Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(2431,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4560.2431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.d (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: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 35x^{10} + 202x^{8} + 362x^{6} + 245x^{4} + 63x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.6 | ||
Root | \(-0.738386i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.2431 |
Dual form | 4560.2.d.j.2431.7 |
$q$-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 \(\left(\mathbb{Z}/4560\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(1711\) | \(1921\) | \(2737\) | \(3041\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.238175i | − | 0.0900215i | −0.998987 | − | 0.0450108i | \(-0.985668\pi\) | ||
0.998987 | − | 0.0450108i | \(-0.0143322\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.02175i | − | 1.51412i | −0.653348 | − | 0.757058i | \(-0.726636\pi\) | ||
0.653348 | − | 0.757058i | \(-0.273364\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.35047i | − | 1.48395i | −0.670426 | − | 0.741977i | \(-0.733889\pi\) | ||
0.670426 | − | 0.741977i | \(-0.266111\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.36324 | 1.05824 | 0.529121 | − | 0.848547i | \(-0.322522\pi\) | ||||
0.529121 | + | 0.848547i | \(0.322522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.72588 | + | 4.00267i | 0.395944 | + | 0.918275i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.238175i | 0.0519739i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.83099i | − | 1.21585i | −0.793996 | − | 0.607923i | \(-0.792003\pi\) | ||
0.793996 | − | 0.607923i | \(-0.207997\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 8.48585i | − | 1.57578i | −0.615814 | − | 0.787892i | \(-0.711173\pi\) | ||
0.615814 | − | 0.787892i | \(-0.288827\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.65870 | −1.01633 | −0.508166 | − | 0.861259i | \(-0.669677\pi\) | ||||
−0.508166 | + | 0.861259i | \(0.669677\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.02175i | 0.874175i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 0.238175i | − | 0.0402588i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.51714i | − | 1.07141i | −0.844405 | − | 0.535706i | \(-0.820046\pi\) | ||
0.844405 | − | 0.535706i | \(-0.179954\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.35047i | 0.856761i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.59282i | 0.873451i | 0.899595 | + | 0.436726i | \(0.143862\pi\) | ||||
−0.899595 | + | 0.436726i | \(0.856138\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.99046i | 1.06604i | 0.846104 | + | 0.533018i | \(0.178942\pi\) | ||||
−0.846104 | + | 0.533018i | \(0.821058\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.328717i | 0.0479484i | 0.999713 | + | 0.0239742i | \(0.00763195\pi\) | ||||
−0.999713 | + | 0.0239742i | \(0.992368\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.94327 | 0.991896 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.36324 | −0.610976 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.29509i | 1.27678i | 0.769713 | + | 0.638390i | \(0.220399\pi\) | ||||
−0.769713 | + | 0.638390i | \(0.779601\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.02175i | − | 0.677133i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.72588 | − | 4.00267i | −0.228598 | − | 0.530166i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.71543 | −0.223330 | −0.111665 | − | 0.993746i | \(-0.535618\pi\) | ||||
−0.111665 | + | 0.993746i | \(0.535618\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.9433 | −1.78525 | −0.892627 | − | 0.450797i | \(-0.851140\pi\) | ||||
−0.892627 | + | 0.450797i | \(0.851140\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 0.238175i | − | 0.0300072i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 5.35047i | − | 0.663644i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.6486 | −1.30094 | −0.650469 | − | 0.759533i | \(-0.725428\pi\) | ||||
−0.650469 | + | 0.759533i | \(0.725428\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.83099i | 0.701969i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.29546 | −0.391099 | −0.195550 | − | 0.980694i | \(-0.562649\pi\) | ||||
−0.195550 | + | 0.980694i | \(0.562649\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.74722 | 1.02378 | 0.511892 | − | 0.859050i | \(-0.328945\pi\) | ||||
0.511892 | + | 0.859050i | \(0.328945\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.19605 | −0.136303 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.52352 | −0.846462 | −0.423231 | − | 0.906022i | \(-0.639104\pi\) | ||||
−0.423231 | + | 0.906022i | \(0.639104\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.08101i | − | 0.777241i | −0.921398 | − | 0.388621i | \(-0.872952\pi\) | ||
0.921398 | − | 0.388621i | \(-0.127048\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.36324 | 0.473260 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.48585i | 0.909779i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.67099i | − | 0.601123i | −0.953762 | − | 0.300562i | \(-0.902826\pi\) | ||
0.953762 | − | 0.300562i | \(-0.0971741\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.27435 | −0.133588 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.65870 | 0.586780 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.72588 | + | 4.00267i | 0.177072 | + | 0.410665i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.4546i | 1.06150i | 0.847528 | + | 0.530750i | \(0.178090\pi\) | ||||
−0.847528 | + | 0.530750i | \(0.821910\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.02175i | − | 0.504705i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.07846 | 0.803837 | 0.401918 | − | 0.915676i | \(-0.368344\pi\) | ||||
0.401918 | + | 0.915676i | \(0.368344\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.6486 | 1.04924 | 0.524621 | − | 0.851336i | \(-0.324207\pi\) | ||||
0.524621 | + | 0.851336i | \(0.324207\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.238175i | 0.0232435i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.3532 | −1.48425 | −0.742124 | − | 0.670263i | \(-0.766181\pi\) | ||||
−0.742124 | + | 0.670263i | \(0.766181\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.2935i | − | 1.08172i | −0.841112 | − | 0.540862i | \(-0.818098\pi\) | ||
0.841112 | − | 0.540862i | \(-0.181902\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.51714i | 0.618580i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.62931i | 0.811778i | 0.913922 | + | 0.405889i | \(0.133038\pi\) | ||||
−0.913922 | + | 0.405889i | \(0.866962\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5.83099i | − | 0.543743i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 5.35047i | − | 0.494651i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1.03921i | − | 0.0952645i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.2180 | −1.29255 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 5.59282i | − | 0.504287i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.90142 | 0.346195 | 0.173098 | − | 0.984905i | \(-0.444622\pi\) | ||||
0.173098 | + | 0.984905i | \(0.444622\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 6.99046i | − | 0.615476i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.53844i | 0.833377i | 0.909049 | + | 0.416689i | \(0.136809\pi\) | ||||
−0.909049 | + | 0.416689i | \(0.863191\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.953333 | − | 0.411061i | 0.0826645 | − | 0.0356435i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.4270 | −1.74520 | −0.872600 | − | 0.488436i | \(-0.837568\pi\) | ||||
−0.872600 | + | 0.488436i | \(0.837568\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 17.7567i | − | 1.50610i | −0.657962 | − | 0.753051i | \(-0.728581\pi\) | ||
0.657962 | − | 0.753051i | \(-0.271419\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 0.328717i | − | 0.0276830i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −26.8687 | −2.24688 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 8.48585i | − | 0.704712i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.94327 | −0.572671 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.6129 | 1.03329 | 0.516643 | − | 0.856201i | \(-0.327181\pi\) | ||||
0.516643 | + | 0.856201i | \(0.327181\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5026 | −1.58710 | −0.793548 | − | 0.608507i | \(-0.791769\pi\) | ||||
−0.793548 | + | 0.608507i | \(0.791769\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.36324 | 0.352747 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.65870 | −0.454518 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.0895 | 1.52351 | 0.761754 | − | 0.647866i | \(-0.224338\pi\) | ||||
0.761754 | + | 0.647866i | \(0.224338\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 9.29509i | − | 0.737149i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.38879 | −0.109452 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5.51818i | − | 0.432218i | −0.976369 | − | 0.216109i | \(-0.930663\pi\) | ||
0.976369 | − | 0.216109i | \(-0.0693366\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.02175i | 0.390943i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.5513 | 0.893869 | 0.446934 | − | 0.894567i | \(-0.352516\pi\) | ||||
0.446934 | + | 0.894567i | \(0.352516\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15.6275 | −1.20212 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.72588 | + | 4.00267i | 0.131981 | + | 0.306092i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.05025i | 0.612049i | 0.952024 | + | 0.306025i | \(0.0989990\pi\) | ||||
−0.952024 | + | 0.306025i | \(0.901001\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 0.238175i | − | 0.0180043i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.71543 | 0.128940 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.79703 | −0.209060 | −0.104530 | − | 0.994522i | \(-0.533334\pi\) | ||||
−0.104530 | + | 0.994522i | \(0.533334\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.70499i | − | 0.572707i | −0.958124 | − | 0.286354i | \(-0.907557\pi\) | ||
0.958124 | − | 0.286354i | \(-0.0924432\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.9433 | 1.03072 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 6.51714i | − | 0.479150i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 21.9111i | − | 1.60230i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.238175i | 0.0173246i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.0287172i | 0.00207791i | 0.999999 | + | 0.00103895i | \(0.000330709\pi\) | ||||
−0.999999 | + | 0.00103895i | \(0.999669\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.18380i | 0.301156i | 0.988598 | + | 0.150578i | \(0.0481135\pi\) | ||||
−0.988598 | + | 0.150578i | \(0.951886\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.35047i | 0.383155i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.155471 | 0.0110768 | 0.00553841 | − | 0.999985i | \(-0.498237\pi\) | ||||
0.00553841 | + | 0.999985i | \(0.498237\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.74291i | 0.123551i | 0.998090 | + | 0.0617757i | \(0.0196764\pi\) | ||||
−0.998090 | + | 0.0617757i | \(0.980324\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.6486 | 0.751097 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.02111 | −0.141854 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.59282i | 0.390619i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 5.83099i | − | 0.405282i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20.1004 | − | 8.66694i | 1.39037 | − | 0.599505i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.7478 | 1.29065 | 0.645327 | − | 0.763906i | \(-0.276721\pi\) | ||||
0.645327 | + | 0.763906i | \(0.276721\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.29546 | 0.225801 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.99046i | 0.476746i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.34776i | 0.0914918i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.74722 | −0.591082 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 23.3454i | − | 1.57038i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.8236 | −0.925695 | −0.462848 | − | 0.886438i | \(-0.653172\pi\) | ||||
−0.462848 | + | 0.886438i | \(0.653172\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.1423 | 1.20414 | 0.602072 | − | 0.798442i | \(-0.294342\pi\) | ||||
0.602072 | + | 0.798442i | \(0.294342\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.92237 | −0.391361 | −0.195681 | − | 0.980668i | \(-0.562692\pi\) | ||||
−0.195681 | + | 0.980668i | \(0.562692\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.19605 | 0.0786945 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.8767 | 1.36768 | 0.683839 | − | 0.729633i | \(-0.260309\pi\) | ||||
0.683839 | + | 0.729633i | \(0.260309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.328717i | 0.0214432i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.52352 | 0.488705 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.58436i | 0.231853i | 0.993258 | + | 0.115927i | \(0.0369837\pi\) | ||||
−0.993258 | + | 0.115927i | \(0.963016\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 16.4985i | − | 1.06276i | −0.847133 | − | 0.531380i | \(-0.821674\pi\) | ||
0.847133 | − | 0.531380i | \(-0.178326\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.94327 | 0.443589 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.4161 | − | 9.23427i | 1.36268 | − | 0.587562i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.08101i | 0.448741i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 14.9787i | − | 0.945450i | −0.881210 | − | 0.472725i | \(-0.843270\pi\) | ||
0.881210 | − | 0.472725i | \(-0.156730\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.2818 | −1.84093 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.36324 | −0.273237 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 13.8363i | − | 0.863086i | −0.902092 | − | 0.431543i | \(-0.857969\pi\) | ||
0.902092 | − | 0.431543i | \(-0.142031\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.55222 | −0.0964501 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 8.48585i | − | 0.525261i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 29.2462i | 1.80340i | 0.432364 | + | 0.901699i | \(0.357680\pi\) | ||||
−0.432364 | + | 0.901699i | \(0.642320\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.29509i | 0.570993i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.67099i | 0.347059i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 24.8947i | − | 1.51786i | −0.651174 | − | 0.758928i | \(-0.725723\pi\) | ||
0.651174 | − | 0.758928i | \(-0.274277\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 14.9419i | − | 0.907655i | −0.891090 | − | 0.453827i | \(-0.850058\pi\) | ||
0.891090 | − | 0.453827i | \(-0.149942\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.27435 | 0.0771269 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 5.02175i | − | 0.302823i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.1722 | −0.971691 | −0.485845 | − | 0.874045i | \(-0.661488\pi\) | ||||
−0.485845 | + | 0.874045i | \(0.661488\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.65870 | −0.338778 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.0827i | − | 0.720792i | −0.932799 | − | 0.360396i | \(-0.882642\pi\) | ||
0.932799 | − | 0.360396i | \(-0.117358\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.35350i | 0.318232i | 0.987260 | + | 0.159116i | \(0.0508645\pi\) | ||||
−0.987260 | + | 0.159116i | \(0.949136\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.72588 | − | 4.00267i | −0.102232 | − | 0.237098i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.33207 | 0.0786294 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.03787 | 0.119875 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 10.4546i | − | 0.612857i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.93582i | − | 0.113092i | −0.998400 | − | 0.0565460i | \(-0.981991\pi\) | ||
0.998400 | − | 0.0565460i | \(-0.0180087\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.71543 | −0.0998761 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.02175i | 0.291392i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31.1985 | −1.80426 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.66495 | 0.0959662 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.07846 | −0.464095 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.9433 | −0.798389 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.6518 | −1.00744 | −0.503720 | − | 0.863867i | \(-0.668036\pi\) | ||||
−0.503720 | + | 0.863867i | \(0.668036\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.6486 | −0.605780 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.01253i | − | 0.454349i | −0.973854 | − | 0.227175i | \(-0.927051\pi\) | ||
0.973854 | − | 0.227175i | \(-0.0729488\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.84580 | −0.273901 | −0.136950 | − | 0.990578i | \(-0.543730\pi\) | ||||
−0.136950 | + | 0.990578i | \(0.543730\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 0.238175i | − | 0.0134196i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.756756i | 0.0425036i | 0.999774 | + | 0.0212518i | \(0.00676517\pi\) | ||||
−0.999774 | + | 0.0212518i | \(0.993235\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −42.6139 | −2.38592 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.3532 | 0.856931 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.53043 | + | 17.4646i | 0.419004 | + | 0.971756i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 5.35047i | − | 0.296791i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.2935i | 0.624533i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.0782921 | 0.00431638 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0857 | 1.10401 | 0.552006 | − | 0.833840i | \(-0.313863\pi\) | ||||
0.552006 | + | 0.833840i | \(0.313863\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 6.51714i | − | 0.357137i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.6486 | −0.581797 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 9.90316i | − | 0.539460i | −0.962936 | − | 0.269730i | \(-0.913066\pi\) | ||
0.962936 | − | 0.269730i | \(-0.0869344\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 8.62931i | − | 0.468680i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.4166i | 1.53885i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 3.32093i | − | 0.179314i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.83099i | 0.313930i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.39677i | 0.236031i | 0.993012 | + | 0.118016i | \(0.0376533\pi\) | ||||
−0.993012 | + | 0.118016i | \(0.962347\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.8909 | −1.65355 | −0.826776 | − | 0.562531i | \(-0.809828\pi\) | ||||
−0.826776 | + | 0.562531i | \(0.809828\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.35047i | 0.285587i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.2106 | −1.66118 | −0.830588 | − | 0.556888i | \(-0.811995\pi\) | ||||
−0.830588 | + | 0.556888i | \(0.811995\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.29546 | −0.174905 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.03921i | 0.0550010i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 16.6056i | − | 0.876408i | −0.898876 | − | 0.438204i | \(-0.855615\pi\) | ||
0.898876 | − | 0.438204i | \(-0.144385\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0427 | + | 13.8162i | −0.686457 | + | 0.727171i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.2180 | 0.746251 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.74722 | 0.457850 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 16.0432i | − | 0.837449i | −0.908113 | − | 0.418724i | \(-0.862477\pi\) | ||
0.908113 | − | 0.418724i | \(-0.137523\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.59282i | 0.291150i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.21385 | 0.114938 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.83604i | 0.146844i | 0.997301 | + | 0.0734222i | \(0.0233921\pi\) | ||||
−0.997301 | + | 0.0734222i | \(0.976608\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −45.4033 | −2.33839 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.8447 | −1.43029 | −0.715143 | − | 0.698978i | \(-0.753638\pi\) | ||||
−0.715143 | + | 0.698978i | \(0.753638\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.90142 | −0.199876 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.3563 | 0.733574 | 0.366787 | − | 0.930305i | \(-0.380458\pi\) | ||||
0.366787 | + | 0.930305i | \(0.380458\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.19605 | −0.0609565 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.99046i | 0.355345i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.6300 | 0.893877 | 0.446938 | − | 0.894565i | \(-0.352514\pi\) | ||||
0.446938 | + | 0.894565i | \(0.352514\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 25.4420i | − | 1.28666i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 9.53844i | − | 0.481151i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.52352 | −0.378549 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.5833 | 1.03305 | 0.516524 | − | 0.856273i | \(-0.327226\pi\) | ||||
0.516524 | + | 0.856273i | \(0.327226\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.953333 | + | 0.411061i | −0.0477264 | + | 0.0205788i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.6997i | 1.93257i | 0.257472 | + | 0.966286i | \(0.417110\pi\) | ||||
−0.257472 | + | 0.966286i | \(0.582890\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.2767i | 1.50819i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −32.7275 | −1.62224 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.3093i | − | 1.10312i | −0.834134 | − | 0.551562i | \(-0.814032\pi\) | ||
0.834134 | − | 0.551562i | \(-0.185968\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.4270 | 1.00759 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.408571i | 0.0201045i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 7.08101i | − | 0.347593i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.7567i | 0.869549i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 16.0263i | − | 0.782936i | −0.920192 | − | 0.391468i | \(-0.871967\pi\) | ||
0.920192 | − | 0.391468i | \(-0.128033\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 32.4549i | − | 1.58175i | −0.611975 | − | 0.790877i | \(-0.709625\pi\) | ||
0.611975 | − | 0.790877i | \(-0.290375\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.328717i | 0.0159828i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.36324 | 0.211648 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.32093i | 0.160711i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 26.8687 | 1.29723 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.3195 | −0.497073 | −0.248536 | − | 0.968623i | \(-0.579950\pi\) | ||||
−0.248536 | + | 0.968623i | \(0.579950\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5.28376i | − | 0.253921i | −0.991908 | − | 0.126961i | \(-0.959478\pi\) | ||
0.991908 | − | 0.126961i | \(-0.0405222\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.48585i | 0.406866i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.3395 | − | 10.0636i | 1.11648 | − | 0.481407i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.5247 | −1.40914 | −0.704569 | − | 0.709635i | \(-0.748860\pi\) | ||||
−0.704569 | + | 0.709635i | \(0.748860\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.94327 | 0.330632 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 6.29905i | − | 0.299277i | −0.988741 | − | 0.149638i | \(-0.952189\pi\) | ||
0.988741 | − | 0.149638i | \(-0.0478110\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 5.67099i | − | 0.268831i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.6129 | −0.596568 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.4136i | 1.43531i | 0.696401 | + | 0.717653i | \(0.254784\pi\) | ||||
−0.696401 | + | 0.717653i | \(0.745216\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.0857 | 1.32251 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.5026 | 0.916311 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.27435 | −0.0597422 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.1217 | −1.31548 | −0.657739 | − | 0.753246i | \(-0.728487\pi\) | ||||
−0.657739 | + | 0.753246i | \(0.728487\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.36324 | −0.203659 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.95794 | −0.184339 | −0.0921697 | − | 0.995743i | \(-0.529380\pi\) | ||||
−0.0921697 | + | 0.995743i | \(0.529380\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 12.2869i | − | 0.571019i | −0.958376 | − | 0.285510i | \(-0.907837\pi\) | ||
0.958376 | − | 0.285510i | \(-0.0921629\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.65870 | 0.262416 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 31.5931i | − | 1.46195i | −0.682403 | − | 0.730976i | \(-0.739065\pi\) | ||
0.682403 | − | 0.730976i | \(-0.260935\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.53624i | 0.117112i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.0895 | −0.879598 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.1044 | 1.61410 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.72588 | + | 4.00267i | 0.0791888 | + | 0.183655i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.29509i | 0.425593i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.6890i | 1.12807i | 0.825752 | + | 0.564034i | \(0.190751\pi\) | ||||
−0.825752 | + | 0.564034i | \(0.809249\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.8698 | −1.58992 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.38879 | 0.0631923 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.4546i | 0.474717i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.9253 | 0.948216 | 0.474108 | − | 0.880467i | \(-0.342771\pi\) | ||||
0.474108 | + | 0.880467i | \(0.342771\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.51818i | 0.249541i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 9.15466i | − | 0.413144i | −0.978431 | − | 0.206572i | \(-0.933769\pi\) | ||
0.978431 | − | 0.206572i | \(-0.0662308\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 37.0258i | − | 1.66756i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 5.02175i | − | 0.225711i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.784895i | 0.0352073i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 32.8579i | − | 1.47092i | −0.677566 | − | 0.735462i | \(-0.736965\pi\) | ||
0.677566 | − | 0.735462i | \(-0.263035\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.5513 | −0.516075 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.3433i | 1.75423i | 0.480278 | + | 0.877116i | \(0.340536\pi\) | ||||
−0.480278 | + | 0.877116i | \(0.659464\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.07846 | 0.359487 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.6275 | 0.694043 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.73039i | − | 0.0766983i | −0.999264 | − | 0.0383492i | \(-0.987790\pi\) | ||
0.999264 | − | 0.0383492i | \(-0.0122099\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 2.08337i | − | 0.0921626i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.72588 | − | 4.00267i | −0.0761994 | − | 0.176722i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.6486 | 0.469235 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.65074 | 0.0725994 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 8.05025i | − | 0.353367i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.5057i | 0.766939i | 0.923554 | + | 0.383470i | \(0.125271\pi\) | ||||
−0.923554 | + | 0.383470i | \(0.874729\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.0971 | 0.747604 | 0.373802 | − | 0.927509i | \(-0.378054\pi\) | ||||
0.373802 | + | 0.927509i | \(0.378054\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.238175i | 0.0103948i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.6903 | −1.07553 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0005 | −0.478280 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.71543 | −0.0744433 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29.9242 | 1.29616 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.3532 | −0.663776 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.79703 | 0.120701 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 34.8674i | − | 1.50185i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.4743 | 1.26720 | 0.633600 | − | 0.773661i | \(-0.281577\pi\) | ||||
0.633600 | + | 0.773661i | \(0.281577\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.70499i | 0.330653i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 11.2935i | − | 0.483761i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.8488 | 1.14797 | 0.573986 | − | 0.818865i | \(-0.305396\pi\) | ||||
0.573986 | + | 0.818865i | \(0.305396\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.9433 | −0.595084 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.9660 | − | 14.6456i | 1.44700 | − | 0.623922i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.79191i | 0.0761998i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.51714i | 0.276637i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.7543 | 0.879387 | 0.439694 | − | 0.898148i | \(-0.355087\pi\) | ||||
0.439694 | + | 0.898148i | \(0.355087\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.4023 | 1.58195 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.9111i | 0.925088i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.5147 | 1.11746 | 0.558730 | − | 0.829350i | \(-0.311289\pi\) | ||||
0.558730 | + | 0.829350i | \(0.311289\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.62931i | 0.363038i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 0.238175i | − | 0.0100024i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.1478i | 1.09617i | 0.836421 | + | 0.548087i | \(0.184644\pi\) | ||||
−0.836421 | + | 0.548087i | \(0.815356\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.8025i | 1.33089i | 0.746445 | + | 0.665447i | \(0.231759\pi\) | ||||
−0.746445 | + | 0.665447i | \(0.768241\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 0.0287172i | − | 0.00119968i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 5.83099i | − | 0.243169i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.2797 | 0.844255 | 0.422127 | − | 0.906537i | \(-0.361284\pi\) | ||||
0.422127 | + | 0.906537i | \(0.361284\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 4.18380i | − | 0.173873i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.68652 | −0.0699685 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 46.6777 | 1.93319 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 5.35047i | − | 0.221215i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 43.6829i | 1.80299i | 0.432794 | + | 0.901493i | \(0.357528\pi\) | ||||
−0.432794 | + | 0.901493i | \(0.642472\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.76624 | − | 22.6499i | −0.402411 | − | 0.933273i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.155471 | −0.00639521 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.1504 | −0.745346 | −0.372673 | − | 0.927963i | \(-0.621559\pi\) | ||||
−0.372673 | + | 0.927963i | \(0.621559\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1.03921i | − | 0.0426036i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1.74291i | − | 0.0713325i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.53126 | −0.226001 | −0.113001 | − | 0.993595i | \(-0.536046\pi\) | ||||
−0.113001 | + | 0.993595i | \(0.536046\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 30.5360i | − | 1.24559i | −0.782386 | − | 0.622794i | \(-0.785997\pi\) | ||
0.782386 | − | 0.622794i | \(-0.214003\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.6486 | −0.433646 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.2180 | −0.578044 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.7869 | 1.45255 | 0.726273 | − | 0.687406i | \(-0.241251\pi\) | ||||
0.726273 | + | 0.687406i | \(0.241251\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.02111 | 0.0818997 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.75879 | 0.0711531 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.9162 | −1.28908 | −0.644542 | − | 0.764569i | \(-0.722952\pi\) | ||||
−0.644542 | + | 0.764569i | \(0.722952\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 5.59282i | − | 0.225524i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.75535 | 0.271960 | 0.135980 | − | 0.990712i | \(-0.456582\pi\) | ||||
0.135980 | + | 0.990712i | \(0.456582\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.1162i | 1.37125i | 0.727956 | + | 0.685624i | \(0.240471\pi\) | ||||
−0.727956 | + | 0.685624i | \(0.759529\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.83099i | 0.233990i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.35068 | −0.0541140 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.1004 | + | 8.66694i | −0.802733 | + | 0.346124i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 28.4359i | − | 1.13381i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 25.8948i | − | 1.03086i | −0.856933 | − | 0.515428i | \(-0.827633\pi\) | ||
0.856933 | − | 0.515428i | \(-0.172367\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.7478 | −0.745160 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.90142 | 0.154823 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 37.1498i | − | 1.47193i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.29546 | −0.130366 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 18.7724i | − | 0.741464i | −0.928740 | − | 0.370732i | \(-0.879107\pi\) | ||
0.928740 | − | 0.370732i | \(-0.120893\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.49043i | 0.177085i | 0.996072 | + | 0.0885427i | \(0.0282210\pi\) | ||||
−0.996072 | + | 0.0885427i | \(0.971779\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 6.99046i | − | 0.275249i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 13.8250i | − | 0.543515i | −0.962366 | − | 0.271757i | \(-0.912395\pi\) | ||
0.962366 | − | 0.271757i | \(-0.0876049\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.61446i | 0.338147i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 1.34776i | − | 0.0528228i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.7480 | 1.04673 | 0.523366 | − | 0.852108i | \(-0.324676\pi\) | ||||
0.523366 | + | 0.852108i | \(0.324676\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.53844i | 0.372698i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.74722 | 0.341262 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.18851 | −0.357934 | −0.178967 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178967 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.0472i | 1.28539i | 0.766123 | + | 0.642694i | \(0.222183\pi\) | ||||
−0.766123 | + | 0.642694i | \(0.777817\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.3454i | 0.906660i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.953333 | − | 0.411061i | 0.0369687 | − | 0.0159402i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −49.4809 | −1.91591 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.8236 | 0.534450 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 70.0197i | 2.70308i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.8213i | 1.07243i | 0.844080 | + | 0.536217i | \(0.180147\pi\) | ||||
−0.844080 | + | 0.536217i | \(0.819853\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 37.1408i | − | 1.42744i | −0.700433 | − | 0.713718i | \(-0.747010\pi\) | ||
0.700433 | − | 0.713718i | \(-0.252990\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.49001 | 0.0955579 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.1423 | −0.695213 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.0081 | 1.37781 | 0.688906 | − | 0.724851i | \(-0.258091\pi\) | ||||
0.688906 | + | 0.724851i | \(0.258091\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.4270 | −0.780477 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.92237 | 0.225953 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 49.7331 | 1.89468 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.782984i | 0.0297861i | 0.999889 | + | 0.0148931i | \(0.00474078\pi\) | ||||
−0.999889 | + | 0.0148931i | \(0.995259\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.19605 | −0.0454343 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 17.7567i | − | 0.673550i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.4028i | 0.924322i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.8767 | −0.789629 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.3563 | −0.466692 | −0.233346 | − | 0.972394i | \(-0.574967\pi\) | ||||
−0.233346 | + | 0.972394i | \(0.574967\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.0859 | − | 11.2478i | 0.983850 | − | 0.424219i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 0.328717i | − | 0.0123802i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1.92408i | − | 0.0723626i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.63067 | −0.211464 | −0.105732 | − | 0.994395i | \(-0.533719\pi\) | ||||
−0.105732 | + | 0.994395i | \(0.533719\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.52352 | −0.282154 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 32.9958i | 1.23570i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.8687 | −1.00483 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 3.58436i | − | 0.133860i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.8084i | 0.962489i | 0.876586 | + | 0.481245i | \(0.159815\pi\) | ||||
−0.876586 | + | 0.481245i | \(0.840185\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 2.53624i | − | 0.0944543i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.4985i | 0.613585i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 8.48585i | − | 0.315157i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 6.92021i | − | 0.256656i | −0.991732 | − | 0.128328i | \(-0.959039\pi\) | ||
0.991732 | − | 0.128328i | \(-0.0409611\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.5011i | 1.12812i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.3083 | 1.11946 | 0.559732 | − | 0.828674i | \(-0.310904\pi\) | ||||
0.559732 | + | 0.828674i | \(0.310904\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.94327 | −0.256106 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 53.4748i | 1.96977i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 37.7028i | − | 1.38692i | −0.720496 | − | 0.693460i | \(-0.756086\pi\) | ||
0.720496 | − | 0.693460i | \(-0.243914\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.4161 | + | 9.23427i | −0.786742 | + | 0.339229i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.4967 | 0.862010 | 0.431005 | − | 0.902349i | \(-0.358159\pi\) | ||||
0.431005 | + | 0.902349i | \(0.358159\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.6129 | 0.462100 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 7.08101i | − | 0.259080i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.65674i | 0.133614i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.7453 | 1.15840 | 0.579201 | − | 0.815185i | \(-0.303365\pi\) | ||||
0.579201 | + | 0.815185i | \(0.303365\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.9787i | 0.545856i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.5026 | −0.709771 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −50.7634 | −1.84503 | −0.922514 | − | 0.385964i | \(-0.873869\pi\) | ||||
−0.922514 | + | 0.385964i | \(0.873869\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29.2818 | 1.06286 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.70934 | 0.351963 | 0.175982 | − | 0.984393i | \(-0.443690\pi\) | ||||
0.175982 | + | 0.984393i | \(0.443690\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.68983 | −0.0973784 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.36324 | 0.157753 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.17835i | 0.331411i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.8126 | −1.39962 | −0.699809 | − | 0.714330i | \(-0.746732\pi\) | ||||
−0.699809 | + | 0.714330i | \(0.746732\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.8363i | 0.498303i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.6751i | 0.959438i | 0.877422 | + | 0.479719i | \(0.159261\pi\) | ||||
−0.877422 | + | 0.479719i | \(0.840739\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.65870 | −0.203267 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.55222 | 0.0556855 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.3862 | + | 9.65253i | −0.802068 | + | 0.345838i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.5490i | 0.592169i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.48585i | 0.303260i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.0895 | 0.681334 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.1398 | 0.610966 | 0.305483 | − | 0.952198i | \(-0.401182\pi\) | ||||
0.305483 | + | 0.952198i | \(0.401182\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 29.2462i | − | 1.04119i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.05528 | 0.0730774 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 74.6031i | 2.64923i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 9.29509i | − | 0.329663i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 5.75453i | − | 0.203836i | −0.994793 | − | 0.101918i | \(-0.967502\pi\) | ||
0.994793 | − | 0.101918i | \(-0.0324979\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.43427i | 0.0507409i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 5.67099i | − | 0.200374i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 43.9264i | − | 1.55013i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.38879 | −0.0489485 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.8947i | 0.876335i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.9654 | 1.40511 | 0.702555 | − | 0.711630i | \(-0.252043\pi\) | ||||
0.702555 | + | 0.711630i | \(0.252043\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.6897 | −0.445594 | −0.222797 | − | 0.974865i | \(-0.571519\pi\) | ||||
−0.222797 | + | 0.974865i | \(0.571519\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.9419i | 0.524035i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 5.51818i | − | 0.193294i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.9805 | + | 12.0647i | −0.978914 | + | 0.422090i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.27435 | −0.0445292 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.2586 | −0.462730 | −0.231365 | − | 0.972867i | \(-0.574319\pi\) | ||||
−0.231365 | + | 0.972867i | \(0.574319\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 3.44493i | − | 0.120083i | −0.998196 | − | 0.0600414i | \(-0.980877\pi\) | ||
0.998196 | − | 0.0600414i | \(-0.0191233\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.02175i | 0.174835i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 51.1260 | 1.77783 | 0.888913 | − | 0.458076i | \(-0.151461\pi\) | ||||
0.888913 | + | 0.458076i | \(0.151461\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 48.2813i | − | 1.67688i | −0.544994 | − | 0.838440i | \(-0.683468\pi\) | ||
0.544994 | − | 0.838440i | \(-0.316532\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.1722 | 0.561006 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.2952 | 1.04967 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.5513 | 0.399750 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.65870 | 0.195593 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47.0092 | −1.62294 | −0.811468 | − | 0.584396i | \(-0.801331\pi\) | ||||
−0.811468 | + | 0.584396i | \(0.801331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −43.0097 | −1.48309 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.0827i | 0.416149i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.6275 | −0.537603 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.38636i | 0.116357i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 5.35350i | − | 0.183732i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38.0014 | −1.30267 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.1722 | −0.553724 | −0.276862 | − | 0.960910i | \(-0.589295\pi\) | ||||
−0.276862 | + | 0.960910i | \(0.589295\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.72588 | + | 4.00267i | 0.0590238 | + | 0.136888i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.0628i | 0.890288i | 0.895459 | + | 0.445144i | \(0.146848\pi\) | ||||
−0.895459 | + | 0.445144i | \(0.853152\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.31302i | 0.215398i | 0.994184 | + | 0.107699i | \(0.0343482\pi\) | ||||
−0.994184 | + | 0.107699i | \(0.965652\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.33207 | −0.0453967 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.2582 | 0.689597 | 0.344799 | − | 0.938677i | \(-0.387947\pi\) | ||||
0.344799 | + | 0.938677i | \(0.387947\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.05025i | 0.273717i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.03787 | −0.0692098 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.7812i | 1.28164i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56.9752i | 1.93053i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.4546i | 0.353833i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 0.238175i | − | 0.00805177i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 21.6235i | − | 0.730174i | −0.930973 | − | 0.365087i | \(-0.881039\pi\) | ||
0.930973 | − | 0.365087i | \(-0.118961\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.93582i | 0.0652937i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.1372 | 0.947967 | 0.473983 | − | 0.880534i | \(-0.342816\pi\) | ||||
0.473983 | + | 0.880534i | \(0.342816\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 29.9128i | − | 1.00665i | −0.864098 | − | 0.503324i | \(-0.832110\pi\) | ||
0.864098 | − | 0.503324i | \(-0.167890\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.71543 | 0.0576635 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.9655 | 1.20760 | 0.603801 | − | 0.797135i | \(-0.293652\pi\) | ||||
0.603801 | + | 0.797135i | \(0.293652\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 0.929219i | − | 0.0311650i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 5.02175i | − | 0.168235i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.31575 | + | 0.567327i | −0.0440298 | + | 0.0189849i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.79703 | −0.0934945 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 31.1985 | 1.04169 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 48.0189i | 1.60152i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.5567i | 1.35114i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.66495 | −0.0554061 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 7.70499i | − | 0.256122i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.3554 | −0.941527 | −0.470764 | − | 0.882259i | \(-0.656021\pi\) | ||||
−0.470764 | + | 0.882259i | \(0.656021\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.07846 | 0.267946 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.1255 | 0.832445 | 0.416222 | − | 0.909263i | \(-0.363354\pi\) | ||||
0.416222 | + | 0.909263i | \(0.363354\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.5591 | −1.17683 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.9433 | 0.460950 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.27181 | 0.0750219 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 23.9029i | − | 0.788485i | −0.919006 | − | 0.394243i | \(-0.871007\pi\) | ||
0.919006 | − | 0.394243i | \(-0.128993\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.6518 | 0.581646 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.6323i | 0.580373i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 6.51714i | − | 0.214282i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.6486 | 0.349747 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.5586 | −1.03540 | −0.517702 | − | 0.855561i | \(-0.673212\pi\) | ||||
−0.517702 | + | 0.855561i | \(0.673212\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.9833 | + | 27.7916i | 0.392735 | + | 0.910833i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.01253i | 0.262319i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 21.9111i | − | 0.716570i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.4540 | 0.374186 | 0.187093 | − | 0.982342i | \(-0.440093\pi\) | ||||
0.187093 | + | 0.982342i | \(0.440093\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.84580 | 0.158137 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 0.140997i | − | 0.00459637i | −0.999997 | − | 0.00229819i | \(-0.999268\pi\) | ||
0.999997 | − | 0.00229819i | \(-0.000731536\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.6117 | 1.06198 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.238175i | 0.00774782i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 25.9714i | − | 0.843957i | −0.906606 | − | 0.421978i | \(-0.861336\pi\) | ||
0.906606 | − | 0.421978i | \(-0.138664\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 46.8017i | − | 1.51925i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 0.756756i | − | 0.0245395i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.6635i | 1.80312i | 0.432656 | + | 0.901559i | \(0.357576\pi\) | ||||
−0.432656 | + | 0.901559i | \(0.642424\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.0287172i | 0.000929268i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 42.6139 | 1.37751 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.86520i | 0.157105i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.02090 | 0.0329323 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.3532 | −0.494749 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.18380i | 0.134681i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 24.9199i | − | 0.801369i | −0.916216 | − | 0.400684i | \(-0.868772\pi\) | ||
0.916216 | − | 0.400684i | \(-0.131228\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.53043 | − | 17.4646i | −0.241912 | − | 0.561044i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.5504 | 1.04459 | 0.522297 | − | 0.852764i | \(-0.325075\pi\) | ||||
0.522297 | + | 0.852764i | \(0.325075\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.22919 | −0.135582 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.35047i | 0.171352i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 18.1618i | − | 0.581047i | −0.956868 | − | 0.290523i | \(-0.906171\pi\) | ||
0.956868 | − | 0.290523i | \(-0.0938294\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.4783 | −0.910170 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 11.2935i | − | 0.360574i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.1146 | 1.34325 | 0.671623 | − | 0.740893i | \(-0.265597\pi\) | ||||
0.671623 | + | 0.740893i | \(0.265597\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.155471 | 0.00495371 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.0782921 | −0.00249207 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 40.7613 | 1.29613 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.4624 | 1.12650 | 0.563250 | − | 0.826287i | \(-0.309551\pi\) | ||||
0.563250 | + | 0.826287i | \(0.309551\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.0857 | −0.637402 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.74291i | 0.0552539i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.3641 | 0.454915 | 0.227457 | − | 0.973788i | \(-0.426959\pi\) | ||||
0.227457 | + | 0.973788i | \(0.426959\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.51714i | 0.206193i |
(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 | 4560.2.d.j.2431.6 | ✓ | 12 | |
4.3 | odd | 2 | 4560.2.d.l.2431.7 | yes | 12 | ||
19.18 | odd | 2 | 4560.2.d.l.2431.6 | yes | 12 | ||
76.75 | even | 2 | inner | 4560.2.d.j.2431.7 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4560.2.d.j.2431.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
4560.2.d.j.2431.7 | yes | 12 | 76.75 | even | 2 | inner | |
4560.2.d.l.2431.6 | yes | 12 | 19.18 | odd | 2 | ||
4560.2.d.l.2431.7 | yes | 12 | 4.3 | odd | 2 |