Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(961,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 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("1560.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.g (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: | \(12.4566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 961.4 | ||
Root | \(2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.961 |
Dual form | 1560.2.g.h.961.1 |
$q$-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 \(\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times\).
\(n\) | \(391\) | \(521\) | \(781\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.56155i | 1.34614i | 0.739579 | + | 0.673070i | \(0.235025\pi\) | ||||
−0.739579 | + | 0.673070i | \(0.764975\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.56155i | 0.470826i | 0.971895 | + | 0.235413i | \(0.0756443\pi\) | ||||
−0.971895 | + | 0.235413i | \(0.924356\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.561553 | − | 3.56155i | −0.155747 | − | 0.987797i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.438447 | 0.106339 | 0.0531695 | − | 0.998586i | \(-0.483068\pi\) | ||||
0.0531695 | + | 0.998586i | \(0.483068\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.12311i | 1.17532i | 0.809108 | + | 0.587661i | \(0.199951\pi\) | ||||
−0.809108 | + | 0.587661i | \(0.800049\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.56155i | 0.777195i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.56155 | 0.325606 | 0.162803 | − | 0.986659i | \(-0.447946\pi\) | ||||
0.162803 | + | 0.986659i | \(0.447946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000i | 0.359211i | 0.983739 | + | 0.179605i | \(0.0574821\pi\) | ||||
−0.983739 | + | 0.179605i | \(0.942518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.56155i | 0.271831i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.56155 | −0.602012 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.56155i | 0.914314i | 0.889386 | + | 0.457157i | \(0.151132\pi\) | ||||
−0.889386 | + | 0.457157i | \(0.848868\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.561553 | − | 3.56155i | −0.0899204 | − | 0.570305i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.68466i | 1.04397i | 0.852955 | + | 0.521984i | \(0.174808\pi\) | ||||
−0.852955 | + | 0.521984i | \(0.825192\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.876894 | 0.133725 | 0.0668626 | − | 0.997762i | \(-0.478701\pi\) | ||||
0.0668626 | + | 0.997762i | \(0.478701\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.68466 | −0.812094 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.438447 | 0.0613949 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.68466 | −0.918208 | −0.459104 | − | 0.888382i | \(-0.651830\pi\) | ||||
−0.459104 | + | 0.888382i | \(0.651830\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.56155 | −0.210560 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.12311i | 0.678572i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 6.24621i | − | 0.813187i | −0.913609 | − | 0.406594i | \(-0.866716\pi\) | ||
0.913609 | − | 0.406594i | \(-0.133284\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.68466 | −0.855883 | −0.427941 | − | 0.903806i | \(-0.640761\pi\) | ||||
−0.427941 | + | 0.903806i | \(0.640761\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.56155i | 0.448713i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.56155 | − | 0.561553i | 0.441756 | − | 0.0696521i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.3693i | 1.87766i | 0.344380 | + | 0.938830i | \(0.388089\pi\) | ||||
−0.344380 | + | 0.938830i | \(0.611911\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.56155 | 0.187989 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.56155i | − | 1.13475i | −0.823460 | − | 0.567374i | \(-0.807959\pi\) | ||
0.823460 | − | 0.567374i | \(-0.192041\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.876894i | 0.102633i | 0.998682 | + | 0.0513164i | \(0.0163417\pi\) | ||||
−0.998682 | + | 0.0513164i | \(0.983658\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.56155 | −0.633798 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.68466 | −0.977100 | −0.488550 | − | 0.872536i | \(-0.662474\pi\) | ||||
−0.488550 | + | 0.872536i | \(0.662474\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.12311i | 0.342805i | 0.985201 | + | 0.171403i | \(0.0548299\pi\) | ||||
−0.985201 | + | 0.171403i | \(0.945170\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.438447i | 0.0475563i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.438447i | 0.0464753i | 0.999730 | + | 0.0232377i | \(0.00739744\pi\) | ||||
−0.999730 | + | 0.0232377i | \(0.992603\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.6847 | − | 2.00000i | 1.32971 | − | 0.209657i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.00000i | 0.207390i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.12311 | −0.525620 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.56155i | 0.158552i | 0.996853 | + | 0.0792758i | \(0.0252608\pi\) | ||||
−0.996853 | + | 0.0792758i | \(0.974739\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.56155i | 0.156942i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.00000 | 0.199007 | 0.0995037 | − | 0.995037i | \(-0.468274\pi\) | ||||
0.0995037 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.2462 | 1.40372 | 0.701860 | − | 0.712314i | \(-0.252353\pi\) | ||||
0.701860 | + | 0.712314i | \(0.252353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.56155 | −0.347572 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.68466 | 0.839578 | 0.419789 | − | 0.907622i | \(-0.362104\pi\) | ||||
0.419789 | + | 0.907622i | \(0.362104\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.87689i | 0.850252i | 0.905134 | + | 0.425126i | \(0.139770\pi\) | ||||
−0.905134 | + | 0.425126i | \(0.860230\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.56155i | 0.527879i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.24621 | 0.399450 | 0.199725 | − | 0.979852i | \(-0.435995\pi\) | ||||
0.199725 | + | 0.979852i | \(0.435995\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.56155i | 0.145616i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.561553 | − | 3.56155i | −0.0519156 | − | 0.329266i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.56155i | 0.143147i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.56155 | 0.778323 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.68466i | 0.602735i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.1231 | 1.69690 | 0.848451 | − | 0.529275i | \(-0.177536\pi\) | ||||
0.848451 | + | 0.529275i | \(0.177536\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.876894 | 0.0772062 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.4924 | 1.79043 | 0.895216 | − | 0.445633i | \(-0.147021\pi\) | ||||
0.895216 | + | 0.445633i | \(0.147021\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.2462 | −1.58215 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.00000i | − | 0.512615i | −0.966595 | − | 0.256307i | \(-0.917494\pi\) | ||
0.966595 | − | 0.256307i | \(-0.0825059\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.56155 | −0.811000 | −0.405500 | − | 0.914095i | \(-0.632903\pi\) | ||||
−0.405500 | + | 0.914095i | \(0.632903\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.56155 | − | 0.876894i | 0.465080 | − | 0.0733296i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.00000i | − | 0.166091i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.68466 | −0.468863 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 20.9309i | − | 1.71472i | −0.514714 | − | 0.857362i | \(-0.672102\pi\) | ||
0.514714 | − | 0.857362i | \(-0.327898\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14.0000i | − | 1.13930i | −0.821886 | − | 0.569652i | \(-0.807078\pi\) | ||
0.821886 | − | 0.569652i | \(-0.192922\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.438447 | 0.0354464 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | −0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.87689 | −0.548836 | −0.274418 | − | 0.961611i | \(-0.588485\pi\) | ||||
−0.274418 | + | 0.961611i | \(0.588485\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.68466 | −0.530128 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.56155i | 0.438312i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.0540i | 1.57075i | 0.619021 | + | 0.785374i | \(0.287529\pi\) | ||||
−0.619021 | + | 0.785374i | \(0.712471\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.56155 | −0.121567 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 6.24621i | − | 0.483346i | −0.970358 | − | 0.241673i | \(-0.922304\pi\) | ||
0.970358 | − | 0.241673i | \(-0.0776962\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3693 | + | 4.00000i | −0.951486 | + | 0.307692i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.12311i | 0.391774i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.4924 | 1.10184 | 0.550919 | − | 0.834559i | \(-0.314277\pi\) | ||||
0.550919 | + | 0.834559i | \(0.314277\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.56155i | − | 0.269228i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 6.24621i | − | 0.469494i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.8078 | −1.02632 | −0.513162 | − | 0.858292i | \(-0.671526\pi\) | ||||
−0.513162 | + | 0.858292i | \(0.671526\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.68466 | −0.494144 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.56155 | −0.408893 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.684658i | 0.0500672i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.56155i | 0.259065i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.75379 | −0.416330 | −0.208165 | − | 0.978094i | \(-0.566749\pi\) | ||||
−0.208165 | + | 0.978094i | \(0.566749\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 10.4384i | − | 0.751376i | −0.926746 | − | 0.375688i | \(-0.877406\pi\) | ||
0.926746 | − | 0.375688i | \(-0.122594\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.56155 | − | 0.561553i | 0.255048 | − | 0.0402136i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 14.4924i | − | 1.03254i | −0.856425 | − | 0.516271i | \(-0.827320\pi\) | ||
0.856425 | − | 0.516271i | \(-0.172680\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.3693i | 1.08407i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 7.12311i | − | 0.499944i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.68466 | −0.466877 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.56155 | 0.108535 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.00000 | −0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.4924 | 1.68613 | 0.843064 | − | 0.537813i | \(-0.180749\pi\) | ||||
0.843064 | + | 0.537813i | \(0.180749\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 9.56155i | − | 0.655147i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.876894i | 0.0598037i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.12311 | −0.483548 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.876894i | 0.0592550i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.246211 | − | 1.56155i | −0.0165620 | − | 0.105041i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.1231i | 0.878788i | 0.898294 | + | 0.439394i | \(0.144807\pi\) | ||||
−0.898294 | + | 0.439394i | \(0.855193\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 26.2462i | − | 1.74202i | −0.491263 | − | 0.871011i | \(-0.663465\pi\) | ||
0.491263 | − | 0.871011i | \(-0.336535\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.63068i | 0.173840i | 0.996215 | + | 0.0869202i | \(0.0277025\pi\) | ||||
−0.996215 | + | 0.0869202i | \(0.972297\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.56155 | −0.365923 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.80776 | 0.380479 | 0.190240 | − | 0.981738i | \(-0.439074\pi\) | ||||
0.190240 | + | 0.981738i | \(0.439074\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.68466 | −0.564129 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.6847i | 0.820502i | 0.911973 | + | 0.410251i | \(0.134559\pi\) | ||||
−0.911973 | + | 0.410251i | \(0.865441\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.12311i | 0.458840i | 0.973328 | + | 0.229420i | \(0.0736829\pi\) | ||||
−0.973328 | + | 0.229420i | \(0.926317\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 5.68466i | − | 0.363180i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.2462 | − | 2.87689i | 1.16098 | − | 0.183052i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.12311i | 0.197919i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.3693 | 0.843864 | 0.421932 | − | 0.906628i | \(-0.361352\pi\) | ||||
0.421932 | + | 0.906628i | \(0.361352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.43845i | 0.153304i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.438447i | 0.0274566i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.4924 | 1.40304 | 0.701519 | − | 0.712650i | \(-0.252505\pi\) | ||||
0.701519 | + | 0.712650i | \(0.252505\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.8078 | −1.23079 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.0000 | 0.986602 | 0.493301 | − | 0.869859i | \(-0.335790\pi\) | ||||
0.493301 | + | 0.869859i | \(0.335790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 6.68466i | − | 0.410635i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.438447i | 0.0268325i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.1231 | −1.77567 | −0.887834 | − | 0.460165i | \(-0.847790\pi\) | ||||
−0.887834 | + | 0.460165i | \(0.847790\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.75379i | − | 0.228026i | −0.993479 | − | 0.114013i | \(-0.963629\pi\) | ||
0.993479 | − | 0.114013i | \(-0.0363706\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.6847 | − | 2.00000i | 0.767710 | − | 0.121046i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1.56155i | − | 0.0941652i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.36932 | −0.202443 | −0.101221 | − | 0.994864i | \(-0.532275\pi\) | ||||
−0.101221 | + | 0.994864i | \(0.532275\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.00000i | 0.119737i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000i | 0.119310i | 0.998219 | + | 0.0596550i | \(0.0190001\pi\) | ||||
−0.998219 | + | 0.0596550i | \(0.981000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.1231 | 0.898975 | 0.449488 | − | 0.893287i | \(-0.351607\pi\) | ||||
0.449488 | + | 0.893287i | \(0.351607\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.12311 | −0.303467 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −23.8078 | −1.40533 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8078 | −0.988692 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.56155i | 0.0915398i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 22.4924i | − | 1.31402i | −0.753881 | − | 0.657011i | \(-0.771821\pi\) | ||
0.753881 | − | 0.657011i | \(-0.228179\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.24621 | 0.363668 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.56155i | 0.0906105i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.876894 | − | 5.56155i | −0.0507121 | − | 0.321633i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.12311i | 0.180013i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.00000 | 0.114897 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 6.68466i | − | 0.382762i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.43845i | − | 0.253316i | −0.991946 | − | 0.126658i | \(-0.959575\pi\) | ||
0.991946 | − | 0.126658i | \(-0.0404250\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.2462 | 0.810439 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.87689 | −0.503362 | −0.251681 | − | 0.967810i | \(-0.580983\pi\) | ||||
−0.251681 | + | 0.967810i | \(0.580983\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.36932 | 0.416538 | 0.208269 | − | 0.978072i | \(-0.433217\pi\) | ||||
0.208269 | + | 0.978072i | \(0.433217\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.56155 | −0.200671 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 10.0000i | − | 0.561656i | −0.959758 | − | 0.280828i | \(-0.909391\pi\) | ||
0.959758 | − | 0.280828i | \(-0.0906090\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.12311i | − | 0.174860i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.68466 | 0.484730 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.24621i | 0.124983i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.561553 | + | 3.56155i | 0.0311493 | + | 0.197559i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.87689i | 0.490893i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 19.3693i | − | 1.06463i | −0.846545 | − | 0.532317i | \(-0.821321\pi\) | ||
0.846545 | − | 0.532317i | \(-0.178679\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.56155i | 0.304771i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.3693 | −0.839715 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.4924 | 1.44313 | 0.721567 | − | 0.692345i | \(-0.243422\pi\) | ||||
0.721567 | + | 0.692345i | \(0.243422\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.24621 | 0.230623 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.12311 | −0.169126 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.68466i | 0.252948i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.56155i | 0.0840712i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.5616 | −1.37222 | −0.686108 | − | 0.727500i | \(-0.740682\pi\) | ||||
−0.686108 | + | 0.727500i | \(0.740682\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 15.6155i | − | 0.835880i | −0.908475 | − | 0.417940i | \(-0.862752\pi\) | ||
0.908475 | − | 0.417940i | \(-0.137248\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.561553 | − | 3.56155i | −0.0299735 | − | 0.190102i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 22.8769i | − | 1.21761i | −0.793318 | − | 0.608807i | \(-0.791648\pi\) | ||
0.793318 | − | 0.608807i | \(-0.208352\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.56155 | 0.507475 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.56155i | 0.0826461i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 12.4924i | − | 0.659325i | −0.944099 | − | 0.329662i | \(-0.893065\pi\) | ||
0.944099 | − | 0.329662i | \(-0.106935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.24621 | −0.381380 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.56155 | 0.449365 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.876894 | −0.0458987 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.8617 | 1.55877 | 0.779385 | − | 0.626545i | \(-0.215532\pi\) | ||||
0.779385 | + | 0.626545i | \(0.215532\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.68466i | 0.347989i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 23.8078i | − | 1.23604i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.8769 | −0.563184 | −0.281592 | − | 0.959534i | \(-0.590863\pi\) | ||||
−0.281592 | + | 0.959534i | \(0.590863\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.00000i | − | 0.0516398i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.12311 | + | 7.12311i | 0.0578429 | + | 0.366859i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 10.4924i | − | 0.538960i | −0.963006 | − | 0.269480i | \(-0.913148\pi\) | ||
0.963006 | − | 0.269480i | \(-0.0868517\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.1231 | 0.979706 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 3.12311i | − | 0.159583i | −0.996812 | − | 0.0797916i | \(-0.974575\pi\) | ||
0.996812 | − | 0.0797916i | \(-0.0254255\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 5.56155i | − | 0.283443i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.876894 | 0.0445750 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.0000 | −0.507020 | −0.253510 | − | 0.967333i | \(-0.581585\pi\) | ||||
−0.253510 | + | 0.967333i | \(0.581585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.684658 | 0.0346247 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.4924 | 1.03371 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 8.68466i | − | 0.436973i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.8078i | 1.39563i | 0.716277 | + | 0.697816i | \(0.245845\pi\) | ||||
−0.716277 | + | 0.697816i | \(0.754155\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.2462 | −0.913453 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.49242i | 0.124466i | 0.998062 | + | 0.0622328i | \(0.0198221\pi\) | ||||
−0.998062 | + | 0.0622328i | \(0.980178\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.12311 | − | 1.12311i | 0.354827 | − | 0.0559459i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.68466 | −0.430483 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 0.492423i | − | 0.0243487i | −0.999926 | − | 0.0121744i | \(-0.996125\pi\) | ||
0.999926 | − | 0.0121744i | \(-0.00387532\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 6.00000i | − | 0.295958i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.2462 | 1.09466 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.12311 | −0.153307 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.56155 | −0.468231 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.8769 | 0.629077 | 0.314539 | − | 0.949245i | \(-0.398150\pi\) | ||||
0.314539 | + | 0.949245i | \(0.398150\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.87689i | 0.432633i | 0.976323 | + | 0.216317i | \(0.0694044\pi\) | ||||
−0.976323 | + | 0.216317i | \(0.930596\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.438447 | −0.0212678 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 23.8078i | − | 1.15214i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.56155 | − | 0.876894i | 0.268514 | − | 0.0423369i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 32.9848i | − | 1.58882i | −0.607379 | − | 0.794412i | \(-0.707779\pi\) | ||
0.607379 | − | 0.794412i | \(-0.292221\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.4924 | 1.65760 | 0.828800 | − | 0.559545i | \(-0.189024\pi\) | ||||
0.828800 | + | 0.559545i | \(0.189024\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 2.00000i | − | 0.0958927i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.00000i | 0.382692i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.4384 | −0.498200 | −0.249100 | − | 0.968478i | \(-0.580135\pi\) | ||||
−0.249100 | + | 0.968478i | \(0.580135\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.68466 | −0.270698 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.93087 | 0.329296 | 0.164648 | − | 0.986352i | \(-0.447351\pi\) | ||||
0.164648 | + | 0.986352i | \(0.447351\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.438447 | −0.0207844 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 20.9309i | − | 0.989996i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 26.6847i | − | 1.25933i | −0.776868 | − | 0.629663i | \(-0.783193\pi\) | ||
0.776868 | − | 0.629663i | \(-0.216807\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.4384 | −0.491527 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 14.0000i | − | 0.657777i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.00000 | + | 12.6847i | 0.0937614 | + | 0.594666i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 22.4384i | − | 1.04963i | −0.851217 | − | 0.524813i | \(-0.824135\pi\) | ||
0.851217 | − | 0.524813i | \(-0.175865\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.438447 | 0.0204650 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.6847i | 0.683933i | 0.939712 | + | 0.341966i | \(0.111093\pi\) | ||||
−0.939712 | + | 0.341966i | \(0.888907\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.3002i | 0.664586i | 0.943176 | + | 0.332293i | \(0.107822\pi\) | ||||
−0.943176 | + | 0.332293i | \(0.892178\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.00000 | −0.0927478 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.4384 | −0.668132 | −0.334066 | − | 0.942550i | \(-0.608421\pi\) | ||||
−0.334066 | + | 0.942550i | \(0.608421\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −54.7386 | −2.52760 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.87689 | −0.316871 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.36932i | 0.0629613i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5.12311i | − | 0.235064i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.68466 | −0.306069 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.6847i | 1.67616i | 0.545544 | + | 0.838082i | \(0.316323\pi\) | ||||
−0.545544 | + | 0.838082i | \(0.683677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.8078 | − | 3.12311i | 0.903156 | − | 0.142401i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.56155i | 0.253059i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.56155 | −0.0709065 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0540i | 0.546218i | 0.961983 | + | 0.273109i | \(0.0880519\pi\) | ||||
−0.961983 | + | 0.273109i | \(0.911948\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.0540i | 0.906872i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.2462 | −0.462405 | −0.231203 | − | 0.972906i | \(-0.574266\pi\) | ||||
−0.231203 | + | 0.972906i | \(0.574266\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.876894 | −0.0394933 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.56155 | −0.0701866 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34.0540 | 1.52753 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 30.1080i | − | 1.34782i | −0.738815 | − | 0.673908i | \(-0.764614\pi\) | ||
0.738815 | − | 0.673908i | \(-0.235386\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 6.24621i | − | 0.279060i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.75379 | −0.434900 | −0.217450 | − | 0.976071i | \(-0.569774\pi\) | ||||
−0.217450 | + | 0.976071i | \(0.569774\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.00000i | 0.0889988i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.3693 | + | 4.00000i | −0.549341 | + | 0.177646i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 32.9309i | − | 1.45964i | −0.683642 | − | 0.729818i | \(-0.739605\pi\) | ||
0.683642 | − | 0.729818i | \(-0.260395\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.12311 | −0.138158 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.12311i | 0.226191i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.2462i | 0.627763i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.4924 | 0.636147 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.6155 | 1.29748 | 0.648740 | − | 0.761010i | \(-0.275296\pi\) | ||||
0.648740 | + | 0.761010i | \(0.275296\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.8617 | −0.781039 | −0.390520 | − | 0.920595i | \(-0.627705\pi\) | ||||
−0.390520 | + | 0.920595i | \(0.627705\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 3.56155i | − | 0.155439i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.876894i | 0.0381981i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5616 | −0.893981 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.24621i | − | 0.271062i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.8078 | − | 3.75379i | 1.03123 | − | 0.162595i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.68466i | 0.375471i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 8.87689i | − | 0.382355i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.4924i | 1.05301i | 0.850172 | + | 0.526506i | \(0.176498\pi\) | ||||
−0.850172 | + | 0.526506i | \(0.823502\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.8078 | −0.592548 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.87689 | −0.380244 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.12311 | −0.304562 | −0.152281 | − | 0.988337i | \(-0.548662\pi\) | ||||
−0.152281 | + | 0.988337i | \(0.548662\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.68466 | −0.285294 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.2462i | − | 0.436503i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 30.9309i | − | 1.31531i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.56155 | −0.236075 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 40.7386i | 1.72615i | 0.505075 | + | 0.863076i | \(0.331465\pi\) | ||||
−0.505075 | + | 0.863076i | \(0.668535\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.492423 | − | 3.12311i | −0.0208273 | − | 0.132093i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.684658i | 0.0289063i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.3153 | 0.645465 | 0.322732 | − | 0.946490i | \(-0.395399\pi\) | ||||
0.322732 | + | 0.946490i | \(0.395399\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.24621i | 0.178639i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.56155i | 0.149571i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 44.7386 | 1.87554 | 0.937771 | − | 0.347256i | \(-0.112886\pi\) | ||||
0.937771 | + | 0.347256i | \(0.112886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.8078 | −1.33111 | −0.665557 | − | 0.746347i | \(-0.731806\pi\) | ||||
−0.665557 | + | 0.746347i | \(0.731806\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.75379 | −0.240368 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.56155 | −0.0651213 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 18.4384i | − | 0.767603i | −0.923416 | − | 0.383801i | \(-0.874615\pi\) | ||
0.923416 | − | 0.383801i | \(-0.125385\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 10.4384i | − | 0.433807i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.1231 | −0.461464 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 10.4384i | − | 0.432316i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.56155 | − | 0.561553i | 0.147252 | − | 0.0232174i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.6307i | 0.934068i | 0.884239 | + | 0.467034i | \(0.154677\pi\) | ||||
−0.884239 | + | 0.467034i | \(0.845323\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.2462 | −0.422188 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 14.4924i | − | 0.596139i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.7386i | 1.34441i | 0.740363 | + | 0.672207i | \(0.234654\pi\) | ||||
−0.740363 | + | 0.672207i | \(0.765346\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.56155 | −0.0640174 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.4924 | −0.510427 | −0.255213 | − | 0.966885i | \(-0.582146\pi\) | ||||
−0.255213 | + | 0.966885i | \(0.582146\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.0540 | −0.818019 | −0.409009 | − | 0.912530i | \(-0.634126\pi\) | ||||
−0.409009 | + | 0.912530i | \(0.634126\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.3693i | 0.625887i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.56155i | 0.348077i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.4924 | 0.831762 | 0.415881 | − | 0.909419i | \(-0.363473\pi\) | ||||
0.415881 | + | 0.909419i | \(0.363473\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 7.12311i | − | 0.288643i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 24.6847i | − | 0.997004i | −0.866889 | − | 0.498502i | \(-0.833884\pi\) | ||
0.866889 | − | 0.498502i | \(-0.166116\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.68466 | −0.269551 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.75379i | 0.312156i | 0.987745 | + | 0.156078i | \(0.0498851\pi\) | ||||
−0.987745 | + | 0.156078i | \(0.950115\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 14.4924i | − | 0.582500i | −0.956647 | − | 0.291250i | \(-0.905929\pi\) | ||
0.956647 | − | 0.291250i | \(-0.0940711\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.56155 | 0.0626630 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.56155 | −0.0625623 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.00000 | −0.319489 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.43845i | 0.0972273i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.0000i | 0.716569i | 0.933613 | + | 0.358284i | \(0.116638\pi\) | ||||
−0.933613 | + | 0.358284i | \(0.883362\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.4924 | 0.973486 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.1231i | 0.758877i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.19224 | + | 20.2462i | 0.126481 | + | 0.802184i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 9.56155i | − | 0.378249i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 49.1231 | 1.94025 | 0.970123 | − | 0.242614i | \(-0.0780047\pi\) | ||||
0.970123 | + | 0.242614i | \(0.0780047\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.9309i | 1.45641i | 0.685359 | + | 0.728206i | \(0.259645\pi\) | ||||
−0.685359 | + | 0.728206i | \(0.740355\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.876894i | 0.0345277i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.05398 | −0.0807501 | −0.0403751 | − | 0.999185i | \(-0.512855\pi\) | ||||
−0.0403751 | + | 0.999185i | \(0.512855\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.75379 | 0.382870 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.12311 | −0.279177 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.4924 | 1.34979 | 0.674896 | − | 0.737912i | \(-0.264188\pi\) | ||||
0.674896 | + | 0.737912i | \(0.264188\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.4924i | 0.800705i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.876894i | 0.0342109i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.6155 | −1.07575 | −0.537874 | − | 0.843025i | \(-0.680772\pi\) | ||||
−0.537874 | + | 0.843025i | \(0.680772\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 6.24621i | − | 0.242949i | −0.992595 | − | 0.121475i | \(-0.961238\pi\) | ||
0.992595 | − | 0.121475i | \(-0.0387623\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.246211 | − | 1.56155i | −0.00956205 | − | 0.0606457i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 18.2462i | − | 0.707558i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.12311 | −0.120927 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.1231i | 0.507369i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 10.4384i | − | 0.402972i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.1080 | 1.16058 | 0.580288 | − | 0.814411i | \(-0.302940\pi\) | ||||
0.580288 | + | 0.814411i | \(0.302940\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.4233 | −1.28456 | −0.642281 | − | 0.766469i | \(-0.722012\pi\) | ||||
−0.642281 | + | 0.766469i | \(0.722012\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.56155 | −0.213433 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 26.2462i | − | 1.00576i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.6155i | 1.36279i | 0.731916 | + | 0.681395i | \(0.238626\pi\) | ||||
−0.731916 | + | 0.681395i | \(0.761374\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.00000 | 0.229248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.63068i | 0.100367i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.75379 | + | 23.8078i | 0.143008 | + | 0.907004i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.2462i | 1.37887i | 0.724347 | + | 0.689435i | \(0.242141\pi\) | ||||
−0.724347 | + | 0.689435i | \(0.757859\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.56155 | −0.211266 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 9.56155i | − | 0.362690i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.93087i | 0.111015i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.80776 | 0.219670 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.3693 | −1.33588 | −0.667940 | − | 0.744215i | \(-0.732824\pi\) | ||||
−0.667940 | + | 0.744215i | \(0.732824\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.4924 | −1.07461 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.12311i | 0.267892i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 26.2462i | − | 0.985697i | −0.870115 | − | 0.492849i | \(-0.835956\pi\) | ||
0.870115 | − | 0.492849i | \(-0.164044\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.68466 | −0.325700 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.12311i | 0.116961i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.876894 | + | 5.56155i | 0.0327940 | + | 0.207990i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.6847i | 0.473717i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.6307 | 0.396458 | 0.198229 | − | 0.980156i | \(-0.436481\pi\) | ||||
0.198229 | + | 0.980156i | \(0.436481\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 50.7386i | 1.88961i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.12311i | 0.264911i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.00000 | 0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.8617 | 1.40421 | 0.702107 | − | 0.712071i | \(-0.252243\pi\) | ||||
0.702107 | + | 0.712071i | \(0.252243\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.384472 | 0.0142202 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 36.3002i | − | 1.34078i | −0.742010 | − | 0.670389i | \(-0.766127\pi\) | ||
0.742010 | − | 0.670389i | \(-0.233873\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 5.68466i | − | 0.209682i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.0000 | −0.884051 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.2462i | 0.744769i | 0.928079 | + | 0.372384i | \(0.121460\pi\) | ||||
−0.928079 | + | 0.372384i | \(0.878540\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.2462 | − | 2.87689i | 0.670291 | − | 0.105685i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.4924i | 0.605048i | 0.953142 | + | 0.302524i | \(0.0978293\pi\) | ||||
−0.953142 | + | 0.302524i | \(0.902171\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.9309 | 0.766848 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.12311i | 0.114268i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.9309i | 1.13019i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.4384 | −0.380904 | −0.190452 | − | 0.981696i | \(-0.560995\pi\) | ||||
−0.190452 | + | 0.981696i | \(0.560995\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.3693 | 0.487205 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.0000 | 0.509512 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.1231 | 1.34926 | 0.674631 | − | 0.738155i | \(-0.264303\pi\) | ||||
0.674631 | + | 0.738155i | \(0.264303\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.43845i | 0.0885100i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.2311i | 1.49462i | 0.664473 | + | 0.747312i | \(0.268656\pi\) | ||||
−0.664473 | + | 0.747312i | \(0.731344\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −31.6155 | −1.14456 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.438447i | 0.0158521i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.2462 | + | 3.50758i | −0.803264 | + | 0.126651i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 24.0000i | − | 0.865462i | −0.901523 | − | 0.432731i | \(-0.857550\pi\) | ||
0.901523 | − | 0.432731i | \(-0.142450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.4924 | 0.810045 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 46.4924i | 1.67222i | 0.548565 | + | 0.836108i | \(0.315174\pi\) | ||||
−0.548565 | + | 0.836108i | \(0.684826\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.00000i | − | 0.0718421i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −19.8078 | −0.710600 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −34.2462 | −1.22700 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.9309 | 0.534269 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 6.87689i | − | 0.245447i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 11.3693i | − | 0.405272i | −0.979254 | − | 0.202636i | \(-0.935049\pi\) | ||
0.979254 | − | 0.202636i | \(-0.0649509\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.0000 | 0.569615 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.1231i | 0.537716i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.75379 | + | 23.8078i | 0.133301 | + | 0.845438i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 6.68466i | − | 0.237080i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.4233 | −0.475477 | −0.237739 | − | 0.971329i | \(-0.576406\pi\) | ||||
−0.237739 | + | 0.971329i | \(0.576406\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.438447i | 0.0154918i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.36932 | −0.0483221 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.56155 | −0.196019 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.1231 | −1.02518 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.8769 | 0.944941 | 0.472471 | − | 0.881346i | \(-0.343362\pi\) | ||||
0.472471 | + | 0.881346i | \(0.343362\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.0000i | 0.351147i | 0.984466 | + | 0.175574i | \(0.0561780\pi\) | ||||
−0.984466 | + | 0.175574i | \(0.943822\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 3.75379i | − | 0.131651i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.0540 | −0.702460 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.49242i | 0.157170i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.6847 | − | 2.00000i | 0.443238 | − | 0.0698857i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.93087i | 0.311690i | 0.987782 | + | 0.155845i | \(0.0498100\pi\) | ||||
−0.987782 | + | 0.155845i | \(0.950190\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.3693 | 1.16318 | 0.581591 | − | 0.813482i | \(-0.302431\pi\) | ||||
0.581591 | + | 0.813482i | \(0.302431\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.56155i | − | 0.0543663i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 5.75379i | − | 0.200079i | −0.994983 | − | 0.100039i | \(-0.968103\pi\) | ||
0.994983 | − | 0.100039i | \(-0.0318969\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.2311 | −1.57094 | −0.785470 | − | 0.618900i | \(-0.787579\pi\) | ||||
−0.785470 | + | 0.618900i | \(0.787579\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.36932 | −0.116880 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.49242 | −0.0863573 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.24621 | 0.216159 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.00000i | 0.0691301i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.5464i | 1.46886i | 0.678682 | + | 0.734432i | \(0.262552\pi\) | ||||
−0.678682 | + | 0.734432i | \(0.737448\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.00000i | 0.0688837i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.00000 | − | 12.3693i | −0.137604 | − | 0.425517i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.4924i | 1.04773i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.1231 | 0.519024 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.68466i | 0.297706i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 14.5464i | − | 0.498059i | −0.968496 | − | 0.249030i | \(-0.919888\pi\) | ||
0.968496 | − | 0.249030i | \(-0.0801116\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.12311 | −0.175207 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.9309 | −0.441710 | −0.220855 | − | 0.975307i | \(-0.570885\pi\) | ||||
−0.220855 | + | 0.975307i | \(0.570885\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.5616 | −1.69102 | −0.845509 | − | 0.533961i | \(-0.820703\pi\) | ||||
−0.845509 | + | 0.533961i | \(0.820703\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.8078 | −0.811366 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.36932i | − | 0.0466121i | −0.999728 | − | 0.0233060i | \(-0.992581\pi\) | ||
0.999728 | − | 0.0233060i | \(-0.00741922\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.4924i | 0.492757i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.8078 | −0.570822 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 13.5616i | − | 0.460044i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.7386 | − | 8.63068i | 1.85475 | − | 0.292440i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.56155i | 0.0528506i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.56155 | 0.120402 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 12.8769i | − | 0.434822i | −0.976080 | − | 0.217411i | \(-0.930239\pi\) | ||
0.976080 | − | 0.217411i | \(-0.0697612\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 22.4924i | − | 0.758651i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.1080 | −0.879599 | −0.439800 | − | 0.898096i | \(-0.644951\pi\) | ||||
−0.439800 | + | 0.898096i | \(0.644951\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.2311 | −1.18562 | −0.592810 | − | 0.805343i | \(-0.701981\pi\) | ||||
−0.592810 | + | 0.805343i | \(0.701981\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.24621 | 0.209964 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.17708 | −0.0395225 | −0.0197613 | − | 0.999805i | \(-0.506291\pi\) | ||||
−0.0197613 | + | 0.999805i | \(0.506291\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 68.1080i | 2.28427i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.56155i | 0.0523140i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.876894 | − | 5.56155i | −0.0292787 | − | 0.185695i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 4.00000i | − | 0.133407i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.93087 | −0.0976414 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.12311i | 0.103930i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 13.8078i | − | 0.458986i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.7386 | 1.02066 | 0.510330 | − | 0.859979i | \(-0.329523\pi\) | ||||
0.510330 | + | 0.859979i | \(0.329523\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.00000 | 0.0663358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.3693 | −1.50315 | −0.751576 | − | 0.659646i | \(-0.770706\pi\) | ||||
−0.751576 | + | 0.659646i | \(0.770706\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.87689 | −0.161402 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 6.68466i | − | 0.220988i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 72.9848i | 2.41017i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.0540 | 0.859441 | 0.429721 | − | 0.902962i | \(-0.358612\pi\) | ||||
0.429721 | + | 0.902962i | \(0.358612\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 4.43845i | − | 0.146252i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34.0540 | + | 5.36932i | −1.12090 | + | 0.176733i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 5.56155i | − | 0.182863i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.2462 | 0.467907 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.5464i | 1.72399i | 0.506916 | + | 0.861996i | \(0.330786\pi\) | ||||
−0.506916 | + | 0.861996i | \(0.669214\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 29.1231i | − | 0.954471i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.87689 | −0.290616 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.684658 | −0.0223907 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.50758 | −0.179925 | −0.0899624 | − | 0.995945i | \(-0.528675\pi\) | ||||
−0.0899624 | + | 0.995945i | \(0.528675\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.36932 | 0.240489 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.80776i | 0.189328i | 0.995509 | + | 0.0946638i | \(0.0301776\pi\) | ||||
−0.995509 | + | 0.0946638i | \(0.969822\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.4384i | 0.339923i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.56155 | −0.115857 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 20.4924i | − | 0.665914i | −0.942942 | − | 0.332957i | \(-0.891954\pi\) | ||
0.942942 | − | 0.332957i | \(-0.108046\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.12311 | − | 0.492423i | 0.101380 | − | 0.0159847i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 10.0000i | − | 0.324272i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.7926 | −1.38619 | −0.693094 | − | 0.720847i | \(-0.743753\pi\) | ||||
−0.693094 | + | 0.720847i | \(0.743753\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 5.75379i | − | 0.186188i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3.12311i | − | 0.100956i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.3693 | 0.690051 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.0000 | 0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.68466 | 0.279859 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.4384 | 0.336026 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 42.8769i | − | 1.37883i | −0.724368 | − | 0.689414i | \(-0.757868\pi\) | ||
0.724368 | − | 0.689414i | \(-0.242132\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.24621i | 0.0721587i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.61553 | −0.116028 | −0.0580139 | − | 0.998316i | \(-0.518477\pi\) | ||||
−0.0580139 | + | 0.998316i | \(0.518477\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 34.0540i | − | 1.09172i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.561553 | + | 3.56155i | 0.0179841 | + | 0.114061i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.3693i | 0.619679i | 0.950789 | + | 0.309840i | \(0.100275\pi\) | ||||
−0.950789 | + | 0.309840i | \(0.899725\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.684658 | −0.0218818 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.87689i | 0.283417i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 20.0000i | − | 0.637901i | −0.947771 | − | 0.318950i | \(-0.896670\pi\) | ||
0.947771 | − | 0.318950i | \(-0.103330\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.4924 | 0.461767 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.36932 | 0.0435417 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.3002 | −0.517792 | −0.258896 | − | 0.965905i | \(-0.583359\pi\) | ||||
−0.258896 | + | 0.965905i | \(0.583359\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 19.3693i | − | 0.614667i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.12311 | −0.162250 | −0.0811252 | − | 0.996704i | \(-0.525851\pi\) | ||||
−0.0811252 | + | 0.996704i | \(0.525851\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.56155i | 0.175960i |
(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 | 1560.2.g.h.961.4 | yes | 4 | |
3.2 | odd | 2 | 4680.2.g.g.2521.2 | 4 | |||
4.3 | odd | 2 | 3120.2.g.p.961.3 | 4 | |||
13.12 | even | 2 | inner | 1560.2.g.h.961.1 | ✓ | 4 | |
39.38 | odd | 2 | 4680.2.g.g.2521.3 | 4 | |||
52.51 | odd | 2 | 3120.2.g.p.961.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.g.h.961.1 | ✓ | 4 | 13.12 | even | 2 | inner | |
1560.2.g.h.961.4 | yes | 4 | 1.1 | even | 1 | trivial | |
3120.2.g.p.961.2 | 4 | 52.51 | odd | 2 | |||
3120.2.g.p.961.3 | 4 | 4.3 | odd | 2 | |||
4680.2.g.g.2521.2 | 4 | 3.2 | odd | 2 | |||
4680.2.g.g.2521.3 | 4 | 39.38 | odd | 2 |