Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(237,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4012.237");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.b (of order \(2\), degree \(1\), 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: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 237.1 | ||
Character | \(\chi\) | \(=\) | 4012.237 |
Dual form | 4012.2.b.a.237.40 |
$q$-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 \(\left(\mathbb{Z}/4012\mathbb{Z}\right)^\times\).
\(n\) | \(2007\) | \(3129\) | \(3777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.27953i | − | 1.89344i | −0.322065 | − | 0.946718i | \(-0.604377\pi\) | ||
0.322065 | − | 0.946718i | \(-0.395623\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.21610i | 1.88550i | 0.333505 | + | 0.942748i | \(0.391769\pi\) | ||||
−0.333505 | + | 0.942748i | \(0.608231\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.547734i | 0.207024i | 0.994628 | + | 0.103512i | \(0.0330080\pi\) | ||||
−0.994628 | + | 0.103512i | \(0.966992\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.75529 | −2.58510 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.860268i | 0.259380i | 0.991555 | + | 0.129690i | \(0.0413983\pi\) | ||||
−0.991555 | + | 0.129690i | \(0.958602\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.171895 | 0.0476751 | 0.0238375 | − | 0.999716i | \(-0.492412\pi\) | ||||
0.0238375 | + | 0.999716i | \(0.492412\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13.8268 | 3.57007 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.68648 | + | 1.84658i | −0.894102 | + | 0.447863i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.806575 | 0.185041 | 0.0925205 | − | 0.995711i | \(-0.470508\pi\) | ||||
0.0925205 | + | 0.995711i | \(0.470508\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.79631 | 0.391987 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.57303i | − | 0.327999i | −0.986460 | − | 0.163999i | \(-0.947561\pi\) | ||
0.986460 | − | 0.163999i | \(-0.0524395\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.7755 | −2.55510 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 15.5951i | 3.00128i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.06772i | 0.198270i | 0.995074 | + | 0.0991350i | \(0.0316076\pi\) | ||||
−0.995074 | + | 0.0991350i | \(0.968392\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.51231i | − | 0.810434i | −0.914221 | − | 0.405217i | \(-0.867196\pi\) | ||
0.914221 | − | 0.405217i | \(-0.132804\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.82127 | 0.491120 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.30930 | −0.390343 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 8.01843i | − | 1.31822i | −0.752046 | − | 0.659111i | \(-0.770933\pi\) | ||
0.752046 | − | 0.659111i | \(-0.229067\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 0.563734i | − | 0.0902696i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.56732i | − | 0.713295i | −0.934239 | − | 0.356647i | \(-0.883920\pi\) | ||
0.934239 | − | 0.356647i | \(-0.116080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0082 | 1.52624 | 0.763118 | − | 0.646259i | \(-0.223667\pi\) | ||||
0.763118 | + | 0.646259i | \(0.223667\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 32.6971i | − | 4.87419i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.00791 | 0.292884 | 0.146442 | − | 0.989219i | \(-0.453218\pi\) | ||||
0.146442 | + | 0.989219i | \(0.453218\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.69999 | 0.957141 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.05592 | + | 12.0899i | 0.847999 | + | 1.69293i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.26805 | −0.586262 | −0.293131 | − | 0.956072i | \(-0.594697\pi\) | ||||
−0.293131 | + | 0.956072i | \(0.594697\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.62697 | −0.489061 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.64518i | − | 0.350363i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.06025i | − | 0.519862i | −0.965627 | − | 0.259931i | \(-0.916300\pi\) | ||
0.965627 | − | 0.259931i | \(-0.0836998\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 4.24784i | − | 0.535177i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.724726i | 0.0898912i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.9086 | −1.57704 | −0.788519 | − | 0.615010i | \(-0.789152\pi\) | ||||
−0.788519 | + | 0.615010i | \(0.789152\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.15878 | −0.621044 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.44608i | − | 0.883687i | −0.897092 | − | 0.441844i | \(-0.854325\pi\) | ||
0.897092 | − | 0.441844i | \(-0.145675\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.64906i | 0.661172i | 0.943776 | + | 0.330586i | \(0.107246\pi\) | ||||
−0.943776 | + | 0.330586i | \(0.892754\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 41.8975i | 4.83791i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.471198 | −0.0536980 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 11.7532i | − | 1.32233i | −0.750239 | − | 0.661167i | \(-0.770061\pi\) | ||
0.750239 | − | 0.661167i | \(-0.229939\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 27.8787 | 3.09763 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.59528 | −0.504398 | −0.252199 | − | 0.967675i | \(-0.581154\pi\) | ||||
−0.252199 | + | 0.967675i | \(0.581154\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.78538 | − | 15.5426i | −0.844443 | − | 1.68583i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.50160 | 0.375411 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.9491 | −1.16060 | −0.580300 | − | 0.814403i | \(-0.697065\pi\) | ||||
−0.580300 | + | 0.814403i | \(0.697065\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0941527i | 0.00986989i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.7982 | −1.53450 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.40060i | 0.348894i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.06247i | − | 0.412482i | −0.978501 | − | 0.206241i | \(-0.933877\pi\) | ||
0.978501 | − | 0.206241i | \(-0.0661230\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 6.67163i | − | 0.670524i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.93186 | −0.789249 | −0.394625 | − | 0.918842i | \(-0.629125\pi\) | ||||
−0.394625 | + | 0.918842i | \(0.629125\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.67163 | 0.755909 | 0.377954 | − | 0.925824i | \(-0.376628\pi\) | ||||
0.377954 | + | 0.925824i | \(0.376628\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.57341i | 0.739090i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.85449i | 0.662648i | 0.943517 | + | 0.331324i | \(0.107495\pi\) | ||||
−0.943517 | + | 0.331324i | \(0.892505\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 16.7832i | − | 1.60754i | −0.594941 | − | 0.803769i | \(-0.702825\pi\) | ||
0.594941 | − | 0.803769i | \(-0.297175\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26.2967 | −2.49597 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 16.9165i | − | 1.59137i | −0.605709 | − | 0.795686i | \(-0.707111\pi\) | ||
0.605709 | − | 0.795686i | \(-0.292889\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.63203 | 0.618440 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.33309 | −0.123245 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.01144 | − | 2.01921i | −0.0927183 | − | 0.185101i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2599 | 0.932722 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.9786 | −1.35058 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 32.7822i | − | 2.93213i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.73624 | 0.420274 | 0.210137 | − | 0.977672i | \(-0.432609\pi\) | ||||
0.210137 | + | 0.977672i | \(0.432609\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 32.8222i | − | 2.88983i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.24147i | − | 0.370579i | −0.982684 | − | 0.185289i | \(-0.940678\pi\) | ||
0.982684 | − | 0.185289i | \(-0.0593223\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.441789i | 0.0383080i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −65.7505 | −5.65890 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.44650 | −0.209019 | −0.104509 | − | 0.994524i | \(-0.533327\pi\) | ||||
−0.104509 | + | 0.994524i | \(0.533327\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 16.8890i | − | 1.43251i | −0.697840 | − | 0.716254i | \(-0.745855\pi\) | ||
0.697840 | − | 0.716254i | \(-0.254145\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 6.58500i | − | 0.554557i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.147876i | 0.0123660i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.50160 | −0.373837 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 21.9728i | − | 1.81228i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.35943 | 0.111369 | 0.0556844 | − | 0.998448i | \(-0.482266\pi\) | ||||
0.0556844 | + | 0.998448i | \(0.482266\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.3037 | −0.838504 | −0.419252 | − | 0.907870i | \(-0.637708\pi\) | ||||
−0.419252 | + | 0.907870i | \(0.637708\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 28.5897 | − | 14.3208i | 2.31134 | − | 1.15777i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.0243 | 1.52807 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.39530 | −0.191166 | −0.0955828 | − | 0.995421i | \(-0.530471\pi\) | ||||
−0.0955828 | + | 0.995421i | \(0.530471\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.9972i | 1.11005i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.861600 | 0.0679036 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 19.1053i | − | 1.49644i | −0.663448 | − | 0.748222i | \(-0.730908\pi\) | ||
0.663448 | − | 0.748222i | \(-0.269092\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.8948i | 0.926005i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2.55660i | − | 0.197836i | −0.995096 | − | 0.0989179i | \(-0.968462\pi\) | ||
0.995096 | − | 0.0989179i | \(-0.0315381\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9705 | −0.997727 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.25523 | −0.478349 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.9882i | 1.59570i | 0.602855 | + | 0.797850i | \(0.294030\pi\) | ||||
−0.602855 | + | 0.797850i | \(0.705970\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 6.99757i | − | 0.528967i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.27953i | 0.246504i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.7844 | −1.25452 | −0.627262 | − | 0.778808i | \(-0.715824\pi\) | ||||
−0.627262 | + | 0.778808i | \(0.715824\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.2329i | 1.13226i | 0.824317 | + | 0.566128i | \(0.191559\pi\) | ||||
−0.824317 | + | 0.566128i | \(0.808441\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.3157 | −0.984325 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 33.8065 | 2.48550 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.58856 | − | 3.17136i | −0.116167 | − | 0.231913i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.54197 | −0.621337 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.25965 | 0.308217 | 0.154109 | − | 0.988054i | \(-0.450749\pi\) | ||||
0.154109 | + | 0.988054i | \(0.450749\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.48174i | 0.106658i | 0.998577 | + | 0.0533289i | \(0.0169832\pi\) | ||||
−0.998577 | + | 0.0533289i | \(0.983017\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.37676 | 0.170203 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.10907i | 0.435253i | 0.976032 | + | 0.217627i | \(0.0698315\pi\) | ||||
−0.976032 | + | 0.217627i | \(0.930169\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 19.2884i | − | 1.36732i | −0.729800 | − | 0.683661i | \(-0.760387\pi\) | ||
0.729800 | − | 0.683661i | \(-0.239613\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 42.3341i | 2.98602i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.584825 | −0.0410467 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.2563 | 1.34492 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.1993i | 0.847908i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.693871i | 0.0479960i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.5418i | 1.27647i | 0.769841 | + | 0.638236i | \(0.220336\pi\) | ||||
−0.769841 | + | 0.638236i | \(0.779664\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −24.4196 | −1.67320 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 42.1956i | 2.87771i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.47154 | 0.167779 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.5262 | 1.25189 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.633687 | + | 0.317418i | −0.0426264 | + | 0.0213519i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.9857 | 0.936555 | 0.468277 | − | 0.883582i | \(-0.344875\pi\) | ||||
0.468277 | + | 0.883582i | \(0.344875\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 99.0776 | 6.60517 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.46318i | 0.495349i | 0.968843 | + | 0.247674i | \(0.0796663\pi\) | ||||
−0.968843 | + | 0.247674i | \(0.920334\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.2348 | −1.07282 | −0.536412 | − | 0.843956i | \(-0.680221\pi\) | ||||
−0.536412 | + | 0.843956i | \(0.680221\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.54531i | 0.101674i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 28.2485i | − | 1.85062i | −0.379214 | − | 0.925309i | \(-0.623805\pi\) | ||
0.379214 | − | 0.925309i | \(-0.376195\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.46556i | 0.552232i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −38.5448 | −2.50375 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.848385 | −0.0548775 | −0.0274387 | − | 0.999623i | \(-0.508735\pi\) | ||||
−0.0274387 | + | 0.999623i | \(0.508735\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0656i | 0.841632i | 0.907146 | + | 0.420816i | \(0.138256\pi\) | ||||
−0.907146 | + | 0.420816i | \(0.861744\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 44.6435i | − | 2.86388i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 28.2478i | 1.80469i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.138646 | 0.00882184 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.0703i | 0.955044i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.08938 | −0.384358 | −0.192179 | − | 0.981360i | \(-0.561555\pi\) | ||||
−0.192179 | + | 0.981360i | \(0.561555\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.35322 | 0.0850764 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −50.9722 | + | 25.5324i | −3.19200 | + | 1.59890i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.57147 | 0.347539 | 0.173769 | − | 0.984786i | \(-0.444405\pi\) | ||||
0.173769 | + | 0.984786i | \(0.444405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.39197 | 0.272904 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 8.28045i | − | 0.512547i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.0863 | −1.48523 | −0.742613 | − | 0.669721i | \(-0.766414\pi\) | ||||
−0.742613 | + | 0.669721i | \(0.766414\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 17.9945i | − | 1.10540i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.9078i | 2.19752i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.8007i | 0.902416i | 0.892419 | + | 0.451208i | \(0.149007\pi\) | ||||
−0.892419 | + | 0.451208i | \(0.850993\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.3764 | 0.934047 | 0.467023 | − | 0.884245i | \(-0.345326\pi\) | ||||
0.467023 | + | 0.884245i | \(0.345326\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.308776 | 0.0186880 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 10.9903i | − | 0.662742i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1.24867i | − | 0.0750254i | −0.999296 | − | 0.0375127i | \(-0.988057\pi\) | ||
0.999296 | − | 0.0375127i | \(-0.0119435\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 34.9942i | 2.09505i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.8069 | 1.00262 | 0.501308 | − | 0.865269i | \(-0.332852\pi\) | ||||
0.501308 | + | 0.865269i | \(0.332852\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 19.8648i | − | 1.18084i | −0.807097 | − | 0.590419i | \(-0.798963\pi\) | ||
0.807097 | − | 0.590419i | \(-0.201037\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.1524 | 0.660609 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.50168 | 0.147669 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.1803 | − | 13.6148i | 0.598838 | − | 0.800870i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.3230 | −0.781007 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.6794 | 1.90915 | 0.954576 | − | 0.297966i | \(-0.0963082\pi\) | ||||
0.954576 | + | 0.297966i | \(0.0963082\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4.21610i | − | 0.245471i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.4160 | −0.778473 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 0.270395i | − | 0.0156373i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.48183i | 0.315968i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 26.0127i | 1.49439i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.1184 | 0.980198 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.26935 | 0.129519 | 0.0647594 | − | 0.997901i | \(-0.479372\pi\) | ||||
0.0647594 | + | 0.997901i | \(0.479372\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 25.1593i | − | 1.43126i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.8502i | 1.06890i | 0.845200 | + | 0.534450i | \(0.179481\pi\) | ||||
−0.845200 | + | 0.534450i | \(0.820519\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 20.9452i | − | 1.18389i | −0.805977 | − | 0.591946i | \(-0.798360\pi\) | ||
0.805977 | − | 0.591946i | \(-0.201640\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 17.9093 | 1.00908 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 17.6609i | − | 0.991936i | −0.868341 | − | 0.495968i | \(-0.834813\pi\) | ||
0.868341 | − | 0.495968i | \(-0.165187\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.918522 | −0.0514274 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.4795 | 1.25468 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.97342 | + | 1.48941i | −0.165446 | + | 0.0828730i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.19604 | −0.121814 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −55.0409 | −3.04377 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.09980i | 0.0606341i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.1135 | −1.16050 | −0.580252 | − | 0.814437i | \(-0.697046\pi\) | ||||
−0.580252 | + | 0.814437i | \(0.697046\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 62.1853i | 3.40773i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 54.4240i | − | 2.97350i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1462i | 0.607172i | 0.952804 | + | 0.303586i | \(0.0981840\pi\) | ||||
−0.952804 | + | 0.303586i | \(0.901816\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −55.4782 | −3.01316 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.88179 | 0.210211 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.50395i | 0.405175i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 21.7499i | − | 1.17098i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.7640i | 1.59782i | 0.601452 | + | 0.798909i | \(0.294589\pi\) | ||||
−0.601452 | + | 0.798909i | \(0.705411\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.1196 | 1.13051 | 0.565253 | − | 0.824917i | \(-0.308778\pi\) | ||||
0.565253 | + | 0.824917i | \(0.308778\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.68072i | 0.143086i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.7091 | −1.42158 | −0.710790 | − | 0.703404i | \(-0.751663\pi\) | ||||
−0.710790 | + | 0.703404i | \(0.751663\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.3934 | 1.66619 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.62205 | + | 3.31704i | −0.350476 | + | 0.175556i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.3817 | −0.759037 | −0.379518 | − | 0.925184i | \(-0.623910\pi\) | ||||
−0.379518 | + | 0.925184i | \(0.623910\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3494 | −0.965760 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 33.6477i | − | 1.76605i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.8170 | −1.24664 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.35410i | 0.175083i | 0.996161 | + | 0.0875414i | \(0.0279010\pi\) | ||||
−0.996161 | + | 0.0875414i | \(0.972099\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 35.4209i | 1.84394i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 2.33776i | − | 0.121370i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.2802 | −1.30896 | −0.654479 | − | 0.756080i | \(-0.727112\pi\) | ||||
−0.654479 | + | 0.756080i | \(0.727112\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −107.510 | −5.55180 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.183535i | 0.00945253i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.8208i | 1.06949i | 0.845013 | + | 0.534746i | \(0.179593\pi\) | ||||
−0.845013 | + | 0.534746i | \(0.820407\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 15.5326i | − | 0.795761i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.0017 | −0.613260 | −0.306630 | − | 0.951829i | \(-0.599201\pi\) | ||||
−0.306630 | + | 0.951829i | \(0.599201\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 1.98662i | − | 0.101247i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −77.6165 | −3.94547 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.06398 | −0.307456 | −0.153728 | − | 0.988113i | \(-0.549128\pi\) | ||||
−0.153728 | + | 0.988113i | \(0.549128\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.90473 | + | 5.79893i | 0.146898 | + | 0.293264i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.9100 | −0.701667 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 49.5525 | 2.49326 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 26.1300i | − | 1.31143i | −0.755009 | − | 0.655715i | \(-0.772367\pi\) | ||
0.755009 | − | 0.655715i | \(-0.227633\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.44886 | 0.0725336 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.13988i | 0.106861i | 0.998572 | + | 0.0534303i | \(0.0170155\pi\) | ||||
−0.998572 | + | 0.0534303i | \(0.982984\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 0.775642i | − | 0.0386375i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 117.539i | 5.84057i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.89800 | 0.341921 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.99171 | −0.0984836 | −0.0492418 | − | 0.998787i | \(-0.515681\pi\) | ||||
−0.0492418 | + | 0.998787i | \(0.515681\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.02338i | 0.395764i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 0.547734i | − | 0.0269522i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 19.3742i | − | 0.951040i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −55.3880 | −2.71236 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.8010i | 1.65129i | 0.564192 | + | 0.825643i | \(0.309188\pi\) | ||||
−0.564192 | + | 0.825643i | \(0.690812\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.94463 | 0.0947755 | 0.0473877 | − | 0.998877i | \(-0.484910\pi\) | ||||
0.0473877 | + | 0.998877i | \(0.484910\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.5720 | −0.757134 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 47.0966 | − | 23.5910i | 2.28452 | − | 1.14433i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.22394 | 0.107624 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.484962 | 0.0234142 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.7047i | 1.67167i | 0.548982 | + | 0.835834i | \(0.315015\pi\) | ||||
−0.548982 | + | 0.835834i | \(0.684985\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.950499 | −0.0456781 | −0.0228390 | − | 0.999739i | \(-0.507271\pi\) | ||||
−0.0228390 | + | 0.999739i | \(0.507271\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.7631i | 0.707837i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.26876i | − | 0.0606932i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.21395i | 0.153394i | 0.997054 | + | 0.0766968i | \(0.0244373\pi\) | ||||
−0.997054 | + | 0.0766968i | \(0.975563\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −51.9604 | −2.47430 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.6989 | 1.22099 | 0.610495 | − | 0.792020i | \(-0.290970\pi\) | ||||
0.610495 | + | 0.792020i | \(0.290970\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 46.1624i | − | 2.18831i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 4.45829i | − | 0.210870i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 19.9069i | − | 0.939464i | −0.882809 | − | 0.469732i | \(-0.844351\pi\) | ||
0.882809 | − | 0.469732i | \(-0.155649\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.92911 | 0.185015 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 33.7913i | 1.58765i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.396957 | −0.0186096 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.50137 | 0.163787 | 0.0818935 | − | 0.996641i | \(-0.473903\pi\) | ||||
0.0818935 | + | 0.996641i | \(0.473903\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −28.7977 | − | 57.4910i | −1.34416 | − | 2.68345i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.9099 | 1.53277 | 0.766383 | − | 0.642384i | \(-0.222055\pi\) | ||||
0.766383 | + | 0.642384i | \(0.222055\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.78529 | −0.268865 | −0.134433 | − | 0.990923i | \(-0.542921\pi\) | ||||
−0.134433 | + | 0.990923i | \(0.542921\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 62.3908i | − | 2.89330i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.9601 | 1.43266 | 0.716332 | − | 0.697759i | \(-0.245820\pi\) | ||||
0.716332 | + | 0.697759i | \(0.245820\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 7.07049i | − | 0.326485i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.85544i | 0.361960i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.60973i | 0.395876i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.3044 | −0.472798 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 33.1000 | 1.51554 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 21.0902i | − | 0.963635i | −0.876272 | − | 0.481817i | \(-0.839977\pi\) | ||
0.876272 | − | 0.481817i | \(-0.160023\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 1.37833i | − | 0.0628463i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 2.82564i | − | 0.128571i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.1278 | 0.777732 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.5548i | 0.614227i | 0.951673 | + | 0.307113i | \(0.0993631\pi\) | ||||
−0.951673 | + | 0.307113i | \(0.900637\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −62.6564 | −2.83342 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.1903 | 1.76863 | 0.884317 | − | 0.466887i | \(-0.154625\pi\) | ||||
0.884317 | + | 0.466887i | \(0.154625\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.97163 | − | 3.93611i | −0.0887977 | − | 0.177274i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 28.1282 | 1.26427 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.07847 | 0.182945 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.119101i | 0.00533171i | 0.999996 | + | 0.00266585i | \(0.000848568\pi\) | ||||
−0.999996 | + | 0.00266585i | \(0.999151\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.38444 | −0.374589 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 31.5384i | − | 1.40623i | −0.711076 | − | 0.703115i | \(-0.751792\pi\) | ||
0.711076 | − | 0.703115i | \(-0.248208\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 33.4415i | − | 1.48813i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 42.5369i | 1.88913i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.3532 | −0.813493 | −0.406746 | − | 0.913541i | \(-0.633337\pi\) | ||||
−0.406746 | + | 0.913541i | \(0.633337\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.09418 | −0.136879 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.5786i | 0.555360i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.3444i | 1.42526i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.72734i | 0.0759684i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 68.8312 | 3.02136 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.8386i | 0.781523i | 0.920492 | + | 0.390762i | \(0.127788\pi\) | ||||
−0.920492 | + | 0.390762i | \(0.872212\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.6052 | 0.944729 | 0.472365 | − | 0.881403i | \(-0.343401\pi\) | ||||
0.472365 | + | 0.881403i | \(0.343401\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.9487 | −1.00156 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.33235 | + | 16.6345i | 0.362963 | + | 0.724611i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.5256 | 0.892417 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.75529 | 0.336551 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 0.785098i | − | 0.0340064i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28.8992 | −1.24942 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 55.0448i | 2.37536i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.76378i | 0.248264i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.8707i | 1.32724i | 0.748072 | + | 0.663618i | \(0.230980\pi\) | ||||
−0.748072 | + | 0.663618i | \(0.769020\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 49.9568 | 2.14385 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 70.7596 | 3.03101 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 13.0862i | − | 0.559526i | −0.960069 | − | 0.279763i | \(-0.909744\pi\) | ||
0.960069 | − | 0.279763i | \(-0.0902559\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 31.4884i | 1.34389i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.861194i | 0.0366881i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.43761 | 0.273755 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 110.869i | − | 4.70614i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.7565 | −0.837111 | −0.418555 | − | 0.908191i | \(-0.637463\pi\) | ||||
−0.418555 | + | 0.908191i | \(0.637463\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.72036 | 0.0727634 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.4006 | + | 5.20971i | −0.439112 | + | 0.219954i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.8113 | −1.76213 | −0.881067 | − | 0.472991i | \(-0.843174\pi\) | ||||
−0.881067 | + | 0.472991i | \(0.843174\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 71.3217 | 3.00053 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.2701i | 0.641284i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.2849 | −0.850386 | −0.425193 | − | 0.905103i | \(-0.639794\pi\) | ||||
−0.425193 | + | 0.905103i | \(0.639794\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 22.4670i | − | 0.940213i | −0.882610 | − | 0.470106i | \(-0.844216\pi\) | ||
0.882610 | − | 0.470106i | \(-0.155784\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 13.9696i | − | 0.583589i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.0962i | 0.838068i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.7152 | −1.07054 | −0.535269 | − | 0.844682i | \(-0.679790\pi\) | ||||
−0.535269 | + | 0.844682i | \(0.679790\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.85940 | 0.201950 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 2.51699i | − | 0.104422i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.67167i | − | 0.152065i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 5.62046i | − | 0.232377i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.04268 | 0.249408 | 0.124704 | − | 0.992194i | \(-0.460202\pi\) | ||||
0.124704 | + | 0.992194i | \(0.460202\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 3.63951i | − | 0.149964i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.0349 | 0.824124 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.888605 | −0.0364906 | −0.0182453 | − | 0.999834i | \(-0.505808\pi\) | ||||
−0.0182453 | + | 0.999834i | \(0.505808\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.51319 | − | 4.26432i | 0.349007 | − | 0.174820i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −63.2570 | −2.58894 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.5835 | −1.20875 | −0.604375 | − | 0.796700i | \(-0.706577\pi\) | ||||
−0.604375 | + | 0.796700i | \(0.706577\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.6368i | 1.00496i | 0.864590 | + | 0.502478i | \(0.167578\pi\) | ||||
−0.864590 | + | 0.502478i | \(0.832422\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 100.110 | 4.07680 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 43.2569i | 1.75864i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 20.5939i | − | 0.835880i | −0.908475 | − | 0.417940i | \(-0.862752\pi\) | ||
0.908475 | − | 0.417940i | \(-0.137248\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.91795i | 0.0777192i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.345150 | 0.0139633 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.9526 | 1.00783 | 0.503914 | − | 0.863754i | \(-0.331893\pi\) | ||||
0.503914 | + | 0.863754i | \(0.331893\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 63.1514i | − | 2.54651i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 47.3422i | − | 1.90593i | −0.303086 | − | 0.952963i | \(-0.598017\pi\) | ||
0.303086 | − | 0.952963i | \(-0.401983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 27.0719i | − | 1.08811i | −0.839049 | − | 0.544056i | \(-0.816888\pi\) | ||
0.839049 | − | 0.544056i | \(-0.183112\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 24.5315 | 0.984415 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 5.99719i | − | 0.240272i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 74.3356 | 2.97342 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.27557 | 0.0908774 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.8067 | + | 29.5598i | 0.590382 | + | 1.17863i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.9128 | 1.78795 | 0.893976 | − | 0.448115i | \(-0.147905\pi\) | ||||
0.893976 | + | 0.448115i | \(0.147905\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 60.8084 | 2.41692 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.9685i | 0.792424i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.15169 | 0.0456318 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 57.7465i | 2.28442i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 0.605421i | − | 0.0239127i | −0.999929 | − | 0.0119563i | \(-0.996194\pi\) | ||
0.999929 | − | 0.0119563i | \(-0.00380591\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 22.5895i | − | 0.890842i | −0.895321 | − | 0.445421i | \(-0.853054\pi\) | ||
0.895321 | − | 0.445421i | \(-0.146946\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 138.381 | 5.44876 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.0415 | −1.57419 | −0.787096 | − | 0.616830i | \(-0.788416\pi\) | ||||
−0.787096 | + | 0.616830i | \(0.788416\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.860268i | − | 0.0337685i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 8.10549i | − | 0.317679i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.1525i | 0.866893i | 0.901179 | + | 0.433447i | \(0.142703\pi\) | ||||
−0.901179 | + | 0.433447i | \(0.857297\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.8825 | 0.698725 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 43.8101i | − | 1.70919i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.41116 | −0.366607 | −0.183303 | − | 0.983056i | \(-0.558679\pi\) | ||||
−0.183303 | + | 0.983056i | \(0.558679\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.7745 | −1.66374 | −0.831869 | − | 0.554973i | \(-0.812729\pi\) | ||||
−0.831869 | + | 0.554973i | \(0.812729\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.04098 | + | 2.07819i | 0.0404284 | + | 0.0807103i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.86263 | −0.0722295 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.67955 | 0.0650323 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 45.8666i | − | 1.77331i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.49290 | 0.134842 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.6152i | 0.563374i | 0.959506 | + | 0.281687i | \(0.0908940\pi\) | ||||
−0.959506 | + | 0.281687i | \(0.909106\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 199.235i | − | 7.66856i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 38.5940i | − | 1.48329i | −0.670794 | − | 0.741644i | \(-0.734047\pi\) | ||
0.670794 | − | 0.741644i | \(-0.265953\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.22516 | 0.0853936 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.4757 | 0.937911 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 34.2970i | − | 1.31234i | −0.754614 | − | 0.656169i | \(-0.772176\pi\) | ||
0.754614 | − | 0.656169i | \(-0.227824\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 10.3147i | − | 0.394105i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 53.2424i | 2.03132i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.733656 | −0.0279501 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 11.1839i | − | 0.425457i | −0.977111 | − | 0.212729i | \(-0.931765\pi\) | ||
0.977111 | − | 0.212729i | \(-0.0682350\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.65428 | 0.138815 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 71.2057 | 2.70099 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.43394 | + | 16.8373i | 0.319458 | + | 0.637759i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −92.6416 | −3.50403 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.1839 | −1.44219 | −0.721093 | − | 0.692839i | \(-0.756360\pi\) | ||||
−0.721093 | + | 0.692839i | \(0.756360\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6.46747i | − | 0.243925i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 27.7630 | 1.04562 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 4.34455i | − | 0.163394i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 12.4630i | − | 0.468057i | −0.972230 | − | 0.234028i | \(-0.924809\pi\) | ||
0.972230 | − | 0.234028i | \(-0.0751908\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 91.1492i | 3.41836i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.09797 | −0.265821 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.623458 | −0.0233160 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.78230i | 0.103907i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.2747i | 0.495062i | 0.968880 | + | 0.247531i | \(0.0796193\pi\) | ||||
−0.968880 | + | 0.247531i | \(0.920381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.20202i | 0.156491i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 42.8491 | 1.59358 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 13.6406i | − | 0.506599i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.1132 | −1.52480 | −0.762402 | − | 0.647104i | \(-0.775980\pi\) | ||||
−0.762402 | + | 0.647104i | \(0.775980\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −62.7736 | −2.32495 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −36.8950 | + | 18.4810i | −1.36461 | + | 0.683544i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.2280 | −0.931818 | −0.465909 | − | 0.884833i | \(-0.654273\pi\) | ||||
−0.465909 | + | 0.884833i | \(0.654273\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 92.6394 | 3.41706 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 11.1049i | − | 0.409053i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.1797 | 1.40446 | 0.702231 | − | 0.711950i | \(-0.252188\pi\) | ||||
0.702231 | + | 0.711950i | \(0.252188\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 0.454694i | − | 0.0167036i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.766960i | 0.0281370i | 0.999901 | + | 0.0140685i | \(0.00447829\pi\) | ||||
−0.999901 | + | 0.0140685i | \(0.995522\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.73149i | 0.209986i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 35.6378 | 1.30392 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.75444 | −0.137184 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0416i | 0.366424i | 0.983073 | + | 0.183212i | \(0.0586494\pi\) | ||||
−0.983073 | + | 0.183212i | \(0.941351\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.9703i | 0.727757i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 43.4415i | − | 1.58100i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.1639 | 0.914599 | 0.457299 | − | 0.889313i | \(-0.348817\pi\) | ||||
0.457299 | + | 0.889313i | \(0.348817\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 4.43793i | − | 0.161087i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.4933 | −0.452883 | −0.226441 | − | 0.974025i | \(-0.572709\pi\) | ||||
−0.226441 | + | 0.974025i | \(0.572709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.19273 | 0.332799 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 60.3779 | + | 120.537i | 2.18297 | + | 4.35803i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.171895 | −0.00620676 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.7374 | −1.07236 | −0.536179 | − | 0.844104i | \(-0.680133\pi\) | ||||
−0.536179 | + | 0.844104i | \(0.680133\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 18.2718i | − | 0.658042i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.05880 | −0.145985 | −0.0729925 | − | 0.997332i | \(-0.523255\pi\) | ||||
−0.0729925 | + | 0.997332i | \(0.523255\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 57.6469i | 2.07074i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 14.4036i | − | 0.516726i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 3.68388i | − | 0.131989i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.40562 | 0.229211 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.6512 | −0.595064 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 10.0988i | − | 0.360442i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 3.55552i | − | 0.126740i | −0.997990 | − | 0.0633702i | \(-0.979815\pi\) | ||
0.997990 | − | 0.0633702i | \(-0.0201849\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 78.9917i | 2.81218i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.26576 | 0.329452 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.697936i | − | 0.0247845i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −59.0135 | −2.09299 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.8515 | 1.34077 | 0.670384 | − | 0.742014i | \(-0.266129\pi\) | ||||
0.670384 | + | 0.742014i | \(0.266129\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.40213 | + | 3.70778i | −0.261868 | + | 0.131172i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 84.9133 | 3.00026 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.85970 | −0.171495 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.63259i | 0.128032i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 48.5394 | 1.70867 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 39.7579i | − | 1.39781i | −0.715212 | − | 0.698907i | \(-0.753670\pi\) | ||
0.715212 | − | 0.698907i | \(-0.246330\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.8644i | 0.416617i | 0.978063 | + | 0.208308i | \(0.0667958\pi\) | ||||
−0.978063 | + | 0.208308i | \(0.933204\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 50.4271i | − | 1.76856i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 80.5499 | 2.82154 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.07237 | 0.282416 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 0.730182i | − | 0.0255146i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 37.6923i | − | 1.31547i | −0.753250 | − | 0.657734i | \(-0.771515\pi\) | ||
0.753250 | − | 0.657734i | \(-0.228485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.43692i | 0.328950i | 0.986381 | + | 0.164475i | \(0.0525931\pi\) | ||||
−0.986381 | + | 0.164475i | \(0.947407\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −36.0431 | −1.25486 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 23.6807i | − | 0.823460i | −0.911306 | − | 0.411730i | \(-0.864925\pi\) | ||
0.911306 | − | 0.411730i | \(-0.135075\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.5718 | −1.27019 | −0.635095 | − | 0.772434i | \(-0.719039\pi\) | ||||
−0.635095 | + | 0.772434i | \(0.719039\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.09505 | −0.142056 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.6994 | + | 12.3721i | −0.855782 | + | 0.428668i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.7789 | 0.373019 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 70.3699 | 2.43234 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 49.1775i | 1.69780i | 0.528557 | + | 0.848898i | \(0.322733\pi\) | ||||
−0.528557 | + | 0.848898i | \(0.677267\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.8600 | 0.960689 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 55.1187i | − | 1.89839i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 54.6847i | − | 1.88121i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.61972i | 0.193096i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −65.1470 | −2.23584 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.6132 | −0.432375 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.31165i | 0.0791494i | 0.999217 | + | 0.0395747i | \(0.0126003\pi\) | ||||
−0.999217 | + | 0.0395747i | \(0.987400\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 26.3726i | − | 0.901926i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 46.4366i | − | 1.58624i | −0.609063 | − | 0.793122i | \(-0.708454\pi\) | ||
0.609063 | − | 0.793122i | \(-0.291546\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.87291 | −0.302740 | −0.151370 | − | 0.988477i | \(-0.548368\pi\) | ||||
−0.151370 | + | 0.988477i | \(0.548368\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 8.20431i | − | 0.279602i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.6477 | −0.566695 | −0.283348 | − | 0.959017i | \(-0.591445\pi\) | ||||
−0.283348 | + | 0.959017i | \(0.591445\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −88.4882 | −3.00869 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −44.6501 | − | 33.3864i | −1.51640 | − | 1.13386i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.1109 | 0.342988 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.21892 | −0.0751854 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 31.5057i | 1.06630i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.9559 | 0.607022 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 51.7439i | − | 1.74727i | −0.486584 | − | 0.873634i | \(-0.661757\pi\) | ||
0.486584 | − | 0.873634i | \(-0.338243\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 107.173i | − | 3.61486i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.30770i | 0.313585i | 0.987632 | + | 0.156792i | \(0.0501153\pi\) | ||||
−0.987632 | + | 0.156792i | \(0.949885\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.3278 | 0.919652 | 0.459826 | − | 0.888009i | \(-0.347912\pi\) | ||||
0.459826 | + | 0.888009i | \(0.347912\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.8268 | −0.464783 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 35.3323i | − | 1.18634i | −0.805076 | − | 0.593172i | \(-0.797876\pi\) | ||
0.805076 | − | 0.593172i | \(-0.202124\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.59420i | 0.0870068i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.9831i | 0.803465i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.61953 | 0.0541956 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 70.7646i | − | 2.36540i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.886768 | −0.0296083 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.81786 | 0.160685 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.7341 | − | 7.88132i | 0.524178 | − | 0.262565i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.9778 | 0.598264 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −64.2236 | −2.13486 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 47.5465i | − | 1.57875i | −0.613908 | − | 0.789377i | \(-0.710404\pi\) | ||
0.613908 | − | 0.789377i | \(-0.289596\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 61.5139 | 2.04029 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.6406i | 1.44588i | 0.690912 | + | 0.722938i | \(0.257209\pi\) | ||||
−0.690912 | + | 0.722938i | \(0.742791\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 3.95317i | − | 0.130831i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 56.1403i | − | 1.85594i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.32320 | 0.0767188 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.68843 | −0.121670 | −0.0608351 | − | 0.998148i | \(-0.519376\pi\) | ||||
−0.0608351 | + | 0.998148i | \(0.519376\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 7.44240i | − | 0.245236i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.27994i | − | 0.0421298i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 102.439i | 3.36819i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −59.4958 | −1.95410 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1.94636i | − | 0.0638579i | −0.999490 | − | 0.0319289i | \(-0.989835\pi\) | ||
0.999490 | − | 0.0319289i | \(-0.0101650\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.40404 | 0.177110 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 61.8199 | 2.02389 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.3708 | − | 6.69751i | 0.437271 | − | 0.219032i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.4794 | −1.12639 | −0.563196 | − | 0.826323i | \(-0.690428\pi\) | ||||
−0.563196 | + | 0.826323i | \(0.690428\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −68.6903 | −2.24162 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 26.1931i | − | 0.853870i | −0.904282 | − | 0.426935i | \(-0.859593\pi\) | ||
0.904282 | − | 0.426935i | \(-0.140407\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.18451 | −0.233960 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 36.0138i | − | 1.17153i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.1518i | 0.459873i | 0.973206 | + | 0.229937i | \(0.0738519\pi\) | ||||
−0.973206 | + | 0.229937i | \(0.926148\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.971044i | 0.0315214i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −57.9194 | −1.87817 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.4551 | −1.05133 | −0.525663 | − | 0.850693i | \(-0.676183\pi\) | ||||
−0.525663 | + | 0.850693i | \(0.676183\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.9591i | 0.581142i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.01232i | 0.0973744i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1.34003i | − | 0.0432720i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.6391 | 0.343197 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 53.1586i | − | 1.71301i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.24715 | −0.201103 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.77681 | −0.153612 | −0.0768059 | − | 0.997046i | \(-0.524472\pi\) | ||||
−0.0768059 | + | 0.997046i | \(0.524472\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.88456 | + | 9.75142i | 0.156915 | + | 0.313261i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.0344 | 1.54150 | 0.770748 | − | 0.637140i | \(-0.219883\pi\) | ||||
0.770748 | + | 0.637140i | \(0.219883\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.25069 | 0.296564 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.20197i | 0.230648i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.4960 | 1.19960 | 0.599801 | − | 0.800149i | \(-0.295246\pi\) | ||||
0.599801 | + | 0.800149i | \(0.295246\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 9.41914i | − | 0.301037i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 130.159i | 4.15564i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.83044i | 0.217857i | 0.994050 | + | 0.108929i | \(0.0347420\pi\) | ||||
−0.994050 | + | 0.108929i | \(0.965258\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.7564 | −0.820668 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.60683 | 0.114807 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 15.7432i | − | 0.500603i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 57.2231i | − | 1.81775i | −0.417068 | − | 0.908875i | \(-0.636942\pi\) | ||
0.417068 | − | 0.908875i | \(-0.363058\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 69.2424i | 2.19734i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 81.3220 | 2.57808 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.2750i | 1.30719i | 0.756843 | + | 0.653596i | \(0.226741\pi\) | ||||
−0.756843 | + | 0.653596i | \(0.773259\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 125.048 | 3.95635 |
(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 | 4012.2.b.a.237.1 | ✓ | 40 | |
17.16 | even | 2 | inner | 4012.2.b.a.237.40 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.b.a.237.1 | ✓ | 40 | 1.1 | even | 1 | trivial | |
4012.2.b.a.237.40 | yes | 40 | 17.16 | even | 2 | inner |