Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,2,Mod(287,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.287");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.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: | \(4.98266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 287.2 | ||
Root | \(1.68614 - 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.287 |
Dual form | 624.2.d.g.287.1 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.68614 | + | 0.396143i | −0.973494 | + | 0.228714i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.25639i | 1.90351i | 0.306851 | + | 0.951757i | \(0.400725\pi\) | ||||
−0.306851 | + | 0.951757i | \(0.599275\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.792287i | − | 0.299456i | −0.988727 | − | 0.149728i | \(-0.952160\pi\) | ||
0.988727 | − | 0.149728i | \(-0.0478399\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.68614 | − | 1.33591i | 0.895380 | − | 0.445302i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.68614 | − | 7.17687i | −0.435360 | − | 1.85306i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.84096i | 1.41664i | 0.705891 | + | 0.708321i | \(0.250547\pi\) | ||||
−0.705891 | + | 0.708321i | \(0.749453\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.46410i | 0.794719i | 0.917663 | + | 0.397360i | \(0.130073\pi\) | ||||
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.313859 | + | 1.33591i | 0.0684897 | + | 0.291519i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.74456 | −1.40634 | −0.703169 | − | 0.711022i | \(-0.748232\pi\) | ||||
−0.703169 | + | 0.711022i | \(0.748232\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.1168 | −2.62337 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | + | 3.31662i | −0.769800 | + | 0.638285i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.63325i | − | 1.19137i | −0.803219 | − | 0.595683i | \(-0.796881\pi\) | ||
0.803219 | − | 0.595683i | \(-0.203119\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.74456 | + | 1.58457i | −1.17408 | + | 0.275839i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.37228 | 0.570020 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.37228 | −0.883198 | −0.441599 | − | 0.897213i | \(-0.645589\pi\) | ||||
−0.441599 | + | 0.897213i | \(0.645589\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.68614 | + | 0.396143i | −0.269999 | + | 0.0634337i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.58457i | 0.247469i | 0.992315 | + | 0.123734i | \(0.0394871\pi\) | ||||
−0.992315 | + | 0.123734i | \(0.960513\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.30506i | 1.41901i | 0.704701 | + | 0.709504i | \(0.251081\pi\) | ||||
−0.704701 | + | 0.709504i | \(0.748919\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.68614 | + | 11.4333i | 0.847640 | + | 1.70437i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.627719 | −0.0915622 | −0.0457811 | − | 0.998951i | \(-0.514578\pi\) | ||||
−0.0457811 | + | 0.998951i | \(0.514578\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.37228 | 0.910326 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.31386 | − | 9.84868i | −0.324005 | − | 1.37909i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.34363i | − | 0.734004i | −0.930220 | − | 0.367002i | \(-0.880384\pi\) | ||
0.930220 | − | 0.367002i | \(-0.119616\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.0256i | 2.29573i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.37228 | − | 5.84096i | −0.181763 | − | 0.773654i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.0000 | −1.56227 | −0.781133 | − | 0.624364i | \(-0.785358\pi\) | ||||
−0.781133 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4891 | 1.47103 | 0.735516 | − | 0.677507i | \(-0.236940\pi\) | ||||
0.735516 | + | 0.677507i | \(0.236940\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.05842 | − | 2.12819i | −0.133349 | − | 0.268127i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.25639i | 0.527940i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.46410i | 0.423207i | 0.977356 | + | 0.211604i | \(0.0678686\pi\) | ||||
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.3723 | − | 2.67181i | 1.36906 | − | 0.321649i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.11684 | −0.725936 | −0.362968 | − | 0.931802i | \(-0.618237\pi\) | ||||
−0.362968 | + | 0.931802i | \(0.618237\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.744563 | 0.0871445 | 0.0435722 | − | 0.999050i | \(-0.486126\pi\) | ||||
0.0435722 | + | 0.999050i | \(0.486126\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 22.1168 | − | 5.19615i | 2.55383 | − | 0.600000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.16915i | − | 0.361158i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.04868i | 0.568020i | 0.958821 | + | 0.284010i | \(0.0916650\pi\) | ||||
−0.958821 | + | 0.284010i | \(0.908335\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.43070 | − | 7.17687i | 0.603411 | − | 0.797430i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.8614 | −2.69660 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.58457i | − | 0.167965i | −0.996467 | − | 0.0839823i | \(-0.973236\pi\) | ||
0.996467 | − | 0.0839823i | \(-0.0267639\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.792287i | − | 0.0830542i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.62772 | + | 11.1846i | 0.272482 | + | 1.15979i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.7446 | −1.51276 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.74456 | 0.887876 | 0.443938 | − | 0.896058i | \(-0.353581\pi\) | ||||
0.443938 | + | 0.896058i | \(0.353581\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.7446 | − | 5.34363i | 1.07987 | − | 0.537055i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 3.16915i | − | 0.315342i | −0.987492 | − | 0.157671i | \(-0.949601\pi\) | ||
0.987492 | − | 0.157671i | \(-0.0503985\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.87953i | 0.185195i | 0.995704 | + | 0.0925977i | \(0.0295170\pi\) | ||||
−0.995704 | + | 0.0925977i | \(0.970483\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.68614 | + | 1.33591i | −0.554911 | + | 0.130371i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.48913 | 0.530654 | 0.265327 | − | 0.964159i | \(-0.414520\pi\) | ||||
0.265327 | + | 0.964159i | \(0.414520\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.62772 | −0.634820 | −0.317410 | − | 0.948288i | \(-0.602813\pi\) | ||||
−0.317410 | + | 0.948288i | \(0.602813\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.05842 | − | 2.12819i | 0.859787 | − | 0.201999i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.33830i | − | 0.596257i | −0.954526 | − | 0.298128i | \(-0.903638\pi\) | ||
0.954526 | − | 0.298128i | \(-0.0963623\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 28.7075i | − | 2.67699i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.68614 | − | 1.33591i | 0.248334 | − | 0.123505i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.62772 | 0.424222 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.627719 | − | 2.67181i | −0.0565995 | − | 0.240909i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 34.5484i | − | 3.09011i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.63325i | − | 0.588606i | −0.955712 | − | 0.294303i | \(-0.904913\pi\) | ||
0.955712 | − | 0.294303i | \(-0.0950874\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.68614 | − | 15.6896i | −0.324547 | − | 1.38140i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.1168 | 0.883913 | 0.441956 | − | 0.897037i | \(-0.354285\pi\) | ||||
0.441956 | + | 0.897037i | \(0.354285\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.74456 | 0.237984 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −14.1168 | − | 17.0256i | −1.21498 | − | 1.46533i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.75372i | 0.406138i | 0.979164 | + | 0.203069i | \(0.0650916\pi\) | ||||
−0.979164 | + | 0.203069i | \(0.934908\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.6434i | 1.32685i | 0.748242 | + | 0.663426i | \(0.230898\pi\) | ||||
−0.748242 | + | 0.663426i | \(0.769102\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.05842 | − | 0.248667i | 0.0891352 | − | 0.0209415i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.7446 | + | 2.52434i | −0.886197 | + | 0.208204i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 3.75906i | − | 0.307954i | −0.988074 | − | 0.153977i | \(-0.950792\pi\) | ||
0.988074 | − | 0.153977i | \(-0.0492081\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.8896i | 0.886186i | 0.896476 | + | 0.443093i | \(0.146119\pi\) | ||||
−0.896476 | + | 0.443093i | \(0.853881\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.80298 | + | 15.6896i | 0.630834 | + | 1.26843i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 28.2337 | 2.26778 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.74456 | −0.697892 | −0.348946 | − | 0.937143i | \(-0.613460\pi\) | ||||
−0.348946 | + | 0.937143i | \(0.613460\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.11684 | + | 9.01011i | 0.167877 | + | 0.714548i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.34363i | 0.421137i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.4897i | 1.60487i | 0.596737 | + | 0.802437i | \(0.296464\pi\) | ||||
−0.596737 | + | 0.802437i | \(0.703536\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.74456 | − | 28.7075i | −0.525063 | − | 2.23487i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.00000 | 0.309529 | 0.154765 | − | 0.987951i | \(-0.450538\pi\) | ||||
0.154765 | + | 0.987951i | \(0.450538\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.62772 | + | 9.30506i | 0.353890 | + | 0.711576i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.1947i | 1.53537i | 0.640825 | + | 0.767687i | \(0.278593\pi\) | ||||
−0.640825 | + | 0.767687i | \(0.721407\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.3923i | 0.785584i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 20.2337 | − | 4.75372i | 1.52086 | − | 0.357312i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.3723 | −0.850004 | −0.425002 | − | 0.905192i | \(-0.639727\pi\) | ||||
−0.425002 | + | 0.905192i | \(0.639727\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.2337 | 0.760664 | 0.380332 | − | 0.924850i | \(-0.375810\pi\) | ||||
0.380332 | + | 0.924850i | \(0.375810\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.3723 | + | 4.55134i | −1.43204 | + | 0.336445i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 22.8665i | − | 1.68118i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.3639i | 1.70853i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.62772 | + | 3.16915i | 0.191138 | + | 0.230522i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.4891 | 1.55490 | 0.777449 | − | 0.628946i | \(-0.216513\pi\) | ||||
0.777449 | + | 0.628946i | \(0.216513\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.2554 | 0.810184 | 0.405092 | − | 0.914276i | \(-0.367239\pi\) | ||||
0.405092 | + | 0.914276i | \(0.367239\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.68614 | − | 7.17687i | −0.120747 | − | 0.513946i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.25639i | 0.303255i | 0.988438 | + | 0.151628i | \(0.0484514\pi\) | ||||
−0.988438 | + | 0.151628i | \(0.951549\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.80240i | − | 0.694874i | −0.937703 | − | 0.347437i | \(-0.887052\pi\) | ||
0.937703 | − | 0.347437i | \(-0.112948\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.37228 | − | 5.84096i | −0.0967933 | − | 0.411990i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.74456 | −0.471061 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.1168 | + | 9.01011i | −1.25921 | + | 0.626246i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.8564i | 0.958468i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 16.2333i | − | 1.11754i | −0.829321 | − | 0.558772i | \(-0.811273\pi\) | ||
0.829321 | − | 0.558772i | \(-0.188727\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.3139 | − | 2.42315i | 0.706694 | − | 0.166031i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −39.6060 | −2.70110 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.25544 | −0.356762 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.25544 | + | 0.294954i | −0.0848346 | + | 0.0199311i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.84096i | 0.392906i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 26.3306i | − | 1.76323i | −0.471971 | − | 0.881614i | \(-0.656457\pi\) | ||
0.471971 | − | 0.881614i | \(-0.343543\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −35.2337 | + | 17.5229i | −2.34891 | + | 1.16819i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.74456 | 0.182163 | 0.0910815 | − | 0.995843i | \(-0.470968\pi\) | ||||
0.0910815 | + | 0.995843i | \(0.470968\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.13859 | −0.0752404 | −0.0376202 | − | 0.999292i | \(-0.511978\pi\) | ||||
−0.0376202 | + | 0.999292i | \(0.511978\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.25544 | + | 5.34363i | 0.0826017 | + | 0.351585i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.497333i | 0.0325814i | 0.999867 | + | 0.0162907i | \(0.00518572\pi\) | ||||
−0.999867 | + | 0.0162907i | \(0.994814\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 2.67181i | − | 0.174290i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.00000 | − | 8.51278i | −0.129914 | − | 0.552964i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.8614 | 1.34941 | 0.674706 | − | 0.738086i | \(-0.264270\pi\) | ||||
0.674706 | + | 0.738086i | \(0.264270\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.0000 | 1.15948 | 0.579741 | − | 0.814801i | \(-0.303154\pi\) | ||||
0.579741 | + | 0.814801i | \(0.303154\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.31386 | + | 14.2525i | −0.405034 | + | 0.914302i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 27.1229i | 1.73282i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.46410i | 0.220416i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −20.2337 | + | 4.75372i | −1.28226 | + | 0.301255i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.0000 | 1.00991 | 0.504956 | − | 0.863145i | \(-0.331509\pi\) | ||||
0.504956 | + | 0.863145i | \(0.331509\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.9783 | −1.69611 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 41.9198 | − | 9.84868i | 2.62512 | − | 0.616749i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 22.8665i | − | 1.42637i | −0.700974 | − | 0.713187i | \(-0.747251\pi\) | ||
0.700974 | − | 0.713187i | \(-0.252749\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.25639i | 0.264479i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.25544 | −0.0774136 | −0.0387068 | − | 0.999251i | \(-0.512324\pi\) | ||||
−0.0387068 | + | 0.999251i | \(0.512324\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.7446 | 1.39719 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.627719 | + | 2.67181i | 0.0384158 | + | 0.163512i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.34363i | 0.325807i | 0.986642 | + | 0.162903i | \(0.0520859\pi\) | ||||
−0.986642 | + | 0.162903i | \(0.947914\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0588i | 0.854010i | 0.904249 | + | 0.427005i | \(0.140431\pi\) | ||||
−0.904249 | + | 0.427005i | \(0.859569\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.313859 | + | 1.33591i | 0.0189956 | + | 0.0808528i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −52.4674 | −3.16390 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.9783 | −1.26046 | −0.630230 | − | 0.776408i | \(-0.717040\pi\) | ||||
−0.630230 | + | 0.776408i | \(0.717040\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.86141 | − | 17.8178i | −0.530519 | − | 1.06673i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.9484i | − | 1.48830i | −0.668014 | − | 0.744149i | \(-0.732855\pi\) | ||
0.668014 | − | 0.744149i | \(-0.267145\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 27.4179i | − | 1.62982i | −0.579586 | − | 0.814911i | \(-0.696786\pi\) | ||
0.579586 | − | 0.814911i | \(-0.303214\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.8614 | − | 5.84096i | 1.47266 | − | 0.345989i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.25544 | 0.0741061 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.1168 | −1.00687 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.7446 | + | 3.46410i | −0.864342 | + | 0.203069i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.7894i | 1.79874i | 0.437193 | + | 0.899368i | \(0.355973\pi\) | ||||
−0.437193 | + | 0.899368i | \(0.644027\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 51.0767i | − | 2.97380i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −16.0000 | + | 13.2665i | −0.928414 | + | 0.769800i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.74456 | −0.390048 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.37228 | 0.424931 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.25544 | + | 5.34363i | 0.0721230 | + | 0.306983i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 48.9022i | 2.80013i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.8333i | 1.47438i | 0.675684 | + | 0.737192i | \(0.263849\pi\) | ||||
−0.675684 | + | 0.737192i | \(0.736151\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.744563 | − | 3.16915i | −0.0423567 | − | 0.180287i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.25544 | 0.524828 | 0.262414 | − | 0.964955i | \(-0.415481\pi\) | ||||
0.262414 | + | 0.964955i | \(0.415481\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.6277 | 0.826808 | 0.413404 | − | 0.910548i | \(-0.364340\pi\) | ||||
0.413404 | + | 0.910548i | \(0.364340\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.05842 | − | 4.50506i | 0.510384 | − | 0.253831i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3.75906i | − | 0.211130i | −0.994412 | − | 0.105565i | \(-0.966335\pi\) | ||
0.994412 | − | 0.105565i | \(-0.0336650\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.25544 | + | 2.17448i | −0.516588 | + | 0.121368i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.2337 | −1.12583 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.1168 | −0.727592 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.1753 | − | 2.62553i | 0.617994 | − | 0.145192i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.497333i | 0.0274189i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 22.0742i | − | 1.21331i | −0.794965 | − | 0.606655i | \(-0.792511\pi\) | ||
0.794965 | − | 0.606655i | \(-0.207489\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.4307 | + | 7.17687i | −0.790798 | + | 0.393290i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.7446 | −0.805582 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.1168 | 1.09583 | 0.547917 | − | 0.836533i | \(-0.315421\pi\) | ||||
0.547917 | + | 0.836533i | \(0.315421\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.51087 | + | 10.6873i | 0.136372 | + | 0.580452i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 26.5330i | − | 1.43684i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 10.5947i | − | 0.572059i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.3723 | + | 48.4048i | 0.612263 | + | 2.60603i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.6060 | 1.26723 | 0.633617 | − | 0.773647i | \(-0.281569\pi\) | ||||
0.633617 | + | 0.773647i | \(0.281569\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.1168 | 1.71918 | 0.859588 | − | 0.510988i | \(-0.170720\pi\) | ||||
0.859588 | + | 0.510988i | \(0.170720\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.00000 | + | 3.31662i | −0.213504 | + | 0.177028i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.6048i | 1.04346i | 0.853111 | + | 0.521729i | \(0.174713\pi\) | ||||
−0.853111 | + | 0.521729i | \(0.825287\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 26.0357i | − | 1.38183i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.80298 | + | 1.83324i | −0.412978 | + | 0.0970254i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.48913 | 0.0785930 | 0.0392965 | − | 0.999228i | \(-0.487488\pi\) | ||||
0.0392965 | + | 0.999228i | \(0.487488\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.43070 | + | 1.98072i | −0.442497 | + | 0.103961i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.16915i | 0.165881i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.04334i | 0.315460i | 0.987482 | + | 0.157730i | \(0.0504175\pi\) | ||||
−0.987482 | + | 0.157730i | \(0.949582\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.11684 | + | 4.25639i | 0.110198 | + | 0.221579i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.23369 | −0.219802 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.7446 | 0.659888 | 0.329944 | − | 0.944000i | \(-0.392970\pi\) | ||||
0.329944 | + | 0.944000i | \(0.392970\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.6861 | + | 58.2535i | 0.706749 | + | 3.00820i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.3205i | 0.889695i | 0.895606 | + | 0.444847i | \(0.146742\pi\) | ||||
−0.895606 | + | 0.444847i | \(0.853258\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.62772 | + | 11.1846i | 0.134622 | + | 0.573004i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.1168 | −1.13012 | −0.565059 | − | 0.825051i | \(-0.691147\pi\) | ||||
−0.565059 | + | 0.825051i | \(0.691147\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.4891 | 0.687469 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.4307 | + | 24.9947i | 0.631888 | + | 1.27055i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.5437i | 1.24441i | 0.782853 | + | 0.622207i | \(0.213764\pi\) | ||||
−0.782853 | + | 0.622207i | \(0.786236\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 39.3947i | − | 1.99228i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.0584 | + | 4.00772i | −0.860484 | + | 0.202163i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.4891 | −1.08124 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.4891 | 1.37964 | 0.689820 | − | 0.723981i | \(-0.257690\pi\) | ||||
0.689820 | + | 0.723981i | \(0.257690\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.62772 | + | 1.08724i | −0.231676 | + | 0.0544301i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 12.2718i | − | 0.612826i | −0.951899 | − | 0.306413i | \(-0.900871\pi\) | ||
0.951899 | − | 0.306413i | \(-0.0991289\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6.63325i | − | 0.330426i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 30.5475 | + | 23.1152i | 1.51792 | + | 1.14860i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.4891 | −1.06518 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.9783 | −1.63067 | −0.815335 | − | 0.578990i | \(-0.803447\pi\) | ||||
−0.815335 | + | 0.578990i | \(0.803447\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.88316 | − | 8.01544i | −0.0928892 | − | 0.395373i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.50744i | 0.467831i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 51.0767i | 2.50725i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.19702 | − | 26.3769i | −0.303469 | − | 1.29168i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.861407 | −0.0420825 | −0.0210412 | − | 0.999779i | \(-0.506698\pi\) | ||||
−0.0210412 | + | 0.999779i | \(0.506698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.1168 | −1.37033 | −0.685166 | − | 0.728387i | \(-0.740270\pi\) | ||||
−0.685166 | + | 0.728387i | \(0.740270\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.68614 | + | 0.838574i | −0.0819830 | + | 0.0407729i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 76.6150i | − | 3.71637i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 9.10268i | − | 0.440510i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.74456 | + | 1.58457i | −0.325631 | + | 0.0765040i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.3505 | 0.883914 | 0.441957 | − | 0.897036i | \(-0.354284\pi\) | ||||
0.441957 | + | 0.897036i | \(0.354284\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.3505 | −0.977984 | −0.488992 | − | 0.872288i | \(-0.662635\pi\) | ||||
−0.488992 | + | 0.872288i | \(0.662635\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 23.3639i | − | 1.11764i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.5817i | 1.50731i | 0.657270 | + | 0.753656i | \(0.271711\pi\) | ||||
−0.657270 | + | 0.753656i | \(0.728289\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.1168 | − | 8.51278i | 0.815088 | − | 0.405370i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.37228 | −0.160222 | −0.0801110 | − | 0.996786i | \(-0.525527\pi\) | ||||
−0.0801110 | + | 0.996786i | \(0.525527\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.74456 | 0.319723 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.48913 | + | 6.33830i | 0.0704332 | + | 0.299791i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6.92820i | − | 0.326962i | −0.986546 | − | 0.163481i | \(-0.947728\pi\) | ||
0.986546 | − | 0.163481i | \(-0.0522723\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.33830i | 0.298459i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.31386 | − | 18.3615i | −0.202683 | − | 0.862697i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.37228 | 0.158095 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.9783 | −0.794209 | −0.397105 | − | 0.917773i | \(-0.629985\pi\) | ||||
−0.397105 | + | 0.917773i | \(0.629985\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.3723 | − | 23.3639i | −0.904221 | − | 1.09053i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 19.1075i | − | 0.889923i | −0.895550 | − | 0.444962i | \(-0.853217\pi\) | ||
0.895550 | − | 0.444962i | \(-0.146783\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.9822i | − | 0.510387i | −0.966890 | − | 0.255193i | \(-0.917861\pi\) | ||
0.966890 | − | 0.255193i | \(-0.0821391\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −47.6060 | + | 11.1846i | −2.20767 | + | 0.518673i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.51087 | −0.116189 | −0.0580947 | − | 0.998311i | \(-0.518503\pi\) | ||||
−0.0580947 | + | 0.998311i | \(0.518503\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.74456 | 0.126732 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.7446 | − | 3.46410i | 0.679394 | − | 0.159617i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 37.2203i | 1.71139i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 45.4381i | − | 2.08484i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.13859 | − | 14.3537i | −0.326854 | − | 0.657213i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.88316 | −0.451573 | −0.225786 | − | 0.974177i | \(-0.572495\pi\) | ||||
−0.225786 | + | 0.974177i | \(0.572495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.37228 | −0.244955 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.11684 | − | 9.01011i | −0.0963197 | − | 0.409974i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 37.2203i | 1.69008i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.884861i | 0.0400969i | 0.999799 | + | 0.0200484i | \(0.00638204\pi\) | ||||
−0.999799 | + | 0.0200484i | \(0.993618\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.11684 | − | 34.5484i | −0.367056 | − | 1.56233i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.3505 | 1.00867 | 0.504333 | − | 0.863509i | \(-0.331739\pi\) | ||||
0.504333 | + | 0.863509i | \(0.331739\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 22.7446 | + | 45.7330i | 1.02229 | + | 2.05555i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.84630i | 0.217386i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 2.87419i | − | 0.128667i | −0.997928 | − | 0.0643333i | \(-0.979508\pi\) | ||
0.997928 | − | 0.0643333i | \(-0.0204921\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.74456 | + | 1.58457i | −0.301325 | + | 0.0707935i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.2337 | 1.25888 | 0.629439 | − | 0.777050i | \(-0.283285\pi\) | ||||
0.629439 | + | 0.777050i | \(0.283285\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.4891 | 0.600258 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.68614 | + | 0.396143i | −0.0748841 | + | 0.0175934i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.6155i | 0.780792i | 0.920647 | + | 0.390396i | \(0.127662\pi\) | ||||
−0.920647 | + | 0.390396i | \(0.872338\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 0.589907i | − | 0.0260960i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11.4891 | − | 13.8564i | −0.507257 | − | 0.611775i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.00000 | −0.352522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.51087 | −0.110428 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.00000 | − | 34.0511i | −0.351161 | − | 1.49468i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.3846i | 1.33117i | 0.746320 | + | 0.665587i | \(0.231819\pi\) | ||||
−0.746320 | + | 0.665587i | \(0.768181\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 23.0689i | − | 1.00873i | −0.863490 | − | 0.504366i | \(-0.831726\pi\) | ||
0.863490 | − | 0.504366i | \(-0.168274\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.11684 | − | 17.5229i | −0.179674 | − | 0.764762i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 38.7446 | 1.68774 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.4891 | 0.977788 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −32.2337 | + | 16.0309i | −1.39882 | + | 0.695681i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.58457i | 0.0686355i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.3639i | 1.01011i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.1753 | − | 4.50506i | 0.827474 | − | 0.194407i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.4891 | 1.09789 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.6277 | −0.972842 | −0.486421 | − | 0.873725i | \(-0.661698\pi\) | ||||
−0.486421 | + | 0.873725i | \(0.661698\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.2554 | + | 4.05401i | −0.740502 | + | 0.173974i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 28.2101i | − | 1.20839i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 43.9461i | − | 1.87900i | −0.342551 | − | 0.939499i | \(-0.611291\pi\) | ||
0.342551 | − | 0.939499i | \(-0.388709\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.8614 | − | 15.3484i | 1.31713 | − | 0.655054i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | 0.170097 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.05842 | + | 38.5562i | 0.384509 | + | 1.63662i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 43.6511i | − | 1.84956i | −0.380505 | − | 0.924779i | \(-0.624250\pi\) | ||
0.380505 | − | 0.924779i | \(-0.375750\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.30506i | 0.393562i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.25544 | − | 39.3947i | −0.390765 | − | 1.66325i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.0951 | −1.22621 | −0.613106 | − | 0.790001i | \(-0.710080\pi\) | ||||
−0.613106 | + | 0.790001i | \(0.710080\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.9783 | 1.13498 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.68614 | − | 4.30268i | −0.238795 | − | 0.180695i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 22.8665i | − | 0.958614i | −0.877647 | − | 0.479307i | \(-0.840888\pi\) | ||
0.877647 | − | 0.479307i | \(-0.159112\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.6434i | 0.654654i | 0.944911 | + | 0.327327i | \(0.106148\pi\) | ||||
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −36.2337 | + | 8.51278i | −1.51368 | + | 0.355626i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 88.4674 | 3.68934 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.74456 | 0.364041 | 0.182020 | − | 0.983295i | \(-0.441736\pi\) | ||||
0.182020 | + | 0.983295i | \(0.441736\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.9783 | + | 4.45877i | −0.788709 | + | 0.185300i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 9.50744i | − | 0.394435i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 21.3745i | − | 0.885242i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.68614 | + | 11.4333i | 0.235093 | + | 0.472707i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.7446 | −0.443476 | −0.221738 | − | 0.975106i | \(-0.571173\pi\) | ||||
−0.221738 | + | 0.975106i | \(0.571173\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.9783 | 0.946802 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.68614 | − | 7.17687i | −0.0693586 | − | 0.295217i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 2.57924i | − | 0.105917i | −0.998597 | − | 0.0529584i | \(-0.983135\pi\) | ||
0.998597 | − | 0.0529584i | \(-0.0168651\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.6974i | 0.807513i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.88316 | + | 16.5282i | 0.158927 | + | 0.676455i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.4891 | 0.878022 | 0.439011 | − | 0.898482i | \(-0.355329\pi\) | ||||
0.439011 | + | 0.898482i | \(0.355329\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.8397 | 1.21719 | 0.608593 | − | 0.793483i | \(-0.291734\pi\) | ||||
0.608593 | + | 0.793483i | \(0.291734\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.62772 | + | 9.30506i | 0.188455 | + | 0.378932i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.2819i | 0.865234i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 5.63858i | − | 0.228863i | −0.993431 | − | 0.114432i | \(-0.963495\pi\) | ||
0.993431 | − | 0.114432i | \(-0.0365046\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.627719 | −0.0253948 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.48913 | −0.302483 | −0.151241 | − | 0.988497i | \(-0.548327\pi\) | ||||
−0.151241 | + | 0.988497i | \(0.548327\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.3723 | − | 2.67181i | 0.458575 | − | 0.107738i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.6155i | 0.709172i | 0.935023 | + | 0.354586i | \(0.115378\pi\) | ||||
−0.935023 | + | 0.354586i | \(0.884622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 6.04334i | − | 0.242902i | −0.992597 | − | 0.121451i | \(-0.961245\pi\) | ||
0.992597 | − | 0.121451i | \(-0.0387548\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.9783 | − | 22.3692i | 1.08260 | − | 0.897644i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.25544 | −0.0502980 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 81.4674 | 3.25870 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.48913 | − | 23.3639i | −0.219215 | − | 0.933062i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 31.3793i | − | 1.25117i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 12.4742i | − | 0.496591i | −0.968684 | − | 0.248295i | \(-0.920130\pi\) | ||
0.968684 | − | 0.248295i | \(-0.0798703\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.43070 | + | 27.3716i | 0.255598 | + | 1.08792i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 28.2337 | 1.12042 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.37228 | 0.252479 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.4307 | + | 8.17154i | −0.649989 | + | 0.323261i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 24.5437i | − | 0.969416i | −0.874676 | − | 0.484708i | \(-0.838926\pi\) | ||
0.874676 | − | 0.484708i | \(-0.161074\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.8535i | 1.72941i | 0.502277 | + | 0.864707i | \(0.332496\pi\) | ||||
−0.502277 | + | 0.864707i | \(0.667504\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 66.7812 | − | 15.6896i | 2.62951 | − | 0.617779i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.9783 | −0.431600 | −0.215800 | − | 0.976438i | \(-0.569236\pi\) | ||||
−0.215800 | + | 0.976438i | \(0.569236\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.0000 | −1.88416 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.86141 | − | 2.08191i | 0.347306 | − | 0.0815964i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.0612i | 1.68254i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000 | − | 0.994667i | 0.0780274 | − | 0.0388056i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.48913 | −0.213826 | −0.106913 | − | 0.994268i | \(-0.534097\pi\) | ||||
−0.106913 | + | 0.994268i | \(0.534097\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.4891 | −0.913621 | −0.456811 | − | 0.889564i | \(-0.651008\pi\) | ||||
−0.456811 | + | 0.889564i | \(0.651008\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.31386 | − | 9.84868i | −0.0898629 | − | 0.382491i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.6819i | 0.453006i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.4307 | + | 44.3971i | 0.403274 | + | 1.71649i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 45.9565 | 1.77413 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.8832 | 0.612251 | 0.306125 | − | 0.951991i | \(-0.400967\pi\) | ||||
0.306125 | + | 0.951991i | \(0.400967\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 52.4674 | − | 43.5036i | 2.01947 | − | 1.67446i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 34.0511i | − | 1.30869i | −0.756196 | − | 0.654345i | \(-0.772944\pi\) | ||
0.756196 | − | 0.654345i | \(-0.227056\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 6.92820i | − | 0.265880i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.62772 | + | 1.08724i | −0.177335 | + | 0.0416632i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.9783 | −0.879238 | −0.439619 | − | 0.898184i | \(-0.644887\pi\) | ||||
−0.439619 | + | 0.898184i | \(0.644887\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.2337 | −0.773089 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.91983 | − | 0.451046i | 0.0732460 | − | 0.0172085i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 5.34363i | − | 0.203576i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.80773i | 0.335062i | 0.985867 | + | 0.167531i | \(0.0535794\pi\) | ||||
−0.985867 | + | 0.167531i | \(0.946421\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.23369 | − | 8.51278i | −0.160825 | − | 0.323374i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −66.5842 | −2.52568 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.25544 | −0.350575 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.197015 | − | 0.838574i | −0.00745181 | − | 0.0317178i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 42.5639i | − | 1.60762i | −0.594889 | − | 0.803808i | \(-0.702804\pi\) | ||
0.594889 | − | 0.803808i | \(-0.297196\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 18.6101i | − | 0.701894i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.05842 | + | 4.50506i | 0.0398625 | + | 0.169670i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.51087 | −0.0944312 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.9783 | −0.787855 | −0.393927 | − | 0.919142i | \(-0.628884\pi\) | ||||
−0.393927 | + | 0.919142i | \(0.628884\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.74456 | + | 13.5615i | 0.252941 | + | 0.508594i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 44.7384i | 1.67547i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.0256i | 0.636720i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −35.1753 | + | 8.26411i | −1.31364 | + | 0.308629i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 49.7228 | 1.85435 | 0.927174 | − | 0.374631i | \(-0.122231\pi\) | ||||
0.927174 | + | 0.374631i | \(0.122231\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.48913 | 0.0554579 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −30.3505 | + | 7.13058i | −1.12875 | + | 0.265189i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 44.8482i | − | 1.66333i | −0.555280 | − | 0.831663i | \(-0.687389\pi\) | ||
0.555280 | − | 0.831663i | \(-0.312611\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.00000 | − | 26.5330i | 0.185185 | − | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −54.3505 | −2.01023 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.3505 | −1.49038 | −0.745190 | − | 0.666852i | \(-0.767641\pi\) | ||||
−0.745190 | + | 0.666852i | \(0.767641\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.7446 | − | 45.7330i | −0.396319 | − | 1.68689i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.8564i | 0.510407i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 19.8997i | − | 0.732024i | −0.930610 | − | 0.366012i | \(-0.880723\pi\) | ||
0.930610 | − | 0.366012i | \(-0.119277\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.37228 | − | 5.84096i | −0.0504120 | − | 0.214573i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.37228 | 0.270463 | 0.135231 | − | 0.990814i | \(-0.456822\pi\) | ||||
0.135231 | + | 0.990814i | \(0.456822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.0000 | 0.586195 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 32.2337 | − | 16.0309i | 1.17937 | − | 0.586540i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 4.34896i | − | 0.158908i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 40.6844i | − | 1.48459i | −0.670071 | − | 0.742297i | \(-0.733737\pi\) | ||
0.670071 | − | 0.742297i | \(-0.266263\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.9783 | + | 6.33830i | −0.983142 | + | 0.230980i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −46.3505 | −1.68687 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.9783 | 0.617085 | 0.308543 | − | 0.951211i | \(-0.400159\pi\) | ||||
0.308543 | + | 0.951211i | \(0.400159\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 45.4891 | − | 10.6873i | 1.65115 | − | 0.387923i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.4463i | 0.523678i | 0.965112 | + | 0.261839i | \(0.0843290\pi\) | ||||
−0.965112 | + | 0.261839i | \(0.915671\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.25106i | 0.190101i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −66.7812 | + | 33.2125i | −2.41448 | + | 1.20080i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0000 | −0.433295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.7228 | −1.72093 | −0.860464 | − | 0.509511i | \(-0.829826\pi\) | ||||
−0.860464 | + | 0.509511i | \(0.829826\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.05842 | + | 38.5562i | 0.326231 | + | 1.38857i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.25106i | 0.188867i | 0.995531 | + | 0.0944337i | \(0.0301040\pi\) | ||||
−0.995531 | + | 0.0944337i | \(0.969896\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 87.0073i | 3.12539i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.68614 | − | 7.17687i | −0.0604900 | − | 0.257469i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.48913 | −0.196668 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.4674 | −0.875512 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 37.2203i | − | 1.32845i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.1514i | 0.504442i | 0.967670 | + | 0.252221i | \(0.0811609\pi\) | ||||
−0.967670 | + | 0.252221i | \(0.918839\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.11684 | − | 0.497333i | 0.0753616 | − | 0.0177055i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.02175 | −0.178553 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.4891 | 0.407991 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −38.3505 | + | 9.01011i | −1.36015 | + | 0.319556i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.2000i | 0.680100i | 0.940407 | + | 0.340050i | \(0.110444\pi\) | ||||
−0.940407 | + | 0.340050i | \(0.889556\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.66648i | − | 0.129711i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.11684 | − | 4.25639i | −0.0747950 | − | 0.150392i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.97825 | 0.105100 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.7446 | −0.801640 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.11684 | − | 9.01011i | −0.0745164 | − | 0.317171i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.66648i | 0.128907i | 0.997921 | + | 0.0644533i | \(0.0205304\pi\) | ||||
−0.997921 | + | 0.0644533i | \(0.979470\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.6897i | 1.39369i | 0.717220 | + | 0.696847i | \(0.245414\pi\) | ||||
−0.717220 | + | 0.696847i | \(0.754586\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.56930 | − | 23.7051i | −0.195324 | − | 0.831374i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −87.2119 | −3.05490 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.2337 | −1.12771 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.05842 | − | 2.12819i | −0.0369843 | − | 0.0743651i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 34.1437i | − | 1.19162i | −0.803124 | − | 0.595811i | \(-0.796831\pi\) | ||
0.803124 | − | 0.595811i | \(-0.203169\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.9051i | 0.658990i | 0.944157 | + | 0.329495i | \(0.106878\pi\) | ||||
−0.944157 | + | 0.329495i | \(0.893122\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 88.4674 | − | 20.7846i | 3.08004 | − | 0.723627i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.2554 | 1.01731 | 0.508656 | − | 0.860970i | \(-0.330143\pi\) | ||||
0.508656 | + | 0.860970i | \(0.330143\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.00000 | −0.0694629 | −0.0347314 | − | 0.999397i | \(-0.511058\pi\) | ||||
−0.0347314 | + | 0.999397i | \(0.511058\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 35.3723 | − | 8.31040i | 1.22705 | − | 0.288284i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 37.2203i | 1.28961i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.0256i | 0.589194i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.0000 | + | 26.5330i | 0.760431 | + | 0.917115i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.9783 | 1.62187 | 0.810935 | − | 0.585137i | \(-0.198959\pi\) | ||||
0.810935 | + | 0.585137i | \(0.198959\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.88316 | + | 42.0666i | 0.340394 | + | 1.44885i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.25639i | 0.146424i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 3.96143i | − | 0.136117i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.8614 | + | 46.2304i | 0.372763 | + | 1.58662i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.2337 | 1.24207 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.6060 | −0.876732 | −0.438366 | − | 0.898797i | \(-0.644443\pi\) | ||||
−0.438366 | + | 0.898797i | \(0.644443\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −39.6060 | + | 19.6974i | −1.35450 | + | 0.673636i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 3.16915i | − | 0.108256i | −0.998534 | − | 0.0541280i | \(-0.982762\pi\) | ||
0.998534 | − | 0.0541280i | \(-0.0172379\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.9715i | 0.442583i | 0.975208 | + | 0.221292i | \(0.0710273\pi\) | ||||
−0.975208 | + | 0.221292i | \(0.928973\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.11684 | + | 0.497333i | −0.0721418 | + | 0.0169491i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.3505 | −1.44163 | −0.720814 | − | 0.693128i | \(-0.756232\pi\) | ||||
−0.720814 | + | 0.693128i | \(0.756232\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −85.9565 | −2.92261 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.8614 | − | 6.78073i | 0.980185 | − | 0.230286i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.1947i | 0.685058i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.46410i | 0.117377i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.4891 | − | 11.6819i | 0.794986 | − | 0.395373i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.3723 | −0.925352 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.1168 | 0.544227 | 0.272114 | − | 0.962265i | \(-0.412277\pi\) | ||||
0.272114 | + | 0.962265i | \(0.412277\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.1970 | − | 51.9152i | −0.411395 | − | 1.75106i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.2101i | 0.950424i | 0.879871 | + | 0.475212i | \(0.157629\pi\) | ||||
−0.879871 | + | 0.475212i | \(0.842371\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.4795i | 0.386317i | 0.981168 | + | 0.193159i | \(0.0618732\pi\) | ||||
−0.981168 | + | 0.193159i | \(0.938127\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20.2337 | + | 86.1224i | 0.680148 | + | 2.89497i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.76631 | −0.126460 | −0.0632302 | − | 0.997999i | \(-0.520140\pi\) | ||||
−0.0632302 | + | 0.997999i | \(0.520140\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.25544 | −0.176262 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.7228 | − | 28.7075i | 0.727742 | − | 0.961737i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 2.17448i | − | 0.0727662i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 48.4048i | − | 1.61800i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.3723 | − | 2.67181i | 0.379709 | − | 0.0892093i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.2119 | 1.03982 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.4307 | + | 2.92048i | −0.413668 | + | 0.0971875i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 43.5586i | 1.44794i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 13.0641i | − | 0.433787i | −0.976195 | − | 0.216893i | \(-0.930408\pi\) | ||
0.976195 | − | 0.216893i | \(-0.0695924\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.23369 | − | 8.51278i | −0.140423 | − | 0.282351i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.9783 | −1.15888 | −0.579441 | − | 0.815014i | \(-0.696729\pi\) | ||||
−0.579441 | + | 0.815014i | \(0.696729\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.0000 | 1.58857 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −19.3723 | − | 82.4560i | −0.640428 | − | 2.72591i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 8.01544i | − | 0.264693i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.2540i | 0.767080i | 0.923524 | + | 0.383540i | \(0.125295\pi\) | ||||
−0.923524 | + | 0.383540i | \(0.874705\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.2337 | − | 43.5586i | −0.337211 | − | 1.43530i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.11684 | −0.201338 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 70.4674 | 2.31695 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.51087 | + | 5.04868i | 0.0824679 | + | 0.165820i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 14.4463i | − | 0.473968i | −0.971514 | − | 0.236984i | \(-0.923841\pi\) | ||
0.971514 | − | 0.236984i | \(-0.0761589\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.0742i | 0.723454i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.6060 | + | 3.66648i | −0.510916 | + | 0.120035i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −99.4456 | −3.25222 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.4891 | −1.15938 | −0.579690 | − | 0.814837i | \(-0.696826\pi\) | ||||
−0.579690 | + | 0.814837i | \(0.696826\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.6644 | + | 5.79468i | −0.804892 | + | 0.189102i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.9383i | 0.519574i | 0.965666 | + | 0.259787i | \(0.0836524\pi\) | ||||
−0.965666 | + | 0.259787i | \(0.916348\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 10.6873i | − | 0.348025i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.4891 | + | 11.1846i | −0.438801 | + | 0.363835i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.9783 | −0.746693 | −0.373346 | − | 0.927692i | \(-0.621790\pi\) | ||||
−0.373346 | + | 0.927692i | \(0.621790\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.744563 | 0.0241695 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.48913 | + | 6.33830i | 0.0482882 | + | 0.205533i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.8921i | 1.29223i | 0.763240 | + | 0.646115i | \(0.223608\pi\) | ||||
−0.763240 | + | 0.646115i | \(0.776392\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 91.4661i | 2.95977i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.76631 | 0.121621 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.0000 | −0.419355 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.7446 | − | 7.33296i | 0.475137 | − | 0.236301i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 47.9075i | 1.54220i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.55134i | 0.146361i | 0.997319 | + | 0.0731806i | \(0.0233150\pi\) | ||||
−0.997319 | + | 0.0731806i | \(0.976685\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 34.1168 | − | 8.01544i | 1.09599 | − | 0.257493i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.8614 | 0.541108 | 0.270554 | − | 0.962705i | \(-0.412793\pi\) | ||||
0.270554 | + | 0.962705i | \(0.412793\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.3940 | 0.397334 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 22.1168 | − | 5.19615i | 0.708306 | − | 0.166410i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.2974i | 0.937306i | 0.883382 | + | 0.468653i | \(0.155261\pi\) | ||||
−0.883382 | + | 0.468653i | \(0.844739\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 6.33830i | − | 0.202573i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.8030 | + | 8.85402i | −0.568406 | + | 0.282687i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.8832 | 1.08070 | 0.540352 | − | 0.841439i | \(-0.318291\pi\) | ||||
0.540352 | + | 0.841439i | \(0.318291\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.1168 | −0.577251 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.197015 | − | 0.838574i | −0.00627107 | − | 0.0266921i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 62.7586i | − | 1.99561i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.7562i | 1.07230i | 0.844123 | + | 0.536150i | \(0.180122\pi\) | ||||
−0.844123 | + | 0.536150i | \(0.819878\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.74456 | + | 37.2203i | 0.277500 | + | 1.18115i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41.7228 | 1.32270 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.2554 | 0.989870 | 0.494935 | − | 0.868930i | \(-0.335192\pi\) | ||||
0.494935 | + | 0.868930i | \(0.335192\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.4891 | − | 17.8178i | 0.679886 | − | 0.563732i |
(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 | 624.2.d.g.287.2 | yes | 4 | |
3.2 | odd | 2 | 624.2.d.i.287.4 | yes | 4 | ||
4.3 | odd | 2 | 624.2.d.i.287.3 | yes | 4 | ||
8.3 | odd | 2 | 2496.2.d.i.1535.2 | 4 | |||
8.5 | even | 2 | 2496.2.d.l.1535.3 | 4 | |||
12.11 | even | 2 | inner | 624.2.d.g.287.1 | ✓ | 4 | |
24.5 | odd | 2 | 2496.2.d.i.1535.1 | 4 | |||
24.11 | even | 2 | 2496.2.d.l.1535.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
624.2.d.g.287.1 | ✓ | 4 | 12.11 | even | 2 | inner | |
624.2.d.g.287.2 | yes | 4 | 1.1 | even | 1 | trivial | |
624.2.d.i.287.3 | yes | 4 | 4.3 | odd | 2 | ||
624.2.d.i.287.4 | yes | 4 | 3.2 | odd | 2 | ||
2496.2.d.i.1535.1 | 4 | 24.5 | odd | 2 | |||
2496.2.d.i.1535.2 | 4 | 8.3 | odd | 2 | |||
2496.2.d.l.1535.3 | 4 | 8.5 | even | 2 | |||
2496.2.d.l.1535.4 | 4 | 24.11 | even | 2 |