Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [480,3,Mod(161,480)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(480, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("480.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 480 = 2^{5} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 480.l (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.0790526893\) |
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: | \( x^{16} - 8 x^{15} + 88 x^{14} - 476 x^{13} + 2434 x^{12} - 8780 x^{11} + 25532 x^{10} - 57568 x^{9} + \cdots + 486 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.7 | ||
Root | \(0.500000 - 0.0650247i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 480.161 |
Dual form | 480.3.l.a.161.8 |
$q$-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 \(\left(\mathbb{Z}/480\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(421\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −0.460323 | − | 2.96447i | −0.153441 | − | 0.988158i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.9698 | 1.56712 | 0.783559 | − | 0.621318i | \(-0.213402\pi\) | ||||
0.783559 | + | 0.621318i | \(0.213402\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.57621 | + | 2.72923i | −0.952912 | + | 0.303248i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.78654i | 0.162412i | 0.996697 | + | 0.0812062i | \(0.0258772\pi\) | ||||
−0.996697 | + | 0.0812062i | \(0.974123\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 22.4485 | 1.72681 | 0.863406 | − | 0.504510i | \(-0.168327\pi\) | ||||
0.863406 | + | 0.504510i | \(0.168327\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.62876 | + | 1.02931i | −0.441918 | + | 0.0686209i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 15.5788i | − | 0.916402i | −0.888849 | − | 0.458201i | \(-0.848494\pi\) | ||
0.888849 | − | 0.458201i | \(-0.151506\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.3809 | 1.38847 | 0.694233 | − | 0.719750i | \(-0.255744\pi\) | ||||
0.694233 | + | 0.719750i | \(0.255744\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.04966 | − | 32.5197i | −0.240460 | − | 1.54856i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 30.1861i | 1.31244i | 0.754570 | + | 0.656220i | \(0.227846\pi\) | ||||
−0.754570 | + | 0.656220i | \(0.772154\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12.0386 | + | 24.1676i | 0.445873 | + | 0.895096i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 44.8246i | − | 1.54567i | −0.634604 | − | 0.772837i | \(-0.718837\pi\) | ||
0.634604 | − | 0.772837i | \(-0.281163\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −51.3786 | −1.65738 | −0.828688 | − | 0.559711i | \(-0.810912\pi\) | ||||
−0.828688 | + | 0.559711i | \(0.810912\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.29614 | − | 0.822384i | 0.160489 | − | 0.0249207i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 24.5293i | − | 0.700836i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −36.3424 | −0.982226 | −0.491113 | − | 0.871096i | \(-0.663410\pi\) | ||||
−0.491113 | + | 0.871096i | \(0.663410\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.3336 | − | 66.5481i | −0.264964 | − | 1.70636i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.93212i | 0.193466i | 0.995310 | + | 0.0967332i | \(0.0308393\pi\) | ||||
−0.995310 | + | 0.0967332i | \(0.969161\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 26.4872 | 0.615982 | 0.307991 | − | 0.951389i | \(-0.400343\pi\) | ||||
0.307991 | + | 0.951389i | \(0.400343\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.10275 | + | 19.1770i | 0.135617 | + | 0.426155i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 31.2242i | − | 0.664344i | −0.943219 | − | 0.332172i | \(-0.892219\pi\) | ||
0.943219 | − | 0.332172i | \(-0.107781\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 71.3370 | 1.45586 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −46.1830 | + | 7.17130i | −0.905550 | + | 0.140614i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 90.5039i | − | 1.70762i | −0.520585 | − | 0.853810i | \(-0.674286\pi\) | ||
0.520585 | − | 0.853810i | \(-0.325714\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.99481 | 0.0726330 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.1437 | − | 78.2054i | −0.213048 | − | 1.37202i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 17.8064i | − | 0.301803i | −0.988549 | − | 0.150902i | \(-0.951782\pi\) | ||
0.988549 | − | 0.150902i | \(-0.0482177\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.6132 | −0.190381 | −0.0951903 | − | 0.995459i | \(-0.530346\pi\) | ||||
−0.0951903 | + | 0.995459i | \(0.530346\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −94.0794 | + | 29.9392i | −1.49332 | + | 0.475225i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 50.1965i | − | 0.772253i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 32.3116 | 0.482262 | 0.241131 | − | 0.970493i | \(-0.422482\pi\) | ||||
0.241131 | + | 0.970493i | \(0.422482\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 89.4859 | − | 13.8954i | 1.29690 | − | 0.201382i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 34.1717i | 0.481292i | 0.970613 | + | 0.240646i | \(0.0773593\pi\) | ||||
−0.970613 | + | 0.240646i | \(0.922641\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −68.9145 | −0.944034 | −0.472017 | − | 0.881590i | \(-0.656474\pi\) | ||||
−0.472017 | + | 0.881590i | \(0.656474\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.30162 | + | 14.8224i | 0.0306882 | + | 0.197632i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 19.5980i | 0.254519i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 29.5267 | 0.373756 | 0.186878 | − | 0.982383i | \(-0.440163\pi\) | ||||
0.186878 | + | 0.982383i | \(0.440163\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 66.1026 | − | 46.8129i | 0.816081 | − | 0.577937i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 76.1626i | 0.917622i | 0.888534 | + | 0.458811i | \(0.151725\pi\) | ||||
−0.888534 | + | 0.458811i | \(0.848275\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −34.8353 | −0.409827 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −132.881 | + | 20.6338i | −1.52737 | + | 0.237170i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 112.955i | 1.26915i | 0.772860 | + | 0.634577i | \(0.218826\pi\) | ||||
−0.772860 | + | 0.634577i | \(0.781174\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 246.257 | 2.70612 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 23.6508 | + | 152.311i | 0.254309 | + | 1.63775i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 58.9894i | − | 0.620941i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −79.5471 | −0.820073 | −0.410037 | − | 0.912069i | \(-0.634484\pi\) | ||||
−0.410037 | + | 0.912069i | \(0.634484\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.87587 | − | 15.3217i | −0.0492512 | − | 0.154765i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 59.3021i | 0.587150i | 0.955936 | + | 0.293575i | \(0.0948450\pi\) | ||||
−0.955936 | + | 0.293575i | \(0.905155\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.9969 | 0.194144 | 0.0970721 | − | 0.995277i | \(-0.469052\pi\) | ||||
0.0970721 | + | 0.995277i | \(0.469052\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −72.7164 | + | 11.2914i | −0.692537 | + | 0.107537i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 39.2253i | 0.366591i | 0.983058 | + | 0.183296i | \(0.0586766\pi\) | ||||
−0.983058 | + | 0.183296i | \(0.941323\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.15707 | 0.0564869 | 0.0282434 | − | 0.999601i | \(-0.491009\pi\) | ||||
0.0282434 | + | 0.999601i | \(0.491009\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.7292 | + | 107.736i | 0.150714 | + | 0.970595i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 88.1167i | − | 0.779794i | −0.920859 | − | 0.389897i | \(-0.872511\pi\) | ||
0.920859 | − | 0.389897i | \(-0.127489\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 67.4982 | 0.586941 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −192.523 | + | 61.2673i | −1.64550 | + | 0.523652i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 170.897i | − | 1.43611i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 117.808 | 0.973622 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 23.5146 | − | 3.65134i | 0.191175 | − | 0.0296857i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.62127 | −0.0363880 | −0.0181940 | − | 0.999834i | \(-0.505792\pi\) | ||||
−0.0181940 | + | 0.999834i | \(0.505792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.1927 | − | 78.5207i | −0.0945170 | − | 0.608688i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 78.8114i | − | 0.601613i | −0.953685 | − | 0.300807i | \(-0.902744\pi\) | ||
0.953685 | − | 0.300807i | \(-0.0972559\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 289.393 | 2.17589 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 54.0404 | − | 26.9190i | 0.400299 | − | 0.199400i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 127.646i | 0.931721i | 0.884858 | + | 0.465861i | \(0.154255\pi\) | ||||
−0.884858 | + | 0.465861i | \(0.845745\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 74.4324 | 0.535485 | 0.267742 | − | 0.963491i | \(-0.413722\pi\) | ||||
0.267742 | + | 0.963491i | \(0.413722\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −92.5632 | + | 14.3732i | −0.656477 | + | 0.101938i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 40.1051i | 0.280455i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −100.231 | −0.691247 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −32.8381 | − | 211.477i | −0.223388 | − | 1.43862i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 120.249i | 0.807038i | 0.914971 | + | 0.403519i | \(0.132213\pi\) | ||||
−0.914971 | + | 0.403519i | \(0.867787\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.1093 | 0.100062 | 0.0500310 | − | 0.998748i | \(-0.484068\pi\) | ||||
0.0500310 | + | 0.998748i | \(0.484068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 42.5182 | + | 133.607i | 0.277897 | + | 0.873250i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 114.886i | 0.741201i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −265.567 | −1.69151 | −0.845754 | − | 0.533573i | \(-0.820849\pi\) | ||||
−0.845754 | + | 0.533573i | \(0.820849\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −268.296 | + | 41.6610i | −1.68740 | + | 0.262019i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 331.136i | 2.05675i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.5655 | 0.150709 | 0.0753544 | − | 0.997157i | \(-0.475991\pi\) | ||||
0.0753544 | + | 0.997157i | \(0.475991\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.83891 | − | 11.8425i | −0.0111449 | − | 0.0717729i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 258.690i | 1.54904i | 0.632549 | + | 0.774520i | \(0.282009\pi\) | ||||
−0.632549 | + | 0.774520i | \(0.717991\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 334.937 | 1.98188 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −226.248 | + | 71.9995i | −1.32309 | + | 0.421050i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 172.804i | 0.998866i | 0.866353 | + | 0.499433i | \(0.166458\pi\) | ||||
−0.866353 | + | 0.499433i | \(0.833542\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −54.8491 | −0.313423 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −52.7866 | + | 8.19670i | −0.298229 | + | 0.0463090i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 274.427i | 1.53311i | 0.642177 | + | 0.766556i | \(0.278031\pi\) | ||||
−0.642177 | + | 0.766556i | \(0.721969\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −136.602 | −0.754710 | −0.377355 | − | 0.926069i | \(-0.623166\pi\) | ||||
−0.377355 | + | 0.926069i | \(0.623166\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.34584 | + | 34.4271i | 0.0292122 | + | 0.188126i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 81.2640i | 0.439265i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.8321 | 0.148835 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 132.061 | + | 265.114i | 0.698735 | + | 1.40272i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 201.748i | − | 1.05627i | −0.849160 | − | 0.528135i | \(-0.822891\pi\) | ||
0.849160 | − | 0.528135i | \(-0.177109\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −29.5623 | −0.153173 | −0.0765863 | − | 0.997063i | \(-0.524402\pi\) | ||||
−0.0765863 | + | 0.997063i | \(0.524402\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −148.806 | + | 23.1066i | −0.763108 | + | 0.118495i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 287.440i | − | 1.45908i | −0.683936 | − | 0.729542i | \(-0.739733\pi\) | ||
0.683936 | − | 0.729542i | \(-0.260267\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 201.363 | 1.01187 | 0.505937 | − | 0.862571i | \(-0.331147\pi\) | ||||
0.505937 | + | 0.862571i | \(0.331147\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.8738 | − | 95.7868i | −0.0739988 | − | 0.476551i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 491.717i | − | 2.42225i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.7368 | 0.0865208 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −82.3849 | − | 258.882i | −0.397995 | − | 1.25064i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 47.1304i | 0.225504i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −126.205 | −0.598128 | −0.299064 | − | 0.954233i | \(-0.596674\pi\) | ||||
−0.299064 | + | 0.954233i | \(0.596674\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 101.301 | − | 15.7300i | 0.475593 | − | 0.0738500i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 59.2273i | − | 0.275476i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −563.614 | −2.59730 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 31.7229 | + | 204.295i | 0.144854 | + | 0.932854i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 349.722i | − | 1.58245i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.22218 | −0.0234178 | −0.0117089 | − | 0.999931i | \(-0.503727\pi\) | ||||
−0.0117089 | + | 0.999931i | \(0.503727\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 42.8810 | − | 13.6462i | 0.190582 | − | 0.0606496i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 170.760i | 0.752248i | 0.926569 | + | 0.376124i | \(0.122743\pi\) | ||||
−0.926569 | + | 0.376124i | \(0.877257\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 352.033 | 1.53726 | 0.768630 | − | 0.639694i | \(-0.220939\pi\) | ||||
0.768630 | + | 0.639694i | \(0.220939\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 58.0977 | − | 9.02140i | 0.251505 | − | 0.0390537i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 266.708i | 1.14467i | 0.820021 | + | 0.572334i | \(0.193962\pi\) | ||||
−0.820021 | + | 0.572334i | \(0.806038\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −69.8194 | −0.297104 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.5918 | − | 87.5311i | −0.0573495 | − | 0.369330i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6.98824i | − | 0.0292395i | −0.999893 | − | 0.0146197i | \(-0.995346\pi\) | ||
0.999893 | − | 0.0146197i | \(-0.00465378\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.2449 | −0.0466593 | −0.0233296 | − | 0.999728i | \(-0.507427\pi\) | ||||
−0.0233296 | + | 0.999728i | \(0.507427\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −169.204 | − | 174.410i | −0.696313 | − | 0.717738i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 159.514i | − | 0.651079i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 592.212 | 2.39762 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 225.782 | − | 35.0594i | 0.906756 | − | 0.140801i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 278.539i | − | 1.10972i | −0.831945 | − | 0.554858i | \(-0.812772\pi\) | ||
0.831945 | − | 0.554858i | \(-0.187228\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −53.9286 | −0.213156 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.0355 | + | 103.268i | 0.0628843 | + | 0.404974i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 296.546i | 1.15388i | 0.816788 | + | 0.576938i | \(0.195753\pi\) | ||||
−0.816788 | + | 0.576938i | \(0.804247\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −398.669 | −1.53926 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 122.337 | + | 384.425i | 0.468723 | + | 1.47289i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 393.054i | 1.49450i | 0.664543 | + | 0.747250i | \(0.268626\pi\) | ||||
−0.664543 | + | 0.747250i | \(0.731374\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −202.373 | −0.763671 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 334.851 | − | 51.9956i | 1.25412 | − | 0.194740i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 235.224i | − | 0.874437i | −0.899355 | − | 0.437219i | \(-0.855964\pi\) | ||
0.899355 | − | 0.437219i | \(-0.144036\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −203.239 | −0.749958 | −0.374979 | − | 0.927033i | \(-0.622350\pi\) | ||||
−0.374979 | + | 0.927033i | \(0.622350\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −113.358 | − | 730.021i | −0.415229 | − | 2.67407i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 8.93268i | − | 0.0324825i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −214.698 | −0.775082 | −0.387541 | − | 0.921852i | \(-0.626675\pi\) | ||||
−0.387541 | + | 0.921852i | \(0.626675\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 440.634 | − | 140.224i | 1.57933 | − | 0.502596i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 343.205i | − | 1.22137i | −0.791874 | − | 0.610685i | \(-0.790894\pi\) | ||
0.791874 | − | 0.610685i | \(-0.209106\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 402.851 | 1.42350 | 0.711751 | − | 0.702432i | \(-0.247903\pi\) | ||||
0.711751 | + | 0.702432i | \(0.247903\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −174.873 | + | 27.1542i | −0.613588 | + | 0.0952779i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 87.0139i | 0.303184i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 46.3000 | 0.160208 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 36.6174 | + | 235.815i | 0.125833 | + | 0.810362i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 121.592i | − | 0.414989i | −0.978236 | − | 0.207494i | \(-0.933469\pi\) | ||
0.978236 | − | 0.207494i | \(-0.0665309\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −39.8163 | −0.134971 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −43.1763 | + | 21.5073i | −0.145375 | + | 0.0724152i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 677.634i | 2.26634i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 290.560 | 0.965316 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 175.800 | − | 27.2981i | 0.580196 | − | 0.0900929i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 25.9680i | 0.0851408i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −551.075 | −1.79503 | −0.897517 | − | 0.440980i | \(-0.854631\pi\) | ||||
−0.897517 | + | 0.440980i | \(0.854631\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.20502 | − | 59.2802i | −0.0297897 | − | 0.191845i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 30.9019i | − | 0.0993631i | −0.998765 | − | 0.0496816i | \(-0.984179\pi\) | ||
0.998765 | − | 0.0496816i | \(-0.0158206\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 471.595 | 1.50669 | 0.753346 | − | 0.657624i | \(-0.228438\pi\) | ||||
0.753346 | + | 0.657624i | \(0.228438\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 66.9460 | + | 210.368i | 0.212527 | + | 0.667835i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 399.347i | − | 1.25977i | −0.776689 | − | 0.629885i | \(-0.783102\pi\) | ||
0.776689 | − | 0.629885i | \(-0.216898\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 80.0807 | 0.251037 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 116.282 | − | 18.0563i | 0.362250 | − | 0.0562502i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 410.983i | − | 1.27239i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −112.243 | −0.345362 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.83424 | − | 18.2525i | −0.00866741 | − | 0.0558179i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 342.524i | − | 1.04111i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −43.3950 | −0.131103 | −0.0655514 | − | 0.997849i | \(-0.520881\pi\) | ||||
−0.0655514 | + | 0.997849i | \(0.520881\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 311.680 | − | 99.1868i | 0.935975 | − | 0.297858i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 72.2509i | − | 0.215674i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 233.859 | 0.693945 | 0.346972 | − | 0.937875i | \(-0.387210\pi\) | ||||
0.346972 | + | 0.937875i | \(0.387210\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −261.220 | + | 40.5621i | −0.770559 | + | 0.119652i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 91.7898i | − | 0.269178i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 245.032 | 0.714380 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −31.0710 | − | 200.097i | −0.0900608 | − | 0.579990i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 200.902i | − | 0.578969i | −0.957183 | − | 0.289485i | \(-0.906516\pi\) | ||
0.957183 | − | 0.289485i | \(-0.0934839\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −106.570 | −0.305358 | −0.152679 | − | 0.988276i | \(-0.548790\pi\) | ||||
−0.152679 | + | 0.988276i | \(0.548790\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 270.248 | + | 542.528i | 0.769938 | + | 1.54566i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 269.597i | 0.763732i | 0.924218 | + | 0.381866i | \(0.124718\pi\) | ||||
−0.924218 | + | 0.381866i | \(0.875282\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 76.4104 | 0.215240 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −506.620 | + | 78.6678i | −1.41910 | + | 0.220358i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.2384i | 0.0870150i | 0.999053 | + | 0.0435075i | \(0.0138532\pi\) | ||||
−0.999053 | + | 0.0435075i | \(0.986147\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 334.950 | 0.927840 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −54.2299 | − | 349.240i | −0.149394 | − | 0.962092i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 154.097i | 0.422185i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −502.908 | −1.37032 | −0.685160 | − | 0.728392i | \(-0.740268\pi\) | ||||
−0.685160 | + | 0.728392i | \(0.740268\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −21.6486 | − | 68.0275i | −0.0586683 | − | 0.184356i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 992.811i | − | 2.67604i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −347.493 | −0.931617 | −0.465808 | − | 0.884886i | \(-0.654236\pi\) | ||||
−0.465808 | + | 0.884886i | \(0.654236\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 33.1438 | − | 5.14657i | 0.0883835 | − | 0.0137242i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1006.25i | − | 2.66909i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −262.136 | −0.691652 | −0.345826 | − | 0.938299i | \(-0.612401\pi\) | ||||
−0.345826 | + | 0.938299i | \(0.612401\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.12728 | + | 13.6996i | 0.00558341 | + | 0.0359570i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 75.5290i | 0.197204i | 0.995127 | + | 0.0986018i | \(0.0314370\pi\) | ||||
−0.995127 | + | 0.0986018i | \(0.968563\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 43.8224 | 0.113824 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −227.160 | + | 72.2898i | −0.586977 | + | 0.186795i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 76.1862i | 0.195852i | 0.995194 | + | 0.0979258i | \(0.0312208\pi\) | ||||
−0.995194 | + | 0.0979258i | \(0.968779\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 470.264 | 1.20272 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −233.634 | + | 36.2787i | −0.594489 | + | 0.0923122i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 66.0237i | − | 0.167149i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 516.613 | 1.30129 | 0.650647 | − | 0.759381i | \(-0.274498\pi\) | ||||
0.650647 | + | 0.759381i | \(0.274498\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −133.214 | − | 857.899i | −0.333871 | − | 2.15012i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 113.732i | − | 0.283621i | −0.989894 | − | 0.141810i | \(-0.954708\pi\) | ||
0.989894 | − | 0.141810i | \(-0.0452923\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1153.38 | −2.86197 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −104.677 | − | 147.810i | −0.258461 | − | 0.364963i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 64.9269i | − | 0.159526i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 101.838 | 0.248994 | 0.124497 | − | 0.992220i | \(-0.460268\pi\) | ||||
0.124497 | + | 0.992220i | \(0.460268\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 378.403 | − | 58.7583i | 0.920688 | − | 0.142964i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 195.333i | − | 0.472961i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 170.305 | 0.410373 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −34.2629 | − | 220.653i | −0.0821653 | − | 0.529143i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 391.559i | 0.934507i | 0.884123 | + | 0.467254i | \(0.154757\pi\) | ||||
−0.884123 | + | 0.467254i | \(0.845243\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −342.755 | −0.814145 | −0.407073 | − | 0.913396i | \(-0.633450\pi\) | ||||
−0.407073 | + | 0.913396i | \(0.633450\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 85.2180 | + | 267.785i | 0.201461 | + | 0.633061i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 77.8942i | 0.183280i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −127.395 | −0.298349 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 118.891 | − | 18.4613i | 0.277134 | − | 0.0430334i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 367.168i | 0.851898i | 0.904747 | + | 0.425949i | \(0.140060\pi\) | ||||
−0.904747 | + | 0.425949i | \(0.859940\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 367.630 | 0.849029 | 0.424515 | − | 0.905421i | \(-0.360445\pi\) | ||||
0.424515 | + | 0.905421i | \(0.360445\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 46.1386 | + | 297.131i | 0.106066 | + | 0.683061i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 796.336i | 1.82228i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −492.913 | −1.12281 | −0.561404 | − | 0.827542i | \(-0.689739\pi\) | ||||
−0.561404 | + | 0.827542i | \(0.689739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −611.800 | + | 194.695i | −1.38730 | + | 0.441485i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 733.159i | 1.65499i | 0.561476 | + | 0.827493i | \(0.310234\pi\) | ||||
−0.561476 | + | 0.827493i | \(0.689766\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 252.574 | 0.567583 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 356.474 | − | 55.3532i | 0.797481 | − | 0.123833i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 704.511i | 1.56907i | 0.620087 | + | 0.784533i | \(0.287097\pi\) | ||||
−0.620087 | + | 0.784533i | \(0.712903\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.1710 | −0.0314213 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.95518 | − | 44.7913i | −0.0153536 | − | 0.0988770i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 550.646i | − | 1.21021i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −755.476 | −1.65312 | −0.826560 | − | 0.562848i | \(-0.809705\pi\) | ||||
−0.826560 | + | 0.562848i | \(0.809705\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 376.503 | − | 187.547i | 0.820268 | − | 0.408598i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 243.102i | − | 0.527335i | −0.964614 | − | 0.263668i | \(-0.915068\pi\) | ||
0.964614 | − | 0.263668i | \(-0.0849322\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −733.057 | −1.58328 | −0.791638 | − | 0.610990i | \(-0.790771\pi\) | ||||
−0.791638 | + | 0.610990i | \(0.790771\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 340.577 | − | 52.8847i | 0.732423 | − | 0.113731i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 580.434i | 1.24290i | 0.783454 | + | 0.621450i | \(0.213456\pi\) | ||||
−0.783454 | + | 0.621450i | \(0.786544\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 354.452 | 0.755761 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 122.246 | + | 787.265i | 0.259547 | + | 1.67148i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 47.3204i | 0.100043i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −131.904 | −0.277693 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 247.006 | + | 776.180i | 0.517832 | + | 1.62721i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 866.763i | − | 1.80953i | −0.425915 | − | 0.904763i | \(-0.640048\pi\) | ||
0.425915 | − | 0.904763i | \(-0.359952\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −815.834 | −1.69612 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 981.645 | − | 152.430i | 2.03239 | − | 0.315589i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 177.873i | 0.366748i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −388.362 | −0.797458 | −0.398729 | − | 0.917069i | \(-0.630549\pi\) | ||||
−0.398729 | + | 0.917069i | \(0.630549\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.3081 | − | 72.8239i | −0.0231249 | − | 0.148924i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 412.624i | 0.840375i | 0.907437 | + | 0.420188i | \(0.138036\pi\) | ||||
−0.907437 | + | 0.420188i | \(0.861964\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −698.314 | −1.41646 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −34.2603 | + | 10.9028i | −0.0692128 | + | 0.0220258i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 374.858i | 0.754241i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 382.658 | 0.766849 | 0.383425 | − | 0.923572i | \(-0.374745\pi\) | ||||
0.383425 | + | 0.923572i | \(0.374745\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 766.879 | − | 119.081i | 1.53070 | − | 0.237686i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 313.069i | 0.622404i | 0.950344 | + | 0.311202i | \(0.100732\pi\) | ||||
−0.950344 | + | 0.311202i | \(0.899268\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 132.604 | 0.262581 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −154.179 | − | 992.913i | −0.304101 | − | 1.95841i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 591.748i | − | 1.16257i | −0.813700 | − | 0.581285i | \(-0.802550\pi\) | ||
0.813700 | − | 0.581285i | \(-0.197450\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −755.979 | −1.47941 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 317.588 | + | 637.562i | 0.619079 | + | 1.24281i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 44.7143i | − | 0.0868240i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 55.7831 | 0.107898 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 512.272 | − | 79.5456i | 0.987037 | − | 0.153267i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 204.448i | 0.392414i | 0.980562 | + | 0.196207i | \(0.0628625\pi\) | ||||
−0.980562 | + | 0.196207i | \(0.937137\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 464.580 | 0.888299 | 0.444150 | − | 0.895953i | \(-0.353506\pi\) | ||||
0.444150 | + | 0.895953i | \(0.353506\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 25.2483 | + | 162.599i | 0.0480920 | + | 0.309712i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 800.419i | 1.51882i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −382.202 | −0.722499 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 48.5978 | + | 152.711i | 0.0915212 | + | 0.287592i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 178.065i | 0.334080i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 87.7104 | 0.163945 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 813.532 | − | 126.325i | 1.51496 | − | 0.235242i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 127.446i | 0.236449i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 260.310 | 0.481165 | 0.240582 | − | 0.970629i | \(-0.422662\pi\) | ||||
0.240582 | + | 0.970629i | \(0.422662\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 62.8813 | + | 404.954i | 0.115803 | + | 0.745772i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 13.7676i | − | 0.0252617i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 736.820 | 1.34702 | 0.673511 | − | 0.739178i | \(-0.264786\pi\) | ||||
0.673511 | + | 0.739178i | \(0.264786\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 99.5974 | − | 31.6952i | 0.181416 | − | 0.0577326i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1182.51i | − | 2.14612i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 323.903 | 0.585719 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 240.905 | − | 37.4077i | 0.434063 | − | 0.0674013i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.1907i | 0.0595883i | 0.999556 | + | 0.0297941i | \(0.00948517\pi\) | ||||
−0.999556 | + | 0.0297941i | \(0.990515\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 594.600 | 1.06369 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.8118 | − | 82.5076i | −0.0228374 | − | 0.147072i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 373.141i | − | 0.662772i | −0.943495 | − | 0.331386i | \(-0.892484\pi\) | ||
0.943495 | − | 0.331386i | \(-0.107516\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −197.035 | −0.348734 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 725.134 | − | 513.529i | 1.27890 | − | 0.905695i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 894.360i | 1.57181i | 0.618347 | + | 0.785905i | \(0.287803\pi\) | ||||
−0.618347 | + | 0.785905i | \(0.712197\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −180.286 | −0.315738 | −0.157869 | − | 0.987460i | \(-0.550462\pi\) | ||||
−0.157869 | + | 0.987460i | \(0.550462\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −598.076 | + | 92.8691i | −1.04376 | + | 0.162075i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 150.931i | − | 0.262488i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 386.559 | 0.669947 | 0.334973 | − | 0.942228i | \(-0.391273\pi\) | ||||
0.334973 | + | 0.942228i | \(0.391273\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.6082 | + | 87.6367i | 0.0235030 | + | 0.151359i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 835.491i | 1.43802i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 161.688 | 0.277338 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 136.998 | + | 430.495i | 0.234184 | + | 0.735889i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 316.118i | 0.538531i | 0.963066 | + | 0.269266i | \(0.0867809\pi\) | ||||
−0.963066 | + | 0.269266i | \(0.913219\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1355.41 | −2.30121 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −852.107 | + | 132.315i | −1.44181 | + | 0.223884i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 482.116i | 0.813012i | 0.913648 | + | 0.406506i | \(0.133253\pi\) | ||||
−0.913648 | + | 0.406506i | \(0.866747\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −382.137 | −0.642247 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −92.6919 | − | 596.935i | −0.155263 | − | 0.999890i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 323.435i | − | 0.539959i | −0.962866 | − | 0.269979i | \(-0.912983\pi\) | ||
0.962866 | − | 0.269979i | \(-0.0870169\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.11704 | 0.00185863 | 0.000929316 | − | 1.00000i | \(-0.499704\pi\) | ||||
0.000929316 | 1.00000i | \(0.499704\pi\) | ||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −277.111 | + | 88.1858i | −0.459553 | + | 0.146245i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 263.427i | − | 0.435417i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −325.831 | −0.536790 | −0.268395 | − | 0.963309i | \(-0.586493\pi\) | ||||
−0.268395 | + | 0.963309i | \(0.586493\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1457.68 | + | 226.349i | −2.39357 | + | 0.371673i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 700.937i | − | 1.14720i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 84.6761 | 0.138134 | 0.0690670 | − | 0.997612i | \(-0.477998\pi\) | ||||
0.0690670 | + | 0.997612i | \(0.477998\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.16464 | − | 52.5802i | −0.0132758 | − | 0.0854962i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1059.47i | 1.71713i | 0.512706 | + | 0.858564i | \(0.328643\pi\) | ||||
−0.512706 | + | 0.858564i | \(0.671357\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −233.336 | −0.376956 | −0.188478 | − | 0.982077i | \(-0.560355\pi\) | ||||
−0.188478 | + | 0.982077i | \(0.560355\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −729.526 | + | 363.397i | −1.17476 | + | 0.585181i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1239.09i | 1.98891i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 139.717 | − | 21.6952i | 0.222834 | − | 0.0346016i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 566.172i | 0.900114i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −179.423 | −0.284347 | −0.142174 | − | 0.989842i | \(-0.545409\pi\) | ||||
−0.142174 | + | 0.989842i | \(0.545409\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 58.0951 | + | 374.132i | 0.0917774 | + | 0.591045i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.3335i | 0.0162732i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1601.41 | 2.51399 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −93.2626 | − | 293.064i | −0.145951 | − | 0.458629i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 469.934i | 0.733126i | 0.930393 | + | 0.366563i | \(0.119466\pi\) | ||||
−0.930393 | + | 0.366563i | \(0.880534\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 408.297 | 0.634988 | 0.317494 | − | 0.948260i | \(-0.397159\pi\) | ||||
0.317494 | + | 0.948260i | \(0.397159\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −175.578 | + | 27.2637i | −0.272213 | + | 0.0422693i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1100.12i | 1.70035i | 0.526502 | + | 0.850174i | \(0.323503\pi\) | ||||
−0.526502 | + | 0.850174i | \(0.676497\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.8118 | 0.0490166 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 259.445 | + | 1670.82i | 0.398533 | + | 2.56654i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 580.056i | − | 0.888295i | −0.895954 | − | 0.444147i | \(-0.853507\pi\) | ||
0.895954 | − | 0.444147i | \(-0.146493\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −176.228 | −0.269050 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 591.025 | − | 188.084i | 0.899581 | − | 0.286276i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.8268i | 0.0376734i | 0.999823 | + | 0.0188367i | \(0.00599626\pi\) | ||||
−0.999823 | + | 0.0188367i | \(0.994004\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 680.704 | 1.02981 | 0.514904 | − | 0.857248i | \(-0.327827\pi\) | ||||
0.514904 | + | 0.857248i | \(0.327827\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1036.74 | + | 160.985i | −1.56371 | + | 0.242813i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 647.103i | − | 0.973088i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1353.08 | 2.02861 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.40389 | + | 15.4810i | 0.00359326 | + | 0.0231405i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 20.7474i | − | 0.0309202i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −803.058 | −1.19325 | −0.596625 | − | 0.802520i | \(-0.703492\pi\) | ||||
−0.596625 | + | 0.802520i | \(0.703492\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −60.1928 | − | 120.838i | −0.0891745 | − | 0.179019i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 229.259i | − | 0.338639i | −0.985561 | − | 0.169319i | \(-0.945843\pi\) | ||
0.985561 | − | 0.169319i | \(-0.0541570\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −872.618 | −1.28515 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 506.214 | − | 78.6049i | 0.743339 | − | 0.115426i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1098.59i | − | 1.60848i | −0.594302 | − | 0.804242i | \(-0.702571\pi\) | ||
0.594302 | − | 0.804242i | \(-0.297429\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 285.425 | 0.416678 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −162.049 | − | 1043.59i | −0.235879 | − | 1.51906i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 2031.68i | − | 2.94874i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1139.91 | −1.64965 | −0.824824 | − | 0.565389i | \(-0.808726\pi\) | ||||
−0.824824 | + | 0.565389i | \(0.808726\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −53.4874 | − | 168.076i | −0.0771824 | − | 0.242534i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 166.436i | − | 0.239476i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 123.573 | 0.177293 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 790.647 | − | 122.772i | 1.13111 | − | 0.175639i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 850.938i | 1.21389i | 0.794743 | + | 0.606946i | \(0.207605\pi\) | ||||
−0.794743 | + | 0.606946i | \(0.792395\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −958.744 | −1.36379 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 32.1395 | + | 206.978i | 0.0455879 | + | 0.293585i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 650.534i | 0.920132i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1057.04 | −1.49088 | −0.745441 | − | 0.666571i | \(-0.767761\pi\) | ||||
−0.745441 | + | 0.666571i | \(0.767761\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −253.227 | + | 80.5852i | −0.356156 | + | 0.113341i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1550.92i | − | 2.17521i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 89.6778 | 0.125423 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.7164 | + | 3.21685i | −0.0288932 | + | 0.00448654i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 671.914i | − | 0.934512i | −0.884122 | − | 0.467256i | \(-0.845243\pi\) | ||
0.884122 | − | 0.467256i | \(-0.154757\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 219.362 | 0.304247 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.17628 | + | 33.3352i | 0.00715945 | + | 0.0461067i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 224.123i | 0.309135i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1318.52 | −1.81364 | −0.906821 | − | 0.421515i | \(-0.861498\pi\) | ||||
−0.906821 | + | 0.421515i | \(0.861498\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −439.146 | + | 581.886i | −0.602395 | + | 0.798198i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 412.640i | − | 0.564487i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −550.561 | −0.751107 | −0.375553 | − | 0.926801i | \(-0.622547\pi\) | ||||
−0.375553 | + | 0.926801i | \(0.622547\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −472.876 | + | 73.4281i | −0.643369 | + | 0.0999022i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 57.7258i | 0.0783253i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 887.354 | 1.20075 | 0.600375 | − | 0.799719i | \(-0.295018\pi\) | ||||
0.600375 | + | 0.799719i | \(0.295018\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −272.609 | − | 1755.60i | −0.367893 | − | 2.36923i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 174.512i | 0.234874i | 0.993080 | + | 0.117437i | \(0.0374679\pi\) | ||||
−0.993080 | + | 0.117437i | \(0.962532\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 268.884 | 0.360918 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −207.866 | − | 653.186i | −0.278267 | − | 0.874413i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 430.294i | 0.574491i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 974.125 | 1.29710 | 0.648552 | − | 0.761170i | \(-0.275375\pi\) | ||||
0.648552 | + | 0.761170i | \(0.275375\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −825.721 | + | 128.218i | −1.09658 | + | 0.170276i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 33.7855i | − | 0.0447490i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1449.71 | 1.91507 | 0.957533 | − | 0.288322i | \(-0.0930974\pi\) | ||||
0.957533 | + | 0.288322i | \(0.0930974\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 24.8246 | + | 159.870i | 0.0327069 | + | 0.210632i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 468.047i | − | 0.615042i | −0.951541 | − | 0.307521i | \(-0.900501\pi\) | ||
0.951541 | − | 0.307521i | \(-0.0994994\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 67.5419 | 0.0885216 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 298.755 | − | 95.0737i | 0.390529 | − | 0.124279i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 399.728i | − | 0.521157i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 707.833 | 0.920459 | 0.460230 | − | 0.887800i | \(-0.347767\pi\) | ||||
0.460230 | + | 0.887800i | \(0.347767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 879.104 | − | 136.507i | 1.14021 | − | 0.177052i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 610.281i | 0.789496i | 0.918789 | + | 0.394748i | \(0.129168\pi\) | ||||
−0.918789 | + | 0.394748i | \(0.870832\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 256.893 | 0.331475 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 183.517 | + | 1181.84i | 0.236186 | + | 1.52104i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 209.256i | 0.268622i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −61.0490 | −0.0781678 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1083.30 | − | 539.623i | 1.38353 | − | 0.689174i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 593.825i | 0.756465i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −561.570 | −0.713557 | −0.356779 | − | 0.934189i | \(-0.616125\pi\) | ||||
−0.356779 | + | 0.934189i | \(0.616125\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1165.20 | − | 180.932i | 1.47680 | − | 0.229318i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 966.624i | − | 1.22203i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −260.700 | −0.328752 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 93.1569 | + | 599.929i | 0.117178 | + | 0.754627i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 789.976i | 0.991187i | 0.868554 | + | 0.495594i | \(0.165049\pi\) | ||||
−0.868554 | + | 0.495594i | \(0.834951\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −486.436 | −0.608806 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −308.279 | − | 968.722i | −0.384868 | − | 1.20939i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 123.118i | − | 0.153323i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 740.443 | 0.919805 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −697.314 | + | 108.279i | −0.864082 | + | 0.134175i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 892.712i | − | 1.10348i | −0.834018 | − | 0.551738i | \(-0.813965\pi\) | ||
0.834018 | − | 0.551738i | \(-0.186035\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 622.708 | 0.767827 | 0.383913 | − | 0.923369i | \(-0.374576\pi\) | ||||
0.383913 | + | 0.923369i | \(0.374576\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 93.5554 | + | 602.495i | 0.115074 | + | 0.741077i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 54.9302i | − | 0.0673990i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 698.756 | 0.855271 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2111.95 | + | 672.091i | −2.57869 | + | 0.820624i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 111.933i | − | 0.136338i | −0.997674 | − | 0.0681690i | \(-0.978284\pi\) | ||
0.997674 | − | 0.0681690i | \(-0.0217157\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1171.63 | 1.42361 | 0.711804 | − | 0.702378i | \(-0.247879\pi\) | ||||
0.711804 | + | 0.702378i | \(0.247879\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −26.4807 | + | 4.11192i | −0.0320978 | + | 0.00498414i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 108.790i | 0.131548i | 0.997835 | + | 0.0657738i | \(0.0209516\pi\) | ||||
−0.997835 | + | 0.0657738i | \(0.979048\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1303.48 | −1.57235 | −0.786177 | − | 0.618001i | \(-0.787943\pi\) | ||||
−0.786177 | + | 0.618001i | \(0.787943\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 98.8304 | + | 636.466i | 0.118929 | + | 0.765904i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1111.35i | − | 1.33415i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 578.448 | 0.692752 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −618.525 | − | 1241.70i | −0.738978 | − | 1.48351i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1190.36i | 1.41878i | 0.704816 | + | 0.709390i | \(0.251029\pi\) | ||||
−0.704816 | + | 0.709390i | \(0.748971\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1168.24 | −1.38911 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1017.42 | + | 157.985i | −1.20691 | + | 0.187408i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 748.942i | − | 0.886322i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1292.34 | 1.52578 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −185.442 | − | 1194.24i | −0.218424 | − | 1.40664i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1097.04i | − | 1.28911i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −291.614 | −0.341869 | −0.170935 | − | 0.985282i | \(-0.554679\pi\) | ||||
−0.170935 | + | 0.985282i | \(0.554679\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 160.996 | + | 505.905i | 0.188299 | + | 0.591702i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1537.66i | − | 1.79423i | −0.441796 | − | 0.897115i | \(-0.645659\pi\) | ||
0.441796 | − | 0.897115i | \(-0.354341\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 488.132 | 0.568256 | 0.284128 | − | 0.958786i | \(-0.408296\pi\) | ||||
0.284128 | + | 0.958786i | \(0.408296\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 257.950 | − | 40.0545i | 0.299594 | − | 0.0465209i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1070.75i | − | 1.24073i | −0.784313 | − | 0.620365i | \(-0.786984\pi\) | ||
0.784313 | − | 0.620365i | \(-0.213016\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 386.401 | 0.446706 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.3130 | − | 137.255i | −0.0245824 | − | 0.158311i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 52.7505i | 0.0607025i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 725.348 | 0.832776 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 682.212 | − | 217.102i | 0.781457 | − | 0.248686i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 122.646i | 0.140167i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 655.738 | 0.747705 | 0.373853 | − | 0.927488i | \(-0.378037\pi\) | ||||
0.373853 | + | 0.927488i | \(0.378037\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −360.455 | + | 55.9715i | −0.410074 | + | 0.0636763i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1051.89i | − | 1.19398i | −0.802249 | − | 0.596989i | \(-0.796364\pi\) | ||
0.802249 | − | 0.596989i | \(-0.203636\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1342.09 | 1.51992 | 0.759960 | − | 0.649970i | \(-0.225219\pi\) | ||||
0.759960 | + | 0.649970i | \(0.225219\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18.3284 | + | 118.034i | 0.0207100 | + | 0.133372i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 773.466i | 0.872002i | 0.899946 | + | 0.436001i | \(0.143606\pi\) | ||||
−0.899946 | + | 0.436001i | \(0.856394\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −50.6945 | −0.0570242 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 83.6329 | + | 118.095i | 0.0938641 | + | 0.132542i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 823.721i | − | 0.922420i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 613.638 | 0.685629 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2008.83 | − | 311.931i | 2.23950 | − | 0.347749i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2303.03i | 2.56176i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1409.94 | −1.56487 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −133.752 | − | 861.358i | −0.148119 | − | 0.953885i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 305.452i | 0.337516i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1397.06 | −1.54031 | −0.770156 | − | 0.637855i | \(-0.779822\pi\) | ||||
−0.770156 | + | 0.637855i | \(0.779822\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −161.849 | − | 508.587i | −0.178052 | − | 0.559502i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1548.07i | 1.69931i | 0.527339 | + | 0.849655i | \(0.323190\pi\) | ||||
−0.527339 | + | 0.849655i | \(0.676810\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −136.067 | −0.149033 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 76.9813 | − | 11.9537i | 0.0841326 | − | 0.0130641i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 864.546i | − | 0.942799i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 469.880 | 0.511294 | 0.255647 | − | 0.966770i | \(-0.417711\pi\) | ||||
0.255647 | + | 0.966770i | \(0.417711\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 253.673 | + | 1633.65i | 0.275432 | + | 1.77378i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 767.106i | 0.831101i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 181.712 | 0.196445 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −171.497 | + | 54.5761i | −0.185002 | + | 0.0588739i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 656.649i | 0.706834i | 0.935466 | + | 0.353417i | \(0.114980\pi\) | ||||
−0.935466 | + | 0.353417i | \(0.885020\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1881.93 | 2.02141 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −91.6080 | + | 14.2249i | −0.0981865 | + | 0.0152464i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 62.2345i | − | 0.0665610i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −759.554 | −0.810623 | −0.405312 | − | 0.914179i | \(-0.632837\pi\) | ||||
−0.405312 | + | 0.914179i | \(0.632837\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −217.086 | − | 1398.03i | −0.231189 | − | 1.48885i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 227.955i | − | 0.242247i | −0.992637 | − | 0.121124i | \(-0.961350\pi\) | ||
0.992637 | − | 0.121124i | \(-0.0386497\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −239.440 | −0.253913 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 592.814 | − | 295.297i | 0.627316 | − | 0.312484i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 150.055i | − | 0.158453i | −0.996857 | − | 0.0792266i | \(-0.974755\pi\) | ||
0.996857 | − | 0.0792266i | \(-0.0252451\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1547.03 | −1.63017 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1183.85 | + | 183.829i | −1.24485 | + | 0.193300i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 216.231i | − | 0.226895i | −0.993544 | − | 0.113447i | \(-0.963811\pi\) | ||
0.993544 | − | 0.113447i | \(-0.0361893\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −451.122 | −0.472379 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −36.8630 | − | 237.397i | −0.0385193 | − | 0.248064i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1400.25i | 1.46012i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1678.76 | 1.74689 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −107.055 | − | 336.404i | −0.111168 | − | 0.349329i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 66.1034i | 0.0685009i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 976.244 | 1.00956 | 0.504780 | − | 0.863248i | \(-0.331574\pi\) | ||||
0.504780 | + | 0.863248i | \(0.331574\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1218.35 | + | 189.185i | −1.25733 | + | 0.195237i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 602.949i | − | 0.620956i | −0.950580 | − | 0.310478i | \(-0.899511\pi\) | ||
0.950580 | − | 0.310478i | \(-0.100489\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 816.510 | 0.839167 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 51.6679 | + | 332.741i | 0.0529928 | + | 0.341272i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 325.588i | 0.333253i | 0.986020 | + | 0.166626i | \(0.0532874\pi\) | ||||
−0.986020 | + | 0.166626i | \(0.946713\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −201.797 | −0.206126 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −52.8043 | + | 16.8041i | −0.0538270 | + | 0.0171295i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1185.68i | − | 1.20619i | −0.797670 | − | 0.603094i | \(-0.793935\pi\) | ||
0.797670 | − | 0.603094i | \(-0.206065\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −642.735 | −0.652523 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1015.40 | + | 157.672i | −1.02878 | + | 0.159748i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 799.547i | 0.808440i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 710.407 | 0.716858 | 0.358429 | − | 0.933557i | \(-0.383312\pi\) | ||||
0.358429 | + | 0.933557i | \(0.383312\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.9757 | + | 128.643i | 0.0201166 | + | 0.129550i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 450.261i | − | 0.452523i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 381.686 | 0.382834 | 0.191417 | − | 0.981509i | \(-0.438692\pi\) | ||||
0.191417 | + | 0.981509i | \(0.438692\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −437.510 | − | 878.308i | −0.437948 | − | 0.879187i |
(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 | 480.3.l.a.161.7 | ✓ | 16 | |
3.2 | odd | 2 | inner | 480.3.l.a.161.8 | yes | 16 | |
4.3 | odd | 2 | inner | 480.3.l.a.161.10 | yes | 16 | |
8.3 | odd | 2 | 960.3.l.i.641.7 | 16 | |||
8.5 | even | 2 | 960.3.l.i.641.10 | 16 | |||
12.11 | even | 2 | inner | 480.3.l.a.161.9 | yes | 16 | |
24.5 | odd | 2 | 960.3.l.i.641.9 | 16 | |||
24.11 | even | 2 | 960.3.l.i.641.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.3.l.a.161.7 | ✓ | 16 | 1.1 | even | 1 | trivial | |
480.3.l.a.161.8 | yes | 16 | 3.2 | odd | 2 | inner | |
480.3.l.a.161.9 | yes | 16 | 12.11 | even | 2 | inner | |
480.3.l.a.161.10 | yes | 16 | 4.3 | odd | 2 | inner | |
960.3.l.i.641.7 | 16 | 8.3 | odd | 2 | |||
960.3.l.i.641.8 | 16 | 24.11 | even | 2 | |||
960.3.l.i.641.9 | 16 | 24.5 | odd | 2 | |||
960.3.l.i.641.10 | 16 | 8.5 | even | 2 |