Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,1,Mod(107,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, base_ring=CyclotomicField(92))
chi = DirichletCharacter(H, H._module([46, 23, 22]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3525.107");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.bg (of order \(92\), degree \(44\), 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: | \(1.75920416953\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{92})\) |
Coefficient field: | \(\Q(\zeta_{184})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{88} - x^{84} + x^{80} - x^{76} + x^{72} - x^{68} + x^{64} - x^{60} + x^{56} - x^{52} + x^{48} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{46}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{46} - \cdots)\) |
Embedding invariants
Embedding label | 557.1 | ||
Root | \(-0.657204 - 0.753713i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.557 |
Dual form | 3525.1.bg.a.443.1 |
$q$-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 \(\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times\).
\(n\) | \(1552\) | \(2026\) | \(2351\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.757993 | − | 0.869303i | −0.757993 | − | 0.869303i | 0.236764 | − | 0.971567i | \(-0.423913\pi\) |
−0.994757 | + | 0.102264i | \(0.967391\pi\) | |||||||
\(3\) | 0.871660 | + | 0.490110i | 0.871660 | + | 0.490110i | ||||
\(4\) | −0.0449678 | + | 0.327165i | −0.0449678 | + | 0.327165i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.234658 | − | 1.12924i | −0.234658 | − | 1.12924i | ||||
\(7\) | 0 | 0 | −0.999417 | − | 0.0341411i | \(-0.989130\pi\) | ||||
0.999417 | + | 0.0341411i | \(0.0108696\pi\) | |||||||
\(8\) | −0.645929 | + | 0.423665i | −0.645929 | + | 0.423665i | ||||
\(9\) | 0.519584 | + | 0.854419i | 0.519584 | + | 0.854419i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.398401 | − | 0.917211i | \(-0.630435\pi\) | ||||
0.398401 | + | 0.917211i | \(0.369565\pi\) | |||||||
\(12\) | −0.199543 | + | 0.263138i | −0.199543 | + | 0.263138i | ||||
\(13\) | 0 | 0 | −0.302515 | − | 0.953145i | \(-0.597826\pi\) | ||||
0.302515 | + | 0.953145i | \(0.402174\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.17590 | + | 0.329471i | 1.17590 | + | 0.329471i | ||||
\(17\) | −1.26993 | + | 0.500795i | −1.26993 | + | 0.500795i | −0.903075 | − | 0.429483i | \(-0.858696\pi\) |
−0.366854 | + | 0.930278i | \(0.619565\pi\) | |||||||
\(18\) | 0.348908 | − | 1.09932i | 0.348908 | − | 1.09932i | ||||
\(19\) | 0.157049 | + | 0.222488i | 0.157049 | + | 0.222488i | 0.887885 | − | 0.460065i | \(-0.152174\pi\) |
−0.730836 | + | 0.682553i | \(0.760870\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.50391 | + | 1.31134i | 1.50391 | + | 1.31134i | 0.796805 | + | 0.604236i | \(0.206522\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(24\) | −0.770673 | + | 0.0527155i | −0.770673 | + | 0.0527155i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.0341411 | + | 0.999417i | 0.0341411 | + | 0.999417i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.460065 | − | 0.887885i | \(-0.652174\pi\) | ||||
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.214975 | + | 0.767255i | −0.214975 | + | 0.767255i | 0.775711 | + | 0.631088i | \(0.217391\pi\) |
−0.990686 | + | 0.136167i | \(0.956522\pi\) | |||||||
\(32\) | −0.273147 | − | 0.574346i | −0.273147 | − | 0.574346i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.39794 | + | 0.724354i | 1.39794 | + | 0.724354i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.302901 | + | 0.131568i | −0.302901 | + | 0.131568i | ||||
\(37\) | 0 | 0 | 0.994757 | − | 0.102264i | \(-0.0326087\pi\) | ||||
−0.994757 | + | 0.102264i | \(0.967391\pi\) | |||||||
\(38\) | 0.0743674 | − | 0.305168i | 0.0743674 | − | 0.305168i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.979084 | − | 0.203456i | \(-0.0652174\pi\) | ||||
−0.979084 | + | 0.203456i | \(0.934783\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.796805 | − | 0.604236i | \(-0.206522\pi\) | ||||
−0.796805 | + | 0.604236i | \(0.793478\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 2.30134i | − | 2.30134i | ||||||
\(47\) | 0.102264 | − | 0.994757i | 0.102264 | − | 0.994757i | ||||
\(48\) | 0.863506 | + | 0.863506i | 0.863506 | + | 0.863506i | ||||
\(49\) | 0.997669 | + | 0.0682424i | 0.997669 | + | 0.0682424i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.35239 | − | 0.185882i | −1.35239 | − | 0.185882i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.937216 | + | 1.42890i | −0.937216 | + | 1.42890i | −0.0341411 | + | 0.999417i | \(0.510870\pi\) |
−0.903075 | + | 0.429483i | \(0.858696\pi\) | |||||||
\(54\) | 0.842917 | − | 0.787230i | 0.842917 | − | 0.787230i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0278499 | + | 0.270906i | 0.0278499 | + | 0.270906i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.136167 | − | 0.990686i | \(-0.543478\pi\) | ||||
0.136167 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.713755 | − | 0.580683i | 0.713755 | − | 0.580683i | −0.203456 | − | 0.979084i | \(-0.565217\pi\) |
0.917211 | + | 0.398401i | \(0.130435\pi\) | |||||||
\(62\) | 0.829926 | − | 0.394695i | 0.829926 | − | 0.394695i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.194283 | − | 0.447285i | 0.194283 | − | 0.447285i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.999417 | − | 0.0341411i | \(-0.0108696\pi\) | ||||
−0.999417 | + | 0.0341411i | \(0.989130\pi\) | |||||||
\(68\) | −0.106737 | − | 0.437996i | −0.106737 | − | 0.437996i | ||||
\(69\) | 0.668198 | + | 1.88013i | 0.668198 | + | 1.88013i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) | ||||
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(72\) | −0.697602 | − | 0.331765i | −0.697602 | − | 0.331765i | ||||
\(73\) | 0 | 0 | 0.971567 | − | 0.236764i | \(-0.0760870\pi\) | ||||
−0.971567 | + | 0.236764i | \(0.923913\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0798525 | + | 0.0413762i | −0.0798525 | + | 0.0413762i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.72850 | + | 0.614311i | 1.72850 | + | 0.614311i | 0.997669 | − | 0.0682424i | \(-0.0217391\pi\) |
0.730836 | + | 0.682553i | \(0.239130\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.460065 | + | 0.887885i | −0.460065 | + | 0.887885i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.378541 | − | 0.149277i | −0.378541 | − | 0.149277i | 0.169910 | − | 0.985460i | \(-0.445652\pi\) |
−0.548452 | + | 0.836182i | \(0.684783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.816970 | − | 0.576680i | \(-0.804348\pi\) | ||||
0.816970 | + | 0.576680i | \(0.195652\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.496653 | + | 0.433059i | −0.496653 | + | 0.433059i | ||||
\(93\) | −0.563424 | + | 0.563424i | −0.563424 | + | 0.563424i | ||||
\(94\) | −0.942261 | + | 0.665120i | −0.942261 | + | 0.665120i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.0434014 | − | 0.634506i | 0.0434014 | − | 0.634506i | ||||
\(97\) | 0 | 0 | 0.490110 | − | 0.871660i | \(-0.336957\pi\) | ||||
−0.490110 | + | 0.871660i | \(0.663043\pi\) | |||||||
\(98\) | −0.696902 | − | 0.919004i | −0.696902 | − | 0.919004i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.682553 | − | 0.730836i | \(-0.739130\pi\) | ||||
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(102\) | 0.863515 | + | 1.31654i | 0.863515 | + | 1.31654i | ||||
\(103\) | 0 | 0 | −0.971567 | − | 0.236764i | \(-0.923913\pi\) | ||||
0.971567 | + | 0.236764i | \(0.0760870\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.95255 | − | 0.268372i | 1.95255 | − | 0.268372i | ||||
\(107\) | 0.514311 | − | 0.163235i | 0.514311 | − | 0.163235i | −0.0341411 | − | 0.999417i | \(-0.510870\pi\) |
0.548452 | + | 0.836182i | \(0.315217\pi\) | |||||||
\(108\) | −0.328509 | − | 0.0337718i | −0.328509 | − | 0.0337718i | ||||
\(109\) | 0.655751 | − | 1.84511i | 0.655751 | − | 1.84511i | 0.136167 | − | 0.990686i | \(-0.456522\pi\) |
0.519584 | − | 0.854419i | \(-0.326087\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.24382 | − | 0.214457i | −1.24382 | − | 0.214457i | −0.490110 | − | 0.871660i | \(-0.663043\pi\) |
−0.753713 | + | 0.657204i | \(0.771739\pi\) | |||||||
\(114\) | 0.214389 | − | 0.229554i | 0.214389 | − | 0.229554i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.682553 | + | 0.730836i | −0.682553 | + | 0.730836i | ||||
\(122\) | −1.04581 | − | 0.180316i | −1.04581 | − | 0.180316i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.241352 | − | 0.104834i | −0.241352 | − | 0.104834i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.994757 | − | 0.102264i | \(-0.967391\pi\) | ||||
0.994757 | + | 0.102264i | \(0.0326087\pi\) | |||||||
\(128\) | −1.14228 | + | 0.362544i | −1.14228 | + | 0.362544i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.775711 | − | 0.631088i | \(-0.782609\pi\) | ||||
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.608115 | − | 0.861502i | 0.608115 | − | 0.861502i | ||||
\(137\) | 1.18320 | + | 1.56028i | 1.18320 | + | 1.56028i | 0.753713 | + | 0.657204i | \(0.228261\pi\) |
0.429483 | + | 0.903075i | \(0.358696\pi\) | |||||||
\(138\) | 1.12791 | − | 2.00599i | 1.12791 | − | 2.00599i | ||||
\(139\) | 0.128604 | − | 1.88013i | 0.128604 | − | 1.88013i | −0.269797 | − | 0.962917i | \(-0.586957\pi\) |
0.398401 | − | 0.917211i | \(-0.369565\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.576680 | − | 0.816970i | 0.576680 | − | 0.816970i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.329471 | + | 1.17590i | 0.329471 | + | 1.17590i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.836182 | + | 0.548452i | 0.836182 | + | 0.548452i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.979084 | − | 0.203456i | \(-0.934783\pi\) | ||||
0.979084 | + | 0.203456i | \(0.0652174\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.12067 | + | 1.37749i | −1.12067 | + | 1.37749i | −0.203456 | + | 0.979084i | \(0.565217\pi\) |
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(152\) | −0.195703 | − | 0.0771753i | −0.195703 | − | 0.0771753i | ||||
\(153\) | −1.08772 | − | 0.824847i | −1.08772 | − | 0.824847i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.871660 | − | 0.490110i | \(-0.163043\pi\) | ||||
−0.871660 | + | 0.490110i | \(0.836957\pi\) | |||||||
\(158\) | −0.776172 | − | 1.96824i | −0.776172 | − | 1.96824i | ||||
\(159\) | −1.51725 | + | 0.786177i | −1.51725 | + | 0.786177i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.12057 | − | 0.273075i | 1.12057 | − | 0.273075i | ||||
\(163\) | 0 | 0 | −0.903075 | − | 0.429483i | \(-0.858696\pi\) | ||||
0.903075 | + | 0.429483i | \(0.141304\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.157164 | + | 0.442218i | 0.157164 | + | 0.442218i | ||||
\(167\) | −0.246038 | − | 1.00962i | −0.246038 | − | 1.00962i | −0.953145 | − | 0.302515i | \(-0.902174\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.816970 | + | 0.576680i | −0.816970 | + | 0.576680i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.108498 | + | 0.249787i | −0.108498 | + | 0.249787i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.40105 | − | 0.666310i | 1.40105 | − | 0.666310i | 0.429483 | − | 0.903075i | \(-0.358696\pi\) |
0.971567 | + | 0.236764i | \(0.0760870\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.922444 | + | 0.861502i | −0.922444 | + | 0.861502i | −0.990686 | − | 0.136167i | \(-0.956522\pi\) |
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.906751 | − | 0.156340i | 0.906751 | − | 0.156340i | ||||
\(184\) | −1.52699 | − | 0.209880i | −1.52699 | − | 0.209880i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.916858 | + | 0.0627148i | 0.916858 | + | 0.0627148i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.320851 | + | 0.0781893i | 0.320851 | + | 0.0781893i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.962917 | − | 0.269797i | \(-0.0869565\pi\) | ||||
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(192\) | 0.388568 | − | 0.294660i | 0.388568 | − | 0.294660i | ||||
\(193\) | 0 | 0 | −0.169910 | − | 0.985460i | \(-0.554348\pi\) | ||||
0.169910 | + | 0.985460i | \(0.445652\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0671895 | + | 0.323333i | −0.0671895 | + | 0.323333i | ||||
\(197\) | 0.217854 | − | 0.893968i | 0.217854 | − | 0.893968i | −0.753713 | − | 0.657204i | \(-0.771739\pi\) |
0.971567 | − | 0.236764i | \(-0.0760870\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.953137 | + | 0.414006i | −0.953137 | + | 0.414006i | −0.816970 | − | 0.576680i | \(-0.804348\pi\) |
−0.136167 | + | 0.990686i | \(0.543478\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.121628 | − | 0.434096i | 0.121628 | − | 0.434096i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.339029 | + | 1.96632i | −0.339029 | + | 1.96632i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.538336 | − | 0.0368232i | 0.538336 | − | 0.0368232i | 0.203456 | − | 0.979084i | \(-0.434783\pi\) |
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(212\) | −0.425342 | − | 0.370879i | −0.425342 | − | 0.370879i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.531744 | − | 0.323361i | −0.531744 | − | 0.323361i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.445471 | − | 0.631088i | −0.445471 | − | 0.631088i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.10101 | + | 0.828531i | −2.10101 | + | 0.828531i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.604236 | − | 0.796805i | \(-0.293478\pi\) | ||||
−0.604236 | + | 0.796805i | \(0.706522\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.756381 | + | 1.24382i | 0.756381 | + | 1.24382i | ||||
\(227\) | 1.48487 | − | 0.973925i | 1.48487 | − | 0.973925i | 0.490110 | − | 0.871660i | \(-0.336957\pi\) |
0.994757 | − | 0.102264i | \(-0.0326087\pi\) | |||||||
\(228\) | −0.0898831 | − | 0.00307050i | −0.0898831 | − | 0.00307050i | ||||
\(229\) | 0.361291 | + | 1.73863i | 0.361291 | + | 1.73863i | 0.631088 | + | 0.775711i | \(0.282609\pi\) |
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.682945 | + | 0.783234i | 0.682945 | + | 0.783234i | 0.985460 | − | 0.169910i | \(-0.0543478\pi\) |
−0.302515 | + | 0.953145i | \(0.597826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.20559 | + | 1.38263i | 1.20559 | + | 1.38263i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.136167 | − | 0.990686i | \(-0.456522\pi\) | ||||
−0.136167 | + | 0.990686i | \(0.543478\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.347674 | − | 1.67310i | −0.347674 | − | 1.67310i | −0.682553 | − | 0.730836i | \(-0.739130\pi\) |
0.334880 | − | 0.942261i | \(-0.391304\pi\) | |||||||
\(242\) | 1.15269 | + | 0.0393770i | 1.15269 | + | 0.0393770i | ||||
\(243\) | −0.836182 | + | 0.548452i | −0.836182 | + | 0.548452i | ||||
\(244\) | 0.157883 | + | 0.259628i | 0.157883 | + | 0.259628i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.186200 | − | 0.586669i | −0.186200 | − | 0.586669i | ||||
\(249\) | −0.256797 | − | 0.315646i | −0.256797 | − | 0.315646i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.962917 | − | 0.269797i | \(-0.913043\pi\) | ||||
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.764337 | + | 0.464804i | 0.764337 | + | 0.464804i | ||||
\(257\) | 0.627764 | − | 1.32000i | 0.627764 | − | 1.32000i | −0.302515 | − | 0.953145i | \(-0.597826\pi\) |
0.930278 | − | 0.366854i | \(-0.119565\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.0231902 | − | 0.134500i | 0.0231902 | − | 0.134500i | −0.971567 | − | 0.236764i | \(-0.923913\pi\) |
0.994757 | + | 0.102264i | \(0.0326087\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | −0.887885 | − | 0.460065i | \(-0.847826\pi\) | ||||
0.887885 | + | 0.460065i | \(0.152174\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.81734 | + | 0.789381i | −1.81734 | + | 0.789381i | −0.854419 | + | 0.519584i | \(0.826087\pi\) |
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(272\) | −1.65830 | + | 0.170479i | −1.65830 | + | 0.170479i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.459500 | − | 2.21124i | 0.459500 | − | 2.21124i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.645159 | + | 0.134066i | −0.645159 | + | 0.134066i | ||||
\(277\) | 0 | 0 | −0.169910 | − | 0.985460i | \(-0.554348\pi\) | ||||
0.169910 | + | 0.985460i | \(0.445652\pi\) | |||||||
\(278\) | −1.73188 | + | 1.31333i | −1.73188 | + | 1.31333i | ||||
\(279\) | −0.767255 | + | 0.214975i | −0.767255 | + | 0.214975i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | −1.14731 | + | 0.117947i | −1.14731 | + | 0.117947i | ||||
\(283\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.348809 | − | 0.531803i | 0.348809 | − | 0.531803i | ||||
\(289\) | 0.631088 | − | 0.589395i | 0.631088 | − | 0.589395i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.599418 | − | 1.52002i | 0.599418 | − | 1.52002i | −0.236764 | − | 0.971567i | \(-0.576087\pi\) |
0.836182 | − | 0.548452i | \(-0.184783\pi\) | |||||||
\(294\) | −0.157049 | − | 1.14262i | −0.157049 | − | 1.14262i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.04691 | − | 0.0699245i | 2.04691 | − | 0.0699245i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.111370 | + | 0.313366i | 0.111370 | + | 0.313366i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.107445 | + | 1.57079i | 0.107445 | + | 1.57079i | ||||
\(307\) | 0 | 0 | −0.903075 | − | 0.429483i | \(-0.858696\pi\) | ||||
0.903075 | + | 0.429483i | \(0.141304\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.887885 | − | 0.460065i | \(-0.152174\pi\) | ||||
−0.887885 | + | 0.460065i | \(0.847826\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.871660 | − | 0.490110i | \(-0.163043\pi\) | ||||
−0.871660 | + | 0.490110i | \(0.836957\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.278708 | + | 0.537882i | −0.278708 | + | 0.537882i | ||||
\(317\) | −0.429951 | − | 0.326042i | −0.429951 | − | 0.326042i | 0.366854 | − | 0.930278i | \(-0.380435\pi\) |
−0.796805 | + | 0.604236i | \(0.793478\pi\) | |||||||
\(318\) | 1.83349 | + | 0.723036i | 1.83349 | + | 0.723036i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.528307 | + | 0.109784i | 0.528307 | + | 0.109784i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.310862 | − | 0.203895i | −0.310862 | − | 0.203895i | ||||
\(324\) | −0.269797 | − | 0.190443i | −0.269797 | − | 0.190443i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.47590 | − | 1.28692i | 1.47590 | − | 1.28692i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.0277687 | − | 0.405963i | 0.0277687 | − | 0.405963i | −0.962917 | − | 0.269797i | \(-0.913043\pi\) |
0.990686 | − | 0.136167i | \(-0.0434783\pi\) | |||||||
\(332\) | 0.0658605 | − | 0.117133i | 0.0658605 | − | 0.117133i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.691172 | + | 0.979167i | −0.691172 | + | 0.979167i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.548452 | − | 0.836182i | \(-0.684783\pi\) | ||||
0.548452 | + | 0.836182i | \(0.315217\pi\) | |||||||
\(338\) | 1.12057 | + | 0.273075i | 1.12057 | + | 0.273075i | ||||
\(339\) | −0.979084 | − | 0.796544i | −0.979084 | − | 0.796544i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.299381 | − | 0.0950194i | 0.299381 | − | 0.0950194i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.64121 | − | 0.712879i | −1.64121 | − | 0.712879i | ||||
\(347\) | −1.47873 | − | 0.469328i | −1.47873 | − | 0.469328i | −0.548452 | − | 0.836182i | \(-0.684783\pi\) |
−0.930278 | + | 0.366854i | \(0.880435\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.28629 | + | 1.37728i | −1.28629 | + | 1.37728i | −0.398401 | + | 0.917211i | \(0.630435\pi\) |
−0.887885 | + | 0.460065i | \(0.847826\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.30216 | − | 1.49339i | 1.30216 | − | 1.49339i | 0.548452 | − | 0.836182i | \(-0.315217\pi\) |
0.753713 | − | 0.657204i | \(-0.228261\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.917211 | − | 0.398401i | \(-0.869565\pi\) | ||||
0.917211 | + | 0.398401i | \(0.130435\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.310043 | − | 0.872378i | 0.310043 | − | 0.872378i | ||||
\(362\) | 1.44811 | + | 0.148870i | 1.44811 | + | 0.148870i | ||||
\(363\) | −0.953145 | + | 0.302515i | −0.953145 | + | 0.302515i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.823217 | − | 0.669737i | −0.823217 | − | 0.669737i | ||||
\(367\) | 0 | 0 | −0.971567 | − | 0.236764i | \(-0.923913\pi\) | ||||
0.971567 | + | 0.236764i | \(0.0760870\pi\) | |||||||
\(368\) | 1.33640 | + | 2.03750i | 1.33640 | + | 2.03750i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.158997 | − | 0.209669i | −0.158997 | − | 0.209669i | ||||
\(373\) | 0 | 0 | 0.490110 | − | 0.871660i | \(-0.336957\pi\) | ||||
−0.490110 | + | 0.871660i | \(0.663043\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.355388 | + | 0.685868i | 0.355388 | + | 0.685868i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.519584 | − | 1.85442i | −0.519584 | − | 1.85442i | −0.519584 | − | 0.854419i | \(-0.673913\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.0529673 | − | 1.55052i | 0.0529673 | − | 1.55052i | −0.604236 | − | 0.796805i | \(-0.706522\pi\) |
0.657204 | − | 0.753713i | \(-0.271739\pi\) | |||||||
\(384\) | −1.17337 | − | 0.243829i | −1.17337 | − | 0.243829i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.460065 | − | 0.887885i | \(-0.347826\pi\) | ||||
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.56658 | − | 0.912161i | −2.56658 | − | 0.912161i | ||||
\(392\) | −0.673335 | + | 0.378597i | −0.673335 | + | 0.378597i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.942261 | + | 0.488240i | −0.942261 | + | 0.488240i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.971567 | − | 0.236764i | \(-0.0760870\pi\) | ||||
−0.971567 | + | 0.236764i | \(0.923913\pi\) | |||||||
\(398\) | 1.08237 | + | 0.514751i | 1.08237 | + | 0.514751i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.334880 | − | 0.942261i | \(-0.608696\pi\) | ||||
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.952300 | − | 0.452894i | 0.952300 | − | 0.452894i | ||||
\(409\) | 1.46184 | − | 1.18930i | 1.46184 | − | 1.18930i | 0.519584 | − | 0.854419i | \(-0.326087\pi\) |
0.942261 | − | 0.334880i | \(-0.108696\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.266637 | + | 1.93993i | 0.266637 | + | 1.93993i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.96631 | − | 1.19574i | 1.96631 | − | 1.19574i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.03357 | − | 1.57580i | 1.03357 | − | 1.57580i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.990686 | − | 0.136167i | \(-0.956522\pi\) | ||||
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.538336 | + | 0.0368232i | 0.538336 | + | 0.0368232i | 0.334880 | − | 0.942261i | \(-0.391304\pi\) |
0.203456 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(422\) | −0.440065 | − | 0.440065i | −0.440065 | − | 0.440065i | ||||
\(423\) | 0.903075 | − | 0.429483i | 0.903075 | − | 0.429483i | ||||
\(424\) | − | 1.32003i | − | 1.32003i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.0302773 | + | 0.175605i | 0.0302773 | + | 0.175605i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(432\) | −0.289132 | + | 1.18646i | −0.289132 | + | 1.18646i | ||||
\(433\) | 0 | 0 | 0.994757 | − | 0.102264i | \(-0.0326087\pi\) | ||||
−0.994757 | + | 0.102264i | \(0.967391\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.574166 | + | 0.297509i | 0.574166 | + | 0.297509i | ||||
\(437\) | −0.0555700 | + | 0.540548i | −0.0555700 | + | 0.540548i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.109784 | + | 0.391823i | −0.109784 | + | 0.391823i | −0.997669 | − | 0.0682424i | \(-0.978261\pi\) |
0.887885 | + | 0.460065i | \(0.152174\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.460065 | + | 0.887885i | 0.460065 | + | 0.887885i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.0668540 | + | 1.95703i | 0.0668540 | + | 1.95703i | 0.236764 | + | 0.971567i | \(0.423913\pi\) |
−0.169910 | + | 0.985460i | \(0.554348\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.854419 | − | 0.519584i | \(-0.826087\pi\) | ||||
0.854419 | + | 0.519584i | \(0.173913\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.126095 | − | 0.397292i | 0.126095 | − | 0.397292i | ||||
\(453\) | −1.65196 | + | 0.651449i | −1.65196 | + | 0.651449i | ||||
\(454\) | −1.97215 | − | 0.552572i | −1.97215 | − | 0.552572i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.132762 | − | 0.163187i | −0.132762 | − | 0.163187i | ||||
\(457\) | 0 | 0 | −0.302515 | − | 0.953145i | \(-0.597826\pi\) | ||||
0.302515 | + | 0.953145i | \(0.402174\pi\) | |||||||
\(458\) | 1.23754 | − | 1.63194i | 1.23754 | − | 1.63194i | ||||
\(459\) | −0.543860 | − | 1.25209i | −0.543860 | − | 1.25209i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.519584 | − | 0.854419i | \(-0.673913\pi\) | ||||
0.519584 | + | 0.854419i | \(0.326087\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.999417 | − | 0.0341411i | \(-0.989130\pi\) | ||||
0.999417 | + | 0.0341411i | \(0.0108696\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.163201 | − | 1.18737i | 0.163201 | − | 1.18737i | ||||
\(467\) | −1.64266 | − | 0.923623i | −1.64266 | − | 0.923623i | −0.985460 | − | 0.169910i | \(-0.945652\pi\) |
−0.657204 | − | 0.753713i | \(-0.728261\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.288095 | − | 2.09604i | 0.288095 | − | 2.09604i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.70784 | − | 0.0583417i | −1.70784 | − | 0.0583417i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.519584 | − | 0.854419i | \(-0.673913\pi\) | ||||
0.519584 | + | 0.854419i | \(0.326087\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1.19089 | + | 1.57043i | −1.19089 | + | 1.57043i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.208411 | − | 0.256171i | −0.208411 | − | 0.256171i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.11059 | + | 0.311173i | 1.11059 | + | 0.311173i | ||||
\(487\) | 0 | 0 | 0.930278 | − | 0.366854i | \(-0.119565\pi\) | ||||
−0.930278 | + | 0.366854i | \(0.880435\pi\) | |||||||
\(488\) | −0.215020 | + | 0.677473i | −0.215020 | + | 0.677473i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.854419 | − | 0.519584i | \(-0.826087\pi\) | ||||
0.854419 | + | 0.519584i | \(0.173913\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.505576 | + | 0.831385i | −0.505576 | + | 0.831385i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.0797417 | + | 0.462492i | −0.0797417 | + | 0.462492i | ||||
\(499\) | −0.917985 | − | 1.77163i | −0.917985 | − | 1.77163i | −0.519584 | − | 0.854419i | \(-0.673913\pi\) |
−0.398401 | − | 0.917211i | \(-0.630435\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.280364 | − | 1.00063i | 0.280364 | − | 1.00063i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.167093 | + | 1.62537i | −0.167093 | + | 1.62537i | 0.490110 | + | 0.871660i | \(0.336957\pi\) |
−0.657204 | + | 0.753713i | \(0.728261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.994757 | + | 0.102264i | −0.994757 | + | 0.102264i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.0283194 | + | 0.164249i | 0.0283194 | + | 0.164249i | ||||
\(513\) | −0.216997 | + | 0.164554i | −0.216997 | + | 0.164554i | ||||
\(514\) | −1.62332 | + | 0.454833i | −1.62332 | + | 0.454833i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.54781 | + | 0.105873i | 1.54781 | + | 0.105873i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.990686 | − | 0.136167i | \(-0.956522\pi\) | ||||
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.548452 | − | 0.836182i | \(-0.315217\pi\) | ||||
−0.548452 | + | 0.836182i | \(0.684783\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.134499 | + | 0.0817909i | −0.134499 | + | 0.0817909i | ||||
\(527\) | −0.111235 | − | 1.08202i | −0.111235 | − | 1.08202i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.405963 | + | 2.95360i | 0.405963 | + | 2.95360i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.125185 | + | 1.83015i | 0.125185 | + | 1.83015i | 0.460065 | + | 0.887885i | \(0.347826\pi\) |
−0.334880 | + | 0.942261i | \(0.608696\pi\) | |||||||
\(542\) | 2.06374 | + | 0.981471i | 2.06374 | + | 0.981471i | ||||
\(543\) | −1.22629 | + | 0.298838i | −1.22629 | + | 0.298838i | ||||
\(544\) | 0.634506 | + | 0.592588i | 0.634506 | + | 0.592588i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.366854 | − | 0.930278i | \(-0.619565\pi\) | ||||
0.366854 | + | 0.930278i | \(0.380435\pi\) | |||||||
\(548\) | −0.563674 | + | 0.316938i | −0.563674 | + | 0.316938i | ||||
\(549\) | 0.867003 | + | 0.308133i | 0.867003 | + | 0.308133i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1.22815 | − | 0.931337i | −1.22815 | − | 0.931337i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.609329 | + | 0.126620i | 0.609329 | + | 0.126620i | ||||
\(557\) | −0.0499031 | + | 1.46082i | −0.0499031 | + | 1.46082i | 0.657204 | + | 0.753713i | \(0.271739\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(558\) | 0.768452 | + | 0.504027i | 0.768452 | + | 0.504027i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.03356 | − | 1.03356i | 1.03356 | − | 1.03356i | 0.0341411 | − | 0.999417i | \(-0.489130\pi\) |
0.999417 | − | 0.0341411i | \(-0.0108696\pi\) | |||||||
\(564\) | 0.241352 | + | 0.225407i | 0.241352 | + | 0.225407i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.576680 | − | 0.816970i | \(-0.304348\pi\) | ||||
−0.576680 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.35239 | − | 1.44806i | −1.35239 | − | 1.44806i | −0.775711 | − | 0.631088i | \(-0.782609\pi\) |
−0.576680 | − | 0.816970i | \(-0.695652\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.483115 | − | 0.0664026i | 0.483115 | − | 0.0664026i | ||||
\(577\) | 0 | 0 | 0.953145 | − | 0.302515i | \(-0.0978261\pi\) | ||||
−0.953145 | + | 0.302515i | \(0.902174\pi\) | |||||||
\(578\) | −0.990723 | − | 0.101849i | −0.990723 | − | 0.101849i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.77571 | + | 0.631088i | −1.77571 | + | 0.631088i | ||||
\(587\) | −0.178978 | + | 0.205261i | −0.178978 | + | 0.205261i | −0.836182 | − | 0.548452i | \(-0.815217\pi\) |
0.657204 | + | 0.753713i | \(0.271739\pi\) | |||||||
\(588\) | −0.217035 | + | 0.248907i | −0.217035 | + | 0.248907i | ||||
\(589\) | −0.204467 | + | 0.0726675i | −0.204467 | + | 0.0726675i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.628038 | − | 0.672464i | 0.628038 | − | 0.672464i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.55738 | − | 0.494291i | −1.55738 | − | 0.494291i | −0.604236 | − | 0.796805i | \(-0.706522\pi\) |
−0.953145 | + | 0.302515i | \(0.902174\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.03372 | − | 0.106270i | −1.03372 | − | 0.106270i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.990686 | − | 0.136167i | \(-0.0434783\pi\) | ||||
−0.990686 | + | 0.136167i | \(0.956522\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.20346 | − | 0.979084i | −1.20346 | − | 0.979084i | −0.203456 | − | 0.979084i | \(-0.565217\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.400271 | − | 0.428585i | −0.400271 | − | 0.428585i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.604236 | − | 0.796805i | \(-0.706522\pi\) | ||||
0.604236 | + | 0.796805i | \(0.293478\pi\) | |||||||
\(608\) | 0.0848876 | − | 0.150972i | 0.0848876 | − | 0.150972i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.318773 | − | 0.318773i | 0.318773 | − | 0.318773i | ||||
\(613\) | 0 | 0 | 0.753713 | − | 0.657204i | \(-0.228261\pi\) | ||||
−0.753713 | + | 0.657204i | \(0.771739\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.53391 | − | 1.00609i | −1.53391 | − | 1.00609i | −0.985460 | − | 0.169910i | \(-0.945652\pi\) |
−0.548452 | − | 0.836182i | \(-0.684783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.900885 | − | 0.187206i | −0.900885 | − | 0.187206i | −0.269797 | − | 0.962917i | \(-0.586957\pi\) |
−0.631088 | + | 0.775711i | \(0.717391\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.25923 | + | 1.54781i | −1.25923 | + | 1.54781i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.45826 | + | 1.36192i | 1.45826 | + | 1.36192i | 0.775711 | + | 0.631088i | \(0.217391\pi\) |
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(632\) | −1.37675 | + | 0.335506i | −1.37675 | + | 0.335506i | ||||
\(633\) | 0.487293 | + | 0.231746i | 0.487293 | + | 0.231746i | ||||
\(634\) | 0.0424704 | + | 0.620895i | 0.0424704 | + | 0.620895i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.188982 | − | 0.531744i | −0.188982 | − | 0.531744i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.398401 | − | 0.917211i | \(-0.369565\pi\) | ||||
−0.398401 | + | 0.917211i | \(0.630435\pi\) | |||||||
\(642\) | −0.305018 | − | 0.542474i | −0.305018 | − | 0.542474i | ||||
\(643\) | 0 | 0 | 0.903075 | − | 0.429483i | \(-0.141304\pi\) | ||||
−0.903075 | + | 0.429483i | \(0.858696\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.0583852 | + | 0.424784i | 0.0583852 | + | 0.424784i | ||||
\(647\) | 0.626895 | − | 1.58970i | 0.626895 | − | 1.58970i | −0.169910 | − | 0.985460i | \(-0.554348\pi\) |
0.796805 | − | 0.604236i | \(-0.206522\pi\) | |||||||
\(648\) | −0.0789964 | − | 0.768424i | −0.0789964 | − | 0.768424i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.95256 | − | 0.336656i | 1.95256 | − | 0.336656i | 0.953145 | − | 0.302515i | \(-0.0978261\pi\) |
0.999417 | − | 0.0341411i | \(-0.0108696\pi\) | |||||||
\(654\) | −2.23744 | − | 0.307529i | −2.23744 | − | 0.307529i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.31448 | + | 0.368301i | −1.31448 | + | 0.368301i | −0.854419 | − | 0.519584i | \(-0.826087\pi\) |
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(662\) | −0.373954 | + | 0.283578i | −0.373954 | + | 0.283578i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.307754 | − | 0.0639521i | 0.307754 | − | 0.0639521i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0.341376 | − | 0.0350946i | 0.341376 | − | 0.0350946i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.429483 | − | 0.903075i | \(-0.641304\pi\) | ||||
0.429483 | + | 0.903075i | \(0.358696\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.151932 | − | 0.293216i | −0.151932 | − | 0.293216i | ||||
\(677\) | −0.320200 | + | 1.85712i | −0.320200 | + | 1.85712i | 0.169910 | + | 0.985460i | \(0.445652\pi\) |
−0.490110 | + | 0.871660i | \(0.663043\pi\) | |||||||
\(678\) | 0.0497007 | + | 1.45490i | 0.0497007 | + | 1.45490i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.77163 | − | 0.121183i | 1.77163 | − | 0.121183i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.0586180 | − | 0.123256i | 0.0586180 | − | 0.123256i | −0.871660 | − | 0.490110i | \(-0.836957\pi\) |
0.930278 | + | 0.366854i | \(0.119565\pi\) | |||||||
\(684\) | −0.0768427 | − | 0.0467291i | −0.0768427 | − | 0.0467291i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.537196 | + | 1.69257i | −0.537196 | + | 1.69257i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.922444 | + | 1.13384i | 0.922444 | + | 1.13384i | 0.990686 | + | 0.136167i | \(0.0434783\pi\) |
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(692\) | 0.154991 | + | 0.488337i | 0.154991 | + | 0.488337i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.712879 | + | 1.64121i | 0.712879 | + | 1.64121i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 2.17227 | + | 0.0742068i | 2.17227 | + | 0.0742068i | ||||
\(699\) | 0.211425 | + | 1.01743i | 0.211425 | + | 1.01743i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.136167 | − | 0.990686i | \(-0.456522\pi\) | ||||
−0.136167 | + | 0.990686i | \(0.543478\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.28524 | −2.28524 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.0185847 | − | 0.135214i | 0.0185847 | − | 0.135214i | −0.979084 | − | 0.203456i | \(-0.934783\pi\) |
0.997669 | + | 0.0682424i | \(0.0217391\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.373224 | + | 1.79605i | 0.373224 | + | 1.79605i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.32944 | + | 0.871978i | −1.32944 | + | 0.871978i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.631088 | − | 0.775711i | \(-0.717391\pi\) | ||||
0.631088 | + | 0.775711i | \(0.282609\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.993371 | + | 0.391735i | −0.993371 | + | 0.391735i | ||||
\(723\) | 0.516949 | − | 1.62877i | 0.516949 | − | 1.62877i | ||||
\(724\) | −0.240373 | − | 0.340531i | −0.240373 | − | 0.340531i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.985454 | + | 0.599268i | 0.985454 | + | 0.599268i | ||||
\(727\) | 0 | 0 | 0.429483 | − | 0.903075i | \(-0.358696\pi\) | ||||
−0.429483 | + | 0.903075i | \(0.641304\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.997669 | + | 0.0682424i | −0.997669 | + | 0.0682424i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.0103743 | + | 0.303687i | 0.0103743 | + | 0.303687i | ||||
\(733\) | 0 | 0 | 0.169910 | − | 0.985460i | \(-0.445652\pi\) | ||||
−0.169910 | + | 0.985460i | \(0.554348\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.342376 | − | 1.22195i | 0.342376 | − | 1.22195i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.37749 | − | 0.713755i | −1.37749 | − | 0.713755i | −0.398401 | − | 0.917211i | \(-0.630435\pi\) |
−0.979084 | + | 0.203456i | \(0.934783\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.0644788 | + | 0.264590i | −0.0644788 | + | 0.264590i | −0.994757 | − | 0.102264i | \(-0.967391\pi\) |
0.930278 | + | 0.366854i | \(0.119565\pi\) | |||||||
\(744\) | 0.125229 | − | 0.602635i | 0.125229 | − | 0.602635i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.0691386 | − | 0.400995i | −0.0691386 | − | 0.400995i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.539594i | 0.539594i | 0.962917 | + | 0.269797i | \(0.0869565\pi\) | ||||
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(752\) | 0.447996 | − | 1.13604i | 0.447996 | − | 1.13604i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.985460 | − | 0.169910i | \(-0.0543478\pi\) | ||||
−0.985460 | + | 0.169910i | \(0.945652\pi\) | |||||||
\(758\) | −1.21821 | + | 1.85731i | −1.21821 | + | 1.85731i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.38802 | + | 1.12924i | −1.38802 | + | 1.12924i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.438437 | + | 0.779760i | 0.438437 | + | 0.779760i | ||||
\(769\) | −0.543860 | + | 1.25209i | −0.543860 | + | 1.25209i | 0.398401 | + | 0.917211i | \(0.369565\pi\) |
−0.942261 | + | 0.334880i | \(0.891304\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.19414 | − | 0.842917i | 1.19414 | − | 0.842917i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.158575 | + | 0.650716i | 0.158575 | + | 0.650716i | 0.994757 | + | 0.102264i | \(0.0326087\pi\) |
−0.836182 | + | 0.548452i | \(0.815217\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.15250 | + | 2.92254i | 1.15250 | + | 2.92254i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.15067 | + | 0.408949i | 1.15067 | + | 0.408949i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.796805 | − | 0.604236i | \(-0.793478\pi\) | ||||
0.796805 | + | 0.604236i | \(0.206522\pi\) | |||||||
\(788\) | 0.282679 | + | 0.111474i | 0.282679 | + | 0.111474i | ||||
\(789\) | 0.0861339 | − | 0.105873i | 0.0861339 | − | 0.105873i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.0925877 | − | 0.330450i | −0.0925877 | − | 0.330450i | ||||
\(797\) | −1.42039 | + | 1.23851i | −1.42039 | + | 1.23851i | −0.490110 | + | 0.871660i | \(0.663043\pi\) |
−0.930278 | + | 0.366854i | \(0.880435\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.368301 | + | 1.31448i | 0.368301 | + | 1.31448i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.775711 | − | 0.631088i | \(-0.782609\pi\) | ||||
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.53697 | − | 0.211252i | 1.53697 | − | 0.211252i | 0.682553 | − | 0.730836i | \(-0.260870\pi\) |
0.854419 | + | 0.519584i | \(0.173913\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.97098 | − | 0.202623i | −1.97098 | − | 0.202623i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.52903 | − | 0.664152i | −1.52903 | − | 0.664152i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −2.14193 | − | 0.369306i | −2.14193 | − | 0.369306i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.942261 | − | 0.334880i | \(-0.108696\pi\) | ||||
−0.942261 | + | 0.334880i | \(0.891304\pi\) | |||||||
\(822\) | 1.48428 | − | 1.70224i | 1.48428 | − | 1.70224i | ||||
\(823\) | 0 | 0 | 0.657204 | − | 0.753713i | \(-0.271739\pi\) | ||||
−0.657204 | + | 0.753713i | \(0.728261\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.660021 | − | 0.113799i | −0.660021 | − | 0.113799i | −0.169910 | − | 0.985460i | \(-0.554348\pi\) |
−0.490110 | + | 0.871660i | \(0.663043\pi\) | |||||||
\(828\) | −0.628067 | − | 0.199339i | −0.628067 | − | 0.199339i | ||||
\(829\) | 1.49867 | + | 0.650963i | 1.49867 | + | 0.650963i | 0.979084 | − | 0.203456i | \(-0.0652174\pi\) |
0.519584 | + | 0.854419i | \(0.326087\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.30114 | + | 0.412965i | −1.30114 | + | 0.412965i | ||||
\(834\) | −2.15329 | + | 0.295963i | −2.15329 | + | 0.295963i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.774147 | − | 0.188654i | −0.774147 | − | 0.188654i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.682553 | − | 0.730836i | \(-0.739130\pi\) | ||||
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.576680 | + | 0.816970i | −0.576680 | + | 0.816970i | ||||
\(842\) | −0.376044 | − | 0.495888i | −0.376044 | − | 0.495888i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.0121605 | + | 0.177780i | −0.0121605 | + | 0.177780i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.05788 | − | 0.459500i | −1.05788 | − | 0.459500i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.57285 | + | 1.37145i | −1.57285 | + | 1.37145i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.0341411 | − | 0.999417i | \(-0.489130\pi\) | ||||
−0.0341411 | + | 0.999417i | \(0.510870\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.263051 | + | 0.323333i | −0.263051 | + | 0.323333i | ||||
\(857\) | 0.501972 | + | 0.197952i | 0.501972 | + | 0.197952i | 0.604236 | − | 0.796805i | \(-0.293478\pi\) |
−0.102264 | + | 0.994757i | \(0.532609\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.751719 | − | 1.45075i | 0.751719 | − | 1.45075i | −0.136167 | − | 0.990686i | \(-0.543478\pi\) |
0.887885 | − | 0.460065i | \(-0.152174\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.672966 | − | 1.70652i | −0.672966 | − | 1.70652i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.0341411 | − | 0.999417i | \(-0.489130\pi\) | |||||||
\(864\) | 0.564685 | − | 0.292596i | 0.564685 | − | 0.292596i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.838963 | − | 0.204450i | 0.838963 | − | 0.204450i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.358138 | + | 1.46963i | 0.358138 | + | 1.46963i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.512022 | − | 0.361424i | 0.512022 | − | 0.361424i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.490110 | − | 0.871660i | \(-0.663043\pi\) | ||||
0.490110 | + | 0.871660i | \(0.336957\pi\) | |||||||
\(878\) | 0.423828 | − | 0.201564i | 0.423828 | − | 0.201564i | ||||
\(879\) | 1.26747 | − | 1.03116i | 1.26747 | − | 1.03116i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.136167 | − | 0.990686i | \(-0.543478\pi\) | ||||
0.136167 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(882\) | 0.423115 | − | 1.07295i | 0.423115 | − | 1.07295i | ||||
\(883\) | 0 | 0 | −0.102264 | − | 0.994757i | \(-0.532609\pi\) | ||||
0.102264 | + | 0.994757i | \(0.467391\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.65057 | − | 1.54153i | 1.65057 | − | 1.54153i | ||||
\(887\) | 0.149362 | − | 0.227720i | 0.149362 | − | 0.227720i | −0.753713 | − | 0.657204i | \(-0.771739\pi\) |
0.903075 | + | 0.429483i | \(0.141304\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.237382 | − | 0.133473i | 0.237382 | − | 0.133473i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.474611 | − | 2.28396i | 0.474611 | − | 2.28396i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.894279 | − | 0.388440i | 0.894279 | − | 0.388440i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.81848 | + | 0.942261i | 1.81848 | + | 0.942261i | ||||
\(907\) | 0 | 0 | 0.102264 | − | 0.994757i | \(-0.467391\pi\) | ||||
−0.102264 | + | 0.994757i | \(0.532609\pi\) | |||||||
\(908\) | 0.251863 | + | 0.529592i | 0.251863 | + | 0.529592i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.460065 | − | 0.887885i | \(-0.652174\pi\) | ||||
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(912\) | −0.0565068 | + | 0.327733i | −0.0565068 | + | 0.327733i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.585065 | + | 0.0400195i | −0.585065 | + | 0.0400195i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.676204 | + | 1.42185i | −0.676204 | + | 1.42185i | ||||
\(919\) | −1.70486 | − | 1.03675i | −1.70486 | − | 1.03675i | −0.887885 | − | 0.460065i | \(-0.847826\pi\) |
−0.816970 | − | 0.576680i | \(-0.804348\pi\) | |||||||
\(920\) | 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 | ||||||||
\(929\) | 0 | 0 | −0.398401 | − | 0.917211i | \(-0.630435\pi\) | ||||
0.398401 | + | 0.917211i | \(0.369565\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.141500 | + | 0.232687i | 0.141500 | + | 0.232687i | ||||
\(932\) | −0.286957 | + | 0.188215i | −0.286957 | + | 0.188215i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.442218 | + | 2.12807i | 0.442218 | + | 2.12807i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.871660 | − | 0.490110i | \(-0.836957\pi\) | ||||
0.871660 | + | 0.490110i | \(0.163043\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.669369 | + | 0.0228663i | 0.669369 | + | 0.0228663i | 0.366854 | − | 0.930278i | \(-0.380435\pi\) |
0.302515 | + | 0.953145i | \(0.402174\pi\) | |||||||
\(948\) | −0.506560 | + | 0.332253i | −0.506560 | + | 0.332253i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.214975 | − | 0.494921i | −0.214975 | − | 0.494921i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.494291 | − | 1.55738i | −0.494291 | − | 1.55738i | −0.796805 | − | 0.604236i | \(-0.793478\pi\) |
0.302515 | − | 0.953145i | \(-0.402174\pi\) | |||||||
\(954\) | 1.24382 | + | 1.52886i | 1.24382 | + | 1.52886i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.311954 | + | 0.189703i | 0.311954 | + | 0.189703i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.406699 | + | 0.354623i | 0.406699 | + | 0.354623i | ||||
\(964\) | 0.563013 | − | 0.0385111i | 0.563013 | − | 0.0385111i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.0341411 | − | 0.999417i | \(-0.510870\pi\) | ||||
0.0341411 | + | 0.999417i | \(0.489130\pi\) | |||||||
\(968\) | 0.131251 | − | 0.761242i | 0.131251 | − | 0.761242i | ||||
\(969\) | −0.171036 | − | 0.330084i | −0.171036 | − | 0.330084i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.269797 | − | 0.962917i | \(-0.413043\pi\) | ||||
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(972\) | −0.141833 | − | 0.298232i | −0.141833 | − | 0.298232i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.03062 | − | 0.447662i | 1.03062 | − | 0.447662i | ||||
\(977\) | 1.54329 | − | 0.158655i | 1.54329 | − | 0.158655i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.836182 | + | 0.548452i | \(0.184783\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.91721 | − | 0.398401i | 1.91721 | − | 0.398401i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.41494 | − | 1.07299i | 1.41494 | − | 1.07299i | 0.429483 | − | 0.903075i | \(-0.358696\pi\) |
0.985460 | − | 0.169910i | \(-0.0543478\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.90790 | − | 0.262234i | −1.90790 | − | 0.262234i | −0.917211 | − | 0.398401i | \(-0.869565\pi\) |
−0.990686 | + | 0.136167i | \(0.956522\pi\) | |||||||
\(992\) | 0.499389 | − | 0.0861034i | 0.499389 | − | 0.0861034i | ||||
\(993\) | 0.223172 | − | 0.340253i | 0.223172 | − | 0.340253i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.114816 | − | 0.0698211i | 0.114816 | − | 0.0698211i | ||||
\(997\) | 0 | 0 | −0.102264 | − | 0.994757i | \(-0.532609\pi\) | ||||
0.102264 | + | 0.994757i | \(0.467391\pi\) | |||||||
\(998\) | −0.844258 | + | 2.14089i | −0.844258 | + | 2.14089i | ||||
\(999\) | 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 | 3525.1.bg.a.557.1 | yes | 88 | |
3.2 | odd | 2 | inner | 3525.1.bg.a.557.2 | yes | 88 | |
5.2 | odd | 4 | inner | 3525.1.bg.a.3518.2 | yes | 88 | |
5.3 | odd | 4 | inner | 3525.1.bg.a.3518.1 | yes | 88 | |
5.4 | even | 2 | inner | 3525.1.bg.a.557.2 | yes | 88 | |
15.2 | even | 4 | inner | 3525.1.bg.a.3518.1 | yes | 88 | |
15.8 | even | 4 | inner | 3525.1.bg.a.3518.2 | yes | 88 | |
15.14 | odd | 2 | CM | 3525.1.bg.a.557.1 | yes | 88 | |
47.20 | odd | 46 | inner | 3525.1.bg.a.1007.2 | yes | 88 | |
141.20 | even | 46 | inner | 3525.1.bg.a.1007.1 | yes | 88 | |
235.67 | even | 92 | inner | 3525.1.bg.a.443.1 | ✓ | 88 | |
235.114 | odd | 46 | inner | 3525.1.bg.a.1007.1 | yes | 88 | |
235.208 | even | 92 | inner | 3525.1.bg.a.443.2 | yes | 88 | |
705.302 | odd | 92 | inner | 3525.1.bg.a.443.2 | yes | 88 | |
705.443 | odd | 92 | inner | 3525.1.bg.a.443.1 | ✓ | 88 | |
705.584 | even | 46 | inner | 3525.1.bg.a.1007.2 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3525.1.bg.a.443.1 | ✓ | 88 | 235.67 | even | 92 | inner | |
3525.1.bg.a.443.1 | ✓ | 88 | 705.443 | odd | 92 | inner | |
3525.1.bg.a.443.2 | yes | 88 | 235.208 | even | 92 | inner | |
3525.1.bg.a.443.2 | yes | 88 | 705.302 | odd | 92 | inner | |
3525.1.bg.a.557.1 | yes | 88 | 1.1 | even | 1 | trivial | |
3525.1.bg.a.557.1 | yes | 88 | 15.14 | odd | 2 | CM | |
3525.1.bg.a.557.2 | yes | 88 | 3.2 | odd | 2 | inner | |
3525.1.bg.a.557.2 | yes | 88 | 5.4 | even | 2 | inner | |
3525.1.bg.a.1007.1 | yes | 88 | 141.20 | even | 46 | inner | |
3525.1.bg.a.1007.1 | yes | 88 | 235.114 | odd | 46 | inner | |
3525.1.bg.a.1007.2 | yes | 88 | 47.20 | odd | 46 | inner | |
3525.1.bg.a.1007.2 | yes | 88 | 705.584 | even | 46 | inner | |
3525.1.bg.a.3518.1 | yes | 88 | 5.3 | odd | 4 | inner | |
3525.1.bg.a.3518.1 | yes | 88 | 15.2 | even | 4 | inner | |
3525.1.bg.a.3518.2 | yes | 88 | 5.2 | odd | 4 | inner | |
3525.1.bg.a.3518.2 | yes | 88 | 15.8 | even | 4 | inner |