Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.r (of order \(3\), degree \(2\), not 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 10.0.6095158642368.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} + 6x^{8} - 7x^{7} + 25x^{6} - 66x^{5} + 75x^{4} - 63x^{3} + 162x^{2} - 324x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 673.1 | ||
Root | \(1.11541 - 1.32509i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.673 |
Dual form | 1008.2.r.n.337.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −1.62713 | − | 0.593666i | −0.939426 | − | 0.342753i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.50470 | + | 2.60622i | 0.672923 | + | 1.16554i | 0.977071 | + | 0.212913i | \(0.0682950\pi\) |
−0.304148 | + | 0.952625i | \(0.598372\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.29512 | + | 1.93195i | 0.765041 | + | 0.643982i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.74254 | + | 4.75022i | −0.826908 | + | 1.43225i | 0.0735450 | + | 0.997292i | \(0.476569\pi\) |
−0.900453 | + | 0.434954i | \(0.856765\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.421867 | − | 0.730695i | −0.117005 | − | 0.202658i | 0.801575 | − | 0.597895i | \(-0.203996\pi\) |
−0.918579 | + | 0.395236i | \(0.870663\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.901126 | − | 5.13396i | −0.232670 | − | 1.32558i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.59024 | −1.11330 | −0.556649 | − | 0.830748i | \(-0.687913\pi\) | ||||
−0.556649 | + | 0.830748i | \(0.687913\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.80203 | 0.872246 | 0.436123 | − | 0.899887i | \(-0.356351\pi\) | ||||
0.436123 | + | 0.899887i | \(0.356351\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.32770 | − | 1.11231i | 0.289727 | − | 0.242725i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.48385 | − | 7.76626i | −0.934948 | − | 1.61938i | −0.774727 | − | 0.632296i | \(-0.782113\pi\) |
−0.160221 | − | 0.987081i | \(-0.551221\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.02826 | + | 3.51305i | −0.405652 | + | 0.702610i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.58754 | − | 4.50607i | −0.497972 | − | 0.867193i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.974447 | + | 1.68779i | −0.180950 | + | 0.313415i | −0.942204 | − | 0.335039i | \(-0.891251\pi\) |
0.761254 | + | 0.648454i | \(0.224584\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.68873 | + | 2.92497i | 0.303305 | + | 0.525339i | 0.976882 | − | 0.213777i | \(-0.0685766\pi\) |
−0.673578 | + | 0.739116i | \(0.735243\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.28252 | − | 6.10109i | 1.26772 | − | 1.06206i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.00941 | −0.508682 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.49050 | −1.23143 | −0.615715 | − | 0.787969i | \(-0.711133\pi\) | ||||
−0.615715 | + | 0.787969i | \(0.711133\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.252645 | + | 1.43939i | 0.0404556 | + | 0.230486i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.69144 | − | 6.39375i | −0.576505 | − | 0.998537i | −0.995876 | − | 0.0907217i | \(-0.971083\pi\) |
0.419371 | − | 0.907815i | \(-0.362251\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.11330 | − | 5.39240i | 0.474774 | − | 0.822333i | −0.524808 | − | 0.851220i | \(-0.675863\pi\) |
0.999583 | + | 0.0288873i | \(0.00919639\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.58160 | + | 8.88860i | −0.235771 | + | 1.32503i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.57013 | + | 11.3798i | −0.958352 | + | 1.65991i | −0.231847 | + | 0.972752i | \(0.574477\pi\) |
−0.726505 | + | 0.687162i | \(0.758856\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.46894 | + | 2.72507i | 1.04586 | + | 0.381586i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.05652 | 1.10665 | 0.553324 | − | 0.832966i | \(-0.313359\pi\) | ||||
0.553324 | + | 0.832966i | \(0.313359\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.5068 | −2.22578 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.18641 | − | 2.25714i | −0.819410 | − | 0.298965i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.04037 | + | 8.73018i | 0.656200 | + | 1.13657i | 0.981591 | + | 0.190993i | \(0.0611707\pi\) |
−0.325391 | + | 0.945580i | \(0.605496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.84423 | + | 4.92635i | −0.364167 | + | 0.630755i | −0.988642 | − | 0.150289i | \(-0.951979\pi\) |
0.624475 | + | 0.781044i | \(0.285313\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.82068 | + | 1.02166i | −0.355372 | + | 0.128717i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.26957 | − | 2.19896i | 0.157471 | − | 0.272747i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.71969 | − | 4.71065i | −0.332264 | − | 0.575497i | 0.650692 | − | 0.759342i | \(-0.274479\pi\) |
−0.982955 | + | 0.183845i | \(0.941146\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.68526 | + | 15.2986i | 0.323267 | + | 1.84174i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.81144 | −0.689691 | −0.344845 | − | 0.938660i | \(-0.612069\pi\) | ||||
−0.344845 | + | 0.938660i | \(0.612069\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.7167 | −1.25429 | −0.627146 | − | 0.778902i | \(-0.715777\pi\) | ||||
−0.627146 | + | 0.778902i | \(0.715777\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.38582 | − | 4.51209i | 0.621901 | − | 0.521011i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.74254 | − | 4.75022i | −0.312542 | − | 0.541338i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.37055 | − | 2.37386i | 0.154199 | − | 0.267080i | −0.778568 | − | 0.627560i | \(-0.784054\pi\) |
0.932767 | + | 0.360480i | \(0.117387\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.53517 | + | 8.86810i | 0.170574 | + | 0.985345i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.35164 | + | 11.0014i | −0.697183 | + | 1.20756i | 0.272256 | + | 0.962225i | \(0.412230\pi\) |
−0.969439 | + | 0.245332i | \(0.921103\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.90695 | − | 11.9632i | −0.749164 | − | 1.29759i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.58754 | − | 2.16776i | 0.277413 | − | 0.232409i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.74898 | −0.927390 | −0.463695 | − | 0.885995i | \(-0.653477\pi\) | ||||
−0.463695 | + | 0.885995i | \(0.653477\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.843734 | 0.0884474 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.01134 | − | 5.76185i | −0.104871 | − | 0.597476i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.72093 | + | 9.90894i | 0.586955 | + | 1.01664i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.83699 | − | 6.64586i | 0.389587 | − | 0.674785i | −0.602807 | − | 0.797887i | \(-0.705951\pi\) |
0.992394 | + | 0.123102i | \(0.0392843\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −15.4716 | + | 5.60390i | −1.55496 | + | 0.563213i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.74033 | + | 6.47845i | −0.372177 | + | 0.644630i | −0.989900 | − | 0.141766i | \(-0.954722\pi\) |
0.617723 | + | 0.786396i | \(0.288055\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.55258 | + | 4.42120i | 0.251513 | + | 0.435634i | 0.963943 | − | 0.266110i | \(-0.0857385\pi\) |
−0.712429 | + | 0.701744i | \(0.752405\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.89670 | + | 1.78658i | 0.477869 | + | 0.174352i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.48256 | −0.143325 | −0.0716623 | − | 0.997429i | \(-0.522830\pi\) | ||||
−0.0716623 | + | 0.997429i | \(0.522830\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.878554 | 0.0841502 | 0.0420751 | − | 0.999114i | \(-0.486603\pi\) | ||||
0.0420751 | + | 0.999114i | \(0.486603\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.1880 | + | 4.44685i | 1.15684 | + | 0.422076i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.30474 | + | 9.18808i | 0.499028 | + | 0.864342i | 0.999999 | − | 0.00112222i | \(-0.000357215\pi\) |
−0.500972 | + | 0.865464i | \(0.667024\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.4937 | − | 23.3718i | 1.25830 | − | 2.17943i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.443427 | − | 2.49206i | 0.0409949 | − | 0.230391i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.29512 | − | 3.97527i | 0.210393 | − | 0.364412i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.54308 | − | 16.5291i | −0.867552 | − | 1.50264i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.21070 | + | 12.5950i | 0.199332 | + | 1.13565i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.83932 | 0.253956 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.55795 | 0.848131 | 0.424065 | − | 0.905632i | \(-0.360603\pi\) | ||||
0.424065 | + | 0.905632i | \(0.360603\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.26704 | + | 6.92589i | −0.727872 | + | 0.609790i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.785008 | − | 1.35967i | −0.0685864 | − | 0.118795i | 0.829693 | − | 0.558220i | \(-0.188516\pi\) |
−0.898279 | + | 0.439425i | \(0.855182\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.90102 | + | 3.29266i | −0.164839 | + | 0.285510i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.85033 | − | 13.5240i | 0.675649 | − | 1.16396i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.15500 | + | 2.00053i | −0.0986787 | + | 0.170916i | −0.911138 | − | 0.412101i | \(-0.864795\pi\) |
0.812459 | + | 0.583018i | \(0.198128\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.11779 | + | 15.7925i | 0.773361 | + | 1.33950i | 0.935711 | + | 0.352768i | \(0.114759\pi\) |
−0.162350 | + | 0.986733i | \(0.551907\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.4463 | − | 14.6160i | 1.46924 | − | 1.23089i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.62795 | 0.387009 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.86501 | −0.487063 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.299437 | + | 1.70597i | 0.0246971 | + | 0.140706i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.64279 | + | 2.84540i | 0.134583 | + | 0.233105i | 0.925438 | − | 0.378899i | \(-0.123697\pi\) |
−0.790855 | + | 0.612003i | \(0.790364\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.12791 | + | 10.6138i | −0.498682 | + | 0.863743i | −0.999999 | − | 0.00152112i | \(-0.999516\pi\) |
0.501317 | + | 0.865264i | \(0.332849\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.5352 | − | 8.86810i | −0.851718 | − | 0.716944i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.08207 | + | 8.80241i | −0.408202 | + | 0.707026i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.58407 | + | 2.74369i | 0.126422 | + | 0.218970i | 0.922288 | − | 0.386503i | \(-0.126317\pi\) |
−0.795866 | + | 0.605473i | \(0.792984\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.1090 | − | 4.78288i | −1.03961 | − | 0.379307i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.96770 | 0.706754 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.06739 | −0.631887 | −0.315943 | − | 0.948778i | \(-0.602321\pi\) | ||||
−0.315943 | + | 0.948778i | \(0.602321\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 26.8588 | + | 9.79955i | 2.09096 | + | 0.762894i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.162965 | + | 0.282264i | 0.0126106 | + | 0.0218422i | 0.872262 | − | 0.489039i | \(-0.162652\pi\) |
−0.859651 | + | 0.510881i | \(0.829319\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.14406 | − | 10.6418i | 0.472620 | − | 0.818601i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.72613 | + | 7.34532i | 0.667304 | + | 0.561711i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.06220 | + | 7.03593i | −0.308843 | + | 0.534932i | −0.978110 | − | 0.208091i | \(-0.933275\pi\) |
0.669267 | + | 0.743022i | \(0.266608\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.02826 | − | 3.51305i | −0.153322 | − | 0.265561i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.01854 | − | 17.1975i | −0.226888 | − | 1.29264i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.5470 | 1.31153 | 0.655763 | − | 0.754967i | \(-0.272347\pi\) | ||||
0.655763 | + | 0.754967i | \(0.272347\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.7991 | 1.10001 | 0.550004 | − | 0.835162i | \(-0.314626\pi\) | ||||
0.550004 | + | 0.835162i | \(0.314626\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.55255 | − | 6.32731i | 0.558301 | − | 0.467728i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.2710 | − | 19.5219i | −0.828658 | − | 1.43528i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.5889 | − | 21.8047i | 0.920594 | − | 1.59452i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.19614 | + | 0.0121603i | 0.377963 | + | 0.000884530i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.6859 | − | 20.2406i | 0.845564 | − | 1.46456i | −0.0395667 | − | 0.999217i | \(-0.512598\pi\) |
0.885131 | − | 0.465343i | \(-0.154069\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.80056 | − | 15.2430i | −0.633478 | − | 1.09722i | −0.986835 | − | 0.161728i | \(-0.948293\pi\) |
0.353357 | − | 0.935488i | \(-0.385040\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.37120 | + | 2.82430i | −0.241417 | + | 0.202252i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.54413 | 0.679991 | 0.339995 | − | 0.940427i | \(-0.389574\pi\) | ||||
0.339995 | + | 0.940427i | \(0.389574\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.05652 | −0.571111 | −0.285556 | − | 0.958362i | \(-0.592178\pi\) | ||||
−0.285556 | + | 0.958362i | \(0.592178\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.62875 | + | 9.27944i | 0.114883 | + | 0.654521i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.974447 | − | 1.68779i | −0.0683928 | − | 0.118460i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1090 | − | 19.2414i | 0.775888 | − | 1.34388i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.71301 | − | 26.4871i | 0.327577 | − | 1.84098i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.4272 | + | 18.0605i | −0.721267 | + | 1.24927i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.08203 | − | 15.7305i | −0.625233 | − | 1.08293i | −0.988496 | − | 0.151248i | \(-0.951671\pi\) |
0.363263 | − | 0.931687i | \(-0.381663\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.45598 | + | 3.45005i | 0.647913 | + | 0.236394i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.7384 | 1.27795 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.37746 | −0.229277 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.4375 | + | 6.36213i | 1.17831 | + | 0.429913i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.93647 | + | 3.35407i | 0.130261 | + | 0.225619i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.47051 | − | 6.01110i | 0.232402 | − | 0.402533i | −0.726112 | − | 0.687576i | \(-0.758675\pi\) |
0.958515 | + | 0.285043i | \(0.0920080\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.4421 | + | 4.14439i | −0.762808 | + | 0.276292i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.01660 | − | 8.68901i | 0.332964 | − | 0.576710i | −0.650128 | − | 0.759825i | \(-0.725285\pi\) |
0.983092 | + | 0.183115i | \(0.0586180\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.24325 | + | 5.61748i | 0.214320 | + | 0.371213i | 0.953062 | − | 0.302775i | \(-0.0979131\pi\) |
−0.738742 | + | 0.673988i | \(0.764580\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.64244 | + | 9.35740i | 0.108064 | + | 0.615671i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.9215 | 0.977538 | 0.488769 | − | 0.872413i | \(-0.337446\pi\) | ||||
0.488769 | + | 0.872413i | \(0.337446\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −39.5444 | −2.57959 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.63934 | + | 3.04894i | −0.236401 | + | 0.198050i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.76389 | − | 8.25130i | −0.308150 | − | 0.533732i | 0.669807 | − | 0.742535i | \(-0.266377\pi\) |
−0.977958 | + | 0.208803i | \(0.933043\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0471 | + | 22.5982i | −0.840436 | + | 1.45568i | 0.0490912 | + | 0.998794i | \(0.484367\pi\) |
−0.889527 | + | 0.456883i | \(0.848966\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.76676 | − | 15.3410i | 0.177488 | − | 0.984123i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.50470 | − | 2.60622i | 0.0961319 | − | 0.166505i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.60395 | − | 2.77813i | −0.102057 | − | 0.176768i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.8661 | − | 14.1299i | 1.06885 | − | 0.895448i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.0711 | −1.64560 | −0.822798 | − | 0.568334i | \(-0.807588\pi\) | ||||
−0.822798 | + | 0.568334i | \(0.807588\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 49.1886 | 3.09246 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.13639 | + | 23.5661i | 0.259031 | + | 1.47577i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.43398 | + | 4.21577i | 0.151827 | + | 0.262973i | 0.931899 | − | 0.362717i | \(-0.118151\pi\) |
−0.780072 | + | 0.625690i | \(0.784818\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.74525 | − | 6.48696i | 0.232718 | − | 0.403080i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.49720 | + | 1.99111i | −0.340268 | + | 0.123247i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.6106 | + | 27.0383i | −0.962588 | + | 1.66725i | −0.246627 | + | 0.969110i | \(0.579322\pi\) |
−0.715961 | + | 0.698141i | \(0.754011\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1227 | + | 20.9971i | 0.744689 | + | 1.28984i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.2357 | + | 5.19397i | 0.871213 | + | 0.317866i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.3736 | 0.693459 | 0.346730 | − | 0.937965i | \(-0.387292\pi\) | ||||
0.346730 | + | 0.937965i | \(0.387292\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.74404 | 0.166689 | 0.0833444 | − | 0.996521i | \(-0.473440\pi\) | ||||
0.0833444 | + | 0.996521i | \(0.473440\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.37287 | − | 0.500896i | −0.0830897 | − | 0.0303156i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.1252 | − | 19.2694i | −0.670873 | − | 1.16199i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.1725 | + | 28.0116i | −0.971710 | + | 1.68305i | −0.281321 | + | 0.959614i | \(0.590773\pi\) |
−0.690389 | + | 0.723438i | \(0.742561\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.77503 | + | 9.97569i | −0.106269 | + | 0.597229i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.74131 | − | 6.48014i | 0.223188 | − | 0.386573i | −0.732586 | − | 0.680674i | \(-0.761687\pi\) |
0.955774 | + | 0.294101i | \(0.0950203\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.02902 | + | 8.71052i | 0.298944 | + | 0.517787i | 0.975895 | − | 0.218242i | \(-0.0700322\pi\) |
−0.676950 | + | 0.736029i | \(0.736699\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.42611 | − | 19.5195i | −0.202945 | − | 1.15623i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.38287 | 0.435797 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.07034 | 0.239432 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.1887 | + | 8.53581i | −0.597273 | + | 0.500378i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.7055 | + | 22.0066i | 0.742263 | + | 1.28564i | 0.951463 | + | 0.307764i | \(0.0995806\pi\) |
−0.209200 | + | 0.977873i | \(0.567086\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.1685 | + | 26.2726i | −0.883145 | + | 1.52965i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 28.5013 | + | 0.0667001i | 1.65381 | + | 0.00387033i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.78318 | + | 6.55266i | −0.218787 | + | 0.378950i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.11330 | + | 5.39240i | 0.179448 | + | 0.310813i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.93205 | − | 8.32079i | 0.570582 | − | 0.478017i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.1189 | −0.980225 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.82625 | 0.560814 | 0.280407 | − | 0.959881i | \(-0.409531\pi\) | ||||
0.280407 | + | 0.959881i | \(0.409531\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.52867 | − | 8.70925i | −0.0869631 | − | 0.495452i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.69543 | + | 2.93657i | 0.0961389 | + | 0.166518i | 0.910083 | − | 0.414425i | \(-0.136017\pi\) |
−0.813944 | + | 0.580943i | \(0.802684\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.6346 | − | 20.1517i | 0.657627 | − | 1.13904i | −0.323601 | − | 0.946193i | \(-0.604894\pi\) |
0.981228 | − | 0.192850i | \(-0.0617730\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.90695 | − | 5.81401i | −0.389163 | − | 0.327582i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.2509 | + | 29.8794i | −0.968904 | + | 1.67819i | −0.270167 | + | 0.962813i | \(0.587079\pi\) |
−0.698737 | + | 0.715378i | \(0.746254\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.34492 | − | 9.25768i | −0.299258 | − | 0.518330i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.41232 | + | 0.880146i | 0.134643 | + | 0.0491249i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.4523 | −0.971070 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.42262 | 0.189853 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.42952 | − | 0.521567i | −0.0790529 | − | 0.0288427i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.57013 | − | 11.3798i | −0.362223 | − | 0.627388i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.99741 | + | 13.8519i | −0.439577 | + | 0.761370i | −0.997657 | − | 0.0684173i | \(-0.978205\pi\) |
0.558080 | + | 0.829787i | \(0.311538\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.1916 | − | 14.4712i | −0.942094 | − | 0.793019i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.18466 | − | 14.1763i | 0.447176 | − | 0.774531i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.83257 | − | 4.90616i | −0.154300 | − | 0.267256i | 0.778504 | − | 0.627640i | \(-0.215979\pi\) |
−0.932804 | + | 0.360384i | \(0.882646\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.17687 | − | 18.0995i | −0.172544 | − | 0.983028i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.5257 | −1.00322 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −35.8311 | + | 30.0183i | −1.92908 | + | 1.61613i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.2090 | − | 24.6107i | −0.762780 | − | 1.32117i | −0.941412 | − | 0.337257i | \(-0.890501\pi\) |
0.178633 | − | 0.983916i | \(-0.442833\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.48661 | + | 14.6992i | −0.454278 | + | 0.786832i | −0.998646 | − | 0.0520138i | \(-0.983436\pi\) |
0.544368 | + | 0.838846i | \(0.316769\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.20096 | + | 3.79166i | −0.117479 | + | 0.202384i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.83029 | + | 15.2945i | −0.469989 | + | 0.814045i | −0.999411 | − | 0.0343137i | \(-0.989075\pi\) |
0.529422 | + | 0.848359i | \(0.322409\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.74448 | − | 15.1459i | −0.464109 | − | 0.803860i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.09445 | + | 5.10575i | −0.322552 | + | 0.270225i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.7147 | 0.723834 | 0.361917 | − | 0.932210i | \(-0.382122\pi\) | ||||
0.361917 | + | 0.932210i | \(0.382122\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.54455 | −0.239187 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.71510 | + | 32.5604i | 0.299965 | + | 1.70898i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.1254 | − | 27.9300i | −0.844043 | − | 1.46192i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.33008 | + | 12.6961i | −0.382627 | + | 0.662730i | −0.991437 | − | 0.130587i | \(-0.958314\pi\) |
0.608810 | + | 0.793316i | \(0.291647\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.88009 | − | 21.8061i | 0.201990 | − | 1.13518i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.02826 | + | 6.97715i | −0.209137 | + | 0.362236i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.10543 | + | 3.64670i | 0.109015 | + | 0.188819i | 0.915371 | − | 0.402610i | \(-0.131897\pi\) |
−0.806357 | + | 0.591430i | \(0.798564\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.61995 | − | 1.68561i | −0.238573 | − | 0.0870443i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.64435 | 0.0846882 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.4637 | 0.897048 | 0.448524 | − | 0.893771i | \(-0.351950\pi\) | ||||
0.448524 | + | 0.893771i | \(0.351950\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.5520 | − | 5.67423i | −0.796756 | − | 0.290699i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.8196 | + | 22.2042i | 0.655050 | + | 1.13458i | 0.981881 | + | 0.189497i | \(0.0606858\pi\) |
−0.326831 | + | 0.945083i | \(0.605981\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.25342 | − | 14.2953i | 0.420633 | − | 0.728558i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.5632 | − | 6.36148i | 0.892789 | − | 0.323372i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.73580 | − | 6.47059i | 0.189413 | − | 0.328072i | −0.755642 | − | 0.654985i | \(-0.772675\pi\) |
0.945055 | + | 0.326913i | \(0.106008\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.5820 | + | 35.6490i | 1.04088 | + | 1.80285i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.470120 | + | 2.67840i | 0.0237144 | + | 0.135107i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.24907 | 0.415056 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.65217 | 0.133109 | 0.0665544 | − | 0.997783i | \(-0.478799\pi\) | ||||
0.0665544 | + | 0.997783i | \(0.478799\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.04794 | − | 4.22902i | 0.252713 | − | 0.211716i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.78586 | + | 15.2175i | 0.438745 | + | 0.759928i | 0.997593 | − | 0.0693419i | \(-0.0220899\pi\) |
−0.558848 | + | 0.829270i | \(0.688757\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.42484 | − | 2.46789i | 0.0709763 | − | 0.122935i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.8023 | + | 17.3448i | −1.03367 | + | 0.861872i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.5430 | − | 35.5815i | 1.01828 | − | 1.76371i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.22907 | + | 9.05702i | 0.258561 | + | 0.447841i | 0.965857 | − | 0.259077i | \(-0.0834184\pi\) |
−0.707296 | + | 0.706918i | \(0.750085\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.06699 | − | 2.56944i | 0.151283 | − | 0.126741i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.0807 | −0.496041 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.2293 | −1.87660 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.46041 | − | 31.1094i | −0.267397 | − | 1.52343i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.44830 | − | 7.70468i | −0.217314 | − | 0.376398i | 0.736672 | − | 0.676250i | \(-0.236396\pi\) |
−0.953986 | + | 0.299852i | \(0.903063\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.5280 | + | 18.2350i | −0.513103 | + | 0.888721i | 0.486781 | + | 0.873524i | \(0.338171\pi\) |
−0.999885 | + | 0.0151973i | \(0.995162\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −37.0644 | + | 13.4249i | −1.80213 | + | 0.652740i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.31020 | − | 16.1257i | 0.451611 | − | 0.782214i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.84423 | − | 4.92635i | −0.137642 | − | 0.238403i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.53029 | − | 2.74746i | −0.363566 | − | 0.132648i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.1233 | 1.25831 | 0.629157 | − | 0.777278i | \(-0.283400\pi\) | ||||
0.629157 | + | 0.777278i | \(0.283400\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.3505 | 1.45855 | 0.729276 | − | 0.684219i | \(-0.239857\pi\) | ||||
0.729276 | + | 0.684219i | \(0.239857\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.54315 | + | 3.48186i | 0.457559 | + | 0.166942i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −17.0477 | − | 29.5276i | −0.815504 | − | 1.41250i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.82759 | − | 8.36162i | 0.230408 | − | 0.399079i | −0.727520 | − | 0.686086i | \(-0.759327\pi\) |
0.957928 | + | 0.287008i | \(0.0926606\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.525553 | − | 2.95361i | 0.0250263 | − | 0.140648i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.35965 | + | 9.28318i | −0.254644 | + | 0.441057i | −0.964799 | − | 0.262989i | \(-0.915292\pi\) |
0.710154 | + | 0.704046i | \(0.248625\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.1646 | − | 22.8018i | −0.624062 | − | 1.08091i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.983826 | − | 5.60512i | −0.0465334 | − | 0.265113i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.1126 | −0.666015 | −0.333008 | − | 0.942924i | \(-0.608064\pi\) | ||||
−0.333008 | + | 0.942924i | \(0.608064\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.4957 | 1.90687 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.2720 | − | 13.6322i | 0.764525 | − | 0.640497i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.26957 | + | 2.19896i | 0.0595183 | + | 0.103089i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.7102 | − | 25.4788i | 0.688114 | − | 1.19185i | −0.284334 | − | 0.958725i | \(-0.591772\pi\) |
0.972447 | − | 0.233123i | \(-0.0748943\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.8774 | + | 20.6840i | 0.554391 | + | 0.965444i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.5313 | + | 26.9009i | −0.723363 | + | 1.25290i | 0.236282 | + | 0.971685i | \(0.424071\pi\) |
−0.959644 | + | 0.281216i | \(0.909262\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.00276 | − | 10.3971i | −0.278972 | − | 0.483194i | 0.692158 | − | 0.721746i | \(-0.256660\pi\) |
−0.971130 | + | 0.238553i | \(0.923327\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.4949 | − | 11.3056i | 0.625811 | − | 0.524286i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.115560 | 0.00534750 | 0.00267375 | − | 0.999996i | \(-0.499149\pi\) | ||||
0.00267375 | + | 0.999996i | \(0.499149\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.43939 | 0.251168 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.948657 | − | 5.40475i | −0.0437118 | − | 0.249038i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.0767 | + | 29.5778i | 0.785189 | + | 1.35999i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.71151 | + | 13.3567i | −0.353828 | + | 0.612848i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.4907 | + | 15.5648i | 0.846631 | + | 0.712661i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.92835 | + | 13.7323i | −0.362256 | + | 0.627445i | −0.988332 | − | 0.152317i | \(-0.951327\pi\) |
0.626076 | + | 0.779762i | \(0.284660\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.15999 | + | 5.47327i | 0.144083 | + | 0.249560i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.5916 | − | 5.32382i | −0.663943 | − | 0.242242i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.0941 | 1.04865 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.9185 | 1.58231 | 0.791154 | − | 0.611617i | \(-0.209481\pi\) | ||||
0.791154 | + | 0.611617i | \(0.209481\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.1267 | + | 4.78933i | 0.593611 | + | 0.216581i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.7104 | − | 20.2831i | −0.528484 | − | 0.915362i | −0.999448 | − | 0.0332092i | \(-0.989427\pi\) |
0.470964 | − | 0.882152i | \(-0.343906\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.47295 | − | 7.74737i | 0.201451 | − | 0.348924i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −37.8852 | − | 31.8903i | −1.70281 | − | 1.43336i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.90572 | − | 5.03285i | 0.130339 | − | 0.225754i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.22661 | + | 3.85659i | 0.0996765 | + | 0.172645i | 0.911551 | − | 0.411188i | \(-0.134886\pi\) |
−0.811874 | + | 0.583832i | \(0.801553\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.0975954 | − | 0.556027i | −0.00436024 | − | 0.0248415i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.1429 | 0.586014 | 0.293007 | − | 0.956110i | \(-0.405344\pi\) | ||||
0.293007 | + | 0.956110i | \(0.405344\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.5124 | −1.00179 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.3149 | + | 13.6681i | −0.724569 | + | 0.607023i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.41360 | − | 9.37662i | −0.239953 | − | 0.415612i | 0.720747 | − | 0.693198i | \(-0.243799\pi\) |
−0.960701 | + | 0.277586i | \(0.910466\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.35834 | − | 9.28092i | 0.237039 | − | 0.410564i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.83790 | − | 17.1322i | −0.434354 | − | 0.756406i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.68175 | + | 13.3052i | −0.338498 | + | 0.586296i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36.0377 | − | 62.4191i | −1.58494 | − | 2.74519i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.7867 | − | 9.03681i | 0.473485 | − | 0.396672i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.9378 | −0.873489 | −0.436745 | − | 0.899586i | \(-0.643869\pi\) | ||||
−0.436745 | + | 0.899586i | \(0.643869\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.6481 | −1.03406 | −0.517029 | − | 0.855968i | \(-0.672962\pi\) | ||||
−0.517029 | + | 0.855968i | \(0.672962\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.21467 | + | 6.92030i | 0.0530126 | + | 0.302027i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.75168 | − | 13.4263i | −0.337669 | − | 0.584859i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −28.7099 | + | 49.7269i | −1.24825 | + | 2.16204i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.29797 | + | 29.7745i | −0.229912 | + | 1.29211i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.11459 | + | 5.39463i | −0.134908 | + | 0.233667i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.23081 | − | 3.86388i | −0.0964465 | − | 0.167050i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.5513 | − | 10.4171i | −1.23208 | − | 0.449529i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.48508 | 0.236259 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.93883 | 0.0833567 | 0.0416783 | − | 0.999131i | \(-0.486730\pi\) | ||||
0.0416783 | + | 0.999131i | \(0.486730\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.0801 | − | 8.78571i | −1.03338 | − | 0.377031i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.32196 | + | 2.28971i | 0.0566266 | + | 0.0980802i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.8625 | + | 34.4029i | −0.849259 | + | 1.47096i | 0.0326112 | + | 0.999468i | \(0.489618\pi\) |
−0.881870 | + | 0.471492i | \(0.843716\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.0453 | + | 5.81168i | −0.684797 | + | 0.248037i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.70488 | + | 6.41704i | −0.157833 | + | 0.273375i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.37055 | + | 2.37386i | 0.0582817 | + | 0.100947i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.74988 | + | 38.4559i | 0.286517 | + | 1.63236i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.8445 | 1.05269 | 0.526347 | − | 0.850270i | \(-0.323561\pi\) | ||||
0.526347 | + | 0.850270i | \(0.323561\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.25360 | −0.222204 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33.4286 | + | 28.0055i | −1.41136 | + | 1.18239i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.7945 | − | 34.2851i | −0.834240 | − | 1.44495i | −0.894648 | − | 0.446772i | \(-0.852574\pi\) |
0.0604081 | − | 0.998174i | \(-0.480760\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.9641 | + | 27.6506i | −0.671615 | + | 1.16327i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.44759 | − | 3.10456i | −0.354765 | − | 0.130379i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.6846 | − | 32.3626i | 0.783298 | − | 1.35671i | −0.146713 | − | 0.989179i | \(-0.546869\pi\) |
0.930011 | − | 0.367532i | \(-0.119797\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.24275 | − | 3.88456i | −0.0938563 | − | 0.162564i | 0.815274 | − | 0.579075i | \(-0.196586\pi\) |
−0.909131 | + | 0.416511i | \(0.863253\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31.0307 | + | 25.9966i | −1.29633 | + | 1.08603i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.3777 | 1.51705 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.6060 | 1.23251 | 0.616256 | − | 0.787546i | \(-0.288649\pi\) | ||||
0.616256 | + | 0.787546i | \(0.288649\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.27042 | + | 30.0270i | 0.219031 | + | 1.24788i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.35164 | − | 11.0014i | −0.263510 | − | 0.456413i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.0953 | + | 38.2703i | −0.915096 | + | 1.58499i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.16208 | − | 2.59414i | 0.296116 | − | 0.107254i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.99150 | − | 12.1096i | 0.288570 | − | 0.499818i | −0.684899 | − | 0.728638i | \(-0.740154\pi\) |
0.973469 | + | 0.228820i | \(0.0734869\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.42061 | + | 11.1208i | 0.264556 | + | 0.458225i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.5296 | − | 5.66602i | −0.638801 | − | 0.233069i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.1799 | 1.11614 | 0.558072 | − | 0.829793i | \(-0.311541\pi\) | ||||
0.558072 | + | 0.829793i | \(0.311541\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.8139 | 0.566315 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.1090 | + | 4.78288i | 0.536517 | + | 0.195750i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.4745 | + | 26.8026i | 0.632270 | + | 1.09512i | 0.987086 | + | 0.160188i | \(0.0512101\pi\) |
−0.354816 | + | 0.934936i | \(0.615457\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.69296 | + | 13.3246i | −0.313803 | + | 0.543522i | −0.979182 | − | 0.202983i | \(-0.934936\pi\) |
0.665380 | + | 0.746505i | \(0.268270\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.85869 | − | 16.0658i | 0.116415 | − | 0.654251i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 28.7190 | − | 49.7427i | 1.16759 | − | 2.02233i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.06075 | − | 12.2296i | −0.286587 | − | 0.496383i | 0.686406 | − | 0.727219i | \(-0.259187\pi\) |
−0.972993 | + | 0.230835i | \(0.925854\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.583570 | + | 3.32476i | 0.0236475 | + | 0.134726i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.0869 | 0.448527 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.9248 | −1.16826 | −0.584130 | − | 0.811660i | \(-0.698564\pi\) | ||||
−0.584130 | + | 0.811660i | \(0.698564\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −29.4988 | + | 24.7133i | −1.18951 | + | 0.996535i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.2196 | − | 21.1649i | −0.491941 | − | 0.852066i | 0.508016 | − | 0.861347i | \(-0.330379\pi\) |
−0.999957 | + | 0.00928127i | \(0.997046\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.6690 | − | 25.4074i | 0.589595 | − | 1.02121i | −0.404690 | − | 0.914454i | \(-0.632621\pi\) |
0.994285 | − | 0.106755i | \(-0.0340461\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23.3932 | + | 40.3000i | −0.938735 | + | 1.61718i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.37449 | − | 7.57684i | 0.175260 | − | 0.303559i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.4136 | + | 24.9651i | 0.576545 | + | 0.998605i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.6884 | − | 23.1965i | 1.10577 | − | 0.926381i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.3832 | 1.37095 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.9995 | 0.517501 | 0.258750 | − | 0.965944i | \(-0.416689\pi\) | ||||
0.258750 | + | 0.965944i | \(0.416689\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.43899 | + | 30.9874i | 0.216180 | + | 1.23164i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.3819 | + | 24.9101i | 0.570727 | + | 0.988528i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.421867 | + | 0.730695i | −0.0167150 | + | 0.0289512i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.3380 | − | 11.2274i | −0.527641 | − | 0.444148i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.02698 | + | 15.6352i | −0.356544 | + | 0.617553i | −0.987381 | − | 0.158363i | \(-0.949378\pi\) |
0.630837 | + | 0.775916i | \(0.282712\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.88663 | − | 3.26773i | −0.0744013 | − | 0.128867i | 0.826424 | − | 0.563048i | \(-0.190371\pi\) |
−0.900826 | + | 0.434181i | \(0.857038\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −30.4898 | − | 11.1243i | −1.20054 | − | 0.438020i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.383345 | 0.0150709 | 0.00753543 | − | 0.999972i | \(-0.497601\pi\) | ||||
0.00753543 | + | 0.999972i | \(0.497601\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −55.2937 | −2.17047 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.49557 | + | 2.00508i | 0.215389 | + | 0.0785854i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.0983475 | − | 0.170343i | −0.00384864 | − | 0.00666603i | 0.864095 | − | 0.503329i | \(-0.167892\pi\) |
−0.867943 | + | 0.496663i | \(0.834558\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.36241 | − | 4.09181i | 0.0923068 | − | 0.159880i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.5961 | − | 20.7040i | −0.959585 | − | 0.807742i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.919372 | + | 1.59240i | −0.0358137 | + | 0.0620311i | −0.883377 | − | 0.468664i | \(-0.844736\pi\) |
0.847563 | + | 0.530695i | \(0.178069\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.5492 | + | 23.4679i | 0.527004 | + | 0.912797i | 0.999505 | + | 0.0314671i | \(0.0100179\pi\) |
−0.472501 | + | 0.881330i | \(0.656649\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.15970 | − | 6.60713i | −0.0450391 | − | 0.256600i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.4419 | −0.443696 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.4771 | 0.676716 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.21556 | + | 7.72053i | −0.356294 | + | 0.298493i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.6009 | − | 27.0215i | −0.602264 | − | 1.04315i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.70611 | − | 8.15122i | 0.181407 | − | 0.314207i | −0.760953 | − | 0.648807i | \(-0.775268\pi\) |
0.942360 | + | 0.334601i | \(0.108601\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 21.0782 | + | 0.0493284i | 0.811301 | + | 0.00189865i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.05519 | − | 13.9520i | 0.309586 | − | 0.536219i | −0.668686 | − | 0.743545i | \(-0.733143\pi\) |
0.978272 | + | 0.207326i | \(0.0664762\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.83699 | + | 6.64586i | 0.147250 | + | 0.255045i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.3210 | + | 11.1600i | −0.510464 | + | 0.427652i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.35812 | 0.281551 | 0.140775 | − | 0.990042i | \(-0.455040\pi\) | ||||
0.140775 | + | 0.990042i | \(0.455040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.95175 | −0.265613 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.94230 | − | 11.0658i | −0.0741033 | − | 0.422186i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.39878 | − | 5.88686i | −0.129483 | − | 0.224271i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.60616 | + | 4.51400i | −0.0991430 | + | 0.171721i | −0.911330 | − | 0.411676i | \(-0.864943\pi\) |
0.812187 | + | 0.583397i | \(0.198277\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.88270 | − | 16.2008i | 0.109505 | − | 0.615417i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.4391 | + | 47.5260i | −1.04083 | + | 1.80276i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.9446 | + | 29.3489i | 0.641822 | + | 1.11167i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.2792 | − | 8.85837i | −0.918325 | − | 0.335054i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.50384 | −0.0567994 | −0.0283997 | − | 0.999597i | \(-0.509041\pi\) | ||||
−0.0283997 | + | 0.999597i | \(0.509041\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.4791 | −1.07411 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 64.3439 | + | 23.4761i | 2.42333 | + | 0.884162i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.74033 | − | 6.47845i | −0.140670 | − | 0.243647i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.8248 | − | 39.5338i | 0.857205 | − | 1.48472i | −0.0173798 | − | 0.999849i | \(-0.505532\pi\) |
0.874585 | − | 0.484873i | \(-0.161134\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.73175 | − | 2.80047i | 0.289963 | − | 0.105026i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.1440 | − | 26.2302i | 0.567148 | − | 0.982330i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.96369 | + | 12.0615i | 0.260427 | + | 0.451073i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.85297 | + | 16.2541i | 0.106546 | + | 0.607021i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.1940 | −0.678522 | −0.339261 | − | 0.940692i | \(-0.610177\pi\) | ||||
−0.339261 | + | 0.940692i | \(0.610177\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.10516 | −0.190126 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.6451 | − | 29.0247i | 1.28846 | − | 1.07944i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.95286 | − | 6.84656i | −0.146806 | − | 0.254275i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.38218 | − | 14.5184i | 0.310878 | − | 0.538456i | −0.667675 | − | 0.744453i | \(-0.732710\pi\) |
0.978553 | + | 0.205997i | \(0.0660436\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.6093 | + | 23.3192i | −0.504048 | + | 0.863676i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.2908 | + | 24.7524i | −0.528565 | + | 0.915501i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.73528 | + | 13.3979i | 0.285709 | + | 0.494862i | 0.972781 | − | 0.231727i | \(-0.0744376\pi\) |
−0.687072 | + | 0.726589i | \(0.741104\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.99557 | + | 3.34738i | −0.147379 | + | 0.123470i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.8355 | 1.09901 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.01244 | −0.257957 | −0.128978 | − | 0.991647i | \(-0.541170\pi\) | ||||
−0.128978 | + | 0.991647i | \(0.541170\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.960564 | + | 5.47259i | 0.0352872 | + | 0.201041i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.29512 | + | 16.0996i | 0.341005 | + | 0.590638i | 0.984620 | − | 0.174712i | \(-0.0558994\pi\) |
−0.643615 | + | 0.765350i | \(0.722566\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.94383 | + | 8.56297i | −0.181128 | + | 0.313723i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −35.8318 | + | 12.9784i | −1.31102 | + | 0.474857i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.741281 | − | 1.28394i | 0.0270858 | − | 0.0469140i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.1237 | + | 46.9797i | 0.989759 | + | 1.71431i | 0.618501 | + | 0.785784i | \(0.287740\pi\) |
0.371259 | + | 0.928529i | \(0.378926\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 42.4212 | + | 15.4775i | 1.54591 | + | 0.564033i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −36.8827 | −1.34230 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.7679 | −0.609439 | −0.304719 | − | 0.952442i | \(-0.598563\pi\) | ||||
−0.304719 | + | 0.952442i | \(0.598563\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −80.0364 | − | 29.2016i | −2.90514 | − | 1.05995i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.762796 | − | 1.32120i | −0.0276514 | − | 0.0478935i | 0.851869 | − | 0.523756i | \(-0.175469\pi\) |
−0.879520 | + | 0.475862i | \(0.842136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.439277 | + | 0.760850i | −0.0159029 | + | 0.0275446i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.25994 | − | 40.8008i | 0.262484 | − | 1.47516i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.25273 | − | 7.36595i | 0.153557 | − | 0.265969i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.9904 | + | 39.8205i | 0.829053 | + | 1.43596i | 0.898782 | + | 0.438397i | \(0.144453\pi\) |
−0.0697283 | + | 0.997566i | \(0.522213\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.45764 | − | 8.30459i | −0.0524958 | − | 0.299083i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.2008 | 0.582701 | 0.291351 | − | 0.956616i | \(-0.405895\pi\) | ||||
0.291351 | + | 0.956616i | \(0.405895\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.7007 | −0.492145 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.94510 | + | 8.33172i | −0.356779 | + | 0.298899i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.0350 | − | 24.3093i | −0.502855 | − | 0.870970i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.9381 | − | 27.6056i | 0.570311 | − | 0.987807i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.1267 | + | 0.0236991i | 0.361899 | + | 0.000846936i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.76710 | + | 8.25686i | −0.170145 | + | 0.294700i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.3187 | − | 17.8726i | −0.367823 | − | 0.637088i | 0.621402 | − | 0.783492i | \(-0.286563\pi\) |
−0.989225 | + | 0.146404i | \(0.953230\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 41.4521 | − | 34.7274i | 1.47574 | − | 1.23633i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.6095 | −0.377230 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.79955 | 0.170437 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.25994 | − | 41.3618i | −0.257484 | − | 1.46695i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.3590 | − | 42.1910i | −0.862839 | − | 1.49448i | −0.869177 | − | 0.494501i | \(-0.835351\pi\) |
0.00633764 | − | 0.999980i | \(-0.497983\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.1585 | − | 52.2360i | 1.06693 | − | 1.84798i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.0800 | − | 16.9025i | −0.709491 | − | 0.597222i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29.3909 | − | 50.9066i | 1.03718 | − | 1.79646i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.4937 | + | 23.3718i | 0.475591 | + | 0.823748i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.5063 | − | 6.75210i | −0.651453 | − | 0.237685i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.903622 | −0.0317696 | −0.0158848 | − | 0.999874i | \(-0.505057\pi\) | ||||
−0.0158848 | + | 0.999874i | \(0.505057\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.7487 | 0.798816 | 0.399408 | − | 0.916773i | \(-0.369216\pi\) | ||||
0.399408 | + | 0.916773i | \(0.369216\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.46492 | − | 1.62905i | −0.156592 | − | 0.0571331i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.1390 | − | 21.0254i | −0.425212 | − | 0.736488i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.8369 | − | 20.5021i | 0.414120 | − | 0.717277i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.93647 | + | 1.63005i | 0.0676658 | + | 0.0569585i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.0367 | + | 46.8290i | −0.943589 | + | 1.63434i | −0.185036 | + | 0.982732i | \(0.559240\pi\) |
−0.758553 | + | 0.651612i | \(0.774093\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.27471 | + | 16.0643i | 0.323296 | + | 0.559966i | 0.981166 | − | 0.193166i | \(-0.0618756\pi\) |
−0.657870 | + | 0.753132i | \(0.728542\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.66257 | + | 37.9584i | 0.231961 | + | 1.32154i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.1856 | −1.39739 | −0.698695 | − | 0.715419i | \(-0.746236\pi\) | ||||
−0.698695 | + | 0.715419i | \(0.746236\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.26946 | −0.0788217 | −0.0394108 | − | 0.999223i | \(-0.512548\pi\) | ||||
−0.0394108 | + | 0.999223i | \(0.512548\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.9443 | − | 35.9775i | 1.48972 | − | 1.24804i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.29512 | + | 3.97527i | 0.0795213 | + | 0.137735i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.490428 | + | 0.849446i | −0.0169720 | + | 0.0293963i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.81044 | − | 15.1780i | 0.304533 | − | 0.524628i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.96058 | − | 13.7881i | 0.274830 | − | 0.476019i | −0.695262 | − | 0.718756i | \(-0.744712\pi\) |
0.970092 | + | 0.242737i | \(0.0780452\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.6009 | + | 21.8254i | 0.434514 | + | 0.752600i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.93464 | + | 8.32296i | −0.342167 | + | 0.286658i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 36.9799 | 1.27215 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.0862 | 0.655808 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.01175 | − | 17.1587i | −0.103363 | − | 0.588886i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.5863 | + | 58.1731i | 1.15132 | + | 1.99415i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.87812 | − | 6.71711i | 0.132784 | − | 0.229989i | −0.791964 | − | 0.610567i | \(-0.790942\pi\) |
0.924749 | + | 0.380578i | \(0.124275\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.01330 | + | 33.7947i | −0.205651 | + | 1.15576i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.17118 | − | 5.49264i | 0.108325 | − | 0.187625i | −0.806767 | − | 0.590870i | \(-0.798785\pi\) |
0.915092 | + | 0.403245i | \(0.132118\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.6252 | + | 25.3315i | 0.499004 | + | 0.864300i | 0.999999 | − | 0.00114976i | \(-0.000365979\pi\) |
−0.500995 | + | 0.865450i | \(0.667033\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0129 | − | 4.38296i | −0.409399 | − | 0.149371i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −41.2373 | −1.40374 | −0.701868 | − | 0.712307i | \(-0.747650\pi\) | ||||
−0.701868 | + | 0.712307i | \(0.747650\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.4496 | −0.831311 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.62298 | − | 2.41642i | −0.224928 | − | 0.0820660i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.51758 | + | 13.0208i | 0.255016 | + | 0.441701i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.29470 | + | 3.97454i | −0.0777529 | + | 0.134672i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.6458 | − | 7.84021i | 0.732600 | − | 0.265351i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.41966 | + | 2.45892i | −0.0479932 | + | 0.0831267i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.7306 | + | 32.4424i | 0.632488 | + | 1.09550i | 0.987041 | + | 0.160466i | \(0.0512997\pi\) |
−0.354553 | + | 0.935036i | \(0.615367\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.60898 | − | 43.3504i | −0.256645 | − | 1.46217i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.2889 | −1.42475 | −0.712375 | − | 0.701799i | \(-0.752380\pi\) | ||||
−0.712375 | + | 0.701799i | \(0.752380\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.1718 | 1.72207 | 0.861034 | − | 0.508547i | \(-0.169817\pi\) | ||||
0.861034 | + | 0.508547i | \(0.169817\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 40.2784 | − | 33.7440i | 1.35394 | − | 1.13429i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.40377 | + | 7.62755i | 0.147864 | + | 0.256108i | 0.930438 | − | 0.366450i | \(-0.119427\pi\) |
−0.782574 | + | 0.622558i | \(0.786094\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.77897 | + | 8.27743i | −0.160282 | + | 0.277616i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −46.3357 | − | 17.0287i | −1.55231 | − | 0.570485i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24.9798 | + | 43.2664i | −0.835918 | + | 1.44785i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.4030 | + | 45.7314i | 0.882556 | + | 1.52863i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.0458 | − | 8.41610i | 0.335420 | − | 0.281005i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.58231 | −0.219532 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.9814 | −1.23203 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.86447 | − | 10.6224i | −0.0620458 | − | 0.353492i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.2682 | + | 38.5697i | 0.740221 | + | 1.28210i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.25169 | − | 14.2923i | 0.273993 | − | 0.474570i | −0.695888 | − | 0.718151i | \(-0.744989\pi\) |
0.969881 | + | 0.243581i | \(0.0783222\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −21.1005 | + | 7.64271i | −0.699861 | + | 0.253493i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.4836 | − | 19.8902i | 0.380469 | − | 0.658992i | −0.610660 | − | 0.791893i | \(-0.709096\pi\) |
0.991129 | + | 0.132901i | \(0.0424292\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34.8393 | − | 60.3434i | −1.15301 | − | 1.99708i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 27.8547 | + | 10.1629i | 0.920848 | + | 0.335975i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.57002 | 0.0518465 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.4537 | 0.773668 | 0.386834 | − | 0.922149i | \(-0.373569\pi\) | ||||
0.386834 | + | 0.922149i | \(0.373569\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.9886 | − | 5.83351i | −0.526843 | − | 0.192221i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.45165 | + | 4.24639i | 0.0806972 | + | 0.139772i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.1927 | − | 26.3145i | 0.499532 | − | 0.865215i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.68303 | + | 15.0786i | −0.0881224 | + | 0.495247i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.8182 | − | 32.5940i | 0.617404 | − | 1.06938i | −0.372553 | − | 0.928011i | \(-0.621518\pi\) |
0.989958 | − | 0.141365i | \(-0.0451491\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.90102 | − | 3.29266i | −0.0623033 | − | 0.107912i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.01535 | − | 5.78471i | −0.0332410 | − | 0.189383i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 75.7704 | 2.47796 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.5719 | 1.35809 | 0.679047 | − | 0.734094i | \(-0.262393\pi\) | ||||
0.679047 | + | 0.734094i | \(0.262393\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.8944 | + | 25.8825i | −1.00820 | + | 0.844643i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.5785 | − | 23.5187i | −0.442647 | − | 0.766686i | 0.555238 | − | 0.831691i | \(-0.312627\pi\) |
−0.997885 | + | 0.0650049i | \(0.979294\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.1037 | + | 57.3373i | −1.07800 | + | 1.86716i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.78695 | + | 13.5606i | 0.253309 | + | 0.441126i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.9444 | − | 27.6166i | 0.518124 | − | 0.897418i | −0.481654 | − | 0.876362i | \(-0.659964\pi\) |
0.999778 | − | 0.0210563i | \(-0.00670293\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.52101 | + | 7.83062i | 0.146758 | + | 0.254193i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 45.8078 | − | 38.3764i | 1.48542 | − | 1.24444i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.5094 | 1.73334 | 0.866670 | − | 0.498881i | \(-0.166256\pi\) | ||||
0.866670 | + | 0.498881i | \(0.166256\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 70.3354 | 2.27600 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.20093 | + | 18.2366i | 0.103471 | + | 0.589505i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.15500 | − | 2.00053i | −0.0372970 | − | 0.0646004i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.79638 | − | 16.9678i | 0.316012 | − | 0.547349i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.40266 | − | 2.86423i | −0.109649 | − | 0.0922985i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.4844 | − | 45.8724i | 0.852565 | − | 1.47669i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.46065 | − | 4.26197i | −0.0791292 | − | 0.137056i | 0.823745 | − | 0.566960i | \(-0.191881\pi\) |
−0.902874 | + | 0.429904i | \(0.858547\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 28.3971 | + | 10.3608i | 0.912248 | + | 0.332837i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.43251 | 0.0780629 | 0.0390315 | − | 0.999238i | \(-0.487573\pi\) | ||||
0.0390315 | + | 0.999238i | \(0.487573\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.2356 | −0.584606 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.56906 | − | 2.03189i | −0.178353 | − | 0.0650727i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.15608 | − | 5.46650i | −0.100972 | − | 0.174889i | 0.811113 | − | 0.584889i | \(-0.198862\pi\) |
−0.912085 | + | 0.410000i | \(0.865529\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.9944 | − | 41.5596i | 0.766865 | − | 1.32825i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.01639 | + | 1.69732i | 0.0643783 | + | 0.0541912i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.9727 | + | 22.4694i | −0.413766 | + | 0.716664i | −0.995298 | − | 0.0968597i | \(-0.969120\pi\) |
0.581532 | + | 0.813524i | \(0.302454\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.3611 | + | 24.8741i | 0.457582 | + | 0.792555i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.93468 | + | 22.4169i | 0.125242 | + | 0.713538i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −55.8384 | −1.77556 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.7413 | −1.29419 | −0.647094 | − | 0.762410i | \(-0.724016\pi\) | ||||
−0.647094 | + | 0.762410i | \(0.724016\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.2363 | − | 17.7911i | 0.673912 | − | 0.564584i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.1227 | − | 20.9971i | −0.384314 | − | 0.665652i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.92260 | + | 3.33004i | −0.0608894 | + | 0.105464i | −0.894863 | − | 0.446340i | \(-0.852727\pi\) |
0.833974 | + | 0.551804i | \(0.186060\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 19.3819 | + | 33.7527i | 0.613218 | + | 1.06789i |
(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 | 1008.2.r.n.673.1 | 10 | ||
3.2 | odd | 2 | 3024.2.r.n.2017.1 | 10 | |||
4.3 | odd | 2 | 504.2.r.f.169.5 | ✓ | 10 | ||
9.2 | odd | 6 | 9072.2.a.cm.1.5 | 5 | |||
9.4 | even | 3 | inner | 1008.2.r.n.337.1 | 10 | ||
9.5 | odd | 6 | 3024.2.r.n.1009.1 | 10 | |||
9.7 | even | 3 | 9072.2.a.cn.1.1 | 5 | |||
12.11 | even | 2 | 1512.2.r.f.505.1 | 10 | |||
36.7 | odd | 6 | 4536.2.a.bd.1.1 | 5 | |||
36.11 | even | 6 | 4536.2.a.bc.1.5 | 5 | |||
36.23 | even | 6 | 1512.2.r.f.1009.1 | 10 | |||
36.31 | odd | 6 | 504.2.r.f.337.5 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.f.169.5 | ✓ | 10 | 4.3 | odd | 2 | ||
504.2.r.f.337.5 | yes | 10 | 36.31 | odd | 6 | ||
1008.2.r.n.337.1 | 10 | 9.4 | even | 3 | inner | ||
1008.2.r.n.673.1 | 10 | 1.1 | even | 1 | trivial | ||
1512.2.r.f.505.1 | 10 | 12.11 | even | 2 | |||
1512.2.r.f.1009.1 | 10 | 36.23 | even | 6 | |||
3024.2.r.n.1009.1 | 10 | 9.5 | odd | 6 | |||
3024.2.r.n.2017.1 | 10 | 3.2 | odd | 2 | |||
4536.2.a.bc.1.5 | 5 | 36.11 | even | 6 | |||
4536.2.a.bd.1.1 | 5 | 36.7 | odd | 6 | |||
9072.2.a.cm.1.5 | 5 | 9.2 | odd | 6 | |||
9072.2.a.cn.1.1 | 5 | 9.7 | even | 3 |