | −0.947884 | − | 0.318617i | \(-0.896782\pi\) | ||||
0.947884 | − | 0.318617i | \(-0.103218\pi\) | |||||||
\(68\) | − 1.68942e22i | − 0.209593i | ||||||||
\(69\) | 1.02563e23 | 1.06017 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.93990e23 | −1.40297 | −0.701486 | − | 0.712683i | \(-0.747480\pi\) | ||||
−0.701486 | + | 0.712683i | \(0.747480\pi\) | |||||||
\(72\) | 2.30419e22i | 0.139914i | ||||||||
\(73\) | − 2.11325e22i | − 0.107998i | −0.998541 | − | 0.0539990i | \(-0.982803\pi\) | ||||
0.998541 | − | 0.0539990i | \(-0.0171968\pi\) | |||||||
\(74\) | −3.01889e23 | −1.30152 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.45397e23 | −0.449143 | ||||||||
\(77\) | 8.99925e23i | 2.36087i | ||||||||
\(78\) | − 4.62006e22i | − 0.103149i | ||||||||
\(79\) | 4.99401e23 | 0.950848 | 0.475424 | − | 0.879757i | \(-0.342295\pi\) | ||||
0.475424 | + | 0.879757i | \(0.342295\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.21371e23 | −0.447656 | ||||||||
\(82\) | 2.69445e23i | 0.321956i | ||||||||
\(83\) | 1.79998e24i | 1.84838i | 0.381937 | + | 0.924189i | \(0.375257\pi\) | ||||
−0.381937 | + | 0.924189i | \(0.624743\pi\) | |||||||
\(84\) | −7.68456e23 | −0.679404 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.84717e24 | 1.21696 | ||||||||
\(87\) | − 2.58149e23i | − 0.147190i | ||||||||
\(88\) | 9.66086e23i | 0.477510i | ||||||||
\(89\) | −2.07122e24 | −0.888898 | −0.444449 | − | 0.895804i | \(-0.646600\pi\) | ||||
−0.444449 | + | 0.895804i | \(0.646600\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00909e24 | −0.328029 | ||||||||
\(92\) | − 2.40482e24i | − 0.681921i | ||||||||
\(93\) | − 6.24624e23i | − 0.154733i | ||||||||
\(94\) | 2.27615e24 | 0.493290 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.24952e23 | −0.137416 | ||||||||
\(97\) | 3.44576e24i | 0.504242i | 0.967696 | + | 0.252121i | \(0.0811281\pi\) | ||||
−0.967696 | + | 0.252121i | \(0.918872\pi\) | |||||||
\(98\) | 1.12912e25i | 1.45349i | ||||||||
\(99\) | 4.71383e24 | 0.534483 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.35804e24 | 0.119921 | 0.0599607 | − | 0.998201i | \(-0.480902\pi\) | ||||
0.0599607 | + | 0.998201i | \(0.480902\pi\) | |||||||
\(102\) | − 2.95126e24i | − 0.230412i | ||||||||
\(103\) | − 1.81348e25i | − 1.25328i | −0.779310 | − | 0.626639i | \(-0.784430\pi\) | ||||
0.779310 | − | 0.626639i | \(-0.215570\pi\) | |||||||
\(104\) | −1.08327e24 | −0.0663471 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.94823e25 | 0.940409 | ||||||||
\(107\) | 4.09213e25i | 1.75652i | 0.478186 | + | 0.878259i | \(0.341295\pi\) | ||||
−0.478186 | + | 0.878259i | \(0.658705\pi\) | |||||||
\(108\) | 1.41966e25i | 0.542484i | ||||||||
\(109\) | −4.31829e25 | −1.47055 | −0.735277 | − | 0.677767i | \(-0.762948\pi\) | ||||
−0.735277 | + | 0.677767i | \(0.762948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.27370e25 | −1.43080 | ||||||||
\(112\) | 1.80181e25i | 0.437003i | ||||||||
\(113\) | − 2.61097e25i | − 0.566659i | −0.959023 | − | 0.283329i | \(-0.908561\pi\) | ||||
0.959023 | − | 0.283329i | \(-0.0914390\pi\) | |||||||
\(114\) | −2.53994e25 | −0.493756 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.05287e24 | −0.0946753 | ||||||||
\(117\) | 5.28563e24i | 0.0742631i | ||||||||
\(118\) | − 8.01888e25i | − 1.01295i | ||||||||
\(119\) | −6.44599e25 | −0.732744 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.92916e25 | 0.824126 | ||||||||
\(122\) | 1.21197e25i | 0.100924i | ||||||||
\(123\) | 4.70694e25i | 0.353936i | ||||||||
\(124\) | −1.46457e25 | −0.0995266 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 8.79160e25 | 0.489144 | ||||||||
\(127\) | − 3.07316e25i | − 0.154895i | −0.996996 | − | 0.0774477i | \(-0.975323\pi\) | ||||
0.996996 | − | 0.0774477i | \(-0.0246771\pi\) | |||||||
\(128\) | 1.93428e25i | 0.0883883i | ||||||||
\(129\) | 3.22682e26 | 1.33784 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.55205e26 | 0.530902 | 0.265451 | − | 0.964124i | \(-0.414479\pi\) | ||||
0.265451 | + | 0.964124i | \(0.414479\pi\) | |||||||
\(132\) | 1.68766e26i | 0.524941i | ||||||||
\(133\) | 5.54760e26i | 1.57022i | ||||||||
\(134\) | −1.74821e26 | −0.450593 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.91988e25 | −0.148205 | ||||||||
\(137\) | − 4.44205e26i | − 0.868112i | −0.900886 | − | 0.434056i | \(-0.857082\pi\) | ||||
0.900886 | − | 0.434056i | \(-0.142918\pi\) | |||||||
\(138\) | − 4.20098e26i | − 0.749656i | ||||||||
\(139\) | −9.86493e26 | −1.60845 | −0.804227 | − | 0.594322i | \(-0.797421\pi\) | ||||
−0.804227 | + | 0.594322i | \(0.797421\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.97621e26 | 0.542288 | ||||||||
\(142\) | 7.94582e26i | 0.992051i | ||||||||
\(143\) | 2.21613e26i | 0.253451i | ||||||||
\(144\) | 9.43795e25 | 0.0989342 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.65589e25 | −0.0763661 | ||||||||
\(147\) | 1.97246e27i | 1.59787i | ||||||||
\(148\) | 1.23654e27i | 0.920313i | ||||||||
\(149\) | −1.38635e27 | −0.948518 | −0.474259 | − | 0.880385i | \(-0.657284\pi\) | ||||
−0.474259 | + | 0.880385i | \(0.657284\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.02182e26 | −0.522495 | −0.261248 | − | 0.965272i | \(-0.584134\pi\) | ||||
−0.261248 | + | 0.965272i | \(0.584134\pi\) | |||||||
\(152\) | 5.95545e26i | 0.317592i | ||||||||
\(153\) | 3.37642e26i | 0.165888i | ||||||||
\(154\) | 3.68609e27 | 1.66939 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.89238e26 | −0.0729373 | ||||||||
\(157\) | − 2.62328e27i | − 0.933466i | −0.884398 | − | 0.466733i | \(-0.845431\pi\) | ||||
0.884398 | − | 0.466733i | \(-0.154569\pi\) | |||||||
\(158\) | − 2.04555e27i | − 0.672351i | ||||||||
\(159\) | 3.40337e27 | 1.03382 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.17555e27 | −2.38401 | ||||||||
\(162\) | 1.31634e27i | 0.316540i | ||||||||
\(163\) | 1.18488e27i | 0.263834i | 0.991261 | + | 0.131917i | \(0.0421133\pi\) | ||||
−0.991261 | + | 0.131917i | \(0.957887\pi\) | |||||||
\(164\) | 1.10365e27 | 0.227657 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.37270e27 | 1.30700 | ||||||||
\(167\) | − 7.47611e27i | − 1.22948i | −0.788732 | − | 0.614738i | \(-0.789262\pi\) | ||||
0.788732 | − | 0.614738i | \(-0.210738\pi\) | |||||||
\(168\) | 3.14760e27i | 0.480411i | ||||||||
\(169\) | 6.80792e27 | 0.964785 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.90585e27 | 0.355485 | ||||||||
\(172\) | − 7.56600e27i | − 0.860519i | ||||||||
\(173\) | − 3.35797e27i | − 0.355223i | −0.984101 | − | 0.177611i | \(-0.943163\pi\) | ||||
0.984101 | − | 0.177611i | \(-0.0568370\pi\) | |||||||
\(174\) | −1.05738e27 | −0.104079 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.95709e27 | 0.337651 | ||||||||
\(177\) | − 1.40082e28i | − 1.11357i | ||||||||
\(178\) | 8.48373e27i | 0.628546i | ||||||||
\(179\) | −6.30645e27 | −0.435634 | −0.217817 | − | 0.975990i | \(-0.569894\pi\) | ||||
−0.217817 | + | 0.975990i | \(0.569894\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.20387e28 | 0.723764 | 0.361882 | − | 0.932224i | \(-0.382134\pi\) | ||||
0.361882 | + | 0.932224i | \(0.382134\pi\) | |||||||
\(182\) | 4.13322e27i | 0.231951i | ||||||||
\(183\) | 2.11720e27i | 0.110949i | ||||||||
\(184\) | −9.85012e27 | −0.482191 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.55846e27 | −0.109413 | ||||||||
\(187\) | 1.41565e28i | 0.566154i | ||||||||
\(188\) | − 9.32310e27i | − 0.348809i | ||||||||
\(189\) | 5.41669e28 | 1.89654 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.13809e28 | 0.656309 | 0.328155 | − | 0.944624i | \(-0.393573\pi\) | ||||
0.328155 | + | 0.944624i | \(0.393573\pi\) | |||||||
\(192\) | 3.37900e27i | 0.0971680i | ||||||||
\(193\) | 2.97996e27i | 0.0803054i | 0.999194 | + | 0.0401527i | \(0.0127844\pi\) | ||||
−0.999194 | + | 0.0401527i | \(0.987216\pi\) | |||||||
\(194\) | 1.41138e28 | 0.356553 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.62487e28 | 1.02778 | ||||||||
\(197\) | − 4.10890e28i | − 0.856836i | −0.903581 | − | 0.428418i | \(-0.859071\pi\) | ||||
0.903581 | − | 0.428418i | \(-0.140929\pi\) | |||||||
\(198\) | − 1.93078e28i | − 0.377937i | ||||||||
\(199\) | 5.34406e28 | 0.982218 | 0.491109 | − | 0.871098i | \(-0.336592\pi\) | ||||
0.491109 | + | 0.871098i | \(0.336592\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.05396e28 | −0.495350 | ||||||||
\(202\) | − 5.56255e27i | − 0.0847973i | ||||||||
\(203\) | 2.30947e28i | 0.330987i | ||||||||
\(204\) | −1.20884e28 | −0.162926 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.42801e28 | −0.886202 | ||||||||
\(207\) | 4.80618e28i | 0.539722i | ||||||||
\(208\) | 4.43709e27i | 0.0469145i | ||||||||
\(209\) | 1.21835e29 | 1.21323 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.77946e28 | 0.422521 | 0.211260 | − | 0.977430i | \(-0.432243\pi\) | ||||
0.211260 | + | 0.977430i | \(0.432243\pi\) | |||||||
\(212\) | − 7.97994e28i | − 0.664969i | ||||||||
\(213\) | 1.38806e29i | 1.09059i | ||||||||
\(214\) | 1.67614e29 | 1.24205 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.81492e28 | 0.383594 | ||||||||
\(217\) | 5.58805e28i | 0.347948i | ||||||||
\(218\) | 1.76877e29i | 1.03984i | ||||||||
\(219\) | −1.51210e28 | −0.0839516 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.58737e28 | −0.0786637 | ||||||||
\(222\) | 2.16011e29i | 1.01173i | ||||||||
\(223\) | 4.45198e29i | 1.97125i | 0.168934 | + | 0.985627i | \(0.445968\pi\) | ||||
−0.168934 | + | 0.985627i | \(0.554032\pi\) | |||||||
\(224\) | 7.38023e28 | 0.309008 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.06945e29 | −0.400688 | ||||||||
\(227\) | 2.11324e29i | 0.749248i | 0.927177 | + | 0.374624i | \(0.122228\pi\) | ||||
−0.927177 | + | 0.374624i | \(0.877772\pi\) | |||||||
\(228\) | 1.04036e29i | 0.349138i | ||||||||
\(229\) | −4.64740e29 | −1.47661 | −0.738307 | − | 0.674465i | \(-0.764374\pi\) | ||||
−0.738307 | + | 0.674465i | \(0.764374\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.43925e29 | 1.83521 | ||||||||
\(232\) | 2.47926e28i | 0.0669455i | ||||||||
\(233\) | 5.21268e29i | 1.33386i | 0.745118 | + | 0.666932i | \(0.232393\pi\) | ||||
−0.745118 | + | 0.666932i | \(0.767607\pi\) | |||||||
\(234\) | 2.16499e28 | 0.0525120 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.28453e29 | −0.716265 | ||||||||
\(237\) | − 3.57337e29i | − 0.739135i | ||||||||
\(238\) | 2.64028e29i | 0.518128i | ||||||||
\(239\) | 9.68016e29 | 1.80264 | 0.901319 | − | 0.433155i | \(-0.142600\pi\) | ||||
0.901319 | + | 0.433155i | \(0.142600\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.30231e29 | −0.218525 | −0.109263 | − | 0.994013i | \(-0.534849\pi\) | ||||
−0.109263 | + | 0.994013i | \(0.534849\pi\) | |||||||
\(242\) | − 3.65738e29i | − 0.582745i | ||||||||
\(243\) | − 4.87009e29i | − 0.736985i | ||||||||
\(244\) | 4.96424e28 | 0.0713641 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.92796e29 | 0.250271 | ||||||||
\(247\) | 1.36613e29i | 0.168570i | ||||||||
\(248\) | 5.99888e28i | 0.0703759i | ||||||||
\(249\) | 1.28794e30 | 1.43682 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.40543e30 | 1.41869 | 0.709345 | − | 0.704862i | \(-0.248991\pi\) | ||||
0.709345 | + | 0.704862i | \(0.248991\pi\) | |||||||
\(252\) | − 3.60104e29i | − 0.345877i | ||||||||
\(253\) | 2.01511e30i | 1.84201i | ||||||||
\(254\) | −1.25877e29 | −0.109528 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | 1.02386e30i | 0.769263i | 0.923070 | + | 0.384632i | \(0.125671\pi\) | ||||
−0.923070 | + | 0.384632i | \(0.874329\pi\) | |||||||
\(258\) | − 1.32171e30i | − 0.945995i | ||||||||
\(259\) | 4.71799e30 | 3.21744 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.20970e29 | 0.0749330 | ||||||||
\(262\) | − 6.35719e29i | − 0.375404i | ||||||||
\(263\) | − 9.94329e29i | − 0.559865i | −0.960020 | − | 0.279933i | \(-0.909688\pi\) | ||||
0.960020 | − | 0.279933i | \(-0.0903121\pi\) | |||||||
\(264\) | 6.91265e29 | 0.371189 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.27230e30 | 1.11031 | ||||||||
\(267\) | 1.48203e30i | 0.690979i | ||||||||
\(268\) | 7.16067e29i | 0.318617i | ||||||||
\(269\) | −9.41553e29 | −0.399891 | −0.199945 | − | 0.979807i | \(-0.564076\pi\) | ||||
−0.199945 | + | 0.979807i | \(0.564076\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.84694e29 | −0.110220 | −0.0551101 | − | 0.998480i | \(-0.517551\pi\) | ||||
−0.0551101 | + | 0.998480i | \(0.517551\pi\) | |||||||
\(272\) | 2.83438e29i | 0.104797i | ||||||||
\(273\) | 7.22034e29i | 0.254991i | ||||||||
\(274\) | −1.81946e30 | −0.613848 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.72072e30 | −0.530087 | ||||||||
\(277\) | − 5.74193e30i | − 1.69068i | −0.534230 | − | 0.845339i | \(-0.679398\pi\) | ||||
0.534230 | − | 0.845339i | \(-0.320602\pi\) | |||||||
\(278\) | 4.04067e30i | 1.13735i | ||||||||
\(279\) | 2.92704e29 | 0.0787726 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.10013e29 | 0.174758 | 0.0873790 | − | 0.996175i | \(-0.472151\pi\) | ||||
0.0873790 | + | 0.996175i | \(0.472151\pi\) | |||||||
\(282\) | − 1.62865e30i | − 0.383456i | ||||||||
\(283\) | 4.98063e30i | 1.12190i | 0.827850 | + | 0.560950i | \(0.189564\pi\) | ||||
−0.827850 | + | 0.560950i | \(0.810436\pi\) | |||||||
\(284\) | 3.25461e30 | 0.701486 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.07726e29 | 0.179217 | ||||||||
\(287\) | − 4.21095e30i | − 0.795896i | ||||||||
\(288\) | − 3.86578e29i | − 0.0699571i | ||||||||
\(289\) | 4.75663e30 | 0.824283 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.46555e30 | 0.391969 | ||||||||
\(292\) | 3.54545e29i | 0.0539990i | ||||||||
\(293\) | − 4.89769e30i | − 0.714736i | −0.933964 | − | 0.357368i | \(-0.883674\pi\) | ||||
0.933964 | − | 0.357368i | \(-0.116326\pi\) | |||||||
\(294\) | 8.07920e30 | 1.12987 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.06485e30 | 0.650759 | ||||||||
\(297\) | − 1.18960e31i | − 1.46536i | ||||||||
\(298\) | 5.67850e30i | 0.670704i | ||||||||
\(299\) | −2.25954e30 | −0.255936 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.88680e31 | −3.00840 | ||||||||
\(302\) | 3.69534e30i | 0.369460i | ||||||||
\(303\) | − 9.71724e29i | − 0.0932202i | ||||||||
\(304\) | 2.43935e30 | 0.224572 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.38298e30 | 0.117300 | ||||||||
\(307\) | 2.34261e31i | 1.90752i | 0.300563 | + | 0.953762i | \(0.402825\pi\) | ||||
−0.300563 | + | 0.953762i | \(0.597175\pi\) | |||||||
\(308\) | − 1.50982e31i | − 1.18044i | ||||||||
\(309\) | −1.29760e31 | −0.974228 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.34425e31 | 0.931054 | 0.465527 | − | 0.885034i | \(-0.345865\pi\) | ||||
0.465527 | + | 0.885034i | \(0.345865\pi\) | |||||||
\(312\) | 7.75117e29i | 0.0515745i | ||||||||
\(313\) | 2.25707e31i | 1.44292i | 0.692458 | + | 0.721458i | \(0.256528\pi\) | ||||
−0.692458 | + | 0.721458i | \(0.743472\pi\) | |||||||
\(314\) | −1.07449e31 | −0.660060 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.37856e30 | −0.475424 | ||||||||
\(317\) | − 4.83401e29i | − 0.0263674i | −0.999913 | − | 0.0131837i | \(-0.995803\pi\) | ||||
0.999913 | − | 0.0131837i | \(-0.00419662\pi\) | |||||||
\(318\) | − 1.39402e31i | − 0.731021i | ||||||||
\(319\) | 5.07198e30 | 0.255737 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.92805e31 | 1.36542 | ||||||||
\(322\) | 3.75831e31i | 1.68575i | ||||||||
\(323\) | 8.72677e30i | 0.376550i | ||||||||
\(324\) | 5.39171e30 | 0.223828 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.85329e30 | 0.186559 | ||||||||
\(327\) | 3.08987e31i | 1.14313i | ||||||||
\(328\) | − 4.52053e30i | − 0.160978i | ||||||||
\(329\) | −3.55722e31 | −1.21944 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.89856e31 | −1.55675 | −0.778375 | − | 0.627800i | \(-0.783956\pi\) | ||||
−0.778375 | + | 0.627800i | \(0.783956\pi\) | |||||||
\(332\) | − 3.01986e31i | − 0.924189i | ||||||||
\(333\) | − 2.47130e31i | − 0.728403i | ||||||||
\(334\) | −3.06221e31 | −0.869370 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.28926e31 | 0.339702 | ||||||||
\(337\) | − 3.74477e31i | − 0.950718i | −0.879792 | − | 0.475359i | \(-0.842318\pi\) | ||||
0.879792 | − | 0.475359i | \(-0.157682\pi\) | |||||||
\(338\) | − 2.78852e31i | − 0.682206i | ||||||||
\(339\) | −1.86823e31 | −0.440489 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.22723e31 | 0.268842 | ||||||||
\(342\) | − 1.19023e31i | − 0.251366i | ||||||||
\(343\) | − 9.06152e31i | − 1.84512i | ||||||||
\(344\) | −3.09903e31 | −0.608479 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.37543e31 | −0.251181 | ||||||||
\(347\) | − 1.26433e31i | − 0.222711i | −0.993781 | − | 0.111356i | \(-0.964481\pi\) | ||||
0.993781 | − | 0.111356i | \(-0.0355193\pi\) | |||||||
\(348\) | 4.33102e30i | 0.0735952i | ||||||||
\(349\) | −5.64423e31 | −0.925308 | −0.462654 | − | 0.886539i | \(-0.653103\pi\) | ||||
−0.462654 | + | 0.886539i | \(0.653103\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.33390e31 | 0.203603 | ||||||||
\(352\) | − 1.62082e31i | − 0.238755i | ||||||||
\(353\) | − 1.66522e31i | − 0.236749i | −0.992969 | − | 0.118374i | \(-0.962232\pi\) | ||||
0.992969 | − | 0.118374i | \(-0.0377683\pi\) | |||||||
\(354\) | −5.73776e31 | −0.787412 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.47494e31 | 0.444449 | ||||||||
\(357\) | 4.61231e31i | 0.569594i | ||||||||
\(358\) | 2.58312e31i | 0.308040i | ||||||||
\(359\) | −1.12363e32 | −1.29403 | −0.647014 | − | 0.762478i | \(-0.723982\pi\) | ||||
−0.647014 | + | 0.762478i | \(0.723982\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.79714e31 | −0.193082 | ||||||||
\(362\) | − 4.93104e31i | − 0.511778i | ||||||||
\(363\) | − 6.38910e31i | − 0.640629i | ||||||||
\(364\) | 1.69297e31 | 0.164014 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.67204e30 | 0.0784527 | ||||||||
\(367\) | 1.62554e32i | 1.42126i | 0.703567 | + | 0.710629i | \(0.251590\pi\) | ||||
−0.703567 | + | 0.710629i | \(0.748410\pi\) | |||||||
\(368\) | 4.03461e31i | 0.340960i | ||||||||
\(369\) | −2.20571e31 | −0.180185 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.04474e32 | −2.32475 | ||||||||
\(372\) | 1.04795e31i | 0.0773663i | ||||||||
\(373\) | 8.65344e31i | 0.617772i | 0.951099 | + | 0.308886i | \(0.0999562\pi\) | ||||
−0.951099 | + | 0.308886i | \(0.900044\pi\) | |||||||
\(374\) | 5.79849e31 | 0.400332 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.81874e31 | −0.246645 | ||||||||
\(377\) | 5.68722e30i | 0.0355331i | ||||||||
\(378\) | − 2.21868e32i | − 1.34105i | ||||||||
\(379\) | 1.30491e32 | 0.763117 | 0.381558 | − | 0.924345i | \(-0.375388\pi\) | ||||
0.381558 | + | 0.924345i | \(0.375388\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.19894e31 | −0.120407 | ||||||||
\(382\) | − 8.75761e31i | − 0.464081i | ||||||||
\(383\) | − 3.19017e31i | − 0.163617i | −0.996648 | − | 0.0818087i | \(-0.973930\pi\) | ||||
0.996648 | − | 0.0818087i | \(-0.0260696\pi\) | |||||||
\(384\) | 1.38404e31 | 0.0687081 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.22059e31 | 0.0567845 | ||||||||
\(387\) | 1.51211e32i | 0.681078i | ||||||||
\(388\) | − 5.78103e31i | − 0.252121i | ||||||||
\(389\) | −1.71823e32 | −0.725622 | −0.362811 | − | 0.931863i | \(-0.618183\pi\) | ||||
−0.362811 | + | 0.931863i | \(0.618183\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.44338e32 | −0.571704 | ||||||||
\(392\) | − 1.89435e32i | − 0.726747i | ||||||||
\(393\) | − 1.11054e32i | − 0.412693i | ||||||||
\(394\) | −1.68301e32 | −0.605874 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.90849e31 | −0.267241 | ||||||||
\(397\) | − 1.44908e32i | − 0.474471i | −0.971452 | − | 0.237236i | \(-0.923759\pi\) | ||||
0.971452 | − | 0.237236i | \(-0.0762414\pi\) | |||||||
\(398\) | − 2.18893e32i | − 0.694533i | ||||||||
\(399\) | 3.96948e32 | 1.22060 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.47108e32 | 1.86927 | 0.934635 | − | 0.355609i | \(-0.115726\pi\) | ||||
0.934635 | + | 0.355609i | \(0.115726\pi\) | |||||||
\(402\) | 1.25090e32i | 0.350265i | ||||||||
\(403\) | 1.37610e31i | 0.0373539i | ||||||||
\(404\) | −2.27842e31 | −0.0599607 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.45958e31 | 0.234043 | ||||||||
\(407\) | − 1.03615e33i | − 2.48595i | ||||||||
\(408\) | 4.95140e31i | 0.115206i | ||||||||
\(409\) | 1.49705e32 | 0.337828 | 0.168914 | − | 0.985631i | \(-0.445974\pi\) | ||||
0.168914 | + | 0.985631i | \(0.445974\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.17842e32 | −0.674822 | ||||||||
\(412\) | 3.04251e32i | 0.626639i | ||||||||
\(413\) | 1.25321e33i | 2.50408i | ||||||||
\(414\) | 1.96861e32 | 0.381641 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.81743e31 | 0.0331735 | ||||||||
\(417\) | 7.05867e32i | 1.25032i | ||||||||
\(418\) | − 4.99035e32i | − 0.857881i | ||||||||
\(419\) | −6.23538e32 | −1.04037 | −0.520185 | − | 0.854054i | \(-0.674137\pi\) | ||||
−0.520185 | + | 0.854054i | \(0.674137\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.35871e32 | 0.685223 | 0.342611 | − | 0.939477i | \(-0.388689\pi\) | ||||
0.342611 | + | 0.939477i | \(0.388689\pi\) | |||||||
\(422\) | − 1.95767e32i | − 0.298767i | ||||||||
\(423\) | 1.86328e32i | 0.276073i | ||||||||
\(424\) | −3.26859e32 | −0.470204 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.68548e32 | 0.771165 | ||||||||
\(427\) | − 1.89410e32i | − 0.249491i | ||||||||
\(428\) | − 6.86546e32i | − 0.878259i | ||||||||
\(429\) | 1.58571e32 | 0.197019 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.60606e32 | −1.12611 | −0.563053 | − | 0.826420i | \(-0.690373\pi\) | ||||
−0.563053 | + | 0.826420i | \(0.690373\pi\) | |||||||
\(432\) | − 2.38179e32i | − 0.271242i | ||||||||
\(433\) | 6.50298e32i | 0.719472i | 0.933054 | + | 0.359736i | \(0.117133\pi\) | ||||
−0.933054 | + | 0.359736i | \(0.882867\pi\) | |||||||
\(434\) | 2.28887e32 | 0.246036 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.24489e32 | 0.735277 | ||||||||
\(437\) | 1.24221e33i | 1.22512i | ||||||||
\(438\) | 6.19356e31i | 0.0593627i | ||||||||
\(439\) | 1.26999e33 | 1.18303 | 0.591515 | − | 0.806294i | \(-0.298530\pi\) | ||||
0.591515 | + | 0.806294i | \(0.298530\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.24309e32 | −0.813458 | ||||||||
\(442\) | 6.50186e31i | 0.0556236i | ||||||||
\(443\) | 3.57910e32i | 0.297665i | 0.988862 | + | 0.148832i | \(0.0475515\pi\) | ||||
−0.988862 | + | 0.148832i | \(0.952449\pi\) | |||||||
\(444\) | 8.84781e32 | 0.715399 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.82353e33 | 1.39389 | ||||||||
\(447\) | 9.91980e32i | 0.737325i | ||||||||
\(448\) | − 3.02294e32i | − 0.218502i | ||||||||
\(449\) | 2.89265e32 | 0.203337 | 0.101669 | − | 0.994818i | \(-0.467582\pi\) | ||||
0.101669 | + | 0.994818i | \(0.467582\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.24796e32 | −0.614949 | ||||||||
\(452\) | 4.38048e32i | 0.283329i | ||||||||
\(453\) | 6.45540e32i | 0.406158i | ||||||||
\(454\) | 8.65583e32 | 0.529798 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.26131e32 | 0.246878 | ||||||||
\(457\) | − 2.55962e33i | − 1.44285i | −0.692491 | − | 0.721427i | \(-0.743487\pi\) | ||||
0.692491 | − | 0.721427i | \(-0.256513\pi\) | |||||||
\(458\) | 1.90358e33i | 1.04412i | ||||||||
\(459\) | 8.52085e32 | 0.454804 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.93005e31 | −0.0400880 | −0.0200440 | − | 0.999799i | \(-0.506381\pi\) | ||||
−0.0200440 | + | 0.999799i | \(0.506381\pi\) | |||||||
\(462\) | − 2.63752e33i | − 1.29769i | ||||||||
\(463\) | 3.30952e32i | 0.158490i | 0.996855 | + | 0.0792452i | \(0.0252510\pi\) | ||||
−0.996855 | + | 0.0792452i | \(0.974749\pi\) | |||||||
\(464\) | 1.01550e32 | 0.0473376 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.13511e33 | 0.943185 | ||||||||
\(467\) | 2.96201e33i | 1.27387i | 0.770917 | + | 0.636936i | \(0.219798\pi\) | ||||
−0.770917 | + | 0.636936i | \(0.780202\pi\) | |||||||
\(468\) | − 8.86781e31i | − 0.0371316i | ||||||||
\(469\) | 2.73215e33 | 1.11389 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.87704e33 | −0.725624 | ||||||||
\(472\) | 1.34535e33i | 0.506476i | ||||||||
\(473\) | 6.33990e33i | 2.32444i | ||||||||
\(474\) | −1.46365e33 | −0.522648 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.08146e33 | 0.366372 | ||||||||
\(477\) | 1.59484e33i | 0.526306i | ||||||||
\(478\) | − 3.96499e33i | − 1.27466i | ||||||||
\(479\) | −1.66525e33 | −0.521537 | −0.260769 | − | 0.965401i | \(-0.583976\pi\) | ||||
−0.260769 | + | 0.965401i | \(0.583976\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.16184e33 | 0.345408 | ||||||||
\(482\) | 5.33427e32i | 0.154521i | ||||||||
\(483\) | 6.56540e33i | 1.85320i | ||||||||
\(484\) | −1.49806e33 | −0.412063 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.99479e33 | −0.521127 | ||||||||
\(487\) | 6.03193e33i | 1.53583i | 0.640549 | + | 0.767917i | \(0.278707\pi\) | ||||
−0.640549 | + | 0.767917i | \(0.721293\pi\) | |||||||
\(488\) | − 2.03335e32i | − 0.0504620i | ||||||||
\(489\) | 8.47822e32 | 0.205090 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.62144e33 | 0.602590 | 0.301295 | − | 0.953531i | \(-0.402581\pi\) | ||||
0.301295 | + | 0.953531i | \(0.402581\pi\) | |||||||
\(492\) | − 7.89693e32i | − 0.176968i | ||||||||
\(493\) | 3.63296e32i | 0.0793732i | ||||||||
\(494\) | 5.59568e32 | 0.119197 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.45714e32 | 0.0497633 | ||||||||
\(497\) | − 1.24179e34i | − 2.45242i | ||||||||
\(498\) | − 5.27540e33i | − 1.01599i | ||||||||
\(499\) | 8.04276e33 | 1.51060 | 0.755298 | − | 0.655382i | \(-0.227492\pi\) | ||||
0.755298 | + | 0.655382i | \(0.227492\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.34939e33 | −0.955725 | ||||||||
\(502\) | − 5.75664e33i | − 1.00316i | ||||||||
\(503\) | 8.35523e33i | 1.42023i | 0.704086 | + | 0.710115i | \(0.251357\pi\) | ||||
−0.704086 | + | 0.710115i | \(0.748643\pi\) | |||||||
\(504\) | −1.47499e33 | −0.244572 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.25387e33 | 1.30250 | ||||||||
\(507\) | − 4.87128e33i | − 0.749969i | ||||||||
\(508\) | 5.15590e32i | 0.0774477i | ||||||||
\(509\) | 7.38135e33 | 1.08184 | 0.540920 | − | 0.841074i | \(-0.318076\pi\) | ||||
0.540920 | + | 0.841074i | \(0.318076\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.35276e33 | 0.188782 | ||||||||
\(512\) | − 3.24519e32i | − 0.0441942i | ||||||||
\(513\) | − 7.33328e33i | − 0.974611i | ||||||||
\(514\) | 4.19371e33 | 0.543951 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.41371e33 | −0.668919 | ||||||||
\(517\) | 7.81225e33i | 0.942203i | ||||||||
\(518\) | − 1.93249e34i | − 2.27507i | ||||||||
\(519\) | −2.40274e33 | −0.276130 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.16894e34 | −1.28032 | −0.640161 | − | 0.768241i | \(-0.721133\pi\) | ||||
−0.640161 | + | 0.768241i | \(0.721133\pi\) | |||||||
\(522\) | − 4.95495e32i | − 0.0529856i | ||||||||
\(523\) | − 1.32178e34i | − 1.38003i | −0.723796 | − | 0.690014i | \(-0.757604\pi\) | ||||
0.723796 | − | 0.690014i | \(-0.242396\pi\) | |||||||
\(524\) | −2.60391e33 | −0.265451 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.07277e33 | −0.395884 | ||||||||
\(527\) | 8.79041e32i | 0.0834404i | ||||||||
\(528\) | − 2.83142e33i | − 0.262470i | ||||||||
\(529\) | −9.50007e33 | −0.860064 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.56435e33 | 0.566905 | ||||||||
\(532\) | − 9.30733e33i | − 0.785108i | ||||||||
\(533\) | − 1.03698e33i | − 0.0854434i | ||||||||
\(534\) | 6.07037e33 | 0.488596 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.93301e33 | 0.225296 | ||||||||
\(537\) | 4.51247e33i | 0.338638i | ||||||||
\(538\) | 3.85660e33i | 0.282765i | ||||||||
\(539\) | −3.87539e34 | −2.77623 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.02274e34 | −0.699522 | −0.349761 | − | 0.936839i | \(-0.613737\pi\) | ||||
−0.349761 | + | 0.936839i | \(0.613737\pi\) | |||||||
\(542\) | 1.16610e33i | 0.0779375i | ||||||||
\(543\) | − 8.61406e33i | − 0.562613i | ||||||||
\(544\) | 1.16096e33 | 0.0741024 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.95745e33 | 0.180306 | ||||||||
\(547\) | 9.41592e33i | 0.561075i | 0.959843 | + | 0.280538i | \(0.0905127\pi\) | ||||
−0.959843 | + | 0.280538i | \(0.909487\pi\) | |||||||
\(548\) | 7.45252e33i | 0.434056i | ||||||||
\(549\) | −9.92134e32 | −0.0564828 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.12663e33 | 0.170091 | ||||||||
\(552\) | 7.04807e33i | 0.374828i | ||||||||
\(553\) | 3.19683e34i | 1.66209i | ||||||||
\(554\) | −2.35190e34 | −1.19549 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.65506e34 | 0.804227 | ||||||||
\(557\) | 1.93891e34i | 0.921227i | 0.887601 | + | 0.460614i | \(0.152371\pi\) | ||||
−0.887601 | + | 0.460614i | \(0.847629\pi\) | |||||||
\(558\) | − 1.19891e33i | − 0.0557007i | ||||||||
\(559\) | −7.10894e33 | −0.322966 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.01294e34 | 0.440097 | ||||||||
\(562\) | − 2.90821e33i | − 0.123573i | ||||||||
\(563\) | − 2.14770e34i | − 0.892520i | −0.894903 | − | 0.446260i | \(-0.852756\pi\) | ||||
0.894903 | − | 0.446260i | \(-0.147244\pi\) | |||||||
\(564\) | −6.67097e33 | −0.271144 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.04007e34 | 0.793303 | ||||||||
\(567\) | − 2.05720e34i | − 0.782508i | ||||||||
\(568\) | − 1.33309e34i | − 0.496026i | ||||||||
\(569\) | 1.35765e33 | 0.0494180 | 0.0247090 | − | 0.999695i | \(-0.492134\pi\) | ||||
0.0247090 | + | 0.999695i | \(0.492134\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.57397e34 | −0.548334 | −0.274167 | − | 0.961682i | \(-0.588402\pi\) | ||||
−0.274167 | + | 0.961682i | \(0.588402\pi\) | |||||||
\(572\) | − 3.71804e33i | − 0.126726i | ||||||||
\(573\) | − 1.52987e34i | − 0.510178i | ||||||||
\(574\) | −1.72481e34 | −0.562784 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.58343e33 | −0.0494671 | ||||||||
\(577\) | 5.82494e34i | 1.78071i | 0.455266 | + | 0.890356i | \(0.349544\pi\) | ||||
−0.455266 | + | 0.890356i | \(0.650456\pi\) | |||||||
\(578\) | − 1.94831e34i | − 0.582856i | ||||||||
\(579\) | 2.13226e33 | 0.0624249 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.15222e35 | −3.23099 | ||||||||
\(582\) | − 1.00989e34i | − 0.277164i | ||||||||
\(583\) | 6.68676e34i | 1.79622i | ||||||||
\(584\) | 1.45222e33 | 0.0381831 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.00609e34 | −0.505395 | ||||||||
\(587\) | − 4.94816e33i | − 0.122030i | −0.998137 | − | 0.0610151i | \(-0.980566\pi\) | ||||
0.998137 | − | 0.0610151i | \(-0.0194338\pi\) | |||||||
\(588\) | − 3.30924e34i | − 0.798935i | ||||||||
\(589\) | 7.56528e33 | 0.178807 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.94005e34 | −0.666056 | ||||||||
\(592\) | − 2.07456e34i | − 0.460156i | ||||||||
\(593\) | − 5.71306e34i | − 1.24075i | −0.784304 | − | 0.620376i | \(-0.786980\pi\) | ||||
0.784304 | − | 0.620376i | \(-0.213020\pi\) | |||||||
\(594\) | −4.87259e34 | −1.03617 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.32592e34 | 0.474259 | ||||||||
\(597\) | − 3.82384e34i | − 0.763521i | ||||||||
\(598\) | 9.25509e33i | 0.180974i | ||||||||
\(599\) | −4.92727e34 | −0.943564 | −0.471782 | − | 0.881715i | \(-0.656389\pi\) | ||||
−0.471782 | + | 0.881715i | \(0.656389\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.24167e34 | 1.33017 | 0.665086 | − | 0.746767i | \(-0.268395\pi\) | ||||
0.665086 | + | 0.746767i | \(0.268395\pi\) | |||||||
\(602\) | 1.18243e35i | 2.12726i | ||||||||
\(603\) | − 1.43111e34i | − 0.252177i | ||||||||
\(604\) | 1.51361e34 | 0.261248 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.98018e33 | −0.0659166 | ||||||||
\(607\) | 2.52292e34i | 0.409304i | 0.978835 | + | 0.204652i | \(0.0656062\pi\) | ||||
−0.978835 | + | 0.204652i | \(0.934394\pi\) | |||||||
\(608\) | − 9.99158e33i | − 0.158796i | ||||||||
\(609\) | 1.65250e34 | 0.257291 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.75990e33 | −0.130913 | ||||||||
\(612\) | − 5.66470e33i | − 0.0829438i | ||||||||
\(613\) | 8.87757e34i | 1.27362i | 0.771023 | + | 0.636808i | \(0.219745\pi\) | ||||
−0.771023 | + | 0.636808i | \(0.780255\pi\) | |||||||
\(614\) | 9.59532e34 | 1.34882 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.18424e34 | −0.834694 | ||||||||
\(617\) | − 3.04657e34i | − 0.402946i | −0.979494 | − | 0.201473i | \(-0.935427\pi\) | ||||
0.979494 | − | 0.201473i | \(-0.0645728\pi\) | |||||||
\(618\) | 5.31498e34i | 0.688883i | ||||||||
\(619\) | −8.61565e34 | −1.09435 | −0.547173 | − | 0.837019i | \(-0.684296\pi\) | ||||
−0.547173 | + | 0.837019i | \(0.684296\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.21290e35 | 1.47972 | ||||||||
\(622\) | − 5.50605e34i | − 0.658355i | ||||||||
\(623\) | − 1.32586e35i | − 1.55381i | ||||||||
\(624\) | 3.17488e33 | 0.0364687 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.24496e34 | 1.02030 | ||||||||
\(627\) | − 8.71765e34i | − 0.943094i | ||||||||
\(628\) | 4.40113e34i | 0.466733i | ||||||||
\(629\) | 7.42174e34 | 0.771566 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.11716e34 | −0.311452 | −0.155726 | − | 0.987800i | \(-0.549772\pi\) | ||||
−0.155726 | + | 0.987800i | \(0.549772\pi\) | |||||||
\(632\) | 3.43186e34i | 0.336175i | ||||||||
\(633\) | − 3.41985e34i | − 0.328444i | ||||||||
\(634\) | −1.98001e33 | −0.0186446 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.70990e34 | −0.516910 | ||||||||
\(637\) | − 4.34548e34i | − 0.385741i | ||||||||
\(638\) | − 2.07748e34i | − 0.180834i | ||||||||
\(639\) | −6.50454e34 | −0.555208 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.40132e35 | 1.15030 | 0.575150 | − | 0.818048i | \(-0.304944\pi\) | ||||
0.575150 | + | 0.818048i | \(0.304944\pi\) | |||||||
\(642\) | − 1.19933e35i | − 0.965496i | ||||||||
\(643\) | 2.61025e34i | 0.206085i | 0.994677 | + | 0.103042i | \(0.0328577\pi\) | ||||
−0.994677 | + | 0.103042i | \(0.967142\pi\) | |||||||
\(644\) | 1.53940e35 | 1.19201 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.57449e34 | 0.266261 | ||||||||
\(647\) | − 1.90009e35i | − 1.38826i | −0.719848 | − | 0.694131i | \(-0.755789\pi\) | ||||
0.719848 | − | 0.694131i | \(-0.244211\pi\) | |||||||
\(648\) | − 2.20844e34i | − 0.158270i | ||||||||
\(649\) | 2.75226e35 | 1.93478 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.99843e34 | 0.270475 | ||||||||
\(652\) | − 1.98791e34i | − 0.131917i | ||||||||
\(653\) | 1.69030e35i | 1.10040i | 0.835034 | + | 0.550198i | \(0.185448\pi\) | ||||
−0.835034 | + | 0.550198i | \(0.814552\pi\) | |||||||
\(654\) | 1.26561e35 | 0.808312 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.85161e34 | −0.113829 | ||||||||
\(657\) | − 7.08581e33i | − 0.0427388i | ||||||||
\(658\) | 1.45704e35i | 0.862277i | ||||||||
\(659\) | 2.20649e35 | 1.28125 | 0.640627 | − | 0.767853i | \(-0.278675\pi\) | ||||
0.640627 | + | 0.767853i | \(0.278675\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.29705e34 | 0.519789 | 0.259894 | − | 0.965637i | \(-0.416312\pi\) | ||||
0.259894 | + | 0.965637i | \(0.416312\pi\) | |||||||
\(662\) | 2.00645e35i | 1.10079i | ||||||||
\(663\) | 1.13581e34i | 0.0611487i | ||||||||
\(664\) | −1.23693e35 | −0.653500 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.01224e35 | −0.515059 | ||||||||
\(667\) | 5.17134e34i | 0.258244i | ||||||||
\(668\) | 1.25428e35i | 0.614738i | ||||||||
\(669\) | 3.18553e35 | 1.53234 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.15976e34 | −0.192769 | ||||||||
\(672\) | − 5.28079e34i | − 0.240205i | ||||||||
\(673\) | − 1.44593e35i | − 0.645593i | −0.946468 | − | 0.322796i | \(-0.895377\pi\) | ||||
0.946468 | − | 0.322796i | \(-0.104623\pi\) | |||||||
\(674\) | −1.53386e35 | −0.672259 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.14218e35 | −0.482392 | ||||||||
\(677\) | 2.51992e35i | 1.04479i | 0.852704 | + | 0.522394i | \(0.174961\pi\) | ||||
−0.852704 | + | 0.522394i | \(0.825039\pi\) | |||||||
\(678\) | 7.65228e34i | 0.311472i | ||||||||
\(679\) | −2.20575e35 | −0.881422 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.51209e35 | 0.582423 | ||||||||
\(682\) | − 5.02674e34i | − 0.190100i | ||||||||
\(683\) | 1.41934e35i | 0.527022i | 0.964656 | + | 0.263511i | \(0.0848806\pi\) | ||||
−0.964656 | + | 0.263511i | \(0.915119\pi\) | |||||||
\(684\) | −4.87520e34 | −0.177742 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.71160e35 | −1.30470 | ||||||||
\(687\) | 3.32536e35i | 1.14784i | ||||||||
\(688\) | 1.26936e35i | 0.430260i | ||||||||
\(689\) | −7.49788e34 | −0.249573 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.26858e34 | 0.137028 | 0.0685138 | − | 0.997650i | \(-0.478174\pi\) | ||||
0.0685138 | + | 0.997650i | \(0.478174\pi\) | |||||||
\(692\) | 5.63374e34i | 0.177611i | ||||||||
\(693\) | 3.01748e35i | 0.934284i | ||||||||
\(694\) | −5.17870e34 | −0.157481 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.77399e34 | 0.0520397 | ||||||||
\(697\) | − 6.62413e34i | − 0.190862i | ||||||||
\(698\) | 2.31187e35i | 0.654292i | ||||||||
\(699\) | 3.72984e35 | 1.03687 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.85276e34 | −0.210643 | −0.105322 | − | 0.994438i | \(-0.533587\pi\) | ||||
−0.105322 | + | 0.994438i | \(0.533587\pi\) | |||||||
\(702\) | − 5.46364e34i | − 0.143969i | ||||||||
\(703\) | − 6.38736e35i | − 1.65341i | ||||||||
\(704\) | −6.63889e34 | −0.168825 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.82074e34 | −0.167407 | ||||||||
\(707\) | 8.69330e34i | 0.209624i | ||||||||
\(708\) | 2.35019e35i | 0.556784i | ||||||||
\(709\) | 3.06083e35 | 0.712461 | 0.356231 | − | 0.934398i | \(-0.384062\pi\) | ||||
0.356231 | + | 0.934398i | \(0.384062\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.67451e35 | 0.376285 | ||||||||
\(712\) | − 1.42333e35i | − 0.314273i | ||||||||
\(713\) | 1.25127e35i | 0.271477i | ||||||||
\(714\) | 1.88920e35 | 0.402764 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.05805e35 | 0.217817 | ||||||||
\(717\) | − 6.92646e35i | − 1.40127i | ||||||||
\(718\) | 4.60240e35i | 0.915016i | ||||||||
\(719\) | −2.20247e35 | −0.430327 | −0.215163 | − | 0.976578i | \(-0.569028\pi\) | ||||
−0.215163 | + | 0.976578i | \(0.569028\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.16087e36 | 2.19075 | ||||||||
\(722\) | 7.36109e34i | 0.136530i | ||||||||
\(723\) | 9.31844e34i | 0.169869i | ||||||||
\(724\) | −2.01976e35 | −0.361882 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.61697e35 | −0.452993 | ||||||||
\(727\) | − 8.70105e33i | − 0.0148044i | −0.999973 | − | 0.00740221i | \(-0.997644\pi\) | ||||
0.999973 | − | 0.00740221i | \(-0.00235622\pi\) | |||||||
\(728\) | − 6.93440e34i | − 0.115976i | ||||||||
\(729\) | −6.20764e35 | −1.02055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.54115e35 | −0.721437 | ||||||||
\(732\) | − 3.55207e34i | − 0.0554744i | ||||||||
\(733\) | − 1.92172e35i | − 0.295046i | −0.989059 | − | 0.147523i | \(-0.952870\pi\) | ||||
0.989059 | − | 0.147523i | \(-0.0471301\pi\) | |||||||
\(734\) | 6.65823e35 | 1.00498 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.65258e35 | 0.241095 | ||||||||
\(737\) | − 6.00026e35i | − 0.860650i | ||||||||
\(738\) | 9.03457e34i | 0.127410i | ||||||||
\(739\) | −9.08434e35 | −1.25961 | −0.629807 | − | 0.776751i | \(-0.716866\pi\) | ||||
−0.629807 | + | 0.776751i | \(0.716866\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.77512e34 | 0.131037 | ||||||||
\(742\) | 1.24713e36i | 1.64385i | ||||||||
\(743\) | − 9.13810e35i | − 1.18439i | −0.805794 | − | 0.592197i | \(-0.798261\pi\) | ||||
0.805794 | − | 0.592197i | \(-0.201739\pi\) | |||||||
\(744\) | 4.29239e34 | 0.0547063 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.54445e35 | 0.436831 | ||||||||
\(747\) | 6.03538e35i | 0.731471i | ||||||||
\(748\) | − 2.37506e35i | − 0.283077i | ||||||||
\(749\) | −2.61951e36 | −3.07042 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.01650e35 | 0.341982 | 0.170991 | − | 0.985273i | \(-0.445303\pi\) | ||||
0.170991 | + | 0.985273i | \(0.445303\pi\) | |||||||
\(752\) | 1.56416e35i | 0.174404i | ||||||||
\(753\) | − 1.00563e36i | − 1.10281i | ||||||||
\(754\) | 2.32949e34 | 0.0251257 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −9.08770e35 | −0.948269 | ||||||||
\(757\) | 1.11391e36i | 1.14328i | 0.820504 | + | 0.571640i | \(0.193693\pi\) | ||||
−0.820504 | + | 0.571640i | \(0.806307\pi\) | |||||||
\(758\) | − 5.34492e35i | − 0.539605i | ||||||||
\(759\) | 1.44187e36 | 1.43187 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.13224e35 | −0.781451 | −0.390726 | − | 0.920507i | \(-0.627776\pi\) | ||||
−0.390726 | + | 0.920507i | \(0.627776\pi\) | |||||||
\(762\) | 9.00686e34i | 0.0851405i | ||||||||
\(763\) | − 2.76428e36i | − 2.57055i | ||||||||
\(764\) | −3.58712e35 | −0.328155 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.30669e35 | −0.115695 | ||||||||
\(767\) | 3.08612e35i | 0.268826i | ||||||||
\(768\) | − 5.66902e34i | − 0.0485840i | ||||||||
\(769\) | 9.19378e35 | 0.775202 | 0.387601 | − | 0.921827i | \(-0.373304\pi\) | ||||
0.387601 | + | 0.921827i | \(0.373304\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.32601e35 | 0.597982 | ||||||||
\(772\) | − 4.99955e34i | − 0.0401527i | ||||||||
\(773\) | 1.53774e36i | 1.21518i | 0.794251 | + | 0.607590i | \(0.207864\pi\) | ||||
−0.794251 | + | 0.607590i | \(0.792136\pi\) | |||||||
\(774\) | 6.19361e35 | 0.481595 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.36791e35 | −0.178276 | ||||||||
\(777\) | − 3.37587e36i | − 2.50106i | ||||||||
\(778\) | 7.03786e35i | 0.513093i | ||||||||
\(779\) | −5.70091e35 | −0.409003 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.72718e36 | −1.89486 | ||||||||
\(782\) | 5.91209e35i | 0.404256i | ||||||||
\(783\) | − 3.05285e35i | − 0.205439i | ||||||||
\(784\) | −7.75924e35 | −0.513888 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.54877e35 | −0.291818 | ||||||||
\(787\) | − 1.78317e36i | − 1.12592i | −0.826484 | − | 0.562960i | \(-0.809663\pi\) | ||||
0.826484 | − | 0.562960i | \(-0.190337\pi\) | |||||||
\(788\) | 6.89359e35i | 0.428418i | ||||||||
\(789\) | −7.11474e35 | −0.435208 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.67137e36 | 0.990527 | ||||||||
\(792\) | 3.23932e35i | 0.188968i | ||||||||
\(793\) | − 4.66435e34i | − 0.0267841i | ||||||||
\(794\) | −5.93542e35 | −0.335502 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.96584e35 | −0.491109 | ||||||||
\(797\) | − 4.10600e35i | − 0.221406i | −0.993854 | − | 0.110703i | \(-0.964690\pi\) | ||||
0.993854 | − | 0.110703i | \(-0.0353103\pi\) | |||||||
\(798\) | − 1.62590e36i | − 0.863093i | ||||||||
\(799\) | −5.59576e35 | −0.292432 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.94488e35 | −0.351770 | ||||||||
\(802\) | − 2.65055e36i | − 1.32177i | ||||||||
\(803\) | − 2.97090e35i | − 0.145862i | ||||||||
\(804\) | 5.12369e35 | 0.247675 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.63649e34 | 0.0264132 | ||||||||
\(807\) | 6.73711e35i | 0.310853i | ||||||||
\(808\) | 9.33241e34i | 0.0423986i | ||||||||
\(809\) | 2.45266e36 | 1.09719 | 0.548593 | − | 0.836090i | \(-0.315164\pi\) | ||||
0.548593 | + | 0.836090i | \(0.315164\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.62915e36 | −1.57414 | −0.787072 | − | 0.616861i | \(-0.788404\pi\) | ||||
−0.787072 | + | 0.616861i | \(0.788404\pi\) | |||||||
\(812\) | − 3.87464e35i | − 0.165494i | ||||||||
\(813\) | 2.03707e35i | 0.0856790i | ||||||||
\(814\) | −4.24407e36 | −1.75783 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.02809e35 | 0.0814630 | ||||||||
\(817\) | 3.90824e36i | 1.54599i | ||||||||
\(818\) | − 6.13193e35i | − 0.238880i | ||||||||
\(819\) | −3.38351e35 | −0.129813 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.84702e36 | 1.80379 | 0.901894 | − | 0.431957i | \(-0.142177\pi\) | ||||
0.901894 | + | 0.431957i | \(0.142177\pi\) | |||||||
\(822\) | 1.30188e36i | 0.477171i | ||||||||
\(823\) | 3.60517e36i | 1.30145i | 0.759312 | + | 0.650726i | \(0.225535\pi\) | ||||
−0.759312 | + | 0.650726i | \(0.774465\pi\) | |||||||
\(824\) | 1.24621e36 | 0.443101 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.13315e36 | 1.77065 | ||||||||
\(827\) | 1.03992e36i | 0.353331i | 0.984271 | + | 0.176665i | \(0.0565311\pi\) | ||||
−0.984271 | + | 0.176665i | \(0.943469\pi\) | |||||||
\(828\) | − 8.06343e35i | − 0.269861i | ||||||||
\(829\) | −3.59238e36 | −1.18427 | −0.592134 | − | 0.805839i | \(-0.701714\pi\) | ||||
−0.592134 | + | 0.805839i | \(0.701714\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.10853e36 | −1.31424 | ||||||||
\(832\) | − 7.44421e34i | − 0.0234572i | ||||||||
\(833\) | − 2.77587e36i | − 0.861660i | ||||||||
\(834\) | 2.89123e36 | 0.884111 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.04405e36 | −0.606613 | ||||||||
\(837\) | − 7.38676e35i | − 0.215966i | ||||||||
\(838\) | 2.55401e36i | 0.735652i | ||||||||
\(839\) | −4.65321e36 | −1.32047 | −0.660234 | − | 0.751060i | \(-0.729543\pi\) | ||||
−0.660234 | + | 0.751060i | \(0.729543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50020e36 | −0.964146 | ||||||||
\(842\) | − 1.78533e36i | − 0.484526i | ||||||||
\(843\) | − 5.08037e35i | − 0.135847i | ||||||||
\(844\) | −8.01860e35 | −0.211260 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.63200e35 | 0.195213 | ||||||||
\(847\) | 5.71585e36i | 1.44058i | ||||||||
\(848\) | 1.33881e36i | 0.332485i | ||||||||
\(849\) | 3.56380e36 | 0.872102 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.05645e37 | 2.51032 | ||||||||
\(852\) | − 2.32877e36i | − 0.545296i | ||||||||
\(853\) | − 5.05930e36i | − 1.16742i | −0.811962 | − | 0.583710i | \(-0.801600\pi\) | ||||
0.811962 | − | 0.583710i | \(-0.198400\pi\) | |||||||
\(854\) | −7.75823e35 | −0.176417 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.81209e36 | −0.621023 | ||||||||
\(857\) | 2.18945e36i | 0.476513i | 0.971202 | + | 0.238257i | \(0.0765760\pi\) | ||||
−0.971202 | + | 0.238257i | \(0.923424\pi\) | |||||||
\(858\) | − 6.49506e35i | − 0.139313i | ||||||||
\(859\) | 5.91491e36 | 1.25035 | 0.625177 | − | 0.780483i | \(-0.285027\pi\) | ||||
0.625177 | + | 0.780483i | \(0.285027\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.01307e36 | −0.618685 | ||||||||
\(862\) | 3.93464e36i | 0.796278i | ||||||||
\(863\) | 3.85509e36i | 0.768952i | 0.923135 | + | 0.384476i | \(0.125618\pi\) | ||||
−0.923135 | + | 0.384476i | \(0.874382\pi\) | |||||||
\(864\) | −9.75581e35 | −0.191797 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.66362e36 | 0.508744 | ||||||||
\(867\) | − 3.40352e36i | − 0.640751i | ||||||||
\(868\) | − 9.37520e35i | − 0.173974i | ||||||||
\(869\) | 7.02078e36 | 1.28422 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.72810e35 | 0.119582 | ||||||||
\(872\) | − 2.96751e36i | − 0.519919i | ||||||||
\(873\) | 1.15538e36i | 0.199547i | ||||||||
\(874\) | 5.08811e36 | 0.866291 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.53688e35 | 0.0419758 | ||||||||
\(877\) | 5.04839e36i | 0.823489i | 0.911299 | + | 0.411744i | \(0.135080\pi\) | ||||
−0.911299 | + | 0.411744i | \(0.864920\pi\) | |||||||
\(878\) | − 5.20190e36i | − 0.836528i | ||||||||
\(879\) | −3.50445e36 | −0.555596 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.50642e36 | 1.15673 | 0.578367 | − | 0.815776i | \(-0.303690\pi\) | ||||
0.578367 | + | 0.815776i | \(0.303690\pi\) | |||||||
\(882\) | 3.78597e36i | 0.575201i | ||||||||
\(883\) | 1.15945e37i | 1.73677i | 0.495893 | + | 0.868384i | \(0.334841\pi\) | ||||
−0.495893 | + | 0.868384i | \(0.665159\pi\) | |||||||
\(884\) | 2.66316e35 | 0.0393318 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.46600e36 | 0.210481 | ||||||||
\(887\) | − 1.11924e37i | − 1.58445i | −0.610228 | − | 0.792226i | \(-0.708922\pi\) | ||||
0.610228 | − | 0.792226i | \(-0.291078\pi\) | |||||||
\(888\) | − 3.62406e36i | − 0.505864i | ||||||||
\(889\) | 1.96723e36 | 0.270759 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.51796e36 | −0.604604 | ||||||||
\(892\) | − 7.46919e36i | − 0.985627i | ||||||||
\(893\) | 4.81587e36i | 0.626660i | ||||||||
\(894\) | 4.06315e36 | 0.521367 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.23820e36 | −0.154504 | ||||||||
\(897\) | 1.61677e36i | 0.198950i | ||||||||
\(898\) | − 1.18483e36i | − 0.143781i | ||||||||
\(899\) | 3.14943e35 | 0.0376908 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.78960e36 | −0.557493 | ||||||||
\(902\) | 3.78796e36i | 0.434835i | ||||||||
\(903\) | 2.06560e37i | 2.33856i | ||||||||
\(904\) | 1.79425e36 | 0.200344 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.64413e36 | 0.287197 | ||||||||
\(907\) | − 1.70146e36i | − 0.182276i | −0.995838 | − | 0.0911381i | \(-0.970950\pi\) | ||||
0.995838 | − | 0.0911381i | \(-0.0290505\pi\) | |||||||
\(908\) | − 3.54543e36i | − 0.374624i | ||||||||
\(909\) | 4.55357e35 | 0.0474573 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.90683e36 | −0.193344 | −0.0966721 | − | 0.995316i | \(-0.530820\pi\) | ||||
−0.0966721 | + | 0.995316i | \(0.530820\pi\) | |||||||
\(912\) | − 1.74543e36i | − 0.174569i | ||||||||
\(913\) | 2.53048e37i | 2.49642i | ||||||||
\(914\) | −1.04842e37 | −1.02025 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.79705e36 | 0.738307 | ||||||||
\(917\) | 9.93518e36i | 0.928024i | ||||||||
\(918\) | − 3.49014e36i | − 0.321595i | ||||||||
\(919\) | 1.39528e37 | 1.26829 | 0.634145 | − | 0.773214i | \(-0.281352\pi\) | ||||
0.634145 | + | 0.773214i | \(0.281352\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.67621e37 | 1.48280 | ||||||||
\(922\) | 3.24815e35i | 0.0283465i | ||||||||
\(923\) | − 3.05800e36i | − 0.263279i | ||||||||
\(924\) | −1.08033e37 | −0.917604 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.35558e36 | 0.112070 | ||||||||
\(927\) | − 6.08066e36i | − 0.495968i | ||||||||
\(928\) | − 4.15950e35i | − 0.0334728i | ||||||||
\(929\) | −3.87552e36 | −0.307704 | −0.153852 | − | 0.988094i | \(-0.549168\pi\) | ||||
−0.153852 | + | 0.988094i | \(0.549168\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.38899e37 | −1.84647 | ||||||||
\(932\) | − 8.74542e36i | − 0.666932i | ||||||||
\(933\) | − 9.61853e36i | − 0.723749i | ||||||||
\(934\) | 1.21324e37 | 0.900763 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.63226e35 | −0.0262560 | ||||||||
\(937\) | 7.59791e36i | 0.541938i | 0.962588 | + | 0.270969i | \(0.0873440\pi\) | ||||
−0.962588 | + | 0.270969i | \(0.912656\pi\) | |||||||
\(938\) | − 1.11909e37i | − 0.787642i | ||||||||
\(939\) | 1.61500e37 | 1.12164 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.56881e37 | −1.73725 | −0.868624 | − | 0.495472i | \(-0.834995\pi\) | ||||
−0.868624 | + | 0.495472i | \(0.834995\pi\) | |||||||
\(942\) | 7.68835e36i | 0.513094i | ||||||||
\(943\) | − 9.42913e36i | − 0.620977i | ||||||||
\(944\) | 5.51053e36 | 0.358133 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.59682e37 | 1.64363 | ||||||||
\(947\) | − 1.90718e37i | − 1.19129i | −0.803247 | − | 0.595645i | \(-0.796896\pi\) | ||||
0.803247 | − | 0.595645i | \(-0.203104\pi\) | |||||||
\(948\) | 5.99512e36i | 0.369568i | ||||||||
\(949\) | 3.33127e35 | 0.0202667 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.45889e35 | −0.0204965 | ||||||||
\(952\) | − 4.42965e36i | − 0.259064i | ||||||||
\(953\) | − 1.68185e36i | − 0.0970791i | −0.998821 | − | 0.0485396i | \(-0.984543\pi\) | ||||
0.998821 | − | 0.0485396i | \(-0.0154567\pi\) | |||||||
\(954\) | 6.53247e36 | 0.372154 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.62406e37 | −0.901319 | ||||||||
\(957\) | − 3.62916e36i | − 0.198796i | ||||||||
\(958\) | 6.82086e36i | 0.368783i | ||||||||
\(959\) | 2.84350e37 | 1.51747 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.84707e37 | −0.960378 | ||||||||
\(962\) | − 4.75889e36i | − 0.244240i | ||||||||
\(963\) | 1.37211e37i | 0.695119i | ||||||||
\(964\) | 2.18492e36 | 0.109263 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.68919e37 | 1.31041 | ||||||||
\(967\) | 4.14643e36i | 0.199454i | 0.995015 | + | 0.0997271i | \(0.0317970\pi\) | ||||
−0.995015 | + | 0.0997271i | \(0.968203\pi\) | |||||||
\(968\) | 6.13607e36i | 0.291373i | ||||||||
\(969\) | 6.24428e36 | 0.292708 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.14239e37 | 0.978720 | 0.489360 | − | 0.872082i | \(-0.337230\pi\) | ||||
0.489360 | + | 0.872082i | \(0.337230\pi\) | |||||||
\(972\) | 8.17066e36i | 0.368493i | ||||||||
\(973\) | − 6.31487e37i | − 2.81160i | ||||||||
\(974\) | 2.47068e37 | 1.08600 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.32861e35 | −0.0356820 | ||||||||
\(977\) | 1.15529e37i | 0.488660i | 0.969692 | + | 0.244330i | \(0.0785681\pi\) | ||||
−0.969692 | + | 0.244330i | \(0.921432\pi\) | |||||||
\(978\) | − 3.47268e36i | − 0.145020i | ||||||||
\(979\) | −2.91181e37 | −1.20055 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.44794e37 | −0.581952 | ||||||||
\(982\) | − 1.07374e37i | − 0.426096i | ||||||||
\(983\) | − 5.38686e36i | − 0.211065i | −0.994416 | − | 0.105533i | \(-0.966345\pi\) | ||||
0.994416 | − | 0.105533i | \(-0.0336547\pi\) | |||||||
\(984\) | −3.23458e36 | −0.125135 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.48806e36 | 0.0561254 | ||||||||
\(987\) | 2.54530e37i | 0.947927i | ||||||||
\(988\) | − 2.29199e36i | − 0.0842852i | ||||||||
\(989\) | −6.46410e37 | −2.34722 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.50366e37 | 1.24051 | 0.620256 | − | 0.784399i | \(-0.287029\pi\) | ||||
0.620256 | + | 0.784399i | \(0.287029\pi\) | |||||||
\(992\) | − 1.00644e36i | − 0.0351880i | ||||||||
\(993\) | 3.50508e37i | 1.21013i | ||||||||
\(994\) | −5.08638e37 | −1.73412 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.16080e37 | −0.718412 | ||||||||
\(997\) | − 4.42953e37i | − 1.45435i | −0.686453 | − | 0.727174i | \(-0.740833\pi\) | ||||
0.686453 | − | 0.727174i | \(-0.259167\pi\) | |||||||
\(998\) | − 3.29431e37i | − 1.06815i | ||||||||
\(999\) | −6.23664e37 | −1.99702 |
(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 | 50.26.b.d.49.1 | 4 | ||
5.2 | odd | 4 | 10.26.a.d.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 50.26.a.d.1.2 | 2 | |||
5.4 | even | 2 | inner | 50.26.b.d.49.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.26.a.d.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
50.26.a.d.1.2 | 2 | 5.3 | odd | 4 | |||
50.26.b.d.49.1 | 4 | 1.1 | even | 1 | trivial | ||
50.26.b.d.49.4 | 4 | 5.4 | even | 2 | inner |