Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3380,1,Mod(187,3380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3380, base_ring=CyclotomicField(52))
chi = DirichletCharacter(H, H._module([26, 13, 31]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3380.187");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3380.bz (of order \(52\), degree \(24\), 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: | \(1.68683974270\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Coefficient field: | \(\Q(\zeta_{52})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{52}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{52} + \cdots)\) |
Embedding invariants
Embedding label | 3047.1 | ||
Root | \(-0.663123 - 0.748511i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3380.3047 |
Dual form | 3380.1.bz.a.203.1 |
$q$-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 \(\left(\mathbb{Z}/3380\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(1691\) | \(1861\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(e\left(\frac{3}{52}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.568065 | − | 0.822984i | −0.568065 | − | 0.822984i | ||||
\(3\) | 0 | 0 | 0.954721 | − | 0.297503i | \(-0.0961538\pi\) | ||||
−0.954721 | + | 0.297503i | \(0.903846\pi\) | |||||||
\(4\) | −0.354605 | + | 0.935016i | −0.354605 | + | 0.935016i | ||||
\(5\) | 0.992709 | − | 0.120537i | 0.992709 | − | 0.120537i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.239316 | − | 0.970942i | \(-0.576923\pi\) | ||||
0.239316 | + | 0.970942i | \(0.423077\pi\) | |||||||
\(8\) | 0.970942 | − | 0.239316i | 0.970942 | − | 0.239316i | ||||
\(9\) | 0.822984 | − | 0.568065i | 0.822984 | − | 0.568065i | ||||
\(10\) | −0.663123 | − | 0.748511i | −0.663123 | − | 0.748511i | ||||
\(11\) | 0 | 0 | 0.983620 | − | 0.180255i | \(-0.0576923\pi\) | ||||
−0.983620 | + | 0.180255i | \(0.942308\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.239316 | − | 0.970942i | 0.239316 | − | 0.970942i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.748511 | − | 0.663123i | −0.748511 | − | 0.663123i | ||||
\(17\) | 0.943521 | − | 1.56077i | 0.943521 | − | 1.56077i | 0.120537 | − | 0.992709i | \(-0.461538\pi\) |
0.822984 | − | 0.568065i | \(-0.192308\pi\) | |||||||
\(18\) | −0.935016 | − | 0.354605i | −0.935016 | − | 0.354605i | ||||
\(19\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(20\) | −0.239316 | + | 0.970942i | −0.239316 | + | 0.970942i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.970942 | − | 0.239316i | 0.970942 | − | 0.239316i | ||||
\(26\) | −0.935016 | + | 0.354605i | −0.935016 | + | 0.354605i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.45743 | + | 1.00599i | −1.45743 | + | 1.00599i | −0.464723 | + | 0.885456i | \(0.653846\pi\) |
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.787183 | − | 0.616719i | \(-0.788462\pi\) | ||||
0.787183 | + | 0.616719i | \(0.211538\pi\) | |||||||
\(32\) | −0.120537 | + | 0.992709i | −0.120537 | + | 0.992709i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.82047 | + | 0.110118i | −1.82047 | + | 0.110118i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.239316 | + | 0.970942i | 0.239316 | + | 0.970942i | ||||
\(37\) | −1.31658 | + | 0.159861i | −1.31658 | + | 0.159861i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.935016 | − | 0.354605i | 0.935016 | − | 0.354605i | ||||
\(41\) | 0.344186 | − | 0.107253i | 0.344186 | − | 0.107253i | −0.120537 | − | 0.992709i | \(-0.538462\pi\) |
0.464723 | + | 0.885456i | \(0.346154\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.787183 | − | 0.616719i | \(-0.211538\pi\) | ||||
−0.787183 | + | 0.616719i | \(0.788462\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.748511 | − | 0.663123i | 0.748511 | − | 0.663123i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.935016 | − | 0.354605i | \(-0.115385\pi\) | ||||
−0.935016 | + | 0.354605i | \(0.884615\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.885456 | + | 0.464723i | −0.885456 | + | 0.464723i | ||||
\(50\) | −0.748511 | − | 0.663123i | −0.748511 | − | 0.663123i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.822984 | + | 0.568065i | 0.822984 | + | 0.568065i | ||||
\(53\) | −0.535277 | + | 0.885456i | −0.535277 | + | 0.885456i | 0.464723 | + | 0.885456i | \(0.346154\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.65583 | + | 0.627974i | 1.65583 | + | 0.627974i | ||||
\(59\) | 0 | 0 | 0.0603785 | − | 0.998176i | \(-0.480769\pi\) | ||||
−0.0603785 | + | 0.998176i | \(0.519231\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.902438 | − | 0.222431i | −0.902438 | − | 0.222431i | −0.239316 | − | 0.970942i | \(-0.576923\pi\) |
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.885456 | − | 0.464723i | 0.885456 | − | 0.464723i | ||||
\(65\) | 0.120537 | − | 0.992709i | 0.120537 | − | 0.992709i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(68\) | 1.12477 | + | 1.43566i | 1.12477 | + | 1.43566i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.954721 | − | 0.297503i | \(-0.0961538\pi\) | ||||
−0.954721 | + | 0.297503i | \(0.903846\pi\) | |||||||
\(72\) | 0.663123 | − | 0.748511i | 0.663123 | − | 0.748511i | ||||
\(73\) | 1.13613 | − | 1.64597i | 1.13613 | − | 1.64597i | 0.568065 | − | 0.822984i | \(-0.307692\pi\) |
0.568065 | − | 0.822984i | \(-0.307692\pi\) | |||||||
\(74\) | 0.879463 | + | 0.992709i | 0.879463 | + | 0.992709i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.935016 | − | 0.354605i | \(-0.115385\pi\) | ||||
−0.935016 | + | 0.354605i | \(0.884615\pi\) | |||||||
\(80\) | −0.822984 | − | 0.568065i | −0.822984 | − | 0.568065i | ||||
\(81\) | 0.354605 | − | 0.935016i | 0.354605 | − | 0.935016i | ||||
\(82\) | −0.283788 | − | 0.222333i | −0.283788 | − | 0.222333i | ||||
\(83\) | 0 | 0 | −0.464723 | − | 0.885456i | \(-0.653846\pi\) | ||||
0.464723 | + | 0.885456i | \(0.346154\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.748511 | − | 1.66312i | 0.748511 | − | 1.66312i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.41163 | + | 1.41163i | −1.41163 | + | 1.41163i | −0.663123 | + | 0.748511i | \(0.730769\pi\) |
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(90\) | −0.970942 | − | 0.239316i | −0.970942 | − | 0.239316i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.48611 | + | 1.31658i | 1.48611 | + | 1.31658i | 0.822984 | + | 0.568065i | \(0.192308\pi\) |
0.663123 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(98\) | 0.885456 | + | 0.464723i | 0.885456 | + | 0.464723i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.120537 | + | 0.992709i | −0.120537 | + | 0.992709i | ||||
\(101\) | 1.97094 | + | 0.239316i | 1.97094 | + | 0.239316i | 1.00000 | \(0\) | ||
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.297503 | − | 0.954721i | \(-0.596154\pi\) | ||||
0.297503 | + | 0.954721i | \(0.403846\pi\) | |||||||
\(104\) | − | 1.00000i | − | 1.00000i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.03279 | − | 0.0624722i | 1.03279 | − | 0.0624722i | ||||
\(107\) | 0 | 0 | −0.998176 | − | 0.0603785i | \(-0.980769\pi\) | ||||
0.998176 | + | 0.0603785i | \(0.0192308\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.646140 | + | 0.506219i | −0.646140 | + | 0.506219i | −0.885456 | − | 0.464723i | \(-0.846154\pi\) |
0.239316 | + | 0.970942i | \(0.423077\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.0359256 | + | 0.115289i | −0.0359256 | + | 0.115289i | −0.970942 | − | 0.239316i | \(-0.923077\pi\) |
0.935016 | + | 0.354605i | \(0.115385\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.423807 | − | 1.71945i | −0.423807 | − | 1.71945i | ||||
\(117\) | −0.354605 | − | 0.935016i | −0.354605 | − | 0.935016i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.935016 | − | 0.354605i | 0.935016 | − | 0.354605i | ||||
\(122\) | 0.329586 | + | 0.869047i | 0.329586 | + | 0.869047i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.935016 | − | 0.354605i | 0.935016 | − | 0.354605i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.911900 | − | 0.410413i | \(-0.865385\pi\) | ||||
0.911900 | + | 0.410413i | \(0.134615\pi\) | |||||||
\(128\) | −0.885456 | − | 0.464723i | −0.885456 | − | 0.464723i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.885456 | + | 0.464723i | −0.885456 | + | 0.464723i | ||||
\(131\) | 0 | 0 | −0.568065 | − | 0.822984i | \(-0.692308\pi\) | ||||
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.542586 | − | 1.74122i | 0.542586 | − | 1.74122i | ||||
\(137\) | −1.48611 | − | 0.180446i | −1.48611 | − | 0.180446i | −0.663123 | − | 0.748511i | \(-0.730769\pi\) |
−0.822984 | + | 0.568065i | \(0.807692\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.663123 | − | 0.748511i | \(-0.269231\pi\) | ||||
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.992709 | − | 0.120537i | −0.992709 | − | 0.120537i | ||||
\(145\) | −1.32555 | + | 1.17433i | −1.32555 | + | 1.17433i | ||||
\(146\) | −2.00000 | −2.00000 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.317391 | − | 1.28771i | 0.317391 | − | 1.28771i | ||||
\(149\) | −0.506219 | + | 1.12477i | −0.506219 | + | 1.12477i | 0.464723 | + | 0.885456i | \(0.346154\pi\) |
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.911900 | − | 0.410413i | \(-0.134615\pi\) | ||||
−0.911900 | + | 0.410413i | \(0.865385\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.110118 | − | 1.82047i | −0.110118 | − | 1.82047i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.57149 | + | 0.0950579i | 1.57149 | + | 0.0950579i | 0.822984 | − | 0.568065i | \(-0.192308\pi\) |
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000i | 1.00000i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.970942 | + | 0.239316i | −0.970942 | + | 0.239316i | ||||
\(163\) | 0 | 0 | −0.120537 | − | 0.992709i | \(-0.538462\pi\) | ||||
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(164\) | −0.0217671 | + | 0.359852i | −0.0217671 | + | 0.359852i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.822984 | − | 0.568065i | \(-0.192308\pi\) | ||||
−0.822984 | + | 0.568065i | \(0.807692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.885456 | − | 0.464723i | −0.885456 | − | 0.464723i | ||||
\(170\) | −1.79393 | + | 0.328749i | −1.79393 | + | 0.328749i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.74122 | − | 0.783659i | 1.74122 | − | 0.783659i | 0.748511 | − | 0.663123i | \(-0.230769\pi\) |
0.992709 | − | 0.120537i | \(-0.0384615\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.96365 | + | 0.359852i | 1.96365 | + | 0.359852i | ||||
\(179\) | 0 | 0 | −0.970942 | − | 0.239316i | \(-0.923077\pi\) | ||||
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(180\) | 0.354605 | + | 0.935016i | 0.354605 | + | 0.935016i | ||||
\(181\) | −1.28771 | − | 1.45352i | −1.28771 | − | 1.45352i | −0.822984 | − | 0.568065i | \(-0.807692\pi\) |
−0.464723 | − | 0.885456i | \(-0.653846\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.28771 | + | 0.317391i | −1.28771 | + | 0.317391i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.92773 | + | 0.475142i | 1.92773 | + | 0.475142i | 0.992709 | + | 0.120537i | \(0.0384615\pi\) |
0.935016 | + | 0.354605i | \(0.115385\pi\) | |||||||
\(194\) | 0.239316 | − | 1.97094i | 0.239316 | − | 1.97094i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.120537 | − | 0.992709i | −0.120537 | − | 0.992709i | ||||
\(197\) | −0.112032 | + | 0.922670i | −0.112032 | + | 0.922670i | 0.822984 | + | 0.568065i | \(0.192308\pi\) |
−0.935016 | + | 0.354605i | \(0.884615\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.748511 | − | 0.663123i | \(-0.769231\pi\) | ||||
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(200\) | 0.885456 | − | 0.464723i | 0.885456 | − | 0.464723i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.922670 | − | 1.75800i | −0.922670 | − | 1.75800i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.328749 | − | 0.147958i | 0.328749 | − | 0.147958i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.822984 | + | 0.568065i | −0.822984 | + | 0.568065i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(212\) | −0.638104 | − | 0.814480i | −0.638104 | − | 0.814480i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.783659 | + | 0.244198i | 0.783659 | + | 0.244198i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.28962 | − | 1.28962i | −1.28962 | − | 1.28962i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.663123 | − | 0.748511i | \(-0.730769\pi\) | ||||
0.663123 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.663123 | − | 0.748511i | 0.663123 | − | 0.748511i | ||||
\(226\) | 0.115289 | − | 0.0359256i | 0.115289 | − | 0.0359256i | ||||
\(227\) | 0 | 0 | 0.354605 | − | 0.935016i | \(-0.384615\pi\) | ||||
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.05555 | + | 1.34731i | 1.05555 | + | 1.34731i | 0.935016 | + | 0.354605i | \(0.115385\pi\) |
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.17433 | + | 1.32555i | −1.17433 | + | 1.32555i | ||||
\(233\) | −1.50308 | − | 0.468379i | −1.50308 | − | 0.468379i | −0.568065 | − | 0.822984i | \(-0.692308\pi\) |
−0.935016 | + | 0.354605i | \(0.884615\pi\) | |||||||
\(234\) | −0.568065 | + | 0.822984i | −0.568065 | + | 0.822984i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.115289 | + | 1.90596i | 0.115289 | + | 1.90596i | 0.354605 | + | 0.935016i | \(0.384615\pi\) |
−0.239316 | + | 0.970942i | \(0.576923\pi\) | |||||||
\(242\) | −0.822984 | − | 0.568065i | −0.822984 | − | 0.568065i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.527986 | − | 0.764919i | 0.527986 | − | 0.764919i | ||||
\(245\) | −0.822984 | + | 0.568065i | −0.822984 | + | 0.568065i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.822984 | − | 0.568065i | −0.822984 | − | 0.568065i | ||||
\(251\) | 0 | 0 | 0.992709 | − | 0.120537i | \(-0.0384615\pi\) | ||||
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.120537 | + | 0.992709i | 0.120537 | + | 0.992709i | ||||
\(257\) | −0.424644 | − | 0.943521i | −0.424644 | − | 0.943521i | −0.992709 | − | 0.120537i | \(-0.961538\pi\) |
0.568065 | − | 0.822984i | \(-0.307692\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.885456 | + | 0.464723i | 0.885456 | + | 0.464723i | ||||
\(261\) | −0.627974 | + | 1.65583i | −0.627974 | + | 1.65583i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.180255 | − | 0.983620i | \(-0.557692\pi\) | ||||
0.180255 | + | 0.983620i | \(0.442308\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.424644 | + | 0.943521i | −0.424644 | + | 0.943521i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.616337 | + | 1.17433i | −0.616337 | + | 1.17433i | 0.354605 | + | 0.935016i | \(0.384615\pi\) |
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.410413 | − | 0.911900i | \(-0.365385\pi\) | ||||
−0.410413 | + | 0.911900i | \(0.634615\pi\) | |||||||
\(272\) | −1.74122 | + | 0.542586i | −1.74122 | + | 0.542586i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.695701 | + | 1.32555i | 0.695701 | + | 1.32555i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.21026 | − | 0.731626i | 1.21026 | − | 0.731626i | 0.239316 | − | 0.970942i | \(-0.423077\pi\) |
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.509195 | + | 1.63406i | 0.509195 | + | 1.63406i | 0.748511 | + | 0.663123i | \(0.230769\pi\) |
−0.239316 | + | 0.970942i | \(0.576923\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.616719 | − | 0.787183i | \(-0.288462\pi\) | ||||
−0.616719 | + | 0.787183i | \(0.711538\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.464723 | + | 0.885456i | 0.464723 | + | 0.885456i | ||||
\(289\) | −1.08106 | − | 2.05979i | −1.08106 | − | 2.05979i | ||||
\(290\) | 1.71945 | + | 0.423807i | 1.71945 | + | 0.423807i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.13613 | + | 1.64597i | 1.13613 | + | 1.64597i | ||||
\(293\) | −0.234068 | − | 0.0576926i | −0.234068 | − | 0.0576926i | 0.120537 | − | 0.992709i | \(-0.461538\pi\) |
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.24006 | + | 0.470293i | −1.24006 | + | 0.470293i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.21323 | − | 0.222333i | 1.21323 | − | 0.222333i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.922670 | − | 0.112032i | −0.922670 | − | 0.112032i | ||||
\(306\) | −1.43566 | + | 1.12477i | −1.43566 | + | 1.12477i | ||||
\(307\) | 0 | 0 | 0.992709 | − | 0.120537i | \(-0.0384615\pi\) | ||||
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.992709 | − | 0.120537i | \(-0.0384615\pi\) | ||||
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.222333 | − | 0.283788i | −0.222333 | − | 0.283788i | 0.663123 | − | 0.748511i | \(-0.269231\pi\) |
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(314\) | −0.814480 | − | 1.34731i | −0.814480 | − | 1.34731i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.88546 | − | 0.464723i | −1.88546 | − | 0.464723i | −0.885456 | − | 0.464723i | \(-0.846154\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.822984 | − | 0.568065i | 0.822984 | − | 0.568065i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.748511 | + | 0.663123i | 0.748511 | + | 0.663123i | ||||
\(325\) | − | 1.00000i | − | 1.00000i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.308518 | − | 0.186505i | 0.308518 | − | 0.186505i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.517338 | − | 0.855781i | \(-0.326923\pi\) | ||||
−0.517338 | + | 0.855781i | \(0.673077\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.992709 | + | 0.879463i | −0.992709 | + | 0.879463i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.872172 | − | 0.872172i | 0.872172 | − | 0.872172i | −0.120537 | − | 0.992709i | \(-0.538462\pi\) |
0.992709 | + | 0.120537i | \(0.0384615\pi\) | |||||||
\(338\) | 0.120537 | + | 0.992709i | 0.120537 | + | 0.992709i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.28962 | + | 1.28962i | 1.28962 | + | 1.28962i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.63406 | − | 0.987826i | −1.63406 | − | 0.987826i | ||||
\(347\) | 0 | 0 | 0.180255 | − | 0.983620i | \(-0.442308\pi\) | ||||
−0.180255 | + | 0.983620i | \(0.557692\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.0217671 | − | 0.118779i | −0.0217671 | − | 0.118779i | 0.970942 | − | 0.239316i | \(-0.0769231\pi\) |
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.114544 | − | 0.464723i | −0.114544 | − | 0.464723i | 0.885456 | − | 0.464723i | \(-0.153846\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.819328 | − | 1.82047i | −0.819328 | − | 1.82047i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.855781 | − | 0.517338i | \(-0.173077\pi\) | ||||
−0.855781 | + | 0.517338i | \(0.826923\pi\) | |||||||
\(360\) | 0.568065 | − | 0.822984i | 0.568065 | − | 0.822984i | ||||
\(361\) | 1.00000i | 1.00000i | ||||||||
\(362\) | −0.464723 | + | 1.88546i | −0.464723 | + | 1.88546i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.929446 | − | 1.77091i | 0.929446 | − | 1.77091i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.180255 | − | 0.983620i | \(-0.442308\pi\) | ||||
−0.180255 | + | 0.983620i | \(0.557692\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.222333 | − | 0.283788i | 0.222333 | − | 0.283788i | ||||
\(370\) | 0.992709 | + | 0.879463i | 0.992709 | + | 0.879463i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.354605 | + | 1.93502i | 0.354605 | + | 1.93502i | 0.354605 | + | 0.935016i | \(0.384615\pi\) |
1.00000i | \(0.500000\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.627974 | + | 1.65583i | 0.627974 | + | 1.65583i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | −0.297503 | − | 0.954721i | \(-0.596154\pi\) | ||||
0.297503 | + | 0.954721i | \(0.403846\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.239316 | − | 0.970942i | \(-0.423077\pi\) | ||||
−0.239316 | + | 0.970942i | \(0.576923\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.704039 | − | 1.85640i | −0.704039 | − | 1.85640i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.75800 | + | 0.922670i | −1.75800 | + | 0.922670i | ||||
\(389\) | 1.45352 | + | 0.358261i | 1.45352 | + | 0.358261i | 0.885456 | − | 0.464723i | \(-0.153846\pi\) |
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.748511 | + | 0.663123i | −0.748511 | + | 0.663123i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.822984 | − | 0.431935i | 0.822984 | − | 0.431935i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.09148 | + | 1.23202i | 1.09148 | + | 1.23202i | 0.970942 | + | 0.239316i | \(0.0769231\pi\) |
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.885456 | − | 0.464723i | −0.885456 | − | 0.464723i | ||||
\(401\) | 0.0950579 | + | 1.57149i | 0.0950579 | + | 1.57149i | 0.663123 | + | 0.748511i | \(0.269231\pi\) |
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.922670 | + | 1.75800i | −0.922670 | + | 1.75800i | ||||
\(405\) | 0.239316 | − | 0.970942i | 0.239316 | − | 0.970942i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.420733 | + | 1.35018i | 0.420733 | + | 1.35018i | 0.885456 | + | 0.464723i | \(0.153846\pi\) |
−0.464723 | + | 0.885456i | \(0.653846\pi\) | |||||||
\(410\) | −0.308518 | − | 0.186505i | −0.308518 | − | 0.186505i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.935016 | + | 0.354605i | 0.935016 | + | 0.354605i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.935016 | − | 0.354605i | \(-0.884615\pi\) | ||||
0.935016 | + | 0.354605i | \(0.115385\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.177016 | − | 0.568065i | 0.177016 | − | 0.568065i | −0.822984 | − | 0.568065i | \(-0.807692\pi\) |
1.00000 | \(0\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.307819 | + | 0.987826i | −0.307819 | + | 0.987826i | ||||
\(425\) | 0.542586 | − | 1.74122i | 0.542586 | − | 1.74122i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.410413 | − | 0.911900i | \(-0.634615\pi\) | ||||
0.410413 | + | 0.911900i | \(0.365385\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.120537 | − | 0.00729113i | −0.120537 | − | 0.00729113i | − | 1.00000i | \(-0.5\pi\) | |
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.244198 | − | 0.783659i | −0.244198 | − | 0.783659i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.120537 | − | 0.992709i | \(-0.461538\pi\) | ||||
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.464723 | + | 0.885456i | −0.464723 | + | 0.885456i | ||||
\(442\) | −0.328749 | + | 1.79393i | −0.328749 | + | 1.79393i | ||||
\(443\) | 0 | 0 | 0.297503 | − | 0.954721i | \(-0.403846\pi\) | ||||
−0.297503 | + | 0.954721i | \(0.596154\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.23119 | + | 1.57149i | −1.23119 | + | 1.57149i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.807380 | − | 1.79393i | −0.807380 | − | 1.79393i | −0.568065 | − | 0.822984i | \(-0.692308\pi\) |
−0.239316 | − | 0.970942i | \(-0.576923\pi\) | |||||||
\(450\) | −0.992709 | − | 0.120537i | −0.992709 | − | 0.120537i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.0950579 | − | 0.0744731i | −0.0950579 | − | 0.0744731i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.423807 | − | 0.222431i | 0.423807 | − | 0.222431i | −0.239316 | − | 0.970942i | \(-0.576923\pi\) |
0.663123 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(458\) | 0.509195 | − | 1.63406i | 0.509195 | − | 1.63406i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.96365 | − | 0.359852i | −1.96365 | − | 0.359852i | −0.992709 | − | 0.120537i | \(-0.961538\pi\) |
−0.970942 | − | 0.239316i | \(-0.923077\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.568065 | − | 0.822984i | \(-0.692308\pi\) | ||||
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(464\) | 1.75800 | + | 0.213460i | 1.75800 | + | 0.213460i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.468379 | + | 1.50308i | 0.468379 | + | 1.50308i | ||||
\(467\) | 0 | 0 | −0.180255 | − | 0.983620i | \(-0.557692\pi\) | ||||
0.180255 | + | 0.983620i | \(0.442308\pi\) | |||||||
\(468\) | 1.00000 | 1.00000 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.0624722 | + | 1.03279i | 0.0624722 | + | 1.03279i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.616719 | − | 0.787183i | \(-0.711538\pi\) | ||||
0.616719 | + | 0.787183i | \(0.288462\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.159861 | + | 1.31658i | −0.159861 | + | 1.31658i | ||||
\(482\) | 1.50308 | − | 1.17759i | 1.50308 | − | 1.17759i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000i | 1.00000i | ||||||||
\(485\) | 1.63397 | + | 1.12785i | 1.63397 | + | 1.12785i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(488\) | −0.929446 | −0.929446 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.935016 | + | 0.354605i | 0.935016 | + | 0.354605i | ||||
\(491\) | 0 | 0 | 0.663123 | − | 0.748511i | \(-0.269231\pi\) | ||||
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.195010 | + | 3.22390i | 0.195010 | + | 3.22390i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | −0.855781 | − | 0.517338i | \(-0.826923\pi\) | ||||
0.855781 | + | 0.517338i | \(0.173077\pi\) | |||||||
\(500\) | 1.00000i | 1.00000i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.410413 | − | 0.911900i | \(-0.634615\pi\) | ||||
0.410413 | + | 0.911900i | \(0.365385\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.98542 | 1.98542 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.344186 | − | 1.87816i | 0.344186 | − | 1.87816i | −0.120537 | − | 0.992709i | \(-0.538462\pi\) |
0.464723 | − | 0.885456i | \(-0.346154\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.748511 | − | 0.663123i | 0.748511 | − | 0.663123i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.535277 | + | 0.885456i | −0.535277 | + | 0.885456i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.120537 | − | 0.992709i | −0.120537 | − | 0.992709i | ||||
\(521\) | 1.23202 | + | 1.09148i | 1.23202 | + | 1.09148i | 0.992709 | + | 0.120537i | \(0.0384615\pi\) |
0.239316 | + | 0.970942i | \(0.423077\pi\) | |||||||
\(522\) | 1.71945 | − | 0.423807i | 1.71945 | − | 0.423807i | ||||
\(523\) | 0 | 0 | 0.998176 | − | 0.0603785i | \(-0.0192308\pi\) | ||||
−0.998176 | + | 0.0603785i | \(0.980769\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000i | 1.00000i | ||||||||
\(530\) | 1.01773 | − | 0.186505i | 1.01773 | − | 0.186505i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0217671 | − | 0.359852i | −0.0217671 | − | 0.359852i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.31658 | − | 0.159861i | 1.31658 | − | 0.159861i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.103342 | − | 1.70844i | −0.103342 | − | 1.70844i | −0.568065 | − | 0.822984i | \(-0.692308\pi\) |
0.464723 | − | 0.885456i | \(-0.346154\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.43566 | + | 1.12477i | 1.43566 | + | 1.12477i | ||||
\(545\) | −0.580411 | + | 0.580411i | −0.580411 | + | 0.580411i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.983620 | − | 0.180255i | \(-0.0576923\pi\) | ||||
−0.983620 | + | 0.180255i | \(0.942308\pi\) | |||||||
\(548\) | 0.695701 | − | 1.32555i | 0.695701 | − | 1.32555i | ||||
\(549\) | −0.869047 | + | 0.329586i | −0.869047 | + | 0.329586i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.28962 | − | 0.580411i | −1.28962 | − | 0.580411i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.885456 | − | 0.464723i | \(-0.153846\pi\) | ||||
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.05555 | − | 1.34731i | 1.05555 | − | 1.34731i | ||||
\(563\) | 0 | 0 | −0.954721 | − | 0.297503i | \(-0.903846\pi\) | ||||
0.954721 | + | 0.297503i | \(0.0961538\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.0217671 | + | 0.118779i | −0.0217671 | + | 0.118779i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.39974 | − | 1.24006i | 1.39974 | − | 1.24006i | 0.464723 | − | 0.885456i | \(-0.346154\pi\) |
0.935016 | − | 0.354605i | \(-0.115385\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.464723 | − | 0.885456i | \(-0.653846\pi\) | ||||
0.464723 | + | 0.885456i | \(0.346154\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.464723 | − | 0.885456i | 0.464723 | − | 0.885456i | ||||
\(577\) | −0.709210 | −0.709210 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(578\) | −1.08106 | + | 2.05979i | −1.08106 | + | 2.05979i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.627974 | − | 1.65583i | −0.627974 | − | 1.65583i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0.709210 | − | 1.87003i | 0.709210 | − | 1.87003i | ||||
\(585\) | −0.464723 | − | 0.885456i | −0.464723 | − | 0.885456i | ||||
\(586\) | 0.0854858 | + | 0.225408i | 0.0854858 | + | 0.225408i | ||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.09148 | + | 0.753393i | 1.09148 | + | 0.753393i | ||||
\(593\) | −1.65583 | + | 0.869047i | −1.65583 | + | 0.869047i | −0.663123 | + | 0.748511i | \(0.730769\pi\) |
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.872172 | − | 0.872172i | −0.872172 | − | 0.872172i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.935016 | − | 0.354605i | \(-0.884615\pi\) | ||||
0.935016 | + | 0.354605i | \(0.115385\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.00599 | − | 1.45743i | 1.00599 | − | 1.45743i | 0.120537 | − | 0.992709i | \(-0.461538\pi\) |
0.885456 | − | 0.464723i | \(-0.153846\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.885456 | − | 0.464723i | 0.885456 | − | 0.464723i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.297503 | − | 0.954721i | \(-0.596154\pi\) | ||||
0.297503 | + | 0.954721i | \(0.403846\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.431935 | + | 0.822984i | 0.431935 | + | 0.822984i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.74122 | + | 0.542586i | 1.74122 | + | 0.542586i | ||||
\(613\) | −1.17433 | + | 1.32555i | −1.17433 | + | 1.32555i | −0.239316 | + | 0.970942i | \(0.576923\pi\) |
−0.935016 | + | 0.354605i | \(0.884615\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.695701 | + | 0.616337i | −0.695701 | + | 0.616337i | −0.935016 | − | 0.354605i | \(-0.884615\pi\) |
0.239316 | + | 0.970942i | \(0.423077\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.954721 | − | 0.297503i | \(-0.0961538\pi\) | ||||
−0.954721 | + | 0.297503i | \(0.903846\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.885456 | − | 0.464723i | 0.885456 | − | 0.464723i | ||||
\(626\) | −0.107253 | + | 0.344186i | −0.107253 | + | 0.344186i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.646140 | + | 1.43566i | −0.646140 | + | 1.43566i | ||||
\(629\) | −0.992709 | + | 2.20571i | −0.992709 | + | 2.20571i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.517338 | − | 0.855781i | \(-0.673077\pi\) | ||||
0.517338 | + | 0.855781i | \(0.326923\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.688601 | + | 1.81569i | 0.688601 | + | 1.81569i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.239316 | + | 0.970942i | 0.239316 | + | 0.970942i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.935016 | − | 0.354605i | −0.935016 | − | 0.354605i | ||||
\(641\) | 0 | 0 | 0.568065 | − | 0.822984i | \(-0.307692\pi\) | ||||
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.464723 | − | 0.885456i | \(-0.653846\pi\) | ||||
0.464723 | + | 0.885456i | \(0.346154\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.983620 | − | 0.180255i | \(-0.942308\pi\) | ||||
0.983620 | + | 0.180255i | \(0.0576923\pi\) | |||||||
\(648\) | 0.120537 | − | 0.992709i | 0.120537 | − | 0.992709i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.822984 | + | 0.568065i | −0.822984 | + | 0.568065i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.731626 | + | 0.731626i | −0.731626 | + | 0.731626i | −0.970942 | − | 0.239316i | \(-0.923077\pi\) |
0.239316 | + | 0.970942i | \(0.423077\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.328749 | − | 0.147958i | −0.328749 | − | 0.147958i | ||||
\(657\) | − | 2.00000i | − | 2.00000i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.239316 | − | 0.970942i | \(-0.576923\pi\) | ||||
0.239316 | + | 0.970942i | \(0.423077\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.56077 | + | 0.943521i | 1.56077 | + | 0.943521i | 0.992709 | + | 0.120537i | \(0.0384615\pi\) |
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.28771 | + | 0.317391i | 1.28771 | + | 0.317391i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.509195 | − | 1.63406i | −0.509195 | − | 1.63406i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
0.239316 | − | 0.970942i | \(-0.423077\pi\) | |||||||
\(674\) | −1.21323 | − | 0.222333i | −1.21323 | − | 0.222333i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.748511 | − | 0.663123i | 0.748511 | − | 0.663123i | ||||
\(677\) | 1.28962 | + | 1.28962i | 1.28962 | + | 1.28962i | 0.935016 | + | 0.354605i | \(0.115385\pi\) |
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.328749 | − | 1.79393i | 0.328749 | − | 1.79393i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.970942 | − | 0.239316i | \(-0.0769231\pi\) | ||||
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.49702 | −1.49702 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.731626 | + | 0.731626i | 0.731626 | + | 0.731626i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.517338 | − | 0.855781i | \(-0.326923\pi\) | ||||
−0.517338 | + | 0.855781i | \(0.673077\pi\) | |||||||
\(692\) | 0.115289 | + | 1.90596i | 0.115289 | + | 1.90596i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.157350 | − | 0.638392i | 0.157350 | − | 0.638392i | ||||
\(698\) | −0.0853881 | + | 0.0853881i | −0.0853881 | + | 0.0853881i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.475142 | + | 0.0576926i | 0.475142 | + | 0.0576926i | 0.354605 | − | 0.935016i | \(-0.384615\pi\) |
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.317391 | + | 0.358261i | −0.317391 | + | 0.358261i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.244198 | − | 0.783659i | 0.244198 | − | 0.783659i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
0.992709 | − | 0.120537i | \(-0.0384615\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.03279 | + | 1.70844i | −1.03279 | + | 1.70844i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.120537 | − | 0.992709i | \(-0.461538\pi\) | ||||
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(720\) | −1.00000 | −1.00000 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.822984 | − | 0.568065i | 0.822984 | − | 0.568065i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.81569 | − | 0.688601i | 1.81569 | − | 0.688601i | ||||
\(725\) | −1.17433 | + | 1.32555i | −1.17433 | + | 1.32555i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.855781 | − | 0.517338i | \(-0.173077\pi\) | ||||
−0.855781 | + | 0.517338i | \(0.826923\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.239316 | − | 0.970942i | −0.239316 | − | 0.970942i | ||||
\(730\) | −1.98542 | + | 0.241073i | −1.98542 | + | 0.241073i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.112032 | + | 0.213460i | −0.112032 | + | 0.213460i | −0.935016 | − | 0.354605i | \(-0.884615\pi\) |
0.822984 | + | 0.568065i | \(0.192308\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.359852 | − | 0.0217671i | −0.359852 | − | 0.0217671i | ||||
\(739\) | 0 | 0 | 0.998176 | − | 0.0603785i | \(-0.0192308\pi\) | ||||
−0.998176 | + | 0.0603785i | \(0.980769\pi\) | |||||||
\(740\) | 0.159861 | − | 1.31658i | 0.159861 | − | 1.31658i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.935016 | − | 0.354605i | \(-0.115385\pi\) | ||||
−0.935016 | + | 0.354605i | \(0.884615\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.366951 | + | 1.17759i | −0.366951 | + | 1.17759i | ||||
\(746\) | 1.39105 | − | 1.39105i | 1.39105 | − | 1.39105i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.822984 | − | 0.568065i | \(-0.807692\pi\) | ||||
0.822984 | + | 0.568065i | \(0.192308\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.00599 | − | 1.45743i | 1.00599 | − | 1.45743i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.542586 | + | 0.244198i | −0.542586 | + | 0.244198i | −0.663123 | − | 0.748511i | \(-0.730769\pi\) |
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.01773 | + | 0.186505i | −1.01773 | + | 0.186505i | −0.663123 | − | 0.748511i | \(-0.730769\pi\) |
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.328749 | − | 1.79393i | −0.328749 | − | 1.79393i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.542586 | − | 0.244198i | 0.542586 | − | 0.244198i | −0.120537 | − | 0.992709i | \(-0.538462\pi\) |
0.663123 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.12785 | + | 1.63397i | −1.12785 | + | 1.63397i | ||||
\(773\) | −1.24006 | + | 1.39974i | −1.24006 | + | 1.39974i | −0.354605 | + | 0.935016i | \(0.615385\pi\) |
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.75800 | + | 0.922670i | 1.75800 | + | 0.922670i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.530851 | − | 1.39974i | −0.530851 | − | 1.39974i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.970942 | + | 0.239316i | 0.970942 | + | 0.239316i | ||||
\(785\) | 1.57149 | − | 0.0950579i | 1.57149 | − | 0.0950579i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.935016 | − | 0.354605i | \(-0.884615\pi\) | ||||
0.935016 | + | 0.354605i | \(0.115385\pi\) | |||||||
\(788\) | −0.822984 | − | 0.431935i | −0.822984 | − | 0.431935i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.431935 | + | 0.822984i | −0.431935 | + | 0.822984i | ||||
\(794\) | 0.393906 | − | 1.59814i | 0.393906 | − | 1.59814i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.79393 | − | 0.807380i | −1.79393 | − | 0.807380i | −0.970942 | − | 0.239316i | \(-0.923077\pi\) |
−0.822984 | − | 0.568065i | \(-0.807692\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.120537 | + | 0.992709i | 0.120537 | + | 0.992709i | ||||
\(801\) | −0.359852 | + | 1.96365i | −0.359852 | + | 1.96365i | ||||
\(802\) | 1.23932 | − | 0.970942i | 1.23932 | − | 0.970942i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.97094 | − | 0.239316i | 1.97094 | − | 0.239316i | ||||
\(809\) | 0.0576926 | + | 0.234068i | 0.0576926 | + | 0.234068i | 0.992709 | − | 0.120537i | \(-0.0384615\pi\) |
−0.935016 | + | 0.354605i | \(0.884615\pi\) | |||||||
\(810\) | −0.935016 | + | 0.354605i | −0.935016 | + | 0.354605i | ||||
\(811\) | 0 | 0 | 0.998176 | − | 0.0603785i | \(-0.0192308\pi\) | ||||
−0.998176 | + | 0.0603785i | \(0.980769\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.872172 | − | 1.11325i | 0.872172 | − | 1.11325i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0217671 | + | 0.359852i | 0.0217671 | + | 0.359852i | ||||
\(821\) | −1.05555 | + | 0.638104i | −1.05555 | + | 0.638104i | −0.935016 | − | 0.354605i | \(-0.884615\pi\) |
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.935016 | − | 0.354605i | \(-0.884615\pi\) | ||||
0.935016 | + | 0.354605i | \(0.115385\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.358261 | − | 0.317391i | −0.358261 | − | 0.317391i | 0.464723 | − | 0.885456i | \(-0.346154\pi\) |
−0.822984 | + | 0.568065i | \(0.807692\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.239316 | − | 0.970942i | −0.239316 | − | 0.970942i | ||||
\(833\) | −0.110118 | + | 1.82047i | −0.110118 | + | 1.82047i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.787183 | − | 0.616719i | \(-0.788462\pi\) | ||||
0.787183 | + | 0.616719i | \(0.211538\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.757482 | − | 1.99732i | 0.757482 | − | 1.99732i | ||||
\(842\) | −0.568065 | + | 0.177016i | −0.568065 | + | 0.177016i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.935016 | − | 0.354605i | −0.935016 | − | 0.354605i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.987826 | − | 0.307819i | 0.987826 | − | 0.307819i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.74122 | + | 0.542586i | −1.74122 | + | 0.542586i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.688601 | + | 0.169725i | −0.688601 | + | 0.169725i | −0.568065 | − | 0.822984i | \(-0.692308\pi\) |
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.0359256 | + | 0.593921i | −0.0359256 | + | 0.593921i | 0.935016 | + | 0.354605i | \(0.115385\pi\) |
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.663123 | − | 0.748511i | \(-0.269231\pi\) | ||||
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.935016 | − | 0.354605i | \(-0.884615\pi\) | ||||
0.935016 | + | 0.354605i | \(0.115385\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.63406 | − | 0.987826i | 1.63406 | − | 0.987826i | ||||
\(866\) | 0.0624722 | + | 0.103342i | 0.0624722 | + | 0.103342i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.506219 | + | 0.646140i | −0.506219 | + | 0.646140i | ||||
\(873\) | 1.97094 | + | 0.239316i | 1.97094 | + | 0.239316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.198399 | − | 1.63397i | 0.198399 | − | 1.63397i | −0.464723 | − | 0.885456i | \(-0.653846\pi\) |
0.663123 | − | 0.748511i | \(-0.269231\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.271894 | − | 1.10312i | −0.271894 | − | 1.10312i | −0.935016 | − | 0.354605i | \(-0.884615\pi\) |
0.663123 | − | 0.748511i | \(-0.269231\pi\) | |||||||
\(882\) | 0.992709 | − | 0.120537i | 0.992709 | − | 0.120537i | ||||
\(883\) | 0 | 0 | 0.180255 | − | 0.983620i | \(-0.442308\pi\) | ||||
−0.180255 | + | 0.983620i | \(0.557692\pi\) | |||||||
\(884\) | 1.66312 | − | 0.748511i | 1.66312 | − | 0.748511i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.410413 | − | 0.911900i | \(-0.365385\pi\) | ||||
−0.410413 | + | 0.911900i | \(0.634615\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.99271 | + | 0.120537i | 1.99271 | + | 0.120537i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.01773 | + | 1.68353i | −1.01773 | + | 1.68353i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.464723 | + | 0.885456i | 0.464723 | + | 0.885456i | ||||
\(901\) | 0.876952 | + | 1.67089i | 0.876952 | + | 1.67089i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.00729113 | + | 0.120537i | −0.00729113 | + | 0.120537i | ||||
\(905\) | −1.45352 | − | 1.28771i | −1.45352 | − | 1.28771i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.0603785 | − | 0.998176i | \(-0.480769\pi\) | ||||
−0.0603785 | + | 0.998176i | \(0.519231\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.75800 | − | 0.922670i | 1.75800 | − | 0.922670i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.885456 | − | 0.464723i | \(-0.846154\pi\) | ||||
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.423807 | − | 0.222431i | −0.423807 | − | 0.222431i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.63406 | + | 0.509195i | −1.63406 | + | 0.509195i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.663123 | − | 0.748511i | \(-0.730769\pi\) | ||||
0.663123 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.819328 | + | 1.82047i | 0.819328 | + | 1.82047i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.24006 | + | 0.470293i | −1.24006 | + | 0.470293i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.822984 | − | 1.56806i | −0.822984 | − | 1.56806i | ||||
\(929\) | −0.807380 | + | 0.147958i | −0.807380 | + | 0.147958i | −0.568065 | − | 0.822984i | \(-0.692308\pi\) |
−0.239316 | + | 0.970942i | \(0.576923\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.970942 | − | 1.23932i | 0.970942 | − | 1.23932i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.568065 | − | 0.822984i | −0.568065 | − | 0.822984i | ||||
\(937\) | −1.28962 | + | 0.580411i | −1.28962 | + | 0.580411i | −0.935016 | − | 0.354605i | \(-0.884615\pi\) |
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.107253 | + | 0.585260i | 0.107253 | + | 0.585260i | 0.992709 | + | 0.120537i | \(0.0384615\pi\) |
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.935016 | − | 0.354605i | \(-0.115385\pi\) | ||||
−0.935016 | + | 0.354605i | \(0.884615\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.32625 | − | 1.49702i | −1.32625 | − | 1.49702i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.307819 | − | 0.509195i | −0.307819 | − | 0.509195i | 0.663123 | − | 0.748511i | \(-0.269231\pi\) |
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(954\) | 0.814480 | − | 0.638104i | 0.814480 | − | 0.638104i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.239316 | + | 0.970942i | 0.239316 | + | 0.970942i | ||||
\(962\) | 1.17433 | − | 0.616337i | 1.17433 | − | 0.616337i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.82298 | − | 0.568065i | −1.82298 | − | 0.568065i | ||||
\(965\) | 1.97094 | + | 0.239316i | 1.97094 | + | 0.239316i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(968\) | 0.822984 | − | 0.568065i | 0.822984 | − | 0.568065i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 1.98542i | − | 1.98542i | ||||||
\(971\) | 0 | 0 | 0.120537 | − | 0.992709i | \(-0.461538\pi\) | ||||
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.527986 | + | 0.764919i | 0.527986 | + | 0.764919i | ||||
\(977\) | 0.0290582 | + | 0.239316i | 0.0290582 | + | 0.239316i | 1.00000 | \(0\) | ||
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.239316 | − | 0.970942i | −0.239316 | − | 0.970942i | ||||
\(981\) | −0.244198 | + | 0.783659i | −0.244198 | + | 0.783659i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.120537 | − | 0.992709i | \(-0.538462\pi\) | ||||
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.929446i | 0.929446i | ||||||||
\(986\) | 2.54244 | − | 1.99187i | 2.54244 | − | 1.99187i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.70844 | − | 1.03279i | −1.70844 | − | 1.03279i | −0.885456 | − | 0.464723i | \(-0.846154\pi\) |
−0.822984 | − | 0.568065i | \(-0.807692\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 3380.1.bz.a.3047.1 | yes | 24 | |
4.3 | odd | 2 | CM | 3380.1.bz.a.3047.1 | yes | 24 | |
5.3 | odd | 4 | 3380.1.cg.a.343.1 | yes | 24 | ||
20.3 | even | 4 | 3380.1.cg.a.343.1 | yes | 24 | ||
169.34 | odd | 52 | 3380.1.cg.a.2907.1 | yes | 24 | ||
676.203 | even | 52 | 3380.1.cg.a.2907.1 | yes | 24 | ||
845.203 | even | 52 | inner | 3380.1.bz.a.203.1 | ✓ | 24 | |
3380.203 | odd | 52 | inner | 3380.1.bz.a.203.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3380.1.bz.a.203.1 | ✓ | 24 | 845.203 | even | 52 | inner | |
3380.1.bz.a.203.1 | ✓ | 24 | 3380.203 | odd | 52 | inner | |
3380.1.bz.a.3047.1 | yes | 24 | 1.1 | even | 1 | trivial | |
3380.1.bz.a.3047.1 | yes | 24 | 4.3 | odd | 2 | CM | |
3380.1.cg.a.343.1 | yes | 24 | 5.3 | odd | 4 | ||
3380.1.cg.a.343.1 | yes | 24 | 20.3 | even | 4 | ||
3380.1.cg.a.2907.1 | yes | 24 | 169.34 | odd | 52 | ||
3380.1.cg.a.2907.1 | yes | 24 | 676.203 | even | 52 |