Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(274,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, 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("525.274");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.9760027530\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.3 | ||
Root | \(-2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.274 |
Dual form | 525.4.d.i.274.2 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.43845i | 0.508568i | 0.967130 | + | 0.254284i | \(0.0818398\pi\) | ||||
−0.967130 | + | 0.254284i | \(0.918160\pi\) | |||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | 5.93087 | 0.741359 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.31534 | 0.293622 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | 20.0388i | 0.885599i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.61553 | 0.208743 | 0.104371 | − | 0.994538i | \(-0.466717\pi\) | ||||
0.104371 | + | 0.994538i | \(0.466717\pi\) | |||||||
\(12\) | − 17.7926i | − 0.428024i | ||||||||
\(13\) | 52.3542i | 1.11696i | 0.829519 | + | 0.558478i | \(0.188615\pi\) | ||||
−0.829519 | + | 0.558478i | \(0.811385\pi\) | |||||||
\(14\) | −10.0691 | −0.192221 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 18.6222 | 0.290971 | ||||||||
\(17\) | 49.7235i | 0.709395i | 0.934981 | + | 0.354697i | \(0.115416\pi\) | ||||
−0.934981 | + | 0.354697i | \(0.884584\pi\) | |||||||
\(18\) | − 12.9460i | − 0.169523i | ||||||||
\(19\) | −140.600 | −1.69768 | −0.848840 | − | 0.528649i | \(-0.822699\pi\) | ||||
−0.848840 | + | 0.528649i | \(0.822699\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 10.9545i | 0.106160i | ||||||||
\(23\) | − 23.4470i | − 0.212566i | −0.994336 | − | 0.106283i | \(-0.966105\pi\) | ||||
0.994336 | − | 0.106283i | \(-0.0338950\pi\) | |||||||
\(24\) | 60.1165 | 0.511301 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −75.3087 | −0.568048 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 41.5161i | 0.280207i | ||||||||
\(29\) | −157.170 | −1.00641 | −0.503204 | − | 0.864168i | \(-0.667845\pi\) | ||||
−0.503204 | + | 0.864168i | \(0.667845\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 127.892 | 0.740971 | 0.370485 | − | 0.928838i | \(-0.379191\pi\) | ||||
0.370485 | + | 0.928838i | \(0.379191\pi\) | |||||||
\(32\) | 187.098i | 1.03358i | ||||||||
\(33\) | − 22.8466i | − 0.120518i | ||||||||
\(34\) | −71.5246 | −0.360776 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −53.3778 | −0.247120 | ||||||||
\(37\) | 115.477i | 0.513090i | 0.966532 | + | 0.256545i | \(0.0825843\pi\) | ||||
−0.966532 | + | 0.256545i | \(0.917416\pi\) | |||||||
\(38\) | − 202.246i | − 0.863386i | ||||||||
\(39\) | 157.062 | 0.644875 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −188.617 | −0.718466 | −0.359233 | − | 0.933248i | \(-0.616962\pi\) | ||||
−0.359233 | + | 0.933248i | \(0.616962\pi\) | |||||||
\(42\) | 30.2074i | 0.110979i | ||||||||
\(43\) | 322.186i | 1.14262i | 0.820733 | + | 0.571312i | \(0.193565\pi\) | ||||
−0.820733 | + | 0.571312i | \(0.806435\pi\) | |||||||
\(44\) | 45.1667 | 0.154753 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 33.7272 | 0.108104 | ||||||||
\(47\) | 76.6477i | 0.237877i | 0.992902 | + | 0.118938i | \(0.0379491\pi\) | ||||
−0.992902 | + | 0.118938i | \(0.962051\pi\) | |||||||
\(48\) | − 55.8665i | − 0.167992i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 149.170 | 0.409569 | ||||||||
\(52\) | 310.506i | 0.828065i | ||||||||
\(53\) | − 424.172i | − 1.09933i | −0.835385 | − | 0.549666i | \(-0.814755\pi\) | ||||
0.835385 | − | 0.549666i | \(-0.185245\pi\) | |||||||
\(54\) | −38.8381 | −0.0978739 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −140.272 | −0.334725 | ||||||||
\(57\) | 421.801i | 0.980157i | ||||||||
\(58\) | − 226.081i | − 0.511827i | ||||||||
\(59\) | −107.784 | −0.237835 | −0.118918 | − | 0.992904i | \(-0.537942\pi\) | ||||
−0.118918 | + | 0.992904i | \(0.537942\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 915.511 | 1.92163 | 0.960813 | − | 0.277197i | \(-0.0894053\pi\) | ||||
0.960813 | + | 0.277197i | \(0.0894053\pi\) | |||||||
\(62\) | 183.966i | 0.376834i | ||||||||
\(63\) | − 63.0000i | − 0.125988i | ||||||||
\(64\) | −120.153 | −0.234673 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 32.8636 | 0.0612914 | ||||||||
\(67\) | 451.723i | 0.823684i | 0.911255 | + | 0.411842i | \(0.135114\pi\) | ||||
−0.911255 | + | 0.411842i | \(0.864886\pi\) | |||||||
\(68\) | 294.903i | 0.525916i | ||||||||
\(69\) | −70.3409 | −0.122725 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 907.312 | 1.51659 | 0.758297 | − | 0.651909i | \(-0.226032\pi\) | ||||
0.758297 | + | 0.651909i | \(0.226032\pi\) | |||||||
\(72\) | − 180.349i | − 0.295200i | ||||||||
\(73\) | 755.956i | 1.21203i | 0.795454 | + | 0.606014i | \(0.207232\pi\) | ||||
−0.795454 | + | 0.606014i | \(0.792768\pi\) | |||||||
\(74\) | −166.108 | −0.260941 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −833.882 | −1.25859 | ||||||||
\(77\) | 53.3087i | 0.0788973i | ||||||||
\(78\) | 225.926i | 0.327963i | ||||||||
\(79\) | −22.5834 | −0.0321624 | −0.0160812 | − | 0.999871i | \(-0.505119\pi\) | ||||
−0.0160812 | + | 0.999871i | \(0.505119\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | − 271.316i | − 0.365389i | ||||||||
\(83\) | 1112.25i | 1.47091i | 0.677575 | + | 0.735454i | \(0.263031\pi\) | ||||
−0.677575 | + | 0.735454i | \(0.736969\pi\) | |||||||
\(84\) | 124.548 | 0.161778 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −463.447 | −0.581102 | ||||||||
\(87\) | 471.511i | 0.581050i | ||||||||
\(88\) | 152.606i | 0.184862i | ||||||||
\(89\) | −1518.81 | −1.80892 | −0.904458 | − | 0.426562i | \(-0.859725\pi\) | ||||
−0.904458 | + | 0.426562i | \(0.859725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −366.479 | −0.422170 | ||||||||
\(92\) | − 139.061i | − 0.157588i | ||||||||
\(93\) | − 383.676i | − 0.427800i | ||||||||
\(94\) | −110.254 | −0.120977 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 561.293 | 0.596736 | ||||||||
\(97\) | 549.987i | 0.575698i | 0.957676 | + | 0.287849i | \(0.0929401\pi\) | ||||
−0.957676 | + | 0.287849i | \(0.907060\pi\) | |||||||
\(98\) | − 70.4839i | − 0.0726526i | ||||||||
\(99\) | −68.5398 | −0.0695809 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −533.299 | −0.525398 | −0.262699 | − | 0.964878i | \(-0.584613\pi\) | ||||
−0.262699 | + | 0.964878i | \(0.584613\pi\) | |||||||
\(102\) | 214.574i | 0.208294i | ||||||||
\(103\) | 1357.79i | 1.29890i | 0.760404 | + | 0.649451i | \(0.225001\pi\) | ||||
−0.760404 | + | 0.649451i | \(0.774999\pi\) | |||||||
\(104\) | −1049.12 | −0.989176 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 610.149 | 0.559084 | ||||||||
\(107\) | − 913.693i | − 0.825515i | −0.910841 | − | 0.412757i | \(-0.864566\pi\) | ||||
0.910841 | − | 0.412757i | \(-0.135434\pi\) | |||||||
\(108\) | 160.133i | 0.142675i | ||||||||
\(109\) | 160.489 | 0.141028 | 0.0705139 | − | 0.997511i | \(-0.477536\pi\) | ||||
0.0705139 | + | 0.997511i | \(0.477536\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 346.432 | 0.296233 | ||||||||
\(112\) | 130.355i | 0.109977i | ||||||||
\(113\) | − 1788.48i | − 1.48891i | −0.667675 | − | 0.744453i | \(-0.732710\pi\) | ||||
0.667675 | − | 0.744453i | \(-0.267290\pi\) | |||||||
\(114\) | −606.739 | −0.498476 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −932.157 | −0.746109 | ||||||||
\(117\) | − 471.187i | − 0.372319i | ||||||||
\(118\) | − 155.042i | − 0.120955i | ||||||||
\(119\) | −348.064 | −0.268126 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1273.00 | −0.956427 | ||||||||
\(122\) | 1316.91i | 0.977277i | ||||||||
\(123\) | 565.852i | 0.414806i | ||||||||
\(124\) | 758.511 | 0.549325 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 90.6222 | 0.0640735 | ||||||||
\(127\) | 271.015i | 0.189360i | 0.995508 | + | 0.0946799i | \(0.0301828\pi\) | ||||
−0.995508 | + | 0.0946799i | \(0.969817\pi\) | |||||||
\(128\) | 1323.95i | 0.914231i | ||||||||
\(129\) | 966.557 | 0.659694 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −763.151 | −0.508984 | −0.254492 | − | 0.967075i | \(-0.581908\pi\) | ||||
−0.254492 | + | 0.967075i | \(0.581908\pi\) | |||||||
\(132\) | − 135.500i | − 0.0893468i | ||||||||
\(133\) | − 984.203i | − 0.641663i | ||||||||
\(134\) | −649.780 | −0.418899 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −996.400 | −0.628240 | ||||||||
\(137\) | 240.934i | 0.150251i | 0.997174 | + | 0.0751254i | \(0.0239357\pi\) | ||||
−0.997174 | + | 0.0751254i | \(0.976064\pi\) | |||||||
\(138\) | − 101.182i | − 0.0624141i | ||||||||
\(139\) | 103.150 | 0.0629427 | 0.0314714 | − | 0.999505i | \(-0.489981\pi\) | ||||
0.0314714 | + | 0.999505i | \(0.489981\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 229.943 | 0.137338 | ||||||||
\(142\) | 1305.12i | 0.771291i | ||||||||
\(143\) | 398.705i | 0.233156i | ||||||||
\(144\) | −167.600 | −0.0969905 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1087.40 | −0.616398 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | 684.881i | 0.380384i | ||||||||
\(149\) | 3256.71 | 1.79061 | 0.895303 | − | 0.445458i | \(-0.146959\pi\) | ||||
0.895303 | + | 0.445458i | \(0.146959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1471.04 | 0.792793 | 0.396396 | − | 0.918080i | \(-0.370261\pi\) | ||||
0.396396 | + | 0.918080i | \(0.370261\pi\) | |||||||
\(152\) | − 2817.47i | − 1.50346i | ||||||||
\(153\) | − 447.511i | − 0.236465i | ||||||||
\(154\) | −76.6817 | −0.0401246 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 931.517 | 0.478084 | ||||||||
\(157\) | 1394.22i | 0.708730i | 0.935107 | + | 0.354365i | \(0.115303\pi\) | ||||
−0.935107 | + | 0.354365i | \(0.884697\pi\) | |||||||
\(158\) | − 32.4850i | − 0.0163567i | ||||||||
\(159\) | −1272.52 | −0.634699 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 164.129 | 0.0803426 | ||||||||
\(162\) | 116.514i | 0.0565075i | ||||||||
\(163\) | − 3674.27i | − 1.76559i | −0.469760 | − | 0.882794i | \(-0.655659\pi\) | ||||
0.469760 | − | 0.882794i | \(-0.344341\pi\) | |||||||
\(164\) | −1118.67 | −0.532641 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1599.91 | −0.748056 | ||||||||
\(167\) | − 4041.09i | − 1.87251i | −0.351325 | − | 0.936254i | \(-0.614269\pi\) | ||||
0.351325 | − | 0.936254i | \(-0.385731\pi\) | |||||||
\(168\) | 420.815i | 0.193254i | ||||||||
\(169\) | −543.958 | −0.247591 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1265.40 | 0.565894 | ||||||||
\(172\) | 1910.84i | 0.847094i | ||||||||
\(173\) | 59.4582i | 0.0261302i | 0.999915 | + | 0.0130651i | \(0.00415886\pi\) | ||||
−0.999915 | + | 0.0130651i | \(0.995841\pi\) | |||||||
\(174\) | −678.244 | −0.295503 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 141.818 | 0.0607381 | ||||||||
\(177\) | 323.352i | 0.137314i | ||||||||
\(178\) | − 2184.73i | − 0.919957i | ||||||||
\(179\) | 2973.32 | 1.24155 | 0.620773 | − | 0.783991i | \(-0.286819\pi\) | ||||
0.620773 | + | 0.783991i | \(0.286819\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −676.220 | −0.277696 | −0.138848 | − | 0.990314i | \(-0.544340\pi\) | ||||
−0.138848 | + | 0.990314i | \(0.544340\pi\) | |||||||
\(182\) | − 527.161i | − 0.214702i | ||||||||
\(183\) | − 2746.53i | − 1.10945i | ||||||||
\(184\) | 469.849 | 0.188249 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 551.898 | 0.217565 | ||||||||
\(187\) | 378.671i | 0.148081i | ||||||||
\(188\) | 454.588i | 0.176352i | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.5589 | 0.00627308 | 0.00313654 | − | 0.999995i | \(-0.499002\pi\) | ||||
0.00313654 | + | 0.999995i | \(0.499002\pi\) | |||||||
\(192\) | 360.458i | 0.135489i | ||||||||
\(193\) | 2694.68i | 1.00501i | 0.864574 | + | 0.502506i | \(0.167589\pi\) | ||||
−0.864574 | + | 0.502506i | \(0.832411\pi\) | |||||||
\(194\) | −791.127 | −0.292781 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −290.613 | −0.105908 | ||||||||
\(197\) | − 1027.38i | − 0.371561i | −0.982591 | − | 0.185781i | \(-0.940519\pi\) | ||||
0.982591 | − | 0.185781i | \(-0.0594814\pi\) | |||||||
\(198\) | − 98.5908i | − 0.0353866i | ||||||||
\(199\) | −2823.77 | −1.00589 | −0.502944 | − | 0.864319i | \(-0.667750\pi\) | ||||
−0.502944 | + | 0.864319i | \(0.667750\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1355.17 | 0.475554 | ||||||||
\(202\) | − 767.123i | − 0.267201i | ||||||||
\(203\) | − 1100.19i | − 0.380386i | ||||||||
\(204\) | 884.710 | 0.303638 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1953.11 | −0.660579 | ||||||||
\(207\) | 211.023i | 0.0708555i | ||||||||
\(208\) | 974.948i | 0.325002i | ||||||||
\(209\) | −1070.75 | −0.354378 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5151.16 | 1.68067 | 0.840333 | − | 0.542071i | \(-0.182360\pi\) | ||||
0.840333 | + | 0.542071i | \(0.182360\pi\) | |||||||
\(212\) | − 2515.71i | − 0.814999i | ||||||||
\(213\) | − 2721.94i | − 0.875606i | ||||||||
\(214\) | 1314.30 | 0.419830 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −541.048 | −0.170434 | ||||||||
\(217\) | 895.244i | 0.280061i | ||||||||
\(218\) | 230.855i | 0.0717222i | ||||||||
\(219\) | 2267.87 | 0.699764 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2603.23 | −0.792363 | ||||||||
\(222\) | 498.324i | 0.150655i | ||||||||
\(223\) | − 114.496i | − 0.0343822i | −0.999852 | − | 0.0171911i | \(-0.994528\pi\) | ||||
0.999852 | − | 0.0171911i | \(-0.00547237\pi\) | |||||||
\(224\) | −1309.68 | −0.390656 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2572.64 | 0.757209 | ||||||||
\(227\) | − 4744.75i | − 1.38731i | −0.720306 | − | 0.693657i | \(-0.755999\pi\) | ||||
0.720306 | − | 0.693657i | \(-0.244001\pi\) | |||||||
\(228\) | 2501.65i | 0.726648i | ||||||||
\(229\) | 5384.47 | 1.55378 | 0.776891 | − | 0.629635i | \(-0.216796\pi\) | ||||
0.776891 | + | 0.629635i | \(0.216796\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 159.926 | 0.0455514 | ||||||||
\(232\) | − 3149.51i | − 0.891274i | ||||||||
\(233\) | − 1608.91i | − 0.452373i | −0.974084 | − | 0.226187i | \(-0.927374\pi\) | ||||
0.974084 | − | 0.226187i | \(-0.0726260\pi\) | |||||||
\(234\) | 677.778 | 0.189349 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −639.253 | −0.176321 | ||||||||
\(237\) | 67.7501i | 0.0185689i | ||||||||
\(238\) | − 500.672i | − 0.136360i | ||||||||
\(239\) | 3113.11 | 0.842554 | 0.421277 | − | 0.906932i | \(-0.361582\pi\) | ||||
0.421277 | + | 0.906932i | \(0.361582\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7136.38 | 1.90745 | 0.953724 | − | 0.300685i | \(-0.0972151\pi\) | ||||
0.953724 | + | 0.300685i | \(0.0972151\pi\) | |||||||
\(242\) | − 1831.15i | − 0.486408i | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 5429.78 | 1.42461 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −813.948 | −0.210957 | ||||||||
\(247\) | − 7361.01i | − 1.89624i | ||||||||
\(248\) | 2562.81i | 0.656203i | ||||||||
\(249\) | 3336.75 | 0.849229 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −225.504 | −0.0567079 | −0.0283539 | − | 0.999598i | \(-0.509027\pi\) | ||||
−0.0283539 | + | 0.999598i | \(0.509027\pi\) | |||||||
\(252\) | − 373.645i | − 0.0934024i | ||||||||
\(253\) | − 178.561i | − 0.0443717i | ||||||||
\(254\) | −389.841 | −0.0963024 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2865.65 | −0.699621 | ||||||||
\(257\) | 4423.05i | 1.07355i | 0.843725 | + | 0.536775i | \(0.180358\pi\) | ||||
−0.843725 | + | 0.536775i | \(0.819642\pi\) | |||||||
\(258\) | 1390.34i | 0.335499i | ||||||||
\(259\) | −808.341 | −0.193930 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1414.53 | 0.335469 | ||||||||
\(262\) | − 1097.75i | − 0.258853i | ||||||||
\(263\) | 6540.56i | 1.53349i | 0.641950 | + | 0.766746i | \(0.278125\pi\) | ||||
−0.641950 | + | 0.766746i | \(0.721875\pi\) | |||||||
\(264\) | 457.819 | 0.106730 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1415.72 | 0.326329 | ||||||||
\(267\) | 4556.43i | 1.04438i | ||||||||
\(268\) | 2679.11i | 0.610645i | ||||||||
\(269\) | −2262.97 | −0.512920 | −0.256460 | − | 0.966555i | \(-0.582556\pi\) | ||||
−0.256460 | + | 0.966555i | \(0.582556\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1615.68 | 0.362160 | 0.181080 | − | 0.983468i | \(-0.442041\pi\) | ||||
0.181080 | + | 0.983468i | \(0.442041\pi\) | |||||||
\(272\) | 925.959i | 0.206414i | ||||||||
\(273\) | 1099.44i | 0.243740i | ||||||||
\(274\) | −346.571 | −0.0764127 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −417.183 | −0.0909835 | ||||||||
\(277\) | − 4691.55i | − 1.01765i | −0.860871 | − | 0.508823i | \(-0.830081\pi\) | ||||
0.860871 | − | 0.508823i | \(-0.169919\pi\) | |||||||
\(278\) | 148.375i | 0.0320107i | ||||||||
\(279\) | −1151.03 | −0.246990 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8119.00 | −1.72363 | −0.861813 | − | 0.507226i | \(-0.830671\pi\) | ||||
−0.861813 | + | 0.507226i | \(0.830671\pi\) | |||||||
\(282\) | 330.761i | 0.0698459i | ||||||||
\(283\) | − 3633.75i | − 0.763265i | −0.924314 | − | 0.381632i | \(-0.875362\pi\) | ||||
0.924314 | − | 0.381632i | \(-0.124638\pi\) | |||||||
\(284\) | 5381.15 | 1.12434 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −573.515 | −0.118576 | ||||||||
\(287\) | − 1320.32i | − 0.271554i | ||||||||
\(288\) | − 1683.88i | − 0.344526i | ||||||||
\(289\) | 2440.58 | 0.496759 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1649.96 | 0.332379 | ||||||||
\(292\) | 4483.48i | 0.898547i | ||||||||
\(293\) | − 7981.99i | − 1.59151i | −0.605618 | − | 0.795756i | \(-0.707074\pi\) | ||||
0.605618 | − | 0.795756i | \(-0.292926\pi\) | |||||||
\(294\) | −211.452 | −0.0419460 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2314.03 | −0.454392 | ||||||||
\(297\) | 205.619i | 0.0401725i | ||||||||
\(298\) | 4684.61i | 0.910645i | ||||||||
\(299\) | 1227.55 | 0.237427 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2255.30 | −0.431871 | ||||||||
\(302\) | 2116.02i | 0.403189i | ||||||||
\(303\) | 1599.90i | 0.303339i | ||||||||
\(304\) | −2618.28 | −0.493977 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 643.721 | 0.120259 | ||||||||
\(307\) | 7118.15i | 1.32330i | 0.749811 | + | 0.661652i | \(0.230144\pi\) | ||||
−0.749811 | + | 0.661652i | \(0.769856\pi\) | |||||||
\(308\) | 316.167i | 0.0584912i | ||||||||
\(309\) | 4073.36 | 0.749921 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9155.92 | −1.66940 | −0.834702 | − | 0.550703i | \(-0.814360\pi\) | ||||
−0.834702 | + | 0.550703i | \(0.814360\pi\) | |||||||
\(312\) | 3147.35i | 0.571101i | ||||||||
\(313\) | − 6163.44i | − 1.11303i | −0.830838 | − | 0.556515i | \(-0.812138\pi\) | ||||
0.830838 | − | 0.556515i | \(-0.187862\pi\) | |||||||
\(314\) | −2005.51 | −0.360438 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −133.939 | −0.0238438 | ||||||||
\(317\) | − 8658.37i | − 1.53408i | −0.641601 | − | 0.767038i | \(-0.721730\pi\) | ||||
0.641601 | − | 0.767038i | \(-0.278270\pi\) | |||||||
\(318\) | − 1830.45i | − 0.322788i | ||||||||
\(319\) | −1196.94 | −0.210080 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2741.08 | −0.476611 | ||||||||
\(322\) | 236.090i | 0.0408597i | ||||||||
\(323\) | − 6991.14i | − 1.20433i | ||||||||
\(324\) | 480.400 | 0.0823732 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5285.24 | 0.897922 | ||||||||
\(327\) | − 481.466i | − 0.0814224i | ||||||||
\(328\) | − 3779.67i | − 0.636272i | ||||||||
\(329\) | −536.534 | −0.0899090 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −128.477 | −0.0213346 | −0.0106673 | − | 0.999943i | \(-0.503396\pi\) | ||||
−0.0106673 | + | 0.999943i | \(0.503396\pi\) | |||||||
\(332\) | 6596.61i | 1.09047i | ||||||||
\(333\) | − 1039.30i | − 0.171030i | ||||||||
\(334\) | 5812.89 | 0.952297 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 391.066 | 0.0634952 | ||||||||
\(337\) | − 7784.57i | − 1.25832i | −0.777277 | − | 0.629158i | \(-0.783400\pi\) | ||||
0.777277 | − | 0.629158i | \(-0.216600\pi\) | |||||||
\(338\) | − 782.455i | − 0.125917i | ||||||||
\(339\) | −5365.45 | −0.859620 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 973.965 | 0.154672 | ||||||||
\(342\) | 1820.22i | 0.287795i | ||||||||
\(343\) | − 343.000i | − 0.0539949i | ||||||||
\(344\) | −6456.22 | −1.01191 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −85.5274 | −0.0132890 | ||||||||
\(347\) | − 3740.26i | − 0.578638i | −0.957233 | − | 0.289319i | \(-0.906571\pi\) | ||||
0.957233 | − | 0.289319i | \(-0.0934289\pi\) | |||||||
\(348\) | 2796.47i | 0.430766i | ||||||||
\(349\) | −5676.86 | −0.870703 | −0.435351 | − | 0.900261i | \(-0.643376\pi\) | ||||
−0.435351 | + | 0.900261i | \(0.643376\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1413.56 | −0.214958 | ||||||||
\(352\) | 1424.85i | 0.215752i | ||||||||
\(353\) | 909.564i | 0.137142i | 0.997646 | + | 0.0685711i | \(0.0218440\pi\) | ||||
−0.997646 | + | 0.0685711i | \(0.978156\pi\) | |||||||
\(354\) | −465.125 | −0.0698337 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9007.87 | −1.34106 | ||||||||
\(357\) | 1044.19i | 0.154803i | ||||||||
\(358\) | 4276.97i | 0.631410i | ||||||||
\(359\) | −2678.57 | −0.393788 | −0.196894 | − | 0.980425i | \(-0.563085\pi\) | ||||
−0.196894 | + | 0.980425i | \(0.563085\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12909.5 | 1.88212 | ||||||||
\(362\) | − 972.706i | − 0.141227i | ||||||||
\(363\) | 3819.01i | 0.552193i | ||||||||
\(364\) | −2173.54 | −0.312979 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3950.74 | 0.564231 | ||||||||
\(367\) | 716.898i | 0.101967i | 0.998700 | + | 0.0509833i | \(0.0162355\pi\) | ||||
−0.998700 | + | 0.0509833i | \(0.983764\pi\) | |||||||
\(368\) | − 436.633i | − 0.0618508i | ||||||||
\(369\) | 1697.56 | 0.239489 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2969.21 | 0.415508 | ||||||||
\(372\) | − 2275.53i | − 0.317153i | ||||||||
\(373\) | − 2006.15i | − 0.278484i | −0.990258 | − | 0.139242i | \(-0.955533\pi\) | ||||
0.990258 | − | 0.139242i | \(-0.0444665\pi\) | |||||||
\(374\) | −544.698 | −0.0753092 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1535.93 | −0.210664 | ||||||||
\(377\) | − 8228.53i | − 1.12411i | ||||||||
\(378\) | − 271.867i | − 0.0369929i | ||||||||
\(379\) | −7277.53 | −0.986336 | −0.493168 | − | 0.869934i | \(-0.664161\pi\) | ||||
−0.493168 | + | 0.869934i | \(0.664161\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 813.045 | 0.109327 | ||||||||
\(382\) | 23.8191i | 0.00319029i | ||||||||
\(383\) | 5953.94i | 0.794339i | 0.917745 | + | 0.397170i | \(0.130008\pi\) | ||||
−0.917745 | + | 0.397170i | \(0.869992\pi\) | |||||||
\(384\) | 3971.84 | 0.527831 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3876.16 | −0.511117 | ||||||||
\(387\) | − 2899.67i | − 0.380875i | ||||||||
\(388\) | 3261.90i | 0.426799i | ||||||||
\(389\) | −1867.98 | −0.243472 | −0.121736 | − | 0.992563i | \(-0.538846\pi\) | ||||
−0.121736 | + | 0.992563i | \(0.538846\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1165.86 | 0.150794 | ||||||||
\(392\) | − 981.902i | − 0.126514i | ||||||||
\(393\) | 2289.45i | 0.293862i | ||||||||
\(394\) | 1477.83 | 0.188964 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −406.500 | −0.0515844 | ||||||||
\(397\) | 2160.07i | 0.273075i | 0.990635 | + | 0.136538i | \(0.0435974\pi\) | ||||
−0.990635 | + | 0.136538i | \(0.956403\pi\) | |||||||
\(398\) | − 4061.85i | − 0.511563i | ||||||||
\(399\) | −2952.61 | −0.370464 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1954.81 | 0.243438 | 0.121719 | − | 0.992565i | \(-0.461159\pi\) | ||||
0.121719 | + | 0.992565i | \(0.461159\pi\) | |||||||
\(402\) | 1949.34i | 0.241851i | ||||||||
\(403\) | 6695.68i | 0.827632i | ||||||||
\(404\) | −3162.93 | −0.389509 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1582.57 | 0.193452 | ||||||||
\(407\) | 879.420i | 0.107104i | ||||||||
\(408\) | 2989.20i | 0.362714i | ||||||||
\(409\) | −14895.1 | −1.80077 | −0.900384 | − | 0.435096i | \(-0.856714\pi\) | ||||
−0.900384 | + | 0.435096i | \(0.856714\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 722.801 | 0.0867474 | ||||||||
\(412\) | 8052.86i | 0.962952i | ||||||||
\(413\) | − 754.489i | − 0.0898934i | ||||||||
\(414\) | −303.545 | −0.0360348 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9795.34 | −1.15446 | ||||||||
\(417\) | − 309.449i | − 0.0363400i | ||||||||
\(418\) | − 1540.21i | − 0.180225i | ||||||||
\(419\) | −12608.9 | −1.47013 | −0.735067 | − | 0.677994i | \(-0.762849\pi\) | ||||
−0.735067 | + | 0.677994i | \(0.762849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7862.86 | −0.910243 | −0.455122 | − | 0.890429i | \(-0.650404\pi\) | ||||
−0.455122 | + | 0.890429i | \(0.650404\pi\) | |||||||
\(422\) | 7409.67i | 0.854732i | ||||||||
\(423\) | − 689.829i | − 0.0792923i | ||||||||
\(424\) | 8499.91 | 0.973567 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3915.36 | 0.445305 | ||||||||
\(427\) | 6408.58i | 0.726307i | ||||||||
\(428\) | − 5419.00i | − 0.612002i | ||||||||
\(429\) | 1196.11 | 0.134613 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14291.0 | 1.59715 | 0.798575 | − | 0.601896i | \(-0.205588\pi\) | ||||
0.798575 | + | 0.601896i | \(0.205588\pi\) | |||||||
\(432\) | 502.799i | 0.0559975i | ||||||||
\(433\) | − 13759.0i | − 1.52705i | −0.645776 | − | 0.763527i | \(-0.723466\pi\) | ||||
0.645776 | − | 0.763527i | \(-0.276534\pi\) | |||||||
\(434\) | −1287.76 | −0.142430 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 951.838 | 0.104552 | ||||||||
\(437\) | 3296.65i | 0.360870i | ||||||||
\(438\) | 3262.21i | 0.355878i | ||||||||
\(439\) | 6093.13 | 0.662436 | 0.331218 | − | 0.943554i | \(-0.392541\pi\) | ||||
0.331218 | + | 0.943554i | \(0.392541\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | − 3744.61i | − 0.402970i | ||||||||
\(443\) | 13449.5i | 1.44244i | 0.692704 | + | 0.721222i | \(0.256419\pi\) | ||||
−0.692704 | + | 0.721222i | \(0.743581\pi\) | |||||||
\(444\) | 2054.64 | 0.219615 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 164.697 | 0.0174857 | ||||||||
\(447\) | − 9770.14i | − 1.03381i | ||||||||
\(448\) | − 841.068i | − 0.0886981i | ||||||||
\(449\) | −6893.83 | −0.724588 | −0.362294 | − | 0.932064i | \(-0.618006\pi\) | ||||
−0.362294 | + | 0.932064i | \(0.618006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1436.42 | −0.149974 | ||||||||
\(452\) | − 10607.3i | − 1.10381i | ||||||||
\(453\) | − 4413.13i | − 0.457719i | ||||||||
\(454\) | 6825.07 | 0.705543 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8452.40 | −0.868026 | ||||||||
\(457\) | 11820.1i | 1.20990i | 0.796265 | + | 0.604948i | \(0.206806\pi\) | ||||
−0.796265 | + | 0.604948i | \(0.793194\pi\) | |||||||
\(458\) | 7745.28i | 0.790203i | ||||||||
\(459\) | −1342.53 | −0.136523 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8443.38 | 0.853031 | 0.426516 | − | 0.904480i | \(-0.359741\pi\) | ||||
0.426516 | + | 0.904480i | \(0.359741\pi\) | |||||||
\(462\) | 230.045i | 0.0231660i | ||||||||
\(463\) | − 1269.74i | − 0.127451i | −0.997967 | − | 0.0637257i | \(-0.979702\pi\) | ||||
0.997967 | − | 0.0637257i | \(-0.0202983\pi\) | |||||||
\(464\) | −2926.86 | −0.292836 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2314.33 | 0.230063 | ||||||||
\(467\) | 16481.8i | 1.63316i | 0.577233 | + | 0.816579i | \(0.304132\pi\) | ||||
−0.577233 | + | 0.816579i | \(0.695868\pi\) | |||||||
\(468\) | − 2794.55i | − 0.276022i | ||||||||
\(469\) | −3162.06 | −0.311323 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4182.65 | 0.409186 | ||||||||
\(472\) | − 2159.87i | − 0.210627i | ||||||||
\(473\) | 2453.61i | 0.238514i | ||||||||
\(474\) | −97.4549 | −0.00944357 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2064.32 | −0.198778 | ||||||||
\(477\) | 3817.55i | 0.366444i | ||||||||
\(478\) | 4478.05i | 0.428496i | ||||||||
\(479\) | 1400.21 | 0.133564 | 0.0667822 | − | 0.997768i | \(-0.478727\pi\) | ||||
0.0667822 | + | 0.997768i | \(0.478727\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6045.72 | −0.573100 | ||||||||
\(482\) | 10265.3i | 0.970066i | ||||||||
\(483\) | − 492.386i | − 0.0463858i | ||||||||
\(484\) | −7550.02 | −0.709055 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 349.543 | 0.0326246 | ||||||||
\(487\) | 14165.9i | 1.31811i | 0.752094 | + | 0.659055i | \(0.229044\pi\) | ||||
−0.752094 | + | 0.659055i | \(0.770956\pi\) | |||||||
\(488\) | 18345.8i | 1.70179i | ||||||||
\(489\) | −11022.8 | −1.01936 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4739.28 | 0.435603 | 0.217801 | − | 0.975993i | \(-0.430112\pi\) | ||||
0.217801 | + | 0.975993i | \(0.430112\pi\) | |||||||
\(492\) | 3356.00i | 0.307520i | ||||||||
\(493\) | − 7815.06i | − 0.713940i | ||||||||
\(494\) | 10588.4 | 0.964364 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2381.63 | 0.215601 | ||||||||
\(497\) | 6351.19i | 0.573219i | ||||||||
\(498\) | 4799.74i | 0.431890i | ||||||||
\(499\) | 11370.0 | 1.02003 | 0.510013 | − | 0.860167i | \(-0.329640\pi\) | ||||
0.510013 | + | 0.860167i | \(0.329640\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12123.3 | −1.08109 | ||||||||
\(502\) | − 324.375i | − 0.0288398i | ||||||||
\(503\) | 9212.48i | 0.816629i | 0.912841 | + | 0.408314i | \(0.133883\pi\) | ||||
−0.912841 | + | 0.408314i | \(0.866117\pi\) | |||||||
\(504\) | 1262.45 | 0.111575 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 256.851 | 0.0225660 | ||||||||
\(507\) | 1631.87i | 0.142947i | ||||||||
\(508\) | 1607.36i | 0.140384i | ||||||||
\(509\) | 15938.3 | 1.38792 | 0.693960 | − | 0.720014i | \(-0.255864\pi\) | ||||
0.693960 | + | 0.720014i | \(0.255864\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5291.69 | −0.458103 | ||||||||
\(512\) | 6469.49i | 0.558426i | ||||||||
\(513\) | − 3796.21i | − 0.326719i | ||||||||
\(514\) | −6362.33 | −0.545973 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5732.52 | 0.489070 | ||||||||
\(517\) | 583.713i | 0.0496550i | ||||||||
\(518\) | − 1162.76i | − 0.0986265i | ||||||||
\(519\) | 178.374 | 0.0150863 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6442.99 | 0.541790 | 0.270895 | − | 0.962609i | \(-0.412680\pi\) | ||||
0.270895 | + | 0.962609i | \(0.412680\pi\) | |||||||
\(522\) | 2034.73i | 0.170609i | ||||||||
\(523\) | 986.655i | 0.0824922i | 0.999149 | + | 0.0412461i | \(0.0131328\pi\) | ||||
−0.999149 | + | 0.0412461i | \(0.986867\pi\) | |||||||
\(524\) | −4526.15 | −0.377339 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9408.26 | −0.779885 | ||||||||
\(527\) | 6359.24i | 0.525641i | ||||||||
\(528\) | − 425.453i | − 0.0350672i | ||||||||
\(529\) | 11617.2 | 0.954815 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 970.057 | 0.0792785 | ||||||||
\(532\) | − 5837.18i | − 0.475703i | ||||||||
\(533\) | − 9874.91i | − 0.802495i | ||||||||
\(534\) | −6554.19 | −0.531137 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9052.01 | −0.729454 | ||||||||
\(537\) | − 8919.97i | − 0.716807i | ||||||||
\(538\) | − 3255.16i | − 0.260855i | ||||||||
\(539\) | −373.161 | −0.0298204 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12681.1 | −1.00777 | −0.503885 | − | 0.863771i | \(-0.668097\pi\) | ||||
−0.503885 | + | 0.863771i | \(0.668097\pi\) | |||||||
\(542\) | 2324.06i | 0.184183i | ||||||||
\(543\) | 2028.66i | 0.160328i | ||||||||
\(544\) | −9303.14 | −0.733215 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1581.48 | −0.123958 | ||||||||
\(547\) | 14826.4i | 1.15892i | 0.814999 | + | 0.579462i | \(0.196737\pi\) | ||||
−0.814999 | + | 0.579462i | \(0.803263\pi\) | |||||||
\(548\) | 1428.95i | 0.111390i | ||||||||
\(549\) | −8239.60 | −0.640542 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22098.2 | 1.70856 | ||||||||
\(552\) | − 1409.55i | − 0.108685i | ||||||||
\(553\) | − 158.083i | − 0.0121562i | ||||||||
\(554\) | 6748.55 | 0.517542 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 611.767 | 0.0466632 | ||||||||
\(557\) | − 1926.46i | − 0.146547i | −0.997312 | − | 0.0732737i | \(-0.976655\pi\) | ||||
0.997312 | − | 0.0732737i | \(-0.0233447\pi\) | |||||||
\(558\) | − 1655.69i | − 0.125611i | ||||||||
\(559\) | −16867.8 | −1.27626 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1136.01 | 0.0854946 | ||||||||
\(562\) | − 11678.8i | − 0.876581i | ||||||||
\(563\) | − 18624.8i | − 1.39422i | −0.716966 | − | 0.697108i | \(-0.754470\pi\) | ||||
0.716966 | − | 0.697108i | \(-0.245530\pi\) | |||||||
\(564\) | 1363.76 | 0.101817 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5226.96 | 0.388172 | ||||||||
\(567\) | 567.000i | 0.0419961i | ||||||||
\(568\) | 18181.5i | 1.34309i | ||||||||
\(569\) | 20093.9 | 1.48045 | 0.740227 | − | 0.672357i | \(-0.234718\pi\) | ||||
0.740227 | + | 0.672357i | \(0.234718\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4535.25 | 0.332389 | 0.166195 | − | 0.986093i | \(-0.446852\pi\) | ||||
0.166195 | + | 0.986093i | \(0.446852\pi\) | |||||||
\(572\) | 2364.66i | 0.172852i | ||||||||
\(573\) | − 49.6766i | − 0.00362176i | ||||||||
\(574\) | 1899.21 | 0.138104 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1081.37 | 0.0782243 | ||||||||
\(577\) | − 10034.6i | − 0.723994i | −0.932179 | − | 0.361997i | \(-0.882095\pi\) | ||||
0.932179 | − | 0.361997i | \(-0.117905\pi\) | |||||||
\(578\) | 3510.64i | 0.252636i | ||||||||
\(579\) | 8084.05 | 0.580244 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7785.75 | −0.555951 | ||||||||
\(582\) | 2373.38i | 0.169037i | ||||||||
\(583\) | − 3230.30i | − 0.229477i | ||||||||
\(584\) | −15148.5 | −1.07337 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11481.7 | 0.809391 | ||||||||
\(587\) | 11192.6i | 0.786999i | 0.919325 | + | 0.393499i | \(0.128736\pi\) | ||||
−0.919325 | + | 0.393499i | \(0.871264\pi\) | |||||||
\(588\) | 871.838i | 0.0611462i | ||||||||
\(589\) | −17981.7 | −1.25793 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3082.13 | −0.214521 | ||||||||
\(592\) | 2150.44i | 0.149295i | ||||||||
\(593\) | 20317.6i | 1.40699i | 0.710703 | + | 0.703493i | \(0.248377\pi\) | ||||
−0.710703 | + | 0.703493i | \(0.751623\pi\) | |||||||
\(594\) | −295.772 | −0.0204305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19315.1 | 1.32748 | ||||||||
\(597\) | 8471.31i | 0.580750i | ||||||||
\(598\) | 1765.76i | 0.120748i | ||||||||
\(599\) | 26376.5 | 1.79919 | 0.899594 | − | 0.436727i | \(-0.143862\pi\) | ||||
0.899594 | + | 0.436727i | \(0.143862\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9266.13 | 0.628907 | 0.314454 | − | 0.949273i | \(-0.398179\pi\) | ||||
0.314454 | + | 0.949273i | \(0.398179\pi\) | |||||||
\(602\) | − 3244.13i | − 0.219636i | ||||||||
\(603\) | − 4065.51i | − 0.274561i | ||||||||
\(604\) | 8724.56 | 0.587744 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2301.37 | −0.154268 | ||||||||
\(607\) | − 11338.0i | − 0.758149i | −0.925366 | − | 0.379075i | \(-0.876242\pi\) | ||||
0.925366 | − | 0.379075i | \(-0.123758\pi\) | |||||||
\(608\) | − 26306.0i | − 1.75469i | ||||||||
\(609\) | −3300.58 | −0.219616 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4012.83 | −0.265698 | ||||||||
\(612\) | − 2654.13i | − 0.175305i | ||||||||
\(613\) | 25712.5i | 1.69416i | 0.531469 | + | 0.847078i | \(0.321640\pi\) | ||||
−0.531469 | + | 0.847078i | \(0.678360\pi\) | |||||||
\(614\) | −10239.1 | −0.672990 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1068.24 | −0.0698714 | ||||||||
\(617\) | − 663.465i | − 0.0432903i | −0.999766 | − | 0.0216451i | \(-0.993110\pi\) | ||||
0.999766 | − | 0.0216451i | \(-0.00689040\pi\) | |||||||
\(618\) | 5859.32i | 0.381386i | ||||||||
\(619\) | 12768.7 | 0.829108 | 0.414554 | − | 0.910025i | \(-0.363938\pi\) | ||||
0.414554 | + | 0.910025i | \(0.363938\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 633.068 | 0.0409084 | ||||||||
\(622\) | − 13170.3i | − 0.849005i | ||||||||
\(623\) | − 10631.7i | − 0.683706i | ||||||||
\(624\) | 2924.84 | 0.187640 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8865.78 | 0.566051 | ||||||||
\(627\) | 3212.24i | 0.204600i | ||||||||
\(628\) | 8268.92i | 0.525423i | ||||||||
\(629\) | −5741.93 | −0.363984 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14937.6 | −0.942400 | −0.471200 | − | 0.882026i | \(-0.656179\pi\) | ||||
−0.471200 | + | 0.882026i | \(0.656179\pi\) | |||||||
\(632\) | − 452.544i | − 0.0284829i | ||||||||
\(633\) | − 15453.5i | − 0.970333i | ||||||||
\(634\) | 12454.6 | 0.780182 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7547.13 | −0.470540 | ||||||||
\(637\) | − 2565.35i | − 0.159565i | ||||||||
\(638\) | − 1721.73i | − 0.106840i | ||||||||
\(639\) | −8165.81 | −0.505531 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10903.0 | 0.671829 | 0.335914 | − | 0.941893i | \(-0.390955\pi\) | ||||
0.335914 | + | 0.941893i | \(0.390955\pi\) | |||||||
\(642\) | − 3942.90i | − 0.242389i | ||||||||
\(643\) | − 7623.47i | − 0.467559i | −0.972290 | − | 0.233779i | \(-0.924891\pi\) | ||||
0.972290 | − | 0.233779i | \(-0.0751094\pi\) | |||||||
\(644\) | 973.426 | 0.0595627 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10056.4 | 0.612482 | ||||||||
\(647\) | − 5384.84i | − 0.327202i | −0.986527 | − | 0.163601i | \(-0.947689\pi\) | ||||
0.986527 | − | 0.163601i | \(-0.0523110\pi\) | |||||||
\(648\) | 1623.14i | 0.0983999i | ||||||||
\(649\) | −820.833 | −0.0496464 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2685.73 | 0.161693 | ||||||||
\(652\) | − 21791.6i | − 1.30893i | ||||||||
\(653\) | 297.318i | 0.0178177i | 0.999960 | + | 0.00890883i | \(0.00283581\pi\) | ||||
−0.999960 | + | 0.00890883i | \(0.997164\pi\) | |||||||
\(654\) | 692.564 | 0.0414088 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3512.47 | −0.209053 | ||||||||
\(657\) | − 6803.61i | − 0.404009i | ||||||||
\(658\) | − 771.776i | − 0.0457248i | ||||||||
\(659\) | −10324.7 | −0.610309 | −0.305155 | − | 0.952303i | \(-0.598708\pi\) | ||||
−0.305155 | + | 0.952303i | \(0.598708\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4272.98 | 0.251437 | 0.125718 | − | 0.992066i | \(-0.459876\pi\) | ||||
0.125718 | + | 0.992066i | \(0.459876\pi\) | |||||||
\(662\) | − 184.808i | − 0.0108501i | ||||||||
\(663\) | 7809.69i | 0.457471i | ||||||||
\(664\) | −22288.2 | −1.30263 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1494.97 | 0.0869804 | ||||||||
\(667\) | 3685.17i | 0.213928i | ||||||||
\(668\) | − 23967.2i | − 1.38820i | ||||||||
\(669\) | −343.488 | −0.0198506 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6972.10 | 0.401125 | ||||||||
\(672\) | 3929.05i | 0.225545i | ||||||||
\(673\) | − 23033.4i | − 1.31927i | −0.751584 | − | 0.659637i | \(-0.770710\pi\) | ||||
0.751584 | − | 0.659637i | \(-0.229290\pi\) | |||||||
\(674\) | 11197.7 | 0.639940 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3226.15 | −0.183554 | ||||||||
\(677\) | − 5113.50i | − 0.290292i | −0.989410 | − | 0.145146i | \(-0.953635\pi\) | ||||
0.989410 | − | 0.145146i | \(-0.0463652\pi\) | |||||||
\(678\) | − 7717.91i | − 0.437175i | ||||||||
\(679\) | −3849.91 | −0.217593 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14234.2 | −0.800966 | ||||||||
\(682\) | 1401.00i | 0.0786613i | ||||||||
\(683\) | 1341.02i | 0.0751286i | 0.999294 | + | 0.0375643i | \(0.0119599\pi\) | ||||
−0.999294 | + | 0.0375643i | \(0.988040\pi\) | |||||||
\(684\) | 7504.94 | 0.419530 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 493.387 | 0.0274601 | ||||||||
\(687\) | − 16153.4i | − 0.897076i | ||||||||
\(688\) | 5999.80i | 0.332471i | ||||||||
\(689\) | 22207.2 | 1.22790 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16809.3 | −0.925404 | −0.462702 | − | 0.886514i | \(-0.653120\pi\) | ||||
−0.462702 | + | 0.886514i | \(0.653120\pi\) | |||||||
\(692\) | 352.639i | 0.0193718i | ||||||||
\(693\) | − 479.778i | − 0.0262991i | ||||||||
\(694\) | 5380.16 | 0.294277 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9448.53 | −0.514577 | ||||||||
\(697\) | − 9378.71i | − 0.509676i | ||||||||
\(698\) | − 8165.86i | − 0.442812i | ||||||||
\(699\) | −4826.72 | −0.261178 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13467.0 | 0.725592 | 0.362796 | − | 0.931869i | \(-0.381822\pi\) | ||||
0.362796 | + | 0.931869i | \(0.381822\pi\) | |||||||
\(702\) | − 2033.33i | − 0.109321i | ||||||||
\(703\) | − 16236.1i | − 0.871064i | ||||||||
\(704\) | −915.025 | −0.0489863 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1308.36 | −0.0697461 | ||||||||
\(707\) | − 3733.09i | − 0.198582i | ||||||||
\(708\) | 1917.76i | 0.101799i | ||||||||
\(709\) | −35514.3 | −1.88119 | −0.940597 | − | 0.339525i | \(-0.889734\pi\) | ||||
−0.940597 | + | 0.339525i | \(0.889734\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 203.250 | 0.0107208 | ||||||||
\(712\) | − 30435.2i | − 1.60198i | ||||||||
\(713\) | − 2998.68i | − 0.157506i | ||||||||
\(714\) | −1502.02 | −0.0787277 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 17634.4 | 0.920431 | ||||||||
\(717\) | − 9339.34i | − 0.486449i | ||||||||
\(718\) | − 3852.99i | − 0.200268i | ||||||||
\(719\) | −4993.61 | −0.259013 | −0.129506 | − | 0.991579i | \(-0.541339\pi\) | ||||
−0.129506 | + | 0.991579i | \(0.541339\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9504.51 | −0.490938 | ||||||||
\(722\) | 18569.6i | 0.957186i | ||||||||
\(723\) | − 21409.1i | − 1.10127i | ||||||||
\(724\) | −4010.57 | −0.205872 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5493.45 | −0.280828 | ||||||||
\(727\) | 4223.35i | 0.215454i | 0.994181 | + | 0.107727i | \(0.0343573\pi\) | ||||
−0.994181 | + | 0.107727i | \(0.965643\pi\) | |||||||
\(728\) | − 7343.81i | − 0.373873i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16020.2 | −0.810572 | ||||||||
\(732\) | − 16289.3i | − 0.822502i | ||||||||
\(733\) | 19030.9i | 0.958968i | 0.877551 | + | 0.479484i | \(0.159176\pi\) | ||||
−0.877551 | + | 0.479484i | \(0.840824\pi\) | |||||||
\(734\) | −1031.22 | −0.0518570 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4386.87 | 0.219704 | ||||||||
\(737\) | 3440.11i | 0.171938i | ||||||||
\(738\) | 2441.85i | 0.121796i | ||||||||
\(739\) | 27772.5 | 1.38245 | 0.691224 | − | 0.722641i | \(-0.257072\pi\) | ||||
0.691224 | + | 0.722641i | \(0.257072\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22083.0 | −1.09479 | ||||||||
\(742\) | 4271.05i | 0.211314i | ||||||||
\(743\) | 26880.7i | 1.32726i | 0.748060 | + | 0.663631i | \(0.230985\pi\) | ||||
−0.748060 | + | 0.663631i | \(0.769015\pi\) | |||||||
\(744\) | 7688.42 | 0.378859 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2885.74 | 0.141628 | ||||||||
\(747\) | − 10010.2i | − 0.490302i | ||||||||
\(748\) | 2245.85i | 0.109781i | ||||||||
\(749\) | 6395.85 | 0.312015 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35166.6 | −1.70872 | −0.854360 | − | 0.519681i | \(-0.826051\pi\) | ||||
−0.854360 | + | 0.519681i | \(0.826051\pi\) | |||||||
\(752\) | 1427.35i | 0.0692154i | ||||||||
\(753\) | 676.512i | 0.0327403i | ||||||||
\(754\) | 11836.3 | 0.571688 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1120.93 | −0.0539259 | ||||||||
\(757\) | − 14589.2i | − 0.700467i | −0.936662 | − | 0.350233i | \(-0.886102\pi\) | ||||
0.936662 | − | 0.350233i | \(-0.113898\pi\) | |||||||
\(758\) | − 10468.3i | − 0.501619i | ||||||||
\(759\) | −535.683 | −0.0256180 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −782.826 | −0.0372897 | −0.0186448 | − | 0.999826i | \(-0.505935\pi\) | ||||
−0.0186448 | + | 0.999826i | \(0.505935\pi\) | |||||||
\(762\) | 1169.52i | 0.0556002i | ||||||||
\(763\) | 1123.42i | 0.0533035i | ||||||||
\(764\) | 98.2085 | 0.00465060 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8564.42 | −0.403975 | ||||||||
\(767\) | − 5642.95i | − 0.265652i | ||||||||
\(768\) | 8596.95i | 0.403927i | ||||||||
\(769\) | 16548.4 | 0.776008 | 0.388004 | − | 0.921658i | \(-0.373165\pi\) | ||||
0.388004 | + | 0.921658i | \(0.373165\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13269.2 | 0.619815 | ||||||||
\(772\) | 15981.8i | 0.745075i | ||||||||
\(773\) | 5744.94i | 0.267310i | 0.991028 | + | 0.133655i | \(0.0426715\pi\) | ||||
−0.991028 | + | 0.133655i | \(0.957329\pi\) | |||||||
\(774\) | 4171.02 | 0.193701 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −11021.1 | −0.509837 | ||||||||
\(777\) | 2425.02i | 0.111966i | ||||||||
\(778\) | − 2687.00i | − 0.123822i | ||||||||
\(779\) | 26519.7 | 1.21973 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6909.66 | 0.316578 | ||||||||
\(782\) | 1677.03i | 0.0766888i | ||||||||
\(783\) | − 4243.60i | − 0.193683i | ||||||||
\(784\) | −912.486 | −0.0415673 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3293.26 | −0.149449 | ||||||||
\(787\) | 34744.3i | 1.57370i | 0.617146 | + | 0.786848i | \(0.288289\pi\) | ||||
−0.617146 | + | 0.786848i | \(0.711711\pi\) | |||||||
\(788\) | − 6093.24i | − 0.275460i | ||||||||
\(789\) | 19621.7 | 0.885362 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12519.4 | 0.562753 | ||||||||
\(792\) | − 1373.46i | − 0.0616207i | ||||||||
\(793\) | 47930.8i | 2.14637i | ||||||||
\(794\) | −3107.15 | −0.138877 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16747.4 | −0.745724 | ||||||||
\(797\) | − 21748.7i | − 0.966600i | −0.875455 | − | 0.483300i | \(-0.839438\pi\) | ||||
0.875455 | − | 0.483300i | \(-0.160562\pi\) | |||||||
\(798\) | − 4247.17i | − 0.188406i | ||||||||
\(799\) | −3811.19 | −0.168749 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13669.3 | 0.602972 | ||||||||
\(802\) | 2811.89i | 0.123805i | ||||||||
\(803\) | 5757.01i | 0.253002i | ||||||||
\(804\) | 8037.34 | 0.352556 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9631.38 | −0.420907 | ||||||||
\(807\) | 6788.90i | 0.296134i | ||||||||
\(808\) | − 10686.7i | − 0.465292i | ||||||||
\(809\) | 42350.6 | 1.84050 | 0.920252 | − | 0.391325i | \(-0.127983\pi\) | ||||
0.920252 | + | 0.391325i | \(0.127983\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18910.7 | −0.818796 | −0.409398 | − | 0.912356i | \(-0.634261\pi\) | ||||
−0.409398 | + | 0.912356i | \(0.634261\pi\) | |||||||
\(812\) | − 6525.10i | − 0.282003i | ||||||||
\(813\) | − 4847.03i | − 0.209093i | ||||||||
\(814\) | −1265.00 | −0.0544696 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2777.88 | 0.119173 | ||||||||
\(817\) | − 45299.4i | − 1.93981i | ||||||||
\(818\) | − 21425.8i | − 0.915813i | ||||||||
\(819\) | 3298.31 | 0.140723 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6593.42 | 0.280283 | 0.140141 | − | 0.990132i | \(-0.455244\pi\) | ||||
0.140141 | + | 0.990132i | \(0.455244\pi\) | |||||||
\(822\) | 1039.71i | 0.0441169i | ||||||||
\(823\) | 26762.4i | 1.13351i | 0.823886 | + | 0.566755i | \(0.191801\pi\) | ||||
−0.823886 | + | 0.566755i | \(0.808199\pi\) | |||||||
\(824\) | −27208.5 | −1.15031 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1085.29 | 0.0457169 | ||||||||
\(827\) | 24016.7i | 1.00985i | 0.863164 | + | 0.504924i | \(0.168479\pi\) | ||||
−0.863164 | + | 0.504924i | \(0.831521\pi\) | |||||||
\(828\) | 1251.55i | 0.0525293i | ||||||||
\(829\) | 28422.3 | 1.19077 | 0.595383 | − | 0.803442i | \(-0.297000\pi\) | ||||
0.595383 | + | 0.803442i | \(0.297000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14074.7 | −0.587538 | ||||||||
\(832\) | − 6290.49i | − 0.262120i | ||||||||
\(833\) | − 2436.45i | − 0.101342i | ||||||||
\(834\) | 445.126 | 0.0184814 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6350.46 | −0.262721 | ||||||||
\(837\) | 3453.09i | 0.142600i | ||||||||
\(838\) | − 18137.3i | − 0.747663i | ||||||||
\(839\) | −6637.09 | −0.273108 | −0.136554 | − | 0.990633i | \(-0.543603\pi\) | ||||
−0.136554 | + | 0.990633i | \(0.543603\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 313.546 | 0.0128560 | ||||||||
\(842\) | − 11310.3i | − 0.462921i | ||||||||
\(843\) | 24357.0i | 0.995136i | ||||||||
\(844\) | 30550.9 | 1.24598 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 992.283 | 0.0403255 | ||||||||
\(847\) | − 8911.03i | − 0.361495i | ||||||||
\(848\) | − 7899.01i | − 0.319874i | ||||||||
\(849\) | −10901.2 | −0.440671 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2707.59 | 0.109066 | ||||||||
\(852\) | − 16143.5i | − 0.649138i | ||||||||
\(853\) | − 1406.88i | − 0.0564720i | −0.999601 | − | 0.0282360i | \(-0.991011\pi\) | ||||
0.999601 | − | 0.0282360i | \(-0.00898899\pi\) | |||||||
\(854\) | −9218.40 | −0.369376 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18309.3 | 0.731075 | ||||||||
\(857\) | − 27943.4i | − 1.11380i | −0.830579 | − | 0.556901i | \(-0.811990\pi\) | ||||
0.830579 | − | 0.556901i | \(-0.188010\pi\) | |||||||
\(858\) | 1720.55i | 0.0684598i | ||||||||
\(859\) | −1936.63 | −0.0769233 | −0.0384616 | − | 0.999260i | \(-0.512246\pi\) | ||||
−0.0384616 | + | 0.999260i | \(0.512246\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3960.97 | −0.156782 | ||||||||
\(862\) | 20556.8i | 0.812259i | ||||||||
\(863\) | 7947.70i | 0.313491i | 0.987639 | + | 0.156746i | \(0.0501003\pi\) | ||||
−0.987639 | + | 0.156746i | \(0.949900\pi\) | |||||||
\(864\) | −5051.63 | −0.198912 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19791.6 | 0.776611 | ||||||||
\(867\) | − 7321.73i | − 0.286804i | ||||||||
\(868\) | 5309.58i | 0.207625i | ||||||||
\(869\) | −171.984 | −0.00671365 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23649.6 | −0.920019 | ||||||||
\(872\) | 3216.00i | 0.124894i | ||||||||
\(873\) | − 4949.88i | − 0.191899i | ||||||||
\(874\) | −4742.06 | −0.183527 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13450.4 | 0.518776 | ||||||||
\(877\) | − 38655.0i | − 1.48835i | −0.667983 | − | 0.744177i | \(-0.732842\pi\) | ||||
0.667983 | − | 0.744177i | \(-0.267158\pi\) | |||||||
\(878\) | 8764.65i | 0.336893i | ||||||||
\(879\) | −23946.0 | −0.918859 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18879.4 | −0.721978 | −0.360989 | − | 0.932570i | \(-0.617561\pi\) | ||||
−0.360989 | + | 0.932570i | \(0.617561\pi\) | |||||||
\(882\) | 634.355i | 0.0242175i | ||||||||
\(883\) | − 35098.1i | − 1.33765i | −0.743420 | − | 0.668825i | \(-0.766798\pi\) | ||||
0.743420 | − | 0.668825i | \(-0.233202\pi\) | |||||||
\(884\) | −15439.4 | −0.587425 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19346.3 | −0.733581 | ||||||||
\(887\) | 48816.4i | 1.84791i | 0.382504 | + | 0.923954i | \(0.375062\pi\) | ||||
−0.382504 | + | 0.923954i | \(0.624938\pi\) | |||||||
\(888\) | 6942.08i | 0.262344i | ||||||||
\(889\) | −1897.11 | −0.0715713 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 616.858 | 0.0231936 | ||||||||
\(892\) | − 679.062i | − 0.0254895i | ||||||||
\(893\) | − 10776.7i | − 0.403839i | ||||||||
\(894\) | 14053.8 | 0.525761 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9267.63 | −0.345547 | ||||||||
\(897\) | − 3682.64i | − 0.137079i | ||||||||
\(898\) | − 9916.41i | − 0.368502i | ||||||||
\(899\) | −20100.8 | −0.745718 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21091.3 | 0.779860 | ||||||||
\(902\) | − 2066.22i | − 0.0762721i | ||||||||
\(903\) | 6765.90i | 0.249341i | ||||||||
\(904\) | 35839.1 | 1.31857 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6348.05 | 0.232781 | ||||||||
\(907\) | 6010.83i | 0.220051i | 0.993929 | + | 0.110026i | \(0.0350933\pi\) | ||||
−0.993929 | + | 0.110026i | \(0.964907\pi\) | |||||||
\(908\) | − 28140.5i | − 1.02850i | ||||||||
\(909\) | 4799.69 | 0.175133 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25780.1 | 0.937576 | 0.468788 | − | 0.883311i | \(-0.344691\pi\) | ||||
0.468788 | + | 0.883311i | \(0.344691\pi\) | |||||||
\(912\) | 7854.85i | 0.285198i | ||||||||
\(913\) | 8470.37i | 0.307041i | ||||||||
\(914\) | −17002.6 | −0.615314 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 31934.6 | 1.15191 | ||||||||
\(917\) | − 5342.06i | − 0.192378i | ||||||||
\(918\) | − 1931.16i | − 0.0694313i | ||||||||
\(919\) | −26731.8 | −0.959522 | −0.479761 | − | 0.877399i | \(-0.659277\pi\) | ||||
−0.479761 | + | 0.877399i | \(0.659277\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21354.4 | 0.764010 | ||||||||
\(922\) | 12145.4i | 0.433824i | ||||||||
\(923\) | 47501.6i | 1.69397i | ||||||||
\(924\) | 948.501 | 0.0337699 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1826.46 | 0.0648177 | ||||||||
\(927\) | − 12220.1i | − 0.432967i | ||||||||
\(928\) | − 29406.2i | − 1.04020i | ||||||||
\(929\) | 30464.6 | 1.07590 | 0.537949 | − | 0.842977i | \(-0.319199\pi\) | ||||
0.537949 | + | 0.842977i | \(0.319199\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6889.42 | 0.242526 | ||||||||
\(932\) | − 9542.22i | − 0.335371i | ||||||||
\(933\) | 27467.7i | 0.963830i | ||||||||
\(934\) | −23708.1 | −0.830572 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9442.04 | 0.329725 | ||||||||
\(937\) | 28533.4i | 0.994819i | 0.867516 | + | 0.497409i | \(0.165715\pi\) | ||||
−0.867516 | + | 0.497409i | \(0.834285\pi\) | |||||||
\(938\) | − 4548.46i | − 0.158329i | ||||||||
\(939\) | −18490.3 | −0.642608 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34455.8 | 1.19365 | 0.596827 | − | 0.802370i | \(-0.296428\pi\) | ||||
0.596827 | + | 0.802370i | \(0.296428\pi\) | |||||||
\(942\) | 6016.52i | 0.208099i | ||||||||
\(943\) | 4422.50i | 0.152722i | ||||||||
\(944\) | −2007.17 | −0.0692033 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3529.39 | −0.121301 | ||||||||
\(947\) | − 2477.68i | − 0.0850198i | −0.999096 | − | 0.0425099i | \(-0.986465\pi\) | ||||
0.999096 | − | 0.0425099i | \(-0.0135354\pi\) | |||||||
\(948\) | 401.817i | 0.0137662i | ||||||||
\(949\) | −39577.5 | −1.35378 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25975.1 | −0.885699 | ||||||||
\(952\) | − 6974.80i | − 0.237452i | ||||||||
\(953\) | 41690.6i | 1.41709i | 0.705663 | + | 0.708547i | \(0.250649\pi\) | ||||
−0.705663 | + | 0.708547i | \(0.749351\pi\) | |||||||
\(954\) | −5491.35 | −0.186361 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 18463.5 | 0.624635 | ||||||||
\(957\) | 3590.81i | 0.121290i | ||||||||
\(958\) | 2014.13i | 0.0679266i | ||||||||
\(959\) | −1686.54 | −0.0567895 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13434.6 | −0.450962 | ||||||||
\(962\) | − 8696.44i | − 0.291460i | ||||||||
\(963\) | 8223.24i | 0.275172i | ||||||||
\(964\) | 42325.0 | 1.41410 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 708.271 | 0.0235903 | ||||||||
\(967\) | 20641.3i | 0.686430i | 0.939257 | + | 0.343215i | \(0.111516\pi\) | ||||
−0.939257 | + | 0.343215i | \(0.888484\pi\) | |||||||
\(968\) | − 25509.5i | − 0.847010i | ||||||||
\(969\) | −20973.4 | −0.695318 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6626.17 | 0.218995 | 0.109497 | − | 0.993987i | \(-0.465076\pi\) | ||||
0.109497 | + | 0.993987i | \(0.465076\pi\) | |||||||
\(972\) | − 1441.20i | − 0.0475582i | ||||||||
\(973\) | 722.048i | 0.0237901i | ||||||||
\(974\) | −20377.0 | −0.670349 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17048.8 | 0.559138 | ||||||||
\(977\) | − 41961.0i | − 1.37405i | −0.726632 | − | 0.687027i | \(-0.758915\pi\) | ||||
0.726632 | − | 0.687027i | \(-0.241085\pi\) | |||||||
\(978\) | − 15855.7i | − 0.518415i | ||||||||
\(979\) | −11566.5 | −0.377598 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1444.40 | −0.0470093 | ||||||||
\(982\) | 6817.21i | 0.221533i | ||||||||
\(983\) | − 16781.7i | − 0.544510i | −0.962225 | − | 0.272255i | \(-0.912231\pi\) | ||||
0.962225 | − | 0.272255i | \(-0.0877695\pi\) | |||||||
\(984\) | −11339.0 | −0.367352 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11241.6 | 0.363087 | ||||||||
\(987\) | 1609.60i | 0.0519090i | ||||||||
\(988\) | − 43657.2i | − 1.40579i | ||||||||
\(989\) | 7554.27 | 0.242884 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50319.8 | 1.61298 | 0.806489 | − | 0.591250i | \(-0.201365\pi\) | ||||
0.806489 | + | 0.591250i | \(0.201365\pi\) | |||||||
\(992\) | 23928.3i | 0.765851i | ||||||||
\(993\) | 385.432i | 0.0123176i | ||||||||
\(994\) | −9135.85 | −0.291521 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 19789.8 | 0.629583 | ||||||||
\(997\) | − 12949.5i | − 0.411348i | −0.978621 | − | 0.205674i | \(-0.934061\pi\) | ||||
0.978621 | − | 0.205674i | \(-0.0659386\pi\) | |||||||
\(998\) | 16355.2i | 0.518753i | ||||||||
\(999\) | −3117.89 | −0.0987443 |
(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 | 525.4.d.i.274.3 | 4 | ||
5.2 | odd | 4 | 105.4.a.c.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 525.4.a.p.1.1 | 2 | |||
5.4 | even | 2 | inner | 525.4.d.i.274.2 | 4 | ||
15.2 | even | 4 | 315.4.a.m.1.1 | 2 | |||
15.8 | even | 4 | 1575.4.a.m.1.2 | 2 | |||
20.7 | even | 4 | 1680.4.a.bk.1.1 | 2 | |||
35.27 | even | 4 | 735.4.a.k.1.2 | 2 | |||
105.62 | odd | 4 | 2205.4.a.bh.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.c.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
315.4.a.m.1.1 | 2 | 15.2 | even | 4 | |||
525.4.a.p.1.1 | 2 | 5.3 | odd | 4 | |||
525.4.d.i.274.2 | 4 | 5.4 | even | 2 | inner | ||
525.4.d.i.274.3 | 4 | 1.1 | even | 1 | trivial | ||
735.4.a.k.1.2 | 2 | 35.27 | even | 4 | |||
1575.4.a.m.1.2 | 2 | 15.8 | even | 4 | |||
1680.4.a.bk.1.1 | 2 | 20.7 | even | 4 | |||
2205.4.a.bh.1.1 | 2 | 105.62 | odd | 4 |