Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(64,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.64");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 37x^{8} + 398x^{6} + 1149x^{4} + 1040x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9}\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.3 | ||
Root | \(-4.40248i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.64 |
Dual form | 105.4.d.b.64.8 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.33774i | − | 1.18007i | −0.807378 | − | 0.590035i | \(-0.799114\pi\) | ||
0.807378 | − | 0.590035i | \(-0.200886\pi\) | |||||||
\(3\) | − | 3.00000i | − | 0.577350i | ||||||
\(4\) | −3.14050 | −0.392563 | ||||||||
\(5\) | 10.1427 | − | 4.70380i | 0.907190 | − | 0.420720i | ||||
\(6\) | −10.0132 | −0.681313 | ||||||||
\(7\) | − | 7.00000i | − | 0.377964i | ||||||
\(8\) | − | 16.2197i | − | 0.716818i | ||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | −15.7000 | − | 33.8537i | −0.496479 | − | 1.07055i | ||||
\(11\) | 18.3258 | 0.502311 | 0.251156 | − | 0.967947i | \(-0.419189\pi\) | ||||
0.251156 | + | 0.967947i | \(0.419189\pi\) | |||||||
\(12\) | 9.42151i | 0.226646i | ||||||||
\(13\) | 10.1457i | 0.216454i | 0.994126 | + | 0.108227i | \(0.0345174\pi\) | ||||
−0.994126 | + | 0.108227i | \(0.965483\pi\) | |||||||
\(14\) | −23.3642 | −0.446024 | ||||||||
\(15\) | −14.1114 | − | 30.4281i | −0.242903 | − | 0.523767i | ||||
\(16\) | −79.2613 | −1.23846 | ||||||||
\(17\) | 24.6984i | 0.352367i | 0.984357 | + | 0.176183i | \(0.0563752\pi\) | ||||
−0.984357 | + | 0.176183i | \(0.943625\pi\) | |||||||
\(18\) | 30.0397i | 0.393356i | ||||||||
\(19\) | −77.4282 | −0.934907 | −0.467454 | − | 0.884018i | \(-0.654829\pi\) | ||||
−0.467454 | + | 0.884018i | \(0.654829\pi\) | |||||||
\(20\) | −31.8532 | + | 14.7723i | −0.356129 | + | 0.165159i | ||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | − | 61.1666i | − | 0.592762i | ||||||
\(23\) | 149.411i | 1.35454i | 0.735735 | + | 0.677270i | \(0.236837\pi\) | ||||
−0.735735 | + | 0.677270i | \(0.763163\pi\) | |||||||
\(24\) | −48.6592 | −0.413855 | ||||||||
\(25\) | 80.7486 | − | 95.4184i | 0.645989 | − | 0.763347i | ||||
\(26\) | 33.8636 | 0.255431 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 21.9835i | 0.148375i | ||||||||
\(29\) | 10.2984 | 0.0659434 | 0.0329717 | − | 0.999456i | \(-0.489503\pi\) | ||||
0.0329717 | + | 0.999456i | \(0.489503\pi\) | |||||||
\(30\) | −101.561 | + | 47.1001i | −0.618081 | + | 0.286642i | ||||
\(31\) | 124.423 | 0.720872 | 0.360436 | − | 0.932784i | \(-0.382628\pi\) | ||||
0.360436 | + | 0.932784i | \(0.382628\pi\) | |||||||
\(32\) | 134.796i | 0.744647i | ||||||||
\(33\) | − | 54.9773i | − | 0.290010i | ||||||
\(34\) | 82.4367 | 0.415817 | ||||||||
\(35\) | −32.9266 | − | 70.9989i | −0.159017 | − | 0.342886i | ||||
\(36\) | 28.2645 | 0.130854 | ||||||||
\(37\) | − | 215.905i | − | 0.959312i | −0.877457 | − | 0.479656i | \(-0.840761\pi\) | ||
0.877457 | − | 0.479656i | \(-0.159239\pi\) | |||||||
\(38\) | 258.435i | 1.10326i | ||||||||
\(39\) | 30.4370 | 0.124970 | ||||||||
\(40\) | −76.2943 | − | 164.512i | −0.301580 | − | 0.650290i | ||||
\(41\) | 495.056 | 1.88573 | 0.942863 | − | 0.333181i | \(-0.108122\pi\) | ||||
0.942863 | + | 0.333181i | \(0.108122\pi\) | |||||||
\(42\) | 70.0925i | 0.257512i | ||||||||
\(43\) | − | 220.606i | − | 0.782375i | −0.920311 | − | 0.391188i | \(-0.872064\pi\) | ||
0.920311 | − | 0.391188i | \(-0.127936\pi\) | |||||||
\(44\) | −57.5521 | −0.197189 | ||||||||
\(45\) | −91.2843 | + | 42.3342i | −0.302397 | + | 0.140240i | ||||
\(46\) | 498.696 | 1.59845 | ||||||||
\(47\) | − | 212.957i | − | 0.660915i | −0.943821 | − | 0.330457i | \(-0.892797\pi\) | ||
0.943821 | − | 0.330457i | \(-0.107203\pi\) | |||||||
\(48\) | 237.784i | 0.715024i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | −318.482 | − | 269.518i | −0.900802 | − | 0.762311i | ||||
\(51\) | 74.0951 | 0.203439 | ||||||||
\(52\) | − | 31.8625i | − | 0.0849719i | ||||||
\(53\) | 532.455i | 1.37997i | 0.723825 | + | 0.689984i | \(0.242382\pi\) | ||||
−0.723825 | + | 0.689984i | \(0.757618\pi\) | |||||||
\(54\) | 90.1190 | 0.227104 | ||||||||
\(55\) | 185.873 | − | 86.2007i | 0.455692 | − | 0.211333i | ||||
\(56\) | −113.538 | −0.270932 | ||||||||
\(57\) | 232.284i | 0.539769i | ||||||||
\(58\) | − | 34.3732i | − | 0.0778177i | ||||||
\(59\) | 324.143 | 0.715252 | 0.357626 | − | 0.933865i | \(-0.383586\pi\) | ||||
0.357626 | + | 0.933865i | \(0.383586\pi\) | |||||||
\(60\) | 44.3169 | + | 95.5595i | 0.0953547 | + | 0.205611i | ||||
\(61\) | 653.967 | 1.37265 | 0.686327 | − | 0.727293i | \(-0.259222\pi\) | ||||
0.686327 | + | 0.727293i | \(0.259222\pi\) | |||||||
\(62\) | − | 415.292i | − | 0.850679i | ||||||
\(63\) | 63.0000i | 0.125988i | ||||||||
\(64\) | −184.178 | −0.359722 | ||||||||
\(65\) | 47.7232 | + | 102.905i | 0.0910667 | + | 0.196365i | ||||
\(66\) | −183.500 | −0.342231 | ||||||||
\(67\) | 819.077i | 1.49353i | 0.665091 | + | 0.746763i | \(0.268393\pi\) | ||||
−0.665091 | + | 0.746763i | \(0.731607\pi\) | |||||||
\(68\) | − | 77.5653i | − | 0.138326i | ||||||
\(69\) | 448.234 | 0.782044 | ||||||||
\(70\) | −236.976 | + | 109.900i | −0.404629 | + | 0.187651i | ||||
\(71\) | −466.940 | −0.780501 | −0.390250 | − | 0.920709i | \(-0.627612\pi\) | ||||
−0.390250 | + | 0.920709i | \(0.627612\pi\) | |||||||
\(72\) | 145.978i | 0.238939i | ||||||||
\(73\) | 173.066i | 0.277478i | 0.990329 | + | 0.138739i | \(0.0443048\pi\) | ||||
−0.990329 | + | 0.138739i | \(0.955695\pi\) | |||||||
\(74\) | −720.634 | −1.13205 | ||||||||
\(75\) | −286.255 | − | 242.246i | −0.440719 | − | 0.372962i | ||||
\(76\) | 243.163 | 0.367010 | ||||||||
\(77\) | − | 128.280i | − | 0.189856i | ||||||
\(78\) | − | 101.591i | − | 0.147473i | ||||||
\(79\) | −810.186 | −1.15384 | −0.576918 | − | 0.816802i | \(-0.695745\pi\) | ||||
−0.576918 | + | 0.816802i | \(0.695745\pi\) | |||||||
\(80\) | −803.923 | + | 372.829i | −1.12352 | + | 0.521044i | ||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | − | 1652.37i | − | 2.22529i | ||||||
\(83\) | 12.3208i | 0.0162937i | 0.999967 | + | 0.00814687i | \(0.00259326\pi\) | ||||
−0.999967 | + | 0.00814687i | \(0.997407\pi\) | |||||||
\(84\) | 65.9506 | 0.0856642 | ||||||||
\(85\) | 116.176 | + | 250.508i | 0.148248 | + | 0.319664i | ||||
\(86\) | −736.326 | −0.923257 | ||||||||
\(87\) | − | 30.8951i | − | 0.0380724i | ||||||
\(88\) | − | 297.239i | − | 0.360066i | ||||||
\(89\) | 33.8297 | 0.0402914 | 0.0201457 | − | 0.999797i | \(-0.493587\pi\) | ||||
0.0201457 | + | 0.999797i | \(0.493587\pi\) | |||||||
\(90\) | 141.300 | + | 304.683i | 0.165493 | + | 0.356849i | ||||
\(91\) | 71.0198 | 0.0818120 | ||||||||
\(92\) | − | 469.227i | − | 0.531742i | ||||||
\(93\) | − | 373.269i | − | 0.416196i | ||||||
\(94\) | −710.795 | −0.779925 | ||||||||
\(95\) | −785.330 | + | 364.206i | −0.848139 | + | 0.393335i | ||||
\(96\) | 404.387 | 0.429922 | ||||||||
\(97\) | 810.761i | 0.848663i | 0.905507 | + | 0.424331i | \(0.139491\pi\) | ||||
−0.905507 | + | 0.424331i | \(0.860509\pi\) | |||||||
\(98\) | 163.549i | 0.168581i | ||||||||
\(99\) | −164.932 | −0.167437 | ||||||||
\(100\) | −253.591 | + | 299.662i | −0.253591 | + | 0.299662i | ||||
\(101\) | 1646.84 | 1.62245 | 0.811223 | − | 0.584737i | \(-0.198802\pi\) | ||||
0.811223 | + | 0.584737i | \(0.198802\pi\) | |||||||
\(102\) | − | 247.310i | − | 0.240072i | ||||||
\(103\) | − | 921.360i | − | 0.881401i | −0.897654 | − | 0.440700i | \(-0.854730\pi\) | ||
0.897654 | − | 0.440700i | \(-0.145270\pi\) | |||||||
\(104\) | 164.560 | 0.155158 | ||||||||
\(105\) | −212.997 | + | 98.7797i | −0.197965 | + | 0.0918087i | ||||
\(106\) | 1777.19 | 1.62846 | ||||||||
\(107\) | 1060.84i | 0.958464i | 0.877688 | + | 0.479232i | \(0.159085\pi\) | ||||
−0.877688 | + | 0.479232i | \(0.840915\pi\) | |||||||
\(108\) | − | 84.7936i | − | 0.0755488i | ||||||
\(109\) | −1533.03 | −1.34713 | −0.673566 | − | 0.739127i | \(-0.735238\pi\) | ||||
−0.673566 | + | 0.739127i | \(0.735238\pi\) | |||||||
\(110\) | −287.715 | − | 620.394i | −0.249387 | − | 0.537748i | ||||
\(111\) | −647.715 | −0.553859 | ||||||||
\(112\) | 554.829i | 0.468093i | ||||||||
\(113\) | − | 2072.67i | − | 1.72549i | −0.505637 | − | 0.862746i | \(-0.668743\pi\) | ||
0.505637 | − | 0.862746i | \(-0.331257\pi\) | |||||||
\(114\) | 775.305 | 0.636965 | ||||||||
\(115\) | 702.801 | + | 1515.43i | 0.569883 | + | 1.22883i | ||||
\(116\) | −32.3420 | −0.0258869 | ||||||||
\(117\) | − | 91.3111i | − | 0.0721514i | ||||||
\(118\) | − | 1081.91i | − | 0.844046i | ||||||
\(119\) | 172.889 | 0.133182 | ||||||||
\(120\) | −493.535 | + | 228.883i | −0.375445 | + | 0.174117i | ||||
\(121\) | −995.166 | −0.747683 | ||||||||
\(122\) | − | 2182.77i | − | 1.61983i | ||||||
\(123\) | − | 1485.17i | − | 1.08872i | ||||||
\(124\) | −390.751 | −0.282988 | ||||||||
\(125\) | 370.180 | − | 1347.62i | 0.264879 | − | 0.964282i | ||||
\(126\) | 210.278 | 0.148675 | ||||||||
\(127\) | 365.145i | 0.255129i | 0.991830 | + | 0.127565i | \(0.0407160\pi\) | ||||
−0.991830 | + | 0.127565i | \(0.959284\pi\) | |||||||
\(128\) | 1693.10i | 1.16914i | ||||||||
\(129\) | −661.819 | −0.451705 | ||||||||
\(130\) | 343.469 | − | 159.288i | 0.231725 | − | 0.107465i | ||||
\(131\) | 1300.83 | 0.867586 | 0.433793 | − | 0.901013i | \(-0.357175\pi\) | ||||
0.433793 | + | 0.901013i | \(0.357175\pi\) | |||||||
\(132\) | 172.656i | 0.113847i | ||||||||
\(133\) | 541.997i | 0.353362i | ||||||||
\(134\) | 2733.87 | 1.76246 | ||||||||
\(135\) | 127.003 | + | 273.853i | 0.0809677 | + | 0.174589i | ||||
\(136\) | 400.601 | 0.252583 | ||||||||
\(137\) | 2578.40i | 1.60794i | 0.594670 | + | 0.803970i | \(0.297283\pi\) | ||||
−0.594670 | + | 0.803970i | \(0.702717\pi\) | |||||||
\(138\) | − | 1496.09i | − | 0.922866i | ||||||
\(139\) | −3065.49 | −1.87059 | −0.935294 | − | 0.353872i | \(-0.884865\pi\) | ||||
−0.935294 | + | 0.353872i | \(0.884865\pi\) | |||||||
\(140\) | 103.406 | + | 222.972i | 0.0624243 | + | 0.134604i | ||||
\(141\) | −638.871 | −0.381579 | ||||||||
\(142\) | 1558.52i | 0.921044i | ||||||||
\(143\) | 185.927i | 0.108727i | ||||||||
\(144\) | 713.351 | 0.412819 | ||||||||
\(145\) | 104.453 | − | 48.4414i | 0.0598232 | − | 0.0277437i | ||||
\(146\) | 577.650 | 0.327443 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | 678.050i | 0.376590i | ||||||||
\(149\) | 2704.34 | 1.48690 | 0.743449 | − | 0.668793i | \(-0.233189\pi\) | ||||
0.743449 | + | 0.668793i | \(0.233189\pi\) | |||||||
\(150\) | −808.553 | + | 955.445i | −0.440121 | + | 0.520078i | ||||
\(151\) | 388.869 | 0.209574 | 0.104787 | − | 0.994495i | \(-0.466584\pi\) | ||||
0.104787 | + | 0.994495i | \(0.466584\pi\) | |||||||
\(152\) | 1255.86i | 0.670158i | ||||||||
\(153\) | − | 222.285i | − | 0.117456i | ||||||
\(154\) | −428.166 | −0.224043 | ||||||||
\(155\) | 1261.98 | − | 585.261i | 0.653968 | − | 0.303286i | ||||
\(156\) | −95.5876 | −0.0490586 | ||||||||
\(157\) | 2885.78i | 1.46694i | 0.679720 | + | 0.733472i | \(0.262101\pi\) | ||||
−0.679720 | + | 0.733472i | \(0.737899\pi\) | |||||||
\(158\) | 2704.19i | 1.36161i | ||||||||
\(159\) | 1597.36 | 0.796725 | ||||||||
\(160\) | 634.051 | + | 1367.19i | 0.313288 | + | 0.675537i | ||||
\(161\) | 1045.88 | 0.511968 | ||||||||
\(162\) | − | 270.357i | − | 0.131119i | ||||||
\(163\) | 571.954i | 0.274840i | 0.990513 | + | 0.137420i | \(0.0438809\pi\) | ||||
−0.990513 | + | 0.137420i | \(0.956119\pi\) | |||||||
\(164\) | −1554.73 | −0.740266 | ||||||||
\(165\) | −258.602 | − | 557.618i | −0.122013 | − | 0.263094i | ||||
\(166\) | 41.1235 | 0.0192277 | ||||||||
\(167\) | − | 2423.96i | − | 1.12319i | −0.827414 | − | 0.561593i | \(-0.810189\pi\) | ||
0.827414 | − | 0.561593i | \(-0.189811\pi\) | |||||||
\(168\) | 340.614i | 0.156422i | ||||||||
\(169\) | 2094.07 | 0.953148 | ||||||||
\(170\) | 836.131 | − | 387.766i | 0.377225 | − | 0.174943i | ||||
\(171\) | 696.853 | 0.311636 | ||||||||
\(172\) | 692.815i | 0.307131i | ||||||||
\(173\) | 626.440i | 0.275303i | 0.990481 | + | 0.137651i | \(0.0439554\pi\) | ||||
−0.990481 | + | 0.137651i | \(0.956045\pi\) | |||||||
\(174\) | −103.120 | −0.0449281 | ||||||||
\(175\) | −667.929 | − | 565.240i | −0.288518 | − | 0.244161i | ||||
\(176\) | −1452.52 | −0.622091 | ||||||||
\(177\) | − | 972.430i | − | 0.412951i | ||||||
\(178\) | − | 112.915i | − | 0.0475467i | ||||||
\(179\) | −2322.11 | −0.969623 | −0.484812 | − | 0.874619i | \(-0.661112\pi\) | ||||
−0.484812 | + | 0.874619i | \(0.661112\pi\) | |||||||
\(180\) | 286.679 | − | 132.951i | 0.118710 | − | 0.0550531i | ||||
\(181\) | −4664.94 | −1.91570 | −0.957852 | − | 0.287263i | \(-0.907255\pi\) | ||||
−0.957852 | + | 0.287263i | \(0.907255\pi\) | |||||||
\(182\) | − | 237.045i | − | 0.0965438i | ||||||
\(183\) | − | 1961.90i | − | 0.792502i | ||||||
\(184\) | 2423.41 | 0.970958 | ||||||||
\(185\) | −1015.57 | − | 2189.86i | −0.403602 | − | 0.870279i | ||||
\(186\) | −1245.87 | −0.491140 | ||||||||
\(187\) | 452.617i | 0.176998i | ||||||||
\(188\) | 668.792i | 0.259451i | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 1215.63 | + | 2621.23i | 0.464162 | + | 1.00086i | ||||
\(191\) | −3730.26 | −1.41315 | −0.706575 | − | 0.707638i | \(-0.749761\pi\) | ||||
−0.706575 | + | 0.707638i | \(0.749761\pi\) | |||||||
\(192\) | 552.533i | 0.207686i | ||||||||
\(193\) | − | 2585.26i | − | 0.964202i | −0.876116 | − | 0.482101i | \(-0.839874\pi\) | ||
0.876116 | − | 0.482101i | \(-0.160126\pi\) | |||||||
\(194\) | 2706.11 | 1.00148 | ||||||||
\(195\) | 308.714 | − | 143.170i | 0.113372 | − | 0.0525774i | ||||
\(196\) | 153.885 | 0.0560804 | ||||||||
\(197\) | − | 2405.91i | − | 0.870122i | −0.900401 | − | 0.435061i | \(-0.856727\pi\) | ||
0.900401 | − | 0.435061i | \(-0.143273\pi\) | |||||||
\(198\) | 550.500i | 0.197587i | ||||||||
\(199\) | −1192.35 | −0.424740 | −0.212370 | − | 0.977189i | \(-0.568118\pi\) | ||||
−0.212370 | + | 0.977189i | \(0.568118\pi\) | |||||||
\(200\) | −1547.66 | − | 1309.72i | −0.547181 | − | 0.463056i | ||||
\(201\) | 2457.23 | 0.862287 | ||||||||
\(202\) | − | 5496.74i | − | 1.91460i | ||||||
\(203\) | − | 72.0885i | − | 0.0249243i | ||||||
\(204\) | −232.696 | −0.0798626 | ||||||||
\(205\) | 5021.20 | − | 2328.64i | 1.71071 | − | 0.793364i | ||||
\(206\) | −3075.26 | −1.04011 | ||||||||
\(207\) | − | 1344.70i | − | 0.451513i | ||||||
\(208\) | − | 804.160i | − | 0.268069i | ||||||
\(209\) | −1418.93 | −0.469615 | ||||||||
\(210\) | 329.701 | + | 710.927i | 0.108341 | + | 0.233613i | ||||
\(211\) | −764.904 | −0.249565 | −0.124782 | − | 0.992184i | \(-0.539823\pi\) | ||||
−0.124782 | + | 0.992184i | \(0.539823\pi\) | |||||||
\(212\) | − | 1672.18i | − | 0.541724i | ||||||
\(213\) | 1400.82i | 0.450622i | ||||||||
\(214\) | 3540.82 | 1.13105 | ||||||||
\(215\) | −1037.69 | − | 2237.54i | −0.329161 | − | 0.709763i | ||||
\(216\) | 437.933 | 0.137952 | ||||||||
\(217\) | − | 870.961i | − | 0.272464i | ||||||
\(218\) | 5116.84i | 1.58971i | ||||||||
\(219\) | 519.199 | 0.160202 | ||||||||
\(220\) | −583.734 | + | 270.713i | −0.178888 | + | 0.0829614i | ||||
\(221\) | −250.582 | −0.0762713 | ||||||||
\(222\) | 2161.90i | 0.653592i | ||||||||
\(223\) | 1585.18i | 0.476016i | 0.971263 | + | 0.238008i | \(0.0764945\pi\) | ||||
−0.971263 | + | 0.238008i | \(0.923506\pi\) | |||||||
\(224\) | 943.569 | 0.281450 | ||||||||
\(225\) | −726.737 | + | 858.765i | −0.215330 | + | 0.254449i | ||||
\(226\) | −6918.04 | −2.03620 | ||||||||
\(227\) | − | 2363.07i | − | 0.690936i | −0.938431 | − | 0.345468i | \(-0.887720\pi\) | ||
0.938431 | − | 0.345468i | \(-0.112280\pi\) | |||||||
\(228\) | − | 729.490i | − | 0.211893i | ||||||
\(229\) | −1626.44 | −0.469337 | −0.234669 | − | 0.972075i | \(-0.575401\pi\) | ||||
−0.234669 | + | 0.972075i | \(0.575401\pi\) | |||||||
\(230\) | 5058.12 | − | 2345.77i | 1.45010 | − | 0.672501i | ||||
\(231\) | −384.841 | −0.109613 | ||||||||
\(232\) | − | 167.037i | − | 0.0472694i | ||||||
\(233\) | 1720.34i | 0.483705i | 0.970313 | + | 0.241853i | \(0.0777551\pi\) | ||||
−0.970313 | + | 0.241853i | \(0.922245\pi\) | |||||||
\(234\) | −304.773 | −0.0851437 | ||||||||
\(235\) | −1001.71 | − | 2159.96i | −0.278060 | − | 0.599575i | ||||
\(236\) | −1017.97 | −0.280781 | ||||||||
\(237\) | 2430.56i | 0.666168i | ||||||||
\(238\) | − | 577.057i | − | 0.157164i | ||||||
\(239\) | −7217.75 | −1.95346 | −0.976732 | − | 0.214466i | \(-0.931199\pi\) | ||||
−0.976732 | + | 0.214466i | \(0.931199\pi\) | |||||||
\(240\) | 1118.49 | + | 2411.77i | 0.300825 | + | 0.648663i | ||||
\(241\) | 5094.78 | 1.36176 | 0.680879 | − | 0.732396i | \(-0.261598\pi\) | ||||
0.680879 | + | 0.732396i | \(0.261598\pi\) | |||||||
\(242\) | 3321.61i | 0.882318i | ||||||||
\(243\) | − | 243.000i | − | 0.0641500i | ||||||
\(244\) | −2053.79 | −0.538853 | ||||||||
\(245\) | −496.992 | + | 230.486i | −0.129599 | + | 0.0601029i | ||||
\(246\) | −4957.10 | −1.28477 | ||||||||
\(247\) | − | 785.561i | − | 0.202365i | ||||||
\(248\) | − | 2018.11i | − | 0.516734i | ||||||
\(249\) | 36.9623 | 0.00940720 | ||||||||
\(250\) | −4498.02 | − | 1235.56i | −1.13792 | − | 0.312575i | ||||
\(251\) | −4346.51 | −1.09303 | −0.546513 | − | 0.837451i | \(-0.684045\pi\) | ||||
−0.546513 | + | 0.837451i | \(0.684045\pi\) | |||||||
\(252\) | − | 197.852i | − | 0.0494583i | ||||||
\(253\) | 2738.08i | 0.680401i | ||||||||
\(254\) | 1218.76 | 0.301070 | ||||||||
\(255\) | 751.524 | − | 348.528i | 0.184558 | − | 0.0855910i | ||||
\(256\) | 4177.71 | 1.01995 | ||||||||
\(257\) | 1428.13i | 0.346632i | 0.984866 | + | 0.173316i | \(0.0554482\pi\) | ||||
−0.984866 | + | 0.173316i | \(0.944552\pi\) | |||||||
\(258\) | 2208.98i | 0.533043i | ||||||||
\(259\) | −1511.33 | −0.362586 | ||||||||
\(260\) | −149.875 | − | 323.172i | −0.0357494 | − | 0.0770857i | ||||
\(261\) | −92.6853 | −0.0219811 | ||||||||
\(262\) | − | 4341.82i | − | 1.02381i | ||||||
\(263\) | 3447.78i | 0.808362i | 0.914679 | + | 0.404181i | \(0.132443\pi\) | ||||
−0.914679 | + | 0.404181i | \(0.867557\pi\) | |||||||
\(264\) | −891.717 | −0.207884 | ||||||||
\(265\) | 2504.56 | + | 5400.53i | 0.580581 | + | 1.25189i | ||||
\(266\) | 1809.05 | 0.416991 | ||||||||
\(267\) | − | 101.489i | − | 0.0232623i | ||||||
\(268\) | − | 2572.31i | − | 0.586303i | ||||||
\(269\) | 22.3975 | 0.00507657 | 0.00253829 | − | 0.999997i | \(-0.499192\pi\) | ||||
0.00253829 | + | 0.999997i | \(0.499192\pi\) | |||||||
\(270\) | 914.049 | − | 423.901i | 0.206027 | − | 0.0955475i | ||||
\(271\) | −1557.33 | −0.349080 | −0.174540 | − | 0.984650i | \(-0.555844\pi\) | ||||
−0.174540 | + | 0.984650i | \(0.555844\pi\) | |||||||
\(272\) | − | 1957.62i | − | 0.436391i | ||||||
\(273\) | − | 213.059i | − | 0.0472342i | ||||||
\(274\) | 8606.03 | 1.89748 | ||||||||
\(275\) | 1479.78 | − | 1748.61i | 0.324487 | − | 0.383438i | ||||
\(276\) | −1407.68 | −0.307001 | ||||||||
\(277\) | 3734.92i | 0.810142i | 0.914285 | + | 0.405071i | \(0.132753\pi\) | ||||
−0.914285 | + | 0.405071i | \(0.867247\pi\) | |||||||
\(278\) | 10231.8i | 2.20742i | ||||||||
\(279\) | −1119.81 | −0.240291 | ||||||||
\(280\) | −1151.58 | + | 534.060i | −0.245787 | + | 0.113986i | ||||
\(281\) | −2422.37 | −0.514258 | −0.257129 | − | 0.966377i | \(-0.582777\pi\) | ||||
−0.257129 | + | 0.966377i | \(0.582777\pi\) | |||||||
\(282\) | 2132.39i | 0.450290i | ||||||||
\(283\) | 283.232i | 0.0594926i | 0.999557 | + | 0.0297463i | \(0.00946994\pi\) | ||||
−0.999557 | + | 0.0297463i | \(0.990530\pi\) | |||||||
\(284\) | 1466.43 | 0.306396 | ||||||||
\(285\) | 1092.62 | + | 2355.99i | 0.227092 | + | 0.489673i | ||||
\(286\) | 620.577 | 0.128306 | ||||||||
\(287\) | − | 3465.39i | − | 0.712737i | ||||||
\(288\) | − | 1213.16i | − | 0.248216i | ||||||
\(289\) | 4302.99 | 0.875838 | ||||||||
\(290\) | −161.685 | − | 348.637i | −0.0327395 | − | 0.0705955i | ||||
\(291\) | 2432.28 | 0.489976 | ||||||||
\(292\) | − | 543.515i | − | 0.108927i | ||||||
\(293\) | 8481.49i | 1.69111i | 0.533892 | + | 0.845553i | \(0.320729\pi\) | ||||
−0.533892 | + | 0.845553i | \(0.679271\pi\) | |||||||
\(294\) | 490.648 | 0.0973305 | ||||||||
\(295\) | 3287.69 | − | 1524.70i | 0.648870 | − | 0.300921i | ||||
\(296\) | −3501.92 | −0.687652 | ||||||||
\(297\) | 494.796i | 0.0966699i | ||||||||
\(298\) | − | 9026.37i | − | 1.75464i | ||||||
\(299\) | −1515.88 | −0.293196 | ||||||||
\(300\) | 898.985 | + | 760.773i | 0.173010 | + | 0.146411i | ||||
\(301\) | −1544.24 | −0.295710 | ||||||||
\(302\) | − | 1297.94i | − | 0.247312i | ||||||
\(303\) | − | 4940.53i | − | 0.936720i | ||||||
\(304\) | 6137.05 | 1.15784 | ||||||||
\(305\) | 6632.99 | − | 3076.13i | 1.24526 | − | 0.577504i | ||||
\(306\) | −741.931 | −0.138606 | ||||||||
\(307\) | 2005.50i | 0.372834i | 0.982471 | + | 0.186417i | \(0.0596875\pi\) | ||||
−0.982471 | + | 0.186417i | \(0.940312\pi\) | |||||||
\(308\) | 402.865i | 0.0745304i | ||||||||
\(309\) | −2764.08 | −0.508877 | ||||||||
\(310\) | −1953.45 | − | 4212.18i | −0.357898 | − | 0.771727i | ||||
\(311\) | 10021.4 | 1.82720 | 0.913602 | − | 0.406609i | \(-0.133289\pi\) | ||||
0.913602 | + | 0.406609i | \(0.133289\pi\) | |||||||
\(312\) | − | 493.681i | − | 0.0895807i | ||||||
\(313\) | − | 631.178i | − | 0.113982i | −0.998375 | − | 0.0569908i | \(-0.981849\pi\) | ||
0.998375 | − | 0.0569908i | \(-0.0181506\pi\) | |||||||
\(314\) | 9631.97 | 1.73109 | ||||||||
\(315\) | 296.339 | + | 638.990i | 0.0530058 | + | 0.114295i | ||||
\(316\) | 2544.39 | 0.452953 | ||||||||
\(317\) | 1202.71i | 0.213095i | 0.994308 | + | 0.106547i | \(0.0339796\pi\) | ||||
−0.994308 | + | 0.106547i | \(0.966020\pi\) | |||||||
\(318\) | − | 5331.58i | − | 0.940190i | ||||||
\(319\) | 188.725 | 0.0331241 | ||||||||
\(320\) | −1868.06 | + | 866.335i | −0.326336 | + | 0.151342i | ||||
\(321\) | 3182.53 | 0.553369 | ||||||||
\(322\) | − | 3490.87i | − | 0.604158i | ||||||
\(323\) | − | 1912.35i | − | 0.329430i | ||||||
\(324\) | −254.381 | −0.0436181 | ||||||||
\(325\) | 968.084 | + | 819.249i | 0.165230 | + | 0.139827i | ||||
\(326\) | 1909.03 | 0.324330 | ||||||||
\(327\) | 4599.08i | 0.777767i | ||||||||
\(328\) | − | 8029.68i | − | 1.35172i | ||||||
\(329\) | −1490.70 | −0.249802 | ||||||||
\(330\) | −1861.18 | + | 863.146i | −0.310469 | + | 0.143984i | ||||
\(331\) | −9297.55 | −1.54393 | −0.771963 | − | 0.635667i | \(-0.780725\pi\) | ||||
−0.771963 | + | 0.635667i | \(0.780725\pi\) | |||||||
\(332\) | − | 38.6934i | − | 0.00639632i | ||||||
\(333\) | 1943.14i | 0.319771i | ||||||||
\(334\) | −8090.56 | −1.32544 | ||||||||
\(335\) | 3852.77 | + | 8307.65i | 0.628357 | + | 1.35491i | ||||
\(336\) | 1664.49 | 0.270254 | ||||||||
\(337\) | − | 507.727i | − | 0.0820702i | −0.999158 | − | 0.0410351i | \(-0.986934\pi\) | ||
0.999158 | − | 0.0410351i | \(-0.0130656\pi\) | |||||||
\(338\) | − | 6989.44i | − | 1.12478i | ||||||
\(339\) | −6218.02 | −0.996213 | ||||||||
\(340\) | −364.852 | − | 786.722i | −0.0581966 | − | 0.125488i | ||||
\(341\) | 2280.15 | 0.362102 | ||||||||
\(342\) | − | 2325.92i | − | 0.367752i | ||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | −3578.17 | −0.560820 | ||||||||
\(345\) | 4546.30 | − | 2108.40i | 0.709463 | − | 0.329022i | ||||
\(346\) | 2090.89 | 0.324876 | ||||||||
\(347\) | − | 6860.59i | − | 1.06137i | −0.847569 | − | 0.530685i | \(-0.821935\pi\) | ||
0.847569 | − | 0.530685i | \(-0.178065\pi\) | |||||||
\(348\) | 97.0261i | 0.0149458i | ||||||||
\(349\) | 9236.45 | 1.41666 | 0.708332 | − | 0.705879i | \(-0.249448\pi\) | ||||
0.708332 | + | 0.705879i | \(0.249448\pi\) | |||||||
\(350\) | −1886.62 | + | 2229.37i | −0.288127 | + | 0.340471i | ||||
\(351\) | −273.933 | −0.0416566 | ||||||||
\(352\) | 2470.23i | 0.374045i | ||||||||
\(353\) | 9419.54i | 1.42026i | 0.704071 | + | 0.710129i | \(0.251364\pi\) | ||||
−0.704071 | + | 0.710129i | \(0.748636\pi\) | |||||||
\(354\) | −3245.72 | −0.487310 | ||||||||
\(355\) | −4736.03 | + | 2196.39i | −0.708063 | + | 0.328373i | ||||
\(356\) | −106.242 | −0.0158169 | ||||||||
\(357\) | − | 518.666i | − | 0.0768927i | ||||||
\(358\) | 7750.59i | 1.14422i | ||||||||
\(359\) | 2890.82 | 0.424990 | 0.212495 | − | 0.977162i | \(-0.431841\pi\) | ||||
0.212495 | + | 0.977162i | \(0.431841\pi\) | |||||||
\(360\) | 686.649 | + | 1480.61i | 0.100527 | + | 0.216763i | ||||
\(361\) | −863.879 | −0.125948 | ||||||||
\(362\) | 15570.4i | 2.26066i | ||||||||
\(363\) | 2985.50i | 0.431675i | ||||||||
\(364\) | −223.038 | −0.0321164 | ||||||||
\(365\) | 814.068 | + | 1755.36i | 0.116740 | + | 0.251725i | ||||
\(366\) | −6548.31 | −0.935207 | ||||||||
\(367\) | 1570.51i | 0.223379i | 0.993743 | + | 0.111690i | \(0.0356262\pi\) | ||||
−0.993743 | + | 0.111690i | \(0.964374\pi\) | |||||||
\(368\) | − | 11842.5i | − | 1.67754i | ||||||
\(369\) | −4455.50 | −0.628575 | ||||||||
\(370\) | −7309.17 | + | 3389.72i | −1.02699 | + | 0.476278i | ||||
\(371\) | 3727.18 | 0.521579 | ||||||||
\(372\) | 1172.25i | 0.163383i | ||||||||
\(373\) | − | 8713.38i | − | 1.20955i | −0.796397 | − | 0.604774i | \(-0.793263\pi\) | ||
0.796397 | − | 0.604774i | \(-0.206737\pi\) | |||||||
\(374\) | 1510.72 | 0.208870 | ||||||||
\(375\) | −4042.87 | − | 1110.54i | −0.556728 | − | 0.152928i | ||||
\(376\) | −3454.11 | −0.473755 | ||||||||
\(377\) | 104.484i | 0.0142737i | ||||||||
\(378\) | − | 630.833i | − | 0.0858374i | ||||||
\(379\) | 5779.65 | 0.783326 | 0.391663 | − | 0.920109i | \(-0.371900\pi\) | ||||
0.391663 | + | 0.920109i | \(0.371900\pi\) | |||||||
\(380\) | 2466.33 | − | 1143.79i | 0.332948 | − | 0.154409i | ||||
\(381\) | 1095.44 | 0.147299 | ||||||||
\(382\) | 12450.6i | 1.66762i | ||||||||
\(383\) | − | 12340.2i | − | 1.64636i | −0.567780 | − | 0.823181i | \(-0.692197\pi\) | ||
0.567780 | − | 0.823181i | \(-0.307803\pi\) | |||||||
\(384\) | 5079.30 | 0.675006 | ||||||||
\(385\) | −603.405 | − | 1301.11i | −0.0798762 | − | 0.172235i | ||||
\(386\) | −8628.92 | −1.13783 | ||||||||
\(387\) | 1985.46i | 0.260792i | ||||||||
\(388\) | − | 2546.20i | − | 0.333153i | ||||||
\(389\) | −7948.44 | −1.03600 | −0.517998 | − | 0.855382i | \(-0.673322\pi\) | ||||
−0.517998 | + | 0.855382i | \(0.673322\pi\) | |||||||
\(390\) | −477.863 | − | 1030.41i | −0.0620450 | − | 0.133786i | ||||
\(391\) | −3690.22 | −0.477295 | ||||||||
\(392\) | 794.767i | 0.102403i | ||||||||
\(393\) | − | 3902.48i | − | 0.500901i | ||||||
\(394\) | −8030.30 | −1.02680 | ||||||||
\(395\) | −8217.47 | + | 3810.95i | −1.04675 | + | 0.485442i | ||||
\(396\) | 517.969 | 0.0657296 | ||||||||
\(397\) | 5363.64i | 0.678069i | 0.940774 | + | 0.339034i | \(0.110100\pi\) | ||||
−0.940774 | + | 0.339034i | \(0.889900\pi\) | |||||||
\(398\) | 3979.75i | 0.501223i | ||||||||
\(399\) | 1625.99 | 0.204014 | ||||||||
\(400\) | −6400.23 | + | 7562.98i | −0.800029 | + | 0.945373i | ||||
\(401\) | 6057.13 | 0.754310 | 0.377155 | − | 0.926150i | \(-0.376902\pi\) | ||||
0.377155 | + | 0.926150i | \(0.376902\pi\) | |||||||
\(402\) | − | 8201.60i | − | 1.01756i | ||||||
\(403\) | 1262.36i | 0.156036i | ||||||||
\(404\) | −5171.92 | −0.636912 | ||||||||
\(405\) | 821.558 | − | 381.008i | 0.100799 | − | 0.0467467i | ||||
\(406\) | −240.613 | −0.0294123 | ||||||||
\(407\) | − | 3956.62i | − | 0.481873i | ||||||
\(408\) | − | 1201.80i | − | 0.145829i | ||||||
\(409\) | −1248.52 | −0.150942 | −0.0754709 | − | 0.997148i | \(-0.524046\pi\) | ||||
−0.0754709 | + | 0.997148i | \(0.524046\pi\) | |||||||
\(410\) | −7772.41 | − | 16759.5i | −0.936224 | − | 2.01876i | ||||
\(411\) | 7735.20 | 0.928344 | ||||||||
\(412\) | 2893.53i | 0.346005i | ||||||||
\(413\) | − | 2269.00i | − | 0.270340i | ||||||
\(414\) | −4488.27 | −0.532817 | ||||||||
\(415\) | 57.9544 | + | 124.966i | 0.00685511 | + | 0.0147815i | ||||
\(416\) | −1367.59 | −0.161182 | ||||||||
\(417\) | 9196.48i | 1.07998i | ||||||||
\(418\) | 4736.02i | 0.554178i | ||||||||
\(419\) | −8324.28 | −0.970567 | −0.485284 | − | 0.874357i | \(-0.661284\pi\) | ||||
−0.485284 | + | 0.874357i | \(0.661284\pi\) | |||||||
\(420\) | 668.917 | − | 310.218i | 0.0777138 | − | 0.0360407i | ||||
\(421\) | 1693.40 | 0.196036 | 0.0980179 | − | 0.995185i | \(-0.468750\pi\) | ||||
0.0980179 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(422\) | 2553.05i | 0.294504i | ||||||||
\(423\) | 1916.61i | 0.220305i | ||||||||
\(424\) | 8636.27 | 0.989185 | ||||||||
\(425\) | 2356.68 | + | 1994.36i | 0.268978 | + | 0.227625i | ||||
\(426\) | 4675.57 | 0.531765 | ||||||||
\(427\) | − | 4577.77i | − | 0.518814i | ||||||
\(428\) | − | 3331.58i | − | 0.376257i | ||||||
\(429\) | 557.782 | 0.0627738 | ||||||||
\(430\) | −7468.33 | + | 3463.53i | −0.837570 | + | 0.388433i | ||||
\(431\) | 11754.6 | 1.31369 | 0.656844 | − | 0.754026i | \(-0.271891\pi\) | ||||
0.656844 | + | 0.754026i | \(0.271891\pi\) | |||||||
\(432\) | − | 2140.05i | − | 0.238341i | ||||||
\(433\) | − | 14614.3i | − | 1.62199i | −0.585056 | − | 0.810993i | \(-0.698927\pi\) | ||
0.585056 | − | 0.810993i | \(-0.301073\pi\) | |||||||
\(434\) | −2907.04 | −0.321526 | ||||||||
\(435\) | −145.324 | − | 313.359i | −0.0160178 | − | 0.0345389i | ||||
\(436\) | 4814.48 | 0.528834 | ||||||||
\(437\) | − | 11568.6i | − | 1.26637i | ||||||
\(438\) | − | 1732.95i | − | 0.189049i | ||||||
\(439\) | −1957.52 | −0.212819 | −0.106409 | − | 0.994322i | \(-0.533935\pi\) | ||||
−0.106409 | + | 0.994322i | \(0.533935\pi\) | |||||||
\(440\) | −1398.15 | − | 3014.80i | −0.151487 | − | 0.326648i | ||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 836.377i | 0.0900054i | ||||||||
\(443\) | − | 356.774i | − | 0.0382637i | −0.999817 | − | 0.0191319i | \(-0.993910\pi\) | ||
0.999817 | − | 0.0191319i | \(-0.00609023\pi\) | |||||||
\(444\) | 2034.15 | 0.217425 | ||||||||
\(445\) | 343.124 | − | 159.128i | 0.0365520 | − | 0.0169514i | ||||
\(446\) | 5290.92 | 0.561732 | ||||||||
\(447\) | − | 8113.01i | − | 0.858461i | ||||||
\(448\) | 1289.24i | 0.135962i | ||||||||
\(449\) | −7395.30 | −0.777296 | −0.388648 | − | 0.921386i | \(-0.627058\pi\) | ||||
−0.388648 | + | 0.921386i | \(0.627058\pi\) | |||||||
\(450\) | 2866.34 | + | 2425.66i | 0.300267 | + | 0.254104i | ||||
\(451\) | 9072.28 | 0.947222 | ||||||||
\(452\) | 6509.23i | 0.677364i | ||||||||
\(453\) | − | 1166.61i | − | 0.120998i | ||||||
\(454\) | −7887.31 | −0.815352 | ||||||||
\(455\) | 720.332 | − | 334.063i | 0.0742191 | − | 0.0344200i | ||||
\(456\) | 3767.59 | 0.386916 | ||||||||
\(457\) | − | 12722.2i | − | 1.30223i | −0.758979 | − | 0.651115i | \(-0.774302\pi\) | ||
0.758979 | − | 0.651115i | \(-0.225698\pi\) | |||||||
\(458\) | 5428.64i | 0.553850i | ||||||||
\(459\) | −666.856 | −0.0678130 | ||||||||
\(460\) | −2207.15 | − | 4759.23i | −0.223715 | − | 0.482391i | ||||
\(461\) | −2206.45 | −0.222916 | −0.111458 | − | 0.993769i | \(-0.535552\pi\) | ||||
−0.111458 | + | 0.993769i | \(0.535552\pi\) | |||||||
\(462\) | 1284.50i | 0.129351i | ||||||||
\(463\) | 15912.0i | 1.59718i | 0.601875 | + | 0.798591i | \(0.294421\pi\) | ||||
−0.601875 | + | 0.798591i | \(0.705579\pi\) | |||||||
\(464\) | −816.261 | −0.0816681 | ||||||||
\(465\) | −1755.78 | − | 3785.95i | −0.175102 | − | 0.377569i | ||||
\(466\) | 5742.05 | 0.570806 | ||||||||
\(467\) | − | 7602.65i | − | 0.753337i | −0.926348 | − | 0.376669i | \(-0.877070\pi\) | ||
0.926348 | − | 0.376669i | \(-0.122930\pi\) | |||||||
\(468\) | 286.763i | 0.0283240i | ||||||||
\(469\) | 5733.54 | 0.564499 | ||||||||
\(470\) | −7209.38 | + | 3343.44i | −0.707540 | + | 0.328130i | ||||
\(471\) | 8657.33 | 0.846940 | ||||||||
\(472\) | − | 5257.52i | − | 0.512705i | ||||||
\(473\) | − | 4042.78i | − | 0.392996i | ||||||
\(474\) | 8112.57 | 0.786124 | ||||||||
\(475\) | −6252.21 | + | 7388.07i | −0.603940 | + | 0.713659i | ||||
\(476\) | −542.957 | −0.0522824 | ||||||||
\(477\) | − | 4792.09i | − | 0.459989i | ||||||
\(478\) | 24091.0i | 2.30522i | ||||||||
\(479\) | −1681.93 | −0.160437 | −0.0802184 | − | 0.996777i | \(-0.525562\pi\) | ||||
−0.0802184 | + | 0.996777i | \(0.525562\pi\) | |||||||
\(480\) | 4101.57 | − | 1902.15i | 0.390021 | − | 0.180877i | ||||
\(481\) | 2190.50 | 0.207647 | ||||||||
\(482\) | − | 17005.0i | − | 1.60697i | ||||||
\(483\) | − | 3137.64i | − | 0.295585i | ||||||
\(484\) | 3125.32 | 0.293513 | ||||||||
\(485\) | 3813.65 | + | 8223.30i | 0.357050 | + | 0.769898i | ||||
\(486\) | −811.071 | −0.0757015 | ||||||||
\(487\) | 14107.0i | 1.31263i | 0.754487 | + | 0.656314i | \(0.227886\pi\) | ||||
−0.754487 | + | 0.656314i | \(0.772114\pi\) | |||||||
\(488\) | − | 10607.2i | − | 0.983943i | ||||||
\(489\) | 1715.86 | 0.158679 | ||||||||
\(490\) | 769.302 | + | 1658.83i | 0.0709256 | + | 0.152935i | ||||
\(491\) | 9010.20 | 0.828156 | 0.414078 | − | 0.910241i | \(-0.364104\pi\) | ||||
0.414078 | + | 0.910241i | \(0.364104\pi\) | |||||||
\(492\) | 4664.18i | 0.427393i | ||||||||
\(493\) | 254.353i | 0.0232363i | ||||||||
\(494\) | −2622.00 | −0.238804 | ||||||||
\(495\) | −1672.85 | + | 775.806i | −0.151897 | + | 0.0704442i | ||||
\(496\) | −9861.92 | −0.892769 | ||||||||
\(497\) | 3268.58i | 0.295001i | ||||||||
\(498\) | − | 123.371i | − | 0.0111011i | ||||||
\(499\) | −2655.07 | −0.238191 | −0.119096 | − | 0.992883i | \(-0.538000\pi\) | ||||
−0.119096 | + | 0.992883i | \(0.538000\pi\) | |||||||
\(500\) | −1162.55 | + | 4232.22i | −0.103982 | + | 0.378541i | ||||
\(501\) | −7271.89 | −0.648471 | ||||||||
\(502\) | 14507.5i | 1.28985i | ||||||||
\(503\) | 16559.4i | 1.46789i | 0.679208 | + | 0.733946i | \(0.262323\pi\) | ||||
−0.679208 | + | 0.733946i | \(0.737677\pi\) | |||||||
\(504\) | 1021.84 | 0.0903105 | ||||||||
\(505\) | 16703.4 | − | 7746.42i | 1.47187 | − | 0.682596i | ||||
\(506\) | 9138.99 | 0.802920 | ||||||||
\(507\) | − | 6282.20i | − | 0.550300i | ||||||
\(508\) | − | 1146.74i | − | 0.100154i | ||||||
\(509\) | 12308.6 | 1.07184 | 0.535922 | − | 0.844268i | \(-0.319964\pi\) | ||||
0.535922 | + | 0.844268i | \(0.319964\pi\) | |||||||
\(510\) | −1163.30 | − | 2508.39i | −0.101003 | − | 0.217791i | ||||
\(511\) | 1211.46 | 0.104877 | ||||||||
\(512\) | − | 399.294i | − | 0.0344658i | ||||||
\(513\) | − | 2090.56i | − | 0.179923i | ||||||
\(514\) | 4766.74 | 0.409050 | ||||||||
\(515\) | −4333.89 | − | 9345.07i | −0.370823 | − | 0.799598i | ||||
\(516\) | 2078.44 | 0.177322 | ||||||||
\(517\) | − | 3902.60i | − | 0.331985i | ||||||
\(518\) | 5044.44i | 0.427876i | ||||||||
\(519\) | 1879.32 | 0.158946 | ||||||||
\(520\) | 1669.08 | − | 774.058i | 0.140758 | − | 0.0652783i | ||||
\(521\) | −15045.9 | −1.26521 | −0.632605 | − | 0.774475i | \(-0.718014\pi\) | ||||
−0.632605 | + | 0.774475i | \(0.718014\pi\) | |||||||
\(522\) | 309.359i | 0.0259392i | ||||||||
\(523\) | 6372.16i | 0.532763i | 0.963868 | + | 0.266381i | \(0.0858281\pi\) | ||||
−0.963868 | + | 0.266381i | \(0.914172\pi\) | |||||||
\(524\) | −4085.25 | −0.340582 | ||||||||
\(525\) | −1695.72 | + | 2003.79i | −0.140966 | + | 0.166576i | ||||
\(526\) | 11507.8 | 0.953923 | ||||||||
\(527\) | 3073.05i | 0.254011i | ||||||||
\(528\) | 4357.57i | 0.359164i | ||||||||
\(529\) | −10156.8 | −0.834779 | ||||||||
\(530\) | 18025.5 | − | 8359.57i | 1.47732 | − | 0.685125i | ||||
\(531\) | −2917.29 | −0.238417 | ||||||||
\(532\) | − | 1702.14i | − | 0.138717i | ||||||
\(533\) | 5022.68i | 0.408173i | ||||||||
\(534\) | −338.744 | −0.0274511 | ||||||||
\(535\) | 4989.99 | + | 10759.8i | 0.403245 | + | 0.869509i | ||||
\(536\) | 13285.2 | 1.07059 | ||||||||
\(537\) | 6966.33i | 0.559812i | ||||||||
\(538\) | − | 74.7569i | − | 0.00599071i | ||||||
\(539\) | −897.962 | −0.0717588 | ||||||||
\(540\) | −398.852 | − | 860.036i | −0.0317849 | − | 0.0685371i | ||||
\(541\) | 4128.72 | 0.328110 | 0.164055 | − | 0.986451i | \(-0.447543\pi\) | ||||
0.164055 | + | 0.986451i | \(0.447543\pi\) | |||||||
\(542\) | 5197.95i | 0.411939i | ||||||||
\(543\) | 13994.8i | 1.10603i | ||||||||
\(544\) | −3329.23 | −0.262389 | ||||||||
\(545\) | −15549.0 | + | 7211.05i | −1.22210 | + | 0.566766i | ||||
\(546\) | −711.136 | −0.0557396 | ||||||||
\(547\) | − | 17987.6i | − | 1.40602i | −0.711179 | − | 0.703011i | \(-0.751838\pi\) | ||
0.711179 | − | 0.703011i | \(-0.248162\pi\) | |||||||
\(548\) | − | 8097.48i | − | 0.631217i | ||||||
\(549\) | −5885.70 | −0.457551 | ||||||||
\(550\) | −5836.42 | − | 4939.12i | −0.452483 | − | 0.382918i | ||||
\(551\) | −797.383 | −0.0616509 | ||||||||
\(552\) | − | 7270.24i | − | 0.560583i | ||||||
\(553\) | 5671.30i | 0.436109i | ||||||||
\(554\) | 12466.2 | 0.956024 | ||||||||
\(555\) | −6569.57 | + | 3046.72i | −0.502456 | + | 0.233020i | ||||
\(556\) | 9627.19 | 0.734323 | ||||||||
\(557\) | 13278.6i | 1.01011i | 0.863086 | + | 0.505057i | \(0.168529\pi\) | ||||
−0.863086 | + | 0.505057i | \(0.831471\pi\) | |||||||
\(558\) | 3737.62i | 0.283560i | ||||||||
\(559\) | 2238.20 | 0.169348 | ||||||||
\(560\) | 2609.80 | + | 5627.46i | 0.196936 | + | 0.424649i | ||||
\(561\) | 1357.85 | 0.102190 | ||||||||
\(562\) | 8085.24i | 0.606860i | ||||||||
\(563\) | 517.822i | 0.0387630i | 0.999812 | + | 0.0193815i | \(0.00616971\pi\) | ||||
−0.999812 | + | 0.0193815i | \(0.993830\pi\) | |||||||
\(564\) | 2006.38 | 0.149794 | ||||||||
\(565\) | −9749.43 | − | 21022.5i | −0.725950 | − | 1.56535i | ||||
\(566\) | 945.355 | 0.0702054 | ||||||||
\(567\) | − | 567.000i | − | 0.0419961i | ||||||
\(568\) | 7573.64i | 0.559477i | ||||||||
\(569\) | −1071.91 | −0.0789750 | −0.0394875 | − | 0.999220i | \(-0.512573\pi\) | ||||
−0.0394875 | + | 0.999220i | \(0.512573\pi\) | |||||||
\(570\) | 7863.68 | − | 3646.88i | 0.577848 | − | 0.267984i | ||||
\(571\) | −24489.8 | −1.79486 | −0.897430 | − | 0.441157i | \(-0.854568\pi\) | ||||
−0.897430 | + | 0.441157i | \(0.854568\pi\) | |||||||
\(572\) | − | 583.905i | − | 0.0426824i | ||||||
\(573\) | 11190.8i | 0.815883i | ||||||||
\(574\) | −11566.6 | −0.841079 | ||||||||
\(575\) | 14256.6 | + | 12064.8i | 1.03398 | + | 0.875018i | ||||
\(576\) | 1657.60 | 0.119907 | ||||||||
\(577\) | − | 22765.1i | − | 1.64250i | −0.570568 | − | 0.821251i | \(-0.693277\pi\) | ||
0.570568 | − | 0.821251i | \(-0.306723\pi\) | |||||||
\(578\) | − | 14362.3i | − | 1.03355i | ||||||
\(579\) | −7755.78 | −0.556682 | ||||||||
\(580\) | −328.035 | + | 152.130i | −0.0234844 | + | 0.0108912i | ||||
\(581\) | 86.2454 | 0.00615846 | ||||||||
\(582\) | − | 8118.32i | − | 0.578205i | ||||||
\(583\) | 9757.64i | 0.693173i | ||||||||
\(584\) | 2807.09 | 0.198901 | ||||||||
\(585\) | −429.509 | − | 926.141i | −0.0303556 | − | 0.0654551i | ||||
\(586\) | 28309.0 | 1.99562 | ||||||||
\(587\) | 10106.8i | 0.710651i | 0.934743 | + | 0.355325i | \(0.115630\pi\) | ||||
−0.934743 | + | 0.355325i | \(0.884370\pi\) | |||||||
\(588\) | − | 461.654i | − | 0.0323780i | ||||||
\(589\) | −9633.85 | −0.673949 | ||||||||
\(590\) | −5089.07 | − | 10973.4i | −0.355108 | − | 0.765711i | ||||
\(591\) | −7217.73 | −0.502365 | ||||||||
\(592\) | 17112.9i | 1.18807i | ||||||||
\(593\) | − | 4241.04i | − | 0.293691i | −0.989159 | − | 0.146845i | \(-0.953088\pi\) | ||
0.989159 | − | 0.146845i | \(-0.0469120\pi\) | |||||||
\(594\) | 1651.50 | 0.114077 | ||||||||
\(595\) | 1753.56 | − | 813.233i | 0.120822 | − | 0.0560324i | ||||
\(596\) | −8492.97 | −0.583701 | ||||||||
\(597\) | 3577.05i | 0.245224i | ||||||||
\(598\) | 5059.61i | 0.345992i | ||||||||
\(599\) | 16536.6 | 1.12799 | 0.563995 | − | 0.825778i | \(-0.309264\pi\) | ||||
0.563995 | + | 0.825778i | \(0.309264\pi\) | |||||||
\(600\) | −3929.16 | + | 4642.98i | −0.267346 | + | 0.315915i | ||||
\(601\) | −6030.83 | −0.409322 | −0.204661 | − | 0.978833i | \(-0.565609\pi\) | ||||
−0.204661 | + | 0.978833i | \(0.565609\pi\) | |||||||
\(602\) | 5154.28i | 0.348958i | ||||||||
\(603\) | − | 7371.69i | − | 0.497842i | ||||||
\(604\) | −1221.24 | −0.0822710 | ||||||||
\(605\) | −10093.7 | + | 4681.06i | −0.678291 | + | 0.314566i | ||||
\(606\) | −16490.2 | −1.10539 | ||||||||
\(607\) | − | 12639.0i | − | 0.845143i | −0.906330 | − | 0.422572i | \(-0.861128\pi\) | ||
0.906330 | − | 0.422572i | \(-0.138872\pi\) | |||||||
\(608\) | − | 10437.0i | − | 0.696176i | ||||||
\(609\) | −216.266 | −0.0143900 | ||||||||
\(610\) | −10267.3 | − | 22139.2i | −0.681494 | − | 1.46949i | ||||
\(611\) | 2160.59 | 0.143058 | ||||||||
\(612\) | 698.088i | 0.0461087i | ||||||||
\(613\) | − | 226.217i | − | 0.0149051i | −0.999972 | − | 0.00745254i | \(-0.997628\pi\) | ||
0.999972 | − | 0.00745254i | \(-0.00237224\pi\) | |||||||
\(614\) | 6693.84 | 0.439970 | ||||||||
\(615\) | −6985.93 | − | 15063.6i | −0.458049 | − | 0.987680i | ||||
\(616\) | −2080.67 | −0.136092 | ||||||||
\(617\) | 6491.49i | 0.423561i | 0.977317 | + | 0.211781i | \(0.0679263\pi\) | ||||
−0.977317 | + | 0.211781i | \(0.932074\pi\) | |||||||
\(618\) | 9225.77i | 0.600510i | ||||||||
\(619\) | −19224.9 | −1.24833 | −0.624163 | − | 0.781294i | \(-0.714560\pi\) | ||||
−0.624163 | + | 0.781294i | \(0.714560\pi\) | |||||||
\(620\) | −3963.27 | + | 1838.01i | −0.256724 | + | 0.119059i | ||||
\(621\) | −4034.11 | −0.260681 | ||||||||
\(622\) | − | 33448.8i | − | 2.15623i | ||||||
\(623\) | − | 236.808i | − | 0.0152287i | ||||||
\(624\) | −2412.48 | −0.154770 | ||||||||
\(625\) | −2584.33 | − | 15409.8i | −0.165397 | − | 0.986227i | ||||
\(626\) | −2106.71 | −0.134506 | ||||||||
\(627\) | 4256.79i | 0.271132i | ||||||||
\(628\) | − | 9062.79i | − | 0.575868i | ||||||
\(629\) | 5332.50 | 0.338030 | ||||||||
\(630\) | 2132.78 | − | 989.103i | 0.134876 | − | 0.0625505i | ||||
\(631\) | 21123.5 | 1.33267 | 0.666334 | − | 0.745653i | \(-0.267862\pi\) | ||||
0.666334 | + | 0.745653i | \(0.267862\pi\) | |||||||
\(632\) | 13141.0i | 0.827090i | ||||||||
\(633\) | 2294.71i | 0.144086i | ||||||||
\(634\) | 4014.34 | 0.251467 | ||||||||
\(635\) | 1717.57 | + | 3703.56i | 0.107338 | + | 0.231451i | ||||
\(636\) | −5016.53 | −0.312765 | ||||||||
\(637\) | − | 497.138i | − | 0.0309220i | ||||||
\(638\) | − | 629.916i | − | 0.0390887i | ||||||
\(639\) | 4202.46 | 0.260167 | ||||||||
\(640\) | 7964.01 | + | 17172.6i | 0.491883 | + | 1.06064i | ||||
\(641\) | −8079.31 | −0.497837 | −0.248918 | − | 0.968524i | \(-0.580075\pi\) | ||||
−0.248918 | + | 0.968524i | \(0.580075\pi\) | |||||||
\(642\) | − | 10622.5i | − | 0.653014i | ||||||
\(643\) | − | 28025.8i | − | 1.71887i | −0.511249 | − | 0.859433i | \(-0.670817\pi\) | ||
0.511249 | − | 0.859433i | \(-0.329183\pi\) | |||||||
\(644\) | −3284.59 | −0.200980 | ||||||||
\(645\) | −6712.63 | + | 3113.06i | −0.409782 | + | 0.190041i | ||||
\(646\) | −6382.93 | −0.388751 | ||||||||
\(647\) | − | 9585.95i | − | 0.582477i | −0.956650 | − | 0.291239i | \(-0.905933\pi\) | ||
0.956650 | − | 0.291239i | \(-0.0940674\pi\) | |||||||
\(648\) | − | 1313.80i | − | 0.0796464i | ||||||
\(649\) | 5940.17 | 0.359279 | ||||||||
\(650\) | 2734.44 | − | 3231.21i | 0.165006 | − | 0.194982i | ||||
\(651\) | −2612.88 | −0.157307 | ||||||||
\(652\) | − | 1796.22i | − | 0.107892i | ||||||
\(653\) | − | 6356.08i | − | 0.380908i | −0.981696 | − | 0.190454i | \(-0.939004\pi\) | ||
0.981696 | − | 0.190454i | \(-0.0609959\pi\) | |||||||
\(654\) | 15350.5 | 0.917819 | ||||||||
\(655\) | 13193.9 | − | 6118.82i | 0.787065 | − | 0.365011i | ||||
\(656\) | −39238.8 | −2.33539 | ||||||||
\(657\) | − | 1557.60i | − | 0.0924925i | ||||||
\(658\) | 4975.57i | 0.294784i | ||||||||
\(659\) | −2394.70 | −0.141554 | −0.0707772 | − | 0.997492i | \(-0.522548\pi\) | ||||
−0.0707772 | + | 0.997492i | \(0.522548\pi\) | |||||||
\(660\) | 812.140 | + | 1751.20i | 0.0478978 | + | 0.103281i | ||||
\(661\) | −23502.0 | −1.38294 | −0.691470 | − | 0.722406i | \(-0.743036\pi\) | ||||
−0.691470 | + | 0.722406i | \(0.743036\pi\) | |||||||
\(662\) | 31032.8i | 1.82194i | ||||||||
\(663\) | 751.745i | 0.0440353i | ||||||||
\(664\) | 199.840 | 0.0116796 | ||||||||
\(665\) | 2549.44 | + | 5497.31i | 0.148667 | + | 0.320566i | ||||
\(666\) | 6485.71 | 0.377351 | ||||||||
\(667\) | 1538.69i | 0.0893229i | ||||||||
\(668\) | 7612.46i | 0.440921i | ||||||||
\(669\) | 4755.54 | 0.274828 | ||||||||
\(670\) | 27728.8 | − | 12859.5i | 1.59889 | − | 0.741504i | ||||
\(671\) | 11984.4 | 0.689500 | ||||||||
\(672\) | − | 2830.71i | − | 0.162495i | ||||||
\(673\) | − | 31304.2i | − | 1.79300i | −0.443047 | − | 0.896498i | \(-0.646103\pi\) | ||
0.443047 | − | 0.896498i | \(-0.353897\pi\) | |||||||
\(674\) | −1694.66 | −0.0968486 | ||||||||
\(675\) | 2576.30 | + | 2180.21i | 0.146906 | + | 0.124321i | ||||
\(676\) | −6576.42 | −0.374170 | ||||||||
\(677\) | − | 16821.3i | − | 0.954940i | −0.878648 | − | 0.477470i | \(-0.841554\pi\) | ||
0.878648 | − | 0.477470i | \(-0.158446\pi\) | |||||||
\(678\) | 20754.1i | 1.17560i | ||||||||
\(679\) | 5675.32 | 0.320764 | ||||||||
\(680\) | 4063.17 | − | 1884.35i | 0.229141 | − | 0.106267i | ||||
\(681\) | −7089.21 | −0.398912 | ||||||||
\(682\) | − | 7610.53i | − | 0.427306i | ||||||
\(683\) | − | 106.287i | − | 0.00595453i | −0.999996 | − | 0.00297726i | \(-0.999052\pi\) | ||
0.999996 | − | 0.00297726i | \(-0.000947694\pi\) | |||||||
\(684\) | −2188.47 | −0.122337 | ||||||||
\(685\) | 12128.3 | + | 26151.9i | 0.676493 | + | 1.45871i | ||||
\(686\) | 1144.84 | 0.0637177 | ||||||||
\(687\) | 4879.32i | 0.270972i | ||||||||
\(688\) | 17485.5i | 0.968938i | ||||||||
\(689\) | −5402.12 | −0.298700 | ||||||||
\(690\) | −7037.30 | − | 15174.4i | −0.388269 | − | 0.837215i | ||||
\(691\) | −19383.5 | −1.06712 | −0.533562 | − | 0.845761i | \(-0.679147\pi\) | ||||
−0.533562 | + | 0.845761i | \(0.679147\pi\) | |||||||
\(692\) | − | 1967.34i | − | 0.108074i | ||||||
\(693\) | 1154.52i | 0.0632853i | ||||||||
\(694\) | −22898.9 | −1.25249 | ||||||||
\(695\) | −31092.4 | + | 14419.5i | −1.69698 | + | 0.786995i | ||||
\(696\) | −501.110 | −0.0272910 | ||||||||
\(697\) | 12227.1i | 0.664467i | ||||||||
\(698\) | − | 30828.9i | − | 1.67176i | ||||||
\(699\) | 5161.03 | 0.279267 | ||||||||
\(700\) | 2097.63 | + | 1775.14i | 0.113261 | + | 0.0958484i | ||||
\(701\) | −13338.2 | −0.718652 | −0.359326 | − | 0.933212i | \(-0.616993\pi\) | ||||
−0.359326 | + | 0.933212i | \(0.616993\pi\) | |||||||
\(702\) | 914.318i | 0.0491577i | ||||||||
\(703\) | 16717.1i | 0.896868i | ||||||||
\(704\) | −3375.20 | −0.180692 | ||||||||
\(705\) | −6479.88 | + | 3005.12i | −0.346165 | + | 0.160538i | ||||
\(706\) | 31440.0 | 1.67600 | ||||||||
\(707\) | − | 11527.9i | − | 0.613227i | ||||||
\(708\) | 3053.92i | 0.162109i | ||||||||
\(709\) | −15225.3 | −0.806487 | −0.403243 | − | 0.915093i | \(-0.632117\pi\) | ||||
−0.403243 | + | 0.915093i | \(0.632117\pi\) | |||||||
\(710\) | 7330.98 | + | 15807.6i | 0.387502 | + | 0.835563i | ||||
\(711\) | 7291.68 | 0.384612 | ||||||||
\(712\) | − | 548.708i | − | 0.0288816i | ||||||
\(713\) | 18590.2i | 0.976450i | ||||||||
\(714\) | −1731.17 | −0.0907387 | ||||||||
\(715\) | 874.565 | + | 1885.80i | 0.0457439 | + | 0.0986365i | ||||
\(716\) | 7292.59 | 0.380638 | ||||||||
\(717\) | 21653.3i | 1.12783i | ||||||||
\(718\) | − | 9648.79i | − | 0.501518i | ||||||
\(719\) | 23884.3 | 1.23885 | 0.619427 | − | 0.785054i | \(-0.287365\pi\) | ||||
0.619427 | + | 0.785054i | \(0.287365\pi\) | |||||||
\(720\) | 7235.31 | − | 3355.46i | 0.374505 | − | 0.173681i | ||||
\(721\) | −6449.52 | −0.333138 | ||||||||
\(722\) | 2883.40i | 0.148628i | ||||||||
\(723\) | − | 15284.3i | − | 0.786211i | ||||||
\(724\) | 14650.3 | 0.752034 | ||||||||
\(725\) | 831.578 | − | 982.653i | 0.0425987 | − | 0.0503377i | ||||
\(726\) | 9964.82 | 0.509406 | ||||||||
\(727\) | 27929.5i | 1.42482i | 0.701761 | + | 0.712412i | \(0.252397\pi\) | ||||
−0.701761 | + | 0.712412i | \(0.747603\pi\) | |||||||
\(728\) | − | 1151.92i | − | 0.0586443i | ||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 5858.93 | − | 2717.15i | 0.297053 | − | 0.137762i | ||||
\(731\) | 5448.62 | 0.275683 | ||||||||
\(732\) | 6161.36i | 0.311107i | ||||||||
\(733\) | − | 17970.8i | − | 0.905548i | −0.891625 | − | 0.452774i | \(-0.850434\pi\) | ||
0.891625 | − | 0.452774i | \(-0.149566\pi\) | |||||||
\(734\) | 5241.97 | 0.263603 | ||||||||
\(735\) | 691.458 | + | 1490.98i | 0.0347004 | + | 0.0748238i | ||||
\(736\) | −20140.0 | −1.00865 | ||||||||
\(737\) | 15010.2i | 0.750215i | ||||||||
\(738\) | 14871.3i | 0.741762i | ||||||||
\(739\) | 1280.61 | 0.0637455 | 0.0318728 | − | 0.999492i | \(-0.489853\pi\) | ||||
0.0318728 | + | 0.999492i | \(0.489853\pi\) | |||||||
\(740\) | 3189.41 | + | 6877.25i | 0.158439 | + | 0.341639i | ||||
\(741\) | −2356.68 | −0.116835 | ||||||||
\(742\) | − | 12440.4i | − | 0.615499i | ||||||
\(743\) | − | 28570.1i | − | 1.41068i | −0.708869 | − | 0.705340i | \(-0.750794\pi\) | ||
0.708869 | − | 0.705340i | \(-0.249206\pi\) | |||||||
\(744\) | −6054.32 | −0.298336 | ||||||||
\(745\) | 27429.3 | − | 12720.6i | 1.34890 | − | 0.625568i | ||||
\(746\) | −29083.0 | −1.42735 | ||||||||
\(747\) | − | 110.887i | − | 0.00543125i | ||||||
\(748\) | − | 1421.44i | − | 0.0694828i | ||||||
\(749\) | 7425.91 | 0.362265 | ||||||||
\(750\) | −3706.69 | + | 13494.1i | −0.180466 | + | 0.656978i | ||||
\(751\) | 32836.7 | 1.59551 | 0.797754 | − | 0.602982i | \(-0.206021\pi\) | ||||
0.797754 | + | 0.602982i | \(0.206021\pi\) | |||||||
\(752\) | 16879.2i | 0.818514i | ||||||||
\(753\) | 13039.5i | 0.631059i | ||||||||
\(754\) | 348.740 | 0.0168440 | ||||||||
\(755\) | 3944.18 | − | 1829.16i | 0.190123 | − | 0.0881721i | ||||
\(756\) | −593.555 | −0.0285547 | ||||||||
\(757\) | 1086.72i | 0.0521763i | 0.999660 | + | 0.0260882i | \(0.00830507\pi\) | ||||
−0.999660 | + | 0.0260882i | \(0.991695\pi\) | |||||||
\(758\) | − | 19291.0i | − | 0.924379i | ||||||
\(759\) | 8214.23 | 0.392830 | ||||||||
\(760\) | 5907.33 | + | 12737.8i | 0.281949 | + | 0.607961i | ||||
\(761\) | −17097.7 | −0.814443 | −0.407221 | − | 0.913329i | \(-0.633502\pi\) | ||||
−0.407221 | + | 0.913329i | \(0.633502\pi\) | |||||||
\(762\) | − | 3656.28i | − | 0.173823i | ||||||
\(763\) | 10731.2i | 0.509168i | ||||||||
\(764\) | 11714.9 | 0.554751 | ||||||||
\(765\) | −1045.59 | − | 2254.57i | −0.0494160 | − | 0.106555i | ||||
\(766\) | −41188.5 | −1.94282 | ||||||||
\(767\) | 3288.65i | 0.154819i | ||||||||
\(768\) | − | 12533.1i | − | 0.588868i | ||||||
\(769\) | 24796.1 | 1.16277 | 0.581386 | − | 0.813628i | \(-0.302511\pi\) | ||||
0.581386 | + | 0.813628i | \(0.302511\pi\) | |||||||
\(770\) | −4342.76 | + | 2014.01i | −0.203250 | + | 0.0942595i | ||||
\(771\) | 4284.40 | 0.200128 | ||||||||
\(772\) | 8119.01i | 0.378510i | ||||||||
\(773\) | − | 33325.8i | − | 1.55064i | −0.631567 | − | 0.775321i | \(-0.717588\pi\) | ||
0.631567 | − | 0.775321i | \(-0.282412\pi\) | |||||||
\(774\) | 6626.93 | 0.307752 | ||||||||
\(775\) | 10047.0 | − | 11872.2i | 0.465675 | − | 0.550275i | ||||
\(776\) | 13150.3 | 0.608336 | ||||||||
\(777\) | 4534.00i | 0.209339i | ||||||||
\(778\) | 26529.8i | 1.22255i | ||||||||
\(779\) | −38331.3 | −1.76298 | ||||||||
\(780\) | −969.516 | + | 449.625i | −0.0445054 | + | 0.0206399i | ||||
\(781\) | −8557.02 | −0.392054 | ||||||||
\(782\) | 12317.0i | 0.563241i | ||||||||
\(783\) | 278.056i | 0.0126908i | ||||||||
\(784\) | 3883.80 | 0.176922 | ||||||||
\(785\) | 13574.1 | + | 29269.6i | 0.617173 | + | 1.33080i | ||||
\(786\) | −13025.5 | −0.591098 | ||||||||
\(787\) | 30195.2i | 1.36765i | 0.729645 | + | 0.683826i | \(0.239685\pi\) | ||||
−0.729645 | + | 0.683826i | \(0.760315\pi\) | |||||||
\(788\) | 7555.77i | 0.341578i | ||||||||
\(789\) | 10343.3 | 0.466708 | ||||||||
\(790\) | 12720.0 | + | 27427.8i | 0.572856 | + | 1.23524i | ||||
\(791\) | −14508.7 | −0.652175 | ||||||||
\(792\) | 2675.15i | 0.120022i | ||||||||
\(793\) | 6634.94i | 0.297117i | ||||||||
\(794\) | 17902.4 | 0.800168 | ||||||||
\(795\) | 16201.6 | − | 7513.68i | 0.722781 | − | 0.335198i | ||||
\(796\) | 3744.57 | 0.166737 | ||||||||
\(797\) | − | 24226.2i | − | 1.07671i | −0.842720 | − | 0.538353i | \(-0.819047\pi\) | ||
0.842720 | − | 0.538353i | \(-0.180953\pi\) | |||||||
\(798\) | − | 5427.14i | − | 0.240750i | ||||||
\(799\) | 5259.69 | 0.232884 | ||||||||
\(800\) | 12862.0 | + | 10884.6i | 0.568424 | + | 0.481034i | ||||
\(801\) | −304.467 | −0.0134305 | ||||||||
\(802\) | − | 20217.1i | − | 0.890138i | ||||||
\(803\) | 3171.57i | 0.139380i | ||||||||
\(804\) | −7716.94 | −0.338502 | ||||||||
\(805\) | 10608.0 | − | 4919.61i | 0.464452 | − | 0.215395i | ||||
\(806\) | 4213.42 | 0.184133 | ||||||||
\(807\) | − | 67.1924i | − | 0.00293096i | ||||||
\(808\) | − | 26711.4i | − | 1.16300i | ||||||
\(809\) | 16039.7 | 0.697065 | 0.348533 | − | 0.937297i | \(-0.386680\pi\) | ||||
0.348533 | + | 0.937297i | \(0.386680\pi\) | |||||||
\(810\) | −1271.70 | − | 2742.15i | −0.0551644 | − | 0.118950i | ||||
\(811\) | 33767.0 | 1.46205 | 0.731024 | − | 0.682352i | \(-0.239043\pi\) | ||||
0.731024 | + | 0.682352i | \(0.239043\pi\) | |||||||
\(812\) | 226.394i | 0.00978434i | ||||||||
\(813\) | 4671.98i | 0.201542i | ||||||||
\(814\) | −13206.2 | −0.568644 | ||||||||
\(815\) | 2690.35 | + | 5801.15i | 0.115631 | + | 0.249332i | ||||
\(816\) | −5872.87 | −0.251951 | ||||||||
\(817\) | 17081.1i | 0.731448i | ||||||||
\(818\) | 4167.22i | 0.178122i | ||||||||
\(819\) | −639.178 | −0.0272707 | ||||||||
\(820\) | −15769.1 | + | 7313.11i | −0.671562 | + | 0.311445i | ||||
\(821\) | 631.743 | 0.0268550 | 0.0134275 | − | 0.999910i | \(-0.495726\pi\) | ||||
0.0134275 | + | 0.999910i | \(0.495726\pi\) | |||||||
\(822\) | − | 25818.1i | − | 1.09551i | ||||||
\(823\) | − | 30565.3i | − | 1.29458i | −0.762244 | − | 0.647290i | \(-0.775902\pi\) | ||
0.762244 | − | 0.647290i | \(-0.224098\pi\) | |||||||
\(824\) | −14944.2 | −0.631804 | ||||||||
\(825\) | −5245.84 | − | 4439.34i | −0.221378 | − | 0.187343i | ||||
\(826\) | −7573.34 | −0.319020 | ||||||||
\(827\) | − | 24472.5i | − | 1.02901i | −0.857487 | − | 0.514505i | \(-0.827976\pi\) | ||
0.857487 | − | 0.514505i | \(-0.172024\pi\) | |||||||
\(828\) | 4223.04i | 0.177247i | ||||||||
\(829\) | 9613.32 | 0.402756 | 0.201378 | − | 0.979514i | \(-0.435458\pi\) | ||||
0.201378 | + | 0.979514i | \(0.435458\pi\) | |||||||
\(830\) | 417.104 | − | 193.437i | 0.0174432 | − | 0.00808951i | ||||
\(831\) | 11204.7 | 0.467736 | ||||||||
\(832\) | − | 1868.61i | − | 0.0778634i | ||||||
\(833\) | − | 1210.22i | − | 0.0503381i | ||||||
\(834\) | 30695.5 | 1.27446 | ||||||||
\(835\) | −11401.8 | − | 24585.5i | −0.472547 | − | 1.01894i | ||||
\(836\) | 4456.15 | 0.184353 | ||||||||
\(837\) | 3359.42i | 0.138732i | ||||||||
\(838\) | 27784.3i | 1.14534i | ||||||||
\(839\) | 23320.5 | 0.959609 | 0.479805 | − | 0.877375i | \(-0.340707\pi\) | ||||
0.479805 | + | 0.877375i | \(0.340707\pi\) | |||||||
\(840\) | 1602.18 | + | 3454.75i | 0.0658101 | + | 0.141905i | ||||
\(841\) | −24282.9 | −0.995651 | ||||||||
\(842\) | − | 5652.11i | − | 0.231336i | ||||||
\(843\) | 7267.11i | 0.296907i | ||||||||
\(844\) | 2402.18 | 0.0979699 | ||||||||
\(845\) | 21239.5 | − | 9850.06i | 0.864686 | − | 0.401009i | ||||
\(846\) | 6397.16 | 0.259975 | ||||||||
\(847\) | 6966.17i | 0.282598i | ||||||||
\(848\) | − | 42203.0i | − | 1.70903i | ||||||
\(849\) | 849.697 | 0.0343481 | ||||||||
\(850\) | 6656.65 | − | 7865.98i | 0.268613 | − | 0.317413i | ||||
\(851\) | 32258.6 | 1.29943 | ||||||||
\(852\) | − | 4399.28i | − | 0.176898i | ||||||
\(853\) | 2992.19i | 0.120106i | 0.998195 | + | 0.0600531i | \(0.0191270\pi\) | ||||
−0.998195 | + | 0.0600531i | \(0.980873\pi\) | |||||||
\(854\) | −15279.4 | −0.612237 | ||||||||
\(855\) | 7067.97 | − | 3277.86i | 0.282713 | − | 0.131112i | ||||
\(856\) | 17206.6 | 0.687044 | ||||||||
\(857\) | − | 20796.2i | − | 0.828919i | −0.910068 | − | 0.414459i | \(-0.863971\pi\) | ||
0.910068 | − | 0.414459i | \(-0.136029\pi\) | |||||||
\(858\) | − | 1861.73i | − | 0.0740774i | ||||||
\(859\) | 5302.17 | 0.210603 | 0.105301 | − | 0.994440i | \(-0.466419\pi\) | ||||
0.105301 | + | 0.994440i | \(0.466419\pi\) | |||||||
\(860\) | 3258.86 | + | 7027.01i | 0.129216 | + | 0.278627i | ||||
\(861\) | −10396.2 | −0.411499 | ||||||||
\(862\) | − | 39233.8i | − | 1.55024i | ||||||
\(863\) | − | 27066.7i | − | 1.06762i | −0.845603 | − | 0.533812i | \(-0.820759\pi\) | ||
0.845603 | − | 0.533812i | \(-0.179241\pi\) | |||||||
\(864\) | −3639.48 | −0.143307 | ||||||||
\(865\) | 2946.65 | + | 6353.79i | 0.115825 | + | 0.249752i | ||||
\(866\) | −48778.8 | −1.91406 | ||||||||
\(867\) | − | 12909.0i | − | 0.505665i | ||||||
\(868\) | 2735.26i | 0.106959i | ||||||||
\(869\) | −14847.3 | −0.579585 | ||||||||
\(870\) | −1045.91 | + | 485.054i | −0.0407583 | + | 0.0189022i | ||||
\(871\) | −8310.09 | −0.323280 | ||||||||
\(872\) | 24865.3i | 0.965648i | ||||||||
\(873\) | − | 7296.85i | − | 0.282888i | ||||||
\(874\) | −38613.1 | −1.49440 | ||||||||
\(875\) | −9433.37 | − | 2591.26i | −0.364464 | − | 0.100115i | ||||
\(876\) | −1630.54 | −0.0628893 | ||||||||
\(877\) | − | 26825.0i | − | 1.03286i | −0.856330 | − | 0.516429i | \(-0.827261\pi\) | ||
0.856330 | − | 0.516429i | \(-0.172739\pi\) | |||||||
\(878\) | 6533.69i | 0.251141i | ||||||||
\(879\) | 25444.5 | 0.976360 | ||||||||
\(880\) | −14732.5 | + | 6832.37i | −0.564355 | + | 0.261726i | ||||
\(881\) | −47701.8 | −1.82420 | −0.912098 | − | 0.409973i | \(-0.865538\pi\) | ||||
−0.912098 | + | 0.409973i | \(0.865538\pi\) | |||||||
\(882\) | − | 1471.94i | − | 0.0561938i | ||||||
\(883\) | 28447.5i | 1.08418i | 0.840319 | + | 0.542092i | \(0.182368\pi\) | ||||
−0.840319 | + | 0.542092i | \(0.817632\pi\) | |||||||
\(884\) | 786.953 | 0.0299413 | ||||||||
\(885\) | −4574.11 | − | 9863.06i | −0.173737 | − | 0.374625i | ||||
\(886\) | −1190.82 | −0.0451538 | ||||||||
\(887\) | 35046.9i | 1.32667i | 0.748321 | + | 0.663337i | \(0.230860\pi\) | ||||
−0.748321 | + | 0.663337i | \(0.769140\pi\) | |||||||
\(888\) | 10505.8i | 0.397016i | ||||||||
\(889\) | 2556.02 | 0.0964297 | ||||||||
\(890\) | −531.128 | − | 1145.26i | −0.0200039 | − | 0.0431339i | ||||
\(891\) | 1484.39 | 0.0558124 | ||||||||
\(892\) | − | 4978.27i | − | 0.186866i | ||||||
\(893\) | 16488.9i | 0.617894i | ||||||||
\(894\) | −27079.1 | −1.01304 | ||||||||
\(895\) | −23552.4 | + | 10922.7i | −0.879633 | + | 0.407940i | ||||
\(896\) | 11851.7 | 0.441895 | ||||||||
\(897\) | 4547.64i | 0.169277i | ||||||||
\(898\) | 24683.6i | 0.917262i | ||||||||
\(899\) | 1281.35 | 0.0475367 | ||||||||
\(900\) | 2282.32 | − | 2696.96i | 0.0845304 | − | 0.0998872i | ||||
\(901\) | −13150.8 | −0.486255 | ||||||||
\(902\) | − | 30280.9i | − | 1.11779i | ||||||
\(903\) | 4632.73i | 0.170728i | ||||||||
\(904\) | −33618.2 | −1.23686 | ||||||||
\(905\) | −47315.1 | + | 21942.9i | −1.73791 | + | 0.805976i | ||||
\(906\) | −3893.83 | −0.142786 | ||||||||
\(907\) | 19761.2i | 0.723439i | 0.932287 | + | 0.361720i | \(0.117810\pi\) | ||||
−0.932287 | + | 0.361720i | \(0.882190\pi\) | |||||||
\(908\) | 7421.23i | 0.271236i | ||||||||
\(909\) | −14821.6 | −0.540815 | ||||||||
\(910\) | −1115.01 | − | 2404.28i | −0.0406180 | − | 0.0875836i | ||||
\(911\) | 23563.4 | 0.856960 | 0.428480 | − | 0.903551i | \(-0.359049\pi\) | ||||
0.428480 | + | 0.903551i | \(0.359049\pi\) | |||||||
\(912\) | − | 18411.2i | − | 0.668481i | ||||||
\(913\) | 225.788i | 0.00818453i | ||||||||
\(914\) | −42463.4 | −1.53672 | ||||||||
\(915\) | −9228.38 | − | 19899.0i | −0.333422 | − | 0.718950i | ||||
\(916\) | 5107.84 | 0.184244 | ||||||||
\(917\) | − | 9105.78i | − | 0.327917i | ||||||
\(918\) | 2225.79i | 0.0800240i | ||||||||
\(919\) | 37601.1 | 1.34967 | 0.674834 | − | 0.737970i | \(-0.264215\pi\) | ||||
0.674834 | + | 0.737970i | \(0.264215\pi\) | |||||||
\(920\) | 24579.9 | − | 11399.2i | 0.880844 | − | 0.408502i | ||||
\(921\) | 6016.50 | 0.215256 | ||||||||
\(922\) | 7364.54i | 0.263057i | ||||||||
\(923\) | − | 4737.42i | − | 0.168943i | ||||||
\(924\) | 1208.59 | 0.0430301 | ||||||||
\(925\) | −20601.3 | − | 17434.0i | −0.732288 | − | 0.619705i | ||||
\(926\) | 53110.2 | 1.88478 | ||||||||
\(927\) | 8292.24i | 0.293800i | ||||||||
\(928\) | 1388.17i | 0.0491046i | ||||||||
\(929\) | 17616.6 | 0.622154 | 0.311077 | − | 0.950385i | \(-0.399310\pi\) | ||||
0.311077 | + | 0.950385i | \(0.399310\pi\) | |||||||
\(930\) | −12636.5 | + | 5860.34i | −0.445557 | + | 0.206632i | ||||
\(931\) | 3793.98 | 0.133558 | ||||||||
\(932\) | − | 5402.74i | − | 0.189885i | ||||||
\(933\) | − | 30064.2i | − | 1.05494i | ||||||
\(934\) | −25375.6 | −0.888990 | ||||||||
\(935\) | 2129.02 | + | 4590.75i | 0.0744666 | + | 0.160571i | ||||
\(936\) | −1481.04 | −0.0517194 | ||||||||
\(937\) | 36717.2i | 1.28015i | 0.768313 | + | 0.640074i | \(0.221096\pi\) | ||||
−0.768313 | + | 0.640074i | \(0.778904\pi\) | |||||||
\(938\) | − | 19137.1i | − | 0.666148i | ||||||
\(939\) | −1893.53 | −0.0658074 | ||||||||
\(940\) | 3145.86 | + | 6783.36i | 0.109156 | + | 0.235371i | ||||
\(941\) | 21861.7 | 0.757354 | 0.378677 | − | 0.925529i | \(-0.376379\pi\) | ||||
0.378677 | + | 0.925529i | \(0.376379\pi\) | |||||||
\(942\) | − | 28895.9i | − | 0.999448i | ||||||
\(943\) | 73967.0i | 2.55429i | ||||||||
\(944\) | −25692.0 | −0.885809 | ||||||||
\(945\) | 1916.97 | − | 889.018i | 0.0659884 | − | 0.0306029i | ||||
\(946\) | −13493.7 | −0.463762 | ||||||||
\(947\) | 17752.1i | 0.609149i | 0.952488 | + | 0.304575i | \(0.0985143\pi\) | ||||
−0.952488 | + | 0.304575i | \(0.901486\pi\) | |||||||
\(948\) | − | 7633.18i | − | 0.261513i | ||||||
\(949\) | −1755.87 | −0.0600612 | ||||||||
\(950\) | 24659.5 | + | 20868.3i | 0.842167 | + | 0.712690i | ||||
\(951\) | 3608.14 | 0.123030 | ||||||||
\(952\) | − | 2804.21i | − | 0.0954673i | ||||||
\(953\) | 26764.9i | 0.909758i | 0.890553 | + | 0.454879i | \(0.150317\pi\) | ||||
−0.890553 | + | 0.454879i | \(0.849683\pi\) | |||||||
\(954\) | −15994.8 | −0.542819 | ||||||||
\(955\) | −37834.9 | + | 17546.4i | −1.28200 | + | 0.594542i | ||||
\(956\) | 22667.4 | 0.766857 | ||||||||
\(957\) | − | 566.176i | − | 0.0191242i | ||||||
\(958\) | 5613.83i | 0.189326i | ||||||||
\(959\) | 18048.8 | 0.607744 | ||||||||
\(960\) | 2599.00 | + | 5604.17i | 0.0873776 | + | 0.188410i | ||||
\(961\) | −14309.9 | −0.480344 | ||||||||
\(962\) | − | 7311.32i | − | 0.245038i | ||||||
\(963\) | − | 9547.59i | − | 0.319488i | ||||||
\(964\) | −16000.2 | −0.534575 | ||||||||
\(965\) | −12160.5 | − | 26221.5i | −0.405660 | − | 0.874715i | ||||
\(966\) | −10472.6 | −0.348811 | ||||||||
\(967\) | 31173.9i | 1.03669i | 0.855170 | + | 0.518347i | \(0.173453\pi\) | ||||
−0.855170 | + | 0.518347i | \(0.826547\pi\) | |||||||
\(968\) | 16141.3i | 0.535953i | ||||||||
\(969\) | −5737.05 | −0.190197 | ||||||||
\(970\) | 27447.2 | − | 12729.0i | 0.908533 | − | 0.421343i | ||||
\(971\) | −35414.7 | −1.17046 | −0.585228 | − | 0.810869i | \(-0.698995\pi\) | ||||
−0.585228 | + | 0.810869i | \(0.698995\pi\) | |||||||
\(972\) | 763.142i | 0.0251829i | ||||||||
\(973\) | 21458.5i | 0.707016i | ||||||||
\(974\) | 47085.6 | 1.54899 | ||||||||
\(975\) | 2457.75 | − | 2904.25i | 0.0807292 | − | 0.0953954i | ||||
\(976\) | −51834.3 | −1.69997 | ||||||||
\(977\) | − | 20952.6i | − | 0.686112i | −0.939315 | − | 0.343056i | \(-0.888538\pi\) | ||
0.939315 | − | 0.343056i | \(-0.111462\pi\) | |||||||
\(978\) | − | 5727.10i | − | 0.187252i | ||||||
\(979\) | 619.955 | 0.0202388 | ||||||||
\(980\) | 1560.81 | − | 723.842i | 0.0508756 | − | 0.0235942i | ||||
\(981\) | 13797.2 | 0.449044 | ||||||||
\(982\) | − | 30073.7i | − | 0.977281i | ||||||
\(983\) | 20858.6i | 0.676793i | 0.941004 | + | 0.338396i | \(0.109884\pi\) | ||||
−0.941004 | + | 0.338396i | \(0.890116\pi\) | |||||||
\(984\) | −24089.0 | −0.780417 | ||||||||
\(985\) | −11316.9 | − | 24402.4i | −0.366078 | − | 0.789366i | ||||
\(986\) | 848.963 | 0.0274204 | ||||||||
\(987\) | 4472.10i | 0.144223i | ||||||||
\(988\) | 2467.06i | 0.0794409i | ||||||||
\(989\) | 32961.1 | 1.05976 | ||||||||
\(990\) | 2589.44 | + | 5583.55i | 0.0831290 | + | 0.179249i | ||||
\(991\) | −13565.0 | −0.434820 | −0.217410 | − | 0.976080i | \(-0.569761\pi\) | ||||
−0.217410 | + | 0.976080i | \(0.569761\pi\) | |||||||
\(992\) | 16771.7i | 0.536795i | ||||||||
\(993\) | 27892.7i | 0.891386i | ||||||||
\(994\) | 10909.7 | 0.348122 | ||||||||
\(995\) | −12093.6 | + | 5608.57i | −0.385320 | + | 0.178697i | ||||
\(996\) | −116.080 | −0.00369292 | ||||||||
\(997\) | − | 12520.7i | − | 0.397727i | −0.980027 | − | 0.198864i | \(-0.936275\pi\) | ||
0.980027 | − | 0.198864i | \(-0.0637251\pi\) | |||||||
\(998\) | 8861.94i | 0.281082i | ||||||||
\(999\) | 5829.43 | 0.184620 |
(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 | 105.4.d.b.64.3 | ✓ | 10 | |
3.2 | odd | 2 | 315.4.d.b.64.8 | 10 | |||
5.2 | odd | 4 | 525.4.a.x.1.4 | 5 | |||
5.3 | odd | 4 | 525.4.a.w.1.2 | 5 | |||
5.4 | even | 2 | inner | 105.4.d.b.64.8 | yes | 10 | |
15.2 | even | 4 | 1575.4.a.bo.1.2 | 5 | |||
15.8 | even | 4 | 1575.4.a.bp.1.4 | 5 | |||
15.14 | odd | 2 | 315.4.d.b.64.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.d.b.64.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
105.4.d.b.64.8 | yes | 10 | 5.4 | even | 2 | inner | |
315.4.d.b.64.3 | 10 | 15.14 | odd | 2 | |||
315.4.d.b.64.8 | 10 | 3.2 | odd | 2 | |||
525.4.a.w.1.2 | 5 | 5.3 | odd | 4 | |||
525.4.a.x.1.4 | 5 | 5.2 | odd | 4 | |||
1575.4.a.bo.1.2 | 5 | 15.2 | even | 4 | |||
1575.4.a.bp.1.4 | 5 | 15.8 | even | 4 |