Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,3,Mod(55,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.55");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.d (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: | \(2.94278685509\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.207360000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.2 | ||
Root | \(0.437016 + 0.756934i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.55 |
Dual form | 108.3.d.d.55.1 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.85123 | + | 0.756934i | −0.925615 | + | 0.378467i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.85410 | − | 2.80252i | 0.713525 | − | 0.700629i | ||||
\(5\) | −1.08036 | −0.216073 | −0.108036 | − | 0.994147i | \(-0.534456\pi\) | ||||
−0.108036 | + | 0.994147i | \(0.534456\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 6.01392i | − | 0.859131i | −0.903036 | − | 0.429565i | \(-0.858667\pi\) | ||
0.903036 | − | 0.429565i | \(-0.141333\pi\) | |||||||
\(8\) | −3.16228 | + | 7.34847i | −0.395285 | + | 0.918559i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | − | 0.817763i | 0.200000 | − | 0.0817763i | ||||
\(11\) | − | 17.7247i | − | 1.61133i | −0.592369 | − | 0.805667i | \(-0.701807\pi\) | ||
0.592369 | − | 0.805667i | \(-0.298193\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.4164 | 0.955108 | 0.477554 | − | 0.878602i | \(-0.341523\pi\) | ||||
0.477554 | + | 0.878602i | \(0.341523\pi\) | |||||||
\(14\) | 4.55214 | + | 11.1331i | 0.325153 | + | 0.795224i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.291796 | − | 15.9973i | 0.0182373 | − | 0.999834i | ||||
\(17\) | 26.3786 | 1.55168 | 0.775841 | − | 0.630929i | \(-0.217326\pi\) | ||||
0.775841 | + | 0.630929i | \(0.217326\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.19615i | − | 0.273482i | −0.990607 | − | 0.136741i | \(-0.956337\pi\) | ||
0.990607 | − | 0.136741i | \(-0.0436628\pi\) | |||||||
\(20\) | −3.08347 | + | 3.02774i | −0.154173 | + | 0.151387i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 13.4164 | + | 32.8124i | 0.609837 | + | 1.49147i | ||||
\(23\) | − | 29.8356i | − | 1.29720i | −0.761129 | − | 0.648600i | \(-0.775355\pi\) | ||
0.761129 | − | 0.648600i | \(-0.224645\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −23.8328 | −0.953313 | ||||||||
\(26\) | −22.9856 | + | 9.39840i | −0.884062 | + | 0.361477i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −16.8541 | − | 17.1643i | −0.601932 | − | 0.613012i | ||||
\(29\) | −4.32145 | −0.149016 | −0.0745078 | − | 0.997220i | \(-0.523739\pi\) | ||||
−0.0745078 | + | 0.997220i | \(0.523739\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 44.8403i | 1.44646i | 0.690607 | + | 0.723230i | \(0.257343\pi\) | ||||
−0.690607 | + | 0.723230i | \(0.742657\pi\) | |||||||
\(32\) | 11.5687 | + | 29.8356i | 0.361523 | + | 0.932363i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −48.8328 | + | 19.9668i | −1.43626 | + | 0.587260i | ||||
\(35\) | 6.49721i | 0.185635i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −20.4164 | −0.551795 | −0.275897 | − | 0.961187i | \(-0.588975\pi\) | ||||
−0.275897 | + | 0.961187i | \(0.588975\pi\) | |||||||
\(38\) | 3.93314 | + | 9.61927i | 0.103504 | + | 0.253139i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.41641 | − | 7.93901i | 0.0854102 | − | 0.198475i | ||||
\(41\) | −59.2393 | −1.44486 | −0.722431 | − | 0.691443i | \(-0.756975\pi\) | ||||
−0.722431 | + | 0.691443i | \(0.756975\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 19.1491i | − | 0.445328i | −0.974895 | − | 0.222664i | \(-0.928525\pi\) | ||
0.974895 | − | 0.222664i | \(-0.0714752\pi\) | |||||||
\(44\) | −49.6737 | − | 50.5880i | −1.12895 | − | 1.14973i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 22.5836 | + | 55.2326i | 0.490948 | + | 1.20071i | ||||
\(47\) | 41.0631i | 0.873683i | 0.899539 | + | 0.436841i | \(0.143903\pi\) | ||||
−0.899539 | + | 0.436841i | \(0.856097\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.8328 | 0.261894 | ||||||||
\(50\) | 44.1200 | − | 18.0399i | 0.882400 | − | 0.360797i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 35.4377 | − | 34.7972i | 0.681494 | − | 0.669177i | ||||
\(53\) | 70.0430 | 1.32157 | 0.660783 | − | 0.750577i | \(-0.270224\pi\) | ||||
0.660783 | + | 0.750577i | \(0.270224\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.1491i | 0.348165i | ||||||||
\(56\) | 44.1931 | + | 19.0177i | 0.789162 | + | 0.339601i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.00000 | − | 3.27105i | 0.137931 | − | 0.0563975i | ||||
\(59\) | 28.9521i | 0.490714i | 0.969433 | + | 0.245357i | \(0.0789052\pi\) | ||||
−0.969433 | + | 0.245357i | \(0.921095\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18.4164 | 0.301908 | 0.150954 | − | 0.988541i | \(-0.451765\pi\) | ||||
0.150954 | + | 0.988541i | \(0.451765\pi\) | |||||||
\(62\) | −33.9411 | − | 83.0096i | −0.547438 | − | 1.33887i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −44.0000 | − | 46.4758i | −0.687500 | − | 0.726184i | ||||
\(65\) | −13.4142 | −0.206373 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 94.8767i | − | 1.41607i | −0.706177 | − | 0.708035i | \(-0.749582\pi\) | ||
0.706177 | − | 0.708035i | \(-0.250418\pi\) | |||||||
\(68\) | 75.2872 | − | 73.9264i | 1.10716 | − | 1.08715i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.91796 | − | 12.0278i | −0.0702566 | − | 0.171826i | ||||
\(71\) | 83.8931i | 1.18159i | 0.806821 | + | 0.590797i | \(0.201186\pi\) | ||||
−0.806821 | + | 0.590797i | \(0.798814\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 55.8328 | 0.764833 | 0.382417 | − | 0.923990i | \(-0.375092\pi\) | ||||
0.382417 | + | 0.923990i | \(0.375092\pi\) | |||||||
\(74\) | 37.7955 | − | 15.4539i | 0.510749 | − | 0.208836i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.5623 | − | 14.8303i | −0.191609 | − | 0.195136i | ||||
\(77\) | −106.595 | −1.38435 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 41.0410i | 0.519507i | 0.965675 | + | 0.259753i | \(0.0836413\pi\) | ||||
−0.965675 | + | 0.259753i | \(0.916359\pi\) | |||||||
\(80\) | −0.315246 | + | 17.2829i | −0.00394057 | + | 0.216037i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 109.666 | − | 44.8403i | 1.33739 | − | 0.546833i | ||||
\(83\) | 35.4493i | 0.427101i | 0.976932 | + | 0.213550i | \(0.0685027\pi\) | ||||
−0.976932 | + | 0.213550i | \(0.931497\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −28.4984 | −0.335276 | ||||||||
\(86\) | 14.4946 | + | 35.4493i | 0.168542 | + | 0.412202i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 130.249 | + | 56.0503i | 1.48010 | + | 0.636936i | ||||
\(89\) | 26.3786 | 0.296389 | 0.148194 | − | 0.988958i | \(-0.452654\pi\) | ||||
0.148194 | + | 0.988958i | \(0.452654\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 74.6712i | − | 0.820563i | ||||||
\(92\) | −83.6148 | − | 85.1539i | −0.908857 | − | 0.925586i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −31.0820 | − | 76.0172i | −0.330660 | − | 0.808693i | ||||
\(95\) | 5.61373i | 0.0590919i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 76.3313 | 0.786920 | 0.393460 | − | 0.919342i | \(-0.371278\pi\) | ||||
0.393460 | + | 0.919342i | \(0.371278\pi\) | |||||||
\(98\) | −23.7565 | + | 9.71359i | −0.242413 | + | 0.0991183i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −68.0213 | + | 66.7919i | −0.680213 | + | 0.667919i | ||||
\(101\) | −72.2037 | −0.714888 | −0.357444 | − | 0.933935i | \(-0.616352\pi\) | ||||
−0.357444 | + | 0.933935i | \(0.616352\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 57.9754i | 0.562868i | 0.959581 | + | 0.281434i | \(0.0908101\pi\) | ||||
−0.959581 | + | 0.281434i | \(0.909190\pi\) | |||||||
\(104\) | −39.2641 | + | 91.2416i | −0.377540 | + | 0.877323i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −129.666 | + | 53.0179i | −1.22326 | + | 0.500169i | ||||
\(107\) | 64.4015i | 0.601883i | 0.953643 | + | 0.300942i | \(0.0973009\pi\) | ||||
−0.953643 | + | 0.300942i | \(0.902699\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −43.1672 | −0.396029 | −0.198015 | − | 0.980199i | \(-0.563449\pi\) | ||||
−0.198015 | + | 0.980199i | \(0.563449\pi\) | |||||||
\(110\) | −14.4946 | − | 35.4493i | −0.131769 | − | 0.322267i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −96.2067 | − | 1.75484i | −0.858988 | − | 0.0156682i | ||||
\(113\) | 81.2965 | 0.719438 | 0.359719 | − | 0.933061i | \(-0.382873\pi\) | ||||
0.359719 | + | 0.933061i | \(0.382873\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 32.2333i | 0.280290i | ||||||||
\(116\) | −12.3339 | + | 12.1109i | −0.106326 | + | 0.104405i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −21.9149 | − | 53.5971i | −0.185719 | − | 0.454212i | ||||
\(119\) | − | 158.639i | − | 1.33310i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −193.164 | −1.59640 | ||||||||
\(122\) | −34.0930 | + | 13.9400i | −0.279451 | + | 0.114262i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 125.666 | + | 127.979i | 1.01343 | + | 1.03209i | ||||
\(125\) | 52.7572 | 0.422057 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 191.968i | 1.51156i | 0.654826 | + | 0.755780i | \(0.272742\pi\) | ||||
−0.654826 | + | 0.755780i | \(0.727258\pi\) | |||||||
\(128\) | 116.633 | + | 52.7323i | 0.911197 | + | 0.411971i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 24.8328 | − | 10.1537i | 0.191022 | − | 0.0781053i | ||||
\(131\) | − | 141.797i | − | 1.08242i | −0.840887 | − | 0.541211i | \(-0.817966\pi\) | ||
0.840887 | − | 0.541211i | \(-0.182034\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −31.2492 | −0.234957 | ||||||||
\(134\) | 71.8154 | + | 175.639i | 0.535936 | + | 1.31074i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −83.4164 | + | 193.842i | −0.613356 | + | 1.42531i | ||||
\(137\) | 87.7787 | 0.640720 | 0.320360 | − | 0.947296i | \(-0.396196\pi\) | ||||
0.320360 | + | 0.947296i | \(0.396196\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 183.501i | − | 1.32015i | −0.751200 | − | 0.660075i | \(-0.770524\pi\) | ||
0.751200 | − | 0.660075i | \(-0.229476\pi\) | |||||||
\(140\) | 18.2085 | + | 18.5437i | 0.130061 | + | 0.132455i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −63.5016 | − | 155.305i | −0.447194 | − | 1.09370i | ||||
\(143\) | − | 220.077i | − | 1.53900i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.66874 | 0.0321982 | ||||||||
\(146\) | −103.359 | + | 42.2618i | −0.707941 | + | 0.289464i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −58.2705 | + | 57.2173i | −0.393720 | + | 0.386604i | ||||
\(149\) | 153.950 | 1.03322 | 0.516611 | − | 0.856220i | \(-0.327193\pi\) | ||||
0.516611 | + | 0.856220i | \(0.327193\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 185.375i | 1.22765i | 0.789442 | + | 0.613825i | \(0.210370\pi\) | ||||
−0.789442 | + | 0.613825i | \(0.789630\pi\) | |||||||
\(152\) | 38.1838 | + | 16.4317i | 0.251209 | + | 0.108103i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 197.331 | − | 80.6851i | 1.28137 | − | 0.523930i | ||||
\(155\) | − | 48.4438i | − | 0.312540i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 196.164 | 1.24945 | 0.624726 | − | 0.780844i | \(-0.285211\pi\) | ||||
0.624726 | + | 0.780844i | \(0.285211\pi\) | |||||||
\(158\) | −31.0653 | − | 75.9764i | −0.196616 | − | 0.480863i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.4984 | − | 32.2333i | −0.0781153 | − | 0.201458i | ||||
\(161\) | −179.429 | −1.11447 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 129.325i | − | 0.793403i | −0.917948 | − | 0.396701i | \(-0.870155\pi\) | ||
0.917948 | − | 0.396701i | \(-0.129845\pi\) | |||||||
\(164\) | −169.075 | + | 166.019i | −1.03095 | + | 1.01231i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −26.8328 | − | 65.6249i | −0.161643 | − | 0.395331i | ||||
\(167\) | 137.951i | 0.826052i | 0.910719 | + | 0.413026i | \(0.135528\pi\) | ||||
−0.910719 | + | 0.413026i | \(0.864472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.8328 | −0.0877681 | ||||||||
\(170\) | 52.7572 | − | 21.5714i | 0.310336 | − | 0.126891i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −53.6656 | − | 54.6534i | −0.312009 | − | 0.317753i | ||||
\(173\) | 160.432 | 0.927354 | 0.463677 | − | 0.886004i | \(-0.346530\pi\) | ||||
0.463677 | + | 0.886004i | \(0.346530\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 143.329i | 0.819020i | ||||||||
\(176\) | −283.548 | − | 5.17199i | −1.61107 | − | 0.0293863i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −48.8328 | + | 19.9668i | −0.274342 | + | 0.112173i | ||||
\(179\) | − | 201.469i | − | 1.12552i | −0.826619 | − | 0.562762i | \(-0.809739\pi\) | ||
0.826619 | − | 0.562762i | \(-0.190261\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −48.2523 | −0.266587 | −0.133294 | − | 0.991077i | \(-0.542555\pi\) | ||||
−0.133294 | + | 0.991077i | \(0.542555\pi\) | |||||||
\(182\) | 56.5212 | + | 138.234i | 0.310556 | + | 0.759525i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 219.246 | + | 94.3485i | 1.19155 | + | 0.512764i | ||||
\(185\) | 22.0571 | 0.119228 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 467.552i | − | 2.50028i | ||||||
\(188\) | 115.080 | + | 117.198i | 0.612128 | + | 0.623395i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.24922 | − | 10.3923i | −0.0223643 | − | 0.0546963i | ||||
\(191\) | 147.411i | 0.771786i | 0.922544 | + | 0.385893i | \(0.126107\pi\) | ||||
−0.922544 | + | 0.385893i | \(0.873893\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.1641 | 0.130384 | 0.0651919 | − | 0.997873i | \(-0.479234\pi\) | ||||
0.0651919 | + | 0.997873i | \(0.479234\pi\) | |||||||
\(194\) | −141.307 | + | 57.7777i | −0.728385 | + | 0.297823i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 36.6262 | − | 35.9642i | 0.186868 | − | 0.183491i | ||||
\(197\) | −385.506 | −1.95688 | −0.978441 | − | 0.206528i | \(-0.933784\pi\) | ||||
−0.978441 | + | 0.206528i | \(0.933784\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 121.386i | − | 0.609978i | −0.952356 | − | 0.304989i | \(-0.901347\pi\) | ||
0.952356 | − | 0.304989i | \(-0.0986528\pi\) | |||||||
\(200\) | 75.3660 | − | 175.135i | 0.376830 | − | 0.875674i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 133.666 | − | 54.6534i | 0.661711 | − | 0.270562i | ||||
\(203\) | 25.9888i | 0.128024i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 64.0000 | 0.312195 | ||||||||
\(206\) | −43.8836 | − | 107.326i | −0.213027 | − | 0.520999i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.62306 | − | 198.629i | 0.0174186 | − | 0.954949i | ||||
\(209\) | −92.1001 | −0.440670 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 261.631i | 1.23996i | 0.784619 | + | 0.619978i | \(0.212859\pi\) | ||||
−0.784619 | + | 0.619978i | \(0.787141\pi\) | |||||||
\(212\) | 199.910 | − | 196.297i | 0.942971 | − | 0.925928i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −48.7477 | − | 119.222i | −0.227793 | − | 0.557112i | ||||
\(215\) | 20.6880i | 0.0962231i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 269.666 | 1.24270 | ||||||||
\(218\) | 79.9124 | − | 32.6747i | 0.366570 | − | 0.149884i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 53.6656 | + | 54.6534i | 0.243935 | + | 0.248425i | ||||
\(221\) | 327.527 | 1.48202 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 70.0542i | 0.314144i | 0.987587 | + | 0.157072i | \(0.0502056\pi\) | ||||
−0.987587 | + | 0.157072i | \(0.949794\pi\) | |||||||
\(224\) | 179.429 | − | 69.5735i | 0.801022 | − | 0.310596i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −150.498 | + | 61.5361i | −0.665922 | + | 0.272283i | ||||
\(227\) | 298.356i | 1.31434i | 0.753740 | + | 0.657172i | \(0.228248\pi\) | ||||
−0.753740 | + | 0.657172i | \(0.771752\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 259.666 | 1.13391 | 0.566956 | − | 0.823748i | \(-0.308121\pi\) | ||||
0.566956 | + | 0.823748i | \(0.308121\pi\) | |||||||
\(230\) | −24.3985 | − | 59.6712i | −0.106080 | − | 0.259440i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.6656 | − | 31.7561i | 0.0589036 | − | 0.136880i | ||||
\(233\) | −7.38192 | −0.0316821 | −0.0158410 | − | 0.999875i | \(-0.505043\pi\) | ||||
−0.0158410 | + | 0.999875i | \(0.505043\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 44.3630i | − | 0.188779i | ||||||
\(236\) | 81.1389 | + | 82.6323i | 0.343809 | + | 0.350137i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 120.079 | + | 293.676i | 0.504533 | + | 1.23393i | ||||
\(239\) | 82.1262i | 0.343624i | 0.985130 | + | 0.171812i | \(0.0549622\pi\) | ||||
−0.985130 | + | 0.171812i | \(0.945038\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −415.827 | −1.72542 | −0.862711 | − | 0.505698i | \(-0.831235\pi\) | ||||
−0.862711 | + | 0.505698i | \(0.831235\pi\) | |||||||
\(242\) | 357.591 | − | 146.212i | 1.47765 | − | 0.604184i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 52.5623 | − | 51.6123i | 0.215419 | − | 0.211526i | ||||
\(245\) | −13.8641 | −0.0565882 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 64.5175i | − | 0.261205i | ||||||
\(248\) | −329.507 | − | 141.797i | −1.32866 | − | 0.571764i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −97.6656 | + | 39.9337i | −0.390663 | + | 0.159735i | ||||
\(251\) | 140.030i | 0.557890i | 0.960307 | + | 0.278945i | \(0.0899847\pi\) | ||||
−0.960307 | + | 0.278945i | \(0.910015\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −528.827 | −2.09022 | ||||||||
\(254\) | −145.307 | − | 355.377i | −0.572075 | − | 1.39912i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −255.830 | − | 9.33592i | −0.999335 | − | 0.0364684i | ||||
\(257\) | 66.9825 | 0.260632 | 0.130316 | − | 0.991472i | \(-0.458401\pi\) | ||||
0.130316 | + | 0.991472i | \(0.458401\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 122.783i | 0.474064i | ||||||||
\(260\) | −38.2856 | + | 37.5936i | −0.147252 | + | 0.144591i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 107.331 | + | 262.500i | 0.409661 | + | 1.00191i | ||||
\(263\) | − | 37.2163i | − | 0.141507i | −0.997494 | − | 0.0707534i | \(-0.977460\pi\) | ||
0.997494 | − | 0.0707534i | \(-0.0225404\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −75.6718 | −0.285554 | ||||||||
\(266\) | 57.8495 | − | 23.6536i | 0.217479 | − | 0.0889233i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −265.894 | − | 270.788i | −0.992140 | − | 1.01040i | ||||
\(269\) | −279.092 | −1.03752 | −0.518758 | − | 0.854921i | \(-0.673605\pi\) | ||||
−0.518758 | + | 0.854921i | \(0.673605\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 406.305i | 1.49928i | 0.661845 | + | 0.749641i | \(0.269774\pi\) | ||||
−0.661845 | + | 0.749641i | \(0.730226\pi\) | |||||||
\(272\) | 7.69717 | − | 421.987i | 0.0282984 | − | 1.55142i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −162.498 | + | 66.4426i | −0.593060 | + | 0.242491i | ||||
\(275\) | 422.429i | 1.53611i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.83282 | 0.0174470 | 0.00872349 | − | 0.999962i | \(-0.497223\pi\) | ||||
0.00872349 | + | 0.999962i | \(0.497223\pi\) | |||||||
\(278\) | 138.898 | + | 339.702i | 0.499633 | + | 1.22195i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −47.7446 | − | 20.5460i | −0.170516 | − | 0.0733785i | ||||
\(281\) | −4.32145 | −0.0153788 | −0.00768942 | − | 0.999970i | \(-0.502448\pi\) | ||||
−0.00768942 | + | 0.999970i | \(0.502448\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 44.3630i | − | 0.156760i | −0.996924 | − | 0.0783799i | \(-0.975025\pi\) | ||
0.996924 | − | 0.0783799i | \(-0.0249747\pi\) | |||||||
\(284\) | 235.112 | + | 239.440i | 0.827859 | + | 0.843097i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 166.584 | + | 407.413i | 0.582460 | + | 1.42452i | ||||
\(287\) | 356.260i | 1.24133i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 406.830 | 1.40772 | ||||||||
\(290\) | −8.64290 | + | 3.53393i | −0.0298031 | + | 0.0121860i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 159.353 | − | 156.472i | 0.545728 | − | 0.535864i | ||||
\(293\) | −388.927 | −1.32740 | −0.663699 | − | 0.748000i | \(-0.731014\pi\) | ||||
−0.663699 | + | 0.748000i | \(0.731014\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 31.2788i | − | 0.106030i | ||||||
\(296\) | 64.5624 | − | 150.029i | 0.218116 | − | 0.506856i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −284.997 | + | 116.530i | −0.956365 | + | 0.391040i | ||||
\(299\) | − | 370.451i | − | 1.23897i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −115.161 | −0.382595 | ||||||||
\(302\) | −140.317 | − | 343.172i | −0.464625 | − | 1.13633i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −83.1246 | − | 1.51622i | −0.273436 | − | 0.00498756i | ||||
\(305\) | −19.8964 | −0.0652341 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 96.6999i | − | 0.314983i | −0.987520 | − | 0.157492i | \(-0.949659\pi\) | ||
0.987520 | − | 0.157492i | \(-0.0503407\pi\) | |||||||
\(308\) | −304.232 | + | 298.733i | −0.987767 | + | 0.969914i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 36.6687 | + | 89.6805i | 0.118286 | + | 0.289292i | ||||
\(311\) | − | 136.184i | − | 0.437890i | −0.975737 | − | 0.218945i | \(-0.929739\pi\) | ||
0.975737 | − | 0.218945i | \(-0.0702615\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 282.161 | 0.901473 | 0.450736 | − | 0.892657i | \(-0.351161\pi\) | ||||
0.450736 | + | 0.892657i | \(0.351161\pi\) | |||||||
\(314\) | −363.145 | + | 148.483i | −1.15651 | + | 0.472877i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 115.018 | + | 117.135i | 0.363982 | + | 0.370681i | ||||
\(317\) | −275.489 | −0.869051 | −0.434526 | − | 0.900659i | \(-0.643084\pi\) | ||||
−0.434526 | + | 0.900659i | \(0.643084\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 76.5963i | 0.240114i | ||||||||
\(320\) | 47.5360 | + | 50.2107i | 0.148550 | + | 0.156909i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 332.164 | − | 135.816i | 1.03157 | − | 0.421788i | ||||
\(323\) | − | 137.067i | − | 0.424356i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −295.918 | −0.910517 | ||||||||
\(326\) | 97.8902 | + | 239.410i | 0.300277 | + | 0.734385i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 187.331 | − | 435.319i | 0.571132 | − | 1.32719i | ||||
\(329\) | 246.950 | 0.750608 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 55.5221i | − | 0.167741i | −0.996477 | − | 0.0838703i | \(-0.973272\pi\) | ||
0.996477 | − | 0.0838703i | \(-0.0267281\pi\) | |||||||
\(332\) | 99.3474 | + | 101.176i | 0.299239 | + | 0.304747i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −104.420 | − | 255.378i | −0.312633 | − | 0.764606i | ||||
\(335\) | 102.501i | 0.305974i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −430.659 | −1.27792 | −0.638961 | − | 0.769239i | \(-0.720635\pi\) | ||||
−0.638961 | + | 0.769239i | \(0.720635\pi\) | |||||||
\(338\) | 27.4589 | − | 11.2275i | 0.0812395 | − | 0.0332173i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −81.3375 | + | 79.8674i | −0.239228 | + | 0.234904i | ||||
\(341\) | 794.779 | 2.33073 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 371.857i | − | 1.08413i | ||||||
\(344\) | 140.716 | + | 60.5547i | 0.409059 | + | 0.176031i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −296.997 | + | 121.437i | −0.858373 | + | 0.350973i | ||||
\(347\) | − | 135.871i | − | 0.391559i | −0.980648 | − | 0.195779i | \(-0.937276\pi\) | ||
0.980648 | − | 0.195779i | \(-0.0627236\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 288.082 | 0.825450 | 0.412725 | − | 0.910856i | \(-0.364577\pi\) | ||||
0.412725 | + | 0.910856i | \(0.364577\pi\) | |||||||
\(350\) | −108.490 | − | 265.334i | −0.309972 | − | 0.758097i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 528.827 | − | 205.052i | 1.50235 | − | 0.582535i | ||||
\(353\) | 198.964 | 0.563638 | 0.281819 | − | 0.959468i | \(-0.409062\pi\) | ||||
0.281819 | + | 0.959468i | \(0.409062\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 90.6350i | − | 0.255310i | ||||||
\(356\) | 75.2872 | − | 73.9264i | 0.211481 | − | 0.207659i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 152.498 | + | 372.965i | 0.425973 | + | 1.04180i | ||||
\(359\) | − | 324.658i | − | 0.904339i | −0.891932 | − | 0.452170i | \(-0.850650\pi\) | ||
0.891932 | − | 0.452170i | \(-0.149350\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 334.000 | 0.925208 | ||||||||
\(362\) | 89.3261 | − | 36.5238i | 0.246757 | − | 0.100895i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −209.267 | − | 213.119i | −0.574910 | − | 0.585493i | ||||
\(365\) | −60.3197 | −0.165259 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 176.141i | 0.479948i | 0.970779 | + | 0.239974i | \(0.0771390\pi\) | ||||
−0.970779 | + | 0.239974i | \(0.922861\pi\) | |||||||
\(368\) | −477.290 | − | 8.70592i | −1.29699 | − | 0.0236574i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −40.8328 | + | 16.6958i | −0.110359 | + | 0.0451238i | ||||
\(371\) | − | 421.233i | − | 1.13540i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 596.580 | 1.59941 | 0.799706 | − | 0.600392i | \(-0.204989\pi\) | ||||
0.799706 | + | 0.600392i | \(0.204989\pi\) | |||||||
\(374\) | 353.906 | + | 865.546i | 0.946272 | + | 2.31429i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −301.751 | − | 129.853i | −0.802529 | − | 0.345353i | ||||
\(377\) | −53.6569 | −0.142326 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.3082i | 0.0799689i | 0.999200 | + | 0.0399844i | \(0.0127308\pi\) | ||||
−0.999200 | + | 0.0399844i | \(0.987269\pi\) | |||||||
\(380\) | 15.7326 | + | 16.0222i | 0.0414015 | + | 0.0421636i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −111.580 | − | 272.892i | −0.292096 | − | 0.714377i | ||||
\(383\) | − | 707.220i | − | 1.84653i | −0.384167 | − | 0.923264i | \(-0.625511\pi\) | ||
0.384167 | − | 0.923264i | \(-0.374489\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 115.161 | 0.299119 | ||||||||
\(386\) | −46.5845 | + | 19.0475i | −0.120685 | + | 0.0493460i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 217.857 | − | 213.920i | 0.561488 | − | 0.551339i | ||||
\(389\) | 577.088 | 1.48352 | 0.741758 | − | 0.670668i | \(-0.233992\pi\) | ||||
0.741758 | + | 0.670668i | \(0.233992\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 787.021i | − | 2.01284i | ||||||
\(392\) | −40.5809 | + | 94.3016i | −0.103523 | + | 0.240565i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 713.659 | − | 291.802i | 1.81132 | − | 0.740615i | ||||
\(395\) | − | 44.3392i | − | 0.112251i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.8266 | 0.0675733 | 0.0337867 | − | 0.999429i | \(-0.489243\pi\) | ||||
0.0337867 | + | 0.999429i | \(0.489243\pi\) | |||||||
\(398\) | 91.8809 | + | 224.713i | 0.230857 | + | 0.564605i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.95432 | + | 381.262i | −0.0173858 | + | 0.953154i | ||||
\(401\) | −505.065 | −1.25951 | −0.629756 | − | 0.776793i | \(-0.716845\pi\) | ||||
−0.629756 | + | 0.776793i | \(0.716845\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 556.755i | 1.38153i | ||||||||
\(404\) | −206.077 | + | 202.352i | −0.510091 | + | 0.500872i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −19.6718 | − | 48.1113i | −0.0484528 | − | 0.118501i | ||||
\(407\) | 361.874i | 0.889126i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −683.328 | −1.67073 | −0.835364 | − | 0.549696i | \(-0.814743\pi\) | ||||
−0.835364 | + | 0.549696i | \(0.814743\pi\) | |||||||
\(410\) | −118.479 | + | 48.4438i | −0.288972 | + | 0.118156i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 162.477 | + | 165.468i | 0.394362 | + | 0.401621i | ||||
\(413\) | 174.116 | 0.421588 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 38.2982i | − | 0.0922847i | ||||||
\(416\) | 143.642 | + | 370.451i | 0.345294 | + | 0.890508i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 170.498 | − | 69.7137i | 0.407891 | − | 0.166779i | ||||
\(419\) | − | 306.620i | − | 0.731791i | −0.930656 | − | 0.365895i | \(-0.880763\pi\) | ||
0.930656 | − | 0.365895i | \(-0.119237\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.5867 | −0.0441489 | −0.0220745 | − | 0.999756i | \(-0.507027\pi\) | ||||
−0.0220745 | + | 0.999756i | \(0.507027\pi\) | |||||||
\(422\) | −198.037 | − | 484.339i | −0.469283 | − | 1.14772i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −221.495 | + | 514.709i | −0.522395 | + | 1.21394i | ||||
\(425\) | −628.676 | −1.47924 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 110.755i | − | 0.259379i | ||||||
\(428\) | 180.486 | + | 183.808i | 0.421697 | + | 0.429459i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15.6594 | − | 38.2982i | −0.0364173 | − | 0.0890655i | ||||
\(431\) | − | 308.130i | − | 0.714918i | −0.933929 | − | 0.357459i | \(-0.883643\pi\) | ||
0.933929 | − | 0.357459i | \(-0.116357\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 174.839 | 0.403785 | 0.201893 | − | 0.979408i | \(-0.435291\pi\) | ||||
0.201893 | + | 0.979408i | \(0.435291\pi\) | |||||||
\(434\) | −499.213 | + | 204.119i | −1.15026 | + | 0.470320i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −123.204 | + | 120.977i | −0.282577 | + | 0.277470i | ||||
\(437\) | −155.030 | −0.354761 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 480.159i | − | 1.09376i | −0.837212 | − | 0.546878i | \(-0.815816\pi\) | ||
0.837212 | − | 0.546878i | \(-0.184184\pi\) | |||||||
\(440\) | −140.716 | − | 60.5547i | −0.319810 | − | 0.137624i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −606.328 | + | 247.917i | −1.37178 | + | 0.560897i | ||||
\(443\) | 555.962i | 1.25499i | 0.778619 | + | 0.627497i | \(0.215920\pi\) | ||||
−0.778619 | + | 0.627497i | \(0.784080\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.4984 | −0.0640415 | ||||||||
\(446\) | −53.0264 | − | 129.686i | −0.118893 | − | 0.290777i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −279.502 | + | 264.612i | −0.623887 | + | 0.590652i | ||||
\(449\) | 801.711 | 1.78555 | 0.892774 | − | 0.450504i | \(-0.148756\pi\) | ||||
0.892774 | + | 0.450504i | \(0.148756\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1050.00i | 2.32816i | ||||||||
\(452\) | 232.028 | − | 227.835i | 0.513337 | − | 0.504059i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −225.836 | − | 552.326i | −0.497436 | − | 1.21658i | ||||
\(455\) | 80.6720i | 0.177301i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −137.830 | −0.301597 | −0.150798 | − | 0.988565i | \(-0.548184\pi\) | ||||
−0.150798 | + | 0.988565i | \(0.548184\pi\) | |||||||
\(458\) | −480.701 | + | 196.550i | −1.04956 | + | 0.429148i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 90.3344 | + | 91.9971i | 0.196379 | + | 0.199994i | ||||
\(461\) | −188.341 | −0.408549 | −0.204274 | − | 0.978914i | \(-0.565483\pi\) | ||||
−0.204274 | + | 0.978914i | \(0.565483\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 548.425i | 1.18450i | 0.805753 | + | 0.592251i | \(0.201761\pi\) | ||||
−0.805753 | + | 0.592251i | \(0.798239\pi\) | |||||||
\(464\) | −1.26098 | + | 69.1317i | −0.00271764 | + | 0.148991i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.6656 | − | 5.58763i | 0.0293254 | − | 0.0119906i | ||||
\(467\) | 618.597i | 1.32462i | 0.749231 | + | 0.662309i | \(0.230423\pi\) | ||||
−0.749231 | + | 0.662309i | \(0.769577\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −570.580 | −1.21659 | ||||||||
\(470\) | 33.5799 | + | 82.1262i | 0.0714466 | + | 0.174737i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −212.754 | − | 91.5547i | −0.450750 | − | 0.193972i | ||||
\(473\) | −339.411 | −0.717571 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 123.839i | 0.260714i | ||||||||
\(476\) | −444.587 | − | 452.771i | −0.934007 | − | 0.951199i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −62.1641 | − | 152.034i | −0.130050 | − | 0.318064i | ||||
\(479\) | − | 770.425i | − | 1.60840i | −0.594357 | − | 0.804202i | \(-0.702593\pi\) | ||
0.594357 | − | 0.804202i | \(-0.297407\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −253.498 | −0.527024 | ||||||||
\(482\) | 769.791 | − | 314.753i | 1.59708 | − | 0.653015i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −551.310 | + | 541.346i | −1.13907 | + | 1.11848i | ||||
\(485\) | −82.4655 | −0.170032 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 549.208i | − | 1.12774i | −0.825865 | − | 0.563868i | \(-0.809313\pi\) | ||
0.825865 | − | 0.563868i | \(-0.190687\pi\) | |||||||
\(488\) | −58.2378 | + | 135.332i | −0.119340 | + | 0.277321i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 25.6656 | − | 10.4942i | 0.0523788 | − | 0.0214168i | ||||
\(491\) | 23.0256i | 0.0468952i | 0.999725 | + | 0.0234476i | \(0.00746429\pi\) | ||||
−0.999725 | + | 0.0234476i | \(0.992536\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −113.994 | −0.231225 | ||||||||
\(494\) | 48.8355 | + | 119.437i | 0.0988573 | + | 0.241775i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 717.325 | + | 13.0842i | 1.44622 | + | 0.0263795i | ||||
\(497\) | 504.526 | 1.01514 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 626.809i | 1.25613i | 0.778160 | + | 0.628065i | \(0.216153\pi\) | ||||
−0.778160 | + | 0.628065i | \(0.783847\pi\) | |||||||
\(500\) | 150.574 | − | 147.853i | 0.301149 | − | 0.295706i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −105.994 | − | 259.228i | −0.211143 | − | 0.516391i | ||||
\(503\) | 732.896i | 1.45705i | 0.685019 | + | 0.728525i | \(0.259794\pi\) | ||||
−0.685019 | + | 0.728525i | \(0.740206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 78.0062 | 0.154468 | ||||||||
\(506\) | 978.979 | − | 400.287i | 1.93474 | − | 0.791081i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 537.994 | + | 547.896i | 1.05904 | + | 1.07854i | ||||
\(509\) | −437.363 | −0.859259 | −0.429630 | − | 0.903005i | \(-0.641356\pi\) | ||||
−0.429630 | + | 0.903005i | \(0.641356\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 335.774i | − | 0.657092i | ||||||
\(512\) | 480.666 | − | 176.363i | 0.938801 | − | 0.344459i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −124.000 | + | 50.7013i | −0.241245 | + | 0.0986407i | ||||
\(515\) | − | 62.6345i | − | 0.121620i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 727.830 | 1.40779 | ||||||||
\(518\) | −92.9383 | − | 227.299i | −0.179418 | − | 0.438801i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 42.4195 | − | 98.5740i | 0.0815760 | − | 0.189565i | ||||
\(521\) | 385.236 | 0.739417 | 0.369709 | − | 0.929148i | \(-0.379458\pi\) | ||||
0.369709 | + | 0.929148i | \(0.379458\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 418.572i | − | 0.800328i | −0.916443 | − | 0.400164i | \(-0.868953\pi\) | ||
0.916443 | − | 0.400164i | \(-0.131047\pi\) | |||||||
\(524\) | −397.390 | − | 404.704i | −0.758377 | − | 0.772336i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.1703 | + | 68.8959i | 0.0535557 | + | 0.130981i | ||||
\(527\) | 1182.82i | 2.24445i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −361.164 | −0.682730 | ||||||||
\(530\) | 140.086 | − | 57.2786i | 0.264313 | − | 0.108073i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −89.1885 | + | 87.5765i | −0.167648 | + | 0.164617i | ||||
\(533\) | −735.540 | −1.38000 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 69.5770i | − | 0.130050i | ||||||
\(536\) | 697.199 | + | 300.026i | 1.30074 | + | 0.559751i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 516.663 | − | 211.254i | 0.960339 | − | 0.392665i | ||||
\(539\) | − | 227.457i | − | 0.421999i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.4257 | −0.0433008 | −0.0216504 | − | 0.999766i | \(-0.506892\pi\) | ||||
−0.0216504 | + | 0.999766i | \(0.506892\pi\) | |||||||
\(542\) | −307.546 | − | 752.164i | −0.567429 | − | 1.38776i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 305.167 | + | 787.021i | 0.560969 | + | 1.44673i | ||||
\(545\) | 46.6362 | 0.0855711 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 722.163i | 1.32023i | 0.751167 | + | 0.660113i | \(0.229491\pi\) | ||||
−0.751167 | + | 0.660113i | \(0.770509\pi\) | |||||||
\(548\) | 250.529 | − | 246.001i | 0.457170 | − | 0.448907i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −319.751 | − | 782.013i | −0.581365 | − | 1.42184i | ||||
\(551\) | 22.4549i | 0.0407530i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 246.817 | 0.446324 | ||||||||
\(554\) | −8.94665 | + | 3.65812i | −0.0161492 | + | 0.00660311i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −514.264 | − | 523.730i | −0.924936 | − | 0.941961i | ||||
\(557\) | 2.34135 | 0.00420349 | 0.00210175 | − | 0.999998i | \(-0.499331\pi\) | ||||
0.00210175 | + | 0.999998i | \(0.499331\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 237.763i | − | 0.425336i | ||||||
\(560\) | 103.938 | + | 1.89586i | 0.185604 | + | 0.00338547i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.00000 | − | 3.27105i | 0.0142349 | − | 0.00582038i | ||||
\(563\) | − | 359.794i | − | 0.639066i | −0.947575 | − | 0.319533i | \(-0.896474\pi\) | ||
0.947575 | − | 0.319533i | \(-0.103526\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −87.8297 | −0.155451 | ||||||||
\(566\) | 33.5799 | + | 82.1262i | 0.0593284 | + | 0.145099i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −616.486 | − | 265.293i | −1.08536 | − | 0.467066i | ||||
\(569\) | −18.6354 | −0.0327512 | −0.0163756 | − | 0.999866i | \(-0.505213\pi\) | ||||
−0.0163756 | + | 0.999866i | \(0.505213\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 284.528i | − | 0.498298i | −0.968465 | − | 0.249149i | \(-0.919849\pi\) | ||
0.968465 | − | 0.249149i | \(-0.0801509\pi\) | |||||||
\(572\) | −616.769 | − | 628.122i | −1.07827 | − | 1.09811i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −269.666 | − | 659.520i | −0.469801 | − | 1.14899i | ||||
\(575\) | 711.067i | 1.23664i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 664.823 | 1.15221 | 0.576104 | − | 0.817377i | \(-0.304572\pi\) | ||||
0.576104 | + | 0.817377i | \(0.304572\pi\) | |||||||
\(578\) | −753.135 | + | 307.943i | −1.30300 | + | 0.532774i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.3251 | − | 13.0842i | 0.0229742 | − | 0.0225590i | ||||
\(581\) | 213.189 | 0.366935 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1241.49i | − | 2.12948i | ||||||
\(584\) | −176.559 | + | 410.286i | −0.302327 | + | 0.702544i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 719.994 | − | 294.392i | 1.22866 | − | 0.502376i | ||||
\(587\) | 754.467i | 1.28529i | 0.766162 | + | 0.642647i | \(0.222164\pi\) | ||||
−0.766162 | + | 0.642647i | \(0.777836\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 232.997 | 0.395580 | ||||||||
\(590\) | 23.6760 | + | 57.9043i | 0.0401288 | + | 0.0981428i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.95743 | + | 326.608i | −0.0100632 | + | 0.551703i | ||||
\(593\) | −550.801 | −0.928838 | −0.464419 | − | 0.885615i | \(-0.653737\pi\) | ||||
−0.464419 | + | 0.885615i | \(0.653737\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 171.387i | 0.288046i | ||||||||
\(596\) | 439.389 | − | 431.448i | 0.737230 | − | 0.723905i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 280.407 | + | 685.790i | 0.468908 | + | 1.14681i | ||||
\(599\) | 25.9888i | 0.0433871i | 0.999765 | + | 0.0216935i | \(0.00690581\pi\) | ||||
−0.999765 | + | 0.0216935i | \(0.993094\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 186.170 | 0.309768 | 0.154884 | − | 0.987933i | \(-0.450500\pi\) | ||||
0.154884 | + | 0.987933i | \(0.450500\pi\) | |||||||
\(602\) | 213.189 | − | 87.1693i | 0.354135 | − | 0.144799i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 519.517 | + | 529.079i | 0.860127 | + | 0.875959i | ||||
\(605\) | 208.687 | 0.344938 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 99.5447i | 0.163994i | 0.996633 | + | 0.0819972i | \(0.0261299\pi\) | ||||
−0.996633 | + | 0.0819972i | \(0.973870\pi\) | |||||||
\(608\) | 155.030 | − | 60.1130i | 0.254984 | − | 0.0988700i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 36.8328 | − | 15.0603i | 0.0603817 | − | 0.0246890i | ||||
\(611\) | 509.856i | 0.834461i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −960.234 | −1.56645 | −0.783225 | − | 0.621739i | \(-0.786427\pi\) | ||||
−0.783225 | + | 0.621739i | \(0.786427\pi\) | |||||||
\(614\) | 73.1954 | + | 179.014i | 0.119211 | + | 0.291553i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 337.082 | − | 783.308i | 0.547211 | − | 1.27160i | ||||
\(617\) | −354.625 | −0.574757 | −0.287378 | − | 0.957817i | \(-0.592784\pi\) | ||||
−0.287378 | + | 0.957817i | \(0.592784\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 360.647i | − | 0.582629i | −0.956627 | − | 0.291314i | \(-0.905907\pi\) | ||
0.956627 | − | 0.291314i | \(-0.0940926\pi\) | |||||||
\(620\) | −135.765 | − | 138.263i | −0.218975 | − | 0.223006i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 103.082 | + | 252.107i | 0.165727 | + | 0.405317i | ||||
\(623\) | − | 158.639i | − | 0.254637i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 538.823 | 0.862118 | ||||||||
\(626\) | −522.345 | + | 213.577i | −0.834417 | + | 0.341178i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 559.872 | − | 549.753i | 0.891516 | − | 0.875403i | ||||
\(629\) | −538.556 | −0.856210 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 82.7121i | − | 0.131081i | −0.997850 | − | 0.0655405i | \(-0.979123\pi\) | ||
0.997850 | − | 0.0655405i | \(-0.0208772\pi\) | |||||||
\(632\) | −301.589 | − | 129.783i | −0.477197 | − | 0.205353i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 509.994 | − | 208.527i | 0.804407 | − | 0.328907i | ||||
\(635\) | − | 207.395i | − | 0.326607i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 159.337 | 0.250137 | ||||||||
\(638\) | −57.9784 | − | 141.797i | −0.0908752 | − | 0.222253i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −126.006 | − | 56.9700i | −0.196885 | − | 0.0890156i | ||||
\(641\) | −760.569 | −1.18653 | −0.593267 | − | 0.805005i | \(-0.702162\pi\) | ||||
−0.593267 | + | 0.805005i | \(0.702162\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 787.021i | 1.22398i | 0.790864 | + | 0.611992i | \(0.209631\pi\) | ||||
−0.790864 | + | 0.611992i | \(0.790369\pi\) | |||||||
\(644\) | −512.108 | + | 502.853i | −0.795199 | + | 0.780827i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 103.751 | + | 253.743i | 0.160605 | + | 0.392791i | ||||
\(647\) | − | 978.962i | − | 1.51308i | −0.653948 | − | 0.756539i | \(-0.726889\pi\) | ||
0.653948 | − | 0.756539i | \(-0.273111\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 513.167 | 0.790704 | ||||||||
\(650\) | 547.812 | − | 223.990i | 0.842788 | − | 0.344601i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −362.435 | − | 369.106i | −0.555881 | − | 0.566113i | ||||
\(653\) | 939.548 | 1.43882 | 0.719409 | − | 0.694587i | \(-0.244413\pi\) | ||||
0.719409 | + | 0.694587i | \(0.244413\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 153.193i | 0.233882i | ||||||||
\(656\) | −17.2858 | + | 947.672i | −0.0263503 | + | 1.44462i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −457.161 | + | 186.925i | −0.694774 | + | 0.284080i | ||||
\(659\) | − | 149.491i | − | 0.226845i | −0.993547 | − | 0.113423i | \(-0.963819\pi\) | ||
0.993547 | − | 0.113423i | \(-0.0361814\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 337.420 | 0.510468 | 0.255234 | − | 0.966879i | \(-0.417847\pi\) | ||||
0.255234 | + | 0.966879i | \(0.417847\pi\) | |||||||
\(662\) | 42.0266 | + | 102.784i | 0.0634843 | + | 0.155263i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −260.498 | − | 112.101i | −0.392317 | − | 0.168826i | ||||
\(665\) | 33.7605 | 0.0507677 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 128.933i | 0.193303i | ||||||||
\(668\) | 386.609 | + | 393.725i | 0.578756 | + | 0.589409i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −77.5867 | − | 189.753i | −0.115801 | − | 0.283214i | ||||
\(671\) | − | 326.425i | − | 0.486475i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −321.341 | −0.477475 | −0.238737 | − | 0.971084i | \(-0.576734\pi\) | ||||
−0.238737 | + | 0.971084i | \(0.576734\pi\) | |||||||
\(674\) | 797.249 | − | 325.981i | 1.18286 | − | 0.483651i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −42.3344 | + | 41.5692i | −0.0626248 | + | 0.0614929i | ||||
\(677\) | 741.841 | 1.09578 | 0.547889 | − | 0.836551i | \(-0.315432\pi\) | ||||
0.547889 | + | 0.836551i | \(0.315432\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 459.050i | − | 0.676067i | ||||||
\(680\) | 90.1200 | − | 209.420i | 0.132529 | − | 0.307971i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1471.32 | + | 601.595i | −2.15736 | + | 0.882105i | ||||
\(683\) | − | 1259.02i | − | 1.84337i | −0.387938 | − | 0.921686i | \(-0.626812\pi\) | ||
0.387938 | − | 0.921686i | \(-0.373188\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −94.8328 | −0.138442 | ||||||||
\(686\) | 281.471 | + | 688.393i | 0.410308 | + | 1.00349i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −306.334 | − | 5.58763i | −0.445253 | − | 0.00812155i | ||||
\(689\) | 869.682 | 1.26224 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 222.770i | 0.322387i | 0.986923 | + | 0.161194i | \(0.0515344\pi\) | ||||
−0.986923 | + | 0.161194i | \(0.948466\pi\) | |||||||
\(692\) | 457.890 | − | 449.614i | 0.661691 | − | 0.649731i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 102.845 | + | 251.528i | 0.148192 | + | 0.362432i | ||||
\(695\) | 198.248i | 0.285248i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1562.65 | −2.24197 | ||||||||
\(698\) | −533.306 | + | 218.059i | −0.764049 | + | 0.312406i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 401.681 | + | 409.074i | 0.573830 | + | 0.584392i | ||||
\(701\) | 2.34135 | 0.00334001 | 0.00167000 | − | 0.999999i | \(-0.499468\pi\) | ||||
0.00167000 | + | 0.999999i | \(0.499468\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 106.087i | 0.150906i | ||||||||
\(704\) | −823.768 | + | 779.886i | −1.17013 | + | 1.10779i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −368.328 | + | 150.603i | −0.521711 | + | 0.213318i | ||||
\(707\) | 434.227i | 0.614182i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −495.085 | −0.698287 | −0.349143 | − | 0.937069i | \(-0.613527\pi\) | ||||
−0.349143 | + | 0.937069i | \(0.613527\pi\) | |||||||
\(710\) | 68.6047 | + | 167.786i | 0.0966264 | + | 0.236319i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −83.4164 | + | 193.842i | −0.117158 | + | 0.272250i | ||||
\(713\) | 1337.84 | 1.87635 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 237.763i | 0.332535i | ||||||||
\(716\) | −564.619 | − | 575.012i | −0.788574 | − | 0.803089i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 245.745 | + | 601.016i | 0.342263 | + | 0.837070i | ||||
\(719\) | − | 962.433i | − | 1.33857i | −0.743005 | − | 0.669286i | \(-0.766600\pi\) | ||
0.743005 | − | 0.669286i | \(-0.233400\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 348.659 | 0.483578 | ||||||||
\(722\) | −618.311 | + | 252.816i | −0.856386 | + | 0.350161i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −137.717 | + | 135.228i | −0.190217 | + | 0.186779i | ||||
\(725\) | 102.992 | 0.142058 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 544.625i | 0.749141i | 0.927198 | + | 0.374570i | \(0.122210\pi\) | ||||
−0.927198 | + | 0.374570i | \(0.877790\pi\) | |||||||
\(728\) | 548.719 | + | 236.131i | 0.753735 | + | 0.324356i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 111.666 | − | 45.6580i | 0.152967 | − | 0.0625453i | ||||
\(731\) | − | 505.126i | − | 0.691006i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −146.170 | −0.199414 | −0.0997069 | − | 0.995017i | \(-0.531791\pi\) | ||||
−0.0997069 | + | 0.995017i | \(0.531791\pi\) | |||||||
\(734\) | −133.327 | − | 326.077i | −0.181645 | − | 0.444247i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 890.164 | − | 345.161i | 1.20946 | − | 0.468968i | ||||
\(737\) | −1681.66 | −2.28176 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1172.87i | 1.58710i | 0.608505 | + | 0.793550i | \(0.291769\pi\) | ||||
−0.608505 | + | 0.793550i | \(0.708231\pi\) | |||||||
\(740\) | 62.9533 | − | 61.8155i | 0.0850720 | − | 0.0835344i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 318.845 | + | 779.798i | 0.429711 | + | 1.05094i | ||||
\(743\) | − | 494.837i | − | 0.665998i | −0.942927 | − | 0.332999i | \(-0.891939\pi\) | ||
0.942927 | − | 0.332999i | \(-0.108061\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −166.322 | −0.223251 | ||||||||
\(746\) | −1104.41 | + | 451.572i | −1.48044 | + | 0.605324i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1310.32 | − | 1334.44i | −1.75177 | − | 1.78401i | ||||
\(749\) | 387.305 | 0.517096 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 927.250i | − | 1.23469i | −0.786693 | − | 0.617344i | \(-0.788209\pi\) | ||
0.786693 | − | 0.617344i | \(-0.211791\pi\) | |||||||
\(752\) | 656.900 | + | 11.9820i | 0.873537 | + | 0.0159336i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 99.3313 | − | 40.6147i | 0.131739 | − | 0.0538657i | ||||
\(755\) | − | 200.272i | − | 0.265261i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −757.748 | −1.00099 | −0.500494 | − | 0.865740i | \(-0.666848\pi\) | ||||
−0.500494 | + | 0.865740i | \(0.666848\pi\) | |||||||
\(758\) | −22.9413 | − | 56.1074i | −0.0302656 | − | 0.0740204i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −41.2523 | − | 17.7522i | −0.0542794 | − | 0.0233581i | ||||
\(761\) | 953.139 | 1.25248 | 0.626241 | − | 0.779629i | \(-0.284592\pi\) | ||||
0.626241 | + | 0.779629i | \(0.284592\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 259.604i | 0.340241i | ||||||||
\(764\) | 413.122 | + | 420.726i | 0.540736 | + | 0.550689i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 535.319 | + | 1309.23i | 0.698850 | + | 1.70917i | ||||
\(767\) | 359.482i | 0.468685i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 145.675 | 0.189434 | 0.0947171 | − | 0.995504i | \(-0.469805\pi\) | ||||
0.0947171 | + | 0.995504i | \(0.469805\pi\) | |||||||
\(770\) | −213.189 | + | 87.1693i | −0.276869 | + | 0.113207i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 71.8208 | − | 70.5228i | 0.0930322 | − | 0.0913507i | ||||
\(773\) | 60.1391 | 0.0777996 | 0.0388998 | − | 0.999243i | \(-0.487615\pi\) | ||||
0.0388998 | + | 0.999243i | \(0.487615\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1068.67i | − | 1.37893i | ||||||
\(776\) | −241.381 | + | 560.918i | −0.311058 | + | 0.722832i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1068.32 | + | 436.817i | −1.37316 | + | 0.561462i | ||||
\(779\) | 307.817i | 0.395143i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1486.98 | 1.90394 | ||||||||
\(782\) | 595.723 | + | 1456.96i | 0.761794 | + | 1.86312i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.74457 | − | 205.291i | 0.00477623 | − | 0.261851i | ||||
\(785\) | −211.928 | −0.269973 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 328.312i | 0.417169i | 0.978004 | + | 0.208585i | \(0.0668856\pi\) | ||||
−0.978004 | + | 0.208585i | \(0.933114\pi\) | |||||||
\(788\) | −1100.27 | + | 1080.39i | −1.39628 | + | 1.37105i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 33.5619 | + | 82.0821i | 0.0424834 | + | 0.103901i | ||||
\(791\) | − | 488.910i | − | 0.618091i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 228.666 | 0.288355 | ||||||||
\(794\) | −49.6622 | + | 20.3060i | −0.0625469 | + | 0.0255743i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −340.185 | − | 346.447i | −0.427369 | − | 0.435235i | ||||
\(797\) | −446.725 | −0.560508 | −0.280254 | − | 0.959926i | \(-0.590419\pi\) | ||||
−0.280254 | + | 0.959926i | \(0.590419\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1083.19i | 1.35568i | ||||||||
\(800\) | −275.716 | − | 711.067i | −0.344645 | − | 0.888833i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 934.991 | − | 382.301i | 1.16582 | − | 0.476684i | ||||
\(803\) | − | 989.618i | − | 1.23240i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 193.848 | 0.240805 | ||||||||
\(806\) | −421.427 | − | 1030.68i | −0.522862 | − | 1.27876i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 228.328 | − | 530.587i | 0.282584 | − | 0.656667i | ||||
\(809\) | −793.341 | −0.980644 | −0.490322 | − | 0.871541i | \(-0.663121\pi\) | ||||
−0.490322 | + | 0.871541i | \(0.663121\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 788.930i | − | 0.972787i | −0.873740 | − | 0.486394i | \(-0.838312\pi\) | ||
0.873740 | − | 0.486394i | \(-0.161688\pi\) | |||||||
\(812\) | 72.8342 | + | 74.1748i | 0.0896973 | + | 0.0913483i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −273.915 | − | 669.912i | −0.336505 | − | 0.822988i | ||||
\(815\) | 139.718i | 0.171433i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −99.5016 | −0.121789 | ||||||||
\(818\) | 1265.00 | − | 517.234i | 1.54645 | − | 0.632316i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 182.663 | − | 179.361i | 0.222759 | − | 0.218733i | ||||
\(821\) | −1448.75 | −1.76462 | −0.882310 | − | 0.470668i | \(-0.844013\pi\) | ||||
−0.882310 | + | 0.470668i | \(0.844013\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 129.939i | − | 0.157884i | −0.996879 | − | 0.0789421i | \(-0.974846\pi\) | ||
0.996879 | − | 0.0789421i | \(-0.0251542\pi\) | |||||||
\(824\) | −426.031 | − | 183.334i | −0.517028 | − | 0.222493i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −322.328 | + | 131.794i | −0.390228 | + | 0.159557i | ||||
\(827\) | 350.389i | 0.423687i | 0.977304 | + | 0.211843i | \(0.0679467\pi\) | ||||
−0.977304 | + | 0.211843i | \(0.932053\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 167.748 | 0.202349 | 0.101175 | − | 0.994869i | \(-0.467740\pi\) | ||||
0.101175 | + | 0.994869i | \(0.467740\pi\) | |||||||
\(830\) | 28.9892 | + | 70.8987i | 0.0349267 | + | 0.0854201i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −546.322 | − | 577.062i | −0.656637 | − | 0.693585i | ||||
\(833\) | 338.512 | 0.406376 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 149.037i | − | 0.178487i | ||||||
\(836\) | −262.863 | + | 258.112i | −0.314430 | + | 0.308747i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 232.091 | + | 567.625i | 0.276959 | + | 0.677356i | ||||
\(839\) | 661.684i | 0.788658i | 0.918969 | + | 0.394329i | \(0.129023\pi\) | ||||
−0.918969 | + | 0.394329i | \(0.870977\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −822.325 | −0.977794 | ||||||||
\(842\) | 34.4082 | − | 14.0689i | 0.0408649 | − | 0.0167089i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 733.225 | + | 746.721i | 0.868750 | + | 0.884741i | ||||
\(845\) | 16.0248 | 0.0189643 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1161.67i | 1.37151i | ||||||||
\(848\) | 20.4383 | − | 1120.50i | 0.0241017 | − | 1.32135i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1163.82 | − | 475.866i | 1.36920 | − | 0.559843i | ||||
\(851\) | 609.136i | 0.715789i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.0789 | 0.0200222 | 0.0100111 | − | 0.999950i | \(-0.496813\pi\) | ||||
0.0100111 | + | 0.999950i | \(0.496813\pi\) | |||||||
\(854\) | 83.8340 | + | 205.032i | 0.0981663 | + | 0.240085i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −473.252 | − | 203.655i | −0.552865 | − | 0.237915i | ||||
\(857\) | 422.419 | 0.492904 | 0.246452 | − | 0.969155i | \(-0.420735\pi\) | ||||
0.246452 | + | 0.969155i | \(0.420735\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1323.18i | − | 1.54037i | −0.637819 | − | 0.770186i | \(-0.720163\pi\) | ||
0.637819 | − | 0.770186i | \(-0.279837\pi\) | |||||||
\(860\) | 57.9784 | + | 59.0456i | 0.0674167 | + | 0.0686576i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 233.234 | + | 570.418i | 0.270573 | + | 0.661738i | ||||
\(863\) | 1455.50i | 1.68656i | 0.537473 | + | 0.843281i | \(0.319379\pi\) | ||||
−0.537473 | + | 0.843281i | \(0.680621\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −173.325 | −0.200376 | ||||||||
\(866\) | −323.667 | + | 132.342i | −0.373750 | + | 0.152819i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 769.653 | − | 755.743i | 0.886697 | − | 0.870671i | ||||
\(869\) | 727.439 | 0.837099 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1178.03i | − | 1.35250i | ||||||
\(872\) | 136.507 | − | 317.213i | 0.156544 | − | 0.363776i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 286.997 | − | 117.348i | 0.328372 | − | 0.134265i | ||||
\(875\) | − | 317.277i | − | 0.362602i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −753.085 | −0.858706 | −0.429353 | − | 0.903137i | \(-0.641258\pi\) | ||||
−0.429353 | + | 0.903137i | \(0.641258\pi\) | |||||||
\(878\) | 363.448 | + | 888.884i | 0.413950 | + | 1.01240i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 306.334 | + | 5.58763i | 0.348107 | + | 0.00634958i | ||||
\(881\) | 996.177 | 1.13073 | 0.565367 | − | 0.824839i | \(-0.308735\pi\) | ||||
0.565367 | + | 0.824839i | \(0.308735\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 950.011i | − | 1.07589i | −0.842980 | − | 0.537945i | \(-0.819201\pi\) | ||
0.842980 | − | 0.537945i | \(-0.180799\pi\) | |||||||
\(884\) | 934.796 | − | 917.901i | 1.05746 | − | 1.03835i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −420.827 | − | 1029.21i | −0.474974 | − | 1.16164i | ||||
\(887\) | − | 433.086i | − | 0.488259i | −0.969743 | − | 0.244129i | \(-0.921498\pi\) | ||
0.969743 | − | 0.244129i | \(-0.0785022\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1154.48 | 1.29863 | ||||||||
\(890\) | 52.7572 | − | 21.5714i | 0.0592777 | − | 0.0242376i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 196.328 | + | 199.942i | 0.220099 | + | 0.224150i | ||||
\(893\) | 213.370 | 0.238936 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 217.659i | 0.243195i | ||||||||
\(896\) | 317.128 | − | 701.422i | 0.353937 | − | 0.782837i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1484.15 | + | 606.842i | −1.65273 | + | 0.675771i | ||||
\(899\) | − | 193.775i | − | 0.215545i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1847.63 | 2.05065 | ||||||||
\(902\) | −794.779 | − | 1943.79i | −0.881130 | − | 2.15498i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −257.082 | + | 597.405i | −0.284383 | + | 0.660846i | ||||
\(905\) | 52.1300 | 0.0576022 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 685.704i | − | 0.756014i | −0.925803 | − | 0.378007i | \(-0.876610\pi\) | ||
0.925803 | − | 0.378007i | \(-0.123390\pi\) | |||||||
\(908\) | 836.148 | + | 851.539i | 0.920868 | + | 0.937818i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −61.0634 | − | 149.342i | −0.0671026 | − | 0.164113i | ||||
\(911\) | 36.0750i | 0.0395994i | 0.999804 | + | 0.0197997i | \(0.00630285\pi\) | ||||
−0.999804 | + | 0.0197997i | \(0.993697\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 628.328 | 0.688202 | ||||||||
\(914\) | 255.154 | − | 104.328i | 0.279162 | − | 0.114144i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 741.112 | − | 727.717i | 0.809074 | − | 0.794451i | ||||
\(917\) | −852.758 | −0.929943 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 953.775i | 1.03784i | 0.854823 | + | 0.518920i | \(0.173666\pi\) | ||||
−0.854823 | + | 0.518920i | \(0.826334\pi\) | |||||||
\(920\) | −236.865 | − | 101.931i | −0.257462 | − | 0.110794i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 348.663 | − | 142.562i | 0.378159 | − | 0.154622i | ||||
\(923\) | 1041.65i | 1.12855i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 486.580 | 0.526033 | ||||||||
\(926\) | −415.121 | − | 1015.26i | −0.448295 | − | 1.09639i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −49.9938 | − | 128.933i | −0.0538726 | − | 0.138937i | ||||
\(929\) | −149.629 | −0.161064 | −0.0805321 | − | 0.996752i | \(-0.525662\pi\) | ||||
−0.0805321 | + | 0.996752i | \(0.525662\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 66.6813i | − | 0.0716233i | ||||||
\(932\) | −21.0688 | + | 20.6880i | −0.0226060 | + | 0.0221974i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −468.237 | − | 1145.16i | −0.501324 | − | 1.22609i | ||||
\(935\) | 505.126i | 0.540241i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −661.158 | −0.705611 | −0.352806 | − | 0.935697i | \(-0.614772\pi\) | ||||
−0.352806 | + | 0.935697i | \(0.614772\pi\) | |||||||
\(938\) | 1056.28 | − | 431.892i | 1.12609 | − | 0.460439i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −124.328 | − | 126.617i | −0.132264 | − | 0.134699i | ||||
\(941\) | −466.713 | −0.495976 | −0.247988 | − | 0.968763i | \(-0.579769\pi\) | ||||
−0.247988 | + | 0.968763i | \(0.579769\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1767.44i | 1.87428i | ||||||||
\(944\) | 463.157 | + | 8.44812i | 0.490633 | + | 0.00894928i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 628.328 | − | 256.912i | 0.664195 | − | 0.271577i | ||||
\(947\) | 1302.74i | 1.37565i | 0.725879 | + | 0.687823i | \(0.241433\pi\) | ||||
−0.725879 | + | 0.687823i | \(0.758567\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 693.243 | 0.730498 | ||||||||
\(950\) | −93.7379 | − | 229.254i | −0.0986715 | − | 0.241320i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1165.75 | + | 501.659i | 1.22453 | + | 0.526953i | ||||
\(953\) | −21.6959 | −0.0227659 | −0.0113829 | − | 0.999935i | \(-0.503623\pi\) | ||||
−0.0113829 | + | 0.999935i | \(0.503623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 159.258i | − | 0.166762i | ||||||
\(956\) | 230.160 | + | 234.396i | 0.240753 | + | 0.245185i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 583.161 | + | 1426.23i | 0.608728 | + | 1.48876i | ||||
\(959\) | − | 527.893i | − | 0.550462i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1049.65 | −1.09225 | ||||||||
\(962\) | 469.284 | − | 191.882i | 0.487821 | − | 0.199461i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1186.81 | + | 1165.36i | −1.23113 | + | 1.20888i | ||||
\(965\) | −27.1863 | −0.0281724 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 640.899i | − | 0.662770i | −0.943496 | − | 0.331385i | \(-0.892484\pi\) | ||
0.943496 | − | 0.331385i | \(-0.107516\pi\) | |||||||
\(968\) | 610.838 | − | 1419.46i | 0.631031 | − | 1.46638i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 152.663 | − | 62.4209i | 0.157384 | − | 0.0643515i | ||||
\(971\) | 1396.09i | 1.43779i | 0.695121 | + | 0.718893i | \(0.255351\pi\) | ||||
−0.695121 | + | 0.718893i | \(0.744649\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1103.56 | −1.13418 | ||||||||
\(974\) | 415.714 | + | 1016.71i | 0.426811 | + | 1.04385i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.37384 | − | 294.614i | 0.00550598 | − | 0.301858i | ||||
\(977\) | −1009.95 | −1.03373 | −0.516864 | − | 0.856068i | \(-0.672901\pi\) | ||||
−0.516864 | + | 0.856068i | \(0.672901\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 467.552i | − | 0.477581i | ||||||
\(980\) | −39.5696 | + | 38.8544i | −0.0403771 | + | 0.0396473i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.4288 | − | 42.6256i | −0.0177483 | − | 0.0434069i | ||||
\(983\) | − | 485.376i | − | 0.493770i | −0.969045 | − | 0.246885i | \(-0.920593\pi\) | ||
0.969045 | − | 0.246885i | \(-0.0794071\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 416.486 | 0.422828 | ||||||||
\(986\) | 211.029 | − | 86.2858i | 0.214025 | − | 0.0875109i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −180.812 | − | 184.140i | −0.183008 | − | 0.186376i | ||||
\(989\) | −571.325 | −0.577679 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 265.720i | − | 0.268133i | −0.990972 | − | 0.134066i | \(-0.957196\pi\) | ||
0.990972 | − | 0.134066i | \(-0.0428035\pi\) | |||||||
\(992\) | −1337.84 | + | 518.746i | −1.34863 | + | 0.522929i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −933.994 | + | 381.893i | −0.939632 | + | 0.384198i | ||||
\(995\) | 131.141i | 0.131800i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1715.81 | −1.72097 | −0.860487 | − | 0.509472i | \(-0.829841\pi\) | ||||
−0.860487 | + | 0.509472i | \(0.829841\pi\) | |||||||
\(998\) | −474.453 | − | 1160.37i | −0.475404 | − | 1.16269i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.3.d.d.55.2 | yes | 8 | |
3.2 | odd | 2 | inner | 108.3.d.d.55.7 | yes | 8 | |
4.3 | odd | 2 | inner | 108.3.d.d.55.1 | ✓ | 8 | |
8.3 | odd | 2 | 1728.3.g.l.703.6 | 8 | |||
8.5 | even | 2 | 1728.3.g.l.703.5 | 8 | |||
9.2 | odd | 6 | 324.3.f.p.271.1 | 8 | |||
9.4 | even | 3 | 324.3.f.o.55.3 | 8 | |||
9.5 | odd | 6 | 324.3.f.o.55.2 | 8 | |||
9.7 | even | 3 | 324.3.f.p.271.4 | 8 | |||
12.11 | even | 2 | inner | 108.3.d.d.55.8 | yes | 8 | |
24.5 | odd | 2 | 1728.3.g.l.703.3 | 8 | |||
24.11 | even | 2 | 1728.3.g.l.703.4 | 8 | |||
36.7 | odd | 6 | 324.3.f.o.271.3 | 8 | |||
36.11 | even | 6 | 324.3.f.o.271.2 | 8 | |||
36.23 | even | 6 | 324.3.f.p.55.2 | 8 | |||
36.31 | odd | 6 | 324.3.f.p.55.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.d.d.55.1 | ✓ | 8 | 4.3 | odd | 2 | inner | |
108.3.d.d.55.2 | yes | 8 | 1.1 | even | 1 | trivial | |
108.3.d.d.55.7 | yes | 8 | 3.2 | odd | 2 | inner | |
108.3.d.d.55.8 | yes | 8 | 12.11 | even | 2 | inner | |
324.3.f.o.55.2 | 8 | 9.5 | odd | 6 | |||
324.3.f.o.55.3 | 8 | 9.4 | even | 3 | |||
324.3.f.o.271.2 | 8 | 36.11 | even | 6 | |||
324.3.f.o.271.3 | 8 | 36.7 | odd | 6 | |||
324.3.f.p.55.2 | 8 | 36.23 | even | 6 | |||
324.3.f.p.55.3 | 8 | 36.31 | odd | 6 | |||
324.3.f.p.271.1 | 8 | 9.2 | odd | 6 | |||
324.3.f.p.271.4 | 8 | 9.7 | even | 3 | |||
1728.3.g.l.703.3 | 8 | 24.5 | odd | 2 | |||
1728.3.g.l.703.4 | 8 | 24.11 | even | 2 | |||
1728.3.g.l.703.5 | 8 | 8.5 | even | 2 | |||
1728.3.g.l.703.6 | 8 | 8.3 | odd | 2 |