Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(165,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.i (of order \(3\), degree \(2\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 14 x^{14} - 8 x^{13} + 136 x^{12} - 87 x^{11} + 706 x^{10} - 568 x^{9} + 2685 x^{8} + \cdots + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 821.1 | ||
Root | \(1.14440 + 1.98216i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.821 |
Dual form | 1148.2.i.d.165.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.14440 | − | 1.98216i | −0.660721 | − | 1.14440i | −0.980426 | − | 0.196886i | \(-0.936917\pi\) |
0.319705 | − | 0.947517i | \(-0.396416\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.175017 | + | 0.303139i | −0.0782701 | + | 0.135568i | −0.902504 | − | 0.430682i | \(-0.858273\pi\) |
0.824234 | + | 0.566250i | \(0.191606\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.303923 | − | 2.62824i | −0.114872 | − | 0.993380i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.11932 | + | 1.93871i | −0.373106 | + | 0.646238i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.55507 | − | 2.69346i | −0.468872 | − | 0.812110i | 0.530495 | − | 0.847688i | \(-0.322006\pi\) |
−0.999367 | + | 0.0355783i | \(0.988673\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.97253 | −1.10178 | −0.550891 | − | 0.834577i | \(-0.685712\pi\) | ||||
−0.550891 | + | 0.834577i | \(0.685712\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.801161 | 0.206859 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.35057 | + | 2.33925i | 0.327561 | + | 0.567352i | 0.982027 | − | 0.188739i | \(-0.0604400\pi\) |
−0.654466 | + | 0.756091i | \(0.727107\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.341367 | − | 0.591264i | 0.0783149 | − | 0.135645i | −0.824208 | − | 0.566287i | \(-0.808379\pi\) |
0.902523 | + | 0.430642i | \(0.141713\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.86179 | + | 3.61019i | −1.06093 | + | 0.787808i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.05756 | − | 3.56379i | 0.429030 | − | 0.743102i | −0.567757 | − | 0.823196i | \(-0.692189\pi\) |
0.996787 | + | 0.0800941i | \(0.0255221\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.43874 | + | 4.22402i | 0.487748 | + | 0.844804i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.74262 | −0.335367 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.74476 | −1.25247 | −0.626236 | − | 0.779634i | \(-0.715405\pi\) | ||||
−0.626236 | + | 0.779634i | \(0.715405\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.232633 | − | 0.402933i | −0.0417822 | − | 0.0723688i | 0.844378 | − | 0.535748i | \(-0.179970\pi\) |
−0.886160 | + | 0.463379i | \(0.846637\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.55926 | + | 6.16482i | −0.619587 | + | 1.07316i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.849913 | + | 0.367856i | 0.143661 | + | 0.0621790i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.16883 | − | 3.75653i | 0.356554 | − | 0.617570i | −0.630829 | − | 0.775922i | \(-0.717285\pi\) |
0.987383 | + | 0.158352i | \(0.0506182\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.54618 | + | 7.87421i | 0.727971 | + | 1.26088i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.58476 | −0.394172 | −0.197086 | − | 0.980386i | \(-0.563148\pi\) | ||||
−0.197086 | + | 0.980386i | \(0.563148\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.391800 | − | 0.678617i | −0.0584061 | − | 0.101162i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.98366 | + | 5.16785i | −0.435211 | + | 0.753808i | −0.997313 | − | 0.0732599i | \(-0.976660\pi\) |
0.562101 | + | 0.827068i | \(0.309993\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.81526 | + | 1.59756i | −0.973609 | + | 0.228223i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.09119 | − | 5.35409i | 0.432853 | − | 0.749723i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.02277 | − | 1.77149i | −0.140489 | − | 0.243333i | 0.787192 | − | 0.616708i | \(-0.211534\pi\) |
−0.927681 | + | 0.373374i | \(0.878201\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.08866 | 0.146795 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.56264 | −0.206977 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.19494 | + | 8.99790i | 0.676324 | + | 1.17143i | 0.976080 | + | 0.217411i | \(0.0697613\pi\) |
−0.299756 | + | 0.954016i | \(0.596905\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.43657 | + | 2.48821i | −0.183934 | + | 0.318583i | −0.943217 | − | 0.332178i | \(-0.892217\pi\) |
0.759283 | + | 0.650761i | \(0.225550\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.43559 | + | 2.35261i | 0.684820 | + | 0.296401i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.695262 | − | 1.20423i | 0.0862366 | − | 0.149366i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.57698 | + | 2.73142i | 0.192659 | + | 0.333696i | 0.946131 | − | 0.323785i | \(-0.104955\pi\) |
−0.753471 | + | 0.657481i | \(0.771622\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.41870 | −1.13388 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.23326 | −0.383717 | −0.191859 | − | 0.981423i | \(-0.561452\pi\) | ||||
−0.191859 | + | 0.981423i | \(0.561452\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.299666 | + | 0.519036i | 0.0350732 | + | 0.0607486i | 0.883029 | − | 0.469318i | \(-0.155500\pi\) |
−0.847956 | + | 0.530067i | \(0.822167\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.58180 | − | 9.66796i | 0.644531 | − | 1.11636i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.60644 | + | 4.90570i | −0.752873 | + | 0.559057i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.428075 | − | 0.741447i | 0.0481622 | − | 0.0834194i | −0.840939 | − | 0.541129i | \(-0.817997\pi\) |
0.889101 | + | 0.457710i | \(0.151330\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.35221 | + | 9.27030i | 0.594690 | + | 1.03003i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.9143 | −1.41753 | −0.708764 | − | 0.705445i | \(-0.750747\pi\) | ||||
−0.708764 | + | 0.705445i | \(0.750747\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.945491 | −0.102553 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.71873 | + | 13.3692i | 0.827535 | + | 1.43333i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.01464 | + | 12.1497i | −0.743551 | + | 1.28787i | 0.207318 | + | 0.978274i | \(0.433526\pi\) |
−0.950869 | + | 0.309594i | \(0.899807\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.20734 | + | 10.4408i | 0.126564 | + | 1.09449i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.532452 | + | 0.922235i | −0.0552128 | + | 0.0956313i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.119490 | + | 0.206963i | 0.0122594 | + | 0.0212339i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.40759 | −0.345988 | −0.172994 | − | 0.984923i | \(-0.555344\pi\) | ||||
−0.172994 | + | 0.984923i | \(0.555344\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.96247 | 0.699755 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.45009 | + | 7.70778i | 0.442801 | + | 0.766953i | 0.997896 | − | 0.0648336i | \(-0.0206517\pi\) |
−0.555096 | + | 0.831787i | \(0.687318\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.32614 | − | 4.02899i | 0.229201 | − | 0.396988i | −0.728370 | − | 0.685184i | \(-0.759722\pi\) |
0.957572 | + | 0.288196i | \(0.0930553\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.243491 | − | 2.10564i | −0.0237623 | − | 0.205490i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.69478 | − | 4.66750i | 0.260514 | − | 0.451224i | −0.705864 | − | 0.708347i | \(-0.749441\pi\) |
0.966379 | + | 0.257123i | \(0.0827746\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.60295 | − | 6.24048i | −0.345100 | − | 0.597730i | 0.640272 | − | 0.768148i | \(-0.278822\pi\) |
−0.985372 | + | 0.170418i | \(0.945488\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.92808 | −0.942332 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.45820 | −0.419392 | −0.209696 | − | 0.977767i | \(-0.567247\pi\) | ||||
−0.209696 | + | 0.977767i | \(0.567247\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.720216 | + | 1.24745i | 0.0671605 | + | 0.116325i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.44652 | − | 7.70161i | 0.411081 | − | 0.712014i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.73764 | − | 4.26056i | 0.525969 | − | 0.390565i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.663505 | − | 1.14922i | 0.0603187 | − | 0.104475i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.14440 | − | 1.98216i | −0.103187 | − | 0.178726i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.45746 | −0.309244 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.3286 | 1.27146 | 0.635730 | − | 0.771912i | \(-0.280699\pi\) | ||||
0.635730 | + | 0.771912i | \(0.280699\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.95801 | + | 5.12342i | 0.260438 | + | 0.451092i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.273936 | + | 0.474472i | −0.0239339 | + | 0.0414548i | −0.877744 | − | 0.479129i | \(-0.840952\pi\) |
0.853810 | + | 0.520584i | \(0.174286\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.65773 | − | 0.717493i | −0.143744 | − | 0.0622146i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.304988 | − | 0.528255i | 0.0262492 | − | 0.0454650i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.19445 | − | 8.99705i | −0.443792 | − | 0.768670i | 0.554175 | − | 0.832400i | \(-0.313034\pi\) |
−0.997967 | + | 0.0637300i | \(0.979700\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.4437 | −1.39474 | −0.697368 | − | 0.716713i | \(-0.745646\pi\) | ||||
−0.697368 | + | 0.716713i | \(0.745646\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.6580 | 1.15021 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.17757 | + | 10.6999i | 0.516595 | + | 0.894768i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.18045 | − | 2.04460i | 0.0980311 | − | 0.169795i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.9660 | + | 11.6807i | 0.904464 | + | 0.963409i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.50883 | − | 2.61338i | 0.123608 | − | 0.214096i | −0.797580 | − | 0.603214i | \(-0.793887\pi\) |
0.921188 | + | 0.389117i | \(0.127220\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.36396 | − | 11.0227i | −0.517892 | − | 0.897015i | −0.999784 | − | 0.0207845i | \(-0.993384\pi\) |
0.481892 | − | 0.876231i | \(-0.339950\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.04686 | −0.488859 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.162859 | 0.0130812 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.1466 | − | 21.0386i | −0.969406 | − | 1.67906i | −0.697280 | − | 0.716799i | \(-0.745606\pi\) |
−0.272126 | − | 0.962262i | \(-0.587727\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.34093 | + | 4.05461i | −0.185648 | + | 0.321551i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.99183 | − | 4.32463i | −0.787466 | − | 0.340828i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.54021 | − | 14.7921i | 0.668921 | − | 1.15861i | −0.309285 | − | 0.950969i | \(-0.600090\pi\) |
0.978206 | − | 0.207636i | \(-0.0665769\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.24586 | − | 2.15790i | −0.0969903 | − | 0.167992i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.3763 | 0.880323 | 0.440162 | − | 0.897919i | \(-0.354921\pi\) | ||||
0.440162 | + | 0.897919i | \(0.354921\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.78101 | 0.213924 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.764195 | + | 1.32362i | 0.0584395 | + | 0.101220i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.884576 | + | 1.53213i | −0.0672531 | + | 0.116486i | −0.897691 | − | 0.440625i | \(-0.854757\pi\) |
0.830438 | + | 0.557111i | \(0.188090\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.3605 | − | 7.69336i | 0.783183 | − | 0.581563i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.8902 | − | 20.5945i | 0.893723 | − | 1.54797i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.63816 | + | 6.30147i | 0.271929 | + | 0.470994i | 0.969356 | − | 0.245662i | \(-0.0790052\pi\) |
−0.697427 | + | 0.716656i | \(0.745672\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.49738 | 0.259958 | 0.129979 | − | 0.991517i | \(-0.458509\pi\) | ||||
0.129979 | + | 0.991517i | \(0.458509\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.57606 | 0.486116 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.759167 | + | 1.31492i | 0.0558151 | + | 0.0966745i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.20046 | − | 7.27541i | 0.307168 | − | 0.532031i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.529622 | + | 4.58001i | 0.0385243 | + | 0.333147i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.447482 | − | 0.775061i | 0.0323786 | − | 0.0560815i | −0.849382 | − | 0.527779i | \(-0.823025\pi\) |
0.881761 | + | 0.471697i | \(0.156358\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.27271 | − | 10.8646i | −0.451519 | − | 0.782054i | 0.546961 | − | 0.837158i | \(-0.315784\pi\) |
−0.998481 | + | 0.0551035i | \(0.982451\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.18264 | −0.227914 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.91618 | 0.706499 | 0.353249 | − | 0.935529i | \(-0.385077\pi\) | ||||
0.353249 | + | 0.935529i | \(0.385077\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.9911 | − | 19.0371i | −0.779137 | − | 1.34951i | −0.932440 | − | 0.361326i | \(-0.882324\pi\) |
0.153302 | − | 0.988179i | \(-0.451009\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.60941 | − | 6.25168i | 0.254588 | − | 0.440960i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.04989 | + | 17.7268i | 0.143874 | + | 1.24418i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.175017 | + | 0.303139i | −0.0122237 | + | 0.0211721i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.60612 | + | 7.97803i | 0.320147 | + | 0.554511i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.12340 | −0.146878 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.4721 | −1.47820 | −0.739101 | − | 0.673595i | \(-0.764749\pi\) | ||||
−0.739101 | + | 0.673595i | \(0.764749\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.70015 | + | 6.40885i | 0.253530 | + | 0.439127i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.452378 | − | 0.783541i | 0.0308519 | − | 0.0534371i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.988300 | + | 0.733876i | −0.0670902 | + | 0.0498187i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.685876 | − | 1.18797i | 0.0463472 | − | 0.0802758i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.36517 | − | 9.29275i | −0.360901 | − | 0.625098i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.30791 | −0.489374 | −0.244687 | − | 0.969602i | \(-0.578685\pi\) | ||||
−0.244687 | + | 0.969602i | \(0.578685\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.9189 | −0.727926 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.22902 | − | 15.9851i | −0.612552 | − | 1.06097i | −0.990809 | − | 0.135270i | \(-0.956810\pi\) |
0.378257 | − | 0.925701i | \(-0.376524\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.50847 | + | 4.34481i | −0.165765 | + | 0.287113i | −0.936927 | − | 0.349526i | \(-0.886343\pi\) |
0.771162 | + | 0.636639i | \(0.219676\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.2843 | + | 7.48094i | 1.13723 | + | 0.492210i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.3778 | − | 23.1710i | 0.876407 | − | 1.51798i | 0.0211515 | − | 0.999776i | \(-0.493267\pi\) |
0.855256 | − | 0.518206i | \(-0.173400\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.04438 | − | 1.80893i | −0.0681281 | − | 0.118001i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.95956 | −0.127287 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.7665 | 1.21390 | 0.606951 | − | 0.794739i | \(-0.292392\pi\) | ||||
0.606951 | + | 0.794739i | \(0.292392\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.6394 | − | 20.1601i | −0.749761 | − | 1.29862i | −0.947937 | − | 0.318458i | \(-0.896835\pi\) |
0.198176 | − | 0.980166i | \(-0.436498\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.63624 | − | 16.6905i | 0.618165 | − | 1.07069i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.708505 | − | 2.34557i | 0.0452647 | − | 0.149853i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.35609 | + | 2.34882i | −0.0862859 | + | 0.149452i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.7792 | + | 25.5983i | 0.936592 | + | 1.62222i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.6641 | −1.30430 | −0.652152 | − | 0.758088i | \(-0.726134\pi\) | ||||
−0.652152 | + | 0.758088i | \(0.726134\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.7986 | −0.804640 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.08202 | + | 1.87412i | 0.0677589 | + | 0.117362i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.55827 | + | 7.89515i | −0.284337 | + | 0.492486i | −0.972448 | − | 0.233119i | \(-0.925107\pi\) |
0.688111 | + | 0.725605i | \(0.258440\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.5322 | − | 4.55851i | −0.654440 | − | 0.283252i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.54953 | − | 13.0762i | 0.467304 | − | 0.809395i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.99284 | − | 10.3799i | −0.369534 | − | 0.640052i | 0.619959 | − | 0.784635i | \(-0.287149\pi\) |
−0.989493 | + | 0.144583i | \(0.953816\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.716012 | 0.0439842 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 32.1103 | 1.96512 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.68655 | − | 4.65325i | −0.163802 | − | 0.283713i | 0.772427 | − | 0.635103i | \(-0.219043\pi\) |
−0.936229 | + | 0.351390i | \(0.885709\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9640 | − | 18.9902i | 0.666014 | − | 1.15357i | −0.312995 | − | 0.949755i | \(-0.601332\pi\) |
0.979009 | − | 0.203815i | \(-0.0653342\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19.3136 | − | 14.3416i | 1.16891 | − | 0.867993i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.58482 | − | 13.1373i | 0.457382 | − | 0.792209i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.71277 | + | 4.69865i | 0.162994 | + | 0.282315i | 0.935941 | − | 0.352156i | \(-0.114551\pi\) |
−0.772947 | + | 0.634471i | \(0.781218\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.04156 | 0.0623567 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.6364 | −1.05210 | −0.526049 | − | 0.850454i | \(-0.676327\pi\) | ||||
−0.526049 | + | 0.850454i | \(0.676327\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.33576 | − | 12.7059i | −0.436066 | − | 0.755288i | 0.561316 | − | 0.827602i | \(-0.310295\pi\) |
−0.997382 | + | 0.0723132i | \(0.976962\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.273490 | − | 0.473698i | 0.0162001 | − | 0.0280595i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.303923 | − | 2.62824i | −0.0179400 | − | 0.155140i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.85193 | − | 8.40380i | 0.285408 | − | 0.494341i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.89965 | + | 6.75439i | 0.228602 | + | 0.395950i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.13441 | 0.416797 | 0.208398 | − | 0.978044i | \(-0.433175\pi\) | ||||
0.208398 | + | 0.978044i | \(0.433175\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.63682 | −0.211744 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.70989 | + | 4.69368i | 0.157244 | + | 0.272355i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.17371 | + | 14.1573i | −0.472698 | + | 0.818737i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.785569 | + | 6.79336i | 0.0452794 | + | 0.391563i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.1854 | − | 17.6416i | 0.585136 | − | 1.01348i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.502849 | − | 0.870960i | −0.0287930 | − | 0.0498710i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.4342 | 0.995024 | 0.497512 | − | 0.867457i | \(-0.334247\pi\) | ||||
0.497512 | + | 0.867457i | \(0.334247\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.6482 | −0.605752 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.147089 | − | 0.254766i | −0.00834067 | − | 0.0144465i | 0.861825 | − | 0.507206i | \(-0.169322\pi\) |
−0.870166 | + | 0.492759i | \(0.835988\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.0419 | + | 27.7854i | −0.906742 | + | 1.57052i | −0.0881805 | + | 0.996105i | \(0.528105\pi\) |
−0.818562 | + | 0.574419i | \(0.805228\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.66449 | + | 1.23599i | −0.0937834 | + | 0.0696402i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.10185 | − | 7.10461i | 0.230383 | − | 0.399035i | −0.727538 | − | 0.686067i | \(-0.759335\pi\) |
0.957921 | + | 0.287033i | \(0.0926688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.4886 | + | 18.1668i | 0.587248 | + | 1.01714i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.3357 | −0.688509 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.84415 | 0.102612 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.68797 | − | 16.7800i | −0.537392 | − | 0.930790i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.24644 | + | 14.2833i | −0.456029 | + | 0.789866i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.4891 | + | 6.27114i | 0.798812 | + | 0.345739i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.22116 | + | 10.7754i | −0.341946 | + | 0.592268i | −0.984794 | − | 0.173726i | \(-0.944419\pi\) |
0.642848 | + | 0.765994i | \(0.277753\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.85523 | + | 8.40950i | 0.266065 | + | 0.460838i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.10400 | −0.0603178 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.6330 | 0.960530 | 0.480265 | − | 0.877123i | \(-0.340540\pi\) | ||||
0.480265 | + | 0.877123i | \(0.340540\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.10198 | + | 8.83689i | 0.277101 | + | 0.479954i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.723523 | + | 1.25318i | −0.0391809 | + | 0.0678634i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.27009 | + | 17.4266i | 0.338553 | + | 0.940947i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.64843 | − | 2.85517i | 0.0887487 | − | 0.153717i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.14857 | + | 5.45348i | 0.169024 | + | 0.292758i | 0.938077 | − | 0.346427i | \(-0.112605\pi\) |
−0.769053 | + | 0.639185i | \(0.779272\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.11133 | 0.0594879 | 0.0297440 | − | 0.999558i | \(-0.490531\pi\) | ||||
0.0297440 | + | 0.999558i | \(0.490531\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.92260 | 0.369501 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.8653 | + | 29.2116i | 0.897651 | + | 1.55478i | 0.830489 | + | 0.557035i | \(0.188061\pi\) |
0.0671614 | + | 0.997742i | \(0.478606\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.565876 | − | 0.980127i | 0.0300336 | − | 0.0520197i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.0113 | − | 6.49714i | −0.794483 | − | 0.343865i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.0242 | + | 20.8264i | −0.634611 | + | 1.09918i | 0.351987 | + | 0.936005i | \(0.385506\pi\) |
−0.986597 | + | 0.163173i | \(0.947827\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.26694 | + | 16.0508i | 0.487734 | + | 0.844779i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.03727 | −0.159415 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.209787 | −0.0109807 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.4142 | + | 24.9661i | 0.752414 | + | 1.30322i | 0.946650 | + | 0.322264i | \(0.104444\pi\) |
−0.194236 | + | 0.980955i | \(0.562223\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.11932 | + | 1.93871i | −0.0582693 | + | 0.100925i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.34506 | + | 3.22649i | −0.225584 | + | 0.167511i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.18345 | − | 15.9062i | 0.475501 | − | 0.823592i | −0.524105 | − | 0.851654i | \(-0.675600\pi\) |
0.999606 | + | 0.0280614i | \(0.00893341\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.95673 | + | 6.85325i | 0.204324 | + | 0.353900i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.7938 | 1.37995 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.6497 | −1.06070 | −0.530352 | − | 0.847778i | \(-0.677940\pi\) | ||||
−0.530352 | + | 0.847778i | \(0.677940\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.3977 | − | 28.4017i | −0.840080 | − | 1.45506i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.88459 | − | 10.1924i | 0.300688 | − | 0.520808i | −0.675604 | − | 0.737265i | \(-0.736117\pi\) |
0.976292 | + | 0.216457i | \(0.0694502\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.330868 | − | 2.86125i | −0.0168626 | − | 0.145823i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.89317 | − | 5.01111i | 0.147068 | − | 0.254729i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.1393 | + | 21.0259i | 0.615489 | + | 1.06606i | 0.990299 | + | 0.138956i | \(0.0443747\pi\) |
−0.374810 | + | 0.927102i | \(0.622292\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.1155 | 0.562134 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.25397 | 0.0632546 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.149841 | + | 0.259532i | 0.00753932 | + | 0.0130585i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.3245 | − | 17.8825i | 0.518171 | − | 0.897498i | −0.481606 | − | 0.876388i | \(-0.659946\pi\) |
0.999777 | − | 0.0211107i | \(-0.00672024\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.474924 | + | 4.10700i | 0.0237759 | + | 0.205607i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.1881 | + | 28.0386i | −0.808396 | + | 1.40018i | 0.105579 | + | 0.994411i | \(0.466330\pi\) |
−0.913975 | + | 0.405771i | \(0.867003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.924143 | + | 1.60066i | 0.0460348 | + | 0.0797347i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.74692 | −0.186186 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.4908 | −0.668712 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.40322 | − | 11.0907i | −0.316619 | − | 0.548400i | 0.663161 | − | 0.748476i | \(-0.269214\pi\) |
−0.979780 | + | 0.200076i | \(0.935881\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.8891 | + | 20.5925i | −0.586446 | + | 1.01575i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.0698 | − | 16.3882i | 1.08598 | − | 0.806411i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.26023 | − | 3.91483i | 0.110950 | − | 0.192171i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.8182 | + | 32.5941i | 0.921532 | + | 1.59614i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.8220 | 1.06608 | 0.533038 | − | 0.846092i | \(-0.321050\pi\) | ||||
0.533038 | + | 0.846092i | \(0.321050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.59928 | −0.224155 | −0.112078 | − | 0.993699i | \(-0.535751\pi\) | ||||
−0.112078 | + | 0.993699i | \(0.535751\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.67932 | − | 11.5689i | −0.324760 | − | 0.562501i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.58736 | + | 11.4096i | −0.319534 | + | 0.553449i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.97621 | + | 3.01942i | 0.337603 | + | 0.146120i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.1393 | − | 24.4899i | 0.682650 | − | 1.18238i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.49297 | + | 12.9782i | 0.360923 | + | 0.625138i | 0.988113 | − | 0.153729i | \(-0.0491282\pi\) |
−0.627190 | + | 0.778867i | \(0.715795\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.5080 | −1.46612 | −0.733060 | − | 0.680164i | \(-0.761909\pi\) | ||||
−0.733060 | + | 0.680164i | \(0.761909\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.40364 | −0.259085 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.40476 | − | 2.43312i | −0.0671989 | − | 0.116392i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.19387 | − | 12.4601i | 0.343345 | − | 0.594690i | −0.641707 | − | 0.766950i | \(-0.721773\pi\) |
0.985052 | + | 0.172260i | \(0.0551068\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.53122 | − | 15.0010i | 0.215772 | − | 0.714335i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.25972 | − | 9.11011i | 0.249897 | − | 0.432834i | −0.713600 | − | 0.700553i | \(-0.752937\pi\) |
0.963497 | + | 0.267719i | \(0.0862699\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.45537 | − | 4.25282i | −0.116396 | − | 0.201603i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.90686 | −0.326683 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.21224 | −0.245981 | −0.122990 | − | 0.992408i | \(-0.539248\pi\) | ||||
−0.122990 | + | 0.992408i | \(0.539248\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.55507 | − | 2.69346i | −0.0732255 | − | 0.126830i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.5659 | + | 25.2288i | −0.684365 | + | 1.18535i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.37631 | − | 1.46132i | −0.158284 | − | 0.0685077i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.12783 | − | 8.88166i | 0.239870 | − | 0.415466i | −0.720807 | − | 0.693136i | \(-0.756229\pi\) |
0.960677 | + | 0.277669i | \(0.0895620\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.35352 | − | 4.07642i | −0.109853 | − | 0.190271i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.59542 | −0.167456 | −0.0837278 | − | 0.996489i | \(-0.526683\pi\) | ||||
−0.0837278 | + | 0.996489i | \(0.526683\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.8730 | −0.923575 | −0.461788 | − | 0.886991i | \(-0.652792\pi\) | ||||
−0.461788 | + | 0.886991i | \(0.652792\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.186377 | − | 0.322814i | −0.00864302 | − | 0.0149701i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.0951 | − | 33.0737i | 0.883617 | − | 1.53047i | 0.0363253 | − | 0.999340i | \(-0.488435\pi\) |
0.847291 | − | 0.531129i | \(-0.178232\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.69953 | − | 4.97483i | 0.309355 | − | 0.229716i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.8013 | + | 48.1532i | −1.28101 | + | 2.21878i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.01949 | + | 6.96196i | 0.184816 | + | 0.320111i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.33001 | 0.152792 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.57923 | 0.209668 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.64907 | − | 16.7127i | −0.440877 | − | 0.763622i | 0.556878 | − | 0.830595i | \(-0.311999\pi\) |
−0.997755 | + | 0.0669729i | \(0.978666\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.61576 | + | 14.9229i | −0.392845 | + | 0.680427i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.86256 | + | 24.7546i | 0.130251 | + | 1.12637i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.596386 | − | 1.03297i | 0.0270805 | − | 0.0469048i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.8801 | − | 36.1653i | −0.946166 | − | 1.63881i | −0.753399 | − | 0.657563i | \(-0.771587\pi\) |
−0.192767 | − | 0.981245i | \(-0.561746\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −39.0938 | −1.76788 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.1057 | −1.53917 | −0.769584 | − | 0.638546i | \(-0.779536\pi\) | ||||
−0.769584 | + | 0.638546i | \(0.779536\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.10926 | − | 15.7777i | −0.410260 | − | 0.710592i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.21855 | + | 2.11060i | −0.0547699 | + | 0.0948643i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.982662 | + | 8.49777i | 0.0440784 | + | 0.381177i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.0229 | + | 19.0923i | −0.493455 | + | 0.854689i | −0.999972 | − | 0.00754120i | \(-0.997600\pi\) |
0.506517 | + | 0.862230i | \(0.330933\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.0191 | − | 22.5497i | −0.581648 | − | 1.00744i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.01342 | −0.0897738 | −0.0448869 | − | 0.998992i | \(-0.514293\pi\) | ||||
−0.0448869 | + | 0.998992i | \(0.514293\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.11537 | −0.138632 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.18260 | − | 5.51243i | −0.141344 | − | 0.244816i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.13871 | + | 12.3646i | −0.316418 | + | 0.548052i | −0.979738 | − | 0.200284i | \(-0.935814\pi\) |
0.663320 | + | 0.748336i | \(0.269147\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.27307 | − | 0.945339i | 0.0563175 | − | 0.0418193i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.594871 | + | 1.03035i | −0.0262642 | + | 0.0454909i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.814228 | + | 1.41028i | 0.0358792 | + | 0.0621446i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.5592 | 0.816233 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.04925 | 0.177742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.84187 | + | 10.1184i | 0.255937 | + | 0.443296i | 0.965150 | − | 0.261699i | \(-0.0842827\pi\) |
−0.709213 | + | 0.704995i | \(0.750949\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.7139 | + | 27.2173i | −0.687122 | + | 1.19013i | 0.285643 | + | 0.958336i | \(0.407793\pi\) |
−0.972765 | + | 0.231794i | \(0.925540\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −27.1061 | − | 11.7320i | −1.18301 | − | 0.512025i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.628374 | − | 1.08838i | 0.0273724 | − | 0.0474104i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.03293 | + | 5.25318i | 0.131866 | + | 0.228399i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.2592 | −1.00936 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.97253 | −0.172069 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.943266 | + | 1.63379i | 0.0407810 | + | 0.0706347i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.32704 | − | 14.4229i | 0.359338 | − | 0.622392i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.9012 | + | 15.8723i | 0.641840 | + | 0.683670i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.9971 | − | 36.3681i | 0.902736 | − | 1.56358i | 0.0788083 | − | 0.996890i | \(-0.474889\pi\) |
0.823928 | − | 0.566695i | \(-0.191778\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.00241 | − | 6.93238i | −0.171760 | − | 0.297497i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.52231 | 0.108044 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.0258 | −1.36933 | −0.684663 | − | 0.728860i | \(-0.740050\pi\) | ||||
−0.684663 | + | 0.728860i | \(0.740050\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.21595 | − | 5.57019i | −0.137254 | − | 0.237730i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.30244 | + | 3.98794i | −0.0980871 | + | 0.169892i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.07880 | − | 0.899739i | −0.0883996 | − | 0.0382608i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.73759 | − | 3.00959i | 0.0737564 | − | 0.127750i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.4282 | − | 30.1865i | −0.738455 | − | 1.27904i | −0.953191 | − | 0.302369i | \(-0.902223\pi\) |
0.214736 | − | 0.976672i | \(-0.431111\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.2680 | 0.434292 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.2281 | −0.811810 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.31680 | − | 4.01281i | −0.0976413 | − | 0.169120i | 0.813067 | − | 0.582171i | \(-0.197796\pi\) |
−0.910708 | + | 0.413051i | \(0.864463\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.780262 | − | 1.35145i | 0.0328259 | − | 0.0568561i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.7379 | − | 16.8843i | 0.954901 | − | 0.709075i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.50425 | − | 9.53364i | 0.230750 | − | 0.399671i | −0.727279 | − | 0.686342i | \(-0.759215\pi\) |
0.958029 | + | 0.286671i | \(0.0925486\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.85342 | − | 11.8705i | −0.286807 | − | 0.496763i | 0.686239 | − | 0.727376i | \(-0.259260\pi\) |
−0.973046 | + | 0.230613i | \(0.925927\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.04840 | −0.0855731 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.0714 | 0.837034 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.28400 | − | 7.42011i | −0.178345 | − | 0.308903i | 0.762969 | − | 0.646436i | \(-0.223741\pi\) |
−0.941314 | + | 0.337532i | \(0.890408\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.3570 | + | 24.8671i | −0.596657 | + | 1.03344i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.92495 | + | 33.9418i | 0.162835 | + | 1.40815i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.18097 | + | 5.50960i | −0.131742 | + | 0.228184i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.55644 | + | 2.69583i | 0.0643508 | + | 0.111459i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.718126 | 0.0296402 | 0.0148201 | − | 0.999890i | \(-0.495282\pi\) | ||||
0.0148201 | + | 0.999890i | \(0.495282\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.317653 | −0.0130887 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.3481 | − | 19.6555i | −0.466799 | − | 0.808519i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.75827 | + | 9.97362i | −0.236464 | + | 0.409567i | −0.959697 | − | 0.281036i | \(-0.909322\pi\) |
0.723233 | + | 0.690604i | \(0.242655\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.287357 | + | 2.48497i | 0.0117805 | + | 0.101874i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25.1565 | + | 43.5723i | −1.02959 | + | 1.78329i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.2112 | + | 38.4709i | 0.907525 | + | 1.57188i | 0.817491 | + | 0.575941i | \(0.195364\pi\) |
0.0900342 | + | 0.995939i | \(0.471302\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.2986 | −1.11353 | −0.556766 | − | 0.830669i | \(-0.687958\pi\) | ||||
−0.556766 | + | 0.830669i | \(0.687958\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.06058 | −0.287529 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.232250 | + | 0.402268i | 0.00944230 | + | 0.0163545i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.34894 | − | 10.9967i | 0.257696 | − | 0.446342i | −0.707929 | − | 0.706284i | \(-0.750370\pi\) |
0.965624 | + | 0.259942i | \(0.0837035\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 32.7916 | − | 24.3499i | 1.32878 | − | 0.986707i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.8527 | − | 20.5295i | 0.479508 | − | 0.830533i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.181551 | + | 0.314456i | 0.00733278 | + | 0.0127007i | 0.869669 | − | 0.493636i | \(-0.164333\pi\) |
−0.862336 | + | 0.506337i | \(0.830999\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.801161 | 0.0323059 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.82313 | 0.395464 | 0.197732 | − | 0.980256i | \(-0.436642\pi\) | ||||
0.197732 | + | 0.980256i | \(0.436642\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.4690 | − | 33.7212i | −0.782524 | − | 1.35537i | −0.930467 | − | 0.366375i | \(-0.880599\pi\) |
0.147944 | − | 0.988996i | \(-0.452734\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.58553 | + | 6.21033i | −0.143883 | + | 0.249212i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 34.0643 | + | 14.7436i | 1.36476 | + | 0.590688i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.5886 | + | 20.0720i | −0.463543 | + | 0.802880i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.43002 | + | 4.20892i | 0.0970458 | + | 0.168088i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.7166 | 0.467173 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.3256 | −0.848959 | −0.424479 | − | 0.905438i | \(-0.639543\pi\) | ||||
−0.424479 | + | 0.905438i | \(0.639543\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.5728 | + | 42.5613i | 0.976679 | + | 1.69166i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.50776 | + | 4.34356i | −0.0995173 | + | 0.172369i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.0738 | − | 6.34638i | 1.07270 | − | 0.251453i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.61904 | − | 6.26837i | 0.143167 | − | 0.247973i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.6802 | + | 37.5513i | 0.856318 | + | 1.48319i | 0.875417 | + | 0.483369i | \(0.160587\pi\) |
−0.0190990 | + | 0.999818i | \(0.506080\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.783742 | −0.0309078 | −0.0154539 | − | 0.999881i | \(-0.504919\pi\) | ||||
−0.0154539 | + | 0.999881i | \(0.504919\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.07081 | −0.0815381 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.4800 | − | 25.0802i | −0.569269 | − | 0.986003i | −0.996638 | − | 0.0819262i | \(-0.973893\pi\) |
0.427369 | − | 0.904077i | \(-0.359440\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.1570 | − | 27.9848i | 0.634218 | − | 1.09850i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.58568 | + | 1.11912i | 0.101341 | + | 0.0438619i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.0168 | + | 19.0817i | −0.431122 | + | 0.746724i | −0.996970 | − | 0.0777847i | \(-0.975215\pi\) |
0.565849 | + | 0.824509i | \(0.308549\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.0958872 | − | 0.166081i | −0.00374662 | − | 0.00648934i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.34168 | −0.0523441 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.7364 | −0.457186 | −0.228593 | − | 0.973522i | \(-0.573413\pi\) | ||||
−0.228593 | + | 0.973522i | \(0.573413\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.6339 | + | 21.8826i | 0.491403 | + | 0.851135i | 0.999951 | − | 0.00989879i | \(-0.00315093\pi\) |
−0.508548 | + | 0.861034i | \(0.669818\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.2798 | + | 21.2693i | −0.476910 | + | 0.826032i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.507632 | − | 0.376949i | 0.0196851 | − | 0.0146175i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.8777 | + | 24.0369i | −0.537348 | + | 0.930714i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.36320 | + | 14.4855i | 0.323340 | + | 0.560041i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.93587 | 0.344965 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.10303 | 0.350896 | 0.175448 | − | 0.984489i | \(-0.443863\pi\) | ||||
0.175448 | + | 0.984489i | \(0.443863\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.24979 | − | 7.36085i | −0.163574 | − | 0.283319i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.5501 | + | 32.1297i | −0.712938 | + | 1.23484i | 0.250812 | + | 0.968036i | \(0.419303\pi\) |
−0.963749 | + | 0.266809i | \(0.914031\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.03564 | + | 8.95594i | 0.0397444 | + | 0.343698i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.1234 | + | 36.5869i | −0.809452 | + | 1.40201i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.51013 | − | 13.0079i | −0.287367 | − | 0.497735i | 0.685813 | − | 0.727778i | \(-0.259447\pi\) |
−0.973180 | + | 0.230043i | \(0.926113\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.63647 | 0.138943 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.4828 | 0.438097 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.06300 | + | 7.03732i | 0.154788 | + | 0.268100i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.7364 | − | 35.9165i | 0.788849 | − | 1.36633i | −0.137823 | − | 0.990457i | \(-0.544011\pi\) |
0.926672 | − | 0.375870i | \(-0.122656\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.11606 | − | 18.2990i | −0.0803824 | − | 0.695123i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.87793 | − | 4.98472i | 0.109166 | − | 0.189081i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.35057 | + | 2.33925i | 0.0511564 | + | 0.0886055i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −61.2383 | −2.31624 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.7161 | −0.593589 | −0.296794 | − | 0.954941i | \(-0.595918\pi\) | ||||
−0.296794 | + | 0.954941i | \(0.595918\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.48073 | − | 2.56471i | −0.0558470 | − | 0.0967298i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.39039 | + | 4.14028i | −0.0900274 | + | 0.155932i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.9054 | − | 14.0385i | 0.711011 | − | 0.527971i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.7957 | − | 34.2872i | 0.743444 | − | 1.28768i | −0.207475 | − | 0.978240i | \(-0.566524\pi\) |
0.950918 | − | 0.309442i | \(-0.100142\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.958303 | + | 1.65983i | 0.0359392 | + | 0.0622485i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.91462 | −0.0717032 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.32473 | −0.161736 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.4764 | − | 37.1982i | −0.802052 | − | 1.38919i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.65262 | − | 9.79062i | 0.210807 | − | 0.365129i | −0.741160 | − | 0.671328i | \(-0.765724\pi\) |
0.951967 | + | 0.306200i | \(0.0990575\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.2961 | − | 4.88914i | −0.420689 | − | 0.182081i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.6404 | + | 46.1425i | −0.990767 | + | 1.71606i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.4487 | − | 28.4900i | −0.610890 | − | 1.05809i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.9056 | 1.07205 | 0.536025 | − | 0.844202i | \(-0.319925\pi\) | ||||
0.536025 | + | 0.844202i | \(0.319925\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.9977 | −0.444361 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.49089 | − | 6.04641i | −0.129115 | − | 0.223634i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.5017 | + | 19.9216i | −0.424826 | + | 0.735820i | −0.996404 | − | 0.0847276i | \(-0.972998\pi\) |
0.571578 | + | 0.820547i | \(0.306331\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.46012 | + | 1.27991i | −0.201400 | + | 0.0472101i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.90464 | − | 8.49509i | 0.180665 | − | 0.312921i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.0399 | + | 26.0498i | 0.553250 | + | 0.958258i | 0.998037 | + | 0.0626212i | \(0.0199460\pi\) |
−0.444787 | + | 0.895636i | \(0.646721\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.20765 | 0.228044 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.24979 | 0.0458503 | 0.0229251 | − | 0.999737i | \(-0.492702\pi\) | ||||
0.0229251 | + | 0.999737i | \(0.492702\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.528144 | + | 0.914772i | 0.0193497 | + | 0.0335147i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.4552 | − | 25.0371i | 0.528888 | − | 0.916061i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.0863 | − | 5.66396i | −0.478163 | − | 0.206957i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.26365 | − | 7.38487i | 0.155583 | − | 0.269478i | −0.777688 | − | 0.628650i | \(-0.783608\pi\) |
0.933271 | + | 0.359173i | \(0.116941\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.6480 | + | 40.9596i | 0.861782 | + | 1.49265i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.45521 | 0.162142 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.0979 | 0.403359 | 0.201679 | − | 0.979452i | \(-0.435360\pi\) | ||||
0.201679 | + | 0.979452i | \(0.435360\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.6467 | + | 25.3689i | 0.531643 | + | 0.920833i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.5149 | + | 26.8726i | −0.562416 | + | 0.974132i | 0.434869 | + | 0.900494i | \(0.356795\pi\) |
−0.997285 | + | 0.0736388i | \(0.976539\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.3065 | + | 11.3660i | −0.554131 | + | 0.411478i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.05830 | − | 1.83304i | 0.0382631 | − | 0.0662736i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.6371 | − | 35.7445i | −0.745162 | − | 1.29066i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.3590 | 1.67175 | 0.835874 | − | 0.548922i | \(-0.184962\pi\) | ||||
0.835874 | + | 0.548922i | \(0.184962\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.8660 | 0.751470 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.420082 | + | 0.727603i | 0.0151093 | + | 0.0261701i | 0.873481 | − | 0.486858i | \(-0.161857\pi\) |
−0.858372 | + | 0.513028i | \(0.828524\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.13466 | − | 1.96529i | 0.0407583 | − | 0.0705954i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.01737 | + | 26.0934i | 0.108248 | + | 0.936094i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.341367 | − | 0.591264i | 0.0122307 | − | 0.0211842i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.02795 | + | 8.70866i | 0.179914 | + | 0.311621i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.7535 | 0.420037 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.50348 | 0.303502 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.16156 | − | 8.94008i | −0.183990 | − | 0.318680i | 0.759246 | − | 0.650804i | \(-0.225568\pi\) |
−0.943236 | + | 0.332124i | \(0.892235\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.7164 | + | 23.7576i | −0.488318 | + | 0.845792i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.35495 | + | 11.7172i | 0.0481765 | + | 0.416616i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.70682 | − | 9.88450i | 0.202655 | − | 0.351009i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.819406 | − | 1.41925i | −0.0290613 | − | 0.0503357i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.5828 | −0.516550 | −0.258275 | − | 0.966071i | \(-0.583154\pi\) | ||||
−0.258275 | + | 0.966071i | \(0.583154\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.1185 | −0.570233 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.7032 | − | 27.1988i | −0.554846 | − | 0.961022i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.932003 | − | 1.61428i | 0.0328897 | − | 0.0569666i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.05971 | − | 2.27203i | 0.107840 | − | 0.0800784i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.14900 | + | 10.6504i | −0.216455 | + | 0.374911i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.8748 | + | 36.1562i | 0.733919 | + | 1.27119i | 0.955196 | + | 0.295974i | \(0.0956442\pi\) |
−0.221277 | + | 0.975211i | \(0.571022\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.25270 | −0.219562 | −0.109781 | − | 0.993956i | \(-0.535015\pi\) | ||||
−0.109781 | + | 0.993956i | \(0.535015\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −50.1888 | −1.76020 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.98937 | + | 5.17774i | 0.104713 | + | 0.181368i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.882351 | + | 1.52828i | −0.0308696 | + | 0.0534676i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −21.5931 | − | 9.34583i | −0.754522 | − | 0.326570i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.0820 | + | 19.1946i | −0.386765 | + | 0.669897i | −0.992012 | − | 0.126141i | \(-0.959741\pi\) |
0.605247 | + | 0.796038i | \(0.293074\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.91758 | − | 13.7137i | −0.275990 | − | 0.478028i | 0.694395 | − | 0.719594i | \(-0.255672\pi\) |
−0.970384 | + | 0.241566i | \(0.922339\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −34.7204 | −1.20881 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.9832 | 1.52945 | 0.764723 | − | 0.644359i | \(-0.222876\pi\) | ||||
0.764723 | + | 0.644359i | \(0.222876\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.0040 | − | 20.7915i | −0.416916 | − | 0.722120i | 0.578711 | − | 0.815532i | \(-0.303556\pi\) |
−0.995627 | + | 0.0934126i | \(0.970222\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.20900 | − | 10.7543i | 0.215388 | − | 0.373063i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.9416 | − | 13.7850i | −0.448399 | − | 0.477622i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.99105 | + | 3.44859i | −0.0689030 | + | 0.119343i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.405391 | + | 0.702157i | 0.0140124 | + | 0.0242701i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.4393 | −0.774690 | −0.387345 | − | 0.921935i | \(-0.626608\pi\) | ||||
−0.387345 | + | 0.921935i | \(0.626608\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.4918 | 0.568684 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.1831 | + | 34.9582i | 0.695144 | + | 1.20402i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.486726 | + | 0.843034i | −0.0167439 | + | 0.0290012i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.22209 | − | 1.39457i | −0.110712 | − | 0.0479181i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.7901 | + | 29.0814i | −0.576236 | + | 0.998070i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.92500 | − | 15.4585i | −0.305945 | − | 0.529912i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 55.6852 | 1.90663 | 0.953313 | − | 0.301984i | \(-0.0976491\pi\) | ||||
0.953313 | + | 0.301984i | \(0.0976491\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.534989 | −0.0182963 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.54767 | − | 4.41269i | −0.0870267 | − | 0.150735i | 0.819226 | − | 0.573470i | \(-0.194403\pi\) |
−0.906253 | + | 0.422736i | \(0.861070\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.11660 | + | 10.5943i | −0.208696 | + | 0.361471i | −0.951304 | − | 0.308255i | \(-0.900255\pi\) |
0.742608 | + | 0.669726i | \(0.233588\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.86179 | + | 3.61019i | −0.165689 | + | 0.123035i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.34977 | + | 10.9981i | −0.216149 | + | 0.374381i | −0.953627 | − | 0.300990i | \(-0.902683\pi\) |
0.737479 | + | 0.675371i | \(0.236016\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.309632 | − | 0.536299i | −0.0105278 | − | 0.0182347i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.2103 | −0.754300 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.66275 | −0.0903275 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.26462 | − | 10.8506i | −0.212269 | − | 0.367660i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.81417 | − | 6.60634i | 0.129090 | − | 0.223591i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.05080 | + | 9.08702i | 0.0355236 | + | 0.307197i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.7643 | − | 30.7687i | 0.599859 | − | 1.03899i | −0.392982 | − | 0.919546i | \(-0.628557\pi\) |
0.992841 | − | 0.119441i | \(-0.0381101\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.16464 | − | 14.1416i | −0.275386 | − | 0.476983i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.8665 | 0.366102 | 0.183051 | − | 0.983103i | \(-0.441403\pi\) | ||||
0.183051 | + | 0.983103i | \(0.441403\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.7307 | 0.596686 | 0.298343 | − | 0.954459i | \(-0.403566\pi\) | ||||
0.298343 | + | 0.954459i | \(0.403566\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.16199 | + | 7.20877i | 0.139904 | + | 0.242320i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.53182 | − | 13.0455i | 0.252894 | − | 0.438025i | −0.711428 | − | 0.702759i | \(-0.751951\pi\) |
0.964321 | + | 0.264735i | \(0.0852844\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.35480 | − | 37.6590i | −0.146055 | − | 1.26304i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.6461 | − | 28.8320i | 0.557667 | − | 0.965907i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.03704 | + | 3.52826i | 0.0681671 | + | 0.118069i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.54696 | −0.0851355 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 37.4161 | 1.24929 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.56906 | + | 2.71769i | 0.0523310 | + | 0.0906399i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.76265 | − | 4.78505i | 0.0920371 | − | 0.159413i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.5666 | − | 9.33147i | 0.418189 | − | 0.310532i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.612102 | + | 1.06019i | −0.0203470 | + | 0.0352420i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.6955 | + | 28.9175i | 0.554366 | + | 0.960190i | 0.997953 | + | 0.0639582i | \(0.0203724\pi\) |
−0.443587 | + | 0.896231i | \(0.646294\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.9243 | −0.660846 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.2548 | −1.53249 | −0.766244 | − | 0.642549i | \(-0.777877\pi\) | ||||
−0.766244 | + | 0.642549i | \(0.777877\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.0827 | + | 34.7842i | 0.664639 | + | 1.15119i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.15092 | + | 1.99346i | −0.0380484 | + | 0.0659017i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.33028 | + | 0.575767i | 0.0439297 | + | 0.0190135i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.1094 | − | 19.2421i | 0.366466 | − | 0.634737i | −0.622544 | − | 0.782584i | \(-0.713901\pi\) |
0.989010 | + | 0.147847i | \(0.0472344\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.9518 | − | 34.5575i | −0.657434 | − | 1.13871i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.8442 | 0.422773 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.1569 | 0.695634 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.20737 | + | 9.01943i | 0.171033 | + | 0.296237i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.1840 | + | 31.4956i | −0.596597 | + | 1.03334i | 0.396722 | + | 0.917939i | \(0.370148\pi\) |
−0.993319 | + | 0.115398i | \(0.963186\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.38192 | + | 4.57498i | −0.0452906 | + | 0.149939i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.336659 | + | 0.583111i | −0.0110217 | + | 0.0190902i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.47031 | + | 2.54664i | 0.0480841 | + | 0.0832842i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.1107 | 1.63704 | 0.818522 | − | 0.574475i | \(-0.194794\pi\) | ||||
0.818522 | + | 0.574475i | \(0.194794\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 73.4336 | 2.39642 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.9476 | + | 27.6220i | 0.519876 | + | 0.900451i | 0.999733 | + | 0.0231045i | \(0.00735506\pi\) |
−0.479857 | + | 0.877346i | \(0.659312\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.05756 | − | 3.56379i | 0.0670032 | − | 0.116053i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.48107 | − | 0.641032i | −0.0481793 | − | 0.0208528i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.8022 | − | 18.7100i | 0.351026 | − | 0.607995i | −0.635404 | − | 0.772180i | \(-0.719166\pi\) |
0.986429 | + | 0.164186i | \(0.0524996\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.19043 | − | 2.06189i | −0.0386430 | − | 0.0669317i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.7767 | −0.608876 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.8795 | 0.805928 | 0.402964 | − | 0.915216i | \(-0.367980\pi\) | ||||
0.402964 | + | 0.915216i | \(0.367980\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.156634 | + | 0.271298i | 0.00506856 | + | 0.00877901i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.0064 | − | 41.5802i | 0.776015 | − | 1.34410i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.0677 | + | 16.3867i | −0.712602 | + | 0.529153i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3918 | − | 26.6593i | 0.496509 | − | 0.859978i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.03263 | + | 10.4488i | 0.194399 | + | 0.336709i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.39133 | 0.141362 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.4487 | 1.30074 | 0.650371 | − | 0.759616i | \(-0.274613\pi\) | ||||
0.650371 | + | 0.759616i | \(0.274613\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.11046 | − | 3.65542i | −0.0677976 | − | 0.117429i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.6747 | − | 20.2212i | 0.374659 | − | 0.648928i | −0.615617 | − | 0.788046i | \(-0.711093\pi\) |
0.990276 | + | 0.139117i | \(0.0444265\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.99762 | + | 43.2179i | 0.160216 | + | 1.38550i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22.1739 | + | 38.4063i | −0.710132 | + | 1.22999i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.3675 | + | 52.5981i | 0.971544 | + | 1.68276i | 0.690899 | + | 0.722951i | \(0.257215\pi\) |
0.280645 | + | 0.959812i | \(0.409452\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43.6331 | 1.39452 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.1314 | 0.515035 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.2799 | − | 42.0541i | −0.774409 | − | 1.34132i | −0.935126 | − | 0.354315i | \(-0.884714\pi\) |
0.160717 | − | 0.987001i | \(-0.448619\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.73550 | + | 3.00598i | −0.0552977 | + | 0.0957785i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.15099 | − | 35.8966i | −0.132128 | − | 1.14260i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.31829 | + | 9.21155i | −0.169112 | + | 0.292910i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.99082 | − | 15.5726i | −0.285603 | − | 0.494678i | 0.687152 | − | 0.726513i | \(-0.258860\pi\) |
−0.972755 | + | 0.231835i | \(0.925527\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.4781 | 0.903724 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.69452 | 0.243933 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.1029 | + | 27.8910i | 0.509983 | + | 0.883317i | 0.999933 | + | 0.0115664i | \(0.00368177\pi\) |
−0.489950 | + | 0.871751i | \(0.662985\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.77945 | + | 6.54620i | −0.119576 | + | 0.207112i |
(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 | 1148.2.i.d.821.1 | yes | 16 | |
7.2 | even | 3 | 8036.2.a.m.1.8 | 8 | |||
7.4 | even | 3 | inner | 1148.2.i.d.165.1 | ✓ | 16 | |
7.5 | odd | 6 | 8036.2.a.n.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.d.165.1 | ✓ | 16 | 7.4 | even | 3 | inner | |
1148.2.i.d.821.1 | yes | 16 | 1.1 | even | 1 | trivial | |
8036.2.a.m.1.8 | 8 | 7.2 | even | 3 | |||
8036.2.a.n.1.1 | 8 | 7.5 | odd | 6 |