Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1471,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("5520.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.be (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: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.6 | ||
Character | \(\chi\) | \(=\) | 5520.1471 |
Dual form | 5520.2.be.c.1471.5 |
$q$-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 \(\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times\).
\(n\) | \(1201\) | \(1381\) | \(1841\) | \(4417\) | \(4831\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.12483 | 1.18108 | 0.590538 | − | 0.807010i | \(-0.298916\pi\) | ||||
0.590538 | + | 0.807010i | \(0.298916\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.96967 | −0.593878 | −0.296939 | − | 0.954896i | \(-0.595966\pi\) | ||||
−0.296939 | + | 0.954896i | \(0.595966\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.52369 | −0.699945 | −0.349972 | − | 0.936760i | \(-0.613809\pi\) | ||||
−0.349972 | + | 0.936760i | \(0.613809\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.66071i | − | 0.887854i | −0.896063 | − | 0.443927i | \(-0.853585\pi\) | ||
0.896063 | − | 0.443927i | \(-0.146415\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.78607 | −1.55683 | −0.778415 | − | 0.627750i | \(-0.783976\pi\) | ||||
−0.778415 | + | 0.627750i | \(0.783976\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.12483i | 0.681895i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.20899 | − | 4.25680i | 0.460606 | − | 0.887605i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.23487 | 0.415005 | 0.207503 | − | 0.978234i | \(-0.433466\pi\) | ||||
0.207503 | + | 0.978234i | \(0.433466\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.377839i | − | 0.0678619i | −0.999424 | − | 0.0339309i | \(-0.989197\pi\) | ||
0.999424 | − | 0.0339309i | \(-0.0108026\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.96967i | − | 0.342875i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.12483i | 0.528193i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.26726i | − | 0.865933i | −0.901410 | − | 0.432966i | \(-0.857467\pi\) | ||
0.901410 | − | 0.432966i | \(-0.142533\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 2.52369i | − | 0.404113i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.40401 | 0.843965 | 0.421982 | − | 0.906604i | \(-0.361334\pi\) | ||||
0.421982 | + | 0.906604i | \(0.361334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.5558 | 1.91475 | 0.957375 | − | 0.288849i | \(-0.0932727\pi\) | ||||
0.957375 | + | 0.288849i | \(0.0932727\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 1.35089i | − | 0.197047i | −0.995135 | − | 0.0985237i | \(-0.968588\pi\) | ||
0.995135 | − | 0.0985237i | \(-0.0314120\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.76459 | 0.394941 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.66071 | 0.512603 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.17126i | 0.435606i | 0.975993 | + | 0.217803i | \(0.0698891\pi\) | ||||
−0.975993 | + | 0.217803i | \(0.930111\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.96967i | − | 0.265590i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.78607i | − | 0.898837i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.9962i | 1.56177i | 0.624675 | + | 0.780885i | \(0.285231\pi\) | ||||
−0.624675 | + | 0.780885i | \(0.714769\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.62698i | − | 0.592424i | −0.955122 | − | 0.296212i | \(-0.904276\pi\) | ||
0.955122 | − | 0.296212i | \(-0.0957235\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.12483 | −0.393692 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.52369i | − | 0.313025i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.4936 | 1.28200 | 0.640998 | − | 0.767543i | \(-0.278521\pi\) | ||||
0.640998 | + | 0.767543i | \(0.278521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.25680 | + | 2.20899i | 0.512459 | + | 0.265931i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 15.1992i | − | 1.80381i | −0.431935 | − | 0.901905i | \(-0.642169\pi\) | ||
0.431935 | − | 0.901905i | \(-0.357831\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.4156 | 1.57017 | 0.785087 | − | 0.619385i | \(-0.212618\pi\) | ||||
0.785087 | + | 0.619385i | \(0.212618\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.15489 | −0.701415 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.38677 | 0.606059 | 0.303029 | − | 0.952981i | \(-0.402002\pi\) | ||||
0.303029 | + | 0.952981i | \(0.402002\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.7579 | 1.61989 | 0.809943 | − | 0.586508i | \(-0.199498\pi\) | ||||
0.809943 | + | 0.586508i | \(0.199498\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.66071 | 0.397060 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.23487i | 0.239604i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.338033i | 0.0358315i | 0.999840 | + | 0.0179157i | \(0.00570306\pi\) | ||||
−0.999840 | + | 0.0179157i | \(0.994297\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.88610 | −0.826688 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.377839 | 0.0391801 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 6.78607i | − | 0.696236i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0882i | 1.12584i | 0.826512 | + | 0.562919i | \(0.190322\pi\) | ||||
−0.826512 | + | 0.562919i | \(0.809678\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.96967 | 0.197959 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.64873 | 0.661573 | 0.330786 | − | 0.943706i | \(-0.392686\pi\) | ||||
0.330786 | + | 0.943706i | \(0.392686\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.583656 | 0.0575093 | 0.0287547 | − | 0.999586i | \(-0.490846\pi\) | ||||
0.0287547 | + | 0.999586i | \(0.490846\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.12483 | −0.304953 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.04526 | 0.197723 | 0.0988615 | − | 0.995101i | \(-0.468480\pi\) | ||||
0.0988615 | + | 0.995101i | \(0.468480\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.7438i | 1.50798i | 0.656884 | + | 0.753992i | \(0.271874\pi\) | ||||
−0.656884 | + | 0.753992i | \(0.728126\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.26726 | 0.499946 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.6691i | − | 1.19180i | −0.803057 | − | 0.595902i | \(-0.796795\pi\) | ||
0.803057 | − | 0.595902i | \(-0.203205\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.25680 | + | 2.20899i | 0.396949 | + | 0.205989i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.52369 | 0.233315 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 11.4391i | − | 1.04862i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.12040 | −0.647309 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.40401i | 0.487263i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 21.2834i | − | 1.88859i | −0.329093 | − | 0.944297i | \(-0.606743\pi\) | ||
0.329093 | − | 0.944297i | \(-0.393257\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.5558i | 1.10548i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 13.9512i | − | 1.21892i | −0.792816 | − | 0.609461i | \(-0.791386\pi\) | ||
0.792816 | − | 0.609461i | \(-0.208614\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21.2053 | −1.83874 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.32226i | 0.198404i | 0.995067 | + | 0.0992021i | \(0.0316290\pi\) | ||||
−0.995067 | + | 0.0992021i | \(0.968371\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.4464i | 1.31014i | 0.755567 | + | 0.655071i | \(0.227361\pi\) | ||||
−0.755567 | + | 0.655071i | \(0.772639\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.35089 | 0.113765 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.97083 | 0.415682 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.23487i | 0.185596i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.76459i | 0.228019i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.84162i | 0.396641i | 0.980137 | + | 0.198320i | \(0.0635487\pi\) | ||||
−0.980137 | + | 0.198320i | \(0.936451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.8598i | 1.61617i | 0.589069 | + | 0.808083i | \(0.299495\pi\) | ||||
−0.589069 | + | 0.808083i | \(0.700505\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.66071i | 0.295951i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.377839 | 0.0303488 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.2502i | 1.29691i | 0.761255 | + | 0.648453i | \(0.224584\pi\) | ||||
−0.761255 | + | 0.648453i | \(0.775416\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.17126 | −0.251497 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.90273 | − | 13.3018i | 0.544011 | − | 1.04833i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 21.5017i | − | 1.68415i | −0.539363 | − | 0.842073i | \(-0.681335\pi\) | ||
0.539363 | − | 0.842073i | \(-0.318665\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.96967 | 0.153339 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 13.7046i | − | 1.06049i | −0.847844 | − | 0.530245i | \(-0.822100\pi\) | ||
0.847844 | − | 0.530245i | \(-0.177900\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.63101 | −0.510078 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.78607 | 0.518944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.6695 | −0.963244 | −0.481622 | − | 0.876379i | \(-0.659952\pi\) | ||||
−0.481622 | + | 0.876379i | \(0.659952\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.12483 | −0.236215 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.9962 | −0.901688 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 19.8164i | − | 1.48115i | −0.671974 | − | 0.740575i | \(-0.734553\pi\) | ||
0.671974 | − | 0.740575i | \(-0.265447\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00943i | 0.149360i | 0.997208 | + | 0.0746801i | \(0.0237936\pi\) | ||||
−0.997208 | + | 0.0746801i | \(0.976206\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.62698 | 0.342036 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.26726 | 0.387257 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.21040i | 0.527277i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 3.12483i | − | 0.227298i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.8616 | 1.36478 | 0.682388 | − | 0.730990i | \(-0.260941\pi\) | ||||
0.682388 | + | 0.730990i | \(0.260941\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.8785 | −1.86277 | −0.931387 | − | 0.364030i | \(-0.881401\pi\) | ||||
−0.931387 | + | 0.364030i | \(0.881401\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.52369 | 0.180725 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.3975 | 0.812040 | 0.406020 | − | 0.913864i | \(-0.366916\pi\) | ||||
0.406020 | + | 0.913864i | \(0.366916\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.1484 | 0.719398 | 0.359699 | − | 0.933068i | \(-0.382879\pi\) | ||||
0.359699 | + | 0.933068i | \(0.382879\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.4936i | 0.740160i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.98361 | 0.490153 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.40401i | 0.377432i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.20899 | + | 4.25680i | −0.153535 | + | 0.295868i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.3663 | 0.924567 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4.20971i | − | 0.289808i | −0.989446 | − | 0.144904i | \(-0.953713\pi\) | ||
0.989446 | − | 0.144904i | \(-0.0462874\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.1992 | 1.04143 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.5558i | 0.856302i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.18068i | − | 0.0801501i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.4156i | 0.906541i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.23850i | 0.621448i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.2218i | 1.35415i | 0.735912 | + | 0.677077i | \(0.236754\pi\) | ||||
−0.735912 | + | 0.677077i | \(0.763246\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −29.8101 | −1.97857 | −0.989284 | − | 0.146005i | \(-0.953359\pi\) | ||||
−0.989284 | + | 0.146005i | \(0.953359\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.3772i | 0.817909i | 0.912555 | + | 0.408955i | \(0.134107\pi\) | ||||
−0.912555 | + | 0.408955i | \(0.865893\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 6.15489i | − | 0.404962i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.5820 | −0.889789 | −0.444895 | − | 0.895583i | \(-0.646759\pi\) | ||||
−0.444895 | + | 0.895583i | \(0.646759\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.35089 | 0.0881222 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.38677i | 0.349908i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.77772i | − | 0.567784i | −0.958856 | − | 0.283892i | \(-0.908374\pi\) | ||
0.958856 | − | 0.283892i | \(-0.0916257\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 13.8466i | − | 0.891935i | −0.895049 | − | 0.445968i | \(-0.852860\pi\) | ||
0.895049 | − | 0.445968i | \(-0.147140\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.76459i | 0.176623i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.1259 | 1.08970 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.7579i | 0.935242i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.2244 | 1.65527 | 0.827635 | − | 0.561267i | \(-0.189686\pi\) | ||||
0.827635 | + | 0.561267i | \(0.189686\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.35098 | + | 8.38449i | −0.273544 | + | 0.527129i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.66071i | 0.229243i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.73811 | −0.233177 | −0.116588 | − | 0.993180i | \(-0.537196\pi\) | ||||
−0.116588 | + | 0.993180i | \(0.537196\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 16.4593i | − | 1.02273i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.23487 | −0.138335 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.3159 | 1.19107 | 0.595536 | − | 0.803328i | \(-0.296940\pi\) | ||||
0.595536 | + | 0.803328i | \(0.296940\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.17126 | −0.194809 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.338033 | −0.0206873 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −32.5176 | −1.98264 | −0.991318 | − | 0.131489i | \(-0.958024\pi\) | ||||
−0.991318 | + | 0.131489i | \(0.958024\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 19.1381i | − | 1.16255i | −0.813706 | − | 0.581277i | \(-0.802553\pi\) | ||
0.813706 | − | 0.581277i | \(-0.197447\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 7.88610i | − | 0.477289i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.96967 | 0.118776 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.32487 | 0.560277 | 0.280139 | − | 0.959960i | \(-0.409620\pi\) | ||||
0.280139 | + | 0.959960i | \(0.409620\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.377839i | 0.0226206i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.4885i | − | 0.745001i | −0.928032 | − | 0.372500i | \(-0.878501\pi\) | ||
0.928032 | − | 0.372500i | \(-0.121499\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.1536 | −0.603567 | −0.301783 | − | 0.953377i | \(-0.597582\pi\) | ||||
−0.301783 | + | 0.953377i | \(0.597582\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.78607 | 0.401972 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.8866 | 0.996787 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.59917 | 0.211716 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.0882 | −0.650003 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 24.8954i | − | 1.45440i | −0.686424 | − | 0.727201i | \(-0.740821\pi\) | ||
0.686424 | − | 0.727201i | \(-0.259179\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.9962 | −0.698444 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.96967i | 0.114292i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.57480 | + | 10.7428i | −0.322399 | + | 0.621274i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 39.2349 | 2.26146 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.64873i | 0.381959i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.62698 | 0.264940 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 14.7305i | − | 0.840712i | −0.907359 | − | 0.420356i | \(-0.861905\pi\) | ||
0.907359 | − | 0.420356i | \(-0.138095\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.583656i | 0.0332030i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.02347i | 0.114740i | 0.998353 | + | 0.0573702i | \(0.0182715\pi\) | ||||
−0.998353 | + | 0.0573702i | \(0.981728\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.6539i | 1.11091i | 0.831548 | + | 0.555453i | \(0.187455\pi\) | ||||
−0.831548 | + | 0.555453i | \(0.812545\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 3.12483i | − | 0.176064i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.0518500 | 0.00291219 | 0.00145609 | − | 0.999999i | \(-0.499537\pi\) | ||||
0.00145609 | + | 0.999999i | \(0.499537\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.40196 | −0.246463 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.04526i | 0.114155i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.8419i | 1.38224i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.52369 | 0.139989 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.7438 | −0.870635 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 4.22130i | − | 0.232728i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 3.22601i | − | 0.177317i | −0.996062 | − | 0.0886586i | \(-0.971742\pi\) | ||
0.996062 | − | 0.0886586i | \(-0.0282580\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.26726i | 0.288644i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.4936i | 0.573326i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.7479i | 1.78389i | 0.452141 | + | 0.891946i | \(0.350660\pi\) | ||||
−0.452141 | + | 0.891946i | \(0.649340\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.6691 | 0.688089 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.744218i | 0.0403017i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.2350 | −0.714621 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.20899 | + | 4.25680i | −0.118928 | + | 0.229179i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 24.5999i | − | 1.32059i | −0.751006 | − | 0.660295i | \(-0.770431\pi\) | ||
0.751006 | − | 0.660295i | \(-0.229569\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.6353 | 1.58634 | 0.793171 | − | 0.608999i | \(-0.208429\pi\) | ||||
0.793171 | + | 0.608999i | \(0.208429\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.52369i | 0.134704i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.6740 | 1.68583 | 0.842917 | − | 0.538043i | \(-0.180836\pi\) | ||||
0.842917 | + | 0.538043i | \(0.180836\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.1992 | 0.806688 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.4391 | 0.605423 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.92427 | 0.259893 | 0.129947 | − | 0.991521i | \(-0.458519\pi\) | ||||
0.129947 | + | 0.991521i | \(0.458519\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.0507 | 1.42372 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 7.12040i | − | 0.373724i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.4156i | 0.702203i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.7214 | 1.02945 | 0.514725 | − | 0.857355i | \(-0.327894\pi\) | ||||
0.514725 | + | 0.857355i | \(0.327894\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.40401 | −0.281322 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.90967i | 0.514484i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.38425i | 0.330564i | 0.986246 | + | 0.165282i | \(0.0528534\pi\) | ||||
−0.986246 | + | 0.165282i | \(0.947147\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.64012 | −0.290481 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.70427 | 0.138909 | 0.0694546 | − | 0.997585i | \(-0.477874\pi\) | ||||
0.0694546 | + | 0.997585i | \(0.477874\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.2834 | 1.09038 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.4327 | 1.55504 | 0.777519 | − | 0.628860i | \(-0.216478\pi\) | ||||
0.777519 | + | 0.628860i | \(0.216478\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 6.15489i | − | 0.313682i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.5558 | −0.638250 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 24.3346i | − | 1.23381i | −0.787037 | − | 0.616906i | \(-0.788386\pi\) | ||
0.787037 | − | 0.616906i | \(-0.211614\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.5829 | − | 8.08648i | −0.788063 | − | 0.408951i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.9512 | 0.703745 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.38677i | 0.271038i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.96983 | 0.500371 | 0.250186 | − | 0.968198i | \(-0.419508\pi\) | ||||
0.250186 | + | 0.968198i | \(0.419508\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 21.2053i | − | 1.06159i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 14.6150i | − | 0.729839i | −0.931039 | − | 0.364920i | \(-0.881096\pi\) | ||
0.931039 | − | 0.364920i | \(-0.118904\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.953547i | 0.0474996i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.3748i | 0.514258i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.77841 | 0.285724 | 0.142862 | − | 0.989743i | \(-0.454369\pi\) | ||||
0.142862 | + | 0.989743i | \(0.454369\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.32226 | −0.114549 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 37.4861i | 1.84457i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.7579i | 0.724435i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.4464 | −0.756411 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.4826 | 1.24491 | 0.622453 | − | 0.782657i | \(-0.286136\pi\) | ||||
0.622453 | + | 0.782657i | \(0.286136\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.35143i | 0.407024i | 0.979072 | + | 0.203512i | \(0.0652356\pi\) | ||||
−0.979072 | + | 0.203512i | \(0.934764\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.35089i | 0.0656824i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.66071i | 0.177571i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 14.4585i | − | 0.699698i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.97083i | 0.239994i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.81003 | −0.135354 | −0.0676771 | − | 0.997707i | \(-0.521559\pi\) | ||||
−0.0676771 | + | 0.997707i | \(0.521559\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 21.5271i | − | 1.03453i | −0.855826 | − | 0.517263i | \(-0.826951\pi\) | ||
0.855826 | − | 0.517263i | \(-0.173049\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.23487 | −0.107154 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.9904 | + | 28.8870i | −0.717086 | + | 1.38185i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 14.5927i | − | 0.696471i | −0.937407 | − | 0.348235i | \(-0.886781\pi\) | ||
0.937407 | − | 0.348235i | \(-0.113219\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.76459 | −0.131647 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.8921i | 0.945101i | 0.881304 | + | 0.472550i | \(0.156667\pi\) | ||||
−0.881304 | + | 0.472550i | \(0.843333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.338033 | −0.0160243 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.84162 | −0.229001 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.8817 | −0.985470 | −0.492735 | − | 0.870180i | \(-0.664003\pi\) | ||||
−0.492735 | + | 0.870180i | \(0.664003\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.6441 | −0.501212 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.8598 | −0.933094 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 7.88610i | − | 0.369706i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 2.71008i | − | 0.126772i | −0.997989 | − | 0.0633861i | \(-0.979810\pi\) | ||
0.997989 | − | 0.0633861i | \(-0.0201900\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.66071 | −0.170868 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.9568 | −1.11578 | −0.557889 | − | 0.829915i | \(-0.688389\pi\) | ||||
−0.557889 | + | 0.829915i | \(0.688389\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.9255i | 1.25133i | 0.780090 | + | 0.625667i | \(0.215173\pi\) | ||||
−0.780090 | + | 0.625667i | \(0.784827\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.377839i | 0.0175219i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.6351 | −0.492134 | −0.246067 | − | 0.969253i | \(-0.579138\pi\) | ||||
−0.246067 | + | 0.969253i | \(0.579138\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.7907 | 1.51413 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.2502 | −0.748769 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24.7309 | −1.13713 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.78607 | 0.311366 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 3.17126i | − | 0.145202i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.4647 | 1.48335 | 0.741676 | − | 0.670759i | \(-0.234031\pi\) | ||||
0.741676 | + | 0.670759i | \(0.234031\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.2929i | 0.606105i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.3018 | + | 6.90273i | 0.605253 | + | 0.314085i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.0882 | −0.503490 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 24.0618i | − | 1.09034i | −0.838324 | − | 0.545172i | \(-0.816464\pi\) | ||
0.838324 | − | 0.545172i | \(-0.183536\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.5017 | 0.972343 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.570628i | 0.0257521i | 0.999917 | + | 0.0128760i | \(0.00409868\pi\) | ||||
−0.999917 | + | 0.0128760i | \(0.995901\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 8.18123i | − | 0.368464i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.96967i | 0.0885301i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 47.4949i | − | 2.13044i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.2429i | 0.995727i | 0.867255 | + | 0.497864i | \(0.165882\pi\) | ||||
−0.867255 | + | 0.497864i | \(0.834118\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.7046 | 0.612275 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.1596 | 1.43392 | 0.716962 | − | 0.697112i | \(-0.245532\pi\) | ||||
0.716962 | + | 0.697112i | \(0.245532\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.64873i | 0.295864i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 6.63101i | − | 0.294493i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.93120 | 0.262896 | 0.131448 | − | 0.991323i | \(-0.458037\pi\) | ||||
0.131448 | + | 0.991323i | \(0.458037\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 41.9215 | 1.85450 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.78607i | 0.299612i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.583656i | 0.0257189i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.66080i | 0.117022i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 12.6695i | − | 0.556129i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.545006i | 0.0238771i | 0.999929 | + | 0.0119386i | \(0.00380025\pi\) | ||||
−0.999929 | + | 0.0119386i | \(0.996200\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.0697 | −1.40231 | −0.701155 | − | 0.713009i | \(-0.747332\pi\) | ||||
−0.701155 | + | 0.713009i | \(0.747332\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 3.12483i | − | 0.136379i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.38316 | −0.0602514 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.2407 | − | 18.8065i | −0.575684 | − | 0.817672i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 11.9962i | − | 0.520590i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.6380 | −0.590728 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.04526i | 0.0884244i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.8164 | 0.855142 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.44533 | −0.234547 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.4749 | −1.56818 | −0.784089 | − | 0.620648i | \(-0.786870\pi\) | ||||
−0.784089 | + | 0.620648i | \(0.786870\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.00943 | −0.0862331 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.7438 | −0.674391 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.286412i | 0.0122461i | 0.999981 | + | 0.00612304i | \(0.00194904\pi\) | ||||
−0.999981 | + | 0.00612304i | \(0.998051\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.62698i | 0.197475i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.1660 | −0.646093 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.8328 | 0.715802 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.26726i | 0.223583i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 7.77446i | − | 0.329414i | −0.986343 | − | 0.164707i | \(-0.947332\pi\) | ||
0.986343 | − | 0.164707i | \(-0.0526679\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.6870 | −1.34022 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.21040 | −0.304423 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.1915 | −0.555955 | −0.277977 | − | 0.960588i | \(-0.589664\pi\) | ||||
−0.277977 | + | 0.960588i | \(0.589664\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.6691 | 0.532991 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.12483 | 0.131231 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.9198i | 0.793159i | 0.918000 | + | 0.396580i | \(0.129803\pi\) | ||||
−0.918000 | + | 0.396580i | \(0.870197\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.35834 | 0.0986933 | 0.0493466 | − | 0.998782i | \(-0.484286\pi\) | ||||
0.0493466 | + | 0.998782i | \(0.484286\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.8616i | 0.787954i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.20899 | + | 4.25680i | −0.0921212 | + | 0.177521i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.1515 | 1.62990 | 0.814949 | − | 0.579533i | \(-0.196765\pi\) | ||||
0.814949 | + | 0.579533i | \(0.196765\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 25.8785i | − | 1.07547i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 46.1159 | 1.91321 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6.24634i | − | 0.258697i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.52369i | 0.104342i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.8938i | 1.19258i | 0.802771 | + | 0.596288i | \(0.203358\pi\) | ||||
−0.802771 | + | 0.596288i | \(0.796642\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.56404i | 0.105649i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.3975i | 0.468832i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.95439 | 0.285583 | 0.142791 | − | 0.989753i | \(-0.454392\pi\) | ||||
0.142791 | + | 0.989753i | \(0.454392\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.4391 | 0.468958 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.1484i | 0.415344i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 39.5319i | − | 1.61523i | −0.589711 | − | 0.807614i | \(-0.700758\pi\) | ||
0.589711 | − | 0.807614i | \(-0.299242\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.3570 | 0.952751 | 0.476376 | − | 0.879242i | \(-0.341950\pi\) | ||||
0.476376 | + | 0.879242i | \(0.341950\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.4936 | −0.427332 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 7.12040i | − | 0.289485i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.94207i | − | 0.281770i | −0.990026 | − | 0.140885i | \(-0.955005\pi\) | ||
0.990026 | − | 0.140885i | \(-0.0449947\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.98361i | 0.282990i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.40922i | 0.137922i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 48.1058i | 1.94298i | 0.237089 | + | 0.971488i | \(0.423807\pi\) | ||||
−0.237089 | + | 0.971488i | \(0.576193\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.40401 | −0.217911 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.62309i | 0.186119i | 0.995661 | + | 0.0930593i | \(0.0296646\pi\) | ||||
−0.995661 | + | 0.0930593i | \(0.970335\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.8837 | −1.40210 | −0.701048 | − | 0.713114i | \(-0.747284\pi\) | ||||
−0.701048 | + | 0.713114i | \(0.747284\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.25680 | − | 2.20899i | −0.170820 | − | 0.0886437i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.05630i | 0.0423197i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.3663i | 0.533799i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.2819 | −0.768821 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.52455 | −0.0606915 | −0.0303458 | − | 0.999539i | \(-0.509661\pi\) | ||||
−0.0303458 | + | 0.999539i | \(0.509661\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.20971 | 0.167321 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.2834 | 0.844605 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.97695 | −0.276437 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.1992i | 0.601270i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 33.0371i | − | 1.30489i | −0.757837 | − | 0.652443i | \(-0.773744\pi\) | ||
0.757837 | − | 0.652443i | \(-0.226256\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.4205 | 0.410943 | 0.205472 | − | 0.978663i | \(-0.434127\pi\) | ||||
0.205472 | + | 0.978663i | \(0.434127\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.5558 | −0.494386 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.28523i | 0.247098i | 0.992338 | + | 0.123549i | \(0.0394276\pi\) | ||||
−0.992338 | + | 0.123549i | \(0.960572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 23.6285i | − | 0.927500i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.18068 | 0.0462747 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.7826 | 0.852419 | 0.426209 | − | 0.904625i | \(-0.359849\pi\) | ||||
0.426209 | + | 0.904625i | \(0.359849\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.9512 | 0.545119 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.4156 | −0.523391 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.2120 | −0.709438 | −0.354719 | − | 0.934973i | \(-0.615424\pi\) | ||||
−0.354719 | + | 0.934973i | \(0.615424\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 17.9091i | − | 0.696583i | −0.937386 | − | 0.348291i | \(-0.886762\pi\) | ||
0.937386 | − | 0.348291i | \(-0.113238\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.23850 | −0.358793 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 21.2053i | − | 0.822308i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.93681 | − | 9.51341i | 0.191154 | − | 0.368361i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.2218 | −0.781821 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.11362i | 0.351828i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.4411 | −1.55889 | −0.779444 | − | 0.626471i | \(-0.784499\pi\) | ||||
−0.779444 | + | 0.626471i | \(0.784499\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 12.0827i | − | 0.464375i | −0.972671 | − | 0.232187i | \(-0.925412\pi\) | ||
0.972671 | − | 0.232187i | \(-0.0745882\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.6489i | 1.32970i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 29.8101i | − | 1.14233i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 44.2598i | − | 1.69356i | −0.531947 | − | 0.846778i | \(-0.678539\pi\) | ||
0.531947 | − | 0.846778i | \(-0.321461\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.32226 | −0.0887290 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.3772 | −0.472220 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 8.00327i | − | 0.304900i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 17.0262i | − | 0.647705i | −0.946108 | − | 0.323853i | \(-0.895022\pi\) | ||
0.946108 | − | 0.323853i | \(-0.104978\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.15489 | 0.233805 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.4464 | −0.585914 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 19.7825i | − | 0.749317i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 13.5820i | − | 0.513720i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 15.2474i | − | 0.575887i | −0.957647 | − | 0.287943i | \(-0.907029\pi\) | ||
0.957647 | − | 0.287943i | \(-0.0929715\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.7440i | 1.34811i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.35089i | 0.0508774i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.7762 | 0.781368 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.8601i | 0.670751i | 0.942085 | + | 0.335375i | \(0.108863\pi\) | ||||
−0.942085 | + | 0.335375i | \(0.891137\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.38677 | −0.202020 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.60839 | − | 0.834642i | −0.0602345 | − | 0.0312576i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.97083i | 0.185898i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.77772 | 0.327810 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.5363i | 0.430231i | 0.976589 | + | 0.215116i | \(0.0690129\pi\) | ||||
−0.976589 | + | 0.215116i | \(0.930987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.82383 | 0.0679229 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.8466 | 0.514959 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.23487 | −0.0830011 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.409166 | 0.0151751 | 0.00758756 | − | 0.999971i | \(-0.497585\pi\) | ||||
0.00758756 | + | 0.999971i | \(0.497585\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 45.9634i | − | 1.70002i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.6370i | 1.05773i | 0.848705 | + | 0.528866i | \(0.177383\pi\) | ||||
−0.848705 | + | 0.528866i | \(0.822617\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.76459 | −0.101973 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.6689 | −0.761348 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.08323i | 0.223775i | 0.993721 | + | 0.111888i | \(0.0356897\pi\) | ||||
−0.993721 | + | 0.111888i | \(0.964310\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.1259i | 0.629136i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.0715 | −0.442860 | −0.221430 | − | 0.975176i | \(-0.571072\pi\) | ||||
−0.221430 | + | 0.975176i | \(0.571072\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.84162 | −0.177383 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.7579 | −0.539962 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.39111 | 0.233526 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −49.1905 | −1.79499 | −0.897493 | − | 0.441029i | \(-0.854614\pi\) | ||||
−0.897493 | + | 0.441029i | \(0.854614\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.2244i | 0.955670i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.8598 | −0.722771 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 21.0572i | − | 0.765335i | −0.923886 | − | 0.382668i | \(-0.875005\pi\) | ||
0.923886 | − | 0.382668i | \(-0.124995\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.38449 | − | 4.35098i | −0.304338 | − | 0.157931i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −44.4485 | −1.61126 | −0.805628 | − | 0.592422i | \(-0.798172\pi\) | ||||
−0.805628 | + | 0.592422i | \(0.798172\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 49.1968i | 1.78104i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.66071 | −0.132353 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 30.2746i | − | 1.09315i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 27.8869i | − | 1.00563i | −0.864395 | − | 0.502814i | \(-0.832298\pi\) | ||
0.864395 | − | 0.502814i | \(-0.167702\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 3.73811i | − | 0.134625i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.96861i | 0.178709i | 0.996000 | + | 0.0893543i | \(0.0284803\pi\) | ||||
−0.996000 | + | 0.0893543i | \(0.971520\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.377839i | 0.0135724i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.4593 | 0.590475 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −36.6720 | −1.31391 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.9373i | 1.07124i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 2.23487i | − | 0.0798678i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.2502 | −0.579994 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.1512 | −0.753957 | −0.376979 | − | 0.926222i | \(-0.623037\pi\) | ||||
−0.376979 | + | 0.926222i | \(0.623037\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.3159i | 0.687666i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 39.5887i | − | 1.40761i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.6770i | 0.414664i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 3.17126i | − | 0.112473i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 4.80963i | − | 0.170366i | −0.996365 | − | 0.0851830i | \(-0.972853\pi\) | ||
0.996365 | − | 0.0851830i | \(-0.0271475\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.94522 | −0.174949 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 0.338033i | − | 0.0119438i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26.4243 | −0.932492 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.3018 | + | 6.90273i | 0.468827 | + | 0.243289i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 32.5176i | − | 1.14468i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.7916 | −1.04742 | −0.523709 | − | 0.851897i | \(-0.675452\pi\) | ||||
−0.523709 | + | 0.851897i | \(0.675452\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 36.0674i | − | 1.26650i | −0.773949 | − | 0.633249i | \(-0.781721\pi\) | ||
0.773949 | − | 0.633249i | \(-0.218279\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.1381 | 0.671201 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.5017 | 0.753173 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −85.2049 | −2.98094 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.88610 | 0.275563 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.3189 | 0.988336 | 0.494168 | − | 0.869366i | \(-0.335473\pi\) | ||||
0.494168 | + | 0.869366i | \(0.335473\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.8822i | 0.414189i | 0.978321 | + | 0.207094i | \(0.0664007\pi\) | ||||
−0.978321 | + | 0.207094i | \(0.933599\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.96967i | 0.0685751i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.8754 | 0.865003 | 0.432501 | − | 0.901633i | \(-0.357631\pi\) | ||||
0.432501 | + | 0.901633i | \(0.357631\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.572815 | −0.0198947 | −0.00994734 | − | 0.999951i | \(-0.503166\pi\) | ||||
−0.00994734 | + | 0.999951i | \(0.503166\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.32487i | 0.323476i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 10.1204i | − | 0.350650i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.7046 | 0.474266 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.377839 | −0.0130600 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.7025 | 1.12902 | 0.564509 | − | 0.825427i | \(-0.309066\pi\) | ||||
0.564509 | + | 0.825427i | \(0.309066\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0053 | −0.827770 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.4885 | 0.430126 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 6.63101i | − | 0.228114i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.2501 | −0.764522 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 10.1536i | − | 0.348469i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.4217 | − | 11.6353i | −0.768606 | − | 0.398854i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.5299 | −0.942606 | −0.471303 | − | 0.881971i | \(-0.656216\pi\) | ||||
−0.471303 | + | 0.881971i | \(0.656216\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.78607i | 0.232079i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.5228 | −0.530249 | −0.265125 | − | 0.964214i | \(-0.585413\pi\) | ||||
−0.265125 | + | 0.964214i | \(0.585413\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 24.2757i | − | 0.828277i | −0.910214 | − | 0.414138i | \(-0.864083\pi\) | ||
0.910214 | − | 0.414138i | \(-0.135917\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.8866i | 0.575495i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.7816i | 1.62651i | 0.581910 | + | 0.813253i | \(0.302305\pi\) | ||||
−0.581910 | + | 0.813253i | \(0.697695\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 12.6695i | − | 0.430776i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.59917i | 0.122234i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.6102 | −0.359925 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.4825 | −0.897326 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 11.0882i | − | 0.375279i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 3.12483i | − | 0.105639i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.7834 | 0.870644 | 0.435322 | − | 0.900275i | \(-0.356635\pi\) | ||||
0.435322 | + | 0.900275i | \(0.356635\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.8954 | 0.839700 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.85252i | 0.331940i | 0.986131 | + | 0.165970i | \(0.0530754\pi\) | ||||
−0.986131 | + | 0.165970i | \(0.946925\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 2.69581i | − | 0.0907212i | −0.998971 | − | 0.0453606i | \(-0.985556\pi\) | ||
0.998971 | − | 0.0453606i | \(-0.0144437\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 11.9962i | − | 0.403247i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.9520i | 0.502038i | 0.967982 | + | 0.251019i | \(0.0807656\pi\) | ||||
−0.967982 | + | 0.251019i | \(0.919234\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 66.5070i | − | 2.23057i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.96967 | −0.0659864 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.16722i | 0.306769i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.8164 | 0.662390 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.7428 | − | 5.57480i | −0.358693 | − | 0.186137i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 0.844422i | − | 0.0281631i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.6091 | 0.386755 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 39.2349i | 1.30566i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.00943 | −0.0667959 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.2046 | −0.438452 | −0.219226 | − | 0.975674i | \(-0.570353\pi\) | ||||
−0.219226 | + | 0.975674i | \(0.570353\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.64873 | −0.220524 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.55943 | 0.0516662 | 0.0258331 | − | 0.999666i | \(-0.491776\pi\) | ||||
0.0258331 | + | 0.999666i | \(0.491776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.0681 | −0.962015 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.62698i | 0.152963i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 43.5952i | − | 1.43964i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.46921 | 0.180413 | 0.0902063 | − | 0.995923i | \(-0.471247\pi\) | ||||
0.0902063 | + | 0.995923i | \(0.471247\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.7305 | 0.485386 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 38.3579i | 1.26257i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.26726i | 0.173187i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.583656 | −0.0191698 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.6885 | −0.350678 | −0.175339 | − | 0.984508i | \(-0.556102\pi\) | ||||
−0.175339 | + | 0.984508i | \(0.556102\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.7607 | −0.614857 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.02347 | −0.0662454 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.21040 | −0.235805 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.41143i | 0.144115i | 0.997400 | + | 0.0720576i | \(0.0229565\pi\) | ||||
−0.997400 | + | 0.0720576i | \(0.977043\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.6539 | −0.641381 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.3983i | 1.25175i | 0.779924 | + | 0.625875i | \(0.215258\pi\) | ||||
−0.779924 | + | 0.625875i | \(0.784742\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.9374 | − | 23.0038i | 0.388735 | − | 0.749107i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.12483 | 0.101651 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 21.6901i | − | 0.704832i | −0.935843 | − | 0.352416i | \(-0.885360\pi\) | ||
0.935843 | − | 0.352416i | \(-0.114640\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.8567 | −1.09904 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.0518500i | 0.00168135i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 21.7352i | − | 0.704072i | −0.935986 | − | 0.352036i | \(-0.885489\pi\) | ||
0.935986 | − | 0.352036i | \(-0.114511\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.8616i | 0.610346i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 4.40196i | − | 0.142295i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.25668i | 0.234330i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.8572 | 0.995395 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.04526 | −0.0659077 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 25.8785i | − | 0.833058i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.1981i | 1.51779i | 0.651215 | + | 0.758894i | \(0.274260\pi\) | ||||
−0.651215 | + | 0.758894i | \(0.725740\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.8419 | −0.798036 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.1263 | 0.357059 | 0.178529 | − | 0.983935i | \(-0.442866\pi\) | ||||
0.178529 | + | 0.983935i | \(0.442866\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48.2673i | 1.54738i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.52369i | 0.0808226i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 59.5577i | − | 1.90542i | −0.303883 | − | 0.952709i | \(-0.598283\pi\) | ||
0.303883 | − | 0.952709i | \(-0.401717\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 0.665814i | − | 0.0212795i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 15.7438i | − | 0.502661i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.3662 | 1.19180 | 0.595898 | − | 0.803060i | \(-0.296796\pi\) | ||||
0.595898 | + | 0.803060i | \(0.296796\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.3975i | 0.363155i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.22130 | 0.134366 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.7357 | − | 53.4478i | 0.881945 | − | 1.69954i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.0206000i | 0.000654379i | 1.00000 | 0.000327190i | \(0.000104148\pi\) | |||||
−1.00000 | 0.000327190i | \(0.999896\pi\) | ||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.22601 | 0.102374 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.1484i | 0.321724i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.0778 | −0.414179 | −0.207089 | − | 0.978322i | \(-0.566399\pi\) | ||||
−0.207089 | + | 0.978322i | \(0.566399\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.26726 | −0.166649 |
(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 | 5520.2.be.c.1471.6 | yes | 32 | |
4.3 | odd | 2 | 5520.2.be.d.1471.5 | yes | 32 | ||
23.22 | odd | 2 | 5520.2.be.d.1471.6 | yes | 32 | ||
92.91 | even | 2 | inner | 5520.2.be.c.1471.5 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5520.2.be.c.1471.5 | ✓ | 32 | 92.91 | even | 2 | inner | |
5520.2.be.c.1471.6 | yes | 32 | 1.1 | even | 1 | trivial | |
5520.2.be.d.1471.5 | yes | 32 | 4.3 | odd | 2 | ||
5520.2.be.d.1471.6 | yes | 32 | 23.22 | odd | 2 |