Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,4,Mod(5,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([11, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.j (of order \(22\), degree \(10\), 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: | \(11.8593839112\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{22})\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{22}]$ |
Embedding invariants
Embedding label | 8.2 | ||
Root | \(0.723734 + 0.690079i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 201.8 |
Dual form | 201.4.j.a.176.2 |
$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{22}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(3\) | 3.92699 | − | 3.40276i | 0.755750 | − | 0.654861i | ||||
\(4\) | 7.67594 | + | 2.25386i | 0.959493 | + | 0.281733i | ||||
\(5\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 35.1868 | + | 5.05910i | 1.89991 | + | 0.273166i | 0.989938 | − | 0.141501i | \(-0.0451929\pi\) |
0.909973 | + | 0.414667i | \(0.136102\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.84250 | − | 26.7252i | 0.142315 | − | 0.989821i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(12\) | 37.8127 | − | 17.2685i | 0.909632 | − | 0.415415i | ||||
\(13\) | −71.0981 | + | 32.4694i | −1.51685 | + | 0.692723i | −0.987780 | − | 0.155855i | \(-0.950187\pi\) |
−0.529071 | + | 0.848578i | \(0.677459\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 53.8402 | + | 34.6010i | 0.841254 | + | 0.540641i | ||||
\(17\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.5471 | + | 80.3116i | 0.139425 | + | 0.969724i | 0.932647 | + | 0.360791i | \(0.117493\pi\) |
−0.793222 | + | 0.608933i | \(0.791598\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 155.393 | − | 99.8652i | 1.61474 | − | 1.03773i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −51.9269 | − | 113.704i | −0.415415 | − | 0.909632i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −75.8498 | − | 118.025i | −0.540641 | − | 0.841254i | ||||
\(28\) | 258.690 | + | 118.140i | 1.74599 | + | 0.797368i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −270.757 | − | 123.651i | −1.56869 | − | 0.716397i | −0.573957 | − | 0.818885i | \(-0.694592\pi\) |
−0.994734 | + | 0.102488i | \(0.967320\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 89.7296 | − | 196.481i | 0.415415 | − | 0.909632i | ||||
\(37\) | 351.338 | 1.56107 | 0.780534 | − | 0.625113i | \(-0.214947\pi\) | ||||
0.780534 | + | 0.625113i | \(0.214947\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −168.716 | + | 369.437i | −0.692723 | + | 1.51685i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −107.720 | − | 366.861i | −0.382027 | − | 1.30107i | −0.896304 | − | 0.443441i | \(-0.853758\pi\) |
0.514276 | − | 0.857625i | \(-0.328061\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(48\) | 329.169 | − | 47.3273i | 0.989821 | − | 0.142315i | ||||
\(49\) | 883.414 | + | 259.394i | 2.57555 | + | 0.756250i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −618.926 | + | 88.9882i | −1.65057 | + | 0.237316i | ||||
\(53\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 318.626 | + | 276.091i | 0.740405 | + | 0.641564i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −256.777 | − | 399.553i | −0.538966 | − | 0.838648i | 0.459814 | − | 0.888015i | \(-0.347916\pi\) |
−0.998781 | + | 0.0493670i | \(0.984280\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 270.411 | − | 920.935i | 0.540771 | − | 1.84170i | ||||
\(64\) | 335.289 | + | 386.944i | 0.654861 | + | 0.755750i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −114.992 | + | 536.227i | −0.209680 | + | 0.977770i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1012.33 | + | 650.584i | −1.62307 | + | 1.04308i | −0.669105 | + | 0.743168i | \(0.733322\pi\) |
−0.953966 | + | 0.299916i | \(0.903041\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −590.823 | − | 269.820i | −0.909632 | − | 0.415415i | ||||
\(76\) | −92.3766 | + | 642.493i | −0.139425 | + | 0.969724i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1143.78 | + | 522.348i | −1.62893 | + | 0.743908i | −0.999452 | − | 0.0331090i | \(-0.989459\pi\) |
−0.629480 | + | 0.777017i | \(0.716732\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −699.470 | − | 205.383i | −0.959493 | − | 0.281733i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(84\) | 1417.87 | − | 416.325i | 1.84170 | − | 0.540771i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2665.98 | + | 782.803i | −3.07111 | + | 0.901759i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1484.01 | + | 435.746i | −1.65468 | + | 0.485857i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 106.819i | 0.111813i | 0.998436 | + | 0.0559065i | \(0.0178049\pi\) | ||||
−0.998436 | + | 0.0559065i | \(0.982195\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −142.315 | − | 989.821i | −0.142315 | − | 0.989821i | ||||
\(101\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 530.642 | − | 1161.94i | 0.507629 | − | 1.11155i | −0.466285 | − | 0.884634i | \(-0.654408\pi\) |
0.973914 | − | 0.226917i | \(-0.0728647\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(108\) | −316.208 | − | 1076.91i | −0.281733 | − | 0.959493i | ||||
\(109\) | 1352.34 | − | 617.591i | 1.18835 | − | 0.542702i | 0.279631 | − | 0.960108i | \(-0.409788\pi\) |
0.908720 | + | 0.417406i | \(0.137061\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1379.70 | − | 1195.52i | 1.17978 | − | 1.02228i | ||||
\(112\) | 1719.42 | + | 1489.88i | 1.45062 | + | 1.25697i | ||||
\(113\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 594.556 | + | 2024.87i | 0.469801 | + | 1.60000i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −552.917 | − | 1210.72i | −0.415415 | − | 0.909632i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1799.63 | − | 1559.38i | −1.30332 | − | 1.12933i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −344.809 | + | 2398.20i | −0.240920 | + | 1.67563i | 0.406616 | + | 0.913599i | \(0.366709\pi\) |
−0.647535 | + | 0.762035i | \(0.724200\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1671.36 | − | 1074.12i | −1.14073 | − | 0.733105i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2884.33i | 1.88048i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1770.00 | + | 2754.17i | −1.08007 | + | 1.68061i | −0.500148 | + | 0.865940i | \(0.666721\pi\) |
−0.579918 | + | 0.814675i | \(0.696915\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1131.60 | − | 1305.94i | 0.654861 | − | 0.755750i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4351.81 | − | 1987.40i | 2.44171 | − | 1.11509i | ||||
\(148\) | 2696.85 | + | 791.866i | 1.49783 | + | 0.439804i | ||||
\(149\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 287.193 | − | 84.3275i | 0.154778 | − | 0.0454469i | −0.203426 | − | 0.979090i | \(-0.565208\pi\) |
0.358204 | + | 0.933644i | \(0.383389\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2127.71 | + | 2455.51i | −1.09201 | + | 1.26025i | ||||
\(157\) | −884.233 | − | 1020.46i | −0.449487 | − | 0.518736i | 0.485106 | − | 0.874456i | \(-0.338781\pi\) |
−0.934593 | + | 0.355720i | \(0.884236\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2585.94 | 1.24262 | 0.621309 | − | 0.783566i | \(-0.286601\pi\) | ||||
0.621309 | + | 0.783566i | \(0.286601\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2561.95 | − | 2956.64i | 1.16611 | − | 1.34576i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2190.71 | 0.979696 | ||||||||
\(172\) | − | 3058.79i | − | 1.35599i | ||||||
\(173\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1251.90 | − | 4263.59i | −0.540771 | − | 1.84170i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3180.21 | + | 3670.16i | 1.30599 | + | 1.50719i | 0.710031 | + | 0.704171i | \(0.248681\pi\) |
0.595955 | + | 0.803018i | \(0.296774\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2367.94 | − | 695.291i | −0.956521 | − | 0.280860i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2071.82 | − | 4536.65i | −0.797368 | − | 1.74599i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(192\) | 2633.35 | + | 378.619i | 0.989821 | + | 0.142315i | ||||
\(193\) | −2085.69 | + | 4567.03i | −0.777884 | + | 1.70333i | −0.0694118 | + | 0.997588i | \(0.522112\pi\) |
−0.708472 | + | 0.705739i | \(0.750615\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6196.40 | + | 3982.18i | 2.25816 | + | 1.45123i | ||||
\(197\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 796.228 | − | 5537.89i | 0.283634 | − | 1.97272i | 0.0590873 | − | 0.998253i | \(-0.481181\pi\) |
0.224547 | − | 0.974463i | \(-0.427910\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1373.08 | + | 2497.05i | 0.481838 | + | 0.876260i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4951.41 | − | 711.906i | −1.65057 | − | 0.237316i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2936.72 | − | 3389.16i | 0.958162 | − | 1.10578i | −0.0361575 | − | 0.999346i | \(-0.511512\pi\) |
0.994320 | − | 0.106432i | \(-0.0339427\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8901.53 | − | 5720.67i | −2.78468 | − | 1.78960i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1761.63 | + | 5999.55i | −0.543560 | + | 1.85120i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1504.50 | − | 1736.28i | 0.451787 | − | 0.521391i | −0.483469 | − | 0.875362i | \(-0.660623\pi\) |
0.935256 | + | 0.353971i | \(0.115169\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3238.29 | + | 950.847i | −0.959493 | + | 0.281733i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(228\) | 1823.49 | + | 2837.40i | 0.529663 | + | 0.824172i | ||||
\(229\) | 5698.07 | + | 2602.22i | 1.64428 | + | 0.750915i | 0.999905 | − | 0.0137984i | \(-0.00439230\pi\) |
0.644370 | + | 0.764714i | \(0.277120\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2714.20 | + | 5943.27i | −0.743908 | + | 1.62893i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1624.08 | + | 1043.73i | −0.434093 | + | 0.278975i | −0.739383 | − | 0.673285i | \(-0.764883\pi\) |
0.305290 | + | 0.952259i | \(0.401246\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3445.68 | + | 1573.59i | −0.909632 | + | 0.415415i | ||||
\(244\) | −1070.47 | − | 3645.69i | −0.280860 | − | 0.956521i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3428.65 | − | 5335.08i | −0.883237 | − | 1.37434i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(252\) | 4151.32 | − | 6459.58i | 1.03773 | − | 1.61474i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1701.54 | + | 3725.85i | 0.415415 | + | 0.909632i | ||||
\(257\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12362.5 | + | 1777.45i | 2.96589 | + | 0.426431i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2091.26 | + | 3856.87i | −0.476656 | + | 0.879090i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −348.244 | + | 301.755i | −0.0780601 | + | 0.0676395i | −0.693017 | − | 0.720921i | \(-0.743719\pi\) |
0.614957 | + | 0.788561i | \(0.289173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7805.60 | + | 12145.8i | −1.73046 | + | 2.69265i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 882.805 | − | 6140.04i | 0.191490 | − | 1.33184i | −0.636579 | − | 0.771212i | \(-0.719651\pi\) |
0.828068 | − | 0.560627i | \(-0.189440\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4344.97 | + | 6760.91i | −0.932354 | + | 1.45077i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −77.9470 | − | 542.133i | −0.0163727 | − | 0.113874i | 0.979996 | − | 0.199016i | \(-0.0637747\pi\) |
−0.996369 | + | 0.0851419i | \(0.972866\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4133.08 | − | 2656.17i | 0.841254 | − | 0.540641i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 363.480 | + | 419.478i | 0.0732219 | + | 0.0845026i | ||||
\(292\) | −9236.91 | + | 2712.20i | −1.85120 | + | 0.543560i | ||||
\(293\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3926.99 | − | 3402.76i | −0.755750 | − | 0.654861i | ||||
\(301\) | −1934.34 | − | 13453.7i | −0.370411 | − | 2.57627i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2157.17 | + | 4723.54i | −0.406980 | + | 0.891163i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4054.88 | + | 8878.96i | −0.753826 | + | 1.65065i | 0.00554079 | + | 0.999985i | \(0.498236\pi\) |
−0.759366 | + | 0.650663i | \(0.774491\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1869.99 | − | 6368.59i | −0.344271 | − | 1.17248i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7997.74 | − | 6930.08i | −1.44428 | − | 1.25147i | −0.915260 | − | 0.402863i | \(-0.868015\pi\) |
−0.529018 | − | 0.848611i | \(-0.677440\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9956.91 | + | 1431.59i | −1.77253 | + | 0.254852i | ||||
\(317\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −4906.19 | − | 3153.02i | −0.841254 | − | 0.540641i | ||||
\(325\) | 7383.80 | + | 6398.10i | 1.26025 | + | 1.09201i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3209.10 | − | 7026.94i | 0.542702 | − | 1.18835i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2425.74 | + | 8261.30i | −0.402811 | + | 1.37185i | 0.469515 | + | 0.882925i | \(0.344429\pi\) |
−0.872326 | + | 0.488925i | \(0.837389\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1350.02 | − | 9389.56i | 0.222163 | − | 1.54518i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 11821.8 | 1.91945 | ||||||||
\(337\) | −227.470 | − | 32.7052i | −0.0367687 | − | 0.00528654i | 0.123906 | − | 0.992294i | \(-0.460458\pi\) |
−0.160675 | + | 0.987007i | \(0.551367\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18680.9 | + | 8531.29i | 2.94074 | + | 1.34299i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3406.77 | − | 1000.32i | −0.522521 | − | 0.153426i | 0.00982661 | − | 0.999952i | \(-0.496872\pi\) |
−0.532348 | + | 0.846526i | \(0.678690\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9224.97 | + | 5928.53i | 1.40283 | + | 0.901542i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 264.538 | − | 77.6755i | 0.0385681 | − | 0.0113246i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6291.09 | − | 2873.04i | −0.909632 | − | 0.415415i | ||||
\(364\) | −22228.3 | −3.20076 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6730.17 | + | 5831.73i | 0.957254 | + | 0.829465i | 0.985420 | − | 0.170138i | \(-0.0544213\pi\) |
−0.0281661 | + | 0.999603i | \(0.508967\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −12373.3 | −1.72453 | ||||||||
\(373\) | − | 13280.3i | − | 1.84350i | −0.387779 | − | 0.921752i | \(-0.626758\pi\) | ||
0.387779 | − | 0.921752i | \(-0.373242\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7712.31 | − | 6682.75i | 1.04526 | − | 0.905726i | 0.0496011 | − | 0.998769i | \(-0.484205\pi\) |
0.995662 | + | 0.0930434i | \(0.0296595\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6806.42 | + | 10591.0i | 0.915232 | + | 1.42413i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10218.3 | + | 1469.18i | −1.34219 | + | 0.192978i | ||||
\(388\) | −240.756 | + | 819.939i | −0.0315013 | + | 0.107284i | ||||
\(389\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2778.39 | − | 1785.56i | −0.351243 | − | 0.225730i | 0.353107 | − | 0.935583i | \(-0.385125\pi\) |
−0.704350 | + | 0.709853i | \(0.748761\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9814.68 | + | 11326.7i | 1.23145 | + | 1.42117i | ||||
\(400\) | 1138.52 | − | 7918.57i | 0.142315 | − | 0.989821i | ||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23265.2 | 2.87574 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7529.19 | + | 1082.53i | 0.910255 | + | 0.130875i | 0.581506 | − | 0.813542i | \(-0.302464\pi\) |
0.328749 | + | 0.944417i | \(0.393373\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6692.04 | − | 7723.03i | 0.800226 | − | 0.923511i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2421.00 | + | 16838.5i | 0.284310 | + | 1.97742i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1295.71 | + | 9011.88i | 0.149998 | + | 1.04326i | 0.916218 | + | 0.400680i | \(0.131226\pi\) |
−0.766220 | + | 0.642579i | \(0.777865\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7013.80 | − | 15358.1i | −0.794898 | − | 1.74058i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | − | 8978.95i | − | 1.00000i | ||||||
\(433\) | 8881.76 | + | 4056.16i | 0.985751 | + | 0.450177i | 0.842024 | − | 0.539440i | \(-0.181364\pi\) |
0.143727 | + | 0.989617i | \(0.454091\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11772.4 | − | 1692.62i | 1.29311 | − | 0.185921i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11289.1 | 1.22734 | 0.613669 | − | 0.789563i | \(-0.289693\pi\) | ||||
0.613669 | + | 0.789563i | \(0.289693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10326.9 | − | 22612.7i | 1.11509 | − | 2.44171i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(444\) | 13285.0 | − | 6067.07i | 1.42000 | − | 0.648491i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9840.16 | + | 15311.6i | 1.03773 | + | 1.61474i | ||||
\(449\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 840.859 | − | 1308.40i | 0.0872119 | − | 0.135704i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6853.51 | − | 15007.1i | −0.701518 | − | 1.53611i | −0.838121 | − | 0.545484i | \(-0.816346\pi\) |
0.136604 | − | 0.990626i | \(-0.456381\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10769.7 | − | 16758.0i | −1.08102 | − | 1.68210i | −0.559036 | − | 0.829143i | \(-0.688829\pi\) |
−0.521983 | − | 0.852956i | \(-0.674808\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(468\) | 16882.9i | 1.66754i | ||||||||
\(469\) | −6759.05 | + | 18286.4i | −0.665467 | + | 1.80040i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6944.75 | − | 998.504i | −0.679399 | − | 0.0976829i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8532.15 | − | 5483.28i | 0.824172 | − | 0.529663i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24979.4 | + | 11407.7i | −2.36791 | + | 1.08139i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1515.37 | − | 10539.6i | −0.142315 | − | 0.989821i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −302.032 | + | 1028.63i | −0.0281034 | + | 0.0957115i | −0.972351 | − | 0.233526i | \(-0.924974\pi\) |
0.944247 | + | 0.329238i | \(0.106792\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10155.0 | − | 8799.33i | 0.939108 | − | 0.813741i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10299.2 | − | 16025.9i | −0.932354 | − | 1.45077i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20567.7i | 1.84516i | 0.385806 | + | 0.922580i | \(0.373923\pi\) | ||||
−0.385806 | + | 0.922580i | \(0.626077\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 20328.4i | − | 1.78070i | ||||||
\(508\) | −8051.93 | + | 17631.3i | −0.703242 | + | 1.53988i | ||||
\(509\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −38912.0 | + | 17770.5i | −3.36863 | + | 1.53840i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8602.91 | − | 7454.46i | 0.740405 | − | 0.641564i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −10408.3 | − | 12011.8i | −0.887987 | − | 1.02479i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7787.55 | + | 17052.4i | 0.651101 | + | 1.42571i | 0.890587 | + | 0.454812i | \(0.150294\pi\) |
−0.239487 | + | 0.970900i | \(0.576979\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −19424.2 | − | 12483.2i | −1.61474 | − | 1.03773i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1731.54 | + | 12043.2i | −0.142315 | + | 0.989821i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6500.88 | + | 22140.0i | −0.529791 | + | 1.80430i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9114.69 | − | 14182.7i | 0.724346 | − | 1.12710i | −0.262421 | − | 0.964954i | \(-0.584521\pi\) |
0.986766 | − | 0.162150i | \(-0.0518429\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24977.3 | + | 3591.20i | 1.97400 | + | 0.283818i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13495.3 | − | 20999.1i | 1.05487 | − | 1.64142i | 0.342653 | − | 0.939462i | \(-0.388674\pi\) |
0.712221 | − | 0.701955i | \(-0.247689\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11664.8 | + | 5327.13i | −0.906815 | + | 0.414128i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −42888.7 | + | 12593.3i | −3.29804 | + | 0.968390i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19793.9 | + | 17151.5i | −1.50980 | + | 1.30825i | ||||
\(557\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19570.5 | + | 22585.5i | 1.48076 | + | 1.70888i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23573.1 | − | 10765.5i | −1.74599 | − | 0.797368i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17017.7 | − | 19639.5i | 1.24723 | − | 1.43938i | 0.392962 | − | 0.919555i | \(-0.371450\pi\) |
0.854270 | − | 0.519829i | \(-0.174004\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 11629.5 | − | 7473.82i | 0.841254 | − | 0.540641i | ||||
\(577\) | −2356.69 | − | 8026.15i | −0.170035 | − | 0.579087i | −0.999781 | − | 0.0209447i | \(-0.993333\pi\) |
0.829745 | − | 0.558142i | \(-0.188486\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7350.00 | + | 25031.8i | 0.527557 | + | 1.79669i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(588\) | 37883.6 | − | 5446.84i | 2.65696 | − | 0.382013i | ||||
\(589\) | 6804.14 | − | 23172.8i | 0.475992 | − | 1.62108i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 18916.1 | + | 12156.6i | 1.31325 | + | 0.843978i | ||||
\(593\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15717.3 | − | 24456.6i | −1.07750 | − | 1.67662i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3748.00 | + | 26067.9i | −0.254383 | + | 1.76927i | 0.316843 | + | 0.948478i | \(0.397377\pi\) |
−0.571226 | + | 0.820793i | \(0.693532\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13888.9 | + | 5133.64i | 0.937977 | + | 0.346697i | ||||
\(604\) | 2394.54 | 0.161312 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4972.50 | + | 1460.06i | 0.332500 | + | 0.0976309i | 0.443721 | − | 0.896165i | \(-0.353658\pi\) |
−0.111221 | + | 0.993796i | \(0.535476\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6336.63 | − | 7312.87i | 0.417511 | − | 0.481833i | −0.507566 | − | 0.861613i | \(-0.669455\pi\) |
0.925077 | + | 0.379779i | \(0.124000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11845.7 | − | 7612.75i | −0.769172 | − | 0.494317i | 0.0962518 | − | 0.995357i | \(-0.469315\pi\) |
−0.865424 | + | 0.501040i | \(0.832951\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −21866.6 | + | 14052.8i | −1.40283 | + | 0.901542i | ||||
\(625\) | −10232.2 | + | 11808.6i | −0.654861 | + | 0.755750i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4487.35 | − | 9825.93i | −0.285135 | − | 0.624358i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17549.4 | + | 8014.56i | 1.10718 | + | 0.505633i | 0.883217 | − | 0.468964i | \(-0.155372\pi\) |
0.223965 | + | 0.974597i | \(0.428100\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 23302.1i | − | 1.46315i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −71231.4 | + | 10241.5i | −4.43060 | + | 0.637024i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3550.99 | − | 2282.08i | 0.217787 | − | 0.139963i | −0.427199 | − | 0.904158i | \(-0.640500\pi\) |
0.644986 | + | 0.764194i | \(0.276863\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −54422.3 | + | 7824.74i | −3.27646 | + | 0.471084i | ||||
\(652\) | 19849.6 | + | 5828.35i | 1.19228 | + | 0.350086i | ||||
\(653\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13497.1 | + | 29554.5i | 0.801480 | + | 1.75500i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31472.0 | − | 4524.99i | −1.85192 | − | 0.266266i | −0.875670 | − | 0.482910i | \(-0.839580\pi\) |
−0.976251 | + | 0.216644i | \(0.930489\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 11937.8i | − | 0.689899i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25921.7 | + | 22461.3i | −1.48471 | + | 1.28651i | −0.619599 | + | 0.784919i | \(0.712705\pi\) |
−0.865108 | + | 0.501586i | \(0.832750\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9481.23 | + | 14753.1i | −0.540641 | + | 0.841254i | ||||
\(676\) | 26329.2 | − | 16920.8i | 1.49802 | − | 0.962720i | ||||
\(677\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −540.410 | + | 3758.63i | −0.0305435 | + | 0.212435i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(684\) | 16815.8 | + | 4937.56i | 0.940011 | + | 0.276012i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 31231.0 | − | 9170.24i | 1.73441 | − | 0.509267i | ||||
\(688\) | 6894.09 | − | 23479.1i | 0.382027 | − | 1.30107i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30547.8 | − | 19631.9i | 1.68176 | − | 1.08080i | 0.824724 | − | 0.565535i | \(-0.191330\pi\) |
0.857031 | − | 0.515264i | \(-0.172306\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 35548.7i | − | 1.91945i | ||||||
\(701\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4056.92 | + | 28216.5i | 0.217652 | + | 1.51381i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13258.9 | − | 29033.0i | 0.702326 | − | 1.53788i | −0.134802 | − | 0.990872i | \(-0.543040\pi\) |
0.837128 | − | 0.547007i | \(-0.184233\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9564.86 | + | 32574.9i | 0.504515 | + | 1.71822i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24550.0 | − | 38200.6i | 1.26809 | − | 1.97318i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2826.18 | + | 9625.09i | −0.145376 | + | 0.495105i | ||||
\(724\) | 16139.1 | + | 35339.7i | 0.828460 | + | 1.81408i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29627.8 | − | 25672.6i | −1.51146 | − | 1.30969i | −0.760341 | − | 0.649524i | \(-0.774968\pi\) |
−0.751121 | − | 0.660165i | \(-0.770486\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8176.61 | + | 17904.3i | −0.415415 | + | 0.909632i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −16609.1 | − | 10674.0i | −0.838648 | − | 0.538966i | ||||
\(733\) | 2724.38 | − | 9278.39i | 0.137282 | − | 0.467538i | −0.861939 | − | 0.507012i | \(-0.830750\pi\) |
0.999221 | + | 0.0394740i | \(0.0125682\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32585.4 | + | 4685.07i | 1.62202 | + | 0.233211i | 0.892598 | − | 0.450854i | \(-0.148881\pi\) |
0.729421 | + | 0.684065i | \(0.239790\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −31618.2 | − | 9283.95i | −1.56751 | − | 0.460262i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30734.7 | − | 9024.51i | −1.49337 | − | 0.438494i | −0.569757 | − | 0.821813i | \(-0.692963\pi\) |
−0.923616 | + | 0.383319i | \(0.874781\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5678.18 | − | 39492.6i | −0.273166 | − | 1.89991i | ||||
\(757\) | −14446.7 | + | 12518.1i | −0.693624 | + | 0.601028i | −0.928648 | − | 0.370961i | \(-0.879028\pi\) |
0.235025 | + | 0.971989i | \(0.424483\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 50708.9 | − | 14889.5i | 2.40601 | − | 0.706468i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 19360.1 | + | 8841.46i | 0.909632 | + | 0.415415i | ||||
\(769\) | 10145.2 | + | 8790.90i | 0.475744 | + | 0.412234i | 0.859449 | − | 0.511221i | \(-0.170807\pi\) |
−0.383705 | + | 0.923456i | \(0.625352\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −26303.1 | + | 30355.4i | −1.22626 | + | 1.41518i | ||||
\(773\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37207.0i | 1.72453i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 54595.5 | − | 35086.4i | 2.52072 | − | 1.61997i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 38587.9 | + | 44532.8i | 1.75783 | + | 2.02865i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12074.6 | − | 41122.3i | −0.546903 | − | 1.86258i | −0.504375 | − | 0.863485i | \(-0.668277\pi\) |
−0.0425282 | − | 0.999095i | \(-0.513541\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31229.6 | + | 20070.1i | 1.39848 | + | 0.898750i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18593.4 | − | 40713.9i | 0.827923 | − | 1.81290i | ||||
\(797\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 4911.66 | + | 22261.9i | 0.215449 | + | 0.976515i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45381.0 | + | 6524.81i | 1.96491 | + | 0.282512i | 0.999785 | + | 0.0207287i | \(0.00659863\pi\) |
0.965127 | + | 0.261783i | \(0.0843105\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −340.751 | + | 2369.98i | −0.0146995 | + | 0.102237i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28219.4 | − | 12887.4i | 1.20841 | − | 0.551862i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10676.5 | + | 74256.8i | 0.455516 | + | 3.16818i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6177.67 | − | 42966.6i | −0.261653 | − | 1.81983i | −0.520439 | − | 0.853899i | \(-0.674232\pi\) |
0.258786 | − | 0.965935i | \(-0.416677\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1584.49 | + | 3469.54i | 0.0663830 | + | 0.145359i | 0.939915 | − | 0.341408i | \(-0.110904\pi\) |
−0.873532 | + | 0.486766i | \(0.838176\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17426.3 | − | 27115.9i | −0.727451 | − | 1.13194i | ||||
\(832\) | −36402.2 | − | 16624.3i | −1.51685 | − | 0.692723i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5943.06 | + | 41334.9i | 0.245427 | + | 1.70698i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24389.0 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 30180.8 | − | 19396.0i | 1.23088 | − | 0.791041i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13330.3 | − | 45398.7i | −0.540771 | − | 1.84170i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2150.84 | − | 1863.72i | −0.0869456 | − | 0.0753388i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3426.46 | + | 1006.10i | 0.137538 | + | 0.0403847i | 0.349777 | − | 0.936833i | \(-0.386257\pi\) |
−0.212239 | + | 0.977218i | \(0.568076\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20305.0 | + | 44461.9i | 0.806518 | + | 1.76603i | 0.621699 | + | 0.783256i | \(0.286443\pi\) |
0.184819 | + | 0.982772i | \(0.440830\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7192.27 | − | 24494.6i | 0.281733 | − | 0.959493i | ||||
\(868\) | −55434.1 | − | 63974.3i | −2.16769 | − | 2.50165i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9235.25 | − | 41858.5i | −0.359270 | − | 1.62838i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2854.76 | + | 410.453i | 0.110675 | + | 0.0159126i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −27044.3 | + | 42081.7i | −1.04308 | + | 1.62307i | ||||
\(877\) | −5262.86 | + | 3382.23i | −0.202639 | + | 0.130228i | −0.638025 | − | 0.770016i | \(-0.720248\pi\) |
0.435386 | + | 0.900244i | \(0.356612\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42946.7 | + | 19613.1i | −1.63677 | + | 0.747490i | −0.999728 | − | 0.0233351i | \(-0.992572\pi\) |
−0.637047 | + | 0.770825i | \(0.719844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24265.5 | + | 82640.6i | −0.915453 | + | 3.11775i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15461.8 | − | 9936.68i | 0.580380 | − | 0.372987i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −27000.0 | −1.00000 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −53375.7 | − | 46250.3i | −1.96703 | − | 1.70444i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8661.17 | − | 18965.3i | 0.317078 | − | 0.694303i | −0.682244 | − | 0.731124i | \(-0.738996\pi\) |
0.999322 | + | 0.0368211i | \(0.0117232\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(912\) | 7601.87 | + | 25889.6i | 0.276012 | + | 0.940011i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 37873.0 | + | 32817.2i | 1.36611 | + | 1.18374i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47814.7 | + | 6874.72i | −1.71628 | + | 0.246764i | −0.929066 | − | 0.369914i | \(-0.879387\pi\) |
−0.787216 | + | 0.616678i | \(0.788478\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14289.4 | + | 48665.4i | 0.511241 | + | 1.74113i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18243.9 | − | 39948.5i | −0.648491 | − | 1.42000i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −29014.2 | − | 18646.3i | −1.02799 | − | 0.660652i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10631.5 | + | 73943.6i | −0.374257 | + | 2.60301i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 29519.1i | − | 1.02919i | −0.857435 | − | 0.514593i | \(-0.827943\pi\) | ||
0.857435 | − | 0.514593i | \(-0.172057\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −54988.4 | −1.91105 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(948\) | −34229.3 | + | 39502.8i | −1.17270 | + | 1.35337i | ||||
\(949\) | 50850.6 | − | 79125.0i | 1.73939 | − | 2.70654i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38511.0 | + | 44444.1i | 1.29271 | + | 1.49186i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14818.8 | + | 4351.19i | −0.495105 | + | 0.145376i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −57991.0 | −1.92850 | −0.964252 | − | 0.264986i | \(-0.914633\pi\) | ||||
−0.964252 | + | 0.264986i | \(0.914633\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(972\) | −29995.5 | + | 4312.70i | −0.989821 | + | 0.142315i | ||||
\(973\) | −76214.2 | + | 87955.9i | −2.51112 | + | 2.89798i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 50767.3 | 1.66754 | ||||||||
\(976\) | − | 30396.8i | − | 0.996903i | ||||||
\(977\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11308.9 | − | 38514.5i | −0.368058 | − | 1.25349i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14293.6 | − | 48679.4i | −0.460262 | − | 1.56751i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3136.37 | − | 10681.5i | 0.100535 | − | 0.342390i | −0.893829 | − | 0.448407i | \(-0.851992\pi\) |
0.994364 | + | 0.106017i | \(0.0338097\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18585.4 | + | 40696.2i | 0.593946 | + | 1.30056i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9695.00 | + | 21229.1i | −0.307967 | + | 0.674355i | −0.998816 | − | 0.0486447i | \(-0.984510\pi\) |
0.690849 | + | 0.722999i | \(0.257237\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26648.9 | − | 41466.5i | −0.843978 | − | 1.31325i |
(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 | 201.4.j.a.8.2 | ✓ | 20 | |
3.2 | odd | 2 | CM | 201.4.j.a.8.2 | ✓ | 20 | |
67.42 | odd | 22 | inner | 201.4.j.a.176.2 | yes | 20 | |
201.176 | even | 22 | inner | 201.4.j.a.176.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.4.j.a.8.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
201.4.j.a.8.2 | ✓ | 20 | 3.2 | odd | 2 | CM | |
201.4.j.a.176.2 | yes | 20 | 67.42 | odd | 22 | inner | |
201.4.j.a.176.2 | yes | 20 | 201.176 | even | 22 | inner |