Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(2157,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.2157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.m (of order \(2\), degree \(1\), 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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2157.6 | ||
Character | \(\chi\) | \(=\) | 4004.2157 |
Dual form | 4004.2.m.c.2157.5 |
$q$-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 \(\left(\mathbb{Z}/4004\mathbb{Z}\right)^\times\).
\(n\) | \(365\) | \(925\) | \(2003\) | \(3433\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.75761 | −1.59211 | −0.796053 | − | 0.605226i | \(-0.793083\pi\) | ||||
−0.796053 | + | 0.605226i | \(0.793083\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.98236i | − | 0.886536i | −0.896389 | − | 0.443268i | \(-0.853819\pi\) | ||
0.896389 | − | 0.443268i | \(-0.146181\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.60441 | 1.53480 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.54138 | − | 2.55761i | −0.704852 | − | 0.709355i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.46656i | 1.41146i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.39189 | −1.79280 | −0.896398 | − | 0.443250i | \(-0.853825\pi\) | ||||
−0.896398 | + | 0.443250i | \(0.853825\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.19788i | 0.963059i | 0.876430 | + | 0.481529i | \(0.159919\pi\) | ||||
−0.876430 | + | 0.481529i | \(0.840081\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.75761i | 0.601760i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.61924 | 0.963178 | 0.481589 | − | 0.876397i | \(-0.340060\pi\) | ||||
0.481589 | + | 0.876397i | \(0.340060\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.07027 | 0.214053 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.42434 | −0.851465 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.07057 | 0.755887 | 0.377943 | − | 0.925829i | \(-0.376631\pi\) | ||||
0.377943 | + | 0.925829i | \(0.376631\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.60497i | − | 0.647472i | −0.946147 | − | 0.323736i | \(-0.895061\pi\) | ||
0.946147 | − | 0.323736i | \(-0.104939\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.75761i | − | 0.480038i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.98236 | −0.335079 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.67276i | 1.59019i | 0.606484 | + | 0.795096i | \(0.292580\pi\) | ||||
−0.606484 | + | 0.795096i | \(0.707420\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.00813 | + | 7.05290i | 1.12220 | + | 1.12937i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.43161i | 0.848275i | 0.905598 | + | 0.424138i | \(0.139423\pi\) | ||||
−0.905598 | + | 0.424138i | \(0.860577\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.3904 | 1.88953 | 0.944763 | − | 0.327755i | \(-0.106292\pi\) | ||||
0.944763 | + | 0.327755i | \(0.106292\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 9.12758i | − | 1.36066i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.284033i | 0.0414305i | 0.999785 | + | 0.0207153i | \(0.00659435\pi\) | ||||
−0.999785 | + | 0.0207153i | \(0.993406\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20.3839 | 2.85432 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.46945 | −0.613926 | −0.306963 | − | 0.951722i | \(-0.599313\pi\) | ||||
−0.306963 | + | 0.951722i | \(0.599313\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.98236 | 0.267301 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 11.5761i | − | 1.53329i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.96978i | 0.256444i | 0.991745 | + | 0.128222i | \(0.0409270\pi\) | ||||
−0.991745 | + | 0.128222i | \(0.959073\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.69145 | −0.344605 | −0.172303 | − | 0.985044i | \(-0.555121\pi\) | ||||
−0.172303 | + | 0.985044i | \(0.555121\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 4.60441i | − | 0.580101i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.07010 | + | 5.03792i | −0.628869 | + | 0.624877i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.8334i | − | 1.56784i | −0.620860 | − | 0.783922i | \(-0.713216\pi\) | ||
0.620860 | − | 0.783922i | \(-0.286784\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.7381 | −1.53348 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00846i | 0.950429i | 0.879870 | + | 0.475214i | \(0.157630\pi\) | ||||
−0.879870 | + | 0.475214i | \(0.842370\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.542368i | 0.0634793i | 0.999496 | + | 0.0317397i | \(0.0101047\pi\) | ||||
−0.999496 | + | 0.0317397i | \(0.989895\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.95137 | −0.340795 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.5068 | −1.51964 | −0.759819 | − | 0.650134i | \(-0.774713\pi\) | ||||
−0.759819 | + | 0.650134i | \(0.774713\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.61263 | −0.179181 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.32443i | − | 0.364903i | −0.983215 | − | 0.182452i | \(-0.941597\pi\) | ||
0.983215 | − | 0.182452i | \(-0.0584033\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.6533i | 1.58938i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.2251 | −1.20345 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.4386i | 1.53048i | 0.643742 | + | 0.765242i | \(0.277381\pi\) | ||||
−0.643742 | + | 0.765242i | \(0.722619\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.55761 | + | 2.54138i | −0.268111 | + | 0.266409i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.94111i | 1.03084i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.32168 | 0.853787 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.3264i | 1.55616i | 0.628164 | + | 0.778081i | \(0.283807\pi\) | ||||
−0.628164 | + | 0.778081i | \(0.716193\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.60441i | 0.462761i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.90146 | −0.686720 | −0.343360 | − | 0.939204i | \(-0.611565\pi\) | ||||
−0.343360 | + | 0.939204i | \(0.611565\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.1336 | 1.29409 | 0.647046 | − | 0.762451i | \(-0.276004\pi\) | ||||
0.647046 | + | 0.762451i | \(0.276004\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.46656 | 0.533482 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.8985 | 1.63364 | 0.816822 | − | 0.576890i | \(-0.195734\pi\) | ||||
0.816822 | + | 0.576890i | \(0.195734\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.6498i | − | 1.21164i | −0.795604 | − | 0.605818i | \(-0.792846\pi\) | ||
0.795604 | − | 0.605818i | \(-0.207154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 26.6737i | − | 2.53176i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.99276 | 0.563752 | 0.281876 | − | 0.959451i | \(-0.409043\pi\) | ||||
0.281876 | + | 0.959451i | \(0.409043\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 9.15698i | − | 0.853892i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.7016 | − | 11.7763i | −1.08181 | − | 1.08872i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.39189i | 0.677613i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 14.9783i | − | 1.35054i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.0334i | − | 1.07630i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.60540 | −0.408664 | −0.204332 | − | 0.978902i | \(-0.565502\pi\) | ||||
−0.204332 | + | 0.978902i | \(0.565502\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −34.1680 | −3.00833 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.5436 | −1.00857 | −0.504283 | − | 0.863538i | \(-0.668243\pi\) | ||||
−0.504283 | + | 0.863538i | \(0.668243\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.19788 | 0.364002 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.77062i | 0.754855i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 7.68246i | − | 0.656357i | −0.944616 | − | 0.328178i | \(-0.893565\pi\) | ||
0.944616 | − | 0.328178i | \(-0.106435\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.55906 | 0.132237 | 0.0661187 | − | 0.997812i | \(-0.478938\pi\) | ||||
0.0661187 | + | 0.997812i | \(0.478938\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 0.783253i | − | 0.0659618i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.55761 | − | 2.54138i | 0.213878 | − | 0.212521i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 8.06932i | − | 0.670121i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.75761 | 0.227444 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.41910i | 0.280103i | 0.990144 | + | 0.140052i | \(0.0447269\pi\) | ||||
−0.990144 | + | 0.140052i | \(0.955273\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.0152i | − | 0.815024i | −0.913200 | − | 0.407512i | \(-0.866397\pi\) | ||
0.913200 | − | 0.407512i | \(-0.133603\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −34.0353 | −2.75159 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.14634 | −0.574008 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.3142 | 1.54144 | 0.770719 | − | 0.637176i | \(-0.219897\pi\) | ||||
0.770719 | + | 0.637176i | \(0.219897\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.3250 | 0.977435 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.61924i | − | 0.364047i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.51917i | − | 0.118990i | −0.998229 | − | 0.0594952i | \(-0.981051\pi\) | ||
0.998229 | − | 0.0594952i | \(-0.0189491\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.46656 | −0.425571 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 4.56617i | − | 0.353340i | −0.984270 | − | 0.176670i | \(-0.943467\pi\) | ||
0.984270 | − | 0.176670i | \(-0.0565326\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.0827857 | + | 12.9997i | −0.00636813 | + | 0.999980i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 19.3288i | 1.47811i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.0406 | 1.59969 | 0.799845 | − | 0.600207i | \(-0.204915\pi\) | ||||
0.799845 | + | 0.600207i | \(0.204915\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.07027i | − | 0.0809045i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 5.43190i | − | 0.408286i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.13541 | −0.383839 | −0.191919 | − | 0.981411i | \(-0.561471\pi\) | ||||
−0.191919 | + | 0.981411i | \(0.561471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.227231 | 0.0168899 | 0.00844497 | − | 0.999964i | \(-0.497312\pi\) | ||||
0.00844497 | + | 0.999964i | \(0.497312\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.42198 | 0.548649 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.1748 | 1.40976 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 7.39189i | − | 0.540548i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.42434i | 0.321824i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.5458 | 1.12486 | 0.562428 | − | 0.826846i | \(-0.309867\pi\) | ||||
0.562428 | + | 0.826846i | \(0.309867\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 24.9751i | − | 1.79775i | −0.438207 | − | 0.898874i | \(-0.644386\pi\) | ||
0.438207 | − | 0.898874i | \(-0.355614\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.9814 | − | 13.8926i | 1.00123 | − | 0.994871i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 20.4952i | − | 1.46022i | −0.683329 | − | 0.730110i | \(-0.739469\pi\) | ||
0.683329 | − | 0.730110i | \(-0.260531\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.18473 | 0.154872 | 0.0774358 | − | 0.996997i | \(-0.475327\pi\) | ||||
0.0774358 | + | 0.996997i | \(0.475327\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 35.3894i | 2.49617i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 4.07057i | − | 0.285698i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.7674 | 0.752027 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 21.2689 | 1.47829 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.19788 | −0.290373 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.26708 | 0.362601 | 0.181300 | − | 0.983428i | \(-0.441969\pi\) | ||||
0.181300 | + | 0.983428i | \(0.441969\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 22.0842i | − | 1.51318i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 24.5623i | − | 1.67513i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.60497 | −0.244721 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1.49564i | − | 0.101066i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.7856 | + | 18.9056i | 1.26366 | + | 1.27173i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.2976i | − | 0.689578i | −0.938680 | − | 0.344789i | \(-0.887950\pi\) | ||
0.938680 | − | 0.344789i | \(-0.112050\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.92794 | 0.328530 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 27.0317i | − | 1.79415i | −0.441874 | − | 0.897077i | \(-0.645686\pi\) | ||
0.441874 | − | 0.897077i | \(-0.354314\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.21512i | 0.146379i | 0.997318 | + | 0.0731896i | \(0.0233178\pi\) | ||||
−0.997318 | + | 0.0731896i | \(0.976682\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.75761 | −0.181437 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.8938 | −1.43431 | −0.717154 | − | 0.696915i | \(-0.754556\pi\) | ||||
−0.717154 | + | 0.696915i | \(0.754556\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.563055 | 0.0367297 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 37.2466 | 2.41943 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.09702i | 0.265014i | 0.991182 | + | 0.132507i | \(0.0423027\pi\) | ||||
−0.991182 | + | 0.132507i | \(0.957697\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.77298i | 0.178623i | 0.996004 | + | 0.0893117i | \(0.0284667\pi\) | ||||
−0.996004 | + | 0.0893117i | \(0.971533\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.7200 | 1.13674 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.98236i | 0.126648i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.7365 | − | 10.6684i | 0.683150 | − | 0.678814i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.16747i | 0.580965i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.7097 | 1.30718 | 0.653592 | − | 0.756847i | \(-0.273261\pi\) | ||||
0.653592 | + | 0.756847i | \(0.273261\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.61924i | 0.290409i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 40.4082i | − | 2.53046i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.54096 | 0.0961227 | 0.0480613 | − | 0.998844i | \(-0.484696\pi\) | ||||
0.0480613 | + | 0.998844i | \(0.484696\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.67276 | 0.601036 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.7426 | 1.16014 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.95053 | 0.490250 | 0.245125 | − | 0.969491i | \(-0.421171\pi\) | ||||
0.245125 | + | 0.969491i | \(0.421171\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.86003i | 0.544267i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 39.8159i | − | 2.43670i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.18925 | 0.499307 | 0.249654 | − | 0.968335i | \(-0.419683\pi\) | ||||
0.249654 | + | 0.968335i | \(0.419683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.8033i | 0.716999i | 0.933530 | + | 0.358500i | \(0.116712\pi\) | ||||
−0.933530 | + | 0.358500i | \(0.883288\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.05290 | − | 7.00813i | 0.426861 | − | 0.424151i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.07027i | 0.0645394i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.29260 | −0.558338 | −0.279169 | − | 0.960242i | \(-0.590059\pi\) | ||||
−0.279169 | + | 0.960242i | \(0.590059\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 16.5988i | − | 0.993743i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.3565i | 1.63195i | 0.578084 | + | 0.815977i | \(0.303801\pi\) | ||||
−0.578084 | + | 0.815977i | \(0.696199\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.0094 | 1.12999 | 0.564995 | − | 0.825094i | \(-0.308878\pi\) | ||||
0.564995 | + | 0.825094i | \(0.308878\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −22.9480 | −1.35932 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.43161 | 0.320618 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.6400 | 2.21412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 42.2643i | − | 2.47758i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 9.11806i | − | 0.532683i | −0.963879 | − | 0.266341i | \(-0.914185\pi\) | ||
0.963879 | − | 0.266341i | \(-0.0858148\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.90481 | 0.227347 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 4.42434i | − | 0.256726i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.7392 | − | 11.8142i | −0.678898 | − | 0.683235i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 12.3904i | − | 0.714173i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.0315 | 1.09333 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.33542i | 0.305505i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.3379i | − | 0.989524i | −0.869028 | − | 0.494762i | \(-0.835255\pi\) | ||
0.869028 | − | 0.494762i | \(-0.164745\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −36.2173 | −2.06033 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.81808 | 0.159799 | 0.0798995 | − | 0.996803i | \(-0.474540\pi\) | ||||
0.0798995 | + | 0.996803i | \(0.474540\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.4075 | −1.49264 | −0.746319 | − | 0.665588i | \(-0.768181\pi\) | ||||
−0.746319 | + | 0.665588i | \(0.768181\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.12758 | −0.514281 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3.99221i | − | 0.224225i | −0.993696 | − | 0.112113i | \(-0.964238\pi\) | ||
0.993696 | − | 0.112113i | \(-0.0357617\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.07057i | 0.227908i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −46.5996 | −2.60094 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 31.0302i | − | 1.72657i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.71995 | − | 2.73733i | −0.150876 | − | 0.151840i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 34.8833i | 1.92905i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.284033 | 0.0156593 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 21.9021i | − | 1.20385i | −0.798554 | − | 0.601923i | \(-0.794401\pi\) | ||
0.798554 | − | 0.601923i | \(-0.205599\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 44.5374i | 2.44063i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.4403 | −1.38995 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.2354 | 1.37466 | 0.687331 | − | 0.726344i | \(-0.258782\pi\) | ||||
0.687331 | + | 0.726344i | \(0.258782\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.5257 | −0.897553 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.60497 | 0.195220 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 25.2514i | 1.35949i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.98169 | −0.213748 | −0.106874 | − | 0.994273i | \(-0.534084\pi\) | ||||
−0.106874 | + | 0.994273i | \(0.534084\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.38283i | 0.0740214i | 0.999315 | + | 0.0370107i | \(0.0117836\pi\) | ||||
−0.999315 | + | 0.0370107i | \(0.988216\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.2439 | + | 11.3158i | 0.600157 | + | 0.603991i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.50659i | − | 0.133412i | −0.997773 | − | 0.0667060i | \(-0.978751\pi\) | ||
0.997773 | − | 0.0667060i | \(-0.0212490\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.8756 | 0.842590 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 20.3839i | − | 1.07883i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.6288i | 0.824859i | 0.910989 | + | 0.412430i | \(0.135320\pi\) | ||||
−0.910989 | + | 0.412430i | \(0.864680\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.37783 | 0.0725176 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.75761 | 0.144737 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.07517 | 0.0562768 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.7136 | 1.02904 | 0.514522 | − | 0.857477i | \(-0.327970\pi\) | ||||
0.514522 | + | 0.857477i | \(0.327970\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 25.0094i | 1.30194i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.46945i | 0.232042i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.5753 | 0.599346 | 0.299673 | − | 0.954042i | \(-0.403122\pi\) | ||||
0.299673 | + | 0.954042i | \(0.403122\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 33.1835i | 1.71359i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.3449 | − | 10.4110i | −0.532788 | − | 0.536192i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 12.2568i | − | 0.629588i | −0.949160 | − | 0.314794i | \(-0.898065\pi\) | ||
0.949160 | − | 0.314794i | \(-0.101935\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.6999 | 0.650636 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.5093i | 1.66115i | 0.556909 | + | 0.830574i | \(0.311987\pi\) | ||||
−0.556909 | + | 0.830574i | \(0.688013\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 1.98236i | − | 0.101030i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 57.0507 | 2.90005 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.79700 | −0.395324 | −0.197662 | − | 0.980270i | \(-0.563335\pi\) | ||||
−0.197662 | + | 0.980270i | \(0.563335\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −34.1449 | −1.72678 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.8327 | 1.60575 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 26.7754i | 1.34722i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 19.6911i | − | 0.988269i | −0.869386 | − | 0.494134i | \(-0.835485\pi\) | ||
0.869386 | − | 0.494134i | \(-0.164515\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.5761 | −0.579530 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.958076i | 0.0478440i | 0.999714 | + | 0.0239220i | \(0.00761534\pi\) | ||||
−0.999714 | + | 0.0239220i | \(0.992385\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.22013 | + | 9.16160i | −0.459287 | + | 0.456372i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.19680i | 0.158850i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.67276 | −0.479461 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 35.2821i | − | 1.74459i | −0.488981 | − | 0.872294i | \(-0.662631\pi\) | ||
0.488981 | − | 0.872294i | \(-0.337369\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.1852i | 1.04499i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.96978 | 0.0969268 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.59019 | −0.323500 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.29927 | −0.210536 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.3266 | 0.504485 | 0.252243 | − | 0.967664i | \(-0.418832\pi\) | ||||
0.252243 | + | 0.967664i | \(0.418832\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.1500i | 0.640892i | 0.947267 | + | 0.320446i | \(0.103833\pi\) | ||||
−0.947267 | + | 0.320446i | \(0.896167\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.30781i | 0.0635878i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.91128 | −0.383753 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.69145i | 0.130249i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.05290 | + | 7.00813i | −0.340517 | + | 0.338356i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 5.88317i | − | 0.283382i | −0.989911 | − | 0.141691i | \(-0.954746\pi\) | ||
0.989911 | − | 0.141691i | \(-0.0452540\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.6669 | −1.76210 | −0.881049 | − | 0.473025i | \(-0.843162\pi\) | ||||
−0.881049 | + | 0.473025i | \(0.843162\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 22.2520i | 1.06690i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.3910i | 0.927597i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.3167 | 1.30376 | 0.651878 | − | 0.758324i | \(-0.273981\pi\) | ||||
0.651878 | + | 0.758324i | \(0.273981\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.60441 | −0.219258 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −33.3749 | −1.58569 | −0.792844 | − | 0.609424i | \(-0.791401\pi\) | ||||
−0.792844 | + | 0.609424i | \(0.791401\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.6224 | 1.35683 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 9.42853i | − | 0.445954i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17.2049i | − | 0.811952i | −0.913884 | − | 0.405976i | \(-0.866932\pi\) | ||
0.913884 | − | 0.405976i | \(-0.133068\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.43161 | −0.255765 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 27.6179i | 1.29760i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.03792 | + | 5.07010i | 0.236181 | + | 0.237690i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 21.5943i | − | 1.01014i | −0.863079 | − | 0.505068i | \(-0.831467\pi\) | ||
0.863079 | − | 0.505068i | \(-0.168533\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 32.7042 | 1.52650 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 28.9024i | − | 1.34612i | −0.739588 | − | 0.673060i | \(-0.764980\pi\) | ||
0.739588 | − | 0.673060i | \(-0.235020\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.3410i | 1.22417i | 0.790792 | + | 0.612085i | \(0.209669\pi\) | ||||
−0.790792 | + | 0.612085i | \(0.790331\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.7068 | 0.913881 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.4092 | −1.31462 | −0.657311 | − | 0.753619i | \(-0.728306\pi\) | ||||
−0.657311 | + | 0.753619i | \(0.728306\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.8334 | −0.592589 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −53.2609 | −2.45413 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.3904i | 0.569713i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.49284i | 0.206146i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.5792 | −0.942256 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.4893i | 1.16464i | 0.812961 | + | 0.582318i | \(0.197854\pi\) | ||||
−0.812961 | + | 0.582318i | \(0.802146\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.7392 | − | 24.5821i | 1.12801 | − | 1.12085i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.7381i | 0.579602i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 30.3824 | 1.37959 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.5089i | 1.51843i | 0.650839 | + | 0.759216i | \(0.274417\pi\) | ||||
−0.650839 | + | 0.759216i | \(0.725583\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.18927i | 0.189445i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.87148 | 0.174717 | 0.0873586 | − | 0.996177i | \(-0.472157\pi\) | ||||
0.0873586 | + | 0.996177i | \(0.472157\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.0892 | −1.35515 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.12758 | 0.410254 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00846 | 0.359228 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 16.7283i | − | 0.748862i | −0.927255 | − | 0.374431i | \(-0.877838\pi\) | ||
0.927255 | − | 0.374431i | \(-0.122162\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.5917i | 0.562556i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 43.5572 | 1.94212 | 0.971059 | − | 0.238839i | \(-0.0767669\pi\) | ||||
0.971059 | + | 0.238839i | \(0.0767669\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.6811i | 0.608803i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.228291 | − | 35.8482i | 0.0101387 | − | 1.59207i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.52062i | 0.289021i | 0.989503 | + | 0.144511i | \(0.0461608\pi\) | ||||
−0.989503 | + | 0.144511i | \(0.953839\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.542368 | 0.0239929 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 18.5728i | − | 0.820011i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 26.0354i | − | 1.14726i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.284033 | −0.0124918 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −58.0218 | −2.54688 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.38853 | −0.148454 | −0.0742270 | − | 0.997241i | \(-0.523649\pi\) | ||||
−0.0742270 | + | 0.997241i | \(0.523649\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.5564 | 1.59850 | 0.799249 | − | 0.601000i | \(-0.205231\pi\) | ||||
0.799249 | + | 0.601000i | \(0.205231\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.95137i | 0.128809i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.6475i | 1.16079i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.66263 | −0.0722881 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.06970i | 0.393591i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.8920 | − | 13.8038i | 0.601728 | − | 0.597908i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 33.4989i | − | 1.44829i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.1615 | 0.611112 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.00000i | − | 0.0430730i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 46.0690i | − | 1.98066i | −0.138734 | − | 0.990330i | \(-0.544303\pi\) | ||
0.138734 | − | 0.990330i | \(-0.455697\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.626614 | −0.0268906 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −25.0765 | −1.07416 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.2186 | −0.479674 | −0.239837 | − | 0.970813i | \(-0.577094\pi\) | ||||
−0.239837 | + | 0.970813i | \(0.577094\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.3926 | −0.528902 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.0878i | 0.727963i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.5068i | 0.574370i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −52.8768 | −2.24449 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 15.3169i | − | 0.648998i | −0.945886 | − | 0.324499i | \(-0.894804\pi\) | ||
0.945886 | − | 0.324499i | \(-0.105196\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.4888 | − | 31.6900i | −1.33184 | − | 1.34034i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.3839i | 0.860611i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.2582 | 1.35952 | 0.679760 | − | 0.733435i | \(-0.262084\pi\) | ||||
0.679760 | + | 0.733435i | \(0.262084\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 11.8798i | − | 0.499786i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.61263i | 0.0677239i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.1639 | 0.761471 | 0.380735 | − | 0.924684i | \(-0.375671\pi\) | ||||
0.380735 | + | 0.924684i | \(0.375671\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.6686 | −1.11605 | −0.558023 | − | 0.829825i | \(-0.688440\pi\) | ||||
−0.558023 | + | 0.829825i | \(0.688440\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −42.8693 | −1.79089 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.94381 | 0.206171 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.9219i | 0.496315i | 0.968720 | + | 0.248157i | \(0.0798250\pi\) | ||||
−0.968720 | + | 0.248157i | \(0.920175\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 68.8716i | 2.86221i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.32443 | −0.137920 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.46945i | − | 0.185106i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −23.3448 | + | 23.1966i | −0.965190 | + | 0.959063i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.09246i | 0.0863651i | 0.999067 | + | 0.0431826i | \(0.0137497\pi\) | ||||
−0.999067 | + | 0.0431826i | \(0.986250\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.1332 | 0.623554 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 56.5177i | 2.32483i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 17.1115i | − | 0.702685i | −0.936247 | − | 0.351343i | \(-0.885725\pi\) | ||
0.936247 | − | 0.351343i | \(-0.114275\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.6533 | 0.600729 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.02464 | −0.246572 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 43.5056 | 1.77759 | 0.888795 | − | 0.458304i | \(-0.151543\pi\) | ||||
0.888795 | + | 0.458304i | \(0.151543\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.7825 | −0.521411 | −0.260705 | − | 0.965418i | \(-0.583955\pi\) | ||||
−0.260705 | + | 0.965418i | \(0.583955\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 59.0900i | − | 2.40633i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.98236i | 0.0805942i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.6720 | 0.960815 | 0.480408 | − | 0.877045i | \(-0.340489\pi\) | ||||
0.480408 | + | 0.877045i | \(0.340489\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.2251i | 0.454862i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.726448 | − | 0.721837i | 0.0293889 | − | 0.0292024i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.2292i | 0.736271i | 0.929772 | + | 0.368135i | \(0.120004\pi\) | ||||
−0.929772 | + | 0.368135i | \(0.879996\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −29.6922 | −1.19731 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.0001i | 1.52983i | 0.644134 | + | 0.764913i | \(0.277218\pi\) | ||||
−0.644134 | + | 0.764913i | \(0.722782\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 14.2348i | − | 0.572147i | −0.958208 | − | 0.286073i | \(-0.907650\pi\) | ||
0.958208 | − | 0.286073i | \(-0.0923501\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.4371 | −0.820112 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.4386 | 0.578469 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.5032 | −0.740128 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.5761 | 0.462305 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 71.4999i | − | 2.85089i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4.63927i | − | 0.184687i | −0.995727 | − | 0.0923433i | \(-0.970564\pi\) | ||
0.995727 | − | 0.0923433i | \(-0.0294357\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.5246 | −0.577299 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.12955i | 0.362295i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.54138 | + | 2.55761i | 0.100693 | + | 0.101336i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 36.8742i | 1.45872i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.60473 | 0.300369 | 0.150184 | − | 0.988658i | \(-0.452013\pi\) | ||||
0.150184 | + | 0.988658i | \(0.452013\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 25.1261i | − | 0.990875i | −0.868643 | − | 0.495438i | \(-0.835008\pi\) | ||
0.868643 | − | 0.495438i | \(-0.164992\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 67.7332i | 2.66699i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.1613 | −1.14645 | −0.573225 | − | 0.819398i | \(-0.694308\pi\) | ||||
−0.573225 | + | 0.819398i | \(0.694308\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.96978 | −0.0773208 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.94111 | 0.389623 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.4154 | −0.838048 | −0.419024 | − | 0.907975i | \(-0.637628\pi\) | ||||
−0.419024 | + | 0.907975i | \(0.637628\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.8835i | 0.894131i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.49728i | 0.0974284i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.27587 | 0.0497008 | 0.0248504 | − | 0.999691i | \(-0.492089\pi\) | ||||
0.0248504 | + | 0.999691i | \(0.492089\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.8826i | 0.695554i | 0.937577 | + | 0.347777i | \(0.113063\pi\) | ||||
−0.937577 | + | 0.347777i | \(0.886937\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −51.8033 | − | 52.1343i | −2.01187 | − | 2.02473i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 8.32168i | − | 0.322701i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.8030 | 0.728053 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.3968i | 1.09788i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.69145i | − | 0.103902i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.0259 | −0.386470 | −0.193235 | − | 0.981152i | \(-0.561898\pi\) | ||||
−0.193235 | + | 0.981152i | \(0.561898\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.73522 | −0.182259 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.6036 | 0.868728 | 0.434364 | − | 0.900737i | \(-0.356973\pi\) | ||||
0.434364 | + | 0.900737i | \(0.356973\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.3264 | 0.588174 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 74.5428i | 2.85648i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.3688i | 1.04724i | 0.851952 | + | 0.523619i | \(0.175419\pi\) | ||||
−0.851952 | + | 0.523619i | \(0.824581\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.2294 | −0.581884 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 6.10844i | − | 0.233051i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.3586 | + | 11.4311i | 0.432727 | + | 0.435491i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.4407i | 0.853683i | 0.904326 | + | 0.426842i | \(0.140374\pi\) | ||||
−0.904326 | + | 0.426842i | \(0.859626\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.60441 | 0.174907 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 3.09060i | − | 0.117233i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 40.1498i | − | 1.52078i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 60.3744 | 2.28357 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.6066 | −1.42038 | −0.710191 | − | 0.704009i | \(-0.751391\pi\) | ||||
−0.710191 | + | 0.704009i | \(0.751391\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −40.6050 | −1.53145 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.55269 | −0.0584776 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.90146i | 0.259556i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.6546i | 1.60193i | 0.598714 | + | 0.800963i | \(0.295679\pi\) | ||||
−0.598714 | + | 0.800963i | \(0.704321\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −62.1911 | −2.33235 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 16.6522i | − | 0.623631i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.03792 | − | 5.07010i | −0.188407 | − | 0.189611i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 11.2980i | − | 0.421931i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 42.2236 | 1.57467 | 0.787337 | − | 0.616523i | \(-0.211459\pi\) | ||||
0.787337 | + | 0.616523i | \(0.211459\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 13.1336i | − | 0.489120i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 7.64680i | − | 0.284388i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.35659 | 0.161800 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.24000 | 0.194341 | 0.0971705 | − | 0.995268i | \(-0.469021\pi\) | ||||
0.0971705 | + | 0.995268i | \(0.469021\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −44.0270 | −1.63063 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −91.5888 | −3.38753 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 24.2788i | − | 0.896757i | −0.893844 | − | 0.448378i | \(-0.852002\pi\) | ||
0.893844 | − | 0.448378i | \(-0.147998\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 5.46656i | − | 0.201637i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.8334 | 0.472723 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 5.37005i | − | 0.197541i | −0.995110 | − | 0.0987703i | \(-0.968509\pi\) | ||
0.995110 | − | 0.0987703i | \(-0.0314909\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −29.6072 | + | 29.4193i | −1.08765 | + | 1.08074i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.4181i | 0.418890i | 0.977820 | + | 0.209445i | \(0.0671658\pi\) | ||||
−0.977820 | + | 0.209445i | \(0.932834\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.77787 | 0.248322 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 15.3070i | − | 0.560055i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 16.8985i | − | 0.617459i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.4887 | 1.76938 | 0.884689 | − | 0.466181i | \(-0.154371\pi\) | ||||
0.884689 | + | 0.466181i | \(0.154371\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −57.1092 | −2.08118 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.8536 | −0.722548 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.79543 | 0.0652559 | 0.0326280 | − | 0.999468i | \(-0.489612\pi\) | ||||
0.0326280 | + | 0.999468i | \(0.489612\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 12.7381i | − | 0.462362i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.79075i | 0.318664i | 0.987225 | + | 0.159332i | \(0.0509341\pi\) | ||||
−0.987225 | + | 0.159332i | \(0.949066\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.6498 | −0.457955 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 67.4701i | 2.43939i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.03795 | − | 5.00597i | 0.181910 | − | 0.180755i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 44.8648i | − | 1.61787i | −0.587901 | − | 0.808933i | \(-0.700045\pi\) | ||
0.587901 | − | 0.808933i | \(-0.299955\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.24938 | −0.153038 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 3.23482i | − | 0.116348i | −0.998306 | − | 0.0581742i | \(-0.981472\pi\) | ||
0.998306 | − | 0.0581742i | \(-0.0185279\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.85828i | − | 0.138593i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −26.6737 | −0.956913 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.8012 | −0.816939 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.00846 | −0.286565 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.0096 | −0.643611 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 38.2875i | − | 1.36654i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 52.0427i | − | 1.85512i | −0.373673 | − | 0.927560i | \(-0.621902\pi\) | ||
0.373673 | − | 0.927560i | \(-0.378098\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.9245 | −0.780531 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 5.99276i | − | 0.213078i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.84001 | + | 6.88370i | 0.242896 | + | 0.244447i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 24.4325i | − | 0.866532i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.8364 | 0.773485 | 0.386743 | − | 0.922188i | \(-0.373600\pi\) | ||||
0.386743 | + | 0.922188i | \(0.373600\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.09954i | − | 0.0742765i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 66.4811i | 2.34899i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.542368 | −0.0191397 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.15698 | −0.322741 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.5827 | −0.794950 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.2028 | 1.09703 | 0.548517 | − | 0.836140i | \(-0.315193\pi\) | ||||
0.548517 | + | 0.836140i | \(0.315193\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3.15331i | − | 0.110728i | −0.998466 | − | 0.0553639i | \(-0.982368\pi\) | ||
0.998466 | − | 0.0553639i | \(-0.0176319\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 32.5489i | − | 1.14154i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.01153 | −0.105489 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 52.0136i | 1.81972i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.7763 | + | 11.7016i | −0.411498 | + | 0.408885i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.9375i | 1.63813i | 0.573702 | + | 0.819064i | \(0.305507\pi\) | ||||
−0.573702 | + | 0.819064i | \(0.694493\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.4979 | −0.470509 | −0.235254 | − | 0.971934i | \(-0.575592\pi\) | ||||
−0.235254 | + | 0.971934i | \(0.575592\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2.95137i | − | 0.102754i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.5564i | 1.58415i | 0.610422 | + | 0.792076i | \(0.291000\pi\) | ||||
−0.610422 | + | 0.792076i | \(0.709000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.9162 | 1.31689 | 0.658443 | − | 0.752631i | \(-0.271215\pi\) | ||||
0.658443 | + | 0.752631i | \(0.271215\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.6254 | 0.888934 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.39189 | 0.256114 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.05176 | −0.313249 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.9496i | 0.551300i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.2968i | 0.907865i | 0.891036 | + | 0.453933i | \(0.149979\pi\) | ||||
−0.891036 | + | 0.453933i | \(0.850021\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.4304 | −0.428636 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 75.4387i | − | 2.59825i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.7701 | + | 0.164111i | 0.886518 | + | 0.00564558i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −52.4204 | −1.79907 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 44.6808i | 1.53164i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.3493i | 1.00490i | 0.864606 | + | 0.502450i | \(0.167568\pi\) | ||||
−0.864606 | + | 0.502450i | \(0.832432\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 38.3165 | 1.31040 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −43.0706 | −1.47126 | −0.735632 | − | 0.677382i | \(-0.763115\pi\) | ||||
−0.735632 | + | 0.677382i | \(0.763115\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 55.4060 | 1.89043 | 0.945215 | − | 0.326450i | \(-0.105852\pi\) | ||||
0.945215 | + | 0.326450i | \(0.105852\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.9783 | −0.510458 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 38.3524i | − | 1.30553i | −0.757560 | − | 0.652766i | \(-0.773609\pi\) | ||
0.757560 | − | 0.652766i | \(-0.226391\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 41.7100i | − | 1.41818i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −103.796 | −3.52511 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 13.5068i | − | 0.458188i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.8228 | + | 32.6144i | −1.11216 | + | 1.10510i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 70.5692i | 2.38840i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.0334 | −0.406804 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.791681i | 0.0267332i | 0.999911 | + | 0.0133666i | \(0.00425484\pi\) | ||||
−0.999911 | + | 0.0133666i | \(0.995745\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.1440i | 0.848088i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.6101 | −0.391153 | −0.195577 | − | 0.980688i | \(-0.562658\pi\) | ||||
−0.195577 | + | 0.980688i | \(0.562658\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.4466 | 0.856347 | 0.428174 | − | 0.903696i | \(-0.359157\pi\) | ||||
0.428174 | + | 0.903696i | \(0.359157\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.7680 | −0.361961 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.0189 | 0.638594 | 0.319297 | − | 0.947655i | \(-0.396553\pi\) | ||||
0.319297 | + | 0.947655i | \(0.396553\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.60540i | 0.154460i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1.61263i | − | 0.0540250i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.19234 | −0.0399000 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.1802i | 0.340287i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.3722 | + | 32.5790i | 1.08088 | + | 1.08778i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 14.6743i | − | 0.489415i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.0376 | 1.10064 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 34.1680i | 1.13704i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 0.450452i | − | 0.0149735i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.7983 | 0.723802 | 0.361901 | − | 0.932217i | \(-0.382128\pi\) | ||||
0.361901 | + | 0.932217i | \(0.382128\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −31.7771 | −1.05398 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.8658 | −0.856972 | −0.428486 | − | 0.903548i | \(-0.640953\pi\) | ||||
−0.428486 | + | 0.903548i | \(0.640953\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.32443 | 0.110022 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 14.7130i | − | 0.486397i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.5436i | 0.381202i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.5222 | 0.446055 | 0.223028 | − | 0.974812i | \(-0.428406\pi\) | ||||
0.223028 | + | 0.974812i | \(0.428406\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 47.8111i | 1.57543i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.4825 | − | 20.3525i | 0.674191 | − | 0.669911i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.3524i | 0.340385i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 60.4725 | 1.98618 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 51.1065i | − | 1.67675i | −0.545095 | − | 0.838374i | \(-0.683506\pi\) | ||
0.545095 | − | 0.838374i | \(-0.316494\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 4.19788i | − | 0.137580i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.77118 | −0.254417 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.6533 | −0.479216 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.0680 | −0.361575 | −0.180788 | − | 0.983522i | \(-0.557865\pi\) | ||||
−0.180788 | + | 0.983522i | \(0.557865\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 72.8215 | 2.37644 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.5464i | 1.06098i | 0.847690 | + | 0.530492i | \(0.177993\pi\) | ||||
−0.847690 | + | 0.530492i | \(0.822007\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.0899i | 0.817040i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.77062 | 0.285308 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.6146i | 0.377422i | 0.982033 | + | 0.188711i | \(0.0604310\pi\) | ||||
−0.982033 | + | 0.188711i | \(0.939569\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.38717 | − | 1.37836i | 0.0450294 | − | 0.0447435i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.0090i | 0.356990i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.5698 | −1.11982 | −0.559912 | − | 0.828552i | \(-0.689165\pi\) | ||||
−0.559912 | + | 0.828552i | \(0.689165\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 30.8173i | − | 0.997226i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 11.2251i | − | 0.362854i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.68246 | −0.248080 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0042 | 0.580780 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 77.8079 | 2.50732 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −49.5096 | −1.59377 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.4031i | 0.559646i | 0.960052 | + | 0.279823i | \(0.0902758\pi\) | ||||
−0.960052 | + | 0.279823i | \(0.909724\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 85.5693i | 2.74888i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.5169 | −0.786785 | −0.393393 | − | 0.919371i | \(-0.628699\pi\) | ||||
−0.393393 | + | 0.919371i | \(0.628699\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.55906i | − | 0.0499810i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.50056 | + | 7.54848i | 0.240210 | + | 0.241745i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.89582i | 0.220617i | 0.993897 | + | 0.110308i | \(0.0351839\pi\) | ||||
−0.993897 | + | 0.110308i | \(0.964816\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.4386 | −0.461458 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 58.2451i | − | 1.85962i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 4.02126i | − | 0.128258i | −0.997942 | − | 0.0641292i | \(-0.979573\pi\) | ||
0.997942 | − | 0.0641292i | \(-0.0204270\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −40.6287 | −1.29454 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.783253 | −0.0249312 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 57.2344 | 1.81995 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.3571 | −1.37728 | −0.688642 | − | 0.725102i | \(-0.741793\pi\) | ||||
−0.688642 | + | 0.725102i | \(0.741793\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 60.3973i | 1.91665i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 4.33092i | − | 0.137299i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.6297 | −0.463328 | −0.231664 | − | 0.972796i | \(-0.574417\pi\) | ||||
−0.231664 | + | 0.972796i | \(0.574417\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 42.7956i | − | 1.35399i |
(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 | 4004.2.m.c.2157.6 | yes | 36 | |
13.12 | even | 2 | inner | 4004.2.m.c.2157.5 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.m.c.2157.5 | ✓ | 36 | 13.12 | even | 2 | inner | |
4004.2.m.c.2157.6 | yes | 36 | 1.1 | even | 1 | trivial |