Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3997,1,Mod(13,3997)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3997, base_ring=CyclotomicField(570))
chi = DirichletCharacter(H, H._module([285, 352]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3997.13");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3997 = 7 \cdot 571 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3997.cz (of order \(570\), degree \(144\), 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: | \(1.99476285549\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Coefficient field: | \(\Q(\zeta_{570})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{144} - x^{143} + x^{142} + x^{139} - x^{138} + x^{137} - x^{129} + x^{128} - x^{127} + x^{125} - 2 x^{124} + 2 x^{123} - x^{122} + x^{120} - x^{119} + x^{118} + x^{114} - x^{113} + x^{112} - x^{110} + 2 x^{109} - 2 x^{108} + x^{107} - x^{105} + x^{104} - x^{103} - x^{99} + x^{98} - x^{97} + x^{95} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{285}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{285} - \cdots)\) |
Embedding invariants
Embedding label | 342.1 | ||
Root | \(-0.761300 - 0.648400i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3997.342 |
Dual form | 3997.1.cz.a.2092.1 |
$q$-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 \(\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times\).
\(n\) | \(1716\) | \(2285\) |
\(\chi(n)\) | \(e\left(\frac{217}{285}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.70487 | + | 0.188695i | −1.70487 | + | 0.188695i | −0.909007 | − | 0.416782i | \(-0.863158\pi\) |
−0.795863 | + | 0.605477i | \(0.792982\pi\) | |||||||
\(3\) | 0 | 0 | 0.731980 | − | 0.681326i | \(-0.238596\pi\) | ||||
−0.731980 | + | 0.681326i | \(0.761404\pi\) | |||||||
\(4\) | 1.89518 | − | 0.424719i | 1.89518 | − | 0.424719i | ||||
\(5\) | 0 | 0 | −0.556143 | − | 0.831087i | \(-0.687719\pi\) | ||||
0.556143 | + | 0.831087i | \(0.312281\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.934564 | + | 0.355794i | −0.934564 | + | 0.355794i | ||||
\(8\) | −1.52855 | + | 0.524751i | −1.52855 | + | 0.524751i | ||||
\(9\) | 0.0715891 | − | 0.997434i | 0.0715891 | − | 0.997434i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.710680 | − | 0.126659i | −0.710680 | − | 0.126659i | −0.191711 | − | 0.981451i | \(-0.561404\pi\) |
−0.518970 | + | 0.854793i | \(0.673684\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.999028 | − | 0.0440782i | \(-0.985965\pi\) | ||||
0.999028 | + | 0.0440782i | \(0.0140351\pi\) | |||||||
\(14\) | 1.52617 | − | 0.782930i | 1.52617 | − | 0.782930i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.750526 | − | 0.354182i | 0.750526 | − | 0.354182i | ||||
\(17\) | 0 | 0 | −0.126427 | − | 0.991976i | \(-0.540351\pi\) | ||||
0.126427 | + | 0.991976i | \(0.459649\pi\) | |||||||
\(18\) | 0.0661607 | + | 1.71400i | 0.0661607 | + | 1.71400i | ||||
\(19\) | 0 | 0 | 0.992658 | − | 0.120958i | \(-0.0385965\pi\) | ||||
−0.992658 | + | 0.120958i | \(0.961404\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.23552 | + | 0.0818350i | 1.23552 | + | 0.0818350i | ||||
\(23\) | −0.00633087 | − | 0.00902376i | −0.00633087 | − | 0.00902376i | 0.815447 | − | 0.578832i | \(-0.196491\pi\) |
−0.821778 | + | 0.569808i | \(0.807018\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.381410 | + | 0.924406i | −0.381410 | + | 0.924406i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.62005 | + | 1.07122i | −1.62005 | + | 1.07122i | ||||
\(29\) | −0.752996 | − | 0.914313i | −0.752996 | − | 0.914313i | 0.245485 | − | 0.969400i | \(-0.421053\pi\) |
−0.998482 | + | 0.0550878i | \(0.982456\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.0825793 | − | 0.996584i | \(-0.473684\pi\) | ||||
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(32\) | 0.164081 | − | 0.100860i | 0.164081 | − | 0.100860i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.287956 | − | 1.92072i | −0.287956 | − | 1.92072i | ||||
\(37\) | 1.20227 | − | 0.957234i | 1.20227 | − | 0.957234i | 0.202517 | − | 0.979279i | \(-0.435088\pi\) |
0.999757 | + | 0.0220445i | \(0.00701754\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.962268 | − | 0.272103i | \(-0.0877193\pi\) | ||||
−0.962268 | + | 0.272103i | \(0.912281\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.918045 | + | 1.47520i | −0.918045 | + | 1.47520i | −0.0385714 | + | 0.999256i | \(0.512281\pi\) |
−0.879474 | + | 0.475947i | \(0.842105\pi\) | |||||||
\(44\) | −1.40066 | + | 0.0617987i | −1.40066 | + | 0.0617987i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0124960 | + | 0.0141897i | 0.0124960 | + | 0.0141897i | ||||
\(47\) | 0 | 0 | −0.821778 | − | 0.569808i | \(-0.807018\pi\) | ||||
0.821778 | + | 0.569808i | \(0.192982\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.746821 | − | 0.665025i | 0.746821 | − | 0.665025i | ||||
\(50\) | 0.475824 | − | 1.64796i | 0.475824 | − | 1.64796i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.740847 | + | 1.63959i | −0.740847 | + | 1.63959i | 0.0275543 | + | 0.999620i | \(0.491228\pi\) |
−0.768401 | + | 0.639969i | \(0.778947\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.24182 | − | 1.03426i | 1.24182 | − | 1.03426i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.45629 | + | 1.41670i | 1.45629 | + | 1.41670i | ||||
\(59\) | 0 | 0 | 0.546948 | − | 0.837166i | \(-0.315789\pi\) | ||||
−0.546948 | + | 0.837166i | \(0.684211\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.00551154 | − | 0.999985i | \(-0.501754\pi\) | ||||
0.00551154 | + | 0.999985i | \(0.498246\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.287976 | + | 0.957638i | 0.287976 | + | 0.957638i | ||||
\(64\) | −0.915613 | + | 0.712650i | −0.915613 | + | 0.712650i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.15955 | + | 1.61463i | 1.15955 | + | 1.61463i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
0.490424 | + | 0.871484i | \(0.336842\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.506840 | + | 0.225660i | −0.506840 | + | 0.225660i | −0.644194 | − | 0.764862i | \(-0.722807\pi\) |
0.137354 | + | 0.990522i | \(0.456140\pi\) | |||||||
\(72\) | 0.413977 | + | 1.56219i | 0.413977 | + | 1.56219i | ||||
\(73\) | 0 | 0 | −0.930586 | − | 0.366074i | \(-0.880702\pi\) | ||||
0.930586 | + | 0.366074i | \(0.119298\pi\) | |||||||
\(74\) | −1.86910 | + | 1.85882i | −1.86910 | + | 1.85882i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.709241 | − | 0.134485i | 0.709241 | − | 0.134485i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.143163 | + | 0.424627i | −0.143163 | + | 0.424627i | −0.995083 | − | 0.0990455i | \(-0.968421\pi\) |
0.851919 | + | 0.523673i | \(0.175439\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.989750 | − | 0.142811i | −0.989750 | − | 0.142811i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.329907 | − | 0.944013i | \(-0.607018\pi\) | ||||
0.329907 | + | 0.944013i | \(0.392982\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.28678 | − | 2.68826i | 1.28678 | − | 2.68826i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.15277 | − | 0.179326i | 1.15277 | − | 0.179326i | ||||
\(89\) | 0 | 0 | −0.982493 | − | 0.186298i | \(-0.940351\pi\) | ||||
0.982493 | + | 0.186298i | \(0.0596491\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.0158307 | − | 0.0144128i | −0.0158307 | − | 0.0144128i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.509516 | − | 0.860461i | \(-0.670175\pi\) | ||||
0.509516 | + | 0.860461i | \(0.329825\pi\) | |||||||
\(98\) | −1.14775 | + | 1.27470i | −1.14775 | + | 1.27470i | ||||
\(99\) | −0.177211 | + | 0.699789i | −0.177211 | + | 0.699789i | ||||
\(100\) | −0.330227 | + | 1.91391i | −0.330227 | + | 1.91391i | ||||
\(101\) | 0 | 0 | −0.0935596 | − | 0.995614i | \(-0.529825\pi\) | ||||
0.0935596 | + | 0.995614i | \(0.470175\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.953665 | − | 2.93508i | 0.953665 | − | 2.93508i | ||||
\(107\) | −1.13438 | − | 0.535328i | −1.13438 | − | 0.535328i | −0.234785 | − | 0.972047i | \(-0.575439\pi\) |
−0.899598 | + | 0.436719i | \(0.856140\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.863256 | + | 1.49520i | −0.863256 | + | 1.49520i | 0.00551154 | + | 0.999985i | \(0.498246\pi\) |
−0.868768 | + | 0.495219i | \(0.835088\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.575399 | + | 0.598038i | −0.575399 | + | 0.598038i | ||||
\(113\) | −0.0674603 | − | 0.243688i | −0.0674603 | − | 0.243688i | 0.922290 | − | 0.386499i | \(-0.126316\pi\) |
−0.989750 | + | 0.142811i | \(0.954386\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.81539 | − | 1.41297i | −1.81539 | − | 1.41297i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.449406 | − | 0.165443i | −0.449406 | − | 0.165443i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.671663 | − | 1.57831i | −0.671663 | − | 1.57831i | ||||
\(127\) | 0.141927 | + | 1.97744i | 0.141927 | + | 1.97744i | 0.202517 | + | 0.979279i | \(0.435088\pi\) |
−0.0605901 | + | 0.998163i | \(0.519298\pi\) | |||||||
\(128\) | 1.28847 | − | 1.25345i | 1.28847 | − | 1.25345i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.677282 | − | 0.735724i | \(-0.736842\pi\) | ||||
0.677282 | + | 0.735724i | \(0.263158\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.28156 | − | 2.53393i | −2.28156 | − | 2.53393i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.678721 | + | 1.64498i | 0.678721 | + | 1.64498i | 0.761300 | + | 0.648400i | \(0.224561\pi\) |
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.899598 | − | 0.436719i | \(-0.856140\pi\) | ||||
0.899598 | + | 0.436719i | \(0.143860\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.821516 | − | 0.480359i | 0.821516 | − | 0.480359i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.299544 | − | 0.773956i | −0.299544 | − | 0.773956i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.87197 | − | 2.32476i | 1.87197 | − | 2.32476i | ||||
\(149\) | 0.943941 | − | 1.34546i | 0.943941 | − | 1.34546i | 0.00551154 | − | 0.999985i | \(-0.498246\pi\) |
0.938430 | − | 0.345471i | \(-0.112281\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.25586 | − | 0.462330i | 1.25586 | − | 0.462330i | 0.371197 | − | 0.928554i | \(-0.378947\pi\) |
0.884667 | + | 0.466224i | \(0.154386\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.18379 | + | 0.363109i | −1.18379 | + | 0.363109i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.795863 | − | 0.605477i | \(-0.207018\pi\) | ||||
−0.795863 | + | 0.605477i | \(0.792982\pi\) | |||||||
\(158\) | 0.163950 | − | 0.750949i | 0.163950 | − | 0.750949i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.00912720 | + | 0.00618080i | 0.00912720 | + | 0.00618080i | ||||
\(162\) | 1.71434 | + | 0.0567129i | 1.71434 | + | 0.0567129i | ||||
\(163\) | 1.86811 | + | 0.711199i | 1.86811 | + | 0.711199i | 0.945817 | + | 0.324699i | \(0.105263\pi\) |
0.922290 | + | 0.386499i | \(0.126316\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.996114 | + | 0.0880708i | 0.996114 | + | 0.0880708i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.11331 | + | 3.18568i | −1.11331 | + | 3.18568i | ||||
\(173\) | 0 | 0 | −0.840168 | − | 0.542326i | \(-0.817544\pi\) | ||||
0.840168 | + | 0.542326i | \(0.182456\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0275543 | − | 0.999620i | 0.0275543 | − | 0.999620i | ||||
\(176\) | −0.578244 | + | 0.156649i | −0.578244 | + | 0.156649i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.949492 | + | 1.68725i | −0.949492 | + | 1.68725i | −0.256156 | + | 0.966635i | \(0.582456\pi\) |
−0.693336 | + | 0.720615i | \(0.743860\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.986361 | − | 0.164595i | \(-0.947368\pi\) | ||||
0.986361 | + | 0.164595i | \(0.0526316\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.0144123 | + | 0.0104711i | 0.0144123 | + | 0.0104711i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.978802 | − | 0.727760i | −0.978802 | − | 0.727760i | −0.0165339 | − | 0.999863i | \(-0.505263\pi\) |
−0.962268 | + | 0.272103i | \(0.912281\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.79510 | − | 0.799232i | −1.79510 | − | 0.799232i | −0.973327 | − | 0.229424i | \(-0.926316\pi\) |
−0.821778 | − | 0.569808i | \(-0.807018\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.13291 | − | 1.57753i | 1.13291 | − | 1.57753i | ||||
\(197\) | −0.0706865 | − | 1.16449i | −0.0706865 | − | 1.16449i | −0.846095 | − | 0.533032i | \(-0.821053\pi\) |
0.775409 | − | 0.631460i | \(-0.217544\pi\) | |||||||
\(198\) | 0.170074 | − | 1.22649i | 0.170074 | − | 1.22649i | ||||
\(199\) | 0 | 0 | −0.775409 | − | 0.631460i | \(-0.782456\pi\) | ||||
0.775409 | + | 0.631460i | \(0.217544\pi\) | |||||||
\(200\) | 0.0979204 | − | 1.61314i | 0.0979204 | − | 1.61314i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.02903 | + | 0.586573i | 1.02903 | + | 0.586573i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.00945383 | + | 0.00566862i | −0.00945383 | + | 0.00566862i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.07786 | + | 1.22395i | −1.07786 | + | 1.22395i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.973327 | + | 0.229424i | \(0.926316\pi\) | |||||||
\(212\) | −0.707671 | + | 3.42196i | −0.707671 | + | 3.42196i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.03499 | + | 0.698612i | 2.03499 | + | 0.698612i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.18960 | − | 2.71202i | 1.18960 | − | 2.71202i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.996114 | − | 0.0880708i | \(-0.0280702\pi\) | ||||
−0.996114 | + | 0.0880708i | \(0.971930\pi\) | |||||||
\(224\) | −0.117459 | + | 0.152640i | −0.117459 | + | 0.152640i | ||||
\(225\) | 0.894729 | + | 0.446609i | 0.894729 | + | 0.446609i | ||||
\(226\) | 0.160994 | + | 0.402728i | 0.160994 | + | 0.402728i | ||||
\(227\) | 0 | 0 | 0.224056 | − | 0.974576i | \(-0.428070\pi\) | ||||
−0.224056 | + | 0.974576i | \(0.571930\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.159156 | − | 0.987253i | \(-0.550877\pi\) | ||||
0.159156 | + | 0.987253i | \(0.449123\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.63078 | + | 1.00243i | 1.63078 | + | 1.00243i | ||||
\(233\) | −1.44850 | + | 0.0319392i | −1.44850 | + | 0.0319392i | −0.739446 | − | 0.673216i | \(-0.764912\pi\) |
−0.709053 | + | 0.705155i | \(0.750877\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.370526 | + | 0.595397i | 0.370526 | + | 0.595397i | 0.980380 | − | 0.197117i | \(-0.0631579\pi\) |
−0.609854 | + | 0.792514i | \(0.708772\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.956036 | − | 0.293250i | \(-0.905263\pi\) | ||||
0.956036 | + | 0.293250i | \(0.0947368\pi\) | |||||||
\(242\) | 0.797396 | + | 0.197258i | 0.797396 | + | 0.197258i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.949339 | − | 0.314254i | \(-0.898246\pi\) | ||||
0.949339 | + | 0.314254i | \(0.101754\pi\) | |||||||
\(252\) | 0.952494 | + | 1.69258i | 0.952494 | + | 1.69258i | ||||
\(253\) | 0.00335628 | + | 0.00721487i | 0.00335628 | + | 0.00721487i | ||||
\(254\) | −0.615101 | − | 3.34450i | −0.615101 | − | 3.34450i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.22255 | + | 1.48446i | −1.22255 | + | 1.48446i | ||||
\(257\) | 0 | 0 | 0.724425 | − | 0.689353i | \(-0.242105\pi\) | ||||
−0.724425 | + | 0.689353i | \(0.757895\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.783025 | + | 1.32236i | −0.783025 | + | 1.32236i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.965873 | + | 0.685609i | −0.965873 | + | 0.685609i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.28743 | + | 0.556280i | −1.28743 | + | 0.556280i | −0.926494 | − | 0.376309i | \(-0.877193\pi\) |
−0.360939 | + | 0.932589i | \(0.617544\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.88333 | + | 2.56752i | 2.88333 | + | 2.56752i | ||||
\(269\) | 0 | 0 | 0.894729 | − | 0.446609i | \(-0.147368\pi\) | ||||
−0.894729 | + | 0.446609i | \(0.852632\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.546948 | − | 0.837166i | \(-0.684211\pi\) | ||||
0.546948 | + | 0.837166i | \(0.315789\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.46753 | − | 2.67641i | −1.46753 | − | 2.67641i | ||||
\(275\) | 0.388145 | − | 0.608648i | 0.388145 | − | 0.608648i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.0316141 | + | 1.91181i | 0.0316141 | + | 1.91181i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.277403 | + | 0.960754i | \(0.589474\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.239087 | + | 1.29999i | −0.239087 | + | 1.29999i | 0.618553 | + | 0.785743i | \(0.287719\pi\) |
−0.857640 | + | 0.514250i | \(0.828070\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.461341 | − | 0.887223i | \(-0.652632\pi\) | ||||
0.461341 | + | 0.887223i | \(0.347368\pi\) | |||||||
\(284\) | −0.864711 | + | 0.642930i | −0.864711 | + | 0.642930i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.0888551 | − | 0.170881i | −0.0888551 | − | 0.170881i | ||||
\(289\) | −0.968033 | + | 0.250825i | −0.968033 | + | 0.250825i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.942181 | − | 0.335105i | \(-0.891228\pi\) | ||||
0.942181 | + | 0.335105i | \(0.108772\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.33542 | + | 2.09407i | −1.33542 | + | 2.09407i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.35542 | + | 2.47194i | −1.35542 | + | 2.47194i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.333104 | − | 1.70531i | 0.333104 | − | 1.70531i | ||||
\(302\) | −2.05384 | + | 1.02519i | −2.05384 | + | 1.02519i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.618553 | − | 0.785743i | \(-0.287719\pi\) | ||||
−0.618553 | + | 0.785743i | \(0.712281\pi\) | |||||||
\(308\) | 1.28702 | − | 0.556101i | 1.28702 | − | 0.556101i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.693336 | − | 0.720615i | \(-0.743860\pi\) | ||||
0.693336 | + | 0.720615i | \(0.256140\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.298515 | − | 0.954405i | \(-0.596491\pi\) | ||||
0.298515 | + | 0.954405i | \(0.403509\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.0909728 | + | 0.865549i | −0.0909728 | + | 0.865549i | ||||
\(317\) | 0.344666 | + | 1.87406i | 0.344666 | + | 1.87406i | 0.471093 | + | 0.882084i | \(0.343860\pi\) |
−0.126427 | + | 0.991976i | \(0.540351\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.419334 | + | 0.745157i | 0.419334 | + | 0.745157i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.0167270 | − | 0.00881521i | −0.0167270 | − | 0.00881521i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.93641 | + | 0.149714i | −1.93641 | + | 0.149714i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.31908 | − | 0.859999i | −3.31908 | − | 0.859999i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.17589 | + | 0.249944i | −1.17589 | + | 0.249944i | −0.754107 | − | 0.656752i | \(-0.771930\pi\) |
−0.421786 | + | 0.906696i | \(0.638596\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.868708 | − | 1.26772i | −0.868708 | − | 1.26772i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.00317439 | − | 0.575944i | 0.00317439 | − | 0.575944i | −0.956036 | − | 0.293250i | \(-0.905263\pi\) |
0.959210 | − | 0.282694i | \(-0.0912281\pi\) | |||||||
\(338\) | −1.71486 | + | 0.0378125i | −1.71486 | + | 0.0378125i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.461341 | + | 0.887223i | −0.461341 | + | 0.887223i | ||||
\(344\) | 0.629161 | − | 2.73666i | 0.629161 | − | 2.73666i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.15362 | + | 1.49915i | −1.15362 | + | 1.49915i | −0.319482 | + | 0.947592i | \(0.603509\pi\) |
−0.834139 | + | 0.551554i | \(0.814035\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.0385714 | − | 0.999256i | \(-0.487719\pi\) | ||||
−0.0385714 | + | 0.999256i | \(0.512281\pi\) | |||||||
\(350\) | 0.141647 | + | 1.70942i | 0.141647 | + | 1.70942i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.129384 | + | 0.0508971i | −0.129384 | + | 0.0508971i | ||||
\(353\) | 0 | 0 | 0.401695 | − | 0.915773i | \(-0.368421\pi\) | ||||
−0.401695 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.30038 | − | 3.05571i | 1.30038 | − | 3.05571i | ||||
\(359\) | −0.0863938 | + | 0.417760i | −0.0863938 | + | 0.417760i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.999939 | + | 0.0110229i | \(0.996491\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.970739 | − | 0.240139i | 0.970739 | − | 0.240139i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.889752 | − | 0.456444i | \(-0.849123\pi\) | ||||
0.889752 | + | 0.456444i | \(0.150877\pi\) | |||||||
\(368\) | −0.00794753 | − | 0.00453029i | −0.00794753 | − | 0.00453029i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.109013 | − | 1.79589i | 0.109013 | − | 1.79589i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.00454199 | + | 0.0327545i | −0.00454199 | + | 0.0327545i | −0.992658 | − | 0.120958i | \(-0.961404\pi\) |
0.988116 | + | 0.153712i | \(0.0491228\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.267435 | − | 1.65892i | 0.267435 | − | 1.65892i | −0.401695 | − | 0.915773i | \(-0.631579\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.80605 | + | 1.05604i | 1.80605 | + | 1.05604i | ||||
\(383\) | 0 | 0 | −0.926494 | − | 0.376309i | \(-0.877193\pi\) | ||||
0.926494 | + | 0.376309i | \(0.122807\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.21123 | + | 1.02386i | 3.21123 | + | 1.02386i | ||||
\(387\) | 1.40570 | + | 1.02130i | 1.40570 | + | 1.02130i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.71290 | − | 0.785368i | 1.71290 | − | 0.785368i | 0.716783 | − | 0.697297i | \(-0.245614\pi\) |
0.996114 | − | 0.0880708i | \(-0.0280702\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.792580 | + | 1.40842i | −0.792580 | + | 1.40842i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.340245 | + | 1.97197i | 0.340245 | + | 1.97197i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.0386318 | + | 1.40149i | −0.0386318 | + | 1.40149i | ||||
\(397\) | 0 | 0 | −0.999757 | − | 0.0220445i | \(-0.992982\pi\) | ||||
0.999757 | + | 0.0220445i | \(0.00701754\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.0411496 | + | 0.828879i | 0.0411496 | + | 0.828879i | ||||
\(401\) | 0.404357 | − | 0.439249i | 0.404357 | − | 0.439249i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.904357 | + | 0.426776i | \(0.140351\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.86505 | − | 0.805857i | −1.86505 | − | 0.805857i | ||||
\(407\) | −0.975675 | + | 0.528009i | −0.975675 | + | 0.528009i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.999453 | − | 0.0330634i | \(-0.989474\pi\) | ||||
0.999453 | + | 0.0330634i | \(0.0105263\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.0150479 | − | 0.0114482i | 0.0150479 | − | 0.0114482i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.899598 | − | 0.436719i | \(-0.143860\pi\) | ||||
−0.899598 | + | 0.436719i | \(0.856140\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.0547169 | − | 0.108124i | −0.0547169 | − | 0.108124i | 0.863256 | − | 0.504766i | \(-0.168421\pi\) |
−0.917973 | + | 0.396642i | \(0.870175\pi\) | |||||||
\(422\) | 1.60665 | − | 2.29005i | 1.60665 | − | 2.29005i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.272043 | − | 2.89495i | 0.272043 | − | 2.89495i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.37722 | − | 0.532748i | −2.37722 | − | 0.532748i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.778017 | − | 0.326040i | −0.778017 | − | 0.326040i | −0.0385714 | − | 0.999256i | \(-0.512281\pi\) |
−0.739446 | + | 0.673216i | \(0.764912\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.995083 | − | 0.0990455i | \(-0.968421\pi\) | ||||
0.995083 | + | 0.0990455i | \(0.0315789\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00098 | + | 3.20032i | −1.00098 | + | 3.20032i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.701237 | − | 0.712928i | \(-0.252632\pi\) | ||||
−0.701237 | + | 0.712928i | \(0.747368\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.609854 | − | 0.792514i | −0.609854 | − | 0.792514i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.43139 | + | 1.39248i | −1.43139 | + | 1.39248i | −0.677282 | + | 0.735724i | \(0.736842\pi\) |
−0.754107 | + | 0.656752i | \(0.771930\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.602143 | − | 0.991787i | 0.602143 | − | 0.991787i | ||||
\(449\) | 0.158295 | + | 1.36153i | 0.158295 | + | 1.36153i | 0.802489 | + | 0.596667i | \(0.203509\pi\) |
−0.644194 | + | 0.764862i | \(0.722807\pi\) | |||||||
\(450\) | −1.60967 | − | 0.592579i | −1.60967 | − | 0.592579i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.231348 | − | 0.433181i | −0.231348 | − | 0.433181i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.412877 | + | 0.616994i | −0.412877 | + | 0.616994i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.565270 | + | 0.824906i | \(0.308772\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.12151 | − | 0.892930i | −1.12151 | − | 0.892930i | −0.126427 | − | 0.991976i | \(-0.540351\pi\) |
−0.995083 | + | 0.0990455i | \(0.968421\pi\) | |||||||
\(464\) | −0.888976 | − | 0.419518i | −0.888976 | − | 0.419518i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.46347 | − | 0.327776i | 2.46347 | − | 0.327776i | ||||
\(467\) | 0 | 0 | 0.959210 | − | 0.282694i | \(-0.0912281\pi\) | ||||
−0.959210 | + | 0.282694i | \(0.908772\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.65815 | − | 1.09641i | −1.65815 | − | 1.09641i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.839284 | − | 0.932119i | 0.839284 | − | 0.932119i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.58235 | + | 0.856323i | 1.58235 | + | 0.856323i | ||||
\(478\) | −0.744047 | − | 0.945157i | −0.744047 | − | 0.945157i | ||||
\(479\) | 0 | 0 | −0.739446 | − | 0.673216i | \(-0.764912\pi\) | ||||
0.739446 | + | 0.673216i | \(0.235088\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.921970 | − | 0.122672i | −0.921970 | − | 0.122672i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.269687 | − | 1.11655i | 0.269687 | − | 1.11655i | −0.660898 | − | 0.750475i | \(-0.729825\pi\) |
0.930586 | − | 0.366074i | \(-0.119298\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.45129 | + | 0.870210i | 1.45129 | + | 0.870210i | 0.999757 | − | 0.0220445i | \(-0.00701754\pi\) |
0.451533 | + | 0.892254i | \(0.350877\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.393387 | − | 0.391224i | 0.393387 | − | 0.391224i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.363256 | + | 1.37079i | 0.363256 | + | 1.37079i | 0.863256 | + | 0.504766i | \(0.168421\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.340293 | − | 0.940319i | \(-0.610526\pi\) | ||||
0.340293 | + | 0.940319i | \(0.389474\pi\) | |||||||
\(504\) | −0.942707 | − | 1.31268i | −0.942707 | − | 1.31268i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.00708344 | − | 0.0116671i | −0.00708344 | − | 0.0116671i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.10884 | + | 3.68732i | 1.10884 | + | 3.68732i | ||||
\(509\) | 0 | 0 | −0.0275543 | − | 0.999620i | \(-0.508772\pi\) | ||||
0.0275543 | + | 0.999620i | \(0.491228\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.820998 | − | 1.25663i | 0.820998 | − | 1.25663i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.08543 | − | 2.40220i | 1.08543 | − | 2.40220i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.277403 | − | 0.960754i | \(-0.410526\pi\) | ||||
−0.277403 | + | 0.960754i | \(0.589474\pi\) | |||||||
\(522\) | 1.51732 | − | 1.35113i | 1.51732 | − | 1.35113i | ||||
\(523\) | 0 | 0 | 0.371197 | − | 0.928554i | \(-0.378947\pi\) | ||||
−0.371197 | + | 0.928554i | \(0.621053\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.08994 | − | 1.19132i | 2.08994 | − | 1.19132i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.340252 | − | 0.940205i | 0.340252 | − | 0.940205i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.61971 | − | 1.85956i | −2.61971 | − | 1.85956i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.614982 | + | 0.378028i | −0.614982 | + | 0.378028i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.69133 | − | 0.206092i | −1.69133 | − | 0.206092i | −0.782322 | − | 0.622874i | \(-0.785965\pi\) |
−0.909007 | + | 0.416782i | \(0.863158\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.291151 | − | 0.545158i | 0.291151 | − | 0.545158i | −0.693336 | − | 0.720615i | \(-0.743860\pi\) |
0.984487 | + | 0.175457i | \(0.0561404\pi\) | |||||||
\(548\) | 1.98495 | + | 2.82927i | 1.98495 | + | 2.82927i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.546887 | + | 1.11091i | −0.546887 | + | 1.11091i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.0172843 | − | 0.447778i | −0.0172843 | − | 0.447778i | ||||
\(554\) | −0.414647 | − | 3.25342i | −0.414647 | − | 3.25342i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.360381 | + | 0.184876i | −0.360381 | + | 0.184876i | −0.627176 | − | 0.778877i | \(-0.715789\pi\) |
0.266796 | + | 0.963753i | \(0.414035\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.162310 | − | 2.26143i | 0.162310 | − | 2.26143i | ||||
\(563\) | 0 | 0 | 0.945817 | − | 0.324699i | \(-0.105263\pi\) | ||||
−0.945817 | + | 0.324699i | \(0.894737\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.975796 | − | 0.218681i | 0.975796 | − | 0.218681i | ||||
\(568\) | 0.656314 | − | 0.610897i | 0.656314 | − | 0.610897i | ||||
\(569\) | 1.51336 | − | 0.167499i | 1.51336 | − | 0.167499i | 0.685350 | − | 0.728214i | \(-0.259649\pi\) |
0.828009 | + | 0.560715i | \(0.189474\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.904357 | − | 0.426776i | 0.904357 | − | 0.426776i | ||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.0107563 | − | 0.00241054i | 0.0107563 | − | 0.00241054i | ||||
\(576\) | 0.645274 | + | 0.964281i | 0.645274 | + | 0.964281i | ||||
\(577\) | 0 | 0 | 0.652586 | − | 0.757715i | \(-0.273684\pi\) | ||||
−0.652586 | + | 0.757715i | \(0.726316\pi\) | |||||||
\(578\) | 1.60304 | − | 0.610286i | 1.60304 | − | 0.610286i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.734173 | − | 1.07139i | 0.734173 | − | 1.07139i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.904357 | − | 0.426776i | \(-0.140351\pi\) | ||||
−0.904357 | + | 0.426776i | \(0.859649\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.563303 | − | 1.14425i | 0.563303 | − | 1.14425i | ||||
\(593\) | 0 | 0 | −0.997814 | − | 0.0660906i | \(-0.978947\pi\) | ||||
0.997814 | + | 0.0660906i | \(0.0210526\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.21750 | − | 2.95079i | 1.21750 | − | 2.95079i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.07469 | − | 0.710615i | 1.07469 | − | 0.710615i | 0.115485 | − | 0.993309i | \(-0.463158\pi\) |
0.959210 | + | 0.282694i | \(0.0912281\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.992658 | − | 0.120958i | \(-0.961404\pi\) | ||||
0.992658 | + | 0.120958i | \(0.0385965\pi\) | |||||||
\(602\) | −0.246116 | + | 2.97018i | −0.246116 | + | 2.97018i | ||||
\(603\) | 1.69350 | − | 1.04099i | 1.69350 | − | 1.04099i | ||||
\(604\) | 2.18373 | − | 1.40959i | 2.18373 | − | 1.40959i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.148264 | − | 0.988948i | \(-0.547368\pi\) | ||||
0.148264 | + | 0.988948i | \(0.452632\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.618657 | − | 1.70951i | 0.618657 | − | 1.70951i | −0.0825793 | − | 0.996584i | \(-0.526316\pi\) |
0.701237 | − | 0.712928i | \(-0.252632\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.01354 | + | 0.577741i | −1.01354 | + | 0.577741i | ||||
\(617\) | 0.504147 | + | 0.572478i | 0.504147 | + | 0.572478i | 0.945817 | − | 0.324699i | \(-0.105263\pi\) |
−0.441671 | + | 0.897177i | \(0.645614\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.371197 | − | 0.928554i | \(-0.378947\pi\) | ||||
−0.371197 | + | 0.928554i | \(0.621053\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.709053 | − | 0.705155i | −0.709053 | − | 0.705155i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.318292 | − | 0.00350872i | −0.318292 | − | 0.00350872i | −0.148264 | − | 0.988948i | \(-0.547368\pi\) |
−0.170028 | + | 0.985439i | \(0.554386\pi\) | |||||||
\(632\) | −0.00399145 | − | 0.724188i | −0.00399145 | − | 0.724188i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.941236 | − | 3.12999i | −0.941236 | − | 3.12999i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.855517 | − | 1.19127i | −0.855517 | − | 1.19127i | ||||
\(639\) | 0.188797 | + | 0.521695i | 0.188797 | + | 0.521695i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.31844 | − | 0.732408i | −1.31844 | − | 0.732408i | −0.340293 | − | 0.940319i | \(-0.610526\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.256156 | − | 0.966635i | \(-0.582456\pi\) | ||||
0.256156 | + | 0.966635i | \(0.417544\pi\) | |||||||
\(644\) | 0.0199228 | + | 0.00783722i | 0.0199228 | + | 0.00783722i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.942181 | − | 0.335105i | \(-0.108772\pi\) | ||||
−0.942181 | + | 0.335105i | \(0.891228\pi\) | |||||||
\(648\) | 1.58782 | − | 0.301079i | 1.58782 | − | 0.301079i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.84245 | + | 0.554427i | 3.84245 | + | 0.554427i | ||||
\(653\) | 1.84747 | − | 0.750379i | 1.84747 | − | 0.750379i | 0.894729 | − | 0.446609i | \(-0.147368\pi\) |
0.952745 | − | 0.303771i | \(-0.0982456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.40125 | + | 0.217980i | −1.40125 | + | 0.217980i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.592235 | + | 0.805765i | \(0.701754\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(662\) | 1.95758 | − | 0.648006i | 1.95758 | − | 0.648006i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.72025 | + | 1.99737i | 1.72025 | + | 1.99737i | ||||
\(667\) | −0.00348342 | + | 0.0125833i | −0.00348342 | + | 0.0125833i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.229144 | − | 0.151516i | −0.229144 | − | 0.151516i | 0.431754 | − | 0.901991i | \(-0.357895\pi\) |
−0.660898 | + | 0.750475i | \(0.729825\pi\) | |||||||
\(674\) | 0.103266 | + | 0.982508i | 0.103266 | + | 0.982508i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.92522 | − | 0.256159i | 1.92522 | − | 0.256159i | ||||
\(677\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.265840 | − | 0.276299i | 0.265840 | − | 0.276299i | −0.574329 | − | 0.818625i | \(-0.694737\pi\) |
0.840168 | + | 0.542326i | \(0.182456\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.619112 | − | 1.59965i | 0.619112 | − | 1.59965i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.166527 | + | 1.43233i | −0.166527 | + | 1.43233i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.995083 | − | 0.0990455i | \(-0.0315789\pi\) | ||||
−0.995083 | + | 0.0990455i | \(0.968421\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0833659 | − | 0.717049i | −0.0833659 | − | 0.717049i | ||||
\(694\) | 1.68389 | − | 2.77353i | 1.68389 | − | 2.77353i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.372338 | − | 1.90616i | −0.372338 | − | 1.90616i | ||||
\(701\) | −0.928564 | − | 1.20668i | −0.928564 | − | 1.20668i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.0495838 | − | 0.998770i | \(-0.484211\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.740971 | − | 0.390496i | 0.740971 | − | 0.390496i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.12498 | − | 0.111975i | −1.12498 | − | 0.111975i | −0.480787 | − | 0.876837i | \(-0.659649\pi\) |
−0.644194 | + | 0.764862i | \(0.722807\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.413289 | + | 0.173195i | 0.413289 | + | 0.173195i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.08285 | + | 3.60091i | −1.08285 | + | 3.60091i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.0684610 | − | 0.728528i | 0.0684610 | − | 0.728528i | ||||
\(719\) | 0 | 0 | 0.627176 | − | 0.778877i | \(-0.284211\pi\) | ||||
−0.627176 | + | 0.778877i | \(0.715789\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.60967 | + | 0.592579i | −1.60967 | + | 0.592579i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.13240 | − | 0.347346i | 1.13240 | − | 0.347346i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.601081 | − | 0.799188i | \(-0.294737\pi\) | ||||
−0.601081 | + | 0.799188i | \(0.705263\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.213300 | + | 0.976987i | −0.213300 | + | 0.976987i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.999453 | − | 0.0330634i | \(-0.989474\pi\) | ||||
0.999453 | + | 0.0330634i | \(0.0105263\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.00194892 | 0.000842096i | −0.00194892 | 0.000842096i | ||||||
\(737\) | −0.619565 | − | 1.29435i | −0.619565 | − | 1.29435i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.160745 | + | 1.26125i | −0.160745 | + | 1.26125i | 0.685350 | + | 0.728214i | \(0.259649\pi\) |
−0.846095 | + | 0.533032i | \(0.821053\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.153022 | + | 3.08233i | 0.153022 | + | 3.08233i | ||||
\(743\) | 0.646869 | − | 1.85098i | 0.646869 | − | 1.85098i | 0.137354 | − | 0.990522i | \(-0.456140\pi\) |
0.509516 | − | 0.860461i | \(-0.329825\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.00156290 | − | 0.0566992i | 0.00156290 | − | 0.0566992i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.25062 | + | 0.0966923i | 1.25062 | + | 0.0966923i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.45872 | − | 1.32807i | 1.45872 | − | 1.32807i | 0.618553 | − | 0.785743i | \(-0.287719\pi\) |
0.840168 | − | 0.542326i | \(-0.182456\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.647019 | − | 0.657806i | −0.647019 | − | 0.657806i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.956036 | + | 0.293250i | \(0.905263\pi\) | |||||||
\(758\) | −0.142913 | + | 2.87870i | −0.142913 | + | 2.87870i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.731980 | − | 0.681326i | \(-0.761404\pi\) | ||||
0.731980 | + | 0.681326i | \(0.238596\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.274784 | − | 1.70451i | 0.274784 | − | 1.70451i | ||||
\(764\) | −2.16410 | − | 0.963518i | −2.16410 | − | 0.963518i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 0.137354 | − | 0.990522i | \(-0.456140\pi\) | ||||
−0.137354 | + | 0.990522i | \(0.543860\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.74149 | − | 0.752271i | −3.74149 | − | 0.752271i | ||||
\(773\) | 0 | 0 | −0.202517 | − | 0.979279i | \(-0.564912\pi\) | ||||
0.202517 | + | 0.979279i | \(0.435088\pi\) | |||||||
\(774\) | −2.58924 | − | 1.47593i | −2.58924 | − | 1.47593i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.77207 | + | 1.66216i | −2.77207 | + | 1.66216i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.388783 | − | 0.0961762i | 0.388783 | − | 0.0961762i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.324969 | − | 0.763629i | 0.324969 | − | 0.763629i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.846095 | − | 0.533032i | \(-0.821053\pi\) | ||||
0.846095 | + | 0.533032i | \(0.178947\pi\) | |||||||
\(788\) | −0.628545 | − | 2.17690i | −0.628545 | − | 2.17690i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.149749 | + | 0.203741i | 0.149749 | + | 0.203741i | ||||
\(792\) | −0.0963401 | − | 1.16265i | −0.0963401 | − | 1.16265i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.371197 | − | 0.928554i | \(-0.621053\pi\) | ||||
0.371197 | + | 0.928554i | \(0.378947\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.0306537 | + | 0.190147i | 0.0306537 | + | 0.190147i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.606492 | + | 0.825162i | −0.606492 | + | 0.825162i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.597333 | + | 0.871695i | 0.597333 | + | 0.871695i | 0.999028 | − | 0.0440782i | \(-0.0140351\pi\) |
−0.401695 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(812\) | 2.19932 | + | 0.674611i | 2.19932 | + | 0.674611i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.56377 | − | 1.08429i | 1.56377 | − | 1.08429i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.30593 | − | 0.416378i | 1.30593 | − | 0.416378i | 0.431754 | − | 0.901991i | \(-0.357895\pi\) |
0.874174 | + | 0.485613i | \(0.161404\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.413707 | − | 0.735159i | −0.413707 | − | 0.735159i | 0.583317 | − | 0.812244i | \(-0.301754\pi\) |
−0.997024 | + | 0.0770854i | \(0.975439\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.523538 | − | 0.635697i | 0.523538 | − | 0.635697i | −0.441671 | − | 0.897177i | \(-0.645614\pi\) |
0.965209 | + | 0.261480i | \(0.0842105\pi\) | |||||||
\(828\) | −0.0155091 | + | 0.0147583i | −0.0155091 | + | 0.0147583i | ||||
\(829\) | 0 | 0 | −0.298515 | − | 0.954405i | \(-0.596491\pi\) | ||||
0.298515 | + | 0.954405i | \(0.403509\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.746821 | − | 0.665025i | \(-0.768421\pi\) | ||||
0.746821 | + | 0.665025i | \(0.231579\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.0772537 | + | 0.395496i | −0.0772537 | + | 0.395496i | ||||
\(842\) | 0.113688 | + | 0.174012i | 0.113688 | + | 0.174012i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.52289 | + | 2.77738i | −1.52289 | + | 2.77738i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.478862 | − | 0.00527877i | 0.478862 | − | 0.00527877i | ||||
\(848\) | 0.0246877 | + | 1.49295i | 0.0246877 | + | 1.49295i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.0162493 | − | 0.00478892i | −0.0162493 | − | 0.00478892i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.968033 | − | 0.250825i | \(-0.0807018\pi\) | ||||
−0.968033 | + | 0.250825i | \(0.919298\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.01487 | + | 0.223006i | 2.01487 | + | 0.223006i | ||||
\(857\) | 0 | 0 | −0.993931 | − | 0.110008i | \(-0.964912\pi\) | ||||
0.993931 | + | 0.110008i | \(0.0350877\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.461341 | − | 0.887223i | \(-0.652632\pi\) | ||||
0.461341 | + | 0.887223i | \(0.347368\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.38794 | + | 0.409047i | 1.38794 | + | 0.409047i | ||||
\(863\) | −0.631370 | − | 0.0982163i | −0.631370 | − | 0.0982163i | −0.170028 | − | 0.985439i | \(-0.554386\pi\) |
−0.461341 | + | 0.887223i | \(0.652632\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.155526 | − | 0.283641i | 0.155526 | − | 0.283641i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.534919 | − | 2.73848i | 0.534919 | − | 2.73848i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.33609 | − | 0.222954i | 1.33609 | − | 0.222954i | 0.546948 | − | 0.837166i | \(-0.315789\pi\) |
0.789141 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.815447 | − | 0.578832i | \(-0.196491\pi\) | ||||
−0.815447 | + | 0.578832i | \(0.803509\pi\) | |||||||
\(882\) | 1.18926 | + | 1.23606i | 1.18926 | + | 1.23606i | ||||
\(883\) | −0.996763 | + | 1.68332i | −0.996763 | + | 1.68332i | −0.319482 | + | 0.947592i | \(0.603509\pi\) |
−0.677282 | + | 0.735724i | \(0.736842\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.17758 | − | 2.64409i | 2.17758 | − | 2.64409i | ||||
\(887\) | 0 | 0 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.836202 | − | 1.79755i | −0.836202 | − | 1.79755i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.685308 | + | 0.226853i | 0.685308 | + | 0.226853i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.758193 | + | 1.62986i | −0.758193 | + | 1.62986i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.526786 | − | 2.29136i | −0.526786 | − | 2.29136i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.88535 | + | 0.466394i | 1.88535 | + | 0.466394i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.230992 | + | 0.337089i | 0.230992 | + | 0.337089i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.0318202 | − | 1.92427i | 0.0318202 | − | 1.92427i | −0.256156 | − | 0.966635i | \(-0.582456\pi\) |
0.287976 | − | 0.957638i | \(-0.407018\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.252647 | − | 0.343739i | 0.252647 | − | 0.343739i | −0.660898 | − | 0.750475i | \(-0.729825\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.587479 | − | 1.12980i | 0.587479 | − | 1.12980i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.78251 | − | 0.157599i | 1.78251 | − | 0.157599i | 0.851919 | − | 0.523673i | \(-0.175439\pi\) |
0.930586 | + | 0.366074i | \(0.119298\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.426313 | + | 1.47649i | 0.426313 | + | 1.47649i | ||||
\(926\) | 2.08052 | + | 1.31071i | 2.08052 | + | 1.31071i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.215770 | − | 0.0740740i | −0.215770 | − | 0.0740740i | ||||
\(929\) | 0 | 0 | 0.391577 | − | 0.920146i | \(-0.371930\pi\) | ||||
−0.391577 | + | 0.920146i | \(0.628070\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.73160 | + | 0.675736i | −2.73160 | + | 0.675736i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.761300 | − | 0.648400i | \(-0.775439\pi\) | ||||
0.761300 | + | 0.648400i | \(0.224561\pi\) | |||||||
\(938\) | 3.03382 | + | 1.55636i | 3.03382 | + | 1.55636i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.980380 | − | 0.197117i | \(-0.936842\pi\) | ||||
0.980380 | + | 0.197117i | \(0.0631579\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.25498 | + | 1.74751i | −1.25498 | + | 1.74751i | ||||
\(947\) | 0.850011 | + | 0.240360i | 0.850011 | + | 0.240360i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.180881 | + | 0.983505i | \(0.442105\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.0475729 | + | 0.0278170i | 0.0475729 | + | 0.0278170i | 0.528360 | − | 0.849020i | \(-0.322807\pi\) |
−0.480787 | + | 0.876837i | \(0.659649\pi\) | |||||||
\(954\) | −2.85928 | − | 1.16134i | −2.85928 | − | 1.16134i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.955089 | + | 0.971013i | 0.955089 | + | 0.971013i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.21958 | − | 1.29586i | −1.21958 | − | 1.29586i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.986361 | − | 0.164595i | −0.986361 | − | 0.164595i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.615164 | + | 1.09315i | −0.615164 | + | 1.09315i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.00576043 | + | 0.208978i | −0.00576043 | + | 0.208978i | 0.991264 | + | 0.131892i | \(0.0421053\pi\) |
−0.997024 | + | 0.0770854i | \(0.975439\pi\) | |||||||
\(968\) | 0.773754 | + | 0.0170611i | 0.773754 | + | 0.0170611i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.0495838 | − | 0.998770i | \(-0.515789\pi\) | ||||
0.0495838 | + | 0.998770i | \(0.484211\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.249095 | + | 1.95446i | −0.249095 | + | 1.95446i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.37112 | − | 0.592442i | −1.37112 | − | 0.592442i | −0.421786 | − | 0.906696i | \(-0.638596\pi\) |
−0.949339 | + | 0.314254i | \(0.898246\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.42957 | + | 0.968082i | 1.42957 | + | 0.968082i | ||||
\(982\) | −2.63846 | − | 1.20974i | −2.63846 | − | 1.20974i | ||||
\(983\) | 0 | 0 | −0.319482 | − | 0.947592i | \(-0.603509\pi\) | ||||
0.319482 | + | 0.947592i | \(0.396491\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.0191239 | − | 0.00105510i | 0.0191239 | − | 0.00105510i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.847465 | − | 0.311983i | 0.847465 | − | 0.311983i | 0.115485 | − | 0.993309i | \(-0.463158\pi\) |
0.731980 | + | 0.681326i | \(0.238596\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.596851 | + | 0.741217i | −0.596851 | + | 0.741217i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.287976 | − | 0.957638i | \(-0.407018\pi\) | ||||
−0.287976 | + | 0.957638i | \(0.592982\pi\) | |||||||
\(998\) | −0.877966 | − | 2.26848i | −0.877966 | − | 2.26848i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3997.1.cz.a.342.1 | ✓ | 144 | |
7.6 | odd | 2 | CM | 3997.1.cz.a.342.1 | ✓ | 144 | |
571.379 | even | 285 | inner | 3997.1.cz.a.2092.1 | yes | 144 | |
3997.2092 | odd | 570 | inner | 3997.1.cz.a.2092.1 | yes | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3997.1.cz.a.342.1 | ✓ | 144 | 1.1 | even | 1 | trivial | |
3997.1.cz.a.342.1 | ✓ | 144 | 7.6 | odd | 2 | CM | |
3997.1.cz.a.2092.1 | yes | 144 | 571.379 | even | 285 | inner | |
3997.1.cz.a.2092.1 | yes | 144 | 3997.2092 | odd | 570 | inner |