Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(298,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.298");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.b (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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 23x^{12} + 201x^{10} + 835x^{8} + 1695x^{6} + 1565x^{4} + 511x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 298.1 | ||
Root | \(-2.73878i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.298 |
Dual form | 429.2.b.b.298.14 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.73878i | − | 1.93661i | −0.249768 | − | 0.968306i | \(-0.580354\pi\) | ||
0.249768 | − | 0.968306i | \(-0.419646\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −5.50093 | −2.75046 | ||||||||
\(5\) | 2.84154i | 1.27078i | 0.772193 | + | 0.635388i | \(0.219160\pi\) | ||||
−0.772193 | + | 0.635388i | \(0.780840\pi\) | |||||||
\(6\) | − | 2.73878i | − | 1.11810i | ||||||
\(7\) | 3.93129i | 1.48589i | 0.669353 | + | 0.742944i | \(0.266571\pi\) | ||||
−0.669353 | + | 0.742944i | \(0.733429\pi\) | |||||||
\(8\) | 9.58828i | 3.38997i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 7.78236 | 2.46100 | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | −5.50093 | −1.58798 | ||||||||
\(13\) | 1.78444 | − | 3.13301i | 0.494915 | − | 0.868941i | ||||
\(14\) | 10.7670 | 2.87759 | ||||||||
\(15\) | 2.84154i | 0.733682i | ||||||||
\(16\) | 15.2584 | 3.81459 | ||||||||
\(17\) | −3.81818 | −0.926044 | −0.463022 | − | 0.886347i | \(-0.653235\pi\) | ||||
−0.463022 | + | 0.886347i | \(0.653235\pi\) | |||||||
\(18\) | − | 2.73878i | − | 0.645537i | ||||||
\(19\) | 2.94082i | 0.674670i | 0.941385 | + | 0.337335i | \(0.109526\pi\) | ||||
−0.941385 | + | 0.337335i | \(0.890474\pi\) | |||||||
\(20\) | − | 15.6311i | − | 3.49522i | ||||||
\(21\) | 3.93129i | 0.857878i | ||||||||
\(22\) | 2.73878 | 0.583910 | ||||||||
\(23\) | 1.89484 | 0.395102 | 0.197551 | − | 0.980293i | \(-0.436701\pi\) | ||||
0.197551 | + | 0.980293i | \(0.436701\pi\) | |||||||
\(24\) | 9.58828i | 1.95720i | ||||||||
\(25\) | −3.07435 | −0.614869 | ||||||||
\(26\) | −8.58064 | − | 4.88720i | −1.68280 | − | 0.958459i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | − | 21.6258i | − | 4.08688i | ||||||
\(29\) | −2.09928 | −0.389826 | −0.194913 | − | 0.980821i | \(-0.562443\pi\) | ||||
−0.194913 | + | 0.980821i | \(0.562443\pi\) | |||||||
\(30\) | 7.78236 | 1.42086 | ||||||||
\(31\) | 6.16032i | 1.10643i | 0.833040 | + | 0.553213i | \(0.186598\pi\) | ||||
−0.833040 | + | 0.553213i | \(0.813402\pi\) | |||||||
\(32\) | − | 22.6127i | − | 3.99741i | ||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | 10.4572i | 1.79339i | ||||||||
\(35\) | −11.1709 | −1.88823 | ||||||||
\(36\) | −5.50093 | −0.916821 | ||||||||
\(37\) | 8.34404i | 1.37175i | 0.727719 | + | 0.685876i | \(0.240581\pi\) | ||||
−0.727719 | + | 0.685876i | \(0.759419\pi\) | |||||||
\(38\) | 8.05426 | 1.30657 | ||||||||
\(39\) | 1.78444 | − | 3.13301i | 0.285740 | − | 0.501683i | ||||
\(40\) | −27.2455 | −4.30789 | ||||||||
\(41\) | − | 6.35787i | − | 0.992933i | −0.868056 | − | 0.496466i | \(-0.834631\pi\) | ||
0.868056 | − | 0.496466i | \(-0.165369\pi\) | |||||||
\(42\) | 10.7670 | 1.66138 | ||||||||
\(43\) | 11.7275 | 1.78842 | 0.894212 | − | 0.447643i | \(-0.147736\pi\) | ||||
0.894212 | + | 0.447643i | \(0.147736\pi\) | |||||||
\(44\) | − | 5.50093i | − | 0.829296i | ||||||
\(45\) | 2.84154i | 0.423592i | ||||||||
\(46\) | − | 5.18956i | − | 0.765159i | ||||||
\(47\) | 5.31137i | 0.774743i | 0.921924 | + | 0.387371i | \(0.126617\pi\) | ||||
−0.921924 | + | 0.387371i | \(0.873383\pi\) | |||||||
\(48\) | 15.2584 | 2.20235 | ||||||||
\(49\) | −8.45506 | −1.20787 | ||||||||
\(50\) | 8.41997i | 1.19076i | ||||||||
\(51\) | −3.81818 | −0.534652 | ||||||||
\(52\) | −9.81609 | + | 17.2345i | −1.36125 | + | 2.38999i | ||||
\(53\) | −2.37985 | −0.326898 | −0.163449 | − | 0.986552i | \(-0.552262\pi\) | ||||
−0.163449 | + | 0.986552i | \(0.552262\pi\) | |||||||
\(54\) | − | 2.73878i | − | 0.372701i | ||||||
\(55\) | −2.84154 | −0.383153 | ||||||||
\(56\) | −37.6943 | −5.03712 | ||||||||
\(57\) | 2.94082i | 0.389521i | ||||||||
\(58\) | 5.74947i | 0.754942i | ||||||||
\(59\) | − | 5.38624i | − | 0.701229i | −0.936520 | − | 0.350615i | \(-0.885973\pi\) | ||
0.936520 | − | 0.350615i | \(-0.114027\pi\) | |||||||
\(60\) | − | 15.6311i | − | 2.01797i | ||||||
\(61\) | −2.34857 | −0.300703 | −0.150352 | − | 0.988633i | \(-0.548041\pi\) | ||||
−0.150352 | + | 0.988633i | \(0.548041\pi\) | |||||||
\(62\) | 16.8718 | 2.14272 | ||||||||
\(63\) | 3.93129i | 0.495296i | ||||||||
\(64\) | −31.4147 | −3.92684 | ||||||||
\(65\) | 8.90258 | + | 5.07056i | 1.10423 | + | 0.628926i | ||||
\(66\) | 2.73878 | 0.337121 | ||||||||
\(67\) | − | 10.4731i | − | 1.27949i | −0.768588 | − | 0.639744i | \(-0.779040\pi\) | ||
0.768588 | − | 0.639744i | \(-0.220960\pi\) | |||||||
\(68\) | 21.0035 | 2.54705 | ||||||||
\(69\) | 1.89484 | 0.228112 | ||||||||
\(70\) | 30.5947i | 3.65677i | ||||||||
\(71\) | − | 10.0939i | − | 1.19793i | −0.800776 | − | 0.598964i | \(-0.795579\pi\) | ||
0.800776 | − | 0.598964i | \(-0.204421\pi\) | |||||||
\(72\) | 9.58828i | 1.12999i | ||||||||
\(73\) | − | 15.1079i | − | 1.76824i | −0.467260 | − | 0.884120i | \(-0.654759\pi\) | ||
0.467260 | − | 0.884120i | \(-0.345241\pi\) | |||||||
\(74\) | 22.8525 | 2.65655 | ||||||||
\(75\) | −3.07435 | −0.354995 | ||||||||
\(76\) | − | 16.1772i | − | 1.85566i | ||||||
\(77\) | −3.93129 | −0.448012 | ||||||||
\(78\) | −8.58064 | − | 4.88720i | −0.971566 | − | 0.553366i | ||||
\(79\) | 1.57120 | 0.176774 | 0.0883872 | − | 0.996086i | \(-0.471829\pi\) | ||||
0.0883872 | + | 0.996086i | \(0.471829\pi\) | |||||||
\(80\) | 43.3572i | 4.84748i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −17.4128 | −1.92293 | ||||||||
\(83\) | − | 10.6736i | − | 1.17157i | −0.810465 | − | 0.585787i | \(-0.800785\pi\) | ||
0.810465 | − | 0.585787i | \(-0.199215\pi\) | |||||||
\(84\) | − | 21.6258i | − | 2.35956i | ||||||
\(85\) | − | 10.8495i | − | 1.17679i | ||||||
\(86\) | − | 32.1190i | − | 3.46348i | ||||||
\(87\) | −2.09928 | −0.225066 | ||||||||
\(88\) | −9.58828 | −1.02211 | ||||||||
\(89\) | 3.23647i | 0.343065i | 0.985178 | + | 0.171533i | \(0.0548719\pi\) | ||||
−0.985178 | + | 0.171533i | \(0.945128\pi\) | |||||||
\(90\) | 7.78236 | 0.820333 | ||||||||
\(91\) | 12.3168 | + | 7.01516i | 1.29115 | + | 0.735389i | ||||
\(92\) | −10.4234 | −1.08671 | ||||||||
\(93\) | 6.16032i | 0.638795i | ||||||||
\(94\) | 14.5467 | 1.50038 | ||||||||
\(95\) | −8.35645 | −0.857354 | ||||||||
\(96\) | − | 22.6127i | − | 2.30790i | ||||||
\(97\) | 17.7914i | 1.80645i | 0.429172 | + | 0.903223i | \(0.358805\pi\) | ||||
−0.429172 | + | 0.903223i | \(0.641195\pi\) | |||||||
\(98\) | 23.1566i | 2.33917i | ||||||||
\(99\) | 1.00000i | 0.100504i | ||||||||
\(100\) | 16.9118 | 1.69118 | ||||||||
\(101\) | 12.1229 | 1.20627 | 0.603136 | − | 0.797638i | \(-0.293917\pi\) | ||||
0.603136 | + | 0.797638i | \(0.293917\pi\) | |||||||
\(102\) | 10.4572i | 1.03541i | ||||||||
\(103\) | 3.40983 | 0.335981 | 0.167990 | − | 0.985789i | \(-0.446272\pi\) | ||||
0.167990 | + | 0.985789i | \(0.446272\pi\) | |||||||
\(104\) | 30.0402 | + | 17.1097i | 2.94568 | + | 1.67775i | ||||
\(105\) | −11.1709 | −1.09017 | ||||||||
\(106\) | 6.51790i | 0.633075i | ||||||||
\(107\) | −12.2352 | −1.18282 | −0.591411 | − | 0.806370i | \(-0.701429\pi\) | ||||
−0.591411 | + | 0.806370i | \(0.701429\pi\) | |||||||
\(108\) | −5.50093 | −0.529327 | ||||||||
\(109\) | 8.72763i | 0.835956i | 0.908457 | + | 0.417978i | \(0.137261\pi\) | ||||
−0.908457 | + | 0.417978i | \(0.862739\pi\) | |||||||
\(110\) | 7.78236i | 0.742019i | ||||||||
\(111\) | 8.34404i | 0.791981i | ||||||||
\(112\) | 59.9850i | 5.66805i | ||||||||
\(113\) | 0.0155525 | 0.00146305 | 0.000731527 | − | 1.00000i | \(-0.499767\pi\) | ||||
0.000731527 | 1.00000i | \(0.499767\pi\) | ||||||||
\(114\) | 8.05426 | 0.754351 | ||||||||
\(115\) | 5.38427i | 0.502086i | ||||||||
\(116\) | 11.5480 | 1.07220 | ||||||||
\(117\) | 1.78444 | − | 3.13301i | 0.164972 | − | 0.289647i | ||||
\(118\) | −14.7517 | −1.35801 | ||||||||
\(119\) | − | 15.0104i | − | 1.37600i | ||||||
\(120\) | −27.2455 | −2.48716 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 6.43222i | 0.582346i | ||||||||
\(123\) | − | 6.35787i | − | 0.573270i | ||||||
\(124\) | − | 33.8875i | − | 3.04318i | ||||||
\(125\) | 5.47182i | 0.489414i | ||||||||
\(126\) | 10.7670 | 0.959196 | ||||||||
\(127\) | 5.91514 | 0.524883 | 0.262442 | − | 0.964948i | \(-0.415472\pi\) | ||||
0.262442 | + | 0.964948i | \(0.415472\pi\) | |||||||
\(128\) | 40.8125i | 3.60735i | ||||||||
\(129\) | 11.7275 | 1.03255 | ||||||||
\(130\) | 13.8872 | − | 24.3822i | 1.21799 | − | 2.13846i | ||||
\(131\) | −1.32191 | −0.115496 | −0.0577481 | − | 0.998331i | \(-0.518392\pi\) | ||||
−0.0577481 | + | 0.998331i | \(0.518392\pi\) | |||||||
\(132\) | − | 5.50093i | − | 0.478794i | ||||||
\(133\) | −11.5612 | −1.00248 | ||||||||
\(134\) | −28.6835 | −2.47787 | ||||||||
\(135\) | 2.84154i | 0.244561i | ||||||||
\(136\) | − | 36.6097i | − | 3.13926i | ||||||
\(137\) | 4.82127i | 0.411909i | 0.978562 | + | 0.205955i | \(0.0660299\pi\) | ||||
−0.978562 | + | 0.205955i | \(0.933970\pi\) | |||||||
\(138\) | − | 5.18956i | − | 0.441765i | ||||||
\(139\) | 17.1877 | 1.45784 | 0.728919 | − | 0.684600i | \(-0.240023\pi\) | ||||
0.728919 | + | 0.684600i | \(0.240023\pi\) | |||||||
\(140\) | 61.4504 | 5.19351 | ||||||||
\(141\) | 5.31137i | 0.447298i | ||||||||
\(142\) | −27.6451 | −2.31992 | ||||||||
\(143\) | 3.13301 | + | 1.78444i | 0.261996 | + | 0.149223i | ||||
\(144\) | 15.2584 | 1.27153 | ||||||||
\(145\) | − | 5.96518i | − | 0.495382i | ||||||
\(146\) | −41.3771 | −3.42439 | ||||||||
\(147\) | −8.45506 | −0.697361 | ||||||||
\(148\) | − | 45.8999i | − | 3.77295i | ||||||
\(149\) | 5.31754i | 0.435629i | 0.975990 | + | 0.217815i | \(0.0698929\pi\) | ||||
−0.975990 | + | 0.217815i | \(0.930107\pi\) | |||||||
\(150\) | 8.41997i | 0.687487i | ||||||||
\(151\) | − | 6.77573i | − | 0.551401i | −0.961244 | − | 0.275700i | \(-0.911090\pi\) | ||
0.961244 | − | 0.275700i | \(-0.0889098\pi\) | |||||||
\(152\) | −28.1974 | −2.28711 | ||||||||
\(153\) | −3.81818 | −0.308681 | ||||||||
\(154\) | 10.7670i | 0.867626i | ||||||||
\(155\) | −17.5048 | −1.40602 | ||||||||
\(156\) | −9.81609 | + | 17.2345i | −0.785916 | + | 1.37986i | ||||
\(157\) | 16.2884 | 1.29995 | 0.649977 | − | 0.759954i | \(-0.274779\pi\) | ||||
0.649977 | + | 0.759954i | \(0.274779\pi\) | |||||||
\(158\) | − | 4.30319i | − | 0.342343i | ||||||
\(159\) | −2.37985 | −0.188735 | ||||||||
\(160\) | 64.2550 | 5.07981 | ||||||||
\(161\) | 7.44918i | 0.587077i | ||||||||
\(162\) | − | 2.73878i | − | 0.215179i | ||||||
\(163\) | 11.4032i | 0.893170i | 0.894741 | + | 0.446585i | \(0.147360\pi\) | ||||
−0.894741 | + | 0.446585i | \(0.852640\pi\) | |||||||
\(164\) | 34.9742i | 2.73103i | ||||||||
\(165\) | −2.84154 | −0.221214 | ||||||||
\(166\) | −29.2325 | −2.26888 | ||||||||
\(167\) | − | 14.7302i | − | 1.13985i | −0.821695 | − | 0.569927i | \(-0.806971\pi\) | ||
0.821695 | − | 0.569927i | \(-0.193029\pi\) | |||||||
\(168\) | −37.6943 | −2.90818 | ||||||||
\(169\) | −6.63153 | − | 11.1814i | −0.510118 | − | 0.860105i | ||||
\(170\) | −29.7144 | −2.27899 | ||||||||
\(171\) | 2.94082i | 0.224890i | ||||||||
\(172\) | −64.5121 | −4.91900 | ||||||||
\(173\) | −0.186647 | −0.0141905 | −0.00709527 | − | 0.999975i | \(-0.502259\pi\) | ||||
−0.00709527 | + | 0.999975i | \(0.502259\pi\) | |||||||
\(174\) | 5.74947i | 0.435866i | ||||||||
\(175\) | − | 12.0862i | − | 0.913627i | ||||||
\(176\) | 15.2584i | 1.15014i | ||||||||
\(177\) | − | 5.38624i | − | 0.404855i | ||||||
\(178\) | 8.86399 | 0.664384 | ||||||||
\(179\) | −10.9555 | −0.818856 | −0.409428 | − | 0.912342i | \(-0.634272\pi\) | ||||
−0.409428 | + | 0.912342i | \(0.634272\pi\) | |||||||
\(180\) | − | 15.6311i | − | 1.16507i | ||||||
\(181\) | 8.52034 | 0.633312 | 0.316656 | − | 0.948540i | \(-0.397440\pi\) | ||||
0.316656 | + | 0.948540i | \(0.397440\pi\) | |||||||
\(182\) | 19.2130 | − | 33.7330i | 1.42416 | − | 2.50046i | ||||
\(183\) | −2.34857 | −0.173611 | ||||||||
\(184\) | 18.1683i | 1.33938i | ||||||||
\(185\) | −23.7099 | −1.74319 | ||||||||
\(186\) | 16.8718 | 1.23710 | ||||||||
\(187\) | − | 3.81818i | − | 0.279213i | ||||||
\(188\) | − | 29.2175i | − | 2.13090i | ||||||
\(189\) | 3.93129i | 0.285959i | ||||||||
\(190\) | 22.8865i | 1.66036i | ||||||||
\(191\) | −11.8003 | −0.853840 | −0.426920 | − | 0.904289i | \(-0.640401\pi\) | ||||
−0.426920 | + | 0.904289i | \(0.640401\pi\) | |||||||
\(192\) | −31.4147 | −2.26716 | ||||||||
\(193\) | 10.9405i | 0.787518i | 0.919214 | + | 0.393759i | \(0.128826\pi\) | ||||
−0.919214 | + | 0.393759i | \(0.871174\pi\) | |||||||
\(194\) | 48.7268 | 3.49838 | ||||||||
\(195\) | 8.90258 | + | 5.07056i | 0.637527 | + | 0.363111i | ||||
\(196\) | 46.5107 | 3.32219 | ||||||||
\(197\) | − | 9.43307i | − | 0.672079i | −0.941848 | − | 0.336039i | \(-0.890912\pi\) | ||
0.941848 | − | 0.336039i | \(-0.109088\pi\) | |||||||
\(198\) | 2.73878 | 0.194637 | ||||||||
\(199\) | 15.3198 | 1.08599 | 0.542996 | − | 0.839735i | \(-0.317290\pi\) | ||||
0.542996 | + | 0.839735i | \(0.317290\pi\) | |||||||
\(200\) | − | 29.4777i | − | 2.08439i | ||||||
\(201\) | − | 10.4731i | − | 0.738713i | ||||||
\(202\) | − | 33.2020i | − | 2.33608i | ||||||
\(203\) | − | 8.25288i | − | 0.579238i | ||||||
\(204\) | 21.0035 | 1.47054 | ||||||||
\(205\) | 18.0661 | 1.26179 | ||||||||
\(206\) | − | 9.33878i | − | 0.650664i | ||||||
\(207\) | 1.89484 | 0.131701 | ||||||||
\(208\) | 27.2277 | − | 47.8046i | 1.88790 | − | 3.31465i | ||||
\(209\) | −2.94082 | −0.203421 | ||||||||
\(210\) | 30.5947i | 2.11124i | ||||||||
\(211\) | 2.91243 | 0.200500 | 0.100250 | − | 0.994962i | \(-0.468036\pi\) | ||||
0.100250 | + | 0.994962i | \(0.468036\pi\) | |||||||
\(212\) | 13.0914 | 0.899122 | ||||||||
\(213\) | − | 10.0939i | − | 0.691625i | ||||||
\(214\) | 33.5096i | 2.29067i | ||||||||
\(215\) | 33.3241i | 2.27269i | ||||||||
\(216\) | 9.58828i | 0.652400i | ||||||||
\(217\) | −24.2180 | −1.64403 | ||||||||
\(218\) | 23.9031 | 1.61892 | ||||||||
\(219\) | − | 15.1079i | − | 1.02089i | ||||||
\(220\) | 15.6311 | 1.05385 | ||||||||
\(221\) | −6.81332 | + | 11.9624i | −0.458313 | + | 0.804677i | ||||
\(222\) | 22.8525 | 1.53376 | ||||||||
\(223\) | − | 10.8511i | − | 0.726641i | −0.931664 | − | 0.363320i | \(-0.881643\pi\) | ||
0.931664 | − | 0.363320i | \(-0.118357\pi\) | |||||||
\(224\) | 88.8973 | 5.93970 | ||||||||
\(225\) | −3.07435 | −0.204956 | ||||||||
\(226\) | − | 0.0425948i | − | 0.00283337i | ||||||
\(227\) | − | 0.322636i | − | 0.0214141i | −0.999943 | − | 0.0107070i | \(-0.996592\pi\) | ||
0.999943 | − | 0.0107070i | \(-0.00340822\pi\) | |||||||
\(228\) | − | 16.1772i | − | 1.07136i | ||||||
\(229\) | − | 5.94060i | − | 0.392566i | −0.980547 | − | 0.196283i | \(-0.937113\pi\) | ||
0.980547 | − | 0.196283i | \(-0.0628871\pi\) | |||||||
\(230\) | 14.7463 | 0.972345 | ||||||||
\(231\) | −3.93129 | −0.258660 | ||||||||
\(232\) | − | 20.1285i | − | 1.32150i | ||||||
\(233\) | 12.6202 | 0.826774 | 0.413387 | − | 0.910555i | \(-0.364346\pi\) | ||||
0.413387 | + | 0.910555i | \(0.364346\pi\) | |||||||
\(234\) | −8.58064 | − | 4.88720i | −0.560934 | − | 0.319486i | ||||
\(235\) | −15.0925 | −0.984524 | ||||||||
\(236\) | 29.6293i | 1.92871i | ||||||||
\(237\) | 1.57120 | 0.102061 | ||||||||
\(238\) | −41.1101 | −2.66477 | ||||||||
\(239\) | − | 20.7706i | − | 1.34354i | −0.740762 | − | 0.671768i | \(-0.765535\pi\) | ||
0.740762 | − | 0.671768i | \(-0.234465\pi\) | |||||||
\(240\) | 43.3572i | 2.79870i | ||||||||
\(241\) | − | 18.2163i | − | 1.17341i | −0.809800 | − | 0.586706i | \(-0.800424\pi\) | ||
0.809800 | − | 0.586706i | \(-0.199576\pi\) | |||||||
\(242\) | 2.73878i | 0.176056i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 12.9193 | 0.827074 | ||||||||
\(245\) | − | 24.0254i | − | 1.53492i | ||||||
\(246\) | −17.4128 | −1.11020 | ||||||||
\(247\) | 9.21362 | + | 5.24772i | 0.586249 | + | 0.333905i | ||||
\(248\) | −59.0668 | −3.75075 | ||||||||
\(249\) | − | 10.6736i | − | 0.676409i | ||||||
\(250\) | 14.9861 | 0.947806 | ||||||||
\(251\) | 22.6662 | 1.43068 | 0.715340 | − | 0.698776i | \(-0.246272\pi\) | ||||
0.715340 | + | 0.698776i | \(0.246272\pi\) | |||||||
\(252\) | − | 21.6258i | − | 1.36229i | ||||||
\(253\) | 1.89484i | 0.119128i | ||||||||
\(254\) | − | 16.2003i | − | 1.01650i | ||||||
\(255\) | − | 10.8495i | − | 0.679422i | ||||||
\(256\) | 48.9471 | 3.05920 | ||||||||
\(257\) | −17.7333 | −1.10617 | −0.553087 | − | 0.833124i | \(-0.686550\pi\) | ||||
−0.553087 | + | 0.833124i | \(0.686550\pi\) | |||||||
\(258\) | − | 32.1190i | − | 1.99964i | ||||||
\(259\) | −32.8028 | −2.03827 | ||||||||
\(260\) | −48.9724 | − | 27.8928i | −3.03714 | − | 1.72984i | ||||
\(261\) | −2.09928 | −0.129942 | ||||||||
\(262\) | 3.62044i | 0.223671i | ||||||||
\(263\) | 29.5107 | 1.81971 | 0.909853 | − | 0.414930i | \(-0.136194\pi\) | ||||
0.909853 | + | 0.414930i | \(0.136194\pi\) | |||||||
\(264\) | −9.58828 | −0.590118 | ||||||||
\(265\) | − | 6.76245i | − | 0.415414i | ||||||
\(266\) | 31.6637i | 1.94142i | ||||||||
\(267\) | 3.23647i | 0.198069i | ||||||||
\(268\) | 57.6116i | 3.51919i | ||||||||
\(269\) | −9.02091 | −0.550015 | −0.275007 | − | 0.961442i | \(-0.588680\pi\) | ||||
−0.275007 | + | 0.961442i | \(0.588680\pi\) | |||||||
\(270\) | 7.78236 | 0.473619 | ||||||||
\(271\) | 4.58320i | 0.278410i | 0.990264 | + | 0.139205i | \(0.0444547\pi\) | ||||
−0.990264 | + | 0.139205i | \(0.955545\pi\) | |||||||
\(272\) | −58.2591 | −3.53248 | ||||||||
\(273\) | 12.3168 | + | 7.01516i | 0.745446 | + | 0.424577i | ||||
\(274\) | 13.2044 | 0.797708 | ||||||||
\(275\) | − | 3.07435i | − | 0.185390i | ||||||
\(276\) | −10.4234 | −0.627414 | ||||||||
\(277\) | −20.9859 | −1.26092 | −0.630461 | − | 0.776221i | \(-0.717134\pi\) | ||||
−0.630461 | + | 0.776221i | \(0.717134\pi\) | |||||||
\(278\) | − | 47.0732i | − | 2.82327i | ||||||
\(279\) | 6.16032i | 0.368809i | ||||||||
\(280\) | − | 107.110i | − | 6.40104i | ||||||
\(281\) | 10.5360i | 0.628524i | 0.949336 | + | 0.314262i | \(0.101757\pi\) | ||||
−0.949336 | + | 0.314262i | \(0.898243\pi\) | |||||||
\(282\) | 14.5467 | 0.866242 | ||||||||
\(283\) | 2.57169 | 0.152871 | 0.0764355 | − | 0.997075i | \(-0.475646\pi\) | ||||
0.0764355 | + | 0.997075i | \(0.475646\pi\) | |||||||
\(284\) | 55.5260i | 3.29486i | ||||||||
\(285\) | −8.35645 | −0.494993 | ||||||||
\(286\) | 4.88720 | − | 8.58064i | 0.288986 | − | 0.507384i | ||||
\(287\) | 24.9947 | 1.47539 | ||||||||
\(288\) | − | 22.6127i | − | 1.33247i | ||||||
\(289\) | −2.42153 | −0.142443 | ||||||||
\(290\) | −16.3373 | −0.959362 | ||||||||
\(291\) | 17.7914i | 1.04295i | ||||||||
\(292\) | 83.1072i | 4.86348i | ||||||||
\(293\) | 5.16162i | 0.301545i | 0.988568 | + | 0.150772i | \(0.0481761\pi\) | ||||
−0.988568 | + | 0.150772i | \(0.951824\pi\) | |||||||
\(294\) | 23.1566i | 1.35052i | ||||||||
\(295\) | 15.3052 | 0.891105 | ||||||||
\(296\) | −80.0050 | −4.65019 | ||||||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | 14.5636 | 0.843645 | ||||||||
\(299\) | 3.38124 | − | 5.93656i | 0.195542 | − | 0.343320i | ||||
\(300\) | 16.9118 | 0.976401 | ||||||||
\(301\) | 46.1042i | 2.65740i | ||||||||
\(302\) | −18.5572 | −1.06785 | ||||||||
\(303\) | 12.1229 | 0.696442 | ||||||||
\(304\) | 44.8720i | 2.57359i | ||||||||
\(305\) | − | 6.67355i | − | 0.382126i | ||||||
\(306\) | 10.4572i | 0.597796i | ||||||||
\(307\) | − | 30.0561i | − | 1.71539i | −0.514156 | − | 0.857697i | \(-0.671895\pi\) | ||
0.514156 | − | 0.857697i | \(-0.328105\pi\) | |||||||
\(308\) | 21.6258 | 1.23224 | ||||||||
\(309\) | 3.40983 | 0.193978 | ||||||||
\(310\) | 47.9418i | 2.72291i | ||||||||
\(311\) | 21.7462 | 1.23311 | 0.616557 | − | 0.787310i | \(-0.288527\pi\) | ||||
0.616557 | + | 0.787310i | \(0.288527\pi\) | |||||||
\(312\) | 30.0402 | + | 17.1097i | 1.70069 | + | 0.968648i | ||||
\(313\) | −24.4361 | −1.38121 | −0.690606 | − | 0.723231i | \(-0.742656\pi\) | ||||
−0.690606 | + | 0.723231i | \(0.742656\pi\) | |||||||
\(314\) | − | 44.6103i | − | 2.51751i | ||||||
\(315\) | −11.1709 | −0.629410 | ||||||||
\(316\) | −8.64309 | −0.486212 | ||||||||
\(317\) | − | 21.1040i | − | 1.18532i | −0.805454 | − | 0.592658i | \(-0.798079\pi\) | ||
0.805454 | − | 0.592658i | \(-0.201921\pi\) | |||||||
\(318\) | 6.51790i | 0.365506i | ||||||||
\(319\) | − | 2.09928i | − | 0.117537i | ||||||
\(320\) | − | 89.2661i | − | 4.99013i | ||||||
\(321\) | −12.2352 | −0.682903 | ||||||||
\(322\) | 20.4017 | 1.13694 | ||||||||
\(323\) | − | 11.2286i | − | 0.624774i | ||||||
\(324\) | −5.50093 | −0.305607 | ||||||||
\(325\) | −5.48600 | + | 9.63196i | −0.304308 | + | 0.534285i | ||||
\(326\) | 31.2310 | 1.72972 | ||||||||
\(327\) | 8.72763i | 0.482639i | ||||||||
\(328\) | 60.9611 | 3.36601 | ||||||||
\(329\) | −20.8805 | −1.15118 | ||||||||
\(330\) | 7.78236i | 0.428405i | ||||||||
\(331\) | − | 0.560518i | − | 0.0308089i | −0.999881 | − | 0.0154044i | \(-0.995096\pi\) | ||
0.999881 | − | 0.0154044i | \(-0.00490358\pi\) | |||||||
\(332\) | 58.7144i | 3.22237i | ||||||||
\(333\) | 8.34404i | 0.457250i | ||||||||
\(334\) | −40.3427 | −2.20745 | ||||||||
\(335\) | 29.7596 | 1.62594 | ||||||||
\(336\) | 59.9850i | 3.27245i | ||||||||
\(337\) | 7.76850 | 0.423177 | 0.211589 | − | 0.977359i | \(-0.432136\pi\) | ||||
0.211589 | + | 0.977359i | \(0.432136\pi\) | |||||||
\(338\) | −30.6233 | + | 18.1623i | −1.66569 | + | 0.987900i | ||||
\(339\) | 0.0155525 | 0.000844695 | ||||||||
\(340\) | 59.6823i | 3.23673i | ||||||||
\(341\) | −6.16032 | −0.333600 | ||||||||
\(342\) | 8.05426 | 0.435525 | ||||||||
\(343\) | − | 5.72025i | − | 0.308864i | ||||||
\(344\) | 112.446i | 6.06270i | ||||||||
\(345\) | 5.38427i | 0.289879i | ||||||||
\(346\) | 0.511186i | 0.0274816i | ||||||||
\(347\) | −10.1357 | −0.544110 | −0.272055 | − | 0.962282i | \(-0.587703\pi\) | ||||
−0.272055 | + | 0.962282i | \(0.587703\pi\) | |||||||
\(348\) | 11.5480 | 0.619037 | ||||||||
\(349\) | − | 20.0030i | − | 1.07074i | −0.844619 | − | 0.535369i | \(-0.820173\pi\) | ||
0.844619 | − | 0.535369i | \(-0.179827\pi\) | |||||||
\(350\) | −33.1013 | −1.76934 | ||||||||
\(351\) | 1.78444 | − | 3.13301i | 0.0952465 | − | 0.167228i | ||||
\(352\) | 22.6127 | 1.20526 | ||||||||
\(353\) | 26.7905i | 1.42591i | 0.701208 | + | 0.712957i | \(0.252645\pi\) | ||||
−0.701208 | + | 0.712957i | \(0.747355\pi\) | |||||||
\(354\) | −14.7517 | −0.784047 | ||||||||
\(355\) | 28.6823 | 1.52230 | ||||||||
\(356\) | − | 17.8036i | − | 0.943589i | ||||||
\(357\) | − | 15.0104i | − | 0.794433i | ||||||
\(358\) | 30.0049i | 1.58581i | ||||||||
\(359\) | 26.7347i | 1.41101i | 0.708707 | + | 0.705503i | \(0.249279\pi\) | ||||
−0.708707 | + | 0.705503i | \(0.750721\pi\) | |||||||
\(360\) | −27.2455 | −1.43596 | ||||||||
\(361\) | 10.3516 | 0.544820 | ||||||||
\(362\) | − | 23.3354i | − | 1.22648i | ||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −67.7537 | − | 38.5899i | −3.55126 | − | 2.02266i | ||||
\(365\) | 42.9296 | 2.24704 | ||||||||
\(366\) | 6.43222i | 0.336218i | ||||||||
\(367\) | 1.89563 | 0.0989512 | 0.0494756 | − | 0.998775i | \(-0.484245\pi\) | ||||
0.0494756 | + | 0.998775i | \(0.484245\pi\) | |||||||
\(368\) | 28.9122 | 1.50715 | ||||||||
\(369\) | − | 6.35787i | − | 0.330978i | ||||||
\(370\) | 64.9363i | 3.37588i | ||||||||
\(371\) | − | 9.35590i | − | 0.485734i | ||||||
\(372\) | − | 33.8875i | − | 1.75698i | ||||||
\(373\) | −36.7517 | −1.90293 | −0.951464 | − | 0.307759i | \(-0.900421\pi\) | ||||
−0.951464 | + | 0.307759i | \(0.900421\pi\) | |||||||
\(374\) | −10.4572 | −0.540726 | ||||||||
\(375\) | 5.47182i | 0.282564i | ||||||||
\(376\) | −50.9269 | −2.62635 | ||||||||
\(377\) | −3.74604 | + | 6.57707i | −0.192931 | + | 0.338736i | ||||
\(378\) | 10.7670 | 0.553792 | ||||||||
\(379\) | 26.1328i | 1.34235i | 0.741298 | + | 0.671176i | \(0.234211\pi\) | ||||
−0.741298 | + | 0.671176i | \(0.765789\pi\) | |||||||
\(380\) | 45.9682 | 2.35812 | ||||||||
\(381\) | 5.91514 | 0.303042 | ||||||||
\(382\) | 32.3185i | 1.65356i | ||||||||
\(383\) | − | 16.9211i | − | 0.864629i | −0.901723 | − | 0.432315i | \(-0.857697\pi\) | ||
0.901723 | − | 0.432315i | \(-0.142303\pi\) | |||||||
\(384\) | 40.8125i | 2.08270i | ||||||||
\(385\) | − | 11.1709i | − | 0.569323i | ||||||
\(386\) | 29.9638 | 1.52512 | ||||||||
\(387\) | 11.7275 | 0.596142 | ||||||||
\(388\) | − | 97.8693i | − | 4.96856i | ||||||
\(389\) | 5.05607 | 0.256353 | 0.128177 | − | 0.991751i | \(-0.459088\pi\) | ||||
0.128177 | + | 0.991751i | \(0.459088\pi\) | |||||||
\(390\) | 13.8872 | − | 24.3822i | 0.703204 | − | 1.23464i | ||||
\(391\) | −7.23484 | −0.365882 | ||||||||
\(392\) | − | 81.0694i | − | 4.09462i | ||||||
\(393\) | −1.32191 | −0.0666818 | ||||||||
\(394\) | −25.8351 | −1.30156 | ||||||||
\(395\) | 4.46464i | 0.224640i | ||||||||
\(396\) | − | 5.50093i | − | 0.276432i | ||||||
\(397\) | 15.7731i | 0.791631i | 0.918330 | + | 0.395815i | \(0.129538\pi\) | ||||
−0.918330 | + | 0.395815i | \(0.870462\pi\) | |||||||
\(398\) | − | 41.9576i | − | 2.10314i | ||||||
\(399\) | −11.5612 | −0.578785 | ||||||||
\(400\) | −46.9095 | −2.34547 | ||||||||
\(401\) | 8.42218i | 0.420584i | 0.977639 | + | 0.210292i | \(0.0674414\pi\) | ||||
−0.977639 | + | 0.210292i | \(0.932559\pi\) | |||||||
\(402\) | −28.6835 | −1.43060 | ||||||||
\(403\) | 19.3003 | + | 10.9927i | 0.961419 | + | 0.547587i | ||||
\(404\) | −66.6872 | −3.31781 | ||||||||
\(405\) | 2.84154i | 0.141197i | ||||||||
\(406\) | −22.6028 | −1.12176 | ||||||||
\(407\) | −8.34404 | −0.413599 | ||||||||
\(408\) | − | 36.6097i | − | 1.81245i | ||||||
\(409\) | − | 31.3861i | − | 1.55194i | −0.630768 | − | 0.775971i | \(-0.717260\pi\) | ||
0.630768 | − | 0.775971i | \(-0.282740\pi\) | |||||||
\(410\) | − | 49.4792i | − | 2.44361i | ||||||
\(411\) | 4.82127i | 0.237816i | ||||||||
\(412\) | −18.7572 | −0.924102 | ||||||||
\(413\) | 21.1749 | 1.04195 | ||||||||
\(414\) | − | 5.18956i | − | 0.255053i | ||||||
\(415\) | 30.3293 | 1.48881 | ||||||||
\(416\) | −70.8460 | − | 40.3512i | −3.47351 | − | 1.97838i | ||||
\(417\) | 17.1877 | 0.841683 | ||||||||
\(418\) | 8.05426i | 0.393947i | ||||||||
\(419\) | −6.62928 | −0.323861 | −0.161931 | − | 0.986802i | \(-0.551772\pi\) | ||||
−0.161931 | + | 0.986802i | \(0.551772\pi\) | |||||||
\(420\) | 61.4504 | 2.99847 | ||||||||
\(421\) | 2.61327i | 0.127363i | 0.997970 | + | 0.0636816i | \(0.0202842\pi\) | ||||
−0.997970 | + | 0.0636816i | \(0.979716\pi\) | |||||||
\(422\) | − | 7.97651i | − | 0.388290i | ||||||
\(423\) | 5.31137i | 0.258248i | ||||||||
\(424\) | − | 22.8187i | − | 1.10817i | ||||||
\(425\) | 11.7384 | 0.569396 | ||||||||
\(426\) | −27.6451 | −1.33941 | ||||||||
\(427\) | − | 9.23291i | − | 0.446812i | ||||||
\(428\) | 67.3050 | 3.25331 | ||||||||
\(429\) | 3.13301 | + | 1.78444i | 0.151263 | + | 0.0861537i | ||||
\(430\) | 91.2675 | 4.40131 | ||||||||
\(431\) | 24.8745i | 1.19816i | 0.800688 | + | 0.599081i | \(0.204467\pi\) | ||||
−0.800688 | + | 0.599081i | \(0.795533\pi\) | |||||||
\(432\) | 15.2584 | 0.734118 | ||||||||
\(433\) | −6.55556 | −0.315040 | −0.157520 | − | 0.987516i | \(-0.550350\pi\) | ||||
−0.157520 | + | 0.987516i | \(0.550350\pi\) | |||||||
\(434\) | 66.3278i | 3.18384i | ||||||||
\(435\) | − | 5.96518i | − | 0.286009i | ||||||
\(436\) | − | 48.0101i | − | 2.29927i | ||||||
\(437\) | 5.57239i | 0.266563i | ||||||||
\(438\) | −41.3771 | −1.97707 | ||||||||
\(439\) | 38.2180 | 1.82405 | 0.912023 | − | 0.410138i | \(-0.134520\pi\) | ||||
0.912023 | + | 0.410138i | \(0.134520\pi\) | |||||||
\(440\) | − | 27.2455i | − | 1.29888i | ||||||
\(441\) | −8.45506 | −0.402622 | ||||||||
\(442\) | 32.7624 | + | 18.6602i | 1.55835 | + | 0.887575i | ||||
\(443\) | −12.7407 | −0.605330 | −0.302665 | − | 0.953097i | \(-0.597876\pi\) | ||||
−0.302665 | + | 0.953097i | \(0.597876\pi\) | |||||||
\(444\) | − | 45.8999i | − | 2.17831i | ||||||
\(445\) | −9.19656 | −0.435959 | ||||||||
\(446\) | −29.7187 | −1.40722 | ||||||||
\(447\) | 5.31754i | 0.251511i | ||||||||
\(448\) | − | 123.500i | − | 5.83484i | ||||||
\(449\) | 25.9513i | 1.22472i | 0.790581 | + | 0.612358i | \(0.209779\pi\) | ||||
−0.790581 | + | 0.612358i | \(0.790221\pi\) | |||||||
\(450\) | 8.41997i | 0.396921i | ||||||||
\(451\) | 6.35787 | 0.299381 | ||||||||
\(452\) | −0.0855531 | −0.00402408 | ||||||||
\(453\) | − | 6.77573i | − | 0.318351i | ||||||
\(454\) | −0.883629 | −0.0414708 | ||||||||
\(455\) | −19.9339 | + | 34.9986i | −0.934514 | + | 1.64076i | ||||
\(456\) | −28.1974 | −1.32046 | ||||||||
\(457\) | − | 16.0372i | − | 0.750190i | −0.926986 | − | 0.375095i | \(-0.877610\pi\) | ||
0.926986 | − | 0.375095i | \(-0.122390\pi\) | |||||||
\(458\) | −16.2700 | −0.760247 | ||||||||
\(459\) | −3.81818 | −0.178217 | ||||||||
\(460\) | − | 29.6185i | − | 1.38097i | ||||||
\(461\) | − | 3.48566i | − | 0.162343i | −0.996700 | − | 0.0811716i | \(-0.974134\pi\) | ||
0.996700 | − | 0.0811716i | \(-0.0258662\pi\) | |||||||
\(462\) | 10.7670i | 0.500924i | ||||||||
\(463\) | − | 27.0784i | − | 1.25844i | −0.777227 | − | 0.629220i | \(-0.783374\pi\) | ||
0.777227 | − | 0.629220i | \(-0.216626\pi\) | |||||||
\(464\) | −32.0315 | −1.48703 | ||||||||
\(465\) | −17.5048 | −0.811765 | ||||||||
\(466\) | − | 34.5639i | − | 1.60114i | ||||||
\(467\) | 15.6899 | 0.726041 | 0.363020 | − | 0.931781i | \(-0.381746\pi\) | ||||
0.363020 | + | 0.931781i | \(0.381746\pi\) | |||||||
\(468\) | −9.81609 | + | 17.2345i | −0.453749 | + | 0.796664i | ||||
\(469\) | 41.1727 | 1.90118 | ||||||||
\(470\) | 41.3350i | 1.90664i | ||||||||
\(471\) | 16.2884 | 0.750529 | ||||||||
\(472\) | 51.6448 | 2.37715 | ||||||||
\(473\) | 11.7275i | 0.539230i | ||||||||
\(474\) | − | 4.30319i | − | 0.197652i | ||||||
\(475\) | − | 9.04109i | − | 0.414834i | ||||||
\(476\) | 82.5709i | 3.78463i | ||||||||
\(477\) | −2.37985 | −0.108966 | ||||||||
\(478\) | −56.8860 | −2.60191 | ||||||||
\(479\) | 33.0061i | 1.50809i | 0.656825 | + | 0.754043i | \(0.271899\pi\) | ||||
−0.656825 | + | 0.754043i | \(0.728101\pi\) | |||||||
\(480\) | 64.2550 | 2.93283 | ||||||||
\(481\) | 26.1420 | + | 14.8895i | 1.19197 | + | 0.678901i | ||||
\(482\) | −49.8904 | −2.27244 | ||||||||
\(483\) | 7.44918i | 0.338949i | ||||||||
\(484\) | 5.50093 | 0.250042 | ||||||||
\(485\) | −50.5550 | −2.29559 | ||||||||
\(486\) | − | 2.73878i | − | 0.124234i | ||||||
\(487\) | − | 18.6684i | − | 0.845945i | −0.906142 | − | 0.422973i | \(-0.860987\pi\) | ||
0.906142 | − | 0.422973i | \(-0.139013\pi\) | |||||||
\(488\) | − | 22.5187i | − | 1.01938i | ||||||
\(489\) | 11.4032i | 0.515672i | ||||||||
\(490\) | −65.8003 | −2.97255 | ||||||||
\(491\) | 6.78238 | 0.306084 | 0.153042 | − | 0.988220i | \(-0.451093\pi\) | ||||
0.153042 | + | 0.988220i | \(0.451093\pi\) | |||||||
\(492\) | 34.9742i | 1.57676i | ||||||||
\(493\) | 8.01542 | 0.360996 | ||||||||
\(494\) | 14.3724 | − | 25.2341i | 0.646643 | − | 1.13534i | ||||
\(495\) | −2.84154 | −0.127718 | ||||||||
\(496\) | 93.9963i | 4.22056i | ||||||||
\(497\) | 39.6822 | 1.77999 | ||||||||
\(498\) | −29.2325 | −1.30994 | ||||||||
\(499\) | 0.212900i | 0.00953070i | 0.999989 | + | 0.00476535i | \(0.00151686\pi\) | ||||
−0.999989 | + | 0.00476535i | \(0.998483\pi\) | |||||||
\(500\) | − | 30.1001i | − | 1.34612i | ||||||
\(501\) | − | 14.7302i | − | 0.658095i | ||||||
\(502\) | − | 62.0779i | − | 2.77067i | ||||||
\(503\) | −10.5282 | −0.469430 | −0.234715 | − | 0.972064i | \(-0.575416\pi\) | ||||
−0.234715 | + | 0.972064i | \(0.575416\pi\) | |||||||
\(504\) | −37.6943 | −1.67904 | ||||||||
\(505\) | 34.4477i | 1.53290i | ||||||||
\(506\) | 5.18956 | 0.230704 | ||||||||
\(507\) | −6.63153 | − | 11.1814i | −0.294517 | − | 0.496582i | ||||
\(508\) | −32.5387 | −1.44367 | ||||||||
\(509\) | 26.1335i | 1.15835i | 0.815204 | + | 0.579175i | \(0.196625\pi\) | ||||
−0.815204 | + | 0.579175i | \(0.803375\pi\) | |||||||
\(510\) | −29.7144 | −1.31578 | ||||||||
\(511\) | 59.3934 | 2.62741 | ||||||||
\(512\) | − | 52.4306i | − | 2.31713i | ||||||
\(513\) | 2.94082i | 0.129840i | ||||||||
\(514\) | 48.5677i | 2.14223i | ||||||||
\(515\) | 9.68917i | 0.426956i | ||||||||
\(516\) | −64.5121 | −2.83999 | ||||||||
\(517\) | −5.31137 | −0.233594 | ||||||||
\(518\) | 89.8398i | 3.94734i | ||||||||
\(519\) | −0.186647 | −0.00819291 | ||||||||
\(520\) | −48.6180 | + | 85.3604i | −2.13204 | + | 3.74330i | ||||
\(521\) | 44.5983 | 1.95389 | 0.976944 | − | 0.213495i | \(-0.0684847\pi\) | ||||
0.976944 | + | 0.213495i | \(0.0684847\pi\) | |||||||
\(522\) | 5.74947i | 0.251647i | ||||||||
\(523\) | −35.9788 | −1.57324 | −0.786622 | − | 0.617435i | \(-0.788172\pi\) | ||||
−0.786622 | + | 0.617435i | \(0.788172\pi\) | |||||||
\(524\) | 7.27176 | 0.317668 | ||||||||
\(525\) | − | 12.0862i | − | 0.527483i | ||||||
\(526\) | − | 80.8233i | − | 3.52406i | ||||||
\(527\) | − | 23.5212i | − | 1.02460i | ||||||
\(528\) | 15.2584i | 0.664035i | ||||||||
\(529\) | −19.4096 | −0.843895 | ||||||||
\(530\) | −18.5209 | −0.804495 | ||||||||
\(531\) | − | 5.38624i | − | 0.233743i | ||||||
\(532\) | 63.5974 | 2.75730 | ||||||||
\(533\) | −19.9193 | − | 11.3453i | −0.862800 | − | 0.491418i | ||||
\(534\) | 8.86399 | 0.383583 | ||||||||
\(535\) | − | 34.7668i | − | 1.50310i | ||||||
\(536\) | 100.419 | 4.33743 | ||||||||
\(537\) | −10.9555 | −0.472767 | ||||||||
\(538\) | 24.7063i | 1.06516i | ||||||||
\(539\) | − | 8.45506i | − | 0.364185i | ||||||
\(540\) | − | 15.6311i | − | 0.672656i | ||||||
\(541\) | 19.2806i | 0.828937i | 0.910064 | + | 0.414469i | \(0.136033\pi\) | ||||
−0.910064 | + | 0.414469i | \(0.863967\pi\) | |||||||
\(542\) | 12.5524 | 0.539172 | ||||||||
\(543\) | 8.52034 | 0.365643 | ||||||||
\(544\) | 86.3395i | 3.70177i | ||||||||
\(545\) | −24.7999 | −1.06231 | ||||||||
\(546\) | 19.2130 | − | 33.7330i | 0.822241 | − | 1.44364i | ||||
\(547\) | −18.3680 | −0.785359 | −0.392679 | − | 0.919675i | \(-0.628452\pi\) | ||||
−0.392679 | + | 0.919675i | \(0.628452\pi\) | |||||||
\(548\) | − | 26.5215i | − | 1.13294i | ||||||
\(549\) | −2.34857 | −0.100234 | ||||||||
\(550\) | −8.41997 | −0.359029 | ||||||||
\(551\) | − | 6.17360i | − | 0.263004i | ||||||
\(552\) | 18.1683i | 0.773293i | ||||||||
\(553\) | 6.17686i | 0.262667i | ||||||||
\(554\) | 57.4759i | 2.44192i | ||||||||
\(555\) | −23.7099 | −1.00643 | ||||||||
\(556\) | −94.5481 | −4.00973 | ||||||||
\(557\) | − | 20.9920i | − | 0.889459i | −0.895665 | − | 0.444730i | \(-0.853300\pi\) | ||
0.895665 | − | 0.444730i | \(-0.146700\pi\) | |||||||
\(558\) | 16.8718 | 0.714239 | ||||||||
\(559\) | 20.9270 | − | 36.7424i | 0.885119 | − | 1.55404i | ||||
\(560\) | −170.450 | −7.20282 | ||||||||
\(561\) | − | 3.81818i | − | 0.161204i | ||||||
\(562\) | 28.8558 | 1.21721 | ||||||||
\(563\) | −3.18924 | −0.134411 | −0.0672053 | − | 0.997739i | \(-0.521408\pi\) | ||||
−0.0672053 | + | 0.997739i | \(0.521408\pi\) | |||||||
\(564\) | − | 29.2175i | − | 1.23028i | ||||||
\(565\) | 0.0441930i | 0.00185921i | ||||||||
\(566\) | − | 7.04329i | − | 0.296052i | ||||||
\(567\) | 3.93129i | 0.165099i | ||||||||
\(568\) | 96.7834 | 4.06094 | ||||||||
\(569\) | −19.0570 | −0.798909 | −0.399455 | − | 0.916753i | \(-0.630800\pi\) | ||||
−0.399455 | + | 0.916753i | \(0.630800\pi\) | |||||||
\(570\) | 22.8865i | 0.958610i | ||||||||
\(571\) | −13.1418 | −0.549967 | −0.274984 | − | 0.961449i | \(-0.588672\pi\) | ||||
−0.274984 | + | 0.961449i | \(0.588672\pi\) | |||||||
\(572\) | −17.2345 | − | 9.81609i | −0.720610 | − | 0.410431i | ||||
\(573\) | −11.8003 | −0.492965 | ||||||||
\(574\) | − | 68.4549i | − | 2.85725i | ||||||
\(575\) | −5.82540 | −0.242936 | ||||||||
\(576\) | −31.4147 | −1.30895 | ||||||||
\(577\) | − | 6.38825i | − | 0.265946i | −0.991120 | − | 0.132973i | \(-0.957548\pi\) | ||
0.991120 | − | 0.132973i | \(-0.0424524\pi\) | |||||||
\(578\) | 6.63205i | 0.275857i | ||||||||
\(579\) | 10.9405i | 0.454674i | ||||||||
\(580\) | 32.8140i | 1.36253i | ||||||||
\(581\) | 41.9608 | 1.74083 | ||||||||
\(582\) | 48.7268 | 2.01979 | ||||||||
\(583\) | − | 2.37985i | − | 0.0985635i | ||||||
\(584\) | 144.858 | 5.99428 | ||||||||
\(585\) | 8.90258 | + | 5.07056i | 0.368076 | + | 0.209642i | ||||
\(586\) | 14.1365 | 0.583975 | ||||||||
\(587\) | 8.66483i | 0.357636i | 0.983882 | + | 0.178818i | \(0.0572273\pi\) | ||||
−0.983882 | + | 0.178818i | \(0.942773\pi\) | |||||||
\(588\) | 46.5107 | 1.91807 | ||||||||
\(589\) | −18.1164 | −0.746472 | ||||||||
\(590\) | − | 41.9177i | − | 1.72572i | ||||||
\(591\) | − | 9.43307i | − | 0.388025i | ||||||
\(592\) | 127.316i | 5.23267i | ||||||||
\(593\) | 5.41552i | 0.222389i | 0.993799 | + | 0.111194i | \(0.0354676\pi\) | ||||
−0.993799 | + | 0.111194i | \(0.964532\pi\) | |||||||
\(594\) | 2.73878 | 0.112374 | ||||||||
\(595\) | 42.6525 | 1.74858 | ||||||||
\(596\) | − | 29.2514i | − | 1.19818i | ||||||
\(597\) | 15.3198 | 0.626997 | ||||||||
\(598\) | −16.2590 | − | 9.26047i | −0.664878 | − | 0.378689i | ||||
\(599\) | 17.1821 | 0.702041 | 0.351021 | − | 0.936368i | \(-0.385835\pi\) | ||||
0.351021 | + | 0.936368i | \(0.385835\pi\) | |||||||
\(600\) | − | 29.4777i | − | 1.20342i | ||||||
\(601\) | 4.44618 | 0.181364 | 0.0906818 | − | 0.995880i | \(-0.471095\pi\) | ||||
0.0906818 | + | 0.995880i | \(0.471095\pi\) | |||||||
\(602\) | 126.269 | 5.14635 | ||||||||
\(603\) | − | 10.4731i | − | 0.426496i | ||||||
\(604\) | 37.2728i | 1.51661i | ||||||||
\(605\) | − | 2.84154i | − | 0.115525i | ||||||
\(606\) | − | 33.2020i | − | 1.34874i | ||||||
\(607\) | 12.1499 | 0.493148 | 0.246574 | − | 0.969124i | \(-0.420695\pi\) | ||||
0.246574 | + | 0.969124i | \(0.420695\pi\) | |||||||
\(608\) | 66.5000 | 2.69693 | ||||||||
\(609\) | − | 8.25288i | − | 0.334423i | ||||||
\(610\) | −18.2774 | −0.740031 | ||||||||
\(611\) | 16.6406 | + | 9.47783i | 0.673206 | + | 0.383432i | ||||
\(612\) | 21.0035 | 0.849017 | ||||||||
\(613\) | 30.6073i | 1.23622i | 0.786093 | + | 0.618108i | \(0.212101\pi\) | ||||
−0.786093 | + | 0.618108i | \(0.787899\pi\) | |||||||
\(614\) | −82.3172 | −3.32205 | ||||||||
\(615\) | 18.0661 | 0.728497 | ||||||||
\(616\) | − | 37.6943i | − | 1.51875i | ||||||
\(617\) | − | 15.3414i | − | 0.617622i | −0.951123 | − | 0.308811i | \(-0.900069\pi\) | ||
0.951123 | − | 0.308811i | \(-0.0999311\pi\) | |||||||
\(618\) | − | 9.33878i | − | 0.375661i | ||||||
\(619\) | − | 10.0391i | − | 0.403505i | −0.979437 | − | 0.201752i | \(-0.935336\pi\) | ||
0.979437 | − | 0.201752i | \(-0.0646636\pi\) | |||||||
\(620\) | 96.2926 | 3.86720 | ||||||||
\(621\) | 1.89484 | 0.0760374 | ||||||||
\(622\) | − | 59.5581i | − | 2.38806i | ||||||
\(623\) | −12.7235 | −0.509757 | ||||||||
\(624\) | 27.2277 | − | 47.8046i | 1.08998 | − | 1.91372i | ||||
\(625\) | −30.9201 | −1.23681 | ||||||||
\(626\) | 66.9253i | 2.67487i | ||||||||
\(627\) | −2.94082 | −0.117445 | ||||||||
\(628\) | −89.6012 | −3.57548 | ||||||||
\(629\) | − | 31.8590i | − | 1.27030i | ||||||
\(630\) | 30.5947i | 1.21892i | ||||||||
\(631\) | 20.8523i | 0.830119i | 0.909794 | + | 0.415059i | \(0.136239\pi\) | ||||
−0.909794 | + | 0.415059i | \(0.863761\pi\) | |||||||
\(632\) | 15.0652i | 0.599260i | ||||||||
\(633\) | 2.91243 | 0.115759 | ||||||||
\(634\) | −57.7991 | −2.29550 | ||||||||
\(635\) | 16.8081i | 0.667009i | ||||||||
\(636\) | 13.0914 | 0.519108 | ||||||||
\(637\) | −15.0876 | + | 26.4898i | −0.597791 | + | 1.04956i | ||||
\(638\) | −5.74947 | −0.227624 | ||||||||
\(639\) | − | 10.0939i | − | 0.399310i | ||||||
\(640\) | −115.970 | −4.58413 | ||||||||
\(641\) | −29.3934 | −1.16097 | −0.580484 | − | 0.814272i | \(-0.697137\pi\) | ||||
−0.580484 | + | 0.814272i | \(0.697137\pi\) | |||||||
\(642\) | 33.5096i | 1.32252i | ||||||||
\(643\) | 7.23812i | 0.285444i | 0.989763 | + | 0.142722i | \(0.0455854\pi\) | ||||
−0.989763 | + | 0.142722i | \(0.954415\pi\) | |||||||
\(644\) | − | 40.9774i | − | 1.61474i | ||||||
\(645\) | 33.3241i | 1.31214i | ||||||||
\(646\) | −30.7526 | −1.20994 | ||||||||
\(647\) | 25.4069 | 0.998848 | 0.499424 | − | 0.866358i | \(-0.333545\pi\) | ||||
0.499424 | + | 0.866358i | \(0.333545\pi\) | |||||||
\(648\) | 9.58828i | 0.376663i | ||||||||
\(649\) | 5.38624 | 0.211429 | ||||||||
\(650\) | 26.3799 | + | 15.0249i | 1.03470 | + | 0.589327i | ||||
\(651\) | −24.2180 | −0.949178 | ||||||||
\(652\) | − | 62.7284i | − | 2.45663i | ||||||
\(653\) | −10.1486 | −0.397146 | −0.198573 | − | 0.980086i | \(-0.563631\pi\) | ||||
−0.198573 | + | 0.980086i | \(0.563631\pi\) | |||||||
\(654\) | 23.9031 | 0.934685 | ||||||||
\(655\) | − | 3.75627i | − | 0.146770i | ||||||
\(656\) | − | 97.0107i | − | 3.78763i | ||||||
\(657\) | − | 15.1079i | − | 0.589413i | ||||||
\(658\) | 57.1873i | 2.22939i | ||||||||
\(659\) | −18.8648 | −0.734869 | −0.367434 | − | 0.930049i | \(-0.619764\pi\) | ||||
−0.367434 | + | 0.930049i | \(0.619764\pi\) | |||||||
\(660\) | 15.6311 | 0.608440 | ||||||||
\(661\) | − | 7.39059i | − | 0.287461i | −0.989617 | − | 0.143730i | \(-0.954090\pi\) | ||
0.989617 | − | 0.143730i | \(-0.0459098\pi\) | |||||||
\(662\) | −1.53514 | −0.0596648 | ||||||||
\(663\) | −6.81332 | + | 11.9624i | −0.264607 | + | 0.464581i | ||||
\(664\) | 102.341 | 3.97160 | ||||||||
\(665\) | − | 32.8516i | − | 1.27393i | ||||||
\(666\) | 22.8525 | 0.885516 | ||||||||
\(667\) | −3.97780 | −0.154021 | ||||||||
\(668\) | 81.0296i | 3.13513i | ||||||||
\(669\) | − | 10.8511i | − | 0.419526i | ||||||
\(670\) | − | 81.5052i | − | 3.14882i | ||||||
\(671\) | − | 2.34857i | − | 0.0906655i | ||||||
\(672\) | 88.8973 | 3.42929 | ||||||||
\(673\) | 13.8241 | 0.532879 | 0.266439 | − | 0.963852i | \(-0.414153\pi\) | ||||
0.266439 | + | 0.963852i | \(0.414153\pi\) | |||||||
\(674\) | − | 21.2762i | − | 0.819530i | ||||||
\(675\) | −3.07435 | −0.118332 | ||||||||
\(676\) | 36.4796 | + | 61.5079i | 1.40306 | + | 2.36569i | ||||
\(677\) | −28.1714 | −1.08272 | −0.541358 | − | 0.840792i | \(-0.682090\pi\) | ||||
−0.541358 | + | 0.840792i | \(0.682090\pi\) | |||||||
\(678\) | − | 0.0425948i | − | 0.00163585i | ||||||
\(679\) | −69.9433 | −2.68418 | ||||||||
\(680\) | 104.028 | 3.98929 | ||||||||
\(681\) | − | 0.322636i | − | 0.0123634i | ||||||
\(682\) | 16.8718i | 0.646053i | ||||||||
\(683\) | − | 20.1458i | − | 0.770856i | −0.922738 | − | 0.385428i | \(-0.874054\pi\) | ||
0.922738 | − | 0.385428i | \(-0.125946\pi\) | |||||||
\(684\) | − | 16.1772i | − | 0.618552i | ||||||
\(685\) | −13.6998 | −0.523444 | ||||||||
\(686\) | −15.6665 | −0.598150 | ||||||||
\(687\) | − | 5.94060i | − | 0.226648i | ||||||
\(688\) | 178.942 | 6.82211 | ||||||||
\(689\) | −4.24671 | + | 7.45611i | −0.161787 | + | 0.284055i | ||||
\(690\) | 14.7463 | 0.561384 | ||||||||
\(691\) | 4.60090i | 0.175026i | 0.996163 | + | 0.0875132i | \(0.0278920\pi\) | ||||
−0.996163 | + | 0.0875132i | \(0.972108\pi\) | |||||||
\(692\) | 1.02673 | 0.0390306 | ||||||||
\(693\) | −3.93129 | −0.149337 | ||||||||
\(694\) | 27.7593i | 1.05373i | ||||||||
\(695\) | 48.8394i | 1.85258i | ||||||||
\(696\) | − | 20.1285i | − | 0.762968i | ||||||
\(697\) | 24.2755i | 0.919499i | ||||||||
\(698\) | −54.7839 | −2.07360 | ||||||||
\(699\) | 12.6202 | 0.477338 | ||||||||
\(700\) | 66.4851i | 2.51290i | ||||||||
\(701\) | 2.14477 | 0.0810067 | 0.0405033 | − | 0.999179i | \(-0.487104\pi\) | ||||
0.0405033 | + | 0.999179i | \(0.487104\pi\) | |||||||
\(702\) | −8.58064 | − | 4.88720i | −0.323855 | − | 0.184455i | ||||
\(703\) | −24.5383 | −0.925479 | ||||||||
\(704\) | − | 31.4147i | − | 1.18399i | ||||||
\(705\) | −15.0925 | −0.568415 | ||||||||
\(706\) | 73.3733 | 2.76144 | ||||||||
\(707\) | 47.6586i | 1.79239i | ||||||||
\(708\) | 29.6293i | 1.11354i | ||||||||
\(709\) | − | 18.0751i | − | 0.678826i | −0.940637 | − | 0.339413i | \(-0.889772\pi\) | ||
0.940637 | − | 0.339413i | \(-0.110228\pi\) | |||||||
\(710\) | − | 78.5546i | − | 2.94810i | ||||||
\(711\) | 1.57120 | 0.0589248 | ||||||||
\(712\) | −31.0322 | −1.16298 | ||||||||
\(713\) | 11.6728i | 0.437151i | ||||||||
\(714\) | −41.1101 | −1.53851 | ||||||||
\(715\) | −5.07056 | + | 8.90258i | −0.189628 | + | 0.332938i | ||||
\(716\) | 60.2657 | 2.25223 | ||||||||
\(717\) | − | 20.7706i | − | 0.775691i | ||||||
\(718\) | 73.2206 | 2.73257 | ||||||||
\(719\) | 5.67258 | 0.211552 | 0.105776 | − | 0.994390i | \(-0.466267\pi\) | ||||
0.105776 | + | 0.994390i | \(0.466267\pi\) | |||||||
\(720\) | 43.3572i | 1.61583i | ||||||||
\(721\) | 13.4050i | 0.499230i | ||||||||
\(722\) | − | 28.3507i | − | 1.05511i | ||||||
\(723\) | − | 18.2163i | − | 0.677470i | ||||||
\(724\) | −46.8698 | −1.74190 | ||||||||
\(725\) | 6.45391 | 0.239692 | ||||||||
\(726\) | 2.73878i | 0.101646i | ||||||||
\(727\) | −20.7279 | −0.768756 | −0.384378 | − | 0.923176i | \(-0.625584\pi\) | ||||
−0.384378 | + | 0.923176i | \(0.625584\pi\) | |||||||
\(728\) | −67.2634 | + | 118.097i | −2.49295 | + | 4.37696i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − | 117.575i | − | 4.35163i | ||||||
\(731\) | −44.7776 | −1.65616 | ||||||||
\(732\) | 12.9193 | 0.477511 | ||||||||
\(733\) | − | 13.8875i | − | 0.512945i | −0.966552 | − | 0.256473i | \(-0.917440\pi\) | ||
0.966552 | − | 0.256473i | \(-0.0825603\pi\) | |||||||
\(734\) | − | 5.19172i | − | 0.191630i | ||||||
\(735\) | − | 24.0254i | − | 0.886189i | ||||||
\(736\) | − | 42.8476i | − | 1.57938i | ||||||
\(737\) | 10.4731 | 0.385780 | ||||||||
\(738\) | −17.4128 | −0.640975 | ||||||||
\(739\) | − | 2.10062i | − | 0.0772725i | −0.999253 | − | 0.0386362i | \(-0.987699\pi\) | ||
0.999253 | − | 0.0386362i | \(-0.0123014\pi\) | |||||||
\(740\) | 130.427 | 4.79457 | ||||||||
\(741\) | 9.21362 | + | 5.24772i | 0.338471 | + | 0.192780i | ||||
\(742\) | −25.6238 | −0.940678 | ||||||||
\(743\) | − | 39.5255i | − | 1.45005i | −0.688722 | − | 0.725025i | \(-0.741828\pi\) | ||
0.688722 | − | 0.725025i | \(-0.258172\pi\) | |||||||
\(744\) | −59.0668 | −2.16550 | ||||||||
\(745\) | −15.1100 | −0.553587 | ||||||||
\(746\) | 100.655i | 3.68523i | ||||||||
\(747\) | − | 10.6736i | − | 0.390525i | ||||||
\(748\) | 21.0035i | 0.767964i | ||||||||
\(749\) | − | 48.1002i | − | 1.75754i | ||||||
\(750\) | 14.9861 | 0.547216 | ||||||||
\(751\) | 7.96076 | 0.290492 | 0.145246 | − | 0.989396i | \(-0.453603\pi\) | ||||
0.145246 | + | 0.989396i | \(0.453603\pi\) | |||||||
\(752\) | 81.0427i | 2.95532i | ||||||||
\(753\) | 22.6662 | 0.826004 | ||||||||
\(754\) | 18.0132 | + | 10.2596i | 0.656000 | + | 0.373632i | ||||
\(755\) | 19.2535 | 0.700707 | ||||||||
\(756\) | − | 21.6258i | − | 0.786521i | ||||||
\(757\) | −21.7720 | −0.791316 | −0.395658 | − | 0.918398i | \(-0.629484\pi\) | ||||
−0.395658 | + | 0.918398i | \(0.629484\pi\) | |||||||
\(758\) | 71.5721 | 2.59962 | ||||||||
\(759\) | 1.89484i | 0.0687784i | ||||||||
\(760\) | − | 80.1240i | − | 2.90640i | ||||||
\(761\) | − | 25.3978i | − | 0.920668i | −0.887746 | − | 0.460334i | \(-0.847730\pi\) | ||
0.887746 | − | 0.460334i | \(-0.152270\pi\) | |||||||
\(762\) | − | 16.2003i | − | 0.586874i | ||||||
\(763\) | −34.3109 | −1.24214 | ||||||||
\(764\) | 64.9126 | 2.34846 | ||||||||
\(765\) | − | 10.8495i | − | 0.392264i | ||||||
\(766\) | −46.3433 | −1.67445 | ||||||||
\(767\) | −16.8752 | − | 9.61144i | −0.609327 | − | 0.347049i | ||||
\(768\) | 48.9471 | 1.76623 | ||||||||
\(769\) | 17.5471i | 0.632763i | 0.948632 | + | 0.316382i | \(0.102468\pi\) | ||||
−0.948632 | + | 0.316382i | \(0.897532\pi\) | |||||||
\(770\) | −30.5947 | −1.10256 | ||||||||
\(771\) | −17.7333 | −0.638649 | ||||||||
\(772\) | − | 60.1832i | − | 2.16604i | ||||||
\(773\) | − | 16.9181i | − | 0.608503i | −0.952592 | − | 0.304251i | \(-0.901594\pi\) | ||
0.952592 | − | 0.304251i | \(-0.0984063\pi\) | |||||||
\(774\) | − | 32.1190i | − | 1.15449i | ||||||
\(775\) | − | 18.9389i | − | 0.680307i | ||||||
\(776\) | −170.589 | −6.12379 | ||||||||
\(777\) | −32.8028 | −1.17680 | ||||||||
\(778\) | − | 13.8475i | − | 0.496456i | ||||||
\(779\) | 18.6974 | 0.669902 | ||||||||
\(780\) | −48.9724 | − | 27.8928i | −1.75349 | − | 0.998723i | ||||
\(781\) | 10.0939 | 0.361189 | ||||||||
\(782\) | 19.8147i | 0.708570i | ||||||||
\(783\) | −2.09928 | −0.0750221 | ||||||||
\(784\) | −129.010 | −4.60751 | ||||||||
\(785\) | 46.2841i | 1.65195i | ||||||||
\(786\) | 3.62044i | 0.129137i | ||||||||
\(787\) | 27.1659i | 0.968361i | 0.874968 | + | 0.484181i | \(0.160882\pi\) | ||||
−0.874968 | + | 0.484181i | \(0.839118\pi\) | |||||||
\(788\) | 51.8907i | 1.84853i | ||||||||
\(789\) | 29.5107 | 1.05061 | ||||||||
\(790\) | 12.2277 | 0.435041 | ||||||||
\(791\) | 0.0611413i | 0.00217394i | ||||||||
\(792\) | −9.58828 | −0.340705 | ||||||||
\(793\) | −4.19089 | + | 7.35810i | −0.148823 | + | 0.261294i | ||||
\(794\) | 43.1992 | 1.53308 | ||||||||
\(795\) | − | 6.76245i | − | 0.239839i | ||||||
\(796\) | −84.2731 | −2.98698 | ||||||||
\(797\) | −12.3253 | −0.436583 | −0.218292 | − | 0.975884i | \(-0.570048\pi\) | ||||
−0.218292 | + | 0.975884i | \(0.570048\pi\) | |||||||
\(798\) | 31.6637i | 1.12088i | ||||||||
\(799\) | − | 20.2797i | − | 0.717446i | ||||||
\(800\) | 69.5194i | 2.45788i | ||||||||
\(801\) | 3.23647i | 0.114355i | ||||||||
\(802\) | 23.0665 | 0.814507 | ||||||||
\(803\) | 15.1079 | 0.533144 | ||||||||
\(804\) | 57.6116i | 2.03180i | ||||||||
\(805\) | −21.1671 | −0.746043 | ||||||||
\(806\) | 30.1067 | − | 52.8594i | 1.06046 | − | 1.86189i | ||||
\(807\) | −9.02091 | −0.317551 | ||||||||
\(808\) | 116.238i | 4.08923i | ||||||||
\(809\) | 51.6306 | 1.81523 | 0.907617 | − | 0.419798i | \(-0.137899\pi\) | ||||
0.907617 | + | 0.419798i | \(0.137899\pi\) | |||||||
\(810\) | 7.78236 | 0.273444 | ||||||||
\(811\) | − | 22.5443i | − | 0.791637i | −0.918329 | − | 0.395818i | \(-0.870461\pi\) | ||
0.918329 | − | 0.395818i | \(-0.129539\pi\) | |||||||
\(812\) | 45.3985i | 1.59317i | ||||||||
\(813\) | 4.58320i | 0.160740i | ||||||||
\(814\) | 22.8525i | 0.800980i | ||||||||
\(815\) | −32.4027 | −1.13502 | ||||||||
\(816\) | −58.2591 | −2.03948 | ||||||||
\(817\) | 34.4884i | 1.20660i | ||||||||
\(818\) | −85.9597 | −3.00551 | ||||||||
\(819\) | 12.3168 | + | 7.01516i | 0.430383 | + | 0.245130i | ||||
\(820\) | −99.3806 | −3.47052 | ||||||||
\(821\) | 18.1907i | 0.634861i | 0.948282 | + | 0.317430i | \(0.102820\pi\) | ||||
−0.948282 | + | 0.317430i | \(0.897180\pi\) | |||||||
\(822\) | 13.2044 | 0.460557 | ||||||||
\(823\) | −44.4631 | −1.54989 | −0.774944 | − | 0.632030i | \(-0.782222\pi\) | ||||
−0.774944 | + | 0.632030i | \(0.782222\pi\) | |||||||
\(824\) | 32.6944i | 1.13896i | ||||||||
\(825\) | − | 3.07435i | − | 0.107035i | ||||||
\(826\) | − | 57.9934i | − | 2.01785i | ||||||
\(827\) | − | 6.33341i | − | 0.220234i | −0.993919 | − | 0.110117i | \(-0.964877\pi\) | ||
0.993919 | − | 0.110117i | \(-0.0351226\pi\) | |||||||
\(828\) | −10.4234 | −0.362238 | ||||||||
\(829\) | −7.54455 | −0.262033 | −0.131017 | − | 0.991380i | \(-0.541824\pi\) | ||||
−0.131017 | + | 0.991380i | \(0.541824\pi\) | |||||||
\(830\) | − | 83.0654i | − | 2.88324i | ||||||
\(831\) | −20.9859 | −0.727994 | ||||||||
\(832\) | −56.0577 | + | 98.4226i | −1.94345 | + | 3.41219i | ||||
\(833\) | 32.2829 | 1.11854 | ||||||||
\(834\) | − | 47.0732i | − | 1.63001i | ||||||
\(835\) | 41.8563 | 1.44850 | ||||||||
\(836\) | 16.1772 | 0.559501 | ||||||||
\(837\) | 6.16032i | 0.212932i | ||||||||
\(838\) | 18.1561i | 0.627194i | ||||||||
\(839\) | 30.1703i | 1.04159i | 0.853681 | + | 0.520797i | \(0.174365\pi\) | ||||
−0.853681 | + | 0.520797i | \(0.825635\pi\) | |||||||
\(840\) | − | 107.110i | − | 3.69564i | ||||||
\(841\) | −24.5930 | −0.848035 | ||||||||
\(842\) | 7.15719 | 0.246653 | ||||||||
\(843\) | 10.5360i | 0.362878i | ||||||||
\(844\) | −16.0211 | −0.551468 | ||||||||
\(845\) | 31.7723 | − | 18.8438i | 1.09300 | − | 0.648245i | ||||
\(846\) | 14.5467 | 0.500125 | ||||||||
\(847\) | − | 3.93129i | − | 0.135081i | ||||||
\(848\) | −36.3127 | −1.24698 | ||||||||
\(849\) | 2.57169 | 0.0882601 | ||||||||
\(850\) | − | 32.1489i | − | 1.10270i | ||||||
\(851\) | 15.8106i | 0.541981i | ||||||||
\(852\) | 55.5260i | 1.90229i | ||||||||
\(853\) | − | 14.6801i | − | 0.502637i | −0.967904 | − | 0.251319i | \(-0.919136\pi\) | ||
0.967904 | − | 0.251319i | \(-0.0808642\pi\) | |||||||
\(854\) | −25.2869 | −0.865301 | ||||||||
\(855\) | −8.35645 | −0.285785 | ||||||||
\(856\) | − | 117.315i | − | 4.00973i | ||||||
\(857\) | 21.1257 | 0.721641 | 0.360821 | − | 0.932635i | \(-0.382497\pi\) | ||||
0.360821 | + | 0.932635i | \(0.382497\pi\) | |||||||
\(858\) | 4.88720 | − | 8.58064i | 0.166846 | − | 0.292938i | ||||
\(859\) | 29.4462 | 1.00469 | 0.502346 | − | 0.864667i | \(-0.332470\pi\) | ||||
0.502346 | + | 0.864667i | \(0.332470\pi\) | |||||||
\(860\) | − | 183.314i | − | 6.25094i | ||||||
\(861\) | 24.9947 | 0.851816 | ||||||||
\(862\) | 68.1258 | 2.32038 | ||||||||
\(863\) | − | 33.8929i | − | 1.15373i | −0.816840 | − | 0.576865i | \(-0.804276\pi\) | ||
0.816840 | − | 0.576865i | \(-0.195724\pi\) | |||||||
\(864\) | − | 22.6127i | − | 0.769301i | ||||||
\(865\) | − | 0.530366i | − | 0.0180330i | ||||||
\(866\) | 17.9543i | 0.610111i | ||||||||
\(867\) | −2.42153 | −0.0822396 | ||||||||
\(868\) | 133.221 | 4.52183 | ||||||||
\(869\) | 1.57120i | 0.0532995i | ||||||||
\(870\) | −16.3373 | −0.553888 | ||||||||
\(871\) | −32.8122 | − | 18.6886i | −1.11180 | − | 0.633239i | ||||
\(872\) | −83.6830 | −2.83386 | ||||||||
\(873\) | 17.7914i | 0.602148i | ||||||||
\(874\) | 15.2616 | 0.516230 | ||||||||
\(875\) | −21.5113 | −0.727215 | ||||||||
\(876\) | 83.1072i | 2.80793i | ||||||||
\(877\) | 6.62356i | 0.223662i | 0.993727 | + | 0.111831i | \(0.0356715\pi\) | ||||
−0.993727 | + | 0.111831i | \(0.964329\pi\) | |||||||
\(878\) | − | 104.671i | − | 3.53247i | ||||||
\(879\) | 5.16162i | 0.174097i | ||||||||
\(880\) | −43.3572 | −1.46157 | ||||||||
\(881\) | −18.7993 | −0.633366 | −0.316683 | − | 0.948531i | \(-0.602569\pi\) | ||||
−0.316683 | + | 0.948531i | \(0.602569\pi\) | |||||||
\(882\) | 23.1566i | 0.779722i | ||||||||
\(883\) | 35.0323 | 1.17893 | 0.589465 | − | 0.807794i | \(-0.299339\pi\) | ||||
0.589465 | + | 0.807794i | \(0.299339\pi\) | |||||||
\(884\) | 37.4796 | − | 65.8043i | 1.26057 | − | 2.21324i | ||||
\(885\) | 15.3052 | 0.514479 | ||||||||
\(886\) | 34.8941i | 1.17229i | ||||||||
\(887\) | 12.8619 | 0.431860 | 0.215930 | − | 0.976409i | \(-0.430722\pi\) | ||||
0.215930 | + | 0.976409i | \(0.430722\pi\) | |||||||
\(888\) | −80.0050 | −2.68479 | ||||||||
\(889\) | 23.2541i | 0.779918i | ||||||||
\(890\) | 25.1874i | 0.844283i | ||||||||
\(891\) | 1.00000i | 0.0335013i | ||||||||
\(892\) | 59.6909i | 1.99860i | ||||||||
\(893\) | −15.6198 | −0.522696 | ||||||||
\(894\) | 14.5636 | 0.487079 | ||||||||
\(895\) | − | 31.1306i | − | 1.04058i | ||||||
\(896\) | −160.446 | −5.36012 | ||||||||
\(897\) | 3.38124 | − | 5.93656i | 0.112896 | − | 0.198216i | ||||
\(898\) | 71.0749 | 2.37180 | ||||||||
\(899\) | − | 12.9322i | − | 0.431314i | ||||||
\(900\) | 16.9118 | 0.563725 | ||||||||
\(901\) | 9.08670 | 0.302722 | ||||||||
\(902\) | − | 17.4128i | − | 0.579784i | ||||||
\(903\) | 46.1042i | 1.53425i | ||||||||
\(904\) | 0.149121i | 0.00495971i | ||||||||
\(905\) | 24.2109i | 0.804797i | ||||||||
\(906\) | −18.5572 | −0.616523 | ||||||||
\(907\) | −47.0378 | −1.56187 | −0.780933 | − | 0.624615i | \(-0.785256\pi\) | ||||
−0.780933 | + | 0.624615i | \(0.785256\pi\) | |||||||
\(908\) | 1.77480i | 0.0588987i | ||||||||
\(909\) | 12.1229 | 0.402091 | ||||||||
\(910\) | 95.8536 | + | 54.5945i | 3.17752 | + | 1.80979i | ||||
\(911\) | 40.3206 | 1.33588 | 0.667940 | − | 0.744215i | \(-0.267176\pi\) | ||||
0.667940 | + | 0.744215i | \(0.267176\pi\) | |||||||
\(912\) | 44.8720i | 1.48586i | ||||||||
\(913\) | 10.6736 | 0.353243 | ||||||||
\(914\) | −43.9225 | −1.45283 | ||||||||
\(915\) | − | 6.67355i | − | 0.220621i | ||||||
\(916\) | 32.6788i | 1.07974i | ||||||||
\(917\) | − | 5.19683i | − | 0.171614i | ||||||
\(918\) | 10.4572i | 0.345137i | ||||||||
\(919\) | −1.80179 | −0.0594356 | −0.0297178 | − | 0.999558i | \(-0.509461\pi\) | ||||
−0.0297178 | + | 0.999558i | \(0.509461\pi\) | |||||||
\(920\) | −51.6259 | −1.70205 | ||||||||
\(921\) | − | 30.0561i | − | 0.990383i | ||||||
\(922\) | −9.54646 | −0.314396 | ||||||||
\(923\) | −31.6244 | − | 18.0120i | −1.04093 | − | 0.592873i | ||||
\(924\) | 21.6258 | 0.711435 | ||||||||
\(925\) | − | 25.6525i | − | 0.843448i | ||||||
\(926\) | −74.1619 | −2.43711 | ||||||||
\(927\) | 3.40983 | 0.111994 | ||||||||
\(928\) | 47.4705i | 1.55829i | ||||||||
\(929\) | − | 26.3015i | − | 0.862924i | −0.902131 | − | 0.431462i | \(-0.857998\pi\) | ||
0.902131 | − | 0.431462i | \(-0.142002\pi\) | |||||||
\(930\) | 47.9418i | 1.57207i | ||||||||
\(931\) | − | 24.8648i | − | 0.814910i | ||||||
\(932\) | −69.4226 | −2.27401 | ||||||||
\(933\) | 21.7462 | 0.711939 | ||||||||
\(934\) | − | 42.9711i | − | 1.40606i | ||||||
\(935\) | 10.8495 | 0.354817 | ||||||||
\(936\) | 30.0402 | + | 17.1097i | 0.981894 | + | 0.559249i | ||||
\(937\) | 8.45280 | 0.276141 | 0.138070 | − | 0.990422i | \(-0.455910\pi\) | ||||
0.138070 | + | 0.990422i | \(0.455910\pi\) | |||||||
\(938\) | − | 112.763i | − | 3.68184i | ||||||
\(939\) | −24.4361 | −0.797443 | ||||||||
\(940\) | 83.0226 | 2.70790 | ||||||||
\(941\) | 8.34188i | 0.271937i | 0.990713 | + | 0.135969i | \(0.0434147\pi\) | ||||
−0.990713 | + | 0.135969i | \(0.956585\pi\) | |||||||
\(942\) | − | 44.6103i | − | 1.45348i | ||||||
\(943\) | − | 12.0472i | − | 0.392310i | ||||||
\(944\) | − | 82.1852i | − | 2.67490i | ||||||
\(945\) | −11.1709 | −0.363390 | ||||||||
\(946\) | 32.1190 | 1.04428 | ||||||||
\(947\) | − | 21.8593i | − | 0.710330i | −0.934804 | − | 0.355165i | \(-0.884425\pi\) | ||
0.934804 | − | 0.355165i | \(-0.115575\pi\) | |||||||
\(948\) | −8.64309 | −0.280714 | ||||||||
\(949\) | −47.3331 | − | 26.9591i | −1.53650 | − | 0.875129i | ||||
\(950\) | −24.7616 | −0.803372 | ||||||||
\(951\) | − | 21.1040i | − | 0.684343i | ||||||
\(952\) | 143.924 | 4.66459 | ||||||||
\(953\) | −57.6509 | −1.86750 | −0.933748 | − | 0.357932i | \(-0.883482\pi\) | ||||
−0.933748 | + | 0.357932i | \(0.883482\pi\) | |||||||
\(954\) | 6.51790i | 0.211025i | ||||||||
\(955\) | − | 33.5310i | − | 1.08504i | ||||||
\(956\) | 114.257i | 3.69535i | ||||||||
\(957\) | − | 2.09928i | − | 0.0678600i | ||||||
\(958\) | 90.3964 | 2.92058 | ||||||||
\(959\) | −18.9538 | −0.612051 | ||||||||
\(960\) | − | 89.2661i | − | 2.88105i | ||||||
\(961\) | −6.94950 | −0.224177 | ||||||||
\(962\) | 40.7790 | − | 71.5972i | 1.31477 | − | 2.30838i | ||||
\(963\) | −12.2352 | −0.394274 | ||||||||
\(964\) | 100.206i | 3.22743i | ||||||||
\(965\) | −31.0880 | −1.00076 | ||||||||
\(966\) | 20.4017 | 0.656413 | ||||||||
\(967\) | − | 41.2637i | − | 1.32695i | −0.748197 | − | 0.663476i | \(-0.769080\pi\) | ||
0.748197 | − | 0.663476i | \(-0.230920\pi\) | |||||||
\(968\) | − | 9.58828i | − | 0.308179i | ||||||
\(969\) | − | 11.2286i | − | 0.360713i | ||||||
\(970\) | 138.459i | 4.44566i | ||||||||
\(971\) | 10.2876 | 0.330146 | 0.165073 | − | 0.986281i | \(-0.447214\pi\) | ||||
0.165073 | + | 0.986281i | \(0.447214\pi\) | |||||||
\(972\) | −5.50093 | −0.176442 | ||||||||
\(973\) | 67.5697i | 2.16618i | ||||||||
\(974\) | −51.1286 | −1.63827 | ||||||||
\(975\) | −5.48600 | + | 9.63196i | −0.175692 | + | 0.308470i | ||||
\(976\) | −35.8353 | −1.14706 | ||||||||
\(977\) | 54.0502i | 1.72922i | 0.502445 | + | 0.864609i | \(0.332434\pi\) | ||||
−0.502445 | + | 0.864609i | \(0.667566\pi\) | |||||||
\(978\) | 31.2310 | 0.998657 | ||||||||
\(979\) | −3.23647 | −0.103438 | ||||||||
\(980\) | 132.162i | 4.22176i | ||||||||
\(981\) | 8.72763i | 0.278652i | ||||||||
\(982\) | − | 18.5755i | − | 0.592766i | ||||||
\(983\) | − | 33.3316i | − | 1.06311i | −0.847022 | − | 0.531557i | \(-0.821607\pi\) | ||
0.847022 | − | 0.531557i | \(-0.178393\pi\) | |||||||
\(984\) | 60.9611 | 1.94337 | ||||||||
\(985\) | 26.8045 | 0.854061 | ||||||||
\(986\) | − | 21.9525i | − | 0.699109i | ||||||
\(987\) | −20.8805 | −0.664635 | ||||||||
\(988\) | −50.6835 | − | 28.8673i | −1.61246 | − | 0.918392i | ||||
\(989\) | 22.2217 | 0.706610 | ||||||||
\(990\) | 7.78236i | 0.247340i | ||||||||
\(991\) | 15.1783 | 0.482155 | 0.241077 | − | 0.970506i | \(-0.422499\pi\) | ||||
0.241077 | + | 0.970506i | \(0.422499\pi\) | |||||||
\(992\) | 139.302 | 4.42283 | ||||||||
\(993\) | − | 0.560518i | − | 0.0177875i | ||||||
\(994\) | − | 108.681i | − | 3.44715i | ||||||
\(995\) | 43.5318i | 1.38005i | ||||||||
\(996\) | 58.7144i | 1.86044i | ||||||||
\(997\) | −23.6131 | −0.747834 | −0.373917 | − | 0.927462i | \(-0.621986\pi\) | ||||
−0.373917 | + | 0.927462i | \(0.621986\pi\) | |||||||
\(998\) | 0.583086 | 0.0184573 | ||||||||
\(999\) | 8.34404i | 0.263994i |
(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 | 429.2.b.b.298.1 | ✓ | 14 | |
3.2 | odd | 2 | 1287.2.b.c.298.14 | 14 | |||
13.5 | odd | 4 | 5577.2.a.x.1.1 | 7 | |||
13.8 | odd | 4 | 5577.2.a.y.1.7 | 7 | |||
13.12 | even | 2 | inner | 429.2.b.b.298.14 | yes | 14 | |
39.38 | odd | 2 | 1287.2.b.c.298.1 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.b.b.298.1 | ✓ | 14 | 1.1 | even | 1 | trivial | |
429.2.b.b.298.14 | yes | 14 | 13.12 | even | 2 | inner | |
1287.2.b.c.298.1 | 14 | 39.38 | odd | 2 | |||
1287.2.b.c.298.14 | 14 | 3.2 | odd | 2 | |||
5577.2.a.x.1.1 | 7 | 13.5 | odd | 4 | |||
5577.2.a.y.1.7 | 7 | 13.8 | odd | 4 |