Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,2,Mod(35,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 9, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.v (of order \(18\), degree \(6\), 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: | \(5.17430605098\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{18})\) |
Coefficient field: | 12.0.101559956668416.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 8x^{6} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 35.2 | ||
Root | \(-0.483690 + 1.32893i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.35 |
Dual form | 648.2.v.a.611.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{13}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.909039 | − | 1.08335i | 0.642788 | − | 0.766044i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.347296 | − | 1.96962i | −0.173648 | − | 0.984808i | ||||
\(5\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(8\) | −2.44949 | − | 1.41421i | −0.866025 | − | 0.500000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.85296 | − | 5.09097i | −0.558689 | − | 1.53498i | −0.821541 | − | 0.570149i | \(-0.806886\pi\) |
0.262853 | − | 0.964836i | \(-0.415337\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.75877 | + | 1.36808i | −0.939693 | + | 0.342020i | ||||
\(17\) | 0.412814 | − | 0.238338i | 0.100122 | − | 0.0578055i | −0.449103 | − | 0.893480i | \(-0.648256\pi\) |
0.549225 | + | 0.835675i | \(0.314923\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.39076 | − | 4.14092i | 0.548478 | − | 0.949992i | −0.449901 | − | 0.893079i | \(-0.648541\pi\) |
0.998379 | − | 0.0569137i | \(-0.0181260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.19972 | − | 2.62048i | −1.53498 | − | 0.558689i | ||||
\(23\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.83022 | − | 3.21394i | −0.766044 | − | 0.642788i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(32\) | −1.93476 | + | 5.31570i | −0.342020 | + | 0.939693i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.117060 | − | 0.663880i | 0.0200756 | − | 0.113855i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(38\) | −2.31277 | − | 6.35429i | −0.375181 | − | 1.03080i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.51466 | + | 6.57212i | 0.861245 | + | 1.02639i | 0.999353 | + | 0.0359748i | \(0.0114536\pi\) |
−0.138108 | + | 0.990417i | \(0.544102\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.3238 | − | 4.48548i | 1.87936 | − | 0.684030i | 0.937795 | − | 0.347190i | \(-0.112864\pi\) |
0.941562 | − | 0.336840i | \(-0.109358\pi\) | |||||||
\(44\) | −9.38372 | + | 5.41770i | −1.41465 | + | 0.816748i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.57785 | − | 2.39414i | −0.939693 | − | 0.342020i | ||||
\(50\) | −6.96364 | + | 1.22788i | −0.984808 | + | 0.173648i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.24706 | + | 14.4162i | −0.683109 | + | 1.87683i | −0.292542 | + | 0.956253i | \(0.594501\pi\) |
−0.390567 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.00000 | + | 6.92820i | 0.500000 | + | 0.866025i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.26366 | − | 6.93404i | 1.00957 | − | 0.847127i | 0.0212861 | − | 0.999773i | \(-0.493224\pi\) |
0.988281 | + | 0.152646i | \(0.0487795\pi\) | |||||||
\(68\) | −0.612803 | − | 0.730310i | −0.0743133 | − | 0.0885631i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.22028 | + | 10.7738i | −0.728028 | + | 1.26098i | 0.229687 | + | 0.973265i | \(0.426230\pi\) |
−0.957715 | + | 0.287718i | \(0.907104\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.98632 | − | 3.27075i | −1.03080 | − | 0.375181i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.1329 | 1.33986 | ||||||||
\(83\) | 9.11103 | − | 10.8581i | 1.00007 | − | 1.19183i | 0.0186715 | − | 0.999826i | \(-0.494056\pi\) |
0.981394 | − | 0.192006i | \(-0.0614992\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.34343 | − | 17.4284i | 0.684030 | − | 1.87936i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.66091 | + | 15.0908i | −0.283654 | + | 1.60868i | ||||
\(89\) | 15.9495 | + | 9.20844i | 1.69064 | + | 0.976093i | 0.953998 | + | 0.299813i | \(0.0969242\pi\) |
0.736644 | + | 0.676280i | \(0.236409\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.3366 | − | 6.31001i | 1.76026 | − | 0.640684i | 0.760304 | − | 0.649567i | \(-0.225050\pi\) |
0.999961 | + | 0.00888289i | \(0.00282755\pi\) | |||||||
\(98\) | −8.57321 | + | 4.94975i | −0.866025 | + | 0.500000i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000 | + | 8.66025i | −0.500000 | + | 0.866025i | ||||
\(101\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 19.0236i | − | 1.83908i | −0.392992 | − | 0.919542i | \(-0.628560\pi\) | ||
0.392992 | − | 0.919542i | \(-0.371440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.39681 | + | 9.33265i | −0.319545 | + | 0.877942i | 0.671087 | + | 0.741379i | \(0.265828\pi\) |
−0.990631 | + | 0.136563i | \(0.956394\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.8480 | + | 18.7893i | 0.998639 | + | 1.72969i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.0580 | + | 11.7961i | −1.27800 | + | 1.07237i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(128\) | 11.1418 | + | 1.96460i | 0.984808 | + | 0.173648i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.3153 | − | 3.93479i | 1.94969 | − | 0.343784i | 0.950213 | − | 0.311602i | \(-0.100866\pi\) |
0.999482 | − | 0.0321817i | \(-0.0102455\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 15.2558i | − | 1.31790i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.34824 | −0.115611 | ||||||||
\(137\) | −6.32378 | + | 7.53639i | −0.540277 | + | 0.643877i | −0.965250 | − | 0.261329i | \(-0.915839\pi\) |
0.424973 | + | 0.905206i | \(0.360284\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.787687 | + | 4.46720i | 0.0668108 | + | 0.378903i | 0.999819 | + | 0.0190466i | \(0.00606310\pi\) |
−0.933008 | + | 0.359856i | \(0.882826\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.01737 | + | 16.5326i | 0.498001 | + | 1.36825i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(152\) | −11.7123 | + | 6.76209i | −0.949992 | + | 0.548478i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.0454 | −1.80506 | −0.902528 | − | 0.430632i | \(-0.858291\pi\) | ||||
−0.902528 | + | 0.430632i | \(0.858291\pi\) | |||||||
\(164\) | 11.0293 | − | 13.1442i | 0.861245 | − | 1.02639i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.48085 | − | 19.7409i | −0.270166 | − | 1.53219i | ||||
\(167\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.25743 | − | 12.8025i | 0.173648 | − | 0.984808i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.1147 | − | 22.7153i | −0.999985 | − | 1.73202i | ||||
\(173\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13.9297 | + | 16.6008i | 1.04999 | + | 1.25133i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 24.4747 | − | 8.90805i | 1.83445 | − | 0.667687i | ||||
\(179\) | −4.92679 | + | 2.84448i | −0.368245 | + | 0.212607i | −0.672692 | − | 0.739923i | \(-0.734862\pi\) |
0.304446 | + | 0.952529i | \(0.401529\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.97830 | − | 1.65999i | −0.144668 | − | 0.121390i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.59777 | + | 26.0753i | 0.330955 | + | 1.87694i | 0.464011 | + | 0.885830i | \(0.346410\pi\) |
−0.133056 | + | 0.991109i | \(0.542479\pi\) | |||||||
\(194\) | 8.92370 | − | 24.5177i | 0.640684 | − | 1.76026i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.43107 | + | 13.7873i | −0.173648 | + | 0.984808i | ||||
\(197\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(200\) | 4.83690 | + | 13.2893i | 0.342020 | + | 0.939693i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −25.5113 | − | 4.49833i | −1.76465 | − | 0.311156i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.2938 | + | 9.93411i | 1.87898 | + | 0.683893i | 0.946595 | + | 0.322424i | \(0.104498\pi\) |
0.932384 | + | 0.361469i | \(0.117725\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −20.6093 | − | 17.2932i | −1.40882 | − | 1.18214i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.02270 | + | 12.1637i | 0.467143 | + | 0.809116i | ||||
\(227\) | −5.85433 | − | 16.0847i | −0.388566 | − | 1.06758i | −0.967647 | − | 0.252306i | \(-0.918811\pi\) |
0.579082 | − | 0.815270i | \(-0.303411\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.28241 | − | 2.47245i | 0.280550 | − | 0.161976i | −0.353122 | − | 0.935577i | \(-0.614880\pi\) |
0.633672 | + | 0.773602i | \(0.281547\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 30.2166 | + | 5.32801i | 1.96693 | + | 0.346824i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.34413 | − | 7.84065i | −0.601908 | − | 0.505061i | 0.290150 | − | 0.956981i | \(-0.406295\pi\) |
−0.892058 | + | 0.451920i | \(0.850739\pi\) | |||||||
\(242\) | 25.9528i | 1.66831i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.3006 | − | 9.98849i | −1.09200 | − | 0.630468i | −0.157894 | − | 0.987456i | \(-0.550470\pi\) |
−0.934109 | + | 0.356988i | \(0.883804\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.2567 | − | 10.2846i | 0.766044 | − | 0.642788i | ||||
\(257\) | −20.2535 | − | 24.1372i | −1.26338 | − | 1.50564i | −0.773427 | − | 0.633885i | \(-0.781459\pi\) |
−0.489951 | − | 0.871750i | \(-0.662985\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.0227 | − | 27.7521i | 0.989886 | − | 1.71453i | ||||
\(263\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −16.5273 | − | 13.8681i | −1.00957 | − | 0.847127i | ||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −1.22561 | + | 1.46062i | −0.0743133 | + | 0.0885631i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.41599 | + | 13.7017i | 0.145955 | + | 0.827752i | ||||
\(275\) | −9.26480 | + | 25.4548i | −0.558689 | + | 1.53498i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(278\) | 5.55558 | + | 3.20751i | 0.333201 | + | 0.192374i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.494671 | + | 1.35910i | 0.0295096 | + | 0.0810770i | 0.953573 | − | 0.301163i | \(-0.0973749\pi\) |
−0.924063 | + | 0.382240i | \(0.875153\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.46127 | + | 7.09985i | −0.502970 | + | 0.422042i | −0.858647 | − | 0.512567i | \(-0.828695\pi\) |
0.355677 | + | 0.934609i | \(0.384250\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.38639 | + | 14.5257i | −0.493317 | + | 0.854450i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 23.3806 | + | 8.50984i | 1.36825 | + | 0.498001i | ||||
\(293\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.32121 | + | 18.8355i | −0.190484 | + | 1.08029i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.5237 | − | 25.1558i | −0.828912 | − | 1.43572i | −0.898893 | − | 0.438169i | \(-0.855627\pi\) |
0.0699810 | − | 0.997548i | \(-0.477706\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.07825 | − | 0.756419i | 0.117469 | − | 0.0427554i | −0.282617 | − | 0.959233i | \(-0.591202\pi\) |
0.400086 | + | 0.916478i | \(0.368980\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.27924i | − | 0.126820i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −20.9492 | + | 24.9663i | −1.16027 | + | 1.38275i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.21373 | − | 23.8972i | −0.232664 | − | 1.31950i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.08557 | + | 34.5130i | −0.334493 | + | 1.89701i | 0.0976852 | + | 0.995217i | \(0.468856\pi\) |
−0.432178 | + | 0.901788i | \(0.642255\pi\) | |||||||
\(332\) | −24.5505 | − | 14.1742i | −1.34738 | − | 0.777913i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.49720 | + | 7.13000i | −0.462872 | + | 0.388396i | −0.844187 | − | 0.536050i | \(-0.819916\pi\) |
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | −11.8175 | − | 14.0836i | −0.642788 | − | 0.766044i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −36.5304 | − | 6.44129i | −1.96959 | − | 0.347291i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.0062 | + | 5.64356i | −1.71818 | + | 0.302962i | −0.943987 | − | 0.329983i | \(-0.892957\pi\) |
−0.774197 | + | 0.632945i | \(0.781846\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 30.6471 | 1.63350 | ||||||||
\(353\) | −23.5371 | + | 28.0504i | −1.25275 | + | 1.49297i | −0.454384 | + | 0.890806i | \(0.650141\pi\) |
−0.798369 | + | 0.602168i | \(0.794304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.5979 | − | 34.6124i | 0.667687 | − | 1.83445i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.39707 | + | 7.92318i | −0.0738375 | + | 0.418753i | ||||
\(359\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.93148 | − | 3.34542i | −0.101657 | − | 0.176075i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(374\) | −3.59670 | + | 0.634196i | −0.185981 | + | 0.0327935i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −38.6105 | −1.98329 | −0.991643 | − | 0.129012i | \(-0.958819\pi\) | ||||
−0.991643 | + | 0.129012i | \(0.958819\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 32.4282 | + | 18.7224i | 1.65055 | + | 0.952947i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.4492 | − | 31.9550i | −0.936617 | − | 1.62227i | ||||
\(389\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 12.7265 | + | 15.1669i | 0.642788 | + | 0.766044i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.7939 | + | 6.84040i | 0.939693 | + | 0.342020i | ||||
\(401\) | 38.6656 | − | 6.81778i | 1.93087 | − | 0.340464i | 0.931158 | − | 0.364615i | \(-0.118800\pi\) |
0.999708 | + | 0.0241516i | \(0.00768844\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.71496 | − | 38.0824i | −0.332033 | − | 1.88305i | −0.454759 | − | 0.890614i | \(-0.650275\pi\) |
0.122726 | − | 0.992441i | \(-0.460836\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −28.0640 | + | 23.5485i | −1.37266 | + | 1.15179i | ||||
\(419\) | 1.79744 | + | 2.14210i | 0.0878107 | + | 0.104649i | 0.808161 | − | 0.588962i | \(-0.200463\pi\) |
−0.720350 | + | 0.693611i | \(0.756019\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(422\) | 35.5732 | − | 20.5382i | 1.73168 | − | 0.999784i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.34717 | − | 0.413870i | −0.113855 | − | 0.0200756i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −37.4692 | + | 6.60684i | −1.81114 | + | 0.319354i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40.0182 | 1.92315 | 0.961575 | − | 0.274543i | \(-0.0885264\pi\) | ||||
0.961575 | + | 0.274543i | \(0.0885264\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.00403 | + | 11.0010i | 0.190237 | + | 0.522672i | 0.997740 | − | 0.0671913i | \(-0.0214038\pi\) |
−0.807503 | + | 0.589863i | \(0.799182\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.6712 | − | 21.1721i | 1.73062 | − | 0.999174i | 0.844990 | − | 0.534783i | \(-0.179606\pi\) |
0.885630 | − | 0.464391i | \(-0.153727\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.2400 | − | 40.2528i | 1.09433 | − | 1.89543i | ||||
\(452\) | 19.5614 | + | 3.44921i | 0.920093 | + | 0.162237i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −22.7471 | − | 8.27928i | −1.06758 | − | 0.388566i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.6087 | − | 23.1664i | −1.29148 | − | 1.08368i | −0.991551 | − | 0.129718i | \(-0.958593\pi\) |
−0.299928 | − | 0.953962i | \(-0.596963\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.21435 | − | 6.88690i | 0.0562535 | − | 0.319030i | ||||
\(467\) | 16.4335 | + | 9.48788i | 0.760452 | + | 0.439047i | 0.829458 | − | 0.558569i | \(-0.188650\pi\) |
−0.0690063 | + | 0.997616i | \(0.521983\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 33.2402 | − | 27.8918i | 1.53000 | − | 1.28383i | ||||
\(473\) | −45.6709 | − | 54.4285i | −2.09995 | − | 2.50262i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.4658 | + | 8.17688i | −1.03080 | + | 0.375181i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −16.9883 | + | 2.99550i | −0.773798 | + | 0.136441i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 28.1160 | + | 23.5921i | 1.27800 | + | 1.07237i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.52827 | + | 15.1888i | −0.249487 | + | 0.685461i | 0.750218 | + | 0.661190i | \(0.229948\pi\) |
−0.999705 | + | 0.0242702i | \(0.992274\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.1065 | − | 24.4232i | 1.30298 | − | 1.09333i | 0.313363 | − | 0.949633i | \(-0.398544\pi\) |
0.989621 | − | 0.143700i | \(-0.0459001\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −26.5479 | + | 9.66266i | −1.18489 | + | 0.431266i | ||||
\(503\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 22.6274i | − | 1.00000i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −44.5602 | −1.96547 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.3627 | + | 19.2620i | 1.46165 | + | 0.843882i | 0.999088 | − | 0.0427062i | \(-0.0135979\pi\) |
0.462559 | + | 0.886588i | \(0.346931\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.5227 | + | 35.5464i | 0.897395 | + | 1.55433i | 0.830812 | + | 0.556553i | \(0.187876\pi\) |
0.0665832 | + | 0.997781i | \(0.478790\pi\) | |||||||
\(524\) | −15.5000 | − | 42.5860i | −0.677122 | − | 1.86038i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.6129 | − | 7.86646i | 0.939693 | − | 0.342020i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −30.0480 | + | 5.29827i | −1.29787 | + | 0.228850i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 37.9239i | 1.63350i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.468240 | + | 2.65552i | 0.0200756 | + | 0.113855i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.06614 | + | 40.0741i | −0.302126 | + | 1.71344i | 0.334606 | + | 0.942358i | \(0.391397\pi\) |
−0.636732 | + | 0.771085i | \(0.719714\pi\) | |||||||
\(548\) | 17.0400 | + | 9.83806i | 0.727913 | + | 0.420261i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 19.1544 | + | 33.1765i | 0.816748 | + | 1.41465i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.52510 | − | 3.10288i | 0.361545 | − | 0.131592i | ||||
\(557\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.92205 | + | 0.699571i | 0.0810770 | + | 0.0295096i | ||||
\(563\) | 35.3834 | − | 6.23904i | 1.49123 | − | 0.262944i | 0.632175 | − | 0.774826i | \(-0.282163\pi\) |
0.859056 | + | 0.511882i | \(0.171051\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.6206i | 0.656581i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.9010 | − | 27.2924i | 0.960061 | − | 1.14416i | −0.0294311 | − | 0.999567i | \(-0.509370\pi\) |
0.989492 | − | 0.144589i | \(-0.0461860\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.80910 | + | 10.2599i | 0.0757085 | + | 0.429364i | 0.998978 | + | 0.0452101i | \(0.0143957\pi\) |
−0.923269 | + | 0.384154i | \(0.874493\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.7607 | − | 23.8343i | −0.572866 | − | 0.992234i | −0.996270 | − | 0.0862925i | \(-0.972498\pi\) |
0.423403 | − | 0.905941i | \(-0.360835\pi\) | |||||||
\(578\) | 8.11282 | + | 22.2898i | 0.337449 | + | 0.927133i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 30.4730 | − | 17.5936i | 1.26098 | − | 0.728028i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.0418 | + | 2.47595i | 0.579567 | + | 0.102193i | 0.455744 | − | 0.890111i | \(-0.349373\pi\) |
0.123823 | + | 0.992304i | \(0.460484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.03896i | 0.289055i | 0.989501 | + | 0.144528i | \(0.0461663\pi\) | ||||
−0.989501 | + | 0.144528i | \(0.953834\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.28921 | + | 24.3253i | −0.174960 | + | 0.992250i | 0.763229 | + | 0.646128i | \(0.223613\pi\) |
−0.938190 | + | 0.346122i | \(0.887498\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(608\) | 17.3864 | + | 20.7203i | 0.705110 | + | 0.840317i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(614\) | −40.4552 | − | 7.13334i | −1.63264 | − | 0.287878i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.3237 | − | 3.93628i | 0.898720 | − | 0.158469i | 0.294843 | − | 0.955546i | \(-0.404733\pi\) |
0.603877 | + | 0.797077i | \(0.293622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.60017 | − | 6.37730i | −0.305477 | − | 0.256325i | 0.477143 | − | 0.878826i | \(-0.341672\pi\) |
−0.782620 | + | 0.622500i | \(0.786117\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.34120 | + | 24.6202i | 0.173648 | + | 0.984808i | ||||
\(626\) | 1.06974 | − | 2.93908i | 0.0427554 | − | 0.117469i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.0281 | + | 2.12088i | 0.475082 | + | 0.0837698i | 0.406062 | − | 0.913845i | \(-0.366902\pi\) |
0.0690201 | + | 0.997615i | \(0.478013\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.0112 | − | 5.82761i | −0.631421 | − | 0.229818i | 0.00642884 | − | 0.999979i | \(-0.497954\pi\) |
−0.637850 | + | 0.770161i | \(0.720176\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.46921 | − | 2.07192i | −0.0971499 | − | 0.0815184i | ||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 83.1149 | 3.26255 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.00359 | + | 45.3906i | 0.313445 | + | 1.77763i | ||||
\(653\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −29.7195 | − | 17.1586i | −1.16035 | − | 0.669930i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.5543 | + | 37.2401i | 0.528000 | + | 1.45067i | 0.861422 | + | 0.507891i | \(0.169575\pi\) |
−0.333422 | + | 0.942778i | \(0.608203\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(662\) | 31.8576 | + | 37.9665i | 1.23818 | + | 1.47561i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −37.6730 | + | 13.7119i | −1.46200 | + | 0.532124i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.6057 | + | 31.5550i | 1.44959 | + | 1.21635i | 0.932875 | + | 0.360200i | \(0.117292\pi\) |
0.516720 | + | 0.856154i | \(0.327153\pi\) | |||||||
\(674\) | 15.6869i | 0.604237i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26.0000 | −1.00000 | ||||||||
\(677\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.4993 | − | 23.3823i | −1.54966 | − | 0.894699i | −0.998167 | − | 0.0605215i | \(-0.980724\pi\) |
−0.551497 | − | 0.834177i | \(-0.685943\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −40.1857 | + | 33.7198i | −1.53207 | + | 1.28556i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.897023 | + | 0.326490i | −0.0341244 | + | 0.0124203i | −0.359026 | − | 0.933328i | \(-0.616891\pi\) |
0.324902 | + | 0.945748i | \(0.394669\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.9809 | + | 39.8042i | −0.872345 | + | 1.51095i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.84291 | + | 1.39871i | 0.145561 | + | 0.0529797i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 27.8594 | − | 33.2016i | 1.04999 | − | 1.25133i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.99230 | + | 50.9979i | 0.338430 | + | 1.91933i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −26.0454 | − | 45.1120i | −0.976093 | − | 1.69064i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.31359 | + | 8.71600i | 0.273322 | + | 0.325732i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.38005 | − | 0.948648i | −0.200225 | − | 0.0353050i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.01836 | − | 4.78889i | 0.148624 | − | 0.177124i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −50.6132 | − | 29.2215i | −1.86436 | − | 1.07639i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.8429 | + | 41.2972i | 0.877077 | + | 1.51914i | 0.854534 | + | 0.519396i | \(0.173843\pi\) |
0.0225433 | + | 0.999746i | \(0.492824\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.58249 | + | 4.47300i | −0.0944250 | + | 0.163549i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | −35.0984 | + | 41.8287i | −1.27483 | + | 1.51929i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.86952 | + | 10.6314i | −0.140270 | + | 0.385388i | −0.989858 | − | 0.142058i | \(-0.954628\pi\) |
0.849589 | + | 0.527446i | \(0.176850\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.2020 | − | 35.4117i | 1.52184 | − | 1.27698i | 0.686709 | − | 0.726932i | \(-0.259055\pi\) |
0.835134 | − | 0.550046i | \(-0.185390\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 49.7614 | − | 18.1117i | 1.79095 | − | 0.651854i | ||||
\(773\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −51.3895 | − | 9.06136i | −1.84478 | − | 0.325284i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 40.3988 | − | 7.12341i | 1.44744 | − | 0.255222i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000 | 1.00000 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.16935 | − | 46.3307i | −0.291206 | − | 1.65151i | −0.682236 | − | 0.731132i | \(-0.738992\pi\) |
0.391030 | − | 0.920378i | \(-0.372119\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 24.4949 | − | 14.1421i | 0.866025 | − | 0.500000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 27.7625 | − | 48.0860i | 0.980327 | − | 1.69798i | ||||
\(803\) | 66.3752 | + | 11.7037i | 2.34233 | + | 0.413016i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.4773i | 1.38795i | 0.720000 | + | 0.693974i | \(0.244142\pi\) | ||||
−0.720000 | + | 0.693974i | \(0.755858\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.1832 | −1.23545 | −0.617725 | − | 0.786394i | \(-0.711946\pi\) | ||||
−0.617725 | + | 0.786394i | \(0.711946\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.8892 | − | 61.7554i | 0.380963 | − | 2.16055i | ||||
\(818\) | −47.3608 | − | 27.3438i | −1.65593 | − | 0.956052i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.1464 | + | 9.89949i | −0.596240 | + | 0.344239i | −0.767561 | − | 0.640976i | \(-0.778530\pi\) |
0.171321 | + | 0.985215i | \(0.445196\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.28604 | + | 0.579418i | −0.113855 | + | 0.0200756i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 51.8097i | 1.79187i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.95459 | 0.136609 | ||||||||
\(839\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.03580 | − | 28.5594i | −0.173648 | − | 0.984808i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.0874 | − | 57.2083i | 0.347221 | − | 1.96919i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.58204 | + | 2.16659i | −0.0885631 | + | 0.0743133i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −26.9035 | + | 46.5982i | −0.919542 | + | 1.59269i | ||||
\(857\) | 22.2837 | + | 3.92921i | 0.761195 | + | 0.134219i | 0.540754 | − | 0.841181i | \(-0.318139\pi\) |
0.220441 | + | 0.975400i | \(0.429250\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.61178 | + | 0.586641i | 0.0549933 | + | 0.0200159i | 0.369370 | − | 0.929282i | \(-0.379573\pi\) |
−0.314377 | + | 0.949298i | \(0.601796\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 36.3781 | − | 43.3537i | 1.23618 | − | 1.47322i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.9949 | + | 21.9364i | −1.28008 | + | 0.739055i | −0.976863 | − | 0.213866i | \(-0.931394\pi\) |
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.3238 | − | 31.7377i | 0.616644 | − | 1.06806i | −0.373450 | − | 0.927650i | \(-0.621825\pi\) |
0.990094 | − | 0.140408i | \(-0.0448416\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.5577 | + | 5.66255i | 0.522672 | + | 0.190237i | ||||
\(887\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.3987 | − | 58.9740i | 0.347009 | − | 1.96799i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −22.4819 | − | 61.7684i | −0.748564 | − | 2.05666i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21.5188 | − | 18.0564i | 0.715705 | − | 0.600548i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −53.3352 | + | 19.4124i | −1.77097 | + | 0.644579i | −0.770996 | + | 0.636841i | \(0.780241\pi\) |
−0.999970 | + | 0.00773827i | \(0.997537\pi\) | |||||||
\(908\) | −29.6474 | + | 17.1169i | −0.983883 | + | 0.568045i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −72.1606 | − | 26.2643i | −2.38817 | − | 0.869222i | ||||
\(914\) | −50.1947 | + | 8.85068i | −1.66029 | + | 0.292755i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.67379 | + | 26.5785i | 0.317387 | + | 0.872013i | 0.991112 | + | 0.133031i | \(0.0424710\pi\) |
−0.673725 | + | 0.738982i | \(0.735307\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.6400 | + | 21.5145i | −0.840317 | + | 0.705110i | ||||
\(932\) | −6.35704 | − | 7.57603i | −0.208232 | − | 0.248161i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 25.2174 | − | 9.17838i | 0.825138 | − | 0.300326i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.5454 | + | 52.9062i | −0.997875 | + | 1.72837i | −0.442509 | + | 0.896764i | \(0.645912\pi\) |
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 61.3655i | − | 1.99728i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −100.482 | −3.26694 | ||||||||
\(947\) | 14.0666 | − | 16.7639i | 0.457102 | − | 0.544753i | −0.487435 | − | 0.873160i | \(-0.662067\pi\) |
0.944536 | + | 0.328407i | \(0.106512\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −11.5639 | + | 31.7714i | −0.375181 | + | 1.03080i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.0149 | − | 16.7518i | −0.939884 | − | 0.542643i | −0.0499603 | − | 0.998751i | \(-0.515909\pi\) |
−0.889924 | + | 0.456109i | \(0.849243\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1305 | + | 10.6026i | −0.939693 | + | 0.342020i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.1979 | + | 21.1274i | −0.392868 | + | 0.680467i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(968\) | 51.1171 | − | 9.01332i | 1.64297 | − | 0.289699i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.1127i | 0.998454i | 0.866471 | + | 0.499227i | \(0.166383\pi\) | ||||
−0.866471 | + | 0.499227i | \(0.833617\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.2970 | − | 53.0180i | 0.617365 | − | 1.69620i | −0.0959785 | − | 0.995383i | \(-0.530598\pi\) |
0.713344 | − | 0.700814i | \(-0.247180\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.3261 | − | 98.2612i | 0.553745 | − | 3.14044i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.4294 | + | 19.7963i | 0.364726 | + | 0.631724i | ||||
\(983\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(998\) | − | 53.7342i | − | 1.70093i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 648.2.v.a.35.2 | 12 | ||
3.2 | odd | 2 | 216.2.v.a.11.1 | ✓ | 12 | ||
8.3 | odd | 2 | CM | 648.2.v.a.35.2 | 12 | ||
12.11 | even | 2 | 864.2.bh.a.335.1 | 12 | |||
24.5 | odd | 2 | 864.2.bh.a.335.1 | 12 | |||
24.11 | even | 2 | 216.2.v.a.11.1 | ✓ | 12 | ||
27.5 | odd | 18 | inner | 648.2.v.a.611.2 | 12 | ||
27.22 | even | 9 | 216.2.v.a.59.1 | yes | 12 | ||
108.103 | odd | 18 | 864.2.bh.a.815.1 | 12 | |||
216.59 | even | 18 | inner | 648.2.v.a.611.2 | 12 | ||
216.157 | even | 18 | 864.2.bh.a.815.1 | 12 | |||
216.211 | odd | 18 | 216.2.v.a.59.1 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.v.a.11.1 | ✓ | 12 | 3.2 | odd | 2 | ||
216.2.v.a.11.1 | ✓ | 12 | 24.11 | even | 2 | ||
216.2.v.a.59.1 | yes | 12 | 27.22 | even | 9 | ||
216.2.v.a.59.1 | yes | 12 | 216.211 | odd | 18 | ||
648.2.v.a.35.2 | 12 | 1.1 | even | 1 | trivial | ||
648.2.v.a.35.2 | 12 | 8.3 | odd | 2 | CM | ||
648.2.v.a.611.2 | 12 | 27.5 | odd | 18 | inner | ||
648.2.v.a.611.2 | 12 | 216.59 | even | 18 | inner | ||
864.2.bh.a.335.1 | 12 | 12.11 | even | 2 | |||
864.2.bh.a.335.1 | 12 | 24.5 | odd | 2 | |||
864.2.bh.a.815.1 | 12 | 108.103 | odd | 18 | |||
864.2.bh.a.815.1 | 12 | 216.157 | even | 18 |