Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.4 | ||
Root | \(0.445042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.2.b.g.337.3 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.445042i | 0.314692i | 0.987544 | + | 0.157346i | \(0.0502938\pi\) | ||||
−0.987544 | + | 0.157346i | \(0.949706\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.80194 | 0.900969 | ||||||||
\(5\) | − 0.246980i | − 0.110453i | −0.998474 | − | 0.0552263i | \(-0.982412\pi\) | ||||
0.998474 | − | 0.0552263i | \(-0.0175880\pi\) | |||||||
\(6\) | 0.445042i | 0.181688i | ||||||||
\(7\) | − 1.75302i | − 0.662579i | −0.943529 | − | 0.331290i | \(-0.892516\pi\) | ||||
0.943529 | − | 0.331290i | \(-0.107484\pi\) | |||||||
\(8\) | 1.69202i | 0.598220i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.109916 | 0.0347586 | ||||||||
\(11\) | − 5.65279i | − 1.70438i | −0.523232 | − | 0.852191i | \(-0.675274\pi\) | ||||
0.523232 | − | 0.852191i | \(-0.324726\pi\) | |||||||
\(12\) | 1.80194 | 0.520175 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.780167 | 0.208509 | ||||||||
\(15\) | − 0.246980i | − 0.0637699i | ||||||||
\(16\) | 2.85086 | 0.712714 | ||||||||
\(17\) | 3.80194 | 0.922105 | 0.461053 | − | 0.887373i | \(-0.347472\pi\) | ||||
0.461053 | + | 0.887373i | \(0.347472\pi\) | |||||||
\(18\) | 0.445042i | 0.104897i | ||||||||
\(19\) | 5.58211i | 1.28062i | 0.768115 | + | 0.640311i | \(0.221195\pi\) | ||||
−0.768115 | + | 0.640311i | \(0.778805\pi\) | |||||||
\(20\) | − 0.445042i | − 0.0995144i | ||||||||
\(21\) | − 1.75302i | − 0.382540i | ||||||||
\(22\) | 2.51573 | 0.536355 | ||||||||
\(23\) | −8.34481 | −1.74001 | −0.870007 | − | 0.493039i | \(-0.835886\pi\) | ||||
−0.870007 | + | 0.493039i | \(0.835886\pi\) | |||||||
\(24\) | 1.69202i | 0.345382i | ||||||||
\(25\) | 4.93900 | 0.987800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | − 3.15883i | − 0.596963i | ||||||||
\(29\) | −5.93900 | −1.10284 | −0.551422 | − | 0.834226i | \(-0.685915\pi\) | ||||
−0.551422 | + | 0.834226i | \(0.685915\pi\) | |||||||
\(30\) | 0.109916 | 0.0200679 | ||||||||
\(31\) | 5.26875i | 0.946295i | 0.880983 | + | 0.473148i | \(0.156882\pi\) | ||||
−0.880983 | + | 0.473148i | \(0.843118\pi\) | |||||||
\(32\) | 4.65279i | 0.822505i | ||||||||
\(33\) | − 5.65279i | − 0.984025i | ||||||||
\(34\) | 1.69202i | 0.290179i | ||||||||
\(35\) | −0.432960 | −0.0731836 | ||||||||
\(36\) | 1.80194 | 0.300323 | ||||||||
\(37\) | − 3.19806i | − 0.525758i | −0.964829 | − | 0.262879i | \(-0.915328\pi\) | ||||
0.964829 | − | 0.262879i | \(-0.0846720\pi\) | |||||||
\(38\) | −2.48427 | −0.403002 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.417895 | 0.0660750 | ||||||||
\(41\) | 0.445042i | 0.0695039i | 0.999396 | + | 0.0347519i | \(0.0110641\pi\) | ||||
−0.999396 | + | 0.0347519i | \(0.988936\pi\) | |||||||
\(42\) | 0.780167 | 0.120382 | ||||||||
\(43\) | −1.71379 | −0.261351 | −0.130675 | − | 0.991425i | \(-0.541715\pi\) | ||||
−0.130675 | + | 0.991425i | \(0.541715\pi\) | |||||||
\(44\) | − 10.1860i | − 1.53559i | ||||||||
\(45\) | − 0.246980i | − 0.0368175i | ||||||||
\(46\) | − 3.71379i | − 0.547569i | ||||||||
\(47\) | 6.73556i | 0.982483i | 0.871024 | + | 0.491241i | \(0.163457\pi\) | ||||
−0.871024 | + | 0.491241i | \(0.836543\pi\) | |||||||
\(48\) | 2.85086 | 0.411485 | ||||||||
\(49\) | 3.92692 | 0.560988 | ||||||||
\(50\) | 2.19806i | 0.310853i | ||||||||
\(51\) | 3.80194 | 0.532378 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.06100 | −0.145739 | −0.0728697 | − | 0.997341i | \(-0.523216\pi\) | ||||
−0.0728697 | + | 0.997341i | \(0.523216\pi\) | |||||||
\(54\) | 0.445042i | 0.0605625i | ||||||||
\(55\) | −1.39612 | −0.188253 | ||||||||
\(56\) | 2.96615 | 0.396368 | ||||||||
\(57\) | 5.58211i | 0.739368i | ||||||||
\(58\) | − 2.64310i | − 0.347057i | ||||||||
\(59\) | 13.7017i | 1.78381i | 0.452222 | + | 0.891905i | \(0.350631\pi\) | ||||
−0.452222 | + | 0.891905i | \(0.649369\pi\) | |||||||
\(60\) | − 0.445042i | − 0.0574547i | ||||||||
\(61\) | −8.51573 | −1.09033 | −0.545164 | − | 0.838330i | \(-0.683533\pi\) | ||||
−0.545164 | + | 0.838330i | \(0.683533\pi\) | |||||||
\(62\) | −2.34481 | −0.297792 | ||||||||
\(63\) | − 1.75302i | − 0.220860i | ||||||||
\(64\) | 3.63102 | 0.453878 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.51573 | 0.309665 | ||||||||
\(67\) | 5.96077i | 0.728224i | 0.931355 | + | 0.364112i | \(0.118627\pi\) | ||||
−0.931355 | + | 0.364112i | \(0.881373\pi\) | |||||||
\(68\) | 6.85086 | 0.830788 | ||||||||
\(69\) | −8.34481 | −1.00460 | ||||||||
\(70\) | − 0.192685i | − 0.0230303i | ||||||||
\(71\) | − 5.71917i | − 0.678740i | −0.940653 | − | 0.339370i | \(-0.889786\pi\) | ||||
0.940653 | − | 0.339370i | \(-0.110214\pi\) | |||||||
\(72\) | 1.69202i | 0.199407i | ||||||||
\(73\) | − 7.35690i | − 0.861060i | −0.902576 | − | 0.430530i | \(-0.858327\pi\) | ||||
0.902576 | − | 0.430530i | \(-0.141673\pi\) | |||||||
\(74\) | 1.42327 | 0.165452 | ||||||||
\(75\) | 4.93900 | 0.570307 | ||||||||
\(76\) | 10.0586i | 1.15380i | ||||||||
\(77\) | −9.90946 | −1.12929 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.45473 | 0.501196 | 0.250598 | − | 0.968091i | \(-0.419373\pi\) | ||||
0.250598 | + | 0.968091i | \(0.419373\pi\) | |||||||
\(80\) | − 0.704103i | − 0.0787211i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.198062 | −0.0218723 | ||||||||
\(83\) | − 10.1860i | − 1.11806i | −0.829149 | − | 0.559028i | \(-0.811174\pi\) | ||||
0.829149 | − | 0.559028i | \(-0.188826\pi\) | |||||||
\(84\) | − 3.15883i | − 0.344657i | ||||||||
\(85\) | − 0.939001i | − 0.101849i | ||||||||
\(86\) | − 0.762709i | − 0.0822450i | ||||||||
\(87\) | −5.93900 | −0.636728 | ||||||||
\(88\) | 9.56465 | 1.01959 | ||||||||
\(89\) | − 0.137063i | − 0.0145287i | −0.999974 | − | 0.00726434i | \(-0.997688\pi\) | ||||
0.999974 | − | 0.00726434i | \(-0.00231233\pi\) | |||||||
\(90\) | 0.109916 | 0.0115862 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −15.0368 | −1.56770 | ||||||||
\(93\) | 5.26875i | 0.546344i | ||||||||
\(94\) | −2.99761 | −0.309180 | ||||||||
\(95\) | 1.37867 | 0.141448 | ||||||||
\(96\) | 4.65279i | 0.474874i | ||||||||
\(97\) | − 13.6896i | − 1.38997i | −0.719024 | − | 0.694986i | \(-0.755411\pi\) | ||||
0.719024 | − | 0.694986i | \(-0.244589\pi\) | |||||||
\(98\) | 1.74764i | 0.176539i | ||||||||
\(99\) | − 5.65279i | − 0.568127i | ||||||||
\(100\) | 8.89977 | 0.889977 | ||||||||
\(101\) | 5.41119 | 0.538434 | 0.269217 | − | 0.963080i | \(-0.413235\pi\) | ||||
0.269217 | + | 0.963080i | \(0.413235\pi\) | |||||||
\(102\) | 1.69202i | 0.167535i | ||||||||
\(103\) | −13.7560 | −1.35542 | −0.677710 | − | 0.735330i | \(-0.737027\pi\) | ||||
−0.677710 | + | 0.735330i | \(0.737027\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.432960 | −0.0422526 | ||||||||
\(106\) | − 0.472189i | − 0.0458630i | ||||||||
\(107\) | −12.8170 | −1.23907 | −0.619533 | − | 0.784970i | \(-0.712678\pi\) | ||||
−0.619533 | + | 0.784970i | \(0.712678\pi\) | |||||||
\(108\) | 1.80194 | 0.173392 | ||||||||
\(109\) | 12.1468i | 1.16345i | 0.813386 | + | 0.581724i | \(0.197622\pi\) | ||||
−0.813386 | + | 0.581724i | \(0.802378\pi\) | |||||||
\(110\) | − 0.621334i | − 0.0592419i | ||||||||
\(111\) | − 3.19806i | − 0.303547i | ||||||||
\(112\) | − 4.99761i | − 0.472229i | ||||||||
\(113\) | −1.63773 | −0.154064 | −0.0770322 | − | 0.997029i | \(-0.524544\pi\) | ||||
−0.0770322 | + | 0.997029i | \(0.524544\pi\) | |||||||
\(114\) | −2.48427 | −0.232673 | ||||||||
\(115\) | 2.06100i | 0.192189i | ||||||||
\(116\) | −10.7017 | −0.993629 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.09783 | −0.561351 | ||||||||
\(119\) | − 6.66487i | − 0.610968i | ||||||||
\(120\) | 0.417895 | 0.0381484 | ||||||||
\(121\) | −20.9541 | −1.90492 | ||||||||
\(122\) | − 3.78986i | − 0.343117i | ||||||||
\(123\) | 0.445042i | 0.0401281i | ||||||||
\(124\) | 9.49396i | 0.852583i | ||||||||
\(125\) | − 2.45473i | − 0.219558i | ||||||||
\(126\) | 0.780167 | 0.0695028 | ||||||||
\(127\) | −10.7995 | −0.958305 | −0.479152 | − | 0.877732i | \(-0.659056\pi\) | ||||
−0.479152 | + | 0.877732i | \(0.659056\pi\) | |||||||
\(128\) | 10.9215i | 0.965337i | ||||||||
\(129\) | −1.71379 | −0.150891 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.907542 | 0.0792923 | 0.0396462 | − | 0.999214i | \(-0.487377\pi\) | ||||
0.0396462 | + | 0.999214i | \(0.487377\pi\) | |||||||
\(132\) | − 10.1860i | − 0.886576i | ||||||||
\(133\) | 9.78554 | 0.848514 | ||||||||
\(134\) | −2.65279 | −0.229166 | ||||||||
\(135\) | − 0.246980i | − 0.0212566i | ||||||||
\(136\) | 6.43296i | 0.551622i | ||||||||
\(137\) | 9.54825i | 0.815762i | 0.913035 | + | 0.407881i | \(0.133732\pi\) | ||||
−0.913035 | + | 0.407881i | \(0.866268\pi\) | |||||||
\(138\) | − 3.71379i | − 0.316139i | ||||||||
\(139\) | −4.09246 | −0.347118 | −0.173559 | − | 0.984823i | \(-0.555527\pi\) | ||||
−0.173559 | + | 0.984823i | \(0.555527\pi\) | |||||||
\(140\) | −0.780167 | −0.0659362 | ||||||||
\(141\) | 6.73556i | 0.567237i | ||||||||
\(142\) | 2.54527 | 0.213594 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.85086 | 0.237571 | ||||||||
\(145\) | 1.46681i | 0.121812i | ||||||||
\(146\) | 3.27413 | 0.270969 | ||||||||
\(147\) | 3.92692 | 0.323887 | ||||||||
\(148\) | − 5.76271i | − 0.473692i | ||||||||
\(149\) | − 15.3884i | − 1.26066i | −0.776326 | − | 0.630332i | \(-0.782919\pi\) | ||||
0.776326 | − | 0.630332i | \(-0.217081\pi\) | |||||||
\(150\) | 2.19806i | 0.179471i | ||||||||
\(151\) | 3.67456i | 0.299032i | 0.988759 | + | 0.149516i | \(0.0477715\pi\) | ||||
−0.988759 | + | 0.149516i | \(0.952228\pi\) | |||||||
\(152\) | −9.44504 | −0.766094 | ||||||||
\(153\) | 3.80194 | 0.307368 | ||||||||
\(154\) | − 4.41013i | − 0.355378i | ||||||||
\(155\) | 1.30127 | 0.104521 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.87800 | −0.389307 | −0.194653 | − | 0.980872i | \(-0.562358\pi\) | ||||
−0.194653 | + | 0.980872i | \(0.562358\pi\) | |||||||
\(158\) | 1.98254i | 0.157723i | ||||||||
\(159\) | −1.06100 | −0.0841427 | ||||||||
\(160\) | 1.14914 | 0.0908479 | ||||||||
\(161\) | 14.6286i | 1.15290i | ||||||||
\(162\) | 0.445042i | 0.0349658i | ||||||||
\(163\) | − 8.63102i | − 0.676034i | −0.941140 | − | 0.338017i | \(-0.890244\pi\) | ||||
0.941140 | − | 0.338017i | \(-0.109756\pi\) | |||||||
\(164\) | 0.801938i | 0.0626208i | ||||||||
\(165\) | −1.39612 | −0.108688 | ||||||||
\(166\) | 4.53319 | 0.351844 | ||||||||
\(167\) | − 9.46980i | − 0.732795i | −0.930458 | − | 0.366397i | \(-0.880591\pi\) | ||||
0.930458 | − | 0.366397i | \(-0.119409\pi\) | |||||||
\(168\) | 2.96615 | 0.228843 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.417895 | 0.0320511 | ||||||||
\(171\) | 5.58211i | 0.426874i | ||||||||
\(172\) | −3.08815 | −0.235469 | ||||||||
\(173\) | −4.77479 | −0.363021 | −0.181510 | − | 0.983389i | \(-0.558099\pi\) | ||||
−0.181510 | + | 0.983389i | \(0.558099\pi\) | |||||||
\(174\) | − 2.64310i | − 0.200373i | ||||||||
\(175\) | − 8.65817i | − 0.654496i | ||||||||
\(176\) | − 16.1153i | − 1.21474i | ||||||||
\(177\) | 13.7017i | 1.02988i | ||||||||
\(178\) | 0.0609989 | 0.00457206 | ||||||||
\(179\) | −3.43535 | −0.256770 | −0.128385 | − | 0.991724i | \(-0.540979\pi\) | ||||
−0.128385 | + | 0.991724i | \(0.540979\pi\) | |||||||
\(180\) | − 0.445042i | − 0.0331715i | ||||||||
\(181\) | 13.4862 | 1.00242 | 0.501210 | − | 0.865326i | \(-0.332888\pi\) | ||||
0.501210 | + | 0.865326i | \(0.332888\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.51573 | −0.629501 | ||||||||
\(184\) | − 14.1196i | − 1.04091i | ||||||||
\(185\) | −0.789856 | −0.0580714 | ||||||||
\(186\) | −2.34481 | −0.171930 | ||||||||
\(187\) | − 21.4916i | − 1.57162i | ||||||||
\(188\) | 12.1371i | 0.885186i | ||||||||
\(189\) | − 1.75302i | − 0.127513i | ||||||||
\(190\) | 0.613564i | 0.0445126i | ||||||||
\(191\) | −1.30127 | −0.0941569 | −0.0470784 | − | 0.998891i | \(-0.514991\pi\) | ||||
−0.0470784 | + | 0.998891i | \(0.514991\pi\) | |||||||
\(192\) | 3.63102 | 0.262046 | ||||||||
\(193\) | 9.19567i | 0.661919i | 0.943645 | + | 0.330959i | \(0.107372\pi\) | ||||
−0.943645 | + | 0.330959i | \(0.892628\pi\) | |||||||
\(194\) | 6.09246 | 0.437413 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.07606 | 0.505433 | ||||||||
\(197\) | 4.11231i | 0.292990i | 0.989211 | + | 0.146495i | \(0.0467992\pi\) | ||||
−0.989211 | + | 0.146495i | \(0.953201\pi\) | |||||||
\(198\) | 2.51573 | 0.178785 | ||||||||
\(199\) | 24.7724 | 1.75607 | 0.878034 | − | 0.478598i | \(-0.158855\pi\) | ||||
0.878034 | + | 0.478598i | \(0.158855\pi\) | |||||||
\(200\) | 8.35690i | 0.590922i | ||||||||
\(201\) | 5.96077i | 0.420440i | ||||||||
\(202\) | 2.40821i | 0.169441i | ||||||||
\(203\) | 10.4112i | 0.730722i | ||||||||
\(204\) | 6.85086 | 0.479656 | ||||||||
\(205\) | 0.109916 | 0.00767688 | ||||||||
\(206\) | − 6.12200i | − 0.426540i | ||||||||
\(207\) | −8.34481 | −0.580005 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 31.5545 | 2.18267 | ||||||||
\(210\) | − 0.192685i | − 0.0132966i | ||||||||
\(211\) | −5.93900 | −0.408858 | −0.204429 | − | 0.978881i | \(-0.565534\pi\) | ||||
−0.204429 | + | 0.978881i | \(0.565534\pi\) | |||||||
\(212\) | −1.91185 | −0.131307 | ||||||||
\(213\) | − 5.71917i | − 0.391871i | ||||||||
\(214\) | − 5.70410i | − 0.389924i | ||||||||
\(215\) | 0.423272i | 0.0288669i | ||||||||
\(216\) | 1.69202i | 0.115127i | ||||||||
\(217\) | 9.23623 | 0.626996 | ||||||||
\(218\) | −5.40581 | −0.366128 | ||||||||
\(219\) | − 7.35690i | − 0.497133i | ||||||||
\(220\) | −2.51573 | −0.169610 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.42327 | 0.0955237 | ||||||||
\(223\) | 14.2010i | 0.950972i | 0.879723 | + | 0.475486i | \(0.157728\pi\) | ||||
−0.879723 | + | 0.475486i | \(0.842272\pi\) | |||||||
\(224\) | 8.15644 | 0.544975 | ||||||||
\(225\) | 4.93900 | 0.329267 | ||||||||
\(226\) | − 0.728857i | − 0.0484829i | ||||||||
\(227\) | 16.0073i | 1.06244i | 0.847233 | + | 0.531221i | \(0.178267\pi\) | ||||
−0.847233 | + | 0.531221i | \(0.821733\pi\) | |||||||
\(228\) | 10.0586i | 0.666147i | ||||||||
\(229\) | − 1.84117i | − 0.121668i | −0.998148 | − | 0.0608339i | \(-0.980624\pi\) | ||||
0.998148 | − | 0.0608339i | \(-0.0193760\pi\) | |||||||
\(230\) | −0.917231 | −0.0604804 | ||||||||
\(231\) | −9.90946 | −0.651995 | ||||||||
\(232\) | − 10.0489i | − 0.659744i | ||||||||
\(233\) | 23.4252 | 1.53464 | 0.767318 | − | 0.641267i | \(-0.221591\pi\) | ||||
0.767318 | + | 0.641267i | \(0.221591\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.66355 | 0.108518 | ||||||||
\(236\) | 24.6896i | 1.60716i | ||||||||
\(237\) | 4.45473 | 0.289366 | ||||||||
\(238\) | 2.96615 | 0.192267 | ||||||||
\(239\) | 14.6015i | 0.944491i | 0.881467 | + | 0.472246i | \(0.156556\pi\) | ||||
−0.881467 | + | 0.472246i | \(0.843444\pi\) | |||||||
\(240\) | − 0.704103i | − 0.0454497i | ||||||||
\(241\) | − 8.63102i | − 0.555973i | −0.960585 | − | 0.277987i | \(-0.910333\pi\) | ||||
0.960585 | − | 0.277987i | \(-0.0896671\pi\) | |||||||
\(242\) | − 9.32544i | − 0.599462i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −15.3448 | −0.982351 | ||||||||
\(245\) | − 0.969869i | − 0.0619627i | ||||||||
\(246\) | −0.198062 | −0.0126280 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8.91484 | −0.566093 | ||||||||
\(249\) | − 10.1860i | − 0.645510i | ||||||||
\(250\) | 1.09246 | 0.0690931 | ||||||||
\(251\) | 3.80194 | 0.239976 | 0.119988 | − | 0.992775i | \(-0.461714\pi\) | ||||
0.119988 | + | 0.992775i | \(0.461714\pi\) | |||||||
\(252\) | − 3.15883i | − 0.198988i | ||||||||
\(253\) | 47.1715i | 2.96565i | ||||||||
\(254\) | − 4.80625i | − 0.301571i | ||||||||
\(255\) | − 0.939001i | − 0.0588025i | ||||||||
\(256\) | 2.40150 | 0.150094 | ||||||||
\(257\) | 20.5961 | 1.28475 | 0.642375 | − | 0.766391i | \(-0.277949\pi\) | ||||
0.642375 | + | 0.766391i | \(0.277949\pi\) | |||||||
\(258\) | − 0.762709i | − 0.0474842i | ||||||||
\(259\) | −5.60627 | −0.348357 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.93900 | −0.367615 | ||||||||
\(262\) | 0.403894i | 0.0249527i | ||||||||
\(263\) | 0.332733 | 0.0205172 | 0.0102586 | − | 0.999947i | \(-0.496735\pi\) | ||||
0.0102586 | + | 0.999947i | \(0.496735\pi\) | |||||||
\(264\) | 9.56465 | 0.588663 | ||||||||
\(265\) | 0.262045i | 0.0160973i | ||||||||
\(266\) | 4.35498i | 0.267021i | ||||||||
\(267\) | − 0.137063i | − 0.00838814i | ||||||||
\(268\) | 10.7409i | 0.656107i | ||||||||
\(269\) | 27.3032 | 1.66471 | 0.832353 | − | 0.554247i | \(-0.186994\pi\) | ||||
0.832353 | + | 0.554247i | \(0.186994\pi\) | |||||||
\(270\) | 0.109916 | 0.00668929 | ||||||||
\(271\) | − 27.9855i | − 1.70000i | −0.526783 | − | 0.850000i | \(-0.676602\pi\) | ||||
0.526783 | − | 0.850000i | \(-0.323398\pi\) | |||||||
\(272\) | 10.8388 | 0.657197 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.24937 | −0.256714 | ||||||||
\(275\) | − 27.9191i | − 1.68359i | ||||||||
\(276\) | −15.0368 | −0.905111 | ||||||||
\(277\) | 2.10321 | 0.126370 | 0.0631849 | − | 0.998002i | \(-0.479874\pi\) | ||||
0.0631849 | + | 0.998002i | \(0.479874\pi\) | |||||||
\(278\) | − 1.82132i | − 0.109235i | ||||||||
\(279\) | 5.26875i | 0.315432i | ||||||||
\(280\) | − 0.732578i | − 0.0437799i | ||||||||
\(281\) | − 27.2349i | − 1.62470i | −0.583172 | − | 0.812349i | \(-0.698189\pi\) | ||||
0.583172 | − | 0.812349i | \(-0.301811\pi\) | |||||||
\(282\) | −2.99761 | −0.178505 | ||||||||
\(283\) | −5.28382 | −0.314090 | −0.157045 | − | 0.987591i | \(-0.550197\pi\) | ||||
−0.157045 | + | 0.987591i | \(0.550197\pi\) | |||||||
\(284\) | − 10.3056i | − 0.611524i | ||||||||
\(285\) | 1.37867 | 0.0816651 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.780167 | 0.0460518 | ||||||||
\(288\) | 4.65279i | 0.274168i | ||||||||
\(289\) | −2.54527 | −0.149722 | ||||||||
\(290\) | −0.652793 | −0.0383333 | ||||||||
\(291\) | − 13.6896i | − 0.802500i | ||||||||
\(292\) | − 13.2567i | − 0.775788i | ||||||||
\(293\) | − 32.6625i | − 1.90816i | −0.299548 | − | 0.954081i | \(-0.596836\pi\) | ||||
0.299548 | − | 0.954081i | \(-0.403164\pi\) | |||||||
\(294\) | 1.74764i | 0.101925i | ||||||||
\(295\) | 3.38404 | 0.197027 | ||||||||
\(296\) | 5.41119 | 0.314519 | ||||||||
\(297\) | − 5.65279i | − 0.328008i | ||||||||
\(298\) | 6.84846 | 0.396721 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 8.89977 | 0.513829 | ||||||||
\(301\) | 3.00431i | 0.173166i | ||||||||
\(302\) | −1.63533 | −0.0941029 | ||||||||
\(303\) | 5.41119 | 0.310865 | ||||||||
\(304\) | 15.9138i | 0.912717i | ||||||||
\(305\) | 2.10321i | 0.120430i | ||||||||
\(306\) | 1.69202i | 0.0967264i | ||||||||
\(307\) | 20.7614i | 1.18491i | 0.805602 | + | 0.592457i | \(0.201842\pi\) | ||||
−0.805602 | + | 0.592457i | \(0.798158\pi\) | |||||||
\(308\) | −17.8562 | −1.01745 | ||||||||
\(309\) | −13.7560 | −0.782552 | ||||||||
\(310\) | 0.579121i | 0.0328919i | ||||||||
\(311\) | 11.3013 | 0.640836 | 0.320418 | − | 0.947276i | \(-0.396177\pi\) | ||||
0.320418 | + | 0.947276i | \(0.396177\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.27173 | −0.241453 | −0.120726 | − | 0.992686i | \(-0.538522\pi\) | ||||
−0.120726 | + | 0.992686i | \(0.538522\pi\) | |||||||
\(314\) | − 2.17092i | − 0.122512i | ||||||||
\(315\) | −0.432960 | −0.0243945 | ||||||||
\(316\) | 8.02715 | 0.451562 | ||||||||
\(317\) | 15.4776i | 0.869307i | 0.900598 | + | 0.434653i | \(0.143129\pi\) | ||||
−0.900598 | + | 0.434653i | \(0.856871\pi\) | |||||||
\(318\) | − 0.472189i | − 0.0264790i | ||||||||
\(319\) | 33.5719i | 1.87967i | ||||||||
\(320\) | − 0.896789i | − 0.0501320i | ||||||||
\(321\) | −12.8170 | −0.715375 | ||||||||
\(322\) | −6.51035 | −0.362808 | ||||||||
\(323\) | 21.2228i | 1.18087i | ||||||||
\(324\) | 1.80194 | 0.100108 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.84117 | 0.212743 | ||||||||
\(327\) | 12.1468i | 0.671717i | ||||||||
\(328\) | −0.753020 | −0.0415786 | ||||||||
\(329\) | 11.8076 | 0.650973 | ||||||||
\(330\) | − 0.621334i | − 0.0342033i | ||||||||
\(331\) | 6.06829i | 0.333544i | 0.985996 | + | 0.166772i | \(0.0533343\pi\) | ||||
−0.985996 | + | 0.166772i | \(0.946666\pi\) | |||||||
\(332\) | − 18.3545i | − 1.00733i | ||||||||
\(333\) | − 3.19806i | − 0.175253i | ||||||||
\(334\) | 4.21446 | 0.230605 | ||||||||
\(335\) | 1.47219 | 0.0804343 | ||||||||
\(336\) | − 4.99761i | − 0.272642i | ||||||||
\(337\) | −12.1239 | −0.660432 | −0.330216 | − | 0.943905i | \(-0.607122\pi\) | ||||
−0.330216 | + | 0.943905i | \(0.607122\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.63773 | −0.0889491 | ||||||||
\(340\) | − 1.69202i | − 0.0917627i | ||||||||
\(341\) | 29.7832 | 1.61285 | ||||||||
\(342\) | −2.48427 | −0.134334 | ||||||||
\(343\) | − 19.1551i | − 1.03428i | ||||||||
\(344\) | − 2.89977i | − 0.156345i | ||||||||
\(345\) | 2.06100i | 0.110960i | ||||||||
\(346\) | − 2.12498i | − 0.114240i | ||||||||
\(347\) | 23.1497 | 1.24274 | 0.621371 | − | 0.783516i | \(-0.286576\pi\) | ||||
0.621371 | + | 0.783516i | \(0.286576\pi\) | |||||||
\(348\) | −10.7017 | −0.573672 | ||||||||
\(349\) | 22.1957i | 1.18811i | 0.804426 | + | 0.594053i | \(0.202473\pi\) | ||||
−0.804426 | + | 0.594053i | \(0.797527\pi\) | |||||||
\(350\) | 3.85325 | 0.205965 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 26.3013 | 1.40186 | ||||||||
\(353\) | − 5.07069i | − 0.269885i | −0.990853 | − | 0.134943i | \(-0.956915\pi\) | ||||
0.990853 | − | 0.134943i | \(-0.0430850\pi\) | |||||||
\(354\) | −6.09783 | −0.324096 | ||||||||
\(355\) | −1.41252 | −0.0749687 | ||||||||
\(356\) | − 0.246980i | − 0.0130899i | ||||||||
\(357\) | − 6.66487i | − 0.352743i | ||||||||
\(358\) | − 1.52888i | − 0.0808036i | ||||||||
\(359\) | 16.6746i | 0.880050i | 0.897986 | + | 0.440025i | \(0.145030\pi\) | ||||
−0.897986 | + | 0.440025i | \(0.854970\pi\) | |||||||
\(360\) | 0.417895 | 0.0220250 | ||||||||
\(361\) | −12.1599 | −0.639995 | ||||||||
\(362\) | 6.00192i | 0.315454i | ||||||||
\(363\) | −20.9541 | −1.09980 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.81700 | −0.0951063 | ||||||||
\(366\) | − 3.78986i | − 0.198099i | ||||||||
\(367\) | −1.17928 | −0.0615577 | −0.0307789 | − | 0.999526i | \(-0.509799\pi\) | ||||
−0.0307789 | + | 0.999526i | \(0.509799\pi\) | |||||||
\(368\) | −23.7899 | −1.24013 | ||||||||
\(369\) | 0.445042i | 0.0231680i | ||||||||
\(370\) | − 0.351519i | − 0.0182746i | ||||||||
\(371\) | 1.85995i | 0.0965639i | ||||||||
\(372\) | 9.49396i | 0.492239i | ||||||||
\(373\) | −30.0925 | −1.55813 | −0.779064 | − | 0.626944i | \(-0.784305\pi\) | ||||
−0.779064 | + | 0.626944i | \(0.784305\pi\) | |||||||
\(374\) | 9.56465 | 0.494576 | ||||||||
\(375\) | − 2.45473i | − 0.126762i | ||||||||
\(376\) | −11.3967 | −0.587741 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.780167 | 0.0401275 | ||||||||
\(379\) | − 19.1631i | − 0.984345i | −0.870498 | − | 0.492172i | \(-0.836203\pi\) | ||||
0.870498 | − | 0.492172i | \(-0.163797\pi\) | |||||||
\(380\) | 2.48427 | 0.127440 | ||||||||
\(381\) | −10.7995 | −0.553277 | ||||||||
\(382\) | − 0.579121i | − 0.0296304i | ||||||||
\(383\) | − 15.3884i | − 0.786308i | −0.919473 | − | 0.393154i | \(-0.871384\pi\) | ||||
0.919473 | − | 0.393154i | \(-0.128616\pi\) | |||||||
\(384\) | 10.9215i | 0.557338i | ||||||||
\(385\) | 2.44743i | 0.124733i | ||||||||
\(386\) | −4.09246 | −0.208301 | ||||||||
\(387\) | −1.71379 | −0.0871169 | ||||||||
\(388\) | − 24.6679i | − 1.25232i | ||||||||
\(389\) | 24.0315 | 1.21844 | 0.609222 | − | 0.793000i | \(-0.291482\pi\) | ||||
0.609222 | + | 0.793000i | \(0.291482\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.7265 | −1.60448 | ||||||||
\(392\) | 6.64443i | 0.335594i | ||||||||
\(393\) | 0.907542 | 0.0457794 | ||||||||
\(394\) | −1.83015 | −0.0922016 | ||||||||
\(395\) | − 1.10023i | − 0.0553585i | ||||||||
\(396\) | − 10.1860i | − 0.511865i | ||||||||
\(397\) | − 29.6015i | − 1.48566i | −0.669482 | − | 0.742828i | \(-0.733484\pi\) | ||||
0.669482 | − | 0.742828i | \(-0.266516\pi\) | |||||||
\(398\) | 11.0248i | 0.552621i | ||||||||
\(399\) | 9.78554 | 0.489890 | ||||||||
\(400\) | 14.0804 | 0.704019 | ||||||||
\(401\) | 21.1032i | 1.05384i | 0.849914 | + | 0.526922i | \(0.176654\pi\) | ||||
−0.849914 | + | 0.526922i | \(0.823346\pi\) | |||||||
\(402\) | −2.65279 | −0.132309 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 9.75063 | 0.485112 | ||||||||
\(405\) | − 0.246980i | − 0.0122725i | ||||||||
\(406\) | −4.63342 | −0.229953 | ||||||||
\(407\) | −18.0780 | −0.896092 | ||||||||
\(408\) | 6.43296i | 0.318479i | ||||||||
\(409\) | − 36.0224i | − 1.78119i | −0.454796 | − | 0.890596i | \(-0.650288\pi\) | ||||
0.454796 | − | 0.890596i | \(-0.349712\pi\) | |||||||
\(410\) | 0.0489173i | 0.00241586i | ||||||||
\(411\) | 9.54825i | 0.470981i | ||||||||
\(412\) | −24.7875 | −1.22119 | ||||||||
\(413\) | 24.0194 | 1.18192 | ||||||||
\(414\) | − 3.71379i | − 0.182523i | ||||||||
\(415\) | −2.51573 | −0.123492 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.09246 | −0.200409 | ||||||||
\(418\) | 14.0431i | 0.686869i | ||||||||
\(419\) | 5.96854 | 0.291582 | 0.145791 | − | 0.989315i | \(-0.453427\pi\) | ||||
0.145791 | + | 0.989315i | \(0.453427\pi\) | |||||||
\(420\) | −0.780167 | −0.0380683 | ||||||||
\(421\) | − 2.09544i | − 0.102126i | −0.998695 | − | 0.0510628i | \(-0.983739\pi\) | ||||
0.998695 | − | 0.0510628i | \(-0.0162609\pi\) | |||||||
\(422\) | − 2.64310i | − 0.128664i | ||||||||
\(423\) | 6.73556i | 0.327494i | ||||||||
\(424\) | − 1.79523i | − 0.0871842i | ||||||||
\(425\) | 18.7778 | 0.910856 | ||||||||
\(426\) | 2.54527 | 0.123319 | ||||||||
\(427\) | 14.9282i | 0.722429i | ||||||||
\(428\) | −23.0954 | −1.11636 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.188374 | −0.00908418 | ||||||||
\(431\) | − 2.88577i | − 0.139003i | −0.997582 | − | 0.0695014i | \(-0.977859\pi\) | ||||
0.997582 | − | 0.0695014i | \(-0.0221408\pi\) | |||||||
\(432\) | 2.85086 | 0.137162 | ||||||||
\(433\) | 12.6485 | 0.607847 | 0.303924 | − | 0.952696i | \(-0.401703\pi\) | ||||
0.303924 | + | 0.952696i | \(0.401703\pi\) | |||||||
\(434\) | 4.11051i | 0.197311i | ||||||||
\(435\) | 1.46681i | 0.0703283i | ||||||||
\(436\) | 21.8877i | 1.04823i | ||||||||
\(437\) | − 46.5816i | − 2.22830i | ||||||||
\(438\) | 3.27413 | 0.156444 | ||||||||
\(439\) | 10.9269 | 0.521513 | 0.260757 | − | 0.965405i | \(-0.416028\pi\) | ||||
0.260757 | + | 0.965405i | \(0.416028\pi\) | |||||||
\(440\) | − 2.36227i | − 0.112617i | ||||||||
\(441\) | 3.92692 | 0.186996 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.2403 | −0.914133 | −0.457067 | − | 0.889433i | \(-0.651100\pi\) | ||||
−0.457067 | + | 0.889433i | \(0.651100\pi\) | |||||||
\(444\) | − 5.76271i | − 0.273486i | ||||||||
\(445\) | −0.0338518 | −0.00160473 | ||||||||
\(446\) | −6.32006 | −0.299264 | ||||||||
\(447\) | − 15.3884i | − 0.727844i | ||||||||
\(448\) | − 6.36526i | − 0.300730i | ||||||||
\(449\) | 28.8200i | 1.36010i | 0.733166 | + | 0.680050i | \(0.238042\pi\) | ||||
−0.733166 | + | 0.680050i | \(0.761958\pi\) | |||||||
\(450\) | 2.19806i | 0.103618i | ||||||||
\(451\) | 2.51573 | 0.118461 | ||||||||
\(452\) | −2.95108 | −0.138807 | ||||||||
\(453\) | 3.67456i | 0.172646i | ||||||||
\(454\) | −7.12392 | −0.334342 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.44504 | −0.442305 | ||||||||
\(457\) | − 18.0707i | − 0.845311i | −0.906290 | − | 0.422656i | \(-0.861098\pi\) | ||||
0.906290 | − | 0.422656i | \(-0.138902\pi\) | |||||||
\(458\) | 0.819396 | 0.0382879 | ||||||||
\(459\) | 3.80194 | 0.177459 | ||||||||
\(460\) | 3.71379i | 0.173156i | ||||||||
\(461\) | − 7.56763i | − 0.352460i | −0.984349 | − | 0.176230i | \(-0.943610\pi\) | ||||
0.984349 | − | 0.176230i | \(-0.0563902\pi\) | |||||||
\(462\) | − 4.41013i | − 0.205178i | ||||||||
\(463\) | − 35.3551i | − 1.64309i | −0.570143 | − | 0.821545i | \(-0.693112\pi\) | ||||
0.570143 | − | 0.821545i | \(-0.306888\pi\) | |||||||
\(464\) | −16.9312 | −0.786013 | ||||||||
\(465\) | 1.30127 | 0.0603451 | ||||||||
\(466\) | 10.4252i | 0.482938i | ||||||||
\(467\) | −13.0000 | −0.601568 | −0.300784 | − | 0.953692i | \(-0.597248\pi\) | ||||
−0.300784 | + | 0.953692i | \(0.597248\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.4494 | 0.482506 | ||||||||
\(470\) | 0.740348i | 0.0341497i | ||||||||
\(471\) | −4.87800 | −0.224766 | ||||||||
\(472\) | −23.1836 | −1.06711 | ||||||||
\(473\) | 9.68771i | 0.445441i | ||||||||
\(474\) | 1.98254i | 0.0910612i | ||||||||
\(475\) | 27.5700i | 1.26500i | ||||||||
\(476\) | − 12.0097i | − 0.550463i | ||||||||
\(477\) | −1.06100 | −0.0485798 | ||||||||
\(478\) | −6.49827 | −0.297224 | ||||||||
\(479\) | 25.5265i | 1.16633i | 0.812352 | + | 0.583167i | \(0.198187\pi\) | ||||
−0.812352 | + | 0.583167i | \(0.801813\pi\) | |||||||
\(480\) | 1.14914 | 0.0524510 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.84117 | 0.174960 | ||||||||
\(483\) | 14.6286i | 0.665626i | ||||||||
\(484\) | −37.7579 | −1.71627 | ||||||||
\(485\) | −3.38106 | −0.153526 | ||||||||
\(486\) | 0.445042i | 0.0201875i | ||||||||
\(487\) | 16.0073i | 0.725360i | 0.931914 | + | 0.362680i | \(0.118138\pi\) | ||||
−0.931914 | + | 0.362680i | \(0.881862\pi\) | |||||||
\(488\) | − 14.4088i | − 0.652256i | ||||||||
\(489\) | − 8.63102i | − 0.390308i | ||||||||
\(490\) | 0.431632 | 0.0194992 | ||||||||
\(491\) | −20.7385 | −0.935917 | −0.467959 | − | 0.883750i | \(-0.655010\pi\) | ||||
−0.467959 | + | 0.883750i | \(0.655010\pi\) | |||||||
\(492\) | 0.801938i | 0.0361541i | ||||||||
\(493\) | −22.5797 | −1.01694 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.39612 | −0.0627511 | ||||||||
\(496\) | 15.0204i | 0.674438i | ||||||||
\(497\) | −10.0258 | −0.449719 | ||||||||
\(498\) | 4.53319 | 0.203137 | ||||||||
\(499\) | − 8.06770i | − 0.361160i | −0.983560 | − | 0.180580i | \(-0.942203\pi\) | ||||
0.983560 | − | 0.180580i | \(-0.0577975\pi\) | |||||||
\(500\) | − 4.42327i | − 0.197815i | ||||||||
\(501\) | − 9.46980i | − 0.423079i | ||||||||
\(502\) | 1.69202i | 0.0755186i | ||||||||
\(503\) | −30.2422 | −1.34843 | −0.674216 | − | 0.738534i | \(-0.735518\pi\) | ||||
−0.674216 | + | 0.738534i | \(0.735518\pi\) | |||||||
\(504\) | 2.96615 | 0.132123 | ||||||||
\(505\) | − 1.33645i | − 0.0594714i | ||||||||
\(506\) | −20.9933 | −0.933266 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −19.4601 | −0.863403 | ||||||||
\(509\) | 16.0495i | 0.711382i | 0.934604 | + | 0.355691i | \(0.115754\pi\) | ||||
−0.934604 | + | 0.355691i | \(0.884246\pi\) | |||||||
\(510\) | 0.417895 | 0.0185047 | ||||||||
\(511\) | −12.8968 | −0.570520 | ||||||||
\(512\) | 22.9119i | 1.01257i | ||||||||
\(513\) | 5.58211i | 0.246456i | ||||||||
\(514\) | 9.16613i | 0.404301i | ||||||||
\(515\) | 3.39745i | 0.149710i | ||||||||
\(516\) | −3.08815 | −0.135948 | ||||||||
\(517\) | 38.0747 | 1.67452 | ||||||||
\(518\) | − 2.49502i | − 0.109625i | ||||||||
\(519\) | −4.77479 | −0.209590 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.69309 | −0.117986 | −0.0589931 | − | 0.998258i | \(-0.518789\pi\) | ||||
−0.0589931 | + | 0.998258i | \(0.518789\pi\) | |||||||
\(522\) | − 2.64310i | − 0.115686i | ||||||||
\(523\) | 35.3957 | 1.54774 | 0.773872 | − | 0.633342i | \(-0.218317\pi\) | ||||
0.773872 | + | 0.633342i | \(0.218317\pi\) | |||||||
\(524\) | 1.63533 | 0.0714399 | ||||||||
\(525\) | − 8.65817i | − 0.377874i | ||||||||
\(526\) | 0.148080i | 0.00645659i | ||||||||
\(527\) | 20.0315i | 0.872584i | ||||||||
\(528\) | − 16.1153i | − 0.701328i | ||||||||
\(529\) | 46.6359 | 2.02765 | ||||||||
\(530\) | −0.116621 | −0.00506569 | ||||||||
\(531\) | 13.7017i | 0.594604i | ||||||||
\(532\) | 17.6329 | 0.764485 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.0609989 | 0.00263968 | ||||||||
\(535\) | 3.16554i | 0.136858i | ||||||||
\(536\) | −10.0858 | −0.435638 | ||||||||
\(537\) | −3.43535 | −0.148246 | ||||||||
\(538\) | 12.1511i | 0.523870i | ||||||||
\(539\) | − 22.1981i | − 0.956138i | ||||||||
\(540\) | − 0.445042i | − 0.0191516i | ||||||||
\(541\) | 34.7338i | 1.49332i | 0.665205 | + | 0.746660i | \(0.268344\pi\) | ||||
−0.665205 | + | 0.746660i | \(0.731656\pi\) | |||||||
\(542\) | 12.4547 | 0.534976 | ||||||||
\(543\) | 13.4862 | 0.578748 | ||||||||
\(544\) | 17.6896i | 0.758437i | ||||||||
\(545\) | 3.00000 | 0.128506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.1183 | −1.11674 | −0.558368 | − | 0.829593i | \(-0.688572\pi\) | ||||
−0.558368 | + | 0.829593i | \(0.688572\pi\) | |||||||
\(548\) | 17.2054i | 0.734976i | ||||||||
\(549\) | −8.51573 | −0.363442 | ||||||||
\(550\) | 12.4252 | 0.529812 | ||||||||
\(551\) | − 33.1521i | − 1.41233i | ||||||||
\(552\) | − 14.1196i | − 0.600970i | ||||||||
\(553\) | − 7.80923i | − 0.332082i | ||||||||
\(554\) | 0.936017i | 0.0397676i | ||||||||
\(555\) | −0.789856 | −0.0335275 | ||||||||
\(556\) | −7.37435 | −0.312742 | ||||||||
\(557\) | − 24.7748i | − 1.04974i | −0.851182 | − | 0.524871i | \(-0.824114\pi\) | ||||
0.851182 | − | 0.524871i | \(-0.175886\pi\) | |||||||
\(558\) | −2.34481 | −0.0992639 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.23431 | −0.0521590 | ||||||||
\(561\) | − 21.4916i | − 0.907375i | ||||||||
\(562\) | 12.1207 | 0.511280 | ||||||||
\(563\) | −5.26098 | −0.221724 | −0.110862 | − | 0.993836i | \(-0.535361\pi\) | ||||
−0.110862 | + | 0.993836i | \(0.535361\pi\) | |||||||
\(564\) | 12.1371i | 0.511063i | ||||||||
\(565\) | 0.404485i | 0.0170168i | ||||||||
\(566\) | − 2.35152i | − 0.0988417i | ||||||||
\(567\) | − 1.75302i | − 0.0736199i | ||||||||
\(568\) | 9.67696 | 0.406036 | ||||||||
\(569\) | 33.7458 | 1.41470 | 0.707350 | − | 0.706864i | \(-0.249891\pi\) | ||||
0.707350 | + | 0.706864i | \(0.249891\pi\) | |||||||
\(570\) | 0.613564i | 0.0256994i | ||||||||
\(571\) | −23.0887 | −0.966234 | −0.483117 | − | 0.875556i | \(-0.660495\pi\) | ||||
−0.483117 | + | 0.875556i | \(0.660495\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.30127 | −0.0543615 | ||||||||
\(574\) | 0.347207i | 0.0144921i | ||||||||
\(575\) | −41.2150 | −1.71879 | ||||||||
\(576\) | 3.63102 | 0.151293 | ||||||||
\(577\) | 3.57002i | 0.148622i | 0.997235 | + | 0.0743110i | \(0.0236758\pi\) | ||||
−0.997235 | + | 0.0743110i | \(0.976324\pi\) | |||||||
\(578\) | − 1.13275i | − 0.0471162i | ||||||||
\(579\) | 9.19567i | 0.382159i | ||||||||
\(580\) | 2.64310i | 0.109749i | ||||||||
\(581\) | −17.8562 | −0.740801 | ||||||||
\(582\) | 6.09246 | 0.252541 | ||||||||
\(583\) | 5.99761i | 0.248396i | ||||||||
\(584\) | 12.4480 | 0.515103 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.5362 | 0.600484 | ||||||||
\(587\) | − 11.4625i | − 0.473108i | −0.971618 | − | 0.236554i | \(-0.923982\pi\) | ||||
0.971618 | − | 0.236554i | \(-0.0760180\pi\) | |||||||
\(588\) | 7.07606 | 0.291812 | ||||||||
\(589\) | −29.4107 | −1.21185 | ||||||||
\(590\) | 1.50604i | 0.0620027i | ||||||||
\(591\) | 4.11231i | 0.169158i | ||||||||
\(592\) | − 9.11721i | − 0.374715i | ||||||||
\(593\) | 21.8538i | 0.897430i | 0.893675 | + | 0.448715i | \(0.148118\pi\) | ||||
−0.893675 | + | 0.448715i | \(0.851882\pi\) | |||||||
\(594\) | 2.51573 | 0.103222 | ||||||||
\(595\) | −1.64609 | −0.0674830 | ||||||||
\(596\) | − 27.7289i | − 1.13582i | ||||||||
\(597\) | 24.7724 | 1.01387 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.0573 | 1.10553 | 0.552765 | − | 0.833337i | \(-0.313573\pi\) | ||||
0.552765 | + | 0.833337i | \(0.313573\pi\) | |||||||
\(600\) | 8.35690i | 0.341169i | ||||||||
\(601\) | 10.8780 | 0.443723 | 0.221861 | − | 0.975078i | \(-0.428787\pi\) | ||||
0.221861 | + | 0.975078i | \(0.428787\pi\) | |||||||
\(602\) | −1.33704 | −0.0544939 | ||||||||
\(603\) | 5.96077i | 0.242741i | ||||||||
\(604\) | 6.62133i | 0.269418i | ||||||||
\(605\) | 5.17523i | 0.210403i | ||||||||
\(606\) | 2.40821i | 0.0978267i | ||||||||
\(607\) | −29.6359 | −1.20289 | −0.601443 | − | 0.798916i | \(-0.705407\pi\) | ||||
−0.601443 | + | 0.798916i | \(0.705407\pi\) | |||||||
\(608\) | −25.9724 | −1.05332 | ||||||||
\(609\) | 10.4112i | 0.421883i | ||||||||
\(610\) | −0.936017 | −0.0378982 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 6.85086 | 0.276929 | ||||||||
\(613\) | 10.2343i | 0.413360i | 0.978409 | + | 0.206680i | \(0.0662659\pi\) | ||||
−0.978409 | + | 0.206680i | \(0.933734\pi\) | |||||||
\(614\) | −9.23968 | −0.372883 | ||||||||
\(615\) | 0.109916 | 0.00443225 | ||||||||
\(616\) | − 16.7670i | − 0.675563i | ||||||||
\(617\) | 26.2828i | 1.05810i | 0.848590 | + | 0.529052i | \(0.177452\pi\) | ||||
−0.848590 | + | 0.529052i | \(0.822548\pi\) | |||||||
\(618\) | − 6.12200i | − 0.246263i | ||||||||
\(619\) | − 29.0834i | − 1.16896i | −0.811408 | − | 0.584479i | \(-0.801299\pi\) | ||||
0.811408 | − | 0.584479i | \(-0.198701\pi\) | |||||||
\(620\) | 2.34481 | 0.0941700 | ||||||||
\(621\) | −8.34481 | −0.334866 | ||||||||
\(622\) | 5.02954i | 0.201666i | ||||||||
\(623\) | −0.240275 | −0.00962641 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.0887 | 0.963549 | ||||||||
\(626\) | − 1.90110i | − 0.0759833i | ||||||||
\(627\) | 31.5545 | 1.26016 | ||||||||
\(628\) | −8.78986 | −0.350753 | ||||||||
\(629\) | − 12.1588i | − 0.484804i | ||||||||
\(630\) | − 0.192685i | − 0.00767677i | ||||||||
\(631\) | − 25.4480i | − 1.01307i | −0.862219 | − | 0.506535i | \(-0.830926\pi\) | ||||
0.862219 | − | 0.506535i | \(-0.169074\pi\) | |||||||
\(632\) | 7.53750i | 0.299826i | ||||||||
\(633\) | −5.93900 | −0.236054 | ||||||||
\(634\) | −6.88816 | −0.273564 | ||||||||
\(635\) | 2.66727i | 0.105847i | ||||||||
\(636\) | −1.91185 | −0.0758099 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.9409 | −0.591517 | ||||||||
\(639\) | − 5.71917i | − 0.226247i | ||||||||
\(640\) | 2.69740 | 0.106624 | ||||||||
\(641\) | 26.7409 | 1.05620 | 0.528102 | − | 0.849181i | \(-0.322904\pi\) | ||||
0.528102 | + | 0.849181i | \(0.322904\pi\) | |||||||
\(642\) | − 5.70410i | − 0.225123i | ||||||||
\(643\) | − 32.9614i | − 1.29987i | −0.759990 | − | 0.649935i | \(-0.774796\pi\) | ||||
0.759990 | − | 0.649935i | \(-0.225204\pi\) | |||||||
\(644\) | 26.3599i | 1.03872i | ||||||||
\(645\) | 0.423272i | 0.0166663i | ||||||||
\(646\) | −9.44504 | −0.371610 | ||||||||
\(647\) | −34.4946 | −1.35612 | −0.678060 | − | 0.735006i | \(-0.737179\pi\) | ||||
−0.678060 | + | 0.735006i | \(0.737179\pi\) | |||||||
\(648\) | 1.69202i | 0.0664689i | ||||||||
\(649\) | 77.4529 | 3.04029 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.23623 | 0.361996 | ||||||||
\(652\) | − 15.5526i | − 0.609085i | ||||||||
\(653\) | 36.1517 | 1.41472 | 0.707362 | − | 0.706852i | \(-0.249885\pi\) | ||||
0.707362 | + | 0.706852i | \(0.249885\pi\) | |||||||
\(654\) | −5.40581 | −0.211384 | ||||||||
\(655\) | − 0.224144i | − 0.00875805i | ||||||||
\(656\) | 1.26875i | 0.0495364i | ||||||||
\(657\) | − 7.35690i | − 0.287020i | ||||||||
\(658\) | 5.25487i | 0.204856i | ||||||||
\(659\) | −6.81700 | −0.265553 | −0.132776 | − | 0.991146i | \(-0.542389\pi\) | ||||
−0.132776 | + | 0.991146i | \(0.542389\pi\) | |||||||
\(660\) | −2.51573 | −0.0979246 | ||||||||
\(661\) | 10.8944i | 0.423743i | 0.977298 | + | 0.211871i | \(0.0679558\pi\) | ||||
−0.977298 | + | 0.211871i | \(0.932044\pi\) | |||||||
\(662\) | −2.70065 | −0.104964 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.2349 | 0.668844 | ||||||||
\(665\) | − 2.41683i | − 0.0937206i | ||||||||
\(666\) | 1.42327 | 0.0551507 | ||||||||
\(667\) | 49.5599 | 1.91897 | ||||||||
\(668\) | − 17.0640i | − 0.660225i | ||||||||
\(669\) | 14.2010i | 0.549044i | ||||||||
\(670\) | 0.655186i | 0.0253120i | ||||||||
\(671\) | 48.1377i | 1.85833i | ||||||||
\(672\) | 8.15644 | 0.314642 | ||||||||
\(673\) | −20.7385 | −0.799412 | −0.399706 | − | 0.916643i | \(-0.630888\pi\) | ||||
−0.399706 | + | 0.916643i | \(0.630888\pi\) | |||||||
\(674\) | − 5.39565i | − 0.207833i | ||||||||
\(675\) | 4.93900 | 0.190102 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.5786 | −0.983067 | −0.491534 | − | 0.870859i | \(-0.663564\pi\) | ||||
−0.491534 | + | 0.870859i | \(0.663564\pi\) | |||||||
\(678\) | − 0.728857i | − 0.0279916i | ||||||||
\(679\) | −23.9982 | −0.920966 | ||||||||
\(680\) | 1.58881 | 0.0609281 | ||||||||
\(681\) | 16.0073i | 0.613401i | ||||||||
\(682\) | 13.2547i | 0.507551i | ||||||||
\(683\) | − 21.6310i | − 0.827688i | −0.910348 | − | 0.413844i | \(-0.864186\pi\) | ||||
0.910348 | − | 0.413844i | \(-0.135814\pi\) | |||||||
\(684\) | 10.0586i | 0.384600i | ||||||||
\(685\) | 2.35822 | 0.0901031 | ||||||||
\(686\) | 8.52483 | 0.325479 | ||||||||
\(687\) | − 1.84117i | − 0.0702449i | ||||||||
\(688\) | −4.88577 | −0.186268 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.917231 | −0.0349184 | ||||||||
\(691\) | 2.62996i | 0.100048i | 0.998748 | + | 0.0500242i | \(0.0159298\pi\) | ||||
−0.998748 | + | 0.0500242i | \(0.984070\pi\) | |||||||
\(692\) | −8.60388 | −0.327070 | ||||||||
\(693\) | −9.90946 | −0.376429 | ||||||||
\(694\) | 10.3026i | 0.391081i | ||||||||
\(695\) | 1.01075i | 0.0383401i | ||||||||
\(696\) | − 10.0489i | − 0.380903i | ||||||||
\(697\) | 1.69202i | 0.0640899i | ||||||||
\(698\) | −9.87800 | −0.373888 | ||||||||
\(699\) | 23.4252 | 0.886022 | ||||||||
\(700\) | − 15.6015i | − 0.589681i | ||||||||
\(701\) | −40.0925 | −1.51427 | −0.757136 | − | 0.653258i | \(-0.773402\pi\) | ||||
−0.757136 | + | 0.653258i | \(0.773402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.8519 | 0.673298 | ||||||||
\(704\) | − 20.5254i | − 0.773581i | ||||||||
\(705\) | 1.66355 | 0.0626528 | ||||||||
\(706\) | 2.25667 | 0.0849308 | ||||||||
\(707\) | − 9.48593i | − 0.356755i | ||||||||
\(708\) | 24.6896i | 0.927893i | ||||||||
\(709\) | − 23.2097i | − 0.871657i | −0.900030 | − | 0.435829i | \(-0.856455\pi\) | ||||
0.900030 | − | 0.435829i | \(-0.143545\pi\) | |||||||
\(710\) | − 0.628630i | − 0.0235921i | ||||||||
\(711\) | 4.45473 | 0.167065 | ||||||||
\(712\) | 0.231914 | 0.00869135 | ||||||||
\(713\) | − 43.9667i | − 1.64657i | ||||||||
\(714\) | 2.96615 | 0.111005 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.19029 | −0.231342 | ||||||||
\(717\) | 14.6015i | 0.545302i | ||||||||
\(718\) | −7.42088 | −0.276945 | ||||||||
\(719\) | 26.0146 | 0.970181 | 0.485090 | − | 0.874464i | \(-0.338787\pi\) | ||||
0.485090 | + | 0.874464i | \(0.338787\pi\) | |||||||
\(720\) | − 0.704103i | − 0.0262404i | ||||||||
\(721\) | 24.1146i | 0.898073i | ||||||||
\(722\) | − 5.41166i | − 0.201401i | ||||||||
\(723\) | − 8.63102i | − 0.320991i | ||||||||
\(724\) | 24.3013 | 0.903150 | ||||||||
\(725\) | −29.3327 | −1.08939 | ||||||||
\(726\) | − 9.32544i | − 0.346099i | ||||||||
\(727\) | 16.5472 | 0.613701 | 0.306851 | − | 0.951758i | \(-0.400725\pi\) | ||||
0.306851 | + | 0.951758i | \(0.400725\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − 0.808643i | − 0.0299292i | ||||||||
\(731\) | −6.51573 | −0.240993 | ||||||||
\(732\) | −15.3448 | −0.567161 | ||||||||
\(733\) | 18.8750i | 0.697165i | 0.937278 | + | 0.348582i | \(0.113337\pi\) | ||||
−0.937278 | + | 0.348582i | \(0.886663\pi\) | |||||||
\(734\) | − 0.524827i | − 0.0193717i | ||||||||
\(735\) | − 0.969869i | − 0.0357742i | ||||||||
\(736\) | − 38.8267i | − 1.43117i | ||||||||
\(737\) | 33.6950 | 1.24117 | ||||||||
\(738\) | −0.198062 | −0.00729077 | ||||||||
\(739\) | − 47.3239i | − 1.74084i | −0.492312 | − | 0.870419i | \(-0.663848\pi\) | ||||
0.492312 | − | 0.870419i | \(-0.336152\pi\) | |||||||
\(740\) | −1.42327 | −0.0523205 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.827757 | −0.0303879 | ||||||||
\(743\) | − 8.88769i | − 0.326058i | −0.986621 | − | 0.163029i | \(-0.947874\pi\) | ||||
0.986621 | − | 0.163029i | \(-0.0521264\pi\) | |||||||
\(744\) | −8.91484 | −0.326834 | ||||||||
\(745\) | −3.80061 | −0.139244 | ||||||||
\(746\) | − 13.3924i | − 0.490331i | ||||||||
\(747\) | − 10.1860i | − 0.372686i | ||||||||
\(748\) | − 38.7265i | − 1.41598i | ||||||||
\(749\) | 22.4685i | 0.820980i | ||||||||
\(750\) | 1.09246 | 0.0398909 | ||||||||
\(751\) | −0.710808 | −0.0259377 | −0.0129689 | − | 0.999916i | \(-0.504128\pi\) | ||||
−0.0129689 | + | 0.999916i | \(0.504128\pi\) | |||||||
\(752\) | 19.2021i | 0.700229i | ||||||||
\(753\) | 3.80194 | 0.138550 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.907542 | 0.0330288 | ||||||||
\(756\) | − 3.15883i | − 0.114886i | ||||||||
\(757\) | 9.78554 | 0.355662 | 0.177831 | − | 0.984061i | \(-0.443092\pi\) | ||||
0.177831 | + | 0.984061i | \(0.443092\pi\) | |||||||
\(758\) | 8.52840 | 0.309766 | ||||||||
\(759\) | 47.1715i | 1.71222i | ||||||||
\(760\) | 2.33273i | 0.0846171i | ||||||||
\(761\) | 18.8810i | 0.684435i | 0.939621 | + | 0.342218i | \(0.111178\pi\) | ||||
−0.939621 | + | 0.342218i | \(0.888822\pi\) | |||||||
\(762\) | − 4.80625i | − 0.174112i | ||||||||
\(763\) | 21.2935 | 0.770877 | ||||||||
\(764\) | −2.34481 | −0.0848324 | ||||||||
\(765\) | − 0.939001i | − 0.0339497i | ||||||||
\(766\) | 6.84846 | 0.247445 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.40150 | 0.0866567 | ||||||||
\(769\) | − 12.4349i | − 0.448413i | −0.974542 | − | 0.224207i | \(-0.928021\pi\) | ||||
0.974542 | − | 0.224207i | \(-0.0719790\pi\) | |||||||
\(770\) | −1.08921 | −0.0392524 | ||||||||
\(771\) | 20.5961 | 0.741751 | ||||||||
\(772\) | 16.5700i | 0.596368i | ||||||||
\(773\) | 45.6746i | 1.64280i | 0.570353 | + | 0.821400i | \(0.306807\pi\) | ||||
−0.570353 | + | 0.821400i | \(0.693193\pi\) | |||||||
\(774\) | − 0.762709i | − 0.0274150i | ||||||||
\(775\) | 26.0224i | 0.934751i | ||||||||
\(776\) | 23.1631 | 0.831508 | ||||||||
\(777\) | −5.60627 | −0.201124 | ||||||||
\(778\) | 10.6950i | 0.383435i | ||||||||
\(779\) | −2.48427 | −0.0890082 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.3293 | −1.15683 | ||||||||
\(782\) | − 14.1196i | − 0.504916i | ||||||||
\(783\) | −5.93900 | −0.212243 | ||||||||
\(784\) | 11.1951 | 0.399824 | ||||||||
\(785\) | 1.20477i | 0.0430000i | ||||||||
\(786\) | 0.403894i | 0.0144064i | ||||||||
\(787\) | 4.51871i | 0.161075i | 0.996752 | + | 0.0805374i | \(0.0256636\pi\) | ||||
−0.996752 | + | 0.0805374i | \(0.974336\pi\) | |||||||
\(788\) | 7.41013i | 0.263975i | ||||||||
\(789\) | 0.332733 | 0.0118456 | ||||||||
\(790\) | 0.489647 | 0.0174209 | ||||||||
\(791\) | 2.87097i | 0.102080i | ||||||||
\(792\) | 9.56465 | 0.339865 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13.1739 | 0.467524 | ||||||||
\(795\) | 0.262045i | 0.00929378i | ||||||||
\(796\) | 44.6383 | 1.58216 | ||||||||
\(797\) | 28.7391 | 1.01799 | 0.508996 | − | 0.860769i | \(-0.330017\pi\) | ||||
0.508996 | + | 0.860769i | \(0.330017\pi\) | |||||||
\(798\) | 4.35498i | 0.154165i | ||||||||
\(799\) | 25.6082i | 0.905953i | ||||||||
\(800\) | 22.9801i | 0.812471i | ||||||||
\(801\) | − 0.137063i | − 0.00484289i | ||||||||
\(802\) | −9.39181 | −0.331636 | ||||||||
\(803\) | −41.5870 | −1.46757 | ||||||||
\(804\) | 10.7409i | 0.378804i | ||||||||
\(805\) | 3.61297 | 0.127341 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.3032 | 0.961118 | ||||||||
\(808\) | 9.15585i | 0.322102i | ||||||||
\(809\) | 5.42891 | 0.190870 | 0.0954352 | − | 0.995436i | \(-0.469576\pi\) | ||||
0.0954352 | + | 0.995436i | \(0.469576\pi\) | |||||||
\(810\) | 0.109916 | 0.00386206 | ||||||||
\(811\) | 0.629104i | 0.0220908i | 0.999939 | + | 0.0110454i | \(0.00351593\pi\) | ||||
−0.999939 | + | 0.0110454i | \(0.996484\pi\) | |||||||
\(812\) | 18.7603i | 0.658358i | ||||||||
\(813\) | − 27.9855i | − 0.981495i | ||||||||
\(814\) | − 8.04546i | − 0.281993i | ||||||||
\(815\) | −2.13169 | −0.0746697 | ||||||||
\(816\) | 10.8388 | 0.379433 | ||||||||
\(817\) | − 9.56657i | − 0.334692i | ||||||||
\(818\) | 16.0315 | 0.560527 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.198062 | 0.00691663 | ||||||||
\(821\) | 36.2640i | 1.26562i | 0.774307 | + | 0.632811i | \(0.218099\pi\) | ||||
−0.774307 | + | 0.632811i | \(0.781901\pi\) | |||||||
\(822\) | −4.24937 | −0.148214 | ||||||||
\(823\) | −41.7396 | −1.45495 | −0.727476 | − | 0.686133i | \(-0.759307\pi\) | ||||
−0.727476 | + | 0.686133i | \(0.759307\pi\) | |||||||
\(824\) | − 23.2755i | − 0.810839i | ||||||||
\(825\) | − 27.9191i | − 0.972020i | ||||||||
\(826\) | 10.6896i | 0.371940i | ||||||||
\(827\) | − 38.1997i | − 1.32833i | −0.747584 | − | 0.664167i | \(-0.768786\pi\) | ||||
0.747584 | − | 0.664167i | \(-0.231214\pi\) | |||||||
\(828\) | −15.0368 | −0.522566 | ||||||||
\(829\) | −15.9788 | −0.554967 | −0.277484 | − | 0.960730i | \(-0.589500\pi\) | ||||
−0.277484 | + | 0.960730i | \(0.589500\pi\) | |||||||
\(830\) | − 1.11960i | − 0.0388621i | ||||||||
\(831\) | 2.10321 | 0.0729596 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.9299 | 0.517290 | ||||||||
\(834\) | − 1.82132i | − 0.0630670i | ||||||||
\(835\) | −2.33885 | −0.0809391 | ||||||||
\(836\) | 56.8592 | 1.96652 | ||||||||
\(837\) | 5.26875i | 0.182115i | ||||||||
\(838\) | 2.65625i | 0.0917587i | ||||||||
\(839\) | 4.63879i | 0.160149i | 0.996789 | + | 0.0800744i | \(0.0255158\pi\) | ||||
−0.996789 | + | 0.0800744i | \(0.974484\pi\) | |||||||
\(840\) | − 0.732578i | − 0.0252763i | ||||||||
\(841\) | 6.27173 | 0.216267 | ||||||||
\(842\) | 0.932559 | 0.0321381 | ||||||||
\(843\) | − 27.2349i | − 0.938020i | ||||||||
\(844\) | −10.7017 | −0.368368 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.99761 | −0.103060 | ||||||||
\(847\) | 36.7329i | 1.26216i | ||||||||
\(848\) | −3.02475 | −0.103870 | ||||||||
\(849\) | −5.28382 | −0.181340 | ||||||||
\(850\) | 8.35690i | 0.286639i | ||||||||
\(851\) | 26.6872i | 0.914827i | ||||||||
\(852\) | − 10.3056i | − 0.353064i | ||||||||
\(853\) | − 18.3884i | − 0.629605i | −0.949157 | − | 0.314803i | \(-0.898062\pi\) | ||||
0.949157 | − | 0.314803i | \(-0.101938\pi\) | |||||||
\(854\) | −6.64370 | −0.227343 | ||||||||
\(855\) | 1.37867 | 0.0471494 | ||||||||
\(856\) | − 21.6866i | − 0.741234i | ||||||||
\(857\) | −28.1849 | −0.962778 | −0.481389 | − | 0.876507i | \(-0.659868\pi\) | ||||
−0.481389 | + | 0.876507i | \(0.659868\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.3957 | 1.13944 | 0.569722 | − | 0.821837i | \(-0.307051\pi\) | ||||
0.569722 | + | 0.821837i | \(0.307051\pi\) | |||||||
\(860\) | 0.762709i | 0.0260082i | ||||||||
\(861\) | 0.780167 | 0.0265880 | ||||||||
\(862\) | 1.28429 | 0.0437431 | ||||||||
\(863\) | − 43.0640i | − 1.46592i | −0.680274 | − | 0.732958i | \(-0.738139\pi\) | ||||
0.680274 | − | 0.732958i | \(-0.261861\pi\) | |||||||
\(864\) | 4.65279i | 0.158291i | ||||||||
\(865\) | 1.17928i | 0.0400966i | ||||||||
\(866\) | 5.62910i | 0.191285i | ||||||||
\(867\) | −2.54527 | −0.0864419 | ||||||||
\(868\) | 16.6431 | 0.564904 | ||||||||
\(869\) | − 25.1817i | − 0.854230i | ||||||||
\(870\) | −0.652793 | −0.0221317 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −20.5526 | −0.695998 | ||||||||
\(873\) | − 13.6896i | − 0.463324i | ||||||||
\(874\) | 20.7308 | 0.701229 | ||||||||
\(875\) | −4.30319 | −0.145474 | ||||||||
\(876\) | − 13.2567i | − 0.447901i | ||||||||
\(877\) | − 30.1702i | − 1.01877i | −0.860537 | − | 0.509387i | \(-0.829872\pi\) | ||||
0.860537 | − | 0.509387i | \(-0.170128\pi\) | |||||||
\(878\) | 4.86294i | 0.164116i | ||||||||
\(879\) | − 32.6625i | − 1.10168i | ||||||||
\(880\) | −3.98015 | −0.134171 | ||||||||
\(881\) | 3.56273 | 0.120031 | 0.0600157 | − | 0.998197i | \(-0.480885\pi\) | ||||
0.0600157 | + | 0.998197i | \(0.480885\pi\) | |||||||
\(882\) | 1.74764i | 0.0588462i | ||||||||
\(883\) | 10.2088 | 0.343554 | 0.171777 | − | 0.985136i | \(-0.445049\pi\) | ||||
0.171777 | + | 0.985136i | \(0.445049\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.38404 | 0.113753 | ||||||||
\(886\) | − 8.56273i | − 0.287670i | ||||||||
\(887\) | −9.33645 | −0.313487 | −0.156744 | − | 0.987639i | \(-0.550100\pi\) | ||||
−0.156744 | + | 0.987639i | \(0.550100\pi\) | |||||||
\(888\) | 5.41119 | 0.181588 | ||||||||
\(889\) | 18.9318i | 0.634953i | ||||||||
\(890\) | − 0.0150655i | 0 0.000504996i | ||||||||
\(891\) | − 5.65279i | − 0.189376i | ||||||||
\(892\) | 25.5894i | 0.856797i | ||||||||
\(893\) | −37.5986 | −1.25819 | ||||||||
\(894\) | 6.84846 | 0.229047 | ||||||||
\(895\) | 0.848462i | 0.0283610i | ||||||||
\(896\) | 19.1457 | 0.639613 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.8261 | −0.428013 | ||||||||
\(899\) | − 31.2911i | − 1.04362i | ||||||||
\(900\) | 8.89977 | 0.296659 | ||||||||
\(901\) | −4.03385 | −0.134387 | ||||||||
\(902\) | 1.11960i | 0.0372788i | ||||||||
\(903\) | 3.00431i | 0.0999772i | ||||||||
\(904\) | − 2.77107i | − 0.0921644i | ||||||||
\(905\) | − 3.33081i | − 0.110720i | ||||||||
\(906\) | −1.63533 | −0.0543303 | ||||||||
\(907\) | 41.0804 | 1.36405 | 0.682026 | − | 0.731328i | \(-0.261099\pi\) | ||||
0.682026 | + | 0.731328i | \(0.261099\pi\) | |||||||
\(908\) | 28.8442i | 0.957227i | ||||||||
\(909\) | 5.41119 | 0.179478 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.9705 | −0.628519 | −0.314260 | − | 0.949337i | \(-0.601756\pi\) | ||||
−0.314260 | + | 0.949337i | \(0.601756\pi\) | |||||||
\(912\) | 15.9138i | 0.526958i | ||||||||
\(913\) | −57.5792 | −1.90559 | ||||||||
\(914\) | 8.04221 | 0.266013 | ||||||||
\(915\) | 2.10321i | 0.0695300i | ||||||||
\(916\) | − 3.31767i | − 0.109619i | ||||||||
\(917\) | − 1.59094i | − 0.0525375i | ||||||||
\(918\) | 1.69202i | 0.0558450i | ||||||||
\(919\) | 29.0019 | 0.956685 | 0.478343 | − | 0.878173i | \(-0.341238\pi\) | ||||
0.478343 | + | 0.878173i | \(0.341238\pi\) | |||||||
\(920\) | −3.48725 | −0.114971 | ||||||||
\(921\) | 20.7614i | 0.684111i | ||||||||
\(922\) | 3.36791 | 0.110916 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −17.8562 | −0.587427 | ||||||||
\(925\) | − 15.7952i | − 0.519344i | ||||||||
\(926\) | 15.7345 | 0.517068 | ||||||||
\(927\) | −13.7560 | −0.451806 | ||||||||
\(928\) | − 27.6329i | − 0.907096i | ||||||||
\(929\) | − 50.7211i | − 1.66410i | −0.554697 | − | 0.832052i | \(-0.687166\pi\) | ||||
0.554697 | − | 0.832052i | \(-0.312834\pi\) | |||||||
\(930\) | 0.579121i | 0.0189901i | ||||||||
\(931\) | 21.9205i | 0.718415i | ||||||||
\(932\) | 42.2107 | 1.38266 | ||||||||
\(933\) | 11.3013 | 0.369987 | ||||||||
\(934\) | − 5.78554i | − 0.189309i | ||||||||
\(935\) | −5.30798 | −0.173589 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.3051 | 1.67606 | 0.838032 | − | 0.545620i | \(-0.183706\pi\) | ||||
0.838032 | + | 0.545620i | \(0.183706\pi\) | |||||||
\(938\) | 4.65040i | 0.151841i | ||||||||
\(939\) | −4.27173 | −0.139403 | ||||||||
\(940\) | 2.99761 | 0.0977712 | ||||||||
\(941\) | − 34.7036i | − 1.13131i | −0.824643 | − | 0.565653i | \(-0.808624\pi\) | ||||
0.824643 | − | 0.565653i | \(-0.191376\pi\) | |||||||
\(942\) | − 2.17092i | − 0.0707322i | ||||||||
\(943\) | − 3.71379i | − 0.120938i | ||||||||
\(944\) | 39.0616i | 1.27135i | ||||||||
\(945\) | −0.432960 | −0.0140842 | ||||||||
\(946\) | −4.31144 | −0.140177 | ||||||||
\(947\) | 13.0127i | 0.422855i | 0.977394 | + | 0.211428i | \(0.0678112\pi\) | ||||
−0.977394 | + | 0.211428i | \(0.932189\pi\) | |||||||
\(948\) | 8.02715 | 0.260710 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −12.2698 | −0.398085 | ||||||||
\(951\) | 15.4776i | 0.501894i | ||||||||
\(952\) | 11.2771 | 0.365493 | ||||||||
\(953\) | −26.0151 | −0.842711 | −0.421355 | − | 0.906896i | \(-0.638445\pi\) | ||||
−0.421355 | + | 0.906896i | \(0.638445\pi\) | |||||||
\(954\) | − 0.472189i | − 0.0152877i | ||||||||
\(955\) | 0.321388i | 0.0103999i | ||||||||
\(956\) | 26.3110i | 0.850957i | ||||||||
\(957\) | 33.5719i | 1.08523i | ||||||||
\(958\) | −11.3604 | −0.367036 | ||||||||
\(959\) | 16.7383 | 0.540507 | ||||||||
\(960\) | − 0.896789i | − 0.0289437i | ||||||||
\(961\) | 3.24027 | 0.104525 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.8170 | −0.413022 | ||||||||
\(964\) | − 15.5526i | − 0.500914i | ||||||||
\(965\) | 2.27114 | 0.0731107 | ||||||||
\(966\) | −6.51035 | −0.209467 | ||||||||
\(967\) | 36.6644i | 1.17905i | 0.807751 | + | 0.589524i | \(0.200685\pi\) | ||||
−0.807751 | + | 0.589524i | \(0.799315\pi\) | |||||||
\(968\) | − 35.4547i | − 1.13956i | ||||||||
\(969\) | 21.2228i | 0.681775i | ||||||||
\(970\) | − 1.50471i | − 0.0483134i | ||||||||
\(971\) | −37.8465 | −1.21455 | −0.607277 | − | 0.794490i | \(-0.707738\pi\) | ||||
−0.607277 | + | 0.794490i | \(0.707738\pi\) | |||||||
\(972\) | 1.80194 | 0.0577972 | ||||||||
\(973\) | 7.17416i | 0.229993i | ||||||||
\(974\) | −7.12392 | −0.228265 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.2771 | −0.777091 | ||||||||
\(977\) | 28.8998i | 0.924586i | 0.886727 | + | 0.462293i | \(0.152973\pi\) | ||||
−0.886727 | + | 0.462293i | \(0.847027\pi\) | |||||||
\(978\) | 3.84117 | 0.122827 | ||||||||
\(979\) | −0.774791 | −0.0247624 | ||||||||
\(980\) | − 1.74764i | − 0.0558264i | ||||||||
\(981\) | 12.1468i | 0.387816i | ||||||||
\(982\) | − 9.22952i | − 0.294526i | ||||||||
\(983\) | 19.3991i | 0.618735i | 0.950942 | + | 0.309368i | \(0.100117\pi\) | ||||
−0.950942 | + | 0.309368i | \(0.899883\pi\) | |||||||
\(984\) | −0.753020 | −0.0240054 | ||||||||
\(985\) | 1.01566 | 0.0323615 | ||||||||
\(986\) | − 10.0489i | − 0.320023i | ||||||||
\(987\) | 11.8076 | 0.375839 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.3013 | 0.454754 | ||||||||
\(990\) | − 0.621334i | − 0.0197473i | ||||||||
\(991\) | −5.18300 | −0.164643 | −0.0823217 | − | 0.996606i | \(-0.526233\pi\) | ||||
−0.0823217 | + | 0.996606i | \(0.526233\pi\) | |||||||
\(992\) | −24.5144 | −0.778333 | ||||||||
\(993\) | 6.06829i | 0.192572i | ||||||||
\(994\) | − 4.46191i | − 0.141523i | ||||||||
\(995\) | − 6.11828i | − 0.193962i | ||||||||
\(996\) | − 18.3545i | − 0.581585i | ||||||||
\(997\) | −49.3642 | −1.56338 | −0.781690 | − | 0.623667i | \(-0.785642\pi\) | ||||
−0.781690 | + | 0.623667i | \(0.785642\pi\) | |||||||
\(998\) | 3.59047 | 0.113654 | ||||||||
\(999\) | − 3.19806i | − 0.101182i |
(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 | 507.2.b.g.337.4 | 6 | ||
3.2 | odd | 2 | 1521.2.b.m.1351.3 | 6 | |||
13.2 | odd | 12 | 507.2.e.j.22.2 | 6 | |||
13.3 | even | 3 | 507.2.j.h.316.3 | 12 | |||
13.4 | even | 6 | 507.2.j.h.361.3 | 12 | |||
13.5 | odd | 4 | 507.2.a.k.1.2 | yes | 3 | ||
13.6 | odd | 12 | 507.2.e.j.484.2 | 6 | |||
13.7 | odd | 12 | 507.2.e.k.484.2 | 6 | |||
13.8 | odd | 4 | 507.2.a.j.1.2 | ✓ | 3 | ||
13.9 | even | 3 | 507.2.j.h.361.4 | 12 | |||
13.10 | even | 6 | 507.2.j.h.316.4 | 12 | |||
13.11 | odd | 12 | 507.2.e.k.22.2 | 6 | |||
13.12 | even | 2 | inner | 507.2.b.g.337.3 | 6 | ||
39.5 | even | 4 | 1521.2.a.p.1.2 | 3 | |||
39.8 | even | 4 | 1521.2.a.q.1.2 | 3 | |||
39.38 | odd | 2 | 1521.2.b.m.1351.4 | 6 | |||
52.31 | even | 4 | 8112.2.a.cf.1.1 | 3 | |||
52.47 | even | 4 | 8112.2.a.by.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.j.1.2 | ✓ | 3 | 13.8 | odd | 4 | ||
507.2.a.k.1.2 | yes | 3 | 13.5 | odd | 4 | ||
507.2.b.g.337.3 | 6 | 13.12 | even | 2 | inner | ||
507.2.b.g.337.4 | 6 | 1.1 | even | 1 | trivial | ||
507.2.e.j.22.2 | 6 | 13.2 | odd | 12 | |||
507.2.e.j.484.2 | 6 | 13.6 | odd | 12 | |||
507.2.e.k.22.2 | 6 | 13.11 | odd | 12 | |||
507.2.e.k.484.2 | 6 | 13.7 | odd | 12 | |||
507.2.j.h.316.3 | 12 | 13.3 | even | 3 | |||
507.2.j.h.316.4 | 12 | 13.10 | even | 6 | |||
507.2.j.h.361.3 | 12 | 13.4 | even | 6 | |||
507.2.j.h.361.4 | 12 | 13.9 | even | 3 | |||
1521.2.a.p.1.2 | 3 | 39.5 | even | 4 | |||
1521.2.a.q.1.2 | 3 | 39.8 | even | 4 | |||
1521.2.b.m.1351.3 | 6 | 3.2 | odd | 2 | |||
1521.2.b.m.1351.4 | 6 | 39.38 | odd | 2 | |||
8112.2.a.by.1.3 | 3 | 52.47 | even | 4 | |||
8112.2.a.cf.1.1 | 3 | 52.31 | even | 4 |