Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,2,Mod(25,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.i (of order \(3\), degree \(2\), 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: | \(0.574922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(1.68614 + 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 72.49 |
Dual form | 72.2.i.b.25.2 |
$q$-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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.68614 | + | 0.396143i | 0.973494 | + | 0.228714i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.18614 | + | 2.05446i | −0.530458 | + | 0.918781i | 0.468910 | + | 0.883246i | \(0.344647\pi\) |
−0.999368 | + | 0.0355348i | \(0.988687\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.18614 | − | 3.78651i | −0.826284 | − | 1.43117i | −0.900934 | − | 0.433955i | \(-0.857118\pi\) |
0.0746509 | − | 0.997210i | \(-0.476216\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.68614 | + | 1.33591i | 0.895380 | + | 0.445302i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | 0.780750 | − | 0.624844i | \(-0.214837\pi\) |
−0.931505 | + | 0.363727i | \(0.881504\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.186141 | − | 0.322405i | 0.0516261 | − | 0.0894191i | −0.839057 | − | 0.544043i | \(-0.816893\pi\) |
0.890684 | + | 0.454624i | \(0.150226\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.81386 | + | 2.99422i | −0.726535 | + | 0.773104i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.37228 | −1.30297 | −0.651485 | − | 0.758662i | \(-0.725854\pi\) | ||||
−0.651485 | + | 0.758662i | \(0.725854\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.627719 | 0.144009 | 0.0720043 | − | 0.997404i | \(-0.477060\pi\) | ||||
0.0720043 | + | 0.997404i | \(0.477060\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.18614 | − | 7.25061i | −0.477055 | − | 1.58221i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.186141 | − | 0.322405i | 0.0388130 | − | 0.0672261i | −0.845966 | − | 0.533236i | \(-0.820976\pi\) |
0.884779 | + | 0.466010i | \(0.154309\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.313859 | − | 0.543620i | −0.0627719 | − | 0.108724i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | + | 3.31662i | 0.769800 | + | 0.638285i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.18614 | + | 3.78651i | 0.405956 | + | 0.703137i | 0.994432 | − | 0.105378i | \(-0.0336052\pi\) |
−0.588476 | + | 0.808515i | \(0.700272\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.18614 | + | 5.51856i | −0.572248 | + | 0.991162i | 0.424087 | + | 0.905621i | \(0.360595\pi\) |
−0.996335 | + | 0.0855407i | \(0.972738\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.500000 | − | 1.65831i | −0.0870388 | − | 0.288675i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.3723 | 1.75324 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.74456 | 1.43760 | 0.718799 | − | 0.695218i | \(-0.244692\pi\) | ||||
0.718799 | + | 0.695218i | \(0.244692\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.441578 | − | 0.469882i | 0.0707091 | − | 0.0752413i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.87228 | − | 10.1711i | 0.917096 | − | 1.58846i | 0.113293 | − | 0.993562i | \(-0.463860\pi\) |
0.803803 | − | 0.594896i | \(-0.202807\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.872281 | + | 1.51084i | 0.133022 | + | 0.230400i | 0.924840 | − | 0.380356i | \(-0.124199\pi\) |
−0.791818 | + | 0.610757i | \(0.790865\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.93070 | + | 3.93398i | −0.884097 | + | 0.586444i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.18614 | − | 3.78651i | −0.318881 | − | 0.552319i | 0.661374 | − | 0.750057i | \(-0.269974\pi\) |
−0.980255 | + | 0.197738i | \(0.936640\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.05842 | + | 10.4935i | −0.865489 | + | 1.49907i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.05842 | − | 2.12819i | −1.26843 | − | 0.298007i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.744563 | 0.102274 | 0.0511368 | − | 0.998692i | \(-0.483716\pi\) | ||||
0.0511368 | + | 0.998692i | \(0.483716\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.37228 | 0.319878 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.05842 | + | 0.248667i | 0.140191 | + | 0.0329367i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.50000 | + | 6.06218i | −0.455661 | + | 0.789228i | −0.998726 | − | 0.0504625i | \(-0.983930\pi\) |
0.543065 | + | 0.839691i | \(0.317264\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.18614 | − | 2.05446i | −0.151870 | − | 0.263046i | 0.780045 | − | 0.625723i | \(-0.215196\pi\) |
−0.931915 | + | 0.362677i | \(0.881863\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.813859 | − | 13.0916i | −0.102537 | − | 1.64938i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.441578 | + | 0.764836i | 0.0547710 | + | 0.0948662i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.87228 | − | 3.24289i | 0.228736 | − | 0.396182i | −0.728698 | − | 0.684835i | \(-0.759874\pi\) |
0.957434 | + | 0.288653i | \(0.0932076\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.441578 | − | 0.469882i | 0.0531597 | − | 0.0565671i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.1168 | −1.41817 | −0.709085 | − | 0.705123i | \(-0.750892\pi\) | ||||
−0.709085 | + | 0.705123i | \(0.750892\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.313859 | − | 1.04095i | −0.0362414 | − | 0.120199i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.18614 | + | 3.78651i | −0.249134 | + | 0.431512i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.18614 | + | 5.51856i | 0.358469 | + | 0.620886i | 0.987705 | − | 0.156328i | \(-0.0499656\pi\) |
−0.629236 | + | 0.777214i | \(0.716632\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.43070 | + | 7.17687i | 0.603411 | + | 0.797430i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.81386 | − | 8.33785i | −0.528390 | − | 0.915198i | −0.999452 | − | 0.0330979i | \(-0.989463\pi\) |
0.471062 | − | 0.882100i | \(-0.343871\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.37228 | − | 11.0371i | 0.691171 | − | 1.19714i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.18614 | + | 7.25061i | 0.234379 | + | 0.777347i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.62772 | −0.170631 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.55842 | + | 8.04290i | −0.783772 | + | 0.834009i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.744563 | + | 1.28962i | −0.0763905 | + | 0.132312i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.872281 | − | 1.51084i | −0.0885667 | − | 0.153402i | 0.818339 | − | 0.574736i | \(-0.194895\pi\) |
−0.906906 | + | 0.421334i | \(0.861562\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.186141 | − | 2.99422i | −0.0187078 | − | 0.300930i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.55842 | + | 6.16337i | 0.354076 | + | 0.613278i | 0.986959 | − | 0.160969i | \(-0.0514620\pi\) |
−0.632883 | + | 0.774247i | \(0.718129\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.18614 | − | 10.7147i | 0.609539 | − | 1.05575i | −0.381778 | − | 0.924254i | \(-0.624688\pi\) |
0.991316 | − | 0.131498i | \(-0.0419786\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 17.4891 | + | 4.10891i | 1.70676 | + | 0.400989i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.8614 | −1.24336 | −0.621680 | − | 0.783272i | \(-0.713549\pi\) | ||||
−0.621680 | + | 0.783272i | \(0.713549\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.74456 | −0.454447 | −0.227223 | − | 0.973843i | \(-0.572965\pi\) | ||||
−0.227223 | + | 0.973843i | \(0.572965\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.7446 | + | 3.46410i | 1.39949 | + | 0.328798i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.18614 | − | 3.78651i | 0.205655 | − | 0.356205i | −0.744686 | − | 0.667415i | \(-0.767401\pi\) |
0.950341 | + | 0.311210i | \(0.100734\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.441578 | + | 0.764836i | 0.0411774 | + | 0.0713213i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.930703 | − | 0.617359i | 0.0860436 | − | 0.0570748i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.7446 | + | 20.3422i | 1.07662 | + | 1.86476i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.9307 | − | 14.8236i | 1.25609 | − | 1.33660i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.3723 | −0.927725 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.74456 | 0.598483 | 0.299242 | − | 0.954177i | \(-0.403266\pi\) | ||||
0.299242 | + | 0.954177i | \(0.403266\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.872281 | + | 2.89303i | 0.0768001 | + | 0.254717i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.18614 | + | 15.9109i | −0.802597 | + | 1.39014i | 0.115305 | + | 0.993330i | \(0.463216\pi\) |
−0.917901 | + | 0.396808i | \(0.870118\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.37228 | − | 2.37686i | −0.118992 | − | 0.206100i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.5584 | + | 4.28384i | −0.994791 | + | 0.368694i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.87228 | − | 15.3672i | −0.758010 | − | 1.31291i | −0.943864 | − | 0.330335i | \(-0.892838\pi\) |
0.185854 | − | 0.982577i | \(-0.440495\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.87228 | + | 4.97494i | −0.243624 | + | 0.421969i | −0.961744 | − | 0.273951i | \(-0.911670\pi\) |
0.718120 | + | 0.695919i | \(0.245003\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.18614 | − | 7.25061i | −0.184106 | − | 0.610611i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.372281 | −0.0311317 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.3723 | −0.861371 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −14.3723 | + | 15.2935i | −1.18541 | + | 1.26139i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.18614 | − | 7.25061i | 0.342942 | − | 0.593993i | −0.642036 | − | 0.766675i | \(-0.721910\pi\) |
0.984978 | + | 0.172682i | \(0.0552432\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.186141 | − | 0.322405i | −0.0151479 | − | 0.0262370i | 0.858352 | − | 0.513061i | \(-0.171489\pi\) |
−0.873500 | + | 0.486824i | \(0.838155\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.4307 | − | 7.17687i | −1.16665 | − | 0.580216i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.55842 | − | 13.0916i | −0.607107 | − | 1.05154i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.55842 | − | 2.69927i | 0.124376 | − | 0.215425i | −0.797113 | − | 0.603830i | \(-0.793641\pi\) |
0.921489 | + | 0.388405i | \(0.126974\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.25544 | + | 0.294954i | 0.0995627 | + | 0.0233913i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.62772 | −0.128282 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0000 | −0.939913 | −0.469956 | − | 0.882690i | \(-0.655730\pi\) | ||||
−0.469956 | + | 0.882690i | \(0.655730\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.00000 | + | 0.939764i | 0.311400 | + | 0.0731605i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.55842 | − | 16.5557i | 0.739653 | − | 1.28112i | −0.212999 | − | 0.977052i | \(-0.568323\pi\) |
0.952652 | − | 0.304064i | \(-0.0983436\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.43070 | + | 11.1383i | 0.494669 | + | 0.856793i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.68614 | + | 0.838574i | 0.128942 | + | 0.0641274i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.18614 | + | 14.1788i | 0.622381 | + | 1.07800i | 0.989041 | + | 0.147640i | \(0.0471678\pi\) |
−0.366660 | + | 0.930355i | \(0.619499\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.37228 | + | 2.37686i | −0.103735 | + | 0.179674i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.30298 | + | 8.83518i | −0.624091 | + | 0.664093i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.9783 | 1.71748 | 0.858738 | − | 0.512416i | \(-0.171249\pi\) | ||||
0.858738 | + | 0.512416i | \(0.171249\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.510875 | −0.0379730 | −0.0189865 | − | 0.999820i | \(-0.506044\pi\) | ||||
−0.0189865 | + | 0.999820i | \(0.506044\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.18614 | − | 3.93398i | −0.0876820 | − | 0.290808i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.3723 | + | 17.9653i | −0.762585 | + | 1.32084i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.68614 | + | 4.65253i | 0.196430 | + | 0.340227i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.81386 | − | 22.3966i | 0.277417 | − | 1.62912i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.93070 | − | 8.54023i | −0.356773 | − | 0.617949i | 0.630647 | − | 0.776070i | \(-0.282790\pi\) |
−0.987420 | + | 0.158121i | \(0.949456\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.872281 | + | 1.51084i | −0.0627882 | + | 0.108752i | −0.895711 | − | 0.444637i | \(-0.853333\pi\) |
0.832923 | + | 0.553390i | \(0.186666\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.441578 | + | 1.46455i | 0.0316221 | + | 0.104879i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.2554 | 1.08690 | 0.543452 | − | 0.839440i | \(-0.317117\pi\) | ||||
0.543452 | + | 0.839440i | \(0.317117\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.2337 | −1.15078 | −0.575388 | − | 0.817881i | \(-0.695149\pi\) | ||||
−0.575388 | + | 0.817881i | \(0.695149\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.44158 | − | 4.72627i | 0.313285 | − | 0.333365i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.55842 | − | 16.5557i | 0.670870 | − | 1.16198i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.9307 | + | 24.1287i | 0.972963 | + | 1.68522i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.930703 | − | 0.617359i | 0.0646884 | − | 0.0429094i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.313859 | − | 0.543620i | −0.0217101 | − | 0.0376030i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.81386 | − | 8.33785i | 0.331400 | − | 0.574001i | −0.651387 | − | 0.758746i | \(-0.725812\pi\) |
0.982787 | + | 0.184745i | \(0.0591458\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.74456 | − | 1.58457i | −0.462130 | − | 0.108573i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.13859 | −0.282250 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.8614 | 1.89136 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20.4307 | − | 4.80001i | −1.38058 | − | 0.324355i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.00000 | + | 1.73205i | −0.0672673 | + | 0.116510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.30298 | + | 12.6491i | 0.489044 | + | 0.847049i | 0.999921 | − | 0.0126050i | \(-0.00401240\pi\) |
−0.510877 | + | 0.859654i | \(0.670679\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.116844 | − | 1.87953i | −0.00778960 | − | 0.125302i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.50000 | + | 12.9904i | 0.497792 | + | 0.862202i | 0.999997 | − | 0.00254715i | \(-0.000810783\pi\) |
−0.502204 | + | 0.864749i | \(0.667477\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.3030 | + | 19.5773i | −0.746922 | + | 1.29371i | 0.202369 | + | 0.979309i | \(0.435136\pi\) |
−0.949291 | + | 0.314398i | \(0.898197\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.18614 | + | 5.51856i | −0.341223 | + | 0.363094i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.37228 | 0.351950 | 0.175975 | − | 0.984395i | \(-0.443692\pi\) | ||||
0.175975 | + | 0.984395i | \(0.443692\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.3723 | 0.676613 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.18614 | + | 10.5672i | 0.206962 | + | 0.686416i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.93070 | − | 12.0043i | 0.448310 | − | 0.776496i | −0.549966 | − | 0.835187i | \(-0.685359\pi\) |
0.998276 | + | 0.0586913i | \(0.0186928\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.87228 | − | 4.97494i | −0.185020 | − | 0.320464i | 0.758563 | − | 0.651599i | \(-0.225902\pi\) |
−0.943583 | + | 0.331135i | \(0.892568\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.31386 | + | 14.2525i | 0.405034 | + | 0.914302i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.3723 | − | 24.8935i | −0.918211 | − | 1.59039i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.116844 | − | 0.202380i | 0.00743460 | − | 0.0128771i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.81386 | − | 15.9658i | −0.305066 | − | 1.01179i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.88316 | 0.623819 | 0.311910 | − | 0.950112i | \(-0.399031\pi\) | ||||
0.311910 | + | 0.950112i | \(0.399031\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.372281 | −0.0234051 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.1168 | − | 16.0858i | 0.946653 | − | 1.00733i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.24456 | + | 3.88770i | −0.140012 | + | 0.242508i | −0.927501 | − | 0.373821i | \(-0.878047\pi\) |
0.787489 | + | 0.616329i | \(0.211381\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.1168 | − | 33.1113i | −1.18786 | − | 2.05744i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.813859 | + | 13.0916i | 0.0503766 | + | 0.810348i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.5584 | + | 18.2877i | 0.651060 | + | 1.12767i | 0.982866 | + | 0.184322i | \(0.0590088\pi\) |
−0.331806 | + | 0.943348i | \(0.607658\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.883156 | + | 1.52967i | −0.0542518 | + | 0.0939669i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.1168 | + | 2.37686i | 0.619141 | + | 0.145462i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.7446 | −0.777050 | −0.388525 | − | 0.921438i | \(-0.627015\pi\) | ||||
−0.388525 | + | 0.921438i | \(0.627015\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.4891 | −1.30537 | −0.652686 | − | 0.757629i | \(-0.726358\pi\) | ||||
−0.652686 | + | 0.757629i | \(0.726358\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.74456 | − | 0.644810i | −0.166108 | − | 0.0390257i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.313859 | + | 0.543620i | −0.0189264 | + | 0.0327815i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.5584 | − | 25.2159i | −0.874731 | − | 1.51508i | −0.857049 | − | 0.515235i | \(-0.827705\pi\) |
−0.0176816 | − | 0.999844i | \(-0.505629\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.9307 | + | 10.5672i | −0.953746 | + | 0.632644i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.93070 | + | 12.0043i | 0.413451 | + | 0.716118i | 0.995264 | − | 0.0972040i | \(-0.0309899\pi\) |
−0.581813 | + | 0.813322i | \(0.697657\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.9307 | + | 20.6646i | −0.709207 | + | 1.22838i | 0.255945 | + | 0.966691i | \(0.417613\pi\) |
−0.965152 | + | 0.261691i | \(0.915720\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.76631 | + | 1.87953i | −0.104627 | + | 0.111334i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −51.3505 | −3.03113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.8614 | 0.697730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.872281 | − | 2.89303i | −0.0511340 | − | 0.169592i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.81386 | + | 16.9981i | −0.573332 | + | 0.993040i | 0.422889 | + | 0.906182i | \(0.361016\pi\) |
−0.996221 | + | 0.0868582i | \(0.972317\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.30298 | − | 14.3812i | −0.483418 | − | 0.837305i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.872281 | − | 5.12241i | 0.0506149 | − | 0.297233i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.0692967 | − | 0.120025i | −0.00400753 | − | 0.00694125i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.81386 | − | 6.60580i | 0.219827 | − | 0.380752i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.55842 | + | 11.8020i | 0.204426 | + | 0.678004i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.62772 | 0.322242 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.3723 | 1.79051 | 0.895255 | − | 0.445553i | \(-0.146993\pi\) | ||||
0.895255 | + | 0.445553i | \(0.146993\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.6753 | − | 15.6159i | 0.834847 | − | 0.888358i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.44158 | − | 9.42509i | 0.308564 | − | 0.534448i | −0.669485 | − | 0.742826i | \(-0.733485\pi\) |
0.978048 | + | 0.208378i | \(0.0668184\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.61684 | − | 9.72866i | −0.317483 | − | 0.549896i | 0.662479 | − | 0.749080i | \(-0.269504\pi\) |
−0.979962 | + | 0.199184i | \(0.936171\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 27.8614 | + | 13.8564i | 1.56981 | + | 0.780720i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.3030 | − | 26.5055i | −0.859501 | − | 1.48870i | −0.872405 | − | 0.488783i | \(-0.837441\pi\) |
0.0129041 | − | 0.999917i | \(-0.495892\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.18614 | − | 3.78651i | 0.122400 | − | 0.212004i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.6861 | − | 5.09496i | −1.21040 | − | 0.284373i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.37228 | −0.187639 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.233688 | −0.0129627 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.00000 | − | 1.87953i | −0.442401 | − | 0.103938i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.55842 | + | 16.5557i | −0.526973 | + | 0.912744i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.9307 | + | 27.5928i | 0.875631 | + | 1.51664i | 0.856089 | + | 0.516828i | \(0.172887\pi\) |
0.0195412 | + | 0.999809i | \(0.493779\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 23.4891 | + | 11.6819i | 1.28720 | + | 0.640166i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.44158 | + | 7.69304i | 0.242669 | + | 0.420316i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.98913 | − | 17.3017i | 0.544142 | − | 0.942482i | −0.454518 | − | 0.890738i | \(-0.650188\pi\) |
0.998660 | − | 0.0517446i | \(-0.0164782\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.18614 | − | 5.51856i | 0.281672 | − | 0.299727i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.37228 | 0.345078 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 22.3723 | 1.20799 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.441578 | + | 1.46455i | 0.0237738 | + | 0.0788486i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.3614 | + | 24.8747i | −0.770961 | + | 1.33534i | 0.166076 | + | 0.986113i | \(0.446890\pi\) |
−0.937037 | + | 0.349230i | \(0.886443\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.44158 | − | 14.6212i | −0.451867 | − | 0.782657i | 0.546635 | − | 0.837371i | \(-0.315909\pi\) |
−0.998502 | + | 0.0547140i | \(0.982575\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.81386 | − | 0.672262i | 0.0968166 | − | 0.0358827i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.9891 | + | 20.7658i | 0.638117 | + | 1.10525i | 0.985846 | + | 0.167656i | \(0.0536196\pi\) |
−0.347729 | + | 0.937595i | \(0.613047\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.74456 | − | 8.21782i | 0.251815 | − | 0.436157i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.7446 | + | 38.9523i | 0.621588 | + | 2.06157i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.2337 | 1.06789 | 0.533947 | − | 0.845518i | \(-0.320708\pi\) | ||||
0.533947 | + | 0.845518i | \(0.320708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6060 | −0.979262 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.8614 | − | 12.6217i | 0.622562 | − | 0.662467i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.3723 | − | 24.8935i | 0.752280 | − | 1.30299i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.81386 | − | 15.2661i | −0.460080 | − | 0.796881i | 0.538885 | − | 0.842380i | \(-0.318846\pi\) |
−0.998964 | + | 0.0454981i | \(0.985513\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 29.3614 | − | 19.4762i | 1.52849 | − | 1.01389i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.62772 | − | 2.81929i | −0.0845069 | − | 0.146370i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.5584 | + | 18.2877i | −0.546694 | + | 0.946902i | 0.451804 | + | 0.892117i | \(0.350781\pi\) |
−0.998498 | + | 0.0547851i | \(0.982553\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.4891 | − | 4.10891i | −0.903135 | − | 0.212183i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.62772 | 0.0838318 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.88316 | −0.302197 | −0.151099 | − | 0.988519i | \(-0.548281\pi\) | ||||
−0.151099 | + | 0.988519i | \(0.548281\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.3723 | + | 2.67181i | 0.582620 | + | 0.136881i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.6753 | + | 18.4901i | −0.545481 | + | 0.944800i | 0.453096 | + | 0.891462i | \(0.350320\pi\) |
−0.998576 | + | 0.0533383i | \(0.983014\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.18614 | − | 8.98266i | −0.264310 | − | 0.457799i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.324734 | + | 5.22360i | 0.0165072 | + | 0.265531i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.30298 | − | 9.18504i | −0.268872 | − | 0.465700i | 0.699699 | − | 0.714438i | \(-0.253318\pi\) |
−0.968571 | + | 0.248738i | \(0.919984\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.00000 | + | 1.73205i | −0.0505722 | + | 0.0875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.7921 | + | 23.1889i | −1.09927 | + | 1.16973i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.1168 | −0.760611 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.2337 | −0.915123 | −0.457561 | − | 0.889178i | \(-0.651277\pi\) | ||||
−0.457561 | + | 0.889178i | \(0.651277\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.37228 | − | 4.55134i | −0.0687000 | − | 0.227852i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.61684 | − | 14.9248i | 0.430305 | − | 0.745310i | −0.566595 | − | 0.823997i | \(-0.691739\pi\) |
0.996899 | + | 0.0786871i | \(0.0250728\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.18614 | + | 2.05446i | 0.0590859 | + | 0.102340i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −21.1861 | + | 2.64436i | −1.05275 | + | 0.131399i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.37228 | − | 7.57301i | −0.216726 | − | 0.375380i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.87228 | + | 4.97494i | −0.142025 | + | 0.245995i | −0.928259 | − | 0.371934i | \(-0.878695\pi\) |
0.786234 | + | 0.617929i | \(0.212028\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.87228 | − | 29.4260i | −0.437637 | − | 1.45148i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 30.6060 | 1.50602 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.8397 | 1.12115 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.81386 | + | 7.25061i | −0.333676 | + | 0.355064i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.30298 | − | 10.9171i | 0.307921 | − | 0.533335i | −0.669986 | − | 0.742373i | \(-0.733700\pi\) |
0.977907 | + | 0.209039i | \(0.0670334\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.5584 | + | 30.4121i | 0.855745 | + | 1.48219i | 0.875952 | + | 0.482398i | \(0.160234\pi\) |
−0.0202069 | + | 0.999796i | \(0.506432\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.813859 | − | 13.0916i | −0.0395712 | − | 0.636534i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.68614 | + | 2.92048i | 0.0817898 | + | 0.141664i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.18614 | + | 8.98266i | −0.250975 | + | 0.434701i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.627719 | − | 0.147477i | −0.0303065 | − | 0.00712025i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.25544 | −0.0604723 | −0.0302361 | − | 0.999543i | \(-0.509626\pi\) | ||||
−0.0302361 | + | 0.999543i | \(0.509626\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.1168 | 1.54344 | 0.771719 | − | 0.635964i | \(-0.219397\pi\) | ||||
0.771719 | + | 0.635964i | \(0.219397\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.4891 | − | 4.10891i | −0.838539 | − | 0.197007i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.116844 | − | 0.202380i | 0.00558941 | − | 0.00968113i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.55842 | − | 6.16337i | −0.169834 | − | 0.294161i | 0.768527 | − | 0.639817i | \(-0.220990\pi\) |
−0.938361 | + | 0.345656i | \(0.887657\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −30.2921 | + | 20.0935i | −1.44248 | + | 0.956834i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.3614 | − | 26.6067i | −0.729842 | − | 1.26412i | −0.956950 | − | 0.290254i | \(-0.906260\pi\) |
0.227107 | − | 0.973870i | \(-0.427073\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.11684 | + | 12.3267i | −0.337371 | + | 0.584343i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.93070 | − | 10.5672i | 0.469706 | − | 0.499813i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.8832 | −0.749572 | −0.374786 | − | 0.927111i | \(-0.622284\pi\) | ||||
−0.374786 | + | 0.927111i | \(0.622284\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.7446 | −0.553030 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.186141 | − | 0.617359i | −0.00874565 | − | 0.0290060i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.93070 | − | 3.34408i | 0.0905128 | − | 0.156773i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.87228 | + | 3.24289i | 0.0875816 | + | 0.151696i | 0.906488 | − | 0.422231i | \(-0.138753\pi\) |
−0.818907 | + | 0.573927i | \(0.805419\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −21.4891 | − | 17.8178i | −1.00303 | − | 0.831666i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.44158 | + | 5.96099i | 0.160290 | + | 0.277631i | 0.934973 | − | 0.354720i | \(-0.115424\pi\) |
−0.774682 | + | 0.632350i | \(0.782090\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.6753 | + | 35.8106i | −0.960861 | + | 1.66426i | −0.240515 | + | 0.970645i | \(0.577316\pi\) |
−0.720346 | + | 0.693615i | \(0.756017\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.55842 | − | 25.0684i | −0.350513 | − | 1.16252i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.37228 | 0.341148 | 0.170574 | − | 0.985345i | \(-0.445438\pi\) | ||||
0.170574 | + | 0.985345i | \(0.445438\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.3723 | −0.756002 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.69702 | − | 3.93398i | 0.170349 | − | 0.181268i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.872281 | − | 1.51084i | 0.0401075 | − | 0.0694683i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.197015 | − | 0.341241i | −0.00903969 | − | 0.0156572i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | + | 0.994667i | 0.0915737 | + | 0.0455427i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.30298 | + | 9.18504i | 0.242300 | + | 0.419675i | 0.961369 | − | 0.275263i | \(-0.0887650\pi\) |
−0.719069 | + | 0.694938i | \(0.755432\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.62772 | − | 2.81929i | 0.0742176 | − | 0.128549i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.74456 | − | 0.644810i | −0.124882 | − | 0.0293399i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.13859 | 0.187924 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.74456 | 0.305625 | 0.152813 | − | 0.988255i | \(-0.451167\pi\) | ||||
0.152813 | + | 0.988255i | \(0.451167\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.2337 | − | 4.75372i | −0.914999 | − | 0.214971i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.127719 | + | 0.221215i | −0.00576386 | + | 0.00998330i | −0.868893 | − | 0.495000i | \(-0.835168\pi\) |
0.863129 | + | 0.504983i | \(0.168501\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.7446 | − | 20.3422i | −0.528948 | − | 0.916166i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.37228 | + | 3.16915i | 0.286413 | + | 0.142443i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.74456 | + | 15.1460i | 0.392247 | + | 0.679392i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.98913 | − | 17.3017i | 0.447175 | − | 0.774529i | −0.551026 | − | 0.834488i | \(-0.685764\pi\) |
0.998201 | + | 0.0599587i | \(0.0190969\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.6753 | − | 24.1287i | 1.01306 | − | 1.07799i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.51087 | 0.290306 | 0.145153 | − | 0.989409i | \(-0.453633\pi\) | ||||
0.145153 | + | 0.989409i | \(0.453633\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.8832 | −0.751291 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.43070 | + | 21.3282i | 0.285598 | + | 0.947220i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.5584 | − | 26.9480i | 0.689615 | − | 1.19445i | −0.282348 | − | 0.959312i | \(-0.591113\pi\) |
0.971962 | − | 0.235136i | \(-0.0755535\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.4891 | + | 45.8805i | 1.17181 | + | 2.02963i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.51087 | + | 2.08191i | 0.110858 | + | 0.0919185i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.6753 | + | 25.4183i | 0.646669 | + | 1.12006i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.18614 | + | 3.78651i | −0.0961464 | + | 0.166530i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.18614 | + | 27.1504i | 0.359332 | + | 1.19177i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.1168 | 0.530849 | 0.265424 | − | 0.964132i | \(-0.414488\pi\) | ||||
0.265424 | + | 0.964132i | \(0.414488\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.4891 | −0.589838 | −0.294919 | − | 0.955522i | \(-0.595293\pi\) | ||||
−0.294919 | + | 0.955522i | \(0.595293\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.25544 | + | 3.46410i | −0.142079 | + | 0.151186i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.1168 | − | 29.6472i | 0.745621 | − | 1.29145i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4307 | + | 19.7986i | 0.496987 | + | 0.860807i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.5000 | + | 11.6082i | −0.759435 | + | 0.503752i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.18614 | − | 3.78651i | −0.0946923 | − | 0.164012i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.2554 | − | 26.4232i | 0.659550 | − | 1.14237i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 38.7446 | + | 9.10268i | 1.67195 | + | 0.392810i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.1168 | 0.521909 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.23369 | 0.0960337 | 0.0480169 | − | 0.998847i | \(-0.484710\pi\) | ||||
0.0480169 | + | 0.998847i | \(0.484710\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.861407 | − | 0.202380i | −0.0369665 | − | 0.00868494i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.62772 | − | 9.74749i | 0.241065 | − | 0.417537i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.12772 | + | 14.0776i | 0.347516 | + | 0.601916i | 0.985808 | − | 0.167879i | \(-0.0536918\pi\) |
−0.638291 | + | 0.769795i | \(0.720359\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.441578 | − | 7.10313i | −0.0188461 | − | 0.303154i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.37228 | + | 2.37686i | 0.0584611 | + | 0.101258i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.9307 | − | 24.1287i | 0.592394 | − | 1.02606i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.6060 | + | 26.1831i | −1.04447 | + | 1.11141i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.0000 | −0.593199 | −0.296600 | − | 0.955002i | \(-0.595853\pi\) | ||||
−0.296600 | + | 0.955002i | \(0.595853\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.649468 | 0.0274696 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.68614 | + | 8.90892i | 0.113409 | + | 0.376135i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.87228 | + | 8.43904i | −0.205342 | + | 0.355663i | −0.950242 | − | 0.311514i | \(-0.899164\pi\) |
0.744900 | + | 0.667177i | \(0.232497\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.18614 | + | 8.98266i | 0.218183 | + | 0.377903i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.3030 | − | 36.2530i | 0.642665 | − | 1.52248i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.6168 | − | 23.5851i | −0.570848 | − | 0.988737i | −0.996479 | − | 0.0838407i | \(-0.973281\pi\) |
0.425631 | − | 0.904897i | \(-0.360052\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.2446 | − | 22.9403i | 0.554268 | − | 0.960020i | −0.443692 | − | 0.896179i | \(-0.646332\pi\) |
0.997960 | − | 0.0638407i | \(-0.0203349\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.93070 | − | 16.3533i | −0.205983 | − | 0.683169i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.233688 | −0.00974546 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.8614 | 0.618688 | 0.309344 | − | 0.950950i | \(-0.399890\pi\) | ||||
0.309344 | + | 0.950950i | \(0.399890\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.06930 | + | 2.20193i | −0.0859970 | + | 0.0915092i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.0475 | + | 36.4554i | −0.873199 | + | 1.51243i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.372281 | − | 0.644810i | −0.0154183 | − | 0.0267053i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.164391 | + | 2.64436i | 0.00679674 | + | 0.109331i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.61684 | − | 7.99661i | −0.190558 | − | 0.330055i | 0.754878 | − | 0.655866i | \(-0.227696\pi\) |
−0.945435 | + | 0.325810i | \(0.894363\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | + | 3.46410i | −0.0824086 | + | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.7228 | + | 6.04334i | 1.05810 | + | 0.248590i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.0000 | −1.06769 | −0.533846 | − | 0.845582i | \(-0.679254\pi\) | ||||
−0.533846 | + | 0.845582i | \(0.679254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −55.7228 | −2.28441 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −27.3723 | − | 6.43087i | −1.12027 | − | 0.263198i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.9307 | + | 34.5210i | −0.814346 | + | 1.41049i | 0.0954498 | + | 0.995434i | \(0.469571\pi\) |
−0.909796 | + | 0.415055i | \(0.863762\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.98913 | − | 5.17732i | −0.121929 | − | 0.211187i | 0.798599 | − | 0.601863i | \(-0.205575\pi\) |
−0.920528 | + | 0.390676i | \(0.872241\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.36141 | − | 6.20965i | 0.381226 | − | 0.252877i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.8614 | + | 20.5446i | 0.482235 | + | 0.835255i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.55842 | − | 9.62747i | 0.225609 | − | 0.390767i | −0.730893 | − | 0.682492i | \(-0.760896\pi\) |
0.956502 | + | 0.291725i | \(0.0942294\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22.6753 | − | 24.1287i | 0.918848 | − | 0.977744i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.62772 | −0.0658504 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.7446 | −0.514748 | −0.257374 | − | 0.966312i | \(-0.582857\pi\) | ||||
−0.257374 | + | 0.966312i | \(0.582857\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.9307 | + | 46.2029i | 0.561740 | + | 1.86308i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.9891 | + | 32.8901i | −0.764473 | + | 1.32411i | 0.176051 | + | 0.984381i | \(0.443668\pi\) |
−0.940525 | + | 0.339726i | \(0.889666\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.6168 | − | 18.3889i | −0.426727 | − | 0.739113i | 0.569853 | − | 0.821747i | \(-0.307000\pi\) |
−0.996580 | + | 0.0826338i | \(0.973667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.81386 | − | 0.672262i | 0.0727877 | − | 0.0269769i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.1168 | − | 22.7190i | −0.525515 | − | 0.910219i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.8723 | − | 24.0275i | 0.554891 | − | 0.961100i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.313859 | − | 1.04095i | −0.0125343 | − | 0.0415717i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −46.9783 | −1.87315 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.0000 | −1.27390 | −0.636950 | − | 0.770905i | \(-0.719804\pi\) | ||||
−0.636950 | + | 0.770905i | \(0.719804\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.4198 | − | 12.1518i | 0.453897 | − | 0.482991i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.00000 | + | 13.8564i | −0.317470 | + | 0.549875i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.25544 | + | 3.90653i | 0.0893637 | + | 0.154782i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.7446 | − | 5.34363i | −0.425048 | − | 0.211391i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.61684 | − | 2.80046i | −0.0638615 | − | 0.110611i | 0.832327 | − | 0.554285i | \(-0.187008\pi\) |
−0.896188 | + | 0.443674i | \(0.853675\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.50000 | + | 2.59808i | −0.0591542 | + | 0.102458i | −0.894086 | − | 0.447895i | \(-0.852174\pi\) |
0.834932 | + | 0.550353i | \(0.185507\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.97825 | − | 1.63948i | −0.274768 | − | 0.0645543i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.7228 | 1.32578 | 0.662890 | − | 0.748717i | \(-0.269330\pi\) | ||||
0.662890 | + | 0.748717i | \(0.269330\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.00000 | 0.274774 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 46.9783 | + | 11.0371i | 1.84122 | + | 0.432579i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.4416 | − | 19.8174i | 0.447744 | − | 0.775515i | −0.550495 | − | 0.834838i | \(-0.685561\pi\) |
0.998239 | + | 0.0593237i | \(0.0188944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.7921 | − | 37.7450i | −0.851488 | − | 1.47482i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −32.5475 | − | 16.1870i | −1.26980 | − | 0.631514i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.55842 | − | 16.5557i | −0.372343 | − | 0.644917i | 0.617582 | − | 0.786506i | \(-0.288112\pi\) |
−0.989926 | + | 0.141589i | \(0.954779\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.0475 | − | 39.9195i | 0.896446 | − | 1.55269i | 0.0644406 | − | 0.997922i | \(-0.479474\pi\) |
0.832005 | − | 0.554768i | \(-0.187193\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.37228 | + | 2.52434i | −0.0921318 | + | 0.0980372i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.51087 | 0.252481 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.62772 | 0.0630255 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.30298 | + | 24.2213i | 0.282350 | + | 0.936448i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.18614 | + | 2.05446i | −0.0457905 | + | 0.0793114i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.186141 | + | 0.322405i | 0.00717520 | + | 0.0124278i | 0.869591 | − | 0.493773i | \(-0.164383\pi\) |
−0.862416 | + | 0.506201i | \(0.831049\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.547547 | − | 3.21543i | 0.0210751 | − | 0.123762i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.3030 | + | 17.8453i | 0.395976 | + | 0.685850i | 0.993225 | − | 0.116205i | \(-0.0370731\pi\) |
−0.597249 | + | 0.802056i | \(0.703740\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.81386 | + | 6.60580i | −0.146362 | + | 0.253507i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.50000 | + | 24.8747i | 0.287401 | + | 0.953200i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.3723 | −0.588204 | −0.294102 | − | 0.955774i | \(-0.595021\pi\) | ||||
−0.294102 | + | 0.955774i | \(0.595021\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 42.0951 | 1.60837 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.8139 | + | 28.5326i | −1.02301 | + | 1.08858i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.138593 | − | 0.240051i | 0.00527999 | − | 0.00914521i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.55842 | − | 13.0916i | −0.287536 | − | 0.498027i | 0.685685 | − | 0.727898i | \(-0.259503\pi\) |
−0.973221 | + | 0.229872i | \(0.926169\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.9307 | + | 7.25061i | −0.415223 | + | 0.275428i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.81386 | − | 11.8020i | −0.258464 | − | 0.447674i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.5475 | + | 54.6420i | −1.19495 | + | 2.06971i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.05842 | + | 2.12819i | 0.342621 | + | 0.0804957i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.4891 | −1.34041 | −0.670203 | − | 0.742178i | \(-0.733793\pi\) | ||||
−0.670203 | + | 0.742178i | \(0.733793\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.48913 | 0.207026 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.4891 | + | 4.10891i | 0.658679 | + | 0.154751i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.5584 | − | 26.9480i | 0.585135 | − | 1.01348i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.3030 | + | 24.7735i | 0.537160 | + | 0.930388i | 0.999055 | + | 0.0434539i | \(0.0138361\pi\) |
−0.461896 | + | 0.886934i | \(0.652831\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.18614 | + | 19.0800i | 0.0444838 | + | 0.715556i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.18614 | + | 2.05446i | 0.0444213 | + | 0.0769400i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.441578 | − | 0.764836i | 0.0165141 | − | 0.0286032i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.4416 | − | 17.4954i | 0.614022 | − | 0.653379i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.4891 | 1.69646 | 0.848229 | − | 0.529630i | \(-0.177669\pi\) | ||||
0.848229 | + | 0.529630i | \(0.177669\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −54.0951 | −2.01461 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.87228 | − | 9.52628i | −0.106821 | − | 0.354286i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.37228 | − | 2.37686i | 0.0509652 | − | 0.0882744i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.44158 | − | 9.42509i | −0.201817 | − | 0.349557i | 0.747297 | − | 0.664490i | \(-0.231351\pi\) |
−0.949114 | + | 0.314933i | \(0.898018\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.00000 | + | 26.5330i | 0.185185 | + | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.68614 | − | 8.11663i | −0.173323 | − | 0.300205i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.9307 | − | 32.7889i | 0.699221 | − | 1.21109i | −0.269515 | − | 0.962996i | \(-0.586863\pi\) |
0.968737 | − | 0.248091i | \(-0.0798032\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.3723 | − | 47.6675i | −0.530130 | − | 1.75824i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.74456 | −0.137933 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.1168 | 1.54929 | 0.774647 | − | 0.632394i | \(-0.217928\pi\) | ||||
0.774647 | + | 0.632394i | \(0.217928\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.277187 | − | 0.294954i | 0.0101827 | − | 0.0108354i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.8139 | + | 30.8545i | −0.653527 | + | 1.13194i | 0.328734 | + | 0.944423i | \(0.393378\pi\) |
−0.982261 | + | 0.187520i | \(0.939955\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.93070 | + | 17.2005i | 0.363833 | + | 0.630177i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.79211 | − | 28.8275i | −0.0655699 | − | 1.05474i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28.1168 | + | 48.6998i | 1.02737 | + | 1.77945i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.8139 | − | 32.5866i | 0.686527 | − | 1.18910i | −0.286427 | − | 0.958102i | \(-0.592467\pi\) |
0.972954 | − | 0.230998i | \(-0.0741992\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.6644 | + | 3.91515i | 0.607284 | + | 0.142676i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.883156 | 0.0321413 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.51087 | 0.309333 | 0.154667 | − | 0.987967i | \(-0.450570\pi\) | ||||
0.154667 | + | 0.987967i | \(0.450570\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.627719 | − | 0.147477i | −0.0227847 | − | 0.00535307i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.67527 | − | 16.7581i | 0.350728 | − | 0.607479i | −0.635649 | − | 0.771978i | \(-0.719267\pi\) |
0.986377 | + | 0.164499i | \(0.0526008\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.3723 | + | 17.9653i | 0.375502 | + | 0.650388i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 31.8614 | − | 21.1345i | 1.15195 | − | 0.764118i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.30298 | + | 2.25684i | 0.0470480 | + | 0.0814896i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.5584 | + | 28.6800i | −0.597112 | + | 1.03423i | 0.396133 | + | 0.918193i | \(0.370352\pi\) |
−0.993245 | + | 0.116035i | \(0.962981\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.32473 | + | 5.66603i | −0.191766 | + | 0.204057i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.9783 | 1.04228 | 0.521138 | − | 0.853473i | \(-0.325508\pi\) | ||||
0.521138 | + | 0.853473i | \(0.325508\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.00000 | 0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −19.1168 | − | 63.4034i | −0.685813 | − | 2.27458i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.68614 | − | 6.38458i | 0.132070 | − | 0.228751i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | + | 3.46410i | 0.0715656 | + | 0.123955i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.81386 | + | 22.3966i | −0.136296 | + | 0.800390i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.69702 | + | 6.40342i | 0.131952 | + | 0.228548i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.4198 | + | 37.1002i | −0.763534 | + | 1.32248i | 0.177484 | + | 0.984124i | \(0.443204\pi\) |
−0.941018 | + | 0.338357i | \(0.890129\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.5584 | + | 35.0183i | 0.375890 | + | 1.24669i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.1168 | −0.679717 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.883156 | −0.0313618 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.09509 | + | 2.22938i | −0.0743053 | + | 0.0790681i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.69702 | + | 2.93932i | −0.0601114 | + | 0.104116i | −0.894515 | − | 0.447038i | \(-0.852479\pi\) |
0.834404 | + | 0.551154i | \(0.185812\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.7446 | + | 20.3422i | 0.415493 | + | 0.719655i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.1168 | + | 8.01544i | 0.569461 | + | 0.283212i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.05842 | + | 10.4935i | 0.213797 | + | 0.370307i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.93070 | − | 3.34408i | 0.0680484 | − | 0.117863i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.4891 | − | 5.04868i | −0.756453 | − | 0.177722i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.1386 | 0.461928 | 0.230964 | − | 0.972962i | \(-0.425812\pi\) | ||||
0.230964 | + | 0.972962i | \(0.425812\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.3505 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −36.2337 | − | 8.51278i | −1.27077 | − | 0.298556i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.2337 | − | 24.6535i | 0.498584 | − | 0.863573i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.547547 | + | 0.948380i | 0.0191563 | + | 0.0331796i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.37228 | − | 2.17448i | −0.152780 | − | 0.0759825i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.81386 | − | 16.9981i | −0.342506 | − | 0.593238i | 0.642391 | − | 0.766377i | \(-0.277942\pi\) |
−0.984897 | + | 0.173139i | \(0.944609\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.4416 | + | 21.5494i | −0.433686 | + | 0.751166i | −0.997187 | − | 0.0749488i | \(-0.976121\pi\) |
0.563501 | + | 0.826115i | \(0.309454\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.744563 | + | 0.792287i | −0.0259223 | + | 0.0275839i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.9783 | 1.07722 | 0.538610 | − | 0.842555i | \(-0.318950\pi\) | ||||
0.538610 | + | 0.842555i | \(0.318950\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.4891 | 0.537960 | 0.268980 | − | 0.963146i | \(-0.413314\pi\) | ||||
0.268980 | + | 0.963146i | \(0.413314\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.5584 | − | 48.2848i | −0.505026 | − | 1.67498i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 32.5475 | − | 56.3740i | 1.12771 | − | 1.95324i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.6753 | + | 39.2747i | 0.784710 | + | 1.35916i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −31.0475 | + | 11.5070i | −1.07316 | + | 0.397740i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.0475 | − | 26.0631i | −0.519499 | − | 0.899799i | −0.999743 | − | 0.0226638i | \(-0.992785\pi\) |
0.480244 | − | 0.877135i | \(-0.340548\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.94158 | − | 8.55906i | 0.170399 | − | 0.295140i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.93070 | + | 22.9865i | 0.238706 | + | 0.791699i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30.5109 | −1.04961 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43.7228 | −1.50233 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.3030 | + | 30.1171i | −0.971356 | + | 1.03362i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.62772 | − | 2.81929i | 0.0557975 | − | 0.0966441i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.5584 | − | 28.6800i | −0.566950 | − | 0.981985i | −0.996865 | − | 0.0791165i | \(-0.974790\pi\) |
0.429916 | − | 0.902869i | \(-0.358543\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.72281 | + | 2.46943i | −0.127318 | + | 0.0844529i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.5584 | − | 32.1441i | −0.633944 | − | 1.09802i | −0.986738 | − | 0.162322i | \(-0.948102\pi\) |
0.352794 | − | 0.935701i | \(-0.385232\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.24456 | − | 2.15565i | 0.0424639 | − | 0.0735497i | −0.844012 | − | 0.536324i | \(-0.819813\pi\) |
0.886476 | + | 0.462774i | \(0.153146\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −86.5842 | − | 20.3422i | −2.95078 | − | 0.693260i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.9783 | −0.646027 | −0.323014 | − | 0.946394i | \(-0.604696\pi\) | ||||
−0.323014 | + | 0.946394i | \(0.604696\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38.8397 | −1.32059 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20.0000 | + | 4.69882i | 0.679236 | + | 0.159580i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.18614 | − | 5.51856i | 0.108082 | − | 0.187204i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.697015 | − | 1.20727i | −0.0236175 | − | 0.0409066i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.324734 | − | 5.22360i | −0.0109906 | − | 0.176792i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.6753 | + | 39.2747i | 0.766564 | + | 1.32773i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.9307 | + | 24.1287i | −0.470406 | + | 0.814768i | −0.999427 | − | 0.0338410i | \(-0.989226\pi\) |
0.529021 | + | 0.848609i | \(0.322559\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.2812 | + | 24.7735i | −0.785257 | + | 0.835589i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.9783 | 0.841539 | 0.420769 | − | 0.907168i | \(-0.361760\pi\) | ||||
0.420769 | + | 0.907168i | \(0.361760\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.8397 | 1.07149 | 0.535745 | − | 0.844380i | \(-0.320031\pi\) | ||||
0.535745 | + | 0.844380i | \(0.320031\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.30298 | − | 27.5379i | −0.279102 | − | 0.925676i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.93070 | + | 10.2723i | −0.199134 | + | 0.344909i | −0.948248 | − | 0.317531i | \(-0.897146\pi\) |
0.749114 | + | 0.662441i | \(0.230479\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.7446 | − | 25.5383i | −0.494517 | − | 0.856528i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.50000 | − | 8.29156i | 0.117254 | − | 0.277778i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.37228 | − | 2.37686i | −0.0459216 | − | 0.0795386i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.2554 | + | 47.2078i | −0.911049 | + | 1.57798i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.0692967 | − | 0.229831i | −0.00231375 | − | 0.00767384i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.8614 | −0.929230 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00000 | −0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.04755 | − | 9.62747i | 0.301084 | − | 0.320382i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.605969 | − | 1.04957i | 0.0201431 | − | 0.0348889i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.5000 | − | 32.0429i | −0.614282 | − | 1.06397i | −0.990510 | − | 0.137441i | \(-0.956112\pi\) |
0.376228 | − | 0.926527i | \(-0.377221\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.32473 | + | 21.3094i | 0.0439387 | + | 0.706788i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.441578 | + | 0.764836i | 0.0146301 | + | 0.0253401i | 0.873248 | − | 0.487276i | \(-0.162010\pi\) |
−0.858618 | + | 0.512617i | \(0.828676\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.81386 | + | 8.33785i | −0.159315 | + | 0.275943i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.48913 | + | 2.22938i | 0.313701 | + | 0.0737012i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 80.3288 | 2.65269 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.2337 | 1.19524 | 0.597620 | − | 0.801780i | \(-0.296113\pi\) | ||||
0.597620 | + | 0.801780i | \(0.296113\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 52.8981 | + | 12.4279i | 1.74305 | + | 0.409514i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.744563 | + | 1.28962i | −0.0245076 | + | 0.0424484i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.74456 | − | 4.75372i | −0.0902407 | − | 0.156301i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 30.9307 | − | 20.5171i | 1.01590 | − | 0.673870i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.7921 | − | 32.5489i | −0.616549 | − | 1.06789i | −0.990111 | − | 0.140289i | \(-0.955197\pi\) |
0.373561 | − | 0.927605i | \(-0.378136\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.80298 | + | 6.58696i | −0.124638 | + | 0.215879i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.9090 | − | 13.7364i | 0.422620 | − | 0.449709i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.7446 | −0.416792 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0000 | 0.980057 | 0.490029 | − | 0.871706i | \(-0.336986\pi\) | ||||
0.490029 | + | 0.871706i | \(0.336986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.61684 | − | 18.6290i | −0.183299 | − | 0.607933i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.4198 | + | 23.2438i | −0.437474 | + | 0.757727i | −0.997494 | − | 0.0707520i | \(-0.977460\pi\) |
0.560020 | + | 0.828479i | \(0.310793\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.18614 | − | 3.78651i | −0.0711905 | − | 0.123306i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 41.4891 | + | 34.4010i | 1.34964 | + | 1.11906i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.8723 | + | 46.5442i | 0.873232 | + | 1.51248i | 0.858634 | + | 0.512588i | \(0.171313\pi\) |
0.0145974 | + | 0.999893i | \(0.495353\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.25544 | + | 3.90653i | −0.0732146 | + | 0.126811i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.3030 | − | 50.7543i | −0.496233 | − | 1.64582i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.88316 | −0.255360 | −0.127680 | − | 0.991815i | \(-0.540753\pi\) | ||||
−0.127680 | + | 0.991815i | \(0.540753\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.3940 | 0.757013 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.18614 | − | 5.51856i | 0.167644 | − | 0.178390i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −38.7921 | + | 67.1899i | −1.25266 | + | 2.16968i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.80298 | − | 8.31901i | −0.154935 | − | 0.268355i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34.5475 | − | 17.1816i | −1.11328 | − | 0.553671i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.06930 | − | 3.58413i | −0.0666130 | − | 0.115377i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.18614 | − | 7.25061i | 0.134617 | − | 0.233164i | −0.790834 | − | 0.612031i | \(-0.790353\pi\) |
0.925451 | + | 0.378867i | \(0.123686\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.68614 | − | 1.33591i | −0.182665 | − | 0.0429155i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.48913 | −0.176154 | −0.0880772 | − | 0.996114i | \(-0.528072\pi\) | ||||
−0.0880772 | + | 0.996114i | \(0.528072\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.1168 | 0.805209 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.394031 | − | 0.0925740i | −0.0126191 | − | 0.00296474i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.127719 | + | 0.221215i | −0.00408608 | + | 0.00707730i | −0.868061 | − | 0.496457i | \(-0.834634\pi\) |
0.863975 | + | 0.503534i | \(0.167967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.00000 | − | 5.19615i | −0.0958804 | − | 0.166070i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.7446 | − | 6.33830i | −0.406903 | − | 0.202366i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.5584 | − | 47.7326i | −0.878977 | − | 1.52243i | −0.852465 | − | 0.522785i | \(-0.824893\pi\) |
−0.0265123 | − | 0.999648i | \(-0.508440\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.0951 | + | 31.3416i | −0.576558 | + | 0.998627i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.6753 | + | 24.1287i | −0.721762 | + | 0.768025i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.649468 | 0.0206519 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.9783 | 1.61938 | 0.809689 | − | 0.586860i | \(-0.199636\pi\) | ||||
0.809689 | + | 0.586860i | \(0.199636\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.9307 | + | 52.8362i | 0.505546 | + | 1.67671i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.2554 | − | 33.3514i | 0.610438 | − | 1.05731i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.6753 | − | 42.7388i | −0.781474 | − | 1.35355i | −0.931083 | − | 0.364807i | \(-0.881135\pi\) |
0.149610 | − | 0.988745i | \(-0.452198\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 34.9783 | + | 29.0024i | 1.10666 | + | 0.917596i |
(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 | 72.2.i.b.49.2 | yes | 4 | |
3.2 | odd | 2 | 216.2.i.b.145.2 | 4 | |||
4.3 | odd | 2 | 144.2.i.d.49.1 | 4 | |||
8.3 | odd | 2 | 576.2.i.l.193.2 | 4 | |||
8.5 | even | 2 | 576.2.i.j.193.1 | 4 | |||
9.2 | odd | 6 | 216.2.i.b.73.2 | 4 | |||
9.4 | even | 3 | 648.2.a.f.1.2 | 2 | |||
9.5 | odd | 6 | 648.2.a.g.1.1 | 2 | |||
9.7 | even | 3 | inner | 72.2.i.b.25.2 | ✓ | 4 | |
12.11 | even | 2 | 432.2.i.d.145.2 | 4 | |||
24.5 | odd | 2 | 1728.2.i.i.577.1 | 4 | |||
24.11 | even | 2 | 1728.2.i.j.577.1 | 4 | |||
36.7 | odd | 6 | 144.2.i.d.97.1 | 4 | |||
36.11 | even | 6 | 432.2.i.d.289.2 | 4 | |||
36.23 | even | 6 | 1296.2.a.p.1.1 | 2 | |||
36.31 | odd | 6 | 1296.2.a.n.1.2 | 2 | |||
72.5 | odd | 6 | 5184.2.a.bp.1.2 | 2 | |||
72.11 | even | 6 | 1728.2.i.j.1153.1 | 4 | |||
72.13 | even | 6 | 5184.2.a.bt.1.1 | 2 | |||
72.29 | odd | 6 | 1728.2.i.i.1153.1 | 4 | |||
72.43 | odd | 6 | 576.2.i.l.385.2 | 4 | |||
72.59 | even | 6 | 5184.2.a.bo.1.2 | 2 | |||
72.61 | even | 6 | 576.2.i.j.385.1 | 4 | |||
72.67 | odd | 6 | 5184.2.a.bs.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.i.b.25.2 | ✓ | 4 | 9.7 | even | 3 | inner | |
72.2.i.b.49.2 | yes | 4 | 1.1 | even | 1 | trivial | |
144.2.i.d.49.1 | 4 | 4.3 | odd | 2 | |||
144.2.i.d.97.1 | 4 | 36.7 | odd | 6 | |||
216.2.i.b.73.2 | 4 | 9.2 | odd | 6 | |||
216.2.i.b.145.2 | 4 | 3.2 | odd | 2 | |||
432.2.i.d.145.2 | 4 | 12.11 | even | 2 | |||
432.2.i.d.289.2 | 4 | 36.11 | even | 6 | |||
576.2.i.j.193.1 | 4 | 8.5 | even | 2 | |||
576.2.i.j.385.1 | 4 | 72.61 | even | 6 | |||
576.2.i.l.193.2 | 4 | 8.3 | odd | 2 | |||
576.2.i.l.385.2 | 4 | 72.43 | odd | 6 | |||
648.2.a.f.1.2 | 2 | 9.4 | even | 3 | |||
648.2.a.g.1.1 | 2 | 9.5 | odd | 6 | |||
1296.2.a.n.1.2 | 2 | 36.31 | odd | 6 | |||
1296.2.a.p.1.1 | 2 | 36.23 | even | 6 | |||
1728.2.i.i.577.1 | 4 | 24.5 | odd | 2 | |||
1728.2.i.i.1153.1 | 4 | 72.29 | odd | 6 | |||
1728.2.i.j.577.1 | 4 | 24.11 | even | 2 | |||
1728.2.i.j.1153.1 | 4 | 72.11 | even | 6 | |||
5184.2.a.bo.1.2 | 2 | 72.59 | even | 6 | |||
5184.2.a.bp.1.2 | 2 | 72.5 | odd | 6 | |||
5184.2.a.bs.1.1 | 2 | 72.67 | odd | 6 | |||
5184.2.a.bt.1.1 | 2 | 72.13 | even | 6 |