Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,3,Mod(721,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.o (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.8502001097\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.219615408.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 22x^{4} - 39x^{3} + 112x^{2} - 93x + 39 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 228) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.5 | ||
Root | \(0.500000 + 3.19918i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.721 |
Dual form | 912.3.o.c.721.2 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.556406 | 0.111281 | 0.0556406 | − | 0.998451i | \(-0.482280\pi\) | ||||
0.0556406 | + | 0.998451i | \(0.482280\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.52587 | 1.36084 | 0.680419 | − | 0.732823i | \(-0.261798\pi\) | ||||
0.680419 | + | 0.732823i | \(0.261798\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.5259 | 1.22962 | 0.614812 | − | 0.788674i | \(-0.289232\pi\) | ||||
0.614812 | + | 0.788674i | \(0.289232\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 10.5348i | − | 0.810370i | −0.914235 | − | 0.405185i | \(-0.867207\pi\) | ||
0.914235 | − | 0.405185i | \(-0.132793\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.963723i | 0.0642482i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.63868 | 0.155216 | 0.0776082 | − | 0.996984i | \(-0.475272\pi\) | ||||
0.0776082 | + | 0.996984i | \(0.475272\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.112811 | − | 18.9997i | −0.00593742 | − | 0.999982i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 16.4993i | 0.785680i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 22.0212 | 0.957443 | 0.478722 | − | 0.877967i | \(-0.341100\pi\) | ||||
0.478722 | + | 0.877967i | \(0.341100\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.6904 | −0.987617 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 48.7824i | − | 1.68215i | −0.540917 | − | 0.841076i | \(-0.681923\pi\) | ||
0.540917 | − | 0.841076i | \(-0.318077\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.248288i | 0.00800930i | 0.999992 | + | 0.00400465i | \(0.00127472\pi\) | ||||
−0.999992 | + | 0.00400465i | \(0.998725\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 23.4275i | 0.709924i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.30025 | 0.151436 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 59.3172i | 1.60317i | 0.597882 | + | 0.801584i | \(0.296009\pi\) | ||||
−0.597882 | + | 0.801584i | \(0.703991\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 18.2468 | 0.467867 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 69.0705i | − | 1.68465i | −0.538974 | − | 0.842323i | \(-0.681188\pi\) | ||
0.538974 | − | 0.842323i | \(-0.318812\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.5869 | 0.641557 | 0.320778 | − | 0.947154i | \(-0.396056\pi\) | ||||
0.320778 | + | 0.947154i | \(0.396056\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.66922 | −0.0370937 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −44.8855 | −0.955011 | −0.477505 | − | 0.878629i | \(-0.658459\pi\) | ||||
−0.477505 | + | 0.878629i | \(0.658459\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 41.7421 | 0.851881 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.57032i | 0.0896142i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.85489i | 0.0727338i | 0.999339 | + | 0.0363669i | \(0.0115785\pi\) | ||||
−0.999339 | + | 0.0363669i | \(0.988422\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.52587 | 0.136834 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 32.9084 | − | 0.195394i | 0.577340 | − | 0.00342797i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 59.3539i | 1.00600i | 0.864287 | + | 0.503000i | \(0.167770\pi\) | ||||
−0.864287 | + | 0.503000i | \(0.832230\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 96.4554 | 1.58124 | 0.790618 | − | 0.612309i | \(-0.209759\pi\) | ||||
0.790618 | + | 0.612309i | \(0.209759\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −28.5776 | −0.453613 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 5.86162i | − | 0.0901788i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.7831i | 0.160942i | 0.996757 | + | 0.0804708i | \(0.0256424\pi\) | ||||
−0.996757 | + | 0.0804708i | \(0.974358\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 38.1418i | 0.552780i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 52.6373i | − | 0.741371i | −0.928759 | − | 0.370685i | \(-0.879123\pi\) | ||
0.928759 | − | 0.370685i | \(-0.120877\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.7362 | 0.188167 | 0.0940835 | − | 0.995564i | \(-0.470008\pi\) | ||||
0.0940835 | + | 0.995564i | \(0.470008\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 42.7650i | − | 0.570201i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 128.846 | 1.67332 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 51.3224i | 0.649651i | 0.945774 | + | 0.324826i | \(0.105306\pi\) | ||||
−0.945774 | + | 0.324826i | \(0.894694\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 63.7744 | 0.768366 | 0.384183 | − | 0.923257i | \(-0.374483\pi\) | ||||
0.384183 | + | 0.923257i | \(0.374483\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.46818 | 0.0172726 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 84.4936 | 0.971191 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 44.9275i | − | 0.504804i | −0.967622 | − | 0.252402i | \(-0.918780\pi\) | ||
0.967622 | − | 0.252402i | \(-0.0812205\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 100.353i | − | 1.10278i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.430048 | −0.00462417 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0627687 | − | 10.5715i | −0.000660723 | − | 0.111279i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 72.6403i | 0.748870i | 0.927253 | + | 0.374435i | \(0.122163\pi\) | ||||
−0.927253 | + | 0.374435i | \(0.877837\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −40.5776 | −0.409875 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 116.783 | 1.15627 | 0.578133 | − | 0.815943i | \(-0.303782\pi\) | ||||
0.578133 | + | 0.815943i | \(0.303782\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 72.3921i | 0.702836i | 0.936219 | + | 0.351418i | \(0.114300\pi\) | ||||
−0.936219 | + | 0.351418i | \(0.885700\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.18029i | 0.0874314i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 154.057i | 1.43979i | 0.694085 | + | 0.719893i | \(0.255809\pi\) | ||||
−0.694085 | + | 0.719893i | \(0.744191\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 159.670i | 1.46487i | 0.680839 | + | 0.732433i | \(0.261615\pi\) | ||||
−0.680839 | + | 0.732433i | \(0.738385\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −102.740 | −0.925590 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 79.6420i | − | 0.704796i | −0.935850 | − | 0.352398i | \(-0.885366\pi\) | ||
0.935850 | − | 0.352398i | \(-0.114634\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.2527 | 0.106545 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 31.6044i | 0.270123i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 25.1357 | 0.211224 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 61.9491 | 0.511976 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 119.634 | 0.972630 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −27.6480 | −0.221184 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 30.2528i | − | 0.238211i | −0.992882 | − | 0.119106i | \(-0.961997\pi\) | ||
0.992882 | − | 0.119106i | \(-0.0380027\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 47.7820i | 0.370403i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 142.842 | 1.09040 | 0.545199 | − | 0.838306i | \(-0.316454\pi\) | ||||
0.545199 | + | 0.838306i | \(0.316454\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.07462 | − | 180.988i | −0.00807987 | − | 1.36081i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 2.89117i | − | 0.0214161i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −165.488 | −1.20795 | −0.603973 | − | 0.797005i | \(-0.706416\pi\) | ||||
−0.603973 | + | 0.797005i | \(0.706416\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 169.324 | 1.21816 | 0.609079 | − | 0.793110i | \(-0.291539\pi\) | ||||
0.609079 | + | 0.793110i | \(0.291539\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 77.7440i | − | 0.551376i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 142.492i | − | 0.996450i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 27.1428i | − | 0.187192i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 72.2995i | 0.491833i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −139.406 | −0.935612 | −0.467806 | − | 0.883831i | \(-0.654955\pi\) | ||||
−0.467806 | + | 0.883831i | \(0.654955\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 152.742i | 1.01154i | 0.862669 | + | 0.505769i | \(0.168791\pi\) | ||||
−0.862669 | + | 0.505769i | \(0.831209\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.91603 | −0.0517388 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.138149i | 0.000891284i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −295.932 | −1.88492 | −0.942459 | − | 0.334321i | \(-0.891493\pi\) | ||||
−0.942459 | + | 0.334321i | \(0.891493\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.67687 | −0.0419929 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 209.771 | 1.30293 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 112.731 | 0.691602 | 0.345801 | − | 0.938308i | \(-0.387607\pi\) | ||||
0.345801 | + | 0.938308i | \(0.387607\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.0352i | 0.0790011i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 297.205i | − | 1.77967i | −0.456284 | − | 0.889834i | \(-0.650820\pi\) | ||
0.456284 | − | 0.889834i | \(-0.349180\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 58.0179 | 0.343301 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.338433 | + | 56.9990i | 0.00197914 | + | 0.333327i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 262.849i | 1.51936i | 0.650299 | + | 0.759678i | \(0.274643\pi\) | ||||
−0.650299 | + | 0.759678i | \(0.725357\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −235.198 | −1.34399 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −102.804 | −0.580814 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 73.9185i | 0.412953i | 0.978452 | + | 0.206476i | \(0.0661996\pi\) | ||||
−0.978452 | + | 0.206476i | \(0.933800\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 34.8893i | − | 0.192759i | −0.995345 | − | 0.0963793i | \(-0.969274\pi\) | ||
0.995345 | − | 0.0963793i | \(-0.0307262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 167.066i | 0.912928i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 33.0044i | 0.178402i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 35.6904 | 0.190858 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 49.4979i | − | 0.261893i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −111.001 | −0.581156 | −0.290578 | − | 0.956851i | \(-0.593848\pi\) | ||||
−0.290578 | + | 0.956851i | \(0.593848\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 83.5616i | − | 0.432962i | −0.976287 | − | 0.216481i | \(-0.930542\pi\) | ||
0.976287 | − | 0.216481i | \(-0.0694579\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.1526 | 0.0520648 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −365.319 | −1.85441 | −0.927205 | − | 0.374554i | \(-0.877796\pi\) | ||||
−0.927205 | + | 0.374554i | \(0.877796\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.6303 | 0.0534184 | 0.0267092 | − | 0.999643i | \(-0.491497\pi\) | ||||
0.0267092 | + | 0.999643i | \(0.491497\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.6769 | −0.0929197 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 464.695i | − | 2.28914i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 38.4312i | − | 0.187469i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −66.0636 | −0.319148 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.52587 | − | 256.987i | −0.00730080 | − | 1.22960i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 230.194i | − | 1.09097i | −0.838122 | − | 0.545483i | \(-0.816346\pi\) | ||
0.838122 | − | 0.545483i | \(-0.183654\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 91.1705 | 0.428031 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.3495 | 0.0713932 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.36516i | 0.0108994i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 23.7918i | 0.108638i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 27.7980i | − | 0.125783i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 263.814i | 1.18302i | 0.806297 | + | 0.591511i | \(0.201468\pi\) | ||||
−0.806297 | + | 0.591511i | \(0.798532\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 74.0712 | 0.329206 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 213.928i | − | 0.942414i | −0.882023 | − | 0.471207i | \(-0.843818\pi\) | ||
0.882023 | − | 0.471207i | \(-0.156182\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −63.4698 | −0.277161 | −0.138580 | − | 0.990351i | \(-0.544254\pi\) | ||||
−0.138580 | + | 0.990351i | \(0.544254\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 223.167i | 0.966092i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 288.449 | 1.23798 | 0.618989 | − | 0.785400i | \(-0.287543\pi\) | ||||
0.618989 | + | 0.785400i | \(0.287543\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.9745 | −0.106275 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −88.8931 | −0.375076 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −279.128 | −1.16790 | −0.583950 | − | 0.811790i | \(-0.698493\pi\) | ||||
−0.583950 | + | 0.811790i | \(0.698493\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 242.687i | 1.00700i | 0.863995 | + | 0.503500i | \(0.167955\pi\) | ||||
−0.863995 | + | 0.503500i | \(0.832045\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23.2256 | 0.0947982 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −200.158 | + | 1.18844i | −0.810355 | + | 0.00481151i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 110.460i | 0.443616i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 162.678 | 0.648118 | 0.324059 | − | 0.946037i | \(-0.394952\pi\) | ||||
0.324059 | + | 0.946037i | \(0.394952\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 297.856 | 1.17730 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.54295i | 0.00997237i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 256.629i | − | 0.998555i | −0.866442 | − | 0.499277i | \(-0.833599\pi\) | ||
0.866442 | − | 0.499277i | \(-0.166401\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 565.048i | 2.18165i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 146.347i | 0.560718i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −71.2027 | −0.270733 | −0.135366 | − | 0.990796i | \(-0.543221\pi\) | ||||
−0.135366 | + | 0.990796i | \(0.543221\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.14488i | 0.00809390i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 77.8168 | 0.291449 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 219.411i | − | 0.815653i | −0.913059 | − | 0.407827i | \(-0.866287\pi\) | ||
0.913059 | − | 0.407827i | \(-0.133713\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −323.913 | −1.19525 | −0.597626 | − | 0.801775i | \(-0.703889\pi\) | ||||
−0.597626 | + | 0.801775i | \(0.703889\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 173.817 | 0.636691 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −333.959 | −1.21440 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −37.4953 | −0.135362 | −0.0676810 | − | 0.997707i | \(-0.521560\pi\) | ||||
−0.0676810 | + | 0.997707i | \(0.521560\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 0.744865i | − | 0.00266977i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 177.483i | 0.631613i | 0.948824 | + | 0.315806i | \(0.102275\pi\) | ||||
−0.948824 | + | 0.315806i | \(0.897725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −72.4063 | −0.255853 | −0.127926 | − | 0.991784i | \(-0.540832\pi\) | ||||
−0.127926 | + | 0.991784i | \(0.540832\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.3104 | − | 0.108719i | 0.0642470 | − | 0.000381469i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 657.956i | − | 2.29253i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −282.037 | −0.975908 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −125.817 | −0.432360 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 57.9819i | − | 0.197891i | −0.995093 | − | 0.0989453i | \(-0.968453\pi\) | ||
0.995093 | − | 0.0989453i | \(-0.0315469\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 33.0249i | 0.111949i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 70.2825i | − | 0.236641i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 231.989i | − | 0.775883i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 262.790 | 0.873055 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 202.274i | 0.667570i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 53.6683 | 0.175962 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 484.604i | 1.57851i | 0.614062 | + | 0.789257i | \(0.289534\pi\) | ||||
−0.614062 | + | 0.789257i | \(0.710466\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −125.387 | −0.405782 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −241.304 | −0.775898 | −0.387949 | − | 0.921681i | \(-0.626816\pi\) | ||||
−0.387949 | + | 0.921681i | \(0.626816\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −313.749 | −1.00239 | −0.501196 | − | 0.865334i | \(-0.667107\pi\) | ||||
−0.501196 | + | 0.865334i | \(0.667107\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −15.9007 | −0.0504785 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 184.282i | − | 0.581331i | −0.956825 | − | 0.290665i | \(-0.906123\pi\) | ||
0.956825 | − | 0.290665i | \(-0.0938767\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 659.825i | − | 2.06842i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −266.835 | −0.831261 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.297672 | − | 50.1340i | −0.000921585 | − | 0.155214i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 260.109i | 0.800334i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −276.557 | −0.845741 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −427.573 | −1.29961 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 460.335i | 1.39074i | 0.718652 | + | 0.695370i | \(0.244759\pi\) | ||||
−0.718652 | + | 0.695370i | \(0.755241\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 177.952i | − | 0.534389i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.99977i | 0.0179098i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 493.633i | 1.46479i | 0.680882 | + | 0.732393i | \(0.261597\pi\) | ||||
−0.680882 | + | 0.732393i | \(0.738403\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 137.944 | 0.406914 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.35831i | 0.00984843i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −69.1373 | −0.201567 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 21.2223i | 0.0615140i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 415.426 | 1.19719 | 0.598596 | − | 0.801051i | \(-0.295725\pi\) | ||||
0.598596 | + | 0.801051i | \(0.295725\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.1332 | 0.0978030 | 0.0489015 | − | 0.998804i | \(-0.484428\pi\) | ||||
0.0489015 | + | 0.998804i | \(0.484428\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −54.7405 | −0.155956 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −154.833 | −0.438620 | −0.219310 | − | 0.975655i | \(-0.570381\pi\) | ||||
−0.219310 | + | 0.975655i | \(0.570381\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 29.2877i | − | 0.0825005i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 43.5363i | 0.121950i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −565.544 | −1.57533 | −0.787665 | − | 0.616103i | \(-0.788710\pi\) | ||||
−0.787665 | + | 0.616103i | \(0.788710\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −360.975 | + | 4.28674i | −0.999929 | + | 0.0118746i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 107.299i | 0.295589i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.64289 | 0.0209394 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −197.695 | −0.538678 | −0.269339 | − | 0.963045i | \(-0.586805\pi\) | ||||
−0.269339 | + | 0.963045i | \(0.586805\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 207.211i | 0.561548i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 36.7212i | 0.0989789i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 198.960i | − | 0.533404i | −0.963779 | − | 0.266702i | \(-0.914066\pi\) | ||
0.963779 | − | 0.266702i | \(-0.0859339\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 47.8878i | − | 0.127701i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −513.913 | −1.36317 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 432.419i | − | 1.14095i | −0.821316 | − | 0.570474i | \(-0.806760\pi\) | ||
0.821316 | − | 0.570474i | \(-0.193240\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 52.3994 | 0.137531 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 543.758i | 1.41973i | 0.704336 | + | 0.709867i | \(0.251245\pi\) | ||||
−0.704336 | + | 0.709867i | \(0.748755\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 71.6904 | 0.186209 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −82.7608 | −0.213852 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 109.783 | 0.282218 | 0.141109 | − | 0.989994i | \(-0.454933\pi\) | ||||
0.141109 | + | 0.989994i | \(0.454933\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 58.1069 | 0.148611 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 247.410i | 0.629542i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.5561i | 0.0722939i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −540.791 | −1.36219 | −0.681097 | − | 0.732193i | \(-0.738497\pi\) | ||||
−0.681097 | + | 0.732193i | \(0.738497\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 313.481 | − | 1.86130i | 0.785666 | − | 0.00466492i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 224.500i | − | 0.559849i | −0.960022 | − | 0.279925i | \(-0.909691\pi\) | ||
0.960022 | − | 0.279925i | \(-0.0903095\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.61567 | 0.00649049 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.00765 | 0.0123646 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 802.317i | 1.97129i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 397.737i | − | 0.972463i | −0.873830 | − | 0.486231i | \(-0.838371\pi\) | ||
0.873830 | − | 0.486231i | \(-0.161629\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 286.634i | − | 0.697408i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 565.398i | 1.36900i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 35.4844 | 0.0855046 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 293.278i | 0.703304i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 769.815 | 1.83727 | 0.918634 | − | 0.395111i | \(-0.129294\pi\) | ||||
0.918634 | + | 0.395111i | \(0.129294\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 515.309i | − | 1.22401i | −0.790853 | − | 0.612006i | \(-0.790363\pi\) | ||
0.790853 | − | 0.612006i | \(-0.209637\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 134.656 | 0.318337 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −65.1501 | −0.153294 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 918.822 | 2.15181 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 246.804 | 0.575301 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 484.686i | 1.12456i | 0.826946 | + | 0.562281i | \(0.190076\pi\) | ||||
−0.826946 | + | 0.562281i | \(0.809924\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 734.040i | 1.69524i | 0.530602 | + | 0.847621i | \(0.321966\pi\) | ||||
−0.530602 | + | 0.847621i | \(0.678034\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 47.0127 | 0.108075 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.48423 | − | 418.395i | −0.00568475 | − | 0.957426i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 108.108i | 0.246260i | 0.992391 | + | 0.123130i | \(0.0392933\pi\) | ||||
−0.992391 | + | 0.123130i | \(0.960707\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −125.226 | −0.283960 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 519.843 | 1.17346 | 0.586730 | − | 0.809782i | \(-0.300415\pi\) | ||||
0.586730 | + | 0.809782i | \(0.300415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 24.9979i | − | 0.0561751i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 241.459i | − | 0.540176i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 810.462i | − | 1.80504i | −0.430651 | − | 0.902519i | \(-0.641716\pi\) | ||
0.430651 | − | 0.902519i | \(-0.358284\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 934.238i | − | 2.07148i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −264.557 | −0.584012 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 55.8371i | − | 0.122719i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 231.412 | 0.506373 | 0.253186 | − | 0.967418i | \(-0.418521\pi\) | ||||
0.253186 | + | 0.967418i | \(0.418521\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 13.7110i | − | 0.0298714i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 766.366 | 1.66240 | 0.831200 | − | 0.555974i | \(-0.187654\pi\) | ||||
0.831200 | + | 0.555974i | \(0.187654\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −152.091 | −0.328490 | −0.164245 | − | 0.986420i | \(-0.552519\pi\) | ||||
−0.164245 | + | 0.986420i | \(0.552519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.239281 | −0.000514583 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −123.992 | −0.265508 | −0.132754 | − | 0.991149i | \(-0.542382\pi\) | ||||
−0.132754 | + | 0.991149i | \(0.542382\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 102.718i | 0.219016i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 512.570i | − | 1.08826i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 373.137 | 0.788874 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.78535 | + | 469.110i | 0.00586390 | + | 0.987599i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 11.5647i | − | 0.0242446i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 443.502 | 0.925892 | 0.462946 | − | 0.886387i | \(-0.346792\pi\) | ||||
0.462946 | + | 0.886387i | \(0.346792\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 624.895 | 1.29916 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 363.334i | 0.752244i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 40.4175i | 0.0833350i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 628.314i | − | 1.29017i | −0.764110 | − | 0.645086i | \(-0.776821\pi\) | ||
0.764110 | − | 0.645086i | \(-0.223179\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 195.256i | 0.399296i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −877.289 | −1.78674 | −0.893370 | − | 0.449322i | \(-0.851666\pi\) | ||||
−0.893370 | + | 0.449322i | \(0.851666\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 128.721i | − | 0.261098i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −22.5776 | −0.0456113 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 501.416i | − | 1.00889i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −206.303 | −0.413433 | −0.206716 | − | 0.978401i | \(-0.566278\pi\) | ||||
−0.206716 | + | 0.978401i | \(0.566278\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 514.773 | 1.02749 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 276.617 | 0.549934 | 0.274967 | − | 0.961454i | \(-0.411333\pi\) | ||||
0.274967 | + | 0.961454i | \(0.411333\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 64.9786 | 0.128671 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 100.490i | 0.198205i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 728.875i | 1.43197i | 0.698114 | + | 0.715987i | \(0.254023\pi\) | ||||
−0.698114 | + | 0.715987i | \(0.745977\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 130.849 | 0.256065 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −98.7252 | + | 0.586183i | −0.192447 | + | 0.00114266i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 40.2793i | 0.0782123i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −607.115 | −1.17430 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −455.267 | −0.877201 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 14.2470i | − | 0.0273455i | −0.999907 | − | 0.0136727i | \(-0.995648\pi\) | ||
0.999907 | − | 0.0136727i | \(-0.00435230\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 535.561i | − | 1.02402i | −0.858981 | − | 0.512008i | \(-0.828902\pi\) | ||
0.858981 | − | 0.512008i | \(-0.171098\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 407.374i | − | 0.775951i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.655153i | 0.00124317i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −44.0669 | −0.0833023 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 178.062i | − | 0.335333i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −727.644 | −1.36519 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 85.7182i | 0.160221i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −128.031 | −0.238418 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 564.599 | 1.04749 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1000.18 | 1.84875 | 0.924376 | − | 0.381482i | \(-0.124586\pi\) | ||||
0.924376 | + | 0.381482i | \(0.124586\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 60.4300 | 0.111289 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 88.8415i | 0.163012i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 675.400i | 1.23473i | 0.786675 | + | 0.617367i | \(0.211801\pi\) | ||||
−0.786675 | + | 0.617367i | \(0.788199\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −289.366 | −0.527079 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −926.850 | + | 5.50320i | −1.68212 | + | 0.00998765i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 488.891i | 0.884070i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −57.1654 | −0.103001 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −366.913 | −0.658730 | −0.329365 | − | 0.944203i | \(-0.606835\pi\) | ||||
−0.329365 | + | 0.944203i | \(0.606835\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 290.623i | − | 0.519898i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 61.8176i | 0.110192i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 50.3339i | 0.0894029i | 0.999000 | + | 0.0447015i | \(0.0142337\pi\) | ||||
−0.999000 | + | 0.0447015i | \(0.985766\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 44.3132i | − | 0.0784305i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 85.7328 | 0.151204 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 61.6165i | 0.108289i | 0.998533 | + | 0.0541446i | \(0.0172432\pi\) | ||||
−0.998533 | + | 0.0541446i | \(0.982757\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −256.504 | −0.449218 | −0.224609 | − | 0.974449i | \(-0.572111\pi\) | ||||
−0.224609 | + | 0.974449i | \(0.572111\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 192.259i | − | 0.335530i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −543.712 | −0.945587 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 429.278 | 0.743983 | 0.371991 | − | 0.928236i | \(-0.378675\pi\) | ||||
0.371991 | + | 0.928236i | \(0.378675\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 144.733 | 0.249970 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 607.506 | 1.04562 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 52.1407i | 0.0894352i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 17.5849i | 0.0300596i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −491.725 | −0.837691 | −0.418845 | − | 0.908058i | \(-0.637565\pi\) | ||||
−0.418845 | + | 0.908058i | \(0.637565\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.71739 | − | 0.0280097i | 0.00800916 | − | 4.75546e-5i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 632.751i | − | 1.07064i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 954.134 | 1.60899 | 0.804497 | − | 0.593956i | \(-0.202435\pi\) | ||||
0.804497 | + | 0.593956i | \(0.202435\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.9856 | 0.0235053 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.4122i | 0.0308411i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 533.310i | 0.890334i | 0.895448 | + | 0.445167i | \(0.146856\pi\) | ||||
−0.895448 | + | 0.445167i | \(0.853144\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 830.453i | − | 1.38179i | −0.722957 | − | 0.690893i | \(-0.757218\pi\) | ||
0.722957 | − | 0.690893i | \(-0.242782\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 32.3493i | − | 0.0536472i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 34.4688 | 0.0569732 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 584.294i | 0.962594i | 0.876558 | + | 0.481297i | \(0.159834\pi\) | ||||
−0.876558 | + | 0.481297i | \(0.840166\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 804.875 | 1.32163 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 472.860i | 0.773912i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −152.216 | −0.248314 | −0.124157 | − | 0.992263i | \(-0.539623\pi\) | ||||
−0.124157 | + | 0.992263i | \(0.539623\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 66.5648 | 0.108235 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 647.334 | 1.04916 | 0.524582 | − | 0.851360i | \(-0.324222\pi\) | ||||
0.524582 | + | 0.851360i | \(0.324222\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 104.700 | 0.169145 | 0.0845723 | − | 0.996417i | \(-0.473048\pi\) | ||||
0.0845723 | + | 0.996417i | \(0.473048\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 114.425i | − | 0.184260i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 427.974i | − | 0.686956i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 601.877 | 0.963003 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 445.114 | − | 2.64288i | 0.709911 | − | 0.00421512i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 156.519i | 0.248838i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −628.425 | −0.995919 | −0.497959 | − | 0.867200i | \(-0.665917\pi\) | ||||
−0.497959 | + | 0.867200i | \(0.665917\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 398.707 | 0.629870 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 16.8328i | − | 0.0265084i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 439.745i | − | 0.690338i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 157.912i | 0.247124i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 462.053i | − | 0.720832i | −0.932792 | − | 0.360416i | \(-0.882635\pi\) | ||
0.932792 | − | 0.360416i | \(-0.117365\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 898.660 | 1.39761 | 0.698803 | − | 0.715314i | \(-0.253716\pi\) | ||||
0.698803 | + | 0.715314i | \(0.253716\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 26.5862i | 0.0412189i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 773.813 | 1.19600 | 0.598001 | − | 0.801495i | \(-0.295962\pi\) | ||||
0.598001 | + | 0.801495i | \(0.295962\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 802.814i | 1.23700i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.09658 | −0.00629275 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −701.376 | −1.07408 | −0.537041 | − | 0.843556i | \(-0.680458\pi\) | ||||
−0.537041 | + | 0.843556i | \(0.680458\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 79.4782 | 0.121341 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −41.2086 | −0.0627223 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1255.87i | − | 1.90572i | −0.303415 | − | 0.952858i | \(-0.598127\pi\) | ||
0.303415 | − | 0.952858i | \(-0.401873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 399.716i | 0.604714i | 0.953195 | + | 0.302357i | \(0.0977735\pi\) | ||||
−0.953195 | + | 0.302357i | \(0.902227\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 48.1475 | 0.0726206 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.597926 | − | 100.703i | −0.000899137 | − | 0.151433i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1074.25i | − | 1.61057i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −456.939 | −0.683018 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1304.64 | 1.94433 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 116.954i | − | 0.173779i | −0.996218 | − | 0.0868897i | \(-0.972307\pi\) | ||
0.996218 | − | 0.0868897i | \(-0.0276928\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 128.295i | 0.190067i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 497.520i | − | 0.734890i | −0.930045 | − | 0.367445i | \(-0.880233\pi\) | ||
0.930045 | − | 0.367445i | \(-0.119767\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 691.962i | 1.01909i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 370.534 | 0.544103 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 803.013i | 1.17572i | 0.808964 | + | 0.587858i | \(0.200028\pi\) | ||||
−0.808964 | + | 0.587858i | \(0.799972\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −92.0787 | −0.134421 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 109.933i | − | 0.160019i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.6105 | 0.0589413 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −891.667 | −1.29040 | −0.645200 | − | 0.764014i | \(-0.723226\pi\) | ||||
−0.645200 | + | 0.764014i | \(0.723226\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −386.537 | −0.557773 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 94.2128 | 0.135558 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 182.255i | − | 0.261485i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 499.608i | 0.714746i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1110.82 | 1.58463 | 0.792313 | − | 0.610114i | \(-0.208876\pi\) | ||||
0.792313 | + | 0.610114i | \(0.208876\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1127.01 | − | 6.69164i | 1.60314 | − | 0.00951869i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 43.2572i | − | 0.0613577i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1112.46 | 1.57349 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.63354 | −0.0135875 | −0.00679375 | − | 0.999977i | \(-0.502163\pi\) | ||||
−0.00679375 | + | 0.999977i | \(0.502163\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 153.967i | − | 0.216550i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.46760i | 0.00766845i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 79.2835i | − | 0.110886i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 483.464i | − | 0.674287i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −97.4316 | −0.135510 | −0.0677549 | − | 0.997702i | \(-0.521584\pi\) | ||||
−0.0677549 | + | 0.997702i | \(0.521584\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 689.597i | 0.956445i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −420.346 | −0.581392 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1204.46i | 1.66132i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 466.358 | 0.641483 | 0.320742 | − | 0.947167i | \(-0.396068\pi\) | ||||
0.320742 | + | 0.947167i | \(0.396068\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 72.7931 | 0.0995801 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 452.839 | 0.617789 | 0.308895 | − | 0.951096i | \(-0.400041\pi\) | ||||
0.308895 | + | 0.951096i | \(0.400041\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 40.2279i | 0.0547318i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 145.851i | 0.197898i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1346.02 | 1.82140 | 0.910701 | − | 0.413066i | \(-0.135542\pi\) | ||||
0.910701 | + | 0.413066i | \(0.135542\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.05844 | − | 346.683i | −0.00277793 | − | 0.467859i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 787.553i | − | 1.05996i | −0.848009 | − | 0.529982i | \(-0.822199\pi\) | ||
0.848009 | − | 0.529982i | \(-0.177801\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −77.5664 | −0.104116 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −191.323 | −0.256122 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1467.53i | 1.95932i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 120.158i | 0.159997i | 0.996795 | + | 0.0799986i | \(0.0254916\pi\) | ||||
−0.996795 | + | 0.0799986i | \(0.974508\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 281.766i | 0.374191i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 84.9866i | 0.112565i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 263.516 | 0.348105 | 0.174053 | − | 0.984736i | \(-0.444314\pi\) | ||||
0.174053 | + | 0.984736i | \(0.444314\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 515.901i | 0.679712i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −60.7691 | −0.0798543 | −0.0399271 | − | 0.999203i | \(-0.512713\pi\) | ||||
−0.0399271 | + | 0.999203i | \(0.512713\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1521.00i | 1.99345i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.40453 | −0.00575755 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 625.282 | 0.815231 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −713.480 | −0.927802 | −0.463901 | − | 0.885887i | \(-0.653551\pi\) | ||||
−0.463901 | + | 0.885887i | \(0.653551\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 444.494 | 0.576516 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 971.062i | 1.25622i | 0.778123 | + | 0.628112i | \(0.216172\pi\) | ||||
−0.778123 | + | 0.628112i | \(0.783828\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 6.13034i | − | 0.00791012i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −978.692 | −1.25958 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1312.32 | + | 7.79191i | −1.68462 | + | 0.0100025i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 711.965i | − | 0.911607i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −253.481 | −0.323730 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −164.658 | −0.209756 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 903.790i | 1.14840i | 0.818716 | + | 0.574199i | \(0.194687\pi\) | ||||
−0.818716 | + | 0.574199i | \(0.805313\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 123.327i | − | 0.156308i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 758.659i | − | 0.959114i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1016.14i | − | 1.28139i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.71505 | −0.00467301 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 836.376i | 1.04941i | 0.851286 | + | 0.524703i | \(0.175823\pi\) | ||||
−0.851286 | + | 0.524703i | \(0.824177\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −118.438 | −0.148233 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 134.783i | 0.168268i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 185.794 | 0.231375 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 116.718 | 0.144991 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 380.031 | 0.470918 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1274.76 | −1.57572 | −0.787861 | − | 0.615853i | \(-0.788811\pi\) | ||||
−0.787861 | + | 0.615853i | \(0.788811\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1452.92i | − | 1.79152i | −0.444539 | − | 0.895759i | \(-0.646633\pi\) | ||
0.444539 | − | 0.895759i | \(-0.353367\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 561.034i | − | 0.690079i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 62.7242 | 0.0769622 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.11211 | − | 524.143i | −0.00380919 | − | 0.641546i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 301.059i | 0.367594i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −579.401 | −0.705726 | −0.352863 | − | 0.935675i | \(-0.614792\pi\) | ||||
−0.352863 | + | 0.935675i | \(0.614792\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −451.801 | −0.548968 | −0.274484 | − | 0.961592i | \(-0.588507\pi\) | ||||
−0.274484 | + | 0.961592i | \(0.588507\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 578.434i | − | 0.701133i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 740.460i | − | 0.895356i | −0.894195 | − | 0.447678i | \(-0.852251\pi\) | ||
0.894195 | − | 0.447678i | \(-0.147749\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1456.61i | − | 1.75707i | −0.477675 | − | 0.878536i | \(-0.658520\pi\) | ||
0.477675 | − | 0.878536i | \(-0.341480\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 64.9437i | − | 0.0781513i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 110.144 | 0.132226 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 165.366i | − | 0.198043i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.29014 | 0.00154139 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 87.8279i | 0.104682i | 0.998629 | + | 0.0523408i | \(0.0166682\pi\) | ||||
−0.998629 | + | 0.0523408i | \(0.983332\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1538.72 | −1.82964 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −307.410 | −0.364662 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 32.2815 | 0.0382029 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 590.119 | 0.696716 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 125.411i | − | 0.147717i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1306.24i | 1.53494i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −870.193 | −1.02016 | −0.510078 | − | 0.860128i | \(-0.670383\pi\) | ||||
−0.510078 | + | 0.860128i | \(0.670383\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.188306 | + | 31.7146i | 0.000220241 | + | 0.0370930i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 143.885i | 0.167894i | 0.996470 | + | 0.0839470i | \(0.0267527\pi\) | ||||
−0.996470 | + | 0.0839470i | \(0.973247\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1378.57 | −1.60485 | −0.802426 | − | 0.596752i | \(-0.796458\pi\) | ||||
−0.802426 | + | 0.596752i | \(0.796458\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1139.61 | 1.32359 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 61.6014i | − | 0.0713805i | −0.999363 | − | 0.0356903i | \(-0.988637\pi\) | ||
0.999363 | − | 0.0356903i | \(-0.0113630\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 146.250i | 0.169076i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 488.503i | − | 0.563441i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 694.181i | 0.798827i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 113.598 | 0.130422 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 217.921i | − | 0.249623i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −263.371 | −0.300996 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1405.80i | 1.60297i | 0.598016 | + | 0.801484i | \(0.295956\pi\) | ||||
−0.598016 | + | 0.801484i | \(0.704044\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 100.428 | 0.114252 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1449.85 | −1.64569 | −0.822846 | − | 0.568264i | \(-0.807615\pi\) | ||||
−0.822846 | + | 0.568264i | \(0.807615\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1177.85 | −1.33392 | −0.666958 | − | 0.745095i | \(-0.732404\pi\) | ||||
−0.666958 | + | 0.745095i | \(0.732404\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −57.2007 | −0.0646336 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1051.90i | 1.18590i | 0.805238 | + | 0.592952i | \(0.202038\pi\) | ||||
−0.805238 | + | 0.592952i | \(0.797962\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 288.185i | − | 0.324167i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 121.733 | 0.136625 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.06358 | + | 852.809i | 0.00567030 | + | 0.954994i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 41.1287i | 0.0459538i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 401.817 | 0.447956 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.1121 | 0.0134729 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.1718i | 0.0112895i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 455.165i | 0.504059i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 19.4126i | − | 0.0214504i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 222.998i | − | 0.245863i | −0.992415 | − | 0.122932i | \(-0.960770\pi\) | ||
0.992415 | − | 0.122932i | \(-0.0392296\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −350.349 | −0.385422 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1400.58i | 1.53741i | 0.639603 | + | 0.768705i | \(0.279099\pi\) | ||||
−0.639603 | + | 0.768705i | \(0.720901\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 862.604 | 0.944802 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 92.9563i | 0.101592i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1360.70 | 1.48386 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 241.714 | 0.263018 | 0.131509 | − | 0.991315i | \(-0.458018\pi\) | ||||
0.131509 | + | 0.991315i | \(0.458018\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −839.359 | −0.911356 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −554.524 | −0.600784 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1464.57i | − | 1.58332i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 217.176i | − | 0.234279i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 704.699 | 0.758556 | 0.379278 | − | 0.925283i | \(-0.376172\pi\) | ||||
0.379278 | + | 0.925283i | \(0.376172\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.70898 | − | 793.087i | −0.00505798 | − | 0.851866i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 417.951i | − | 0.447965i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.8583 | 0.0212389 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −212.822 | −0.227131 | −0.113566 | − | 0.993531i | \(-0.536227\pi\) | ||||
−0.113566 | + | 0.993531i | \(0.536227\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 543.429i | − | 0.578732i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 863.837i | 0.917999i | 0.888437 | + | 0.458999i | \(0.151792\pi\) | ||||
−0.888437 | + | 0.458999i | \(0.848208\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1521.01i | − | 1.61295i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 27.5409i | − | 0.0291438i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −595.986 | −0.629341 | −0.314671 | − | 0.949201i | \(-0.601894\pi\) | ||||
−0.314671 | + | 0.949201i | \(0.601894\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 144.708i | − | 0.152485i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 319.186 | 0.335632 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1057.19i | 1.10933i | 0.832073 | + | 0.554666i | \(0.187154\pi\) | ||||
−0.832073 | + | 0.554666i | \(0.812846\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −61.7614 | −0.0646717 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1142.85 | 1.19420 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1576.42 | −1.64382 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 960.938 | 0.999936 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 462.171i | − | 0.479929i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 46.4941i | − | 0.0481804i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −635.416 | −0.657100 | −0.328550 | − | 0.944487i | \(-0.606560\pi\) | ||||
−0.328550 | + | 0.944487i | \(0.606560\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 86.8346 | − | 0.515583i | 0.0896126 | − | 0.000532078i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1498.44i | 1.54320i | 0.636111 | + | 0.771598i | \(0.280542\pi\) | ||||
−0.636111 | + | 0.771598i | \(0.719458\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1612.96 | 1.65772 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −450.521 | −0.462073 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 892.040i | − | 0.913039i | −0.889713 | − | 0.456520i | \(-0.849096\pi\) | ||
0.889713 | − | 0.456520i | \(-0.150904\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 607.684i | − | 0.620719i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 479.011i | − | 0.488289i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 708.551i | − | 0.720805i | −0.932797 | − | 0.360402i | \(-0.882639\pi\) | ||
0.932797 | − | 0.360402i | \(-0.117361\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −203.265 | −0.206361 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 740.579i | − | 0.750333i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 607.498 | 0.614254 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 730.885i | − | 0.737523i | −0.929524 | − | 0.368762i | \(-0.879782\pi\) | ||
0.929524 | − | 0.368762i | \(-0.120218\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −797.323 | −0.802944 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.91474 | 0.00594446 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −841.726 | −0.844259 | −0.422129 | − | 0.906536i | \(-0.638717\pi\) | ||||
−0.422129 | + | 0.906536i | \(0.638717\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 308.221 | 0.308530 |
(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 | 912.3.o.c.721.5 | 6 | ||
3.2 | odd | 2 | 2736.3.o.m.721.3 | 6 | |||
4.3 | odd | 2 | 228.3.h.a.37.2 | ✓ | 6 | ||
12.11 | even | 2 | 684.3.h.e.37.3 | 6 | |||
19.18 | odd | 2 | inner | 912.3.o.c.721.2 | 6 | ||
57.56 | even | 2 | 2736.3.o.m.721.4 | 6 | |||
76.75 | even | 2 | 228.3.h.a.37.5 | yes | 6 | ||
228.227 | odd | 2 | 684.3.h.e.37.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.3.h.a.37.2 | ✓ | 6 | 4.3 | odd | 2 | ||
228.3.h.a.37.5 | yes | 6 | 76.75 | even | 2 | ||
684.3.h.e.37.3 | 6 | 12.11 | even | 2 | |||
684.3.h.e.37.4 | 6 | 228.227 | odd | 2 | |||
912.3.o.c.721.2 | 6 | 19.18 | odd | 2 | inner | ||
912.3.o.c.721.5 | 6 | 1.1 | even | 1 | trivial | ||
2736.3.o.m.721.3 | 6 | 3.2 | odd | 2 | |||
2736.3.o.m.721.4 | 6 | 57.56 | even | 2 |