Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(865,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.i (of order \(3\), degree \(2\), 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: | \(18.1100711784\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 10x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 756) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2053.1 | ||
Root | \(-1.58114 - 2.73861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.2053 |
Dual form | 2268.2.i.i.865.1 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.58114 | − | 2.73861i | −0.707107 | − | 1.22474i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.16228 | + | 5.47723i | −0.953463 | + | 1.65145i | −0.215615 | + | 0.976478i | \(0.569176\pi\) |
−0.737848 | + | 0.674967i | \(0.764158\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.58114 | + | 2.73861i | 0.383482 | + | 0.664211i | 0.991557 | − | 0.129668i | \(-0.0413913\pi\) |
−0.608075 | + | 0.793880i | \(0.708058\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.50000 | − | 6.06218i | 0.802955 | − | 1.39076i | −0.114708 | − | 0.993399i | \(-0.536593\pi\) |
0.917663 | − | 0.397360i | \(-0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.58114 | + | 2.73861i | 0.329690 | + | 0.571040i | 0.982450 | − | 0.186524i | \(-0.0597224\pi\) |
−0.652760 | + | 0.757565i | \(0.726389\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.50000 | + | 4.33013i | −0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.58114 | − | 2.73861i | −0.293610 | − | 0.508548i | 0.681051 | − | 0.732236i | \(-0.261523\pi\) |
−0.974661 | + | 0.223689i | \(0.928190\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | 0.538816 | 0.269408 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269408 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.32456 | + | 5.47723i | 1.06904 | + | 0.925820i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | − | 3.46410i | 0.328798 | − | 0.569495i | −0.653476 | − | 0.756948i | \(-0.726690\pi\) |
0.982274 | + | 0.187453i | \(0.0600231\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.74342 | + | 8.21584i | −0.740797 | + | 1.28310i | 0.211336 | + | 0.977414i | \(0.432219\pi\) |
−0.952133 | + | 0.305685i | \(0.901115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.50000 | − | 4.33013i | −0.381246 | − | 0.660338i | 0.609994 | − | 0.792406i | \(-0.291172\pi\) |
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.48683 | 1.38380 | 0.691898 | − | 0.721995i | \(-0.256775\pi\) | ||||
0.691898 | + | 0.721995i | \(0.256775\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.74342 | − | 8.21584i | −0.651558 | − | 1.12853i | −0.982745 | − | 0.184967i | \(-0.940782\pi\) |
0.331186 | − | 0.943565i | \(-0.392551\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 20.0000 | 2.69680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.6491 | 1.64677 | 0.823387 | − | 0.567480i | \(-0.192082\pi\) | ||||
0.823387 | + | 0.567480i | \(0.192082\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | −0.384111 | −0.192055 | − | 0.981384i | \(-0.561515\pi\) | ||||
−0.192055 | + | 0.981384i | \(0.561515\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0000 | 1.22169 | 0.610847 | − | 0.791748i | \(-0.290829\pi\) | ||||
0.610847 | + | 0.791748i | \(0.290829\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.6491 | −1.50117 | −0.750587 | − | 0.660772i | \(-0.770229\pi\) | ||||
−0.750587 | + | 0.660772i | \(0.770229\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.50000 | + | 4.33013i | 0.292603 | + | 0.506803i | 0.974424 | − | 0.224716i | \(-0.0721453\pi\) |
−0.681822 | + | 0.731519i | \(0.738812\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.16228 | − | 16.4317i | 0.360375 | − | 1.87256i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000 | 1.35011 | 0.675053 | − | 0.737769i | \(-0.264121\pi\) | ||||
0.675053 | + | 0.737769i | \(0.264121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.16228 | − | 5.47723i | −0.347105 | − | 0.601204i | 0.638629 | − | 0.769515i | \(-0.279502\pi\) |
−0.985734 | + | 0.168311i | \(0.946169\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.00000 | − | 8.66025i | 0.542326 | − | 0.939336i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.74342 | − | 8.21584i | 0.502801 | − | 0.870877i | −0.497194 | − | 0.867640i | \(-0.665636\pi\) |
0.999995 | − | 0.00323751i | \(-0.00103053\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −22.1359 | −2.27110 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.50000 | + | 4.33013i | 0.253837 | + | 0.439658i | 0.964579 | − | 0.263795i | \(-0.0849741\pi\) |
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.16228 | − | 5.47723i | 0.314658 | − | 0.545004i | −0.664706 | − | 0.747105i | \(-0.731443\pi\) |
0.979365 | + | 0.202100i | \(0.0647767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.00000 | − | 1.73205i | −0.0985329 | − | 0.170664i | 0.812545 | − | 0.582899i | \(-0.198082\pi\) |
−0.911078 | + | 0.412235i | \(0.864748\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.50000 | − | 6.06218i | −0.335239 | − | 0.580651i | 0.648292 | − | 0.761392i | \(-0.275484\pi\) |
−0.983531 | + | 0.180741i | \(0.942150\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.16228 | − | 5.47723i | 0.297482 | − | 0.515254i | −0.678077 | − | 0.734991i | \(-0.737186\pi\) |
0.975559 | + | 0.219737i | \(0.0705198\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.00000 | − | 8.66025i | 0.466252 | − | 0.807573i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.32456 | − | 5.47723i | −0.579771 | − | 0.502096i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.5000 | − | 25.1147i | −1.31818 | − | 2.28316i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.0000 | 1.86345 | 0.931724 | − | 0.363166i | \(-0.118304\pi\) | ||||
0.931724 | + | 0.363166i | \(0.118304\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.90569 | + | 13.6931i | 0.690724 | + | 1.19637i | 0.971601 | + | 0.236625i | \(0.0760412\pi\) |
−0.280877 | + | 0.959744i | \(0.590625\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.50000 | + | 18.1865i | −0.303488 | + | 1.57697i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.58114 | + | 2.73861i | −0.135086 | + | 0.233975i | −0.925630 | − | 0.378429i | \(-0.876464\pi\) |
0.790544 | + | 0.612405i | \(0.209798\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.00000 | − | 1.73205i | 0.0848189 | − | 0.146911i | −0.820495 | − | 0.571654i | \(-0.806302\pi\) |
0.905314 | + | 0.424743i | \(0.139635\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.00000 | + | 8.66025i | −0.415227 | + | 0.719195i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.74342 | + | 8.21584i | 0.388596 | + | 0.673068i | 0.992261 | − | 0.124170i | \(-0.0396269\pi\) |
−0.603665 | + | 0.797238i | \(0.706294\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.50000 | − | 14.7224i | 0.691720 | − | 1.19809i | −0.279554 | − | 0.960130i | \(-0.590186\pi\) |
0.971274 | − | 0.237964i | \(-0.0764802\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.74342 | − | 8.21584i | −0.381000 | − | 0.659912i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.0000 | −1.27694 | −0.638470 | − | 0.769647i | \(-0.720432\pi\) | ||||
−0.638470 | + | 0.769647i | \(0.720432\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.32456 | − | 5.47723i | −0.498445 | − | 0.431666i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.50000 | + | 14.7224i | −0.665771 | + | 1.15315i | 0.313304 | + | 0.949653i | \(0.398564\pi\) |
−0.979076 | + | 0.203497i | \(0.934769\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.16228 | − | 5.47723i | 0.244704 | − | 0.423840i | −0.717344 | − | 0.696719i | \(-0.754642\pi\) |
0.962048 | + | 0.272879i | \(0.0879758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.50000 | + | 11.2583i | 0.500000 | + | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.16228 | 0.240424 | 0.120212 | − | 0.992748i | \(-0.461643\pi\) | ||||
0.120212 | + | 0.992748i | \(0.461643\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.50000 | − | 12.9904i | 0.188982 | − | 0.981981i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.74342 | + | 8.21584i | 0.354540 | + | 0.614081i | 0.987039 | − | 0.160480i | \(-0.0513043\pi\) |
−0.632499 | + | 0.774561i | \(0.717971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.0000 | 1.56092 | 0.780459 | − | 0.625207i | \(-0.214986\pi\) | ||||
0.780459 | + | 0.625207i | \(0.214986\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.6491 | −0.929981 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.0000 | −1.46254 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.48683 | 0.686443 | 0.343222 | − | 0.939254i | \(-0.388482\pi\) | ||||
0.343222 | + | 0.939254i | \(0.388482\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.00000 | 0.575853 | 0.287926 | − | 0.957653i | \(-0.407034\pi\) | ||||
0.287926 | + | 0.957653i | \(0.407034\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.2982 | 1.80242 | 0.901212 | − | 0.433379i | \(-0.142679\pi\) | ||||
0.901212 | + | 0.433379i | \(0.142679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.50000 | + | 11.2583i | 0.460773 | + | 0.798082i | 0.999000 | − | 0.0447181i | \(-0.0142390\pi\) |
−0.538227 | + | 0.842800i | \(0.680906\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.32456 | + | 5.47723i | 0.443897 | + | 0.384426i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 30.0000 | 2.09529 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.1359 | + | 38.3406i | 1.53118 | + | 2.65207i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.500000 | − | 0.866025i | 0.0344214 | − | 0.0596196i | −0.848301 | − | 0.529514i | \(-0.822374\pi\) |
0.882723 | + | 0.469894i | \(0.155708\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.90569 | + | 13.6931i | −0.539164 | + | 0.933859i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.50000 | + | 2.59808i | −0.509133 | + | 0.176369i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | − | 1.73205i | −0.0669650 | − | 0.115987i | 0.830599 | − | 0.556871i | \(-0.187998\pi\) |
−0.897564 | + | 0.440884i | \(0.854665\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.74342 | + | 8.21584i | −0.314832 | + | 0.545304i | −0.979402 | − | 0.201922i | \(-0.935281\pi\) |
0.664570 | + | 0.747226i | \(0.268615\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.50000 | − | 11.2583i | −0.429532 | − | 0.743971i | 0.567300 | − | 0.823511i | \(-0.307988\pi\) |
−0.996832 | + | 0.0795401i | \(0.974655\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.90569 | + | 13.6931i | −0.517919 | + | 0.897062i | 0.481864 | + | 0.876246i | \(0.339960\pi\) |
−0.999783 | + | 0.0208165i | \(0.993373\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.0000 | − | 25.9808i | −0.978492 | − | 1.69480i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.74342 | − | 8.21584i | 0.306826 | − | 0.531438i | −0.670840 | − | 0.741602i | \(-0.734066\pi\) |
0.977666 | + | 0.210164i | \(0.0673997\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | − | 0.866025i | 0.0322078 | − | 0.0557856i | −0.849472 | − | 0.527633i | \(-0.823079\pi\) |
0.881680 | + | 0.471848i | \(0.156413\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −20.5548 | − | 8.21584i | −1.31320 | − | 0.524891i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.48683 | −0.598804 | −0.299402 | − | 0.954127i | \(-0.596787\pi\) | ||||
−0.299402 | + | 0.954127i | \(0.596787\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.0000 | −1.25739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.48683 | + | 16.4317i | 0.591772 | + | 1.02498i | 0.993994 | + | 0.109437i | \(0.0349049\pi\) |
−0.402221 | + | 0.915542i | \(0.631762\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.00000 | + | 10.3923i | −0.124274 | + | 0.645746i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.48683 | + | 16.4317i | −0.584983 | + | 1.01322i | 0.409894 | + | 0.912133i | \(0.365566\pi\) |
−0.994878 | + | 0.101088i | \(0.967768\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.0000 | + | 25.9808i | −0.921443 | + | 1.59599i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.16228 | + | 5.47723i | 0.192807 | + | 0.333952i | 0.946180 | − | 0.323642i | \(-0.104907\pi\) |
−0.753372 | + | 0.657594i | \(0.771574\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.50000 | + | 7.79423i | −0.273356 | + | 0.473466i | −0.969719 | − | 0.244224i | \(-0.921467\pi\) |
0.696363 | + | 0.717689i | \(0.254800\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.8114 | − | 27.3861i | −0.953463 | − | 1.65145i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.500000 | − | 0.866025i | 0.0300421 | − | 0.0520344i | −0.850613 | − | 0.525792i | \(-0.823769\pi\) |
0.880656 | + | 0.473757i | \(0.157103\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.16228 | − | 5.47723i | −0.188646 | − | 0.326744i | 0.756153 | − | 0.654395i | \(-0.227076\pi\) |
−0.944799 | + | 0.327651i | \(0.893743\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.0000 | 0.772770 | 0.386385 | − | 0.922338i | \(-0.373724\pi\) | ||||
0.386385 | + | 0.922338i | \(0.373724\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.74342 | − | 24.6475i | 0.279995 | − | 1.45490i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.50000 | − | 6.06218i | 0.205882 | − | 0.356599i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.0000 | − | 34.6410i | −1.16445 | − | 2.01688i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0000 | + | 8.66025i | 0.576390 | + | 0.499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.74342 | + | 8.21584i | 0.271607 | + | 0.470438i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.0000 | 1.42683 | 0.713413 | − | 0.700744i | \(-0.247149\pi\) | ||||
0.713413 | + | 0.700744i | \(0.247149\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.32456 | −0.358633 | −0.179316 | − | 0.983791i | \(-0.557389\pi\) | ||||
−0.179316 | + | 0.983791i | \(0.557389\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.0000 | −0.960897 | −0.480448 | − | 0.877023i | \(-0.659526\pi\) | ||||
−0.480448 | + | 0.877023i | \(0.659526\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.9737 | −1.06567 | −0.532834 | − | 0.846220i | \(-0.678873\pi\) | ||||
−0.532834 | + | 0.846220i | \(0.678873\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.0000 | 1.11979 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.1359 | 1.23168 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −23.7171 | + | 8.21584i | −1.30757 | + | 0.452954i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.0000 | 0.934405 | 0.467202 | − | 0.884150i | \(-0.345262\pi\) | ||||
0.467202 | + | 0.884150i | \(0.345262\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.8114 | − | 27.3861i | −0.863868 | − | 1.49626i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.5000 | + | 18.1865i | −0.571971 | + | 0.990684i | 0.424392 | + | 0.905479i | \(0.360488\pi\) |
−0.996363 | + | 0.0852050i | \(0.972845\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.48683 | + | 16.4317i | −0.513741 | + | 0.889825i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.50000 | + | 14.7224i | 0.454995 | + | 0.788074i | 0.998688 | − | 0.0512103i | \(-0.0163079\pi\) |
−0.543693 | + | 0.839284i | \(0.682975\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.48683 | − | 16.4317i | 0.504933 | − | 0.874570i | −0.495051 | − | 0.868864i | \(-0.664850\pi\) |
0.999984 | − | 0.00570573i | \(-0.00181620\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.0000 | + | 34.6410i | 1.06149 | + | 1.83855i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.6491 | − | 21.9089i | 0.667595 | − | 1.15631i | −0.310980 | − | 0.950416i | \(-0.600657\pi\) |
0.978575 | − | 0.205891i | \(-0.0660093\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | − | 25.9808i | −0.789474 | − | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.90569 | − | 13.6931i | 0.413803 | − | 0.716728i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.50000 | − | 16.4545i | 0.495896 | − | 0.858917i | −0.504093 | − | 0.863649i | \(-0.668173\pi\) |
0.999989 | + | 0.00473247i | \(0.00150640\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.9737 | + | 16.4317i | 0.985064 | + | 0.853090i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.50000 | + | 14.7224i | 0.440113 | + | 0.762299i | 0.997697 | − | 0.0678218i | \(-0.0216049\pi\) |
−0.557584 | + | 0.830120i | \(0.688272\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.0000 | −1.33553 | −0.667765 | − | 0.744372i | \(-0.732749\pi\) | ||||
−0.667765 | + | 0.744372i | \(0.732749\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.32456 | + | 10.9545i | 0.323170 | + | 0.559746i | 0.981140 | − | 0.193297i | \(-0.0619182\pi\) |
−0.657971 | + | 0.753044i | \(0.728585\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −50.0000 | + | 17.3205i | −2.54824 | + | 0.882735i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.3925 | − | 30.1247i | 0.881836 | − | 1.52738i | 0.0325386 | − | 0.999470i | \(-0.489641\pi\) |
0.849298 | − | 0.527915i | \(-0.177026\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.00000 | + | 8.66025i | −0.252861 | + | 0.437968i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.9737 | − | 32.8634i | −0.954669 | − | 1.65353i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.50000 | − | 12.9904i | 0.376414 | − | 0.651969i | −0.614123 | − | 0.789210i | \(-0.710490\pi\) |
0.990538 | + | 0.137241i | \(0.0438236\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.48683 | + | 16.4317i | 0.473750 | + | 0.820559i | 0.999548 | − | 0.0300503i | \(-0.00956676\pi\) |
−0.525799 | + | 0.850609i | \(0.676233\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.6491 | + | 21.9089i | 0.626993 | + | 1.08598i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0000 | −0.791149 | −0.395575 | − | 0.918434i | \(-0.629455\pi\) | ||||
−0.395575 | + | 0.918434i | \(0.629455\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −31.6228 | + | 10.9545i | −1.55606 | + | 0.539033i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.0000 | + | 17.3205i | −0.490881 | + | 0.850230i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.74342 | − | 8.21584i | 0.231731 | − | 0.401370i | −0.726587 | − | 0.687075i | \(-0.758894\pi\) |
0.958318 | + | 0.285705i | \(0.0922277\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.50000 | − | 2.59808i | −0.0731055 | − | 0.126622i | 0.827155 | − | 0.561973i | \(-0.189958\pi\) |
−0.900261 | + | 0.435351i | \(0.856624\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.8114 | −0.766965 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.50000 | − | 2.59808i | 0.362950 | − | 0.125730i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.00000 | 0.240285 | 0.120142 | − | 0.992757i | \(-0.461665\pi\) | ||||
0.120142 | + | 0.992757i | \(0.461665\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.1359 | 1.05891 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.0000 | −0.859093 | −0.429547 | − | 0.903045i | \(-0.641327\pi\) | ||||
−0.429547 | + | 0.903045i | \(0.641327\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.7851 | 1.65269 | 0.826344 | − | 0.563166i | \(-0.190417\pi\) | ||||
0.826344 | + | 0.563166i | \(0.190417\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.0000 | −1.42214 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.7851 | −1.64161 | −0.820804 | − | 0.571210i | \(-0.806474\pi\) | ||||
−0.820804 | + | 0.571210i | \(0.806474\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.0000 | − | 51.9615i | −1.41264 | − | 2.44677i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.0000 | −1.35656 | −0.678281 | − | 0.734802i | \(-0.737275\pi\) | ||||
−0.678281 | + | 0.734802i | \(0.737275\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.32456 | − | 10.9545i | −0.294564 | − | 0.510200i | 0.680319 | − | 0.732916i | \(-0.261841\pi\) |
−0.974883 | + | 0.222716i | \(0.928508\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.5000 | + | 21.6506i | −0.580924 | + | 1.00619i | 0.414446 | + | 0.910074i | \(0.363975\pi\) |
−0.995370 | + | 0.0961164i | \(0.969358\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.16228 | − | 5.47723i | 0.146333 | − | 0.253456i | −0.783537 | − | 0.621346i | \(-0.786586\pi\) |
0.929869 | + | 0.367890i | \(0.119920\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.0000 | + | 8.66025i | −1.15439 | + | 0.399893i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.6228 | 1.45402 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.5000 | + | 30.3109i | 0.802955 | + | 1.39076i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.0680 | − | 19.1703i | 0.505709 | − | 0.875913i | −0.494270 | − | 0.869309i | \(-0.664564\pi\) |
0.999978 | − | 0.00660425i | \(-0.00210221\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.90569 | − | 13.6931i | 0.358979 | − | 0.621770i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.500000 | + | 0.866025i | 0.0226572 | + | 0.0392434i | 0.877132 | − | 0.480250i | \(-0.159454\pi\) |
−0.854475 | + | 0.519493i | \(0.826121\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.48683 | + | 16.4317i | −0.428135 | + | 0.741551i | −0.996707 | − | 0.0810819i | \(-0.974162\pi\) |
0.568573 | + | 0.822633i | \(0.307496\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.00000 | − | 8.66025i | 0.225189 | − | 0.390038i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.6228 | − | 10.9545i | 1.41848 | − | 0.491374i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.50000 | − | 6.06218i | −0.156682 | − | 0.271380i | 0.776989 | − | 0.629515i | \(-0.216746\pi\) |
−0.933670 | + | 0.358134i | \(0.883413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.4605 | 1.26899 | 0.634495 | − | 0.772927i | \(-0.281208\pi\) | ||||
0.634495 | + | 0.772927i | \(0.281208\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.0000 | −0.889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.9737 | − | 32.8634i | −0.840993 | − | 1.45664i | −0.889056 | − | 0.457798i | \(-0.848638\pi\) |
0.0480632 | − | 0.998844i | \(-0.484695\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0000 | − | 8.66025i | −0.442374 | − | 0.383107i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.16228 | + | 5.47723i | −0.139347 | + | 0.241355i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.0000 | + | 51.9615i | −1.31940 | + | 2.28527i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.0000 | + | 27.7128i | −0.699631 | + | 1.21180i | 0.268963 | + | 0.963150i | \(0.413319\pi\) |
−0.968594 | + | 0.248646i | \(0.920014\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.74342 | + | 8.21584i | 0.206626 | + | 0.357888i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50000 | − | 11.2583i | 0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.32456 | + | 43.8178i | 0.272418 | + | 1.88737i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.5000 | − | 18.1865i | 0.451430 | − | 0.781900i | −0.547045 | − | 0.837103i | \(-0.684247\pi\) |
0.998475 | + | 0.0552031i | \(0.0175806\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.0680 | + | 19.1703i | −0.474100 | + | 0.821165i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.5000 | − | 18.1865i | −0.448948 | − | 0.777600i | 0.549370 | − | 0.835579i | \(-0.314868\pi\) |
−0.998318 | + | 0.0579790i | \(0.981534\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.1359 | −0.943023 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.0000 | + | 10.3923i | −1.27573 | + | 0.441926i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.58114 | − | 2.73861i | −0.0669950 | − | 0.116039i | 0.830582 | − | 0.556896i | \(-0.188008\pi\) |
−0.897577 | + | 0.440857i | \(0.854674\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.1096 | −1.73256 | −0.866282 | − | 0.499556i | \(-0.833497\pi\) | ||||
−0.866282 | + | 0.499556i | \(0.833497\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.0000 | −0.841406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −37.9473 | −1.59083 | −0.795417 | − | 0.606062i | \(-0.792748\pi\) | ||||
−0.795417 | + | 0.606062i | \(0.792748\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.0000 | 1.63210 | 0.816050 | − | 0.577982i | \(-0.196160\pi\) | ||||
0.816050 | + | 0.577982i | \(0.196160\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.8114 | −0.659380 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.0000 | + | 38.1051i | 0.915872 | + | 1.58634i | 0.805620 | + | 0.592433i | \(0.201833\pi\) |
0.110252 | + | 0.993904i | \(0.464834\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.6491 | + | 10.9545i | 0.524774 | + | 0.454467i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 60.0000 | 2.48495 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.3925 | − | 30.1247i | −0.717866 | − | 1.24338i | −0.961844 | − | 0.273600i | \(-0.911786\pi\) |
0.243977 | − | 0.969781i | \(-0.421548\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.5000 | − | 18.1865i | 0.432645 | − | 0.749363i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.48683 | − | 16.4317i | 0.389578 | − | 0.674768i | −0.602815 | − | 0.797881i | \(-0.705954\pi\) |
0.992393 | + | 0.123113i | \(0.0392877\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.00000 | + | 25.9808i | −0.204980 | + | 1.06511i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.4605 | 1.16286 | 0.581432 | − | 0.813595i | \(-0.302493\pi\) | ||||
0.581432 | + | 0.813595i | \(0.302493\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.50000 | + | 16.4545i | 0.387513 | + | 0.671192i | 0.992114 | − | 0.125336i | \(-0.0400009\pi\) |
−0.604601 | + | 0.796528i | \(0.706668\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −45.8530 | + | 79.4198i | −1.86419 | + | 3.22887i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.50000 | − | 12.9904i | −0.304416 | − | 0.527263i | 0.672715 | − | 0.739901i | \(-0.265128\pi\) |
−0.977131 | + | 0.212638i | \(0.931794\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.5000 | − | 28.5788i | −0.666429 | − | 1.15429i | −0.978896 | − | 0.204360i | \(-0.934489\pi\) |
0.312467 | − | 0.949929i | \(-0.398845\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.6491 | + | 21.9089i | −0.509234 | + | 0.882019i | 0.490709 | + | 0.871324i | \(0.336738\pi\) |
−0.999943 | + | 0.0106956i | \(0.996595\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.0000 | + | 19.0526i | −0.442127 | + | 0.765787i | −0.997847 | − | 0.0655827i | \(-0.979109\pi\) |
0.555720 | + | 0.831370i | \(0.312443\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.74342 | + | 24.6475i | −0.190041 | + | 0.987482i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5000 | + | 21.6506i | 0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.6491 | 0.504353 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.0000 | −1.23409 | −0.617045 | − | 0.786928i | \(-0.711670\pi\) | ||||
−0.617045 | + | 0.786928i | \(0.711670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −33.2039 | − | 57.5109i | −1.31766 | − | 2.28225i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.58114 | − | 2.73861i | 0.0624512 | − | 0.108169i | −0.833109 | − | 0.553108i | \(-0.813442\pi\) |
0.895561 | + | 0.444940i | \(0.146775\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.5000 | − | 32.0429i | 0.729569 | − | 1.26365i | −0.227497 | − | 0.973779i | \(-0.573054\pi\) |
0.957066 | − | 0.289871i | \(-0.0936125\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.9737 | + | 32.8634i | 0.745932 | + | 1.29199i | 0.949758 | + | 0.312985i | \(0.101329\pi\) |
−0.203826 | + | 0.979007i | \(0.565338\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −40.0000 | + | 69.2820i | −1.57014 | + | 2.71956i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.2302 | − | 24.6475i | −0.556873 | − | 0.964532i | −0.997755 | − | 0.0669670i | \(-0.978668\pi\) |
0.440882 | − | 0.897565i | \(-0.354666\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.0000 | − | 43.3013i | 0.976831 | − | 1.69192i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.58114 | + | 2.73861i | 0.0615924 | + | 0.106681i | 0.895177 | − | 0.445710i | \(-0.147049\pi\) |
−0.833585 | + | 0.552391i | \(0.813715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0000 | −0.661223 | −0.330612 | − | 0.943767i | \(-0.607255\pi\) | ||||
−0.330612 | + | 0.943767i | \(0.607255\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 55.3399 | − | 19.1703i | 2.14599 | − | 0.743392i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.00000 | − | 8.66025i | 0.193601 | − | 0.335326i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.48683 | − | 16.4317i | 0.366235 | − | 0.634338i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.50000 | − | 4.33013i | −0.0963679 | − | 0.166914i | 0.813811 | − | 0.581130i | \(-0.197389\pi\) |
−0.910179 | + | 0.414216i | \(0.864056\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 37.9473 | 1.45843 | 0.729217 | − | 0.684282i | \(-0.239884\pi\) | ||||
0.729217 | + | 0.684282i | \(0.239884\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0000 | − | 8.66025i | −0.383765 | − | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.48683 | − | 16.4317i | −0.363004 | − | 0.628741i | 0.625450 | − | 0.780264i | \(-0.284915\pi\) |
−0.988454 | + | 0.151524i | \(0.951582\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.0000 | 0.382080 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.0000 | 0.418460 | 0.209230 | − | 0.977866i | \(-0.432904\pi\) | ||||
0.209230 | + | 0.977866i | \(0.432904\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.32456 | −0.239904 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.0000 | −1.13633 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.16228 | 0.119438 | 0.0597188 | − | 0.998215i | \(-0.480980\pi\) | ||||
0.0597188 | + | 0.998215i | \(0.480980\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.0000 | − | 24.2487i | −0.528020 | − | 0.914557i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.16228 | + | 16.4317i | −0.118930 | + | 0.617977i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.00000 | −0.0375558 | −0.0187779 | − | 0.999824i | \(-0.505978\pi\) | ||||
−0.0187779 | + | 0.999824i | \(0.505978\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.74342 | + | 8.21584i | 0.177642 | + | 0.307686i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.00000 | + | 3.46410i | 0.148968 | + | 0.129010i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.8114 | 0.587220 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.5000 | + | 25.1147i | 0.537775 | + | 0.931454i | 0.999023 | + | 0.0441829i | \(0.0140684\pi\) |
−0.461248 | + | 0.887271i | \(0.652598\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.90569 | − | 13.6931i | 0.292403 | − | 0.506456i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.50000 | − | 2.59808i | −0.0554038 | − | 0.0959621i | 0.836993 | − | 0.547213i | \(-0.184311\pi\) |
−0.892397 | + | 0.451251i | \(0.850978\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −31.6228 | + | 54.7723i | −1.16484 | + | 2.01756i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.50000 | − | 2.59808i | −0.0551784 | − | 0.0955718i | 0.837117 | − | 0.547024i | \(-0.184239\pi\) |
−0.892295 | + | 0.451452i | \(0.850906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.2302 | + | 24.6475i | −0.522057 | + | 0.904230i | 0.477614 | + | 0.878570i | \(0.341502\pi\) |
−0.999671 | + | 0.0256596i | \(0.991831\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.0000 | − | 25.9808i | 0.549557 | − | 0.951861i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.50000 | − | 2.59808i | −0.0547358 | − | 0.0948051i | 0.837359 | − | 0.546653i | \(-0.184098\pi\) |
−0.892095 | + | 0.451848i | \(0.850765\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −53.7587 | −1.95648 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.0000 | 0.545184 | 0.272592 | − | 0.962130i | \(-0.412119\pi\) | ||||
0.272592 | + | 0.962130i | \(0.412119\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.6491 | − | 21.9089i | −0.458530 | − | 0.794197i | 0.540354 | − | 0.841438i | \(-0.318290\pi\) |
−0.998884 | + | 0.0472409i | \(0.984957\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0000 | + | 12.1244i | 0.506834 | + | 0.438931i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.5000 | − | 19.9186i | 0.414701 | − | 0.718283i | −0.580696 | − | 0.814120i | \(-0.697220\pi\) |
0.995397 | + | 0.0958377i | \(0.0305530\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.3925 | + | 30.1247i | 0.625566 | + | 1.08351i | 0.988431 | + | 0.151670i | \(0.0484651\pi\) |
−0.362865 | + | 0.931842i | \(0.618202\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.50000 | + | 12.9904i | −0.269408 | + | 0.466628i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.2039 | + | 57.5109i | 1.18965 | + | 2.06054i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.0000 | − | 69.2820i | 1.43131 | − | 2.47911i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.2982 | + | 43.8178i | 0.902932 | + | 1.56392i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.0000 | 0.534692 | 0.267346 | − | 0.963601i | \(-0.413853\pi\) | ||||
0.267346 | + | 0.963601i | \(0.413853\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.16228 | + | 16.4317i | −0.112438 | + | 0.584243i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.48683 | − | 16.4317i | 0.336041 | − | 0.582040i | −0.647643 | − | 0.761944i | \(-0.724245\pi\) |
0.983684 | + | 0.179904i | \(0.0575786\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.0000 | + | 25.9808i | 0.530662 | + | 0.919133i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −31.6228 | −1.11594 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.00000 | + | 25.9808i | −0.176227 | + | 0.915702i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.8114 | − | 27.3861i | −0.555899 | − | 0.962845i | −0.997833 | − | 0.0657975i | \(-0.979041\pi\) |
0.441934 | − | 0.897047i | \(-0.354292\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.0000 | −0.491606 | −0.245803 | − | 0.969320i | \(-0.579052\pi\) | ||||
−0.245803 | + | 0.969320i | \(0.579052\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 53.7587 | 1.88309 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −35.0000 | −1.22449 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.2982 | 0.882914 | 0.441457 | − | 0.897282i | \(-0.354462\pi\) | ||||
0.441457 | + | 0.897282i | \(0.354462\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.0000 | −0.801730 | −0.400865 | − | 0.916137i | \(-0.631290\pi\) | ||||
−0.400865 | + | 0.916137i | \(0.631290\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.9737 | −0.659779 | −0.329890 | − | 0.944020i | \(-0.607011\pi\) | ||||
−0.329890 | + | 0.944020i | \(0.607011\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.50000 | + | 9.52628i | 0.191023 | + | 0.330861i | 0.945589 | − | 0.325362i | \(-0.105486\pi\) |
−0.754567 | + | 0.656223i | \(0.772153\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.5548 | + | 8.21584i | 0.712182 | + | 0.284662i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.0000 | −0.692129 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.8114 | + | 27.3861i | 0.545870 | + | 0.945474i | 0.998552 | + | 0.0538020i | \(0.0171340\pi\) |
−0.452682 | + | 0.891672i | \(0.649533\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.50000 | − | 16.4545i | 0.327586 | − | 0.567396i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.5548 | − | 35.6020i | 0.707107 | − | 1.22474i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 58.0000 | + | 50.2295i | 1.99290 | + | 1.72591i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.6491 | 0.433606 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.5000 | + | 37.2391i | 0.736146 | + | 1.27504i | 0.954219 | + | 0.299110i | \(0.0966897\pi\) |
−0.218073 | + | 0.975933i | \(0.569977\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.9737 | − | 32.8634i | 0.648128 | − | 1.12259i | −0.335441 | − | 0.942061i | \(-0.608885\pi\) |
0.983570 | − | 0.180530i | \(-0.0577812\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.50000 | − | 14.7224i | −0.290016 | − | 0.502323i | 0.683797 | − | 0.729672i | \(-0.260327\pi\) |
−0.973813 | + | 0.227349i | \(0.926994\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.90569 | − | 13.6931i | 0.269113 | − | 0.466117i | −0.699520 | − | 0.714613i | \(-0.746603\pi\) |
0.968633 | + | 0.248496i | \(0.0799362\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.00000 | − | 8.66025i | −0.170005 | − | 0.294457i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −37.9473 | + | 65.7267i | −1.28728 | + | 2.22963i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.50000 | + | 4.33013i | 0.0844190 | + | 0.146218i | 0.905143 | − | 0.425106i | \(-0.139763\pi\) |
−0.820724 | + | 0.571324i | \(0.806430\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.4342 | 1.59810 | 0.799049 | − | 0.601266i | \(-0.205337\pi\) | ||||
0.799049 | + | 0.601266i | \(0.205337\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.0000 | 0.774012 | 0.387006 | − | 0.922077i | \(-0.373509\pi\) | ||||
0.387006 | + | 0.922077i | \(0.373509\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −52.5000 | + | 18.1865i | −1.76079 | + | 0.609957i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.2039 | − | 57.5109i | 1.11113 | − | 1.92453i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.0000 | − | 25.9808i | 0.501395 | − | 0.868441i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.74342 | − | 8.21584i | −0.158202 | − | 0.274014i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.0000 | − | 25.9808i | 0.499722 | − | 0.865545i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.2039 | − | 57.5109i | −1.10374 | − | 1.91173i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.0000 | − | 20.7846i | 0.398453 | − | 0.690142i | −0.595082 | − | 0.803665i | \(-0.702880\pi\) |
0.993535 | + | 0.113523i | \(0.0362137\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.7171 | − | 41.0792i | −0.785782 | − | 1.36101i | −0.928531 | − | 0.371255i | \(-0.878927\pi\) |
0.142749 | − | 0.989759i | \(-0.454406\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.0000 | 1.32381 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −31.6228 | − | 27.3861i | −1.04428 | − | 0.904370i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.50000 | − | 9.52628i | 0.181428 | − | 0.314243i | −0.760939 | − | 0.648824i | \(-0.775261\pi\) |
0.942367 | + | 0.334581i | \(0.108595\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0000 | + | 17.3205i | 0.328798 | + | 0.569495i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.4605 | −0.933759 | −0.466879 | − | 0.884321i | \(-0.654622\pi\) | ||||
−0.466879 | + | 0.884321i | \(0.654622\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.00000 | − | 48.4974i | −0.229416 | − | 1.58944i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.6228 | + | 54.7723i | 1.03418 | + | 1.79124i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.0000 | 1.43742 | 0.718709 | − | 0.695311i | \(-0.244734\pi\) | ||||
0.718709 | + | 0.695311i | \(0.244734\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.2982 | −0.824698 | −0.412349 | − | 0.911026i | \(-0.635292\pi\) | ||||
−0.412349 | + | 0.911026i | \(0.635292\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.0000 | −0.976934 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.7851 | −1.13036 | −0.565181 | − | 0.824967i | \(-0.691194\pi\) | ||||
−0.565181 | + | 0.824967i | \(0.691194\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.16228 | −0.102436 | −0.0512181 | − | 0.998687i | \(-0.516310\pi\) | ||||
−0.0512181 | + | 0.998687i | \(0.516310\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.0000 | − | 25.9808i | −0.485389 | − | 0.840718i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.58114 | − | 8.21584i | 0.0510576 | − | 0.265303i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.6491 | − | 21.9089i | −0.407189 | − | 0.705273i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.0000 | + | 22.5167i | −0.418052 | + | 0.724087i | −0.995743 | − | 0.0921681i | \(-0.970620\pi\) |
0.577692 | + | 0.816255i | \(0.303954\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.7171 | − | 41.0792i | 0.761117 | − | 1.31829i | −0.181158 | − | 0.983454i | \(-0.557984\pi\) |
0.942275 | − | 0.334840i | \(-0.108682\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.00000 | + | 5.19615i | −0.0320585 | + | 0.166581i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.9473 | −1.21404 | −0.607021 | − | 0.794686i | \(-0.707636\pi\) | ||||
−0.607021 | + | 0.794686i | \(0.707636\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.0000 | + | 51.9615i | 0.958804 | + | 1.66070i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −40.0000 | − | 69.2820i | −1.27451 | − | 2.20751i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.90569 | − | 13.6931i | 0.251386 | − | 0.435414i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.00000 | − | 12.1244i | −0.222362 | − | 0.385143i | 0.733163 | − | 0.680053i | \(-0.238043\pi\) |
−0.955525 | + | 0.294911i | \(0.904710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.5548 | − | 35.6020i | 0.651631 | − | 1.12866i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.5000 | + | 35.5070i | −0.649242 | + | 1.12452i | 0.334063 | + | 0.942551i | \(0.391580\pi\) |
−0.983304 | + | 0.181968i | \(0.941753\pi\) | |||||||
\(998\) | 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 | 2268.2.i.i.2053.1 | 4 | ||
3.2 | odd | 2 | inner | 2268.2.i.i.2053.2 | 4 | ||
7.4 | even | 3 | 2268.2.l.i.109.2 | 4 | |||
9.2 | odd | 6 | 2268.2.l.i.541.1 | 4 | |||
9.4 | even | 3 | 756.2.k.d.541.1 | yes | 4 | ||
9.5 | odd | 6 | 756.2.k.d.541.2 | yes | 4 | ||
9.7 | even | 3 | 2268.2.l.i.541.2 | 4 | |||
21.11 | odd | 6 | 2268.2.l.i.109.1 | 4 | |||
63.4 | even | 3 | 756.2.k.d.109.1 | ✓ | 4 | ||
63.5 | even | 6 | 5292.2.a.r.1.2 | 2 | |||
63.11 | odd | 6 | inner | 2268.2.i.i.865.2 | 4 | ||
63.23 | odd | 6 | 5292.2.a.q.1.1 | 2 | |||
63.25 | even | 3 | inner | 2268.2.i.i.865.1 | 4 | ||
63.32 | odd | 6 | 756.2.k.d.109.2 | yes | 4 | ||
63.40 | odd | 6 | 5292.2.a.r.1.1 | 2 | |||
63.58 | even | 3 | 5292.2.a.q.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.k.d.109.1 | ✓ | 4 | 63.4 | even | 3 | ||
756.2.k.d.109.2 | yes | 4 | 63.32 | odd | 6 | ||
756.2.k.d.541.1 | yes | 4 | 9.4 | even | 3 | ||
756.2.k.d.541.2 | yes | 4 | 9.5 | odd | 6 | ||
2268.2.i.i.865.1 | 4 | 63.25 | even | 3 | inner | ||
2268.2.i.i.865.2 | 4 | 63.11 | odd | 6 | inner | ||
2268.2.i.i.2053.1 | 4 | 1.1 | even | 1 | trivial | ||
2268.2.i.i.2053.2 | 4 | 3.2 | odd | 2 | inner | ||
2268.2.l.i.109.1 | 4 | 21.11 | odd | 6 | |||
2268.2.l.i.109.2 | 4 | 7.4 | even | 3 | |||
2268.2.l.i.541.1 | 4 | 9.2 | odd | 6 | |||
2268.2.l.i.541.2 | 4 | 9.7 | even | 3 | |||
5292.2.a.q.1.1 | 2 | 63.23 | odd | 6 | |||
5292.2.a.q.1.2 | 2 | 63.58 | even | 3 | |||
5292.2.a.r.1.1 | 2 | 63.40 | odd | 6 | |||
5292.2.a.r.1.2 | 2 | 63.5 | even | 6 |