Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2432,2,Mod(1217,2432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2432, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2432.1217");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2432 = 2^{7} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2432.c (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: | \(19.4196177716\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 8 x^{14} - 8 x^{13} - 3 x^{12} + 20 x^{11} - 24 x^{10} + 28 x^{8} - 96 x^{6} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1217.7 | ||
Root | \(-1.07547 - 0.918353i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2432.1217 |
Dual form | 2432.2.c.i.1217.10 |
$q$-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 \(\left(\mathbb{Z}/2432\mathbb{Z}\right)^\times\).
\(n\) | \(1407\) | \(1921\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 0.222191i | − 0.128282i | −0.997941 | − | 0.0641411i | \(-0.979569\pi\) | ||||
0.997941 | − | 0.0641411i | \(-0.0204308\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.55081i | − 0.693543i | −0.937950 | − | 0.346772i | \(-0.887278\pi\) | ||||
0.937950 | − | 0.346772i | \(-0.112722\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.06334 | −1.15783 | −0.578917 | − | 0.815387i | \(-0.696524\pi\) | ||||
−0.578917 | + | 0.815387i | \(0.696524\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.95063 | 0.983544 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.950631i | 0.286626i | 0.989677 | + | 0.143313i | \(0.0457756\pi\) | ||||
−0.989677 | + | 0.143313i | \(0.954224\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.36113i | 0.932209i | 0.884730 | + | 0.466105i | \(0.154343\pi\) | ||||
−0.884730 | + | 0.466105i | \(0.845657\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.344577 | −0.0889693 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.82843 | 0.443459 | 0.221729 | − | 0.975108i | \(-0.428830\pi\) | ||||
0.221729 | + | 0.975108i | \(0.428830\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.00000i | − 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.680647i | 0.148529i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.36113 | −0.700844 | −0.350422 | − | 0.936592i | \(-0.613962\pi\) | ||||
−0.350422 | + | 0.936592i | \(0.613962\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.59499 | 0.518998 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.32218i | − 0.254453i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.95873i | 0.920812i | 0.887708 | + | 0.460406i | \(0.152296\pi\) | ||||
−0.887708 | + | 0.460406i | \(0.847704\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.44620 | 0.618955 | 0.309478 | − | 0.950907i | \(-0.399846\pi\) | ||||
0.309478 | + | 0.950907i | \(0.399846\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.211222 | 0.0367690 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.75066i | 0.803007i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.95889i | 0.486439i | 0.969971 | + | 0.243219i | \(0.0782035\pi\) | ||||
−0.969971 | + | 0.243219i | \(0.921797\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.746814 | 0.119586 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.55687 | 0.711663 | 0.355832 | − | 0.934550i | \(-0.384198\pi\) | ||||
0.355832 | + | 0.934550i | \(0.384198\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.69373i | − 0.258291i | −0.991626 | − | 0.129145i | \(-0.958777\pi\) | ||||
0.991626 | − | 0.129145i | \(-0.0412234\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 4.57587i | − 0.682130i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.39941 | 0.495855 | 0.247927 | − | 0.968779i | \(-0.420251\pi\) | ||||
0.247927 | + | 0.968779i | \(0.420251\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.38404 | 0.340578 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 0.406261i | − 0.0568879i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 4.47142i | − 0.614197i | −0.951678 | − | 0.307098i | \(-0.900642\pi\) | ||||
0.951678 | − | 0.307098i | \(-0.0993581\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.47425 | 0.198788 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.222191 | −0.0294300 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.395014i | 0.0514264i | 0.999669 | + | 0.0257132i | \(0.00818567\pi\) | ||||
−0.999669 | + | 0.0257132i | \(0.991814\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.34158i | 0.683920i | 0.939715 | + | 0.341960i | \(0.111091\pi\) | ||||
−0.939715 | + | 0.341960i | \(0.888909\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.03878 | −1.13878 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.21247 | 0.646528 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.85064i | 0.836939i | 0.908231 | + | 0.418470i | \(0.137433\pi\) | ||||
−0.908231 | + | 0.418470i | \(0.862567\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.746814i | 0.0899058i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.15207 | 0.611438 | 0.305719 | − | 0.952122i | \(-0.401103\pi\) | ||||
0.305719 | + | 0.952122i | \(0.401103\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.19998 | 0.140446 | 0.0702232 | − | 0.997531i | \(-0.477629\pi\) | ||||
0.0702232 | + | 0.997531i | \(0.477629\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 0.576584i | − 0.0665782i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.91210i | − 0.331865i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.7249 | 1.65669 | 0.828343 | − | 0.560222i | \(-0.189284\pi\) | ||||
0.828343 | + | 0.560222i | \(0.189284\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.55812 | 0.950902 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.35564i | 0.368330i | 0.982895 | + | 0.184165i | \(0.0589580\pi\) | ||||
−0.982895 | + | 0.184165i | \(0.941042\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 2.83554i | − 0.307558i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.10179 | 0.118124 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.64561 | 1.02243 | 0.511216 | − | 0.859452i | \(-0.329195\pi\) | ||||
0.511216 | + | 0.859452i | \(0.329195\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 10.2963i | − 1.07934i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 0.765715i | − 0.0794010i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.55081 | −0.159110 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.55562 | 0.361018 | 0.180509 | − | 0.983573i | \(-0.442225\pi\) | ||||
0.180509 | + | 0.983573i | \(0.442225\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.80496i | 0.281909i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 13.5381i | − 1.34709i | −0.739146 | − | 0.673545i | \(-0.764771\pi\) | ||||
0.739146 | − | 0.673545i | \(-0.235229\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.64570 | 0.654820 | 0.327410 | − | 0.944882i | \(-0.393824\pi\) | ||||
0.327410 | + | 0.944882i | \(0.393824\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.05555 | 0.103012 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 15.8519i | − 1.53246i | −0.642566 | − | 0.766230i | \(-0.722130\pi\) | ||||
0.642566 | − | 0.766230i | \(-0.277870\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 13.4213i | − 1.28553i | −0.766064 | − | 0.642764i | \(-0.777788\pi\) | ||||
0.766064 | − | 0.642764i | \(-0.222212\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.657440 | 0.0624015 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.65810 | 0.626342 | 0.313171 | − | 0.949697i | \(-0.398609\pi\) | ||||
0.313171 | + | 0.949697i | \(0.398609\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.21247i | 0.486065i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.91745i | 0.916869i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.60109 | −0.513451 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.0963 | 0.917846 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.01250i | − 0.0912937i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 11.7784i | − 1.05349i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.54782 | −0.581025 | −0.290512 | − | 0.956871i | \(-0.593826\pi\) | ||||
−0.290512 | + | 0.956871i | \(0.593826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.376331 | −0.0331341 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.2838i | 1.24798i | 0.781432 | + | 0.623990i | \(0.214489\pi\) | ||||
−0.781432 | + | 0.623990i | \(0.785511\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.06334i | 0.265625i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.05045 | −0.176474 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.9138 | 1.01786 | 0.508931 | − | 0.860808i | \(-0.330041\pi\) | ||||
0.508931 | + | 0.860808i | \(0.330041\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 11.1950i | − 0.949551i | −0.880107 | − | 0.474775i | \(-0.842529\pi\) | ||||
0.880107 | − | 0.474775i | \(-0.157471\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 0.755320i | − 0.0636094i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.19519 | −0.267195 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.69004 | 0.638623 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 0.529714i | − 0.0436901i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.67749i | 0.628964i | 0.949263 | + | 0.314482i | \(0.101831\pi\) | ||||
−0.949263 | + | 0.314482i | \(0.898169\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.10162 | 0.252406 | 0.126203 | − | 0.992004i | \(-0.459721\pi\) | ||||
0.126203 | + | 0.992004i | \(0.459721\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.39501 | 0.436161 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 5.34440i | − 0.429272i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8994i | 1.18910i | 0.804059 | + | 0.594550i | \(0.202670\pi\) | ||||
−0.804059 | + | 0.594550i | \(0.797330\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.993511 | −0.0787905 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.2963 | 0.811460 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.5481i | 1.45280i | 0.687272 | + | 0.726400i | \(0.258808\pi\) | ||||
−0.687272 | + | 0.726400i | \(0.741192\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 0.327565i | − 0.0255009i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.4532 | −0.886274 | −0.443137 | − | 0.896454i | \(-0.646135\pi\) | ||||
−0.443137 | + | 0.896454i | \(0.646135\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.70281 | 0.130986 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 2.95063i | − 0.225640i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 7.20956i | − 0.548133i | −0.961711 | − | 0.274066i | \(-0.911631\pi\) | ||||
0.961711 | − | 0.274066i | \(-0.0883688\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.94933 | −0.600913 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0877686 | 0.00659710 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 4.90251i | − 0.366431i | −0.983073 | − | 0.183215i | \(-0.941349\pi\) | ||||
0.983073 | − | 0.183215i | \(-0.0586506\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.1775i | 1.42545i | 0.701444 | + | 0.712725i | \(0.252539\pi\) | ||||
−0.701444 | + | 0.712725i | \(0.747461\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.18685 | 0.0877347 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.58868 | 0.337366 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.73816i | 0.127107i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.05028i | 0.294615i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.8812 | −1.65563 | −0.827814 | − | 0.561003i | \(-0.810416\pi\) | ||||
−0.827814 | + | 0.561003i | \(0.810416\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.11248 | −0.152060 | −0.0760300 | − | 0.997106i | \(-0.524224\pi\) | ||||
−0.0760300 | + | 0.997106i | \(0.524224\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 1.15817i | − 0.0829380i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 6.05012i | − 0.431053i | −0.976498 | − | 0.215526i | \(-0.930853\pi\) | ||||
0.976498 | − | 0.215526i | \(-0.0691467\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.03090 | 0.285743 | 0.142872 | − | 0.989741i | \(-0.454366\pi\) | ||||
0.142872 | + | 0.989741i | \(0.454366\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.52215 | 0.107364 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 15.1903i | − 1.06615i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 7.06683i | − 0.493569i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.91745 | −0.689310 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.950631 | 0.0657565 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.66532i | 0.114646i | 0.998356 | + | 0.0573228i | \(0.0182564\pi\) | ||||
−0.998356 | + | 0.0573228i | \(0.981744\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.14475i | − 0.0784366i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.62665 | −0.179136 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.5569 | −0.716647 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 0.266624i | − 0.0180168i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.14558i | 0.413396i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.9352 | 1.93764 | 0.968821 | − | 0.247761i | \(-0.0796948\pi\) | ||||
0.968821 | + | 0.247761i | \(0.0796948\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.65685 | 0.510457 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.0519i | 1.33089i | 0.746447 | + | 0.665445i | \(0.231758\pi\) | ||||
−0.746447 | + | 0.665445i | \(0.768242\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.9953i | 0.990919i | 0.868631 | + | 0.495459i | \(0.165000\pi\) | ||||
−0.868631 | + | 0.495459i | \(0.835000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.647045 | −0.0425724 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.2738 | −0.738570 | −0.369285 | − | 0.929316i | \(-0.620397\pi\) | ||||
−0.369285 | + | 0.929316i | \(0.620397\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 5.27184i | − 0.343897i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 3.27176i | − 0.212523i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.9049 | 1.28754 | 0.643770 | − | 0.765219i | \(-0.277369\pi\) | ||||
0.643770 | + | 0.765219i | \(0.277369\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.8163 | −1.01882 | −0.509408 | − | 0.860525i | \(-0.670135\pi\) | ||||
−0.509408 | + | 0.860525i | \(0.670135\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 5.86808i | − 0.376437i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3.69720i | − 0.236205i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.36113 | 0.213863 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.745595 | 0.0472501 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.5087i | 0.663306i | 0.943401 | + | 0.331653i | \(0.107606\pi\) | ||||
−0.943401 | + | 0.331653i | \(0.892394\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 3.19519i | − 0.200880i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.630033 | −0.0394542 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.70129 | −0.106123 | −0.0530617 | − | 0.998591i | \(-0.516898\pi\) | ||||
−0.0530617 | + | 0.998591i | \(0.516898\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 9.06409i | − 0.563215i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.6314i | 0.905659i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.8359 | −0.853157 | −0.426578 | − | 0.904451i | \(-0.640281\pi\) | ||||
−0.426578 | + | 0.904451i | \(0.640281\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.93432 | −0.425972 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 2.14317i | − 0.131160i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.9655i | 0.912466i | 0.889860 | + | 0.456233i | \(0.150802\pi\) | ||||
−0.889860 | + | 0.456233i | \(0.849198\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.12684 | −0.250688 | −0.125344 | − | 0.992113i | \(-0.540003\pi\) | ||||
−0.125344 | + | 0.992113i | \(0.540003\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.28774 | −0.138461 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.46688i | 0.148758i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 25.7721i | − 1.54849i | −0.632884 | − | 0.774247i | \(-0.718129\pi\) | ||||
0.632884 | − | 0.774247i | \(-0.281871\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.1685 | 0.608769 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.2694 | 0.612621 | 0.306311 | − | 0.951932i | \(-0.400905\pi\) | ||||
0.306311 | + | 0.951932i | \(0.400905\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.99506i | 0.415813i | 0.978149 | + | 0.207907i | \(0.0666650\pi\) | ||||
−0.978149 | + | 0.207907i | \(0.933335\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.344577i | 0.0204110i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.9592 | −0.823987 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.6569 | −0.803344 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 0.790027i | − 0.0463122i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 31.8434i | − 1.86031i | −0.367162 | − | 0.930157i | \(-0.619670\pi\) | ||||
0.367162 | − | 0.930157i | \(-0.380330\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.612591 | 0.0356664 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.25690 | 0.0729330 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 11.2972i | − 0.653333i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.18846i | 0.299058i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.00805 | −0.172808 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.28378 | 0.474328 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.45813i | 0.368585i | 0.982871 | + | 0.184292i | \(0.0589993\pi\) | ||||
−0.982871 | + | 0.184292i | \(0.941001\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 1.47662i | − 0.0840018i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.1973 | 1.59892 | 0.799462 | − | 0.600716i | \(-0.205118\pi\) | ||||
0.799462 | + | 0.600716i | \(0.205118\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.1212 | −0.967746 | −0.483873 | − | 0.875138i | \(-0.660770\pi\) | ||||
−0.483873 | + | 0.875138i | \(0.660770\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.0174i | 0.789793i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.5841i | 1.66161i | 0.556564 | + | 0.830804i | \(0.312119\pi\) | ||||
−0.556564 | + | 0.830804i | \(0.687881\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.71392 | −0.263929 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.52215 | −0.196587 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.82843i | − 0.101736i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.72209i | 0.483815i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.98210 | −0.164910 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.4135 | −0.574117 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 20.5519i | − 1.12964i | −0.825215 | − | 0.564818i | \(-0.808946\pi\) | ||||
0.825215 | − | 0.564818i | \(-0.191054\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.73060i | 0.478434i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.6240 | 0.580454 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.1832 | −1.04497 | −0.522487 | − | 0.852647i | \(-0.674996\pi\) | ||||
−0.522487 | + | 0.852647i | \(0.674996\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 1.47937i | − 0.0803485i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.27606i | 0.177409i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.1402 | 0.763501 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.15817 | 0.0623536 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 10.5507i | − 0.566390i | −0.959062 | − | 0.283195i | \(-0.908606\pi\) | ||||
0.959062 | − | 0.283195i | \(-0.0913944\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 29.4693i | − 1.57745i | −0.614744 | − | 0.788727i | \(-0.710741\pi\) | ||||
0.614744 | − | 0.788727i | \(-0.289259\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.44401 | 0.237204 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.98903 | −0.212315 | −0.106157 | − | 0.994349i | \(-0.533855\pi\) | ||||
−0.106157 | + | 0.994349i | \(0.533855\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 7.98988i | − 0.424059i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.24451i | 0.0658667i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.9377 | 0.788380 | 0.394190 | − | 0.919029i | \(-0.371025\pi\) | ||||
0.394190 | + | 0.919029i | \(0.371025\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2.24331i | − 0.117743i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1.86093i | − 0.0974057i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.1009 | −0.997059 | −0.498529 | − | 0.866873i | \(-0.666126\pi\) | ||||
−0.498529 | + | 0.866873i | \(0.666126\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.4456 | 0.699952 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.6975i | 0.711137i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.461357i | 0.0238882i | 0.999929 | + | 0.0119441i | \(0.00380201\pi\) | ||||
−0.999929 | + | 0.0119441i | \(0.996198\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.61706 | −0.135144 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.6669 | −0.858390 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.9622i | 1.53906i | 0.638613 | + | 0.769528i | \(0.279508\pi\) | ||||
−0.638613 | + | 0.769528i | \(0.720492\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.45487i | 0.0745352i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.9077 | 0.863944 | 0.431972 | − | 0.901887i | \(-0.357818\pi\) | ||||
0.431972 | + | 0.901887i | \(0.357818\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.51612 | −0.230163 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 4.99756i | − 0.254040i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.92418i | 0.401772i | 0.979615 | + | 0.200886i | \(0.0643821\pi\) | ||||
−0.979615 | + | 0.200886i | \(0.935618\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.14558 | −0.310795 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.17373 | 0.160094 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 22.8356i | − 1.14898i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.6718i | 0.686170i | 0.939304 | + | 0.343085i | \(0.111472\pi\) | ||||
−0.939304 | + | 0.343085i | \(0.888528\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.680647 | 0.0340750 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0107 | 0.599785 | 0.299893 | − | 0.953973i | \(-0.403049\pi\) | ||||
0.299893 | + | 0.953973i | \(0.403049\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.5831i | 0.576996i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 13.2720i | − 0.659492i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.81281 | −0.139426 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.47063 | −0.468292 | −0.234146 | − | 0.972201i | \(-0.575229\pi\) | ||||
−0.234146 | + | 0.972201i | \(0.575229\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 2.64713i | − 0.130574i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.21006i | − 0.0595432i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.20396 | 0.255453 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.48744 | −0.121811 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.0843i | 1.37201i | 0.727598 | + | 0.686004i | \(0.240637\pi\) | ||||
−0.727598 | + | 0.686004i | \(0.759363\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 9.83238i | − 0.479201i | −0.970872 | − | 0.239601i | \(-0.922984\pi\) | ||||
0.970872 | − | 0.239601i | \(-0.0770165\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.0304 | 0.487695 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.74475 | 0.230154 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 16.3631i | − 0.791865i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.709944i | 0.0342764i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.94284 | 0.430761 | 0.215381 | − | 0.976530i | \(-0.430901\pi\) | ||||
0.215381 | + | 0.976530i | \(0.430901\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.5274 | −1.41900 | −0.709499 | − | 0.704707i | \(-0.751079\pi\) | ||||
−0.709499 | + | 0.704707i | \(0.751079\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 1.70866i | − 0.0819240i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.36113i | 0.160785i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.5113 | −0.978953 | −0.489477 | − | 0.872016i | \(-0.662812\pi\) | ||||
−0.489477 | + | 0.872016i | \(0.662812\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.03444 | 0.334973 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.3188i | 0.632794i | 0.948627 | + | 0.316397i | \(0.102473\pi\) | ||||
−0.948627 | + | 0.316397i | \(0.897527\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 14.9585i | − 0.709101i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.70587 | 0.0806850 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.5138 | 0.496177 | 0.248089 | − | 0.968737i | \(-0.420198\pi\) | ||||
0.248089 | + | 0.968737i | \(0.420198\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.33190i | 0.203981i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 0.689153i | − 0.0323792i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15.9676 | −0.748571 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.5831 | −1.24351 | −0.621753 | − | 0.783214i | \(-0.713579\pi\) | ||||
−0.621753 | + | 0.783214i | \(0.713579\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 2.41751i | − 0.112840i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.2417i | 0.896175i | 0.893990 | + | 0.448087i | \(0.147895\pi\) | ||||
−0.893990 | + | 0.448087i | \(0.852105\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.24701 | −0.104427 | −0.0522137 | − | 0.998636i | \(-0.516628\pi\) | ||||
−0.0522137 | + | 0.998636i | \(0.516628\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.18748 | −0.0550680 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.5682i | 1.27570i | 0.770159 | + | 0.637852i | \(0.220177\pi\) | ||||
−0.770159 | + | 0.637852i | \(0.779823\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 20.9858i | − 0.969036i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.31051 | 0.152540 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.61011 | 0.0740329 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 2.59499i | − 0.119066i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 13.1935i | − 0.604089i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.5447 | −0.481802 | −0.240901 | − | 0.970550i | \(-0.577443\pi\) | ||||
−0.240901 | + | 0.970550i | \(0.577443\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.94521 | −0.453463 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 2.28774i | − 0.104096i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 5.51409i | − 0.250382i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.7294 | −1.80031 | −0.900154 | − | 0.435571i | \(-0.856546\pi\) | ||||
−0.900154 | + | 0.435571i | \(0.856546\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.12123 | 0.186369 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 31.0150i | − 1.39969i | −0.714296 | − | 0.699844i | \(-0.753253\pi\) | ||||
0.714296 | − | 0.699844i | \(-0.246747\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.06667i | 0.408342i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.34996 | 0.195516 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.7825 | −0.707943 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 4.90620i | − 0.219632i | −0.993952 | − | 0.109816i | \(-0.964974\pi\) | ||||
0.993952 | − | 0.109816i | \(-0.0350261\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.54480i | 0.113693i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.6847 | −0.654759 | −0.327380 | − | 0.944893i | \(-0.606166\pi\) | ||||
−0.327380 | + | 0.944893i | \(0.606166\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.9950 | −0.934265 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 0.378351i | − 0.0168031i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 20.3988i | − 0.904159i | −0.891978 | − | 0.452080i | \(-0.850682\pi\) | ||||
0.891978 | − | 0.452080i | \(-0.149318\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.67593 | −0.162614 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.32218 | −0.0583756 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 10.3062i | − 0.454146i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.23158i | 0.142125i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.60190 | −0.0703157 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.4356 | −0.982923 | −0.491462 | − | 0.870899i | \(-0.663537\pi\) | ||||
−0.491462 | + | 0.870899i | \(0.663537\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.71531i | 0.424821i | 0.977181 | + | 0.212410i | \(0.0681314\pi\) | ||||
−0.977181 | + | 0.212410i | \(0.931869\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.76627i | 0.0770865i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.30112 | 0.274481 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.7028 | −0.508818 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.16554i | 0.0505801i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.3162i | 0.663419i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.5833 | −1.06283 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.08930 | −0.0470066 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.26635i | 0.0976185i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 14.7230i | − 0.632991i | −0.948594 | − | 0.316496i | \(-0.897494\pi\) | ||||
0.948594 | − | 0.316496i | \(-0.102506\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.26107 | 0.182860 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.8139 | −0.891569 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 10.9906i | − 0.469922i | −0.972005 | − | 0.234961i | \(-0.924504\pi\) | ||||
0.972005 | − | 0.234961i | \(-0.0754963\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.7610i | 0.672665i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.95873 | 0.211249 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −45.1075 | −1.91817 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 1.01956i | − 0.0432781i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 25.9252i | − 1.09849i | −0.835663 | − | 0.549243i | \(-0.814916\pi\) | ||||
0.835663 | − | 0.549243i | \(-0.185084\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.69283 | 0.240781 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.386204 | 0.0163055 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 21.0775i | − 0.888310i | −0.895950 | − | 0.444155i | \(-0.853504\pi\) | ||||
0.895950 | − | 0.444155i | \(-0.146496\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 10.3255i | − 0.434395i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −26.2164 | −1.10099 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.2369 | 0.471076 | 0.235538 | − | 0.971865i | \(-0.424315\pi\) | ||||
0.235538 | + | 0.971865i | \(0.424315\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.5037i | 1.77872i | 0.457204 | + | 0.889362i | \(0.348851\pi\) | ||||
−0.457204 | + | 0.889362i | \(0.651149\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.08401i | 0.212388i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.72209 | −0.363736 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.6503 | −1.10947 | −0.554733 | − | 0.832029i | \(-0.687179\pi\) | ||||
−0.554733 | + | 0.832029i | \(0.687179\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.469376i | 0.0195066i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 10.2795i | − 0.426464i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.25067 | 0.176045 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.3801 | 0.635888 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 33.2195i | − 1.37111i | −0.728019 | − | 0.685557i | \(-0.759559\pi\) | ||||
0.728019 | − | 0.685557i | \(-0.240441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 3.44620i | − 0.141998i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.34428 | −0.0552964 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.4149 | −1.04367 | −0.521833 | − | 0.853047i | \(-0.674752\pi\) | ||||
−0.521833 | + | 0.853047i | \(0.674752\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.68623i | 0.356101i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 0.895632i | − 0.0366558i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 46.6431 | 1.90578 | 0.952892 | − | 0.303310i | \(-0.0980918\pi\) | ||||
0.952892 | + | 0.303310i | \(0.0980918\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −47.4644 | −1.93611 | −0.968056 | − | 0.250734i | \(-0.919328\pi\) | ||||
−0.968056 | + | 0.250734i | \(0.919328\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.2137i | 0.823166i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 15.6574i | − 0.636566i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.4897 | 0.994006 | 0.497003 | − | 0.867749i | \(-0.334434\pi\) | ||||
0.497003 | + | 0.867749i | \(0.334434\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.37514 | −0.136768 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.4259i | 0.462241i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.9950i | 0.767201i | 0.923499 | + | 0.383600i | \(0.125316\pi\) | ||||
−0.923499 | + | 0.383600i | \(0.874684\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.57019 | −0.0633162 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.219907 | 0.00885311 | 0.00442656 | − | 0.999990i | \(-0.498591\pi\) | ||||
0.00442656 | + | 0.999990i | \(0.498591\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.9136i | 0.639623i | 0.947481 | + | 0.319811i | \(0.103620\pi\) | ||||
−0.947481 | + | 0.319811i | \(0.896380\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.44401i | 0.178332i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.5478 | −1.18381 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.29109 | −0.211644 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 0.211222i | − 0.00843539i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.41012i | 0.215716i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.6207 | −1.09956 | −0.549781 | − | 0.835309i | \(-0.685289\pi\) | ||||
−0.549781 | + | 0.835309i | \(0.685289\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.370021 | 0.0147070 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.1544i | 0.402966i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.01308i | 0.317490i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.2019 | 0.601376 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.17066 | −0.164731 | −0.0823656 | − | 0.996602i | \(-0.526248\pi\) | ||||
−0.0823656 | + | 0.996602i | \(0.526248\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 20.8643i | − 0.822806i | −0.911453 | − | 0.411403i | \(-0.865039\pi\) | ||||
0.911453 | − | 0.411403i | \(-0.134961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.583619i | 0.0229800i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.7924 | 1.24989 | 0.624943 | − | 0.780670i | \(-0.285122\pi\) | ||||
0.624943 | + | 0.780670i | \(0.285122\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.375512 | −0.0147401 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.34564i | 0.0919331i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.2099i | 1.06481i | 0.846491 | + | 0.532403i | \(0.178711\pi\) | ||||
−0.846491 | + | 0.532403i | \(0.821289\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.1514 | 0.865528 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.54068 | 0.138135 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 32.8090i | − 1.27806i | −0.769182 | − | 0.639030i | \(-0.779336\pi\) | ||||
0.769182 | − | 0.639030i | \(-0.220664\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5824i | 0.489398i | 0.969599 | + | 0.244699i | \(0.0786891\pi\) | ||||
−0.969599 | + | 0.244699i | \(0.921311\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.36549 | 0.0530314 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.75066 | 0.184223 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 16.6669i | − 0.645345i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 6.42915i | − 0.248565i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.07787 | −0.196029 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.58049 | −0.0994704 | −0.0497352 | − | 0.998762i | \(-0.515838\pi\) | ||||
−0.0497352 | + | 0.998762i | \(0.515838\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 3.43104i | − 0.132061i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.86443i | 0.225388i | 0.993630 | + | 0.112694i | \(0.0359480\pi\) | ||||
−0.993630 | + | 0.112694i | \(0.964052\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.8921 | −0.417999 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.45535 | 0.170729 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.3162i | 0.509531i | 0.967003 | + | 0.254765i | \(0.0819982\pi\) | ||||
−0.967003 | + | 0.254765i | \(0.918002\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 18.4760i | − 0.705931i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.33183 | 0.127117 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.0290 | 0.572560 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 34.9751i | − 1.33051i | −0.746614 | − | 0.665257i | \(-0.768322\pi\) | ||||
0.746614 | − | 0.665257i | \(-0.231678\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 8.59255i | − 0.326404i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.3614 | −0.658555 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.33190 | 0.315593 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.50494i | 0.0947454i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 4.91851i | − 0.185769i | −0.995677 | − | 0.0928847i | \(-0.970391\pi\) | ||||
0.995677 | − | 0.0928847i | \(-0.0296088\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.95889 | 0.111597 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.17136 | −0.0441159 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 41.4717i | 1.55971i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.4930i | 1.03252i | 0.856431 | + | 0.516261i | \(0.172676\pi\) | ||||
−0.856431 | + | 0.516261i | \(0.827324\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 43.4479 | 1.62942 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.5831 | −0.433791 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.95514i | 0.185312i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 4.42270i | − 0.165169i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.8746 | −0.405553 | −0.202777 | − | 0.979225i | \(-0.564996\pi\) | ||||
−0.202777 | + | 0.979225i | \(0.564996\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.3580 | −0.758172 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.51424i | 0.130696i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.8678i | 0.477899i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.13818 | −0.0422127 | −0.0211063 | − | 0.999777i | \(-0.506719\pi\) | ||||
−0.0211063 | + | 0.999777i | \(0.506719\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.3705 | 0.902612 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 3.09686i | − 0.114541i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.9950i | 1.03402i | 0.855980 | + | 0.517010i | \(0.172955\pi\) | ||||
−0.855980 | + | 0.517010i | \(0.827045\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.821486 | −0.0303010 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.51243 | −0.239889 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 44.2375i | − 1.62730i | −0.581352 | − | 0.813652i | \(-0.697476\pi\) | ||||
0.581352 | − | 0.813652i | \(-0.302524\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 0.746814i | − 0.0274349i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 49.4810 | 1.81528 | 0.907640 | − | 0.419749i | \(-0.137882\pi\) | ||||
0.907640 | + | 0.419749i | \(0.137882\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.9063 | 0.436214 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.90126i | 0.362268i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.5597i | 1.77433i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.9833 | −0.948145 | −0.474073 | − | 0.880486i | \(-0.657217\pi\) | ||||
−0.474073 | + | 0.880486i | \(0.657217\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.33495 | 0.0850904 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 4.81002i | − 0.175055i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.1605i | 1.56869i | 0.620322 | + | 0.784347i | \(0.287002\pi\) | ||||
−0.620322 | + | 0.784347i | \(0.712998\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.709944 | −0.0257693 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.16498 | −0.150981 | −0.0754903 | − | 0.997147i | \(-0.524052\pi\) | ||||
−0.0754903 | + | 0.997147i | \(0.524052\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 41.1140i | 1.48843i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 8.36664i | − 0.302497i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.32769 | −0.0479402 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.24441 | 0.189118 | 0.0945591 | − | 0.995519i | \(-0.469856\pi\) | ||||
0.0945591 | + | 0.995519i | \(0.469856\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.378011i | 0.0136137i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.91186i | 0.140700i | 0.997522 | + | 0.0703499i | \(0.0224116\pi\) | ||||
−0.997522 | + | 0.0703499i | \(0.977588\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.94284 | 0.321236 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.01396 | −0.0722505 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 4.55687i | − 0.163267i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.89772i | 0.175254i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.55632 | 0.234304 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.1061 | 0.824692 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 16.8869i | − 0.601952i | −0.953632 | − | 0.300976i | \(-0.902688\pi\) | ||||
0.953632 | − | 0.300976i | \(-0.0973125\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.07421i | 0.109445i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.3960 | −0.725199 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.9537 | −0.637556 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.54075i | 0.0546447i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 25.3722i | − 0.898729i | −0.893348 | − | 0.449365i | \(-0.851650\pi\) | ||||
0.893348 | − | 0.449365i | \(-0.148350\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.21557 | 0.219891 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28.4606 | 1.00561 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.14073i | 0.0402556i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 15.9676i | − 0.562783i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.32522 | 0.117053 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.5640 | 1.10973 | 0.554866 | − | 0.831940i | \(-0.312770\pi\) | ||||
0.554866 | + | 0.831940i | \(0.312770\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 44.1203i | − 1.54927i | −0.632407 | − | 0.774636i | \(-0.717933\pi\) | ||||
0.632407 | − | 0.774636i | \(-0.282067\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.916949i | 0.0321588i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.7646 | 1.00758 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.69373 | −0.0592560 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 30.3805i | − 1.06158i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.81015i | 0.132975i | 0.997787 | + | 0.0664876i | \(0.0211793\pi\) | ||||
−0.997787 | + | 0.0664876i | \(0.978821\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.3301 | 1.19667 | 0.598336 | − | 0.801245i | \(-0.295829\pi\) | ||||
0.598336 | + | 0.801245i | \(0.295829\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.548119 | 0.0190830 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.7484i | 1.06923i | 0.845097 | + | 0.534613i | \(0.179543\pi\) | ||||
−0.845097 | + | 0.534613i | \(0.820457\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.1917i | 0.353971i | 0.984213 | + | 0.176986i | \(0.0566346\pi\) | ||||
−0.984213 | + | 0.176986i | \(0.943365\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.72633 | −0.198644 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.35905 | 0.151032 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.7617i | 0.614669i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 4.55649i | − 0.157495i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.81123 | −0.269674 | −0.134837 | − | 0.990868i | \(-0.543051\pi\) | ||||
−0.134837 | + | 0.990868i | \(0.543051\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.41104 | 0.152105 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 2.28177i | − 0.0785884i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 2.64074i | − 0.0908442i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.9284 | −1.06271 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.55424 | 0.0533415 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 9.94521i | − 0.340918i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 46.9706i | − 1.60824i | −0.594465 | − | 0.804122i | \(-0.702636\pi\) | ||||
0.594465 | − | 0.804122i | \(-0.297364\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.57587 | −0.156491 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.24191 | −0.0765821 | −0.0382911 | − | 0.999267i | \(-0.512191\pi\) | ||||
−0.0382911 | + | 0.999267i | \(0.512191\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.9456i | 1.70412i | 0.523442 | + | 0.852061i | \(0.324648\pi\) | ||||
−0.523442 | + | 0.852061i | \(0.675352\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.10162i | 0.105703i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.4322 | 0.355115 | 0.177557 | − | 0.984110i | \(-0.443180\pi\) | ||||
0.177557 | + | 0.984110i | \(0.443180\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.1807 | −0.380154 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.03444i | 0.103055i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.9980i | 0.474849i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.0259 | −0.780203 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.4913 | 0.355077 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.0812i | 1.21977i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 23.6385i | − 0.798215i | −0.916904 | − | 0.399107i | \(-0.869320\pi\) | ||||
0.916904 | − | 0.399107i | \(-0.130680\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.07534 | −0.238645 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.2713 | −0.986175 | −0.493087 | − | 0.869980i | \(-0.664132\pi\) | ||||
−0.493087 | + | 0.869980i | \(0.664132\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 42.1875i | − 1.41972i | −0.704341 | − | 0.709862i | \(-0.748757\pi\) | ||||
0.704341 | − | 0.709862i | \(-0.251243\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 0.136112i | − 0.00457537i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.32254 | 0.0444064 | 0.0222032 | − | 0.999753i | \(-0.492932\pi\) | ||||
0.0222032 | + | 0.999753i | \(0.492932\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0582 | 0.672730 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.13561i | 0.272553i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 3.39941i | − 0.113757i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.60286 | −0.254136 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.51014 | −0.0838110 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.0887i | 0.569941i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 8.17567i | − 0.272371i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.15283 | 0.0383638 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 29.7406 | 0.988611 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.58771i | 0.119128i | 0.998224 | + | 0.0595639i | \(0.0189710\pi\) | ||||
−0.998224 | + | 0.0595639i | \(0.981029\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 39.9459i | − 1.32492i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.6828 | −0.486464 | −0.243232 | − | 0.969968i | \(-0.578208\pi\) | ||||
−0.243232 | + | 0.969968i | \(0.578208\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.18998 | −0.105573 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 1.84058i | − 0.0608478i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 43.7561i | − 1.44495i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.2168 | 1.26066 | 0.630328 | − | 0.776329i | \(-0.282920\pi\) | ||||
0.630328 | + | 0.776329i | \(0.282920\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.43494 | 0.0472829 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.3168i | 0.569988i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.67829i | 0.252461i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.6090 | 0.644044 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.8919 | 1.21038 | 0.605192 | − | 0.796080i | \(-0.293096\pi\) | ||||
0.605192 | + | 0.796080i | \(0.293096\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 2.38404i | − 0.0781339i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 6.26521i | − 0.205114i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.69555 | 0.0881541 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.7347 | −1.10206 | −0.551032 | − | 0.834484i | \(-0.685766\pi\) | ||||
−0.551032 | + | 0.834484i | \(0.685766\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.80418i | 0.124145i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 3.91029i | − 0.127472i | −0.997967 | − | 0.0637360i | \(-0.979698\pi\) | ||||
0.997967 | − | 0.0637360i | \(-0.0203015\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.3162 | −0.498765 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.28122 | 0.204328 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 46.8518i | − 1.52248i | −0.648470 | − | 0.761240i | \(-0.724591\pi\) | ||||
0.648470 | − | 0.761240i | \(-0.275409\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.03327i | 0.130925i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.57333 | 0.213155 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.5470 | −0.859941 | −0.429971 | − | 0.902843i | \(-0.641476\pi\) | ||||
−0.429971 | + | 0.902843i | \(0.641476\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 35.4844i | 1.14825i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.04739i | 0.0338574i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −36.4959 | −1.17851 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.1237 | −0.616895 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 46.7731i | − 1.50724i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.27606i | 0.105460i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.80878 | −0.218956 | −0.109478 | − | 0.993989i | \(-0.534918\pi\) | ||||
−0.109478 | + | 0.993989i | \(0.534918\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.406261 | −0.0130510 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 48.4549i | − 1.55499i | −0.628887 | − | 0.777496i | \(-0.716489\pi\) | ||||
0.628887 | − | 0.777496i | \(-0.283511\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.2942i | 1.09942i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.93797 | 0.0620648 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46.0137 | 1.47211 | 0.736055 | − | 0.676922i | \(-0.236686\pi\) | ||||
0.736055 | + | 0.676922i | \(0.236686\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.16941i | 0.293056i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 39.6013i | − 1.26437i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.8031 | −0.886782 | −0.443391 | − | 0.896328i | \(-0.646225\pi\) | ||||
−0.443391 | + | 0.896328i | \(0.646225\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.38258 | −0.298954 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.31380i | 0.0736490i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.69283i | 0.181022i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.16951 | 0.164215 | 0.0821074 | − | 0.996623i | \(-0.473835\pi\) | ||||
0.0821074 | + | 0.996623i | \(0.473835\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.56646 | −0.144912 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 6.25116i | − 0.198175i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.7227i | 0.592953i | 0.955040 | + | 0.296476i | \(0.0958116\pi\) | ||||
−0.955040 | + | 0.296476i | \(0.904188\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.91218 | 0.123776 |
(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 | 2432.2.c.i.1217.7 | ✓ | 16 | |
4.3 | odd | 2 | inner | 2432.2.c.i.1217.9 | yes | 16 | |
8.3 | odd | 2 | inner | 2432.2.c.i.1217.8 | yes | 16 | |
8.5 | even | 2 | inner | 2432.2.c.i.1217.10 | yes | 16 | |
16.3 | odd | 4 | 4864.2.a.br.1.3 | 8 | |||
16.5 | even | 4 | 4864.2.a.br.1.4 | 8 | |||
16.11 | odd | 4 | 4864.2.a.bm.1.6 | 8 | |||
16.13 | even | 4 | 4864.2.a.bm.1.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.i.1217.7 | ✓ | 16 | 1.1 | even | 1 | trivial | |
2432.2.c.i.1217.8 | yes | 16 | 8.3 | odd | 2 | inner | |
2432.2.c.i.1217.9 | yes | 16 | 4.3 | odd | 2 | inner | |
2432.2.c.i.1217.10 | yes | 16 | 8.5 | even | 2 | inner | |
4864.2.a.bm.1.5 | 8 | 16.13 | even | 4 | |||
4864.2.a.bm.1.6 | 8 | 16.11 | odd | 4 | |||
4864.2.a.br.1.3 | 8 | 16.3 | odd | 4 | |||
4864.2.a.br.1.4 | 8 | 16.5 | even | 4 |