Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [520,2,Mod(19,520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(520, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 6, 6, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("520.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 520 = 2^{3} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 520.cz (of order \(12\), degree \(4\), 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: | \(4.15222090511\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
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: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{12}]$ |
Embedding invariants
Embedding label | 379.2 | ||
Root | \(0.578737 + 2.15988i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 520.379 |
Dual form | 520.2.cz.a.59.2 |
$q$-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 \(\left(\mathbb{Z}/520\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(261\) | \(391\) | \(417\) |
\(\chi(n)\) | \(e\left(\frac{1}{12}\right)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36603 | − | 0.366025i | −0.965926 | − | 0.258819i | ||||
\(3\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(4\) | 1.73205 | + | 1.00000i | 0.866025 | + | 0.500000i | ||||
\(5\) | 1.58114 | − | 1.58114i | 0.707107 | − | 0.707107i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.52590 | − | 1.21271i | 1.71063 | − | 0.458362i | 0.735051 | − | 0.678012i | \(-0.237158\pi\) |
0.975579 | + | 0.219650i | \(0.0704915\pi\) | |||||||
\(8\) | −2.00000 | − | 2.00000i | −0.707107 | − | 0.707107i | ||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | −2.73861 | + | 1.58114i | −0.866025 | + | 0.500000i | ||||
\(11\) | 0.923665 | − | 3.44716i | 0.278495 | − | 1.03936i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.42783 | − | 3.31079i | 0.396007 | − | 0.918247i | ||||
\(14\) | −6.62638 | −1.77097 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.707107 | − | 0.707107i | ||||
\(19\) | 1.17922 | + | 4.40089i | 0.270530 | + | 1.00963i | 0.958778 | + | 0.284157i | \(0.0917138\pi\) |
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | 4.31975 | − | 1.15747i | 0.965926 | − | 0.258819i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.52350 | + | 4.37083i | −0.538012 | + | 0.931864i | ||||
\(23\) | −7.93477 | + | 4.58114i | −1.65451 | + | 0.955233i | −0.679330 | + | 0.733833i | \(0.737729\pi\) |
−0.975183 | + | 0.221401i | \(0.928937\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 5.00000i | − | 1.00000i | ||||||
\(26\) | −3.16228 | + | 4.00000i | −0.620174 | + | 0.784465i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.05180 | + | 2.42542i | 1.71063 | + | 0.458362i | ||||
\(29\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(32\) | −1.46410 | − | 5.46410i | −0.258819 | − | 0.965926i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.23861 | − | 9.07354i | 0.885487 | − | 1.53371i | ||||
\(36\) | −5.19615 | + | 3.00000i | −0.866025 | + | 0.500000i | ||||
\(37\) | 0.461700 | − | 1.72309i | 0.0759030 | − | 0.283274i | −0.917534 | − | 0.397658i | \(-0.869823\pi\) |
0.993437 | + | 0.114385i | \(0.0364896\pi\) | |||||||
\(38\) | − | 6.44335i | − | 1.04525i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.32456 | −1.00000 | ||||||||
\(41\) | 7.27348 | + | 1.94892i | 1.13593 | + | 0.304371i | 0.777312 | − | 0.629115i | \(-0.216583\pi\) |
0.358614 | + | 0.933486i | \(0.383249\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(44\) | 5.04700 | − | 5.04700i | 0.760864 | − | 0.760864i | ||||
\(45\) | 1.73621 | + | 6.47963i | 0.258819 | + | 0.965926i | ||||
\(46\) | 12.5159 | − | 3.35363i | 1.84537 | − | 0.494465i | ||||
\(47\) | −9.21584 | − | 9.21584i | −1.34427 | − | 1.34427i | −0.891761 | − | 0.452508i | \(-0.850530\pi\) |
−0.452508 | − | 0.891761i | \(-0.649470\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.9509 | − | 7.47723i | 1.85013 | − | 1.06818i | ||||
\(50\) | −1.83013 | + | 6.83013i | −0.258819 | + | 0.965926i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.78385 | − | 4.30663i | 0.802076 | − | 0.597222i | ||||
\(53\) | 14.4234 | 1.98120 | 0.990600 | − | 0.136789i | \(-0.0436783\pi\) | ||||
0.990600 | + | 0.136789i | \(0.0436783\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.99000 | − | 6.91089i | −0.538012 | − | 0.931864i | ||||
\(56\) | −11.4772 | − | 6.62638i | −1.53371 | − | 0.885487i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.24243 | + | 1.40470i | −0.682506 | + | 0.182877i | −0.583382 | − | 0.812198i | \(-0.698271\pi\) |
−0.0991242 | + | 0.995075i | \(0.531604\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.63813 | + | 13.5777i | −0.458362 | + | 1.71063i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −2.97723 | − | 7.49240i | −0.369279 | − | 0.929318i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −10.4772 | + | 10.4772i | −1.25227 | + | 1.25227i | ||||
\(71\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(72\) | 8.19615 | − | 2.19615i | 0.965926 | − | 0.258819i | ||||
\(73\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(74\) | −1.26139 | + | 2.18479i | −0.146633 | + | 0.253976i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.35843 | + | 8.80178i | −0.270530 | + | 1.00963i | ||||
\(77\) | − | 16.7217i | − | 1.90561i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 8.63950 | + | 2.31495i | 0.965926 | + | 0.258819i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | −9.22240 | − | 5.32456i | −1.01844 | − | 0.587999i | ||||
\(83\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.74166 | + | 5.04700i | −0.931864 | + | 0.538012i | ||||
\(89\) | −4.10010 | + | 15.3018i | −0.434610 | + | 1.62199i | 0.307389 | + | 0.951584i | \(0.400545\pi\) |
−0.741999 | + | 0.670402i | \(0.766122\pi\) | |||||||
\(90\) | − | 9.48683i | − | 1.00000i | ||||||
\(91\) | 2.44716 | − | 16.7158i | 0.256533 | − | 1.75230i | ||||
\(92\) | −18.3246 | −1.91047 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.21584 | + | 15.9623i | 0.950541 | + | 1.64639i | ||||
\(95\) | 8.82292 | + | 5.09392i | 0.905213 | + | 0.522625i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(98\) | −20.4282 | + | 5.47371i | −2.06356 | + | 0.552928i | ||||
\(99\) | 7.57050 | + | 7.57050i | 0.760864 | + | 0.760864i | ||||
\(100\) | 5.00000 | − | 8.66025i | 0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 20.2818i | 1.99843i | 0.0396400 | + | 0.999214i | \(0.487379\pi\) | ||||
−0.0396400 | + | 0.999214i | \(0.512621\pi\) | |||||||
\(104\) | −9.47723 | + | 3.76593i | −0.929318 | + | 0.369279i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −19.7027 | − | 5.27931i | −1.91369 | − | 0.512772i | ||||
\(107\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(110\) | 2.92088 | + | 10.9009i | 0.278495 | + | 1.03936i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 13.2528 | + | 13.2528i | 1.25227 | + | 1.25227i | ||||
\(113\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.30255 | + | 19.7894i | −0.494465 | + | 1.84537i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.45994 | + | 8.67578i | 0.597222 | + | 0.802076i | ||||
\(118\) | 7.67544 | 0.706582 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.50351 | − | 0.868049i | −0.136682 | − | 0.0789135i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.90569 | − | 7.90569i | −0.707107 | − | 0.707107i | ||||
\(126\) | 9.93957 | − | 17.2158i | 0.885487 | − | 1.53371i | ||||
\(127\) | −18.0711 | + | 10.4334i | −1.60355 | + | 0.925810i | −0.612781 | + | 0.790253i | \(0.709949\pi\) |
−0.990769 | + | 0.135558i | \(0.956717\pi\) | |||||||
\(128\) | 2.92820 | − | 10.9282i | 0.258819 | − | 0.965926i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.32456 | + | 11.3246i | 0.116171 | + | 0.993229i | ||||
\(131\) | 15.8903 | 1.38834 | 0.694170 | − | 0.719811i | \(-0.255772\pi\) | ||||
0.694170 | + | 0.719811i | \(0.255772\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.6740 | + | 18.4879i | 0.925555 | + | 1.60311i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.31876 | + | 2.28416i | −0.111856 | + | 0.193740i | −0.916519 | − | 0.399992i | \(-0.869013\pi\) |
0.804663 | + | 0.593732i | \(0.202346\pi\) | |||||||
\(140\) | 18.1471 | − | 10.4772i | 1.53371 | − | 0.885487i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.0940 | − | 7.98001i | −0.844102 | − | 0.667322i | ||||
\(144\) | −12.0000 | −1.00000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.52277 | − | 2.52277i | 0.207371 | − | 0.207371i | ||||
\(149\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(152\) | 6.44335 | − | 11.1602i | 0.522625 | − | 0.905213i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.12055 | + | 22.8422i | −0.493208 | + | 1.84068i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.14083 | −0.410283 | −0.205142 | − | 0.978732i | \(-0.565765\pi\) | ||||
−0.205142 | + | 0.978732i | \(0.565765\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.9545 | − | 6.32456i | −0.866025 | − | 0.500000i | ||||
\(161\) | −30.3564 | + | 30.3564i | −2.39242 | + | 2.39242i | ||||
\(162\) | 3.29423 | + | 12.2942i | 0.258819 | + | 0.965926i | ||||
\(163\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(164\) | 10.6491 | + | 10.6491i | 0.831556 | + | 0.831556i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.29663 | + | 16.0352i | −0.332483 | + | 1.24084i | 0.574089 | + | 0.818793i | \(0.305356\pi\) |
−0.906572 | + | 0.422051i | \(0.861310\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.92263 | − | 9.45445i | −0.686356 | − | 0.727265i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.2027 | − | 3.53765i | −1.00963 | − | 0.270530i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.9354 | − | 12.6644i | −1.66772 | − | 0.962858i | −0.968864 | − | 0.247593i | \(-0.920360\pi\) |
−0.698854 | − | 0.715264i | \(-0.746306\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.06356 | − | 22.6295i | −0.458362 | − | 1.71063i | ||||
\(176\) | 13.7887 | − | 3.69466i | 1.03936 | − | 0.278495i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.2017 | − | 19.4019i | 0.839601 | − | 1.45423i | ||||
\(179\) | −5.47723 | + | 3.16228i | −0.409387 | + | 0.236360i | −0.690526 | − | 0.723307i | \(-0.742621\pi\) |
0.281139 | + | 0.959667i | \(0.409288\pi\) | |||||||
\(180\) | −3.47242 | + | 12.9593i | −0.258819 | + | 0.965926i | ||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | −9.46131 | + | 21.9385i | −0.701319 | + | 1.62619i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 25.0318 | + | 6.70725i | 1.84537 | + | 0.494465i | ||||
\(185\) | −1.99443 | − | 3.45445i | −0.146633 | − | 0.253976i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.74646 | − | 25.1781i | −0.492036 | − | 1.83630i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.1878 | − | 10.1878i | −0.739103 | − | 0.739103i | ||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 29.9089 | 2.13635 | ||||||||
\(197\) | 26.9012 | + | 7.20816i | 1.91663 | + | 0.513560i | 0.990740 | + | 0.135775i | \(0.0433525\pi\) |
0.925893 | + | 0.377785i | \(0.123314\pi\) | |||||||
\(198\) | −7.57050 | − | 13.1125i | −0.538012 | − | 0.931864i | ||||
\(199\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | −10.0000 | + | 10.0000i | −0.707107 | + | 0.707107i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.5819 | − | 8.41886i | 1.01844 | − | 0.587999i | ||||
\(206\) | 7.42366 | − | 27.7055i | 0.517231 | − | 1.93033i | ||||
\(207\) | − | 27.4868i | − | 1.91047i | ||||||
\(208\) | 14.3246 | − | 1.67544i | 0.993229 | − | 0.116171i | ||||
\(209\) | 16.2598 | 1.12471 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.71584 | + | 4.70397i | 0.186966 | + | 0.323835i | 0.944237 | − | 0.329266i | \(-0.106801\pi\) |
−0.757271 | + | 0.653101i | \(0.773468\pi\) | |||||||
\(212\) | 24.9820 | + | 14.4234i | 1.71577 | + | 0.990600i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 15.9600i | − | 1.07602i | ||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.14290 | + | 2.44983i | 0.612254 | + | 0.164053i | 0.551604 | − | 0.834106i | \(-0.314016\pi\) |
0.0606498 | + | 0.998159i | \(0.480683\pi\) | |||||||
\(224\) | −13.2528 | − | 22.9545i | −0.885487 | − | 1.53371i | ||||
\(225\) | 12.9904 | + | 7.50000i | 0.866025 | + | 0.500000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(230\) | 14.4868 | − | 25.0919i | 0.955233 | − | 1.65451i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | −5.64889 | − | 14.2158i | −0.369279 | − | 0.929318i | ||||
\(235\) | −29.1430 | −1.90108 | ||||||||
\(236\) | −10.4849 | − | 2.80941i | −0.682506 | − | 0.182877i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.4697 | + | 2.80534i | −0.674411 | + | 0.180708i | −0.579741 | − | 0.814801i | \(-0.696846\pi\) |
−0.0946700 | + | 0.995509i | \(0.530180\pi\) | |||||||
\(242\) | 1.73610 | + | 1.73610i | 0.111601 | + | 0.111601i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.65469 | − | 32.2998i | 0.552928 | − | 2.06356i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.2541 | + | 2.37957i | 1.03423 | + | 0.151408i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.90569 | + | 13.6931i | 0.500000 | + | 0.866025i | ||||
\(251\) | −22.8511 | − | 13.1931i | −1.44235 | − | 0.832739i | −0.444340 | − | 0.895858i | \(-0.646562\pi\) |
−0.998006 | + | 0.0631194i | \(0.979895\pi\) | |||||||
\(252\) | −19.8791 | + | 19.8791i | −1.25227 | + | 1.25227i | ||||
\(253\) | 8.46287 | + | 31.5839i | 0.532056 | + | 1.98566i | ||||
\(254\) | 28.5045 | − | 7.63774i | 1.78853 | − | 0.479235i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.35843i | − | 0.519368i | ||||||
\(260\) | 2.33570 | − | 15.9545i | 0.144854 | − | 0.989453i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −21.7065 | − | 5.81625i | −1.34103 | − | 0.359329i | ||||
\(263\) | −0.0469174 | − | 0.0812633i | −0.00289305 | − | 0.00501091i | 0.864575 | − | 0.502503i | \(-0.167588\pi\) |
−0.867468 | + | 0.497492i | \(0.834254\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.8053 | − | 22.8053i | 1.40092 | − | 1.40092i | ||||
\(266\) | −7.81393 | − | 29.1620i | −0.479103 | − | 1.78804i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −17.2358 | − | 4.61832i | −1.03936 | − | 0.278495i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.6512 | − | 13.6550i | −1.42106 | − | 0.820451i | −0.424673 | − | 0.905347i | \(-0.639611\pi\) |
−0.996390 | + | 0.0848955i | \(0.972944\pi\) | |||||||
\(278\) | 2.63752 | − | 2.63752i | 0.158188 | − | 0.158188i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −28.6243 | + | 7.66986i | −1.71063 | + | 0.458362i | ||||
\(281\) | 23.6491 | + | 23.6491i | 1.41079 | + | 1.41079i | 0.754583 | + | 0.656205i | \(0.227839\pi\) |
0.656205 | + | 0.754583i | \(0.272161\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.8678 | + | 14.5955i | 0.642625 | + | 0.863053i | ||||
\(287\) | 35.2825 | 2.08266 | ||||||||
\(288\) | 16.3923 | + | 4.39230i | 0.965926 | + | 0.258819i | ||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.2324 | + | 7.02896i | −1.53251 | + | 0.410636i | −0.923838 | − | 0.382782i | \(-0.874966\pi\) |
−0.608676 | + | 0.793419i | \(0.708299\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.06797 | + | 10.5100i | −0.353291 | + | 0.611918i | ||||
\(296\) | −4.36957 | + | 2.52277i | −0.253976 | + | 0.146633i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.83772 | + | 32.8114i | 0.221941 | + | 1.89753i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.8867 | + | 12.8867i | −0.739103 | + | 0.739103i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(308\) | 16.7217 | − | 28.9628i | 0.952805 | − | 1.65031i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 7.02251 | + | 1.88168i | 0.396303 | + | 0.106189i | ||||
\(315\) | 15.7158 | + | 27.2206i | 0.885487 | + | 1.53371i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.675667 | − | 0.675667i | 0.0379492 | − | 0.0379492i | −0.687878 | − | 0.725827i | \(-0.741457\pi\) |
0.725827 | + | 0.687878i | \(0.241457\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 12.6491 | + | 12.6491i | 0.707107 | + | 0.707107i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 52.5788 | − | 30.3564i | 2.93010 | − | 1.69169i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | − | 18.0000i | − | 1.00000i | ||||||
\(325\) | −16.5539 | − | 7.13913i | −0.918247 | − | 0.396007i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.6491 | − | 18.4448i | −0.587999 | − | 1.01844i | ||||
\(329\) | −52.8861 | − | 30.5338i | −2.91571 | − | 1.68338i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.49314 | − | 9.30453i | −0.137035 | − | 0.511423i | −0.999981 | − | 0.00612670i | \(-0.998050\pi\) |
0.862946 | − | 0.505296i | \(-0.168617\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.78416 | + | 3.78416i | 0.207371 | + | 0.207371i | ||||
\(334\) | 11.7386 | − | 20.3319i | 0.642308 | − | 1.11251i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | 8.72797 | + | 16.1809i | 0.474739 | + | 0.880127i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 16.7403 | + | 9.66503i | 0.905213 | + | 0.522625i | ||||
\(343\) | 26.3546 | − | 26.3546i | 1.42301 | − | 1.42301i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 25.3288 | + | 25.3288i | 1.36169 | + | 1.36169i | ||||
\(347\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(350\) | 33.1319i | 1.77097i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −20.1880 | −1.07602 | ||||||||
\(353\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −22.4034 | + | 22.4034i | −1.18738 | + | 1.18738i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.63950 | − | 2.31495i | 0.456612 | − | 0.122349i | ||||
\(359\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(360\) | 9.48683 | − | 16.4317i | 0.500000 | − | 0.866025i | ||||
\(361\) | −1.52281 | + | 0.879192i | −0.0801477 | + | 0.0462733i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 20.9545 | − | 26.5055i | 1.09831 | − | 1.38927i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.09431 | − | 5.35949i | −0.161521 | − | 0.279763i | 0.773893 | − | 0.633316i | \(-0.218307\pi\) |
−0.935415 | + | 0.353553i | \(0.884973\pi\) | |||||||
\(368\) | −31.7391 | − | 18.3246i | −1.65451 | − | 0.955233i | ||||
\(369\) | −15.9737 | + | 15.9737i | −0.831556 | + | 0.831556i | ||||
\(370\) | 1.46002 | + | 5.44888i | 0.0759030 | + | 0.283274i | ||||
\(371\) | 65.2787 | − | 17.4914i | 3.38910 | − | 0.908107i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.0680 | + | 33.0267i | −0.987302 | + | 1.71006i | −0.356080 | + | 0.934456i | \(0.615887\pi\) |
−0.631222 | + | 0.775602i | \(0.717446\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 36.8634i | 1.90108i | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.2027 | − | 7.02098i | −1.34594 | − | 0.360644i | −0.487306 | − | 0.873231i | \(-0.662020\pi\) |
−0.858635 | + | 0.512588i | \(0.828687\pi\) | |||||||
\(380\) | 10.1878 | + | 17.6458i | 0.522625 | + | 0.905213i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.47242 | + | 12.9593i | 0.177432 | + | 0.662187i | 0.996125 | + | 0.0879542i | \(0.0280329\pi\) |
−0.818692 | + | 0.574233i | \(0.805300\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.4393 | − | 26.4393i | −1.34747 | − | 1.34747i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −40.8563 | − | 10.9474i | −2.06356 | − | 0.552928i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −34.1094 | − | 19.6931i | −1.71841 | − | 0.992122i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.54199 | + | 20.6830i | 0.278495 | + | 1.03936i | ||||
\(397\) | 35.2842 | − | 9.45438i | 1.77086 | − | 0.474502i | 0.781995 | − | 0.623285i | \(-0.214202\pi\) |
0.988870 | + | 0.148783i | \(0.0475356\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.3205 | − | 10.0000i | 0.866025 | − | 0.500000i | ||||
\(401\) | −0.616760 | + | 2.30178i | −0.0307995 | + | 0.114945i | −0.979614 | − | 0.200888i | \(-0.935617\pi\) |
0.948815 | + | 0.315833i | \(0.102284\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.4389 | − | 5.20863i | −0.965926 | − | 0.258819i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.51331 | − | 3.18311i | −0.273285 | − | 0.157781i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.958011 | − | 3.57534i | −0.0473706 | − | 0.176789i | 0.938187 | − | 0.346128i | \(-0.112504\pi\) |
−0.985558 | + | 0.169338i | \(0.945837\pi\) | |||||||
\(410\) | −23.0008 | + | 6.16303i | −1.13593 | + | 0.304371i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20.2818 | + | 35.1292i | −0.999214 | + | 1.73069i | ||||
\(413\) | −22.0232 | + | 12.7151i | −1.08369 | + | 0.625669i | ||||
\(414\) | −10.0609 | + | 37.5477i | −0.494465 | + | 1.84537i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −20.1810 | − | 2.95445i | −0.989453 | − | 0.144854i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −22.2113 | − | 5.95150i | −1.08639 | − | 0.291097i | ||||
\(419\) | 15.8114 | + | 27.3861i | 0.772437 | + | 1.33790i | 0.936224 | + | 0.351404i | \(0.114296\pi\) |
−0.163787 | + | 0.986496i | \(0.552371\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(422\) | −1.98813 | − | 7.41981i | −0.0967807 | − | 0.361191i | ||||
\(423\) | 37.7672 | − | 10.1197i | 1.83630 | − | 0.492036i | ||||
\(424\) | −28.8467 | − | 28.8467i | −1.40092 | − | 1.40092i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −29.5179 | − | 29.5179i | −1.41203 | − | 1.41203i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | −5.84177 | + | 21.8018i | −0.278495 | + | 1.03936i | ||||
\(441\) | 44.8634i | 2.13635i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.7114 | + | 30.6771i | 0.839601 | + | 1.45423i | ||||
\(446\) | −11.5927 | − | 6.69306i | −0.548932 | − | 0.316926i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.70169 | + | 36.2072i | 0.458362 | + | 1.71063i | ||||
\(449\) | 38.0470 | − | 10.1947i | 1.79555 | − | 0.481116i | 0.802280 | − | 0.596948i | \(-0.203620\pi\) |
0.993269 | + | 0.115833i | \(0.0369536\pi\) | |||||||
\(450\) | −15.0000 | − | 15.0000i | −0.707107 | − | 0.707107i | ||||
\(451\) | 13.4365 | − | 23.2727i | 0.632701 | − | 1.09587i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −22.5608 | − | 30.2994i | −1.05766 | − | 1.42046i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −28.9737 | + | 28.9737i | −1.35090 | + | 1.35090i | ||||
\(461\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.8114 | − | 15.8114i | −0.734818 | − | 0.734818i | 0.236752 | − | 0.971570i | \(-0.423917\pi\) |
−0.971570 | + | 0.236752i | \(0.923917\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 2.51317 | + | 21.4868i | 0.116171 | + | 0.993229i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 39.8101 | + | 10.6671i | 1.83630 | + | 0.492036i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.2943 | + | 7.67544i | 0.611918 | + | 0.353291i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.0045 | − | 5.89608i | 1.00963 | − | 0.270530i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.6350 | + | 37.4730i | −0.990600 | + | 1.71577i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.04555 | − | 3.98886i | −0.230057 | − | 0.181876i | ||||
\(482\) | 15.3287 | 0.698202 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.73610 | − | 3.00701i | −0.0789135 | − | 0.136682i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.0431 | + | 41.2134i | 0.500410 | + | 1.86756i | 0.497330 | + | 0.867561i | \(0.334314\pi\) |
0.00308010 | + | 0.999995i | \(0.499020\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −23.6451 | + | 40.9545i | −1.06818 | + | 1.85013i | ||||
\(491\) | −20.6703 | + | 11.9340i | −0.932837 | + | 0.538574i | −0.887708 | − | 0.460407i | \(-0.847703\pi\) |
−0.0451294 | + | 0.998981i | \(0.514370\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −21.3326 | − | 9.19998i | −0.959798 | − | 0.413927i | ||||
\(495\) | 23.9400 | 1.07602 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.1359 | − | 25.1359i | 1.12524 | − | 1.12524i | 0.134298 | − | 0.990941i | \(-0.457122\pi\) |
0.990941 | − | 0.134298i | \(-0.0428781\pi\) | |||||||
\(500\) | −5.78737 | − | 21.5988i | −0.258819 | − | 0.965926i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 26.3861 | + | 26.3861i | 1.17767 | + | 1.17767i | ||||
\(503\) | −16.8767 | + | 29.2313i | −0.752495 | + | 1.30336i | 0.194115 | + | 0.980979i | \(0.437817\pi\) |
−0.946610 | + | 0.322381i | \(0.895517\pi\) | |||||||
\(504\) | 34.4317 | − | 19.8791i | 1.53371 | − | 0.885487i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 46.2420i | − | 2.05571i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −41.7334 | −1.85162 | ||||||||
\(509\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.707107 | − | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.0684 | + | 32.0684i | 1.41310 | + | 1.41310i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −40.2809 | + | 23.2562i | −1.77155 | + | 1.02280i | ||||
\(518\) | −3.05940 | + | 11.4178i | −0.134422 | + | 0.501671i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.03036 | + | 20.9393i | −0.396007 | + | 0.918247i | ||||
\(521\) | 2.90890 | 0.127441 | 0.0637207 | − | 0.997968i | \(-0.479703\pi\) | ||||
0.0637207 | + | 0.997968i | \(0.479703\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(524\) | 27.5228 | + | 15.8903i | 1.20234 | + | 0.694170i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.0343459 | + | 0.128181i | 0.00149755 | + | 0.00558894i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.4737 | − | 52.7819i | 1.32494 | − | 2.29487i | ||||
\(530\) | −39.5000 | + | 22.8053i | −1.71577 | + | 0.990600i | ||||
\(531\) | 4.21411 | − | 15.7273i | 0.182877 | − | 0.682506i | ||||
\(532\) | 42.6961i | 1.85111i | ||||||||
\(533\) | 16.8377 | − | 21.2982i | 0.729323 | − | 0.922528i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.8129 | − | 51.5504i | −0.594964 | − | 2.22044i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 21.8541 | + | 12.6175i | 0.931864 | + | 0.538012i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 27.3101 | + | 27.3101i | 1.16029 | + | 1.16029i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.56832 | + | 2.63752i | −0.193740 | + | 0.111856i | ||||
\(557\) | −11.8798 | + | 44.3360i | −0.503363 | + | 1.87858i | −0.0264067 | + | 0.999651i | \(0.508406\pi\) |
−0.476957 | + | 0.878927i | \(0.658260\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 41.9089 | 1.77097 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.6491 | − | 40.9615i | −0.997578 | − | 1.72785i | ||||
\(563\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −29.8187 | − | 29.8187i | −1.25227 | − | 1.25227i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.4054 | − | 16.9772i | 1.23274 | − | 0.711722i | 0.265139 | − | 0.964210i | \(-0.414582\pi\) |
0.967600 | + | 0.252488i | \(0.0812488\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 47.3406i | − | 1.98114i | −0.137002 | − | 0.990571i | \(-0.543747\pi\) | ||
0.137002 | − | 0.990571i | \(-0.456253\pi\) | |||||||
\(572\) | −9.50331 | − | 23.9158i | −0.397353 | − | 0.999969i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −48.1968 | − | 12.9143i | −2.01170 | − | 0.539032i | ||||
\(575\) | 22.9057 | + | 39.6738i | 0.955233 | + | 1.65451i | ||||
\(576\) | −20.7846 | − | 12.0000i | −0.866025 | − | 0.500000i | ||||
\(577\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(578\) | −6.22243 | − | 23.2224i | −0.258819 | − | 0.965926i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.3223 | − | 49.7197i | 0.551755 | − | 2.05918i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 23.9317 | + | 3.50355i | 0.989453 | + | 0.144854i | ||||
\(586\) | 38.4069 | 1.58658 | ||||||||
\(587\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 12.1359 | − | 12.1359i | 0.499629 | − | 0.499629i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.89235 | − | 1.84680i | 0.283274 | − | 0.0759030i | ||||
\(593\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.76738 | − | 46.2259i | 0.276739 | − | 1.89032i | ||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.5111 | − | 42.4545i | −0.999828 | − | 1.73175i | −0.515968 | − | 0.856608i | \(-0.672568\pi\) |
−0.483860 | − | 0.875145i | \(-0.660766\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.74976 | + | 1.00474i | −0.152449 | + | 0.0408487i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.00008 | − | 8.66039i | 0.202947 | − | 0.351515i | −0.746530 | − | 0.665352i | \(-0.768281\pi\) |
0.949477 | + | 0.313838i | \(0.101615\pi\) | |||||||
\(608\) | 22.3204 | − | 12.8867i | 0.905213 | − | 0.522625i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −43.6703 | + | 17.3531i | −1.76671 | + | 0.702030i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.0266 | − | 5.09816i | −0.768476 | − | 0.205913i | −0.146778 | − | 0.989169i | \(-0.546890\pi\) |
−0.621698 | + | 0.783257i | \(0.713557\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −33.4433 | + | 33.4433i | −1.34747 | + | 1.34747i | ||||
\(617\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.9462 | − | 27.9462i | −1.12325 | − | 1.12325i | −0.991250 | − | 0.132002i | \(-0.957860\pi\) |
−0.132002 | − | 0.991250i | \(-0.542140\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 74.2266i | 2.97383i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.90418 | − | 5.14083i | −0.355316 | − | 0.205142i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −11.5048 | − | 42.9365i | −0.458362 | − | 1.71063i | ||||
\(631\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.17029 | + | 0.675667i | −0.0464781 | + | 0.0268342i | ||||
\(635\) | −12.0763 | + | 45.0695i | −0.479235 | + | 1.78853i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.26384 | − | 53.5540i | −0.248182 | − | 2.12189i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −12.6491 | − | 21.9089i | −0.500000 | − | 0.866025i | ||||
\(641\) | 38.8134 | + | 22.4089i | 1.53304 | + | 0.885098i | 0.999220 | + | 0.0394976i | \(0.0125758\pi\) |
0.533816 | + | 0.845601i | \(0.320758\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(644\) | −82.9351 | + | 22.2224i | −3.26810 | + | 0.875685i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.0479 | − | 20.2349i | 1.37787 | − | 0.795516i | 0.385972 | − | 0.922511i | \(-0.373866\pi\) |
0.991903 | + | 0.126994i | \(0.0405330\pi\) | |||||||
\(648\) | −6.58846 | + | 24.5885i | −0.258819 | + | 0.965926i | ||||
\(649\) | 19.3690i | 0.760299i | ||||||||
\(650\) | 20.0000 | + | 15.8114i | 0.784465 | + | 0.620174i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.74833 | − | 15.1526i | −0.342349 | − | 0.592965i | 0.642520 | − | 0.766269i | \(-0.277889\pi\) |
−0.984868 | + | 0.173304i | \(0.944556\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.1247 | − | 25.1247i | 0.981705 | − | 0.981705i | ||||
\(656\) | 7.79569 | + | 29.0939i | 0.304371 | + | 1.13593i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 61.0676 | + | 61.0676i | 2.38066 | + | 2.38066i | ||||
\(659\) | −22.1359 | + | 38.3406i | −0.862294 | + | 1.49354i | 0.00741531 | + | 0.999973i | \(0.497640\pi\) |
−0.869709 | + | 0.493564i | \(0.835694\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(662\) | 13.6228i | 0.529464i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 46.1091 | + | 12.3549i | 1.78804 | + | 0.479103i | ||||
\(666\) | −3.78416 | − | 6.55436i | −0.146633 | − | 0.253976i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −23.4772 | + | 23.4772i | −0.908361 | + | 0.908361i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.00000 | − | 25.2982i | −0.230769 | − | 0.973009i | ||||
\(677\) | 22.7851 | 0.875701 | 0.437850 | − | 0.899048i | \(-0.355740\pi\) | ||||
0.437850 | + | 0.899048i | \(0.355740\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(684\) | −19.3301 | − | 19.3301i | −0.739103 | − | 0.739103i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −45.6475 | + | 26.3546i | −1.74283 | + | 1.00622i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.5940 | − | 47.7527i | 0.784570 | − | 1.81923i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.2808 | + | 8.38168i | 1.18998 | + | 0.318854i | 0.798878 | − | 0.601494i | \(-0.205427\pi\) |
0.391102 | + | 0.920348i | \(0.372094\pi\) | |||||||
\(692\) | −25.3288 | − | 43.8708i | −0.962858 | − | 1.66772i | ||||
\(693\) | 43.4442 | + | 25.0825i | 1.65031 | + | 0.952805i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.52643 | + | 5.69672i | 0.0579009 | + | 0.216089i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 12.1271 | − | 45.2590i | 0.458362 | − | 1.71063i | ||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.12756 | 0.306537 | ||||||||
\(704\) | 27.5773 | + | 7.38932i | 1.03936 | + | 0.278495i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 38.8038 | − | 22.4034i | 1.45423 | − | 0.839601i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.5775 | + | 3.34251i | −1.06874 | + | 0.125003i | ||||
\(716\) | −12.6491 | −0.472719 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | −18.9737 | + | 18.9737i | −0.707107 | + | 0.707107i | ||||
\(721\) | 24.5960 | + | 91.7936i | 0.916003 | + | 3.41857i | ||||
\(722\) | 2.40200 | − | 0.643614i | 0.0893931 | − | 0.0239528i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 50.7515i | − | 1.88227i | −0.338033 | − | 0.941134i | \(-0.609761\pi\) | ||
0.338033 | − | 0.941134i | \(-0.390239\pi\) | |||||||
\(728\) | −38.3260 | + | 28.5373i | −1.42046 | + | 1.05766i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.1247 | − | 38.1247i | 1.40817 | − | 1.40817i | 0.638780 | − | 0.769390i | \(-0.279439\pi\) |
0.769390 | − | 0.638780i | \(-0.220561\pi\) | |||||||
\(734\) | 2.26519 | + | 8.45380i | 0.0836097 | + | 0.312035i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.6491 | + | 36.6491i | 1.35090 | + | 1.35090i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 27.6672 | − | 15.9737i | 1.01844 | − | 0.587999i | ||||
\(739\) | 13.9237 | − | 51.9638i | 0.512190 | − | 1.91152i | 0.116326 | − | 0.993211i | \(-0.462888\pi\) |
0.395864 | − | 0.918309i | \(-0.370445\pi\) | |||||||
\(740\) | − | 7.97771i | − | 0.293267i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −95.5746 | −3.50866 | ||||||||
\(743\) | −38.8778 | − | 10.4173i | −1.42629 | − | 0.382172i | −0.538577 | − | 0.842576i | \(-0.681038\pi\) |
−0.887710 | + | 0.460404i | \(0.847705\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 38.1359 | − | 38.1359i | 1.39626 | − | 1.39626i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(752\) | 13.4929 | − | 50.3563i | 0.492036 | − | 1.83630i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.8052 | − | 30.8396i | −0.647143 | − | 1.12088i | −0.983802 | − | 0.179258i | \(-0.942630\pi\) |
0.336659 | − | 0.941626i | \(-0.390703\pi\) | |||||||
\(758\) | 33.2237 | + | 19.1817i | 1.20674 | + | 0.696710i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.45801 | − | 27.8337i | −0.270530 | − | 1.00963i | ||||
\(761\) | −41.7071 | + | 11.1754i | −1.51188 | + | 0.405108i | −0.917060 | − | 0.398750i | \(-0.869444\pi\) |
−0.594822 | + | 0.803857i | \(0.702778\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 18.9737i | − | 0.685546i | ||||||
\(767\) | −2.83459 | + | 19.3622i | −0.102351 | + | 0.699130i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.2432 | − | 7.56774i | −1.01848 | − | 0.272900i | −0.289309 | − | 0.957236i | \(-0.593425\pi\) |
−0.729167 | + | 0.684336i | \(0.760092\pi\) | |||||||
\(770\) | 26.4393 | + | 45.7942i | 0.952805 | + | 1.65031i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.3052 | − | 53.3878i | −0.514523 | − | 1.92023i | −0.363067 | − | 0.931763i | \(-0.618270\pi\) |
−0.151456 | − | 0.988464i | \(-0.548396\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.3080i | 1.22921i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 51.8037 | + | 29.9089i | 1.85013 | + | 1.06818i | ||||
\(785\) | −8.12837 | + | 8.12837i | −0.290114 | + | 0.290114i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(788\) | 39.3861 | + | 39.3861i | 1.40307 | + | 1.40307i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 30.2820i | − | 1.07602i | ||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −51.6597 | −1.83333 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 48.8962 | + | 28.2302i | 1.73199 | + | 0.999967i | 0.870075 | + | 0.492920i | \(0.164071\pi\) |
0.861919 | + | 0.507047i | \(0.169263\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −27.3205 | + | 7.32051i | −0.965926 | + | 0.258819i | ||||
\(801\) | −33.6050 | − | 33.6050i | −1.18738 | − | 1.18738i | ||||
\(802\) | 1.68502 | − | 2.91854i | 0.0595001 | − | 0.103057i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 95.9952i | 3.38339i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.2982 | − | 43.8178i | −0.889438 | − | 1.54055i | −0.840541 | − | 0.541748i | \(-0.817763\pi\) |
−0.0488972 | − | 0.998804i | \(-0.515571\pi\) | |||||||
\(810\) | 24.6475 | + | 14.2302i | 0.866025 | + | 0.500000i | ||||
\(811\) | 38.5117 | − | 38.5117i | 1.35233 | − | 1.35233i | 0.469281 | − | 0.883049i | \(-0.344513\pi\) |
0.883049 | − | 0.469281i | \(-0.155487\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.36622 | + | 6.36622i | 0.223136 | + | 0.223136i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 5.23467i | 0.183026i | ||||||||
\(819\) | 39.7583 | + | 31.4317i | 1.38927 | + | 1.09831i | ||||
\(820\) | 33.6754 | 1.17600 | ||||||||
\(821\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.4095 | − | 8.89670i | −0.537143 | − | 0.310119i | 0.206778 | − | 0.978388i | \(-0.433702\pi\) |
−0.743920 | + | 0.668269i | \(0.767036\pi\) | |||||||
\(824\) | 40.5637 | − | 40.5637i | 1.41310 | − | 1.41310i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 34.7383 | − | 9.30810i | 1.20870 | − | 0.323870i | ||||
\(827\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(828\) | 27.4868 | − | 47.6086i | 0.955233 | − | 1.65451i | ||||
\(829\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 26.4863 | + | 11.4226i | 0.918247 | + | 0.396007i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.5604 | + | 32.1475i | 0.642308 | + | 1.11251i | ||||
\(836\) | 28.1628 | + | 16.2598i | 0.974030 | + | 0.562357i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.5747 | − | 43.1975i | −0.399843 | − | 1.49223i | ||||
\(839\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.5000 | + | 25.1147i | −0.500000 | + | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.8634i | 0.373932i | ||||||||
\(845\) | −29.0567 | − | 0.840881i | −0.999582 | − | 0.0289272i | ||||
\(846\) | −55.2950 | −1.90108 | ||||||||
\(847\) | −7.85741 | − | 2.10539i | −0.269984 | − | 0.0723419i | ||||
\(848\) | 28.8467 | + | 49.9640i | 0.990600 | + | 1.71577i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.23022 | + | 15.7874i | 0.145010 | + | 0.541185i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.00000 | − | 4.00000i | −0.136957 | − | 0.136957i | 0.635304 | − | 0.772262i | \(-0.280875\pi\) |
−0.772262 | + | 0.635304i | \(0.780875\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −26.4688 | + | 15.2817i | −0.905213 | + | 0.522625i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.2950 | −1.44309 | −0.721544 | − | 0.692369i | \(-0.756567\pi\) | ||||
−0.721544 | + | 0.692369i | \(0.756567\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.00000 | − | 6.00000i | 0.204242 | − | 0.204242i | −0.597573 | − | 0.801815i | \(-0.703868\pi\) |
0.801815 | + | 0.597573i | \(0.203868\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −54.7071 | + | 14.6587i | −1.86010 | + | 0.498412i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 29.5179 | + | 51.1265i | 0.998457 | + | 1.72938i | ||||
\(875\) | −45.3677 | − | 26.1931i | −1.53371 | − | 0.885487i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.92820 | − | 10.9282i | −0.0988784 | − | 0.369019i | 0.898701 | − | 0.438563i | \(-0.144512\pi\) |
−0.997579 | + | 0.0695437i | \(0.977846\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 15.9600 | − | 27.6436i | 0.538012 | − | 0.931864i | ||||
\(881\) | −15.6279 | + | 9.02277i | −0.526517 | + | 0.303985i | −0.739597 | − | 0.673050i | \(-0.764984\pi\) |
0.213080 | + | 0.977035i | \(0.431651\pi\) | |||||||
\(882\) | 16.4211 | − | 61.2845i | 0.552928 | − | 2.06356i | ||||
\(883\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.52666 | + | 9.57245i | 0.185567 | + | 0.321411i | 0.943767 | − | 0.330610i | \(-0.107254\pi\) |
−0.758200 | + | 0.652022i | \(0.773921\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −69.1354 | + | 69.1354i | −2.31873 | + | 2.31873i | ||||
\(890\) | −12.9657 | − | 48.3885i | −0.434610 | − | 1.62199i | ||||
\(891\) | −31.0245 | + | 8.31298i | −1.03936 | + | 0.278495i | ||||
\(892\) | 13.3861 | + | 13.3861i | 0.448201 | + | 0.448201i | ||||
\(893\) | 29.6904 | − | 51.4254i | 0.993553 | − | 1.72088i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.66025 | + | 13.6603i | −0.122349 | + | 0.456612i | ||||
\(896\) | − | 53.0110i | − | 1.77097i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −55.7047 | −1.85889 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 15.0000 | + | 25.9808i | 0.500000 | + | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −26.8730 | + | 26.8730i | −0.894774 | + | 0.894774i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 19.7282 | + | 49.6475i | 0.653984 | + | 1.64580i | ||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 71.9178 | − | 19.2703i | 2.37494 | − | 0.636362i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(920\) | 50.1839 | − | 28.9737i | 1.65451 | − | 0.955233i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.61543 | − | 2.30850i | −0.283274 | − | 0.0759030i | ||||
\(926\) | 15.8114 | + | 27.3861i | 0.519594 | + | 0.899964i | ||||
\(927\) | −52.6937 | − | 30.4227i | −1.73069 | − | 0.999214i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.03736 | + | 11.3356i | 0.0996525 | + | 0.371908i | 0.997684 | − | 0.0680235i | \(-0.0216693\pi\) |
−0.898031 | + | 0.439932i | \(0.855003\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 48.1784 | + | 48.1784i | 1.57898 | + | 1.57898i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.43168 | − | 30.2714i | 0.144854 | − | 0.989453i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −50.4772 | − | 29.1430i | −1.64639 | − | 0.950541i | ||||
\(941\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −66.6416 | + | 17.8566i | −2.17015 | + | 0.581490i | ||||
\(944\) | −15.3509 | − | 15.3509i | −0.499629 | − | 0.499629i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −32.2168 | −1.04525 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(954\) | 43.2701 | − | 43.2701i | 1.40092 | − | 1.40092i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 31.0000i | − | 1.00000i | ||||||
\(962\) | 5.43233 | + | 7.29568i | 0.175145 | + | 0.235222i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20.9393 | − | 5.61068i | −0.674411 | − | 0.180708i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.8410 | + | 21.8410i | −0.702359 | + | 0.702359i | −0.964916 | − | 0.262557i | \(-0.915434\pi\) |
0.262557 | + | 0.964916i | \(0.415434\pi\) | |||||||
\(968\) | 1.27091 | + | 4.74311i | 0.0408487 | + | 0.152449i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.2386 | − | 31.5902i | 0.585305 | − | 1.01378i | −0.409532 | − | 0.912296i | \(-0.634308\pi\) |
0.994837 | − | 0.101482i | \(-0.0323585\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.19855 | + | 11.9372i | −0.102541 | + | 0.382688i | ||||
\(974\) | − | 60.3406i | − | 1.93344i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.9606 | + | 28.2674i | 1.56479 | + | 0.903431i | ||||
\(980\) | 47.2901 | − | 47.2901i | 1.51063 | − | 1.51063i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 32.6043 | − | 8.73629i | 1.04044 | − | 0.278786i | ||||
\(983\) | 15.2146 | + | 15.2146i | 0.485271 | + | 0.485271i | 0.906810 | − | 0.421539i | \(-0.138510\pi\) |
−0.421539 | + | 0.906810i | \(0.638510\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 53.9317 | − | 31.1375i | 1.71841 | − | 0.992122i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 25.7734 | + | 20.3757i | 0.819961 | + | 0.648236i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −32.7027 | − | 8.76265i | −1.03936 | − | 0.278495i | ||||
\(991\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.7582 | + | 22.0979i | −0.404058 | + | 0.699849i | −0.994211 | − | 0.107442i | \(-0.965734\pi\) |
0.590154 | + | 0.807291i | \(0.299067\pi\) | |||||||
\(998\) | −43.5367 | + | 25.1359i | −1.37813 | + | 0.795664i | ||||
\(999\) | 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 | 520.2.cz.a.379.2 | yes | 8 | |
5.4 | even | 2 | 520.2.cz.b.379.1 | yes | 8 | ||
8.3 | odd | 2 | 520.2.cz.b.379.1 | yes | 8 | ||
13.7 | odd | 12 | inner | 520.2.cz.a.59.2 | ✓ | 8 | |
40.19 | odd | 2 | CM | 520.2.cz.a.379.2 | yes | 8 | |
65.59 | odd | 12 | 520.2.cz.b.59.1 | yes | 8 | ||
104.59 | even | 12 | 520.2.cz.b.59.1 | yes | 8 | ||
520.59 | even | 12 | inner | 520.2.cz.a.59.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
520.2.cz.a.59.2 | ✓ | 8 | 13.7 | odd | 12 | inner | |
520.2.cz.a.59.2 | ✓ | 8 | 520.59 | even | 12 | inner | |
520.2.cz.a.379.2 | yes | 8 | 1.1 | even | 1 | trivial | |
520.2.cz.a.379.2 | yes | 8 | 40.19 | odd | 2 | CM | |
520.2.cz.b.59.1 | yes | 8 | 65.59 | odd | 12 | ||
520.2.cz.b.59.1 | yes | 8 | 104.59 | even | 12 | ||
520.2.cz.b.379.1 | yes | 8 | 5.4 | even | 2 | ||
520.2.cz.b.379.1 | yes | 8 | 8.3 | odd | 2 |