Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2940,2,Mod(361,2940)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2940, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2940.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2940.q (of order \(3\), degree \(2\), 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: | \(23.4760181943\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2940.961 |
Dual form | 2940.2.q.q.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(1177\) | \(1471\) | \(1961\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.12132 | − | 3.67423i | −0.639602 | − | 1.10782i | −0.985520 | − | 0.169559i | \(-0.945766\pi\) |
0.345918 | − | 0.938265i | \(-0.387568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.24264 | 1.45405 | 0.727023 | − | 0.686613i | \(-0.240903\pi\) | ||||
0.727023 | + | 0.686613i | \(0.240903\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.12132 | − | 3.67423i | −0.514496 | − | 0.891133i | −0.999859 | − | 0.0168199i | \(-0.994646\pi\) |
0.485363 | − | 0.874313i | \(-0.338688\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | + | 6.06218i | −0.802955 | + | 1.39076i | 0.114708 | + | 0.993399i | \(0.463407\pi\) |
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.12132 | + | 3.67423i | −0.442326 | + | 0.766131i | −0.997862 | − | 0.0653618i | \(-0.979180\pi\) |
0.555536 | + | 0.831493i | \(0.312513\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.2426 | −1.90201 | −0.951005 | − | 0.309175i | \(-0.899947\pi\) | ||||
−0.951005 | + | 0.309175i | \(0.899947\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.74264 | + | 6.48244i | 0.672198 | + | 1.16428i | 0.977279 | + | 0.211955i | \(0.0679830\pi\) |
−0.305081 | + | 0.952326i | \(0.598684\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.12132 | − | 3.67423i | 0.369274 | − | 0.639602i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.62132 | − | 4.54026i | 0.430942 | − | 0.746414i | −0.566012 | − | 0.824397i | \(-0.691515\pi\) |
0.996955 | + | 0.0779826i | \(0.0248479\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.62132 | + | 4.54026i | 0.419747 | + | 0.727023i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.24264 | −0.662589 | −0.331295 | − | 0.943527i | \(-0.607485\pi\) | ||||
−0.331295 | + | 0.943527i | \(0.607485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.24264 | −0.799495 | −0.399748 | − | 0.916625i | \(-0.630902\pi\) | ||||
−0.399748 | + | 0.916625i | \(0.630902\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.500000 | − | 0.866025i | −0.0745356 | − | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | + | 5.19615i | −0.437595 | + | 0.757937i | −0.997503 | − | 0.0706177i | \(-0.977503\pi\) |
0.559908 | + | 0.828554i | \(0.310836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.12132 | − | 3.67423i | 0.297044 | − | 0.514496i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.24264 | + | 7.34847i | 0.582772 | + | 1.00939i | 0.995149 | + | 0.0983769i | \(0.0313651\pi\) |
−0.412378 | + | 0.911013i | \(0.635302\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.24264 | 0.572078 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.00000 | −0.927173 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.878680 | − | 1.52192i | −0.114394 | − | 0.198137i | 0.803143 | − | 0.595786i | \(-0.203159\pi\) |
−0.917537 | + | 0.397649i | \(0.869826\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.24264 | + | 10.8126i | −0.799288 | + | 1.38441i | 0.120792 | + | 0.992678i | \(0.461457\pi\) |
−0.920080 | + | 0.391730i | \(0.871877\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.62132 | + | 4.54026i | −0.325135 | + | 0.563150i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.62132 | − | 2.80821i | −0.198076 | − | 0.343077i | 0.749829 | − | 0.661632i | \(-0.230136\pi\) |
−0.947904 | + | 0.318555i | \(0.896803\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.24264 | −0.510754 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7279 | 1.51053 | 0.755263 | − | 0.655422i | \(-0.227509\pi\) | ||||
0.755263 | + | 0.655422i | \(0.227509\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.378680 | + | 0.655892i | 0.0443211 | + | 0.0767664i | 0.887335 | − | 0.461125i | \(-0.152554\pi\) |
−0.843014 | + | 0.537892i | \(0.819221\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.50000 | + | 9.52628i | −0.618798 | + | 1.07179i | 0.370907 | + | 0.928670i | \(0.379047\pi\) |
−0.989705 | + | 0.143120i | \(0.954286\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.75736 | 0.192895 | 0.0964476 | − | 0.995338i | \(-0.469252\pi\) | ||||
0.0964476 | + | 0.995338i | \(0.469252\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.24264 | 0.460179 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.12132 | − | 8.87039i | −0.549063 | − | 0.951005i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.878680 | + | 1.52192i | −0.0931399 | + | 0.161323i | −0.908831 | − | 0.417165i | \(-0.863024\pi\) |
0.815691 | + | 0.578488i | \(0.196357\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.74264 | + | 6.48244i | −0.388094 | + | 0.672198i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.50000 | − | 6.06218i | −0.359092 | − | 0.621966i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.4853 | −1.67383 | −0.836913 | − | 0.547335i | \(-0.815642\pi\) | ||||
−0.836913 | + | 0.547335i | \(0.815642\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.24264 | 0.426401 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.12132 | − | 14.0665i | −0.808102 | − | 1.39967i | −0.914177 | − | 0.405315i | \(-0.867162\pi\) |
0.106076 | − | 0.994358i | \(-0.466171\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.37868 | + | 7.58410i | −0.431444 | + | 0.747283i | −0.996998 | − | 0.0774283i | \(-0.975329\pi\) |
0.565554 | + | 0.824711i | \(0.308662\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.36396 | − | 11.0227i | 0.615227 | − | 1.06561i | −0.375117 | − | 0.926977i | \(-0.622398\pi\) |
0.990345 | − | 0.138628i | \(-0.0442691\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.74264 | − | 6.48244i | −0.358480 | − | 0.620906i | 0.629227 | − | 0.777221i | \(-0.283372\pi\) |
−0.987707 | + | 0.156316i | \(0.950038\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.24264 | 0.497609 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.12132 | − | 3.67423i | −0.197814 | − | 0.342624i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.62132 | + | 4.54026i | −0.242341 | + | 0.419747i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.50000 | + | 6.06218i | −0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.12132 | − | 3.67423i | −0.191273 | − | 0.331295i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.2426 | −0.997623 | −0.498812 | − | 0.866710i | \(-0.666230\pi\) | ||||
−0.498812 | + | 0.866710i | \(0.666230\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.62132 | − | 4.54026i | −0.230794 | − | 0.399748i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.24264 | + | 2.15232i | −0.108570 | + | 0.188049i | −0.915191 | − | 0.403020i | \(-0.867961\pi\) |
0.806621 | + | 0.591069i | \(0.201294\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.500000 | − | 0.866025i | 0.0430331 | − | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.12132 | + | 3.67423i | 0.181237 | + | 0.313911i | 0.942302 | − | 0.334764i | \(-0.108657\pi\) |
−0.761065 | + | 0.648675i | \(0.775323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.48528 | −0.125980 | −0.0629900 | − | 0.998014i | \(-0.520064\pi\) | ||||
−0.0629900 | + | 0.998014i | \(0.520064\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.1213 | − | 19.2627i | −0.930012 | − | 1.61083i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.12132 | − | 8.87039i | 0.425303 | − | 0.736646i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | − | 10.3923i | 0.491539 | − | 0.851371i | −0.508413 | − | 0.861113i | \(-0.669768\pi\) |
0.999953 | + | 0.00974235i | \(0.00310113\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.75736 | − | 4.77589i | −0.224391 | − | 0.388656i | 0.731746 | − | 0.681578i | \(-0.238706\pi\) |
−0.956136 | + | 0.292922i | \(0.905373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.24264 | 0.342997 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.48528 | −0.601232 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.24264 | + | 9.08052i | 0.418408 | + | 0.724704i | 0.995780 | − | 0.0917773i | \(-0.0292548\pi\) |
−0.577371 | + | 0.816482i | \(0.695921\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.24264 | + | 7.34847i | −0.336463 | + | 0.582772i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | + | 6.92820i | −0.313304 | + | 0.542659i | −0.979076 | − | 0.203497i | \(-0.934769\pi\) |
0.665771 | + | 0.746156i | \(0.268103\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.12132 | + | 3.67423i | 0.165145 | + | 0.286039i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.72792 | 0.520622 | 0.260311 | − | 0.965525i | \(-0.416175\pi\) | ||||
0.260311 | + | 0.965525i | \(0.416175\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.4853 | 1.11425 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.50000 | − | 6.06218i | −0.267652 | − | 0.463586i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.75736 | + | 3.04384i | −0.133610 | + | 0.231419i | −0.925065 | − | 0.379808i | \(-0.875990\pi\) |
0.791456 | + | 0.611226i | \(0.209323\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.878680 | − | 1.52192i | 0.0660456 | − | 0.114394i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.00000 | + | 5.19615i | 0.224231 | + | 0.388379i | 0.956088 | − | 0.293079i | \(-0.0946798\pi\) |
−0.731858 | + | 0.681457i | \(0.761346\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.0000 | 0.966282 | 0.483141 | − | 0.875542i | \(-0.339496\pi\) | ||||
0.483141 | + | 0.875542i | \(0.339496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.4853 | −0.922939 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.62132 | + | 4.54026i | 0.192723 | + | 0.333807i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00000 | + | 15.5885i | −0.658145 | + | 1.13994i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | + | 5.19615i | −0.217072 | + | 0.375980i | −0.953912 | − | 0.300088i | \(-0.902984\pi\) |
0.736839 | + | 0.676068i | \(0.236317\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.62132 | − | 13.2005i | −0.548595 | − | 0.950194i | −0.998371 | − | 0.0570527i | \(-0.981830\pi\) |
0.449777 | − | 0.893141i | \(-0.351504\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.24264 | −0.375433 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.75736 | −0.552689 | −0.276344 | − | 0.961059i | \(-0.589123\pi\) | ||||
−0.276344 | + | 0.961059i | \(0.589123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.24264 | − | 5.61642i | −0.229865 | − | 0.398137i | 0.727903 | − | 0.685680i | \(-0.240495\pi\) |
−0.957768 | + | 0.287543i | \(0.907162\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.62132 | − | 2.80821i | 0.114359 | − | 0.198076i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.12132 | − | 3.67423i | 0.148159 | − | 0.256620i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.12132 | − | 3.67423i | −0.147442 | − | 0.255377i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 29.6985 | 2.05429 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.51472 | 0.379649 | 0.189824 | − | 0.981818i | \(-0.439208\pi\) | ||||
0.189824 | + | 0.981818i | \(0.439208\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.36396 | + | 11.0227i | 0.436051 | + | 0.755263i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.62132 | − | 4.54026i | 0.178773 | − | 0.309643i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.378680 | + | 0.655892i | −0.0255888 | + | 0.0443211i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.1213 | − | 19.2627i | −0.748101 | − | 1.29575i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.4853 | 1.63966 | 0.819828 | − | 0.572610i | \(-0.194069\pi\) | ||||
0.819828 | + | 0.572610i | \(0.194069\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.6066 | + | 23.5673i | 0.903102 | + | 1.56422i | 0.823445 | + | 0.567396i | \(0.192049\pi\) |
0.0796568 | + | 0.996822i | \(0.474618\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.50000 | + | 6.06218i | −0.231287 | + | 0.400600i | −0.958187 | − | 0.286143i | \(-0.907627\pi\) |
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.24264 | − | 2.15232i | 0.0814081 | − | 0.141003i | −0.822447 | − | 0.568842i | \(-0.807392\pi\) |
0.903855 | + | 0.427839i | \(0.140725\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.00000 | − | 5.19615i | −0.195698 | − | 0.338960i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.0000 | −0.714527 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.9706 | −1.48584 | −0.742921 | − | 0.669379i | \(-0.766560\pi\) | ||||
−0.742921 | + | 0.669379i | \(0.766560\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | − | 3.46410i | −0.128831 | − | 0.223142i | 0.794393 | − | 0.607404i | \(-0.207789\pi\) |
−0.923224 | + | 0.384262i | \(0.874456\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.3492 | + | 31.7818i | −1.16753 | + | 2.02223i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.878680 | + | 1.52192i | 0.0556841 | + | 0.0964476i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.72792 | −0.424663 | −0.212331 | − | 0.977198i | \(-0.568106\pi\) | ||||
−0.212331 | + | 0.977198i | \(0.568106\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.12132 | + | 3.67423i | 0.132842 | + | 0.230089i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.878680 | − | 1.52192i | 0.0548105 | − | 0.0949346i | −0.837318 | − | 0.546716i | \(-0.815878\pi\) |
0.892129 | + | 0.451781i | \(0.149211\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.12132 | − | 8.87039i | 0.317002 | − | 0.549063i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.24264 | − | 7.34847i | −0.261612 | − | 0.453126i | 0.705058 | − | 0.709150i | \(-0.250921\pi\) |
−0.966671 | + | 0.256023i | \(0.917588\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.48528 | −0.521247 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.75736 | −0.107549 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.24264 | + | 12.5446i | 0.441592 | + | 0.764859i | 0.997808 | − | 0.0661785i | \(-0.0210807\pi\) |
−0.556216 | + | 0.831038i | \(0.687747\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.7279 | − | 23.7775i | 0.833912 | − | 1.44438i | −0.0610014 | − | 0.998138i | \(-0.519429\pi\) |
0.894913 | − | 0.446240i | \(-0.147237\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.12132 | + | 3.67423i | −0.127920 | + | 0.221565i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.86396 | + | 6.69258i | 0.232163 | + | 0.402118i | 0.958444 | − | 0.285279i | \(-0.0920864\pi\) |
−0.726281 | + | 0.687397i | \(0.758753\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.48528 | −0.448132 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.97056 | −0.296519 | −0.148259 | − | 0.988948i | \(-0.547367\pi\) | ||||
−0.148259 | + | 0.988948i | \(0.547367\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.863961 | − | 1.49642i | −0.0513572 | − | 0.0889532i | 0.839204 | − | 0.543817i | \(-0.183021\pi\) |
−0.890561 | + | 0.454864i | \(0.849688\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.50000 | − | 6.06218i | 0.207322 | − | 0.359092i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.500000 | + | 0.866025i | −0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.24264 | − | 14.2767i | −0.483192 | − | 0.836913i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.9706 | −1.69248 | −0.846239 | − | 0.532803i | \(-0.821139\pi\) | ||||
−0.846239 | + | 0.532803i | \(0.821139\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.75736 | 0.102317 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.12132 | + | 3.67423i | 0.123091 | + | 0.213201i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.1213 | + | 19.2627i | −0.643163 | + | 1.11399i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.12132 | − | 14.0665i | 0.466558 | − | 0.808102i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.24264 | − | 10.8126i | −0.357453 | − | 0.619126i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.24264 | 0.299213 | 0.149607 | − | 0.988746i | \(-0.452199\pi\) | ||||
0.149607 | + | 0.988746i | \(0.452199\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.75736 | −0.498189 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.6066 | − | 18.3712i | −0.601445 | − | 1.04173i | −0.992602 | − | 0.121410i | \(-0.961258\pi\) |
0.391157 | − | 0.920324i | \(-0.372075\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.863961 | + | 1.49642i | −0.0488340 | + | 0.0845829i | −0.889409 | − | 0.457112i | \(-0.848884\pi\) |
0.840575 | + | 0.541695i | \(0.182217\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.363961 | + | 0.630399i | −0.0204421 | + | 0.0354067i | −0.876065 | − | 0.482192i | \(-0.839841\pi\) |
0.855623 | + | 0.517599i | \(0.173174\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.7279 | + | 37.6339i | 1.21653 | + | 2.10709i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.7279 | 0.710403 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.6985 | 1.65247 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.62132 | − | 4.54026i | −0.145405 | − | 0.251848i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.74264 | − | 6.48244i | 0.206969 | − | 0.358480i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.50000 | + | 14.7224i | −0.467202 | + | 0.809218i | −0.999298 | − | 0.0374662i | \(-0.988071\pi\) |
0.532096 | + | 0.846684i | \(0.321405\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.62132 | + | 4.54026i | 0.143647 | + | 0.248805i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.24264 | 0.177164 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.7279 | 0.638861 | 0.319430 | − | 0.947610i | \(-0.396508\pi\) | ||||
0.319430 | + | 0.947610i | \(0.396508\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.00000 | − | 15.5885i | −0.488813 | − | 0.846649i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.8787 | − | 27.5027i | 0.859879 | − | 1.48935i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.12132 | − | 3.67423i | 0.114208 | − | 0.197814i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.0000 | + | 20.7846i | 0.644194 | + | 1.11578i | 0.984487 | + | 0.175457i | \(0.0561403\pi\) |
−0.340293 | + | 0.940319i | \(0.610526\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.24264 | −0.279831 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.878680 | − | 1.52192i | −0.0467674 | − | 0.0810035i | 0.841694 | − | 0.539955i | \(-0.181559\pi\) |
−0.888462 | + | 0.458951i | \(0.848225\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.36396 | + | 11.0227i | −0.337764 | + | 0.585024i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.12132 | + | 8.87039i | −0.270293 | + | 0.468161i | −0.968937 | − | 0.247309i | \(-0.920454\pi\) |
0.698644 | + | 0.715470i | \(0.253787\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | − | 25.9808i | −0.789474 | − | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.757359 | −0.0396420 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.13604 | + | 8.89588i | 0.268099 | + | 0.464361i | 0.968371 | − | 0.249515i | \(-0.0802712\pi\) |
−0.700272 | + | 0.713876i | \(0.746938\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.12132 | − | 3.67423i | 0.110432 | − | 0.191273i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.86396 | − | 6.69258i | 0.200068 | − | 0.346528i | −0.748482 | − | 0.663155i | \(-0.769217\pi\) |
0.948550 | + | 0.316627i | \(0.102550\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −53.6985 | −2.76561 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.4558 | 1.56441 | 0.782206 | − | 0.623020i | \(-0.214095\pi\) | ||||
0.782206 | + | 0.623020i | \(0.214095\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.62132 | − | 9.73641i | −0.287989 | − | 0.498812i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.7279 | + | 22.0454i | −0.650366 | + | 1.12647i | 0.332668 | + | 0.943044i | \(0.392051\pi\) |
−0.983034 | + | 0.183424i | \(0.941282\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.62132 | − | 4.54026i | 0.133249 | − | 0.230794i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.6066 | − | 18.3712i | −0.537776 | − | 0.931455i | −0.999023 | − | 0.0441839i | \(-0.985931\pi\) |
0.461247 | − | 0.887272i | \(-0.347402\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000 | 0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.48528 | −0.125366 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.50000 | − | 9.52628i | −0.276735 | − | 0.479319i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.62132 | + | 14.9326i | −0.432692 | + | 0.749444i | −0.997104 | − | 0.0760490i | \(-0.975769\pi\) |
0.564412 | + | 0.825493i | \(0.309103\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.2426 | − | 17.7408i | 0.511493 | − | 0.885932i | −0.488418 | − | 0.872610i | \(-0.662426\pi\) |
0.999911 | − | 0.0133223i | \(-0.00424074\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.6213 | + | 33.9851i | 0.977408 | + | 1.69292i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.2426 | −1.10253 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.50000 | + | 14.7224i | 0.420298 | + | 0.727977i | 0.995968 | − | 0.0897044i | \(-0.0285922\pi\) |
−0.575670 | + | 0.817682i | \(0.695259\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.12132 | + | 3.67423i | −0.104637 | + | 0.181237i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.878680 | + | 1.52192i | −0.0431327 | + | 0.0747080i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.742641 | − | 1.28629i | −0.0363673 | − | 0.0629900i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.48528 | −0.121414 | −0.0607070 | − | 0.998156i | \(-0.519336\pi\) | ||||
−0.0607070 | + | 0.998156i | \(0.519336\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.5147 | 0.707404 | 0.353702 | − | 0.935358i | \(-0.384923\pi\) | ||||
0.353702 | + | 0.935358i | \(0.384923\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00000 | − | 5.19615i | −0.145865 | − | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.12132 | + | 3.67423i | −0.102899 | + | 0.178227i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.1213 | − | 19.2627i | 0.536942 | − | 0.930012i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.7279 | + | 27.2416i | 0.757587 | + | 1.31218i | 0.944078 | + | 0.329723i | \(0.106955\pi\) |
−0.186490 | + | 0.982457i | \(0.559711\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.7574 | −1.18976 | −0.594881 | − | 0.803814i | \(-0.702801\pi\) | ||||
−0.594881 | + | 0.803814i | \(0.702801\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.2426 | 0.491097 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.8492 | − | 25.7196i | −0.710336 | − | 1.23034i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.00000 | + | 8.66025i | −0.238637 | + | 0.413331i | −0.960323 | − | 0.278889i | \(-0.910034\pi\) |
0.721686 | + | 0.692220i | \(0.243367\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.75736 | + | 3.04384i | −0.0834947 | + | 0.144617i | −0.904749 | − | 0.425946i | \(-0.859941\pi\) |
0.821254 | + | 0.570563i | \(0.193275\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.878680 | − | 1.52192i | −0.0416534 | − | 0.0721458i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0000 | 0.567581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | + | 15.5885i | 0.423793 | + | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.75736 | − | 4.77589i | 0.129552 | − | 0.224391i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.10660 | − | 8.84489i | 0.238877 | − | 0.413747i | −0.721516 | − | 0.692398i | \(-0.756554\pi\) |
0.960392 | + | 0.278652i | \(0.0898875\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.12132 | + | 3.67423i | 0.0990148 | + | 0.171499i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.72792 | 0.313351 | 0.156675 | − | 0.987650i | \(-0.449922\pi\) | ||||
0.156675 | + | 0.987650i | \(0.449922\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.7279 | 1.66042 | 0.830209 | − | 0.557453i | \(-0.188221\pi\) | ||||
0.830209 | + | 0.557453i | \(0.188221\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.74264 | − | 6.48244i | −0.173561 | − | 0.300616i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.4853 | − | 19.8931i | 0.531475 | − | 0.920542i | −0.467850 | − | 0.883808i | \(-0.654971\pi\) |
0.999325 | − | 0.0367344i | \(-0.0116955\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.24264 | + | 9.08052i | −0.241568 | + | 0.418408i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.1213 | + | 19.2627i | 0.511359 | + | 0.885700i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.00000 | 0.321182 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.48528 | −0.388514 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.00000 | + | 10.3923i | 0.274147 | + | 0.474837i | 0.969920 | − | 0.243426i | \(-0.0782712\pi\) |
−0.695773 | + | 0.718262i | \(0.744938\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.7426 | − | 23.8030i | 0.626610 | − | 1.08532i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.24264 | − | 14.2767i | 0.374279 | − | 0.648270i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.13604 | + | 10.6279i | 0.278050 | + | 0.481598i | 0.970900 | − | 0.239484i | \(-0.0769784\pi\) |
−0.692850 | + | 0.721082i | \(0.743645\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.00000 | −0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.4853 | 1.46604 | 0.733020 | − | 0.680207i | \(-0.238110\pi\) | ||||
0.733020 | + | 0.680207i | \(0.238110\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.7279 | + | 37.6339i | 0.978576 | + | 1.69494i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.12132 | + | 3.67423i | −0.0953463 | + | 0.165145i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.25736 | + | 2.17781i | −0.0562871 | + | 0.0974922i | −0.892796 | − | 0.450461i | \(-0.851260\pi\) |
0.836509 | + | 0.547953i | \(0.184593\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.36396 | + | 5.82655i | 0.150291 | + | 0.260311i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.51472 | 0.424240 | 0.212120 | − | 0.977244i | \(-0.431963\pi\) | ||||
0.212120 | + | 0.977244i | \(0.431963\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.2426 | 0.722788 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.24264 | + | 12.5446i | 0.321657 | + | 0.557126i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.7279 | − | 27.2416i | 0.697128 | − | 1.20746i | −0.272330 | − | 0.962204i | \(-0.587794\pi\) |
0.969458 | − | 0.245257i | \(-0.0788724\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.50000 | − | 6.06218i | 0.154529 | − | 0.267652i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.37868 | − | 7.58410i | −0.192948 | − | 0.334195i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.4558 | 1.11955 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.51472 | −0.154279 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.7279 | + | 32.4377i | 0.820485 | + | 1.42112i | 0.905321 | + | 0.424727i | \(0.139630\pi\) |
−0.0848363 | + | 0.996395i | \(0.527037\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.62132 | − | 2.80821i | 0.0708954 | − | 0.122794i | −0.828399 | − | 0.560139i | \(-0.810748\pi\) |
0.899294 | + | 0.437345i | \(0.144081\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.8787 | − | 27.5027i | 0.691686 | − | 1.19804i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.50000 | + | 4.33013i | 0.108696 | + | 0.188266i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.75736 | 0.0762629 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.2426 | −0.963436 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.36396 | + | 11.0227i | 0.275138 | + | 0.476553i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.00000 | + | 5.19615i | −0.129460 | + | 0.224231i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.4706 | + | 23.3317i | −0.579145 | + | 1.00311i | 0.416433 | + | 0.909166i | \(0.363280\pi\) |
−0.995578 | + | 0.0939417i | \(0.970053\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.50000 | + | 11.2583i | 0.278942 | + | 0.483141i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.48528 | 0.320634 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.4558 | −0.746358 | −0.373179 | − | 0.927759i | \(-0.621732\pi\) | ||||
−0.373179 | + | 0.927759i | \(0.621732\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.24264 | − | 10.8126i | −0.266429 | − | 0.461469i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.8492 | − | 62.0927i | 1.52723 | − | 2.64524i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.62132 | + | 4.54026i | −0.111269 | + | 0.192723i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.0000 | + | 25.9808i | 0.635570 | + | 1.10084i | 0.986394 | + | 0.164399i | \(0.0525683\pi\) |
−0.350824 | + | 0.936442i | \(0.614098\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.4853 | −1.16250 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.0000 | −0.759961 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.00000 | − | 5.19615i | −0.126435 | − | 0.218992i | 0.795858 | − | 0.605483i | \(-0.207020\pi\) |
−0.922293 | + | 0.386492i | \(0.873687\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.00000 | − | 15.5885i | 0.378633 | − | 0.655811i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.84924 | + | 15.3273i | −0.370980 | + | 0.642555i | −0.989717 | − | 0.143043i | \(-0.954311\pi\) |
0.618737 | + | 0.785598i | \(0.287645\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.4706 | − | 33.7240i | −0.814818 | − | 1.41131i | −0.909459 | − | 0.415794i | \(-0.863504\pi\) |
0.0946410 | − | 0.995511i | \(-0.469830\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.00000 | −0.250654 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.24264 | 0.176930 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.6213 | + | 18.3967i | 0.442171 | + | 0.765863i | 0.997850 | − | 0.0655337i | \(-0.0208750\pi\) |
−0.555679 | + | 0.831397i | \(0.687542\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.62132 | − | 13.2005i | 0.316731 | − | 0.548595i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0000 | − | 31.1769i | 0.745484 | − | 1.29122i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.62132 | − | 4.54026i | −0.108378 | − | 0.187717i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.78680 | −0.115023 | −0.0575117 | − | 0.998345i | \(-0.518317\pi\) | ||||
−0.0575117 | + | 0.998345i | \(0.518317\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −52.3970 | −2.15898 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.87868 | − | 6.71807i | −0.159548 | − | 0.276344i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.6066 | + | 33.9596i | −0.805147 | + | 1.39455i | 0.111045 | + | 0.993815i | \(0.464580\pi\) |
−0.916192 | + | 0.400740i | \(0.868753\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.24264 | − | 5.61642i | 0.132712 | − | 0.229865i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.75736 | + | 13.4361i | 0.316957 | + | 0.548986i | 0.979852 | − | 0.199727i | \(-0.0640055\pi\) |
−0.662894 | + | 0.748713i | \(0.730672\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.4853 | −0.550076 | −0.275038 | − | 0.961433i | \(-0.588690\pi\) | ||||
−0.275038 | + | 0.961433i | \(0.588690\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.24264 | 0.132051 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.50000 | − | 6.06218i | −0.142295 | − | 0.246463i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.3787 | + | 17.9764i | −0.421258 | + | 0.729640i | −0.996063 | − | 0.0886507i | \(-0.971745\pi\) |
0.574805 | + | 0.818290i | \(0.305078\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.7279 | + | 27.2416i | −0.636284 | + | 1.10208i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.7279 | − | 39.3659i | −0.917972 | − | 1.58997i | −0.802491 | − | 0.596665i | \(-0.796492\pi\) |
−0.115482 | − | 0.993310i | \(-0.536841\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.24264 | 0.171080 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.51472 | −0.383048 | −0.191524 | − | 0.981488i | \(-0.561343\pi\) | ||||
−0.191524 | + | 0.981488i | \(0.561343\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.9853 | + | 19.0271i | 0.441536 | + | 0.764762i | 0.997804 | − | 0.0662407i | \(-0.0211005\pi\) |
−0.556268 | + | 0.831003i | \(0.687767\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.12132 | − | 3.67423i | 0.0851257 | − | 0.147442i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.8492 | + | 25.7196i | 0.593022 | + | 1.02714i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.2426 | −0.886872 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.75736 | + | 4.77589i | 0.109595 | + | 0.189824i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.62132 | − | 9.73641i | 0.223075 | − | 0.386378i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.36396 | + | 11.0227i | −0.251754 | + | 0.436051i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.8787 | − | 22.3065i | −0.508677 | − | 0.881055i | −0.999950 | − | 0.0100488i | \(-0.996801\pi\) |
0.491272 | − | 0.871006i | \(-0.336532\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.72792 | −0.225887 | −0.112944 | − | 0.993601i | \(-0.536028\pi\) | ||||
−0.112944 | + | 0.993601i | \(0.536028\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.24264 | 0.206429 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.878680 | + | 1.52192i | 0.0345445 | + | 0.0598328i | 0.882781 | − | 0.469785i | \(-0.155669\pi\) |
−0.848236 | + | 0.529618i | \(0.822335\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.72792 | + | 6.45695i | −0.146334 | + | 0.253457i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.878680 | + | 1.52192i | −0.0343854 | + | 0.0595572i | −0.882706 | − | 0.469926i | \(-0.844281\pi\) |
0.848321 | + | 0.529483i | \(0.177614\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.24264 | − | 2.15232i | −0.0485540 | − | 0.0840980i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.757359 | −0.0295474 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.02944 | 0.273828 | 0.136914 | − | 0.990583i | \(-0.456282\pi\) | ||||
0.136914 | + | 0.990583i | \(0.456282\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.9853 | − | 31.1514i | −0.699546 | − | 1.21165i | −0.968624 | − | 0.248531i | \(-0.920052\pi\) |
0.269077 | − | 0.963119i | \(-0.413281\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.1213 | − | 19.2627i | 0.431916 | − | 0.748101i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.7279 | − | 37.6339i | 0.841309 | − | 1.45719i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.2426 | + | 21.2049i | 0.473328 | + | 0.819828i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 52.9706 | 2.04491 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.27208 | 0.164677 | 0.0823383 | − | 0.996604i | \(-0.473761\pi\) | ||||
0.0823383 | + | 0.996604i | \(0.473761\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.500000 | + | 0.866025i | 0.0192450 | + | 0.0333333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.36396 | + | 11.0227i | −0.244587 | + | 0.423637i | −0.962015 | − | 0.272995i | \(-0.911986\pi\) |
0.717428 | + | 0.696632i | \(0.245319\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.6066 | + | 23.5673i | −0.521406 | + | 0.903102i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.60660 | + | 7.97887i | 0.176267 | + | 0.305303i | 0.940599 | − | 0.339520i | \(-0.110265\pi\) |
−0.764332 | + | 0.644823i | \(0.776931\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.24264 | −0.162103 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.00000 | −0.267067 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.2426 | + | 38.5254i | 0.847377 | + | 1.46770i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.4706 | + | 35.4561i | −0.778737 | + | 1.34881i | 0.153933 | + | 0.988081i | \(0.450806\pi\) |
−0.932670 | + | 0.360731i | \(0.882527\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.742641 | − | 1.28629i | 0.0281700 | − | 0.0487918i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | + | 15.5885i | 0.340899 | + | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.48528 | 0.0940020 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 51.2132 | 1.93430 | 0.967148 | − | 0.254214i | \(-0.0818167\pi\) | ||||
0.967148 | + | 0.254214i | \(0.0818167\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.3492 | + | 31.7818i | 0.692055 | + | 1.19867i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.00000 | − | 5.19615i | 0.112987 | − | 0.195698i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.75736 | − | 16.9002i | 0.366445 | − | 0.634702i | −0.622562 | − | 0.782571i | \(-0.713908\pi\) |
0.989007 | + | 0.147869i | \(0.0472413\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.50000 | − | 9.52628i | −0.206266 | − | 0.357263i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31.7574 | −1.18932 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.2426 | 0.831828 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.4853 | − | 19.8931i | −0.428926 | − | 0.742921i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.75736 | − | 8.23999i | 0.177420 | − | 0.307300i | −0.763576 | − | 0.645718i | \(-0.776558\pi\) |
0.940996 | + | 0.338418i | \(0.109892\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.00000 | − | 3.46410i | 0.0743808 | − | 0.128831i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.12132 | + | 8.87039i | 0.190201 | + | 0.329438i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.24264 | −0.342791 | −0.171395 | − | 0.985202i | \(-0.554828\pi\) | ||||
−0.171395 | + | 0.985202i | \(0.554828\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.1213 | + | 19.2627i | 0.411337 | + | 0.712456i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.1066 | − | 38.2898i | 0.816526 | − | 1.41426i | −0.0917010 | − | 0.995787i | \(-0.529230\pi\) |
0.908227 | − | 0.418478i | \(-0.137436\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.87868 | + | 11.9142i | −0.253379 | + | 0.438866i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.742641 | − | 1.28629i | −0.0273185 | − | 0.0473170i | 0.852043 | − | 0.523472i | \(-0.175363\pi\) |
−0.879361 | + | 0.476155i | \(0.842030\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −36.6985 | −1.34815 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.2132 | −0.998356 | −0.499178 | − | 0.866500i | \(-0.666365\pi\) | ||||
−0.499178 | + | 0.866500i | \(0.666365\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | + | 10.3923i | 0.219823 | + | 0.380745i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.878680 | + | 1.52192i | −0.0321492 | + | 0.0556841i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.4706 | − | 19.8676i | 0.418567 | − | 0.724979i | −0.577229 | − | 0.816582i | \(-0.695866\pi\) |
0.995796 | + | 0.0916035i | \(0.0291992\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.36396 | − | 5.82655i | −0.122590 | − | 0.212331i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.51472 | 0.200701 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.9706 | 1.56179 | 0.780896 | − | 0.624661i | \(-0.214763\pi\) | ||||
0.780896 | + | 0.624661i | \(0.214763\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.00000 | + | 15.5885i | 0.326679 | + | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.8787 | − | 32.6988i | 0.684352 | − | 1.18533i | −0.289288 | − | 0.957242i | \(-0.593419\pi\) |
0.973640 | − | 0.228090i | \(-0.0732480\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.12132 | + | 3.67423i | −0.0766965 | + | 0.132842i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.60660 | − | 7.97887i | −0.166335 | − | 0.288100i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.00000 | −0.180305 | −0.0901523 | − | 0.995928i | \(-0.528735\pi\) | ||||
−0.0901523 | + | 0.995928i | \(0.528735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.75736 | 0.0632897 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.8492 | − | 41.3081i | −0.857798 | − | 1.48575i | −0.874025 | − | 0.485881i | \(-0.838499\pi\) |
0.0162275 | − | 0.999868i | \(-0.494834\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.74264 | − | 6.48244i | 0.134440 | − | 0.232856i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.8492 | − | 25.7196i | 0.532029 | − | 0.921502i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.0000 | − | 46.7654i | −0.966136 | − | 1.67340i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.2426 | 0.366042 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.4853 | −0.374236 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.75736 | + | 9.97204i | 0.205228 | + | 0.355465i | 0.950205 | − | 0.311625i | \(-0.100873\pi\) |
−0.744978 | + | 0.667090i | \(0.767540\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.24264 | − | 7.34847i | 0.151042 | − | 0.261612i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.7279 | + | 56.6864i | −1.16220 | + | 2.01299i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.24264 | − | 7.34847i | −0.150471 | − | 0.260623i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.2426 | 1.42547 | 0.712734 | − | 0.701435i | \(-0.247457\pi\) | ||||
0.712734 | + | 0.701435i | \(0.247457\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.4558 | 0.900563 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.878680 | − | 1.52192i | −0.0310466 | − | 0.0537743i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.60660 | − | 2.78272i | 0.0566957 | − | 0.0981999i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.24264 | + | 12.5446i | −0.254953 | + | 0.441592i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.9706 | + | 34.5900i | 0.702128 | + | 1.21612i | 0.967718 | + | 0.252035i | \(0.0810997\pi\) |
−0.265591 | + | 0.964086i | \(0.585567\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 55.9411 | 1.96436 | 0.982179 | − | 0.187946i | \(-0.0601831\pi\) | ||||
0.982179 | + | 0.187946i | \(0.0601831\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.4558 | 0.962918 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.00000 | − | 6.92820i | −0.140114 | − | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.3492 | − | 31.7818i | 0.641959 | − | 1.11191i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.8492 | − | 46.5043i | 0.937045 | − | 1.62301i | 0.166099 | − | 0.986109i | \(-0.446883\pi\) |
0.770946 | − | 0.636901i | \(-0.219784\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.51472 | + | 4.35562i | 0.0876576 | + | 0.151827i | 0.906521 | − | 0.422162i | \(-0.138729\pi\) |
−0.818863 | + | 0.573989i | \(0.805395\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.24264 | −0.147710 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.45584 | −0.259265 | −0.129633 | − | 0.991562i | \(-0.541380\pi\) | ||||
−0.129633 | + | 0.991562i | \(0.541380\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.50000 | + | 9.52628i | 0.191023 | + | 0.330861i | 0.945589 | − | 0.325362i | \(-0.105486\pi\) |
−0.754567 | + | 0.656223i | \(0.772153\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.86396 | + | 6.69258i | −0.134039 | + | 0.232163i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.36396 | + | 5.82655i | −0.116415 | + | 0.201636i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.74264 | − | 6.48244i | −0.129365 | − | 0.224066i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.2426 | −1.18219 | −0.591094 | − | 0.806603i | \(-0.701304\pi\) | ||||
−0.591094 | + | 0.806603i | \(0.701304\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 75.9117 | 2.61764 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.48528 | − | 4.30463i | −0.0855976 | − | 0.148259i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.24264 | + | 12.5446i | −0.249154 | + | 0.431548i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.863961 | − | 1.49642i | 0.0296511 | − | 0.0513572i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.1213 | + | 19.2627i | 0.381234 | + | 0.660317i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.272078 | 0.00931577 | 0.00465789 | − | 0.999989i | \(-0.498517\pi\) | ||||
0.00465789 | + | 0.999989i | \(0.498517\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.00000 | 0.239395 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.12132 | − | 3.67423i | −0.0724629 | − | 0.125509i | 0.827517 | − | 0.561440i | \(-0.189753\pi\) |
−0.899980 | + | 0.435931i | \(0.856419\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.0000 | + | 19.0526i | −0.375315 | + | 0.650065i | −0.990374 | − | 0.138416i | \(-0.955799\pi\) |
0.615059 | + | 0.788481i | \(0.289132\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.2426 | − | 33.3292i | 0.655027 | − | 1.13454i | −0.326860 | − | 0.945073i | \(-0.605991\pi\) |
0.981887 | − | 0.189467i | \(-0.0606761\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.75736 | − | 3.04384i | −0.0597520 | − | 0.103494i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46.6690 | 1.58314 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.50000 | − | 14.7224i | −0.288012 | − | 0.498851i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.24264 | − | 14.2767i | 0.278971 | − | 0.483192i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.00000 | − | 8.66025i | 0.168838 | − | 0.292436i | −0.769174 | − | 0.639040i | \(-0.779332\pi\) |
0.938012 | + | 0.346604i | \(0.112665\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.4853 | − | 25.0892i | −0.488576 | − | 0.846239i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.02944 | −0.236828 | −0.118414 | − | 0.992964i | \(-0.537781\pi\) | ||||
−0.118414 | + | 0.992964i | \(0.537781\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.7279 | −0.663897 | −0.331949 | − | 0.943297i | \(-0.607706\pi\) | ||||
−0.331949 | + | 0.943297i | \(0.607706\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.878680 | + | 1.52192i | 0.0295365 | + | 0.0511587i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.6066 | + | 23.5673i | −0.456865 | + | 0.791313i | −0.998793 | − | 0.0491114i | \(-0.984361\pi\) |
0.541928 | + | 0.840425i | \(0.317694\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.12132 | + | 3.67423i | −0.0710669 | + | 0.123091i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.0000 | − | 36.3731i | −0.702738 | − | 1.21718i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.00000 | −0.200558 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.2426 | −0.742660 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.3345 | − | 66.3973i | −1.27853 | − | 2.21448i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.0000 | − | 31.1769i | 0.599667 | − | 1.03865i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.50000 | + | 11.2583i | −0.216067 | + | 0.374240i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.8640 | + | 48.2618i | 0.925208 | + | 1.60251i | 0.791227 | + | 0.611523i | \(0.209443\pi\) |
0.133981 | + | 0.990984i | \(0.457224\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.2426 | 0.538734 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.78680 | 0.291120 | 0.145560 | − | 0.989349i | \(-0.453502\pi\) | ||||
0.145560 | + | 0.989349i | \(0.453502\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.72792 | − | 6.45695i | −0.123376 | − | 0.213694i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.24264 | − | 10.8126i | 0.206375 | − | 0.357453i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.0147186 | + | 0.0254934i | −0.000485523 | + | 0.000840950i | −0.866268 | − | 0.499579i | \(-0.833488\pi\) |
0.865783 | + | 0.500420i | \(0.166821\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.62132 | + | 4.54026i | 0.0863754 | + | 0.149607i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 66.7279 | 2.19638 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.24264 | −0.172377 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.37868 | − | 7.58410i | −0.143815 | − | 0.249094i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.63604 | − | 9.76191i | 0.184912 | − | 0.320278i | −0.758635 | − | 0.651516i | \(-0.774133\pi\) |
0.943547 | + | 0.331239i | \(0.107467\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.6066 | − | 18.3712i | 0.347245 | − | 0.601445i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.00000 | − | 15.5885i | −0.294331 | − | 0.509797i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.6985 | −1.32956 | −0.664781 | − | 0.747039i | \(-0.731475\pi\) | ||||
−0.664781 | + | 0.747039i | \(0.731475\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.72792 | −0.0563886 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.84924 | + | 10.1312i | 0.190680 | + | 0.330267i | 0.945476 | − | 0.325693i | \(-0.105597\pi\) |
−0.754796 | + | 0.655960i | \(0.772264\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.00000 | − | 15.5885i | 0.293080 | − | 0.507630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.6066 | + | 33.9596i | −0.637129 | + | 1.10354i | 0.348931 | + | 0.937148i | \(0.386545\pi\) |
−0.986060 | + | 0.166391i | \(0.946789\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.98528 | + | 3.43861i | 0.0644450 | + | 0.111622i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.727922 | −0.0236045 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.4853 | −1.44102 | −0.720510 | − | 0.693445i | \(-0.756092\pi\) | ||||
−0.720510 | + | 0.693445i | \(0.756092\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.00000 | − | 5.19615i | −0.0970777 | − | 0.168144i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21.7279 | + | 37.6339i | −0.702364 | + | 1.21653i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.5147 | + | 21.6761i | −0.403701 | + | 0.699230i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.36396 | + | 11.0227i | 0.205076 | + | 0.355202i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.2426 | 0.490678 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.7574 | −0.860459 | −0.430229 | − | 0.902720i | \(-0.641567\pi\) | ||||
−0.430229 | + | 0.902720i | \(0.641567\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.8492 | + | 25.7196i | 0.477026 | + | 0.826234i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.51472 | − | 16.4800i | 0.305342 | − | 0.528868i | −0.671996 | − | 0.740555i | \(-0.734563\pi\) |
0.977337 | + | 0.211688i | \(0.0678959\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.62132 | − | 4.54026i | 0.0839494 | − | 0.145405i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.6066 | + | 44.3519i | 0.819228 | + | 1.41894i | 0.906252 | + | 0.422738i | \(0.138931\pi\) |
−0.0870242 | + | 0.996206i | \(0.527736\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.45584 | 0.238290 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.48528 | 0.238987 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.84924 | + | 15.3273i | 0.282247 | + | 0.488866i | 0.971938 | − | 0.235238i | \(-0.0755869\pi\) |
−0.689691 | + | 0.724104i | \(0.742254\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.87868 | − | 6.71807i | 0.123585 | − | 0.214056i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.1213 | − | 19.2627i | 0.353637 | − | 0.612518i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.4706 | + | 45.8484i | 0.840865 | + | 1.45642i | 0.889164 | + | 0.457588i | \(0.151287\pi\) |
−0.0482991 | + | 0.998833i | \(0.515380\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.0000 | −0.539479 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.48528 | 0.205597 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.136039 | − | 0.235626i | −0.00430840 | − | 0.00746236i | 0.863863 | − | 0.503727i | \(-0.168038\pi\) |
−0.868172 | + | 0.496264i | \(0.834705\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.62132 | + | 4.54026i | −0.0829349 | + | 0.143647i |
(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 | 2940.2.q.q.961.1 | 4 | ||
7.2 | even | 3 | 2940.2.a.p.1.2 | 2 | |||
7.3 | odd | 6 | 420.2.q.d.361.1 | yes | 4 | ||
7.4 | even | 3 | inner | 2940.2.q.q.361.1 | 4 | ||
7.5 | odd | 6 | 2940.2.a.r.1.2 | 2 | |||
7.6 | odd | 2 | 420.2.q.d.121.1 | ✓ | 4 | ||
21.2 | odd | 6 | 8820.2.a.bf.1.1 | 2 | |||
21.5 | even | 6 | 8820.2.a.bk.1.1 | 2 | |||
21.17 | even | 6 | 1260.2.s.e.361.1 | 4 | |||
21.20 | even | 2 | 1260.2.s.e.541.1 | 4 | |||
28.3 | even | 6 | 1680.2.bg.t.1201.2 | 4 | |||
28.27 | even | 2 | 1680.2.bg.t.961.2 | 4 | |||
35.3 | even | 12 | 2100.2.bc.f.949.2 | 8 | |||
35.13 | even | 4 | 2100.2.bc.f.1549.3 | 8 | |||
35.17 | even | 12 | 2100.2.bc.f.949.3 | 8 | |||
35.24 | odd | 6 | 2100.2.q.k.1201.2 | 4 | |||
35.27 | even | 4 | 2100.2.bc.f.1549.2 | 8 | |||
35.34 | odd | 2 | 2100.2.q.k.1801.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.q.d.121.1 | ✓ | 4 | 7.6 | odd | 2 | ||
420.2.q.d.361.1 | yes | 4 | 7.3 | odd | 6 | ||
1260.2.s.e.361.1 | 4 | 21.17 | even | 6 | |||
1260.2.s.e.541.1 | 4 | 21.20 | even | 2 | |||
1680.2.bg.t.961.2 | 4 | 28.27 | even | 2 | |||
1680.2.bg.t.1201.2 | 4 | 28.3 | even | 6 | |||
2100.2.q.k.1201.2 | 4 | 35.24 | odd | 6 | |||
2100.2.q.k.1801.2 | 4 | 35.34 | odd | 2 | |||
2100.2.bc.f.949.2 | 8 | 35.3 | even | 12 | |||
2100.2.bc.f.949.3 | 8 | 35.17 | even | 12 | |||
2100.2.bc.f.1549.2 | 8 | 35.27 | even | 4 | |||
2100.2.bc.f.1549.3 | 8 | 35.13 | even | 4 | |||
2940.2.a.p.1.2 | 2 | 7.2 | even | 3 | |||
2940.2.a.r.1.2 | 2 | 7.5 | odd | 6 | |||
2940.2.q.q.361.1 | 4 | 7.4 | even | 3 | inner | ||
2940.2.q.q.961.1 | 4 | 1.1 | even | 1 | trivial | ||
8820.2.a.bf.1.1 | 2 | 21.2 | odd | 6 | |||
8820.2.a.bk.1.1 | 2 | 21.5 | even | 6 |