Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4410,2,Mod(4409,4410)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4410, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4410.4409");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4410.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: | \(35.2140272914\) |
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: | \( x^{16} - 6 x^{15} + 21 x^{14} - 54 x^{13} + 113 x^{12} - 168 x^{11} + 186 x^{10} - 84 x^{9} + \cdots + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4409.3 | ||
Root | \(1.98669 + 1.02619i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4410.4409 |
Dual form | 4410.2.d.a.4409.4 |
$q$-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 \(\left(\mathbb{Z}/4410\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(2647\) | \(3431\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.88205 | − | 1.20743i | −0.841680 | − | 0.539977i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.88205 | + | 1.20743i | 0.595157 | + | 0.381821i | ||||
\(11\) | 1.59230i | 0.480097i | 0.970761 | + | 0.240049i | \(0.0771634\pi\) | ||||
−0.970761 | + | 0.240049i | \(0.922837\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.925091 | 0.256574 | 0.128287 | − | 0.991737i | \(-0.459052\pi\) | ||||
0.128287 | + | 0.991737i | \(0.459052\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 3.95765i | − | 0.959871i | −0.877304 | − | 0.479936i | \(-0.840660\pi\) | ||
0.877304 | − | 0.479936i | \(-0.159340\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.625477i | − | 0.143494i | −0.997423 | − | 0.0717472i | \(-0.977143\pi\) | ||
0.997423 | − | 0.0717472i | \(-0.0228575\pi\) | |||||||
\(20\) | −1.88205 | − | 1.20743i | −0.420840 | − | 0.269988i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 1.59230i | − | 0.339480i | ||||||
\(23\) | 7.78564 | 1.62342 | 0.811709 | − | 0.584062i | \(-0.198537\pi\) | ||||
0.811709 | + | 0.584062i | \(0.198537\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.08425 | + | 4.54488i | 0.416850 | + | 0.908975i | ||||
\(26\) | −0.925091 | −0.181425 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 9.34805i | − | 1.73589i | −0.496661 | − | 0.867945i | \(-0.665441\pi\) | ||
0.496661 | − | 0.867945i | \(-0.334559\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.3302i | 1.85535i | 0.373388 | + | 0.927675i | \(0.378196\pi\) | ||||
−0.373388 | + | 0.927675i | \(0.621804\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.95765i | 0.678732i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.426383i | 0.0700970i | 0.999386 | + | 0.0350485i | \(0.0111586\pi\) | ||||
−0.999386 | + | 0.0350485i | \(0.988841\pi\) | |||||||
\(38\) | 0.625477i | 0.101466i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.88205 | + | 1.20743i | 0.297579 | + | 0.190911i | ||||
\(41\) | −8.35463 | −1.30477 | −0.652387 | − | 0.757886i | \(-0.726232\pi\) | ||||
−0.652387 | + | 0.757886i | \(0.726232\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.27133i | 0.956369i | 0.878259 | + | 0.478184i | \(0.158705\pi\) | ||||
−0.878259 | + | 0.478184i | \(0.841295\pi\) | |||||||
\(44\) | 1.59230i | 0.240049i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.78564 | −1.14793 | ||||||||
\(47\) | 2.78130i | 0.405695i | 0.979210 | + | 0.202847i | \(0.0650195\pi\) | ||||
−0.979210 | + | 0.202847i | \(0.934980\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.08425 | − | 4.54488i | −0.294757 | − | 0.642743i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.925091 | 0.128287 | ||||||||
\(53\) | −3.35114 | −0.460315 | −0.230157 | − | 0.973153i | \(-0.573924\pi\) | ||||
−0.230157 | + | 0.973153i | \(0.573924\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.92259 | − | 2.99680i | 0.259241 | − | 0.404088i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.34805i | 1.22746i | ||||||||
\(59\) | −6.21360 | −0.808941 | −0.404471 | − | 0.914551i | \(-0.632544\pi\) | ||||
−0.404471 | + | 0.914551i | \(0.632544\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 11.0005i | − | 1.40847i | −0.709967 | − | 0.704235i | \(-0.751290\pi\) | ||
0.709967 | − | 0.704235i | \(-0.248710\pi\) | |||||||
\(62\) | − | 10.3302i | − | 1.31193i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.74107 | − | 1.11698i | −0.215953 | − | 0.138544i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 0.356178i | − | 0.0435141i | −0.999763 | − | 0.0217570i | \(-0.993074\pi\) | ||
0.999763 | − | 0.0217570i | \(-0.00692603\pi\) | |||||||
\(68\) | − | 3.95765i | − | 0.479936i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.07975i | 1.07757i | 0.842444 | + | 0.538784i | \(0.181116\pi\) | ||||
−0.842444 | + | 0.538784i | \(0.818884\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.83023 | 0.799418 | 0.399709 | − | 0.916642i | \(-0.369111\pi\) | ||||
0.399709 | + | 0.916642i | \(0.369111\pi\) | |||||||
\(74\) | − | 0.426383i | − | 0.0495661i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 0.625477i | − | 0.0717472i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.05164 | 1.01839 | 0.509195 | − | 0.860651i | \(-0.329943\pi\) | ||||
0.509195 | + | 0.860651i | \(0.329943\pi\) | |||||||
\(80\) | −1.88205 | − | 1.20743i | −0.210420 | − | 0.134994i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.35463 | 0.922614 | ||||||||
\(83\) | − | 0.809898i | − | 0.0888978i | −0.999012 | − | 0.0444489i | \(-0.985847\pi\) | ||
0.999012 | − | 0.0444489i | \(-0.0141532\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.77857 | + | 7.44851i | −0.518308 | + | 0.807904i | ||||
\(86\) | − | 6.27133i | − | 0.676255i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 1.59230i | − | 0.169740i | ||||||
\(89\) | −4.01442 | −0.425528 | −0.212764 | − | 0.977104i | \(-0.568247\pi\) | ||||
−0.212764 | + | 0.977104i | \(0.568247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.78564 | 0.811709 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 2.78130i | − | 0.286869i | ||||||
\(95\) | −0.755217 | + | 1.17718i | −0.0774836 | + | 0.120776i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.87721 | 0.799809 | 0.399905 | − | 0.916557i | \(-0.369043\pi\) | ||||
0.399905 | + | 0.916557i | \(0.369043\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.08425 | + | 4.54488i | 0.208425 | + | 0.454488i | ||||
\(101\) | −7.52821 | −0.749085 | −0.374543 | − | 0.927210i | \(-0.622200\pi\) | ||||
−0.374543 | + | 0.927210i | \(0.622200\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.66361 | 0.163920 | 0.0819601 | − | 0.996636i | \(-0.473882\pi\) | ||||
0.0819601 | + | 0.996636i | \(0.473882\pi\) | |||||||
\(104\) | −0.925091 | −0.0907127 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.35114 | 0.325492 | ||||||||
\(107\) | 19.4028 | 1.87574 | 0.937869 | − | 0.346990i | \(-0.112796\pi\) | ||||
0.937869 | + | 0.346990i | \(0.112796\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | −1.92259 | + | 2.99680i | −0.183311 | + | 0.285734i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.0750 | 1.51221 | 0.756104 | − | 0.654451i | \(-0.227100\pi\) | ||||
0.756104 | + | 0.654451i | \(0.227100\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.6530 | − | 9.40058i | −1.36640 | − | 0.876608i | ||||
\(116\) | − | 9.34805i | − | 0.867945i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.21360 | 0.572008 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.46457 | 0.769507 | ||||||||
\(122\) | 11.0005i | 0.995938i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.3302i | 0.927675i | ||||||||
\(125\) | 1.56493 | − | 11.0703i | 0.139972 | − | 0.990156i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2173i | 1.17285i | 0.810004 | + | 0.586424i | \(0.199465\pi\) | ||||
−0.810004 | + | 0.586424i | \(0.800535\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.74107 | + | 1.11698i | 0.152702 | + | 0.0979655i | ||||
\(131\) | 9.40160 | 0.821422 | 0.410711 | − | 0.911766i | \(-0.365281\pi\) | ||||
0.410711 | + | 0.911766i | \(0.365281\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.356178i | 0.0307691i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.95765i | 0.339366i | ||||||||
\(137\) | −9.37271 | −0.800765 | −0.400382 | − | 0.916348i | \(-0.631123\pi\) | ||||
−0.400382 | + | 0.916348i | \(0.631123\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 14.1106i | − | 1.19685i | −0.801180 | − | 0.598423i | \(-0.795794\pi\) | ||
0.801180 | − | 0.598423i | \(-0.204206\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 9.07975i | − | 0.761956i | ||||||
\(143\) | 1.47303i | 0.123181i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.2871 | + | 17.5935i | −0.937340 | + | 1.46106i | ||||
\(146\) | −6.83023 | −0.565274 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.426383i | 0.0350485i | ||||||||
\(149\) | − | 2.47225i | − | 0.202535i | −0.994859 | − | 0.101267i | \(-0.967710\pi\) | ||
0.994859 | − | 0.101267i | \(-0.0322897\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.8849 | −1.69959 | −0.849796 | − | 0.527112i | \(-0.823275\pi\) | ||||
−0.849796 | + | 0.527112i | \(0.823275\pi\) | |||||||
\(152\) | 0.625477i | 0.0507329i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.4729 | − | 19.4419i | 1.00185 | − | 1.56161i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.4475 | 1.95113 | 0.975563 | − | 0.219721i | \(-0.0705146\pi\) | ||||
0.975563 | + | 0.219721i | \(0.0705146\pi\) | |||||||
\(158\) | −9.05164 | −0.720110 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.88205 | + | 1.20743i | 0.148789 | + | 0.0954553i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5.91515i | − | 0.463310i | −0.972798 | − | 0.231655i | \(-0.925586\pi\) | ||
0.972798 | − | 0.231655i | \(-0.0744141\pi\) | |||||||
\(164\) | −8.35463 | −0.652387 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.809898i | 0.0628602i | ||||||||
\(167\) | − | 12.1440i | − | 0.939733i | −0.882737 | − | 0.469867i | \(-0.844302\pi\) | ||
0.882737 | − | 0.469867i | \(-0.155698\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.1442 | −0.934170 | ||||||||
\(170\) | 4.77857 | − | 7.44851i | 0.366499 | − | 0.571275i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.27133i | 0.478184i | ||||||||
\(173\) | − | 16.3984i | − | 1.24674i | −0.781925 | − | 0.623372i | \(-0.785762\pi\) | ||
0.781925 | − | 0.623372i | \(-0.214238\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.59230i | 0.120024i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.01442 | 0.300894 | ||||||||
\(179\) | 3.15693i | 0.235960i | 0.993016 | + | 0.117980i | \(0.0376419\pi\) | ||||
−0.993016 | + | 0.117980i | \(0.962358\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 8.17916i | − | 0.607952i | −0.952680 | − | 0.303976i | \(-0.901686\pi\) | ||
0.952680 | − | 0.303976i | \(-0.0983143\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.78564 | −0.573965 | ||||||||
\(185\) | 0.514826 | − | 0.802476i | 0.0378508 | − | 0.0589992i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.30178 | 0.460832 | ||||||||
\(188\) | 2.78130i | 0.202847i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.755217 | − | 1.17718i | 0.0547892 | − | 0.0854017i | ||||
\(191\) | − | 2.82843i | − | 0.204658i | −0.994751 | − | 0.102329i | \(-0.967371\pi\) | ||
0.994751 | − | 0.102329i | \(-0.0326294\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 17.7154i | − | 1.27519i | −0.770374 | − | 0.637593i | \(-0.779930\pi\) | ||
0.770374 | − | 0.637593i | \(-0.220070\pi\) | |||||||
\(194\) | −7.87721 | −0.565550 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.30350 | 0.306612 | 0.153306 | − | 0.988179i | \(-0.451008\pi\) | ||||
0.153306 | + | 0.988179i | \(0.451008\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.46410i | − | 0.245564i | −0.992434 | − | 0.122782i | \(-0.960818\pi\) | ||
0.992434 | − | 0.122782i | \(-0.0391815\pi\) | |||||||
\(200\) | −2.08425 | − | 4.54488i | −0.147379 | − | 0.321371i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.52821 | 0.529683 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.7239 | + | 10.0876i | 1.09820 | + | 0.704548i | ||||
\(206\) | −1.66361 | −0.115909 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.925091 | 0.0641435 | ||||||||
\(209\) | 0.995949 | 0.0688912 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3886 | 0.715183 | 0.357592 | − | 0.933878i | \(-0.383598\pi\) | ||||
0.357592 | + | 0.933878i | \(0.383598\pi\) | |||||||
\(212\) | −3.35114 | −0.230157 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −19.4028 | −1.32635 | ||||||||
\(215\) | 7.57216 | − | 11.8030i | 0.516417 | − | 0.804956i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.92259 | − | 2.99680i | 0.129621 | − | 0.202044i | ||||
\(221\) | − | 3.66119i | − | 0.246278i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.3555 | 1.22918 | 0.614589 | − | 0.788848i | \(-0.289322\pi\) | ||||
0.614589 | + | 0.788848i | \(0.289322\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.0750 | −1.06929 | ||||||||
\(227\) | − | 3.02304i | − | 0.200647i | −0.994955 | − | 0.100323i | \(-0.968012\pi\) | ||
0.994955 | − | 0.100323i | \(-0.0319877\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.6465i | − | 0.703541i | −0.936086 | − | 0.351770i | \(-0.885580\pi\) | ||
0.936086 | − | 0.351770i | \(-0.114420\pi\) | |||||||
\(230\) | 14.6530 | + | 9.40058i | 0.966190 | + | 0.619856i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.34805i | 0.613730i | ||||||||
\(233\) | −3.98585 | −0.261122 | −0.130561 | − | 0.991440i | \(-0.541678\pi\) | ||||
−0.130561 | + | 0.991440i | \(0.541678\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.35821 | − | 5.23456i | 0.219066 | − | 0.341465i | ||||
\(236\) | −6.21360 | −0.404471 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.24699i | − | 0.533453i | −0.963772 | − | 0.266727i | \(-0.914058\pi\) | ||
0.963772 | − | 0.266727i | \(-0.0859421\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 10.9556i | − | 0.705714i | −0.935677 | − | 0.352857i | \(-0.885210\pi\) | ||
0.935677 | − | 0.352857i | \(-0.114790\pi\) | |||||||
\(242\) | −8.46457 | −0.544123 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 11.0005i | − | 0.704235i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.578623i | − | 0.0368169i | ||||||
\(248\) | − | 10.3302i | − | 0.655965i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.56493 | + | 11.0703i | −0.0989750 | + | 0.700146i | ||||
\(251\) | −21.7369 | −1.37202 | −0.686012 | − | 0.727590i | \(-0.740640\pi\) | ||||
−0.686012 | + | 0.727590i | \(0.740640\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.3971i | 0.779399i | ||||||||
\(254\) | − | 13.2173i | − | 0.829329i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.4352i | 1.08757i | 0.839223 | + | 0.543787i | \(0.183010\pi\) | ||||
−0.839223 | + | 0.543787i | \(0.816990\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.74107 | − | 1.11698i | −0.107977 | − | 0.0692721i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.40160 | −0.580833 | ||||||||
\(263\) | 18.3511 | 1.13158 | 0.565790 | − | 0.824549i | \(-0.308571\pi\) | ||||
0.565790 | + | 0.824549i | \(0.308571\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.30703 | + | 4.04625i | 0.387438 | + | 0.248559i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 0.356178i | − | 0.0217570i | ||||||
\(269\) | 24.8371 | 1.51434 | 0.757171 | − | 0.653217i | \(-0.226581\pi\) | ||||
0.757171 | + | 0.653217i | \(0.226581\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 24.4408i | − | 1.48467i | −0.670029 | − | 0.742335i | \(-0.733718\pi\) | ||
0.670029 | − | 0.742335i | \(-0.266282\pi\) | |||||||
\(272\) | − | 3.95765i | − | 0.239968i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.37271 | 0.566226 | ||||||||
\(275\) | −7.23682 | + | 3.31876i | −0.436397 | + | 0.200128i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 23.1970i | − | 1.39378i | −0.717180 | − | 0.696888i | \(-0.754568\pi\) | ||
0.717180 | − | 0.696888i | \(-0.245432\pi\) | |||||||
\(278\) | 14.1106i | 0.846298i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.0801i | − | 0.839949i | −0.907536 | − | 0.419974i | \(-0.862039\pi\) | ||
0.907536 | − | 0.419974i | \(-0.137961\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.79820 | −0.166335 | −0.0831677 | − | 0.996536i | \(-0.526504\pi\) | ||||
−0.0831677 | + | 0.996536i | \(0.526504\pi\) | |||||||
\(284\) | 9.07975i | 0.538784i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 1.47303i | − | 0.0871018i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.33700 | 0.0786468 | ||||||||
\(290\) | 11.2871 | − | 17.5935i | 0.662800 | − | 1.03313i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.83023 | 0.399709 | ||||||||
\(293\) | − | 25.5598i | − | 1.49322i | −0.665263 | − | 0.746609i | \(-0.731681\pi\) | ||
0.665263 | − | 0.746609i | \(-0.268319\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.6943 | + | 7.50245i | 0.680870 | + | 0.436810i | ||||
\(296\) | − | 0.426383i | − | 0.0247830i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.47225i | 0.143214i | ||||||||
\(299\) | 7.20243 | 0.416527 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 20.8849 | 1.20179 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 0.625477i | − | 0.0358736i | ||||||
\(305\) | −13.2823 | + | 20.7035i | −0.760541 | + | 1.18548i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −34.2860 | −1.95681 | −0.978403 | − | 0.206704i | \(-0.933726\pi\) | ||||
−0.978403 | + | 0.206704i | \(0.933726\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.4729 | + | 19.4419i | −0.708412 | + | 1.10423i | ||||
\(311\) | 8.68041 | 0.492221 | 0.246110 | − | 0.969242i | \(-0.420847\pi\) | ||||
0.246110 | + | 0.969242i | \(0.420847\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.0213 | −1.69690 | −0.848452 | − | 0.529273i | \(-0.822465\pi\) | ||||
−0.848452 | + | 0.529273i | \(0.822465\pi\) | |||||||
\(314\) | −24.4475 | −1.37965 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.05164 | 0.509195 | ||||||||
\(317\) | 27.7256 | 1.55723 | 0.778613 | − | 0.627504i | \(-0.215923\pi\) | ||||
0.778613 | + | 0.627504i | \(0.215923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.8849 | 0.833396 | ||||||||
\(320\) | −1.88205 | − | 1.20743i | −0.105210 | − | 0.0674971i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.47542 | −0.137736 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.92812 | + | 4.20443i | 0.106953 | + | 0.233220i | ||||
\(326\) | 5.91515i | 0.327610i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.35463 | 0.461307 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.30350 | 0.346472 | 0.173236 | − | 0.984880i | \(-0.444578\pi\) | ||||
0.173236 | + | 0.984880i | \(0.444578\pi\) | |||||||
\(332\) | − | 0.809898i | − | 0.0444489i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.1440i | 0.664492i | ||||||||
\(335\) | −0.430058 | + | 0.670346i | −0.0234966 | + | 0.0366249i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 27.4097i | − | 1.49310i | −0.665329 | − | 0.746550i | \(-0.731709\pi\) | ||
0.665329 | − | 0.746550i | \(-0.268291\pi\) | |||||||
\(338\) | 12.1442 | 0.660558 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.77857 | + | 7.44851i | −0.259154 | + | 0.403952i | ||||
\(341\) | −16.4487 | −0.890749 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 6.27133i | − | 0.338127i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.3984i | 0.881581i | ||||||||
\(347\) | 8.16672 | 0.438412 | 0.219206 | − | 0.975679i | \(-0.429653\pi\) | ||||
0.219206 | + | 0.975679i | \(0.429653\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.5885i | 1.47678i | 0.674374 | + | 0.738390i | \(0.264413\pi\) | ||||
−0.674374 | + | 0.738390i | \(0.735587\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 1.59230i | − | 0.0848700i | ||||||
\(353\) | 7.04285i | 0.374853i | 0.982279 | + | 0.187426i | \(0.0600146\pi\) | ||||
−0.982279 | + | 0.187426i | \(0.939985\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.9631 | − | 17.0886i | 0.581862 | − | 0.906967i | ||||
\(356\) | −4.01442 | −0.212764 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 3.15693i | − | 0.166849i | ||||||
\(359\) | 16.3443i | 0.862617i | 0.902205 | + | 0.431308i | \(0.141948\pi\) | ||||
−0.902205 | + | 0.431308i | \(0.858052\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.6088 | 0.979409 | ||||||||
\(362\) | 8.17916i | 0.429887i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.8549 | − | 8.24699i | −0.672854 | − | 0.431667i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.00798 | 0.157015 | 0.0785076 | − | 0.996914i | \(-0.474985\pi\) | ||||
0.0785076 | + | 0.996914i | \(0.474985\pi\) | |||||||
\(368\) | 7.78564 | 0.405855 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.514826 | + | 0.802476i | −0.0267645 | + | 0.0417188i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.1970i | 1.20110i | 0.799588 | + | 0.600549i | \(0.205051\pi\) | ||||
−0.799588 | + | 0.600549i | \(0.794949\pi\) | |||||||
\(374\) | −6.30178 | −0.325857 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 2.78130i | − | 0.143435i | ||||||
\(377\) | − | 8.64780i | − | 0.445384i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.2718 | 1.40086 | 0.700429 | − | 0.713722i | \(-0.252992\pi\) | ||||
0.700429 | + | 0.713722i | \(0.252992\pi\) | |||||||
\(380\) | −0.755217 | + | 1.17718i | −0.0387418 | + | 0.0603881i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.82843i | 0.144715i | ||||||||
\(383\) | 4.26195i | 0.217776i | 0.994054 | + | 0.108888i | \(0.0347289\pi\) | ||||
−0.994054 | + | 0.108888i | \(0.965271\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.7154i | 0.901692i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.87721 | 0.399905 | ||||||||
\(389\) | 2.08172i | 0.105547i | 0.998607 | + | 0.0527736i | \(0.0168062\pi\) | ||||
−0.998607 | + | 0.0527736i | \(0.983194\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 30.8129i | − | 1.55827i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.30350 | −0.216807 | ||||||||
\(395\) | −17.0357 | − | 10.9292i | −0.857158 | − | 0.549907i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.3771 | 1.12307 | 0.561537 | − | 0.827452i | \(-0.310210\pi\) | ||||
0.561537 | + | 0.827452i | \(0.310210\pi\) | |||||||
\(398\) | 3.46410i | 0.173640i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.08425 | + | 4.54488i | 0.104212 | + | 0.227244i | ||||
\(401\) | 19.6639i | 0.981970i | 0.871168 | + | 0.490985i | \(0.163363\pi\) | ||||
−0.871168 | + | 0.490985i | \(0.836637\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.55634i | 0.476035i | ||||||||
\(404\) | −7.52821 | −0.374543 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.678932 | −0.0336534 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.53956i | 0.125573i | 0.998027 | + | 0.0627866i | \(0.0199987\pi\) | ||||
−0.998027 | + | 0.0627866i | \(0.980001\pi\) | |||||||
\(410\) | −15.7239 | − | 10.0876i | −0.776546 | − | 0.498190i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.66361 | 0.0819601 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.977891 | + | 1.52427i | −0.0480028 | + | 0.0748235i | ||||
\(416\) | −0.925091 | −0.0453563 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.995949 | −0.0487135 | ||||||||
\(419\) | 32.0568 | 1.56608 | 0.783039 | − | 0.621973i | \(-0.213669\pi\) | ||||
0.783039 | + | 0.621973i | \(0.213669\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.2201 | −1.22915 | −0.614577 | − | 0.788857i | \(-0.710673\pi\) | ||||
−0.614577 | + | 0.788857i | \(0.710673\pi\) | |||||||
\(422\) | −10.3886 | −0.505711 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.35114 | 0.162746 | ||||||||
\(425\) | 17.9870 | − | 8.24873i | 0.872500 | − | 0.400122i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 19.4028 | 0.937869 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.57216 | + | 11.8030i | −0.365162 | + | 0.569190i | ||||
\(431\) | 33.6710i | 1.62187i | 0.585133 | + | 0.810937i | \(0.301042\pi\) | ||||
−0.585133 | + | 0.810937i | \(0.698958\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.7610 | 1.09382 | 0.546912 | − | 0.837190i | \(-0.315803\pi\) | ||||
0.546912 | + | 0.837190i | \(0.315803\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | − | 4.86974i | − | 0.232951i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.15100i | − | 0.102661i | −0.998682 | − | 0.0513307i | \(-0.983654\pi\) | ||
0.998682 | − | 0.0513307i | \(-0.0163463\pi\) | |||||||
\(440\) | −1.92259 | + | 2.99680i | −0.0916557 | + | 0.142867i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.66119i | 0.174145i | ||||||||
\(443\) | −7.66479 | −0.364165 | −0.182082 | − | 0.983283i | \(-0.558284\pi\) | ||||
−0.182082 | + | 0.983283i | \(0.558284\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.55535 | + | 4.84711i | 0.358158 | + | 0.229775i | ||||
\(446\) | −18.3555 | −0.869160 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 18.8337i | − | 0.888817i | −0.895824 | − | 0.444408i | \(-0.853414\pi\) | ||
0.895824 | − | 0.444408i | \(-0.146586\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 13.3031i | − | 0.626418i | ||||||
\(452\) | 16.0750 | 0.756104 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.02304i | 0.141879i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 29.2649i | − | 1.36896i | −0.729034 | − | 0.684478i | \(-0.760030\pi\) | ||
0.729034 | − | 0.684478i | \(-0.239970\pi\) | |||||||
\(458\) | 10.6465i | 0.497478i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14.6530 | − | 9.40058i | −0.683199 | − | 0.438304i | ||||
\(461\) | −14.1963 | −0.661188 | −0.330594 | − | 0.943773i | \(-0.607249\pi\) | ||||
−0.330594 | + | 0.943773i | \(0.607249\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7.65787i | − | 0.355891i | −0.984040 | − | 0.177946i | \(-0.943055\pi\) | ||
0.984040 | − | 0.177946i | \(-0.0569451\pi\) | |||||||
\(464\) | − | 9.34805i | − | 0.433972i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.98585 | 0.184641 | ||||||||
\(467\) | − | 17.7143i | − | 0.819718i | −0.912149 | − | 0.409859i | \(-0.865578\pi\) | ||
0.912149 | − | 0.409859i | \(-0.134422\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.35821 | + | 5.23456i | −0.154903 | + | 0.241452i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.21360 | 0.286004 | ||||||||
\(473\) | −9.98585 | −0.459150 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.84272 | − | 1.30365i | 0.130433 | − | 0.0598156i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.24699i | 0.377209i | ||||||||
\(479\) | −12.8399 | −0.586671 | −0.293336 | − | 0.956010i | \(-0.594765\pi\) | ||||
−0.293336 | + | 0.956010i | \(0.594765\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.394444i | 0.0179851i | ||||||||
\(482\) | 10.9556i | 0.499015i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.46457 | 0.384753 | ||||||||
\(485\) | −14.8253 | − | 9.51114i | −0.673183 | − | 0.431878i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 3.77858i | − | 0.171224i | −0.996329 | − | 0.0856119i | \(-0.972715\pi\) | ||
0.996329 | − | 0.0856119i | \(-0.0272845\pi\) | |||||||
\(488\) | 11.0005i | 0.497969i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.1664i | 1.45165i | 0.687880 | + | 0.725824i | \(0.258541\pi\) | ||||
−0.687880 | + | 0.725824i | \(0.741459\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −36.9963 | −1.66623 | ||||||||
\(494\) | 0.578623i | 0.0260335i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.3302i | 0.463838i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.9366 | 1.42968 | 0.714839 | − | 0.699290i | \(-0.246500\pi\) | ||||
0.714839 | + | 0.699290i | \(0.246500\pi\) | |||||||
\(500\) | 1.56493 | − | 11.0703i | 0.0699859 | − | 0.495078i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.7369 | 0.970167 | ||||||||
\(503\) | − | 5.29834i | − | 0.236241i | −0.992999 | − | 0.118121i | \(-0.962313\pi\) | ||
0.992999 | − | 0.118121i | \(-0.0376870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.1685 | + | 9.08975i | 0.630490 | + | 0.404489i | ||||
\(506\) | − | 12.3971i | − | 0.551118i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.2173i | 0.586424i | ||||||||
\(509\) | 37.2643 | 1.65171 | 0.825854 | − | 0.563883i | \(-0.190693\pi\) | ||||
0.825854 | + | 0.563883i | \(0.190693\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 17.4352i | − | 0.769032i | ||||||
\(515\) | −3.13100 | − | 2.00868i | −0.137968 | − | 0.0885132i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.42867 | −0.194773 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.74107 | + | 1.11698i | 0.0763510 | + | 0.0489828i | ||||
\(521\) | 12.0135 | 0.526322 | 0.263161 | − | 0.964752i | \(-0.415235\pi\) | ||||
0.263161 | + | 0.964752i | \(0.415235\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.0357 | −1.18219 | −0.591093 | − | 0.806603i | \(-0.701304\pi\) | ||||
−0.591093 | + | 0.806603i | \(0.701304\pi\) | |||||||
\(524\) | 9.40160 | 0.410711 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.3511 | −0.800148 | ||||||||
\(527\) | 40.8831 | 1.78090 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37.6162 | 1.63549 | ||||||||
\(530\) | −6.30703 | − | 4.04625i | −0.273960 | − | 0.175758i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.72879 | −0.334771 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −36.5171 | − | 23.4274i | −1.57877 | − | 1.01286i | ||||
\(536\) | 0.356178i | 0.0153846i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −24.8371 | −1.07080 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.7090 | −0.503409 | −0.251705 | − | 0.967804i | \(-0.580991\pi\) | ||||
−0.251705 | + | 0.967804i | \(0.580991\pi\) | |||||||
\(542\) | 24.4408i | 1.04982i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.95765i | 0.169683i | ||||||||
\(545\) | −3.76411 | − | 2.41485i | −0.161237 | − | 0.103441i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 17.6050i | − | 0.752737i | −0.926470 | − | 0.376369i | \(-0.877173\pi\) | ||
0.926470 | − | 0.376369i | \(-0.122827\pi\) | |||||||
\(548\) | −9.37271 | −0.400382 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.23682 | − | 3.31876i | 0.308579 | − | 0.141512i | ||||
\(551\) | −5.84699 | −0.249090 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 23.1970i | 0.985548i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 14.1106i | − | 0.598423i | ||||||
\(557\) | 20.0817 | 0.850890 | 0.425445 | − | 0.904984i | \(-0.360118\pi\) | ||||
0.425445 | + | 0.904984i | \(0.360118\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.80155i | 0.245380i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.0801i | 0.593933i | ||||||||
\(563\) | − | 23.8077i | − | 1.00337i | −0.865050 | − | 0.501687i | \(-0.832713\pi\) | ||
0.865050 | − | 0.501687i | \(-0.167287\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.2540 | − | 19.4094i | −1.27280 | − | 0.816558i | ||||
\(566\) | 2.79820 | 0.117617 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 9.07975i | − | 0.380978i | ||||||
\(569\) | − | 41.4267i | − | 1.73670i | −0.495952 | − | 0.868350i | \(-0.665181\pi\) | ||
0.495952 | − | 0.868350i | \(-0.334819\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.1567 | 1.72235 | 0.861177 | − | 0.508305i | \(-0.169728\pi\) | ||||
0.861177 | + | 0.508305i | \(0.169728\pi\) | |||||||
\(572\) | 1.47303i | 0.0615903i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.2272 | + | 35.3848i | 0.676722 | + | 1.47565i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.4167 | 0.516914 | 0.258457 | − | 0.966023i | \(-0.416786\pi\) | ||||
0.258457 | + | 0.966023i | \(0.416786\pi\) | |||||||
\(578\) | −1.33700 | −0.0556117 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11.2871 | + | 17.5935i | −0.468670 | + | 0.730532i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5.33603i | − | 0.220996i | ||||||
\(584\) | −6.83023 | −0.282637 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.5598i | 1.05586i | ||||||||
\(587\) | − | 4.01980i | − | 0.165915i | −0.996553 | − | 0.0829575i | \(-0.973563\pi\) | ||
0.996553 | − | 0.0829575i | \(-0.0264366\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.46127 | 0.266232 | ||||||||
\(590\) | −11.6943 | − | 7.50245i | −0.481447 | − | 0.308871i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.426383i | 0.0175243i | ||||||||
\(593\) | − | 43.5334i | − | 1.78770i | −0.448366 | − | 0.893850i | \(-0.647994\pi\) | ||
0.448366 | − | 0.893850i | \(-0.352006\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 2.47225i | − | 0.101267i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.20243 | −0.294529 | ||||||||
\(599\) | − | 32.1259i | − | 1.31263i | −0.754488 | − | 0.656314i | \(-0.772115\pi\) | ||
0.754488 | − | 0.656314i | \(-0.227885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 8.21681i | − | 0.335171i | −0.985858 | − | 0.167585i | \(-0.946403\pi\) | ||
0.985858 | − | 0.167585i | \(-0.0535970\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20.8849 | −0.849796 | ||||||||
\(605\) | −15.9308 | − | 10.2203i | −0.647678 | − | 0.415516i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.2361 | 1.14607 | 0.573034 | − | 0.819532i | \(-0.305766\pi\) | ||||
0.573034 | + | 0.819532i | \(0.305766\pi\) | |||||||
\(608\) | 0.625477i | 0.0253664i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13.2823 | − | 20.7035i | 0.537784 | − | 0.838261i | ||||
\(611\) | 2.57296i | 0.104091i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 30.7924i | − | 1.24369i | −0.783139 | − | 0.621846i | \(-0.786383\pi\) | ||
0.783139 | − | 0.621846i | \(-0.213617\pi\) | |||||||
\(614\) | 34.2860 | 1.38367 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.42613 | −0.178189 | −0.0890947 | − | 0.996023i | \(-0.528397\pi\) | ||||
−0.0890947 | + | 0.996023i | \(0.528397\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.9356i | 0.439537i | 0.975552 | + | 0.219768i | \(0.0705302\pi\) | ||||
−0.975552 | + | 0.219768i | \(0.929470\pi\) | |||||||
\(620\) | 12.4729 | − | 19.4419i | 0.500923 | − | 0.780805i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.68041 | −0.348053 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.3118 | + | 18.9453i | −0.652473 | + | 0.757812i | ||||
\(626\) | 30.0213 | 1.19989 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24.4475 | 0.975563 | ||||||||
\(629\) | 1.68748 | 0.0672841 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.2293 | −1.52189 | −0.760943 | − | 0.648819i | \(-0.775263\pi\) | ||||
−0.760943 | + | 0.648819i | \(0.775263\pi\) | |||||||
\(632\) | −9.05164 | −0.360055 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −27.7256 | −1.10113 | ||||||||
\(635\) | 15.9589 | − | 24.8757i | 0.633311 | − | 0.987163i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.8849 | −0.589300 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.88205 | + | 1.20743i | 0.0743947 | + | 0.0477277i | ||||
\(641\) | 33.5254i | 1.32418i | 0.749426 | + | 0.662088i | \(0.230329\pi\) | ||||
−0.749426 | + | 0.662088i | \(0.769671\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.4072 | −0.686474 | −0.343237 | − | 0.939249i | \(-0.611523\pi\) | ||||
−0.343237 | + | 0.939249i | \(0.611523\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.47542 | 0.0973941 | ||||||||
\(647\) | 38.2602i | 1.50416i | 0.659070 | + | 0.752082i | \(0.270950\pi\) | ||||
−0.659070 | + | 0.752082i | \(0.729050\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 9.89393i | − | 0.388371i | ||||||
\(650\) | −1.92812 | − | 4.20443i | −0.0756271 | − | 0.164911i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 5.91515i | − | 0.231655i | ||||||
\(653\) | −32.3343 | −1.26534 | −0.632669 | − | 0.774422i | \(-0.718041\pi\) | ||||
−0.632669 | + | 0.774422i | \(0.718041\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.6943 | − | 11.3517i | −0.691374 | − | 0.443549i | ||||
\(656\) | −8.35463 | −0.326193 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.4516i | 0.640865i | 0.947271 | + | 0.320433i | \(0.103828\pi\) | ||||
−0.947271 | + | 0.320433i | \(0.896172\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 2.47741i | − | 0.0963600i | −0.998839 | − | 0.0481800i | \(-0.984658\pi\) | ||
0.998839 | − | 0.0481800i | \(-0.0153421\pi\) | |||||||
\(662\) | −6.30350 | −0.244992 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.809898i | 0.0314301i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 72.7806i | − | 2.81807i | ||||||
\(668\) | − | 12.1440i | − | 0.469867i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.430058 | − | 0.670346i | 0.0166146 | − | 0.0258977i | ||||
\(671\) | 17.5161 | 0.676202 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.0784i | 0.658326i | 0.944273 | + | 0.329163i | \(0.106767\pi\) | ||||
−0.944273 | + | 0.329163i | \(0.893233\pi\) | |||||||
\(674\) | 27.4097i | 1.05578i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.1442 | −0.467085 | ||||||||
\(677\) | 46.6082i | 1.79130i | 0.444759 | + | 0.895650i | \(0.353289\pi\) | ||||
−0.444759 | + | 0.895650i | \(0.646711\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.77857 | − | 7.44851i | 0.183250 | − | 0.285637i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 16.4487 | 0.629854 | ||||||||
\(683\) | 2.36707 | 0.0905734 | 0.0452867 | − | 0.998974i | \(-0.485580\pi\) | ||||
0.0452867 | + | 0.998974i | \(0.485580\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.6399 | + | 11.3168i | 0.673988 | + | 0.432395i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.27133i | 0.239092i | ||||||||
\(689\) | −3.10011 | −0.118105 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.0010i | 0.836957i | 0.908227 | + | 0.418479i | \(0.137437\pi\) | ||||
−0.908227 | + | 0.418479i | \(0.862563\pi\) | |||||||
\(692\) | − | 16.3984i | − | 0.623372i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.16672 | −0.310004 | ||||||||
\(695\) | −17.0375 | + | 26.5569i | −0.646269 | + | 1.00736i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.0647i | 1.25241i | ||||||||
\(698\) | − | 27.5885i | − | 1.04424i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.7909i | 1.08742i | 0.839274 | + | 0.543708i | \(0.182980\pi\) | ||||
−0.839274 | + | 0.543708i | \(0.817020\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.266693 | 0.0100585 | ||||||||
\(704\) | 1.59230i | 0.0600122i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 7.04285i | − | 0.265061i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.2810 | −0.573890 | −0.286945 | − | 0.957947i | \(-0.592640\pi\) | ||||
−0.286945 | + | 0.957947i | \(0.592640\pi\) | |||||||
\(710\) | −10.9631 | + | 17.0886i | −0.411439 | + | 0.641323i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.01442 | 0.150447 | ||||||||
\(713\) | 80.4269i | 3.01201i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.77857 | − | 2.77231i | 0.0665147 | − | 0.103679i | ||||
\(716\) | 3.15693i | 0.117980i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 16.3443i | − | 0.609962i | ||||||
\(719\) | −16.6746 | −0.621858 | −0.310929 | − | 0.950433i | \(-0.600640\pi\) | ||||
−0.310929 | + | 0.950433i | \(0.600640\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −18.6088 | −0.692547 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 8.17916i | − | 0.303976i | ||||||
\(725\) | 42.4857 | − | 19.4837i | 1.57788 | − | 0.723605i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.4228 | −1.20250 | −0.601248 | − | 0.799062i | \(-0.705330\pi\) | ||||
−0.601248 | + | 0.799062i | \(0.705330\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.8549 | + | 8.24699i | 0.475779 | + | 0.305235i | ||||
\(731\) | 24.8197 | 0.917991 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.3274 | 1.71114 | 0.855570 | − | 0.517687i | \(-0.173207\pi\) | ||||
0.855570 | + | 0.517687i | \(0.173207\pi\) | |||||||
\(734\) | −3.00798 | −0.111026 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.78564 | −0.286983 | ||||||||
\(737\) | 0.567143 | 0.0208910 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.4738 | −0.605998 | −0.302999 | − | 0.952991i | \(-0.597988\pi\) | ||||
−0.302999 | + | 0.952991i | \(0.597988\pi\) | |||||||
\(740\) | 0.514826 | − | 0.802476i | 0.0189254 | − | 0.0294996i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.4778 | −1.41161 | −0.705806 | − | 0.708405i | \(-0.749415\pi\) | ||||
−0.705806 | + | 0.708405i | \(0.749415\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.98506 | + | 4.65290i | −0.109364 | + | 0.170469i | ||||
\(746\) | − | 23.1970i | − | 0.849304i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.30178 | 0.230416 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.8289 | 1.38040 | 0.690198 | − | 0.723620i | \(-0.257523\pi\) | ||||
0.690198 | + | 0.723620i | \(0.257523\pi\) | |||||||
\(752\) | 2.78130i | 0.101424i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.64780i | 0.314934i | ||||||||
\(755\) | 39.3065 | + | 25.2170i | 1.43051 | + | 0.917740i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.1485i | 0.405197i | 0.979262 | + | 0.202599i | \(0.0649387\pi\) | ||||
−0.979262 | + | 0.202599i | \(0.935061\pi\) | |||||||
\(758\) | −27.2718 | −0.990556 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.755217 | − | 1.17718i | 0.0273946 | − | 0.0427009i | ||||
\(761\) | −29.2478 | −1.06023 | −0.530117 | − | 0.847925i | \(-0.677852\pi\) | ||||
−0.530117 | + | 0.847925i | \(0.677852\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 2.82843i | − | 0.102329i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 4.26195i | − | 0.153991i | ||||||
\(767\) | −5.74814 | −0.207553 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 0.892823i | − | 0.0321960i | −0.999870 | − | 0.0160980i | \(-0.994876\pi\) | ||
0.999870 | − | 0.0160980i | \(-0.00512438\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 17.7154i | − | 0.637593i | ||||||
\(773\) | − | 19.7802i | − | 0.711445i | −0.934592 | − | 0.355723i | \(-0.884235\pi\) | ||
0.934592 | − | 0.355723i | \(-0.115765\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −46.9493 | + | 21.5306i | −1.68647 | + | 0.773402i | ||||
\(776\) | −7.87721 | −0.282775 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 2.08172i | − | 0.0746332i | ||||||
\(779\) | 5.22563i | 0.187228i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.4577 | −0.517338 | ||||||||
\(782\) | 30.8129i | 1.10187i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −46.0116 | − | 29.5186i | −1.64222 | − | 1.05356i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.5957 | 0.948034 | 0.474017 | − | 0.880516i | \(-0.342804\pi\) | ||||
0.474017 | + | 0.880516i | \(0.342804\pi\) | |||||||
\(788\) | 4.30350 | 0.153306 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 17.0357 | + | 10.9292i | 0.606102 | + | 0.388843i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 10.1765i | − | 0.361377i | ||||||
\(794\) | −22.3771 | −0.794133 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 3.46410i | − | 0.122782i | ||||||
\(797\) | 21.4698i | 0.760499i | 0.924884 | + | 0.380250i | \(0.124162\pi\) | ||||
−0.924884 | + | 0.380250i | \(0.875838\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.0074 | 0.389415 | ||||||||
\(800\) | −2.08425 | − | 4.54488i | −0.0736893 | − | 0.160686i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 19.6639i | − | 0.694357i | ||||||
\(803\) | 10.8758i | 0.383798i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 9.55634i | − | 0.336608i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.52821 | 0.264842 | ||||||||
\(809\) | − | 21.1230i | − | 0.742645i | −0.928504 | − | 0.371322i | \(-0.878904\pi\) | ||
0.928504 | − | 0.371322i | \(-0.121096\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 13.3784i | − | 0.469779i | −0.972022 | − | 0.234889i | \(-0.924527\pi\) | ||
0.972022 | − | 0.234889i | \(-0.0754728\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.678932 | 0.0237965 | ||||||||
\(815\) | −7.14210 | + | 11.1326i | −0.250177 | + | 0.389959i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.92257 | 0.137233 | ||||||||
\(818\) | − | 2.53956i | − | 0.0887936i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.7239 | + | 10.0876i | 0.549101 | + | 0.352274i | ||||
\(821\) | 6.55398i | 0.228735i | 0.993438 | + | 0.114368i | \(0.0364842\pi\) | ||||
−0.993438 | + | 0.114368i | \(0.963516\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.8688i | 1.52917i | 0.644523 | + | 0.764585i | \(0.277056\pi\) | ||||
−0.644523 | + | 0.764585i | \(0.722944\pi\) | |||||||
\(824\) | −1.66361 | −0.0579546 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.1611 | 0.666296 | 0.333148 | − | 0.942875i | \(-0.391889\pi\) | ||||
0.333148 | + | 0.942875i | \(0.391889\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.9319i | 0.588071i | 0.955795 | + | 0.294035i | \(0.0949983\pi\) | ||||
−0.955795 | + | 0.294035i | \(0.905002\pi\) | |||||||
\(830\) | 0.977891 | − | 1.52427i | 0.0339431 | − | 0.0529082i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.925091 | 0.0320718 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.6630 | + | 22.8557i | −0.507434 | + | 0.790954i | ||||
\(836\) | 0.995949 | 0.0344456 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −32.0568 | −1.10738 | ||||||||
\(839\) | 10.5028 | 0.362596 | 0.181298 | − | 0.983428i | \(-0.441970\pi\) | ||||
0.181298 | + | 0.983428i | \(0.441970\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −58.3861 | −2.01331 | ||||||||
\(842\) | 25.2201 | 0.869143 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.3886 | 0.357592 | ||||||||
\(845\) | 22.8560 | + | 14.6632i | 0.786272 | + | 0.504430i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.35114 | −0.115079 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −17.9870 | + | 8.24873i | −0.616950 | + | 0.282929i | ||||
\(851\) | 3.31967i | 0.113797i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.2419 | −1.03546 | −0.517731 | − | 0.855544i | \(-0.673223\pi\) | ||||
−0.517731 | + | 0.855544i | \(0.673223\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19.4028 | −0.663173 | ||||||||
\(857\) | 22.2644i | 0.760539i | 0.924876 | + | 0.380270i | \(0.124169\pi\) | ||||
−0.924876 | + | 0.380270i | \(0.875831\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 30.8374i | − | 1.05216i | −0.850436 | − | 0.526078i | \(-0.823662\pi\) | ||
0.850436 | − | 0.526078i | \(-0.176338\pi\) | |||||||
\(860\) | 7.57216 | − | 11.8030i | 0.258209 | − | 0.402478i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 33.6710i | − | 1.14684i | ||||||
\(863\) | 23.1159 | 0.786875 | 0.393437 | − | 0.919351i | \(-0.371286\pi\) | ||||
0.393437 | + | 0.919351i | \(0.371286\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.7998 | + | 30.8626i | −0.673213 | + | 1.04936i | ||||
\(866\) | −22.7610 | −0.773450 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.4130i | 0.488926i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 0.329497i | − | 0.0111646i | ||||||
\(872\) | −2.00000 | −0.0677285 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.86974i | 0.164721i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 25.2147i | − | 0.851441i | −0.904855 | − | 0.425720i | \(-0.860021\pi\) | ||
0.904855 | − | 0.425720i | \(-0.139979\pi\) | |||||||
\(878\) | 2.15100i | 0.0725926i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.92259 | − | 2.99680i | 0.0648104 | − | 0.101022i | ||||
\(881\) | 20.5142 | 0.691140 | 0.345570 | − | 0.938393i | \(-0.387686\pi\) | ||||
0.345570 | + | 0.938393i | \(0.387686\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 43.0491i | − | 1.44872i | −0.689424 | − | 0.724358i | \(-0.742136\pi\) | ||
0.689424 | − | 0.724358i | \(-0.257864\pi\) | |||||||
\(884\) | − | 3.66119i | − | 0.123139i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.66479 | 0.257504 | ||||||||
\(887\) | 33.3905i | 1.12114i | 0.828106 | + | 0.560571i | \(0.189418\pi\) | ||||
−0.828106 | + | 0.560571i | \(0.810582\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −7.55535 | − | 4.84711i | −0.253256 | − | 0.162476i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18.3555 | 0.614589 | ||||||||
\(893\) | 1.73964 | 0.0582149 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.81176 | − | 5.94151i | 0.127413 | − | 0.198603i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.8337i | 0.628488i | ||||||||
\(899\) | 96.5668 | 3.22068 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.2626i | 0.441843i | ||||||||
\(902\) | 13.3031i | 0.442945i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.0750 | −0.534646 | ||||||||
\(905\) | −9.87572 | + | 15.3936i | −0.328280 | + | 0.511701i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 27.3797i | − | 0.909127i | −0.890714 | − | 0.454563i | \(-0.849795\pi\) | ||
0.890714 | − | 0.454563i | \(-0.150205\pi\) | |||||||
\(908\) | − | 3.02304i | − | 0.100323i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 33.0422i | − | 1.09474i | −0.836892 | − | 0.547368i | \(-0.815630\pi\) | ||
0.836892 | − | 0.547368i | \(-0.184370\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.28960 | 0.0426796 | ||||||||
\(914\) | 29.2649i | 0.967998i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 10.6465i | − | 0.351770i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.4889 | −0.873787 | −0.436893 | − | 0.899513i | \(-0.643921\pi\) | ||||
−0.436893 | + | 0.899513i | \(0.643921\pi\) | |||||||
\(920\) | 14.6530 | + | 9.40058i | 0.483095 | + | 0.309928i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.1963 | 0.467531 | ||||||||
\(923\) | 8.39960i | 0.276476i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.93786 | + | 0.888689i | −0.0637165 | + | 0.0292199i | ||||
\(926\) | 7.65787i | 0.251653i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.34805i | 0.306865i | ||||||||
\(929\) | −31.1904 | −1.02333 | −0.511663 | − | 0.859186i | \(-0.670970\pi\) | ||||
−0.511663 | + | 0.859186i | \(0.670970\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.98585 | −0.130561 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.7143i | 0.579628i | ||||||||
\(935\) | −11.8603 | − | 7.60893i | −0.387873 | − | 0.248838i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.40017 | 0.209084 | 0.104542 | − | 0.994520i | \(-0.466662\pi\) | ||||
0.104542 | + | 0.994520i | \(0.466662\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.35821 | − | 5.23456i | 0.109533 | − | 0.170732i | ||||
\(941\) | −5.12485 | −0.167065 | −0.0835327 | − | 0.996505i | \(-0.526620\pi\) | ||||
−0.0835327 | + | 0.996505i | \(0.526620\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −65.0461 | −2.11819 | ||||||||
\(944\) | −6.21360 | −0.202235 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.98585 | 0.324668 | ||||||||
\(947\) | −42.2250 | −1.37213 | −0.686064 | − | 0.727541i | \(-0.740663\pi\) | ||||
−0.686064 | + | 0.727541i | \(0.740663\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.31858 | 0.205110 | ||||||||
\(950\) | −2.84272 | + | 1.30365i | −0.0922299 | + | 0.0422960i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.12428 | 0.263171 | 0.131586 | − | 0.991305i | \(-0.457993\pi\) | ||||
0.131586 | + | 0.991305i | \(0.457993\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.41511 | + | 5.32325i | −0.110510 | + | 0.172256i | ||||
\(956\) | − | 8.24699i | − | 0.266727i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.8399 | 0.414839 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −75.7121 | −2.44232 | ||||||||
\(962\) | − | 0.394444i | − | 0.0127174i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 10.9556i | − | 0.352857i | ||||||
\(965\) | −21.3901 | + | 33.3414i | −0.688571 | + | 1.07330i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 52.3097i | − | 1.68217i | −0.540905 | − | 0.841084i | \(-0.681918\pi\) | ||
0.540905 | − | 0.841084i | \(-0.318082\pi\) | |||||||
\(968\) | −8.46457 | −0.272062 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.8253 | + | 9.51114i | 0.476012 | + | 0.305384i | ||||
\(971\) | 17.1056 | 0.548945 | 0.274473 | − | 0.961595i | \(-0.411497\pi\) | ||||
0.274473 | + | 0.961595i | \(0.411497\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.77858i | 0.121073i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 11.0005i | − | 0.352117i | ||||||
\(977\) | 36.3978 | 1.16447 | 0.582235 | − | 0.813020i | \(-0.302178\pi\) | ||||
0.582235 | + | 0.813020i | \(0.302178\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 6.39217i | − | 0.204295i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 32.1664i | − | 1.02647i | ||||||
\(983\) | 25.7283i | 0.820604i | 0.911950 | + | 0.410302i | \(0.134577\pi\) | ||||
−0.911950 | + | 0.410302i | \(0.865423\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.09941 | − | 5.19615i | −0.258069 | − | 0.165563i | ||||
\(986\) | 36.9963 | 1.17820 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 0.578623i | − | 0.0184085i | ||||||
\(989\) | 48.8263i | 1.55259i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.1475 | −0.385878 | −0.192939 | − | 0.981211i | \(-0.561802\pi\) | ||||
−0.192939 | + | 0.981211i | \(0.561802\pi\) | |||||||
\(992\) | − | 10.3302i | − | 0.327983i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.18264 | + | 6.51962i | −0.132599 | + | 0.206686i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.1533 | 0.543249 | 0.271625 | − | 0.962403i | \(-0.412439\pi\) | ||||
0.271625 | + | 0.962403i | \(0.412439\pi\) | |||||||
\(998\) | −31.9366 | −1.01093 | ||||||||
\(999\) | 0 | 0 |
(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 | 4410.2.d.a.4409.3 | 16 | ||
3.2 | odd | 2 | 4410.2.d.b.4409.14 | 16 | |||
5.4 | even | 2 | 4410.2.d.b.4409.4 | 16 | |||
7.4 | even | 3 | 630.2.bo.b.89.7 | yes | 16 | ||
7.5 | odd | 6 | 630.2.bo.b.269.4 | yes | 16 | ||
7.6 | odd | 2 | inner | 4410.2.d.a.4409.14 | 16 | ||
15.14 | odd | 2 | inner | 4410.2.d.a.4409.13 | 16 | ||
21.5 | even | 6 | 630.2.bo.a.269.5 | yes | 16 | ||
21.11 | odd | 6 | 630.2.bo.a.89.2 | ✓ | 16 | ||
21.20 | even | 2 | 4410.2.d.b.4409.3 | 16 | |||
35.4 | even | 6 | 630.2.bo.a.89.5 | yes | 16 | ||
35.12 | even | 12 | 3150.2.bf.f.1151.6 | 32 | |||
35.18 | odd | 12 | 3150.2.bf.f.1601.5 | 32 | |||
35.19 | odd | 6 | 630.2.bo.a.269.2 | yes | 16 | ||
35.32 | odd | 12 | 3150.2.bf.f.1601.14 | 32 | |||
35.33 | even | 12 | 3150.2.bf.f.1151.15 | 32 | |||
35.34 | odd | 2 | 4410.2.d.b.4409.13 | 16 | |||
105.32 | even | 12 | 3150.2.bf.f.1601.6 | 32 | |||
105.47 | odd | 12 | 3150.2.bf.f.1151.16 | 32 | |||
105.53 | even | 12 | 3150.2.bf.f.1601.13 | 32 | |||
105.68 | odd | 12 | 3150.2.bf.f.1151.5 | 32 | |||
105.74 | odd | 6 | 630.2.bo.b.89.4 | yes | 16 | ||
105.89 | even | 6 | 630.2.bo.b.269.7 | yes | 16 | ||
105.104 | even | 2 | inner | 4410.2.d.a.4409.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.bo.a.89.2 | ✓ | 16 | 21.11 | odd | 6 | ||
630.2.bo.a.89.5 | yes | 16 | 35.4 | even | 6 | ||
630.2.bo.a.269.2 | yes | 16 | 35.19 | odd | 6 | ||
630.2.bo.a.269.5 | yes | 16 | 21.5 | even | 6 | ||
630.2.bo.b.89.4 | yes | 16 | 105.74 | odd | 6 | ||
630.2.bo.b.89.7 | yes | 16 | 7.4 | even | 3 | ||
630.2.bo.b.269.4 | yes | 16 | 7.5 | odd | 6 | ||
630.2.bo.b.269.7 | yes | 16 | 105.89 | even | 6 | ||
3150.2.bf.f.1151.5 | 32 | 105.68 | odd | 12 | |||
3150.2.bf.f.1151.6 | 32 | 35.12 | even | 12 | |||
3150.2.bf.f.1151.15 | 32 | 35.33 | even | 12 | |||
3150.2.bf.f.1151.16 | 32 | 105.47 | odd | 12 | |||
3150.2.bf.f.1601.5 | 32 | 35.18 | odd | 12 | |||
3150.2.bf.f.1601.6 | 32 | 105.32 | even | 12 | |||
3150.2.bf.f.1601.13 | 32 | 105.53 | even | 12 | |||
3150.2.bf.f.1601.14 | 32 | 35.32 | odd | 12 | |||
4410.2.d.a.4409.3 | 16 | 1.1 | even | 1 | trivial | ||
4410.2.d.a.4409.4 | 16 | 105.104 | even | 2 | inner | ||
4410.2.d.a.4409.13 | 16 | 15.14 | odd | 2 | inner | ||
4410.2.d.a.4409.14 | 16 | 7.6 | odd | 2 | inner | ||
4410.2.d.b.4409.3 | 16 | 21.20 | even | 2 | |||
4410.2.d.b.4409.4 | 16 | 5.4 | even | 2 | |||
4410.2.d.b.4409.13 | 16 | 35.34 | odd | 2 | |||
4410.2.d.b.4409.14 | 16 | 3.2 | odd | 2 |