Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(353,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.353");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.t (of order \(6\), degree \(2\), 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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.3317760000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 25x^{4} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 353.2 | ||
Root | \(0.578737 + 2.15988i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.353 |
Dual form | 1216.2.t.b.1185.2 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −2.59808 | − | 1.50000i | −1.50000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.73861 | + | 1.58114i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.16228 | 1.19523 | 0.597614 | − | 0.801784i | \(-0.296115\pi\) | ||||
0.597614 | + | 0.801784i | \(0.296115\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | + | 5.19615i | 1.00000 | + | 1.73205i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.00000i | − | 0.904534i | −0.891883 | − | 0.452267i | \(-0.850615\pi\) | ||
0.891883 | − | 0.452267i | \(-0.149385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.47723 | − | 3.16228i | 1.51911 | − | 0.877058i | 0.519362 | − | 0.854554i | \(-0.326170\pi\) |
0.999747 | − | 0.0225039i | \(-0.00716381\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.74342 | − | 8.21584i | −1.22474 | − | 2.12132i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | + | 3.46410i | −0.485071 | + | 0.840168i | −0.999853 | − | 0.0171533i | \(-0.994540\pi\) |
0.514782 | + | 0.857321i | \(0.327873\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.59808 | + | 3.50000i | −0.596040 | + | 0.802955i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.21584 | − | 4.74342i | −1.79284 | − | 1.03510i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.74342 | + | 8.21584i | 0.989071 | + | 1.71312i | 0.622224 | + | 0.782839i | \(0.286229\pi\) |
0.366847 | + | 0.930281i | \(0.380437\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | + | 4.33013i | 0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 9.00000i | − | 1.73205i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.73861 | + | 1.58114i | −0.508548 | + | 0.293610i | −0.732236 | − | 0.681051i | \(-0.761523\pi\) |
0.223689 | + | 0.974661i | \(0.428190\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.16228 | 0.567962 | 0.283981 | − | 0.958830i | \(-0.408345\pi\) | ||||
0.283981 | + | 0.958830i | \(0.408345\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.50000 | + | 7.79423i | −0.783349 | + | 1.35680i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.66025 | + | 5.00000i | 1.46385 | + | 0.845154i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.16228i | 0.519875i | 0.965625 | + | 0.259938i | \(0.0837020\pi\) | ||||
−0.965625 | + | 0.259938i | \(0.916298\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −18.9737 | −3.03822 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50000 | − | 2.59808i | 0.234261 | − | 0.405751i | −0.724797 | − | 0.688963i | \(-0.758066\pi\) |
0.959058 | + | 0.283211i | \(0.0913998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.66025 | − | 5.00000i | −1.32068 | − | 0.762493i | −0.336840 | − | 0.941562i | \(-0.609358\pi\) |
−0.983836 | + | 0.179069i | \(0.942691\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 18.9737i | 2.82843i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.58114 | + | 2.73861i | 0.230633 | + | 0.399468i | 0.957995 | − | 0.286787i | \(-0.0925871\pi\) |
−0.727362 | + | 0.686254i | \(0.759254\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.3923 | − | 6.00000i | 1.45521 | − | 0.840168i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.74342 | − | 8.21584i | 0.639602 | − | 1.10782i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.0000 | − | 5.19615i | 1.58944 | − | 0.688247i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.06218 | + | 3.50000i | 0.789228 | + | 0.455661i | 0.839691 | − | 0.543065i | \(-0.182736\pi\) |
−0.0504625 | + | 0.998726i | \(0.516070\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.73861 | + | 1.58114i | −0.350643 | + | 0.202444i | −0.664969 | − | 0.746871i | \(-0.731555\pi\) |
0.314325 | + | 0.949315i | \(0.398222\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.48683 | + | 16.4317i | 1.19523 | + | 2.07020i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 20.0000 | 2.48069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.33013 | − | 2.50000i | 0.529009 | − | 0.305424i | −0.211604 | − | 0.977356i | \(-0.567869\pi\) |
0.740613 | + | 0.671932i | \(0.234535\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 28.4605i | − | 3.42624i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.50000 | − | 6.06218i | 0.409644 | − | 0.709524i | −0.585206 | − | 0.810885i | \(-0.698986\pi\) |
0.994850 | + | 0.101361i | \(0.0323196\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 15.0000i | − | 1.73205i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 9.48683i | − | 1.08112i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.16228 | − | 5.47723i | 0.355784 | − | 0.616236i | −0.631468 | − | 0.775402i | \(-0.717547\pi\) |
0.987252 | + | 0.159166i | \(0.0508805\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.00000i | 0.768350i | 0.923260 | + | 0.384175i | \(0.125514\pi\) | ||||
−0.923260 | + | 0.384175i | \(0.874486\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.9545 | + | 6.32456i | −1.18818 | + | 0.685994i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.48683 | 1.01710 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.00000 | − | 6.92820i | −0.423999 | − | 0.734388i | 0.572327 | − | 0.820025i | \(-0.306041\pi\) |
−0.996326 | + | 0.0856373i | \(0.972707\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.3205 | − | 10.0000i | 1.81568 | − | 1.04828i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.21584 | − | 4.74342i | −0.851943 | − | 0.491869i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.6491 | + | 5.47723i | −1.29777 | + | 0.561951i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.50000 | − | 7.79423i | 0.456906 | − | 0.791384i | −0.541890 | − | 0.840450i | \(-0.682291\pi\) |
0.998796 | + | 0.0490655i | \(0.0156243\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.5885 | − | 9.00000i | 1.56670 | − | 0.904534i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.21584 | − | 4.74342i | 0.817506 | − | 0.471988i | −0.0320494 | − | 0.999486i | \(-0.510203\pi\) |
0.849556 | + | 0.527499i | \(0.176870\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.32456 | −0.623177 | −0.311588 | − | 0.950217i | \(-0.600861\pi\) | ||||
−0.311588 | + | 0.950217i | \(0.600861\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −15.0000 | − | 25.9808i | −1.46385 | − | 2.53546i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6.00000i | − | 0.580042i | −0.957020 | − | 0.290021i | \(-0.906338\pi\) | ||
0.957020 | − | 0.290021i | \(-0.0936623\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.4317 | + | 9.48683i | 1.57387 | + | 0.908674i | 0.995688 | + | 0.0927654i | \(0.0295707\pi\) |
0.578181 | + | 0.815908i | \(0.303763\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.74342 | − | 8.21584i | 0.450225 | − | 0.779813i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.0000 | −1.22294 | −0.611469 | − | 0.791269i | \(-0.709421\pi\) | ||||
−0.611469 | + | 0.791269i | \(0.709421\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 30.0000i | 2.79751i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 32.8634 | + | 18.9737i | 3.03822 | + | 1.75412i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.32456 | + | 10.9545i | −0.579771 | + | 1.00419i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.00000 | 0.181818 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.79423 | + | 4.50000i | −0.702782 | + | 0.405751i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.16228 | − | 5.47723i | −0.280607 | − | 0.486025i | 0.690928 | − | 0.722924i | \(-0.257202\pi\) |
−0.971534 | + | 0.236899i | \(0.923869\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.0000 | + | 25.9808i | 1.32068 | + | 2.28748i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.79423 | + | 4.50000i | 0.680985 | + | 0.393167i | 0.800226 | − | 0.599699i | \(-0.204713\pi\) |
−0.119241 | + | 0.992865i | \(0.538046\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.21584 | + | 11.0680i | −0.712404 | + | 0.959715i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 14.2302 | − | 24.6475i | 1.22474 | − | 2.12132i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.50000 | + | 7.79423i | 0.384461 | + | 0.665906i | 0.991694 | − | 0.128618i | \(-0.0410540\pi\) |
−0.607233 | + | 0.794524i | \(0.707721\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.52628 | + | 5.50000i | −0.808008 | + | 0.466504i | −0.846264 | − | 0.532764i | \(-0.821153\pi\) |
0.0382553 | + | 0.999268i | \(0.487820\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 9.48683i | − | 0.798935i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.48683 | − | 16.4317i | −0.793329 | − | 1.37409i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.0000 | −0.830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.79423 | − | 4.50000i | −0.642857 | − | 0.371154i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.21584 | + | 4.74342i | 0.673068 | + | 0.388596i | 0.797238 | − | 0.603665i | \(-0.206294\pi\) |
−0.124170 | + | 0.992261i | \(0.539627\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.16228 | 0.257343 | 0.128671 | − | 0.991687i | \(-0.458929\pi\) | ||||
0.128671 | + | 0.991687i | \(0.458929\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −24.0000 | −1.94029 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.66025 | + | 5.00000i | 0.695608 | + | 0.401610i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.47723 | − | 3.16228i | −0.437130 | − | 0.252377i | 0.265249 | − | 0.964180i | \(-0.414546\pi\) |
−0.702380 | + | 0.711803i | \(0.747879\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.0000 | + | 25.9808i | 1.18217 | + | 2.04757i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.00000i | 0.391630i | 0.980641 | + | 0.195815i | \(0.0627352\pi\) | ||||
−0.980641 | + | 0.195815i | \(0.937265\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −24.6475 | + | 14.2302i | −1.91881 | + | 1.10782i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.16228 | + | 5.47723i | 0.244704 | + | 0.423840i | 0.962048 | − | 0.272879i | \(-0.0879758\pi\) |
−0.717344 | + | 0.696719i | \(0.754642\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.5000 | − | 23.3827i | 1.03846 | − | 1.79867i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −25.9808 | − | 3.00000i | −1.98680 | − | 0.229416i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.9545 | − | 6.32456i | −0.832851 | − | 0.480847i | 0.0219765 | − | 0.999758i | \(-0.493004\pi\) |
−0.854828 | + | 0.518911i | \(0.826337\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.90569 | + | 13.6931i | 0.597614 | + | 1.03510i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.5000 | − | 18.1865i | −0.789228 | − | 1.36698i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.00000i | 0.224231i | 0.993695 | + | 0.112115i | \(0.0357626\pi\) | ||||
−0.993695 | + | 0.112115i | \(0.964237\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.21584 | + | 4.74342i | −0.610678 | + | 0.352575i | −0.773231 | − | 0.634125i | \(-0.781361\pi\) |
0.162552 | + | 0.986700i | \(0.448027\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.48683 | 0.701287 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.00000 | + | 8.66025i | −0.367607 | + | 0.636715i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.3923 | + | 6.00000i | 0.759961 | + | 0.438763i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 28.4605i | − | 2.07020i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.32456 | −0.457629 | −0.228814 | − | 0.973470i | \(-0.573485\pi\) | ||||
−0.228814 | + | 0.973470i | \(0.573485\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.00000 | + | 6.92820i | −0.287926 | + | 0.498703i | −0.973315 | − | 0.229475i | \(-0.926299\pi\) |
0.685388 | + | 0.728178i | \(0.259632\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −51.9615 | − | 30.0000i | −3.72104 | − | 2.14834i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 22.1359i | − | 1.57712i | −0.614957 | − | 0.788560i | \(-0.710827\pi\) | ||
0.614957 | − | 0.788560i | \(-0.289173\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.16228 | − | 5.47723i | −0.224168 | − | 0.388270i | 0.731902 | − | 0.681410i | \(-0.238633\pi\) |
−0.956069 | + | 0.293140i | \(0.905300\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.0000 | −1.05802 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.66025 | + | 5.00000i | −0.607831 | + | 0.350931i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.21584 | − | 4.74342i | 0.573819 | − | 0.331295i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −28.4605 | + | 49.2950i | −1.97814 | + | 3.42624i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.5000 | + | 7.79423i | 0.726300 | + | 0.539138i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.8564 | − | 8.00000i | −0.953914 | − | 0.550743i | −0.0596196 | − | 0.998221i | \(-0.518989\pi\) |
−0.894295 | + | 0.447478i | \(0.852322\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.8114 | − | 27.3861i | −1.07833 | − | 1.86772i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.0000 | 0.678844 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.1865 | + | 10.5000i | −1.22893 | + | 0.709524i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.2982i | 1.70174i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.90569 | − | 13.6931i | 0.529404 | − | 0.916955i | −0.470007 | − | 0.882662i | \(-0.655749\pi\) |
0.999412 | − | 0.0342929i | \(-0.0109179\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15.0000 | + | 25.9808i | −1.00000 | + | 1.73205i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.0000i | 0.730096i | 0.930989 | + | 0.365048i | \(0.118947\pi\) | ||||
−0.930989 | + | 0.365048i | \(0.881053\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.2982i | 1.67175i | 0.548917 | + | 0.835877i | \(0.315040\pi\) | ||||
−0.548917 | + | 0.835877i | \(0.684960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.2302 | + | 24.6475i | −0.936282 | + | 1.62169i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.50000 | − | 2.59808i | 0.0982683 | − | 0.170206i | −0.812700 | − | 0.582683i | \(-0.802003\pi\) |
0.910968 | + | 0.412477i | \(0.135336\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.0000i | 0.652328i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.4317 | + | 9.48683i | −1.06735 | + | 0.616236i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.32456 | 0.409101 | 0.204551 | − | 0.978856i | \(-0.434427\pi\) | ||||
0.204551 | + | 0.978856i | \(0.434427\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.50000 | − | 11.2583i | −0.418702 | − | 0.725213i | 0.577107 | − | 0.816668i | \(-0.304181\pi\) |
−0.995809 | + | 0.0914555i | \(0.970848\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.21584 | + | 4.74342i | 0.524891 | + | 0.303046i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.16228 | + | 27.3861i | −0.201211 | + | 1.74254i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.5000 | − | 18.1865i | 0.665410 | − | 1.15252i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.06218 | − | 3.50000i | 0.382641 | − | 0.220918i | −0.296326 | − | 0.955087i | \(-0.595761\pi\) |
0.678967 | + | 0.734169i | \(0.262428\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.6475 | − | 14.2302i | 1.54958 | − | 0.894648i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 37.9473 | 2.37635 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.5000 | − | 18.1865i | −0.654972 | − | 1.13444i | −0.981901 | − | 0.189396i | \(-0.939347\pi\) |
0.326929 | − | 0.945049i | \(-0.393986\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.0000i | 0.621370i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.4317 | − | 9.48683i | −1.01710 | − | 0.587220i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.74342 | − | 8.21584i | 0.292492 | − | 0.506610i | −0.681907 | − | 0.731439i | \(-0.738849\pi\) |
0.974398 | + | 0.224829i | \(0.0721823\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.0000i | 1.46878i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.9089 | − | 12.6491i | −1.33581 | − | 0.771230i | −0.349626 | − | 0.936889i | \(-0.613691\pi\) |
−0.986183 | + | 0.165659i | \(0.947025\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0680 | − | 19.1703i | 0.672331 | − | 1.16451i | −0.304910 | − | 0.952381i | \(-0.598626\pi\) |
0.977241 | − | 0.212131i | \(-0.0680403\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −60.0000 | −3.63137 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.9904 | − | 7.50000i | 0.783349 | − | 0.452267i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 28.4605i | − | 1.71003i | −0.518607 | − | 0.855013i | \(-0.673549\pi\) | ||
0.518607 | − | 0.855013i | \(-0.326451\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.48683 | + | 16.4317i | 0.567962 | + | 0.983739i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.50000 | + | 16.4545i | 0.566722 | + | 0.981592i | 0.996887 | + | 0.0788417i | \(0.0251222\pi\) |
−0.430165 | + | 0.902750i | \(0.641545\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.9904 | − | 7.50000i | −0.772198 | − | 0.445829i | 0.0614601 | − | 0.998110i | \(-0.480424\pi\) |
−0.833658 | + | 0.552281i | \(0.813758\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 41.0792 | + | 4.74342i | 2.43332 | + | 0.280976i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.74342 | − | 8.21584i | 0.279995 | − | 0.484966i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.3827 | + | 13.5000i | −1.37072 | + | 0.791384i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.8114i | 0.923711i | 0.886955 | + | 0.461856i | \(0.152816\pi\) | ||||
−0.886955 | + | 0.461856i | \(0.847184\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.0680 | + | 19.1703i | 0.644402 | + | 1.11614i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −27.0000 | −1.56670 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 51.9615 | + | 30.0000i | 3.00501 | + | 1.73494i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.3861 | − | 15.8114i | −1.57851 | − | 0.911353i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −28.4605 | −1.63501 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.0000 | −0.572598 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.1865 | − | 10.5000i | −1.03796 | − | 0.599267i | −0.118705 | − | 0.992930i | \(-0.537874\pi\) |
−0.919255 | + | 0.393663i | \(0.871208\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.4317 | + | 9.48683i | 0.934765 | + | 0.539687i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.1359 | 1.25521 | 0.627607 | − | 0.778530i | \(-0.284034\pi\) | ||||
0.627607 | + | 0.778530i | \(0.284034\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.50000 | + | 2.59808i | 0.0847850 | + | 0.146852i | 0.905300 | − | 0.424774i | \(-0.139646\pi\) |
−0.820515 | + | 0.571626i | \(0.806313\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 60.0000i | 3.38062i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.3861 | + | 15.8114i | −1.53816 | + | 0.888056i | −0.539211 | + | 0.842170i | \(0.681278\pi\) |
−0.998947 | + | 0.0458856i | \(0.985389\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.74342 | + | 8.21584i | 0.265580 | + | 0.459999i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.00000 | + | 15.5885i | −0.502331 | + | 0.870063i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.92820 | − | 16.0000i | −0.385496 | − | 0.890264i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.3861 | + | 15.8114i | 1.51911 | + | 0.877058i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −28.4605 | − | 49.2950i | −1.57387 | − | 2.72602i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.00000 | + | 8.66025i | 0.275659 | + | 0.477455i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 29.0000i | − | 1.59398i | −0.603990 | − | 0.796992i | \(-0.706423\pi\) | ||
0.603990 | − | 0.796992i | \(-0.293577\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.4317 | + | 9.48683i | −0.900450 | + | 0.519875i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.8114 | 0.863868 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.5000 | − | 21.6506i | 0.680918 | − | 1.17939i | −0.293783 | − | 0.955872i | \(-0.594914\pi\) |
0.974701 | − | 0.223513i | \(-0.0717525\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 33.7750 | + | 19.5000i | 1.83441 | + | 1.05909i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 9.48683i | − | 0.513741i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.6491 | −0.682988 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 45.0000 | − | 77.9423i | 2.42272 | − | 4.19627i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.33013 | − | 2.50000i | −0.232453 | − | 0.134207i | 0.379250 | − | 0.925294i | \(-0.376182\pi\) |
−0.611703 | + | 0.791087i | \(0.709515\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.6491i | − | 0.677091i | −0.940950 | − | 0.338546i | \(-0.890065\pi\) | ||
0.940950 | − | 0.338546i | \(-0.109935\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −28.4605 | − | 49.2950i | −1.51911 | − | 2.63117i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.0000 | −0.691920 | −0.345960 | − | 0.938249i | \(-0.612447\pi\) | ||||
−0.345960 | + | 0.938249i | \(0.612447\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 32.8634 | − | 18.9737i | 1.73931 | − | 1.00419i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.74342 | − | 8.21584i | 0.250348 | − | 0.433615i | −0.713274 | − | 0.700886i | \(-0.752788\pi\) |
0.963622 | + | 0.267270i | \(0.0861217\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.50000 | − | 18.1865i | −0.289474 | − | 0.957186i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.19615 | − | 3.00000i | −0.272727 | − | 0.157459i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.1703 | − | 11.0680i | 1.00342 | − | 0.579324i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.58114 | + | 2.73861i | 0.0825348 | + | 0.142954i | 0.904338 | − | 0.426817i | \(-0.140365\pi\) |
−0.821803 | + | 0.569771i | \(0.807032\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.0000 | 0.937043 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.0000 | + | 17.3205i | −0.515026 | + | 0.892052i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.0000i | 1.64373i | 0.569683 | + | 0.821865i | \(0.307066\pi\) | ||||
−0.569683 | + | 0.821865i | \(0.692934\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.9737i | 0.972050i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.2302 | + | 24.6475i | −0.727132 | + | 1.25943i | 0.230959 | + | 0.972964i | \(0.425814\pi\) |
−0.958091 | + | 0.286466i | \(0.907520\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.0000 | − | 25.9808i | 0.764471 | − | 1.32410i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 60.0000i | − | 3.04997i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −37.9473 | −1.91908 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.5000 | − | 23.3827i | −0.680985 | − | 1.17950i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.3205 | − | 10.0000i | 0.871489 | − | 0.503155i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.6931 | + | 7.90569i | 0.687235 | + | 0.396775i | 0.802575 | − | 0.596551i | \(-0.203463\pi\) |
−0.115340 | + | 0.993326i | \(0.536796\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 37.9473 | − | 16.4317i | 1.89974 | − | 0.822613i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.50000 | − | 11.2583i | 0.324595 | − | 0.562214i | −0.656836 | − | 0.754034i | \(-0.728105\pi\) |
0.981430 | + | 0.191820i | \(0.0614388\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.3205 | − | 10.0000i | 0.862796 | − | 0.498135i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −24.6475 | + | 14.2302i | −1.22474 | + | 0.707107i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.48683 | 0.470245 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.50000 | − | 7.79423i | −0.222511 | − | 0.385400i | 0.733059 | − | 0.680165i | \(-0.238092\pi\) |
−0.955570 | + | 0.294765i | \(0.904759\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 27.0000i | − | 1.33181i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.1703 | + | 11.0680i | 0.943308 | + | 0.544619i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.0680 | + | 19.1703i | −0.543305 | + | 0.941033i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 33.0000 | 1.61602 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0000i | 0.879358i | 0.898155 | + | 0.439679i | \(0.144908\pi\) | ||||
−0.898155 | + | 0.439679i | \(0.855092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.6475 | − | 14.2302i | −1.20125 | − | 0.693540i | −0.240414 | − | 0.970670i | \(-0.577283\pi\) |
−0.960832 | + | 0.277130i | \(0.910617\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.48683 | + | 16.4317i | −0.461266 | + | 0.798935i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.0000 | −0.970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.66025 | + | 5.00000i | −0.419099 | + | 0.241967i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 56.9210i | 2.74817i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.32456 | − | 10.9545i | −0.304643 | − | 0.527657i | 0.672539 | − | 0.740062i | \(-0.265204\pi\) |
−0.977182 | + | 0.212405i | \(0.931871\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.0000 | + | 24.2487i | 0.672797 | + | 1.16532i | 0.977108 | + | 0.212746i | \(0.0682406\pi\) |
−0.304311 | + | 0.952573i | \(0.598426\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 25.9808 | + | 15.0000i | 1.24568 | + | 0.719195i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −41.0792 | − | 4.74342i | −1.96508 | − | 0.226908i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.90569 | + | 13.6931i | −0.377318 | + | 0.653534i | −0.990671 | − | 0.136275i | \(-0.956487\pi\) |
0.613353 | + | 0.789809i | \(0.289820\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | + | 15.5885i | 0.428571 | + | 0.742307i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.3109 | − | 17.5000i | 1.44011 | − | 0.831450i | 0.442257 | − | 0.896888i | \(-0.354178\pi\) |
0.997857 | + | 0.0654382i | \(0.0208445\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 25.2982i | − | 1.19925i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.2302 | − | 24.6475i | −0.673068 | − | 1.16579i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.0000 | 0.802280 | 0.401140 | − | 0.916017i | \(-0.368614\pi\) | ||||
0.401140 | + | 0.916017i | \(0.368614\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.79423 | − | 4.50000i | −0.367016 | − | 0.211897i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.21584 | − | 4.74342i | −0.386014 | − | 0.222865i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 63.2456 | 2.96500 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.0000 | −1.45012 | −0.725059 | − | 0.688686i | \(-0.758188\pi\) | ||||
−0.725059 | + | 0.688686i | \(0.758188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 31.1769 | + | 18.0000i | 1.45521 | + | 0.840168i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.3861 | + | 15.8114i | 1.27550 | + | 0.736410i | 0.976017 | − | 0.217692i | \(-0.0698529\pi\) |
0.299482 | + | 0.954102i | \(0.403186\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.6228 | −1.46964 | −0.734818 | − | 0.678265i | \(-0.762732\pi\) | ||||
−0.734818 | + | 0.678265i | \(0.762732\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.0000 | − | 25.9808i | −0.695608 | − | 1.20483i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.0000i | 0.971764i | 0.874024 | + | 0.485882i | \(0.161502\pi\) | ||||
−0.874024 | + | 0.485882i | \(0.838498\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.6931 | − | 7.90569i | 0.632287 | − | 0.365051i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.48683 | + | 16.4317i | 0.437130 | + | 0.757132i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.0000 | + | 25.9808i | −0.689701 | + | 1.19460i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.6506 | − | 2.50000i | −0.993399 | − | 0.114708i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.48683 | + | 16.4317i | 0.433464 | + | 0.750782i | 0.997169 | − | 0.0751941i | \(-0.0239576\pi\) |
−0.563704 | + | 0.825977i | \(0.690624\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.0000 | + | 17.3205i | 0.455961 | + | 0.789747i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 90.0000i | − | 4.09514i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.6475 | − | 14.2302i | 1.11919 | − | 0.646162i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.48683 | −0.429889 | −0.214945 | − | 0.976626i | \(-0.568957\pi\) | ||||
−0.214945 | + | 0.976626i | \(0.568957\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.50000 | − | 12.9904i | 0.339162 | − | 0.587445i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.5885 | + | 9.00000i | 0.703497 | + | 0.406164i | 0.808649 | − | 0.588292i | \(-0.200199\pi\) |
−0.105151 | + | 0.994456i | \(0.533533\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 12.6491i | − | 0.569687i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 56.9210 | 2.55841 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.2583 | + | 6.50000i | 0.503992 | + | 0.290980i | 0.730361 | − | 0.683062i | \(-0.239352\pi\) |
−0.226369 | + | 0.974042i | \(0.572685\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 18.9737i | − | 0.847681i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.58114 | + | 2.73861i | 0.0704995 | + | 0.122109i | 0.899120 | − | 0.437702i | \(-0.144207\pi\) |
−0.828621 | + | 0.559810i | \(0.810874\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.0000 | 1.33498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −70.1481 | + | 40.5000i | −3.11538 | + | 1.79867i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.3861 | + | 15.8114i | −1.21387 | + | 0.700827i | −0.963600 | − | 0.267349i | \(-0.913852\pi\) |
−0.250269 | + | 0.968176i | \(0.580519\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.0680 | − | 19.1703i | 0.489618 | − | 0.848044i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 31.5000 | + | 23.3827i | 1.39076 | + | 1.03237i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.3205 | − | 10.0000i | −0.763233 | − | 0.440653i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.21584 | − | 4.74342i | 0.361332 | − | 0.208615i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.9737 | + | 32.8634i | 0.832851 | + | 1.44254i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.0000 | −1.44576 | −0.722878 | − | 0.690976i | \(-0.757181\pi\) | ||||
−0.722878 | + | 0.690976i | \(0.757181\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.0526 | − | 11.0000i | 0.833110 | − | 0.480996i | −0.0218062 | − | 0.999762i | \(-0.506942\pi\) |
0.854916 | + | 0.518766i | \(0.173608\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 47.4342i | − | 2.07020i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.32456 | + | 10.9545i | −0.275502 | + | 0.477183i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −33.5000 | + | 58.0237i | −1.45652 | + | 2.52277i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 42.0000i | 1.82264i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 18.9737i | − | 0.821841i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.48683 | − | 16.4317i | 0.410152 | − | 0.710403i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.50000 | − | 7.79423i | 0.194189 | − | 0.336346i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 9.00000i | − | 0.387657i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.9089 | + | 12.6491i | −0.941937 | + | 0.543828i | −0.890567 | − | 0.454852i | \(-0.849692\pi\) |
−0.0513702 | + | 0.998680i | \(0.516359\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 28.4605 | 1.22136 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.0000 | + | 51.9615i | 1.28506 | + | 2.22579i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.5167 | + | 13.0000i | −0.962743 | + | 0.555840i | −0.897016 | − | 0.441998i | \(-0.854270\pi\) |
−0.0657267 | + | 0.997838i | \(0.520937\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.4317 | − | 9.48683i | −0.701287 | − | 0.404888i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.58114 | − | 13.6931i | 0.0673588 | − | 0.583344i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.0000 | − | 17.3205i | 0.425243 | − | 0.736543i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 25.9808 | − | 15.0000i | 1.10282 | − | 0.636715i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.4317 | + | 9.48683i | −0.696232 | + | 0.401970i | −0.805943 | − | 0.591994i | \(-0.798341\pi\) |
0.109710 | + | 0.993964i | \(0.465008\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −63.2456 | −2.67500 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.0000 | − | 31.1769i | −0.759961 | − | 1.31629i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.00000i | 0.126435i | 0.998000 | + | 0.0632175i | \(0.0201362\pi\) | ||||
−0.998000 | + | 0.0632175i | \(0.979864\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −35.6020 | − | 20.5548i | −1.49779 | − | 0.864747i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.2302 | + | 24.6475i | −0.597614 | + | 1.03510i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.0000 | 0.503066 | 0.251533 | − | 0.967849i | \(-0.419065\pi\) | ||||
0.251533 | + | 0.967849i | \(0.419065\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 29.0000i | − | 1.21361i | −0.794850 | − | 0.606806i | \(-0.792450\pi\) | ||
0.794850 | − | 0.606806i | \(-0.207550\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.4317 | + | 9.48683i | 0.686443 | + | 0.396318i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.7171 | + | 41.0792i | −0.989071 | + | 1.71312i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.0000 | −1.87337 | −0.936687 | − | 0.350167i | \(-0.886125\pi\) | ||||
−0.936687 | + | 0.350167i | \(0.886125\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.7846 | − | 12.0000i | 0.863779 | − | 0.498703i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.1359i | 0.918354i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 60.0000 | + | 103.923i | 2.48069 | + | 4.29669i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.4449 | − | 17.0000i | −1.21532 | − | 0.701665i | −0.251406 | − | 0.967882i | \(-0.580893\pi\) |
−0.963913 | + | 0.266217i | \(0.914226\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.21584 | + | 11.0680i | −0.338528 | + | 0.456048i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −33.2039 | + | 57.5109i | −1.36583 | + | 2.36568i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.5000 | + | 30.3109i | 0.718639 | + | 1.24472i | 0.961539 | + | 0.274668i | \(0.0885679\pi\) |
−0.242900 | + | 0.970051i | \(0.578099\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −34.6410 | + | 20.0000i | −1.42014 | + | 0.819920i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.9737i | 0.776540i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.2302 | − | 24.6475i | −0.581432 | − | 1.00707i | −0.995310 | − | 0.0967377i | \(-0.969159\pi\) |
0.413878 | − | 0.910333i | \(-0.364174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.0000 | −1.26452 | −0.632258 | − | 0.774758i | \(-0.717872\pi\) | ||||
−0.632258 | + | 0.774758i | \(0.717872\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.9808 | + | 15.0000i | 1.05802 | + | 0.610847i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.47723 | + | 3.16228i | 0.222681 | + | 0.128565i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.1359 | 0.898470 | 0.449235 | − | 0.893414i | \(-0.351697\pi\) | ||||
0.449235 | + | 0.893414i | \(0.351697\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 30.0000 | 1.21566 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.3205 | + | 10.0000i | 0.700713 | + | 0.404557i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.4317 | − | 9.48683i | −0.663669 | − | 0.383170i | 0.130004 | − | 0.991513i | \(-0.458501\pi\) |
−0.793674 | + | 0.608344i | \(0.791834\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −28.4605 | −1.14764 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.5000 | + | 18.1865i | 0.422714 | + | 0.732162i | 0.996204 | − | 0.0870504i | \(-0.0277441\pi\) |
−0.573490 | + | 0.819213i | \(0.694411\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 14.0000i | − | 0.562708i | −0.959604 | − | 0.281354i | \(-0.909217\pi\) | ||
0.959604 | − | 0.281354i | \(-0.0907834\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 73.9425 | − | 42.6907i | 2.96721 | − | 1.71312i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.6491 | − | 21.9089i | −0.506776 | − | 0.877762i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5000 | − | 21.6506i | 0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.5885 | − | 36.0000i | −0.622543 | − | 1.43770i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.9545 | − | 6.32456i | −0.436783 | − | 0.252177i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.58114 | + | 2.73861i | 0.0629441 | + | 0.109022i | 0.895780 | − | 0.444497i | \(-0.146618\pi\) |
−0.832836 | + | 0.553520i | \(0.813284\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.0000 | + | 41.5692i | 0.953914 | + | 1.65223i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 20.0000i | − | 0.793676i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.4317 | − | 9.48683i | 0.651047 | − | 0.375882i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.50000 | − | 9.52628i | 0.217237 | − | 0.376265i | −0.736725 | − | 0.676192i | \(-0.763629\pi\) |
0.953962 | + | 0.299927i | \(0.0969622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.2391 | − | 21.5000i | −1.46857 | − | 0.847877i | −0.469187 | − | 0.883099i | \(-0.655453\pi\) |
−0.999380 | + | 0.0352216i | \(0.988786\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 94.8683i | 3.73544i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.2982 | −0.994576 | −0.497288 | − | 0.867586i | \(-0.665671\pi\) | ||||
−0.497288 | + | 0.867586i | \(0.665671\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.5000 | − | 18.1865i | 0.412161 | − | 0.713884i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.9808 | − | 15.0000i | −1.01827 | − | 0.587896i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.2302 | + | 24.6475i | 0.556022 | + | 0.963058i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 42.0000 | 1.63858 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.5885 | − | 9.00000i | 0.607240 | − | 0.350590i | −0.164644 | − | 0.986353i | \(-0.552648\pi\) |
0.771885 | + | 0.635763i | \(0.219314\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.6931 | + | 7.90569i | −0.532598 | + | 0.307496i | −0.742074 | − | 0.670318i | \(-0.766158\pi\) |
0.209475 | + | 0.977814i | \(0.432824\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 37.9473 | − | 65.7267i | 1.47375 | − | 2.55261i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −40.0000 | + | 17.3205i | −1.55113 | + | 0.671660i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.9808 | − | 15.0000i | −1.00598 | − | 0.580802i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −41.0792 | + | 23.7171i | −1.58821 | + | 0.916955i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.74342 | + | 8.21584i | 0.183118 | + | 0.317169i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.0000 | −0.770943 | −0.385472 | − | 0.922720i | \(-0.625961\pi\) | ||||
−0.385472 | + | 0.922720i | \(0.625961\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 38.9711 | − | 22.5000i | 1.50000 | − | 0.866025i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.6228i | 1.21536i | 0.794181 | + | 0.607681i | \(0.207900\pi\) | ||||
−0.794181 | + | 0.607681i | \(0.792100\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.2302 | − | 24.6475i | 0.546107 | − | 0.945885i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.5000 | − | 28.5788i | 0.632281 | − | 1.09514i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 38.0000i | − | 1.45403i | −0.686622 | − | 0.727015i | \(-0.740907\pi\) | ||
0.686622 | − | 0.727015i | \(-0.259093\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.4605i | 1.08742i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 37.9473 | − | 65.7267i | 1.44778 | − | 2.50763i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 6.00000i | − | 0.228251i | −0.993466 | − | 0.114125i | \(-0.963593\pi\) | ||
0.993466 | − | 0.114125i | \(-0.0364066\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 49.2950 | − | 28.4605i | 1.87256 | − | 1.08112i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −34.7851 | −1.31947 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.00000 | + | 10.3923i | 0.227266 | + | 0.393637i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.79423 | + | 4.50000i | −0.294805 | + | 0.170206i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.6020 | + | 20.5548i | 1.34467 | + | 0.776344i | 0.987488 | − | 0.157692i | \(-0.0504052\pi\) |
0.357179 | + | 0.934036i | \(0.383739\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.0680 | − | 8.21584i | −0.417436 | − | 0.309866i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.0000 | − | 25.9808i | 0.564933 | − | 0.978492i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.9808 | − | 15.0000i | 0.977107 | − | 0.564133i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.6931 | − | 7.90569i | 0.514254 | − | 0.296905i | −0.220327 | − | 0.975426i | \(-0.570712\pi\) |
0.734580 | + | 0.678522i | \(0.237379\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 37.9473 | 1.42314 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.0000 | + | 25.9808i | 0.561754 | + | 0.972987i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 60.0000i | − | 2.24387i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.4317 | − | 9.48683i | −0.613652 | − | 0.354292i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.9737 | − | 32.8634i | 0.707598 | − | 1.22560i | −0.258147 | − | 0.966106i | \(-0.583112\pi\) |
0.965746 | − | 0.259491i | \(-0.0835547\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.0000 | −0.744839 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 39.0000i | 1.45043i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.6931 | − | 7.90569i | −0.508548 | − | 0.293610i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.1359 | − | 38.3406i | 0.820977 | − | 1.42197i | −0.0839790 | − | 0.996468i | \(-0.526763\pi\) |
0.904956 | − | 0.425506i | \(-0.139904\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.6410 | − | 20.0000i | 1.28124 | − | 0.739727i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 41.1096i | − | 1.51842i | −0.650847 | − | 0.759209i | \(-0.725586\pi\) | ||
0.650847 | − | 0.759209i | \(-0.274414\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.2302 | − | 24.6475i | −0.524891 | − | 0.909137i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.50000 | − | 12.9904i | −0.276266 | − | 0.478507i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.2583 | − | 6.50000i | −0.414144 | − | 0.239106i | 0.278425 | − | 0.960458i | \(-0.410188\pi\) |
−0.692569 | + | 0.721352i | \(0.743521\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 49.2950 | − | 66.4078i | 1.81090 | − | 2.43955i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.2302 | − | 24.6475i | 0.522057 | − | 0.904230i | −0.477614 | − | 0.878570i | \(-0.658498\pi\) |
0.999671 | − | 0.0256596i | \(-0.00816860\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.0000 | + | 25.9808i | 0.549557 | + | 0.951861i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −36.3731 | + | 21.0000i | −1.33082 | + | 0.768350i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 18.9737i | − | 0.693283i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.2982 | + | 43.8178i | 0.923145 | + | 1.59893i | 0.794517 | + | 0.607241i | \(0.207724\pi\) |
0.128628 | + | 0.991693i | \(0.458943\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.0000 | −0.765283 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.66025 | + | 5.00000i | 0.315179 | + | 0.181969i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.9089 | + | 12.6491i | 0.796293 | + | 0.459740i | 0.842173 | − | 0.539207i | \(-0.181276\pi\) |
−0.0458805 | + | 0.998947i | \(0.514609\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −85.3815 | −3.09915 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.0000 | −0.616250 | −0.308125 | − | 0.951346i | \(-0.599701\pi\) | ||||
−0.308125 | + | 0.951346i | \(0.599701\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 51.9615 | + | 30.0000i | 1.88113 | + | 1.08607i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −65.7267 | − | 37.9473i | −2.37635 | − | 1.37199i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 44.2719 | 1.59857 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.00000 | − | 6.92820i | −0.144244 | − | 0.249837i | 0.784847 | − | 0.619690i | \(-0.212742\pi\) |
−0.929091 | + | 0.369852i | \(0.879408\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 63.0000i | 2.26889i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.1247 | − | 17.3925i | 1.08351 | − | 0.625566i | 0.151670 | − | 0.988431i | \(-0.451535\pi\) |
0.931842 | + | 0.362865i | \(0.118202\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.90569 | + | 13.6931i | 0.283981 | + | 0.491869i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.0000 | − | 25.9808i | 0.538122 | − | 0.932055i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.19615 | + | 12.0000i | 0.186171 | + | 0.429945i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.2302 | + | 24.6475i | 0.508548 | + | 0.880830i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.0000 | − | 17.3205i | −0.356915 | − | 0.618195i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.0000i | 1.10503i | 0.833503 | + | 0.552515i | \(0.186332\pi\) | ||||
−0.833503 | + | 0.552515i | \(0.813668\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.6475 | + | 14.2302i | −0.877475 | + | 0.506610i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −41.1096 | −1.46169 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.0000 | + | 17.3205i | −0.355110 | + | 0.615069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.4605i | 1.00812i | 0.863668 | + | 0.504061i | \(0.168161\pi\) | ||||
−0.863668 | + | 0.504061i | \(0.831839\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.6491 | −0.447493 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.0000 | − | 41.5692i | 0.847998 | − | 1.46878i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.1865 | − | 10.5000i | −0.641789 | − | 0.370537i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 94.8683i | 3.34367i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 37.9473 | + | 65.7267i | 1.33581 | + | 2.31369i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.0000 | 0.457056 | 0.228528 | − | 0.973537i | \(-0.426609\pi\) | ||||
0.228528 | + | 0.973537i | \(0.426609\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.73205 | − | 1.00000i | 0.0608205 | − | 0.0351147i | −0.469281 | − | 0.883049i | \(-0.655487\pi\) |
0.530102 | + | 0.847934i | \(0.322154\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −57.5109 | + | 33.2039i | −2.01699 | + | 1.16451i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.90569 | + | 13.6931i | −0.276924 | + | 0.479647i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40.0000 | − | 17.3205i | 1.39942 | − | 0.605968i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 103.923 | + | 60.0000i | 3.63137 | + | 2.09657i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.9089 | − | 12.6491i | 0.764626 | − | 0.441457i | −0.0663282 | − | 0.997798i | \(-0.521128\pi\) |
0.830954 | + | 0.556341i | \(0.187795\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −45.0000 | −1.56670 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.33013 | + | 2.50000i | −0.150573 | + | 0.0869335i | −0.573394 | − | 0.819280i | \(-0.694373\pi\) |
0.422820 | + | 0.906213i | \(0.361040\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.6491i | 0.439322i | 0.975576 | + | 0.219661i | \(0.0704951\pi\) | ||||
−0.975576 | + | 0.219661i | \(0.929505\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −42.6907 | + | 73.9425i | −1.48093 | + | 2.56504i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.00000 | + | 10.3923i | −0.207888 | + | 0.360072i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.0000i | 0.692129i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 28.4605i | − | 0.983739i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.3925 | + | 30.1247i | −0.600457 | + | 1.04002i | 0.392295 | + | 0.919839i | \(0.371681\pi\) |
−0.992752 | + | 0.120182i | \(0.961652\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.50000 | + | 16.4545i | −0.327586 | + | 0.567396i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 57.0000i | − | 1.96318i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 73.9425 | − | 42.6907i | 2.54370 | − | 1.46861i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.32456 | 0.217314 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.5000 | + | 38.9711i | 0.772198 | + | 1.33749i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.9808 | + | 15.0000i | −0.890609 | + | 0.514193i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.47723 | + | 3.16228i | 0.187537 | + | 0.108274i | 0.590829 | − | 0.806797i | \(-0.298801\pi\) |
−0.403292 | + | 0.915071i | \(0.632134\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −66.4078 | − | 49.2950i | −2.27110 | − | 1.68585i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.5000 | + | 30.3109i | −0.597789 | + | 1.03540i | 0.395358 | + | 0.918527i | \(0.370620\pi\) |
−0.993147 | + | 0.116873i | \(0.962713\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.9186 | − | 11.5000i | 0.679613 | − | 0.392375i | −0.120096 | − | 0.992762i | \(-0.538320\pi\) |
0.799709 | + | 0.600387i | \(0.204987\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −24.6475 | + | 14.2302i | −0.839985 | + | 0.484966i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −53.7587 | −1.82997 | −0.914984 | − | 0.403490i | \(-0.867797\pi\) | ||||
−0.914984 | + | 0.403490i | \(0.867797\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.0000 | − | 34.6410i | −0.680020 | − | 1.17783i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 3.00000i | − | 0.101885i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.4317 | − | 9.48683i | −0.557406 | − | 0.321819i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.8114 | − | 27.3861i | 0.535748 | − | 0.927944i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 54.0000 | 1.82762 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.73861 | + | 1.58114i | 0.0924764 | + | 0.0533913i | 0.545525 | − | 0.838095i | \(-0.316330\pi\) |
−0.453049 | + | 0.891486i | \(0.649664\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.7171 | − | 41.0792i | 0.799957 | − | 1.38557i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −59.0000 | −1.98776 | −0.993880 | − | 0.110463i | \(-0.964767\pi\) | ||||
−0.993880 | + | 0.110463i | \(0.964767\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.2391 | − | 21.5000i | 1.25320 | − | 0.723533i | 0.281453 | − | 0.959575i | \(-0.409184\pi\) |
0.971743 | + | 0.236043i | \(0.0758505\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 66.4078i | − | 2.23227i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.16228 | − | 5.47723i | −0.106179 | − | 0.183907i | 0.808040 | − | 0.589127i | \(-0.200528\pi\) |
−0.914219 | + | 0.405220i | \(0.867195\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.0000 | − | 17.3205i | −0.335389 | − | 0.580911i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.3827 | + | 13.5000i | 0.783349 | + | 0.452267i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.6931 | − | 1.58114i | −0.458221 | − | 0.0529108i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.74342 | + | 8.21584i | −0.158555 | + | 0.274625i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −90.0000 | − | 155.885i | −3.00501 | − | 5.20483i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.66025 | + | 5.00000i | −0.288836 | + | 0.166759i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 47.4342 | + | 82.1584i | 1.57851 | + | 2.73406i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.0000 | −0.997234 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.866025 | − | 0.500000i | −0.0287559 | − | 0.0166022i | 0.485553 | − | 0.874207i | \(-0.338618\pi\) |
−0.514309 | + | 0.857605i | \(0.671952\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 49.2950 | + | 28.4605i | 1.63501 | + | 0.943975i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.4605 | 0.942938 | 0.471469 | − | 0.881883i | \(-0.343724\pi\) | ||||
0.471469 | + | 0.881883i | \(0.343724\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.0000 | 0.694999 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 25.9808 | + | 15.0000i | 0.858898 | + | 0.495885i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.6475 | + | 14.2302i | 0.813933 | + | 0.469924i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.6228 | 1.04314 | 0.521570 | − | 0.853209i | \(-0.325347\pi\) | ||||
0.521570 | + | 0.853209i | \(0.325347\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.5000 | + | 54.5596i | 1.03796 | + | 1.79780i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.6931 | + | 7.90569i | −0.450225 | + | 0.259938i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.9737 | − | 32.8634i | −0.623177 | − | 1.07937i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.50000 | − | 11.2583i | 0.213258 | − | 0.369374i | −0.739474 | − | 0.673185i | \(-0.764926\pi\) |
0.952732 | + | 0.303811i | \(0.0982592\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.79423 | + | 10.5000i | −0.255446 | + | 0.344124i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −57.5109 | − | 33.2039i | −1.88282 | − | 1.08705i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.9737 | + | 32.8634i | 0.620505 | + | 1.07475i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.500000 | − | 0.866025i | −0.0163343 | − | 0.0282918i | 0.857743 | − | 0.514079i | \(-0.171866\pi\) |
−0.874077 | + | 0.485787i | \(0.838533\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 9.00000i | − | 0.293704i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.4605 | 0.926801 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 45.0000 | − | 77.9423i | 1.46385 | − | 2.53546i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.9808 | + | 15.0000i | 0.844261 | + | 0.487435i | 0.858710 | − | 0.512461i | \(-0.171266\pi\) |
−0.0144491 | + | 0.999896i | \(0.504599\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 44.2719i | − | 1.43713i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 94.8683 | 3.07632 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.50000 | − | 12.9904i | 0.242949 | − | 0.420800i | −0.718604 | − | 0.695419i | \(-0.755219\pi\) |
0.961553 | + | 0.274620i | \(0.0885520\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.3205 | − | 10.0000i | −0.560478 | − | 0.323592i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 28.4605i | − | 0.919997i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.2302 | + | 24.6475i | 0.459519 | + | 0.795910i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.0000 | −0.677419 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31.1769 | − | 18.0000i | 1.00466 | − | 0.580042i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.9089 | + | 12.6491i | −0.705273 | + | 0.407189i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.16228 | − | 5.47723i | 0.101692 | − | 0.176136i | −0.810690 | − | 0.585476i | \(-0.800908\pi\) |
0.912382 | + | 0.409340i | \(0.134241\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.00000 | + | 51.9615i | −0.192748 | + | 1.66924i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.866025 | − | 0.500000i | −0.0277921 | − | 0.0160458i | 0.486040 | − | 0.873937i | \(-0.338441\pi\) |
−0.513832 | + | 0.857891i | \(0.671774\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30.1247 | + | 17.3925i | −0.965755 | + | 0.557579i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −47.4342 | − | 82.1584i | −1.51911 | − | 2.63117i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35.0000 | 1.11975 | 0.559875 | − | 0.828577i | \(-0.310849\pi\) | ||||
0.559875 | + | 0.828577i | \(0.310849\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.7846 | + | 12.0000i | −0.664279 | + | 0.383522i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 113.842i | 3.63470i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.9737 | + | 32.8634i | −0.605166 | + | 1.04818i | 0.386859 | + | 0.922139i | \(0.373560\pi\) |
−0.992025 | + | 0.126039i | \(0.959773\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.0000 | − | 60.6218i | 1.11519 | − | 1.93157i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 30.0000i | − | 0.954911i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 94.8683i | − | 3.01664i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.6491 | − | 21.9089i | 0.401812 | − | 0.695959i | −0.592132 | − | 0.805841i | \(-0.701714\pi\) |
0.993945 | + | 0.109881i | \(0.0350471\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −43.5000 | + | 75.3442i | −1.38043 | + | 2.39098i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 20.0000i | − | 0.634043i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.6020 | + | 20.5548i | −1.12753 | + | 0.650977i | −0.943311 | − | 0.331909i | \(-0.892307\pi\) |
−0.184214 | + | 0.982886i | \(0.558974\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 28.4605 | 0.900450 |
(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 | 1216.2.t.b.353.2 | yes | 8 | |
4.3 | odd | 2 | inner | 1216.2.t.b.353.4 | yes | 8 | |
8.3 | odd | 2 | inner | 1216.2.t.b.353.1 | ✓ | 8 | |
8.5 | even | 2 | inner | 1216.2.t.b.353.3 | yes | 8 | |
19.7 | even | 3 | inner | 1216.2.t.b.1185.3 | yes | 8 | |
76.7 | odd | 6 | inner | 1216.2.t.b.1185.1 | yes | 8 | |
152.45 | even | 6 | inner | 1216.2.t.b.1185.2 | yes | 8 | |
152.83 | odd | 6 | inner | 1216.2.t.b.1185.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.t.b.353.1 | ✓ | 8 | 8.3 | odd | 2 | inner | |
1216.2.t.b.353.2 | yes | 8 | 1.1 | even | 1 | trivial | |
1216.2.t.b.353.3 | yes | 8 | 8.5 | even | 2 | inner | |
1216.2.t.b.353.4 | yes | 8 | 4.3 | odd | 2 | inner | |
1216.2.t.b.1185.1 | yes | 8 | 76.7 | odd | 6 | inner | |
1216.2.t.b.1185.2 | yes | 8 | 152.45 | even | 6 | inner | |
1216.2.t.b.1185.3 | yes | 8 | 19.7 | even | 3 | inner | |
1216.2.t.b.1185.4 | yes | 8 | 152.83 | odd | 6 | inner |