Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [56,3,Mod(5,56)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(56, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("56.5");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 56 = 2^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 56.j (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.52588948042\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 45.2 | ||
Character | \(\chi\) | \(=\) | 56.45 |
Dual form | 56.3.j.a.5.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/56\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(29\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.87135 | + | 0.705725i | −0.935675 | + | 0.352863i | ||||
\(3\) | −0.126628 | + | 0.219326i | −0.0422093 | + | 0.0731087i | −0.886358 | − | 0.463000i | \(-0.846773\pi\) |
0.844149 | + | 0.536109i | \(0.180106\pi\) | |||||||
\(4\) | 3.00390 | − | 2.64132i | 0.750976 | − | 0.660330i | ||||
\(5\) | 1.78589 | + | 3.09325i | 0.357178 | + | 0.618650i | 0.987488 | − | 0.157693i | \(-0.0504056\pi\) |
−0.630310 | + | 0.776343i | \(0.717072\pi\) | |||||||
\(6\) | 0.0821813 | − | 0.499801i | 0.0136969 | − | 0.0833001i | ||||
\(7\) | 2.89466 | + | 6.37346i | 0.413522 | + | 0.910494i | ||||
\(8\) | −3.75731 | + | 7.06276i | −0.469664 | + | 0.882845i | ||||
\(9\) | 4.46793 | + | 7.73868i | 0.496437 | + | 0.859854i | ||||
\(10\) | −5.52501 | − | 4.52821i | −0.552501 | − | 0.452821i | ||||
\(11\) | −6.82675 | − | 3.94142i | −0.620613 | − | 0.358311i | 0.156494 | − | 0.987679i | \(-0.449981\pi\) |
−0.777108 | + | 0.629368i | \(0.783314\pi\) | |||||||
\(12\) | 0.198932 | + | 0.993300i | 0.0165777 | + | 0.0827750i | ||||
\(13\) | 18.1529 | 1.39638 | 0.698189 | − | 0.715914i | \(-0.253990\pi\) | ||||
0.698189 | + | 0.715914i | \(0.253990\pi\) | |||||||
\(14\) | −9.91483 | − | 9.88414i | −0.708202 | − | 0.706010i | ||||
\(15\) | −0.904575 | −0.0603050 | ||||||||
\(16\) | 2.04687 | − | 15.8685i | 0.127929 | − | 0.991783i | ||||
\(17\) | −8.26180 | − | 4.76995i | −0.485988 | − | 0.280585i | 0.236920 | − | 0.971529i | \(-0.423862\pi\) |
−0.722909 | + | 0.690944i | \(0.757195\pi\) | |||||||
\(18\) | −13.8224 | − | 11.3287i | −0.767914 | − | 0.629370i | ||||
\(19\) | −12.4094 | − | 21.4938i | −0.653129 | − | 1.13125i | −0.982359 | − | 0.187003i | \(-0.940123\pi\) |
0.329231 | − | 0.944250i | \(-0.393211\pi\) | |||||||
\(20\) | 13.5349 | + | 4.57472i | 0.676745 | + | 0.228736i | ||||
\(21\) | −1.76441 | − | 0.172184i | −0.0840196 | − | 0.00819925i | ||||
\(22\) | 15.5568 | + | 2.55798i | 0.707127 | + | 0.116272i | ||||
\(23\) | 2.14949 | + | 3.72303i | 0.0934563 | + | 0.161871i | 0.908963 | − | 0.416876i | \(-0.136875\pi\) |
−0.815507 | + | 0.578747i | \(0.803542\pi\) | |||||||
\(24\) | −1.07327 | − | 1.71842i | −0.0447195 | − | 0.0716008i | ||||
\(25\) | 6.12120 | − | 10.6022i | 0.244848 | − | 0.424089i | ||||
\(26\) | −33.9704 | + | 12.8110i | −1.30656 | + | 0.492729i | ||||
\(27\) | −4.54237 | −0.168236 | ||||||||
\(28\) | 25.5296 | + | 11.4995i | 0.911772 | + | 0.410698i | ||||
\(29\) | 28.3630i | 0.978035i | 0.872274 | + | 0.489017i | \(0.162644\pi\) | ||||
−0.872274 | + | 0.489017i | \(0.837356\pi\) | |||||||
\(30\) | 1.69278 | − | 0.638381i | 0.0564259 | − | 0.0212794i | ||||
\(31\) | −28.2372 | − | 16.3027i | −0.910876 | − | 0.525895i | −0.0301634 | − | 0.999545i | \(-0.509603\pi\) |
−0.880713 | + | 0.473650i | \(0.842936\pi\) | |||||||
\(32\) | 7.36842 | + | 31.1401i | 0.230263 | + | 0.973128i | ||||
\(33\) | 1.72891 | − | 0.998189i | 0.0523914 | − | 0.0302482i | ||||
\(34\) | 18.8270 | + | 3.09569i | 0.553735 | + | 0.0910497i | ||||
\(35\) | −14.5452 | + | 20.3362i | −0.415576 | + | 0.581034i | ||||
\(36\) | 33.8616 | + | 11.4450i | 0.940599 | + | 0.317917i | ||||
\(37\) | 25.9006 | − | 14.9537i | 0.700017 | − | 0.404155i | −0.107337 | − | 0.994223i | \(-0.534232\pi\) |
0.807354 | + | 0.590068i | \(0.200899\pi\) | |||||||
\(38\) | 38.3911 | + | 31.4648i | 1.01029 | + | 0.828020i | ||||
\(39\) | −2.29867 | + | 3.98141i | −0.0589402 | + | 0.102087i | ||||
\(40\) | −28.5570 | + | 0.991016i | −0.713926 | + | 0.0247754i | ||||
\(41\) | − | 45.2606i | − | 1.10392i | −0.833872 | − | 0.551958i | \(-0.813881\pi\) | ||
0.833872 | − | 0.551958i | \(-0.186119\pi\) | |||||||
\(42\) | 3.42334 | − | 0.922973i | 0.0815082 | − | 0.0219755i | ||||
\(43\) | 24.9109i | 0.579323i | 0.957129 | + | 0.289661i | \(0.0935427\pi\) | ||||
−0.957129 | + | 0.289661i | \(0.906457\pi\) | |||||||
\(44\) | −30.9174 | + | 6.19196i | −0.702669 | + | 0.140726i | ||||
\(45\) | −15.9585 | + | 27.6409i | −0.354632 | + | 0.614242i | ||||
\(46\) | −6.64990 | − | 5.45015i | −0.144563 | − | 0.118481i | ||||
\(47\) | 44.0432 | − | 25.4284i | 0.937090 | − | 0.541029i | 0.0480430 | − | 0.998845i | \(-0.484702\pi\) |
0.889047 | + | 0.457816i | \(0.151368\pi\) | |||||||
\(48\) | 3.22119 | + | 2.45833i | 0.0671082 | + | 0.0512153i | ||||
\(49\) | −32.2419 | + | 36.8979i | −0.657998 | + | 0.753019i | ||||
\(50\) | −3.97264 | + | 24.1604i | −0.0794529 | + | 0.483207i | ||||
\(51\) | 2.09235 | − | 1.20802i | 0.0410265 | − | 0.0236867i | ||||
\(52\) | 54.5296 | − | 47.9476i | 1.04865 | − | 0.922069i | ||||
\(53\) | −54.3930 | − | 31.4038i | −1.02628 | − | 0.592525i | −0.110365 | − | 0.993891i | \(-0.535202\pi\) |
−0.915918 | + | 0.401366i | \(0.868535\pi\) | |||||||
\(54\) | 8.50036 | − | 3.20566i | 0.157414 | − | 0.0593641i | ||||
\(55\) | − | 28.1558i | − | 0.511924i | ||||||
\(56\) | −55.8903 | − | 3.50277i | −0.998042 | − | 0.0625494i | ||||
\(57\) | 6.28554 | 0.110273 | ||||||||
\(58\) | −20.0165 | − | 53.0771i | −0.345112 | − | 0.915123i | ||||
\(59\) | 37.0048 | − | 64.0942i | 0.627200 | − | 1.08634i | −0.360912 | − | 0.932600i | \(-0.617534\pi\) |
0.988111 | − | 0.153741i | \(-0.0491323\pi\) | |||||||
\(60\) | −2.71725 | + | 2.38927i | −0.0452876 | + | 0.0398212i | ||||
\(61\) | −25.2994 | − | 43.8198i | −0.414743 | − | 0.718357i | 0.580658 | − | 0.814148i | \(-0.302795\pi\) |
−0.995401 | + | 0.0957908i | \(0.969462\pi\) | |||||||
\(62\) | 64.3469 | + | 10.5804i | 1.03785 | + | 0.170652i | ||||
\(63\) | −36.3890 | + | 50.8770i | −0.577604 | + | 0.807571i | ||||
\(64\) | −35.7653 | − | 53.0740i | −0.558832 | − | 0.829281i | ||||
\(65\) | 32.4191 | + | 56.1515i | 0.498755 | + | 0.863869i | ||||
\(66\) | −2.53096 | + | 3.08810i | −0.0383478 | + | 0.0467894i | ||||
\(67\) | 108.673 | + | 62.7422i | 1.62198 | + | 0.936451i | 0.986389 | + | 0.164426i | \(0.0525772\pi\) |
0.635592 | + | 0.772025i | \(0.280756\pi\) | |||||||
\(68\) | −37.4166 | + | 7.49357i | −0.550244 | + | 0.110200i | ||||
\(69\) | −1.08875 | −0.0157789 | ||||||||
\(70\) | 12.8673 | − | 48.3210i | 0.183819 | − | 0.690301i | ||||
\(71\) | −5.33822 | −0.0751863 | −0.0375931 | − | 0.999293i | \(-0.511969\pi\) | ||||
−0.0375931 | + | 0.999293i | \(0.511969\pi\) | |||||||
\(72\) | −71.4439 | + | 2.47932i | −0.992276 | + | 0.0344350i | ||||
\(73\) | −23.6569 | − | 13.6583i | −0.324067 | − | 0.187100i | 0.329137 | − | 0.944282i | \(-0.393242\pi\) |
−0.653204 | + | 0.757182i | \(0.726576\pi\) | |||||||
\(74\) | −37.9159 | + | 46.2624i | −0.512378 | + | 0.625168i | ||||
\(75\) | 1.55023 | + | 2.68508i | 0.0206697 | + | 0.0358010i | ||||
\(76\) | −94.0487 | − | 31.7880i | −1.23748 | − | 0.418263i | ||||
\(77\) | 5.35941 | − | 54.9191i | 0.0696027 | − | 0.713234i | ||||
\(78\) | 1.49183 | − | 9.07283i | 0.0191260 | − | 0.116318i | ||||
\(79\) | 51.5380 | + | 89.2664i | 0.652380 | + | 1.12995i | 0.982544 | + | 0.186031i | \(0.0595626\pi\) |
−0.330164 | + | 0.943924i | \(0.607104\pi\) | |||||||
\(80\) | 52.7408 | − | 22.0080i | 0.659261 | − | 0.275100i | ||||
\(81\) | −39.6362 | + | 68.6519i | −0.489336 | + | 0.847554i | ||||
\(82\) | 31.9415 | + | 84.6984i | 0.389531 | + | 1.03291i | ||||
\(83\) | −51.5695 | −0.621319 | −0.310660 | − | 0.950521i | \(-0.600550\pi\) | ||||
−0.310660 | + | 0.950521i | \(0.600550\pi\) | |||||||
\(84\) | −5.75491 | + | 4.14315i | −0.0685109 | + | 0.0493232i | ||||
\(85\) | − | 34.0744i | − | 0.400876i | ||||||
\(86\) | −17.5802 | − | 46.6170i | −0.204421 | − | 0.542058i | ||||
\(87\) | −6.22075 | − | 3.59155i | −0.0715029 | − | 0.0412822i | ||||
\(88\) | 53.4875 | − | 33.4066i | 0.607813 | − | 0.379620i | ||||
\(89\) | 133.222 | − | 76.9158i | 1.49688 | − | 0.864222i | 0.496883 | − | 0.867818i | \(-0.334478\pi\) |
0.999994 | + | 0.00359545i | \(0.00114447\pi\) | |||||||
\(90\) | 10.3570 | − | 62.9880i | 0.115078 | − | 0.699867i | ||||
\(91\) | 52.5464 | + | 115.697i | 0.577433 | + | 1.27139i | ||||
\(92\) | 16.2906 | + | 5.50613i | 0.177072 | + | 0.0598493i | ||||
\(93\) | 7.15123 | − | 4.12877i | 0.0768950 | − | 0.0443953i | ||||
\(94\) | −64.4749 | + | 78.6678i | −0.685903 | + | 0.836892i | ||||
\(95\) | 44.3238 | − | 76.7711i | 0.466566 | − | 0.808117i | ||||
\(96\) | −7.76289 | − | 2.32712i | −0.0808634 | − | 0.0242409i | ||||
\(97\) | 47.0436i | 0.484986i | 0.970153 | + | 0.242493i | \(0.0779651\pi\) | ||||
−0.970153 | + | 0.242493i | \(0.922035\pi\) | |||||||
\(98\) | 34.2961 | − | 91.8029i | 0.349960 | − | 0.936765i | ||||
\(99\) | − | 70.4400i | − | 0.711516i | ||||||
\(100\) | −9.61637 | − | 48.0161i | −0.0961637 | − | 0.480161i | ||||
\(101\) | −74.6727 | + | 129.337i | −0.739333 | + | 1.28056i | 0.213462 | + | 0.976951i | \(0.431526\pi\) |
−0.952796 | + | 0.303612i | \(0.901807\pi\) | |||||||
\(102\) | −3.06299 | + | 3.73725i | −0.0300293 | + | 0.0366397i | ||||
\(103\) | −17.1847 | + | 9.92160i | −0.166842 | + | 0.0963262i | −0.581096 | − | 0.813835i | \(-0.697376\pi\) |
0.414254 | + | 0.910161i | \(0.364043\pi\) | |||||||
\(104\) | −68.2061 | + | 128.210i | −0.655827 | + | 1.23279i | ||||
\(105\) | −2.61843 | − | 5.76527i | −0.0249375 | − | 0.0549073i | ||||
\(106\) | 123.951 | + | 20.3810i | 1.16935 | + | 0.192274i | ||||
\(107\) | 7.91877 | − | 4.57190i | 0.0740072 | − | 0.0427281i | −0.462540 | − | 0.886599i | \(-0.653062\pi\) |
0.536547 | + | 0.843870i | \(0.319728\pi\) | |||||||
\(108\) | −13.6448 | + | 11.9978i | −0.126341 | + | 0.111091i | ||||
\(109\) | −103.229 | − | 59.5992i | −0.947053 | − | 0.546781i | −0.0548888 | − | 0.998492i | \(-0.517480\pi\) |
−0.892164 | + | 0.451711i | \(0.850814\pi\) | |||||||
\(110\) | 19.8703 | + | 52.6894i | 0.180639 | + | 0.478994i | ||||
\(111\) | 7.57425i | 0.0682365i | ||||||||
\(112\) | 107.062 | − | 32.8883i | 0.955914 | − | 0.293646i | ||||
\(113\) | −124.011 | −1.09744 | −0.548720 | − | 0.836006i | \(-0.684885\pi\) | ||||
−0.548720 | + | 0.836006i | \(0.684885\pi\) | |||||||
\(114\) | −11.7624 | + | 4.43586i | −0.103179 | + | 0.0389111i | ||||
\(115\) | −7.67752 | + | 13.2979i | −0.0667611 | + | 0.115634i | ||||
\(116\) | 74.9157 | + | 85.1997i | 0.645825 | + | 0.734480i | ||||
\(117\) | 81.1059 | + | 140.480i | 0.693213 | + | 1.20068i | ||||
\(118\) | −24.0160 | + | 146.058i | −0.203526 | + | 1.23778i | ||||
\(119\) | 6.48601 | − | 66.4636i | 0.0545043 | − | 0.558518i | ||||
\(120\) | 3.39877 | − | 6.38880i | 0.0283231 | − | 0.0532400i | ||||
\(121\) | −29.4303 | − | 50.9749i | −0.243226 | − | 0.421280i | ||||
\(122\) | 78.2687 | + | 64.1477i | 0.641546 | + | 0.525801i | ||||
\(123\) | 9.92683 | + | 5.73126i | 0.0807059 | + | 0.0465956i | ||||
\(124\) | −127.882 | + | 25.6115i | −1.03131 | + | 0.206545i | ||||
\(125\) | 133.022 | 1.06417 | ||||||||
\(126\) | 32.1914 | − | 120.889i | 0.255488 | − | 0.959439i | ||||
\(127\) | −57.6144 | −0.453656 | −0.226828 | − | 0.973935i | \(-0.572836\pi\) | ||||
−0.226828 | + | 0.973935i | \(0.572836\pi\) | |||||||
\(128\) | 104.385 | + | 74.0795i | 0.815508 | + | 0.578746i | ||||
\(129\) | −5.46361 | − | 3.15441i | −0.0423535 | − | 0.0244528i | ||||
\(130\) | −100.295 | − | 82.2001i | −0.771500 | − | 0.632309i | ||||
\(131\) | −62.1497 | − | 107.646i | −0.474425 | − | 0.821728i | 0.525146 | − | 0.851012i | \(-0.324011\pi\) |
−0.999571 | + | 0.0292837i | \(0.990677\pi\) | |||||||
\(132\) | 2.55696 | − | 7.56508i | 0.0193709 | − | 0.0573112i | ||||
\(133\) | 101.069 | − | 141.308i | 0.759915 | − | 1.06247i | ||||
\(134\) | −247.644 | − | 40.7196i | −1.84809 | − | 0.303877i | ||||
\(135\) | −8.11216 | − | 14.0507i | −0.0600901 | − | 0.104079i | ||||
\(136\) | 64.7312 | − | 40.4290i | 0.475965 | − | 0.297272i | ||||
\(137\) | 84.7404 | − | 146.775i | 0.618543 | − | 1.07135i | −0.371208 | − | 0.928550i | \(-0.621056\pi\) |
0.989752 | − | 0.142799i | \(-0.0456102\pi\) | |||||||
\(138\) | 2.03742 | − | 0.768355i | 0.0147639 | − | 0.00556779i | ||||
\(139\) | −266.497 | −1.91725 | −0.958624 | − | 0.284677i | \(-0.908114\pi\) | ||||
−0.958624 | + | 0.284677i | \(0.908114\pi\) | |||||||
\(140\) | 10.0221 | + | 99.5064i | 0.0715864 | + | 0.710760i | ||||
\(141\) | 12.8798i | 0.0913459i | ||||||||
\(142\) | 9.98969 | − | 3.76732i | 0.0703499 | − | 0.0265304i | ||||
\(143\) | −123.925 | − | 71.5483i | −0.866610 | − | 0.500338i | ||||
\(144\) | 131.947 | − | 55.0594i | 0.916297 | − | 0.382357i | ||||
\(145\) | −87.7339 | + | 50.6532i | −0.605061 | + | 0.349332i | ||||
\(146\) | 53.9093 | + | 8.86421i | 0.369242 | + | 0.0607138i | ||||
\(147\) | −4.00996 | − | 11.7438i | −0.0272786 | − | 0.0798899i | ||||
\(148\) | 38.3054 | − | 113.331i | 0.258820 | − | 0.765753i | ||||
\(149\) | 26.6902 | − | 15.4096i | 0.179129 | − | 0.103420i | −0.407754 | − | 0.913092i | \(-0.633688\pi\) |
0.586883 | + | 0.809672i | \(0.300355\pi\) | |||||||
\(150\) | −4.79595 | − | 3.93068i | −0.0319730 | − | 0.0262046i | ||||
\(151\) | −11.7448 | + | 20.3425i | −0.0777800 | + | 0.134719i | −0.902292 | − | 0.431126i | \(-0.858116\pi\) |
0.824512 | + | 0.565845i | \(0.191450\pi\) | |||||||
\(152\) | 198.432 | − | 6.88618i | 1.30547 | − | 0.0453038i | ||||
\(153\) | − | 85.2473i | − | 0.557172i | ||||||
\(154\) | 28.7284 | + | 106.555i | 0.186548 | + | 0.691916i | ||||
\(155\) | − | 116.460i | − | 0.751352i | ||||||
\(156\) | 3.61119 | + | 18.0313i | 0.0231487 | + | 0.115585i | ||||
\(157\) | −63.8147 | + | 110.530i | −0.406463 | + | 0.704015i | −0.994491 | − | 0.104826i | \(-0.966571\pi\) |
0.588028 | + | 0.808841i | \(0.299905\pi\) | |||||||
\(158\) | −159.443 | − | 130.677i | −1.00913 | − | 0.827070i | ||||
\(159\) | 13.7754 | − | 7.95320i | 0.0866374 | − | 0.0500202i | ||||
\(160\) | −83.1650 | + | 78.4052i | −0.519781 | + | 0.490032i | ||||
\(161\) | −17.5065 | + | 24.4766i | −0.108736 | + | 0.152029i | ||||
\(162\) | 25.7238 | − | 156.444i | 0.158789 | − | 0.965704i | ||||
\(163\) | −138.291 | + | 79.8421i | −0.848409 | + | 0.489829i | −0.860114 | − | 0.510103i | \(-0.829607\pi\) |
0.0117050 | + | 0.999931i | \(0.496274\pi\) | |||||||
\(164\) | −119.548 | − | 135.958i | −0.728949 | − | 0.829015i | ||||
\(165\) | 6.17530 | + | 3.56531i | 0.0374261 | + | 0.0216080i | ||||
\(166\) | 96.5046 | − | 36.3939i | 0.581353 | − | 0.219240i | ||||
\(167\) | 142.792i | 0.855042i | 0.904005 | + | 0.427521i | \(0.140613\pi\) | ||||
−0.904005 | + | 0.427521i | \(0.859387\pi\) | |||||||
\(168\) | 7.84553 | − | 11.8147i | 0.0466996 | − | 0.0703254i | ||||
\(169\) | 160.528 | 0.949869 | ||||||||
\(170\) | 24.0472 | + | 63.7652i | 0.141454 | + | 0.375089i | ||||
\(171\) | 110.889 | − | 192.066i | 0.648474 | − | 1.12319i | ||||
\(172\) | 65.7976 | + | 74.8299i | 0.382544 | + | 0.435057i | ||||
\(173\) | 97.8898 | + | 169.550i | 0.565837 | + | 0.980059i | 0.996971 | + | 0.0777710i | \(0.0247803\pi\) |
−0.431134 | + | 0.902288i | \(0.641886\pi\) | |||||||
\(174\) | 14.1758 | + | 2.33091i | 0.0814704 | + | 0.0133960i | ||||
\(175\) | 85.2916 | + | 8.32338i | 0.487380 | + | 0.0475622i | ||||
\(176\) | −76.5181 | + | 100.263i | −0.434762 | + | 0.569675i | ||||
\(177\) | 9.37168 | + | 16.2322i | 0.0529474 | + | 0.0917075i | ||||
\(178\) | −195.024 | + | 237.955i | −1.09564 | + | 1.33682i | ||||
\(179\) | 129.477 | + | 74.7535i | 0.723334 | + | 0.417617i | 0.815979 | − | 0.578082i | \(-0.196199\pi\) |
−0.0926444 | + | 0.995699i | \(0.529532\pi\) | |||||||
\(180\) | 25.0707 | + | 125.182i | 0.139282 | + | 0.695455i | ||||
\(181\) | 91.2994 | 0.504417 | 0.252208 | − | 0.967673i | \(-0.418843\pi\) | ||||
0.252208 | + | 0.967673i | \(0.418843\pi\) | |||||||
\(182\) | −179.983 | − | 179.426i | −0.988917 | − | 0.985856i | ||||
\(183\) | 12.8144 | 0.0700242 | ||||||||
\(184\) | −34.3712 | + | 1.19279i | −0.186800 | + | 0.00648253i | ||||
\(185\) | 92.5114 | + | 53.4115i | 0.500062 | + | 0.288711i | ||||
\(186\) | −10.4687 | + | 12.7732i | −0.0562833 | + | 0.0686730i | ||||
\(187\) | 37.6008 | + | 65.1265i | 0.201074 | + | 0.348270i | ||||
\(188\) | 65.1372 | − | 192.717i | 0.346474 | − | 1.02509i | ||||
\(189\) | −13.1486 | − | 28.9506i | −0.0695693 | − | 0.153178i | ||||
\(190\) | −28.7661 | + | 174.946i | −0.151400 | + | 0.920769i | ||||
\(191\) | −13.9140 | − | 24.0997i | −0.0728480 | − | 0.126176i | 0.827300 | − | 0.561760i | \(-0.189875\pi\) |
−0.900148 | + | 0.435583i | \(0.856542\pi\) | |||||||
\(192\) | 16.1694 | − | 1.12361i | 0.0842156 | − | 0.00585212i | ||||
\(193\) | −121.192 | + | 209.911i | −0.627938 | + | 1.08762i | 0.360027 | + | 0.932942i | \(0.382767\pi\) |
−0.987965 | + | 0.154678i | \(0.950566\pi\) | |||||||
\(194\) | −33.1999 | − | 88.0351i | −0.171133 | − | 0.453789i | ||||
\(195\) | −16.4207 | −0.0842085 | ||||||||
\(196\) | 0.607652 | + | 195.999i | 0.00310026 | + | 0.999995i | ||||
\(197\) | 94.7050i | 0.480736i | 0.970682 | + | 0.240368i | \(0.0772682\pi\) | ||||
−0.970682 | + | 0.240368i | \(0.922732\pi\) | |||||||
\(198\) | 49.7113 | + | 131.818i | 0.251067 | + | 0.665747i | ||||
\(199\) | 267.738 | + | 154.579i | 1.34542 | + | 0.776778i | 0.987597 | − | 0.157011i | \(-0.0501859\pi\) |
0.357823 | + | 0.933790i | \(0.383519\pi\) | |||||||
\(200\) | 51.8818 | + | 83.0684i | 0.259409 | + | 0.415342i | ||||
\(201\) | −27.5220 | + | 15.8899i | −0.136926 | + | 0.0790540i | ||||
\(202\) | 48.4624 | − | 294.733i | 0.239913 | − | 1.45907i | ||||
\(203\) | −180.770 | + | 82.1012i | −0.890494 | + | 0.404439i | ||||
\(204\) | 3.09445 | − | 9.15534i | 0.0151689 | − | 0.0448791i | ||||
\(205\) | 140.002 | − | 80.8304i | 0.682938 | − | 0.394295i | ||||
\(206\) | 25.1567 | − | 30.6945i | 0.122120 | − | 0.149002i | ||||
\(207\) | −19.2076 | + | 33.2685i | −0.0927903 | + | 0.160717i | ||||
\(208\) | 37.1566 | − | 288.060i | 0.178637 | − | 1.38490i | ||||
\(209\) | 195.644i | 0.936094i | ||||||||
\(210\) | 8.96870 | + | 8.94094i | 0.0427081 | + | 0.0425759i | ||||
\(211\) | 125.864i | 0.596514i | 0.954486 | + | 0.298257i | \(0.0964052\pi\) | ||||
−0.954486 | + | 0.298257i | \(0.903595\pi\) | |||||||
\(212\) | −246.339 | + | 49.3352i | −1.16198 | + | 0.232713i | ||||
\(213\) | 0.675969 | − | 1.17081i | 0.00317356 | − | 0.00549677i | ||||
\(214\) | −11.5923 | + | 14.1441i | −0.0541695 | + | 0.0660940i | ||||
\(215\) | −77.0556 | + | 44.4881i | −0.358398 | + | 0.206921i | ||||
\(216\) | 17.0671 | − | 32.0817i | 0.0790142 | − | 0.148526i | ||||
\(217\) | 22.1679 | − | 227.159i | 0.102156 | − | 1.04682i | ||||
\(218\) | 235.238 | + | 38.6797i | 1.07907 | + | 0.177430i | ||||
\(219\) | 5.99125 | − | 3.45905i | 0.0273573 | − | 0.0157947i | ||||
\(220\) | −74.3684 | − | 84.5773i | −0.338038 | − | 0.384442i | ||||
\(221\) | −149.976 | − | 86.5885i | −0.678623 | − | 0.391803i | ||||
\(222\) | −5.34534 | − | 14.1741i | −0.0240781 | − | 0.0638472i | ||||
\(223\) | − | 8.94619i | − | 0.0401174i | −0.999799 | − | 0.0200587i | \(-0.993615\pi\) | ||
0.999799 | − | 0.0200587i | \(-0.00638532\pi\) | |||||||
\(224\) | −177.141 | + | 137.102i | −0.790809 | + | 0.612064i | ||||
\(225\) | 109.396 | 0.486206 | ||||||||
\(226\) | 232.067 | − | 87.5175i | 1.02685 | − | 0.387246i | ||||
\(227\) | 136.347 | − | 236.160i | 0.600647 | − | 1.04035i | −0.392076 | − | 0.919933i | \(-0.628243\pi\) |
0.992723 | − | 0.120419i | \(-0.0384237\pi\) | |||||||
\(228\) | 18.8811 | − | 16.6021i | 0.0828120 | − | 0.0728162i | ||||
\(229\) | −165.611 | − | 286.846i | −0.723191 | − | 1.25260i | −0.959714 | − | 0.280978i | \(-0.909341\pi\) |
0.236523 | − | 0.971626i | \(-0.423992\pi\) | |||||||
\(230\) | 4.98269 | − | 30.3032i | 0.0216639 | − | 0.131753i | ||||
\(231\) | 11.3665 | + | 8.12975i | 0.0492058 | + | 0.0351937i | ||||
\(232\) | −200.321 | − | 106.569i | −0.863453 | − | 0.459347i | ||||
\(233\) | −79.1185 | − | 137.037i | −0.339564 | − | 0.588143i | 0.644786 | − | 0.764363i | \(-0.276946\pi\) |
−0.984351 | + | 0.176220i | \(0.943613\pi\) | |||||||
\(234\) | −250.918 | − | 205.648i | −1.07230 | − | 0.878837i | ||||
\(235\) | 157.313 | + | 90.8245i | 0.669416 | + | 0.386487i | ||||
\(236\) | −58.1343 | − | 290.274i | −0.246332 | − | 1.22997i | ||||
\(237\) | −26.1046 | −0.110146 | ||||||||
\(238\) | 34.7675 | + | 128.954i | 0.146082 | + | 0.541824i | ||||
\(239\) | 48.9981 | 0.205013 | 0.102507 | − | 0.994732i | \(-0.467314\pi\) | ||||
0.102507 | + | 0.994732i | \(0.467314\pi\) | |||||||
\(240\) | −1.85154 | + | 14.3543i | −0.00771477 | + | 0.0598095i | ||||
\(241\) | 170.914 | + | 98.6771i | 0.709186 | + | 0.409449i | 0.810759 | − | 0.585379i | \(-0.199054\pi\) |
−0.101574 | + | 0.994828i | \(0.532388\pi\) | |||||||
\(242\) | 91.0487 | + | 74.6221i | 0.376234 | + | 0.308356i | ||||
\(243\) | −30.4787 | − | 52.7907i | −0.125427 | − | 0.217246i | ||||
\(244\) | −191.739 | − | 64.8067i | −0.785815 | − | 0.265601i | ||||
\(245\) | −171.715 | − | 33.8367i | −0.700878 | − | 0.138109i | ||||
\(246\) | −22.6213 | − | 3.71957i | −0.0919564 | − | 0.0151202i | ||||
\(247\) | −225.267 | − | 390.175i | −0.912014 | − | 1.57965i | ||||
\(248\) | 221.238 | − | 138.178i | 0.892089 | − | 0.557170i | ||||
\(249\) | 6.53014 | − | 11.3105i | 0.0262255 | − | 0.0454239i | ||||
\(250\) | −248.930 | + | 93.8767i | −0.995720 | + | 0.375507i | ||||
\(251\) | 315.497 | 1.25696 | 0.628480 | − | 0.777826i | \(-0.283677\pi\) | ||||
0.628480 | + | 0.777826i | \(0.283677\pi\) | |||||||
\(252\) | 25.0732 | + | 248.945i | 0.0994970 | + | 0.987876i | ||||
\(253\) | − | 33.8883i | − | 0.133946i | ||||||
\(254\) | 107.817 | − | 40.6599i | 0.424475 | − | 0.160078i | ||||
\(255\) | 7.47341 | + | 4.31478i | 0.0293075 | + | 0.0169207i | ||||
\(256\) | −247.621 | − | 64.9616i | −0.967268 | − | 0.253756i | ||||
\(257\) | −329.533 | + | 190.256i | −1.28223 | + | 0.740296i | −0.977256 | − | 0.212065i | \(-0.931981\pi\) |
−0.304974 | + | 0.952361i | \(0.598648\pi\) | |||||||
\(258\) | 12.4505 | + | 2.04721i | 0.0482576 | + | 0.00793492i | ||||
\(259\) | 170.281 | + | 121.791i | 0.657454 | + | 0.470234i | ||||
\(260\) | 245.698 | + | 83.0445i | 0.944991 | + | 0.319402i | ||||
\(261\) | −219.492 | + | 126.724i | −0.840967 | + | 0.485532i | ||||
\(262\) | 192.273 | + | 157.584i | 0.733865 | + | 0.601464i | ||||
\(263\) | −98.1636 | + | 170.024i | −0.373246 | + | 0.646480i | −0.990063 | − | 0.140626i | \(-0.955088\pi\) |
0.616817 | + | 0.787106i | \(0.288422\pi\) | |||||||
\(264\) | 0.553910 | + | 15.9614i | 0.00209814 | + | 0.0604599i | ||||
\(265\) | − | 224.335i | − | 0.846547i | ||||||
\(266\) | −89.4101 | + | 335.764i | −0.336128 | + | 1.26227i | ||||
\(267\) | 38.9588i | 0.145913i | ||||||||
\(268\) | 492.165 | − | 98.5678i | 1.83644 | − | 0.367790i | ||||
\(269\) | 51.1557 | − | 88.6043i | 0.190170 | − | 0.329384i | −0.755137 | − | 0.655568i | \(-0.772429\pi\) |
0.945306 | + | 0.326184i | \(0.105763\pi\) | |||||||
\(270\) | 25.0966 | + | 20.5688i | 0.0929504 | + | 0.0761807i | ||||
\(271\) | −221.981 | + | 128.161i | −0.819118 | + | 0.472918i | −0.850112 | − | 0.526602i | \(-0.823466\pi\) |
0.0309944 | + | 0.999520i | \(0.490133\pi\) | |||||||
\(272\) | −92.6030 | + | 121.339i | −0.340452 | + | 0.446100i | ||||
\(273\) | −32.0292 | − | 3.12564i | −0.117323 | − | 0.0114492i | ||||
\(274\) | −54.9964 | + | 334.470i | −0.200717 | + | 1.22070i | ||||
\(275\) | −83.5757 | + | 48.2525i | −0.303912 | + | 0.175464i | ||||
\(276\) | −3.27048 | + | 2.87572i | −0.0118496 | + | 0.0104193i | ||||
\(277\) | −170.372 | − | 98.3646i | −0.615063 | − | 0.355107i | 0.159881 | − | 0.987136i | \(-0.448889\pi\) |
−0.774944 | + | 0.632029i | \(0.782222\pi\) | |||||||
\(278\) | 498.710 | − | 188.074i | 1.79392 | − | 0.676525i | ||||
\(279\) | − | 291.358i | − | 1.04429i | ||||||
\(280\) | −88.9790 | − | 179.138i | −0.317782 | − | 0.639780i | ||||
\(281\) | −70.2923 | −0.250151 | −0.125075 | − | 0.992147i | \(-0.539917\pi\) | ||||
−0.125075 | + | 0.992147i | \(0.539917\pi\) | |||||||
\(282\) | −9.08959 | − | 24.1026i | −0.0322326 | − | 0.0854701i | ||||
\(283\) | −148.495 | + | 257.201i | −0.524718 | + | 0.908838i | 0.474868 | + | 0.880057i | \(0.342496\pi\) |
−0.999586 | + | 0.0287807i | \(0.990838\pi\) | |||||||
\(284\) | −16.0355 | + | 14.1000i | −0.0564631 | + | 0.0496477i | ||||
\(285\) | 11.2253 | + | 19.4427i | 0.0393869 | + | 0.0682201i | ||||
\(286\) | 282.401 | + | 46.4347i | 0.987416 | + | 0.162359i | ||||
\(287\) | 288.466 | − | 131.014i | 1.00511 | − | 0.456494i | ||||
\(288\) | −208.062 | + | 196.154i | −0.722437 | + | 0.681089i | ||||
\(289\) | −98.9951 | − | 171.465i | −0.342544 | − | 0.593303i | ||||
\(290\) | 128.434 | − | 156.706i | 0.442874 | − | 0.540365i | ||||
\(291\) | −10.3179 | − | 5.95704i | −0.0354567 | − | 0.0204709i | ||||
\(292\) | −107.139 | + | 21.4571i | −0.366914 | + | 0.0734834i | ||||
\(293\) | 135.561 | 0.462665 | 0.231333 | − | 0.972875i | \(-0.425691\pi\) | ||||
0.231333 | + | 0.972875i | \(0.425691\pi\) | |||||||
\(294\) | 15.7919 | + | 19.1469i | 0.0537141 | + | 0.0651254i | ||||
\(295\) | 264.346 | 0.896087 | ||||||||
\(296\) | 8.29805 | + | 239.116i | 0.0280339 | + | 0.807824i | ||||
\(297\) | 31.0096 | + | 17.9034i | 0.104409 | + | 0.0602808i | ||||
\(298\) | −39.0718 | + | 47.6727i | −0.131113 | + | 0.159976i | ||||
\(299\) | 39.0196 | + | 67.5839i | 0.130500 | + | 0.226033i | ||||
\(300\) | 11.7489 | + | 3.97106i | 0.0391630 | + | 0.0132369i | ||||
\(301\) | −158.768 | + | 72.1084i | −0.527470 | + | 0.239563i | ||||
\(302\) | 7.62233 | − | 46.3566i | 0.0252395 | − | 0.153499i | ||||
\(303\) | −18.9113 | − | 32.7553i | −0.0624136 | − | 0.108103i | ||||
\(304\) | −366.475 | + | 152.925i | −1.20551 | + | 0.503042i | ||||
\(305\) | 90.3637 | − | 156.515i | 0.296274 | − | 0.513162i | ||||
\(306\) | 60.1612 | + | 159.527i | 0.196605 | + | 0.521332i | ||||
\(307\) | 76.2052 | 0.248225 | 0.124113 | − | 0.992268i | \(-0.460392\pi\) | ||||
0.124113 | + | 0.992268i | \(0.460392\pi\) | |||||||
\(308\) | −128.960 | − | 179.127i | −0.418700 | − | 0.581583i | ||||
\(309\) | − | 5.02541i | − | 0.0162635i | ||||||
\(310\) | 82.1885 | + | 217.937i | 0.265124 | + | 0.703021i | ||||
\(311\) | −171.554 | − | 99.0468i | −0.551621 | − | 0.318479i | 0.198154 | − | 0.980171i | \(-0.436505\pi\) |
−0.749776 | + | 0.661692i | \(0.769839\pi\) | |||||||
\(312\) | −19.4829 | − | 31.1943i | −0.0624453 | − | 0.0999817i | ||||
\(313\) | −47.9693 | + | 27.6951i | −0.153257 | + | 0.0884827i | −0.574667 | − | 0.818387i | \(-0.694868\pi\) |
0.421411 | + | 0.906870i | \(0.361535\pi\) | |||||||
\(314\) | 41.4156 | − | 251.877i | 0.131897 | − | 0.802155i | ||||
\(315\) | −222.362 | − | 21.6997i | −0.705912 | − | 0.0688881i | ||||
\(316\) | 390.596 | + | 132.019i | 1.23606 | + | 0.417783i | ||||
\(317\) | −259.080 | + | 149.580i | −0.817289 | + | 0.471862i | −0.849481 | − | 0.527620i | \(-0.823085\pi\) |
0.0321920 | + | 0.999482i | \(0.489751\pi\) | |||||||
\(318\) | −20.1657 | + | 24.6048i | −0.0634143 | + | 0.0773737i | ||||
\(319\) | 111.791 | − | 193.627i | 0.350441 | − | 0.606981i | ||||
\(320\) | 100.298 | − | 205.415i | 0.313432 | − | 0.641923i | ||||
\(321\) | 2.31572i | 0.00721409i | ||||||||
\(322\) | 15.4871 | − | 58.1591i | 0.0480966 | − | 0.180618i | ||||
\(323\) | 236.770i | 0.733034i | ||||||||
\(324\) | 62.2683 | + | 310.915i | 0.192186 | + | 0.959616i | ||||
\(325\) | 111.117 | − | 192.461i | 0.341900 | − | 0.592188i | ||||
\(326\) | 202.444 | − | 247.008i | 0.620992 | − | 0.757693i | ||||
\(327\) | 26.1433 | − | 15.0938i | 0.0799490 | − | 0.0461586i | ||||
\(328\) | 319.665 | + | 170.058i | 0.974588 | + | 0.518469i | ||||
\(329\) | 289.557 | + | 207.101i | 0.880111 | + | 0.629487i | ||||
\(330\) | −14.0723 | − | 2.31388i | −0.0426433 | − | 0.00701176i | ||||
\(331\) | 325.087 | − | 187.689i | 0.982135 | − | 0.567036i | 0.0792209 | − | 0.996857i | \(-0.474757\pi\) |
0.902914 | + | 0.429821i | \(0.141423\pi\) | |||||||
\(332\) | −154.910 | + | 136.212i | −0.466596 | + | 0.410276i | ||||
\(333\) | 231.445 | + | 133.625i | 0.695029 | + | 0.401275i | ||||
\(334\) | −100.772 | − | 267.214i | −0.301712 | − | 0.800041i | ||||
\(335\) | 448.203i | 1.33792i | ||||||||
\(336\) | −6.34383 | + | 27.6462i | −0.0188804 | + | 0.0822803i | ||||
\(337\) | −4.99043 | −0.0148084 | −0.00740419 | − | 0.999973i | \(-0.502357\pi\) | ||||
−0.00740419 | + | 0.999973i | \(0.502357\pi\) | |||||||
\(338\) | −300.404 | + | 113.289i | −0.888769 | + | 0.335173i | ||||
\(339\) | 15.7032 | − | 27.1988i | 0.0463222 | − | 0.0802324i | ||||
\(340\) | −90.0014 | − | 102.356i | −0.264710 | − | 0.301048i | ||||
\(341\) | 128.512 | + | 222.589i | 0.376868 | + | 0.652755i | ||||
\(342\) | −71.9668 | + | 437.679i | −0.210429 | + | 1.27976i | ||||
\(343\) | −328.497 | − | 98.6856i | −0.957717 | − | 0.287713i | ||||
\(344\) | −175.940 | − | 93.5978i | −0.511452 | − | 0.272087i | ||||
\(345\) | −1.94438 | − | 3.36776i | −0.00563588 | − | 0.00976163i | ||||
\(346\) | −302.842 | − | 248.204i | −0.875266 | − | 0.717354i | ||||
\(347\) | −320.772 | − | 185.198i | −0.924414 | − | 0.533711i | −0.0393734 | − | 0.999225i | \(-0.512536\pi\) |
−0.885041 | + | 0.465514i | \(0.845870\pi\) | |||||||
\(348\) | −28.1730 | + | 5.64231i | −0.0809568 | + | 0.0162135i | ||||
\(349\) | 25.6801 | 0.0735821 | 0.0367910 | − | 0.999323i | \(-0.488286\pi\) | ||||
0.0367910 | + | 0.999323i | \(0.488286\pi\) | |||||||
\(350\) | −165.484 | + | 44.6165i | −0.472813 | + | 0.127476i | ||||
\(351\) | −82.4571 | −0.234921 | ||||||||
\(352\) | 72.4340 | − | 241.628i | 0.205779 | − | 0.686442i | ||||
\(353\) | −229.938 | − | 132.755i | −0.651383 | − | 0.376076i | 0.137603 | − | 0.990487i | \(-0.456060\pi\) |
−0.788986 | + | 0.614411i | \(0.789394\pi\) | |||||||
\(354\) | −28.9932 | − | 23.7624i | −0.0819017 | − | 0.0671253i | ||||
\(355\) | −9.53348 | − | 16.5125i | −0.0268549 | − | 0.0465140i | ||||
\(356\) | 197.027 | − | 582.929i | 0.553446 | − | 1.63744i | ||||
\(357\) | 13.7559 | + | 9.83871i | 0.0385319 | + | 0.0275594i | ||||
\(358\) | −295.052 | − | 48.5148i | −0.824167 | − | 0.135516i | ||||
\(359\) | 275.228 | + | 476.709i | 0.766651 | + | 1.32788i | 0.939369 | + | 0.342908i | \(0.111412\pi\) |
−0.172718 | + | 0.984971i | \(0.555255\pi\) | |||||||
\(360\) | −135.260 | − | 216.566i | −0.375722 | − | 0.601573i | ||||
\(361\) | −127.489 | + | 220.817i | −0.353155 | + | 0.611682i | ||||
\(362\) | −170.853 | + | 64.4323i | −0.471970 | + | 0.177990i | ||||
\(363\) | 14.9068 | 0.0410656 | ||||||||
\(364\) | 463.436 | + | 208.750i | 1.27318 | + | 0.573489i | ||||
\(365\) | − | 97.5689i | − | 0.267312i | ||||||
\(366\) | −23.9803 | + | 9.04347i | −0.0655199 | + | 0.0247089i | ||||
\(367\) | 180.099 | + | 103.980i | 0.490732 | + | 0.283324i | 0.724878 | − | 0.688877i | \(-0.241896\pi\) |
−0.234146 | + | 0.972201i | \(0.575229\pi\) | |||||||
\(368\) | 63.4788 | − | 26.4888i | 0.172497 | − | 0.0719803i | ||||
\(369\) | 350.257 | − | 202.221i | 0.949207 | − | 0.548025i | ||||
\(370\) | −210.815 | − | 34.6639i | −0.569770 | − | 0.0936863i | ||||
\(371\) | 42.7018 | − | 437.575i | 0.115099 | − | 1.17945i | ||||
\(372\) | 10.5762 | − | 31.2911i | 0.0284307 | − | 0.0841159i | ||||
\(373\) | 393.539 | − | 227.210i | 1.05507 | − | 0.609142i | 0.131002 | − | 0.991382i | \(-0.458180\pi\) |
0.924063 | + | 0.382240i | \(0.124847\pi\) | |||||||
\(374\) | −116.326 | − | 95.3387i | −0.311031 | − | 0.254916i | ||||
\(375\) | −16.8443 | + | 29.1751i | −0.0449180 | + | 0.0778003i | ||||
\(376\) | 14.1106 | + | 406.609i | 0.0375281 | + | 1.08141i | ||||
\(377\) | 514.871i | 1.36570i | ||||||||
\(378\) | 45.0368 | + | 44.8974i | 0.119145 | + | 0.118776i | ||||
\(379\) | − | 373.244i | − | 0.984813i | −0.870365 | − | 0.492406i | \(-0.836117\pi\) | ||
0.870365 | − | 0.492406i | \(-0.163883\pi\) | |||||||
\(380\) | −69.6325 | − | 347.686i | −0.183243 | − | 0.914964i | ||||
\(381\) | 7.29559 | − | 12.6363i | 0.0191485 | − | 0.0331662i | ||||
\(382\) | 43.0457 | + | 35.2796i | 0.112685 | + | 0.0923549i | ||||
\(383\) | −270.298 | + | 156.056i | −0.705738 | + | 0.407458i | −0.809481 | − | 0.587146i | \(-0.800251\pi\) |
0.103743 | + | 0.994604i | \(0.466918\pi\) | |||||||
\(384\) | −29.4656 | + | 13.5138i | −0.0767334 | + | 0.0351922i | ||||
\(385\) | 179.450 | − | 81.5014i | 0.466103 | − | 0.211692i | ||||
\(386\) | 78.6533 | − | 478.345i | 0.203765 | − | 1.23923i | ||||
\(387\) | −192.777 | + | 111.300i | −0.498133 | + | 0.287597i | ||||
\(388\) | 124.257 | + | 141.314i | 0.320251 | + | 0.364213i | ||||
\(389\) | 439.628 | + | 253.819i | 1.13015 | + | 0.652492i | 0.943973 | − | 0.330024i | \(-0.107057\pi\) |
0.186177 | + | 0.982516i | \(0.440390\pi\) | |||||||
\(390\) | 30.7288 | − | 11.5885i | 0.0787918 | − | 0.0297140i | ||||
\(391\) | − | 41.0120i | − | 0.104890i | ||||||
\(392\) | −139.459 | − | 366.354i | −0.355762 | − | 0.934577i | ||||
\(393\) | 31.4796 | 0.0801007 | ||||||||
\(394\) | −66.8358 | − | 177.226i | −0.169634 | − | 0.449813i | ||||
\(395\) | −184.082 | + | 318.840i | −0.466031 | + | 0.807190i | ||||
\(396\) | −186.055 | − | 211.595i | −0.469835 | − | 0.534331i | ||||
\(397\) | −95.6487 | − | 165.668i | −0.240929 | − | 0.417301i | 0.720050 | − | 0.693922i | \(-0.244119\pi\) |
−0.960979 | + | 0.276621i | \(0.910785\pi\) | |||||||
\(398\) | −610.123 | − | 100.321i | −1.53297 | − | 0.252064i | ||||
\(399\) | 18.1945 | + | 40.0606i | 0.0456002 | + | 0.100402i | ||||
\(400\) | −155.712 | − | 118.836i | −0.389281 | − | 0.297089i | ||||
\(401\) | 61.2011 | + | 106.004i | 0.152621 | + | 0.264348i | 0.932190 | − | 0.361968i | \(-0.117895\pi\) |
−0.779569 | + | 0.626316i | \(0.784562\pi\) | |||||||
\(402\) | 40.2895 | − | 49.1585i | 0.100223 | − | 0.122285i | ||||
\(403\) | −512.587 | − | 295.942i | −1.27193 | − | 0.734347i | ||||
\(404\) | 117.310 | + | 585.750i | 0.290372 | + | 1.44988i | ||||
\(405\) | −283.143 | −0.699120 | ||||||||
\(406\) | 280.344 | − | 281.214i | 0.690502 | − | 0.692646i | ||||
\(407\) | −235.756 | −0.579254 | ||||||||
\(408\) | 0.670347 | + | 19.3167i | 0.00164301 | + | 0.0473448i | ||||
\(409\) | −4.57744 | − | 2.64279i | −0.0111918 | − | 0.00646158i | 0.494394 | − | 0.869238i | \(-0.335390\pi\) |
−0.505585 | + | 0.862777i | \(0.668723\pi\) | |||||||
\(410\) | −204.949 | + | 250.065i | −0.499877 | + | 0.609915i | ||||
\(411\) | 21.4610 | + | 37.1716i | 0.0522166 | + | 0.0904418i | ||||
\(412\) | −25.4151 | + | 75.1939i | −0.0616872 | + | 0.182509i | ||||
\(413\) | 515.617 | + | 50.3178i | 1.24847 | + | 0.121835i | ||||
\(414\) | 12.4657 | − | 75.8123i | 0.0301103 | − | 0.183122i | ||||
\(415\) | −92.0975 | − | 159.517i | −0.221922 | − | 0.384379i | ||||
\(416\) | 133.758 | + | 565.283i | 0.321534 | + | 1.35885i | ||||
\(417\) | 33.7460 | − | 58.4498i | 0.0809257 | − | 0.140167i | ||||
\(418\) | −138.071 | − | 366.118i | −0.330313 | − | 0.875880i | ||||
\(419\) | −34.7160 | −0.0828545 | −0.0414272 | − | 0.999142i | \(-0.513190\pi\) | ||||
−0.0414272 | + | 0.999142i | \(0.513190\pi\) | |||||||
\(420\) | −23.0934 | − | 10.4022i | −0.0549844 | − | 0.0247671i | ||||
\(421\) | 394.337i | 0.936669i | 0.883551 | + | 0.468334i | \(0.155146\pi\) | ||||
−0.883551 | + | 0.468334i | \(0.844854\pi\) | |||||||
\(422\) | −88.8257 | − | 235.536i | −0.210487 | − | 0.558143i | ||||
\(423\) | 393.564 | + | 227.224i | 0.930412 | + | 0.537173i | ||||
\(424\) | 426.169 | − | 266.171i | 1.00512 | − | 0.627762i | ||||
\(425\) | −101.144 | + | 58.3956i | −0.237986 | + | 0.137401i | ||||
\(426\) | −0.438702 | + | 2.66805i | −0.00102982 | + | 0.00626302i | ||||
\(427\) | 206.050 | − | 288.088i | 0.482554 | − | 0.674678i | ||||
\(428\) | 11.7114 | − | 34.6495i | 0.0273630 | − | 0.0809569i | ||||
\(429\) | 31.3848 | − | 18.1200i | 0.0731581 | − | 0.0422378i | ||||
\(430\) | 112.802 | − | 137.633i | 0.262329 | − | 0.320076i | ||||
\(431\) | 215.872 | − | 373.901i | 0.500862 | − | 0.867519i | −0.499137 | − | 0.866523i | \(-0.666350\pi\) |
1.00000 | 0.000995912i | \(-0.000317009\pi\) | ||||||||
\(432\) | −9.29762 | + | 72.0807i | −0.0215223 | + | 0.166853i | ||||
\(433\) | − | 318.535i | − | 0.735647i | −0.929896 | − | 0.367823i | \(-0.880103\pi\) | ||
0.929896 | − | 0.367823i | \(-0.119897\pi\) | |||||||
\(434\) | 118.828 | + | 440.739i | 0.273798 | + | 1.01553i | ||||
\(435\) | − | 25.6565i | − | 0.0589803i | ||||||
\(436\) | −467.510 | + | 93.6300i | −1.07227 | + | 0.214748i | ||||
\(437\) | 53.3481 | − | 92.4016i | 0.122078 | − | 0.211445i | ||||
\(438\) | −8.77058 | + | 10.7013i | −0.0200242 | + | 0.0244321i | ||||
\(439\) | 532.799 | − | 307.612i | 1.21366 | − | 0.700710i | 0.250109 | − | 0.968218i | \(-0.419533\pi\) |
0.963556 | + | 0.267508i | \(0.0862001\pi\) | |||||||
\(440\) | 198.858 | + | 105.790i | 0.451949 | + | 0.240432i | ||||
\(441\) | −429.596 | − | 84.6525i | −0.974141 | − | 0.191956i | ||||
\(442\) | 341.765 | + | 56.1957i | 0.773223 | + | 0.127140i | ||||
\(443\) | −86.4553 | + | 49.9150i | −0.195159 | + | 0.112675i | −0.594395 | − | 0.804173i | \(-0.702609\pi\) |
0.399237 | + | 0.916848i | \(0.369275\pi\) | |||||||
\(444\) | 20.0060 | + | 22.7523i | 0.0450586 | + | 0.0512440i | ||||
\(445\) | 475.840 | + | 274.726i | 1.06930 | + | 0.617362i | ||||
\(446\) | 6.31355 | + | 16.7415i | 0.0141559 | + | 0.0375369i | ||||
\(447\) | 7.80515i | 0.0174612i | ||||||||
\(448\) | 234.736 | − | 381.579i | 0.523965 | − | 0.851740i | ||||
\(449\) | −75.3168 | −0.167743 | −0.0838717 | − | 0.996477i | \(-0.526729\pi\) | ||||
−0.0838717 | + | 0.996477i | \(0.526729\pi\) | |||||||
\(450\) | −204.719 | + | 77.2038i | −0.454931 | + | 0.171564i | ||||
\(451\) | −178.391 | + | 308.983i | −0.395546 | + | 0.685105i | ||||
\(452\) | −372.516 | + | 327.552i | −0.824151 | + | 0.724672i | ||||
\(453\) | −2.97443 | − | 5.15187i | −0.00656608 | − | 0.0113728i | ||||
\(454\) | −88.4889 | + | 538.161i | −0.194909 | + | 1.18538i | ||||
\(455\) | −264.037 | + | 369.161i | −0.580301 | + | 0.811343i | ||||
\(456\) | −23.6167 | + | 44.3932i | −0.0517910 | + | 0.0973536i | ||||
\(457\) | 104.447 | + | 180.907i | 0.228549 | + | 0.395858i | 0.957378 | − | 0.288837i | \(-0.0932687\pi\) |
−0.728830 | + | 0.684695i | \(0.759935\pi\) | |||||||
\(458\) | 512.351 | + | 419.914i | 1.11867 | + | 0.916843i | ||||
\(459\) | 37.5281 | + | 21.6669i | 0.0817606 | + | 0.0472045i | ||||
\(460\) | 12.0614 | + | 60.2243i | 0.0262203 | + | 0.130922i | ||||
\(461\) | −751.461 | −1.63007 | −0.815034 | − | 0.579413i | \(-0.803282\pi\) | ||||
−0.815034 | + | 0.579413i | \(0.803282\pi\) | |||||||
\(462\) | −27.0081 | − | 7.19195i | −0.0584592 | − | 0.0155670i | ||||
\(463\) | −3.56075 | −0.00769060 | −0.00384530 | − | 0.999993i | \(-0.501224\pi\) | ||||
−0.00384530 | + | 0.999993i | \(0.501224\pi\) | |||||||
\(464\) | 450.079 | + | 58.0553i | 0.969998 | + | 0.125119i | ||||
\(465\) | 25.5426 | + | 14.7470i | 0.0549304 | + | 0.0317141i | ||||
\(466\) | 244.769 | + | 200.609i | 0.525256 | + | 0.430491i | ||||
\(467\) | 206.945 | + | 358.440i | 0.443138 | + | 0.767537i | 0.997920 | − | 0.0644583i | \(-0.0205320\pi\) |
−0.554783 | + | 0.831995i | \(0.687199\pi\) | |||||||
\(468\) | 614.686 | + | 207.760i | 1.31343 | + | 0.443932i | ||||
\(469\) | −85.3146 | + | 874.238i | −0.181908 | + | 1.86405i | ||||
\(470\) | −358.484 | − | 58.9449i | −0.762733 | − | 0.125415i | ||||
\(471\) | −16.1615 | − | 27.9925i | −0.0343131 | − | 0.0594320i | ||||
\(472\) | 313.643 | + | 502.177i | 0.664499 | + | 1.06394i | ||||
\(473\) | 98.1843 | − | 170.060i | 0.207578 | − | 0.359535i | ||||
\(474\) | 48.8509 | − | 18.4227i | 0.103061 | − | 0.0388664i | ||||
\(475\) | −303.843 | −0.639669 | ||||||||
\(476\) | −156.068 | − | 216.782i | −0.327874 | − | 0.455424i | ||||
\(477\) | − | 561.240i | − | 1.17660i | ||||||
\(478\) | −91.6927 | + | 34.5792i | −0.191826 | + | 0.0723415i | ||||
\(479\) | −785.798 | − | 453.681i | −1.64050 | − | 0.947142i | −0.980657 | − | 0.195737i | \(-0.937290\pi\) |
−0.659841 | − | 0.751405i | \(-0.729376\pi\) | |||||||
\(480\) | −6.66529 | − | 28.1686i | −0.0138860 | − | 0.0586845i | ||||
\(481\) | 470.172 | − | 271.454i | 0.977488 | − | 0.564353i | ||||
\(482\) | −389.478 | − | 64.0412i | −0.808047 | − | 0.132866i | ||||
\(483\) | −3.15154 | − | 6.93907i | −0.00652494 | − | 0.0143666i | ||||
\(484\) | −223.047 | − | 75.3886i | −0.460840 | − | 0.155762i | ||||
\(485\) | −145.518 | + | 84.0147i | −0.300037 | + | 0.173226i | ||||
\(486\) | 94.2922 | + | 77.2803i | 0.194017 | + | 0.159013i | ||||
\(487\) | −421.452 | + | 729.977i | −0.865405 | + | 1.49893i | 0.00123943 | + | 0.999999i | \(0.499605\pi\) |
−0.866644 | + | 0.498926i | \(0.833728\pi\) | |||||||
\(488\) | 404.546 | − | 14.0390i | 0.828988 | − | 0.0287684i | ||||
\(489\) | − | 40.4410i | − | 0.0827014i | ||||||
\(490\) | 345.219 | − | 57.8634i | 0.704528 | − | 0.118089i | ||||
\(491\) | 144.126i | 0.293535i | 0.989171 | + | 0.146768i | \(0.0468870\pi\) | ||||
−0.989171 | + | 0.146768i | \(0.953113\pi\) | |||||||
\(492\) | 44.9573 | − | 9.00378i | 0.0913766 | − | 0.0183004i | ||||
\(493\) | 135.290 | − | 234.329i | 0.274422 | − | 0.475313i | ||||
\(494\) | 696.911 | + | 571.177i | 1.41075 | + | 1.15623i | ||||
\(495\) | 217.889 | − | 125.798i | 0.440179 | − | 0.254138i | ||||
\(496\) | −316.498 | + | 414.713i | −0.638101 | + | 0.836115i | ||||
\(497\) | −15.4523 | − | 34.0229i | −0.0310912 | − | 0.0684566i | ||||
\(498\) | −4.23805 | + | 25.7745i | −0.00851014 | + | 0.0517560i | ||||
\(499\) | 330.101 | − | 190.584i | 0.661526 | − | 0.381932i | −0.131332 | − | 0.991338i | \(-0.541926\pi\) |
0.792858 | + | 0.609406i | \(0.208592\pi\) | |||||||
\(500\) | 399.584 | − | 351.352i | 0.799168 | − | 0.702705i | ||||
\(501\) | −31.3180 | − | 18.0815i | −0.0625110 | − | 0.0360908i | ||||
\(502\) | −590.405 | + | 222.654i | −1.17611 | + | 0.443534i | ||||
\(503\) | − | 936.429i | − | 1.86169i | −0.365418 | − | 0.930843i | \(-0.619074\pi\) | ||
0.365418 | − | 0.930843i | \(-0.380926\pi\) | |||||||
\(504\) | −222.607 | − | 448.168i | −0.441681 | − | 0.889222i | ||||
\(505\) | −533.429 | −1.05629 | ||||||||
\(506\) | 23.9158 | + | 63.4168i | 0.0472645 | + | 0.125330i | ||||
\(507\) | −20.3273 | + | 35.2080i | −0.0400933 | + | 0.0694437i | ||||
\(508\) | −173.068 | + | 152.178i | −0.340685 | + | 0.299563i | ||||
\(509\) | −167.592 | − | 290.278i | −0.329258 | − | 0.570291i | 0.653107 | − | 0.757265i | \(-0.273465\pi\) |
−0.982365 | + | 0.186975i | \(0.940132\pi\) | |||||||
\(510\) | −17.0304 | − | 2.80028i | −0.0333930 | − | 0.00549075i | ||||
\(511\) | 18.5721 | − | 190.312i | 0.0363446 | − | 0.372431i | ||||
\(512\) | 509.230 | − | 53.1863i | 0.994590 | − | 0.103880i | ||||
\(513\) | 56.3682 | + | 97.6327i | 0.109880 | + | 0.190317i | ||||
\(514\) | 482.403 | − | 588.596i | 0.938528 | − | 1.14513i | ||||
\(515\) | −61.3800 | − | 35.4378i | −0.119185 | − | 0.0688112i | ||||
\(516\) | −24.7440 | + | 4.95557i | −0.0479534 | + | 0.00960382i | ||||
\(517\) | −400.896 | −0.775427 | ||||||||
\(518\) | −404.605 | − | 107.742i | −0.781091 | − | 0.207996i | ||||
\(519\) | −49.5824 | −0.0955345 | ||||||||
\(520\) | −518.393 | + | 17.9898i | −0.996910 | + | 0.0345958i | ||||
\(521\) | −421.675 | − | 243.454i | −0.809357 | − | 0.467283i | 0.0373754 | − | 0.999301i | \(-0.488100\pi\) |
−0.846733 | + | 0.532019i | \(0.821434\pi\) | |||||||
\(522\) | 321.315 | − | 392.046i | 0.615545 | − | 0.751046i | ||||
\(523\) | 86.3132 | + | 149.499i | 0.165035 | + | 0.285849i | 0.936668 | − | 0.350220i | \(-0.113893\pi\) |
−0.771633 | + | 0.636068i | \(0.780560\pi\) | |||||||
\(524\) | −471.020 | − | 159.202i | −0.898894 | − | 0.303821i | ||||
\(525\) | −12.6258 | + | 17.6527i | −0.0240492 | + | 0.0336242i | ||||
\(526\) | 63.7080 | − | 387.452i | 0.121118 | − | 0.736600i | ||||
\(527\) | 155.527 | + | 269.380i | 0.295117 | + | 0.511157i | ||||
\(528\) | −12.3009 | − | 29.4785i | −0.0232972 | − | 0.0558305i | ||||
\(529\) | 255.259 | − | 442.122i | 0.482532 | − | 0.835770i | ||||
\(530\) | 158.319 | + | 419.809i | 0.298715 | + | 0.792093i | ||||
\(531\) | 661.339 | 1.24546 | ||||||||
\(532\) | −69.6396 | − | 691.431i | −0.130902 | − | 1.29968i | ||||
\(533\) | − | 821.611i | − | 1.54148i | ||||||
\(534\) | −27.4942 | − | 72.9055i | −0.0514872 | − | 0.136527i | ||||
\(535\) | 28.2841 | + | 16.3298i | 0.0528675 | + | 0.0305230i | ||||
\(536\) | −851.451 | + | 531.788i | −1.58853 | + | 0.992142i | ||||
\(537\) | −32.7908 | + | 18.9318i | −0.0610629 | + | 0.0352547i | ||||
\(538\) | −33.1999 | + | 201.912i | −0.0617099 | + | 0.375300i | ||||
\(539\) | 365.538 | − | 124.814i | 0.678178 | − | 0.231566i | ||||
\(540\) | −61.4805 | − | 20.7801i | −0.113853 | − | 0.0384816i | ||||
\(541\) | −500.736 | + | 289.100i | −0.925574 | + | 0.534381i | −0.885409 | − | 0.464812i | \(-0.846122\pi\) |
−0.0401652 | + | 0.999193i | \(0.512788\pi\) | |||||||
\(542\) | 324.958 | − | 396.491i | 0.599553 | − | 0.731534i | ||||
\(543\) | −11.5611 | + | 20.0244i | −0.0212911 | + | 0.0368773i | ||||
\(544\) | 87.6604 | − | 292.420i | 0.161140 | − | 0.537537i | ||||
\(545\) | − | 425.750i | − | 0.781193i | ||||||
\(546\) | 62.1436 | − | 16.7546i | 0.113816 | − | 0.0306861i | ||||
\(547\) | − | 454.579i | − | 0.831040i | −0.909584 | − | 0.415520i | \(-0.863600\pi\) | ||
0.909584 | − | 0.415520i | \(-0.136400\pi\) | |||||||
\(548\) | −133.127 | − | 664.724i | −0.242932 | − | 1.21300i | ||||
\(549\) | 226.071 | − | 391.567i | 0.411788 | − | 0.713237i | ||||
\(550\) | 122.346 | − | 149.279i | 0.222448 | − | 0.271416i | ||||
\(551\) | 609.629 | − | 351.969i | 1.10640 | − | 0.638783i | ||||
\(552\) | 4.09075 | − | 7.68955i | 0.00741078 | − | 0.0139303i | ||||
\(553\) | −419.751 | + | 586.871i | −0.759043 | + | 1.06125i | ||||
\(554\) | 388.245 | + | 63.8384i | 0.700803 | + | 0.115232i | ||||
\(555\) | −23.4291 | + | 13.5268i | −0.0422145 | + | 0.0243726i | ||||
\(556\) | −800.532 | + | 703.905i | −1.43981 | + | 1.26602i | ||||
\(557\) | −25.2401 | − | 14.5724i | −0.0453143 | − | 0.0261622i | 0.477172 | − | 0.878810i | \(-0.341662\pi\) |
−0.522486 | + | 0.852648i | \(0.674995\pi\) | |||||||
\(558\) | 205.619 | + | 545.233i | 0.368492 | + | 0.977120i | ||||
\(559\) | 452.205i | 0.808953i | ||||||||
\(560\) | 292.934 | + | 272.436i | 0.523096 | + | 0.486493i | ||||
\(561\) | −19.0453 | −0.0339488 | ||||||||
\(562\) | 131.542 | − | 49.6071i | 0.234060 | − | 0.0882688i | ||||
\(563\) | −514.005 | + | 890.283i | −0.912975 | + | 1.58132i | −0.103136 | + | 0.994667i | \(0.532888\pi\) |
−0.809839 | + | 0.586652i | \(0.800446\pi\) | |||||||
\(564\) | 34.0196 | + | 38.6896i | 0.0603184 | + | 0.0685986i | ||||
\(565\) | −221.469 | − | 383.596i | −0.391981 | − | 0.678931i | ||||
\(566\) | 96.3730 | − | 586.110i | 0.170270 | − | 1.03553i | ||||
\(567\) | −552.283 | − | 53.8959i | −0.974044 | − | 0.0950544i | ||||
\(568\) | 20.0574 | − | 37.7026i | 0.0353122 | − | 0.0663778i | ||||
\(569\) | 409.852 | + | 709.885i | 0.720303 | + | 1.24760i | 0.960878 | + | 0.276971i | \(0.0893305\pi\) |
−0.240576 | + | 0.970630i | \(0.577336\pi\) | |||||||
\(570\) | −34.7277 | − | 28.4622i | −0.0609257 | − | 0.0499337i | ||||
\(571\) | −140.820 | − | 81.3023i | −0.246620 | − | 0.142386i | 0.371596 | − | 0.928395i | \(-0.378811\pi\) |
−0.618215 | + | 0.786009i | \(0.712144\pi\) | |||||||
\(572\) | −561.241 | + | 112.402i | −0.981191 | + | 0.196507i | ||||
\(573\) | 7.04760 | 0.0122995 | ||||||||
\(574\) | −447.362 | + | 448.751i | −0.779376 | + | 0.781796i | ||||
\(575\) | 52.6299 | 0.0915303 | ||||||||
\(576\) | 250.926 | − | 513.907i | 0.435635 | − | 0.892199i | ||||
\(577\) | 131.878 | + | 76.1400i | 0.228559 | + | 0.131958i | 0.609907 | − | 0.792473i | \(-0.291207\pi\) |
−0.381348 | + | 0.924431i | \(0.624540\pi\) | |||||||
\(578\) | 306.261 | + | 251.007i | 0.529864 | + | 0.434268i | ||||
\(579\) | −30.6926 | − | 53.1611i | −0.0530097 | − | 0.0918154i | ||||
\(580\) | −129.753 | + | 383.890i | −0.223712 | + | 0.661880i | ||||
\(581\) | −149.276 | − | 328.676i | −0.256930 | − | 0.565708i | ||||
\(582\) | 23.5124 | + | 3.86611i | 0.0403994 | + | 0.00664279i | ||||
\(583\) | 247.551 | + | 428.772i | 0.424617 | + | 0.735457i | ||||
\(584\) | 185.352 | − | 115.764i | 0.317383 | − | 0.198227i | ||||
\(585\) | −289.692 | + | 501.762i | −0.495201 | + | 0.857713i | ||||
\(586\) | −253.682 | + | 95.6688i | −0.432905 | + | 0.163257i | ||||
\(587\) | 894.404 | 1.52369 | 0.761843 | − | 0.647761i | \(-0.224295\pi\) | ||||
0.761843 | + | 0.647761i | \(0.224295\pi\) | |||||||
\(588\) | −43.0647 | − | 24.6857i | −0.0732392 | − | 0.0419825i | ||||
\(589\) | 809.232i | 1.37391i | ||||||||
\(590\) | −494.684 | + | 186.556i | −0.838447 | + | 0.316196i | ||||
\(591\) | −20.7713 | − | 11.9923i | −0.0351460 | − | 0.0202916i | ||||
\(592\) | −184.279 | − | 441.614i | −0.311282 | − | 0.745969i | ||||
\(593\) | 164.729 | − | 95.1064i | 0.277789 | − | 0.160382i | −0.354633 | − | 0.935006i | \(-0.615394\pi\) |
0.632422 | + | 0.774624i | \(0.282061\pi\) | |||||||
\(594\) | −70.6647 | − | 11.6193i | −0.118964 | − | 0.0195610i | ||||
\(595\) | 217.172 | − | 98.6338i | 0.364995 | − | 0.165771i | ||||
\(596\) | 39.4731 | − | 116.786i | 0.0662301 | − | 0.195950i | ||||
\(597\) | −67.8064 | + | 39.1480i | −0.113579 | + | 0.0655746i | ||||
\(598\) | −120.715 | − | 98.9360i | −0.201864 | − | 0.165445i | ||||
\(599\) | 146.832 | − | 254.320i | 0.245128 | − | 0.424574i | −0.717040 | − | 0.697033i | \(-0.754503\pi\) |
0.962168 | + | 0.272458i | \(0.0878366\pi\) | |||||||
\(600\) | −24.7888 | + | 0.860245i | −0.0413146 | + | 0.00143374i | ||||
\(601\) | 597.574i | 0.994299i | 0.867665 | + | 0.497150i | \(0.165620\pi\) | ||||
−0.867665 | + | 0.497150i | \(0.834380\pi\) | |||||||
\(602\) | 246.223 | − | 246.987i | 0.409008 | − | 0.410278i | ||||
\(603\) | 1121.31i | 1.85956i | ||||||||
\(604\) | 18.4510 | + | 92.1287i | 0.0305480 | + | 0.152531i | ||||
\(605\) | 105.119 | − | 182.071i | 0.173750 | − | 0.300944i | ||||
\(606\) | 58.5060 | + | 47.9505i | 0.0965445 | + | 0.0791263i | ||||
\(607\) | −10.6620 | + | 6.15569i | −0.0175650 | + | 0.0101412i | −0.508757 | − | 0.860910i | \(-0.669895\pi\) |
0.491192 | + | 0.871051i | \(0.336561\pi\) | |||||||
\(608\) | 577.881 | − | 544.807i | 0.950462 | − | 0.896064i | ||||
\(609\) | 4.88366 | − | 50.0440i | 0.00801915 | − | 0.0821740i | ||||
\(610\) | −58.6458 | + | 356.665i | −0.0961407 | + | 0.584697i | ||||
\(611\) | 799.512 | − | 461.599i | 1.30853 | − | 0.755481i | ||||
\(612\) | −225.165 | − | 256.075i | −0.367917 | − | 0.418422i | ||||
\(613\) | 118.897 | + | 68.6451i | 0.193959 | + | 0.111982i | 0.593835 | − | 0.804587i | \(-0.297613\pi\) |
−0.399876 | + | 0.916569i | \(0.630947\pi\) | |||||||
\(614\) | −142.607 | + | 53.7800i | −0.232258 | + | 0.0875895i | ||||
\(615\) | 40.9416i | 0.0665717i | ||||||||
\(616\) | 367.743 | + | 244.200i | 0.596986 | + | 0.396429i | ||||
\(617\) | 290.516 | 0.470853 | 0.235427 | − | 0.971892i | \(-0.424351\pi\) | ||||
0.235427 | + | 0.971892i | \(0.424351\pi\) | |||||||
\(618\) | 3.54656 | + | 9.40430i | 0.00573877 | + | 0.0152173i | ||||
\(619\) | 51.1586 | − | 88.6092i | 0.0826471 | − | 0.143149i | −0.821739 | − | 0.569864i | \(-0.806996\pi\) |
0.904386 | + | 0.426715i | \(0.140329\pi\) | |||||||
\(620\) | −307.607 | − | 349.833i | −0.496140 | − | 0.564247i | ||||
\(621\) | −9.76379 | − | 16.9114i | −0.0157227 | − | 0.0272325i | ||||
\(622\) | 390.938 | + | 64.2812i | 0.628517 | + | 0.103346i | ||||
\(623\) | 875.851 | + | 626.440i | 1.40586 | + | 1.00552i | ||||
\(624\) | 58.4740 | + | 44.6259i | 0.0937083 | + | 0.0715158i | ||||
\(625\) | 84.5320 | + | 146.414i | 0.135251 | + | 0.234262i | ||||
\(626\) | 70.2222 | − | 85.6804i | 0.112176 | − | 0.136870i | ||||
\(627\) | −42.9098 | − | 24.7740i | −0.0684366 | − | 0.0395119i | ||||
\(628\) | 100.253 | + | 500.577i | 0.159638 | + | 0.797097i | ||||
\(629\) | −285.315 | −0.453600 | ||||||||
\(630\) | 431.432 | − | 116.319i | 0.684812 | − | 0.184633i | ||||
\(631\) | −562.739 | −0.891820 | −0.445910 | − | 0.895078i | \(-0.647120\pi\) | ||||
−0.445910 | + | 0.895078i | \(0.647120\pi\) | |||||||
\(632\) | −824.112 | + | 28.5992i | −1.30397 | + | 0.0452519i | ||||
\(633\) | −27.6054 | − | 15.9380i | −0.0436104 | − | 0.0251785i | ||||
\(634\) | 379.268 | − | 462.757i | 0.598214 | − | 0.729900i | ||||
\(635\) | −102.893 | − | 178.216i | −0.162036 | − | 0.280655i | ||||
\(636\) | 20.3729 | − | 60.2758i | 0.0320328 | − | 0.0947732i | ||||
\(637\) | −585.284 | + | 669.805i | −0.918814 | + | 1.05150i | ||||
\(638\) | −72.5519 | + | 441.237i | −0.113718 | + | 0.691595i | ||||
\(639\) | −23.8508 | − | 41.3108i | −0.0373252 | − | 0.0646492i | ||||
\(640\) | −42.7265 | + | 455.187i | −0.0667602 | + | 0.711229i | ||||
\(641\) | 376.275 | − | 651.727i | 0.587012 | − | 1.01673i | −0.407610 | − | 0.913156i | \(-0.633638\pi\) |
0.994621 | − | 0.103578i | \(-0.0330291\pi\) | |||||||
\(642\) | −1.63427 | − | 4.33353i | −0.00254558 | − | 0.00675005i | ||||
\(643\) | −253.143 | −0.393690 | −0.196845 | − | 0.980435i | \(-0.563070\pi\) | ||||
−0.196845 | + | 0.980435i | \(0.563070\pi\) | |||||||
\(644\) | 12.0626 | + | 119.766i | 0.0187307 | + | 0.185972i | ||||
\(645\) | − | 22.5337i | − | 0.0349360i | ||||||
\(646\) | −167.095 | − | 443.079i | −0.258660 | − | 0.685881i | ||||
\(647\) | 485.492 | + | 280.299i | 0.750374 | + | 0.433229i | 0.825829 | − | 0.563921i | \(-0.190708\pi\) |
−0.0754551 | + | 0.997149i | \(0.524041\pi\) | |||||||
\(648\) | −335.947 | − | 537.887i | −0.518436 | − | 0.830073i | ||||
\(649\) | −505.244 | + | 291.703i | −0.778497 | + | 0.449465i | ||||
\(650\) | −72.1150 | + | 438.581i | −0.110946 | + | 0.674739i | ||||
\(651\) | 47.0149 | + | 33.6267i | 0.0722195 | + | 0.0516539i | ||||
\(652\) | −204.523 | + | 605.108i | −0.313686 | + | 0.928079i | ||||
\(653\) | 602.396 | − | 347.793i | 0.922505 | − | 0.532609i | 0.0380717 | − | 0.999275i | \(-0.487878\pi\) |
0.884433 | + | 0.466666i | \(0.154545\pi\) | |||||||
\(654\) | −38.2712 | + | 46.6959i | −0.0585186 | + | 0.0714004i | ||||
\(655\) | 221.985 | − | 384.489i | 0.338908 | − | 0.587007i | ||||
\(656\) | −718.219 | − | 92.6424i | −1.09485 | − | 0.141223i | ||||
\(657\) | − | 244.097i | − | 0.371533i | ||||||
\(658\) | −688.019 | − | 183.211i | −1.04562 | − | 0.278437i | ||||
\(659\) | 323.387i | 0.490724i | 0.969432 | + | 0.245362i | \(0.0789068\pi\) | ||||
−0.969432 | + | 0.245362i | \(0.921093\pi\) | |||||||
\(660\) | 27.9671 | − | 5.60109i | 0.0423745 | − | 0.00848650i | ||||
\(661\) | 15.5168 | − | 26.8758i | 0.0234747 | − | 0.0406593i | −0.854049 | − | 0.520192i | \(-0.825860\pi\) |
0.877524 | + | 0.479533i | \(0.159194\pi\) | |||||||
\(662\) | −475.894 | + | 580.654i | −0.718873 | + | 0.877120i | ||||
\(663\) | 37.9822 | − | 21.9291i | 0.0572884 | − | 0.0330755i | ||||
\(664\) | 193.763 | − | 364.223i | 0.291811 | − | 0.548529i | ||||
\(665\) | 617.600 | + | 60.2699i | 0.928721 | + | 0.0906315i | ||||
\(666\) | −527.416 | − | 86.7221i | −0.791916 | − | 0.130213i | ||||
\(667\) | −105.596 | + | 60.9661i | −0.158315 | + | 0.0914035i | ||||
\(668\) | 377.159 | + | 428.933i | 0.564610 | + | 0.642116i | ||||
\(669\) | 1.96213 | + | 1.13284i | 0.00293293 | + | 0.00169333i | ||||
\(670\) | −316.308 | − | 838.745i | −0.472102 | − | 1.25186i | ||||
\(671\) | 398.862i | 0.594429i | ||||||||
\(672\) | −7.63908 | − | 56.2127i | −0.0113677 | − | 0.0836498i | ||||
\(673\) | 1011.75 | 1.50334 | 0.751670 | − | 0.659539i | \(-0.229249\pi\) | ||||
0.751670 | + | 0.659539i | \(0.229249\pi\) | |||||||
\(674\) | 9.33884 | − | 3.52187i | 0.0138558 | − | 0.00522533i | ||||
\(675\) | −27.8047 | + | 48.1592i | −0.0411922 | + | 0.0713469i | ||||
\(676\) | 482.210 | − | 424.005i | 0.713328 | − | 0.627227i | ||||
\(677\) | −34.7377 | − | 60.1674i | −0.0513112 | − | 0.0888736i | 0.839229 | − | 0.543778i | \(-0.183007\pi\) |
−0.890540 | + | 0.454905i | \(0.849673\pi\) | |||||||
\(678\) | −10.1914 | + | 61.9806i | −0.0150315 | + | 0.0914169i | ||||
\(679\) | −299.831 | + | 136.175i | −0.441577 | + | 0.200553i | ||||
\(680\) | 240.660 | + | 128.028i | 0.353911 | + | 0.188277i | ||||
\(681\) | 34.5307 | + | 59.8089i | 0.0507058 | + | 0.0878251i | ||||
\(682\) | −397.578 | − | 325.848i | −0.582959 | − | 0.477784i | ||||
\(683\) | −824.530 | − | 476.042i | −1.20722 | − | 0.696987i | −0.245067 | − | 0.969506i | \(-0.578810\pi\) |
−0.962150 | + | 0.272519i | \(0.912143\pi\) | |||||||
\(684\) | −174.206 | − | 869.840i | −0.254688 | − | 1.27170i | ||||
\(685\) | 605.348 | 0.883720 | ||||||||
\(686\) | 684.378 | − | 47.1533i | 0.997635 | − | 0.0687366i | ||||
\(687\) | 83.8839 | 0.122102 | ||||||||
\(688\) | 395.299 | + | 50.9893i | 0.574563 | + | 0.0741123i | ||||
\(689\) | −987.391 | − | 570.070i | −1.43308 | − | 0.827388i | ||||
\(690\) | 6.01533 | + | 4.93007i | 0.00871787 | + | 0.00714502i | ||||
\(691\) | −34.0754 | − | 59.0204i | −0.0493132 | − | 0.0854130i | 0.840315 | − | 0.542098i | \(-0.182370\pi\) |
−0.889628 | + | 0.456685i | \(0.849037\pi\) | |||||||
\(692\) | 741.888 | + | 250.754i | 1.07209 | + | 0.362361i | ||||
\(693\) | 448.947 | − | 203.900i | 0.647831 | − | 0.294228i | ||||
\(694\) | 730.975 | + | 120.193i | 1.05328 | + | 0.173189i | ||||
\(695\) | −475.935 | − | 824.343i | −0.684798 | − | 1.18611i | ||||
\(696\) | 48.7395 | − | 30.4411i | 0.0700281 | − | 0.0437372i | ||||
\(697\) | −215.891 | + | 373.934i | −0.309743 | + | 0.536490i | ||||
\(698\) | −48.0565 | + | 18.1231i | −0.0688489 | + | 0.0259644i | ||||
\(699\) | 40.0745 | 0.0573311 | ||||||||
\(700\) | 278.192 | − | 200.280i | 0.397418 | − | 0.286114i | ||||
\(701\) | − | 1.67276i | − | 0.00238625i | −0.999999 | − | 0.00119312i | \(-0.999620\pi\) | ||
0.999999 | − | 0.00119312i | \(-0.000379783\pi\) | |||||||
\(702\) | 154.306 | − | 58.1921i | 0.219809 | − | 0.0828947i | ||||
\(703\) | −642.825 | − | 371.135i | −0.914403 | − | 0.527931i | ||||
\(704\) | 34.9734 | + | 503.289i | 0.0496781 | + | 0.714899i | ||||
\(705\) | −39.8404 | + | 23.0019i | −0.0565112 | + | 0.0326267i | ||||
\(706\) | 523.984 | + | 86.1577i | 0.742186 | + | 0.122036i | ||||
\(707\) | −1040.47 | − | 101.537i | −1.47168 | − | 0.143617i | ||||
\(708\) | 71.0261 | + | 24.0064i | 0.100319 | + | 0.0339074i | ||||
\(709\) | 45.7969 | − | 26.4408i | 0.0645936 | − | 0.0372931i | −0.467355 | − | 0.884070i | \(-0.654793\pi\) |
0.531949 | + | 0.846776i | \(0.321460\pi\) | |||||||
\(710\) | 29.4937 | + | 24.1726i | 0.0415405 | + | 0.0340459i | ||||
\(711\) | −460.536 | + | 797.673i | −0.647731 | + | 1.12190i | ||||
\(712\) | 42.6817 | + | 1229.91i | 0.0599461 | + | 1.72740i | ||||
\(713\) | − | 140.171i | − | 0.196593i | ||||||
\(714\) | −32.6855 | − | 8.70378i | −0.0457780 | − | 0.0121902i | ||||
\(715\) | − | 511.109i | − | 0.714838i | ||||||
\(716\) | 586.384 | − | 117.437i | 0.818972 | − | 0.164019i | ||||
\(717\) | −6.20454 | + | 10.7466i | −0.00865347 | + | 0.0149882i | ||||
\(718\) | −851.473 | − | 697.853i | −1.18590 | − | 0.971941i | ||||
\(719\) | −824.178 | + | 475.840i | −1.14628 | + | 0.661808i | −0.947979 | − | 0.318333i | \(-0.896877\pi\) |
−0.198305 | + | 0.980140i | \(0.563544\pi\) | |||||||
\(720\) | 405.955 | + | 309.815i | 0.563827 | + | 0.430298i | ||||
\(721\) | −112.979 | − | 80.8064i | −0.156697 | − | 0.112075i | ||||
\(722\) | 82.7399 | − | 503.198i | 0.114598 | − | 0.696950i | ||||
\(723\) | −43.2849 | + | 24.9906i | −0.0598685 | + | 0.0345651i | ||||
\(724\) | 274.255 | − | 241.151i | 0.378805 | − | 0.333081i | ||||
\(725\) | 300.711 | + | 173.615i | 0.414774 | + | 0.239470i | ||||
\(726\) | −27.8959 | + | 10.5201i | −0.0384241 | + | 0.0144905i | ||||
\(727\) | − | 1061.98i | − | 1.46078i | −0.683032 | − | 0.730388i | \(-0.739339\pi\) | ||
0.683032 | − | 0.730388i | \(-0.260661\pi\) | |||||||
\(728\) | −1014.57 | − | 63.5854i | −1.39364 | − | 0.0873426i | ||||
\(729\) | −698.013 | −0.957494 | ||||||||
\(730\) | 68.8569 | + | 182.586i | 0.0943245 | + | 0.250117i | ||||
\(731\) | 118.824 | − | 205.809i | 0.162550 | − | 0.281544i | ||||
\(732\) | 38.4933 | − | 33.8470i | 0.0525865 | − | 0.0462391i | ||||
\(733\) | −0.148102 | − | 0.256519i | −0.000202048 | − | 0.000349958i | 0.865924 | − | 0.500175i | \(-0.166731\pi\) |
−0.866126 | + | 0.499825i | \(0.833398\pi\) | |||||||
\(734\) | −410.409 | − | 67.4828i | −0.559140 | − | 0.0919384i | ||||
\(735\) | 29.1652 | − | 33.3769i | 0.0396806 | − | 0.0454108i | ||||
\(736\) | −100.097 | + | 94.3684i | −0.136002 | + | 0.128218i | ||||
\(737\) | −494.588 | − | 856.651i | −0.671082 | − | 1.16235i | ||||
\(738\) | −512.741 | + | 625.612i | −0.694772 | + | 0.847713i | ||||
\(739\) | 176.276 | + | 101.773i | 0.238533 | + | 0.137717i | 0.614502 | − | 0.788915i | \(-0.289357\pi\) |
−0.375969 | + | 0.926632i | \(0.622690\pi\) | |||||||
\(740\) | 418.972 | − | 83.9092i | 0.566178 | − | 0.113391i | ||||
\(741\) | 114.101 | 0.153982 | ||||||||
\(742\) | 228.898 | + | 848.991i | 0.308487 | + | 1.14419i | ||||
\(743\) | 1142.13 | 1.53718 | 0.768592 | − | 0.639739i | \(-0.220958\pi\) | ||||
0.768592 | + | 0.639739i | \(0.220958\pi\) | |||||||
\(744\) | 2.29111 | + | 66.0205i | 0.00307945 | + | 0.0887373i | ||||
\(745\) | 95.3315 | + | 55.0397i | 0.127962 | + | 0.0738788i | ||||
\(746\) | −576.102 | + | 702.920i | −0.772255 | + | 0.942253i | ||||
\(747\) | −230.409 | − | 399.080i | −0.308446 | − | 0.534244i | ||||
\(748\) | 284.969 | + | 96.3180i | 0.380975 | + | 0.128767i | ||||
\(749\) | 52.0610 | + | 37.2358i | 0.0695073 | + | 0.0497141i | ||||
\(750\) | 10.9319 | − | 66.4843i | 0.0145759 | − | 0.0886457i | ||||
\(751\) | 396.068 | + | 686.010i | 0.527387 | + | 0.913462i | 0.999490 | + | 0.0319185i | \(0.0101617\pi\) |
−0.472103 | + | 0.881543i | \(0.656505\pi\) | |||||||
\(752\) | −313.360 | − | 750.950i | −0.416702 | − | 0.998604i | ||||
\(753\) | −39.9508 | + | 69.1967i | −0.0530554 | + | 0.0918947i | ||||
\(754\) | −363.357 | − | 963.503i | −0.481906 | − | 1.27786i | ||||
\(755\) | −83.8995 | −0.111125 | ||||||||
\(756\) | −115.965 | − | 52.2351i | −0.153393 | − | 0.0690940i | ||||
\(757\) | 1179.34i | 1.55792i | 0.627076 | + | 0.778958i | \(0.284252\pi\) | ||||
−0.627076 | + | 0.778958i | \(0.715748\pi\) | |||||||
\(758\) | 263.408 | + | 698.470i | 0.347504 | + | 0.921465i | ||||
\(759\) | 7.43259 | + | 4.29121i | 0.00979260 | + | 0.00565376i | ||||
\(760\) | 375.678 | + | 601.501i | 0.494313 | + | 0.791449i | ||||
\(761\) | 197.869 | − | 114.240i | 0.260011 | − | 0.150118i | −0.364328 | − | 0.931271i | \(-0.618701\pi\) |
0.624340 | + | 0.781153i | \(0.285368\pi\) | |||||||
\(762\) | −4.73482 | + | 28.7957i | −0.00621368 | + | 0.0377896i | ||||
\(763\) | 81.0408 | − | 830.443i | 0.106213 | − | 1.08839i | ||||
\(764\) | −105.451 | − | 35.6420i | −0.138025 | − | 0.0466518i | ||||
\(765\) | 263.691 | − | 152.242i | 0.344694 | − | 0.199009i | ||||
\(766\) | 395.689 | − | 482.792i | 0.516565 | − | 0.630277i | ||||
\(767\) | 671.744 | − | 1163.49i | 0.875807 | − | 1.51694i | ||||
\(768\) | 45.6035 | − | 46.0837i | 0.0593795 | − | 0.0600049i | ||||
\(769\) | − | 83.4232i | − | 0.108483i | −0.998528 | − | 0.0542414i | \(-0.982726\pi\) | ||
0.998528 | − | 0.0542414i | \(-0.0172740\pi\) | |||||||
\(770\) | −278.296 | + | 279.160i | −0.361423 | + | 0.362545i | ||||
\(771\) | − | 96.3670i | − | 0.124990i | ||||||
\(772\) | 190.392 | + | 950.658i | 0.246622 | + | 1.23142i | ||||
\(773\) | −285.318 | + | 494.186i | −0.369105 | + | 0.639309i | −0.989426 | − | 0.145039i | \(-0.953669\pi\) |
0.620321 | + | 0.784348i | \(0.287002\pi\) | |||||||
\(774\) | 282.207 | − | 344.329i | 0.364608 | − | 0.444870i | ||||
\(775\) | −345.691 | + | 199.585i | −0.446052 | + | 0.257528i | ||||
\(776\) | −332.258 | − | 176.757i | −0.428168 | − | 0.227780i | ||||
\(777\) | −48.2742 | + | 21.9249i | −0.0621289 | + | 0.0282173i | ||||
\(778\) | −1001.83 | − | 164.728i | −1.28769 | − | 0.211733i | ||||
\(779\) | −972.822 | + | 561.659i | −1.24881 | + | 0.721000i | ||||
\(780\) | −49.3261 | + | 43.3722i | −0.0632385 | + | 0.0556054i | ||||
\(781\) | 36.4427 | + | 21.0402i | 0.0466616 | + | 0.0269401i | ||||
\(782\) | 28.9432 | + | 76.7477i | 0.0370117 | + | 0.0981429i | ||||
\(783\) | − | 128.835i | − | 0.164540i | ||||||
\(784\) | 519.521 | + | 587.157i | 0.662655 | + | 0.748925i | ||||
\(785\) | −455.864 | −0.580718 | ||||||||
\(786\) | −58.9093 | + | 22.2159i | −0.0749482 | + | 0.0282645i | ||||
\(787\) | 382.719 | − | 662.888i | 0.486301 | − | 0.842298i | −0.513575 | − | 0.858045i | \(-0.671679\pi\) |
0.999876 | + | 0.0157470i | \(0.00501262\pi\) | |||||||
\(788\) | 250.146 | + | 284.485i | 0.317444 | + | 0.361021i | ||||
\(789\) | −24.8605 | − | 43.0597i | −0.0315089 | − | 0.0545750i | ||||
\(790\) | 119.469 | − | 726.573i | 0.151227 | − | 0.919713i | ||||
\(791\) | −358.968 | − | 790.377i | −0.453816 | − | 0.999212i | ||||
\(792\) | 497.501 | + | 264.665i | 0.628158 | + | 0.334173i | ||||
\(793\) | −459.257 | − | 795.456i | −0.579138 | − | 1.00310i | ||||
\(794\) | 295.909 | + | 242.522i | 0.372681 | + | 0.305443i | ||||
\(795\) | 49.2025 | + | 28.4071i | 0.0618900 | + | 0.0357322i | ||||
\(796\) | 1212.55 | − | 242.843i | 1.52331 | − | 0.305079i | ||||
\(797\) | 577.729 | 0.724880 | 0.362440 | − | 0.932007i | \(-0.381944\pi\) | ||||
0.362440 | + | 0.932007i | \(0.381944\pi\) | |||||||
\(798\) | −62.3200 | − | 62.1271i | −0.0780952 | − | 0.0778535i | ||||
\(799\) | −485.168 | −0.607220 | ||||||||
\(800\) | 375.258 | + | 112.493i | 0.469072 | + | 0.140616i | ||||
\(801\) | 1190.45 | + | 687.309i | 1.48621 | + | 0.858063i | ||||
\(802\) | −189.338 | − | 155.178i | −0.236082 | − | 0.193489i | ||||
\(803\) | 107.666 | + | 186.484i | 0.134080 | + | 0.232234i | ||||
\(804\) | −40.7033 | + | 120.426i | −0.0506260 | + | 0.149784i | ||||
\(805\) | −106.977 | − | 10.4396i | −0.132891 | − | 0.0129685i | ||||
\(806\) | 1168.08 | + | 192.066i | 1.44923 | + | 0.238295i | ||||
\(807\) | 12.9555 | + | 22.4396i | 0.0160539 | + | 0.0278062i | ||||
\(808\) | −632.908 | − | 1013.35i | −0.783301 | − | 1.25415i | ||||
\(809\) | 41.4824 | − | 71.8496i | 0.0512761 | − | 0.0888128i | −0.839248 | − | 0.543749i | \(-0.817004\pi\) |
0.890524 | + | 0.454936i | \(0.150338\pi\) | |||||||
\(810\) | 529.860 | − | 199.822i | 0.654149 | − | 0.246693i | ||||
\(811\) | −525.164 | −0.647552 | −0.323776 | − | 0.946134i | \(-0.604952\pi\) | ||||
−0.323776 | + | 0.946134i | \(0.604952\pi\) | |||||||
\(812\) | −326.161 | + | 724.096i | −0.401677 | + | 0.891744i | ||||
\(813\) | − | 64.9150i | − | 0.0798462i | ||||||
\(814\) | 441.182 | − | 166.379i | 0.541993 | − | 0.204397i | ||||
\(815\) | −493.944 | − | 285.178i | −0.606066 | − | 0.349912i | ||||
\(816\) | −14.8867 | − | 35.6752i | −0.0182435 | − | 0.0437196i | ||||
\(817\) | 535.429 | − | 309.130i | 0.655360 | − | 0.378372i | ||||
\(818\) | 10.4311 | + | 1.71516i | 0.0127519 | + | 0.00209677i | ||||
\(819\) | −660.567 | + | 923.565i | −0.806553 | + | 1.12767i | ||||
\(820\) | 207.055 | − | 612.598i | 0.252506 | − | 0.747070i | ||||
\(821\) | −506.369 | + | 292.352i | −0.616771 | + | 0.356093i | −0.775611 | − | 0.631211i | \(-0.782558\pi\) |
0.158840 | + | 0.987304i | \(0.449225\pi\) | |||||||
\(822\) | −66.3940 | − | 54.4155i | −0.0807713 | − | 0.0661989i | ||||
\(823\) | −590.484 | + | 1022.75i | −0.717478 | + | 1.24271i | 0.244518 | + | 0.969645i | \(0.421370\pi\) |
−0.961996 | + | 0.273063i | \(0.911963\pi\) | |||||||
\(824\) | −5.50564 | − | 158.650i | −0.00668160 | − | 0.192537i | ||||
\(825\) | − | 24.4405i | − | 0.0296248i | ||||||
\(826\) | −1000.41 | + | 269.722i | −1.21115 | + | 0.326540i | ||||
\(827\) | 336.806i | 0.407262i | 0.979048 | + | 0.203631i | \(0.0652743\pi\) | ||||
−0.979048 | + | 0.203631i | \(0.934726\pi\) | |||||||
\(828\) | 30.1750 | + | 150.669i | 0.0364433 | + | 0.181967i | ||||
\(829\) | 184.145 | − | 318.949i | 0.222130 | − | 0.384740i | −0.733325 | − | 0.679878i | \(-0.762033\pi\) |
0.955454 | + | 0.295139i | \(0.0953658\pi\) | |||||||
\(830\) | 284.922 | + | 233.518i | 0.343280 | + | 0.281346i | ||||
\(831\) | 43.1479 | − | 24.9114i | 0.0519228 | − | 0.0299777i | ||||
\(832\) | −649.243 | − | 963.446i | −0.780340 | − | 1.15799i | ||||
\(833\) | 442.378 | − | 151.051i | 0.531066 | − | 0.181334i | ||||
\(834\) | −21.9011 | + | 133.196i | −0.0262603 | + | 0.159707i | ||||
\(835\) | −441.692 | + | 255.011i | −0.528972 | + | 0.305402i | ||||
\(836\) | 516.757 | + | 587.694i | 0.618131 | + | 0.702984i | ||||
\(837\) | 128.264 | + | 74.0530i | 0.153242 | + | 0.0884743i | ||||
\(838\) | 64.9658 | − | 24.5000i | 0.0775249 | − | 0.0292363i | ||||
\(839\) | 709.889i | 0.846113i | 0.906103 | + | 0.423056i | \(0.139043\pi\) | ||||
−0.906103 | + | 0.423056i | \(0.860957\pi\) | |||||||
\(840\) | 50.5570 | + | 3.16851i | 0.0601869 | + | 0.00377204i | ||||
\(841\) | 36.5402 | 0.0434485 | ||||||||
\(842\) | −278.294 | − | 737.943i | −0.330515 | − | 0.876417i | ||||
\(843\) | 8.90098 | − | 15.4169i | 0.0105587 | − | 0.0182882i | ||||
\(844\) | 332.448 | + | 378.084i | 0.393896 | + | 0.447967i | ||||
\(845\) | 286.685 | + | 496.553i | 0.339272 | + | 0.587637i | ||||
\(846\) | −896.854 | − | 147.468i | −1.06011 | − | 0.174312i | ||||
\(847\) | 239.695 | − | 335.128i | 0.282993 | − | 0.395664i | ||||
\(848\) | −609.668 | + | 798.858i | −0.718948 | + | 0.942049i | ||||
\(849\) | −37.6073 | − | 65.1377i | −0.0442960 | − | 0.0767229i | ||||
\(850\) | 148.065 | − | 180.659i | 0.174194 | − | 0.212540i | ||||
\(851\) | 111.347 | + | 64.2860i | 0.130842 | + | 0.0755417i | ||||
\(852\) | −1.06194 | − | 5.30246i | −0.00124641 | − | 0.00622354i | ||||
\(853\) | 1136.65 | 1.33253 | 0.666267 | − | 0.745713i | \(-0.267891\pi\) | ||||
0.666267 | + | 0.745713i | \(0.267891\pi\) | |||||||
\(854\) | −182.282 | + | 684.528i | −0.213445 | + | 0.801555i | ||||
\(855\) | 792.143 | 0.926483 | ||||||||
\(856\) | 2.53701 | + | 73.1064i | 0.00296380 | + | 0.0854047i | ||||
\(857\) | 578.645 | + | 334.081i | 0.675198 | + | 0.389826i | 0.798043 | − | 0.602600i | \(-0.205869\pi\) |
−0.122845 | + | 0.992426i | \(0.539202\pi\) | |||||||
\(858\) | −45.9442 | + | 56.0580i | −0.0535480 | + | 0.0653357i | ||||
\(859\) | 100.378 | + | 173.859i | 0.116854 | + | 0.202397i | 0.918519 | − | 0.395376i | \(-0.129386\pi\) |
−0.801665 | + | 0.597773i | \(0.796052\pi\) | |||||||
\(860\) | −113.960 | + | 337.166i | −0.132512 | + | 0.392054i | ||||
\(861\) | −7.79316 | + | 79.8582i | −0.00905129 | + | 0.0927506i | ||||
\(862\) | −140.100 | + | 852.045i | −0.162529 | + | 0.988451i | ||||
\(863\) | −21.7855 | − | 37.7337i | −0.0252440 | − | 0.0437238i | 0.853127 | − | 0.521703i | \(-0.174703\pi\) |
−0.878371 | + | 0.477979i | \(0.841370\pi\) | |||||||
\(864\) | −33.4701 | − | 141.450i | −0.0387385 | − | 0.163715i | ||||
\(865\) | −349.641 | + | 605.596i | −0.404209 | + | 0.700111i | ||||
\(866\) | 224.798 | + | 596.091i | 0.259582 | + | 0.688326i | ||||
\(867\) | 50.1422 | 0.0578342 | ||||||||
\(868\) | −533.410 | − | 740.917i | −0.614527 | − | 0.853591i | ||||
\(869\) | − | 812.533i | − | 0.935020i | ||||||
\(870\) | 18.1064 | + | 48.0122i | 0.0208120 | + | 0.0551864i | ||||
\(871\) | 1972.73 | + | 1138.95i | 2.26490 | + | 1.30764i | ||||
\(872\) | 808.797 | − | 505.148i | 0.927520 | − | 0.579298i | ||||
\(873\) | −364.056 | + | 210.188i | −0.417017 | + | 0.240765i | ||||
\(874\) | −34.6228 | + | 210.565i | −0.0396142 | + | 0.240921i | ||||
\(875\) | 385.052 | + | 847.808i | 0.440059 | + | 0.968923i | ||||
\(876\) | 8.86068 | − | 26.2154i | 0.0101149 | − | 0.0299263i | ||||
\(877\) | −129.242 | + | 74.6180i | −0.147368 | + | 0.0850832i | −0.571871 | − | 0.820343i | \(-0.693782\pi\) |
0.424503 | + | 0.905427i | \(0.360449\pi\) | |||||||
\(878\) | −779.964 | + | 951.659i | −0.888342 | + | 1.08389i | ||||
\(879\) | −17.1658 | + | 29.7321i | −0.0195288 | + | 0.0338249i | ||||
\(880\) | −446.791 | − | 57.6312i | −0.507717 | − | 0.0654900i | ||||
\(881\) | 865.257i | 0.982130i | 0.871123 | + | 0.491065i | \(0.163392\pi\) | ||||
−0.871123 | + | 0.491065i | \(0.836608\pi\) | |||||||
\(882\) | 863.666 | − | 144.762i | 0.979214 | − | 0.164130i | ||||
\(883\) | − | 1476.24i | − | 1.67184i | −0.548850 | − | 0.835921i | \(-0.684934\pi\) | ||
0.548850 | − | 0.835921i | \(-0.315066\pi\) | |||||||
\(884\) | −679.220 | + | 136.030i | −0.768348 | + | 0.153880i | ||||
\(885\) | −33.4736 | + | 57.9779i | −0.0378233 | + | 0.0655118i | ||||
\(886\) | 126.562 | − | 154.422i | 0.142846 | − | 0.174291i | ||||
\(887\) | −518.166 | + | 299.163i | −0.584178 | + | 0.337275i | −0.762792 | − | 0.646644i | \(-0.776172\pi\) |
0.178614 | + | 0.983919i | \(0.442839\pi\) | |||||||
\(888\) | −53.4951 | − | 28.4588i | −0.0602423 | − | 0.0320482i | ||||
\(889\) | −166.774 | − | 367.203i | −0.187597 | − | 0.413051i | ||||
\(890\) | −1084.34 | − | 178.297i | −1.21836 | − | 0.200333i | ||||
\(891\) | 541.172 | − | 312.446i | 0.607376 | − | 0.350669i | ||||
\(892\) | −23.6297 | − | 26.8735i | −0.0264907 | − | 0.0301272i | ||||
\(893\) | −1093.10 | − | 631.104i | −1.22408 | − | 0.706723i | ||||
\(894\) | −5.50829 | − | 14.6062i | −0.00616140 | − | 0.0163380i | ||||
\(895\) | 534.006i | 0.596655i | ||||||||
\(896\) | −169.984 | + | 879.728i | −0.189714 | + | 0.981839i | ||||
\(897\) | −19.7639 | −0.0220333 | ||||||||
\(898\) | 140.944 | − | 53.1530i | 0.156953 | − | 0.0591904i | ||||
\(899\) | 462.395 | − | 800.891i | 0.514343 | − | 0.890869i | ||||
\(900\) | 328.616 | − | 288.951i | 0.365129 | − | 0.321056i | ||||
\(901\) | 299.589 | + | 518.904i | 0.332508 | + | 0.575920i | ||||
\(902\) | 115.775 | − | 704.110i | 0.128354 | − | 0.780609i | ||||
\(903\) | 4.28926 | − | 43.9530i | 0.00475001 | − | 0.0486744i | ||||
\(904\) | 465.946 | − | 875.858i | 0.515428 | − | 0.968870i | ||||
\(905\) | 163.051 | + | 282.412i | 0.180167 | + | 0.312058i | ||||
\(906\) | 9.20202 | + | 7.54182i | 0.0101568 | + | 0.00832431i | ||||
\(907\) | 1463.00 | + | 844.666i | 1.61301 | + | 0.931274i | 0.988667 | + | 0.150128i | \(0.0479687\pi\) |
0.624348 | + | 0.781146i | \(0.285365\pi\) | |||||||
\(908\) | −214.200 | − | 1069.54i | −0.235904 | − | 1.17790i | ||||
\(909\) | −1334.53 | −1.46813 | ||||||||
\(910\) | 233.579 | − | 877.167i | 0.256681 | − | 0.963920i | ||||
\(911\) | −813.339 | −0.892798 | −0.446399 | − | 0.894834i | \(-0.647294\pi\) | ||||
−0.446399 | + | 0.894834i | \(0.647294\pi\) | |||||||
\(912\) | 12.8657 | − | 99.7422i | 0.0141071 | − | 0.109366i | ||||
\(913\) | 352.052 | + | 203.257i | 0.385599 | + | 0.222626i | ||||
\(914\) | −323.127 | − | 264.830i | −0.353531 | − | 0.289748i | ||||
\(915\) | 22.8852 | + | 39.6382i | 0.0250111 | + | 0.0433205i | ||||
\(916\) | −1255.13 | − | 424.228i | −1.37023 | − | 0.463131i | ||||
\(917\) | 506.178 | − | 707.708i | 0.551993 | − | 0.771764i | ||||
\(918\) | −85.5191 | − | 14.0617i | −0.0931581 | − | 0.0153178i | ||||
\(919\) | −751.489 | − | 1301.62i | −0.817724 | − | 1.41634i | −0.907355 | − | 0.420365i | \(-0.861902\pi\) |
0.0896310 | − | 0.995975i | \(-0.471431\pi\) | |||||||
\(920\) | −65.0728 | − | 104.189i | −0.0707313 | − | 0.113249i | ||||
\(921\) | −9.64971 | + | 16.7138i | −0.0104774 | + | 0.0181474i | ||||
\(922\) | 1406.25 | − | 530.325i | 1.52521 | − | 0.575190i | ||||
\(923\) | −96.9043 | −0.104988 | ||||||||
\(924\) | 55.6172 | − | 5.60166i | 0.0601918 | − | 0.00606241i | ||||
\(925\) | − | 366.139i | − | 0.395826i | ||||||
\(926\) | 6.66340 | − | 2.51291i | 0.00719590 | − | 0.00271373i | ||||
\(927\) | −153.560 | − | 88.6581i | −0.165653 | − | 0.0956398i | ||||
\(928\) | −883.227 | + | 208.991i | −0.951753 | + | 0.225205i | ||||
\(929\) | −1301.71 | + | 751.543i | −1.40120 | + | 0.808981i | −0.994515 | − | 0.104589i | \(-0.966647\pi\) |
−0.406681 | + | 0.913570i | \(0.633314\pi\) | |||||||
\(930\) | −58.2066 | − | 9.57080i | −0.0625877 | − | 0.0102912i | ||||
\(931\) | 1193.18 | + | 235.118i | 1.28161 | + | 0.252543i | ||||
\(932\) | −599.623 | − | 202.669i | −0.643373 | − | 0.217456i | ||||
\(933\) | 43.4471 | − | 25.0842i | 0.0465671 | − | 0.0268855i | ||||
\(934\) | −640.227 | − | 524.720i | −0.685468 | − | 0.561798i | ||||
\(935\) | −134.302 | + | 232.618i | −0.143638 | + | 0.248789i | ||||
\(936\) | −1296.91 | + | 45.0068i | −1.38559 | + | 0.0480842i | ||||
\(937\) | − | 419.349i | − | 0.447545i | −0.974641 | − | 0.223772i | \(-0.928163\pi\) | ||
0.974641 | − | 0.223772i | \(-0.0718372\pi\) | |||||||
\(938\) | −457.319 | − | 1696.21i | −0.487547 | − | 1.80833i | ||||
\(939\) | − | 14.0279i | − | 0.0149392i | ||||||
\(940\) | 712.449 | − | 142.685i | 0.757924 | − | 0.151792i | ||||
\(941\) | −261.680 | + | 453.243i | −0.278087 | + | 0.481661i | −0.970909 | − | 0.239448i | \(-0.923034\pi\) |
0.692822 | + | 0.721108i | \(0.256367\pi\) | |||||||
\(942\) | 49.9987 | + | 40.9781i | 0.0530772 | + | 0.0435012i | ||||
\(943\) | 168.507 | − | 97.2874i | 0.178692 | − | 0.103168i | ||||
\(944\) | −941.336 | − | 718.404i | −0.997178 | − | 0.761021i | ||||
\(945\) | 66.0695 | − | 92.3744i | 0.0699148 | − | 0.0977507i | ||||
\(946\) | −63.7214 | + | 387.533i | −0.0673588 | + | 0.409655i | ||||
\(947\) | 311.949 | − | 180.104i | 0.329408 | − | 0.190184i | −0.326170 | − | 0.945311i | \(-0.605758\pi\) |
0.655578 | + | 0.755127i | \(0.272425\pi\) | |||||||
\(948\) | −78.4157 | + | 68.9506i | −0.0827170 | + | 0.0727327i | ||||
\(949\) | −429.441 | − | 247.938i | −0.452520 | − | 0.261262i | ||||
\(950\) | 568.596 | − | 214.430i | 0.598522 | − | 0.225715i | ||||
\(951\) | − | 75.7642i | − | 0.0796679i | ||||||
\(952\) | 445.047 | + | 295.533i | 0.467486 | + | 0.310434i | ||||
\(953\) | 1242.81 | 1.30410 | 0.652051 | − | 0.758175i | \(-0.273909\pi\) | ||||
0.652051 | + | 0.758175i | \(0.273909\pi\) | |||||||
\(954\) | 396.081 | + | 1050.28i | 0.415180 | + | 1.10092i | ||||
\(955\) | 49.6976 | − | 86.0789i | 0.0520394 | − | 0.0901349i | ||||
\(956\) | 147.186 | − | 129.420i | 0.153960 | − | 0.135376i | ||||
\(957\) | 28.3116 | + | 49.0372i | 0.0295838 | + | 0.0512406i | ||||
\(958\) | 1790.68 | + | 294.438i | 1.86918 | + | 0.307346i | ||||
\(959\) | 1180.76 | + | 115.227i | 1.23124 | + | 0.120153i | ||||
\(960\) | 32.3524 | + | 48.0094i | 0.0337004 | + | 0.0500098i | ||||
\(961\) | 51.0585 | + | 88.4359i | 0.0531306 | + | 0.0920248i | ||||
\(962\) | −688.284 | + | 839.797i | −0.715472 | + | 0.872970i | ||||
\(963\) | 70.7610 | + | 40.8539i | 0.0734798 | + | 0.0424236i | ||||
\(964\) | 774.046 | − | 155.021i | 0.802952 | − | 0.160810i | ||||
\(965\) | −865.742 | −0.897142 | ||||||||
\(966\) | 10.7947 | + | 10.7613i | 0.0111747 | + | 0.0111401i | ||||
\(967\) | 81.8793 | 0.0846735 | 0.0423368 | − | 0.999103i | \(-0.486520\pi\) | ||||
0.0423368 | + | 0.999103i | \(0.486520\pi\) | |||||||
\(968\) | 470.602 | − | 16.3313i | 0.486159 | − | 0.0168712i | ||||
\(969\) | −51.9298 | − | 29.9817i | −0.0535912 | − | 0.0309409i | ||||
\(970\) | 213.023 | − | 259.917i | 0.219612 | − | 0.267955i | ||||
\(971\) | −409.052 | − | 708.499i | −0.421269 | − | 0.729660i | 0.574795 | − | 0.818298i | \(-0.305082\pi\) |
−0.996064 | + | 0.0886380i | \(0.971749\pi\) | |||||||
\(972\) | −230.992 | − | 78.0742i | −0.237646 | − | 0.0803232i | ||||
\(973\) | −771.419 | − | 1698.51i | −0.792825 | − | 1.74564i | ||||
\(974\) | 273.522 | − | 1663.47i | 0.280823 | − | 1.70788i | ||||
\(975\) | 28.1412 | + | 48.7419i | 0.0288627 | + | 0.0499917i | ||||
\(976\) | −747.140 | + | 311.770i | −0.765512 | + | 0.319437i | ||||
\(977\) | −448.155 | + | 776.227i | −0.458705 | + | 0.794500i | −0.998893 | − | 0.0470441i | \(-0.985020\pi\) |
0.540188 | + | 0.841544i | \(0.318353\pi\) | |||||||
\(978\) | 28.5402 | + | 75.6793i | 0.0291823 | + | 0.0773817i | ||||
\(979\) | −1212.63 | −1.23864 | ||||||||
\(980\) | −605.189 | + | 351.912i | −0.617540 | + | 0.359094i | ||||
\(981\) | − | 1065.14i | − | 1.08577i | ||||||
\(982\) | −101.713 | − | 269.710i | −0.103578 | − | 0.274654i | ||||
\(983\) | 852.404 | + | 492.136i | 0.867146 | + | 0.500647i | 0.866399 | − | 0.499353i | \(-0.166429\pi\) |
0.000746983 | 1.00000i | \(0.499762\pi\) | ||||||||
\(984\) | −77.7767 | + | 48.5767i | −0.0790413 | + | 0.0493666i | ||||
\(985\) | −292.947 | + | 169.133i | −0.297408 | + | 0.171708i | ||||
\(986\) | −87.8030 | + | 533.990i | −0.0890497 | + | 0.541572i | ||||
\(987\) | −82.0887 | + | 37.2825i | −0.0831699 | + | 0.0377736i | ||||
\(988\) | −1707.26 | − | 577.044i | −1.72799 | − | 0.584052i | ||||
\(989\) | −92.7440 | + | 53.5458i | −0.0937756 | + | 0.0541414i | ||||
\(990\) | −318.967 | + | 389.182i | −0.322189 | + | 0.393113i | ||||
\(991\) | 612.037 | − | 1060.08i | 0.617596 | − | 1.06971i | −0.372327 | − | 0.928101i | \(-0.621440\pi\) |
0.989923 | − | 0.141606i | \(-0.0452265\pi\) | |||||||
\(992\) | 299.606 | − | 999.434i | 0.302022 | − | 1.00749i | ||||
\(993\) | 95.0667i | 0.0957368i | ||||||||
\(994\) | 52.9276 | + | 52.7637i | 0.0532471 | + | 0.0530822i | ||||
\(995\) | 1104.24i | 1.10979i | ||||||||
\(996\) | −10.2588 | − | 51.2240i | −0.0103000 | − | 0.0514297i | ||||
\(997\) | −186.825 | + | 323.590i | −0.187387 | + | 0.324563i | −0.944378 | − | 0.328861i | \(-0.893335\pi\) |
0.756991 | + | 0.653425i | \(0.226668\pi\) | |||||||
\(998\) | −483.235 | + | 589.610i | −0.484203 | + | 0.590792i | ||||
\(999\) | −117.650 | + | 67.9254i | −0.117768 | + | 0.0679934i |
(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 | 56.3.j.a.45.2 | yes | 28 | |
4.3 | odd | 2 | 224.3.n.a.17.8 | 28 | |||
7.2 | even | 3 | 392.3.j.e.117.12 | 28 | |||
7.3 | odd | 6 | 392.3.h.a.293.13 | 28 | |||
7.4 | even | 3 | 392.3.h.a.293.14 | 28 | |||
7.5 | odd | 6 | inner | 56.3.j.a.5.12 | yes | 28 | |
7.6 | odd | 2 | 392.3.j.e.325.2 | 28 | |||
8.3 | odd | 2 | 224.3.n.a.17.7 | 28 | |||
8.5 | even | 2 | inner | 56.3.j.a.45.12 | yes | 28 | |
28.3 | even | 6 | 1568.3.h.a.881.15 | 28 | |||
28.11 | odd | 6 | 1568.3.h.a.881.13 | 28 | |||
28.19 | even | 6 | 224.3.n.a.145.7 | 28 | |||
56.3 | even | 6 | 1568.3.h.a.881.14 | 28 | |||
56.5 | odd | 6 | inner | 56.3.j.a.5.2 | ✓ | 28 | |
56.11 | odd | 6 | 1568.3.h.a.881.16 | 28 | |||
56.13 | odd | 2 | 392.3.j.e.325.12 | 28 | |||
56.19 | even | 6 | 224.3.n.a.145.8 | 28 | |||
56.37 | even | 6 | 392.3.j.e.117.2 | 28 | |||
56.45 | odd | 6 | 392.3.h.a.293.16 | 28 | |||
56.53 | even | 6 | 392.3.h.a.293.15 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.j.a.5.2 | ✓ | 28 | 56.5 | odd | 6 | inner | |
56.3.j.a.5.12 | yes | 28 | 7.5 | odd | 6 | inner | |
56.3.j.a.45.2 | yes | 28 | 1.1 | even | 1 | trivial | |
56.3.j.a.45.12 | yes | 28 | 8.5 | even | 2 | inner | |
224.3.n.a.17.7 | 28 | 8.3 | odd | 2 | |||
224.3.n.a.17.8 | 28 | 4.3 | odd | 2 | |||
224.3.n.a.145.7 | 28 | 28.19 | even | 6 | |||
224.3.n.a.145.8 | 28 | 56.19 | even | 6 | |||
392.3.h.a.293.13 | 28 | 7.3 | odd | 6 | |||
392.3.h.a.293.14 | 28 | 7.4 | even | 3 | |||
392.3.h.a.293.15 | 28 | 56.53 | even | 6 | |||
392.3.h.a.293.16 | 28 | 56.45 | odd | 6 | |||
392.3.j.e.117.2 | 28 | 56.37 | even | 6 | |||
392.3.j.e.117.12 | 28 | 7.2 | even | 3 | |||
392.3.j.e.325.2 | 28 | 7.6 | odd | 2 | |||
392.3.j.e.325.12 | 28 | 56.13 | odd | 2 | |||
1568.3.h.a.881.13 | 28 | 28.11 | odd | 6 | |||
1568.3.h.a.881.14 | 28 | 56.3 | even | 6 | |||
1568.3.h.a.881.15 | 28 | 28.3 | even | 6 | |||
1568.3.h.a.881.16 | 28 | 56.11 | odd | 6 |