Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1567,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1567");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.p (of order \(2\), degree \(1\), 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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1567.8 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.1567 |
Dual form | 4032.2.p.i.1567.7 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.82843 | 1.26491 | 0.632456 | − | 0.774597i | \(-0.282047\pi\) | ||||
0.632456 | + | 0.774597i | \(0.282047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | + | 2.00000i | 0.654654 | + | 0.755929i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.89898 | −1.47710 | −0.738549 | − | 0.674200i | \(-0.764489\pi\) | ||||
−0.738549 | + | 0.674200i | \(0.764489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000 | 1.66410 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.89898i | − | 1.18818i | −0.804400 | − | 0.594089i | \(-0.797513\pi\) | ||
0.804400 | − | 0.594089i | \(-0.202487\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.48528i | 1.76930i | 0.466252 | + | 0.884652i | \(0.345604\pi\) | ||||
−0.466252 | + | 0.884652i | \(0.654396\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.46410 | 0.622171 | 0.311086 | − | 0.950382i | \(-0.399307\pi\) | ||||
0.311086 | + | 0.950382i | \(0.399307\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.89898 | + | 5.65685i | 0.828079 | + | 0.956183i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.92820i | − | 1.13899i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) | ||
0.821995 | − | 0.569495i | \(-0.192861\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.89898i | − | 0.765092i | −0.923936 | − | 0.382546i | \(-0.875047\pi\) | ||
0.923936 | − | 0.382546i | \(-0.124953\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.46410 | 0.528271 | 0.264135 | − | 0.964486i | \(-0.414913\pi\) | ||||
0.264135 | + | 0.964486i | \(0.414913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.79796 | 1.42918 | 0.714590 | − | 0.699544i | \(-0.246613\pi\) | ||||
0.714590 | + | 0.699544i | \(0.246613\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | + | 6.92820i | −0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.79796i | 1.34585i | 0.739709 | + | 0.672927i | \(0.234963\pi\) | ||||
−0.739709 | + | 0.672927i | \(0.765037\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.8564 | −1.86840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 5.65685i | − | 0.736460i | −0.929735 | − | 0.368230i | \(-0.879964\pi\) | ||
0.929735 | − | 0.368230i | \(-0.120036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.9706 | 2.10494 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3923 | 1.26962 | 0.634811 | − | 0.772667i | \(-0.281078\pi\) | ||||
0.634811 | + | 0.772667i | \(0.281078\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.48528i | − | 1.00702i | −0.863990 | − | 0.503509i | \(-0.832042\pi\) | ||
0.863990 | − | 0.503509i | \(-0.167958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.8564i | 1.62177i | 0.585206 | + | 0.810885i | \(0.301014\pi\) | ||||
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.48528 | − | 9.79796i | −0.966988 | − | 1.11658i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000i | 0.450035i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.65685i | 0.620920i | 0.950586 | + | 0.310460i | \(0.100483\pi\) | ||||
−0.950586 | + | 0.310460i | \(0.899517\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 13.8564i | − | 1.50294i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.6969i | 1.55787i | 0.627103 | + | 0.778936i | \(0.284240\pi\) | ||||
−0.627103 | + | 0.778936i | \(0.715760\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.3923 | + | 12.0000i | 1.08941 | + | 1.25794i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.8564i | − | 1.40690i | −0.710742 | − | 0.703452i | \(-0.751641\pi\) | ||
0.710742 | − | 0.703452i | \(-0.248359\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.1421 | 1.40720 | 0.703598 | − | 0.710599i | \(-0.251576\pi\) | ||||
0.703598 | + | 0.710599i | \(0.251576\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.3923 | −1.02398 | −0.511992 | − | 0.858990i | \(-0.671092\pi\) | ||||
−0.511992 | + | 0.858990i | \(0.671092\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.89898 | −0.473602 | −0.236801 | − | 0.971558i | \(-0.576099\pi\) | ||||
−0.236801 | + | 0.971558i | \(0.576099\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.92820i | − | 0.663602i | −0.943349 | − | 0.331801i | \(-0.892344\pi\) | ||
0.943349 | − | 0.331801i | \(-0.107656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.9706 | −1.59646 | −0.798228 | − | 0.602355i | \(-0.794229\pi\) | ||||
−0.798228 | + | 0.602355i | \(0.794229\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.0000i | 2.23801i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.79796 | − | 8.48528i | 0.898177 | − | 0.777844i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000i | 0.354943i | 0.984126 | + | 0.177471i | \(0.0567917\pi\) | ||||
−0.984126 | + | 0.177471i | \(0.943208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 5.65685i | − | 0.494242i | −0.968985 | − | 0.247121i | \(-0.920516\pi\) | ||
0.968985 | − | 0.247121i | \(-0.0794845\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −29.3939 | −2.45804 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.79796i | 0.802680i | 0.915929 | + | 0.401340i | \(0.131455\pi\) | ||||
−0.915929 | + | 0.401340i | \(0.868545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0000i | 1.62758i | 0.581161 | + | 0.813788i | \(0.302599\pi\) | ||||
−0.581161 | + | 0.813788i | \(0.697401\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.79796 | 0.786991 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.00000 | 0.478852 | 0.239426 | − | 0.970915i | \(-0.423041\pi\) | ||||
0.239426 | + | 0.970915i | \(0.423041\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.9706 | + | 14.6969i | −1.33747 | + | 1.15828i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.3205 | 1.35665 | 0.678323 | − | 0.734763i | \(-0.262707\pi\) | ||||
0.678323 | + | 0.734763i | \(0.262707\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.5959 | −1.51638 | −0.758189 | − | 0.652035i | \(-0.773915\pi\) | ||||
−0.758189 | + | 0.652035i | \(0.773915\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.1421 | −1.07521 | −0.537603 | − | 0.843198i | \(-0.680670\pi\) | ||||
−0.537603 | + | 0.843198i | \(0.680670\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.19615 | + | 6.00000i | 0.392792 | + | 0.453557i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.89898 | 0.366167 | 0.183083 | − | 0.983097i | \(-0.441392\pi\) | ||||
0.183083 | + | 0.983097i | \(0.441392\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.0000 | 1.33793 | 0.668965 | − | 0.743294i | \(-0.266738\pi\) | ||||
0.668965 | + | 0.743294i | \(0.266738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 19.5959i | − | 1.44072i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.0000i | 1.75505i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.48528i | 0.613973i | 0.951714 | + | 0.306987i | \(0.0993207\pi\) | ||||
−0.951714 | + | 0.306987i | \(0.900679\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0000 | −0.719816 | −0.359908 | − | 0.932988i | \(-0.617192\pi\) | ||||
−0.359908 | + | 0.932988i | \(0.617192\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 19.5959i | − | 1.39615i | −0.716024 | − | 0.698076i | \(-0.754040\pi\) | ||
0.716024 | − | 0.698076i | \(-0.245960\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.46410 | −0.245564 | −0.122782 | − | 0.992434i | \(-0.539182\pi\) | ||||
−0.122782 | + | 0.992434i | \(0.539182\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 13.8564i | − | 0.967773i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.3923 | −0.715436 | −0.357718 | − | 0.933830i | \(-0.616445\pi\) | ||||
−0.357718 | + | 0.933830i | \(0.616445\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.79796 | 0.668215 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.00000 | + | 6.92820i | 0.407307 | + | 0.470317i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 29.3939i | − | 1.97725i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.3923 | −0.695920 | −0.347960 | − | 0.937509i | \(-0.613126\pi\) | ||||
−0.347960 | + | 0.937509i | \(0.613126\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 22.6274i | − | 1.50183i | −0.660396 | − | 0.750917i | \(-0.729612\pi\) | ||
0.660396 | − | 0.750917i | \(-0.270388\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.0000 | 1.18947 | 0.594737 | − | 0.803921i | \(-0.297256\pi\) | ||||
0.594737 | + | 0.803921i | \(0.297256\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.9706 | −1.11178 | −0.555889 | − | 0.831256i | \(-0.687622\pi\) | ||||
−0.555889 | + | 0.831256i | \(0.687622\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.7128 | 1.80778 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.48528i | − | 0.548867i | −0.961606 | − | 0.274434i | \(-0.911510\pi\) | ||
0.961606 | − | 0.274434i | \(-0.0884904\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.82843 | + | 19.5959i | −0.180702 | + | 1.25194i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 22.6274i | − | 1.42823i | −0.700028 | − | 0.714115i | \(-0.746829\pi\) | ||
0.700028 | − | 0.714115i | \(-0.253171\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 41.5692i | − | 2.61343i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.6969i | 0.916770i | 0.888754 | + | 0.458385i | \(0.151572\pi\) | ||||
−0.888754 | + | 0.458385i | \(0.848428\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.8564 | − | 12.0000i | 0.860995 | − | 0.745644i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.48528i | 0.523225i | 0.965173 | + | 0.261612i | \(0.0842542\pi\) | ||||
−0.965173 | + | 0.261612i | \(0.915746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.7128i | 1.70238i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.82843 | 0.172452 | 0.0862261 | − | 0.996276i | \(-0.472519\pi\) | ||||
0.0862261 | + | 0.996276i | \(0.472519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.46410 | −0.210429 | −0.105215 | − | 0.994450i | \(-0.533553\pi\) | ||||
−0.105215 | + | 0.994450i | \(0.533553\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.6969 | −0.886259 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.92820i | 0.416275i | 0.978100 | + | 0.208138i | \(0.0667402\pi\) | ||||
−0.978100 | + | 0.208138i | \(0.933260\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.9706 | 1.01238 | 0.506189 | − | 0.862422i | \(-0.331054\pi\) | ||||
0.506189 | + | 0.862422i | \(0.331054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 24.0000i | − | 1.42665i | −0.700832 | − | 0.713326i | \(-0.747188\pi\) | ||
0.700832 | − | 0.713326i | \(-0.252812\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.79796 | − | 8.48528i | 0.578355 | − | 0.500870i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.7990 | 1.15667 | 0.578335 | − | 0.815800i | \(-0.303703\pi\) | ||||
0.578335 | + | 0.815800i | \(0.303703\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 16.0000i | − | 0.931556i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 50.9117i | 2.94430i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | + | 6.92820i | 0.345834 | + | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.9706 | 0.971732 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.0000i | 1.36975i | 0.728659 | + | 0.684876i | \(0.240144\pi\) | ||||
−0.728659 | + | 0.684876i | \(0.759856\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.79796 | −0.555591 | −0.277796 | − | 0.960640i | \(-0.589604\pi\) | ||||
−0.277796 | + | 0.960640i | \(0.589604\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.7128i | 1.56642i | 0.621757 | + | 0.783210i | \(0.286419\pi\) | ||||
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.79796i | 0.550308i | 0.961400 | + | 0.275154i | \(0.0887289\pi\) | ||||
−0.961400 | + | 0.275154i | \(0.911271\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.0000 | 0.998460 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.9706 | + | 19.5959i | 0.935617 | + | 1.08036i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.46410 | −0.190404 | −0.0952021 | − | 0.995458i | \(-0.530350\pi\) | ||||
−0.0952021 | + | 0.995458i | \(0.530350\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 29.3939 | 1.60596 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.9706 | −0.919007 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5885 | + | 10.0000i | −0.841698 | + | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.4949 | 1.31495 | 0.657477 | − | 0.753474i | \(-0.271623\pi\) | ||||
0.657477 | + | 0.753474i | \(0.271623\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.00000 | −0.321173 | −0.160586 | − | 0.987022i | \(-0.551338\pi\) | ||||
−0.160586 | + | 0.987022i | \(0.551338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 34.2929i | − | 1.82522i | −0.408826 | − | 0.912612i | \(-0.634062\pi\) | ||
0.408826 | − | 0.912612i | \(-0.365938\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 24.0000i | − | 1.27379i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 25.4558i | − | 1.34351i | −0.740774 | − | 0.671754i | \(-0.765541\pi\) | ||
0.740774 | − | 0.671754i | \(-0.234459\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 39.1918i | 2.05139i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.3205 | −0.904123 | −0.452062 | − | 0.891987i | \(-0.649311\pi\) | ||||
−0.452062 | + | 0.891987i | \(0.649311\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.5959 | + | 16.9706i | −1.01737 | + | 0.881068i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 6.92820i | − | 0.358729i | −0.983783 | − | 0.179364i | \(-0.942596\pi\) | ||
0.983783 | − | 0.179364i | \(-0.0574041\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.2487 | −1.24557 | −0.622786 | − | 0.782392i | \(-0.713999\pi\) | ||||
−0.622786 | + | 0.782392i | \(0.713999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.79796 | 0.500652 | 0.250326 | − | 0.968162i | \(-0.419462\pi\) | ||||
0.250326 | + | 0.968162i | \(0.419462\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.0000 | − | 27.7128i | −1.22315 | − | 1.41238i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.5959i | 0.993552i | 0.867879 | + | 0.496776i | \(0.165483\pi\) | ||||
−0.867879 | + | 0.496776i | \(0.834517\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.5692 | 2.10225 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.3137i | 0.569254i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.00000 | −0.301131 | −0.150566 | − | 0.988600i | \(-0.548110\pi\) | ||||
−0.150566 | + | 0.988600i | \(0.548110\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.7846 | 1.03536 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.9411i | 1.68240i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 13.8564i | − | 0.685155i | −0.939490 | − | 0.342578i | \(-0.888700\pi\) | ||
0.939490 | − | 0.342578i | \(-0.111300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.3137 | − | 9.79796i | 0.556711 | − | 0.482126i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.0000i | 0.785409i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.65685i | 0.276355i | 0.990407 | + | 0.138178i | \(0.0441245\pi\) | ||||
−0.990407 | + | 0.138178i | \(0.955875\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 20.7846i | − | 1.01298i | −0.862246 | − | 0.506490i | \(-0.830943\pi\) | ||
0.862246 | − | 0.506490i | \(-0.169057\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 14.6969i | − | 0.712906i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.3923 | + | 12.0000i | 0.502919 | + | 0.580721i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.48528i | 0.408722i | 0.978896 | + | 0.204361i | \(0.0655116\pi\) | ||||
−0.978896 | + | 0.204361i | \(0.934488\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.8564i | 0.665896i | 0.942945 | + | 0.332948i | \(0.108043\pi\) | ||||
−0.942945 | + | 0.332948i | \(0.891957\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.2487 | 1.15733 | 0.578664 | − | 0.815566i | \(-0.303574\pi\) | ||||
0.578664 | + | 0.815566i | \(0.303574\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.6969 | 0.698273 | 0.349136 | − | 0.937072i | \(-0.386475\pi\) | ||||
0.349136 | + | 0.937072i | \(0.386475\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 41.5692i | 1.97057i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.9706 | 0.800890 | 0.400445 | − | 0.916321i | \(-0.368855\pi\) | ||||
0.400445 | + | 0.916321i | \(0.368855\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.0000i | 1.13012i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 29.3939 | + | 33.9411i | 1.37801 | + | 1.59118i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0000 | 1.02912 | 0.514558 | − | 0.857455i | \(-0.327956\pi\) | ||||
0.514558 | + | 0.857455i | \(0.327956\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.7990 | 0.922131 | 0.461065 | − | 0.887366i | \(-0.347467\pi\) | ||||
0.461065 | + | 0.887366i | \(0.347467\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 28.0000i | − | 1.30127i | −0.759390 | − | 0.650635i | \(-0.774503\pi\) | ||
0.759390 | − | 0.650635i | \(-0.225497\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 22.6274i | − | 1.04707i | −0.852004 | − | 0.523536i | \(-0.824613\pi\) | ||
0.852004 | − | 0.523536i | \(-0.175387\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.0000 | + | 20.7846i | 0.831163 | + | 0.959744i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.9706 | −0.780307 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.79796 | −0.447680 | −0.223840 | − | 0.974626i | \(-0.571859\pi\) | ||||
−0.223840 | + | 0.974626i | \(0.571859\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 41.5692i | − | 1.89539i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 39.1918i | − | 1.77961i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0000i | 0.906287i | 0.891438 | + | 0.453143i | \(0.149697\pi\) | ||||
−0.891438 | + | 0.453143i | \(0.850303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.2929 | −1.54761 | −0.773807 | − | 0.633421i | \(-0.781650\pi\) | ||||
−0.773807 | + | 0.633421i | \(0.781650\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.9706 | − | 14.6969i | 0.761234 | − | 0.659248i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.1051 | −1.70582 | −0.852910 | − | 0.522059i | \(-0.825164\pi\) | ||||
−0.852910 | + | 0.522059i | \(0.825164\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.79796 | −0.436869 | −0.218435 | − | 0.975852i | \(-0.570095\pi\) | ||||
−0.218435 | + | 0.975852i | \(0.570095\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 40.0000 | 1.77998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.82843 | −0.125368 | −0.0626839 | − | 0.998033i | \(-0.519966\pi\) | ||||
−0.0626839 | + | 0.998033i | \(0.519966\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.7128 | + | 24.0000i | −1.22594 | + | 1.06170i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −29.3939 | −1.29525 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −48.0000 | −2.11104 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 4.89898i | − | 0.214628i | −0.994225 | − | 0.107314i | \(-0.965775\pi\) | ||
0.994225 | − | 0.107314i | \(-0.0342250\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.0000i | 1.04945i | 0.851273 | + | 0.524723i | \(0.175831\pi\) | ||||
−0.851273 | + | 0.524723i | \(0.824169\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 16.9706i | − | 0.739249i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −49.0000 | −2.13043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 29.3939i | − | 1.27319i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.8564 | −0.599065 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.89898 | − | 33.9411i | 0.211014 | − | 1.46195i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 6.92820i | − | 0.297867i | −0.988847 | − | 0.148933i | \(-0.952416\pi\) | ||
0.988847 | − | 0.148933i | \(-0.0475840\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 19.5959i | − | 0.839397i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.1051 | −1.62926 | −0.814629 | − | 0.579983i | \(-0.803059\pi\) | ||||
−0.814629 | + | 0.579983i | \(0.803059\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.00000 | + | 6.92820i | −0.340195 | + | 0.294617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.79796i | 0.415153i | 0.978219 | + | 0.207576i | \(0.0665576\pi\) | ||||
−0.978219 | + | 0.207576i | \(0.933442\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.7846 | 0.879095 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.65685i | 0.238408i | 0.992870 | + | 0.119204i | \(0.0380342\pi\) | ||||
−0.992870 | + | 0.119204i | \(0.961966\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −48.0000 | −2.01938 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.9706 | −0.711443 | −0.355722 | − | 0.934592i | \(-0.615765\pi\) | ||||
−0.355722 | + | 0.934592i | \(0.615765\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.46410 | 0.144968 | 0.0724841 | − | 0.997370i | \(-0.476907\pi\) | ||||
0.0724841 | + | 0.997370i | \(0.476907\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 25.4558i | 1.06158i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 41.5692i | − | 1.73055i | −0.501298 | − | 0.865275i | \(-0.667144\pi\) | ||
0.501298 | − | 0.865275i | \(-0.332856\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.3137 | + | 9.79796i | −0.469372 | + | 0.406488i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 48.0000i | − | 1.98796i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 11.3137i | − | 0.466967i | −0.972361 | − | 0.233483i | \(-0.924988\pi\) | ||
0.972361 | − | 0.233483i | \(-0.0750124\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.89898i | 0.201177i | 0.994928 | + | 0.100588i | \(0.0320726\pi\) | ||||
−0.994928 | + | 0.100588i | \(0.967927\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.7128 | − | 24.0000i | 1.13611 | − | 0.983904i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 42.4264i | − | 1.73350i | −0.498746 | − | 0.866748i | \(-0.666206\pi\) | ||
0.498746 | − | 0.866748i | \(-0.333794\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.8564i | 0.565215i | 0.959236 | + | 0.282607i | \(0.0911993\pi\) | ||||
−0.959236 | + | 0.282607i | \(0.908801\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 36.7696 | 1.49489 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.3923 | −0.421811 | −0.210905 | − | 0.977506i | \(-0.567641\pi\) | ||||
−0.210905 | + | 0.977506i | \(0.567641\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 58.7878 | 2.37830 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.7846i | 0.839482i | 0.907644 | + | 0.419741i | \(0.137879\pi\) | ||||
−0.907644 | + | 0.419741i | \(0.862121\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 48.0000i | − | 1.92928i | −0.263566 | − | 0.964641i | \(-0.584899\pi\) | ||
0.263566 | − | 0.964641i | \(-0.415101\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.3939 | + | 25.4558i | −1.17764 | + | 1.01987i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33.9411 | −1.35332 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4.00000i | − | 0.159237i | −0.996825 | − | 0.0796187i | \(-0.974630\pi\) | ||
0.996825 | − | 0.0796187i | \(-0.0253703\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.3137i | 0.448971i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.00000 | + | 41.5692i | −0.237729 | + | 1.64703i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.9411 | −1.34059 | −0.670297 | − | 0.742093i | \(-0.733833\pi\) | ||||
−0.670297 | + | 0.742093i | \(0.733833\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.7128i | 1.08782i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 9.79796i | − | 0.383424i | −0.981451 | − | 0.191712i | \(-0.938596\pi\) | ||
0.981451 | − | 0.191712i | \(-0.0614039\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 16.0000i | − | 0.625172i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.89898 | 0.190837 | 0.0954186 | − | 0.995437i | \(-0.469581\pi\) | ||||
0.0954186 | + | 0.995437i | \(0.469581\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.0000 | −1.16686 | −0.583432 | − | 0.812162i | \(-0.698291\pi\) | ||||
−0.583432 | + | 0.812162i | \(0.698291\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.3939 | −1.13474 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.0000 | −0.848038 | −0.424019 | − | 0.905653i | \(-0.639381\pi\) | ||||
−0.424019 | + | 0.905653i | \(0.639381\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.82843 | −0.108705 | −0.0543526 | − | 0.998522i | \(-0.517310\pi\) | ||||
−0.0543526 | + | 0.998522i | \(0.517310\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.7128 | − | 24.0000i | 1.06352 | − | 0.921035i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −44.0908 | −1.68709 | −0.843544 | − | 0.537060i | \(-0.819535\pi\) | ||||
−0.843544 | + | 0.537060i | \(0.819535\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 58.7878i | 2.23964i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 24.0000i | − | 0.913003i | −0.889723 | − | 0.456502i | \(-0.849102\pi\) | ||
0.889723 | − | 0.456502i | \(-0.150898\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.0000 | −0.909065 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.9898i | 1.85032i | 0.379579 | + | 0.925160i | \(0.376069\pi\) | ||||
−0.379579 | + | 0.925160i | \(0.623931\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.4949 | + | 28.2843i | 0.921225 | + | 1.06374i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.92820i | 0.260194i | 0.991501 | + | 0.130097i | \(0.0415289\pi\) | ||||
−0.991501 | + | 0.130097i | \(0.958471\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.3939i | 1.10081i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −83.1384 | −3.10920 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.79796 | −0.365402 | −0.182701 | − | 0.983169i | \(-0.558484\pi\) | ||||
−0.182701 | + | 0.983169i | \(0.558484\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.0000 | − | 20.7846i | −0.670355 | − | 0.774059i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.3205 | −0.642382 | −0.321191 | − | 0.947014i | \(-0.604083\pi\) | ||||
−0.321191 | + | 0.947014i | \(0.604083\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 16.9706i | − | 0.627679i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.00000 | 0.221615 | 0.110808 | − | 0.993842i | \(-0.464656\pi\) | ||||
0.110808 | + | 0.993842i | \(0.464656\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −50.9117 | −1.87536 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.3923 | 0.382287 | 0.191144 | − | 0.981562i | \(-0.438780\pi\) | ||||
0.191144 | + | 0.981562i | \(0.438780\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 42.4264i | − | 1.55647i | −0.627971 | − | 0.778237i | \(-0.716114\pi\) | ||
0.627971 | − | 0.778237i | \(-0.283886\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.7128i | 1.01532i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.48528 | − | 9.79796i | −0.310045 | − | 0.358010i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 20.0000i | − | 0.729810i | −0.931045 | − | 0.364905i | \(-0.881101\pi\) | ||
0.931045 | − | 0.364905i | \(-0.118899\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 56.5685i | 2.05874i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 48.4974i | − | 1.76267i | −0.472493 | − | 0.881334i | \(-0.656646\pi\) | ||
0.472493 | − | 0.881334i | \(-0.343354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.89898i | 0.177588i | 0.996050 | + | 0.0887939i | \(0.0283013\pi\) | ||||
−0.996050 | + | 0.0887939i | \(0.971699\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.8564 | − | 12.0000i | 0.501636 | − | 0.434429i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 33.9411i | − | 1.22554i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 27.7128i | − | 0.999350i | −0.866213 | − | 0.499675i | \(-0.833453\pi\) | ||
0.866213 | − | 0.499675i | \(-0.166547\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −48.0833 | −1.72943 | −0.864717 | − | 0.502259i | \(-0.832502\pi\) | ||||
−0.864717 | + | 0.502259i | \(0.832502\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.3923 | 0.373303 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.5692i | 1.48746i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.9706 | 0.605705 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 24.0000i | − | 0.855508i | −0.903895 | − | 0.427754i | \(-0.859305\pi\) | ||
0.903895 | − | 0.427754i | \(-0.140695\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.3939 | − | 33.9411i | −1.04513 | − | 1.20681i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.0000 | 1.27840 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.7990 | −0.701316 | −0.350658 | − | 0.936504i | \(-0.614042\pi\) | ||||
−0.350658 | + | 0.936504i | \(0.614042\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 48.0000i | − | 1.69812i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 67.8823i | − | 2.39551i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −48.0000 | + | 41.5692i | −1.69178 | + | 1.46512i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.9706 | 0.596653 | 0.298327 | − | 0.954464i | \(-0.403572\pi\) | ||||
0.298327 | + | 0.954464i | \(0.403572\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 24.0000i | − | 0.842754i | −0.906886 | − | 0.421377i | \(-0.861547\pi\) | ||
0.906886 | − | 0.421377i | \(-0.138453\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 48.9898 | 1.71604 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 29.3939i | − | 1.02585i | −0.858432 | − | 0.512927i | \(-0.828561\pi\) | ||
0.858432 | − | 0.512927i | \(-0.171439\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.0000i | 1.53374i | 0.641800 | + | 0.766872i | \(0.278188\pi\) | ||||
−0.641800 | + | 0.766872i | \(0.721812\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.6969 | 0.511063 | 0.255531 | − | 0.966801i | \(-0.417750\pi\) | ||||
0.255531 | + | 0.966801i | \(0.417750\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.00000 | −0.208389 | −0.104194 | − | 0.994557i | \(-0.533226\pi\) | ||||
−0.104194 | + | 0.994557i | \(0.533226\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.9411 | + | 4.89898i | 1.17599 | + | 0.169740i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −55.4256 | −1.91808 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.5959 | 0.676526 | 0.338263 | − | 0.941052i | \(-0.390161\pi\) | ||||
0.338263 | + | 0.941052i | \(0.390161\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 65.0538 | 2.23792 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.5167 | + | 26.0000i | 0.773682 | + | 0.893371i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 58.7878 | 2.01522 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.0000 | 1.02718 | 0.513590 | − | 0.858036i | \(-0.328315\pi\) | ||||
0.513590 | + | 0.858036i | \(0.328315\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.4949i | 0.836730i | 0.908279 | + | 0.418365i | \(0.137397\pi\) | ||||
−0.908279 | + | 0.418365i | \(0.862603\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 48.0000i | − | 1.63774i | −0.573980 | − | 0.818869i | \(-0.694601\pi\) | ||
0.573980 | − | 0.818869i | \(-0.305399\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 25.4558i | − | 0.866527i | −0.901267 | − | 0.433264i | \(-0.857362\pi\) | ||
0.901267 | − | 0.433264i | \(-0.142638\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40.0000 | −1.36004 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 19.5959i | − | 0.664746i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 62.3538 | 2.11278 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.79796 | − | 11.3137i | −0.331231 | − | 0.382473i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.6410i | 1.16974i | 0.811126 | + | 0.584872i | \(0.198855\pi\) | ||||
−0.811126 | + | 0.584872i | \(0.801145\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.6969i | 0.495152i | 0.968868 | + | 0.247576i | \(0.0796341\pi\) | ||||
−0.968868 | + | 0.247576i | \(0.920366\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.0333 | −1.51549 | −0.757746 | − | 0.652550i | \(-0.773699\pi\) | ||||
−0.757746 | + | 0.652550i | \(0.773699\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.5959 | −0.657967 | −0.328983 | − | 0.944336i | \(-0.606706\pi\) | ||||
−0.328983 | + | 0.944336i | \(0.606706\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.00000 | + | 6.92820i | −0.268311 | + | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.8564 | 0.463169 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48.0000 | 1.59911 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 50.9117 | 1.69236 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.46410 | 0.115024 | 0.0575118 | − | 0.998345i | \(-0.481683\pi\) | ||||
0.0575118 | + | 0.998345i | \(0.481683\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 8.48528i | − | 0.281130i | −0.990071 | − | 0.140565i | \(-0.955108\pi\) | ||
0.990071 | − | 0.140565i | \(-0.0448919\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 27.7128i | − | 0.917160i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.3137 | − | 9.79796i | 0.373612 | − | 0.323557i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.00000i | 0.131948i | 0.997821 | + | 0.0659739i | \(0.0210154\pi\) | ||||
−0.997821 | + | 0.0659739i | \(0.978985\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 50.9117i | − | 1.67578i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 20.7846i | − | 0.683394i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.89898i | 0.160730i | 0.996765 | + | 0.0803652i | \(0.0256086\pi\) | ||||
−0.996765 | + | 0.0803652i | \(0.974391\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 67.8823i | 2.21999i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 27.7128i | − | 0.905338i | −0.891679 | − | 0.452669i | \(-0.850472\pi\) | ||
0.891679 | − | 0.452669i | \(-0.149528\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53.7401 | −1.75188 | −0.875939 | − | 0.482422i | \(-0.839757\pi\) | ||||
−0.875939 | + | 0.482422i | \(0.839757\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41.5692 | 1.35368 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53.8888 | −1.75115 | −0.875575 | − | 0.483082i | \(-0.839517\pi\) | ||||
−0.875575 | + | 0.483082i | \(0.839517\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 83.1384i | 2.69879i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.9411 | −1.09946 | −0.549730 | − | 0.835342i | \(-0.685270\pi\) | ||||
−0.549730 | + | 0.835342i | \(0.685270\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.0000i | 0.776622i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.0000 | −0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.2843 | −0.910503 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 52.0000i | − | 1.67221i | −0.548572 | − | 0.836104i | \(-0.684828\pi\) | ||
0.548572 | − | 0.836104i | \(-0.315172\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.3137i | 0.363074i | 0.983384 | + | 0.181537i | \(0.0581072\pi\) | ||||
−0.983384 | + | 0.181537i | \(0.941893\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.9706 | −0.542936 | −0.271468 | − | 0.962447i | \(-0.587509\pi\) | ||||
−0.271468 | + | 0.962447i | \(0.587509\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 72.0000i | − | 2.30113i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.5959 | 0.625013 | 0.312506 | − | 0.949916i | \(-0.398831\pi\) | ||||
0.312506 | + | 0.949916i | \(0.398831\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 55.4256i | − | 1.76601i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.3939i | 0.934671i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 4.00000i | − | 0.127064i | −0.997980 | − | 0.0635321i | \(-0.979763\pi\) | ||
0.997980 | − | 0.0635321i | \(-0.0202365\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.79796 | −0.310616 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.0000 | −0.570066 | −0.285033 | − | 0.958518i | \(-0.592005\pi\) | ||||
−0.285033 | + | 0.958518i | \(0.592005\pi\) | |||||||
\(998\) | 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 | 4032.2.p.i.1567.8 | yes | 8 | |
3.2 | odd | 2 | inner | 4032.2.p.i.1567.4 | yes | 8 | |
4.3 | odd | 2 | inner | 4032.2.p.i.1567.5 | yes | 8 | |
7.6 | odd | 2 | 4032.2.p.e.1567.2 | yes | 8 | ||
8.3 | odd | 2 | 4032.2.p.e.1567.1 | ✓ | 8 | ||
8.5 | even | 2 | 4032.2.p.e.1567.4 | yes | 8 | ||
12.11 | even | 2 | inner | 4032.2.p.i.1567.1 | yes | 8 | |
21.20 | even | 2 | 4032.2.p.e.1567.6 | yes | 8 | ||
24.5 | odd | 2 | 4032.2.p.e.1567.8 | yes | 8 | ||
24.11 | even | 2 | 4032.2.p.e.1567.5 | yes | 8 | ||
28.27 | even | 2 | 4032.2.p.e.1567.3 | yes | 8 | ||
56.13 | odd | 2 | inner | 4032.2.p.i.1567.6 | yes | 8 | |
56.27 | even | 2 | inner | 4032.2.p.i.1567.7 | yes | 8 | |
84.83 | odd | 2 | 4032.2.p.e.1567.7 | yes | 8 | ||
168.83 | odd | 2 | inner | 4032.2.p.i.1567.3 | yes | 8 | |
168.125 | even | 2 | inner | 4032.2.p.i.1567.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4032.2.p.e.1567.1 | ✓ | 8 | 8.3 | odd | 2 | ||
4032.2.p.e.1567.2 | yes | 8 | 7.6 | odd | 2 | ||
4032.2.p.e.1567.3 | yes | 8 | 28.27 | even | 2 | ||
4032.2.p.e.1567.4 | yes | 8 | 8.5 | even | 2 | ||
4032.2.p.e.1567.5 | yes | 8 | 24.11 | even | 2 | ||
4032.2.p.e.1567.6 | yes | 8 | 21.20 | even | 2 | ||
4032.2.p.e.1567.7 | yes | 8 | 84.83 | odd | 2 | ||
4032.2.p.e.1567.8 | yes | 8 | 24.5 | odd | 2 | ||
4032.2.p.i.1567.1 | yes | 8 | 12.11 | even | 2 | inner | |
4032.2.p.i.1567.2 | yes | 8 | 168.125 | even | 2 | inner | |
4032.2.p.i.1567.3 | yes | 8 | 168.83 | odd | 2 | inner | |
4032.2.p.i.1567.4 | yes | 8 | 3.2 | odd | 2 | inner | |
4032.2.p.i.1567.5 | yes | 8 | 4.3 | odd | 2 | inner | |
4032.2.p.i.1567.6 | yes | 8 | 56.13 | odd | 2 | inner | |
4032.2.p.i.1567.7 | yes | 8 | 56.27 | even | 2 | inner | |
4032.2.p.i.1567.8 | yes | 8 | 1.1 | even | 1 | trivial |