Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,4,Mod(649,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.649");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.b (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: | \(39.8262892539\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.12559936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 6x^{3} + 49x^{2} - 42x + 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.1 | ||
Root | \(-2.05655 - 2.05655i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.649 |
Dual form | 675.4.b.m.649.6 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 5.45876i | − 1.92996i | −0.262320 | − | 0.964981i | \(-0.584487\pi\) | ||||
0.262320 | − | 0.964981i | \(-0.415513\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −21.7980 | −2.72475 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 11.8065i | − 0.637492i | −0.947840 | − | 0.318746i | \(-0.896738\pi\) | ||||
0.947840 | − | 0.318746i | \(-0.103262\pi\) | |||||||
\(8\) | 75.3201i | 3.32871i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 56.2376 | 1.54148 | 0.770740 | − | 0.637150i | \(-0.219887\pi\) | ||||
0.770740 | + | 0.637150i | \(0.219887\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 34.5961i | − 0.738094i | −0.929411 | − | 0.369047i | \(-0.879684\pi\) | ||||
0.929411 | − | 0.369047i | \(-0.120316\pi\) | |||||||
\(14\) | −64.4489 | −1.23034 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 236.770 | 3.69953 | ||||||||
\(17\) | − 39.2675i | − 0.560221i | −0.959968 | − | 0.280111i | \(-0.909629\pi\) | ||||
0.959968 | − | 0.280111i | \(-0.0903712\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 146.561 | 1.76965 | 0.884825 | − | 0.465924i | \(-0.154278\pi\) | ||||
0.884825 | + | 0.465924i | \(0.154278\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 306.987i | − 2.97500i | ||||||||
\(23\) | − 23.5777i | − 0.213752i | −0.994272 | − | 0.106876i | \(-0.965915\pi\) | ||||
0.994272 | − | 0.106876i | \(-0.0340848\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −188.851 | −1.42449 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 257.359i | 1.73701i | ||||||||
\(29\) | 161.003 | 1.03095 | 0.515473 | − | 0.856906i | \(-0.327616\pi\) | ||||
0.515473 | + | 0.856906i | \(0.327616\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −29.5465 | −0.171184 | −0.0855921 | − | 0.996330i | \(-0.527278\pi\) | ||||
−0.0855921 | + | 0.996330i | \(0.527278\pi\) | |||||||
\(32\) | − 689.908i | − 3.81124i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −214.352 | −1.08121 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 217.688i | − 0.967233i | −0.875280 | − | 0.483617i | \(-0.839323\pi\) | ||||
0.875280 | − | 0.483617i | \(-0.160677\pi\) | |||||||
\(38\) | − 800.039i | − 3.41536i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −142.290 | −0.541999 | −0.270999 | − | 0.962580i | \(-0.587354\pi\) | ||||
−0.270999 | + | 0.962580i | \(0.587354\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 468.030i | 1.65986i | 0.557869 | + | 0.829929i | \(0.311619\pi\) | ||||
−0.557869 | + | 0.829929i | \(0.688381\pi\) | |||||||
\(44\) | −1225.87 | −4.20015 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −128.705 | −0.412533 | ||||||||
\(47\) | − 394.318i | − 1.22377i | −0.790946 | − | 0.611886i | \(-0.790411\pi\) | ||||
0.790946 | − | 0.611886i | \(-0.209589\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 203.606 | 0.593604 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 754.126i | 2.01112i | ||||||||
\(53\) | − 134.780i | − 0.349311i | −0.984630 | − | 0.174655i | \(-0.944119\pi\) | ||||
0.984630 | − | 0.174655i | \(-0.0558811\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 889.268 | 2.12203 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 878.875i | − 1.98969i | ||||||||
\(59\) | −131.195 | −0.289495 | −0.144747 | − | 0.989469i | \(-0.546237\pi\) | ||||
−0.144747 | + | 0.989469i | \(0.546237\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 259.801 | 0.545313 | 0.272657 | − | 0.962111i | \(-0.412098\pi\) | ||||
0.272657 | + | 0.962111i | \(0.412098\pi\) | |||||||
\(62\) | 161.287i | 0.330379i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1871.88 | −3.65602 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 445.244i | 0.811869i | 0.913902 | + | 0.405935i | \(0.133054\pi\) | ||||
−0.913902 | + | 0.405935i | \(0.866946\pi\) | |||||||
\(68\) | 855.954i | 1.52647i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −560.841 | −0.937459 | −0.468729 | − | 0.883342i | \(-0.655288\pi\) | ||||
−0.468729 | + | 0.883342i | \(0.655288\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 88.6681i | 0.142162i | 0.997471 | + | 0.0710809i | \(0.0226448\pi\) | ||||
−0.997471 | + | 0.0710809i | \(0.977355\pi\) | |||||||
\(74\) | −1188.30 | −1.86672 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3194.74 | −4.82186 | ||||||||
\(77\) | − 663.970i | − 0.982681i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −450.342 | −0.641360 | −0.320680 | − | 0.947188i | \(-0.603911\pi\) | ||||
−0.320680 | + | 0.947188i | \(0.603911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 776.726i | 1.04604i | ||||||||
\(83\) | 284.295i | 0.375969i | 0.982172 | + | 0.187985i | \(0.0601955\pi\) | ||||
−0.982172 | + | 0.187985i | \(0.939804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2554.86 | 3.20346 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4235.82i | 5.13114i | ||||||||
\(89\) | 625.305 | 0.744744 | 0.372372 | − | 0.928083i | \(-0.378545\pi\) | ||||
0.372372 | + | 0.928083i | \(0.378545\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −408.459 | −0.470529 | ||||||||
\(92\) | 513.948i | 0.582421i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2152.49 | −2.36183 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 193.261i | − 0.202296i | −0.994871 | − | 0.101148i | \(-0.967748\pi\) | ||||
0.994871 | − | 0.101148i | \(-0.0322516\pi\) | |||||||
\(98\) | − 1111.44i | − 1.14563i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1374.86 | −1.35449 | −0.677245 | − | 0.735758i | \(-0.736826\pi\) | ||||
−0.677245 | + | 0.735758i | \(0.736826\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 2029.60i | − 1.94158i | −0.239935 | − | 0.970789i | \(-0.577126\pi\) | ||||
0.239935 | − | 0.970789i | \(-0.422874\pi\) | |||||||
\(104\) | 2605.78 | 2.45690 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −735.732 | −0.674156 | ||||||||
\(107\) | 823.062i | 0.743630i | 0.928307 | + | 0.371815i | \(0.121264\pi\) | ||||
−0.928307 | + | 0.371815i | \(0.878736\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 829.868 | 0.729238 | 0.364619 | − | 0.931157i | \(-0.381199\pi\) | ||||
0.364619 | + | 0.931157i | \(0.381199\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 2795.43i | − 2.35842i | ||||||||
\(113\) | − 1503.37i | − 1.25155i | −0.780005 | − | 0.625773i | \(-0.784784\pi\) | ||||
0.780005 | − | 0.625773i | \(-0.215216\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3509.54 | −2.80908 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 716.164i | 0.558714i | ||||||||
\(119\) | −463.612 | −0.357137 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1831.67 | 1.37616 | ||||||||
\(122\) | − 1418.19i | − 1.05243i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 644.056 | 0.466435 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 576.348i | − 0.402698i | −0.979520 | − | 0.201349i | \(-0.935468\pi\) | ||||
0.979520 | − | 0.201349i | \(-0.0645325\pi\) | |||||||
\(128\) | 4698.89i | 3.24474i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2390.04 | −1.59403 | −0.797017 | − | 0.603957i | \(-0.793590\pi\) | ||||
−0.797017 | + | 0.603957i | \(0.793590\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1730.37i | − 1.12814i | ||||||||
\(134\) | 2430.48 | 1.56688 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2957.63 | 1.86481 | ||||||||
\(137\) | − 1002.46i | − 0.625152i | −0.949893 | − | 0.312576i | \(-0.898808\pi\) | ||||
0.949893 | − | 0.312576i | \(-0.101192\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −131.817 | −0.0804356 | −0.0402178 | − | 0.999191i | \(-0.512805\pi\) | ||||
−0.0402178 | + | 0.999191i | \(0.512805\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3061.50i | 1.80926i | ||||||||
\(143\) | − 1945.60i | − 1.13776i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 484.017 | 0.274367 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4745.16i | 2.63547i | ||||||||
\(149\) | 1019.49 | 0.560533 | 0.280267 | − | 0.959922i | \(-0.409577\pi\) | ||||
0.280267 | + | 0.959922i | \(0.409577\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2822.38 | 1.52107 | 0.760537 | − | 0.649295i | \(-0.224936\pi\) | ||||
0.760537 | + | 0.649295i | \(0.224936\pi\) | |||||||
\(152\) | 11039.0i | 5.89065i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3624.45 | −1.89654 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 476.499i | 0.242222i | 0.992639 | + | 0.121111i | \(0.0386456\pi\) | ||||
−0.992639 | + | 0.121111i | \(0.961354\pi\) | |||||||
\(158\) | 2458.31i | 1.23780i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −278.371 | −0.136265 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2242.26i | 1.07747i | 0.842476 | + | 0.538734i | \(0.181097\pi\) | ||||
−0.842476 | + | 0.538734i | \(0.818903\pi\) | |||||||
\(164\) | 3101.64 | 1.47681 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1551.90 | 0.725607 | ||||||||
\(167\) | − 95.0390i | − 0.0440380i | −0.999758 | − | 0.0220190i | \(-0.992991\pi\) | ||||
0.999758 | − | 0.0220190i | \(-0.00700943\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1000.11 | 0.455217 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 10202.1i | − 4.52270i | ||||||||
\(173\) | − 2133.76i | − 0.937727i | −0.883271 | − | 0.468864i | \(-0.844664\pi\) | ||||
0.883271 | − | 0.468864i | \(-0.155336\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13315.4 | 5.70275 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 3413.39i | − 1.43733i | ||||||||
\(179\) | −1704.68 | −0.711808 | −0.355904 | − | 0.934523i | \(-0.615827\pi\) | ||||
−0.355904 | + | 0.934523i | \(0.615827\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1360.98 | −0.558902 | −0.279451 | − | 0.960160i | \(-0.590152\pi\) | ||||
−0.279451 | + | 0.960160i | \(0.590152\pi\) | |||||||
\(182\) | 2229.68i | 0.908103i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1775.88 | 0.711518 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2208.31i | − 0.863570i | ||||||||
\(188\) | 8595.36i | 3.33447i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1096.84 | 0.415522 | 0.207761 | − | 0.978180i | \(-0.433382\pi\) | ||||
0.207761 | + | 0.978180i | \(0.433382\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2867.27i | 1.06938i | 0.845048 | + | 0.534691i | \(0.179572\pi\) | ||||
−0.845048 | + | 0.534691i | \(0.820428\pi\) | |||||||
\(194\) | −1054.97 | −0.390424 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4438.21 | −1.61742 | ||||||||
\(197\) | − 724.139i | − 0.261892i | −0.991389 | − | 0.130946i | \(-0.958199\pi\) | ||||
0.991389 | − | 0.130946i | \(-0.0418015\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1693.65 | 0.603315 | 0.301658 | − | 0.953416i | \(-0.402460\pi\) | ||||
0.301658 | + | 0.953416i | \(0.402460\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7505.02i | 2.61411i | ||||||||
\(203\) | − 1900.88i | − 0.657220i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11079.1 | −3.74717 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 8191.30i | − 2.73060i | ||||||||
\(209\) | 8242.22 | 2.72788 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 947.452 | 0.309124 | 0.154562 | − | 0.987983i | \(-0.450603\pi\) | ||||
0.154562 | + | 0.987983i | \(0.450603\pi\) | |||||||
\(212\) | 2937.94i | 0.951785i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4492.89 | 1.43518 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 348.841i | 0.109129i | ||||||||
\(218\) | − 4530.05i | − 1.40740i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1358.50 | −0.413496 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 111.866i | − 0.0335923i | −0.999859 | − | 0.0167961i | \(-0.994653\pi\) | ||||
0.999859 | − | 0.0167961i | \(-0.00534663\pi\) | |||||||
\(224\) | −8145.41 | −2.42964 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8206.51 | −2.41544 | ||||||||
\(227\) | − 1200.70i | − 0.351072i | −0.984473 | − | 0.175536i | \(-0.943834\pi\) | ||||
0.984473 | − | 0.175536i | \(-0.0561658\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −822.380 | −0.237312 | −0.118656 | − | 0.992935i | \(-0.537859\pi\) | ||||
−0.118656 | + | 0.992935i | \(0.537859\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12126.7i | 3.43172i | ||||||||
\(233\) | − 5329.21i | − 1.49840i | −0.662341 | − | 0.749202i | \(-0.730437\pi\) | ||||
0.662341 | − | 0.749202i | \(-0.269563\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2859.80 | 0.788802 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2530.75i | 0.689260i | ||||||||
\(239\) | −7085.61 | −1.91770 | −0.958850 | − | 0.283914i | \(-0.908367\pi\) | ||||
−0.958850 | + | 0.283914i | \(0.908367\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6560.09 | −1.75341 | −0.876707 | − | 0.481025i | \(-0.840265\pi\) | ||||
−0.876707 | + | 0.481025i | \(0.840265\pi\) | |||||||
\(242\) | − 9998.63i | − 2.65593i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5663.15 | −1.48584 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 5070.42i | − 1.30617i | ||||||||
\(248\) | − 2225.45i | − 0.569822i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −714.222 | −0.179607 | −0.0898033 | − | 0.995960i | \(-0.528624\pi\) | ||||
−0.0898033 | + | 0.995960i | \(0.528624\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1325.95i | − 0.329494i | ||||||||
\(254\) | −3146.14 | −0.777191 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10675.0 | 2.60621 | ||||||||
\(257\) | − 4396.59i | − 1.06713i | −0.845760 | − | 0.533563i | \(-0.820853\pi\) | ||||
0.845760 | − | 0.533563i | \(-0.179147\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2570.13 | −0.616604 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13046.6i | 3.07643i | ||||||||
\(263\) | − 7550.31i | − 1.77024i | −0.465367 | − | 0.885118i | \(-0.654078\pi\) | ||||
0.465367 | − | 0.885118i | \(-0.345922\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9445.68 | −2.17726 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 9705.45i | − 2.21214i | ||||||||
\(269\) | −5536.86 | −1.25497 | −0.627487 | − | 0.778627i | \(-0.715917\pi\) | ||||
−0.627487 | + | 0.778627i | \(0.715917\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3058.25 | 0.685518 | 0.342759 | − | 0.939423i | \(-0.388639\pi\) | ||||
0.342759 | + | 0.939423i | \(0.388639\pi\) | |||||||
\(272\) | − 9297.36i | − 2.07256i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5472.18 | −1.20652 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 4070.19i | − 0.882865i | −0.897294 | − | 0.441433i | \(-0.854470\pi\) | ||||
0.897294 | − | 0.441433i | \(-0.145530\pi\) | |||||||
\(278\) | 719.556i | 0.155238i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7446.19 | −1.58079 | −0.790396 | − | 0.612597i | \(-0.790125\pi\) | ||||
−0.790396 | + | 0.612597i | \(0.790125\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 774.651i | 0.162715i | 0.996685 | + | 0.0813573i | \(0.0259255\pi\) | ||||
−0.996685 | + | 0.0813573i | \(0.974075\pi\) | |||||||
\(284\) | 12225.2 | 2.55434 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10620.6 | −2.19583 | ||||||||
\(287\) | 1679.95i | 0.345520i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3371.06 | 0.686152 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 1932.79i | − 0.387356i | ||||||||
\(293\) | 6749.23i | 1.34571i | 0.739772 | + | 0.672857i | \(0.234933\pi\) | ||||
−0.739772 | + | 0.672857i | \(0.765067\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 16396.3 | 3.21964 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 5565.12i | − 1.08181i | ||||||||
\(299\) | −815.696 | −0.157769 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5525.80 | 1.05815 | ||||||||
\(302\) | − 15406.7i | − 2.93561i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 34701.2 | 6.54687 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2204.39i | − 0.409808i | −0.978782 | − | 0.204904i | \(-0.934312\pi\) | ||||
0.978782 | − | 0.204904i | \(-0.0656883\pi\) | |||||||
\(308\) | 14473.2i | 2.67756i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6032.98 | 1.10000 | 0.549998 | − | 0.835166i | \(-0.314628\pi\) | ||||
0.549998 | + | 0.835166i | \(0.314628\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5772.96i | 1.04251i | 0.853400 | + | 0.521257i | \(0.174537\pi\) | ||||
−0.853400 | + | 0.521257i | \(0.825463\pi\) | |||||||
\(314\) | 2601.09 | 0.467479 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9816.57 | 1.74755 | ||||||||
\(317\) | 3302.07i | 0.585057i | 0.956257 | + | 0.292528i | \(0.0944966\pi\) | ||||
−0.956257 | + | 0.292528i | \(0.905503\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9054.41 | 1.58918 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1519.56i | 0.262986i | ||||||||
\(323\) | − 5755.07i | − 0.991395i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12239.9 | 2.07947 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 10717.3i | − 1.80416i | ||||||||
\(329\) | −4655.53 | −0.780144 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8053.15 | 1.33728 | 0.668642 | − | 0.743584i | \(-0.266876\pi\) | ||||
0.668642 | + | 0.743584i | \(0.266876\pi\) | |||||||
\(332\) | − 6197.08i | − 1.02442i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −518.795 | −0.0849916 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3460.33i | 0.559335i | 0.960097 | + | 0.279668i | \(0.0902242\pi\) | ||||
−0.960097 | + | 0.279668i | \(0.909776\pi\) | |||||||
\(338\) | − 5459.37i | − 0.878552i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1661.62 | −0.263877 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 6453.51i | − 1.01591i | ||||||||
\(344\) | −35252.0 | −5.52518 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11647.7 | −1.80978 | ||||||||
\(347\) | 9328.27i | 1.44314i | 0.692344 | + | 0.721568i | \(0.256578\pi\) | ||||
−0.692344 | + | 0.721568i | \(0.743422\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8899.42 | −1.36497 | −0.682486 | − | 0.730899i | \(-0.739101\pi\) | ||||
−0.682486 | + | 0.730899i | \(0.739101\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 38798.8i | − 5.87495i | ||||||||
\(353\) | 3722.45i | 0.561264i | 0.959816 | + | 0.280632i | \(0.0905440\pi\) | ||||
−0.959816 | + | 0.280632i | \(0.909456\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −13630.4 | −2.02924 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9305.42i | 1.37376i | ||||||||
\(359\) | 11029.3 | 1.62145 | 0.810727 | − | 0.585425i | \(-0.199072\pi\) | ||||
0.810727 | + | 0.585425i | \(0.199072\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14621.1 | 2.13166 | ||||||||
\(362\) | 7429.29i | 1.07866i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8903.60 | 1.28208 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 4853.11i | − 0.690274i | −0.938552 | − | 0.345137i | \(-0.887833\pi\) | ||||
0.938552 | − | 0.345137i | \(-0.112167\pi\) | |||||||
\(368\) | − 5582.49i | − 0.790781i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1591.28 | −0.222683 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12373.8i | 1.71767i | 0.512254 | + | 0.858834i | \(0.328811\pi\) | ||||
−0.512254 | + | 0.858834i | \(0.671189\pi\) | |||||||
\(374\) | −12054.6 | −1.66666 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 29700.1 | 4.07358 | ||||||||
\(377\) | − 5570.06i | − 0.760935i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11150.6 | −1.51127 | −0.755634 | − | 0.654994i | \(-0.772671\pi\) | ||||
−0.755634 | + | 0.654994i | \(0.772671\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 5987.39i | − 0.801941i | ||||||||
\(383\) | 2199.59i | 0.293457i | 0.989177 | + | 0.146728i | \(0.0468743\pi\) | ||||
−0.989177 | + | 0.146728i | \(0.953126\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15651.7 | 2.06386 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4212.72i | 0.551207i | ||||||||
\(389\) | 9218.92 | 1.20159 | 0.600794 | − | 0.799404i | \(-0.294851\pi\) | ||||
0.600794 | + | 0.799404i | \(0.294851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −925.838 | −0.119748 | ||||||||
\(392\) | 15335.6i | 1.97594i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3952.90 | −0.505442 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1119.36i | 0.141509i | 0.997494 | + | 0.0707544i | \(0.0225407\pi\) | ||||
−0.997494 | + | 0.0707544i | \(0.977459\pi\) | |||||||
\(398\) | − 9245.23i | − 1.16438i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12296.9 | −1.53137 | −0.765683 | − | 0.643218i | \(-0.777599\pi\) | ||||
−0.765683 | + | 0.643218i | \(0.777599\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1022.19i | 0.126350i | ||||||||
\(404\) | 29969.2 | 3.69065 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10376.4 | −1.26841 | ||||||||
\(407\) | − 12242.2i | − 1.49097i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2500.22 | −0.302269 | −0.151134 | − | 0.988513i | \(-0.548293\pi\) | ||||
−0.151134 | + | 0.988513i | \(0.548293\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 44241.3i | 5.29032i | ||||||||
\(413\) | 1548.96i | 0.184551i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −23868.1 | −2.81305 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 44992.3i | − 5.26470i | ||||||||
\(419\) | −8332.97 | −0.971581 | −0.485790 | − | 0.874075i | \(-0.661468\pi\) | ||||
−0.485790 | + | 0.874075i | \(0.661468\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11374.2 | 1.31673 | 0.658367 | − | 0.752697i | \(-0.271248\pi\) | ||||
0.658367 | + | 0.752697i | \(0.271248\pi\) | |||||||
\(422\) | − 5171.91i | − 0.596598i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10151.6 | 1.16275 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3067.35i | − 0.347633i | ||||||||
\(428\) | − 17941.1i | − 2.02621i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10030.2 | 1.12097 | 0.560484 | − | 0.828165i | \(-0.310615\pi\) | ||||
0.560484 | + | 0.828165i | \(0.310615\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 7609.38i | − 0.844535i | −0.906471 | − | 0.422267i | \(-0.861234\pi\) | ||||
0.906471 | − | 0.422267i | \(-0.138766\pi\) | |||||||
\(434\) | 1904.24 | 0.210614 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18089.5 | −1.98699 | ||||||||
\(437\) | − 3455.57i | − 0.378266i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12370.5 | 1.34490 | 0.672450 | − | 0.740143i | \(-0.265242\pi\) | ||||
0.672450 | + | 0.740143i | \(0.265242\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7415.72i | 0.798032i | ||||||||
\(443\) | − 12084.4i | − 1.29605i | −0.761621 | − | 0.648023i | \(-0.775596\pi\) | ||||
0.761621 | − | 0.648023i | \(-0.224404\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −610.647 | −0.0648318 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 22100.4i | 2.33068i | ||||||||
\(449\) | −625.550 | −0.0657495 | −0.0328747 | − | 0.999459i | \(-0.510466\pi\) | ||||
−0.0328747 | + | 0.999459i | \(0.510466\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8002.04 | −0.835480 | ||||||||
\(452\) | 32770.4i | 3.41016i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6554.33 | −0.677555 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1811.22i | 0.185395i | 0.995694 | + | 0.0926974i | \(0.0295489\pi\) | ||||
−0.995694 | + | 0.0926974i | \(0.970451\pi\) | |||||||
\(458\) | 4489.17i | 0.458003i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11625.0 | 1.17447 | 0.587233 | − | 0.809418i | \(-0.300217\pi\) | ||||
0.587233 | + | 0.809418i | \(0.300217\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 7291.88i | − 0.731928i | −0.930629 | − | 0.365964i | \(-0.880739\pi\) | ||||
0.930629 | − | 0.365964i | \(-0.119261\pi\) | |||||||
\(464\) | 38120.6 | 3.81402 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −29090.9 | −2.89186 | ||||||||
\(467\) | 11637.6i | 1.15316i | 0.817042 | + | 0.576579i | \(0.195613\pi\) | ||||
−0.817042 | + | 0.576579i | \(0.804387\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5256.78 | 0.517560 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 9881.66i | − 0.963644i | ||||||||
\(473\) | 26320.9i | 2.55864i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10105.8 | 0.973109 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 38678.6i | 3.70109i | ||||||||
\(479\) | 12041.4 | 1.14862 | 0.574309 | − | 0.818639i | \(-0.305271\pi\) | ||||
0.574309 | + | 0.818639i | \(0.305271\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7531.14 | −0.713909 | ||||||||
\(482\) | 35810.0i | 3.38402i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −39926.7 | −3.74969 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7037.81i | 0.654853i | 0.944877 | + | 0.327427i | \(0.106181\pi\) | ||||
−0.944877 | + | 0.327427i | \(0.893819\pi\) | |||||||
\(488\) | 19568.2i | 1.81519i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6603.07 | −0.606909 | −0.303454 | − | 0.952846i | \(-0.598140\pi\) | ||||
−0.303454 | + | 0.952846i | \(0.598140\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 6322.17i | − 0.577558i | ||||||||
\(494\) | −27678.2 | −2.52085 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6995.72 | −0.633301 | ||||||||
\(497\) | 6621.58i | 0.597623i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.7047 | 0.00329284 | 0.00164642 | − | 0.999999i | \(-0.499476\pi\) | ||||
0.00164642 | + | 0.999999i | \(0.499476\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3898.76i | 0.346634i | ||||||||
\(503\) | 21242.5i | 1.88302i | 0.336990 | + | 0.941508i | \(0.390591\pi\) | ||||
−0.336990 | + | 0.941508i | \(0.609409\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7238.06 | −0.635911 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12563.2i | 1.09725i | ||||||||
\(509\) | −11280.4 | −0.982309 | −0.491155 | − | 0.871072i | \(-0.663425\pi\) | ||||
−0.491155 | + | 0.871072i | \(0.663425\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1046.86 | 0.0906270 | ||||||||
\(512\) | − 20681.3i | − 1.78514i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −23999.9 | −2.05951 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 22175.5i | − 1.88642i | ||||||||
\(518\) | 14029.7i | 1.19002i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10239.3 | 0.861023 | 0.430511 | − | 0.902585i | \(-0.358333\pi\) | ||||
0.430511 | + | 0.902585i | \(0.358333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2822.00i | 0.235942i | 0.993017 | + | 0.117971i | \(0.0376389\pi\) | ||||
−0.993017 | + | 0.117971i | \(0.962361\pi\) | |||||||
\(524\) | 52098.1 | 4.34335 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −41215.3 | −3.41649 | ||||||||
\(527\) | 1160.22i | 0.0959010i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11611.1 | 0.954310 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 37718.7i | 3.07390i | ||||||||
\(533\) | 4922.67i | 0.400046i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −33535.8 | −2.70248 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 30224.4i | 2.42205i | ||||||||
\(539\) | 11450.3 | 0.915028 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9409.63 | −0.747785 | −0.373892 | − | 0.927472i | \(-0.621977\pi\) | ||||
−0.373892 | + | 0.927472i | \(0.621977\pi\) | |||||||
\(542\) | − 16694.2i | − 1.32302i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −27091.0 | −2.13514 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3836.43i | − 0.299879i | −0.988695 | − | 0.149940i | \(-0.952092\pi\) | ||||
0.988695 | − | 0.149940i | \(-0.0479079\pi\) | |||||||
\(548\) | 21851.6i | 1.70339i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23596.7 | 1.82441 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5316.97i | 0.408862i | ||||||||
\(554\) | −22218.2 | −1.70390 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2873.35 | 0.219167 | ||||||||
\(557\) | − 6145.92i | − 0.467524i | −0.972294 | − | 0.233762i | \(-0.924896\pi\) | ||||
0.972294 | − | 0.233762i | \(-0.0751036\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16192.0 | 1.22513 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 40646.9i | 3.05087i | ||||||||
\(563\) | 13247.9i | 0.991707i | 0.868406 | + | 0.495854i | \(0.165145\pi\) | ||||
−0.868406 | + | 0.495854i | \(0.834855\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4228.63 | 0.314033 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 42242.6i | − 3.12053i | ||||||||
\(569\) | 6544.89 | 0.482208 | 0.241104 | − | 0.970499i | \(-0.422491\pi\) | ||||
0.241104 | + | 0.970499i | \(0.422491\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20362.1 | 1.49234 | 0.746170 | − | 0.665755i | \(-0.231890\pi\) | ||||
0.746170 | + | 0.665755i | \(0.231890\pi\) | |||||||
\(572\) | 42410.2i | 3.10011i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9170.43 | 0.666840 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 26247.4i | − 1.89375i | −0.321600 | − | 0.946876i | \(-0.604221\pi\) | ||||
0.321600 | − | 0.946876i | \(-0.395779\pi\) | |||||||
\(578\) | − 18401.8i | − 1.32425i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3356.54 | 0.239677 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 7579.71i | − 0.538455i | ||||||||
\(584\) | −6678.49 | −0.473215 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36842.4 | 2.59718 | ||||||||
\(587\) | 14098.2i | 0.991301i | 0.868522 | + | 0.495650i | \(0.165070\pi\) | ||||
−0.868522 | + | 0.495650i | \(0.834930\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4330.36 | −0.302936 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 51541.9i | − 3.57831i | ||||||||
\(593\) | 3476.71i | 0.240761i | 0.992728 | + | 0.120380i | \(0.0384115\pi\) | ||||
−0.992728 | + | 0.120380i | \(0.961589\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22222.8 | −1.52732 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4452.69i | 0.304488i | ||||||||
\(599\) | −16179.0 | −1.10360 | −0.551798 | − | 0.833978i | \(-0.686058\pi\) | ||||
−0.551798 | + | 0.833978i | \(0.686058\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8112.16 | 0.550586 | 0.275293 | − | 0.961360i | \(-0.411225\pi\) | ||||
0.275293 | + | 0.961360i | \(0.411225\pi\) | |||||||
\(602\) | − 30164.0i | − 2.04218i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −61522.3 | −4.14455 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21139.2i | 1.41353i | 0.707449 | + | 0.706765i | \(0.249846\pi\) | ||||
−0.707449 | + | 0.706765i | \(0.750154\pi\) | |||||||
\(608\) | − 101113.i | − 6.74456i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13641.9 | −0.903258 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11440.3i | 0.753785i | 0.926257 | + | 0.376892i | \(0.123007\pi\) | ||||
−0.926257 | + | 0.376892i | \(0.876993\pi\) | |||||||
\(614\) | −12033.2 | −0.790915 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 50010.3 | 3.27106 | ||||||||
\(617\) | − 21566.2i | − 1.40717i | −0.710612 | − | 0.703584i | \(-0.751582\pi\) | ||||
0.710612 | − | 0.703584i | \(-0.248418\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15198.3 | 0.986866 | 0.493433 | − | 0.869784i | \(-0.335742\pi\) | ||||
0.493433 | + | 0.869784i | \(0.335742\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 32932.6i | − 2.12295i | ||||||||
\(623\) | − 7382.68i | − 0.474769i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 31513.2 | 2.01201 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 10386.7i | − 0.659994i | ||||||||
\(629\) | −8548.05 | −0.541865 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4929.66 | −0.311009 | −0.155504 | − | 0.987835i | \(-0.549700\pi\) | ||||
−0.155504 | + | 0.987835i | \(0.549700\pi\) | |||||||
\(632\) | − 33919.8i | − 2.13490i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18025.2 | 1.12914 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 7043.97i | − 0.438135i | ||||||||
\(638\) | − 49425.8i | − 3.06706i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7535.73 | 0.464342 | 0.232171 | − | 0.972675i | \(-0.425417\pi\) | ||||
0.232171 | + | 0.972675i | \(0.425417\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15997.2i | 0.981135i | 0.871403 | + | 0.490568i | \(0.163211\pi\) | ||||
−0.871403 | + | 0.490568i | \(0.836789\pi\) | |||||||
\(644\) | 6067.93 | 0.371289 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31415.5 | −1.91336 | ||||||||
\(647\) | − 6020.46i | − 0.365825i | −0.983129 | − | 0.182913i | \(-0.941447\pi\) | ||||
0.983129 | − | 0.182913i | \(-0.0585525\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7378.12 | −0.446250 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 48876.8i | − 2.93583i | ||||||||
\(653\) | 10948.7i | 0.656133i | 0.944655 | + | 0.328067i | \(0.106397\pi\) | ||||
−0.944655 | + | 0.328067i | \(0.893603\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −33690.0 | −2.00514 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 25413.4i | 1.50565i | ||||||||
\(659\) | −12338.3 | −0.729334 | −0.364667 | − | 0.931138i | \(-0.618817\pi\) | ||||
−0.364667 | + | 0.931138i | \(0.618817\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20016.8 | 1.17786 | 0.588928 | − | 0.808186i | \(-0.299550\pi\) | ||||
0.588928 | + | 0.808186i | \(0.299550\pi\) | |||||||
\(662\) | − 43960.2i | − 2.58091i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21413.1 | −1.25149 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 3796.08i | − 0.220367i | ||||||||
\(668\) | 2071.66i | 0.119993i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14610.6 | 0.840589 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8419.22i | 0.482225i | 0.970497 | + | 0.241112i | \(0.0775122\pi\) | ||||
−0.970497 | + | 0.241112i | \(0.922488\pi\) | |||||||
\(674\) | 18889.1 | 1.07950 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −21800.5 | −1.24036 | ||||||||
\(677\) | 25707.1i | 1.45938i | 0.683776 | + | 0.729692i | \(0.260337\pi\) | ||||
−0.683776 | + | 0.729692i | \(0.739663\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2281.74 | −0.128962 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9070.41i | 0.509272i | ||||||||
\(683\) | 19624.3i | 1.09942i | 0.835357 | + | 0.549708i | \(0.185261\pi\) | ||||
−0.835357 | + | 0.549708i | \(0.814739\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −35228.2 | −1.96067 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 110815.i | 6.14069i | ||||||||
\(689\) | −4662.86 | −0.257824 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7273.23 | 0.400415 | 0.200207 | − | 0.979754i | \(-0.435838\pi\) | ||||
0.200207 | + | 0.979754i | \(0.435838\pi\) | |||||||
\(692\) | 46511.8i | 2.55508i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 50920.8 | 2.78520 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5587.37i | 0.303639i | ||||||||
\(698\) | 48579.8i | 2.63434i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17644.3 | 0.950664 | 0.475332 | − | 0.879807i | \(-0.342328\pi\) | ||||
0.475332 | + | 0.879807i | \(0.342328\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 31904.5i | − 1.71166i | ||||||||
\(704\) | −105270. | −5.63568 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20320.0 | 1.08322 | ||||||||
\(707\) | 16232.3i | 0.863476i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24304.4 | −1.28741 | −0.643703 | − | 0.765276i | \(-0.722603\pi\) | ||||
−0.643703 | + | 0.765276i | \(0.722603\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 47098.1i | 2.47904i | ||||||||
\(713\) | 696.639i | 0.0365909i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 37158.6 | 1.93950 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 60206.0i | − 3.12934i | ||||||||
\(719\) | 15170.2 | 0.786863 | 0.393431 | − | 0.919354i | \(-0.371288\pi\) | ||||
0.393431 | + | 0.919354i | \(0.371288\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23962.5 | −1.23774 | ||||||||
\(722\) | − 79812.8i | − 4.11402i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 29666.8 | 1.52287 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 17487.0i | − 0.892102i | −0.895008 | − | 0.446051i | \(-0.852830\pi\) | ||||
0.895008 | − | 0.446051i | \(-0.147170\pi\) | |||||||
\(728\) | − 30765.2i | − 1.56625i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18378.4 | 0.929888 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 18698.0i | − 0.942194i | −0.882082 | − | 0.471097i | \(-0.843858\pi\) | ||||
0.882082 | − | 0.471097i | \(-0.156142\pi\) | |||||||
\(734\) | −26492.0 | −1.33220 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16266.5 | −0.814660 | ||||||||
\(737\) | 25039.5i | 1.25148i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35250.3 | 1.75467 | 0.877336 | − | 0.479876i | \(-0.159318\pi\) | ||||
0.877336 | + | 0.479876i | \(0.159318\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8686.43i | 0.429769i | ||||||||
\(743\) | 11133.6i | 0.549731i | 0.961483 | + | 0.274866i | \(0.0886334\pi\) | ||||
−0.961483 | + | 0.274866i | \(0.911367\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 67545.5 | 3.31503 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 48136.8i | 2.35301i | ||||||||
\(749\) | 9717.49 | 0.474058 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17197.6 | 0.835619 | 0.417809 | − | 0.908535i | \(-0.362798\pi\) | ||||
0.417809 | + | 0.908535i | \(0.362798\pi\) | |||||||
\(752\) | − 93362.7i | − 4.52738i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −30405.6 | −1.46858 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 804.647i | 0.0386333i | 0.999813 | + | 0.0193166i | \(0.00614906\pi\) | ||||
−0.999813 | + | 0.0193166i | \(0.993851\pi\) | |||||||
\(758\) | 60868.7i | 2.91669i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26208.9 | −1.24845 | −0.624225 | − | 0.781245i | \(-0.714585\pi\) | ||||
−0.624225 | + | 0.781245i | \(0.714585\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 9797.85i | − 0.464883i | ||||||||
\(764\) | −23909.0 | −1.13219 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12007.0 | 0.566360 | ||||||||
\(767\) | 4538.85i | 0.213674i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36544.2 | −1.71367 | −0.856837 | − | 0.515587i | \(-0.827574\pi\) | ||||
−0.856837 | + | 0.515587i | \(0.827574\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 62500.8i | − 2.91380i | ||||||||
\(773\) | − 42387.4i | − 1.97228i | −0.165923 | − | 0.986139i | \(-0.553060\pi\) | ||||
0.165923 | − | 0.986139i | \(-0.446940\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14556.5 | 0.673385 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 50323.8i | − 2.31902i | ||||||||
\(779\) | −20854.1 | −0.959148 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31540.4 | −1.44507 | ||||||||
\(782\) | 5053.92i | 0.231110i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 48207.8 | 2.19606 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26849.4i | 1.21611i | 0.793896 | + | 0.608054i | \(0.208050\pi\) | ||||
−0.793896 | + | 0.608054i | \(0.791950\pi\) | |||||||
\(788\) | 15784.8i | 0.713592i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17749.5 | −0.797851 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 8988.09i | − 0.402492i | ||||||||
\(794\) | 6110.31 | 0.273107 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −36918.3 | −1.64389 | ||||||||
\(797\) | 31307.0i | 1.39141i | 0.718328 | + | 0.695704i | \(0.244908\pi\) | ||||
−0.718328 | + | 0.695704i | \(0.755092\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15483.9 | −0.685583 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 67125.7i | 2.95548i | ||||||||
\(803\) | 4986.48i | 0.219140i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5579.90 | 0.243851 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 103554.i | − 4.50870i | ||||||||
\(809\) | −10011.9 | −0.435106 | −0.217553 | − | 0.976049i | \(-0.569807\pi\) | ||||
−0.217553 | + | 0.976049i | \(0.569807\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4603.68 | 0.199331 | 0.0996653 | − | 0.995021i | \(-0.468223\pi\) | ||||
0.0996653 | + | 0.995021i | \(0.468223\pi\) | |||||||
\(812\) | 41435.5i | 1.79076i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −66827.4 | −2.87752 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 68594.8i | 2.93737i | ||||||||
\(818\) | 13648.1i | 0.583367i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35429.0 | 1.50607 | 0.753033 | − | 0.657983i | \(-0.228590\pi\) | ||||
0.753033 | + | 0.657983i | \(0.228590\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28297.6i | 1.19853i | 0.800550 | + | 0.599265i | \(0.204541\pi\) | ||||
−0.800550 | + | 0.599265i | \(0.795459\pi\) | |||||||
\(824\) | 152870. | 6.46295 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8455.40 | 0.356176 | ||||||||
\(827\) | − 41059.9i | − 1.72647i | −0.504800 | − | 0.863236i | \(-0.668434\pi\) | ||||
0.504800 | − | 0.863236i | \(-0.331566\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9030.68 | −0.378345 | −0.189173 | − | 0.981944i | \(-0.560581\pi\) | ||||
−0.189173 | + | 0.981944i | \(0.560581\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 64759.8i | 2.69849i | ||||||||
\(833\) | − 7995.10i | − 0.332550i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −179664. | −7.43280 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 45487.7i | 1.87511i | ||||||||
\(839\) | 5227.81 | 0.215118 | 0.107559 | − | 0.994199i | \(-0.465697\pi\) | ||||
0.107559 | + | 0.994199i | \(0.465697\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1532.87 | 0.0628508 | ||||||||
\(842\) | − 62089.0i | − 2.54125i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −20652.6 | −0.842288 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 21625.6i | − 0.877290i | ||||||||
\(848\) | − 31911.8i | − 1.29228i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5132.58 | −0.206748 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30002.9i | 1.20432i | 0.798377 | + | 0.602158i | \(0.205692\pi\) | ||||
−0.798377 | + | 0.602158i | \(0.794308\pi\) | |||||||
\(854\) | −16743.9 | −0.670918 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −61993.1 | −2.47533 | ||||||||
\(857\) | − 15671.7i | − 0.624662i | −0.949973 | − | 0.312331i | \(-0.898890\pi\) | ||||
0.949973 | − | 0.312331i | \(-0.101110\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31306.8 | 1.24351 | 0.621755 | − | 0.783212i | \(-0.286420\pi\) | ||||
0.621755 | + | 0.783212i | \(0.286420\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 54752.3i | − 2.16342i | ||||||||
\(863\) | 13212.3i | 0.521150i | 0.965454 | + | 0.260575i | \(0.0839121\pi\) | ||||
−0.965454 | + | 0.260575i | \(0.916088\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −41537.8 | −1.62992 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 7604.05i | − 0.297348i | ||||||||
\(869\) | −25326.2 | −0.988643 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15403.7 | 0.599236 | ||||||||
\(872\) | 62505.7i | 2.42742i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −18863.1 | −0.730039 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15440.6i | 0.594519i | 0.954797 | + | 0.297260i | \(0.0960727\pi\) | ||||
−0.954797 | + | 0.297260i | \(0.903927\pi\) | |||||||
\(878\) | − 67527.5i | − 2.59561i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27563.1 | 1.05406 | 0.527029 | − | 0.849847i | \(-0.323306\pi\) | ||||
0.527029 | + | 0.849847i | \(0.323306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 19897.7i | − 0.758337i | −0.925328 | − | 0.379169i | \(-0.876210\pi\) | ||||
0.925328 | − | 0.379169i | \(-0.123790\pi\) | |||||||
\(884\) | 29612.6 | 1.12667 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −65965.9 | −2.50132 | ||||||||
\(887\) | − 40061.6i | − 1.51650i | −0.651963 | − | 0.758251i | \(-0.726054\pi\) | ||||
0.651963 | − | 0.758251i | \(-0.273946\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6804.66 | −0.256716 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2438.45i | 0.0915306i | ||||||||
\(893\) | − 57791.6i | − 2.16565i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 55477.5 | 2.06850 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3414.72i | 0.126894i | ||||||||
\(899\) | −4757.07 | −0.176482 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5292.47 | −0.195691 | ||||||||
\(902\) | 43681.2i | 1.61244i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 113234. | 4.16603 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27839.6i | 1.01918i | 0.860417 | + | 0.509591i | \(0.170203\pi\) | ||||
−0.860417 | + | 0.509591i | \(0.829797\pi\) | |||||||
\(908\) | 26172.9i | 0.956584i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22251.0 | −0.809232 | −0.404616 | − | 0.914487i | \(-0.632595\pi\) | ||||
−0.404616 | + | 0.914487i | \(0.632595\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15988.1i | 0.579549i | ||||||||
\(914\) | 9887.02 | 0.357805 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17926.3 | 0.646616 | ||||||||
\(917\) | 28218.0i | 1.01618i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29480.5 | −1.05819 | −0.529093 | − | 0.848564i | \(-0.677468\pi\) | ||||
−0.529093 | + | 0.848564i | \(0.677468\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 63457.9i | − 2.26668i | ||||||||
\(923\) | 19402.9i | 0.691933i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −39804.6 | −1.41259 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 111077.i | − 3.92919i | ||||||||
\(929\) | 42351.8 | 1.49571 | 0.747857 | − | 0.663860i | \(-0.231083\pi\) | ||||
0.747857 | + | 0.663860i | \(0.231083\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29840.7 | 1.05047 | ||||||||
\(932\) | 116166.i | 4.08278i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 63526.9 | 2.22555 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 35930.6i | − 1.25272i | −0.779532 | − | 0.626362i | \(-0.784543\pi\) | ||||
0.779532 | − | 0.626362i | \(-0.215457\pi\) | |||||||
\(938\) | − 28695.5i | − 0.998872i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21564.0 | 0.747041 | 0.373521 | − | 0.927622i | \(-0.378151\pi\) | ||||
0.373521 | + | 0.927622i | \(0.378151\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3354.87i | 0.115853i | ||||||||
\(944\) | −31063.1 | −1.07099 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 143679. | 4.93807 | ||||||||
\(947\) | 16632.4i | 0.570729i | 0.958419 | + | 0.285364i | \(0.0921146\pi\) | ||||
−0.958419 | + | 0.285364i | \(0.907885\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3067.57 | 0.104929 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 34919.3i | − 1.18880i | ||||||||
\(953\) | 39557.8i | 1.34460i | 0.740279 | + | 0.672299i | \(0.234693\pi\) | ||||
−0.740279 | + | 0.672299i | \(0.765307\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 154452. | 5.22526 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 65731.4i | − 2.21679i | ||||||||
\(959\) | −11835.5 | −0.398529 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28918.0 | −0.970696 | ||||||||
\(962\) | 41110.6i | 1.37782i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 142997. | 4.77762 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 10666.2i | − 0.354707i | −0.984147 | − | 0.177354i | \(-0.943246\pi\) | ||||
0.984147 | − | 0.177354i | \(-0.0567536\pi\) | |||||||
\(968\) | 137961.i | 4.58083i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31821.8 | −1.05171 | −0.525855 | − | 0.850574i | \(-0.676254\pi\) | ||||
−0.525855 | + | 0.850574i | \(0.676254\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1556.30i | 0.0512771i | ||||||||
\(974\) | 38417.7 | 1.26384 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 61513.0 | 2.01740 | ||||||||
\(977\) | − 11126.5i | − 0.364347i | −0.983266 | − | 0.182173i | \(-0.941687\pi\) | ||||
0.983266 | − | 0.182173i | \(-0.0583132\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35165.7 | 1.14801 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36044.5i | 1.17131i | ||||||||
\(983\) | − 991.225i | − 0.0321619i | −0.999871 | − | 0.0160810i | \(-0.994881\pi\) | ||||
0.999871 | − | 0.0160810i | \(-0.00511895\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −34511.2 | −1.11467 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 110525.i | 3.55898i | ||||||||
\(989\) | 11035.1 | 0.354798 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48714.9 | −1.56153 | −0.780767 | − | 0.624822i | \(-0.785171\pi\) | ||||
−0.780767 | + | 0.624822i | \(0.785171\pi\) | |||||||
\(992\) | 20384.4i | 0.652424i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 36145.6 | 1.15339 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 42207.2i | − 1.34074i | −0.742028 | − | 0.670369i | \(-0.766136\pi\) | ||||
0.742028 | − | 0.670369i | \(-0.233864\pi\) | |||||||
\(998\) | − 200.362i | − 0.00635505i | ||||||||
\(999\) | 0 | 0 |
(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 | 675.4.b.m.649.1 | 6 | ||
3.2 | odd | 2 | 675.4.b.n.649.6 | 6 | |||
5.2 | odd | 4 | 675.4.a.s.1.3 | 3 | |||
5.3 | odd | 4 | 135.4.a.e.1.1 | ✓ | 3 | ||
5.4 | even | 2 | inner | 675.4.b.m.649.6 | 6 | ||
15.2 | even | 4 | 675.4.a.p.1.1 | 3 | |||
15.8 | even | 4 | 135.4.a.h.1.3 | yes | 3 | ||
15.14 | odd | 2 | 675.4.b.n.649.1 | 6 | |||
20.3 | even | 4 | 2160.4.a.bi.1.2 | 3 | |||
45.13 | odd | 12 | 405.4.e.v.136.3 | 6 | |||
45.23 | even | 12 | 405.4.e.q.136.1 | 6 | |||
45.38 | even | 12 | 405.4.e.q.271.1 | 6 | |||
45.43 | odd | 12 | 405.4.e.v.271.3 | 6 | |||
60.23 | odd | 4 | 2160.4.a.bq.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.a.e.1.1 | ✓ | 3 | 5.3 | odd | 4 | ||
135.4.a.h.1.3 | yes | 3 | 15.8 | even | 4 | ||
405.4.e.q.136.1 | 6 | 45.23 | even | 12 | |||
405.4.e.q.271.1 | 6 | 45.38 | even | 12 | |||
405.4.e.v.136.3 | 6 | 45.13 | odd | 12 | |||
405.4.e.v.271.3 | 6 | 45.43 | odd | 12 | |||
675.4.a.p.1.1 | 3 | 15.2 | even | 4 | |||
675.4.a.s.1.3 | 3 | 5.2 | odd | 4 | |||
675.4.b.m.649.1 | 6 | 1.1 | even | 1 | trivial | ||
675.4.b.m.649.6 | 6 | 5.4 | even | 2 | inner | ||
675.4.b.n.649.1 | 6 | 15.14 | odd | 2 | |||
675.4.b.n.649.6 | 6 | 3.2 | odd | 2 | |||
2160.4.a.bi.1.2 | 3 | 20.3 | even | 4 | |||
2160.4.a.bq.1.2 | 3 | 60.23 | odd | 4 |