Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1084,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1805.1084");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 22x^{14} + 190x^{12} + 820x^{10} + 1862x^{8} + 2154x^{6} + 1163x^{4} + 256x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1084.13 | ||
Root | \(1.85244i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1084 |
Dual form | 1805.2.b.i.1084.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).
\(n\) | \(362\) | \(1446\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.85244i | 1.30987i | 0.755685 | + | 0.654936i | \(0.227304\pi\) | ||||
−0.755685 | + | 0.654936i | \(0.772696\pi\) | |||||||
\(3\) | 1.45440i | 0.839696i | 0.907594 | + | 0.419848i | \(0.137917\pi\) | ||||
−0.907594 | + | 0.419848i | \(0.862083\pi\) | |||||||
\(4\) | −1.43152 | −0.715762 | ||||||||
\(5\) | −0.323421 | − | 2.21255i | −0.144638 | − | 0.989485i | ||||
\(6\) | −2.69418 | −1.09989 | ||||||||
\(7\) | − | 0.477604i | − | 0.180517i | −0.995918 | − | 0.0902586i | \(-0.971231\pi\) | ||
0.995918 | − | 0.0902586i | \(-0.0287694\pi\) | |||||||
\(8\) | 1.05306i | 0.372315i | ||||||||
\(9\) | 0.884731 | 0.294910 | ||||||||
\(10\) | 4.09862 | − | 0.599118i | 1.29610 | − | 0.189458i | ||||
\(11\) | 1.95728 | 0.590142 | 0.295071 | − | 0.955475i | \(-0.404657\pi\) | ||||
0.295071 | + | 0.955475i | \(0.404657\pi\) | |||||||
\(12\) | − | 2.08200i | − | 0.601023i | ||||||
\(13\) | − | 3.06043i | − | 0.848812i | −0.905472 | − | 0.424406i | \(-0.860483\pi\) | ||
0.905472 | − | 0.424406i | \(-0.139517\pi\) | |||||||
\(14\) | 0.884731 | 0.236454 | ||||||||
\(15\) | 3.21793 | − | 0.470383i | 0.830866 | − | 0.121452i | ||||
\(16\) | −4.81379 | −1.20345 | ||||||||
\(17\) | − | 0.973502i | − | 0.236109i | −0.993007 | − | 0.118054i | \(-0.962334\pi\) | ||
0.993007 | − | 0.118054i | \(-0.0376657\pi\) | |||||||
\(18\) | 1.63891i | 0.386295i | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0.462986 | + | 3.16733i | 0.103527 | + | 0.708236i | ||||
\(21\) | 0.694625 | 0.151580 | ||||||||
\(22\) | 3.62574i | 0.773010i | ||||||||
\(23\) | − | 5.59328i | − | 1.16628i | −0.812372 | − | 0.583140i | \(-0.801824\pi\) | ||
0.812372 | − | 0.583140i | \(-0.198176\pi\) | |||||||
\(24\) | −1.53157 | −0.312631 | ||||||||
\(25\) | −4.79080 | + | 1.43117i | −0.958159 | + | 0.286235i | ||||
\(26\) | 5.66926 | 1.11183 | ||||||||
\(27\) | 5.64994i | 1.08733i | ||||||||
\(28\) | 0.683702i | 0.129207i | ||||||||
\(29\) | 10.1756 | 1.88955 | 0.944777 | − | 0.327714i | \(-0.106278\pi\) | ||||
0.944777 | + | 0.327714i | \(0.106278\pi\) | |||||||
\(30\) | 0.871355 | + | 5.96102i | 0.159087 | + | 1.08833i | ||||
\(31\) | 5.60367 | 1.00645 | 0.503225 | − | 0.864156i | \(-0.332147\pi\) | ||||
0.503225 | + | 0.864156i | \(0.332147\pi\) | |||||||
\(32\) | − | 6.81111i | − | 1.20405i | ||||||
\(33\) | 2.84666i | 0.495540i | ||||||||
\(34\) | 1.80335 | 0.309272 | ||||||||
\(35\) | −1.05672 | + | 0.154467i | −0.178619 | + | 0.0261097i | ||||
\(36\) | −1.26651 | −0.211086 | ||||||||
\(37\) | − | 5.65754i | − | 0.930094i | −0.885286 | − | 0.465047i | \(-0.846037\pi\) | ||
0.885286 | − | 0.465047i | \(-0.153963\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.45108 | 0.712744 | ||||||||
\(40\) | 2.32996 | − | 0.340584i | 0.368400 | − | 0.0538510i | ||||
\(41\) | 10.4679 | 1.63481 | 0.817404 | − | 0.576065i | \(-0.195413\pi\) | ||||
0.817404 | + | 0.576065i | \(0.195413\pi\) | |||||||
\(42\) | 1.28675i | 0.198550i | ||||||||
\(43\) | 6.20983i | 0.946990i | 0.880796 | + | 0.473495i | \(0.157008\pi\) | ||||
−0.880796 | + | 0.473495i | \(0.842992\pi\) | |||||||
\(44\) | −2.80189 | −0.422401 | ||||||||
\(45\) | −0.286141 | − | 1.95752i | −0.0426554 | − | 0.291809i | ||||
\(46\) | 10.3612 | 1.52768 | ||||||||
\(47\) | − | 2.47845i | − | 0.361519i | −0.983527 | − | 0.180759i | \(-0.942144\pi\) | ||
0.983527 | − | 0.180759i | \(-0.0578555\pi\) | |||||||
\(48\) | − | 7.00115i | − | 1.01053i | ||||||
\(49\) | 6.77189 | 0.967414 | ||||||||
\(50\) | −2.65116 | − | 8.87465i | −0.374931 | − | 1.25507i | ||||
\(51\) | 1.41586 | 0.198260 | ||||||||
\(52\) | 4.38109i | 0.607547i | ||||||||
\(53\) | 10.7711i | 1.47953i | 0.672866 | + | 0.739764i | \(0.265063\pi\) | ||||
−0.672866 | + | 0.739764i | \(0.734937\pi\) | |||||||
\(54\) | −10.4662 | −1.42426 | ||||||||
\(55\) | −0.633026 | − | 4.33059i | −0.0853572 | − | 0.583936i | ||||
\(56\) | 0.502948 | 0.0672092 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 18.8496i | 2.47507i | ||||||||
\(59\) | −7.32031 | −0.953024 | −0.476512 | − | 0.879168i | \(-0.658099\pi\) | ||||
−0.476512 | + | 0.879168i | \(0.658099\pi\) | |||||||
\(60\) | −4.60655 | + | 0.673365i | −0.594703 | + | 0.0869310i | ||||
\(61\) | 8.76766 | 1.12258 | 0.561292 | − | 0.827618i | \(-0.310305\pi\) | ||||
0.561292 | + | 0.827618i | \(0.310305\pi\) | |||||||
\(62\) | 10.3805i | 1.31832i | ||||||||
\(63\) | − | 0.422551i | − | 0.0532364i | ||||||
\(64\) | 2.98958 | 0.373698 | ||||||||
\(65\) | −6.77138 | + | 0.989809i | −0.839886 | + | 0.122771i | ||||
\(66\) | −5.27326 | −0.649093 | ||||||||
\(67\) | 8.82042i | 1.07759i | 0.842438 | + | 0.538793i | \(0.181120\pi\) | ||||
−0.842438 | + | 0.538793i | \(0.818880\pi\) | |||||||
\(68\) | 1.39359i | 0.168998i | ||||||||
\(69\) | 8.13485 | 0.979321 | ||||||||
\(70\) | −0.286141 | − | 1.95752i | −0.0342004 | − | 0.233968i | ||||
\(71\) | −13.1846 | −1.56472 | −0.782362 | − | 0.622825i | \(-0.785985\pi\) | ||||
−0.782362 | + | 0.622825i | \(0.785985\pi\) | |||||||
\(72\) | 0.931679i | 0.109799i | ||||||||
\(73\) | 4.97121i | 0.581836i | 0.956748 | + | 0.290918i | \(0.0939606\pi\) | ||||
−0.956748 | + | 0.290918i | \(0.906039\pi\) | |||||||
\(74\) | 10.4802 | 1.21830 | ||||||||
\(75\) | −2.08150 | − | 6.96772i | −0.240350 | − | 0.804563i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.934804i | − | 0.106531i | ||||||
\(78\) | 8.24535i | 0.933603i | ||||||||
\(79\) | 0.707984 | 0.0796544 | 0.0398272 | − | 0.999207i | \(-0.487319\pi\) | ||||
0.0398272 | + | 0.999207i | \(0.487319\pi\) | |||||||
\(80\) | 1.55688 | + | 10.6508i | 0.174065 | + | 1.19079i | ||||
\(81\) | −5.56306 | −0.618118 | ||||||||
\(82\) | 19.3911i | 2.14139i | ||||||||
\(83\) | − | 11.8783i | − | 1.30382i | −0.758297 | − | 0.651909i | \(-0.773968\pi\) | ||
0.758297 | − | 0.651909i | \(-0.226032\pi\) | |||||||
\(84\) | −0.994373 | −0.108495 | ||||||||
\(85\) | −2.15393 | + | 0.314851i | −0.233626 | + | 0.0341504i | ||||
\(86\) | −11.5033 | −1.24043 | ||||||||
\(87\) | 14.7993i | 1.58665i | ||||||||
\(88\) | 2.06114i | 0.219718i | ||||||||
\(89\) | −2.14855 | −0.227746 | −0.113873 | − | 0.993495i | \(-0.536326\pi\) | ||||
−0.113873 | + | 0.993495i | \(0.536326\pi\) | |||||||
\(90\) | 3.62618 | − | 0.530058i | 0.382232 | − | 0.0558730i | ||||
\(91\) | −1.46167 | −0.153225 | ||||||||
\(92\) | 8.00692i | 0.834779i | ||||||||
\(93\) | 8.14996i | 0.845112i | ||||||||
\(94\) | 4.59117 | 0.473543 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.90605 | 1.01103 | ||||||||
\(97\) | 5.89541i | 0.598588i | 0.954161 | + | 0.299294i | \(0.0967512\pi\) | ||||
−0.954161 | + | 0.299294i | \(0.903249\pi\) | |||||||
\(98\) | 12.5445i | 1.26719i | ||||||||
\(99\) | 1.73167 | 0.174039 | ||||||||
\(100\) | 6.85815 | − | 2.04876i | 0.685815 | − | 0.204876i | ||||
\(101\) | 0.258211 | 0.0256930 | 0.0128465 | − | 0.999917i | \(-0.495911\pi\) | ||||
0.0128465 | + | 0.999917i | \(0.495911\pi\) | |||||||
\(102\) | 2.62279i | 0.259695i | ||||||||
\(103\) | − | 14.3714i | − | 1.41605i | −0.706186 | − | 0.708026i | \(-0.749586\pi\) | ||
0.706186 | − | 0.708026i | \(-0.250414\pi\) | |||||||
\(104\) | 3.22283 | 0.316025 | ||||||||
\(105\) | −0.224657 | − | 1.53690i | −0.0219242 | − | 0.149986i | ||||
\(106\) | −19.9529 | −1.93799 | ||||||||
\(107\) | − | 5.73115i | − | 0.554051i | −0.960863 | − | 0.277026i | \(-0.910651\pi\) | ||
0.960863 | − | 0.277026i | \(-0.0893487\pi\) | |||||||
\(108\) | − | 8.08803i | − | 0.778271i | ||||||
\(109\) | 5.77812 | 0.553444 | 0.276722 | − | 0.960950i | \(-0.410752\pi\) | ||||
0.276722 | + | 0.960950i | \(0.410752\pi\) | |||||||
\(110\) | 8.02214 | − | 1.17264i | 0.764881 | − | 0.111807i | ||||
\(111\) | 8.22830 | 0.780996 | ||||||||
\(112\) | 2.29908i | 0.217243i | ||||||||
\(113\) | 13.9762i | 1.31477i | 0.753554 | + | 0.657386i | \(0.228338\pi\) | ||||
−0.753554 | + | 0.657386i | \(0.771662\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.3754 | + | 1.80899i | −1.15402 | + | 0.168689i | ||||
\(116\) | −14.5666 | −1.35247 | ||||||||
\(117\) | − | 2.70766i | − | 0.250323i | ||||||
\(118\) | − | 13.5604i | − | 1.24834i | ||||||
\(119\) | −0.464948 | −0.0426217 | ||||||||
\(120\) | 0.495344 | + | 3.38869i | 0.0452185 | + | 0.309344i | ||||
\(121\) | −7.16906 | −0.651733 | ||||||||
\(122\) | 16.2415i | 1.47044i | ||||||||
\(123\) | 15.2244i | 1.37274i | ||||||||
\(124\) | −8.02180 | −0.720379 | ||||||||
\(125\) | 4.71600 | + | 10.1370i | 0.421812 | + | 0.906683i | ||||
\(126\) | 0.782749 | 0.0697328 | ||||||||
\(127\) | − | 9.23319i | − | 0.819313i | −0.912240 | − | 0.409657i | \(-0.865649\pi\) | ||
0.912240 | − | 0.409657i | \(-0.134351\pi\) | |||||||
\(128\) | − | 8.08421i | − | 0.714550i | ||||||
\(129\) | −9.03155 | −0.795184 | ||||||||
\(130\) | −1.83356 | − | 12.5436i | −0.160814 | − | 1.10014i | ||||
\(131\) | −13.9316 | −1.21721 | −0.608603 | − | 0.793475i | \(-0.708270\pi\) | ||||
−0.608603 | + | 0.793475i | \(0.708270\pi\) | |||||||
\(132\) | − | 4.07506i | − | 0.354689i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −16.3393 | −1.41150 | ||||||||
\(135\) | 12.5008 | − | 1.82731i | 1.07590 | − | 0.157270i | ||||
\(136\) | 1.02516 | 0.0879068 | ||||||||
\(137\) | − | 3.84336i | − | 0.328360i | −0.986430 | − | 0.164180i | \(-0.947502\pi\) | ||
0.986430 | − | 0.164180i | \(-0.0524978\pi\) | |||||||
\(138\) | 15.0693i | 1.28278i | ||||||||
\(139\) | 18.8730 | 1.60079 | 0.800395 | − | 0.599473i | \(-0.204623\pi\) | ||||
0.800395 | + | 0.599473i | \(0.204623\pi\) | |||||||
\(140\) | 1.51273 | − | 0.221124i | 0.127849 | − | 0.0186884i | ||||
\(141\) | 3.60464 | 0.303566 | ||||||||
\(142\) | − | 24.4236i | − | 2.04959i | ||||||
\(143\) | − | 5.99012i | − | 0.500919i | ||||||
\(144\) | −4.25891 | −0.354909 | ||||||||
\(145\) | −3.29099 | − | 22.5140i | −0.273302 | − | 1.86968i | ||||
\(146\) | −9.20885 | −0.762130 | ||||||||
\(147\) | 9.84902i | 0.812333i | ||||||||
\(148\) | 8.09891i | 0.665726i | ||||||||
\(149\) | 23.9268 | 1.96016 | 0.980082 | − | 0.198594i | \(-0.0636375\pi\) | ||||
0.980082 | + | 0.198594i | \(0.0636375\pi\) | |||||||
\(150\) | 12.9073 | − | 3.85584i | 1.05387 | − | 0.314828i | ||||
\(151\) | −5.90301 | −0.480380 | −0.240190 | − | 0.970726i | \(-0.577210\pi\) | ||||
−0.240190 | + | 0.970726i | \(0.577210\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.861288i | − | 0.0696310i | ||||||
\(154\) | 1.73167 | 0.139542 | ||||||||
\(155\) | −1.81235 | − | 12.3984i | −0.145571 | − | 0.995866i | ||||
\(156\) | −6.37184 | −0.510155 | ||||||||
\(157\) | − | 10.5707i | − | 0.843631i | −0.906682 | − | 0.421815i | \(-0.861393\pi\) | ||
0.906682 | − | 0.421815i | \(-0.138607\pi\) | |||||||
\(158\) | 1.31150i | 0.104337i | ||||||||
\(159\) | −15.6655 | −1.24235 | ||||||||
\(160\) | −15.0700 | + | 2.20286i | −1.19138 | + | 0.174151i | ||||
\(161\) | −2.67137 | −0.210534 | ||||||||
\(162\) | − | 10.3052i | − | 0.809654i | ||||||
\(163\) | − | 18.6090i | − | 1.45757i | −0.684743 | − | 0.728785i | \(-0.740085\pi\) | ||
0.684743 | − | 0.728785i | \(-0.259915\pi\) | |||||||
\(164\) | −14.9850 | −1.17013 | ||||||||
\(165\) | 6.29839 | − | 0.920670i | 0.490329 | − | 0.0716741i | ||||
\(166\) | 22.0039 | 1.70783 | ||||||||
\(167\) | 2.77731i | 0.214914i | 0.994210 | + | 0.107457i | \(0.0342708\pi\) | ||||
−0.994210 | + | 0.107457i | \(0.965729\pi\) | |||||||
\(168\) | 0.731485i | 0.0564353i | ||||||||
\(169\) | 3.63375 | 0.279519 | ||||||||
\(170\) | −0.583242 | − | 3.99001i | −0.0447327 | − | 0.306020i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 8.88952i | − | 0.677820i | ||||||
\(173\) | 8.92075i | 0.678232i | 0.940745 | + | 0.339116i | \(0.110128\pi\) | ||||
−0.940745 | + | 0.339116i | \(0.889872\pi\) | |||||||
\(174\) | −27.4148 | −2.07831 | ||||||||
\(175\) | 0.683534 | + | 2.28810i | 0.0516703 | + | 0.172964i | ||||
\(176\) | −9.42192 | −0.710204 | ||||||||
\(177\) | − | 10.6466i | − | 0.800250i | ||||||
\(178\) | − | 3.98006i | − | 0.298318i | ||||||
\(179\) | −15.2646 | −1.14093 | −0.570467 | − | 0.821321i | \(-0.693238\pi\) | ||||
−0.570467 | + | 0.821321i | \(0.693238\pi\) | |||||||
\(180\) | 0.409618 | + | 2.80223i | 0.0305311 | + | 0.208866i | ||||
\(181\) | −8.54101 | −0.634848 | −0.317424 | − | 0.948284i | \(-0.602818\pi\) | ||||
−0.317424 | + | 0.948284i | \(0.602818\pi\) | |||||||
\(182\) | − | 2.70766i | − | 0.200705i | ||||||
\(183\) | 12.7516i | 0.942629i | ||||||||
\(184\) | 5.89009 | 0.434223 | ||||||||
\(185\) | −12.5176 | + | 1.82977i | −0.920313 | + | 0.134527i | ||||
\(186\) | −15.0973 | −1.10699 | ||||||||
\(187\) | − | 1.90542i | − | 0.139338i | ||||||
\(188\) | 3.54796i | 0.258761i | ||||||||
\(189\) | 2.69843 | 0.196282 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.2967 | −1.17919 | −0.589594 | − | 0.807700i | \(-0.700712\pi\) | ||||
−0.589594 | + | 0.807700i | \(0.700712\pi\) | |||||||
\(192\) | 4.34804i | 0.313792i | ||||||||
\(193\) | 16.4692i | 1.18548i | 0.805394 | + | 0.592739i | \(0.201954\pi\) | ||||
−0.805394 | + | 0.592739i | \(0.798046\pi\) | |||||||
\(194\) | −10.9209 | −0.784074 | ||||||||
\(195\) | −1.43958 | − | 9.84827i | −0.103090 | − | 0.705249i | ||||
\(196\) | −9.69414 | −0.692438 | ||||||||
\(197\) | 10.0229i | 0.714102i | 0.934085 | + | 0.357051i | \(0.116218\pi\) | ||||
−0.934085 | + | 0.357051i | \(0.883782\pi\) | |||||||
\(198\) | 3.20780i | 0.227969i | ||||||||
\(199\) | 12.6643 | 0.897748 | 0.448874 | − | 0.893595i | \(-0.351825\pi\) | ||||
0.448874 | + | 0.893595i | \(0.351825\pi\) | |||||||
\(200\) | −1.50712 | − | 5.04502i | −0.106569 | − | 0.356737i | ||||
\(201\) | −12.8284 | −0.904845 | ||||||||
\(202\) | 0.478321i | 0.0336545i | ||||||||
\(203\) | − | 4.85988i | − | 0.341097i | ||||||
\(204\) | −2.02684 | −0.141907 | ||||||||
\(205\) | −3.38553 | − | 23.1607i | −0.236456 | − | 1.61762i | ||||
\(206\) | 26.6221 | 1.85485 | ||||||||
\(207\) | − | 4.94855i | − | 0.343948i | ||||||
\(208\) | 14.7323i | 1.02150i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.84700 | − | 0.416162i | 0.196462 | − | 0.0287179i | ||||
\(211\) | 5.73609 | 0.394888 | 0.197444 | − | 0.980314i | \(-0.436736\pi\) | ||||
0.197444 | + | 0.980314i | \(0.436736\pi\) | |||||||
\(212\) | − | 15.4191i | − | 1.05899i | ||||||
\(213\) | − | 19.1756i | − | 1.31389i | ||||||
\(214\) | 10.6166 | 0.725736 | ||||||||
\(215\) | 13.7396 | − | 2.00839i | 0.937032 | − | 0.136971i | ||||
\(216\) | −5.94975 | −0.404829 | ||||||||
\(217\) | − | 2.67634i | − | 0.181682i | ||||||
\(218\) | 10.7036i | 0.724940i | ||||||||
\(219\) | −7.23010 | −0.488565 | ||||||||
\(220\) | 0.906192 | + | 6.19934i | 0.0610955 | + | 0.417960i | ||||
\(221\) | −2.97934 | −0.200412 | ||||||||
\(222\) | 15.2424i | 1.02300i | ||||||||
\(223\) | 12.8478i | 0.860353i | 0.902745 | + | 0.430176i | \(0.141549\pi\) | ||||
−0.902745 | + | 0.430176i | \(0.858451\pi\) | |||||||
\(224\) | −3.25301 | −0.217351 | ||||||||
\(225\) | −4.23857 | + | 1.26620i | −0.282571 | + | 0.0844136i | ||||
\(226\) | −25.8901 | −1.72218 | ||||||||
\(227\) | − | 15.5808i | − | 1.03413i | −0.855945 | − | 0.517067i | \(-0.827024\pi\) | ||
0.855945 | − | 0.517067i | \(-0.172976\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.77930 | 0.249743 | 0.124871 | − | 0.992173i | \(-0.460148\pi\) | ||||
0.124871 | + | 0.992173i | \(0.460148\pi\) | |||||||
\(230\) | −3.35103 | − | 22.9247i | −0.220961 | − | 1.51161i | ||||
\(231\) | 1.35958 | 0.0894535 | ||||||||
\(232\) | 10.7155i | 0.703508i | ||||||||
\(233\) | − | 11.0745i | − | 0.725512i | −0.931884 | − | 0.362756i | \(-0.881836\pi\) | ||
0.931884 | − | 0.362756i | \(-0.118164\pi\) | |||||||
\(234\) | 5.01577 | 0.327891 | ||||||||
\(235\) | −5.48370 | + | 0.801583i | −0.357717 | + | 0.0522895i | ||||
\(236\) | 10.4792 | 0.682139 | ||||||||
\(237\) | 1.02969i | 0.0668855i | ||||||||
\(238\) | − | 0.861288i | − | 0.0558290i | ||||||
\(239\) | 10.6496 | 0.688865 | 0.344433 | − | 0.938811i | \(-0.388071\pi\) | ||||
0.344433 | + | 0.938811i | \(0.388071\pi\) | |||||||
\(240\) | −15.4904 | + | 2.26432i | −0.999903 | + | 0.146161i | ||||
\(241\) | 5.01271 | 0.322897 | 0.161448 | − | 0.986881i | \(-0.448383\pi\) | ||||
0.161448 | + | 0.986881i | \(0.448383\pi\) | |||||||
\(242\) | − | 13.2802i | − | 0.853686i | ||||||
\(243\) | 8.85892i | 0.568300i | ||||||||
\(244\) | −12.5511 | −0.803503 | ||||||||
\(245\) | −2.19018 | − | 14.9832i | −0.139925 | − | 0.957241i | ||||
\(246\) | −28.2023 | −1.79811 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5.90103i | 0.374716i | ||||||||
\(249\) | 17.2758 | 1.09481 | ||||||||
\(250\) | −18.7782 | + | 8.73609i | −1.18764 | + | 0.552519i | ||||
\(251\) | −26.1721 | −1.65197 | −0.825986 | − | 0.563691i | \(-0.809381\pi\) | ||||
−0.825986 | + | 0.563691i | \(0.809381\pi\) | |||||||
\(252\) | 0.604892i | 0.0381046i | ||||||||
\(253\) | − | 10.9476i | − | 0.688271i | ||||||
\(254\) | 17.1039 | 1.07319 | ||||||||
\(255\) | −0.457919 | − | 3.13266i | −0.0286760 | − | 0.196175i | ||||
\(256\) | 20.9546 | 1.30967 | ||||||||
\(257\) | 22.4024i | 1.39742i | 0.715403 | + | 0.698712i | \(0.246243\pi\) | ||||
−0.715403 | + | 0.698712i | \(0.753757\pi\) | |||||||
\(258\) | − | 16.7304i | − | 1.04159i | ||||||
\(259\) | −2.70206 | −0.167898 | ||||||||
\(260\) | 9.69339 | − | 1.41694i | 0.601159 | − | 0.0878747i | ||||
\(261\) | 9.00263 | 0.557249 | ||||||||
\(262\) | − | 25.8074i | − | 1.59438i | ||||||
\(263\) | 25.9338i | 1.59915i | 0.600569 | + | 0.799573i | \(0.294941\pi\) | ||||
−0.600569 | + | 0.799573i | \(0.705059\pi\) | |||||||
\(264\) | −2.99772 | −0.184497 | ||||||||
\(265\) | 23.8317 | − | 3.48361i | 1.46397 | − | 0.213997i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3.12485i | − | 0.191238i | ||||||
\(268\) | − | 12.6267i | − | 0.771296i | ||||||
\(269\) | 9.24978 | 0.563969 | 0.281985 | − | 0.959419i | \(-0.409007\pi\) | ||||
0.281985 | + | 0.959419i | \(0.409007\pi\) | |||||||
\(270\) | 3.38498 | + | 23.1569i | 0.206003 | + | 1.40929i | ||||
\(271\) | −22.4688 | −1.36488 | −0.682441 | − | 0.730941i | \(-0.739082\pi\) | ||||
−0.682441 | + | 0.730941i | \(0.739082\pi\) | |||||||
\(272\) | 4.68623i | 0.284145i | ||||||||
\(273\) | − | 2.12585i | − | 0.128663i | ||||||
\(274\) | 7.11958 | 0.430110 | ||||||||
\(275\) | −9.37693 | + | 2.80121i | −0.565450 | + | 0.168919i | ||||
\(276\) | −11.6452 | −0.700961 | ||||||||
\(277\) | − | 9.16598i | − | 0.550730i | −0.961340 | − | 0.275365i | \(-0.911201\pi\) | ||
0.961340 | − | 0.275365i | \(-0.0887987\pi\) | |||||||
\(278\) | 34.9611i | 2.09683i | ||||||||
\(279\) | 4.95774 | 0.296812 | ||||||||
\(280\) | −0.162664 | − | 1.11280i | −0.00972103 | − | 0.0665025i | ||||
\(281\) | −19.3577 | −1.15479 | −0.577393 | − | 0.816467i | \(-0.695930\pi\) | ||||
−0.577393 | + | 0.816467i | \(0.695930\pi\) | |||||||
\(282\) | 6.67738i | 0.397632i | ||||||||
\(283\) | 8.72514i | 0.518656i | 0.965789 | + | 0.259328i | \(0.0835010\pi\) | ||||
−0.965789 | + | 0.259328i | \(0.916499\pi\) | |||||||
\(284\) | 18.8741 | 1.11997 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.0963 | 0.656140 | ||||||||
\(287\) | − | 4.99950i | − | 0.295111i | ||||||
\(288\) | − | 6.02600i | − | 0.355085i | ||||||
\(289\) | 16.0523 | 0.944253 | ||||||||
\(290\) | 41.7057 | − | 6.09636i | 2.44905 | − | 0.357990i | ||||
\(291\) | −8.57427 | −0.502632 | ||||||||
\(292\) | − | 7.11641i | − | 0.416456i | ||||||
\(293\) | − | 16.7749i | − | 0.980002i | −0.871722 | − | 0.490001i | \(-0.836996\pi\) | ||
0.871722 | − | 0.490001i | \(-0.163004\pi\) | |||||||
\(294\) | −18.2447 | −1.06405 | ||||||||
\(295\) | 2.36755 | + | 16.1966i | 0.137844 | + | 0.943002i | ||||
\(296\) | 5.95776 | 0.346287 | ||||||||
\(297\) | 11.0585i | 0.641680i | ||||||||
\(298\) | 44.3230i | 2.56756i | ||||||||
\(299\) | −17.1179 | −0.989952 | ||||||||
\(300\) | 2.97971 | + | 9.97446i | 0.172034 | + | 0.575876i | ||||
\(301\) | 2.96584 | 0.170948 | ||||||||
\(302\) | − | 10.9350i | − | 0.629236i | ||||||
\(303\) | 0.375542i | 0.0215743i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.83565 | − | 19.3989i | −0.162369 | − | 1.11078i | ||||
\(306\) | 1.59548 | 0.0912076 | ||||||||
\(307\) | 6.40893i | 0.365777i | 0.983134 | + | 0.182889i | \(0.0585448\pi\) | ||||
−0.983134 | + | 0.182889i | \(0.941455\pi\) | |||||||
\(308\) | 1.33819i | 0.0762507i | ||||||||
\(309\) | 20.9017 | 1.18905 | ||||||||
\(310\) | 22.9673 | − | 3.35726i | 1.30446 | − | 0.190680i | ||||
\(311\) | 10.6248 | 0.602477 | 0.301238 | − | 0.953549i | \(-0.402600\pi\) | ||||
0.301238 | + | 0.953549i | \(0.402600\pi\) | |||||||
\(312\) | 4.68728i | 0.265365i | ||||||||
\(313\) | − | 4.75656i | − | 0.268857i | −0.990923 | − | 0.134428i | \(-0.957080\pi\) | ||
0.990923 | − | 0.134428i | \(-0.0429198\pi\) | |||||||
\(314\) | 19.5815 | 1.10505 | ||||||||
\(315\) | −0.934917 | + | 0.136662i | −0.0526766 | + | 0.00770003i | ||||
\(316\) | −1.01350 | −0.0570136 | ||||||||
\(317\) | 0.0612218i | 0.00343856i | 0.999999 | + | 0.00171928i | \(0.000547264\pi\) | ||||
−0.999999 | + | 0.00171928i | \(0.999453\pi\) | |||||||
\(318\) | − | 29.0194i | − | 1.62732i | ||||||
\(319\) | 19.9164 | 1.11510 | ||||||||
\(320\) | −0.966894 | − | 6.61461i | −0.0540510 | − | 0.369768i | ||||
\(321\) | 8.33536 | 0.465235 | ||||||||
\(322\) | − | 4.94855i | − | 0.275772i | ||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 7.96366 | 0.442425 | ||||||||
\(325\) | 4.38002 | + | 14.6619i | 0.242960 | + | 0.813297i | ||||
\(326\) | 34.4720 | 1.90923 | ||||||||
\(327\) | 8.40368i | 0.464724i | ||||||||
\(328\) | 11.0234i | 0.608663i | ||||||||
\(329\) | −1.18372 | −0.0652603 | ||||||||
\(330\) | 1.70548 | + | 11.6674i | 0.0938838 | + | 0.642268i | ||||
\(331\) | 17.6067 | 0.967752 | 0.483876 | − | 0.875137i | \(-0.339229\pi\) | ||||
0.483876 | + | 0.875137i | \(0.339229\pi\) | |||||||
\(332\) | 17.0041i | 0.933224i | ||||||||
\(333\) | − | 5.00540i | − | 0.274294i | ||||||
\(334\) | −5.14478 | −0.281510 | ||||||||
\(335\) | 19.5157 | − | 2.85271i | 1.06625 | − | 0.155860i | ||||
\(336\) | −3.34378 | −0.182418 | ||||||||
\(337\) | 6.90874i | 0.376343i | 0.982136 | + | 0.188171i | \(0.0602560\pi\) | ||||
−0.982136 | + | 0.188171i | \(0.939744\pi\) | |||||||
\(338\) | 6.73129i | 0.366134i | ||||||||
\(339\) | −20.3270 | −1.10401 | ||||||||
\(340\) | 3.08340 | − | 0.450718i | 0.167221 | − | 0.0244436i | ||||
\(341\) | 10.9680 | 0.593948 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6.57751i | − | 0.355152i | ||||||
\(344\) | −6.53935 | −0.352578 | ||||||||
\(345\) | −2.63098 | − | 17.9988i | −0.141647 | − | 0.969023i | ||||
\(346\) | −16.5251 | −0.888396 | ||||||||
\(347\) | − | 7.32576i | − | 0.393267i | −0.980477 | − | 0.196634i | \(-0.936999\pi\) | ||
0.980477 | − | 0.196634i | \(-0.0630010\pi\) | |||||||
\(348\) | − | 21.1856i | − | 1.13567i | ||||||
\(349\) | 2.16127 | 0.115690 | 0.0578452 | − | 0.998326i | \(-0.481577\pi\) | ||||
0.0578452 | + | 0.998326i | \(0.481577\pi\) | |||||||
\(350\) | −4.23857 | + | 1.26620i | −0.226561 | + | 0.0676815i | ||||
\(351\) | 17.2913 | 0.922939 | ||||||||
\(352\) | − | 13.3312i | − | 0.710557i | ||||||
\(353\) | − | 16.6022i | − | 0.883644i | −0.897103 | − | 0.441822i | \(-0.854332\pi\) | ||
0.897103 | − | 0.441822i | \(-0.145668\pi\) | |||||||
\(354\) | 19.7222 | 1.04822 | ||||||||
\(355\) | 4.26418 | + | 29.1716i | 0.226319 | + | 1.54827i | ||||
\(356\) | 3.07571 | 0.163012 | ||||||||
\(357\) | − | 0.676219i | − | 0.0357893i | ||||||
\(358\) | − | 28.2768i | − | 1.49448i | ||||||
\(359\) | −17.0830 | −0.901608 | −0.450804 | − | 0.892623i | \(-0.648863\pi\) | ||||
−0.450804 | + | 0.892623i | \(0.648863\pi\) | |||||||
\(360\) | 2.06139 | − | 0.301325i | 0.108645 | − | 0.0158812i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | − | 15.8217i | − | 0.831569i | ||||||
\(363\) | − | 10.4267i | − | 0.547257i | ||||||
\(364\) | 2.09242 | 0.109673 | ||||||||
\(365\) | 10.9991 | − | 1.60779i | 0.575717 | − | 0.0841558i | ||||
\(366\) | −23.6216 | −1.23472 | ||||||||
\(367\) | − | 19.5631i | − | 1.02119i | −0.859822 | − | 0.510594i | \(-0.829426\pi\) | ||
0.859822 | − | 0.510594i | \(-0.170574\pi\) | |||||||
\(368\) | 26.9249i | 1.40356i | ||||||||
\(369\) | 9.26125 | 0.482122 | ||||||||
\(370\) | −3.38953 | − | 23.1881i | −0.176213 | − | 1.20549i | ||||
\(371\) | 5.14433 | 0.267080 | ||||||||
\(372\) | − | 11.6669i | − | 0.604899i | ||||||
\(373\) | − | 6.59700i | − | 0.341580i | −0.985307 | − | 0.170790i | \(-0.945368\pi\) | ||
0.985307 | − | 0.170790i | \(-0.0546320\pi\) | |||||||
\(374\) | 3.52966 | 0.182515 | ||||||||
\(375\) | −14.7433 | + | 6.85893i | −0.761339 | + | 0.354194i | ||||
\(376\) | 2.60997 | 0.134599 | ||||||||
\(377\) | − | 31.1416i | − | 1.60387i | ||||||
\(378\) | 4.99868i | 0.257104i | ||||||||
\(379\) | −21.6574 | −1.11246 | −0.556232 | − | 0.831027i | \(-0.687753\pi\) | ||||
−0.556232 | + | 0.831027i | \(0.687753\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.4287 | 0.687974 | ||||||||
\(382\) | − | 30.1886i | − | 1.54458i | ||||||
\(383\) | − | 24.3214i | − | 1.24277i | −0.783507 | − | 0.621383i | \(-0.786571\pi\) | ||
0.783507 | − | 0.621383i | \(-0.213429\pi\) | |||||||
\(384\) | 11.7576 | 0.600005 | ||||||||
\(385\) | −2.06830 | + | 0.302335i | −0.105411 | + | 0.0154084i | ||||
\(386\) | −30.5082 | −1.55282 | ||||||||
\(387\) | 5.49403i | 0.279277i | ||||||||
\(388\) | − | 8.43943i | − | 0.428447i | ||||||
\(389\) | −15.8227 | −0.802241 | −0.401120 | − | 0.916025i | \(-0.631379\pi\) | ||||
−0.401120 | + | 0.916025i | \(0.631379\pi\) | |||||||
\(390\) | 18.2433 | − | 2.66672i | 0.923785 | − | 0.135035i | ||||
\(391\) | −5.44507 | −0.275369 | ||||||||
\(392\) | 7.13124i | 0.360182i | ||||||||
\(393\) | − | 20.2620i | − | 1.02208i | ||||||
\(394\) | −18.5668 | −0.935381 | ||||||||
\(395\) | −0.228977 | − | 1.56645i | −0.0115211 | − | 0.0788168i | ||||
\(396\) | −2.47892 | −0.124571 | ||||||||
\(397\) | 35.4753i | 1.78046i | 0.455515 | + | 0.890228i | \(0.349455\pi\) | ||||
−0.455515 | + | 0.890228i | \(0.650545\pi\) | |||||||
\(398\) | 23.4598i | 1.17593i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 23.0619 | − | 6.88937i | 1.15309 | − | 0.344468i | ||||
\(401\) | −11.2107 | −0.559837 | −0.279919 | − | 0.960024i | \(-0.590307\pi\) | ||||
−0.279919 | + | 0.960024i | \(0.590307\pi\) | |||||||
\(402\) | − | 23.7638i | − | 1.18523i | ||||||
\(403\) | − | 17.1497i | − | 0.854286i | ||||||
\(404\) | −0.369636 | −0.0183901 | ||||||||
\(405\) | 1.79921 | + | 12.3086i | 0.0894035 | + | 0.611618i | ||||
\(406\) | 9.00263 | 0.446793 | ||||||||
\(407\) | − | 11.0734i | − | 0.548887i | ||||||
\(408\) | 1.49099i | 0.0738150i | ||||||||
\(409\) | −1.91450 | −0.0946660 | −0.0473330 | − | 0.998879i | \(-0.515072\pi\) | ||||
−0.0473330 | + | 0.998879i | \(0.515072\pi\) | |||||||
\(410\) | 42.9038 | − | 6.27149i | 2.11887 | − | 0.309727i | ||||
\(411\) | 5.58977 | 0.275723 | ||||||||
\(412\) | 20.5730i | 1.01356i | ||||||||
\(413\) | 3.49621i | 0.172037i | ||||||||
\(414\) | 9.16688 | 0.450528 | ||||||||
\(415\) | −26.2815 | + | 3.84171i | −1.29011 | + | 0.188582i | ||||
\(416\) | −20.8449 | −1.02201 | ||||||||
\(417\) | 27.4489i | 1.34418i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.1856 | 1.08384 | 0.541918 | − | 0.840431i | \(-0.317698\pi\) | ||||
0.541918 | + | 0.840431i | \(0.317698\pi\) | |||||||
\(420\) | 0.321601 | + | 2.20010i | 0.0156925 | + | 0.107354i | ||||
\(421\) | 13.3793 | 0.652069 | 0.326034 | − | 0.945358i | \(-0.394287\pi\) | ||||
0.326034 | + | 0.945358i | \(0.394287\pi\) | |||||||
\(422\) | 10.6257i | 0.517253i | ||||||||
\(423\) | − | 2.19276i | − | 0.106616i | ||||||
\(424\) | −11.3427 | −0.550850 | ||||||||
\(425\) | 1.39325 | + | 4.66385i | 0.0675826 | + | 0.226230i | ||||
\(426\) | 35.5216 | 1.72103 | ||||||||
\(427\) | − | 4.18747i | − | 0.202646i | ||||||
\(428\) | 8.20428i | 0.396569i | ||||||||
\(429\) | 8.71201 | 0.420620 | ||||||||
\(430\) | 3.72042 | + | 25.4517i | 0.179415 | + | 1.22739i | ||||
\(431\) | −37.1687 | −1.79035 | −0.895177 | − | 0.445711i | \(-0.852951\pi\) | ||||
−0.895177 | + | 0.445711i | \(0.852951\pi\) | |||||||
\(432\) | − | 27.1976i | − | 1.30855i | ||||||
\(433\) | − | 8.32630i | − | 0.400137i | −0.979782 | − | 0.200068i | \(-0.935884\pi\) | ||
0.979782 | − | 0.200068i | \(-0.0641164\pi\) | |||||||
\(434\) | 4.95774 | 0.237979 | ||||||||
\(435\) | 32.7443 | − | 4.78641i | 1.56997 | − | 0.229491i | ||||
\(436\) | −8.27152 | −0.396134 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | − | 13.3933i | − | 0.639957i | ||||||
\(439\) | 17.0746 | 0.814928 | 0.407464 | − | 0.913221i | \(-0.366413\pi\) | ||||
0.407464 | + | 0.913221i | \(0.366413\pi\) | |||||||
\(440\) | 4.56039 | − | 0.666617i | 0.217408 | − | 0.0317797i | ||||
\(441\) | 5.99131 | 0.285300 | ||||||||
\(442\) | − | 5.51904i | − | 0.262514i | ||||||
\(443\) | − | 7.18135i | − | 0.341196i | −0.985341 | − | 0.170598i | \(-0.945430\pi\) | ||
0.985341 | − | 0.170598i | \(-0.0545700\pi\) | |||||||
\(444\) | −11.7790 | −0.559008 | ||||||||
\(445\) | 0.694888 | + | 4.75379i | 0.0329409 | + | 0.225351i | ||||
\(446\) | −23.7998 | −1.12695 | ||||||||
\(447\) | 34.7991i | 1.64594i | ||||||||
\(448\) | − | 1.42784i | − | 0.0674589i | ||||||
\(449\) | −23.1024 | −1.09027 | −0.545134 | − | 0.838349i | \(-0.683521\pi\) | ||||
−0.545134 | + | 0.838349i | \(0.683521\pi\) | |||||||
\(450\) | −2.34557 | − | 7.85168i | −0.110571 | − | 0.370132i | ||||
\(451\) | 20.4886 | 0.964768 | ||||||||
\(452\) | − | 20.0073i | − | 0.941065i | ||||||
\(453\) | − | 8.58532i | − | 0.403373i | ||||||
\(454\) | 28.8625 | 1.35458 | ||||||||
\(455\) | 0.472737 | + | 3.23403i | 0.0221622 | + | 0.151614i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 13.7430i | − | 0.642872i | −0.946931 | − | 0.321436i | \(-0.895834\pi\) | ||
0.946931 | − | 0.321436i | \(-0.104166\pi\) | |||||||
\(458\) | 7.00091i | 0.327131i | ||||||||
\(459\) | 5.50023 | 0.256729 | ||||||||
\(460\) | 17.7158 | − | 2.58961i | 0.826001 | − | 0.120741i | ||||
\(461\) | −26.0522 | −1.21337 | −0.606686 | − | 0.794942i | \(-0.707501\pi\) | ||||
−0.606686 | + | 0.794942i | \(0.707501\pi\) | |||||||
\(462\) | 2.51853i | 0.117173i | ||||||||
\(463\) | − | 4.24698i | − | 0.197374i | −0.995119 | − | 0.0986869i | \(-0.968536\pi\) | ||
0.995119 | − | 0.0986869i | \(-0.0314642\pi\) | |||||||
\(464\) | −48.9830 | −2.27398 | ||||||||
\(465\) | 18.0322 | − | 2.63587i | 0.836225 | − | 0.122236i | ||||
\(466\) | 20.5147 | 0.950327 | ||||||||
\(467\) | 27.7571i | 1.28444i | 0.766519 | + | 0.642222i | \(0.221987\pi\) | ||||
−0.766519 | + | 0.642222i | \(0.778013\pi\) | |||||||
\(468\) | 3.87608i | 0.179172i | ||||||||
\(469\) | 4.21267 | 0.194523 | ||||||||
\(470\) | −1.48488 | − | 10.1582i | −0.0684925 | − | 0.468563i | ||||
\(471\) | 15.3739 | 0.708394 | ||||||||
\(472\) | − | 7.70877i | − | 0.354825i | ||||||
\(473\) | 12.1544i | 0.558858i | ||||||||
\(474\) | −1.90744 | −0.0876114 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.665585 | 0.0305070 | ||||||||
\(477\) | 9.52956i | 0.436328i | ||||||||
\(478\) | 19.7277i | 0.902325i | ||||||||
\(479\) | 7.11883 | 0.325268 | 0.162634 | − | 0.986686i | \(-0.448001\pi\) | ||||
0.162634 | + | 0.986686i | \(0.448001\pi\) | |||||||
\(480\) | −3.20383 | − | 21.9177i | −0.146234 | − | 1.00040i | ||||
\(481\) | −17.3145 | −0.789474 | ||||||||
\(482\) | 9.28573i | 0.422953i | ||||||||
\(483\) | − | 3.88523i | − | 0.176784i | ||||||
\(484\) | 10.2627 | 0.466486 | ||||||||
\(485\) | 13.0439 | − | 1.90670i | 0.592294 | − | 0.0865789i | ||||
\(486\) | −16.4106 | −0.744400 | ||||||||
\(487\) | − | 3.54621i | − | 0.160694i | −0.996767 | − | 0.0803470i | \(-0.974397\pi\) | ||
0.996767 | − | 0.0803470i | \(-0.0256028\pi\) | |||||||
\(488\) | 9.23291i | 0.417954i | ||||||||
\(489\) | 27.0649 | 1.22392 | ||||||||
\(490\) | 27.7554 | − | 4.05716i | 1.25386 | − | 0.183284i | ||||
\(491\) | −32.1308 | −1.45004 | −0.725020 | − | 0.688727i | \(-0.758170\pi\) | ||||
−0.725020 | + | 0.688727i | \(0.758170\pi\) | |||||||
\(492\) | − | 21.7942i | − | 0.982557i | ||||||
\(493\) | − | 9.90593i | − | 0.446141i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.560057 | − | 3.83140i | −0.0251727 | − | 0.172209i | ||||
\(496\) | −26.9749 | −1.21121 | ||||||||
\(497\) | 6.29701i | 0.282459i | ||||||||
\(498\) | 32.0024i | 1.43406i | ||||||||
\(499\) | 11.9147 | 0.533376 | 0.266688 | − | 0.963783i | \(-0.414071\pi\) | ||||
0.266688 | + | 0.963783i | \(0.414071\pi\) | |||||||
\(500\) | −6.75107 | − | 14.5114i | −0.301917 | − | 0.648970i | ||||
\(501\) | −4.03930 | −0.180463 | ||||||||
\(502\) | − | 48.4823i | − | 2.16387i | ||||||
\(503\) | 0.239744i | 0.0106896i | 0.999986 | + | 0.00534482i | \(0.00170132\pi\) | ||||
−0.999986 | + | 0.00534482i | \(0.998299\pi\) | |||||||
\(504\) | 0.444973 | 0.0198207 | ||||||||
\(505\) | −0.0835111 | − | 0.571307i | −0.00371620 | − | 0.0254228i | ||||
\(506\) | 20.2798 | 0.901546 | ||||||||
\(507\) | 5.28491i | 0.234711i | ||||||||
\(508\) | 13.2175i | 0.586434i | ||||||||
\(509\) | 29.3663 | 1.30164 | 0.650819 | − | 0.759233i | \(-0.274426\pi\) | ||||
0.650819 | + | 0.759233i | \(0.274426\pi\) | |||||||
\(510\) | 5.80306 | − | 0.848266i | 0.256964 | − | 0.0375618i | ||||
\(511\) | 2.37427 | 0.105031 | ||||||||
\(512\) | 22.6488i | 1.00094i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −41.4991 | −1.83045 | ||||||||
\(515\) | −31.7974 | + | 4.64801i | −1.40116 | + | 0.204816i | ||||
\(516\) | 12.9289 | 0.569163 | ||||||||
\(517\) | − | 4.85101i | − | 0.213347i | ||||||
\(518\) | − | 5.00540i | − | 0.219925i | ||||||
\(519\) | −12.9743 | −0.569509 | ||||||||
\(520\) | −1.04233 | − | 7.13070i | −0.0457093 | − | 0.312702i | ||||
\(521\) | 12.1069 | 0.530414 | 0.265207 | − | 0.964191i | \(-0.414560\pi\) | ||||
0.265207 | + | 0.964191i | \(0.414560\pi\) | |||||||
\(522\) | 16.6768i | 0.729924i | ||||||||
\(523\) | 6.43779i | 0.281505i | 0.990045 | + | 0.140752i | \(0.0449522\pi\) | ||||
−0.990045 | + | 0.140752i | \(0.955048\pi\) | |||||||
\(524\) | 19.9434 | 0.871231 | ||||||||
\(525\) | −3.32781 | + | 0.994130i | −0.145237 | + | 0.0433874i | ||||
\(526\) | −48.0407 | −2.09467 | ||||||||
\(527\) | − | 5.45519i | − | 0.237632i | ||||||
\(528\) | − | 13.7032i | − | 0.596356i | ||||||
\(529\) | −8.28480 | −0.360209 | ||||||||
\(530\) | 6.45318 | + | 44.1468i | 0.280308 | + | 1.91761i | ||||
\(531\) | −6.47651 | −0.281057 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 32.0362i | − | 1.38764i | ||||||
\(534\) | 5.78859 | 0.250497 | ||||||||
\(535\) | −12.6805 | + | 1.85358i | −0.548225 | + | 0.0801371i | ||||
\(536\) | −9.28848 | −0.401201 | ||||||||
\(537\) | − | 22.2008i | − | 0.958037i | ||||||
\(538\) | 17.1346i | 0.738727i | ||||||||
\(539\) | 13.2545 | 0.570911 | ||||||||
\(540\) | −17.8952 | + | 2.61584i | −0.770087 | + | 0.112568i | ||||
\(541\) | −15.1179 | −0.649969 | −0.324985 | − | 0.945719i | \(-0.605359\pi\) | ||||
−0.324985 | + | 0.945719i | \(0.605359\pi\) | |||||||
\(542\) | − | 41.6220i | − | 1.78782i | ||||||
\(543\) | − | 12.4220i | − | 0.533079i | ||||||
\(544\) | −6.63063 | −0.284286 | ||||||||
\(545\) | −1.86877 | − | 12.7844i | −0.0800492 | − | 0.547624i | ||||
\(546\) | 3.93801 | 0.168531 | ||||||||
\(547\) | 36.1694i | 1.54649i | 0.634106 | + | 0.773246i | \(0.281368\pi\) | ||||
−0.634106 | + | 0.773246i | \(0.718632\pi\) | |||||||
\(548\) | 5.50186i | 0.235028i | ||||||||
\(549\) | 7.75702 | 0.331061 | ||||||||
\(550\) | −5.18906 | − | 17.3702i | −0.221262 | − | 0.740667i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 8.56652i | 0.364615i | ||||||||
\(553\) | − | 0.338136i | − | 0.0143790i | ||||||
\(554\) | 16.9794 | 0.721386 | ||||||||
\(555\) | −2.66121 | − | 18.2056i | −0.112962 | − | 0.772784i | ||||
\(556\) | −27.0172 | −1.14579 | ||||||||
\(557\) | − | 37.0585i | − | 1.57022i | −0.619358 | − | 0.785109i | \(-0.712607\pi\) | ||
0.619358 | − | 0.785109i | \(-0.287393\pi\) | |||||||
\(558\) | 9.18391i | 0.388786i | ||||||||
\(559\) | 19.0048 | 0.803816 | ||||||||
\(560\) | 5.08685 | − | 0.743572i | 0.214958 | − | 0.0314217i | ||||
\(561\) | 2.77123 | 0.117001 | ||||||||
\(562\) | − | 35.8590i | − | 1.51262i | ||||||
\(563\) | 12.9283i | 0.544863i | 0.962175 | + | 0.272432i | \(0.0878279\pi\) | ||||
−0.962175 | + | 0.272432i | \(0.912172\pi\) | |||||||
\(564\) | −5.16014 | −0.217281 | ||||||||
\(565\) | 30.9232 | − | 4.52021i | 1.30095 | − | 0.190167i | ||||
\(566\) | −16.1628 | −0.679372 | ||||||||
\(567\) | 2.65694i | 0.111581i | ||||||||
\(568\) | − | 13.8842i | − | 0.582569i | ||||||
\(569\) | −18.5114 | −0.776038 | −0.388019 | − | 0.921651i | \(-0.626841\pi\) | ||||
−0.388019 | + | 0.921651i | \(0.626841\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.2207 | 0.678816 | 0.339408 | − | 0.940639i | \(-0.389773\pi\) | ||||
0.339408 | + | 0.940639i | \(0.389773\pi\) | |||||||
\(572\) | 8.57501i | 0.358539i | ||||||||
\(573\) | − | 23.7019i | − | 0.990160i | ||||||
\(574\) | 9.26125 | 0.386557 | ||||||||
\(575\) | 8.00496 | + | 26.7963i | 0.333830 | + | 1.11748i | ||||
\(576\) | 2.64498 | 0.110207 | ||||||||
\(577\) | − | 17.7980i | − | 0.740939i | −0.928845 | − | 0.370470i | \(-0.879197\pi\) | ||
0.928845 | − | 0.370470i | \(-0.120803\pi\) | |||||||
\(578\) | 29.7359i | 1.23685i | ||||||||
\(579\) | −23.9527 | −0.995442 | ||||||||
\(580\) | 4.71114 | + | 32.2293i | 0.195619 | + | 1.33825i | ||||
\(581\) | −5.67314 | −0.235362 | ||||||||
\(582\) | − | 15.8833i | − | 0.658384i | ||||||
\(583\) | 21.0821i | 0.873132i | ||||||||
\(584\) | −5.23500 | −0.216626 | ||||||||
\(585\) | −5.99085 | + | 0.875715i | −0.247691 | + | 0.0362064i | ||||
\(586\) | 31.0745 | 1.28368 | ||||||||
\(587\) | − | 35.8593i | − | 1.48007i | −0.672567 | − | 0.740036i | \(-0.734809\pi\) | ||
0.672567 | − | 0.740036i | \(-0.265191\pi\) | |||||||
\(588\) | − | 14.0991i | − | 0.581438i | ||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −30.0032 | + | 4.38573i | −1.23521 | + | 0.180558i | ||||
\(591\) | −14.5773 | −0.599628 | ||||||||
\(592\) | 27.2342i | 1.11932i | ||||||||
\(593\) | 18.2848i | 0.750868i | 0.926849 | + | 0.375434i | \(0.122506\pi\) | ||||
−0.926849 | + | 0.375434i | \(0.877494\pi\) | |||||||
\(594\) | −20.4852 | −0.840518 | ||||||||
\(595\) | 0.150374 | + | 1.02872i | 0.00616474 | + | 0.0421735i | ||||
\(596\) | −34.2519 | −1.40301 | ||||||||
\(597\) | 18.4189i | 0.753836i | ||||||||
\(598\) | − | 31.7098i | − | 1.29671i | ||||||
\(599\) | 7.85141 | 0.320800 | 0.160400 | − | 0.987052i | \(-0.448722\pi\) | ||||
0.160400 | + | 0.987052i | \(0.448722\pi\) | |||||||
\(600\) | 7.33746 | − | 2.19195i | 0.299551 | − | 0.0894860i | ||||
\(601\) | 17.3527 | 0.707833 | 0.353917 | − | 0.935277i | \(-0.384850\pi\) | ||||
0.353917 | + | 0.935277i | \(0.384850\pi\) | |||||||
\(602\) | 5.49403i | 0.223920i | ||||||||
\(603\) | 7.80370i | 0.317791i | ||||||||
\(604\) | 8.45030 | 0.343838 | ||||||||
\(605\) | 2.31863 | + | 15.8619i | 0.0942656 | + | 0.644879i | ||||
\(606\) | −0.695668 | −0.0282596 | ||||||||
\(607\) | − | 40.7364i | − | 1.65344i | −0.562614 | − | 0.826720i | \(-0.690204\pi\) | ||
0.562614 | − | 0.826720i | \(-0.309796\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.06820 | 0.286418 | ||||||||
\(610\) | 35.9353 | − | 5.25286i | 1.45498 | − | 0.212682i | ||||
\(611\) | −7.58512 | −0.306861 | ||||||||
\(612\) | 1.23295i | 0.0498392i | ||||||||
\(613\) | − | 27.0535i | − | 1.09268i | −0.837564 | − | 0.546340i | \(-0.816021\pi\) | ||
0.837564 | − | 0.546340i | \(-0.183979\pi\) | |||||||
\(614\) | −11.8721 | −0.479121 | ||||||||
\(615\) | 33.6849 | − | 4.92391i | 1.35831 | − | 0.198551i | ||||
\(616\) | 0.984409 | 0.0396630 | ||||||||
\(617\) | 19.8932i | 0.800871i | 0.916325 | + | 0.400436i | \(0.131141\pi\) | ||||
−0.916325 | + | 0.400436i | \(0.868859\pi\) | |||||||
\(618\) | 38.7190i | 1.55751i | ||||||||
\(619\) | −16.8447 | −0.677044 | −0.338522 | − | 0.940958i | \(-0.609927\pi\) | ||||
−0.338522 | + | 0.940958i | \(0.609927\pi\) | |||||||
\(620\) | 2.59442 | + | 17.7487i | 0.104194 | + | 0.712804i | ||||
\(621\) | 31.6017 | 1.26813 | ||||||||
\(622\) | 19.6818i | 0.789167i | ||||||||
\(623\) | 1.02616i | 0.0411121i | ||||||||
\(624\) | −21.4266 | −0.857749 | ||||||||
\(625\) | 20.9035 | − | 13.7129i | 0.836139 | − | 0.548517i | ||||
\(626\) | 8.81123 | 0.352168 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.1322i | 0.603839i | ||||||||
\(629\) | −5.50763 | −0.219603 | ||||||||
\(630\) | −0.253158 | − | 1.73187i | −0.0100860 | − | 0.0689995i | ||||
\(631\) | 27.2013 | 1.08287 | 0.541433 | − | 0.840744i | \(-0.317882\pi\) | ||||
0.541433 | + | 0.840744i | \(0.317882\pi\) | |||||||
\(632\) | 0.745553i | 0.0296565i | ||||||||
\(633\) | 8.34254i | 0.331586i | ||||||||
\(634\) | −0.113410 | −0.00450407 | ||||||||
\(635\) | −20.4289 | + | 2.98621i | −0.810698 | + | 0.118504i | ||||
\(636\) | 22.4255 | 0.889231 | ||||||||
\(637\) | − | 20.7249i | − | 0.821152i | ||||||
\(638\) | 36.8939i | 1.46064i | ||||||||
\(639\) | −11.6648 | −0.461453 | ||||||||
\(640\) | −17.8867 | + | 2.61460i | −0.707036 | + | 0.103351i | ||||
\(641\) | −17.6090 | −0.695514 | −0.347757 | − | 0.937585i | \(-0.613057\pi\) | ||||
−0.347757 | + | 0.937585i | \(0.613057\pi\) | |||||||
\(642\) | 15.4407i | 0.609398i | ||||||||
\(643\) | 8.95765i | 0.353255i | 0.984278 | + | 0.176628i | \(0.0565188\pi\) | ||||
−0.984278 | + | 0.176628i | \(0.943481\pi\) | |||||||
\(644\) | 3.82414 | 0.150692 | ||||||||
\(645\) | 2.92100 | + | 19.9828i | 0.115014 | + | 0.786822i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 49.1850i | 1.93366i | 0.255416 | + | 0.966831i | \(0.417788\pi\) | ||||
−0.255416 | + | 0.966831i | \(0.582212\pi\) | |||||||
\(648\) | − | 5.85826i | − | 0.230134i | ||||||
\(649\) | −14.3279 | −0.562419 | ||||||||
\(650\) | −27.1603 | + | 8.11371i | −1.06531 | + | 0.318246i | ||||
\(651\) | 3.89245 | 0.152557 | ||||||||
\(652\) | 26.6393i | 1.04327i | ||||||||
\(653\) | − | 11.7035i | − | 0.457993i | −0.973427 | − | 0.228997i | \(-0.926456\pi\) | ||
0.973427 | − | 0.228997i | \(-0.0735445\pi\) | |||||||
\(654\) | −15.5673 | −0.608729 | ||||||||
\(655\) | 4.50576 | + | 30.8243i | 0.176055 | + | 1.20441i | ||||
\(656\) | −50.3901 | −1.96740 | ||||||||
\(657\) | 4.39818i | 0.171589i | ||||||||
\(658\) | − | 2.19276i | − | 0.0854826i | ||||||
\(659\) | −34.7573 | −1.35395 | −0.676976 | − | 0.736005i | \(-0.736710\pi\) | ||||
−0.676976 | + | 0.736005i | \(0.736710\pi\) | |||||||
\(660\) | −9.01630 | + | 1.31796i | −0.350959 | + | 0.0513016i | ||||
\(661\) | −17.9064 | −0.696477 | −0.348239 | − | 0.937406i | \(-0.613220\pi\) | ||||
−0.348239 | + | 0.937406i | \(0.613220\pi\) | |||||||
\(662\) | 32.6153i | 1.26763i | ||||||||
\(663\) | − | 4.33314i | − | 0.168285i | ||||||
\(664\) | 12.5087 | 0.485431 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.27219 | 0.359290 | ||||||||
\(667\) | − | 56.9148i | − | 2.20375i | ||||||
\(668\) | − | 3.97578i | − | 0.153828i | ||||||
\(669\) | −18.6858 | −0.722435 | ||||||||
\(670\) | 5.28447 | + | 36.1516i | 0.204157 | + | 1.39666i | ||||
\(671\) | 17.1607 | 0.662483 | ||||||||
\(672\) | − | 4.73117i | − | 0.182509i | ||||||
\(673\) | 10.9828i | 0.423355i | 0.977340 | + | 0.211677i | \(0.0678926\pi\) | ||||
−0.977340 | + | 0.211677i | \(0.932107\pi\) | |||||||
\(674\) | −12.7980 | −0.492961 | ||||||||
\(675\) | −8.08605 | − | 27.0677i | −0.311232 | − | 1.04184i | ||||
\(676\) | −5.20180 | −0.200069 | ||||||||
\(677\) | − | 4.77520i | − | 0.183526i | −0.995781 | − | 0.0917630i | \(-0.970750\pi\) | ||
0.995781 | − | 0.0917630i | \(-0.0292502\pi\) | |||||||
\(678\) | − | 37.6544i | − | 1.44611i | ||||||
\(679\) | 2.81567 | 0.108056 | ||||||||
\(680\) | −0.331559 | − | 2.26822i | −0.0127147 | − | 0.0869824i | ||||
\(681\) | 22.6607 | 0.868359 | ||||||||
\(682\) | 20.3175i | 0.777995i | ||||||||
\(683\) | − | 46.0853i | − | 1.76341i | −0.471805 | − | 0.881703i | \(-0.656397\pi\) | ||
0.471805 | − | 0.881703i | \(-0.343603\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.50364 | + | 1.24302i | −0.324907 | + | 0.0474935i | ||||
\(686\) | 12.1844 | 0.465203 | ||||||||
\(687\) | 5.49660i | 0.209708i | ||||||||
\(688\) | − | 29.8928i | − | 1.13965i | ||||||
\(689\) | 32.9643 | 1.25584 | ||||||||
\(690\) | 33.3417 | − | 4.87373i | 1.26930 | − | 0.185540i | ||||
\(691\) | 15.2699 | 0.580893 | 0.290447 | − | 0.956891i | \(-0.406196\pi\) | ||||
0.290447 | + | 0.956891i | \(0.406196\pi\) | |||||||
\(692\) | − | 12.7703i | − | 0.485453i | ||||||
\(693\) | − | 0.827050i | − | 0.0314170i | ||||||
\(694\) | 13.5705 | 0.515130 | ||||||||
\(695\) | −6.10394 | − | 41.7576i | −0.231536 | − | 1.58396i | ||||
\(696\) | −15.5846 | −0.590733 | ||||||||
\(697\) | − | 10.1905i | − | 0.385993i | ||||||
\(698\) | 4.00362i | 0.151539i | ||||||||
\(699\) | 16.1067 | 0.609210 | ||||||||
\(700\) | −0.978496 | − | 3.27548i | −0.0369837 | − | 0.123801i | ||||
\(701\) | −16.6852 | −0.630191 | −0.315096 | − | 0.949060i | \(-0.602037\pi\) | ||||
−0.315096 | + | 0.949060i | \(0.602037\pi\) | |||||||
\(702\) | 32.0310i | 1.20893i | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 5.85144 | 0.220535 | ||||||||
\(705\) | −1.16582 | − | 7.97547i | −0.0439073 | − | 0.300374i | ||||
\(706\) | 30.7545 | 1.15746 | ||||||||
\(707\) | − | 0.123323i | − | 0.00463803i | ||||||
\(708\) | 15.2409i | 0.572789i | ||||||||
\(709\) | −1.95870 | −0.0735604 | −0.0367802 | − | 0.999323i | \(-0.511710\pi\) | ||||
−0.0367802 | + | 0.999323i | \(0.511710\pi\) | |||||||
\(710\) | −54.0386 | + | 7.89912i | −2.02803 | + | 0.296449i | ||||
\(711\) | 0.626375 | 0.0234909 | ||||||||
\(712\) | − | 2.26257i | − | 0.0847933i | ||||||
\(713\) | − | 31.3429i | − | 1.17380i | ||||||
\(714\) | 1.25265 | 0.0468794 | ||||||||
\(715\) | −13.2535 | + | 1.93733i | −0.495652 | + | 0.0724522i | ||||
\(716\) | 21.8517 | 0.816637 | ||||||||
\(717\) | 15.4887i | 0.578438i | ||||||||
\(718\) | − | 31.6452i | − | 1.18099i | ||||||
\(719\) | 23.0165 | 0.858370 | 0.429185 | − | 0.903217i | \(-0.358801\pi\) | ||||
0.429185 | + | 0.903217i | \(0.358801\pi\) | |||||||
\(720\) | 1.37742 | + | 9.42306i | 0.0513334 | + | 0.351177i | ||||
\(721\) | −6.86382 | −0.255622 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.29046i | 0.271135i | ||||||||
\(724\) | 12.2267 | 0.454400 | ||||||||
\(725\) | −48.7490 | + | 14.5630i | −1.81049 | + | 0.540856i | ||||
\(726\) | 19.3147 | 0.716837 | ||||||||
\(727\) | 10.3883i | 0.385279i | 0.981270 | + | 0.192640i | \(0.0617048\pi\) | ||||
−0.981270 | + | 0.192640i | \(0.938295\pi\) | |||||||
\(728\) | − | 1.53924i | − | 0.0570479i | ||||||
\(729\) | −29.5736 | −1.09532 | ||||||||
\(730\) | 2.97834 | + | 20.3751i | 0.110233 | + | 0.754116i | ||||
\(731\) | 6.04528 | 0.223593 | ||||||||
\(732\) | − | 18.2543i | − | 0.674698i | ||||||
\(733\) | 40.7900i | 1.50661i | 0.657670 | + | 0.753306i | \(0.271542\pi\) | ||||
−0.657670 | + | 0.753306i | \(0.728458\pi\) | |||||||
\(734\) | 36.2395 | 1.33762 | ||||||||
\(735\) | 21.7915 | − | 3.18538i | 0.803791 | − | 0.117495i | ||||
\(736\) | −38.0965 | −1.40425 | ||||||||
\(737\) | 17.2640i | 0.635929i | ||||||||
\(738\) | 17.1559i | 0.631517i | ||||||||
\(739\) | 7.92965 | 0.291697 | 0.145848 | − | 0.989307i | \(-0.453409\pi\) | ||||
0.145848 | + | 0.989307i | \(0.453409\pi\) | |||||||
\(740\) | 17.9193 | − | 2.61936i | 0.658726 | − | 0.0962896i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.52956i | 0.349841i | ||||||||
\(743\) | − | 7.27911i | − | 0.267045i | −0.991046 | − | 0.133522i | \(-0.957371\pi\) | ||
0.991046 | − | 0.133522i | \(-0.0426288\pi\) | |||||||
\(744\) | −8.58244 | −0.314648 | ||||||||
\(745\) | −7.73845 | − | 52.9395i | −0.283515 | − | 1.93955i | ||||
\(746\) | 12.2205 | 0.447426 | ||||||||
\(747\) | − | 10.5091i | − | 0.384509i | ||||||
\(748\) | 2.72765i | 0.0997327i | ||||||||
\(749\) | −2.73722 | −0.100016 | ||||||||
\(750\) | −12.7057 | − | 27.3110i | −0.463948 | − | 0.997255i | ||||
\(751\) | −37.8815 | −1.38232 | −0.691158 | − | 0.722704i | \(-0.742899\pi\) | ||||
−0.691158 | + | 0.722704i | \(0.742899\pi\) | |||||||
\(752\) | 11.9307i | 0.435068i | ||||||||
\(753\) | − | 38.0647i | − | 1.38715i | ||||||
\(754\) | 57.6879 | 2.10087 | ||||||||
\(755\) | 1.90916 | + | 13.0607i | 0.0694814 | + | 0.475329i | ||||
\(756\) | −3.86287 | −0.140491 | ||||||||
\(757\) | − | 51.1527i | − | 1.85917i | −0.368602 | − | 0.929587i | \(-0.620163\pi\) | ||
0.368602 | − | 0.929587i | \(-0.379837\pi\) | |||||||
\(758\) | − | 40.1189i | − | 1.45718i | ||||||
\(759\) | 15.9222 | 0.577938 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.8749 | −0.394213 | −0.197107 | − | 0.980382i | \(-0.563155\pi\) | ||||
−0.197107 | + | 0.980382i | \(0.563155\pi\) | |||||||
\(762\) | 24.8759i | 0.901158i | ||||||||
\(763\) | − | 2.75965i | − | 0.0999061i | ||||||
\(764\) | 23.3291 | 0.844019 | ||||||||
\(765\) | −1.90565 | + | 0.278559i | −0.0688988 | + | 0.0100713i | ||||
\(766\) | 45.0539 | 1.62786 | ||||||||
\(767\) | 22.4033i | 0.808938i | ||||||||
\(768\) | 30.4764i | 1.09972i | ||||||||
\(769\) | 18.8020 | 0.678016 | 0.339008 | − | 0.940783i | \(-0.389909\pi\) | ||||
0.339008 | + | 0.940783i | \(0.389909\pi\) | |||||||
\(770\) | −0.560057 | − | 3.83140i | −0.0201831 | − | 0.138074i | ||||
\(771\) | −32.5820 | −1.17341 | ||||||||
\(772\) | − | 23.5761i | − | 0.848521i | ||||||
\(773\) | − | 24.3856i | − | 0.877090i | −0.898709 | − | 0.438545i | \(-0.855494\pi\) | ||
0.898709 | − | 0.438545i | \(-0.144506\pi\) | |||||||
\(774\) | −10.1773 | −0.365817 | ||||||||
\(775\) | −26.8461 | + | 8.01984i | −0.964339 | + | 0.288081i | ||||
\(776\) | −6.20825 | −0.222863 | ||||||||
\(777\) | − | 3.92987i | − | 0.140983i | ||||||
\(778\) | − | 29.3105i | − | 1.05083i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 2.06079 | + | 14.0980i | 0.0737880 | + | 0.504791i | ||||
\(781\) | −25.8059 | −0.923408 | ||||||||
\(782\) | − | 10.0867i | − | 0.360698i | ||||||
\(783\) | 57.4913i | 2.05457i | ||||||||
\(784\) | −32.5985 | −1.16423 | ||||||||
\(785\) | −23.3882 | + | 3.41878i | −0.834760 | + | 0.122021i | ||||
\(786\) | 37.5341 | 1.33880 | ||||||||
\(787\) | − | 9.17617i | − | 0.327095i | −0.986535 | − | 0.163547i | \(-0.947706\pi\) | ||
0.986535 | − | 0.163547i | \(-0.0522937\pi\) | |||||||
\(788\) | − | 14.3480i | − | 0.511127i | ||||||
\(789\) | −37.7180 | −1.34280 | ||||||||
\(790\) | 2.90176 | − | 0.424166i | 0.103240 | − | 0.0150911i | ||||
\(791\) | 6.67510 | 0.237339 | ||||||||
\(792\) | 1.82356i | 0.0647972i | ||||||||
\(793\) | − | 26.8328i | − | 0.952862i | ||||||
\(794\) | −65.7158 | −2.33217 | ||||||||
\(795\) | 5.06656 | + | 34.6608i | 0.179692 | + | 1.22929i | ||||
\(796\) | −18.1293 | −0.642574 | ||||||||
\(797\) | 46.8095i | 1.65808i | 0.559191 | + | 0.829039i | \(0.311112\pi\) | ||||
−0.559191 | + | 0.829039i | \(0.688888\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.41277 | −0.0853578 | ||||||||
\(800\) | 9.74789 | + | 32.6306i | 0.344640 | + | 1.15367i | ||||
\(801\) | −1.90089 | −0.0671647 | ||||||||
\(802\) | − | 20.7672i | − | 0.733314i | ||||||
\(803\) | 9.73004i | 0.343366i | ||||||||
\(804\) | 18.3642 | 0.647654 | ||||||||
\(805\) | 0.863979 | + | 5.91056i | 0.0304512 | + | 0.208320i | ||||
\(806\) | 31.7687 | 1.11900 | ||||||||
\(807\) | 13.4529i | 0.473563i | ||||||||
\(808\) | 0.271913i | 0.00956588i | ||||||||
\(809\) | −11.7440 | −0.412898 | −0.206449 | − | 0.978457i | \(-0.566191\pi\) | ||||
−0.206449 | + | 0.978457i | \(0.566191\pi\) | |||||||
\(810\) | −22.8009 | + | 3.33293i | −0.801141 | + | 0.117107i | ||||
\(811\) | 41.3856 | 1.45324 | 0.726622 | − | 0.687038i | \(-0.241089\pi\) | ||||
0.726622 | + | 0.687038i | \(0.241089\pi\) | |||||||
\(812\) | 6.95704i | 0.244144i | ||||||||
\(813\) | − | 32.6785i | − | 1.14609i | ||||||
\(814\) | 20.5127 | 0.718971 | ||||||||
\(815\) | −41.1734 | + | 6.01855i | −1.44224 | + | 0.210821i | ||||
\(816\) | −6.81564 | −0.238595 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 3.54650i | − | 0.124000i | ||||||
\(819\) | −1.29319 | −0.0451877 | ||||||||
\(820\) | 4.84648 | + | 33.1552i | 0.169246 | + | 1.15783i | ||||
\(821\) | −15.6567 | −0.546424 | −0.273212 | − | 0.961954i | \(-0.588086\pi\) | ||||
−0.273212 | + | 0.961954i | \(0.588086\pi\) | |||||||
\(822\) | 10.3547i | 0.361161i | ||||||||
\(823\) | 42.0847i | 1.46698i | 0.679700 | + | 0.733490i | \(0.262110\pi\) | ||||
−0.679700 | + | 0.733490i | \(0.737890\pi\) | |||||||
\(824\) | 15.1340 | 0.527217 | ||||||||
\(825\) | −4.07407 | − | 13.6378i | −0.141841 | − | 0.474806i | ||||
\(826\) | −6.47651 | −0.225347 | ||||||||
\(827\) | 23.0974i | 0.803175i | 0.915821 | + | 0.401588i | \(0.131541\pi\) | ||||
−0.915821 | + | 0.401588i | \(0.868459\pi\) | |||||||
\(828\) | 7.08397i | 0.246185i | ||||||||
\(829\) | −44.6607 | −1.55113 | −0.775566 | − | 0.631267i | \(-0.782535\pi\) | ||||
−0.775566 | + | 0.631267i | \(0.782535\pi\) | |||||||
\(830\) | −7.11653 | − | 48.6848i | −0.247018 | − | 1.68988i | ||||
\(831\) | 13.3310 | 0.462446 | ||||||||
\(832\) | − | 9.14941i | − | 0.317199i | ||||||
\(833\) | − | 6.59245i | − | 0.228415i | ||||||
\(834\) | −50.8473 | −1.76070 | ||||||||
\(835\) | 6.14494 | − | 0.898240i | 0.212654 | − | 0.0310849i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31.6604i | 1.09434i | ||||||||
\(838\) | 41.0974i | 1.41969i | ||||||||
\(839\) | −27.2641 | −0.941260 | −0.470630 | − | 0.882331i | \(-0.655973\pi\) | ||||
−0.470630 | + | 0.882331i | \(0.655973\pi\) | |||||||
\(840\) | 1.61845 | − | 0.236578i | 0.0558419 | − | 0.00816271i | ||||
\(841\) | 74.5420 | 2.57041 | ||||||||
\(842\) | 24.7844i | 0.854126i | ||||||||
\(843\) | − | 28.1538i | − | 0.969669i | ||||||
\(844\) | −8.21135 | −0.282646 | ||||||||
\(845\) | −1.17523 | − | 8.03986i | −0.0404292 | − | 0.276580i | ||||
\(846\) | 4.06195 | 0.139653 | ||||||||
\(847\) | 3.42397i | 0.117649i | ||||||||
\(848\) | − | 51.8499i | − | 1.78053i | ||||||
\(849\) | −12.6898 | −0.435513 | ||||||||
\(850\) | −8.63949 | + | 2.58091i | −0.296332 | + | 0.0885245i | ||||
\(851\) | −31.6442 | −1.08475 | ||||||||
\(852\) | 27.4504i | 0.940434i | ||||||||
\(853\) | − | 6.64990i | − | 0.227688i | −0.993499 | − | 0.113844i | \(-0.963684\pi\) | ||
0.993499 | − | 0.113844i | \(-0.0363165\pi\) | |||||||
\(854\) | 7.75702 | 0.265440 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.03527 | 0.206281 | ||||||||
\(857\) | 47.5875i | 1.62556i | 0.582571 | + | 0.812780i | \(0.302047\pi\) | ||||
−0.582571 | + | 0.812780i | \(0.697953\pi\) | |||||||
\(858\) | 16.1385i | 0.550958i | ||||||||
\(859\) | −47.5779 | −1.62334 | −0.811669 | − | 0.584118i | \(-0.801441\pi\) | ||||
−0.811669 | + | 0.584118i | \(0.801441\pi\) | |||||||
\(860\) | −19.6686 | + | 2.87506i | −0.670692 | + | 0.0980388i | ||||
\(861\) | 7.27125 | 0.247804 | ||||||||
\(862\) | − | 68.8527i | − | 2.34513i | ||||||
\(863\) | − | 0.387407i | − | 0.0131875i | −0.999978 | − | 0.00659374i | \(-0.997901\pi\) | ||
0.999978 | − | 0.00659374i | \(-0.00209887\pi\) | |||||||
\(864\) | 38.4823 | 1.30920 | ||||||||
\(865\) | 19.7376 | − | 2.88516i | 0.671100 | − | 0.0980984i | ||||
\(866\) | 15.4240 | 0.524127 | ||||||||
\(867\) | 23.3464i | 0.792885i | ||||||||
\(868\) | 3.83124i | 0.130041i | ||||||||
\(869\) | 1.38572 | 0.0470074 | ||||||||
\(870\) | 8.86652 | + | 60.6567i | 0.300603 | + | 2.05645i | ||||
\(871\) | 26.9943 | 0.914667 | ||||||||
\(872\) | 6.08473i | 0.206055i | ||||||||
\(873\) | 5.21585i | 0.176530i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.84148 | − | 2.25238i | 0.163672 | − | 0.0761443i | ||||
\(876\) | 10.3501 | 0.349697 | ||||||||
\(877\) | 39.0509i | 1.31865i | 0.751856 | + | 0.659327i | \(0.229159\pi\) | ||||
−0.751856 | + | 0.659327i | \(0.770841\pi\) | |||||||
\(878\) | 31.6297i | 1.06745i | ||||||||
\(879\) | 24.3974 | 0.822904 | ||||||||
\(880\) | 3.04725 | + | 20.8465i | 0.102723 | + | 0.702736i | ||||
\(881\) | 22.9067 | 0.771747 | 0.385873 | − | 0.922552i | \(-0.373900\pi\) | ||||
0.385873 | + | 0.922552i | \(0.373900\pi\) | |||||||
\(882\) | 11.0985i | 0.373707i | ||||||||
\(883\) | − | 28.5966i | − | 0.962353i | −0.876624 | − | 0.481176i | \(-0.840210\pi\) | ||
0.876624 | − | 0.481176i | \(-0.159790\pi\) | |||||||
\(884\) | 4.26500 | 0.143447 | ||||||||
\(885\) | −23.5563 | + | 3.44335i | −0.791835 | + | 0.115747i | ||||
\(886\) | 13.3030 | 0.446923 | ||||||||
\(887\) | − | 8.79919i | − | 0.295448i | −0.989029 | − | 0.147724i | \(-0.952805\pi\) | ||
0.989029 | − | 0.147724i | \(-0.0471947\pi\) | |||||||
\(888\) | 8.66494i | 0.290776i | ||||||||
\(889\) | −4.40981 | −0.147900 | ||||||||
\(890\) | −8.80610 | + | 1.28724i | −0.295181 | + | 0.0431483i | ||||
\(891\) | −10.8885 | −0.364777 | ||||||||
\(892\) | − | 18.3919i | − | 0.615808i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −64.4632 | −2.15597 | ||||||||
\(895\) | 4.93691 | + | 33.7739i | 0.165023 | + | 1.12894i | ||||
\(896\) | −3.86105 | −0.128989 | ||||||||
\(897\) | − | 24.8962i | − | 0.831259i | ||||||
\(898\) | − | 42.7957i | − | 1.42811i | ||||||
\(899\) | 57.0205 | 1.90174 | ||||||||
\(900\) | 6.06761 | − | 1.81260i | 0.202254 | − | 0.0604201i | ||||
\(901\) | 10.4857 | 0.349330 | ||||||||
\(902\) | 37.9538i | 1.26372i | ||||||||
\(903\) | 4.31350i | 0.143544i | ||||||||
\(904\) | −14.7179 | −0.489509 | ||||||||
\(905\) | 2.76234 | + | 18.8974i | 0.0918234 | + | 0.628172i | ||||
\(906\) | 15.9038 | 0.528367 | ||||||||
\(907\) | − | 23.7448i | − | 0.788432i | −0.919018 | − | 0.394216i | \(-0.871016\pi\) | ||
0.919018 | − | 0.394216i | \(-0.128984\pi\) | |||||||
\(908\) | 22.3043i | 0.740194i | ||||||||
\(909\) | 0.228448 | 0.00757713 | ||||||||
\(910\) | −5.99085 | + | 0.875715i | −0.198595 | + | 0.0290297i | ||||
\(911\) | −8.14760 | −0.269942 | −0.134971 | − | 0.990850i | \(-0.543094\pi\) | ||||
−0.134971 | + | 0.990850i | \(0.543094\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 23.2492i | − | 0.769438i | ||||||
\(914\) | 25.4581 | 0.842080 | ||||||||
\(915\) | 28.2137 | − | 4.12416i | 0.932717 | − | 0.136340i | ||||
\(916\) | −5.41016 | −0.178757 | ||||||||
\(917\) | 6.65377i | 0.219727i | ||||||||
\(918\) | 10.1888i | 0.336281i | ||||||||
\(919\) | 4.38700 | 0.144714 | 0.0723569 | − | 0.997379i | \(-0.476948\pi\) | ||||
0.0723569 | + | 0.997379i | \(0.476948\pi\) | |||||||
\(920\) | −1.90498 | − | 13.0321i | −0.0628053 | − | 0.429657i | ||||
\(921\) | −9.32113 | −0.307142 | ||||||||
\(922\) | − | 48.2601i | − | 1.58936i | ||||||
\(923\) | 40.3506i | 1.32816i | ||||||||
\(924\) | −1.94627 | −0.0640274 | ||||||||
\(925\) | 8.09693 | + | 27.1041i | 0.266225 | + | 0.891178i | ||||
\(926\) | 7.86726 | 0.258534 | ||||||||
\(927\) | − | 12.7148i | − | 0.417609i | ||||||
\(928\) | − | 69.3068i | − | 2.27511i | ||||||
\(929\) | 0.394075 | 0.0129292 | 0.00646459 | − | 0.999979i | \(-0.497942\pi\) | ||||
0.00646459 | + | 0.999979i | \(0.497942\pi\) | |||||||
\(930\) | 4.88279 | + | 33.4036i | 0.160113 | + | 1.09535i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.8534i | 0.519294i | ||||||||
\(933\) | 15.4527i | 0.505898i | ||||||||
\(934\) | −51.4182 | −1.68246 | ||||||||
\(935\) | −4.21584 | + | 0.616252i | −0.137873 | + | 0.0201536i | ||||
\(936\) | 2.85134 | 0.0931990 | ||||||||
\(937\) | 28.6351i | 0.935468i | 0.883869 | + | 0.467734i | \(0.154930\pi\) | ||||
−0.883869 | + | 0.467734i | \(0.845070\pi\) | |||||||
\(938\) | 7.80370i | 0.254800i | ||||||||
\(939\) | 6.91792 | 0.225758 | ||||||||
\(940\) | 7.85005 | − | 1.14749i | 0.256040 | − | 0.0374268i | ||||
\(941\) | −26.6636 | −0.869208 | −0.434604 | − | 0.900622i | \(-0.643112\pi\) | ||||
−0.434604 | + | 0.900622i | \(0.643112\pi\) | |||||||
\(942\) | 28.4793i | 0.927904i | ||||||||
\(943\) | − | 58.5498i | − | 1.90664i | ||||||
\(944\) | 35.2384 | 1.14691 | ||||||||
\(945\) | −0.872730 | − | 5.97043i | −0.0283899 | − | 0.194218i | ||||
\(946\) | −22.5152 | −0.732032 | ||||||||
\(947\) | 18.0730i | 0.587295i | 0.955914 | + | 0.293648i | \(0.0948692\pi\) | ||||
−0.955914 | + | 0.293648i | \(0.905131\pi\) | |||||||
\(948\) | − | 1.47403i | − | 0.0478741i | ||||||
\(949\) | 15.2140 | 0.493869 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.0890408 | −0.00288735 | ||||||||
\(952\) | − | 0.489621i | − | 0.0158687i | ||||||
\(953\) | − | 23.2504i | − | 0.753155i | −0.926385 | − | 0.376577i | \(-0.877101\pi\) | ||
0.926385 | − | 0.376577i | \(-0.122899\pi\) | |||||||
\(954\) | −17.6529 | −0.571534 | ||||||||
\(955\) | 5.27070 | + | 36.0574i | 0.170556 | + | 1.16679i | ||||
\(956\) | −15.2452 | −0.493064 | ||||||||
\(957\) | 28.9663i | 0.936349i | ||||||||
\(958\) | 13.1872i | 0.426059i | ||||||||
\(959\) | −1.83560 | −0.0592747 | ||||||||
\(960\) | 9.62027 | − | 1.40625i | 0.310493 | − | 0.0453864i | ||||
\(961\) | 0.401173 | 0.0129411 | ||||||||
\(962\) | − | 32.0741i | − | 1.03411i | ||||||
\(963\) | − | 5.07053i | − | 0.163395i | ||||||
\(964\) | −7.17581 | −0.231117 | ||||||||
\(965\) | 36.4390 | − | 5.32649i | 1.17301 | − | 0.171466i | ||||
\(966\) | 7.19715 | 0.231565 | ||||||||
\(967\) | 38.9509i | 1.25258i | 0.779591 | + | 0.626289i | \(0.215427\pi\) | ||||
−0.779591 | + | 0.626289i | \(0.784573\pi\) | |||||||
\(968\) | − | 7.54948i | − | 0.242650i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.53205 | + | 24.1631i | 0.113407 | + | 0.775829i | ||||
\(971\) | 11.0320 | 0.354034 | 0.177017 | − | 0.984208i | \(-0.443355\pi\) | ||||
0.177017 | + | 0.984208i | \(0.443355\pi\) | |||||||
\(972\) | − | 12.6818i | − | 0.406768i | ||||||
\(973\) | − | 9.01384i | − | 0.288970i | ||||||
\(974\) | 6.56913 | 0.210488 | ||||||||
\(975\) | −21.3242 | + | 6.37028i | −0.682922 | + | 0.204012i | ||||
\(976\) | −42.2056 | −1.35097 | ||||||||
\(977\) | 26.3934i | 0.844401i | 0.906502 | + | 0.422201i | \(0.138742\pi\) | ||||
−0.906502 | + | 0.422201i | \(0.861258\pi\) | |||||||
\(978\) | 50.1360i | 1.60317i | ||||||||
\(979\) | −4.20532 | −0.134403 | ||||||||
\(980\) | 3.13529 | + | 21.4488i | 0.100153 | + | 0.685157i | ||||
\(981\) | 5.11208 | 0.163216 | ||||||||
\(982\) | − | 59.5202i | − | 1.89937i | ||||||
\(983\) | 47.2339i | 1.50653i | 0.657719 | + | 0.753264i | \(0.271522\pi\) | ||||
−0.657719 | + | 0.753264i | \(0.728478\pi\) | |||||||
\(984\) | −16.0323 | −0.511092 | ||||||||
\(985\) | 22.1762 | − | 3.24162i | 0.706593 | − | 0.103287i | ||||
\(986\) | 18.3501 | 0.584387 | ||||||||
\(987\) | − | 1.72159i | − | 0.0547989i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.7333 | 1.10446 | ||||||||
\(990\) | 7.09744 | − | 1.03747i | 0.225571 | − | 0.0329730i | ||||
\(991\) | −45.6843 | −1.45121 | −0.725604 | − | 0.688112i | \(-0.758440\pi\) | ||||
−0.725604 | + | 0.688112i | \(0.758440\pi\) | |||||||
\(992\) | − | 38.1672i | − | 1.21181i | ||||||
\(993\) | 25.6071i | 0.812618i | ||||||||
\(994\) | −11.6648 | −0.369986 | ||||||||
\(995\) | −4.09590 | − | 28.0205i | −0.129849 | − | 0.888308i | ||||
\(996\) | −24.7308 | −0.783625 | ||||||||
\(997\) | − | 28.9871i | − | 0.918031i | −0.888428 | − | 0.459016i | \(-0.848202\pi\) | ||
0.888428 | − | 0.459016i | \(-0.151798\pi\) | |||||||
\(998\) | 22.0713i | 0.698654i | ||||||||
\(999\) | 31.9648 | 1.01132 |
(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 | 1805.2.b.i.1084.13 | yes | 16 | |
5.2 | odd | 4 | 9025.2.a.cl.1.4 | 16 | |||
5.3 | odd | 4 | 9025.2.a.cl.1.13 | 16 | |||
5.4 | even | 2 | inner | 1805.2.b.i.1084.4 | ✓ | 16 | |
19.18 | odd | 2 | 1805.2.b.j.1084.4 | yes | 16 | ||
95.18 | even | 4 | 9025.2.a.ck.1.4 | 16 | |||
95.37 | even | 4 | 9025.2.a.ck.1.13 | 16 | |||
95.94 | odd | 2 | 1805.2.b.j.1084.13 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.b.i.1084.4 | ✓ | 16 | 5.4 | even | 2 | inner | |
1805.2.b.i.1084.13 | yes | 16 | 1.1 | even | 1 | trivial | |
1805.2.b.j.1084.4 | yes | 16 | 19.18 | odd | 2 | ||
1805.2.b.j.1084.13 | yes | 16 | 95.94 | odd | 2 | ||
9025.2.a.ck.1.4 | 16 | 95.18 | even | 4 | |||
9025.2.a.ck.1.13 | 16 | 95.37 | even | 4 | |||
9025.2.a.cl.1.4 | 16 | 5.2 | odd | 4 | |||
9025.2.a.cl.1.13 | 16 | 5.3 | odd | 4 |