Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,4,Mod(1,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.a (trivial) |
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: | yes |
Analytic conductor: | \(18.5856016518\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 315.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.00000 | −1.00000 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −42.0000 | −1.15123 | −0.575613 | − | 0.817723i | \(-0.695236\pi\) | ||||
−0.575613 | + | 0.817723i | \(0.695236\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 20.0000 | 0.426692 | 0.213346 | − | 0.976977i | \(-0.431564\pi\) | ||||
0.213346 | + | 0.976977i | \(0.431564\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000 | 1.00000 | ||||||||
\(17\) | −66.0000 | −0.941609 | −0.470804 | − | 0.882238i | \(-0.656036\pi\) | ||||
−0.470804 | + | 0.882238i | \(0.656036\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 38.0000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 40.0000 | 0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −12.0000 | −0.108790 | −0.0543951 | − | 0.998519i | \(-0.517323\pi\) | ||||
−0.0543951 | + | 0.998519i | \(0.517323\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −56.0000 | −0.377964 | ||||||||
\(29\) | 258.000 | 1.65205 | 0.826024 | − | 0.563635i | \(-0.190597\pi\) | ||||
0.826024 | + | 0.563635i | \(0.190597\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 146.000 | 0.845883 | 0.422942 | − | 0.906157i | \(-0.360998\pi\) | ||||
0.422942 | + | 0.906157i | \(0.360998\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −35.0000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 434.000 | 1.92836 | 0.964178 | − | 0.265257i | \(-0.0854567\pi\) | ||||
0.964178 | + | 0.265257i | \(0.0854567\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 282.000 | 1.07417 | 0.537085 | − | 0.843528i | \(-0.319525\pi\) | ||||
0.537085 | + | 0.843528i | \(0.319525\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20.0000 | 0.0709296 | 0.0354648 | − | 0.999371i | \(-0.488709\pi\) | ||||
0.0354648 | + | 0.999371i | \(0.488709\pi\) | |||||||
\(44\) | 336.000 | 1.15123 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 72.0000 | 0.223453 | 0.111726 | − | 0.993739i | \(-0.464362\pi\) | ||||
0.111726 | + | 0.993739i | \(0.464362\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −160.000 | −0.426692 | ||||||||
\(53\) | −336.000 | −0.870814 | −0.435407 | − | 0.900234i | \(-0.643396\pi\) | ||||
−0.435407 | + | 0.900234i | \(0.643396\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 210.000 | 0.514844 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 360.000 | 0.794373 | 0.397187 | − | 0.917738i | \(-0.369987\pi\) | ||||
0.397187 | + | 0.917738i | \(0.369987\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −682.000 | −1.43149 | −0.715747 | − | 0.698360i | \(-0.753914\pi\) | ||||
−0.715747 | + | 0.698360i | \(0.753914\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | −100.000 | −0.190823 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 812.000 | 1.48062 | 0.740310 | − | 0.672265i | \(-0.234679\pi\) | ||||
0.740310 | + | 0.672265i | \(0.234679\pi\) | |||||||
\(68\) | 528.000 | 0.941609 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −810.000 | −1.35393 | −0.676967 | − | 0.736013i | \(-0.736706\pi\) | ||||
−0.676967 | + | 0.736013i | \(0.736706\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −124.000 | −0.198810 | −0.0994048 | − | 0.995047i | \(-0.531694\pi\) | ||||
−0.0994048 | + | 0.995047i | \(0.531694\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −304.000 | −0.458831 | ||||||||
\(77\) | −294.000 | −0.435122 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1136.00 | 1.61785 | 0.808924 | − | 0.587913i | \(-0.200050\pi\) | ||||
0.808924 | + | 0.587913i | \(0.200050\pi\) | |||||||
\(80\) | −320.000 | −0.447214 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −156.000 | −0.206304 | −0.103152 | − | 0.994666i | \(-0.532893\pi\) | ||||
−0.103152 | + | 0.994666i | \(0.532893\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 330.000 | 0.421100 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1038.00 | 1.23627 | 0.618134 | − | 0.786073i | \(-0.287889\pi\) | ||||
0.618134 | + | 0.786073i | \(0.287889\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 140.000 | 0.161275 | ||||||||
\(92\) | 96.0000 | 0.108790 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −190.000 | −0.205196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1208.00 | 1.26447 | 0.632236 | − | 0.774776i | \(-0.282137\pi\) | ||||
0.632236 | + | 0.774776i | \(0.282137\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −200.000 | −0.200000 | ||||||||
\(101\) | −546.000 | −0.537911 | −0.268956 | − | 0.963153i | \(-0.586678\pi\) | ||||
−0.268956 | + | 0.963153i | \(0.586678\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −520.000 | −0.497448 | −0.248724 | − | 0.968574i | \(-0.580011\pi\) | ||||
−0.248724 | + | 0.968574i | \(0.580011\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1212.00 | −1.09503 | −0.547516 | − | 0.836795i | \(-0.684427\pi\) | ||||
−0.547516 | + | 0.836795i | \(0.684427\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1078.00 | −0.947281 | −0.473641 | − | 0.880718i | \(-0.657060\pi\) | ||||
−0.473641 | + | 0.880718i | \(0.657060\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 448.000 | 0.377964 | ||||||||
\(113\) | 1452.00 | 1.20878 | 0.604392 | − | 0.796687i | \(-0.293416\pi\) | ||||
0.604392 | + | 0.796687i | \(0.293416\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 60.0000 | 0.0486524 | ||||||||
\(116\) | −2064.00 | −1.65205 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −462.000 | −0.355895 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 433.000 | 0.325319 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1168.00 | −0.845883 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1312.00 | −0.916702 | −0.458351 | − | 0.888771i | \(-0.651560\pi\) | ||||
−0.458351 | + | 0.888771i | \(0.651560\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1356.00 | 0.904384 | 0.452192 | − | 0.891921i | \(-0.350642\pi\) | ||||
0.452192 | + | 0.891921i | \(0.350642\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 266.000 | 0.173422 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 984.000 | 0.613641 | 0.306820 | − | 0.951767i | \(-0.400735\pi\) | ||||
0.306820 | + | 0.951767i | \(0.400735\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −394.000 | −0.240422 | −0.120211 | − | 0.992748i | \(-0.538357\pi\) | ||||
−0.120211 | + | 0.992748i | \(0.538357\pi\) | |||||||
\(140\) | 280.000 | 0.169031 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −840.000 | −0.491219 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1290.00 | −0.738818 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3472.00 | −1.92836 | ||||||||
\(149\) | 1014.00 | 0.557518 | 0.278759 | − | 0.960361i | \(-0.410077\pi\) | ||||
0.278759 | + | 0.960361i | \(0.410077\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1996.00 | −1.07571 | −0.537855 | − | 0.843037i | \(-0.680765\pi\) | ||||
−0.537855 | + | 0.843037i | \(0.680765\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −730.000 | −0.378290 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2392.00 | −1.21594 | −0.607969 | − | 0.793960i | \(-0.708016\pi\) | ||||
−0.607969 | + | 0.793960i | \(0.708016\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −84.0000 | −0.0411188 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2036.00 | 0.978355 | 0.489177 | − | 0.872184i | \(-0.337297\pi\) | ||||
0.489177 | + | 0.872184i | \(0.337297\pi\) | |||||||
\(164\) | −2256.00 | −1.07417 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3936.00 | 1.82381 | 0.911907 | − | 0.410398i | \(-0.134610\pi\) | ||||
0.911907 | + | 0.410398i | \(0.134610\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1797.00 | −0.817934 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −160.000 | −0.0709296 | ||||||||
\(173\) | −378.000 | −0.166120 | −0.0830601 | − | 0.996545i | \(-0.526469\pi\) | ||||
−0.0830601 | + | 0.996545i | \(0.526469\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 175.000 | 0.0755929 | ||||||||
\(176\) | −2688.00 | −1.15123 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 222.000 | 0.0926987 | 0.0463493 | − | 0.998925i | \(-0.485241\pi\) | ||||
0.0463493 | + | 0.998925i | \(0.485241\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2590.00 | −1.06361 | −0.531804 | − | 0.846867i | \(-0.678486\pi\) | ||||
−0.531804 | + | 0.846867i | \(0.678486\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2170.00 | −0.862387 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2772.00 | 1.08400 | ||||||||
\(188\) | −576.000 | −0.223453 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2214.00 | −0.838740 | −0.419370 | − | 0.907815i | \(-0.637749\pi\) | ||||
−0.419370 | + | 0.907815i | \(0.637749\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4178.00 | 1.55823 | 0.779117 | − | 0.626879i | \(-0.215668\pi\) | ||||
0.779117 | + | 0.626879i | \(0.215668\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −392.000 | −0.142857 | ||||||||
\(197\) | 3060.00 | 1.10668 | 0.553340 | − | 0.832955i | \(-0.313353\pi\) | ||||
0.553340 | + | 0.832955i | \(0.313353\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2666.00 | 0.949687 | 0.474844 | − | 0.880070i | \(-0.342505\pi\) | ||||
0.474844 | + | 0.880070i | \(0.342505\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1806.00 | 0.624416 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1410.00 | −0.480384 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1280.00 | 0.426692 | ||||||||
\(209\) | −1596.00 | −0.528218 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1348.00 | −0.439811 | −0.219906 | − | 0.975521i | \(-0.570575\pi\) | ||||
−0.219906 | + | 0.975521i | \(0.570575\pi\) | |||||||
\(212\) | 2688.00 | 0.870814 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −100.000 | −0.0317207 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1022.00 | 0.319714 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1680.00 | −0.514844 | ||||||||
\(221\) | −1320.00 | −0.401777 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3188.00 | 0.957329 | 0.478664 | − | 0.877998i | \(-0.341121\pi\) | ||||
0.478664 | + | 0.877998i | \(0.341121\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3396.00 | 0.992953 | 0.496477 | − | 0.868050i | \(-0.334627\pi\) | ||||
0.496477 | + | 0.868050i | \(0.334627\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5294.00 | 1.52767 | 0.763837 | − | 0.645409i | \(-0.223313\pi\) | ||||
0.763837 | + | 0.645409i | \(0.223313\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −852.000 | −0.239555 | −0.119778 | − | 0.992801i | \(-0.538218\pi\) | ||||
−0.119778 | + | 0.992801i | \(0.538218\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −360.000 | −0.0999311 | ||||||||
\(236\) | −2880.00 | −0.794373 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4866.00 | −1.31697 | −0.658484 | − | 0.752595i | \(-0.728802\pi\) | ||||
−0.658484 | + | 0.752595i | \(0.728802\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2050.00 | −0.547934 | −0.273967 | − | 0.961739i | \(-0.588336\pi\) | ||||
−0.273967 | + | 0.961739i | \(0.588336\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5456.00 | 1.43149 | ||||||||
\(245\) | −245.000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 760.000 | 0.195780 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1152.00 | 0.289696 | 0.144848 | − | 0.989454i | \(-0.453731\pi\) | ||||
0.144848 | + | 0.989454i | \(0.453731\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 504.000 | 0.125242 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | 6450.00 | 1.56553 | 0.782763 | − | 0.622321i | \(-0.213810\pi\) | ||||
0.782763 | + | 0.622321i | \(0.213810\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3038.00 | 0.728850 | ||||||||
\(260\) | 800.000 | 0.190823 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1968.00 | −0.461415 | −0.230707 | − | 0.973023i | \(-0.574104\pi\) | ||||
−0.230707 | + | 0.973023i | \(0.574104\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1680.00 | 0.389440 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6496.00 | −1.48062 | ||||||||
\(269\) | 3894.00 | 0.882607 | 0.441304 | − | 0.897358i | \(-0.354516\pi\) | ||||
0.441304 | + | 0.897358i | \(0.354516\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7094.00 | 1.59015 | 0.795073 | − | 0.606513i | \(-0.207432\pi\) | ||||
0.795073 | + | 0.606513i | \(0.207432\pi\) | |||||||
\(272\) | −4224.00 | −0.941609 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1050.00 | −0.230245 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3310.00 | −0.717973 | −0.358987 | − | 0.933343i | \(-0.616878\pi\) | ||||
−0.358987 | + | 0.933343i | \(0.616878\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7158.00 | −1.51961 | −0.759805 | − | 0.650151i | \(-0.774706\pi\) | ||||
−0.759805 | + | 0.650151i | \(0.774706\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5164.00 | −1.08469 | −0.542346 | − | 0.840155i | \(-0.682464\pi\) | ||||
−0.542346 | + | 0.840155i | \(0.682464\pi\) | |||||||
\(284\) | 6480.00 | 1.35393 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1974.00 | 0.405998 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −557.000 | −0.113373 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 992.000 | 0.198810 | ||||||||
\(293\) | 8598.00 | 1.71434 | 0.857168 | − | 0.515037i | \(-0.172222\pi\) | ||||
0.857168 | + | 0.515037i | \(0.172222\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1800.00 | −0.355254 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −240.000 | −0.0464199 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 140.000 | 0.0268089 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2432.00 | 0.458831 | ||||||||
\(305\) | 3410.00 | 0.640184 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −448.000 | −0.0832857 | −0.0416429 | − | 0.999133i | \(-0.513259\pi\) | ||||
−0.0416429 | + | 0.999133i | \(0.513259\pi\) | |||||||
\(308\) | 2352.00 | 0.435122 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5832.00 | 1.06335 | 0.531676 | − | 0.846948i | \(-0.321562\pi\) | ||||
0.531676 | + | 0.846948i | \(0.321562\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9848.00 | 1.77841 | 0.889204 | − | 0.457510i | \(-0.151259\pi\) | ||||
0.889204 | + | 0.457510i | \(0.151259\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9088.00 | −1.61785 | ||||||||
\(317\) | 5616.00 | 0.995035 | 0.497517 | − | 0.867454i | \(-0.334245\pi\) | ||||
0.497517 | + | 0.867454i | \(0.334245\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10836.0 | −1.90188 | ||||||||
\(320\) | 2560.00 | 0.447214 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2508.00 | −0.432040 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 500.000 | 0.0853385 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 504.000 | 0.0844572 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 452.000 | 0.0750579 | 0.0375290 | − | 0.999296i | \(-0.488051\pi\) | ||||
0.0375290 | + | 0.999296i | \(0.488051\pi\) | |||||||
\(332\) | 1248.00 | 0.206304 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4060.00 | −0.662154 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2302.00 | −0.372101 | −0.186050 | − | 0.982540i | \(-0.559569\pi\) | ||||
−0.186050 | + | 0.982540i | \(0.559569\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2640.00 | −0.421100 | ||||||||
\(341\) | −6132.00 | −0.973802 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1584.00 | −0.245054 | −0.122527 | − | 0.992465i | \(-0.539100\pi\) | ||||
−0.122527 | + | 0.992465i | \(0.539100\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8174.00 | 1.25371 | 0.626854 | − | 0.779137i | \(-0.284342\pi\) | ||||
0.626854 | + | 0.779137i | \(0.284342\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8610.00 | −1.29820 | −0.649099 | − | 0.760704i | \(-0.724854\pi\) | ||||
−0.649099 | + | 0.760704i | \(0.724854\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4050.00 | 0.605498 | ||||||||
\(356\) | −8304.00 | −1.23627 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2154.00 | 0.316668 | 0.158334 | − | 0.987386i | \(-0.449388\pi\) | ||||
0.158334 | + | 0.987386i | \(0.449388\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5415.00 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1120.00 | −0.161275 | ||||||||
\(365\) | 620.000 | 0.0889104 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6644.00 | 0.944997 | 0.472499 | − | 0.881331i | \(-0.343352\pi\) | ||||
0.472499 | + | 0.881331i | \(0.343352\pi\) | |||||||
\(368\) | −768.000 | −0.108790 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2352.00 | −0.329137 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7958.00 | 1.10469 | 0.552345 | − | 0.833615i | \(-0.313733\pi\) | ||||
0.552345 | + | 0.833615i | \(0.313733\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5160.00 | 0.704917 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3440.00 | 0.466229 | 0.233115 | − | 0.972449i | \(-0.425108\pi\) | ||||
0.233115 | + | 0.972449i | \(0.425108\pi\) | |||||||
\(380\) | 1520.00 | 0.205196 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12936.0 | −1.72585 | −0.862923 | − | 0.505336i | \(-0.831369\pi\) | ||||
−0.862923 | + | 0.505336i | \(0.831369\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1470.00 | 0.194593 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9664.00 | −1.26447 | ||||||||
\(389\) | 14862.0 | 1.93710 | 0.968552 | − | 0.248812i | \(-0.0800401\pi\) | ||||
0.968552 | + | 0.248812i | \(0.0800401\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 792.000 | 0.102438 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5680.00 | −0.723524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10460.0 | 1.32235 | 0.661174 | − | 0.750232i | \(-0.270058\pi\) | ||||
0.661174 | + | 0.750232i | \(0.270058\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1600.00 | 0.200000 | ||||||||
\(401\) | 9150.00 | 1.13947 | 0.569737 | − | 0.821827i | \(-0.307045\pi\) | ||||
0.569737 | + | 0.821827i | \(0.307045\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2920.00 | 0.360932 | ||||||||
\(404\) | 4368.00 | 0.537911 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18228.0 | −2.21997 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4894.00 | −0.591669 | −0.295835 | − | 0.955239i | \(-0.595598\pi\) | ||||
−0.295835 | + | 0.955239i | \(0.595598\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4160.00 | 0.497448 | ||||||||
\(413\) | 2520.00 | 0.300245 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 780.000 | 0.0922619 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1668.00 | 0.194480 | 0.0972400 | − | 0.995261i | \(-0.468999\pi\) | ||||
0.0972400 | + | 0.995261i | \(0.468999\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12418.0 | −1.43757 | −0.718784 | − | 0.695233i | \(-0.755301\pi\) | ||||
−0.718784 | + | 0.695233i | \(0.755301\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1650.00 | −0.188322 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4774.00 | −0.541054 | ||||||||
\(428\) | 9696.00 | 1.09503 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15186.0 | −1.69718 | −0.848589 | − | 0.529052i | \(-0.822548\pi\) | ||||
−0.848589 | + | 0.529052i | \(0.822548\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5704.00 | −0.633064 | −0.316532 | − | 0.948582i | \(-0.602518\pi\) | ||||
−0.316532 | + | 0.948582i | \(0.602518\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8624.00 | 0.947281 | ||||||||
\(437\) | −456.000 | −0.0499163 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17206.0 | −1.87061 | −0.935305 | − | 0.353843i | \(-0.884875\pi\) | ||||
−0.935305 | + | 0.353843i | \(0.884875\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3456.00 | −0.370654 | −0.185327 | − | 0.982677i | \(-0.559334\pi\) | ||||
−0.185327 | + | 0.982677i | \(0.559334\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5190.00 | −0.552875 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3584.00 | −0.377964 | ||||||||
\(449\) | −16074.0 | −1.68949 | −0.844743 | − | 0.535173i | \(-0.820247\pi\) | ||||
−0.844743 | + | 0.535173i | \(0.820247\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11844.0 | −1.23661 | ||||||||
\(452\) | −11616.0 | −1.20878 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −700.000 | −0.0721242 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7526.00 | 0.770353 | 0.385177 | − | 0.922843i | \(-0.374141\pi\) | ||||
0.385177 | + | 0.922843i | \(0.374141\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −480.000 | −0.0486524 | ||||||||
\(461\) | 2274.00 | 0.229741 | 0.114871 | − | 0.993380i | \(-0.463355\pi\) | ||||
0.114871 | + | 0.993380i | \(0.463355\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10024.0 | −1.00617 | −0.503083 | − | 0.864238i | \(-0.667801\pi\) | ||||
−0.503083 | + | 0.864238i | \(0.667801\pi\) | |||||||
\(464\) | 16512.0 | 1.65205 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2460.00 | 0.243759 | 0.121879 | − | 0.992545i | \(-0.461108\pi\) | ||||
0.121879 | + | 0.992545i | \(0.461108\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5684.00 | 0.559622 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −840.000 | −0.0816559 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 950.000 | 0.0917663 | ||||||||
\(476\) | 3696.00 | 0.355895 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19320.0 | −1.84291 | −0.921454 | − | 0.388486i | \(-0.872998\pi\) | ||||
−0.921454 | + | 0.388486i | \(0.872998\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8680.00 | 0.822815 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3464.00 | −0.325319 | ||||||||
\(485\) | −6040.00 | −0.565489 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12544.0 | −1.16719 | −0.583596 | − | 0.812044i | \(-0.698355\pi\) | ||||
−0.583596 | + | 0.812044i | \(0.698355\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15510.0 | 1.42557 | 0.712787 | − | 0.701381i | \(-0.247433\pi\) | ||||
0.712787 | + | 0.701381i | \(0.247433\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17028.0 | −1.55558 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9344.00 | 0.845883 | ||||||||
\(497\) | −5670.00 | −0.511739 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14344.0 | −1.28682 | −0.643412 | − | 0.765520i | \(-0.722482\pi\) | ||||
−0.643412 | + | 0.765520i | \(0.722482\pi\) | |||||||
\(500\) | 1000.00 | 0.0894427 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21384.0 | 1.89556 | 0.947779 | − | 0.318929i | \(-0.103323\pi\) | ||||
0.947779 | + | 0.318929i | \(0.103323\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2730.00 | 0.240561 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10496.0 | 0.916702 | ||||||||
\(509\) | 7134.00 | 0.621236 | 0.310618 | − | 0.950535i | \(-0.399464\pi\) | ||||
0.310618 | + | 0.950535i | \(0.399464\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −868.000 | −0.0751430 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2600.00 | 0.222465 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3024.00 | −0.257244 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19122.0 | 1.60797 | 0.803983 | − | 0.594653i | \(-0.202710\pi\) | ||||
0.803983 | + | 0.594653i | \(0.202710\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15640.0 | −1.30763 | −0.653814 | − | 0.756655i | \(-0.726832\pi\) | ||||
−0.653814 | + | 0.756655i | \(0.726832\pi\) | |||||||
\(524\) | −10848.0 | −0.904384 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9636.00 | −0.796491 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12023.0 | −0.988165 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2128.00 | −0.173422 | ||||||||
\(533\) | 5640.00 | 0.458341 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6060.00 | 0.489713 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2058.00 | −0.164461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2846.00 | 0.226172 | 0.113086 | − | 0.993585i | \(-0.463926\pi\) | ||||
0.113086 | + | 0.993585i | \(0.463926\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5390.00 | 0.423637 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4444.00 | −0.347371 | −0.173685 | − | 0.984801i | \(-0.555568\pi\) | ||||
−0.173685 | + | 0.984801i | \(0.555568\pi\) | |||||||
\(548\) | −7872.00 | −0.613641 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9804.00 | 0.758012 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7952.00 | 0.611489 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3152.00 | 0.240422 | ||||||||
\(557\) | −18552.0 | −1.41126 | −0.705631 | − | 0.708579i | \(-0.749337\pi\) | ||||
−0.705631 | + | 0.708579i | \(0.749337\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 400.000 | 0.0302651 | ||||||||
\(560\) | −2240.00 | −0.169031 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16452.0 | 1.23156 | 0.615781 | − | 0.787918i | \(-0.288841\pi\) | ||||
0.615781 | + | 0.787918i | \(0.288841\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7260.00 | −0.540585 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7722.00 | −0.568933 | −0.284467 | − | 0.958686i | \(-0.591817\pi\) | ||||
−0.284467 | + | 0.958686i | \(0.591817\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2576.00 | 0.188796 | 0.0943978 | − | 0.995535i | \(-0.469907\pi\) | ||||
0.0943978 | + | 0.995535i | \(0.469907\pi\) | |||||||
\(572\) | 6720.00 | 0.491219 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −300.000 | −0.0217580 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2464.00 | −0.177778 | −0.0888888 | − | 0.996042i | \(-0.528332\pi\) | ||||
−0.0888888 | + | 0.996042i | \(0.528332\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10320.0 | 0.738818 | ||||||||
\(581\) | −1092.00 | −0.0779755 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14112.0 | 1.00250 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1452.00 | −0.102096 | −0.0510481 | − | 0.998696i | \(-0.516256\pi\) | ||||
−0.0510481 | + | 0.998696i | \(0.516256\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5548.00 | 0.388118 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 27776.0 | 1.92836 | ||||||||
\(593\) | −10698.0 | −0.740833 | −0.370417 | − | 0.928866i | \(-0.620785\pi\) | ||||
−0.370417 | + | 0.928866i | \(0.620785\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2310.00 | 0.159161 | ||||||||
\(596\) | −8112.00 | −0.557518 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8730.00 | 0.595489 | 0.297745 | − | 0.954646i | \(-0.403766\pi\) | ||||
0.297745 | + | 0.954646i | \(0.403766\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1910.00 | 0.129635 | 0.0648174 | − | 0.997897i | \(-0.479354\pi\) | ||||
0.0648174 | + | 0.997897i | \(0.479354\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 15968.0 | 1.07571 | ||||||||
\(605\) | −2165.00 | −0.145487 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5596.00 | −0.374192 | −0.187096 | − | 0.982342i | \(-0.559908\pi\) | ||||
−0.187096 | + | 0.982342i | \(0.559908\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1440.00 | 0.0953456 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28586.0 | 1.88349 | 0.941744 | − | 0.336332i | \(-0.109186\pi\) | ||||
0.941744 | + | 0.336332i | \(0.109186\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19236.0 | 1.25513 | 0.627563 | − | 0.778566i | \(-0.284053\pi\) | ||||
0.627563 | + | 0.778566i | \(0.284053\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6734.00 | 0.437257 | 0.218629 | − | 0.975808i | \(-0.429842\pi\) | ||||
0.218629 | + | 0.975808i | \(0.429842\pi\) | |||||||
\(620\) | 5840.00 | 0.378290 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7266.00 | 0.467265 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19136.0 | 1.21594 | ||||||||
\(629\) | −28644.0 | −1.81576 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7184.00 | 0.453234 | 0.226617 | − | 0.973984i | \(-0.427233\pi\) | ||||
0.226617 | + | 0.973984i | \(0.427233\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6560.00 | 0.409962 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 980.000 | 0.0609561 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −510.000 | −0.0314256 | −0.0157128 | − | 0.999877i | \(-0.505002\pi\) | ||||
−0.0157128 | + | 0.999877i | \(0.505002\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20752.0 | −1.27275 | −0.636376 | − | 0.771379i | \(-0.719567\pi\) | ||||
−0.636376 | + | 0.771379i | \(0.719567\pi\) | |||||||
\(644\) | 672.000 | 0.0411188 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21072.0 | −1.28041 | −0.640205 | − | 0.768204i | \(-0.721151\pi\) | ||||
−0.640205 | + | 0.768204i | \(0.721151\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15120.0 | −0.914502 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16288.0 | −0.978355 | ||||||||
\(653\) | −2892.00 | −0.173312 | −0.0866560 | − | 0.996238i | \(-0.527618\pi\) | ||||
−0.0866560 | + | 0.996238i | \(0.527618\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6780.00 | −0.404453 | ||||||||
\(656\) | 18048.0 | 1.07417 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −750.000 | −0.0443336 | −0.0221668 | − | 0.999754i | \(-0.507056\pi\) | ||||
−0.0221668 | + | 0.999754i | \(0.507056\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30062.0 | 1.76895 | 0.884475 | − | 0.466587i | \(-0.154517\pi\) | ||||
0.884475 | + | 0.466587i | \(0.154517\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1330.00 | −0.0775567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3096.00 | −0.179727 | ||||||||
\(668\) | −31488.0 | −1.82381 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28644.0 | 1.64797 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15446.0 | 0.884695 | 0.442347 | − | 0.896844i | \(-0.354146\pi\) | ||||
0.442347 | + | 0.896844i | \(0.354146\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14376.0 | 0.817934 | ||||||||
\(677\) | 25110.0 | 1.42549 | 0.712744 | − | 0.701424i | \(-0.247452\pi\) | ||||
0.712744 | + | 0.701424i | \(0.247452\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8456.00 | 0.477926 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7968.00 | −0.446394 | −0.223197 | − | 0.974773i | \(-0.571649\pi\) | ||||
−0.223197 | + | 0.974773i | \(0.571649\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4920.00 | −0.274429 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1280.00 | 0.0709296 | ||||||||
\(689\) | −6720.00 | −0.371570 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14398.0 | −0.792657 | −0.396328 | − | 0.918109i | \(-0.629716\pi\) | ||||
−0.396328 | + | 0.918109i | \(0.629716\pi\) | |||||||
\(692\) | 3024.00 | 0.166120 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1970.00 | 0.107520 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18612.0 | −1.01145 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1400.00 | −0.0755929 | ||||||||
\(701\) | 9234.00 | 0.497523 | 0.248761 | − | 0.968565i | \(-0.419977\pi\) | ||||
0.248761 | + | 0.968565i | \(0.419977\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16492.0 | 0.884790 | ||||||||
\(704\) | 21504.0 | 1.15123 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3822.00 | −0.203311 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8030.00 | 0.425350 | 0.212675 | − | 0.977123i | \(-0.431782\pi\) | ||||
0.212675 | + | 0.977123i | \(0.431782\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1752.00 | −0.0920237 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4200.00 | 0.219680 | ||||||||
\(716\) | −1776.00 | −0.0926987 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27060.0 | −1.40357 | −0.701786 | − | 0.712388i | \(-0.747614\pi\) | ||||
−0.701786 | + | 0.712388i | \(0.747614\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3640.00 | −0.188018 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20720.0 | 1.06361 | ||||||||
\(725\) | 6450.00 | 0.330410 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3724.00 | −0.189980 | −0.0949900 | − | 0.995478i | \(-0.530282\pi\) | ||||
−0.0949900 | + | 0.995478i | \(0.530282\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1320.00 | −0.0667879 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5668.00 | −0.285610 | −0.142805 | − | 0.989751i | \(-0.545612\pi\) | ||||
−0.142805 | + | 0.989751i | \(0.545612\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −34104.0 | −1.70453 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16072.0 | −0.800024 | −0.400012 | − | 0.916510i | \(-0.630994\pi\) | ||||
−0.400012 | + | 0.916510i | \(0.630994\pi\) | |||||||
\(740\) | 17360.0 | 0.862387 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8256.00 | 0.407649 | 0.203825 | − | 0.979007i | \(-0.434663\pi\) | ||||
0.203825 | + | 0.979007i | \(0.434663\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5070.00 | −0.249329 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −22176.0 | −1.08400 | ||||||||
\(749\) | −8484.00 | −0.413883 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6352.00 | −0.308639 | −0.154319 | − | 0.988021i | \(-0.549318\pi\) | ||||
−0.154319 | + | 0.988021i | \(0.549318\pi\) | |||||||
\(752\) | 4608.00 | 0.223453 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9980.00 | 0.481072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11558.0 | 0.554931 | 0.277465 | − | 0.960736i | \(-0.410506\pi\) | ||||
0.277465 | + | 0.960736i | \(0.410506\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7770.00 | −0.370121 | −0.185061 | − | 0.982727i | \(-0.559248\pi\) | ||||
−0.185061 | + | 0.982727i | \(0.559248\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7546.00 | −0.358039 | ||||||||
\(764\) | 17712.0 | 0.838740 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7200.00 | 0.338953 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22646.0 | 1.06194 | 0.530972 | − | 0.847389i | \(-0.321827\pi\) | ||||
0.530972 | + | 0.847389i | \(0.321827\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −33424.0 | −1.55823 | ||||||||
\(773\) | 35502.0 | 1.65190 | 0.825950 | − | 0.563744i | \(-0.190639\pi\) | ||||
0.825950 | + | 0.563744i | \(0.190639\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3650.00 | 0.169177 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10716.0 | 0.492863 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34020.0 | 1.55868 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3136.00 | 0.142857 | ||||||||
\(785\) | 11960.0 | 0.543784 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17080.0 | −0.773617 | −0.386808 | − | 0.922160i | \(-0.626422\pi\) | ||||
−0.386808 | + | 0.922160i | \(0.626422\pi\) | |||||||
\(788\) | −24480.0 | −1.10668 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10164.0 | 0.456878 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13640.0 | −0.610808 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −21328.0 | −0.949687 | ||||||||
\(797\) | −5730.00 | −0.254664 | −0.127332 | − | 0.991860i | \(-0.540641\pi\) | ||||
−0.127332 | + | 0.991860i | \(0.540641\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4752.00 | −0.210405 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5208.00 | 0.228875 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 420.000 | 0.0183889 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2550.00 | −0.110820 | −0.0554099 | − | 0.998464i | \(-0.517647\pi\) | ||||
−0.0554099 | + | 0.998464i | \(0.517647\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27538.0 | −1.19234 | −0.596171 | − | 0.802857i | \(-0.703312\pi\) | ||||
−0.596171 | + | 0.802857i | \(0.703312\pi\) | |||||||
\(812\) | −14448.0 | −0.624416 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10180.0 | −0.437534 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 760.000 | 0.0325447 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11280.0 | 0.480384 | ||||||||
\(821\) | 19242.0 | 0.817966 | 0.408983 | − | 0.912542i | \(-0.365883\pi\) | ||||
0.408983 | + | 0.912542i | \(0.365883\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11752.0 | −0.497751 | −0.248875 | − | 0.968536i | \(-0.580061\pi\) | ||||
−0.248875 | + | 0.968536i | \(0.580061\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28692.0 | 1.20643 | 0.603216 | − | 0.797578i | \(-0.293886\pi\) | ||||
0.603216 | + | 0.797578i | \(0.293886\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28442.0 | 1.19159 | 0.595797 | − | 0.803135i | \(-0.296836\pi\) | ||||
0.595797 | + | 0.803135i | \(0.296836\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −10240.0 | −0.426692 | ||||||||
\(833\) | −3234.00 | −0.134516 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19680.0 | −0.815634 | ||||||||
\(836\) | 12768.0 | 0.528218 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20172.0 | −0.830053 | −0.415027 | − | 0.909809i | \(-0.636228\pi\) | ||||
−0.415027 | + | 0.909809i | \(0.636228\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42175.0 | 1.72926 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10784.0 | 0.439811 | ||||||||
\(845\) | 8985.00 | 0.365791 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3031.00 | 0.122959 | ||||||||
\(848\) | −21504.0 | −0.870814 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5208.00 | −0.209786 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19820.0 | 0.795573 | 0.397787 | − | 0.917478i | \(-0.369778\pi\) | ||||
0.397787 | + | 0.917478i | \(0.369778\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10290.0 | 0.410151 | 0.205076 | − | 0.978746i | \(-0.434256\pi\) | ||||
0.205076 | + | 0.978746i | \(0.434256\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31606.0 | −1.25539 | −0.627697 | − | 0.778458i | \(-0.716002\pi\) | ||||
−0.627697 | + | 0.778458i | \(0.716002\pi\) | |||||||
\(860\) | 800.000 | 0.0317207 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23172.0 | −0.914002 | −0.457001 | − | 0.889466i | \(-0.651076\pi\) | ||||
−0.457001 | + | 0.889466i | \(0.651076\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1890.00 | 0.0742912 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8176.00 | −0.319714 | ||||||||
\(869\) | −47712.0 | −1.86251 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16240.0 | 0.631770 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −875.000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15550.0 | −0.598730 | −0.299365 | − | 0.954139i | \(-0.596775\pi\) | ||||
−0.299365 | + | 0.954139i | \(0.596775\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 13440.0 | 0.514844 | ||||||||
\(881\) | −28530.0 | −1.09103 | −0.545517 | − | 0.838100i | \(-0.683666\pi\) | ||||
−0.545517 | + | 0.838100i | \(0.683666\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28780.0 | −1.09686 | −0.548428 | − | 0.836198i | \(-0.684774\pi\) | ||||
−0.548428 | + | 0.836198i | \(0.684774\pi\) | |||||||
\(884\) | 10560.0 | 0.401777 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22872.0 | −0.865802 | −0.432901 | − | 0.901441i | \(-0.642510\pi\) | ||||
−0.432901 | + | 0.901441i | \(0.642510\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9184.00 | −0.346481 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −25504.0 | −0.957329 | ||||||||
\(893\) | 2736.00 | 0.102527 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1110.00 | −0.0414561 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37668.0 | 1.39744 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22176.0 | 0.819966 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12950.0 | 0.475660 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10708.0 | −0.392010 | −0.196005 | − | 0.980603i | \(-0.562797\pi\) | ||||
−0.196005 | + | 0.980603i | \(0.562797\pi\) | |||||||
\(908\) | −27168.0 | −0.992953 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1326.00 | −0.0482243 | −0.0241122 | − | 0.999709i | \(-0.507676\pi\) | ||||
−0.0241122 | + | 0.999709i | \(0.507676\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6552.00 | 0.237502 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −42352.0 | −1.52767 | ||||||||
\(917\) | 9492.00 | 0.341825 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13696.0 | −0.491610 | −0.245805 | − | 0.969319i | \(-0.579052\pi\) | ||||
−0.245805 | + | 0.969319i | \(0.579052\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16200.0 | −0.577713 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10850.0 | 0.385671 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42354.0 | −1.49579 | −0.747895 | − | 0.663817i | \(-0.768936\pi\) | ||||
−0.747895 | + | 0.663817i | \(0.768936\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1862.00 | 0.0655474 | ||||||||
\(932\) | 6816.00 | 0.239555 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13860.0 | −0.484781 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6644.00 | 0.231644 | 0.115822 | − | 0.993270i | \(-0.463050\pi\) | ||||
0.115822 | + | 0.993270i | \(0.463050\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2880.00 | 0.0999311 | ||||||||
\(941\) | −1350.00 | −0.0467681 | −0.0233840 | − | 0.999727i | \(-0.507444\pi\) | ||||
−0.0233840 | + | 0.999727i | \(0.507444\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3384.00 | −0.116859 | ||||||||
\(944\) | 23040.0 | 0.794373 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49320.0 | −1.69238 | −0.846190 | − | 0.532881i | \(-0.821109\pi\) | ||||
−0.846190 | + | 0.532881i | \(0.821109\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2480.00 | −0.0848306 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5940.00 | −0.201905 | −0.100953 | − | 0.994891i | \(-0.532189\pi\) | ||||
−0.100953 | + | 0.994891i | \(0.532189\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11070.0 | 0.375096 | ||||||||
\(956\) | 38928.0 | 1.31697 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6888.00 | 0.231934 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8475.00 | −0.284482 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16400.0 | 0.547934 | ||||||||
\(965\) | −20890.0 | −0.696863 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47216.0 | 1.57018 | 0.785090 | − | 0.619382i | \(-0.212617\pi\) | ||||
0.785090 | + | 0.619382i | \(0.212617\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12552.0 | −0.414843 | −0.207422 | − | 0.978252i | \(-0.566507\pi\) | ||||
−0.207422 | + | 0.978252i | \(0.566507\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2758.00 | −0.0908709 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −43648.0 | −1.43149 | ||||||||
\(977\) | −46908.0 | −1.53605 | −0.768025 | − | 0.640420i | \(-0.778760\pi\) | ||||
−0.768025 | + | 0.640420i | \(0.778760\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −43596.0 | −1.42322 | ||||||||
\(980\) | 1960.00 | 0.0638877 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46128.0 | 1.49670 | 0.748349 | − | 0.663305i | \(-0.230847\pi\) | ||||
0.748349 | + | 0.663305i | \(0.230847\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15300.0 | −0.494922 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6080.00 | −0.195780 | ||||||||
\(989\) | −240.000 | −0.00771644 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12184.0 | −0.390552 | −0.195276 | − | 0.980748i | \(-0.562560\pi\) | ||||
−0.195276 | + | 0.980748i | \(0.562560\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13330.0 | −0.424713 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5164.00 | −0.164038 | −0.0820188 | − | 0.996631i | \(-0.526137\pi\) | ||||
−0.0820188 | + | 0.996631i | \(0.526137\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 315.4.a.d.1.1 | 1 | ||
3.2 | odd | 2 | 105.4.a.a.1.1 | ✓ | 1 | ||
5.4 | even | 2 | 1575.4.a.f.1.1 | 1 | |||
7.6 | odd | 2 | 2205.4.a.o.1.1 | 1 | |||
12.11 | even | 2 | 1680.4.a.s.1.1 | 1 | |||
15.2 | even | 4 | 525.4.d.f.274.2 | 2 | |||
15.8 | even | 4 | 525.4.d.f.274.1 | 2 | |||
15.14 | odd | 2 | 525.4.a.e.1.1 | 1 | |||
21.20 | even | 2 | 735.4.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
315.4.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
525.4.a.e.1.1 | 1 | 15.14 | odd | 2 | |||
525.4.d.f.274.1 | 2 | 15.8 | even | 4 | |||
525.4.d.f.274.2 | 2 | 15.2 | even | 4 | |||
735.4.a.c.1.1 | 1 | 21.20 | even | 2 | |||
1575.4.a.f.1.1 | 1 | 5.4 | even | 2 | |||
1680.4.a.s.1.1 | 1 | 12.11 | even | 2 | |||
2205.4.a.o.1.1 | 1 | 7.6 | odd | 2 |