Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(160,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.160");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.h (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: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 14x^{10} + 67x^{8} + 141x^{6} + 129x^{4} + 39x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 160.9 | ||
Root | \(2.61062i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.160 |
Dual form | 483.2.h.b.160.11 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.86081 | 1.31579 | 0.657894 | − | 0.753110i | \(-0.271447\pi\) | ||||
0.657894 | + | 0.753110i | \(0.271447\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 1.46260 | 0.731299 | ||||||||
\(5\) | −4.10256 | −1.83472 | −0.917361 | − | 0.398057i | \(-0.869685\pi\) | ||||
−0.917361 | + | 0.398057i | \(0.869685\pi\) | |||||||
\(6\) | − | 1.86081i | − | 0.759671i | ||||||
\(7\) | −0.663393 | − | 2.56123i | −0.250739 | − | 0.968055i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −7.63407 | −2.41411 | ||||||||
\(11\) | − | 1.89784i | − | 0.572220i | −0.958197 | − | 0.286110i | \(-0.907638\pi\) | ||
0.958197 | − | 0.286110i | \(-0.0923623\pi\) | |||||||
\(12\) | − | 1.46260i | − | 0.422216i | ||||||
\(13\) | − | 2.18421i | − | 0.605791i | −0.953024 | − | 0.302895i | \(-0.902047\pi\) | ||
0.953024 | − | 0.302895i | \(-0.0979533\pi\) | |||||||
\(14\) | −1.23445 | − | 4.76596i | −0.329920 | − | 1.27376i | ||||
\(15\) | 4.10256i | 1.05928i | ||||||||
\(16\) | −4.78600 | −1.19650 | ||||||||
\(17\) | 1.18482 | 0.287362 | 0.143681 | − | 0.989624i | \(-0.454106\pi\) | ||||
0.143681 | + | 0.989624i | \(0.454106\pi\) | |||||||
\(18\) | −1.86081 | −0.438596 | ||||||||
\(19\) | 4.98050 | 1.14261 | 0.571303 | − | 0.820740i | \(-0.306438\pi\) | ||||
0.571303 | + | 0.820740i | \(0.306438\pi\) | |||||||
\(20\) | −6.00040 | −1.34173 | ||||||||
\(21\) | −2.56123 | + | 0.663393i | −0.558907 | + | 0.144764i | ||||
\(22\) | − | 3.53151i | − | 0.752920i | ||||||
\(23\) | −4.25901 | + | 2.20472i | −0.888066 | + | 0.459717i | ||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | 11.8310 | 2.36620 | ||||||||
\(26\) | − | 4.06439i | − | 0.797093i | ||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −0.970278 | − | 3.74605i | −0.183365 | − | 0.707938i | ||||
\(29\) | 2.39821 | 0.445336 | 0.222668 | − | 0.974894i | \(-0.428523\pi\) | ||||
0.222668 | + | 0.974894i | \(0.428523\pi\) | |||||||
\(30\) | 7.63407i | 1.39378i | ||||||||
\(31\) | − | 9.32340i | − | 1.67453i | −0.546795 | − | 0.837266i | \(-0.684152\pi\) | ||
0.546795 | − | 0.837266i | \(-0.315848\pi\) | |||||||
\(32\) | −6.90582 | −1.22079 | ||||||||
\(33\) | −1.89784 | −0.330371 | ||||||||
\(34\) | 2.20472 | 0.378107 | ||||||||
\(35\) | 2.72161 | + | 10.5076i | 0.460036 | + | 1.77611i | ||||
\(36\) | −1.46260 | −0.243766 | ||||||||
\(37\) | 6.92106i | 1.13781i | 0.822402 | + | 0.568907i | \(0.192634\pi\) | ||||
−0.822402 | + | 0.568907i | \(0.807366\pi\) | |||||||
\(38\) | 9.26774 | 1.50343 | ||||||||
\(39\) | −2.18421 | −0.349754 | ||||||||
\(40\) | 4.10256 | 0.648672 | ||||||||
\(41\) | 5.60179i | 0.874853i | 0.899254 | + | 0.437427i | \(0.144110\pi\) | ||||
−0.899254 | + | 0.437427i | \(0.855890\pi\) | |||||||
\(42\) | −4.76596 | + | 1.23445i | −0.735403 | + | 0.190479i | ||||
\(43\) | − | 5.38663i | − | 0.821454i | −0.911758 | − | 0.410727i | \(-0.865275\pi\) | ||
0.911758 | − | 0.410727i | \(-0.134725\pi\) | |||||||
\(44\) | − | 2.77578i | − | 0.418464i | ||||||
\(45\) | 4.10256 | 0.611574 | ||||||||
\(46\) | −7.92520 | + | 4.10256i | −1.16851 | + | 0.604890i | ||||
\(47\) | − | 9.57201i | − | 1.39622i | −0.715990 | − | 0.698110i | \(-0.754025\pi\) | ||
0.715990 | − | 0.698110i | \(-0.245975\pi\) | |||||||
\(48\) | 4.78600i | 0.690800i | ||||||||
\(49\) | −6.11982 | + | 3.39821i | −0.874260 | + | 0.485458i | ||||
\(50\) | 22.0152 | 3.11342 | ||||||||
\(51\) | − | 1.18482i | − | 0.165908i | ||||||
\(52\) | − | 3.19462i | − | 0.443014i | ||||||
\(53\) | − | 5.85844i | − | 0.804718i | −0.915482 | − | 0.402359i | \(-0.868190\pi\) | ||
0.915482 | − | 0.402359i | \(-0.131810\pi\) | |||||||
\(54\) | 1.86081i | 0.253224i | ||||||||
\(55\) | 7.78600i | 1.04986i | ||||||||
\(56\) | 0.663393 | + | 2.56123i | 0.0886496 | + | 0.342259i | ||||
\(57\) | − | 4.98050i | − | 0.659683i | ||||||
\(58\) | 4.46260 | 0.585968 | ||||||||
\(59\) | 3.50761i | 0.456652i | 0.973585 | + | 0.228326i | \(0.0733253\pi\) | ||||
−0.973585 | + | 0.228326i | \(0.926675\pi\) | |||||||
\(60\) | 6.00040i | 0.774648i | ||||||||
\(61\) | −1.49171 | −0.190993 | −0.0954967 | − | 0.995430i | \(-0.530444\pi\) | ||||
−0.0954967 | + | 0.995430i | \(0.530444\pi\) | |||||||
\(62\) | − | 17.3490i | − | 2.20333i | ||||||
\(63\) | 0.663393 | + | 2.56123i | 0.0835797 | + | 0.322685i | ||||
\(64\) | −3.27839 | −0.409799 | ||||||||
\(65\) | 8.96086i | 1.11146i | ||||||||
\(66\) | −3.53151 | −0.434699 | ||||||||
\(67\) | − | 3.48879i | − | 0.426224i | −0.977028 | − | 0.213112i | \(-0.931640\pi\) | ||
0.977028 | − | 0.213112i | \(-0.0683599\pi\) | |||||||
\(68\) | 1.73292 | 0.210147 | ||||||||
\(69\) | 2.20472 | + | 4.25901i | 0.265418 | + | 0.512725i | ||||
\(70\) | 5.06439 | + | 19.5526i | 0.605311 | + | 2.33699i | ||||
\(71\) | 1.81579 | 0.215495 | 0.107747 | − | 0.994178i | \(-0.465636\pi\) | ||||
0.107747 | + | 0.994178i | \(0.465636\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 7.97021i | 0.932843i | 0.884563 | + | 0.466421i | \(0.154457\pi\) | ||||
−0.884563 | + | 0.466421i | \(0.845543\pi\) | |||||||
\(74\) | 12.8787i | 1.49712i | ||||||||
\(75\) | − | 11.8310i | − | 1.36613i | ||||||
\(76\) | 7.28447 | 0.835586 | ||||||||
\(77\) | −4.86081 | + | 1.25901i | −0.553940 | + | 0.143478i | ||||
\(78\) | −4.06439 | −0.460202 | ||||||||
\(79\) | − | 14.0833i | − | 1.58450i | −0.610198 | − | 0.792249i | \(-0.708910\pi\) | ||
0.610198 | − | 0.792249i | \(-0.291090\pi\) | |||||||
\(80\) | 19.6349 | 2.19525 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.4238i | 1.15112i | ||||||||
\(83\) | −2.51161 | −0.275685 | −0.137842 | − | 0.990454i | \(-0.544017\pi\) | ||||
−0.137842 | + | 0.990454i | \(0.544017\pi\) | |||||||
\(84\) | −3.74605 | + | 0.970278i | −0.408728 | + | 0.105866i | ||||
\(85\) | −4.86081 | −0.527228 | ||||||||
\(86\) | − | 10.0235i | − | 1.08086i | ||||||
\(87\) | − | 2.39821i | − | 0.257115i | ||||||
\(88\) | 1.89784i | 0.202310i | ||||||||
\(89\) | 4.57437 | 0.484882 | 0.242441 | − | 0.970166i | \(-0.422052\pi\) | ||||
0.242441 | + | 0.970166i | \(0.422052\pi\) | |||||||
\(90\) | 7.63407 | 0.804702 | ||||||||
\(91\) | −5.59427 | + | 1.44899i | −0.586439 | + | 0.151895i | ||||
\(92\) | −6.22923 | + | 3.22463i | −0.649442 | + | 0.336190i | ||||
\(93\) | −9.32340 | −0.966792 | ||||||||
\(94\) | − | 17.8116i | − | 1.83713i | ||||||
\(95\) | −20.4328 | −2.09636 | ||||||||
\(96\) | 6.90582i | 0.704822i | ||||||||
\(97\) | −7.44939 | −0.756371 | −0.378186 | − | 0.925730i | \(-0.623452\pi\) | ||||
−0.378186 | + | 0.925730i | \(0.623452\pi\) | |||||||
\(98\) | −11.3878 | + | 6.32340i | −1.15034 | + | 0.638760i | ||||
\(99\) | 1.89784i | 0.190740i | ||||||||
\(100\) | 17.3040 | 1.73040 | ||||||||
\(101\) | − | 17.1004i | − | 1.70156i | −0.525524 | − | 0.850779i | \(-0.676131\pi\) | ||
0.525524 | − | 0.850779i | \(-0.323869\pi\) | |||||||
\(102\) | − | 2.20472i | − | 0.218300i | ||||||
\(103\) | 8.91814 | 0.878731 | 0.439365 | − | 0.898308i | \(-0.355203\pi\) | ||||
0.439365 | + | 0.898308i | \(0.355203\pi\) | |||||||
\(104\) | 2.18421i | 0.214179i | ||||||||
\(105\) | 10.5076 | − | 2.72161i | 1.02544 | − | 0.265602i | ||||
\(106\) | − | 10.9014i | − | 1.05884i | ||||||
\(107\) | − | 6.51492i | − | 0.629821i | −0.949121 | − | 0.314911i | \(-0.898025\pi\) | ||
0.949121 | − | 0.314911i | \(-0.101975\pi\) | |||||||
\(108\) | 1.46260i | 0.140739i | ||||||||
\(109\) | − | 16.2880i | − | 1.56011i | −0.625710 | − | 0.780056i | \(-0.715191\pi\) | ||
0.625710 | − | 0.780056i | \(-0.284809\pi\) | |||||||
\(110\) | 14.4882i | 1.38140i | ||||||||
\(111\) | 6.92106 | 0.656917 | ||||||||
\(112\) | 3.17500 | + | 12.2581i | 0.300009 | + | 1.15828i | ||||
\(113\) | 15.5750i | 1.46518i | 0.680673 | + | 0.732588i | \(0.261688\pi\) | ||||
−0.680673 | + | 0.732588i | \(0.738312\pi\) | |||||||
\(114\) | − | 9.26774i | − | 0.868004i | ||||||
\(115\) | 17.4729 | − | 9.04502i | 1.62935 | − | 0.843452i | ||||
\(116\) | 3.50761 | 0.325674 | ||||||||
\(117\) | 2.18421i | 0.201930i | ||||||||
\(118\) | 6.52699i | 0.600858i | ||||||||
\(119\) | −0.786003 | − | 3.03460i | −0.0720527 | − | 0.278182i | ||||
\(120\) | − | 4.10256i | − | 0.374511i | ||||||
\(121\) | 7.39821 | 0.672564 | ||||||||
\(122\) | −2.77578 | −0.251307 | ||||||||
\(123\) | 5.60179 | 0.505097 | ||||||||
\(124\) | − | 13.6364i | − | 1.22458i | ||||||
\(125\) | −28.0247 | −2.50660 | ||||||||
\(126\) | 1.23445 | + | 4.76596i | 0.109973 | + | 0.424585i | ||||
\(127\) | 1.10941 | 0.0984440 | 0.0492220 | − | 0.998788i | \(-0.484326\pi\) | ||||
0.0492220 | + | 0.998788i | \(0.484326\pi\) | |||||||
\(128\) | 7.71120 | 0.681580 | ||||||||
\(129\) | −5.38663 | −0.474267 | ||||||||
\(130\) | 16.6744i | 1.46244i | ||||||||
\(131\) | 3.04502i | 0.266044i | 0.991113 | + | 0.133022i | \(0.0424681\pi\) | ||||
−0.991113 | + | 0.133022i | \(0.957532\pi\) | |||||||
\(132\) | −2.77578 | −0.241600 | ||||||||
\(133\) | −3.30403 | − | 12.7562i | −0.286496 | − | 1.10610i | ||||
\(134\) | − | 6.49197i | − | 0.560821i | ||||||
\(135\) | − | 4.10256i | − | 0.353092i | ||||||
\(136\) | −1.18482 | −0.101598 | ||||||||
\(137\) | − | 4.45216i | − | 0.380374i | −0.981748 | − | 0.190187i | \(-0.939091\pi\) | ||
0.981748 | − | 0.190187i | \(-0.0609094\pi\) | |||||||
\(138\) | 4.10256 | + | 7.92520i | 0.349233 | + | 0.674638i | ||||
\(139\) | 7.35801i | 0.624098i | 0.950066 | + | 0.312049i | \(0.101015\pi\) | ||||
−0.950066 | + | 0.312049i | \(0.898985\pi\) | |||||||
\(140\) | 3.98062 | + | 15.3684i | 0.336424 | + | 1.29887i | ||||
\(141\) | −9.57201 | −0.806108 | ||||||||
\(142\) | 3.37883 | 0.283545 | ||||||||
\(143\) | −4.14528 | −0.346646 | ||||||||
\(144\) | 4.78600 | 0.398834 | ||||||||
\(145\) | −9.83880 | −0.817068 | ||||||||
\(146\) | 14.8310i | 1.22742i | ||||||||
\(147\) | 3.39821 | + | 6.11982i | 0.280279 | + | 0.504754i | ||||
\(148\) | 10.1227i | 0.832083i | ||||||||
\(149\) | 20.7204i | 1.69749i | 0.528806 | + | 0.848743i | \(0.322640\pi\) | ||||
−0.528806 | + | 0.848743i | \(0.677360\pi\) | |||||||
\(150\) | − | 22.0152i | − | 1.79754i | ||||||
\(151\) | 21.6620 | 1.76283 | 0.881416 | − | 0.472341i | \(-0.156591\pi\) | ||||
0.881416 | + | 0.472341i | \(0.156591\pi\) | |||||||
\(152\) | −4.98050 | −0.403972 | ||||||||
\(153\) | −1.18482 | −0.0957872 | ||||||||
\(154\) | −9.04502 | + | 2.34278i | −0.728868 | + | 0.188787i | ||||
\(155\) | 38.2498i | 3.07230i | ||||||||
\(156\) | −3.19462 | −0.255774 | ||||||||
\(157\) | −12.2847 | −0.980428 | −0.490214 | − | 0.871602i | \(-0.663081\pi\) | ||||
−0.490214 | + | 0.871602i | \(0.663081\pi\) | |||||||
\(158\) | − | 26.2063i | − | 2.08486i | ||||||
\(159\) | −5.85844 | −0.464604 | ||||||||
\(160\) | 28.3316 | 2.23981 | ||||||||
\(161\) | 8.47221 | + | 9.44572i | 0.667704 | + | 0.744427i | ||||
\(162\) | 1.86081 | 0.146199 | ||||||||
\(163\) | −10.4328 | −0.817161 | −0.408580 | − | 0.912722i | \(-0.633976\pi\) | ||||
−0.408580 | + | 0.912722i | \(0.633976\pi\) | |||||||
\(164\) | 8.19317i | 0.639779i | ||||||||
\(165\) | 7.78600 | 0.606139 | ||||||||
\(166\) | −4.67362 | −0.362743 | ||||||||
\(167\) | 11.9702i | 0.926283i | 0.886284 | + | 0.463141i | \(0.153278\pi\) | ||||
−0.886284 | + | 0.463141i | \(0.846722\pi\) | |||||||
\(168\) | 2.56123 | − | 0.663393i | 0.197603 | − | 0.0511819i | ||||
\(169\) | 8.22923 | 0.633017 | ||||||||
\(170\) | −9.04502 | −0.693721 | ||||||||
\(171\) | −4.98050 | −0.380868 | ||||||||
\(172\) | − | 7.87848i | − | 0.600728i | ||||||
\(173\) | − | 5.17380i | − | 0.393357i | −0.980468 | − | 0.196678i | \(-0.936985\pi\) | ||
0.980468 | − | 0.196678i | \(-0.0630155\pi\) | |||||||
\(174\) | − | 4.46260i | − | 0.338309i | ||||||
\(175\) | −7.84862 | − | 30.3020i | −0.593300 | − | 2.29061i | ||||
\(176\) | 9.08306i | 0.684662i | ||||||||
\(177\) | 3.50761 | 0.263648 | ||||||||
\(178\) | 8.51201 | 0.638002 | ||||||||
\(179\) | −14.5616 | −1.08838 | −0.544192 | − | 0.838961i | \(-0.683164\pi\) | ||||
−0.544192 | + | 0.838961i | \(0.683164\pi\) | |||||||
\(180\) | 6.00040 | 0.447244 | ||||||||
\(181\) | −17.4499 | −1.29704 | −0.648521 | − | 0.761197i | \(-0.724612\pi\) | ||||
−0.648521 | + | 0.761197i | \(0.724612\pi\) | |||||||
\(182\) | −10.4098 | + | 2.69629i | −0.771629 | + | 0.199862i | ||||
\(183\) | 1.49171i | 0.110270i | ||||||||
\(184\) | 4.25901 | − | 2.20472i | 0.313979 | − | 0.162534i | ||||
\(185\) | − | 28.3941i | − | 2.08757i | ||||||
\(186\) | −17.3490 | −1.27209 | ||||||||
\(187\) | − | 2.24860i | − | 0.164434i | ||||||
\(188\) | − | 14.0000i | − | 1.02105i | ||||||
\(189\) | 2.56123 | − | 0.663393i | 0.186302 | − | 0.0482547i | ||||
\(190\) | −38.0215 | −2.75837 | ||||||||
\(191\) | 4.07961i | 0.295190i | 0.989048 | + | 0.147595i | \(0.0471532\pi\) | ||||
−0.989048 | + | 0.147595i | \(0.952847\pi\) | |||||||
\(192\) | 3.27839i | 0.236597i | ||||||||
\(193\) | 22.8864 | 1.64740 | 0.823701 | − | 0.567024i | \(-0.191905\pi\) | ||||
0.823701 | + | 0.567024i | \(0.191905\pi\) | |||||||
\(194\) | −13.8619 | −0.995224 | ||||||||
\(195\) | 8.96086 | 0.641700 | ||||||||
\(196\) | −8.95084 | + | 4.97021i | −0.639346 | + | 0.355015i | ||||
\(197\) | −0.702237 | −0.0500323 | −0.0250161 | − | 0.999687i | \(-0.507964\pi\) | ||||
−0.0250161 | + | 0.999687i | \(0.507964\pi\) | |||||||
\(198\) | 3.53151i | 0.250973i | ||||||||
\(199\) | 23.6947 | 1.67967 | 0.839837 | − | 0.542838i | \(-0.182650\pi\) | ||||
0.839837 | + | 0.542838i | \(0.182650\pi\) | |||||||
\(200\) | −11.8310 | −0.836579 | ||||||||
\(201\) | −3.48879 | −0.246081 | ||||||||
\(202\) | − | 31.8206i | − | 2.23889i | ||||||
\(203\) | −1.59095 | − | 6.14237i | −0.111663 | − | 0.431110i | ||||
\(204\) | − | 1.73292i | − | 0.121329i | ||||||
\(205\) | − | 22.9817i | − | 1.60511i | ||||||
\(206\) | 16.5949 | 1.15622 | ||||||||
\(207\) | 4.25901 | − | 2.20472i | 0.296022 | − | 0.153239i | ||||
\(208\) | 10.4536i | 0.724829i | ||||||||
\(209\) | − | 9.45219i | − | 0.653821i | ||||||
\(210\) | 19.5526 | − | 5.06439i | 1.34926 | − | 0.349476i | ||||
\(211\) | −20.7666 | −1.42963 | −0.714817 | − | 0.699312i | \(-0.753490\pi\) | ||||
−0.714817 | + | 0.699312i | \(0.753490\pi\) | |||||||
\(212\) | − | 8.56854i | − | 0.588490i | ||||||
\(213\) | − | 1.81579i | − | 0.124416i | ||||||
\(214\) | − | 12.1230i | − | 0.828712i | ||||||
\(215\) | 22.0990i | 1.50714i | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −23.8794 | + | 6.18508i | −1.62104 | + | 0.419871i | ||||
\(218\) | − | 30.3089i | − | 2.05278i | ||||||
\(219\) | 7.97021 | 0.538577 | ||||||||
\(220\) | 11.3878i | 0.767765i | ||||||||
\(221\) | − | 2.58790i | − | 0.174081i | ||||||
\(222\) | 12.8787 | 0.864364 | ||||||||
\(223\) | 24.5228i | 1.64217i | 0.570805 | + | 0.821086i | \(0.306631\pi\) | ||||
−0.570805 | + | 0.821086i | \(0.693369\pi\) | |||||||
\(224\) | 4.58127 | + | 17.6874i | 0.306099 | + | 1.18179i | ||||
\(225\) | −11.8310 | −0.788735 | ||||||||
\(226\) | 28.9821i | 1.92786i | ||||||||
\(227\) | −21.5098 | −1.42765 | −0.713826 | − | 0.700323i | \(-0.753039\pi\) | ||||
−0.713826 | + | 0.700323i | \(0.753039\pi\) | |||||||
\(228\) | − | 7.28447i | − | 0.482426i | ||||||
\(229\) | 10.4526 | 0.690725 | 0.345362 | − | 0.938469i | \(-0.387756\pi\) | ||||
0.345362 | + | 0.938469i | \(0.387756\pi\) | |||||||
\(230\) | 32.5136 | − | 16.8310i | 2.14388 | − | 1.10980i | ||||
\(231\) | 1.25901 | + | 4.86081i | 0.0828370 | + | 0.319818i | ||||
\(232\) | −2.39821 | −0.157450 | ||||||||
\(233\) | 4.19317 | 0.274704 | 0.137352 | − | 0.990522i | \(-0.456141\pi\) | ||||
0.137352 | + | 0.990522i | \(0.456141\pi\) | |||||||
\(234\) | 4.06439i | 0.265698i | ||||||||
\(235\) | 39.2697i | 2.56168i | ||||||||
\(236\) | 5.13023i | 0.333950i | ||||||||
\(237\) | −14.0833 | −0.914810 | ||||||||
\(238\) | −1.46260 | − | 5.64681i | −0.0948062 | − | 0.366028i | ||||
\(239\) | 21.8552 | 1.41370 | 0.706848 | − | 0.707365i | \(-0.250116\pi\) | ||||
0.706848 | + | 0.707365i | \(0.250116\pi\) | |||||||
\(240\) | − | 19.6349i | − | 1.26743i | ||||||
\(241\) | 19.8196 | 1.27669 | 0.638345 | − | 0.769750i | \(-0.279619\pi\) | ||||
0.638345 | + | 0.769750i | \(0.279619\pi\) | |||||||
\(242\) | 13.7666 | 0.884952 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −2.18177 | −0.139673 | ||||||||
\(245\) | 25.1069 | − | 13.9414i | 1.60402 | − | 0.890681i | ||||
\(246\) | 10.4238 | 0.664600 | ||||||||
\(247\) | − | 10.8785i | − | 0.692180i | ||||||
\(248\) | 9.32340i | 0.592037i | ||||||||
\(249\) | 2.51161i | 0.159167i | ||||||||
\(250\) | −52.1485 | −3.29816 | ||||||||
\(251\) | −7.92120 | −0.499981 | −0.249991 | − | 0.968248i | \(-0.580428\pi\) | ||||
−0.249991 | + | 0.968248i | \(0.580428\pi\) | |||||||
\(252\) | 0.970278 | + | 3.74605i | 0.0611218 | + | 0.235979i | ||||
\(253\) | 4.18421 | + | 8.08292i | 0.263059 | + | 0.508169i | ||||
\(254\) | 2.06439 | 0.129531 | ||||||||
\(255\) | 4.86081i | 0.304395i | ||||||||
\(256\) | 20.9058 | 1.30661 | ||||||||
\(257\) | − | 12.0900i | − | 0.754155i | −0.926182 | − | 0.377078i | \(-0.876929\pi\) | ||
0.926182 | − | 0.377078i | \(-0.123071\pi\) | |||||||
\(258\) | −10.0235 | −0.624034 | ||||||||
\(259\) | 17.7264 | − | 4.59138i | 1.10147 | − | 0.285294i | ||||
\(260\) | 13.1061i | 0.812808i | ||||||||
\(261\) | −2.39821 | −0.148445 | ||||||||
\(262\) | 5.66618i | 0.350058i | ||||||||
\(263\) | 13.3703i | 0.824448i | 0.911082 | + | 0.412224i | \(0.135248\pi\) | ||||
−0.911082 | + | 0.412224i | \(0.864752\pi\) | |||||||
\(264\) | 1.89784 | 0.116804 | ||||||||
\(265\) | 24.0346i | 1.47643i | ||||||||
\(266\) | −6.14816 | − | 23.7368i | −0.376968 | − | 1.45540i | ||||
\(267\) | − | 4.57437i | − | 0.279947i | ||||||
\(268\) | − | 5.10270i | − | 0.311697i | ||||||
\(269\) | − | 15.6066i | − | 0.951552i | −0.879567 | − | 0.475776i | \(-0.842167\pi\) | ||
0.879567 | − | 0.475776i | \(-0.157833\pi\) | |||||||
\(270\) | − | 7.63407i | − | 0.464595i | ||||||
\(271\) | − | 2.78745i | − | 0.169326i | −0.996410 | − | 0.0846628i | \(-0.973019\pi\) | ||
0.996410 | − | 0.0846628i | \(-0.0269813\pi\) | |||||||
\(272\) | −5.67056 | −0.343828 | ||||||||
\(273\) | 1.44899 | + | 5.59427i | 0.0876969 | + | 0.338581i | ||||
\(274\) | − | 8.28461i | − | 0.500492i | ||||||
\(275\) | − | 22.4534i | − | 1.35399i | ||||||
\(276\) | 3.22463 | + | 6.22923i | 0.194100 | + | 0.374955i | ||||
\(277\) | −26.1246 | −1.56968 | −0.784839 | − | 0.619700i | \(-0.787254\pi\) | ||||
−0.784839 | + | 0.619700i | \(0.787254\pi\) | |||||||
\(278\) | 13.6918i | 0.821181i | ||||||||
\(279\) | 9.32340i | 0.558178i | ||||||||
\(280\) | −2.72161 | − | 10.5076i | −0.162647 | − | 0.627950i | ||||
\(281\) | − | 25.4138i | − | 1.51606i | −0.652219 | − | 0.758031i | \(-0.726162\pi\) | ||
0.652219 | − | 0.758031i | \(-0.273838\pi\) | |||||||
\(282\) | −17.8116 | −1.06067 | ||||||||
\(283\) | 5.24467 | 0.311763 | 0.155882 | − | 0.987776i | \(-0.450178\pi\) | ||||
0.155882 | + | 0.987776i | \(0.450178\pi\) | |||||||
\(284\) | 2.65577 | 0.157591 | ||||||||
\(285\) | 20.4328i | 1.21034i | ||||||||
\(286\) | −7.71356 | −0.456112 | ||||||||
\(287\) | 14.3475 | − | 3.71619i | 0.846906 | − | 0.219360i | ||||
\(288\) | 6.90582 | 0.406929 | ||||||||
\(289\) | −15.5962 | −0.917423 | ||||||||
\(290\) | −18.3081 | −1.07509 | ||||||||
\(291\) | 7.44939i | 0.436691i | ||||||||
\(292\) | 11.6572i | 0.682187i | ||||||||
\(293\) | 24.5161 | 1.43225 | 0.716124 | − | 0.697973i | \(-0.245915\pi\) | ||||
0.716124 | + | 0.697973i | \(0.245915\pi\) | |||||||
\(294\) | 6.32340 | + | 11.3878i | 0.368788 | + | 0.664150i | ||||
\(295\) | − | 14.3902i | − | 0.837830i | ||||||
\(296\) | − | 6.92106i | − | 0.402278i | ||||||
\(297\) | 1.89784 | 0.110124 | ||||||||
\(298\) | 38.5567i | 2.23353i | ||||||||
\(299\) | 4.81558 | + | 9.30258i | 0.278492 | + | 0.537982i | ||||
\(300\) | − | 17.3040i | − | 0.999049i | ||||||
\(301\) | −13.7964 | + | 3.57345i | −0.795212 | + | 0.205971i | ||||
\(302\) | 40.3088 | 2.31951 | ||||||||
\(303\) | −17.1004 | −0.982395 | ||||||||
\(304\) | −23.8367 | −1.36713 | ||||||||
\(305\) | 6.11982 | 0.350420 | ||||||||
\(306\) | −2.20472 | −0.126036 | ||||||||
\(307\) | − | 33.2043i | − | 1.89507i | −0.319657 | − | 0.947533i | \(-0.603568\pi\) | ||
0.319657 | − | 0.947533i | \(-0.396432\pi\) | |||||||
\(308\) | −7.10941 | + | 1.84143i | −0.405096 | + | 0.104925i | ||||
\(309\) | − | 8.91814i | − | 0.507335i | ||||||
\(310\) | 71.1755i | 4.04250i | ||||||||
\(311\) | − | 22.5526i | − | 1.27884i | −0.768857 | − | 0.639421i | \(-0.779174\pi\) | ||
0.768857 | − | 0.639421i | \(-0.220826\pi\) | |||||||
\(312\) | 2.18421 | 0.123657 | ||||||||
\(313\) | −4.07961 | −0.230593 | −0.115296 | − | 0.993331i | \(-0.536782\pi\) | ||||
−0.115296 | + | 0.993331i | \(0.536782\pi\) | |||||||
\(314\) | −22.8595 | −1.29004 | ||||||||
\(315\) | −2.72161 | − | 10.5076i | −0.153345 | − | 0.592037i | ||||
\(316\) | − | 20.5982i | − | 1.15874i | ||||||
\(317\) | −12.8608 | −0.722335 | −0.361167 | − | 0.932501i | \(-0.617622\pi\) | ||||
−0.361167 | + | 0.932501i | \(0.617622\pi\) | |||||||
\(318\) | −10.9014 | −0.611321 | ||||||||
\(319\) | − | 4.55141i | − | 0.254830i | ||||||
\(320\) | 13.4498 | 0.751866 | ||||||||
\(321\) | −6.51492 | −0.363628 | ||||||||
\(322\) | 15.7651 | + | 17.5767i | 0.878557 | + | 0.979509i | ||||
\(323\) | 5.90101 | 0.328341 | ||||||||
\(324\) | 1.46260 | 0.0812555 | ||||||||
\(325\) | − | 25.8414i | − | 1.43342i | ||||||
\(326\) | −19.4134 | −1.07521 | ||||||||
\(327\) | −16.2880 | −0.900731 | ||||||||
\(328\) | − | 5.60179i | − | 0.309307i | ||||||
\(329\) | −24.5161 | + | 6.35000i | −1.35162 | + | 0.350087i | ||||
\(330\) | 14.4882 | 0.797551 | ||||||||
\(331\) | 24.6081 | 1.35258 | 0.676291 | − | 0.736635i | \(-0.263586\pi\) | ||||
0.676291 | + | 0.736635i | \(0.263586\pi\) | |||||||
\(332\) | −3.67347 | −0.201608 | ||||||||
\(333\) | − | 6.92106i | − | 0.379271i | ||||||
\(334\) | 22.2742i | 1.21879i | ||||||||
\(335\) | 14.3130i | 0.782002i | ||||||||
\(336\) | 12.2581 | − | 3.17500i | 0.668732 | − | 0.173211i | ||||
\(337\) | − | 1.77564i | − | 0.0967250i | −0.998830 | − | 0.0483625i | \(-0.984600\pi\) | ||
0.998830 | − | 0.0483625i | \(-0.0154003\pi\) | |||||||
\(338\) | 15.3130 | 0.832917 | ||||||||
\(339\) | 15.5750 | 0.845919 | ||||||||
\(340\) | −7.10941 | −0.385562 | ||||||||
\(341\) | −17.6943 | −0.958201 | ||||||||
\(342\) | −9.26774 | −0.501142 | ||||||||
\(343\) | 12.7634 | + | 13.4199i | 0.689161 | + | 0.724608i | ||||
\(344\) | 5.38663i | 0.290428i | ||||||||
\(345\) | −9.04502 | − | 17.4729i | −0.486967 | − | 0.940708i | ||||
\(346\) | − | 9.62743i | − | 0.517574i | ||||||
\(347\) | 0.766628 | 0.0411547 | 0.0205774 | − | 0.999788i | \(-0.493450\pi\) | ||||
0.0205774 | + | 0.999788i | \(0.493450\pi\) | |||||||
\(348\) | − | 3.50761i | − | 0.188028i | ||||||
\(349\) | − | 12.9896i | − | 0.695317i | −0.937621 | − | 0.347658i | \(-0.886977\pi\) | ||
0.937621 | − | 0.347658i | \(-0.113023\pi\) | |||||||
\(350\) | −14.6048 | − | 56.3861i | −0.780657 | − | 3.01396i | ||||
\(351\) | 2.18421 | 0.116585 | ||||||||
\(352\) | 13.1061i | 0.698559i | ||||||||
\(353\) | − | 0.736170i | − | 0.0391824i | −0.999808 | − | 0.0195912i | \(-0.993764\pi\) | ||
0.999808 | − | 0.0195912i | \(-0.00623647\pi\) | |||||||
\(354\) | 6.52699 | 0.346906 | ||||||||
\(355\) | −7.44939 | −0.395373 | ||||||||
\(356\) | 6.69046 | 0.354594 | ||||||||
\(357\) | −3.03460 | + | 0.786003i | −0.160608 | + | 0.0415997i | ||||
\(358\) | −27.0963 | −1.43208 | ||||||||
\(359\) | 24.8230i | 1.31011i | 0.755582 | + | 0.655054i | \(0.227354\pi\) | ||||
−0.755582 | + | 0.655054i | \(0.772646\pi\) | |||||||
\(360\) | −4.10256 | −0.216224 | ||||||||
\(361\) | 5.80538 | 0.305546 | ||||||||
\(362\) | −32.4709 | −1.70663 | ||||||||
\(363\) | − | 7.39821i | − | 0.388305i | ||||||
\(364\) | −8.18217 | + | 2.11929i | −0.428862 | + | 0.111081i | ||||
\(365\) | − | 32.6983i | − | 1.71151i | ||||||
\(366\) | 2.77578i | 0.145092i | ||||||||
\(367\) | −22.7405 | −1.18704 | −0.593522 | − | 0.804818i | \(-0.702263\pi\) | ||||
−0.593522 | + | 0.804818i | \(0.702263\pi\) | |||||||
\(368\) | 20.3836 | − | 10.5518i | 1.06257 | − | 0.550051i | ||||
\(369\) | − | 5.60179i | − | 0.291618i | ||||||
\(370\) | − | 52.8358i | − | 2.74680i | ||||||
\(371\) | −15.0048 | + | 3.88645i | −0.779011 | + | 0.201774i | ||||
\(372\) | −13.6364 | −0.707014 | ||||||||
\(373\) | 28.9224i | 1.49754i | 0.662828 | + | 0.748772i | \(0.269356\pi\) | ||||
−0.662828 | + | 0.748772i | \(0.730644\pi\) | |||||||
\(374\) | − | 4.18421i | − | 0.216360i | ||||||
\(375\) | 28.0247i | 1.44719i | ||||||||
\(376\) | 9.57201i | 0.493638i | ||||||||
\(377\) | − | 5.23819i | − | 0.269780i | ||||||
\(378\) | 4.76596 | − | 1.23445i | 0.245134 | − | 0.0634930i | ||||
\(379\) | − | 5.53774i | − | 0.284454i | −0.989834 | − | 0.142227i | \(-0.954574\pi\) | ||
0.989834 | − | 0.142227i | \(-0.0454264\pi\) | |||||||
\(380\) | −29.8850 | −1.53307 | ||||||||
\(381\) | − | 1.10941i | − | 0.0568366i | ||||||
\(382\) | 7.59136i | 0.388408i | ||||||||
\(383\) | 25.6550 | 1.31091 | 0.655456 | − | 0.755234i | \(-0.272477\pi\) | ||||
0.655456 | + | 0.755234i | \(0.272477\pi\) | |||||||
\(384\) | − | 7.71120i | − | 0.393511i | ||||||
\(385\) | 19.9418 | − | 5.16518i | 1.01633 | − | 0.263242i | ||||
\(386\) | 42.5872 | 2.16763 | ||||||||
\(387\) | 5.38663i | 0.273818i | ||||||||
\(388\) | −10.8955 | −0.553134 | ||||||||
\(389\) | − | 9.10602i | − | 0.461693i | −0.972990 | − | 0.230847i | \(-0.925850\pi\) | ||
0.972990 | − | 0.230847i | \(-0.0741496\pi\) | |||||||
\(390\) | 16.6744 | 0.844342 | ||||||||
\(391\) | −5.04617 | + | 2.61220i | −0.255196 | + | 0.132105i | ||||
\(392\) | 6.11982 | − | 3.39821i | 0.309098 | − | 0.171635i | ||||
\(393\) | 3.04502 | 0.153601 | ||||||||
\(394\) | −1.30673 | −0.0658319 | ||||||||
\(395\) | 57.7777i | 2.90711i | ||||||||
\(396\) | 2.77578i | 0.139488i | ||||||||
\(397\) | 18.6468i | 0.935856i | 0.883766 | + | 0.467928i | \(0.154999\pi\) | ||||
−0.883766 | + | 0.467928i | \(0.845001\pi\) | |||||||
\(398\) | 44.0913 | 2.21010 | ||||||||
\(399\) | −12.7562 | + | 3.30403i | −0.638610 | + | 0.165408i | ||||
\(400\) | −56.6233 | −2.83116 | ||||||||
\(401\) | − | 28.7377i | − | 1.43509i | −0.696511 | − | 0.717546i | \(-0.745265\pi\) | ||
0.696511 | − | 0.717546i | \(-0.254735\pi\) | |||||||
\(402\) | −6.49197 | −0.323790 | ||||||||
\(403\) | −20.3643 | −1.01442 | ||||||||
\(404\) | − | 25.0111i | − | 1.24435i | ||||||
\(405\) | −4.10256 | −0.203858 | ||||||||
\(406\) | −2.96046 | − | 11.4298i | −0.146925 | − | 0.567249i | ||||
\(407\) | 13.1350 | 0.651080 | ||||||||
\(408\) | 1.18482i | 0.0586574i | ||||||||
\(409\) | 20.6170i | 1.01945i | 0.860339 | + | 0.509723i | \(0.170252\pi\) | ||||
−0.860339 | + | 0.509723i | \(0.829748\pi\) | |||||||
\(410\) | − | 42.7645i | − | 2.11199i | ||||||
\(411\) | −4.45216 | −0.219609 | ||||||||
\(412\) | 13.0437 | 0.642615 | ||||||||
\(413\) | 8.98381 | − | 2.32693i | 0.442065 | − | 0.114501i | ||||
\(414\) | 7.92520 | − | 4.10256i | 0.389502 | − | 0.201630i | ||||
\(415\) | 10.3040 | 0.505805 | ||||||||
\(416\) | 15.0838i | 0.739542i | ||||||||
\(417\) | 7.35801 | 0.360323 | ||||||||
\(418\) | − | 17.5887i | − | 0.860291i | ||||||
\(419\) | 36.4940 | 1.78285 | 0.891424 | − | 0.453171i | \(-0.149707\pi\) | ||||
0.891424 | + | 0.453171i | \(0.149707\pi\) | |||||||
\(420\) | 15.3684 | − | 3.98062i | 0.749902 | − | 0.194235i | ||||
\(421\) | − | 16.7599i | − | 0.816825i | −0.912797 | − | 0.408413i | \(-0.866082\pi\) | ||
0.912797 | − | 0.408413i | \(-0.133918\pi\) | |||||||
\(422\) | −38.6427 | −1.88110 | ||||||||
\(423\) | 9.57201i | 0.465407i | ||||||||
\(424\) | 5.85844i | 0.284511i | ||||||||
\(425\) | 14.0177 | 0.679956 | ||||||||
\(426\) | − | 3.37883i | − | 0.163705i | ||||||
\(427\) | 0.989588 | + | 3.82061i | 0.0478895 | + | 0.184892i | ||||
\(428\) | − | 9.52872i | − | 0.460588i | ||||||
\(429\) | 4.14528i | 0.200136i | ||||||||
\(430\) | 41.1219i | 1.98308i | ||||||||
\(431\) | 13.6910i | 0.659472i | 0.944073 | + | 0.329736i | \(0.106960\pi\) | ||||
−0.944073 | + | 0.329736i | \(0.893040\pi\) | |||||||
\(432\) | − | 4.78600i | − | 0.230267i | ||||||
\(433\) | −8.81889 | −0.423809 | −0.211905 | − | 0.977290i | \(-0.567967\pi\) | ||||
−0.211905 | + | 0.977290i | \(0.567967\pi\) | |||||||
\(434\) | −44.4349 | + | 11.5092i | −2.13294 | + | 0.552461i | ||||
\(435\) | 9.83880i | 0.471734i | ||||||||
\(436\) | − | 23.8229i | − | 1.14091i | ||||||
\(437\) | −21.2120 | + | 10.9806i | −1.01471 | + | 0.525275i | ||||
\(438\) | 14.8310 | 0.708653 | ||||||||
\(439\) | 19.0034i | 0.906981i | 0.891261 | + | 0.453491i | \(0.149821\pi\) | ||||
−0.891261 | + | 0.453491i | \(0.850179\pi\) | |||||||
\(440\) | − | 7.78600i | − | 0.371183i | ||||||
\(441\) | 6.11982 | − | 3.39821i | 0.291420 | − | 0.161819i | ||||
\(442\) | − | 4.81558i | − | 0.229054i | ||||||
\(443\) | 20.3476 | 0.966743 | 0.483372 | − | 0.875415i | \(-0.339412\pi\) | ||||
0.483372 | + | 0.875415i | \(0.339412\pi\) | |||||||
\(444\) | 10.1227 | 0.480403 | ||||||||
\(445\) | −18.7666 | −0.889623 | ||||||||
\(446\) | 45.6323i | 2.16075i | ||||||||
\(447\) | 20.7204 | 0.980044 | ||||||||
\(448\) | 2.17486 | + | 8.39671i | 0.102752 | + | 0.396707i | ||||
\(449\) | −20.6724 | −0.975593 | −0.487797 | − | 0.872957i | \(-0.662199\pi\) | ||||
−0.487797 | + | 0.872957i | \(0.662199\pi\) | |||||||
\(450\) | −22.0152 | −1.03781 | ||||||||
\(451\) | 10.6313 | 0.500608 | ||||||||
\(452\) | 22.7800i | 1.07148i | ||||||||
\(453\) | − | 21.6620i | − | 1.01777i | ||||||
\(454\) | −40.0255 | −1.87849 | ||||||||
\(455\) | 22.9508 | − | 5.94457i | 1.07595 | − | 0.278686i | ||||
\(456\) | 4.98050i | 0.233233i | ||||||||
\(457\) | 33.5565i | 1.56971i | 0.619682 | + | 0.784853i | \(0.287261\pi\) | ||||
−0.619682 | + | 0.784853i | \(0.712739\pi\) | |||||||
\(458\) | 19.4502 | 0.908848 | ||||||||
\(459\) | 1.18482i | 0.0553028i | ||||||||
\(460\) | 25.5558 | − | 13.2292i | 1.19154 | − | 0.616816i | ||||
\(461\) | 3.26798i | 0.152205i | 0.997100 | + | 0.0761024i | \(0.0242476\pi\) | ||||
−0.997100 | + | 0.0761024i | \(0.975752\pi\) | |||||||
\(462\) | 2.34278 | + | 9.04502i | 0.108996 | + | 0.420812i | ||||
\(463\) | −4.65577 | −0.216372 | −0.108186 | − | 0.994131i | \(-0.534504\pi\) | ||||
−0.108186 | + | 0.994131i | \(0.534504\pi\) | |||||||
\(464\) | −11.4778 | −0.532845 | ||||||||
\(465\) | 38.2498 | 1.77379 | ||||||||
\(466\) | 7.80268 | 0.361452 | ||||||||
\(467\) | 17.2514 | 0.798300 | 0.399150 | − | 0.916886i | \(-0.369305\pi\) | ||||
0.399150 | + | 0.916886i | \(0.369305\pi\) | |||||||
\(468\) | 3.19462i | 0.147671i | ||||||||
\(469\) | −8.93561 | + | 2.31444i | −0.412608 | + | 0.106871i | ||||
\(470\) | 73.0734i | 3.37062i | ||||||||
\(471\) | 12.2847i | 0.566051i | ||||||||
\(472\) | − | 3.50761i | − | 0.161451i | ||||||
\(473\) | −10.2230 | −0.470052 | ||||||||
\(474\) | −26.2063 | −1.20370 | ||||||||
\(475\) | 58.9244 | 2.70364 | ||||||||
\(476\) | −1.14961 | − | 4.43841i | −0.0526921 | − | 0.203434i | ||||
\(477\) | 5.85844i | 0.268239i | ||||||||
\(478\) | 40.6683 | 1.86012 | ||||||||
\(479\) | 20.4333 | 0.933622 | 0.466811 | − | 0.884357i | \(-0.345403\pi\) | ||||
0.466811 | + | 0.884357i | \(0.345403\pi\) | |||||||
\(480\) | − | 28.3316i | − | 1.29315i | ||||||
\(481\) | 15.1170 | 0.689278 | ||||||||
\(482\) | 36.8803 | 1.67985 | ||||||||
\(483\) | 9.44572 | − | 8.47221i | 0.429795 | − | 0.385499i | ||||
\(484\) | 10.8206 | 0.491846 | ||||||||
\(485\) | 30.5616 | 1.38773 | ||||||||
\(486\) | − | 1.86081i | − | 0.0844079i | ||||||
\(487\) | 3.36215 | 0.152354 | 0.0761769 | − | 0.997094i | \(-0.475729\pi\) | ||||
0.0761769 | + | 0.997094i | \(0.475729\pi\) | |||||||
\(488\) | 1.49171 | 0.0675264 | ||||||||
\(489\) | 10.4328i | 0.471788i | ||||||||
\(490\) | 46.7191 | − | 25.9422i | 2.11056 | − | 1.17195i | ||||
\(491\) | 2.76181 | 0.124639 | 0.0623194 | − | 0.998056i | \(-0.480150\pi\) | ||||
0.0623194 | + | 0.998056i | \(0.480150\pi\) | |||||||
\(492\) | 8.19317 | 0.369377 | ||||||||
\(493\) | 2.84145 | 0.127972 | ||||||||
\(494\) | − | 20.2427i | − | 0.910762i | ||||||
\(495\) | − | 7.78600i | − | 0.349955i | ||||||
\(496\) | 44.6218i | 2.00358i | ||||||||
\(497\) | −1.20458 | − | 4.65066i | −0.0540329 | − | 0.208611i | ||||
\(498\) | 4.67362i | 0.209430i | ||||||||
\(499\) | 38.4328 | 1.72049 | 0.860244 | − | 0.509882i | \(-0.170311\pi\) | ||||
0.860244 | + | 0.509882i | \(0.170311\pi\) | |||||||
\(500\) | −40.9889 | −1.83308 | ||||||||
\(501\) | 11.9702 | 0.534790 | ||||||||
\(502\) | −14.7398 | −0.657870 | ||||||||
\(503\) | −11.5092 | −0.513172 | −0.256586 | − | 0.966521i | \(-0.582598\pi\) | ||||
−0.256586 | + | 0.966521i | \(0.582598\pi\) | |||||||
\(504\) | −0.663393 | − | 2.56123i | −0.0295499 | − | 0.114086i | ||||
\(505\) | 70.1556i | 3.12189i | ||||||||
\(506\) | 7.78600 | + | 15.0407i | 0.346130 | + | 0.668643i | ||||
\(507\) | − | 8.22923i | − | 0.365473i | ||||||
\(508\) | 1.62262 | 0.0719920 | ||||||||
\(509\) | 2.12878i | 0.0943566i | 0.998886 | + | 0.0471783i | \(0.0150229\pi\) | ||||
−0.998886 | + | 0.0471783i | \(0.984977\pi\) | |||||||
\(510\) | 9.04502i | 0.400520i | ||||||||
\(511\) | 20.4136 | − | 5.28738i | 0.903043 | − | 0.233900i | ||||
\(512\) | 23.4793 | 1.03765 | ||||||||
\(513\) | 4.98050i | 0.219894i | ||||||||
\(514\) | − | 22.4972i | − | 0.992309i | ||||||
\(515\) | −36.5872 | −1.61223 | ||||||||
\(516\) | −7.87848 | −0.346831 | ||||||||
\(517\) | −18.1661 | −0.798945 | ||||||||
\(518\) | 32.9854 | − | 8.54367i | 1.44930 | − | 0.375387i | ||||
\(519\) | −5.17380 | −0.227105 | ||||||||
\(520\) | − | 8.96086i | − | 0.392960i | ||||||
\(521\) | 24.4702 | 1.07206 | 0.536030 | − | 0.844199i | \(-0.319923\pi\) | ||||
0.536030 | + | 0.844199i | \(0.319923\pi\) | |||||||
\(522\) | −4.46260 | −0.195323 | ||||||||
\(523\) | 27.4141 | 1.19874 | 0.599368 | − | 0.800474i | \(-0.295419\pi\) | ||||
0.599368 | + | 0.800474i | \(0.295419\pi\) | |||||||
\(524\) | 4.45364i | 0.194558i | ||||||||
\(525\) | −30.3020 | + | 7.84862i | −1.32249 | + | 0.342542i | ||||
\(526\) | 24.8795i | 1.08480i | ||||||||
\(527\) | − | 11.0466i | − | 0.481196i | ||||||
\(528\) | 9.08306 | 0.395290 | ||||||||
\(529\) | 13.2784 | − | 18.7799i | 0.577321 | − | 0.816517i | ||||
\(530\) | 44.7237i | 1.94267i | ||||||||
\(531\) | − | 3.50761i | − | 0.152217i | ||||||
\(532\) | −4.83247 | − | 18.6572i | −0.209514 | − | 0.808893i | ||||
\(533\) | 12.2355 | 0.529978 | ||||||||
\(534\) | − | 8.51201i | − | 0.368351i | ||||||
\(535\) | 26.7279i | 1.15555i | ||||||||
\(536\) | 3.48879i | 0.150693i | ||||||||
\(537\) | 14.5616i | 0.628379i | ||||||||
\(538\) | − | 29.0409i | − | 1.25204i | ||||||
\(539\) | 6.44925 | + | 11.6144i | 0.277789 | + | 0.500269i | ||||
\(540\) | − | 6.00040i | − | 0.258216i | ||||||
\(541\) | −22.6468 | −0.973662 | −0.486831 | − | 0.873496i | \(-0.661847\pi\) | ||||
−0.486831 | + | 0.873496i | \(0.661847\pi\) | |||||||
\(542\) | − | 5.18691i | − | 0.222797i | ||||||
\(543\) | 17.4499i | 0.748847i | ||||||||
\(544\) | −8.18217 | −0.350808 | ||||||||
\(545\) | 66.8227i | 2.86237i | ||||||||
\(546\) | 2.69629 | + | 10.4098i | 0.115391 | + | 0.445500i | ||||
\(547\) | 24.1544 | 1.03277 | 0.516384 | − | 0.856357i | \(-0.327278\pi\) | ||||
0.516384 | + | 0.856357i | \(0.327278\pi\) | |||||||
\(548\) | − | 6.51173i | − | 0.278167i | ||||||
\(549\) | 1.49171 | 0.0636645 | ||||||||
\(550\) | − | 41.7814i | − | 1.78156i | ||||||
\(551\) | 11.9443 | 0.508843 | ||||||||
\(552\) | −2.20472 | − | 4.25901i | −0.0938393 | − | 0.181276i | ||||
\(553\) | −36.0707 | + | 9.34278i | −1.53388 | + | 0.397295i | ||||
\(554\) | −48.6129 | −2.06536 | ||||||||
\(555\) | −28.3941 | −1.20526 | ||||||||
\(556\) | 10.7618i | 0.456402i | ||||||||
\(557\) | 12.6008i | 0.533911i | 0.963709 | + | 0.266956i | \(0.0860177\pi\) | ||||
−0.963709 | + | 0.266956i | \(0.913982\pi\) | |||||||
\(558\) | 17.3490i | 0.734444i | ||||||||
\(559\) | −11.7655 | −0.497629 | ||||||||
\(560\) | −13.0256 | − | 50.2895i | −0.550434 | − | 2.12512i | ||||
\(561\) | −2.24860 | −0.0949360 | ||||||||
\(562\) | − | 47.2902i | − | 1.99482i | ||||||
\(563\) | −2.96365 | −0.124903 | −0.0624515 | − | 0.998048i | \(-0.519892\pi\) | ||||
−0.0624515 | + | 0.998048i | \(0.519892\pi\) | |||||||
\(564\) | −14.0000 | −0.589506 | ||||||||
\(565\) | − | 63.8975i | − | 2.68819i | ||||||
\(566\) | 9.75931 | 0.410214 | ||||||||
\(567\) | −0.663393 | − | 2.56123i | −0.0278599 | − | 0.107562i | ||||
\(568\) | −1.81579 | −0.0761889 | ||||||||
\(569\) | 14.1399i | 0.592774i | 0.955068 | + | 0.296387i | \(0.0957817\pi\) | ||||
−0.955068 | + | 0.296387i | \(0.904218\pi\) | |||||||
\(570\) | 38.0215i | 1.59255i | ||||||||
\(571\) | − | 19.0211i | − | 0.796009i | −0.917384 | − | 0.398004i | \(-0.869703\pi\) | ||
0.917384 | − | 0.398004i | \(-0.130297\pi\) | |||||||
\(572\) | −6.06288 | −0.253502 | ||||||||
\(573\) | 4.07961 | 0.170428 | ||||||||
\(574\) | 26.6979 | − | 6.91511i | 1.11435 | − | 0.288631i | ||||
\(575\) | −50.3885 | + | 26.0841i | −2.10134 | + | 1.08778i | ||||
\(576\) | 3.27839 | 0.136600 | ||||||||
\(577\) | 7.11355i | 0.296141i | 0.988977 | + | 0.148071i | \(0.0473063\pi\) | ||||
−0.988977 | + | 0.148071i | \(0.952694\pi\) | |||||||
\(578\) | −29.0215 | −1.20714 | ||||||||
\(579\) | − | 22.8864i | − | 0.951128i | ||||||
\(580\) | −14.3902 | −0.597521 | ||||||||
\(581\) | 1.66618 | + | 6.43281i | 0.0691249 | + | 0.266878i | ||||
\(582\) | 13.8619i | 0.574593i | ||||||||
\(583\) | −11.1184 | −0.460476 | ||||||||
\(584\) | − | 7.97021i | − | 0.329810i | ||||||
\(585\) | − | 8.96086i | − | 0.370486i | ||||||
\(586\) | 45.6198 | 1.88453 | ||||||||
\(587\) | − | 30.9419i | − | 1.27711i | −0.769577 | − | 0.638554i | \(-0.779533\pi\) | ||
0.769577 | − | 0.638554i | \(-0.220467\pi\) | |||||||
\(588\) | 4.97021 | + | 8.95084i | 0.204968 | + | 0.369126i | ||||
\(589\) | − | 46.4352i | − | 1.91333i | ||||||
\(590\) | − | 26.7774i | − | 1.10241i | ||||||
\(591\) | 0.702237i | 0.0288862i | ||||||||
\(592\) | − | 33.1242i | − | 1.36140i | ||||||
\(593\) | − | 25.4253i | − | 1.04409i | −0.852917 | − | 0.522046i | \(-0.825169\pi\) | ||
0.852917 | − | 0.522046i | \(-0.174831\pi\) | |||||||
\(594\) | 3.53151 | 0.144900 | ||||||||
\(595\) | 3.22463 | + | 12.4497i | 0.132197 | + | 0.510386i | ||||
\(596\) | 30.3057i | 1.24137i | ||||||||
\(597\) | − | 23.6947i | − | 0.969760i | ||||||
\(598\) | 8.96086 | + | 17.3103i | 0.366437 | + | 0.707871i | ||||
\(599\) | 5.08858 | 0.207914 | 0.103957 | − | 0.994582i | \(-0.466850\pi\) | ||||
0.103957 | + | 0.994582i | \(0.466850\pi\) | |||||||
\(600\) | 11.8310i | 0.482999i | ||||||||
\(601\) | 29.1004i | 1.18703i | 0.804822 | + | 0.593516i | \(0.202261\pi\) | ||||
−0.804822 | + | 0.593516i | \(0.797739\pi\) | |||||||
\(602\) | −25.6724 | + | 6.64951i | −1.04633 | + | 0.271014i | ||||
\(603\) | 3.48879i | 0.142075i | ||||||||
\(604\) | 31.6829 | 1.28916 | ||||||||
\(605\) | −30.3516 | −1.23397 | ||||||||
\(606\) | −31.8206 | −1.29262 | ||||||||
\(607\) | 19.5679i | 0.794235i | 0.917768 | + | 0.397117i | \(0.129989\pi\) | ||||
−0.917768 | + | 0.397117i | \(0.870011\pi\) | |||||||
\(608\) | −34.3944 | −1.39488 | ||||||||
\(609\) | −6.14237 | + | 1.59095i | −0.248901 | + | 0.0644687i | ||||
\(610\) | 11.3878 | 0.461078 | ||||||||
\(611\) | −20.9073 | −0.845818 | ||||||||
\(612\) | −1.73292 | −0.0700491 | ||||||||
\(613\) | 1.89784i | 0.0766530i | 0.999265 | + | 0.0383265i | \(0.0122027\pi\) | ||||
−0.999265 | + | 0.0383265i | \(0.987797\pi\) | |||||||
\(614\) | − | 61.7867i | − | 2.49351i | ||||||
\(615\) | −22.9817 | −0.926712 | ||||||||
\(616\) | 4.86081 | − | 1.25901i | 0.195847 | − | 0.0507271i | ||||
\(617\) | − | 26.4903i | − | 1.06646i | −0.845971 | − | 0.533229i | \(-0.820978\pi\) | ||
0.845971 | − | 0.533229i | \(-0.179022\pi\) | |||||||
\(618\) | − | 16.5949i | − | 0.667546i | ||||||
\(619\) | −28.9058 | −1.16182 | −0.580911 | − | 0.813967i | \(-0.697304\pi\) | ||||
−0.580911 | + | 0.813967i | \(0.697304\pi\) | |||||||
\(620\) | 55.9442i | 2.24677i | ||||||||
\(621\) | −2.20472 | − | 4.25901i | −0.0884725 | − | 0.170908i | ||||
\(622\) | − | 41.9661i | − | 1.68269i | ||||||
\(623\) | −3.03460 | − | 11.7160i | −0.121579 | − | 0.469392i | ||||
\(624\) | 10.4536 | 0.418480 | ||||||||
\(625\) | 55.8179 | 2.23272 | ||||||||
\(626\) | −7.59136 | −0.303412 | ||||||||
\(627\) | −9.45219 | −0.377484 | ||||||||
\(628\) | −17.9676 | −0.716986 | ||||||||
\(629\) | 8.20022i | 0.326964i | ||||||||
\(630\) | −5.06439 | − | 19.5526i | −0.201770 | − | 0.778995i | ||||
\(631\) | − | 11.9976i | − | 0.477617i | −0.971067 | − | 0.238809i | \(-0.923243\pi\) | ||
0.971067 | − | 0.238809i | \(-0.0767569\pi\) | |||||||
\(632\) | 14.0833i | 0.560204i | ||||||||
\(633\) | 20.7666i | 0.825399i | ||||||||
\(634\) | −23.9315 | −0.950440 | ||||||||
\(635\) | −4.55141 | −0.180617 | ||||||||
\(636\) | −8.56854 | −0.339765 | ||||||||
\(637\) | 7.42240 | + | 13.3670i | 0.294086 | + | 0.529619i | ||||
\(638\) | − | 8.46929i | − | 0.335303i | ||||||
\(639\) | −1.81579 | −0.0718315 | ||||||||
\(640\) | −31.6357 | −1.25051 | ||||||||
\(641\) | − | 24.2520i | − | 0.957895i | −0.877844 | − | 0.478947i | \(-0.841018\pi\) | ||
0.877844 | − | 0.478947i | \(-0.158982\pi\) | |||||||
\(642\) | −12.1230 | −0.478457 | ||||||||
\(643\) | −22.8931 | −0.902815 | −0.451407 | − | 0.892318i | \(-0.649078\pi\) | ||||
−0.451407 | + | 0.892318i | \(0.649078\pi\) | |||||||
\(644\) | 12.3914 | + | 13.8153i | 0.488291 | + | 0.544399i | ||||
\(645\) | 22.0990 | 0.870147 | ||||||||
\(646\) | 10.9806 | 0.432027 | ||||||||
\(647\) | − | 22.0948i | − | 0.868638i | −0.900759 | − | 0.434319i | \(-0.856989\pi\) | ||
0.900759 | − | 0.434319i | \(-0.143011\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 6.65689 | 0.261306 | ||||||||
\(650\) | − | 48.0859i | − | 1.88608i | ||||||
\(651\) | 6.18508 | + | 23.8794i | 0.242412 | + | 0.935908i | ||||
\(652\) | −15.2590 | −0.597589 | ||||||||
\(653\) | 0.680742 | 0.0266395 | 0.0133197 | − | 0.999911i | \(-0.495760\pi\) | ||||
0.0133197 | + | 0.999911i | \(0.495760\pi\) | |||||||
\(654\) | −30.3089 | −1.18517 | ||||||||
\(655\) | − | 12.4924i | − | 0.488117i | ||||||
\(656\) | − | 26.8102i | − | 1.04676i | ||||||
\(657\) | − | 7.97021i | − | 0.310948i | ||||||
\(658\) | −45.6198 | + | 11.8161i | −1.77844 | + | 0.460640i | ||||
\(659\) | 10.1425i | 0.395095i | 0.980293 | + | 0.197548i | \(0.0632977\pi\) | ||||
−0.980293 | + | 0.197548i | \(0.936702\pi\) | |||||||
\(660\) | 11.3878 | 0.443269 | ||||||||
\(661\) | −3.93764 | −0.153157 | −0.0765783 | − | 0.997064i | \(-0.524400\pi\) | ||||
−0.0765783 | + | 0.997064i | \(0.524400\pi\) | |||||||
\(662\) | 45.7908 | 1.77971 | ||||||||
\(663\) | −2.58790 | −0.100506 | ||||||||
\(664\) | 2.51161 | 0.0974693 | ||||||||
\(665\) | 13.5550 | + | 52.3332i | 0.525640 | + | 2.02939i | ||||
\(666\) | − | 12.8787i | − | 0.499041i | ||||||
\(667\) | −10.2140 | + | 5.28738i | −0.395488 | + | 0.204728i | ||||
\(668\) | 17.5076i | 0.677390i | ||||||||
\(669\) | 24.5228 | 0.948108 | ||||||||
\(670\) | 26.6337i | 1.02895i | ||||||||
\(671\) | 2.83102i | 0.109290i | ||||||||
\(672\) | 17.6874 | − | 4.58127i | 0.682307 | − | 0.176727i | ||||
\(673\) | 14.5062 | 0.559172 | 0.279586 | − | 0.960121i | \(-0.409803\pi\) | ||||
0.279586 | + | 0.960121i | \(0.409803\pi\) | |||||||
\(674\) | − | 3.30411i | − | 0.127270i | ||||||
\(675\) | 11.8310i | 0.455376i | ||||||||
\(676\) | 12.0361 | 0.462925 | ||||||||
\(677\) | −7.46596 | −0.286940 | −0.143470 | − | 0.989655i | \(-0.545826\pi\) | ||||
−0.143470 | + | 0.989655i | \(0.545826\pi\) | |||||||
\(678\) | 28.9821 | 1.11305 | ||||||||
\(679\) | 4.94187 | + | 19.0796i | 0.189652 | + | 0.732209i | ||||
\(680\) | 4.86081 | 0.186403 | ||||||||
\(681\) | 21.5098i | 0.824256i | ||||||||
\(682\) | −32.9257 | −1.26079 | ||||||||
\(683\) | 17.5243 | 0.670548 | 0.335274 | − | 0.942121i | \(-0.391171\pi\) | ||||
0.335274 | + | 0.942121i | \(0.391171\pi\) | |||||||
\(684\) | −7.28447 | −0.278529 | ||||||||
\(685\) | 18.2653i | 0.697880i | ||||||||
\(686\) | 23.7503 | + | 24.9719i | 0.906790 | + | 0.953431i | ||||
\(687\) | − | 10.4526i | − | 0.398790i | ||||||
\(688\) | 25.7804i | 0.982870i | ||||||||
\(689\) | −12.7961 | −0.487491 | ||||||||
\(690\) | −16.8310 | − | 32.5136i | −0.640746 | − | 1.23777i | ||||
\(691\) | 23.4391i | 0.891665i | 0.895117 | + | 0.445832i | \(0.147092\pi\) | ||||
−0.895117 | + | 0.445832i | \(0.852908\pi\) | |||||||
\(692\) | − | 7.56719i | − | 0.287661i | ||||||
\(693\) | 4.86081 | − | 1.25901i | 0.184647 | − | 0.0478260i | ||||
\(694\) | 1.42655 | 0.0541509 | ||||||||
\(695\) | − | 30.1867i | − | 1.14505i | ||||||
\(696\) | 2.39821i | 0.0909038i | ||||||||
\(697\) | 6.63713i | 0.251399i | ||||||||
\(698\) | − | 24.1711i | − | 0.914890i | ||||||
\(699\) | − | 4.19317i | − | 0.158600i | ||||||
\(700\) | −11.4794 | − | 44.3196i | −0.433880 | − | 1.67512i | ||||
\(701\) | 5.57451i | 0.210546i | 0.994443 | + | 0.105273i | \(0.0335717\pi\) | ||||
−0.994443 | + | 0.105273i | \(0.966428\pi\) | |||||||
\(702\) | 4.06439 | 0.153401 | ||||||||
\(703\) | 34.4703i | 1.30007i | ||||||||
\(704\) | 6.22185i | 0.234495i | ||||||||
\(705\) | 39.2697 | 1.47898 | ||||||||
\(706\) | − | 1.36987i | − | 0.0515557i | ||||||
\(707\) | −43.7982 | + | 11.3443i | −1.64720 | + | 0.426647i | ||||
\(708\) | 5.13023 | 0.192806 | ||||||||
\(709\) | 10.9244i | 0.410273i | 0.978733 | + | 0.205137i | \(0.0657639\pi\) | ||||
−0.978733 | + | 0.205137i | \(0.934236\pi\) | |||||||
\(710\) | −13.8619 | −0.520227 | ||||||||
\(711\) | 14.0833i | 0.528166i | ||||||||
\(712\) | −4.57437 | −0.171432 | ||||||||
\(713\) | 20.5555 | + | 39.7085i | 0.769811 | + | 1.48710i | ||||
\(714\) | −5.64681 | + | 1.46260i | −0.211326 | + | 0.0547364i | ||||
\(715\) | 17.0063 | 0.635998 | ||||||||
\(716\) | −21.2978 | −0.795935 | ||||||||
\(717\) | − | 21.8552i | − | 0.816198i | ||||||
\(718\) | 46.1908i | 1.72383i | ||||||||
\(719\) | − | 40.9162i | − | 1.52592i | −0.646447 | − | 0.762959i | \(-0.723746\pi\) | ||
0.646447 | − | 0.762959i | \(-0.276254\pi\) | |||||||
\(720\) | −19.6349 | −0.731749 | ||||||||
\(721\) | −5.91623 | − | 22.8414i | −0.220332 | − | 0.850659i | ||||
\(722\) | 10.8027 | 0.402034 | ||||||||
\(723\) | − | 19.8196i | − | 0.737097i | ||||||
\(724\) | −25.5222 | −0.948526 | ||||||||
\(725\) | 28.3732 | 1.05376 | ||||||||
\(726\) | − | 13.7666i | − | 0.510927i | ||||||
\(727\) | −20.8165 | −0.772041 | −0.386021 | − | 0.922490i | \(-0.626151\pi\) | ||||
−0.386021 | + | 0.922490i | \(0.626151\pi\) | |||||||
\(728\) | 5.59427 | − | 1.44899i | 0.207337 | − | 0.0537031i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | − | 60.8452i | − | 2.25198i | ||||||
\(731\) | − | 6.38220i | − | 0.236054i | ||||||
\(732\) | 2.18177i | 0.0806405i | ||||||||
\(733\) | −43.2639 | −1.59799 | −0.798995 | − | 0.601338i | \(-0.794635\pi\) | ||||
−0.798995 | + | 0.601338i | \(0.794635\pi\) | |||||||
\(734\) | −42.3156 | −1.56190 | ||||||||
\(735\) | −13.9414 | − | 25.1069i | −0.514235 | − | 0.926083i | ||||
\(736\) | 29.4120 | − | 15.2254i | 1.08414 | − | 0.561217i | ||||
\(737\) | −6.62117 | −0.243894 | ||||||||
\(738\) | − | 10.4238i | − | 0.383707i | ||||||
\(739\) | −17.4343 | −0.641330 | −0.320665 | − | 0.947193i | \(-0.603906\pi\) | ||||
−0.320665 | + | 0.947193i | \(0.603906\pi\) | |||||||
\(740\) | − | 41.5291i | − | 1.52664i | ||||||
\(741\) | −10.8785 | −0.399630 | ||||||||
\(742\) | −27.9211 | + | 7.23192i | −1.02501 | + | 0.265492i | ||||
\(743\) | − | 45.3129i | − | 1.66237i | −0.555998 | − | 0.831184i | \(-0.687664\pi\) | ||
0.555998 | − | 0.831184i | \(-0.312336\pi\) | |||||||
\(744\) | 9.32340 | 0.341813 | ||||||||
\(745\) | − | 85.0069i | − | 3.11441i | ||||||
\(746\) | 53.8189i | 1.97045i | ||||||||
\(747\) | 2.51161 | 0.0918949 | ||||||||
\(748\) | − | 3.28880i | − | 0.120250i | ||||||
\(749\) | −16.6862 | + | 4.32195i | −0.609702 | + | 0.157921i | ||||
\(750\) | 52.1485i | 1.90419i | ||||||||
\(751\) | 7.41582i | 0.270607i | 0.990804 | + | 0.135303i | \(0.0432009\pi\) | ||||
−0.990804 | + | 0.135303i | \(0.956799\pi\) | |||||||
\(752\) | 45.8116i | 1.67058i | ||||||||
\(753\) | 7.92120i | 0.288664i | ||||||||
\(754\) | − | 9.74725i | − | 0.354974i | ||||||
\(755\) | −88.8699 | −3.23431 | ||||||||
\(756\) | 3.74605 | − | 0.970278i | 0.136243 | − | 0.0352887i | ||||
\(757\) | − | 37.6558i | − | 1.36862i | −0.729189 | − | 0.684312i | \(-0.760102\pi\) | ||
0.729189 | − | 0.684312i | \(-0.239898\pi\) | |||||||
\(758\) | − | 10.3047i | − | 0.374282i | ||||||
\(759\) | 8.08292 | − | 4.18421i | 0.293391 | − | 0.151877i | ||||
\(760\) | 20.4328 | 0.741176 | ||||||||
\(761\) | 31.7312i | 1.15026i | 0.818063 | + | 0.575128i | \(0.195048\pi\) | ||||
−0.818063 | + | 0.575128i | \(0.804952\pi\) | |||||||
\(762\) | − | 2.06439i | − | 0.0747850i | ||||||
\(763\) | −41.7175 | + | 10.8054i | −1.51027 | + | 0.391181i | ||||
\(764\) | 5.96683i | 0.215872i | ||||||||
\(765\) | 4.86081 | 0.175743 | ||||||||
\(766\) | 47.7390 | 1.72488 | ||||||||
\(767\) | 7.66137 | 0.276636 | ||||||||
\(768\) | − | 20.9058i | − | 0.754374i | ||||||
\(769\) | 19.4332 | 0.700779 | 0.350389 | − | 0.936604i | \(-0.386049\pi\) | ||||
0.350389 | + | 0.936604i | \(0.386049\pi\) | |||||||
\(770\) | 37.1077 | − | 9.61140i | 1.33727 | − | 0.346371i | ||||
\(771\) | −12.0900 | −0.435412 | ||||||||
\(772\) | 33.4737 | 1.20474 | ||||||||
\(773\) | −25.3849 | −0.913032 | −0.456516 | − | 0.889715i | \(-0.650903\pi\) | ||||
−0.456516 | + | 0.889715i | \(0.650903\pi\) | |||||||
\(774\) | 10.0235i | 0.360286i | ||||||||
\(775\) | − | 110.305i | − | 3.96229i | ||||||
\(776\) | 7.44939 | 0.267418 | ||||||||
\(777\) | −4.59138 | − | 17.7264i | −0.164715 | − | 0.635932i | ||||
\(778\) | − | 16.9445i | − | 0.607491i | ||||||
\(779\) | 27.8997i | 0.999611i | ||||||||
\(780\) | 13.1061 | 0.469275 | ||||||||
\(781\) | − | 3.44608i | − | 0.123310i | ||||||
\(782\) | −9.38995 | + | 4.86081i | −0.335784 | + | 0.173822i | ||||
\(783\) | 2.39821i | 0.0857049i | ||||||||
\(784\) | 29.2895 | − | 16.2638i | 1.04605 | − | 0.580851i | ||||
\(785\) | 50.3989 | 1.79881 | ||||||||
\(786\) | 5.66618 | 0.202106 | ||||||||
\(787\) | 25.9054 | 0.923427 | 0.461714 | − | 0.887029i | \(-0.347235\pi\) | ||||
0.461714 | + | 0.887029i | \(0.347235\pi\) | |||||||
\(788\) | −1.02709 | −0.0365886 | ||||||||
\(789\) | 13.3703 | 0.475995 | ||||||||
\(790\) | 107.513i | 3.82514i | ||||||||
\(791\) | 39.8913 | − | 10.3324i | 1.41837 | − | 0.367377i | ||||
\(792\) | − | 1.89784i | − | 0.0674368i | ||||||
\(793\) | 3.25820i | 0.115702i | ||||||||
\(794\) | 34.6981i | 1.23139i | ||||||||
\(795\) | 24.0346 | 0.852420 | ||||||||
\(796\) | 34.6559 | 1.22834 | ||||||||
\(797\) | −16.5949 | −0.587823 | −0.293911 | − | 0.955833i | \(-0.594957\pi\) | ||||
−0.293911 | + | 0.955833i | \(0.594957\pi\) | |||||||
\(798\) | −23.7368 | + | 6.14816i | −0.840275 | + | 0.217642i | ||||
\(799\) | − | 11.3411i | − | 0.401220i | ||||||
\(800\) | −81.7029 | −2.88863 | ||||||||
\(801\) | −4.57437 | −0.161627 | ||||||||
\(802\) | − | 53.4753i | − | 1.88828i | ||||||
\(803\) | 15.1262 | 0.533791 | ||||||||
\(804\) | −5.10270 | −0.179958 | ||||||||
\(805\) | −34.7578 | − | 38.7517i | −1.22505 | − | 1.36582i | ||||
\(806\) | −37.8940 | −1.33476 | ||||||||
\(807\) | −15.6066 | −0.549379 | ||||||||
\(808\) | 17.1004i | 0.601592i | ||||||||
\(809\) | −32.2742 | −1.13470 | −0.567351 | − | 0.823476i | \(-0.692032\pi\) | ||||
−0.567351 | + | 0.823476i | \(0.692032\pi\) | |||||||
\(810\) | −7.63407 | −0.268234 | ||||||||
\(811\) | 21.3926i | 0.751196i | 0.926783 | + | 0.375598i | \(0.122563\pi\) | ||||
−0.926783 | + | 0.375598i | \(0.877437\pi\) | |||||||
\(812\) | −2.32693 | − | 8.98381i | −0.0816591 | − | 0.315270i | ||||
\(813\) | −2.78745 | −0.0977602 | ||||||||
\(814\) | 24.4418 | 0.856684 | ||||||||
\(815\) | 42.8013 | 1.49926 | ||||||||
\(816\) | 5.67056i | 0.198509i | ||||||||
\(817\) | − | 26.8281i | − | 0.938597i | ||||||
\(818\) | 38.3643i | 1.34138i | ||||||||
\(819\) | 5.59427 | − | 1.44899i | 0.195480 | − | 0.0506318i | ||||
\(820\) | − | 33.6130i | − | 1.17382i | ||||||
\(821\) | −1.82957 | −0.0638524 | −0.0319262 | − | 0.999490i | \(-0.510164\pi\) | ||||
−0.0319262 | + | 0.999490i | \(0.510164\pi\) | |||||||
\(822\) | −8.28461 | −0.288959 | ||||||||
\(823\) | −15.9564 | −0.556206 | −0.278103 | − | 0.960551i | \(-0.589706\pi\) | ||||
−0.278103 | + | 0.960551i | \(0.589706\pi\) | |||||||
\(824\) | −8.91814 | −0.310678 | ||||||||
\(825\) | −22.4534 | −0.781726 | ||||||||
\(826\) | 16.7171 | − | 4.32996i | 0.581663 | − | 0.150659i | ||||
\(827\) | 14.5322i | 0.505333i | 0.967553 | + | 0.252667i | \(0.0813076\pi\) | ||||
−0.967553 | + | 0.252667i | \(0.918692\pi\) | |||||||
\(828\) | 6.22923 | − | 3.22463i | 0.216481 | − | 0.112063i | ||||
\(829\) | − | 12.7279i | − | 0.442057i | −0.975267 | − | 0.221029i | \(-0.929059\pi\) | ||
0.975267 | − | 0.221029i | \(-0.0709415\pi\) | |||||||
\(830\) | 19.1738 | 0.665532 | ||||||||
\(831\) | 26.1246i | 0.906254i | ||||||||
\(832\) | 7.16069i | 0.248252i | ||||||||
\(833\) | −7.25090 | + | 4.02627i | −0.251229 | + | 0.139502i | ||||
\(834\) | 13.6918 | 0.474109 | ||||||||
\(835\) | − | 49.1085i | − | 1.69947i | ||||||
\(836\) | − | 13.8248i | − | 0.478139i | ||||||
\(837\) | 9.32340 | 0.322264 | ||||||||
\(838\) | 67.9082 | 2.34585 | ||||||||
\(839\) | −5.04298 | −0.174103 | −0.0870514 | − | 0.996204i | \(-0.527744\pi\) | ||||
−0.0870514 | + | 0.996204i | \(0.527744\pi\) | |||||||
\(840\) | −10.5076 | + | 2.72161i | −0.362547 | + | 0.0939045i | ||||
\(841\) | −23.2486 | −0.801676 | ||||||||
\(842\) | − | 31.1868i | − | 1.07477i | ||||||
\(843\) | −25.4138 | −0.875299 | ||||||||
\(844\) | −30.3732 | −1.04549 | ||||||||
\(845\) | −33.7609 | −1.16141 | ||||||||
\(846\) | 17.8116i | 0.612377i | ||||||||
\(847\) | −4.90792 | − | 18.9485i | −0.168638 | − | 0.651079i | ||||
\(848\) | 28.0385i | 0.962846i | ||||||||
\(849\) | − | 5.24467i | − | 0.179997i | ||||||
\(850\) | 26.0841 | 0.894678 | ||||||||
\(851\) | −15.2590 | − | 29.4769i | −0.523072 | − | 1.01045i | ||||
\(852\) | − | 2.65577i | − | 0.0909852i | ||||||
\(853\) | − | 2.16753i | − | 0.0742149i | −0.999311 | − | 0.0371074i | \(-0.988186\pi\) | ||
0.999311 | − | 0.0371074i | \(-0.0118144\pi\) | |||||||
\(854\) | 1.84143 | + | 7.10941i | 0.0630125 | + | 0.243279i | ||||
\(855\) | 20.4328 | 0.698787 | ||||||||
\(856\) | 6.51492i | 0.222675i | ||||||||
\(857\) | − | 27.9709i | − | 0.955467i | −0.878505 | − | 0.477734i | \(-0.841458\pi\) | ||
0.878505 | − | 0.477734i | \(-0.158542\pi\) | |||||||
\(858\) | 7.71356i | 0.263337i | ||||||||
\(859\) | − | 9.46405i | − | 0.322909i | −0.986880 | − | 0.161455i | \(-0.948381\pi\) | ||
0.986880 | − | 0.161455i | \(-0.0516185\pi\) | |||||||
\(860\) | 32.3220i | 1.10217i | ||||||||
\(861\) | −3.71619 | − | 14.3475i | −0.126647 | − | 0.488961i | ||||
\(862\) | 25.4763i | 0.867726i | ||||||||
\(863\) | −23.2549 | −0.791605 | −0.395802 | − | 0.918336i | \(-0.629533\pi\) | ||||
−0.395802 | + | 0.918336i | \(0.629533\pi\) | |||||||
\(864\) | − | 6.90582i | − | 0.234941i | ||||||
\(865\) | 21.2258i | 0.721700i | ||||||||
\(866\) | −16.4102 | −0.557643 | ||||||||
\(867\) | 15.5962i | 0.529675i | ||||||||
\(868\) | −34.9260 | + | 9.04629i | −1.18546 | + | 0.307051i | ||||
\(869\) | −26.7279 | −0.906681 | ||||||||
\(870\) | 18.3081i | 0.620702i | ||||||||
\(871\) | −7.62026 | −0.258203 | ||||||||
\(872\) | 16.2880i | 0.551583i | ||||||||
\(873\) | 7.44939 | 0.252124 | ||||||||
\(874\) | −39.4714 | + | 20.4328i | −1.33514 | + | 0.691150i | ||||
\(875\) | 18.5914 | + | 71.7777i | 0.628503 | + | 2.42653i | ||||
\(876\) | 11.6572 | 0.393861 | ||||||||
\(877\) | 32.6981 | 1.10414 | 0.552068 | − | 0.833799i | \(-0.313839\pi\) | ||||
0.552068 | + | 0.833799i | \(0.313839\pi\) | |||||||
\(878\) | 35.3616i | 1.19340i | ||||||||
\(879\) | − | 24.5161i | − | 0.826908i | ||||||
\(880\) | − | 37.2638i | − | 1.25616i | ||||||
\(881\) | 28.9651 | 0.975859 | 0.487929 | − | 0.872883i | \(-0.337752\pi\) | ||||
0.487929 | + | 0.872883i | \(0.337752\pi\) | |||||||
\(882\) | 11.3878 | − | 6.32340i | 0.383447 | − | 0.212920i | ||||
\(883\) | −18.6427 | −0.627376 | −0.313688 | − | 0.949526i | \(-0.601565\pi\) | ||||
−0.313688 | + | 0.949526i | \(0.601565\pi\) | |||||||
\(884\) | − | 3.78506i | − | 0.127305i | ||||||
\(885\) | −14.3902 | −0.483722 | ||||||||
\(886\) | 37.8629 | 1.27203 | ||||||||
\(887\) | − | 37.4570i | − | 1.25768i | −0.777533 | − | 0.628842i | \(-0.783529\pi\) | ||
0.777533 | − | 0.628842i | \(-0.216471\pi\) | |||||||
\(888\) | −6.92106 | −0.232255 | ||||||||
\(889\) | −0.735973 | − | 2.84145i | −0.0246837 | − | 0.0952991i | ||||
\(890\) | −34.9211 | −1.17056 | ||||||||
\(891\) | − | 1.89784i | − | 0.0635800i | ||||||
\(892\) | 35.8671i | 1.20092i | ||||||||
\(893\) | − | 47.6734i | − | 1.59533i | ||||||
\(894\) | 38.5567 | 1.28953 | ||||||||
\(895\) | 59.7398 | 1.99688 | ||||||||
\(896\) | −5.11556 | − | 19.7502i | −0.170899 | − | 0.659807i | ||||
\(897\) | 9.30258 | − | 4.81558i | 0.310604 | − | 0.160788i | ||||
\(898\) | −38.4674 | −1.28367 | ||||||||
\(899\) | − | 22.3595i | − | 0.745730i | ||||||
\(900\) | −17.3040 | −0.576801 | ||||||||
\(901\) | − | 6.94120i | − | 0.231245i | ||||||
\(902\) | 19.7828 | 0.658695 | ||||||||
\(903\) | 3.57345 | + | 13.7964i | 0.118917 | + | 0.459116i | ||||
\(904\) | − | 15.5750i | − | 0.518018i | ||||||
\(905\) | 71.5894 | 2.37971 | ||||||||
\(906\) | − | 40.3088i | − | 1.33917i | ||||||
\(907\) | 32.3151i | 1.07301i | 0.843898 | + | 0.536503i | \(0.180255\pi\) | ||||
−0.843898 | + | 0.536503i | \(0.819745\pi\) | |||||||
\(908\) | −31.4601 | −1.04404 | ||||||||
\(909\) | 17.1004i | 0.567186i | ||||||||
\(910\) | 42.7071 | − | 11.0617i | 1.41573 | − | 0.366692i | ||||
\(911\) | − | 19.5922i | − | 0.649117i | −0.945866 | − | 0.324559i | \(-0.894784\pi\) | ||
0.945866 | − | 0.324559i | \(-0.105216\pi\) | |||||||
\(912\) | 23.8367i | 0.789312i | ||||||||
\(913\) | 4.76663i | 0.157752i | ||||||||
\(914\) | 62.4421i | 2.06540i | ||||||||
\(915\) | − | 6.11982i | − | 0.202315i | ||||||
\(916\) | 15.2879 | 0.505127 | ||||||||
\(917\) | 7.79899 | − | 2.02004i | 0.257545 | − | 0.0667077i | ||||
\(918\) | 2.20472i | 0.0727667i | ||||||||
\(919\) | 13.3565i | 0.440590i | 0.975433 | + | 0.220295i | \(0.0707020\pi\) | ||||
−0.975433 | + | 0.220295i | \(0.929298\pi\) | |||||||
\(920\) | −17.4729 | + | 9.04502i | −0.576063 | + | 0.298205i | ||||
\(921\) | −33.2043 | −1.09412 | ||||||||
\(922\) | 6.08107i | 0.200269i | ||||||||
\(923\) | − | 3.96607i | − | 0.130545i | ||||||
\(924\) | 1.84143 | + | 7.10941i | 0.0605786 | + | 0.233882i | ||||
\(925\) | 81.8831i | 2.69230i | ||||||||
\(926\) | −8.66349 | −0.284700 | ||||||||
\(927\) | −8.91814 | −0.292910 | ||||||||
\(928\) | −16.5616 | −0.543661 | ||||||||
\(929\) | 13.2984i | 0.436307i | 0.975914 | + | 0.218154i | \(0.0700034\pi\) | ||||
−0.975914 | + | 0.218154i | \(0.929997\pi\) | |||||||
\(930\) | 71.1755 | 2.33394 | ||||||||
\(931\) | −30.4798 | + | 16.9248i | −0.998934 | + | 0.554687i | ||||
\(932\) | 6.13293 | 0.200891 | ||||||||
\(933\) | −22.5526 | −0.738340 | ||||||||
\(934\) | 32.1015 | 1.05039 | ||||||||
\(935\) | 9.22503i | 0.301691i | ||||||||
\(936\) | − | 2.18421i | − | 0.0713931i | ||||||
\(937\) | −17.8652 | −0.583630 | −0.291815 | − | 0.956475i | \(-0.594259\pi\) | ||||
−0.291815 | + | 0.956475i | \(0.594259\pi\) | |||||||
\(938\) | −16.6274 | + | 4.30673i | −0.542905 | + | 0.140620i | ||||
\(939\) | 4.07961i | 0.133133i | ||||||||
\(940\) | 57.4359i | 1.87335i | ||||||||
\(941\) | 49.6994 | 1.62015 | 0.810076 | − | 0.586324i | \(-0.199426\pi\) | ||||
0.810076 | + | 0.586324i | \(0.199426\pi\) | |||||||
\(942\) | 22.8595i | 0.744803i | ||||||||
\(943\) | −12.3504 | − | 23.8581i | −0.402184 | − | 0.776927i | ||||
\(944\) | − | 16.7875i | − | 0.546385i | ||||||
\(945\) | −10.5076 | + | 2.72161i | −0.341813 | + | 0.0885340i | ||||
\(946\) | −19.0229 | −0.618489 | ||||||||
\(947\) | −23.8116 | −0.773774 | −0.386887 | − | 0.922127i | \(-0.626450\pi\) | ||||
−0.386887 | + | 0.922127i | \(0.626450\pi\) | |||||||
\(948\) | −20.5982 | −0.669000 | ||||||||
\(949\) | 17.4086 | 0.565108 | ||||||||
\(950\) | 109.647 | 3.55741 | ||||||||
\(951\) | 12.8608i | 0.417040i | ||||||||
\(952\) | 0.786003 | + | 3.03460i | 0.0254745 | + | 0.0983521i | ||||
\(953\) | − | 55.6859i | − | 1.80384i | −0.431898 | − | 0.901922i | \(-0.642156\pi\) | ||
0.431898 | − | 0.901922i | \(-0.357844\pi\) | |||||||
\(954\) | 10.9014i | 0.352946i | ||||||||
\(955\) | − | 16.7368i | − | 0.541591i | ||||||
\(956\) | 31.9654 | 1.03383 | ||||||||
\(957\) | −4.55141 | −0.147126 | ||||||||
\(958\) | 38.0225 | 1.22845 | ||||||||
\(959\) | −11.4030 | + | 2.95353i | −0.368223 | + | 0.0953746i | ||||
\(960\) | − | 13.4498i | − | 0.434090i | ||||||
\(961\) | −55.9259 | −1.80406 | ||||||||
\(962\) | 28.1299 | 0.906944 | ||||||||
\(963\) | 6.51492i | 0.209940i | ||||||||
\(964\) | 28.9881 | 0.933642 | ||||||||
\(965\) | −93.8931 | −3.02253 | ||||||||
\(966\) | 17.5767 | − | 15.7651i | 0.565520 | − | 0.507235i | ||||
\(967\) | 34.2188 | 1.10040 | 0.550201 | − | 0.835032i | \(-0.314551\pi\) | ||||
0.550201 | + | 0.835032i | \(0.314551\pi\) | |||||||
\(968\) | −7.39821 | −0.237787 | ||||||||
\(969\) | − | 5.90101i | − | 0.189568i | ||||||
\(970\) | 56.8692 | 1.82596 | ||||||||
\(971\) | 60.1092 | 1.92900 | 0.964498 | − | 0.264090i | \(-0.0850715\pi\) | ||||
0.964498 | + | 0.264090i | \(0.0850715\pi\) | |||||||
\(972\) | − | 1.46260i | − | 0.0469129i | ||||||
\(973\) | 18.8456 | − | 4.88125i | 0.604161 | − | 0.156486i | ||||
\(974\) | 6.25632 | 0.200465 | ||||||||
\(975\) | −25.8414 | −0.827588 | ||||||||
\(976\) | 7.13931 | 0.228524 | ||||||||
\(977\) | − | 50.3329i | − | 1.61029i | −0.593077 | − | 0.805146i | \(-0.702087\pi\) | ||
0.593077 | − | 0.805146i | \(-0.297913\pi\) | |||||||
\(978\) | 19.4134i | 0.620773i | ||||||||
\(979\) | − | 8.68141i | − | 0.277459i | ||||||
\(980\) | 36.7214 | − | 20.3906i | 1.17302 | − | 0.651354i | ||||
\(981\) | 16.2880i | 0.520037i | ||||||||
\(982\) | 5.13919 | 0.163998 | ||||||||
\(983\) | −29.3653 | −0.936607 | −0.468304 | − | 0.883568i | \(-0.655135\pi\) | ||||
−0.468304 | + | 0.883568i | \(0.655135\pi\) | |||||||
\(984\) | −5.60179 | −0.178579 | ||||||||
\(985\) | 2.88097 | 0.0917953 | ||||||||
\(986\) | 5.28738 | 0.168385 | ||||||||
\(987\) | 6.35000 | + | 24.5161i | 0.202123 | + | 0.780357i | ||||
\(988\) | − | 15.9108i | − | 0.506190i | ||||||
\(989\) | 11.8760 | + | 22.9417i | 0.377636 | + | 0.729505i | ||||
\(990\) | − | 14.4882i | − | 0.460466i | ||||||
\(991\) | −33.0319 | −1.04929 | −0.524647 | − | 0.851320i | \(-0.675803\pi\) | ||||
−0.524647 | + | 0.851320i | \(0.675803\pi\) | |||||||
\(992\) | 64.3858i | 2.04425i | ||||||||
\(993\) | − | 24.6081i | − | 0.780913i | ||||||
\(994\) | −2.24149 | − | 8.65397i | −0.0710959 | − | 0.274487i | ||||
\(995\) | −97.2091 | −3.08173 | ||||||||
\(996\) | 3.67347i | 0.116398i | ||||||||
\(997\) | 26.5962i | 0.842310i | 0.906989 | + | 0.421155i | \(0.138375\pi\) | ||||
−0.906989 | + | 0.421155i | \(0.861625\pi\) | |||||||
\(998\) | 71.5160 | 2.26380 | ||||||||
\(999\) | −6.92106 | −0.218972 |
(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 | 483.2.h.b.160.9 | ✓ | 12 | |
3.2 | odd | 2 | 1449.2.h.h.1126.3 | 12 | |||
7.6 | odd | 2 | inner | 483.2.h.b.160.12 | yes | 12 | |
21.20 | even | 2 | 1449.2.h.h.1126.1 | 12 | |||
23.22 | odd | 2 | inner | 483.2.h.b.160.10 | yes | 12 | |
69.68 | even | 2 | 1449.2.h.h.1126.2 | 12 | |||
161.160 | even | 2 | inner | 483.2.h.b.160.11 | yes | 12 | |
483.482 | odd | 2 | 1449.2.h.h.1126.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.h.b.160.9 | ✓ | 12 | 1.1 | even | 1 | trivial | |
483.2.h.b.160.10 | yes | 12 | 23.22 | odd | 2 | inner | |
483.2.h.b.160.11 | yes | 12 | 161.160 | even | 2 | inner | |
483.2.h.b.160.12 | yes | 12 | 7.6 | odd | 2 | inner | |
1449.2.h.h.1126.1 | 12 | 21.20 | even | 2 | |||
1449.2.h.h.1126.2 | 12 | 69.68 | even | 2 | |||
1449.2.h.h.1126.3 | 12 | 3.2 | odd | 2 | |||
1449.2.h.h.1126.4 | 12 | 483.482 | odd | 2 |