Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,3,Mod(321,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.321");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.k (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(50.1363686423\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 64 x^{14} - 16 x^{13} + 2252 x^{12} + 648 x^{11} - 30106 x^{10} + 12360 x^{9} + \cdots + 1535848276 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 460) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 321.5 | ||
Root | \(2.47022 - 2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.321 |
Dual form | 1840.3.k.c.321.6 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −2.47022 | −0.823406 | −0.411703 | − | 0.911318i | \(-0.635066\pi\) | ||||
−0.411703 | + | 0.911318i | \(0.635066\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.25674i | 1.17953i | 0.807573 | + | 0.589767i | \(0.200781\pi\) | ||||
−0.807573 | + | 0.589767i | \(0.799219\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.89803 | −0.322003 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.596769i | 0.0542517i | 0.999632 | + | 0.0271258i | \(0.00863548\pi\) | ||||
−0.999632 | + | 0.0271258i | \(0.991365\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.219868 | −0.0169129 | −0.00845647 | − | 0.999964i | \(-0.502692\pi\) | ||||
−0.00845647 | + | 0.999964i | \(0.502692\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.52357i | 0.368238i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 25.0471i | − | 1.47336i | −0.676243 | − | 0.736679i | \(-0.736393\pi\) | ||
0.676243 | − | 0.736679i | \(-0.263607\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.81284i | − | 0.0954126i | −0.998861 | − | 0.0477063i | \(-0.984809\pi\) | ||
0.998861 | − | 0.0477063i | \(-0.0151912\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 20.3959i | − | 0.971236i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 22.4752 | + | 4.88514i | 0.977183 | + | 0.212397i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 29.3907 | 1.08854 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.88636 | −0.0650469 | −0.0325235 | − | 0.999471i | \(-0.510354\pi\) | ||||
−0.0325235 | + | 0.999471i | \(0.510354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −18.8533 | −0.608171 | −0.304086 | − | 0.952645i | \(-0.598351\pi\) | ||||
−0.304086 | + | 0.952645i | \(0.598351\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.47415i | − | 0.0446711i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 18.4626 | 0.527504 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 19.4877i | − | 0.526696i | −0.964701 | − | 0.263348i | \(-0.915173\pi\) | ||
0.964701 | − | 0.263348i | \(-0.0848267\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.543122 | 0.0139262 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 33.6825 | 0.821524 | 0.410762 | − | 0.911743i | \(-0.365263\pi\) | ||||
0.410762 | + | 0.911743i | \(0.365263\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19.3697i | 0.450458i | 0.974306 | + | 0.225229i | \(0.0723130\pi\) | ||||
−0.974306 | + | 0.225229i | \(0.927687\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.48019i | 0.144004i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −74.0247 | −1.57499 | −0.787497 | − | 0.616319i | \(-0.788623\pi\) | ||||
−0.787497 | + | 0.616319i | \(0.788623\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −19.1738 | −0.391303 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 61.8717i | 1.21317i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 18.1176i | − | 0.341841i | −0.985285 | − | 0.170920i | \(-0.945326\pi\) | ||
0.985285 | − | 0.170920i | \(-0.0546741\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.33441 | 0.0242621 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.47811i | 0.0785633i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 27.5793 | 0.467445 | 0.233723 | − | 0.972303i | \(-0.424909\pi\) | ||||
0.233723 | + | 0.972303i | \(0.424909\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 37.6457i | 0.617143i | 0.951201 | + | 0.308571i | \(0.0998508\pi\) | ||||
−0.951201 | + | 0.308571i | \(0.900149\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 23.9283i | − | 0.379814i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.491641i | 0.00756370i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.5802i | 0.232541i | 0.993218 | + | 0.116271i | \(0.0370940\pi\) | ||||
−0.993218 | + | 0.116271i | \(0.962906\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −55.5187 | − | 12.0674i | −0.804618 | − | 0.174889i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −49.8789 | −0.702519 | −0.351260 | − | 0.936278i | \(-0.614247\pi\) | ||||
−0.351260 | + | 0.936278i | \(0.614247\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.8538 | −0.189777 | −0.0948887 | − | 0.995488i | \(-0.530250\pi\) | ||||
−0.0948887 | + | 0.995488i | \(0.530250\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.3511 | 0.164681 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.92737 | −0.0639918 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 46.8236i | 0.592704i | 0.955079 | + | 0.296352i | \(0.0957701\pi\) | ||||
−0.955079 | + | 0.296352i | \(0.904230\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −46.5192 | −0.574311 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.5849i | 0.139577i | 0.997562 | + | 0.0697884i | \(0.0222324\pi\) | ||||
−0.997562 | + | 0.0697884i | \(0.977768\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −56.0070 | −0.658906 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.65972 | 0.0535600 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 32.4824i | − | 0.364970i | −0.983209 | − | 0.182485i | \(-0.941586\pi\) | ||
0.983209 | − | 0.182485i | \(-0.0584142\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.81540i | − | 0.0199494i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 46.5718 | 0.500772 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.05363 | −0.0426698 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 101.474i | 1.04612i | 0.852295 | + | 0.523062i | \(0.175210\pi\) | ||||
−0.852295 | + | 0.523062i | \(0.824790\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.72945i | − | 0.0174692i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 122.925 | 1.21708 | 0.608539 | − | 0.793524i | \(-0.291756\pi\) | ||||
0.608539 | + | 0.793524i | \(0.291756\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 26.7742i | − | 0.259944i | −0.991518 | − | 0.129972i | \(-0.958511\pi\) | ||
0.991518 | − | 0.129972i | \(-0.0414887\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −45.6067 | −0.434350 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 100.317i | 0.937544i | 0.883319 | + | 0.468772i | \(0.155303\pi\) | ||||
−0.883319 | + | 0.468772i | \(0.844697\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 148.064i | 1.35838i | 0.733961 | + | 0.679192i | \(0.237670\pi\) | ||||
−0.733961 | + | 0.679192i | \(0.762330\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 48.1389i | 0.433684i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 72.5714i | − | 0.642225i | −0.947041 | − | 0.321112i | \(-0.895943\pi\) | ||
0.947041 | − | 0.321112i | \(-0.104057\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.9235 | − | 50.2561i | 0.0949870 | − | 0.437010i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.637185 | 0.00544602 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 206.807 | 1.73788 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 120.644 | 0.997057 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −83.2031 | −0.676448 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −188.604 | −1.48507 | −0.742536 | − | 0.669806i | \(-0.766377\pi\) | ||||
−0.742536 | + | 0.669806i | \(0.766377\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 47.8473i | − | 0.370909i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 157.588 | 1.20297 | 0.601483 | − | 0.798886i | \(-0.294577\pi\) | ||||
0.601483 | + | 0.798886i | \(0.294577\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.9682 | 0.112543 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 65.7196i | − | 0.486812i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 241.444i | 1.76237i | 0.472774 | + | 0.881184i | \(0.343253\pi\) | ||||
−0.472774 | + | 0.881184i | \(0.656747\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 77.6599 | 0.558704 | 0.279352 | − | 0.960189i | \(-0.409880\pi\) | ||||
0.279352 | + | 0.960189i | \(0.409880\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 182.857 | 1.29686 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.131211i | − | 0.000917556i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.21803i | 0.0290899i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 47.3635 | 0.322201 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 111.378i | 0.747505i | 0.927529 | + | 0.373752i | \(0.121929\pi\) | ||||
−0.927529 | + | 0.373752i | \(0.878071\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.7575 | −0.0778641 | −0.0389321 | − | 0.999242i | \(-0.512396\pi\) | ||||
−0.0389321 | + | 0.999242i | \(0.512396\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 72.5872i | 0.474426i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 42.1573i | 0.271982i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 186.009i | 1.18477i | 0.805654 | + | 0.592386i | \(0.201814\pi\) | ||||
−0.805654 | + | 0.592386i | \(0.798186\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 44.7543i | 0.281474i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −40.3353 | + | 185.572i | −0.250530 | + | 1.15262i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −188.029 | −1.15355 | −0.576775 | − | 0.816903i | \(-0.695689\pi\) | ||||
−0.576775 | + | 0.816903i | \(0.695689\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.29629 | −0.0199775 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.0962 | −0.126325 | −0.0631624 | − | 0.998003i | \(-0.520119\pi\) | ||||
−0.0631624 | + | 0.998003i | \(0.520119\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −168.952 | −0.999714 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.25366i | 0.0307232i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 244.057 | 1.41073 | 0.705366 | − | 0.708843i | \(-0.250783\pi\) | ||||
0.705366 | + | 0.708843i | \(0.250783\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 41.2837i | − | 0.235907i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −68.1268 | −0.384897 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 204.186 | 1.14070 | 0.570351 | − | 0.821401i | \(-0.306807\pi\) | ||||
0.570351 | + | 0.821401i | \(0.306807\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 224.135i | 1.23832i | 0.785267 | + | 0.619158i | \(0.212526\pi\) | ||||
−0.785267 | + | 0.619158i | \(0.787474\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 92.9930i | − | 0.508159i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −43.5759 | −0.235545 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.9473 | 0.0799322 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 242.672i | 1.28398i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 117.560i | 0.615497i | 0.951468 | + | 0.307749i | \(0.0995756\pi\) | ||||
−0.951468 | + | 0.307749i | \(0.900424\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 204.891 | 1.06161 | 0.530806 | − | 0.847493i | \(-0.321889\pi\) | ||||
0.530806 | + | 0.847493i | \(0.321889\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 1.21446i | − | 0.00622799i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −125.626 | −0.637698 | −0.318849 | − | 0.947806i | \(-0.603296\pi\) | ||||
−0.318849 | + | 0.947806i | \(0.603296\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 119.866i | − | 0.602344i | −0.953570 | − | 0.301172i | \(-0.902622\pi\) | ||
0.953570 | − | 0.301172i | \(-0.0973778\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 38.4866i | − | 0.191476i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 15.5752i | − | 0.0767251i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 75.3163i | − | 0.367397i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −65.1338 | − | 14.1573i | −0.314656 | − | 0.0683926i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.08185 | 0.00517629 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −60.5329 | −0.286886 | −0.143443 | − | 0.989659i | \(-0.545817\pi\) | ||||
−0.143443 | + | 0.989659i | \(0.545817\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 123.212 | 0.578458 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 43.3119 | 0.201451 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 155.667i | − | 0.717359i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 34.2218 | 0.156264 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.50706i | 0.0249188i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −44.2442 | −0.198405 | −0.0992024 | − | 0.995067i | \(-0.531629\pi\) | ||||
−0.0992024 | + | 0.995067i | \(0.531629\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.4901 | 0.0644006 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 436.822i | 1.92432i | 0.272478 | + | 0.962162i | \(0.412157\pi\) | ||||
−0.272478 | + | 0.962162i | \(0.587843\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 165.166i | 0.721247i | 0.932712 | + | 0.360623i | \(0.117436\pi\) | ||||
−0.932712 | + | 0.360623i | \(0.882564\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.1717 | 0.0526912 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 220.867 | 0.947928 | 0.473964 | − | 0.880544i | \(-0.342823\pi\) | ||||
0.473964 | + | 0.880544i | \(0.342823\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 165.524i | 0.704359i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 115.664i | − | 0.488035i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 150.110 | 0.628076 | 0.314038 | − | 0.949410i | \(-0.398318\pi\) | ||||
0.314038 | + | 0.949410i | \(0.398318\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 264.391i | 1.09706i | 0.836132 | + | 0.548529i | \(0.184812\pi\) | ||||
−0.836132 | + | 0.548529i | \(0.815188\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −149.604 | −0.615654 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 42.8740i | 0.174996i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.398586i | 0.00161371i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 28.6171i | − | 0.114928i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 418.511i | 1.66737i | 0.552237 | + | 0.833687i | \(0.313774\pi\) | ||||
−0.552237 | + | 0.833687i | \(0.686226\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.91530 | + | 13.4125i | −0.0115229 | + | 0.0530138i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 138.349 | 0.542547 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −203.107 | −0.790300 | −0.395150 | − | 0.918617i | \(-0.629307\pi\) | ||||
−0.395150 | + | 0.918617i | \(0.629307\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 160.905 | 0.621256 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.46673 | 0.0209453 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 182.612i | 0.694344i | 0.937801 | + | 0.347172i | \(0.112858\pi\) | ||||
−0.937801 | + | 0.347172i | \(0.887142\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −40.5121 | −0.152876 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 80.2385i | 0.300519i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −92.2556 | −0.342958 | −0.171479 | − | 0.985188i | \(-0.554855\pi\) | ||||
−0.171479 | + | 0.985188i | \(0.554855\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 167.824 | 0.619277 | 0.309639 | − | 0.950854i | \(-0.399792\pi\) | ||||
0.309639 | + | 0.950854i | \(0.399792\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.48442i | 0.0164265i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2.98384i | − | 0.0108503i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −130.608 | −0.471510 | −0.235755 | − | 0.971812i | \(-0.575756\pi\) | ||||
−0.235755 | + | 0.971812i | \(0.575756\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 54.6374 | 0.195833 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 465.802i | − | 1.65766i | −0.559501 | − | 0.828830i | \(-0.689007\pi\) | ||
0.559501 | − | 0.828830i | \(-0.310993\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 400.983i | 1.41690i | 0.705760 | + | 0.708451i | \(0.250606\pi\) | ||||
−0.705760 | + | 0.708451i | \(0.749394\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.0134 | 0.0351346 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 278.108i | 0.969016i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −338.357 | −1.17078 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 250.663i | − | 0.861384i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 33.3297i | 0.113753i | 0.998381 | + | 0.0568767i | \(0.0181142\pi\) | ||||
−0.998381 | + | 0.0568767i | \(0.981886\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 61.6691i | − | 0.209048i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.5395i | 0.0590554i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.94159 | − | 1.07409i | −0.0165271 | − | 0.00359227i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −159.931 | −0.531331 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −303.651 | −1.00215 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 84.1783 | 0.275995 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −408.916 | −1.33197 | −0.665987 | − | 0.745963i | \(-0.731990\pi\) | ||||
−0.665987 | + | 0.745963i | \(0.731990\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 66.1381i | 0.214039i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −78.9088 | −0.253726 | −0.126863 | − | 0.991920i | \(-0.540491\pi\) | ||||
−0.126863 | + | 0.991920i | \(0.540491\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 421.949i | − | 1.34808i | −0.738695 | − | 0.674040i | \(-0.764558\pi\) | ||
0.738695 | − | 0.674040i | \(-0.235442\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −53.5053 | −0.169858 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.40226 | 0.00757810 | 0.00378905 | − | 0.999993i | \(-0.498794\pi\) | ||||
0.00378905 | + | 0.999993i | \(0.498794\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.12572i | − | 0.00352891i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 247.805i | − | 0.771979i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −45.4064 | −0.140577 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.09934 | 0.00338259 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 365.750i | − | 1.11850i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 611.203i | − | 1.85776i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 369.886 | 1.11748 | 0.558739 | − | 0.829343i | \(-0.311285\pi\) | ||||
0.558739 | + | 0.829343i | \(0.311285\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 56.4760i | 0.169598i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 34.8385 | 0.103996 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 91.2849i | − | 0.270875i | −0.990786 | − | 0.135438i | \(-0.956756\pi\) | ||
0.990786 | − | 0.135438i | \(-0.0432440\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 179.267i | 0.528812i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 11.2511i | − | 0.0329943i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 246.267i | 0.717980i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −26.9834 | + | 124.143i | −0.0782128 | + | 0.359836i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −357.398 | −1.02996 | −0.514982 | − | 0.857201i | \(-0.672202\pi\) | ||||
−0.514982 | + | 0.857201i | \(0.672202\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −158.842 | −0.455135 | −0.227568 | − | 0.973762i | \(-0.573077\pi\) | ||||
−0.227568 | + | 0.973762i | \(0.573077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.46209 | −0.0184105 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 125.964 | 0.356837 | 0.178419 | − | 0.983955i | \(-0.442902\pi\) | ||||
0.178419 | + | 0.983955i | \(0.442902\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 111.533i | 0.314176i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −510.859 | −1.43098 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 409.017i | 1.13932i | 0.821879 | + | 0.569662i | \(0.192926\pi\) | ||||
−0.821879 | + | 0.569662i | \(0.807074\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 357.714 | 0.990896 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −298.017 | −0.820982 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.9779i | 0.0848710i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 686.483i | − | 1.87053i | −0.353955 | − | 0.935263i | \(-0.615163\pi\) | ||
0.353955 | − | 0.935263i | \(-0.384837\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −97.6128 | −0.264533 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 149.592 | 0.403213 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 492.015i | 1.31907i | 0.751672 | + | 0.659537i | \(0.229248\pi\) | ||||
−0.751672 | + | 0.659537i | \(0.770752\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 27.6179i | − | 0.0736476i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.414751 | 0.00110014 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.63529i | − | 0.00431474i | −0.999998 | − | 0.00215737i | \(-0.999313\pi\) | ||
0.999998 | − | 0.00215737i | \(-0.000686713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 465.893 | 1.22282 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 223.309i | 0.583051i | 0.956563 | + | 0.291526i | \(0.0941628\pi\) | ||||
−0.956563 | + | 0.291526i | \(0.905837\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.0179i | 0.0286180i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 56.1339i | − | 0.145049i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 296.882i | − | 0.763192i | −0.924329 | − | 0.381596i | \(-0.875375\pi\) | ||
0.924329 | − | 0.381596i | \(-0.124625\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 122.359 | − | 562.939i | 0.312937 | − | 1.43974i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −389.278 | −0.990529 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 104.701 | 0.265065 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.3096 | −0.0687899 | −0.0343950 | − | 0.999408i | \(-0.510950\pi\) | ||||
−0.0343950 | + | 0.999408i | \(0.510950\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −36.9746 | −0.0926681 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 622.315i | − | 1.55191i | −0.630789 | − | 0.775954i | \(-0.717269\pi\) | ||
0.630789 | − | 0.775954i | \(-0.282731\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.14525 | 0.0102860 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 104.020i | 0.256840i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.6297 | 0.0285741 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 679.902 | 1.66235 | 0.831175 | − | 0.556010i | \(-0.187668\pi\) | ||||
0.831175 | + | 0.556010i | \(0.187668\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 596.420i | − | 1.45114i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 227.715i | 0.551368i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.9046 | 0.0624206 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −191.837 | −0.460040 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 538.609i | − | 1.28546i | −0.766092 | − | 0.642731i | \(-0.777801\pi\) | ||
0.766092 | − | 0.642731i | \(-0.222199\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 298.554i | − | 0.709154i | −0.935027 | − | 0.354577i | \(-0.884625\pi\) | ||
0.935027 | − | 0.354577i | \(-0.115375\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 214.526 | 0.507153 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 125.235i | 0.294672i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −310.831 | −0.727941 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.324118i | 0.000755521i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 271.961i | 0.630999i | 0.948926 | + | 0.315499i | \(0.102172\pi\) | ||||
−0.948926 | + | 0.315499i | \(0.897828\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 50.1785i | − | 0.115886i | −0.998320 | − | 0.0579428i | \(-0.981546\pi\) | ||
0.998320 | − | 0.0579428i | \(-0.0184541\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 10.4195i | − | 0.0239528i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.85597 | − | 40.7440i | 0.0202654 | − | 0.0932356i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 572.063 | 1.30310 | 0.651552 | − | 0.758604i | \(-0.274118\pi\) | ||||
0.651552 | + | 0.758604i | \(0.274118\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 55.5663 | 0.126001 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 436.287 | 0.984848 | 0.492424 | − | 0.870356i | \(-0.336111\pi\) | ||||
0.492424 | + | 0.870356i | \(0.336111\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −72.6328 | −0.163220 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 275.128i | − | 0.615499i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −391.151 | −0.871161 | −0.435581 | − | 0.900150i | \(-0.643457\pi\) | ||||
−0.435581 | + | 0.900150i | \(0.643457\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.1006i | 0.0445691i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 29.0435 | 0.0641138 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.05935 | −0.00892165 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 148.735i | − | 0.325460i | −0.986671 | − | 0.162730i | \(-0.947970\pi\) | ||
0.986671 | − | 0.162730i | \(-0.0520299\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 736.152i | − | 1.60382i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 463.228 | 1.00483 | 0.502416 | − | 0.864626i | \(-0.332444\pi\) | ||||
0.502416 | + | 0.864626i | \(0.332444\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 710.802 | 1.53521 | 0.767605 | − | 0.640923i | \(-0.221448\pi\) | ||||
0.767605 | + | 0.640923i | \(0.221448\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 104.138i | − | 0.223952i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 286.551i | 0.613600i | 0.951774 | + | 0.306800i | \(0.0992582\pi\) | ||||
−0.951774 | + | 0.306800i | \(0.900742\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −128.642 | −0.274290 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 459.483i | − | 0.975549i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.5592 | −0.0244381 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.06420i | 0.0190825i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 52.5052i | 0.110074i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.6682i | 0.0327102i | 0.999866 | + | 0.0163551i | \(0.00520623\pi\) | ||||
−0.999866 | + | 0.0163551i | \(0.994794\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.28474i | 0.00890798i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 99.6371 | − | 458.403i | 0.206288 | − | 0.949075i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 226.903 | 0.467841 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −845.442 | −1.73602 | −0.868010 | − | 0.496546i | \(-0.834601\pi\) | ||||
−0.868010 | + | 0.496546i | \(0.834601\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 464.471 | 0.949839 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.3768 | −0.0455739 | −0.0227870 | − | 0.999740i | \(-0.507254\pi\) | ||||
−0.0227870 | + | 0.999740i | \(0.507254\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 47.2478i | 0.0958374i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.86717 | −0.00781247 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 411.837i | − | 0.828646i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −624.639 | −1.25178 | −0.625891 | − | 0.779911i | \(-0.715264\pi\) | ||||
−0.625891 | + | 0.779911i | \(0.715264\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 52.1123 | 0.104017 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 221.993i | − | 0.441338i | −0.975349 | − | 0.220669i | \(-0.929176\pi\) | ||
0.975349 | − | 0.220669i | \(-0.0708240\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 274.869i | − | 0.544294i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 417.347 | 0.823170 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 122.910 | 0.241473 | 0.120737 | − | 0.992685i | \(-0.461474\pi\) | ||||
0.120737 | + | 0.992685i | \(0.461474\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 114.387i | − | 0.223849i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 53.2806i | − | 0.103861i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −59.8690 | −0.116250 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 44.1756i | − | 0.0854461i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −602.873 | −1.16160 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 370.245i | − | 0.710643i | −0.934744 | − | 0.355321i | \(-0.884371\pi\) | ||
0.934744 | − | 0.355321i | \(-0.115629\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 149.485i | 0.285823i | 0.989735 | + | 0.142912i | \(0.0456464\pi\) | ||||
−0.989735 | + | 0.142912i | \(0.954354\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 101.980i | 0.194247i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 472.221i | 0.896054i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 481.271 | + | 219.589i | 0.909775 | + | 0.415102i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −79.9255 | −0.150519 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.40571 | −0.0138944 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 224.316 | 0.419283 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −504.383 | −0.939261 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 11.4423i | − | 0.0212288i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 222.304 | 0.410913 | 0.205456 | − | 0.978666i | \(-0.434132\pi\) | ||||
0.205456 | + | 0.978666i | \(0.434132\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 553.662i | − | 1.01964i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 331.081 | 0.607488 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −289.014 | −0.528362 | −0.264181 | − | 0.964473i | \(-0.585102\pi\) | ||||
−0.264181 | + | 0.964473i | \(0.585102\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 109.098i | − | 0.198722i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.41967i | 0.00620630i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −386.610 | −0.699115 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 107.642 | 0.193949 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 976.361i | 1.75289i | 0.481500 | + | 0.876446i | \(0.340092\pi\) | ||||
−0.481500 | + | 0.876446i | \(0.659908\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.25878i | − | 0.00761857i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −36.9231 | −0.0658166 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 203.128i | − | 0.360797i | −0.983594 | − | 0.180398i | \(-0.942261\pi\) | ||
0.983594 | − | 0.180398i | \(-0.0577387\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −162.275 | −0.287212 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 384.097i | − | 0.677420i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 54.0125i | 0.0949254i | 0.998873 | + | 0.0474627i | \(0.0151135\pi\) | ||||
−0.998873 | + | 0.0474627i | \(0.984886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 782.388i | − | 1.37021i | −0.728446 | − | 0.685103i | \(-0.759757\pi\) | ||
0.728446 | − | 0.685103i | \(-0.240243\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 290.399i | − | 0.506804i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −112.376 | − | 24.4257i | −0.195437 | − | 0.0424795i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −161.020 | −0.279064 | −0.139532 | − | 0.990218i | \(-0.544560\pi\) | ||||
−0.139532 | + | 0.990218i | \(0.544560\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −506.126 | −0.874137 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −95.6533 | −0.164636 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.8120 | 0.0185454 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 1.42479i | − | 0.00243554i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 340.427 | 0.579943 | 0.289972 | − | 0.957035i | \(-0.406354\pi\) | ||||
0.289972 | + | 0.957035i | \(0.406354\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 34.1780i | 0.0580272i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 310.325 | 0.525084 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −823.560 | −1.38880 | −0.694401 | − | 0.719588i | \(-0.744331\pi\) | ||||
−0.694401 | + | 0.719588i | \(0.744331\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 462.435i | − | 0.777202i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 296.096i | 0.495973i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −487.521 | −0.813892 | −0.406946 | − | 0.913452i | \(-0.633406\pi\) | ||||
−0.406946 | + | 0.913452i | \(0.633406\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −600.376 | −0.998962 | −0.499481 | − | 0.866325i | \(-0.666476\pi\) | ||||
−0.499481 | + | 0.866325i | \(0.666476\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 45.1520i | − | 0.0748790i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 269.768i | − | 0.445897i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −440.562 | −0.725802 | −0.362901 | − | 0.931828i | \(-0.618214\pi\) | ||||
−0.362901 | + | 0.931828i | \(0.618214\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 38.4741i | 0.0631759i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.2757 | 0.0266378 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 552.134i | 0.900708i | 0.892850 | + | 0.450354i | \(0.148702\pi\) | ||||
−0.892850 | + | 0.450354i | \(0.851298\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 186.048i | 0.302517i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 824.577i | − | 1.33643i | −0.743968 | − | 0.668215i | \(-0.767059\pi\) | ||
0.743968 | − | 0.668215i | \(-0.232941\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 87.5843i | 0.141493i | 0.997494 | + | 0.0707466i | \(0.0225382\pi\) | ||||
−0.997494 | + | 0.0707466i | \(0.977462\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 660.563 | + | 143.578i | 1.06371 | + | 0.231204i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 268.199 | 0.430495 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.67239 | −0.00426219 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −488.111 | −0.776011 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 73.4341i | − | 0.116377i | −0.998306 | − | 0.0581887i | \(-0.981468\pi\) | ||
0.998306 | − | 0.0581887i | \(-0.0185325\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 149.529 | 0.236223 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 421.732i | 0.664145i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.21572 | 0.00661808 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 144.550 | 0.226213 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1027.28i | 1.60262i | 0.598252 | + | 0.801308i | \(0.295862\pi\) | ||||
−0.598252 | + | 0.801308i | \(0.704138\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 860.413i | − | 1.33812i | −0.743207 | − | 0.669062i | \(-0.766696\pi\) | ||
0.743207 | − | 0.669062i | \(-0.233304\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −106.990 | −0.165876 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −349.194 | −0.539713 | −0.269856 | − | 0.962901i | \(-0.586976\pi\) | ||||
−0.269856 | + | 0.962901i | \(0.586976\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.4584i | 0.0253597i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 384.531i | 0.590678i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −515.430 | −0.789326 | −0.394663 | − | 0.918826i | \(-0.629139\pi\) | ||||
−0.394663 | + | 0.918826i | \(0.629139\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 352.379i | − | 0.537983i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 40.1486 | 0.0611089 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 81.1143i | − | 0.123087i | −0.998104 | − | 0.0615435i | \(-0.980398\pi\) | ||
0.998104 | − | 0.0615435i | \(-0.0196023\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 213.989i | − | 0.323735i | −0.986812 | − | 0.161868i | \(-0.948248\pi\) | ||
0.986812 | − | 0.161868i | \(-0.0517518\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 13.6036i | − | 0.0205183i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 33.4698i | − | 0.0503305i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −42.3964 | − | 9.21514i | −0.0635628 | − | 0.0138158i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 109.293 | 0.163368 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.4658 | −0.0334810 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −573.388 | −0.851988 | −0.425994 | − | 0.904726i | \(-0.640076\pi\) | ||||
−0.425994 | + | 0.904726i | \(0.640076\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −146.954 | −0.217709 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 798.023i | 1.17876i | 0.807855 | + | 0.589382i | \(0.200629\pi\) | ||||
−0.807855 | + | 0.589382i | \(0.799371\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −837.845 | −1.23394 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 1079.04i | − | 1.58450i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 808.667 | 1.18399 | 0.591997 | − | 0.805940i | \(-0.298340\pi\) | ||||
0.591997 | + | 0.805940i | \(0.298340\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 539.886 | 0.788155 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 407.995i | − | 0.593879i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.98348i | 0.00578154i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1127.48 | 1.63167 | 0.815834 | − | 0.578286i | \(-0.196278\pi\) | ||||
0.815834 | + | 0.578286i | \(0.196278\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.2796 | 0.0206056 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 173.653i | − | 0.249860i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 843.648i | − | 1.21040i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −545.590 | −0.780529 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1055.92i | 1.50631i | 0.657845 | + | 0.753153i | \(0.271468\pi\) | ||||
−0.657845 | + | 0.753153i | \(0.728532\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −35.3281 | −0.0502534 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 408.881i | − | 0.579973i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1014.96i | 1.43559i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.7402i | 0.0560510i | 0.999607 | + | 0.0280255i | \(0.00892196\pi\) | ||||
−0.999607 | + | 0.0280255i | \(0.991078\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 135.696i | − | 0.190852i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −423.732 | − | 92.1011i | −0.594295 | − | 0.129174i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.293396 | −0.000410344 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −370.805 | −0.517161 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1158.15 | −1.61078 | −0.805389 | − | 0.592746i | \(-0.798044\pi\) | ||||
−0.805389 | + | 0.592746i | \(0.798044\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 221.068 | 0.306613 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 653.103i | − | 0.903324i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.43180 | 0.0130094 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 180.994i | 0.248960i | 0.992222 | + | 0.124480i | \(0.0397262\pi\) | ||||
−0.992222 | + | 0.124480i | \(0.960274\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 788.227 | 1.08124 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 485.154 | 0.663686 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 334.983i | 0.457003i | 0.973544 | + | 0.228501i | \(0.0733825\pi\) | ||||
−0.973544 | + | 0.228501i | \(0.926617\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 105.908i | − | 0.144093i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.29780 | −0.0126157 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −959.742 | −1.29870 | −0.649352 | − | 0.760488i | \(-0.724960\pi\) | ||||
−0.649352 | + | 0.760488i | \(0.724960\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 0.984594i | − | 0.00132874i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 705.966i | 0.950156i | 0.879944 | + | 0.475078i | \(0.157580\pi\) | ||||
−0.879944 | + | 0.475078i | \(0.842420\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 249.049 | 0.334294 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 33.5733i | − | 0.0449442i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −828.294 | −1.10587 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1480.59i | 1.97149i | 0.168241 | + | 0.985746i | \(0.446191\pi\) | ||||
−0.168241 | + | 0.985746i | \(0.553809\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1033.81i | − | 1.37293i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.2905i | 0.0348219i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 911.552i | − | 1.20416i | −0.798434 | − | 0.602082i | \(-0.794338\pi\) | ||
0.798434 | − | 0.602082i | \(-0.205662\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.20142 | − | 33.1318i | 0.00948803 | − | 0.0436519i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1129.29 | 1.48396 | 0.741979 | − | 0.670423i | \(-0.233887\pi\) | ||||
0.741979 | + | 0.670423i | \(0.233887\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1222.53 | −1.60226 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 162.310 | 0.212170 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.06381 | −0.00790588 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 264.516i | 0.343974i | 0.985099 | + | 0.171987i | \(0.0550187\pi\) | ||||
−0.985099 | + | 0.171987i | \(0.944981\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 501.718 | 0.650737 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1379.04i | − | 1.78401i | −0.452027 | − | 0.892004i | \(-0.649299\pi\) | ||
0.452027 | − | 0.892004i | \(-0.350701\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 94.2666 | 0.121634 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −397.471 | −0.511546 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 61.0609i | − | 0.0783838i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 29.7661i | − | 0.0381128i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −55.4415 | −0.0708065 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 415.929 | 0.529846 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1080.69i | − | 1.37318i | −0.727045 | − | 0.686590i | \(-0.759107\pi\) | ||
0.727045 | − | 0.686590i | \(-0.240893\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 451.092i | − | 0.571727i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 599.204 | 0.757527 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 8.27710i | − | 0.0104377i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 100.074 | 0.125879 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 673.128i | 0.844577i | 0.906462 | + | 0.422288i | \(0.138773\pi\) | ||||
−0.906462 | + | 0.422288i | \(0.861227\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1854.10i | 2.32053i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 94.1349i | 0.117522i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 8.26748i | − | 0.0102957i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 414.952 | + | 90.1926i | 0.515468 | + | 0.112040i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 227.891 | 0.282393 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −662.758 | −0.819231 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1286.90 | 1.58681 | 0.793405 | − | 0.608694i | \(-0.208306\pi\) | ||||
0.793405 | + | 0.608694i | \(0.208306\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −414.562 | −0.509916 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 420.445i | 0.515883i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.1141 | 0.0429793 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.26107i | 0.00642378i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −90.1269 | −0.109777 | −0.0548885 | − | 0.998492i | \(-0.517480\pi\) | ||||
−0.0548885 | + | 0.998492i | \(0.517480\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1014.08 | 1.23218 | 0.616088 | − | 0.787677i | \(-0.288717\pi\) | ||||
0.616088 | + | 0.787677i | \(0.288717\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.37074i | 0.00893423i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 310.832i | − | 0.375855i | −0.982183 | − | 0.187928i | \(-0.939823\pi\) | ||
0.982183 | − | 0.187928i | \(-0.0601770\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 804.117 | 0.969985 | 0.484992 | − | 0.874518i | \(-0.338822\pi\) | ||||
0.484992 | + | 0.874518i | \(0.338822\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 322.631 | 0.388244 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 480.249i | 0.576529i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 47.1726i | 0.0564942i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −554.112 | −0.662022 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1075.82i | 1.28227i | 0.767430 | + | 0.641133i | \(0.221535\pi\) | ||||
−0.767430 | + | 0.641133i | \(0.778465\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −837.442 | −0.995769 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1150.63i | 1.36493i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 377.787i | 0.447086i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 996.126i | 1.17606i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 990.515i | − | 1.16668i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 95.2003 | − | 437.991i | 0.111869 | − | 0.514678i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −127.475 | −0.149443 | −0.0747214 | − | 0.997204i | \(-0.523807\pi\) | ||||
−0.0747214 | + | 0.997204i | \(0.523807\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.7475 | 0.0137398 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −618.354 | −0.721533 | −0.360767 | − | 0.932656i | \(-0.617485\pi\) | ||||
−0.360767 | + | 0.932656i | \(0.617485\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 745.538 | 0.867914 | 0.433957 | − | 0.900934i | \(-0.357117\pi\) | ||||
0.433957 | + | 0.900934i | \(0.357117\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 686.986i | − | 0.797894i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −64.5791 | −0.0748310 | −0.0374155 | − | 0.999300i | \(-0.511912\pi\) | ||||
−0.0374155 | + | 0.999300i | \(0.511912\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 545.727i | − | 0.630899i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 835.814 | 0.964030 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.9428 | −0.0321552 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 3.42560i | − | 0.00393295i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 294.075i | − | 0.336855i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −92.3132 | −0.105501 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 601.465 | 0.685821 | 0.342910 | − | 0.939368i | \(-0.388587\pi\) | ||||
0.342910 | + | 0.939368i | \(0.388587\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 82.3317i | − | 0.0936652i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 863.232i | − | 0.979832i | −0.871770 | − | 0.489916i | \(-0.837027\pi\) | ||
0.871770 | − | 0.489916i | \(-0.162973\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −933.043 | −1.05667 | −0.528337 | − | 0.849035i | \(-0.677184\pi\) | ||||
−0.528337 | + | 0.849035i | \(0.677184\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 152.336i | 0.172131i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 55.1069 | 0.0621273 | 0.0310637 | − | 0.999517i | \(-0.490111\pi\) | ||||
0.0310637 | + | 0.999517i | \(0.490111\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1557.26i | − | 1.75169i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 27.7612i | − | 0.0311573i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 134.195i | 0.150274i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 456.573i | − | 0.510138i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.2068 | + | 2.65323i | 0.0136085 | + | 0.00295789i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.5642 | 0.0395597 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −453.792 | −0.503654 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 395.063 | 0.437501 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 501.181 | 0.553791 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1046.63i | − | 1.15395i | −0.816763 | − | 0.576974i | \(-0.804234\pi\) | ||
0.816763 | − | 0.576974i | \(-0.195766\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −356.240 | −0.391903 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 842.705i | 0.925033i | 0.886611 | + | 0.462516i | \(0.153053\pi\) | ||||
−0.886611 | + | 0.462516i | \(0.846947\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.91349 | −0.00757228 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −207.939 | −0.227255 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1301.17i | 1.41894i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 981.227i | − | 1.06771i | −0.845576 | − | 0.533856i | \(-0.820743\pi\) | ||
0.845576 | − | 0.533856i | \(-0.179257\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1010.11 | 1.09676 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.9668 | 0.0118817 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 97.4387i | 0.105339i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 77.5925i | 0.0837028i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 745.480 | 0.802454 | 0.401227 | − | 0.915979i | \(-0.368584\pi\) | ||||
0.401227 | + | 0.915979i | \(0.368584\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.7591i | 0.0373352i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 194.922 | 0.208920 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 33.4232i | − | 0.0357467i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 847.258i | − | 0.904224i | −0.891961 | − | 0.452112i | \(-0.850671\pi\) | ||
0.891961 | − | 0.452112i | \(-0.149329\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1042.31i | 1.11002i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1395.97i | 1.48349i | 0.670681 | + | 0.741746i | \(0.266002\pi\) | ||||
−0.670681 | + | 0.741746i | \(0.733998\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 757.021 | + | 164.544i | 0.802780 | + | 0.174490i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 542.630 | 0.574212 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54.4962 | 0.0575461 | 0.0287730 | − | 0.999586i | \(-0.490840\pi\) | ||||
0.0287730 | + | 0.999586i | \(0.490840\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.04600 | 0.00320970 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.93409 | −0.00623985 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 126.158i | − | 0.132380i | −0.997807 | − | 0.0661901i | \(-0.978916\pi\) | ||
0.997807 | − | 0.0661901i | \(-0.0210844\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 262.872 | 0.275259 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.78077i | 0.00290572i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1993.54 | −2.07877 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −605.553 | −0.630128 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 290.722i | − | 0.301892i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 458.151i | − | 0.474767i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −462.481 | −0.478263 | −0.239132 | − | 0.970987i | \(-0.576863\pi\) | ||||
−0.239132 | + | 0.970987i | \(0.576863\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 112.164 | 0.115752 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 737.368i | − | 0.759390i | −0.925112 | − | 0.379695i | \(-0.876029\pi\) | ||
0.925112 | − | 0.379695i | \(-0.123971\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 641.218i | 0.659011i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.71561 | −0.00278524 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 915.226i | 0.936771i | 0.883524 | + | 0.468386i | \(0.155164\pi\) | ||||
−0.883524 | + | 0.468386i | \(0.844836\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.3845 | 0.0198003 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 429.093i | − | 0.437404i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 674.233i | 0.685893i | 0.939355 | + | 0.342946i | \(0.111425\pi\) | ||||
−0.939355 | + | 0.342946i | \(0.888575\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 280.909i | 0.285187i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1509.80i | 1.52969i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −94.6236 | + | 435.338i | −0.0956760 | + | 0.440180i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 970.677 | 0.979493 | 0.489746 | − | 0.871865i | \(-0.337089\pi\) | ||||
0.489746 | + | 0.871865i | \(0.337089\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −913.697 | −0.920138 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −268.029 | −0.269376 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 653.389 | 0.655355 | 0.327678 | − | 0.944790i | \(-0.393734\pi\) | ||||
0.327678 | + | 0.944790i | \(0.393734\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 572.758i | − | 0.573332i |
(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 | 1840.3.k.c.321.5 | 16 | ||
4.3 | odd | 2 | 460.3.f.a.321.11 | ✓ | 16 | ||
12.11 | even | 2 | 4140.3.d.a.2161.9 | 16 | |||
20.3 | even | 4 | 2300.3.d.b.1149.6 | 32 | |||
20.7 | even | 4 | 2300.3.d.b.1149.27 | 32 | |||
20.19 | odd | 2 | 2300.3.f.e.1701.6 | 16 | |||
23.22 | odd | 2 | inner | 1840.3.k.c.321.6 | 16 | ||
92.91 | even | 2 | 460.3.f.a.321.12 | yes | 16 | ||
276.275 | odd | 2 | 4140.3.d.a.2161.8 | 16 | |||
460.183 | odd | 4 | 2300.3.d.b.1149.28 | 32 | |||
460.367 | odd | 4 | 2300.3.d.b.1149.5 | 32 | |||
460.459 | even | 2 | 2300.3.f.e.1701.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.3.f.a.321.11 | ✓ | 16 | 4.3 | odd | 2 | ||
460.3.f.a.321.12 | yes | 16 | 92.91 | even | 2 | ||
1840.3.k.c.321.5 | 16 | 1.1 | even | 1 | trivial | ||
1840.3.k.c.321.6 | 16 | 23.22 | odd | 2 | inner | ||
2300.3.d.b.1149.5 | 32 | 460.367 | odd | 4 | |||
2300.3.d.b.1149.6 | 32 | 20.3 | even | 4 | |||
2300.3.d.b.1149.27 | 32 | 20.7 | even | 4 | |||
2300.3.d.b.1149.28 | 32 | 460.183 | odd | 4 | |||
2300.3.f.e.1701.5 | 16 | 460.459 | even | 2 | |||
2300.3.f.e.1701.6 | 16 | 20.19 | odd | 2 | |||
4140.3.d.a.2161.8 | 16 | 276.275 | odd | 2 | |||
4140.3.d.a.2161.9 | 16 | 12.11 | even | 2 |