Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [371,1,Mod(6,371)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(371, base_ring=CyclotomicField(26))
chi = DirichletCharacter(H, H._module([13, 9]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("371.6");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 371 = 7 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 371.o (of order \(26\), degree \(12\), 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: | \(0.185153119687\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\Q(\zeta_{26})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{26}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{26} - \cdots)\) |
Embedding invariants
Embedding label | 62.1 | ||
Root | \(0.970942 + 0.239316i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 371.62 |
Dual form | 371.1.o.a.6.1 |
$q$-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 \(\left(\mathbb{Z}/371\mathbb{Z}\right)^\times\).
\(n\) | \(213\) | \(267\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{17}{26}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.922670 | − | 1.75800i | 0.922670 | − | 1.75800i | 0.354605 | − | 0.935016i | \(-0.384615\pi\) |
0.568065 | − | 0.822984i | \(-0.307692\pi\) | |||||||
\(3\) | 0 | 0 | −0.935016 | − | 0.354605i | \(-0.884615\pi\) | ||||
0.935016 | + | 0.354605i | \(0.115385\pi\) | |||||||
\(4\) | −1.67118 | − | 2.42112i | −1.67118 | − | 2.42112i | ||||
\(5\) | 0 | 0 | 0.663123 | − | 0.748511i | \(-0.269231\pi\) | ||||
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.885456 | + | 0.464723i | 0.885456 | + | 0.464723i | ||||
\(8\) | −3.82734 | + | 0.464723i | −3.82734 | + | 0.464723i | ||||
\(9\) | 0.748511 | + | 0.663123i | 0.748511 | + | 0.663123i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.45352 | + | 0.358261i | −1.45352 | + | 0.358261i | −0.885456 | − | 0.464723i | \(-0.846154\pi\) |
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.568065 | − | 0.822984i | \(-0.307692\pi\) | ||||
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(14\) | 1.63397 | − | 1.12785i | 1.63397 | − | 1.12785i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.67118 | + | 4.40654i | −1.67118 | + | 4.40654i | ||||
\(17\) | 0 | 0 | 0.120537 | − | 0.992709i | \(-0.461538\pi\) | ||||
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(18\) | 1.85640 | − | 0.704039i | 1.85640 | − | 0.704039i | ||||
\(19\) | 0 | 0 | −0.822984 | − | 0.568065i | \(-0.807692\pi\) | ||||
0.822984 | + | 0.568065i | \(0.192308\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.711297 | + | 2.88585i | −0.711297 | + | 2.88585i | ||||
\(23\) | 0.478631i | 0.478631i | 0.970942 | + | 0.239316i | \(0.0769231\pi\) | ||||
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.120537 | − | 0.992709i | −0.120537 | − | 0.992709i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.354605 | − | 2.92043i | −0.354605 | − | 2.92043i | ||||
\(29\) | −0.234068 | − | 0.0576926i | −0.234068 | − | 0.0576926i | 0.120537 | − | 0.992709i | \(-0.461538\pi\) |
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.239316 | − | 0.970942i | \(-0.423077\pi\) | ||||
−0.239316 | + | 0.970942i | \(0.576923\pi\) | |||||||
\(32\) | 3.64811 | + | 4.11787i | 3.64811 | + | 4.11787i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.354605 | − | 2.92043i | 0.354605 | − | 2.92043i | ||||
\(37\) | 0.402877 | − | 1.06230i | 0.402877 | − | 1.06230i | −0.568065 | − | 0.822984i | \(-0.692308\pi\) |
0.970942 | − | 0.239316i | \(-0.0769231\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.239316 | − | 0.970942i | \(-0.576923\pi\) | ||||
0.239316 | + | 0.970942i | \(0.423077\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.251489 | − | 0.663123i | −0.251489 | − | 0.663123i | 0.748511 | − | 0.663123i | \(-0.230769\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(44\) | 3.29649 | + | 2.92043i | 3.29649 | + | 2.92043i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.841434 | + | 0.441619i | 0.841434 | + | 0.441619i | ||||
\(47\) | 0 | 0 | 0.748511 | − | 0.663123i | \(-0.230769\pi\) | ||||
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.568065 | + | 0.822984i | 0.568065 | + | 0.822984i | ||||
\(50\) | −1.85640 | − | 0.704039i | −1.85640 | − | 0.704039i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.748511 | + | 0.663123i | −0.748511 | + | 0.663123i | ||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.60491 | − | 1.36716i | −3.60491 | − | 1.36716i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.317391 | + | 0.358261i | −0.317391 | + | 0.358261i | ||||
\(59\) | 0 | 0 | 0.748511 | − | 0.663123i | \(-0.230769\pi\) | ||||
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.992709 | − | 0.120537i | \(-0.0384615\pi\) | ||||
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.354605 | + | 0.935016i | 0.354605 | + | 0.935016i | ||||
\(64\) | 6.02937 | − | 1.48611i | 6.02937 | − | 1.48611i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.09148 | + | 0.753393i | −1.09148 | + | 0.753393i | −0.970942 | − | 0.239316i | \(-0.923077\pi\) |
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.869047 | + | 0.329586i | −0.869047 | + | 0.329586i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(72\) | −3.17297 | − | 2.19015i | −3.17297 | − | 2.19015i | ||||
\(73\) | 0 | 0 | −0.992709 | − | 0.120537i | \(-0.961538\pi\) | ||||
0.992709 | + | 0.120537i | \(0.0384615\pi\) | |||||||
\(74\) | −1.49580 | − | 1.68841i | −1.49580 | − | 1.68841i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.45352 | − | 0.358261i | −1.45352 | − | 0.358261i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.431935 | − | 0.822984i | −0.431935 | − | 0.822984i | 0.568065 | − | 0.822984i | \(-0.307692\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.120537 | + | 0.992709i | 0.120537 | + | 0.992709i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.39781 | − | 0.169725i | −1.39781 | − | 0.169725i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.39663 | − | 2.04667i | 5.39663 | − | 2.04667i | ||||
\(89\) | 0 | 0 | 0.120537 | − | 0.992709i | \(-0.461538\pi\) | ||||
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.15883 | − | 0.799879i | 1.15883 | − | 0.799879i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.748511 | − | 0.663123i | \(-0.769231\pi\) | ||||
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(98\) | 1.97094 | − | 0.239316i | 1.97094 | − | 0.239316i | ||||
\(99\) | −1.32555 | − | 0.695701i | −1.32555 | − | 0.695701i | ||||
\(100\) | −2.20203 | + | 1.95083i | −2.20203 | + | 1.95083i | ||||
\(101\) | 0 | 0 | 0.663123 | − | 0.748511i | \(-0.269231\pi\) | ||||
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.935016 | − | 0.354605i | \(-0.884615\pi\) | ||||
0.935016 | + | 0.354605i | \(0.115385\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.475142 | + | 1.92773i | 0.475142 | + | 1.92773i | ||||
\(107\) | 0.709210 | 0.709210 | 0.354605 | − | 0.935016i | \(-0.384615\pi\) | ||||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 0.354605 | − | 0.935016i | \(-0.384615\pi\) | ||||
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.52758 | + | 3.12516i | −3.52758 | + | 3.12516i | ||||
\(113\) | 1.00599 | + | 0.527986i | 1.00599 | + | 0.527986i | 0.885456 | − | 0.464723i | \(-0.153846\pi\) |
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.251489 | + | 0.663123i | 0.251489 | + | 0.663123i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.09892 | − | 0.576756i | 1.09892 | − | 0.576756i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.97094 | + | 0.239316i | 1.97094 | + | 0.239316i | ||||
\(127\) | 0.317391 | + | 0.358261i | 0.317391 | + | 0.358261i | 0.885456 | − | 0.464723i | \(-0.153846\pi\) |
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(128\) | 1.63397 | − | 6.62926i | 1.63397 | − | 6.62926i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.120537 | − | 0.992709i | \(-0.538462\pi\) | ||||
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.317391 | + | 2.61395i | 0.317391 | + | 2.61395i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.447528 | − | 1.81569i | 0.447528 | − | 1.81569i | −0.120537 | − | 0.992709i | \(-0.538462\pi\) |
0.568065 | − | 0.822984i | \(-0.307692\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.992709 | − | 0.120537i | \(-0.961538\pi\) | ||||
0.992709 | + | 0.120537i | \(0.0384615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.222431 | + | 1.83188i | −0.222431 | + | 1.83188i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.17297 | + | 2.19015i | −4.17297 | + | 2.19015i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.24524 | + | 0.799879i | −3.24524 | + | 0.799879i | ||||
\(149\) | −0.627974 | − | 1.65583i | −0.627974 | − | 1.65583i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
0.120537 | − | 0.992709i | \(-0.461538\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.85640 | + | 0.225408i | −1.85640 | + | 0.225408i | −0.970942 | − | 0.239316i | \(-0.923077\pi\) |
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.97094 | + | 2.22473i | −1.97094 | + | 2.22473i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.464723 | − | 0.885456i | \(-0.346154\pi\) | ||||
−0.464723 | + | 0.885456i | \(0.653846\pi\) | |||||||
\(158\) | −1.84534 | −1.84534 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.222431 | + | 0.423807i | −0.222431 | + | 0.423807i | ||||
\(162\) | 1.85640 | + | 0.704039i | 1.85640 | + | 0.704039i | ||||
\(163\) | 1.00599 | + | 1.45743i | 1.00599 | + | 1.45743i | 0.885456 | + | 0.464723i | \(0.153846\pi\) |
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.992709 | − | 0.120537i | \(-0.0384615\pi\) | ||||
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.354605 | − | 0.935016i | −0.354605 | − | 0.935016i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.18522 | + | 1.71708i | −1.18522 | + | 1.71708i | ||||
\(173\) | 0 | 0 | 0.822984 | − | 0.568065i | \(-0.192308\pi\) | ||||
−0.822984 | + | 0.568065i | \(0.807692\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.354605 | − | 0.935016i | 0.354605 | − | 0.935016i | ||||
\(176\) | 0.850405 | − | 7.00372i | 0.850405 | − | 7.00372i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.63397 | − | 0.198399i | −1.63397 | − | 0.198399i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.239316 | − | 0.970942i | \(-0.423077\pi\) | ||||
−0.239316 | + | 0.970942i | \(0.576923\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.222431 | − | 1.83188i | −0.222431 | − | 1.83188i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.748511 | − | 0.663123i | \(-0.230769\pi\) | ||||
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.35460 | + | 0.935016i | 1.35460 | + | 0.935016i | 1.00000 | \(0\) | ||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.04321 | − | 2.75071i | 1.04321 | − | 2.75071i | ||||
\(197\) | 1.71945 | − | 0.902438i | 1.71945 | − | 0.902438i | 0.748511 | − | 0.663123i | \(-0.230769\pi\) |
0.970942 | − | 0.239316i | \(-0.0769231\pi\) | |||||||
\(198\) | −2.44608 | + | 1.68841i | −2.44608 | + | 1.68841i | ||||
\(199\) | 0 | 0 | 0.568065 | − | 0.822984i | \(-0.307692\pi\) | ||||
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(200\) | 0.922670 | + | 3.74342i | 0.922670 | + | 3.74342i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.180446 | − | 0.159861i | −0.180446 | − | 0.159861i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.317391 | + | 0.358261i | −0.317391 | + | 0.358261i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.94188 | 1.94188 | 0.970942 | − | 0.239316i | \(-0.0769231\pi\) | ||||
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(212\) | 2.85640 | + | 0.704039i | 2.85640 | + | 0.704039i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.654366 | − | 1.24679i | 0.654366 | − | 1.24679i | ||||
\(215\) | 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 | 0.970942 | − | 0.239316i | \(-0.0769231\pi\) | ||||
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(224\) | 1.31658 | + | 5.34156i | 1.31658 | + | 5.34156i | ||||
\(225\) | 0.568065 | − | 0.822984i | 0.568065 | − | 0.822984i | ||||
\(226\) | 1.85640 | − | 1.28138i | 1.85640 | − | 1.28138i | ||||
\(227\) | 0 | 0 | 0.885456 | − | 0.464723i | \(-0.153846\pi\) | ||||
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.120537 | − | 0.992709i | \(-0.461538\pi\) | ||||
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.922670 | + | 0.112032i | 0.922670 | + | 0.112032i | ||||
\(233\) | 0.879463 | + | 0.992709i | 0.879463 | + | 0.992709i | 1.00000 | \(0\) | ||
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.764919 | − | 1.45743i | −0.764919 | − | 1.45743i | −0.885456 | − | 0.464723i | \(-0.846154\pi\) |
0.120537 | − | 0.992709i | \(-0.461538\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.970942 | − | 0.239316i | \(-0.923077\pi\) | ||||
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(242\) | − | 2.46405i | − | 2.46405i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.822984 | − | 0.568065i | \(-0.192308\pi\) | ||||
−0.822984 | + | 0.568065i | \(0.807692\pi\) | |||||||
\(252\) | 1.67118 | − | 2.42112i | 1.67118 | − | 2.42112i | ||||
\(253\) | −0.171475 | − | 0.695701i | −0.171475 | − | 0.695701i | ||||
\(254\) | 0.922670 | − | 0.227418i | 0.922670 | − | 0.227418i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.49852 | − | 4.87126i | −5.49852 | − | 4.87126i | ||||
\(257\) | 0 | 0 | 0.992709 | − | 0.120537i | \(-0.0384615\pi\) | ||||
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.850405 | − | 0.753393i | 0.850405 | − | 0.753393i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.136945 | − | 0.198399i | −0.136945 | − | 0.198399i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.616337 | − | 1.17433i | 0.616337 | − | 1.17433i | −0.354605 | − | 0.935016i | \(-0.615385\pi\) |
0.970942 | − | 0.239316i | \(-0.0769231\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.64811 | + | 1.38355i | 3.64811 | + | 1.38355i | ||||
\(269\) | 0 | 0 | −0.568065 | − | 0.822984i | \(-0.692308\pi\) | ||||
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.748511 | − | 0.663123i | \(-0.230769\pi\) | ||||
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.77907 | − | 2.46204i | −2.77907 | − | 2.46204i | ||||
\(275\) | 0.530851 | + | 1.39974i | 0.530851 | + | 1.39974i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.222431 | + | 0.902438i | 0.222431 | + | 0.902438i | 0.970942 | + | 0.239316i | \(0.0769231\pi\) |
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.251489 | + | 0.663123i | −0.251489 | + | 0.663123i | 0.748511 | + | 0.663123i | \(0.230769\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.935016 | − | 0.354605i | \(-0.115385\pi\) | ||||
−0.935016 | + | 0.354605i | \(0.884615\pi\) | |||||||
\(284\) | 2.25030 | + | 1.55327i | 2.25030 | + | 1.55327i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.50142i | 5.50142i | ||||||||
\(289\) | −0.970942 | − | 0.239316i | −0.970942 | − | 0.239316i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.120537 | − | 0.992709i | \(-0.538462\pi\) | ||||
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.04827 | + | 4.25301i | −1.04827 | + | 4.25301i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.49036 | − | 0.423807i | −3.49036 | − | 0.423807i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0854858 | − | 0.704039i | 0.0854858 | − | 0.704039i | ||||
\(302\) | −1.31658 | + | 3.47152i | −1.31658 | + | 3.47152i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.970942 | − | 0.239316i | \(-0.0769231\pi\) | ||||
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(308\) | 1.56170 | + | 4.11787i | 1.56170 | + | 4.11787i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.885456 | − | 0.464723i | \(-0.846154\pi\) | ||||
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.663123 | − | 0.748511i | \(-0.269231\pi\) | ||||
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.27070 | + | 2.42112i | −1.27070 | + | 2.42112i | ||||
\(317\) | −1.77091 | −1.77091 | −0.885456 | − | 0.464723i | \(-0.846154\pi\) | ||||
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.360892 | 0.360892 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.539822 | + | 0.782068i | 0.539822 | + | 0.782068i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2.20203 | − | 1.95083i | 2.20203 | − | 1.95083i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.49036 | − | 0.423807i | 3.49036 | − | 0.423807i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.00599 | − | 1.45743i | 1.00599 | − | 1.45743i | 0.120537 | − | 0.992709i | \(-0.461538\pi\) |
0.885456 | − | 0.464723i | \(-0.153846\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.00599 | − | 0.527986i | 1.00599 | − | 0.527986i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.09148 | − | 0.753393i | −1.09148 | − | 0.753393i | −0.120537 | − | 0.992709i | \(-0.538462\pi\) |
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(338\) | −1.97094 | − | 0.239316i | −1.97094 | − | 0.239316i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.120537 | + | 0.992709i | 0.120537 | + | 0.992709i | ||||
\(344\) | 1.27070 | + | 2.42112i | 1.27070 | + | 2.42112i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.45352 | + | 0.358261i | 1.45352 | + | 0.358261i | 0.885456 | − | 0.464723i | \(-0.153846\pi\) |
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.239316 | − | 0.970942i | \(-0.423077\pi\) | ||||
−0.239316 | + | 0.970942i | \(0.576923\pi\) | |||||||
\(350\) | −1.31658 | − | 1.48611i | −1.31658 | − | 1.48611i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.77788 | − | 4.67843i | −6.77788 | − | 4.67843i | ||||
\(353\) | 0 | 0 | 0.935016 | − | 0.354605i | \(-0.115385\pi\) | ||||
−0.935016 | + | 0.354605i | \(0.884615\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.85640 | + | 2.68946i | −1.85640 | + | 2.68946i | ||||
\(359\) | −0.475142 | − | 1.92773i | −0.475142 | − | 1.92773i | −0.354605 | − | 0.935016i | \(-0.615385\pi\) |
−0.120537 | − | 0.992709i | \(-0.538462\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.354605 | + | 0.935016i | 0.354605 | + | 0.935016i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.568065 | − | 0.822984i | \(-0.692308\pi\) | ||||
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(368\) | −2.10911 | − | 0.799879i | −2.10911 | − | 0.799879i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.970942 | + | 0.239316i | −0.970942 | + | 0.239316i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.922670 | + | 1.75800i | −0.922670 | + | 1.75800i | −0.354605 | + | 0.935016i | \(0.615385\pi\) |
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.31658 | − | 0.159861i | 1.31658 | − | 0.159861i | 0.568065 | − | 0.822984i | \(-0.307692\pi\) |
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.239316 | − | 0.970942i | \(-0.576923\pi\) | ||||
0.239316 | + | 0.970942i | \(0.423077\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.89361 | − | 1.51868i | 2.89361 | − | 1.51868i | ||||
\(387\) | 0.251489 | − | 0.663123i | 0.251489 | − | 0.663123i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.24006 | − | 0.470293i | 1.24006 | − | 0.470293i | 0.354605 | − | 0.935016i | \(-0.384615\pi\) |
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2.55664 | − | 2.88585i | −2.55664 | − | 2.88585i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 3.85545i | − | 3.85545i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.530851 | + | 4.37195i | 0.530851 | + | 4.37195i | ||||
\(397\) | 0 | 0 | −0.464723 | − | 0.885456i | \(-0.653846\pi\) | ||||
0.464723 | + | 0.885456i | \(0.346154\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.57585 | + | 1.12785i | 4.57585 | + | 1.12785i | ||||
\(401\) | 1.64597i | 1.64597i | 0.568065 | + | 0.822984i | \(0.307692\pi\) | ||||
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.447528 | + | 0.169725i | −0.447528 | + | 0.169725i | ||||
\(407\) | −0.205010 | + | 1.68841i | −0.205010 | + | 1.68841i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.885456 | − | 0.464723i | \(-0.153846\pi\) | ||||
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.336975 | + | 0.888530i | 0.336975 | + | 0.888530i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.663123 | − | 0.748511i | \(-0.269231\pi\) | ||||
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.53901 | − | 0.583668i | −1.53901 | − | 0.583668i | −0.568065 | − | 0.822984i | \(-0.692308\pi\) |
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(422\) | 1.79172 | − | 3.41383i | 1.79172 | − | 3.41383i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.55664 | − | 2.88585i | 2.55664 | − | 2.88585i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.18522 | − | 1.71708i | −1.18522 | − | 1.71708i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.56806 | − | 0.822984i | −1.56806 | − | 0.822984i | −0.568065 | − | 0.822984i | \(-0.692308\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.748511 | − | 0.663123i | \(-0.769231\pi\) | ||||
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.885456 | − | 0.464723i | \(-0.153846\pi\) | ||||
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.120537 | + | 0.992709i | −0.120537 | + | 0.992709i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.35460 | + | 0.935016i | 1.35460 | + | 0.935016i | 1.00000 | \(0\) | ||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.02937 | + | 1.48611i | 6.02937 | + | 1.48611i | ||||
\(449\) | 0.234068 | + | 1.92773i | 0.234068 | + | 1.92773i | 0.354605 | + | 0.935016i | \(0.384615\pi\) |
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(450\) | −0.922670 | − | 1.75800i | −0.922670 | − | 1.75800i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.402877 | − | 3.31799i | −0.402877 | − | 3.31799i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.97094 | − | 0.239316i | −1.97094 | − | 0.239316i | −0.970942 | − | 0.239316i | \(-0.923077\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.354605 | − | 0.935016i | \(-0.384615\pi\) | ||||
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.35460 | − | 0.935016i | 1.35460 | − | 0.935016i | 0.354605 | − | 0.935016i | \(-0.384615\pi\) |
1.00000 | \(0\) | |||||||||
\(464\) | 0.645395 | − | 0.935016i | 0.645395 | − | 0.935016i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.55664 | − | 0.630154i | 2.55664 | − | 0.630154i | ||||
\(467\) | 0 | 0 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.31658 | + | 0.159861i | −1.31658 | + | 0.159861i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.603116 | + | 0.873764i | 0.603116 | + | 0.873764i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.00000 | −1.00000 | ||||||||
\(478\) | −3.26793 | −3.26793 | ||||||||
\(479\) | 0 | 0 | 0.464723 | − | 0.885456i | \(-0.346154\pi\) | ||||
−0.464723 | + | 0.885456i | \(0.653846\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.23288 | − | 1.69675i | −3.23288 | − | 1.69675i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.627974 | + | 1.65583i | 0.627974 | + | 1.65583i | 0.748511 | + | 0.663123i | \(0.230769\pi\) |
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.568065 | − | 0.822984i | \(-0.692308\pi\) | ||||
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.922670 | − | 0.112032i | −0.922670 | − | 0.112032i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.475142 | + | 1.92773i | −0.475142 | + | 1.92773i | −0.120537 | + | 0.992709i | \(0.538462\pi\) |
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.464723 | − | 0.885456i | \(-0.653846\pi\) | ||||
0.464723 | + | 0.885456i | \(0.346154\pi\) | |||||||
\(504\) | −1.79172 | − | 3.41383i | −1.79172 | − | 3.41383i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.38126 | − | 0.340449i | −1.38126 | − | 0.340449i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.336975 | − | 1.36716i | 0.336975 | − | 1.36716i | ||||
\(509\) | 0 | 0 | −0.663123 | − | 0.748511i | \(-0.730769\pi\) | ||||
0.663123 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −7.25302 | + | 2.75071i | −7.25302 | + | 2.75071i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.539822 | − | 2.19015i | −0.539822 | − | 2.19015i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.748511 | − | 0.663123i | \(-0.769231\pi\) | ||||
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(522\) | −0.475142 | + | 0.0576926i | −0.475142 | + | 0.0576926i | ||||
\(523\) | 0 | 0 | −0.885456 | − | 0.464723i | \(-0.846154\pi\) | ||||
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.49580 | − | 2.16704i | −1.49580 | − | 2.16704i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.770912 | 0.770912 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.82734 | − | 3.39073i | 3.82734 | − | 3.39073i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.12054 | − | 0.992709i | −1.12054 | − | 0.992709i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.688601 | + | 0.169725i | −0.688601 | + | 0.169725i | −0.568065 | − | 0.822984i | \(-0.692308\pi\) |
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.136945 | + | 1.12785i | −0.136945 | + | 1.12785i | 0.748511 | + | 0.663123i | \(0.230769\pi\) |
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(548\) | −5.14392 | + | 1.95083i | −5.14392 | + | 1.95083i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.95054 | + | 0.358261i | 2.95054 | + | 0.358261i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 0.929446i | − | 0.929446i | ||||||
\(554\) | 1.79172 | + | 0.441619i | 1.79172 | + | 0.441619i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.222431 | − | 0.423807i | −0.222431 | − | 0.423807i | 0.748511 | − | 0.663123i | \(-0.230769\pi\) |
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.933728 | + | 1.05396i | 0.933728 | + | 1.05396i | ||||
\(563\) | 0 | 0 | −0.992709 | − | 0.120537i | \(-0.961538\pi\) | ||||
0.992709 | + | 0.120537i | \(0.0384615\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.354605 | + | 0.935016i | −0.354605 | + | 0.935016i | ||||
\(568\) | 3.17297 | − | 1.66530i | 3.17297 | − | 1.66530i | ||||
\(569\) | −0.764919 | + | 0.527986i | −0.764919 | + | 0.527986i | −0.885456 | − | 0.464723i | \(-0.846154\pi\) |
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.447528 | − | 1.81569i | −0.447528 | − | 1.81569i | −0.568065 | − | 0.822984i | \(-0.692308\pi\) |
0.120537 | − | 0.992709i | \(-0.461538\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.475142 | − | 0.0576926i | 0.475142 | − | 0.0576926i | ||||
\(576\) | 5.49852 | + | 2.88585i | 5.49852 | + | 2.88585i | ||||
\(577\) | 0 | 0 | 0.748511 | − | 0.663123i | \(-0.230769\pi\) | ||||
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(578\) | −1.31658 | + | 1.48611i | −1.31658 | + | 1.48611i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.850405 | − | 1.23202i | 0.850405 | − | 1.23202i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.568065 | − | 0.822984i | \(-0.692308\pi\) | ||||
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.00779 | + | 3.55059i | 4.00779 | + | 3.55059i | ||||
\(593\) | 0 | 0 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.95951 | + | 4.28760i | −2.95951 | + | 4.28760i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.402877 | + | 1.06230i | −0.402877 | + | 1.06230i | 0.568065 | + | 0.822984i | \(0.307692\pi\) |
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.935016 | − | 0.354605i | \(-0.115385\pi\) | ||||
−0.935016 | + | 0.354605i | \(0.884615\pi\) | |||||||
\(602\) | −1.15883 | − | 0.799879i | −1.15883 | − | 0.799879i | ||||
\(603\) | −1.31658 | − | 0.159861i | −1.31658 | − | 0.159861i | ||||
\(604\) | 3.64811 | + | 4.11787i | 3.64811 | + | 4.11787i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.970942 | − | 0.239316i | \(-0.923077\pi\) | ||||
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.87003i | 1.87003i | 0.354605 | + | 0.935016i | \(0.384615\pi\) | ||||
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.72961 | + | 0.695701i | 5.72961 | + | 0.695701i | ||||
\(617\) | 1.53901 | + | 1.06230i | 1.53901 | + | 1.06230i | 0.970942 | + | 0.239316i | \(0.0769231\pi\) |
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.120537 | − | 0.992709i | \(-0.461538\pi\) | ||||
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.970942 | + | 0.239316i | −0.970942 | + | 0.239316i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.24006 | + | 1.39974i | −1.24006 | + | 1.39974i | −0.354605 | + | 0.935016i | \(0.615385\pi\) |
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(632\) | 2.03562 | + | 2.94911i | 2.03562 | + | 2.94911i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.63397 | + | 3.11326i | −1.63397 | + | 3.11326i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.332984 | − | 0.634448i | 0.332984 | − | 0.634448i | ||||
\(639\) | −0.869047 | − | 0.329586i | −0.869047 | − | 0.329586i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.616337 | − | 0.695701i | 0.616337 | − | 0.695701i | −0.354605 | − | 0.935016i | \(-0.615385\pi\) |
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.885456 | − | 0.464723i | \(-0.846154\pi\) | ||||
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(644\) | 1.39781 | − | 0.169725i | 1.39781 | − | 0.169725i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.970942 | − | 0.239316i | \(-0.0769231\pi\) | ||||
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(648\) | −0.922670 | − | 3.74342i | −0.922670 | − | 3.74342i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.84743 | − | 4.87126i | 1.84743 | − | 4.87126i | ||||
\(653\) | −0.0290582 | + | 0.239316i | −0.0290582 | + | 0.239316i | 0.970942 | + | 0.239316i | \(0.0769231\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 0.478631i | − | 0.478631i | −0.970942 | − | 0.239316i | \(-0.923077\pi\) | ||
0.970942 | − | 0.239316i | \(-0.0769231\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.120537 | − | 0.992709i | \(-0.538462\pi\) | ||||
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(662\) | −1.63397 | − | 3.11326i | −1.63397 | − | 3.11326i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 2.25569i | − | 2.25569i | ||||||
\(667\) | 0.0276135 | − | 0.112032i | 0.0276135 | − | 0.112032i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.627974 | − | 1.65583i | 0.627974 | − | 1.65583i | −0.120537 | − | 0.992709i | \(-0.538462\pi\) |
0.748511 | − | 0.663123i | \(-0.230769\pi\) | |||||||
\(674\) | −2.33154 | + | 1.22369i | −2.33154 | + | 1.22369i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.67118 | + | 2.42112i | −1.67118 | + | 2.42112i | ||||
\(677\) | 0 | 0 | −0.239316 | − | 0.970942i | \(-0.576923\pi\) | ||||
0.239316 | + | 0.970942i | \(0.423077\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.180446 | − | 0.159861i | 0.180446 | − | 0.159861i | −0.568065 | − | 0.822984i | \(-0.692308\pi\) |
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.85640 | + | 0.704039i | 1.85640 | + | 0.704039i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.34236 | 3.34236 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.464723 | − | 0.885456i | \(-0.346154\pi\) | ||||
−0.464723 | + | 0.885456i | \(0.653846\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.850405 | − | 1.23202i | −0.850405 | − | 1.23202i | ||||
\(694\) | 1.97094 | − | 2.22473i | 1.97094 | − | 2.22473i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.85640 | + | 0.704039i | −2.85640 | + | 0.704039i | ||||
\(701\) | 0.317391 | + | 1.28771i | 0.317391 | + | 1.28771i | 0.885456 | + | 0.464723i | \(0.153846\pi\) |
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −8.23140 | + | 4.32017i | −8.23140 | + | 4.32017i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.85640 | − | 0.225408i | −1.85640 | − | 0.225408i | −0.885456 | − | 0.464723i | \(-0.846154\pi\) |
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.222431 | − | 0.902438i | 0.222431 | − | 0.902438i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.25030 | + | 4.28760i | 2.25030 | + | 4.28760i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.82734 | − | 0.943355i | −3.82734 | − | 0.943355i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.97094 | + | 0.239316i | 1.97094 | + | 0.239316i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.0290582 | + | 0.239316i | −0.0290582 | + | 0.239316i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.885456 | − | 0.464723i | \(-0.153846\pi\) | ||||
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.568065 | + | 0.822984i | −0.568065 | + | 0.822984i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.748511 | − | 0.663123i | \(-0.769231\pi\) | ||||
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.97094 | + | 1.74610i | −1.97094 | + | 1.74610i | ||||
\(737\) | 1.31658 | − | 1.48611i | 1.31658 | − | 1.48611i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.53901 | + | 0.583668i | 1.53901 | + | 0.583668i | 0.970942 | − | 0.239316i | \(-0.0769231\pi\) |
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.475142 | + | 1.92773i | −0.475142 | + | 1.92773i | ||||
\(743\) | 1.77091 | 1.77091 | 0.885456 | − | 0.464723i | \(-0.153846\pi\) | ||||
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.23925 | + | 3.24411i | 2.23925 | + | 3.24411i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.627974 | + | 0.329586i | 0.627974 | + | 0.329586i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.180446 | − | 0.159861i | −0.180446 | − | 0.159861i | 0.568065 | − | 0.822984i | \(-0.307692\pi\) |
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.00599 | + | 0.527986i | −1.00599 | + | 0.527986i | −0.885456 | − | 0.464723i | \(-0.846154\pi\) |
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(758\) | 0.933728 | − | 2.46204i | 0.933728 | − | 2.46204i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.822984 | − | 0.568065i | \(-0.807692\pi\) | ||||
0.822984 | + | 0.568065i | \(0.192308\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | −0.464723 | − | 0.885456i | \(-0.653846\pi\) | ||||
0.464723 | + | 0.885456i | \(0.346154\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 4.84225i | − | 4.84225i | ||||||
\(773\) | 0 | 0 | 0.239316 | − | 0.970942i | \(-0.423077\pi\) | ||||
−0.239316 | + | 0.970942i | \(0.576923\pi\) | |||||||
\(774\) | −0.933728 | − | 1.05396i | −0.933728 | − | 1.05396i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.317391 | − | 2.61395i | 0.317391 | − | 2.61395i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.14510 | − | 0.790406i | 1.14510 | − | 0.790406i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.57585 | + | 1.12785i | −4.57585 | + | 1.12785i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.992709 | − | 0.120537i | \(-0.0384615\pi\) | ||||
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(788\) | −5.05843 | − | 2.65487i | −5.05843 | − | 2.65487i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.645395 | + | 0.935016i | 0.645395 | + | 0.935016i | ||||
\(792\) | 5.39663 | + | 2.04667i | 5.39663 | + | 2.04667i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.464723 | − | 0.885456i | \(-0.346154\pi\) | ||||
−0.464723 | + | 0.885456i | \(0.653846\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 3.64811 | − | 4.11787i | 3.64811 | − | 4.11787i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.89361 | + | 1.51868i | 2.89361 | + | 1.51868i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.35460 | − | 0.935016i | 1.35460 | − | 0.935016i | 0.354605 | − | 0.935016i | \(-0.384615\pi\) |
1.00000 | \(0\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.354605 | − | 0.935016i | \(-0.384615\pi\) | ||||
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(812\) | −0.0854858 | + | 0.704039i | −0.0854858 | + | 0.704039i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.77907 | + | 1.91825i | 2.77907 | + | 1.91825i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.616337 | − | 1.17433i | −0.616337 | − | 1.17433i | −0.970942 | − | 0.239316i | \(-0.923077\pi\) |
0.354605 | − | 0.935016i | \(-0.384615\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.0854858 | + | 0.704039i | 0.0854858 | + | 0.704039i | 0.970942 | + | 0.239316i | \(0.0769231\pi\) |
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.24006 | − | 1.39974i | −1.24006 | − | 1.39974i | −0.885456 | − | 0.464723i | \(-0.846154\pi\) |
−0.354605 | − | 0.935016i | \(-0.615385\pi\) | |||||||
\(828\) | 1.39781 | + | 0.169725i | 1.39781 | + | 0.169725i | ||||
\(829\) | 0 | 0 | −0.822984 | − | 0.568065i | \(-0.807692\pi\) | ||||
0.822984 | + | 0.568065i | \(0.192308\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.748511 | − | 0.663123i | \(-0.769231\pi\) | ||||
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.833997 | − | 0.437715i | −0.833997 | − | 0.437715i | ||||
\(842\) | −2.44608 | + | 2.16704i | −2.44608 | + | 2.16704i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.24524 | − | 4.70154i | −3.24524 | − | 4.70154i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.24107 | 1.24107 | ||||||||
\(848\) | −1.67118 | − | 4.40654i | −1.67118 | − | 4.40654i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.508450 | + | 0.192830i | 0.508450 | + | 0.192830i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.663123 | − | 0.748511i | \(-0.269231\pi\) | ||||
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.71439 | + | 0.329586i | −2.71439 | + | 0.329586i | ||||
\(857\) | 0 | 0 | −0.748511 | − | 0.663123i | \(-0.769231\pi\) | ||||
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.970942 | − | 0.239316i | \(-0.0769231\pi\) | ||||
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.89361 | + | 1.99732i | −2.89361 | + | 1.99732i | ||||
\(863\) | 0.627974 | − | 0.329586i | 0.627974 | − | 0.329586i | −0.120537 | − | 0.992709i | \(-0.538462\pi\) |
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.922670 | + | 1.04148i | 0.922670 | + | 1.04148i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.10312 | − | 0.271894i | −1.10312 | − | 0.271894i | −0.354605 | − | 0.935016i | \(-0.615385\pi\) |
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.992709 | − | 0.120537i | \(-0.961538\pi\) | ||||
0.992709 | + | 0.120537i | \(0.0384615\pi\) | |||||||
\(882\) | 1.63397 | + | 1.12785i | 1.63397 | + | 1.12785i | ||||
\(883\) | 0.447528 | − | 0.169725i | 0.447528 | − | 0.169725i | −0.120537 | − | 0.992709i | \(-0.538462\pi\) |
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.89361 | − | 1.51868i | 2.89361 | − | 1.51868i | ||||
\(887\) | 0 | 0 | 0.822984 | − | 0.568065i | \(-0.192308\pi\) | ||||
−0.822984 | + | 0.568065i | \(0.807692\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.114544 | + | 0.464723i | 0.114544 | + | 0.464723i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.530851 | − | 1.39974i | −0.530851 | − | 1.39974i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.52758 | − | 5.11058i | 4.52758 | − | 5.11058i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.60491 | + | 1.36716i | 3.60491 | + | 1.36716i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −2.94188 | −2.94188 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.09564 | − | 1.55327i | −4.09564 | − | 1.55327i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.12054 | − | 0.992709i | 1.12054 | − | 0.992709i | 0.120537 | − | 0.992709i | \(-0.461538\pi\) |
1.00000 | \(0\) | |||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.688601 | + | 1.81569i | 0.688601 | + | 1.81569i | 0.568065 | + | 0.822984i | \(0.307692\pi\) |
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −2.23925 | + | 3.24411i | −2.23925 | + | 3.24411i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.53901 | − | 0.583668i | 1.53901 | − | 0.583668i | 0.568065 | − | 0.822984i | \(-0.307692\pi\) |
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.10312 | − | 0.271894i | −1.10312 | − | 0.271894i | ||||
\(926\) | −0.393906 | − | 3.24411i | −0.393906 | − | 3.24411i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.616337 | − | 1.17433i | −0.616337 | − | 1.17433i | ||||
\(929\) | 0 | 0 | −0.120537 | − | 0.992709i | \(-0.538462\pi\) | ||||
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.933728 | − | 3.78828i | 0.933728 | − | 3.78828i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.120537 | − | 0.992709i | \(-0.461538\pi\) | ||||
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(938\) | −0.933728 | + | 2.46204i | −0.933728 | + | 2.46204i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.568065 | − | 0.822984i | \(-0.307692\pi\) | ||||
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.09255 | − | 0.254082i | 2.09255 | − | 0.254082i | ||||
\(947\) | 1.00599 | + | 0.527986i | 1.00599 | + | 0.527986i | 0.885456 | − | 0.464723i | \(-0.153846\pi\) |
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.709210 | 0.709210 | 0.354605 | − | 0.935016i | \(-0.384615\pi\) | ||||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(954\) | −0.922670 | + | 1.75800i | −0.922670 | + | 1.75800i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.25030 | + | 4.28760i | −2.25030 | + | 4.28760i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.24006 | − | 1.39974i | 1.24006 | − | 1.39974i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.885456 | − | 0.464723i | −0.885456 | − | 0.464723i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.530851 | + | 0.470293i | 0.530851 | + | 0.470293i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.136945 | − | 0.198399i | 0.136945 | − | 0.198399i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(968\) | −3.93789 | + | 2.71813i | −3.93789 | + | 2.71813i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.120537 | − | 0.992709i | \(-0.461538\pi\) | ||||
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.49036 | + | 0.423807i | 3.49036 | + | 0.423807i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.32625i | 1.32625i | 0.748511 | + | 0.663123i | \(0.230769\pi\) | ||||
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.970942 | − | 0.239316i | \(-0.923077\pi\) | ||||
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.317391 | − | 0.120371i | 0.317391 | − | 0.120371i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.530851 | − | 1.39974i | 0.530851 | − | 1.39974i | −0.354605 | − | 0.935016i | \(-0.615385\pi\) |
0.885456 | − | 0.464723i | \(-0.153846\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.04827 | + | 1.51868i | −1.04827 | + | 1.51868i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(998\) | 2.95054 | + | 2.61395i | 2.95054 | + | 2.61395i | ||||
\(999\) | 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 | 371.1.o.a.62.1 | yes | 12 | |
3.2 | odd | 2 | 3339.1.cm.a.433.1 | 12 | |||
7.2 | even | 3 | 2597.1.be.a.1599.1 | 24 | |||
7.3 | odd | 6 | 2597.1.be.a.1440.1 | 24 | |||
7.4 | even | 3 | 2597.1.be.a.1440.1 | 24 | |||
7.5 | odd | 6 | 2597.1.be.a.1599.1 | 24 | |||
7.6 | odd | 2 | CM | 371.1.o.a.62.1 | yes | 12 | |
21.20 | even | 2 | 3339.1.cm.a.433.1 | 12 | |||
53.6 | even | 26 | inner | 371.1.o.a.6.1 | ✓ | 12 | |
159.59 | odd | 26 | 3339.1.cm.a.748.1 | 12 | |||
371.6 | odd | 26 | inner | 371.1.o.a.6.1 | ✓ | 12 | |
371.59 | odd | 78 | 2597.1.be.a.2126.1 | 24 | |||
371.165 | even | 78 | 2597.1.be.a.2126.1 | 24 | |||
371.271 | odd | 78 | 2597.1.be.a.2285.1 | 24 | |||
371.324 | even | 78 | 2597.1.be.a.2285.1 | 24 | |||
1113.377 | even | 26 | 3339.1.cm.a.748.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
371.1.o.a.6.1 | ✓ | 12 | 53.6 | even | 26 | inner | |
371.1.o.a.6.1 | ✓ | 12 | 371.6 | odd | 26 | inner | |
371.1.o.a.62.1 | yes | 12 | 1.1 | even | 1 | trivial | |
371.1.o.a.62.1 | yes | 12 | 7.6 | odd | 2 | CM | |
2597.1.be.a.1440.1 | 24 | 7.3 | odd | 6 | |||
2597.1.be.a.1440.1 | 24 | 7.4 | even | 3 | |||
2597.1.be.a.1599.1 | 24 | 7.2 | even | 3 | |||
2597.1.be.a.1599.1 | 24 | 7.5 | odd | 6 | |||
2597.1.be.a.2126.1 | 24 | 371.59 | odd | 78 | |||
2597.1.be.a.2126.1 | 24 | 371.165 | even | 78 | |||
2597.1.be.a.2285.1 | 24 | 371.271 | odd | 78 | |||
2597.1.be.a.2285.1 | 24 | 371.324 | even | 78 | |||
3339.1.cm.a.433.1 | 12 | 3.2 | odd | 2 | |||
3339.1.cm.a.433.1 | 12 | 21.20 | even | 2 | |||
3339.1.cm.a.748.1 | 12 | 159.59 | odd | 26 | |||
3339.1.cm.a.748.1 | 12 | 1113.377 | even | 26 |