Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(119,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.119");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 119.61 | ||
Character | \(\chi\) | \(=\) | 177.119 |
Dual form | 177.5.b.a.119.18 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.04906i | 1.26227i | 0.775675 | + | 0.631133i | \(0.217410\pi\) | ||||
−0.775675 | + | 0.631133i | \(0.782590\pi\) | |||||||
\(3\) | −3.85410 | + | 8.13301i | −0.428233 | + | 0.903668i | ||||
\(4\) | −9.49305 | −0.593316 | ||||||||
\(5\) | − | 33.9624i | − | 1.35850i | −0.733909 | − | 0.679248i | \(-0.762306\pi\) | ||
0.733909 | − | 0.679248i | \(-0.237694\pi\) | |||||||
\(6\) | −41.0641 | − | 19.4596i | −1.14067 | − | 0.540544i | ||||
\(7\) | 88.4932 | 1.80598 | 0.902992 | − | 0.429657i | \(-0.141366\pi\) | ||||
0.902992 | + | 0.429657i | \(0.141366\pi\) | |||||||
\(8\) | 32.8540i | 0.513344i | ||||||||
\(9\) | −51.2919 | − | 62.6909i | −0.633233 | − | 0.773961i | ||||
\(10\) | 171.478 | 1.71478 | ||||||||
\(11\) | 111.430i | 0.920906i | 0.887684 | + | 0.460453i | \(0.152313\pi\) | ||||
−0.887684 | + | 0.460453i | \(0.847687\pi\) | |||||||
\(12\) | 36.5871 | − | 77.2071i | 0.254077 | − | 0.536161i | ||||
\(13\) | 6.16984 | 0.0365079 | 0.0182539 | − | 0.999833i | \(-0.494189\pi\) | ||||
0.0182539 | + | 0.999833i | \(0.494189\pi\) | |||||||
\(14\) | 446.808i | 2.27963i | ||||||||
\(15\) | 276.217 | + | 130.894i | 1.22763 | + | 0.581753i | ||||
\(16\) | −317.771 | −1.24129 | ||||||||
\(17\) | 288.710i | 0.998996i | 0.866315 | + | 0.499498i | \(0.166482\pi\) | ||||
−0.866315 | + | 0.499498i | \(0.833518\pi\) | |||||||
\(18\) | 316.530 | − | 258.976i | 0.976945 | − | 0.799308i | ||||
\(19\) | 261.438 | 0.724205 | 0.362103 | − | 0.932138i | \(-0.382059\pi\) | ||||
0.362103 | + | 0.932138i | \(0.382059\pi\) | |||||||
\(20\) | 322.407i | 0.806017i | ||||||||
\(21\) | −341.062 | + | 719.717i | −0.773382 | + | 1.63201i | ||||
\(22\) | −562.615 | −1.16243 | ||||||||
\(23\) | 401.655i | 0.759273i | 0.925136 | + | 0.379636i | \(0.123951\pi\) | ||||
−0.925136 | + | 0.379636i | \(0.876049\pi\) | |||||||
\(24\) | −267.202 | − | 126.623i | −0.463893 | − | 0.219831i | ||||
\(25\) | −528.444 | −0.845511 | ||||||||
\(26\) | 31.1519i | 0.0460827i | ||||||||
\(27\) | 707.550 | − | 175.541i | 0.970576 | − | 0.240797i | ||||
\(28\) | −840.071 | −1.07152 | ||||||||
\(29\) | 696.014i | 0.827603i | 0.910367 | + | 0.413801i | \(0.135799\pi\) | ||||
−0.910367 | + | 0.413801i | \(0.864201\pi\) | |||||||
\(30\) | −660.894 | + | 1394.64i | −0.734327 | + | 1.54960i | ||||
\(31\) | 1230.65 | 1.28059 | 0.640295 | − | 0.768129i | \(-0.278812\pi\) | ||||
0.640295 | + | 0.768129i | \(0.278812\pi\) | |||||||
\(32\) | − | 1078.78i | − | 1.05350i | ||||||
\(33\) | −906.259 | − | 429.461i | −0.832194 | − | 0.394362i | ||||
\(34\) | −1457.71 | −1.26100 | ||||||||
\(35\) | − | 3005.44i | − | 2.45342i | ||||||
\(36\) | 486.916 | + | 595.128i | 0.375707 | + | 0.459203i | ||||
\(37\) | −1133.89 | −0.828264 | −0.414132 | − | 0.910217i | \(-0.635915\pi\) | ||||
−0.414132 | + | 0.910217i | \(0.635915\pi\) | |||||||
\(38\) | 1320.02i | 0.914140i | ||||||||
\(39\) | −23.7791 | + | 50.1794i | −0.0156339 | + | 0.0329910i | ||||
\(40\) | 1115.80 | 0.697375 | ||||||||
\(41\) | − | 1509.67i | − | 0.898081i | −0.893511 | − | 0.449040i | \(-0.851766\pi\) | ||
0.893511 | − | 0.449040i | \(-0.148234\pi\) | |||||||
\(42\) | −3633.90 | − | 1722.04i | −2.06003 | − | 0.976214i | ||||
\(43\) | −1234.10 | −0.667443 | −0.333722 | − | 0.942672i | \(-0.608305\pi\) | ||||
−0.333722 | + | 0.942672i | \(0.608305\pi\) | |||||||
\(44\) | − | 1057.81i | − | 0.546388i | ||||||
\(45\) | −2129.13 | + | 1741.99i | −1.05142 | + | 0.860244i | ||||
\(46\) | −2027.98 | −0.958405 | ||||||||
\(47\) | − | 148.995i | − | 0.0674489i | −0.999431 | − | 0.0337244i | \(-0.989263\pi\) | ||
0.999431 | − | 0.0337244i | \(-0.0107369\pi\) | |||||||
\(48\) | 1224.72 | − | 2584.43i | 0.531562 | − | 1.12172i | ||||
\(49\) | 5430.05 | 2.26158 | ||||||||
\(50\) | − | 2668.15i | − | 1.06726i | ||||||
\(51\) | −2348.08 | − | 1112.72i | −0.902761 | − | 0.427803i | ||||
\(52\) | −58.5706 | −0.0216607 | ||||||||
\(53\) | 4971.34i | 1.76979i | 0.465792 | + | 0.884894i | \(0.345769\pi\) | ||||
−0.465792 | + | 0.884894i | \(0.654231\pi\) | |||||||
\(54\) | 886.317 | + | 3572.46i | 0.303950 | + | 1.22512i | ||||
\(55\) | 3784.42 | 1.25105 | ||||||||
\(56\) | 2907.36i | 0.927091i | ||||||||
\(57\) | −1007.61 | + | 2126.28i | −0.310129 | + | 0.654441i | ||||
\(58\) | −3514.22 | −1.04465 | ||||||||
\(59\) | 453.188i | 0.130189i | ||||||||
\(60\) | −2622.14 | − | 1242.59i | −0.728372 | − | 0.345163i | ||||
\(61\) | 2566.52 | 0.689740 | 0.344870 | − | 0.938651i | \(-0.387923\pi\) | ||||
0.344870 | + | 0.938651i | \(0.387923\pi\) | |||||||
\(62\) | 6213.62i | 1.61645i | ||||||||
\(63\) | −4538.98 | − | 5547.72i | −1.14361 | − | 1.39776i | ||||
\(64\) | 362.503 | 0.0885017 | ||||||||
\(65\) | − | 209.542i | − | 0.0495958i | ||||||
\(66\) | 2168.37 | − | 4575.76i | 0.497790 | − | 1.05045i | ||||
\(67\) | −7694.85 | −1.71416 | −0.857079 | − | 0.515185i | \(-0.827723\pi\) | ||||
−0.857079 | + | 0.515185i | \(0.827723\pi\) | |||||||
\(68\) | − | 2740.74i | − | 0.592720i | ||||||
\(69\) | −3266.67 | − | 1548.02i | −0.686131 | − | 0.325146i | ||||
\(70\) | 15174.7 | 3.09687 | ||||||||
\(71\) | 7593.28i | 1.50630i | 0.657846 | + | 0.753152i | \(0.271468\pi\) | ||||
−0.657846 | + | 0.753152i | \(0.728532\pi\) | |||||||
\(72\) | 2059.65 | − | 1685.14i | 0.397308 | − | 0.325066i | ||||
\(73\) | −4759.98 | −0.893221 | −0.446611 | − | 0.894728i | \(-0.647369\pi\) | ||||
−0.446611 | + | 0.894728i | \(0.647369\pi\) | |||||||
\(74\) | − | 5725.10i | − | 1.04549i | ||||||
\(75\) | 2036.68 | − | 4297.84i | 0.362076 | − | 0.764061i | ||||
\(76\) | −2481.85 | −0.429682 | ||||||||
\(77\) | 9860.77i | 1.66314i | ||||||||
\(78\) | −253.359 | − | 120.062i | −0.0416435 | − | 0.0197341i | ||||
\(79\) | 8166.54 | 1.30853 | 0.654266 | − | 0.756265i | \(-0.272978\pi\) | ||||
0.654266 | + | 0.756265i | \(0.272978\pi\) | |||||||
\(80\) | 10792.3i | 1.68629i | ||||||||
\(81\) | −1299.29 | + | 6431.06i | −0.198032 | + | 0.980196i | ||||
\(82\) | 7622.44 | 1.13362 | ||||||||
\(83\) | − | 7869.62i | − | 1.14235i | −0.820830 | − | 0.571173i | \(-0.806489\pi\) | ||
0.820830 | − | 0.571173i | \(-0.193511\pi\) | |||||||
\(84\) | 3237.71 | − | 6832.31i | 0.458860 | − | 0.968298i | ||||
\(85\) | 9805.27 | 1.35713 | ||||||||
\(86\) | − | 6231.06i | − | 0.842491i | ||||||
\(87\) | −5660.69 | − | 2682.50i | −0.747878 | − | 0.354407i | ||||
\(88\) | −3660.91 | −0.472741 | ||||||||
\(89\) | − | 5351.59i | − | 0.675620i | −0.941214 | − | 0.337810i | \(-0.890314\pi\) | ||
0.941214 | − | 0.337810i | \(-0.109686\pi\) | |||||||
\(90\) | −8795.44 | − | 10750.1i | −1.08586 | − | 1.32718i | ||||
\(91\) | 545.989 | 0.0659327 | ||||||||
\(92\) | − | 3812.94i | − | 0.450489i | ||||||
\(93\) | −4743.04 | + | 10008.9i | −0.548391 | + | 1.15723i | ||||
\(94\) | 752.283 | 0.0851384 | ||||||||
\(95\) | − | 8879.07i | − | 0.983830i | ||||||
\(96\) | 8773.74 | + | 4157.73i | 0.952012 | + | 0.451142i | ||||
\(97\) | −7987.92 | −0.848966 | −0.424483 | − | 0.905436i | \(-0.639544\pi\) | ||||
−0.424483 | + | 0.905436i | \(0.639544\pi\) | |||||||
\(98\) | 27416.7i | 2.85472i | ||||||||
\(99\) | 6985.62 | − | 5715.43i | 0.712746 | − | 0.583148i | ||||
\(100\) | 5016.55 | 0.501655 | ||||||||
\(101\) | 3277.52i | 0.321294i | 0.987012 | + | 0.160647i | \(0.0513580\pi\) | ||||
−0.987012 | + | 0.160647i | \(0.948642\pi\) | |||||||
\(102\) | 5618.17 | − | 11855.6i | 0.540001 | − | 1.13952i | ||||
\(103\) | 14838.0 | 1.39862 | 0.699310 | − | 0.714819i | \(-0.253491\pi\) | ||||
0.699310 | + | 0.714819i | \(0.253491\pi\) | |||||||
\(104\) | 202.704i | 0.0187411i | ||||||||
\(105\) | 24443.3 | + | 11583.3i | 2.21708 | + | 1.05064i | ||||
\(106\) | −25100.6 | −2.23394 | ||||||||
\(107\) | − | 3771.28i | − | 0.329398i | −0.986344 | − | 0.164699i | \(-0.947335\pi\) | ||
0.986344 | − | 0.164699i | \(-0.0526653\pi\) | |||||||
\(108\) | −6716.80 | + | 1666.42i | −0.575858 | + | 0.142868i | ||||
\(109\) | 17882.7 | 1.50515 | 0.752577 | − | 0.658504i | \(-0.228810\pi\) | ||||
0.752577 | + | 0.658504i | \(0.228810\pi\) | |||||||
\(110\) | 19107.8i | 1.57915i | ||||||||
\(111\) | 4370.14 | − | 9221.97i | 0.354690 | − | 0.748476i | ||||
\(112\) | −28120.6 | −2.24175 | ||||||||
\(113\) | 2411.73i | 0.188874i | 0.995531 | + | 0.0944370i | \(0.0301051\pi\) | ||||
−0.995531 | + | 0.0944370i | \(0.969895\pi\) | |||||||
\(114\) | −10735.7 | − | 5087.48i | −0.826079 | − | 0.391465i | ||||
\(115\) | 13641.2 | 1.03147 | ||||||||
\(116\) | − | 6607.29i | − | 0.491030i | ||||||
\(117\) | −316.462 | − | 386.792i | −0.0231180 | − | 0.0282557i | ||||
\(118\) | −2288.17 | −0.164333 | ||||||||
\(119\) | 25548.9i | 1.80417i | ||||||||
\(120\) | −4300.40 | + | 9074.82i | −0.298639 | + | 0.630196i | ||||
\(121\) | 2224.44 | 0.151932 | ||||||||
\(122\) | 12958.5i | 0.870635i | ||||||||
\(123\) | 12278.2 | + | 5818.43i | 0.811567 | + | 0.384588i | ||||
\(124\) | −11682.6 | −0.759794 | ||||||||
\(125\) | − | 3279.27i | − | 0.209873i | ||||||
\(126\) | 28010.8 | − | 22917.6i | 1.76435 | − | 1.44354i | ||||
\(127\) | 3307.85 | 0.205087 | 0.102543 | − | 0.994729i | \(-0.467302\pi\) | ||||
0.102543 | + | 0.994729i | \(0.467302\pi\) | |||||||
\(128\) | − | 15430.2i | − | 0.941785i | ||||||
\(129\) | 4756.35 | − | 10037.0i | 0.285821 | − | 0.603147i | ||||
\(130\) | 1057.99 | 0.0626031 | ||||||||
\(131\) | − | 24056.8i | − | 1.40183i | −0.713245 | − | 0.700915i | \(-0.752775\pi\) | ||
0.713245 | − | 0.700915i | \(-0.247225\pi\) | |||||||
\(132\) | 8603.16 | + | 4076.89i | 0.493754 | + | 0.233981i | ||||
\(133\) | 23135.5 | 1.30790 | ||||||||
\(134\) | − | 38851.8i | − | 2.16372i | ||||||
\(135\) | −5961.79 | − | 24030.1i | −0.327121 | − | 1.31852i | ||||
\(136\) | −9485.27 | −0.512828 | ||||||||
\(137\) | − | 15669.2i | − | 0.834845i | −0.908713 | − | 0.417422i | \(-0.862934\pi\) | ||
0.908713 | − | 0.417422i | \(-0.137066\pi\) | |||||||
\(138\) | 7816.05 | − | 16493.6i | 0.410421 | − | 0.866080i | ||||
\(139\) | 22577.2 | 1.16853 | 0.584267 | − | 0.811562i | \(-0.301382\pi\) | ||||
0.584267 | + | 0.811562i | \(0.301382\pi\) | |||||||
\(140\) | 28530.8i | 1.45565i | ||||||||
\(141\) | 1211.77 | + | 574.239i | 0.0609514 | + | 0.0288838i | ||||
\(142\) | −38339.0 | −1.90136 | ||||||||
\(143\) | 687.502i | 0.0336203i | ||||||||
\(144\) | 16299.1 | + | 19921.3i | 0.786027 | + | 0.960712i | ||||
\(145\) | 23638.3 | 1.12429 | ||||||||
\(146\) | − | 24033.4i | − | 1.12748i | ||||||
\(147\) | −20928.0 | + | 44162.7i | −0.968483 | + | 2.04372i | ||||
\(148\) | 10764.1 | 0.491422 | ||||||||
\(149\) | 1485.69i | 0.0669201i | 0.999440 | + | 0.0334600i | \(0.0106526\pi\) | ||||
−0.999440 | + | 0.0334600i | \(0.989347\pi\) | |||||||
\(150\) | 21700.1 | + | 10283.3i | 0.964449 | + | 0.457036i | ||||
\(151\) | −20410.8 | −0.895170 | −0.447585 | − | 0.894241i | \(-0.647716\pi\) | ||||
−0.447585 | + | 0.894241i | \(0.647716\pi\) | |||||||
\(152\) | 8589.29i | 0.371766i | ||||||||
\(153\) | 18099.5 | − | 14808.5i | 0.773184 | − | 0.632597i | ||||
\(154\) | −49787.7 | −2.09933 | ||||||||
\(155\) | − | 41795.7i | − | 1.73968i | ||||||
\(156\) | 225.737 | − | 476.355i | 0.00927583 | − | 0.0195741i | ||||
\(157\) | −45940.4 | −1.86378 | −0.931891 | − | 0.362738i | \(-0.881842\pi\) | ||||
−0.931891 | + | 0.362738i | \(0.881842\pi\) | |||||||
\(158\) | 41233.4i | 1.65171i | ||||||||
\(159\) | −40431.9 | − | 19160.0i | −1.59930 | − | 0.757882i | ||||
\(160\) | −36638.0 | −1.43117 | ||||||||
\(161\) | 35543.8i | 1.37124i | ||||||||
\(162\) | −32470.9 | − | 6560.19i | −1.23727 | − | 0.249969i | ||||
\(163\) | 25058.4 | 0.943145 | 0.471573 | − | 0.881827i | \(-0.343687\pi\) | ||||
0.471573 | + | 0.881827i | \(0.343687\pi\) | |||||||
\(164\) | 14331.4i | 0.532846i | ||||||||
\(165\) | −14585.5 | + | 30778.7i | −0.535740 | + | 1.13053i | ||||
\(166\) | 39734.2 | 1.44194 | ||||||||
\(167\) | 32413.6i | 1.16224i | 0.813819 | + | 0.581118i | \(0.197385\pi\) | ||||
−0.813819 | + | 0.581118i | \(0.802615\pi\) | |||||||
\(168\) | −23645.6 | − | 11205.2i | −0.837783 | − | 0.397011i | ||||
\(169\) | −28522.9 | −0.998667 | ||||||||
\(170\) | 49507.5i | 1.71306i | ||||||||
\(171\) | −13409.7 | − | 16389.8i | −0.458591 | − | 0.560507i | ||||
\(172\) | 11715.4 | 0.396005 | ||||||||
\(173\) | − | 55290.6i | − | 1.84739i | −0.383126 | − | 0.923696i | \(-0.625153\pi\) | ||
0.383126 | − | 0.923696i | \(-0.374847\pi\) | |||||||
\(174\) | 13544.1 | − | 28581.2i | 0.447356 | − | 0.944021i | ||||
\(175\) | −46763.7 | −1.52698 | ||||||||
\(176\) | − | 35409.1i | − | 1.14311i | ||||||
\(177\) | −3685.78 | − | 1746.63i | −0.117648 | − | 0.0557512i | ||||
\(178\) | 27020.5 | 0.852812 | ||||||||
\(179\) | 17012.3i | 0.530955i | 0.964117 | + | 0.265477i | \(0.0855295\pi\) | ||||
−0.964117 | + | 0.265477i | \(0.914470\pi\) | |||||||
\(180\) | 20212.0 | − | 16536.8i | 0.623826 | − | 0.510396i | ||||
\(181\) | 17714.0 | 0.540703 | 0.270352 | − | 0.962762i | \(-0.412860\pi\) | ||||
0.270352 | + | 0.962762i | \(0.412860\pi\) | |||||||
\(182\) | 2756.73i | 0.0832246i | ||||||||
\(183\) | −9891.62 | + | 20873.6i | −0.295369 | + | 0.623296i | ||||
\(184\) | −13196.0 | −0.389768 | ||||||||
\(185\) | 38509.7i | 1.12519i | ||||||||
\(186\) | −50535.5 | − | 23947.9i | −1.46073 | − | 0.692216i | ||||
\(187\) | −32170.8 | −0.919981 | ||||||||
\(188\) | 1414.41i | 0.0400185i | ||||||||
\(189\) | 62613.4 | − | 15534.2i | 1.75284 | − | 0.434875i | ||||
\(190\) | 44831.0 | 1.24186 | ||||||||
\(191\) | − | 48580.3i | − | 1.33166i | −0.746103 | − | 0.665830i | \(-0.768077\pi\) | ||
0.746103 | − | 0.665830i | \(-0.231923\pi\) | |||||||
\(192\) | −1397.12 | + | 2948.24i | −0.0378993 | + | 0.0799761i | ||||
\(193\) | 32320.8 | 0.867697 | 0.433848 | − | 0.900986i | \(-0.357155\pi\) | ||||
0.433848 | + | 0.900986i | \(0.357155\pi\) | |||||||
\(194\) | − | 40331.5i | − | 1.07162i | ||||||
\(195\) | 1704.21 | + | 807.597i | 0.0448182 | + | 0.0212386i | ||||
\(196\) | −51547.8 | −1.34183 | ||||||||
\(197\) | 24102.9i | 0.621066i | 0.950563 | + | 0.310533i | \(0.100507\pi\) | ||||
−0.950563 | + | 0.310533i | \(0.899493\pi\) | |||||||
\(198\) | 28857.6 | + | 35270.8i | 0.736088 | + | 0.899675i | ||||
\(199\) | 42180.4 | 1.06513 | 0.532567 | − | 0.846388i | \(-0.321228\pi\) | ||||
0.532567 | + | 0.846388i | \(0.321228\pi\) | |||||||
\(200\) | − | 17361.5i | − | 0.434038i | ||||||
\(201\) | 29656.7 | − | 62582.4i | 0.734059 | − | 1.54903i | ||||
\(202\) | −16548.4 | −0.405558 | ||||||||
\(203\) | 61592.5i | 1.49464i | ||||||||
\(204\) | 22290.5 | + | 10563.1i | 0.535622 | + | 0.253822i | ||||
\(205\) | −51272.1 | −1.22004 | ||||||||
\(206\) | 74917.8i | 1.76543i | ||||||||
\(207\) | 25180.1 | − | 20601.7i | 0.587648 | − | 0.480797i | ||||
\(208\) | −1960.59 | −0.0453170 | ||||||||
\(209\) | 29132.0i | 0.666925i | ||||||||
\(210\) | −58484.7 | + | 123416.i | −1.32618 | + | 2.79854i | ||||
\(211\) | −40533.0 | −0.910425 | −0.455212 | − | 0.890383i | \(-0.650437\pi\) | ||||
−0.455212 | + | 0.890383i | \(0.650437\pi\) | |||||||
\(212\) | − | 47193.1i | − | 1.05004i | ||||||
\(213\) | −61756.3 | − | 29265.2i | −1.36120 | − | 0.645049i | ||||
\(214\) | 19041.4 | 0.415788 | ||||||||
\(215\) | 41913.1i | 0.906719i | ||||||||
\(216\) | 5767.22 | + | 23245.8i | 0.123611 | + | 0.498239i | ||||
\(217\) | 108904. | 2.31273 | ||||||||
\(218\) | 90291.1i | 1.89991i | ||||||||
\(219\) | 18345.4 | − | 38713.0i | 0.382507 | − | 0.807176i | ||||
\(220\) | −35925.7 | −0.742266 | ||||||||
\(221\) | 1781.29i | 0.0364712i | ||||||||
\(222\) | 46562.3 | + | 22065.1i | 0.944776 | + | 0.447713i | ||||
\(223\) | 16360.3 | 0.328989 | 0.164494 | − | 0.986378i | \(-0.447401\pi\) | ||||
0.164494 | + | 0.986378i | \(0.447401\pi\) | |||||||
\(224\) | − | 95464.8i | − | 1.90260i | ||||||
\(225\) | 27104.9 | + | 33128.6i | 0.535405 | + | 0.654393i | ||||
\(226\) | −12177.0 | −0.238409 | ||||||||
\(227\) | 87068.2i | 1.68969i | 0.535009 | + | 0.844846i | \(0.320308\pi\) | ||||
−0.535009 | + | 0.844846i | \(0.679692\pi\) | |||||||
\(228\) | 9565.28 | − | 20184.9i | 0.184004 | − | 0.388290i | ||||
\(229\) | −16660.9 | −0.317707 | −0.158854 | − | 0.987302i | \(-0.550780\pi\) | ||||
−0.158854 | + | 0.987302i | \(0.550780\pi\) | |||||||
\(230\) | 68875.2i | 1.30199i | ||||||||
\(231\) | −80197.8 | − | 38004.4i | −1.50293 | − | 0.712212i | ||||
\(232\) | −22866.8 | −0.424845 | ||||||||
\(233\) | − | 26333.3i | − | 0.485059i | −0.970144 | − | 0.242529i | \(-0.922023\pi\) | ||
0.970144 | − | 0.242529i | \(-0.0779771\pi\) | |||||||
\(234\) | 1952.94 | − | 1597.84i | 0.0356662 | − | 0.0291811i | ||||
\(235\) | −5060.21 | −0.0916290 | ||||||||
\(236\) | − | 4302.13i | − | 0.0772431i | ||||||
\(237\) | −31474.7 | + | 66418.6i | −0.560356 | + | 1.18248i | ||||
\(238\) | −128998. | −2.27734 | ||||||||
\(239\) | − | 66473.4i | − | 1.16373i | −0.813285 | − | 0.581865i | \(-0.802323\pi\) | ||
0.813285 | − | 0.581865i | \(-0.197677\pi\) | |||||||
\(240\) | −87773.6 | − | 41594.4i | −1.52385 | − | 0.722125i | ||||
\(241\) | 15975.1 | 0.275048 | 0.137524 | − | 0.990498i | \(-0.456086\pi\) | ||||
0.137524 | + | 0.990498i | \(0.456086\pi\) | |||||||
\(242\) | 11231.3i | 0.191779i | ||||||||
\(243\) | −47296.3 | − | 35353.1i | −0.800968 | − | 0.598708i | ||||
\(244\) | −24364.1 | −0.409233 | ||||||||
\(245\) | − | 184418.i | − | 3.07235i | ||||||
\(246\) | −29377.6 | + | 61993.4i | −0.485452 | + | 1.02441i | ||||
\(247\) | 1613.03 | 0.0264392 | ||||||||
\(248\) | 40431.7i | 0.657383i | ||||||||
\(249\) | 64003.7 | + | 30330.3i | 1.03230 | + | 0.489190i | ||||
\(250\) | 16557.2 | 0.264916 | ||||||||
\(251\) | − | 60374.2i | − | 0.958306i | −0.877732 | − | 0.479153i | \(-0.840944\pi\) | ||
0.877732 | − | 0.479153i | \(-0.159056\pi\) | |||||||
\(252\) | 43088.8 | + | 52664.8i | 0.678521 | + | 0.829314i | ||||
\(253\) | −44756.3 | −0.699219 | ||||||||
\(254\) | 16701.5i | 0.258874i | ||||||||
\(255\) | −37790.5 | + | 79746.4i | −0.581169 | + | 1.22640i | ||||
\(256\) | 83708.1 | 1.27728 | ||||||||
\(257\) | − | 42564.2i | − | 0.644434i | −0.946666 | − | 0.322217i | \(-0.895572\pi\) | ||
0.946666 | − | 0.322217i | \(-0.104428\pi\) | |||||||
\(258\) | 50677.3 | + | 24015.1i | 0.761333 | + | 0.360783i | ||||
\(259\) | −100342. | −1.49583 | ||||||||
\(260\) | 1989.20i | 0.0294260i | ||||||||
\(261\) | 43633.7 | − | 35699.8i | 0.640532 | − | 0.524065i | ||||
\(262\) | 121464. | 1.76948 | ||||||||
\(263\) | − | 75835.7i | − | 1.09638i | −0.836353 | − | 0.548191i | \(-0.815317\pi\) | ||
0.836353 | − | 0.548191i | \(-0.184683\pi\) | |||||||
\(264\) | 14109.5 | − | 29774.2i | 0.202444 | − | 0.427201i | ||||
\(265\) | 168838. | 2.40425 | ||||||||
\(266\) | 116813.i | 1.65092i | ||||||||
\(267\) | 43524.5 | + | 20625.5i | 0.610536 | + | 0.289323i | ||||
\(268\) | 73047.6 | 1.01704 | ||||||||
\(269\) | 107497.i | 1.48557i | 0.669533 | + | 0.742783i | \(0.266494\pi\) | ||||
−0.669533 | + | 0.742783i | \(0.733506\pi\) | |||||||
\(270\) | 121329. | − | 30101.4i | 1.66433 | − | 0.412914i | ||||
\(271\) | 13069.1 | 0.177953 | 0.0889767 | − | 0.996034i | \(-0.471640\pi\) | ||||
0.0889767 | + | 0.996034i | \(0.471640\pi\) | |||||||
\(272\) | − | 91743.5i | − | 1.24005i | ||||||
\(273\) | −2104.29 | + | 4440.53i | −0.0282346 | + | 0.0595813i | ||||
\(274\) | 79114.8 | 1.05380 | ||||||||
\(275\) | − | 58884.3i | − | 0.778636i | ||||||
\(276\) | 31010.7 | + | 14695.4i | 0.407092 | + | 0.192914i | ||||
\(277\) | 36791.8 | 0.479503 | 0.239751 | − | 0.970834i | \(-0.422934\pi\) | ||||
0.239751 | + | 0.970834i | \(0.422934\pi\) | |||||||
\(278\) | 113994.i | 1.47500i | ||||||||
\(279\) | −63122.2 | − | 77150.4i | −0.810912 | − | 0.991127i | ||||
\(280\) | 98740.8 | 1.25945 | ||||||||
\(281\) | − | 116425.i | − | 1.47447i | −0.675638 | − | 0.737233i | \(-0.736132\pi\) | ||
0.675638 | − | 0.737233i | \(-0.263868\pi\) | |||||||
\(282\) | −2899.37 | + | 6118.33i | −0.0364591 | + | 0.0769369i | ||||
\(283\) | −75649.7 | −0.944570 | −0.472285 | − | 0.881446i | \(-0.656571\pi\) | ||||
−0.472285 | + | 0.881446i | \(0.656571\pi\) | |||||||
\(284\) | − | 72083.4i | − | 0.893714i | ||||||
\(285\) | 72213.6 | + | 34220.8i | 0.889056 | + | 0.421309i | ||||
\(286\) | −3471.24 | −0.0424378 | ||||||||
\(287\) | − | 133596.i | − | 1.62192i | ||||||
\(288\) | −67629.7 | + | 55332.7i | −0.815366 | + | 0.667109i | ||||
\(289\) | 167.676 | 0.00200759 | ||||||||
\(290\) | 119351.i | 1.41916i | ||||||||
\(291\) | 30786.2 | − | 64965.9i | 0.363555 | − | 0.767184i | ||||
\(292\) | 45186.7 | 0.529962 | ||||||||
\(293\) | − | 136522.i | − | 1.59026i | −0.606439 | − | 0.795130i | \(-0.707402\pi\) | ||
0.606439 | − | 0.795130i | \(-0.292598\pi\) | |||||||
\(294\) | −222980. | − | 105667.i | −2.57972 | − | 1.22248i | ||||
\(295\) | 15391.3 | 0.176861 | ||||||||
\(296\) | − | 37252.9i | − | 0.425184i | ||||||
\(297\) | 19560.4 | + | 78842.0i | 0.221751 | + | 0.893809i | ||||
\(298\) | −7501.36 | −0.0844709 | ||||||||
\(299\) | 2478.15i | 0.0277195i | ||||||||
\(300\) | −19334.3 | + | 40799.7i | −0.214825 | + | 0.453330i | ||||
\(301\) | −109210. | −1.20539 | ||||||||
\(302\) | − | 103055.i | − | 1.12994i | ||||||
\(303\) | −26656.1 | − | 12631.9i | −0.290343 | − | 0.137589i | ||||
\(304\) | −83077.4 | −0.898951 | ||||||||
\(305\) | − | 87165.2i | − | 0.937008i | ||||||
\(306\) | 74768.9 | + | 91385.4i | 0.798506 | + | 0.975964i | ||||
\(307\) | 40342.3 | 0.428039 | 0.214020 | − | 0.976829i | \(-0.431344\pi\) | ||||
0.214020 | + | 0.976829i | \(0.431344\pi\) | |||||||
\(308\) | − | 93608.8i | − | 0.986768i | ||||||
\(309\) | −57186.9 | + | 120677.i | −0.598935 | + | 1.26389i | ||||
\(310\) | 211029. | 2.19594 | ||||||||
\(311\) | 2156.57i | 0.0222968i | 0.999938 | + | 0.0111484i | \(0.00354872\pi\) | ||||
−0.999938 | + | 0.0111484i | \(0.996451\pi\) | |||||||
\(312\) | −1648.59 | − | 781.240i | −0.0169357 | − | 0.00802556i | ||||
\(313\) | 140844. | 1.43763 | 0.718817 | − | 0.695199i | \(-0.244684\pi\) | ||||
0.718817 | + | 0.695199i | \(0.244684\pi\) | |||||||
\(314\) | − | 231956.i | − | 2.35259i | ||||||
\(315\) | −188414. | + | 154155.i | −1.89885 | + | 1.55359i | ||||
\(316\) | −77525.4 | −0.776372 | ||||||||
\(317\) | − | 101071.i | − | 1.00579i | −0.864346 | − | 0.502897i | \(-0.832268\pi\) | ||
0.864346 | − | 0.502897i | \(-0.167732\pi\) | |||||||
\(318\) | 96740.1 | − | 204143.i | 0.956649 | − | 2.01874i | ||||
\(319\) | −77556.6 | −0.762144 | ||||||||
\(320\) | − | 12311.5i | − | 0.120229i | ||||||
\(321\) | 30671.9 | + | 14534.9i | 0.297667 | + | 0.141059i | ||||
\(322\) | −179463. | −1.73086 | ||||||||
\(323\) | 75479.7i | 0.723478i | ||||||||
\(324\) | 12334.2 | − | 61050.4i | 0.117496 | − | 0.581565i | ||||
\(325\) | −3260.41 | −0.0308678 | ||||||||
\(326\) | 126522.i | 1.19050i | ||||||||
\(327\) | −68921.8 | + | 145441.i | −0.644557 | + | 1.36016i | ||||
\(328\) | 49598.8 | 0.461024 | ||||||||
\(329\) | − | 13185.0i | − | 0.121812i | ||||||
\(330\) | −155404. | − | 73643.2i | −1.42703 | − | 0.676246i | ||||
\(331\) | 40959.7 | 0.373853 | 0.186926 | − | 0.982374i | \(-0.440147\pi\) | ||||
0.186926 | + | 0.982374i | \(0.440147\pi\) | |||||||
\(332\) | 74706.7i | 0.677771i | ||||||||
\(333\) | 58159.5 | + | 71084.8i | 0.524484 | + | 0.641044i | ||||
\(334\) | −163658. | −1.46705 | ||||||||
\(335\) | 261336.i | 2.32868i | ||||||||
\(336\) | 108379. | − | 228705.i | 0.959993 | − | 2.02580i | ||||
\(337\) | −105275. | −0.926965 | −0.463483 | − | 0.886106i | \(-0.653400\pi\) | ||||
−0.463483 | + | 0.886106i | \(0.653400\pi\) | |||||||
\(338\) | − | 144014.i | − | 1.26058i | ||||||
\(339\) | −19614.7 | − | 9295.06i | −0.170680 | − | 0.0808821i | ||||
\(340\) | −93082.0 | −0.805207 | ||||||||
\(341\) | 137131.i | 1.17930i | ||||||||
\(342\) | 82753.1 | − | 67706.2i | 0.707509 | − | 0.578863i | ||||
\(343\) | 268051. | 2.27839 | ||||||||
\(344\) | − | 40545.2i | − | 0.342628i | ||||||
\(345\) | −52574.4 | + | 110944.i | −0.441709 | + | 0.932106i | ||||
\(346\) | 279166. | 2.33190 | ||||||||
\(347\) | − | 36624.9i | − | 0.304171i | −0.988367 | − | 0.152085i | \(-0.951401\pi\) | ||
0.988367 | − | 0.152085i | \(-0.0485989\pi\) | |||||||
\(348\) | 53737.2 | + | 25465.2i | 0.443728 | + | 0.210275i | ||||
\(349\) | 11886.3 | 0.0975879 | 0.0487939 | − | 0.998809i | \(-0.484462\pi\) | ||||
0.0487939 | + | 0.998809i | \(0.484462\pi\) | |||||||
\(350\) | − | 236113.i | − | 1.92745i | ||||||
\(351\) | 4365.46 | − | 1083.06i | 0.0354337 | − | 0.00879098i | ||||
\(352\) | 120208. | 0.970172 | ||||||||
\(353\) | − | 128488.i | − | 1.03113i | −0.856850 | − | 0.515565i | \(-0.827582\pi\) | ||
0.856850 | − | 0.515565i | \(-0.172418\pi\) | |||||||
\(354\) | 8818.84 | − | 18609.7i | 0.0703728 | − | 0.148503i | ||||
\(355\) | 257886. | 2.04631 | ||||||||
\(356\) | 50802.9i | 0.400856i | ||||||||
\(357\) | −207789. | − | 98467.8i | −1.63037 | − | 0.772605i | ||||
\(358\) | −85896.3 | −0.670206 | ||||||||
\(359\) | 207156.i | 1.60735i | 0.595071 | + | 0.803673i | \(0.297124\pi\) | ||||
−0.595071 | + | 0.803673i | \(0.702876\pi\) | |||||||
\(360\) | −57231.5 | − | 69950.5i | −0.441601 | − | 0.539742i | ||||
\(361\) | −61971.1 | −0.475527 | ||||||||
\(362\) | 89439.0i | 0.682511i | ||||||||
\(363\) | −8573.19 | + | 18091.4i | −0.0650623 | + | 0.137296i | ||||
\(364\) | −5183.10 | −0.0391189 | ||||||||
\(365\) | 161660.i | 1.21344i | ||||||||
\(366\) | −105392. | − | 49943.4i | −0.786765 | − | 0.372835i | ||||
\(367\) | −123091. | −0.913892 | −0.456946 | − | 0.889494i | \(-0.651057\pi\) | ||||
−0.456946 | + | 0.889494i | \(0.651057\pi\) | |||||||
\(368\) | − | 127634.i | − | 0.942480i | ||||||
\(369\) | −94642.8 | + | 77434.0i | −0.695080 | + | 0.568694i | ||||
\(370\) | −194438. | −1.42029 | ||||||||
\(371\) | 439930.i | 3.19621i | ||||||||
\(372\) | 45025.9 | − | 95014.8i | 0.325369 | − | 0.686602i | ||||
\(373\) | −215834. | −1.55132 | −0.775662 | − | 0.631149i | \(-0.782584\pi\) | ||||
−0.775662 | + | 0.631149i | \(0.782584\pi\) | |||||||
\(374\) | − | 162433.i | − | 1.16126i | ||||||
\(375\) | 26670.3 | + | 12638.6i | 0.189656 | + | 0.0898745i | ||||
\(376\) | 4895.07 | 0.0346245 | ||||||||
\(377\) | 4294.29i | 0.0302140i | ||||||||
\(378\) | 78433.0 | + | 316139.i | 0.548928 | + | 2.21256i | ||||
\(379\) | 170916. | 1.18988 | 0.594942 | − | 0.803769i | \(-0.297175\pi\) | ||||
0.594942 | + | 0.803769i | \(0.297175\pi\) | |||||||
\(380\) | 84289.4i | 0.583722i | ||||||||
\(381\) | −12748.8 | + | 26902.8i | −0.0878250 | + | 0.185331i | ||||
\(382\) | 245285. | 1.68091 | ||||||||
\(383\) | − | 41171.9i | − | 0.280675i | −0.990104 | − | 0.140337i | \(-0.955181\pi\) | ||
0.990104 | − | 0.140337i | \(-0.0448187\pi\) | |||||||
\(384\) | 125494. | + | 59469.5i | 0.851061 | + | 0.403303i | ||||
\(385\) | 334895. | 2.25937 | ||||||||
\(386\) | 163190.i | 1.09526i | ||||||||
\(387\) | 63299.4 | + | 77367.0i | 0.422647 | + | 0.516575i | ||||
\(388\) | 75829.8 | 0.503705 | ||||||||
\(389\) | − | 11993.0i | − | 0.0792552i | −0.999215 | − | 0.0396276i | \(-0.987383\pi\) | ||
0.999215 | − | 0.0396276i | \(-0.0126172\pi\) | |||||||
\(390\) | −4077.61 | + | 8604.67i | −0.0268087 | + | 0.0565725i | ||||
\(391\) | −115962. | −0.758510 | ||||||||
\(392\) | 178399.i | 1.16097i | ||||||||
\(393\) | 195654. | + | 92717.3i | 1.26679 | + | 0.600310i | ||||
\(394\) | −121697. | −0.783950 | ||||||||
\(395\) | − | 277355.i | − | 1.77763i | ||||||
\(396\) | −66314.9 | + | 54256.9i | −0.422883 | + | 0.345991i | ||||
\(397\) | −65587.3 | −0.416139 | −0.208070 | − | 0.978114i | \(-0.566718\pi\) | ||||
−0.208070 | + | 0.978114i | \(0.566718\pi\) | |||||||
\(398\) | 212971.i | 1.34448i | ||||||||
\(399\) | −89166.5 | + | 188161.i | −0.560088 | + | 1.18191i | ||||
\(400\) | 167924. | 1.04953 | ||||||||
\(401\) | − | 155422.i | − | 0.966551i | −0.875468 | − | 0.483275i | \(-0.839447\pi\) | ||
0.875468 | − | 0.483275i | \(-0.160553\pi\) | |||||||
\(402\) | 315982. | + | 149739.i | 1.95529 | + | 0.926578i | ||||
\(403\) | 7592.89 | 0.0467517 | ||||||||
\(404\) | − | 31113.6i | − | 0.190629i | ||||||
\(405\) | 218414. | + | 44127.0i | 1.33159 | + | 0.269026i | ||||
\(406\) | −310985. | −1.88663 | ||||||||
\(407\) | − | 126349.i | − | 0.762753i | ||||||
\(408\) | 36557.2 | − | 77143.9i | 0.219610 | − | 0.463427i | ||||
\(409\) | −4099.29 | −0.0245054 | −0.0122527 | − | 0.999925i | \(-0.503900\pi\) | ||||
−0.0122527 | + | 0.999925i | \(0.503900\pi\) | |||||||
\(410\) | − | 258876.i | − | 1.54001i | ||||||
\(411\) | 127438. | + | 60390.6i | 0.754423 | + | 0.357508i | ||||
\(412\) | −140857. | −0.829823 | ||||||||
\(413\) | 40104.0i | 0.235119i | ||||||||
\(414\) | 104019. | + | 127136.i | 0.606893 | + | 0.741768i | ||||
\(415\) | −267271. | −1.55187 | ||||||||
\(416\) | − | 6655.90i | − | 0.0384610i | ||||||
\(417\) | −87014.9 | + | 183621.i | −0.500405 | + | 1.05597i | ||||
\(418\) | −147089. | −0.841837 | ||||||||
\(419\) | − | 13136.9i | − | 0.0748281i | −0.999300 | − | 0.0374141i | \(-0.988088\pi\) | ||
0.999300 | − | 0.0374141i | \(-0.0119120\pi\) | |||||||
\(420\) | −232042. | − | 109961.i | −1.31543 | − | 0.623359i | ||||
\(421\) | 87174.3 | 0.491840 | 0.245920 | − | 0.969290i | \(-0.420910\pi\) | ||||
0.245920 | + | 0.969290i | \(0.420910\pi\) | |||||||
\(422\) | − | 204654.i | − | 1.14920i | ||||||
\(423\) | −9340.60 | + | 7642.21i | −0.0522028 | + | 0.0427108i | ||||
\(424\) | −163328. | −0.908510 | ||||||||
\(425\) | − | 152567.i | − | 0.844662i | ||||||
\(426\) | 147762. | − | 311811.i | 0.814224 | − | 1.71820i | ||||
\(427\) | 227120. | 1.24566 | ||||||||
\(428\) | 35800.9i | 0.195437i | ||||||||
\(429\) | −5591.47 | − | 2649.70i | −0.0303816 | − | 0.0143973i | ||||
\(430\) | −211622. | −1.14452 | ||||||||
\(431\) | − | 32749.0i | − | 0.176297i | −0.996107 | − | 0.0881483i | \(-0.971905\pi\) | ||
0.996107 | − | 0.0881483i | \(-0.0280949\pi\) | |||||||
\(432\) | −224839. | + | 55781.7i | −1.20477 | + | 0.298899i | ||||
\(433\) | −48.9144 | −0.000260892 | −0.000130446 | − | 1.00000i | \(-0.500042\pi\) | ||||
−0.000130446 | 1.00000i | \(0.500042\pi\) | ||||||||
\(434\) | 549863.i | 2.91928i | ||||||||
\(435\) | −91104.3 | + | 192251.i | −0.481460 | + | 1.01599i | ||||
\(436\) | −169762. | −0.893032 | ||||||||
\(437\) | 105008.i | 0.549870i | ||||||||
\(438\) | 195464. | + | 92627.2i | 1.01887 | + | 0.482825i | ||||
\(439\) | −359966. | −1.86781 | −0.933905 | − | 0.357522i | \(-0.883622\pi\) | ||||
−0.933905 | + | 0.357522i | \(0.883622\pi\) | |||||||
\(440\) | 124333.i | 0.642217i | ||||||||
\(441\) | −278518. | − | 340415.i | −1.43211 | − | 1.75038i | ||||
\(442\) | −8993.86 | −0.0460364 | ||||||||
\(443\) | − | 271249.i | − | 1.38217i | −0.722775 | − | 0.691083i | \(-0.757134\pi\) | ||
0.722775 | − | 0.691083i | \(-0.242866\pi\) | |||||||
\(444\) | −41485.9 | + | 87544.7i | −0.210443 | + | 0.444083i | ||||
\(445\) | −181753. | −0.917827 | ||||||||
\(446\) | 82604.1i | 0.415271i | ||||||||
\(447\) | −12083.2 | − | 5726.00i | −0.0604736 | − | 0.0286574i | ||||
\(448\) | 32079.0 | 0.159833 | ||||||||
\(449\) | 12238.5i | 0.0607064i | 0.999539 | + | 0.0303532i | \(0.00966321\pi\) | ||||
−0.999539 | + | 0.0303532i | \(0.990337\pi\) | |||||||
\(450\) | −167269. | + | 136854.i | −0.826018 | + | 0.675824i | ||||
\(451\) | 168222. | 0.827048 | ||||||||
\(452\) | − | 22894.7i | − | 0.112062i | ||||||
\(453\) | 78665.1 | − | 166001.i | 0.383341 | − | 0.808937i | ||||
\(454\) | −439613. | −2.13284 | ||||||||
\(455\) | − | 18543.1i | − | 0.0895693i | ||||||
\(456\) | −69856.8 | − | 33104.0i | −0.335953 | − | 0.159203i | ||||
\(457\) | −364846. | −1.74694 | −0.873469 | − | 0.486879i | \(-0.838135\pi\) | ||||
−0.873469 | + | 0.486879i | \(0.838135\pi\) | |||||||
\(458\) | − | 84121.9i | − | 0.401031i | ||||||
\(459\) | 50680.3 | + | 204276.i | 0.240555 | + | 0.969601i | ||||
\(460\) | −129496. | −0.611987 | ||||||||
\(461\) | − | 219775.i | − | 1.03413i | −0.855945 | − | 0.517066i | \(-0.827024\pi\) | ||
0.855945 | − | 0.517066i | \(-0.172976\pi\) | |||||||
\(462\) | 191886. | − | 404924.i | 0.899002 | − | 1.89710i | ||||
\(463\) | 190085. | 0.886717 | 0.443359 | − | 0.896344i | \(-0.353787\pi\) | ||||
0.443359 | + | 0.896344i | \(0.353787\pi\) | |||||||
\(464\) | − | 221173.i | − | 1.02730i | ||||||
\(465\) | 339925. | + | 161085.i | 1.57209 | + | 0.744987i | ||||
\(466\) | 132959. | 0.612273 | ||||||||
\(467\) | 427960.i | 1.96232i | 0.193207 | + | 0.981158i | \(0.438111\pi\) | ||||
−0.193207 | + | 0.981158i | \(0.561889\pi\) | |||||||
\(468\) | 3004.19 | + | 3671.84i | 0.0137163 | + | 0.0167646i | ||||
\(469\) | −680943. | −3.09574 | ||||||||
\(470\) | − | 25549.3i | − | 0.115660i | ||||||
\(471\) | 177059. | − | 373634.i | 0.798133 | − | 1.68424i | ||||
\(472\) | −14889.0 | −0.0668317 | ||||||||
\(473\) | − | 137516.i | − | 0.614653i | ||||||
\(474\) | −335352. | − | 158918.i | −1.49260 | − | 0.707319i | ||||
\(475\) | −138155. | −0.612323 | ||||||||
\(476\) | − | 242537.i | − | 1.07044i | ||||||
\(477\) | 311657. | − | 254989.i | 1.36975 | − | 1.12069i | ||||
\(478\) | 335629. | 1.46894 | ||||||||
\(479\) | − | 62417.6i | − | 0.272042i | −0.990706 | − | 0.136021i | \(-0.956569\pi\) | ||
0.990706 | − | 0.136021i | \(-0.0434315\pi\) | |||||||
\(480\) | 141206. | − | 297977.i | 0.612875 | − | 1.29330i | ||||
\(481\) | −6995.94 | −0.0302382 | ||||||||
\(482\) | 80659.2i | 0.347184i | ||||||||
\(483\) | −289078. | − | 136989.i | −1.23914 | − | 0.587208i | ||||
\(484\) | −21116.7 | −0.0901436 | ||||||||
\(485\) | 271289.i | 1.15332i | ||||||||
\(486\) | 178500. | − | 238802.i | 0.755728 | − | 1.01103i | ||||
\(487\) | 469157. | 1.97816 | 0.989078 | − | 0.147395i | \(-0.0470888\pi\) | ||||
0.989078 | + | 0.147395i | \(0.0470888\pi\) | |||||||
\(488\) | 84320.5i | 0.354074i | ||||||||
\(489\) | −96577.6 | + | 203801.i | −0.403886 | + | 0.852290i | ||||
\(490\) | 931136. | 3.87812 | ||||||||
\(491\) | 106092.i | 0.440068i | 0.975492 | + | 0.220034i | \(0.0706168\pi\) | ||||
−0.975492 | + | 0.220034i | \(0.929383\pi\) | |||||||
\(492\) | −116558. | − | 55234.7i | −0.481516 | − | 0.228182i | ||||
\(493\) | −200946. | −0.826771 | ||||||||
\(494\) | 8144.29i | 0.0333733i | ||||||||
\(495\) | −194110. | − | 237248.i | −0.792204 | − | 0.968262i | ||||
\(496\) | −391064. | −1.58959 | ||||||||
\(497\) | 671954.i | 2.72036i | ||||||||
\(498\) | −153139. | + | 323159.i | −0.617488 | + | 1.30304i | ||||
\(499\) | −384086. | −1.54251 | −0.771254 | − | 0.636527i | \(-0.780370\pi\) | ||||
−0.771254 | + | 0.636527i | \(0.780370\pi\) | |||||||
\(500\) | 31130.2i | 0.124521i | ||||||||
\(501\) | −263620. | − | 124925.i | −1.05028 | − | 0.497708i | ||||
\(502\) | 304833. | 1.20964 | ||||||||
\(503\) | − | 136712.i | − | 0.540343i | −0.962812 | − | 0.270172i | \(-0.912920\pi\) | ||
0.962812 | − | 0.270172i | \(-0.0870804\pi\) | |||||||
\(504\) | 182265. | − | 149124.i | 0.717532 | − | 0.587064i | ||||
\(505\) | 111312. | 0.436476 | ||||||||
\(506\) | − | 225978.i | − | 0.882601i | ||||||
\(507\) | 109930. | − | 231977.i | 0.427662 | − | 0.902464i | ||||
\(508\) | −31401.6 | −0.121681 | ||||||||
\(509\) | − | 282297.i | − | 1.08961i | −0.838563 | − | 0.544805i | \(-0.816604\pi\) | ||
0.838563 | − | 0.544805i | \(-0.183396\pi\) | |||||||
\(510\) | −402645. | − | 190807.i | −1.54804 | − | 0.733589i | ||||
\(511\) | −421226. | −1.61314 | ||||||||
\(512\) | 175764.i | 0.670488i | ||||||||
\(513\) | 184980. | − | 45893.1i | 0.702896 | − | 0.174386i | ||||
\(514\) | 214910. | 0.813447 | ||||||||
\(515\) | − | 503933.i | − | 1.90002i | ||||||
\(516\) | −45152.3 | + | 95281.5i | −0.169582 | + | 0.357857i | ||||
\(517\) | 16602.4 | 0.0621141 | ||||||||
\(518\) | − | 506633.i | − | 1.88814i | ||||||
\(519\) | 449679. | + | 213095.i | 1.66943 | + | 0.791114i | ||||
\(520\) | 6884.31 | 0.0254597 | ||||||||
\(521\) | 337551.i | 1.24355i | 0.783195 | + | 0.621776i | \(0.213589\pi\) | ||||
−0.783195 | + | 0.621776i | \(0.786411\pi\) | |||||||
\(522\) | 180251. | + | 220309.i | 0.661510 | + | 0.808522i | ||||
\(523\) | −316302. | −1.15637 | −0.578187 | − | 0.815904i | \(-0.696240\pi\) | ||||
−0.578187 | + | 0.815904i | \(0.696240\pi\) | |||||||
\(524\) | 228372.i | 0.831728i | ||||||||
\(525\) | 180232. | − | 380330.i | 0.653903 | − | 1.37988i | ||||
\(526\) | 382899. | 1.38393 | ||||||||
\(527\) | 355300.i | 1.27930i | ||||||||
\(528\) | 287983. | + | 136470.i | 1.03300 | + | 0.489519i | ||||
\(529\) | 118514. | 0.423505 | ||||||||
\(530\) | 852476.i | 3.03480i | ||||||||
\(531\) | 28410.7 | − | 23244.8i | 0.100761 | − | 0.0824399i | ||||
\(532\) | −219627. | −0.776000 | ||||||||
\(533\) | − | 9314.44i | − | 0.0327870i | ||||||
\(534\) | −104140. | + | 219758.i | −0.365202 | + | 0.770659i | ||||
\(535\) | −128082. | −0.447486 | ||||||||
\(536\) | − | 252807.i | − | 0.879952i | ||||||
\(537\) | −138361. | − | 65567.1i | −0.479807 | − | 0.227372i | ||||
\(538\) | −542759. | −1.87518 | ||||||||
\(539\) | 605069.i | 2.08270i | ||||||||
\(540\) | 56595.5 | + | 228119.i | 0.194086 | + | 0.782300i | ||||
\(541\) | 66158.9 | 0.226044 | 0.113022 | − | 0.993592i | \(-0.463947\pi\) | ||||
0.113022 | + | 0.993592i | \(0.463947\pi\) | |||||||
\(542\) | 65986.6i | 0.224624i | ||||||||
\(543\) | −68271.4 | + | 144068.i | −0.231547 | + | 0.488616i | ||||
\(544\) | 311455. | 1.05244 | ||||||||
\(545\) | − | 607341.i | − | 2.04475i | ||||||
\(546\) | −22420.5 | − | 10624.7i | −0.0752074 | − | 0.0356395i | ||||
\(547\) | −167080. | −0.558407 | −0.279204 | − | 0.960232i | \(-0.590070\pi\) | ||||
−0.279204 | + | 0.960232i | \(0.590070\pi\) | |||||||
\(548\) | 148748.i | 0.495326i | ||||||||
\(549\) | −131642. | − | 160897.i | −0.436766 | − | 0.533832i | ||||
\(550\) | 297311. | 0.982846 | ||||||||
\(551\) | 181965.i | 0.599354i | ||||||||
\(552\) | 50858.6 | − | 107323.i | 0.166912 | − | 0.352221i | ||||
\(553\) | 722684. | 2.36319 | ||||||||
\(554\) | 185764.i | 0.605260i | ||||||||
\(555\) | −313200. | − | 148420.i | −1.01680 | − | 0.481845i | ||||
\(556\) | −214327. | −0.693309 | ||||||||
\(557\) | 302225.i | 0.974135i | 0.873364 | + | 0.487068i | \(0.161933\pi\) | ||||
−0.873364 | + | 0.487068i | \(0.838067\pi\) | |||||||
\(558\) | 389537. | − | 318708.i | 1.25107 | − | 1.02359i | ||||
\(559\) | −7614.21 | −0.0243670 | ||||||||
\(560\) | 955042.i | 3.04541i | ||||||||
\(561\) | 123989. | − | 261646.i | 0.393966 | − | 0.831358i | ||||
\(562\) | 587839. | 1.86117 | ||||||||
\(563\) | 33389.3i | 0.105339i | 0.998612 | + | 0.0526697i | \(0.0167730\pi\) | ||||
−0.998612 | + | 0.0526697i | \(0.983227\pi\) | |||||||
\(564\) | −11503.4 | − | 5451.28i | −0.0361634 | − | 0.0171372i | ||||
\(565\) | 81908.2 | 0.256585 | ||||||||
\(566\) | − | 381960.i | − | 1.19230i | ||||||
\(567\) | −114978. | + | 569106.i | −0.357643 | + | 1.77022i | ||||
\(568\) | −249470. | −0.773252 | ||||||||
\(569\) | − | 462649.i | − | 1.42898i | −0.699644 | − | 0.714491i | \(-0.746658\pi\) | ||
0.699644 | − | 0.714491i | \(-0.253342\pi\) | |||||||
\(570\) | −172783. | + | 364611.i | −0.531803 | + | 1.12223i | ||||
\(571\) | −149876. | −0.459685 | −0.229842 | − | 0.973228i | \(-0.573821\pi\) | ||||
−0.229842 | + | 0.973228i | \(0.573821\pi\) | |||||||
\(572\) | − | 6526.50i | − | 0.0199475i | ||||||
\(573\) | 395104. | + | 187233.i | 1.20338 | + | 0.570261i | ||||
\(574\) | 674535. | 2.04729 | ||||||||
\(575\) | − | 212252.i | − | 0.641973i | ||||||
\(576\) | −18593.4 | − | 22725.6i | −0.0560422 | − | 0.0684969i | ||||
\(577\) | −101628. | −0.305253 | −0.152627 | − | 0.988284i | \(-0.548773\pi\) | ||||
−0.152627 | + | 0.988284i | \(0.548773\pi\) | |||||||
\(578\) | 846.608i | 0.00253412i | ||||||||
\(579\) | −124568. | + | 262866.i | −0.371577 | + | 0.784110i | ||||
\(580\) | −224400. | −0.667062 | ||||||||
\(581\) | − | 696408.i | − | 2.06306i | ||||||
\(582\) | 328017. | + | 155442.i | 0.968390 | + | 0.458904i | ||||
\(583\) | −553954. | −1.62981 | ||||||||
\(584\) | − | 156384.i | − | 0.458530i | ||||||
\(585\) | −13136.4 | + | 10747.8i | −0.0383853 | + | 0.0314057i | ||||
\(586\) | 689310. | 2.00733 | ||||||||
\(587\) | − | 163854.i | − | 0.475533i | −0.971322 | − | 0.237766i | \(-0.923585\pi\) | ||
0.971322 | − | 0.237766i | \(-0.0764153\pi\) | |||||||
\(588\) | 198670. | − | 419239.i | 0.574616 | − | 1.21257i | ||||
\(589\) | 321738. | 0.927411 | ||||||||
\(590\) | 77711.8i | 0.223246i | ||||||||
\(591\) | −196030. | − | 92895.1i | −0.561237 | − | 0.265961i | ||||
\(592\) | 360318. | 1.02812 | ||||||||
\(593\) | 366216.i | 1.04142i | 0.853733 | + | 0.520712i | \(0.174333\pi\) | ||||
−0.853733 | + | 0.520712i | \(0.825667\pi\) | |||||||
\(594\) | −398078. | + | 98762.0i | −1.12822 | + | 0.279909i | ||||
\(595\) | 867700. | 2.45096 | ||||||||
\(596\) | − | 14103.8i | − | 0.0397047i | ||||||
\(597\) | −162567. | + | 343053.i | −0.456125 | + | 0.962528i | ||||
\(598\) | −12512.3 | −0.0349893 | ||||||||
\(599\) | − | 630279.i | − | 1.75663i | −0.478087 | − | 0.878313i | \(-0.658670\pi\) | ||
0.478087 | − | 0.878313i | \(-0.341330\pi\) | |||||||
\(600\) | 141201. | + | 66912.9i | 0.392226 | + | 0.185869i | ||||
\(601\) | 494937. | 1.37025 | 0.685127 | − | 0.728424i | \(-0.259747\pi\) | ||||
0.685127 | + | 0.728424i | \(0.259747\pi\) | |||||||
\(602\) | − | 551407.i | − | 1.52153i | ||||||
\(603\) | 394683. | + | 482397.i | 1.08546 | + | 1.32669i | ||||
\(604\) | 193761. | 0.531119 | ||||||||
\(605\) | − | 75547.2i | − | 0.206399i | ||||||
\(606\) | 63779.1 | − | 134588.i | 0.173673 | − | 0.366490i | ||||
\(607\) | 465849. | 1.26435 | 0.632175 | − | 0.774825i | \(-0.282162\pi\) | ||||
0.632175 | + | 0.774825i | \(0.282162\pi\) | |||||||
\(608\) | − | 282035.i | − | 0.762948i | ||||||
\(609\) | −500933. | − | 237384.i | −1.35066 | − | 0.640053i | ||||
\(610\) | 440103. | 1.18275 | ||||||||
\(611\) | − | 919.272i | − | 0.00246242i | ||||||
\(612\) | −171819. | + | 140577.i | −0.458742 | + | 0.375330i | ||||
\(613\) | 453160. | 1.20595 | 0.602976 | − | 0.797759i | \(-0.293981\pi\) | ||||
0.602976 | + | 0.797759i | \(0.293981\pi\) | |||||||
\(614\) | 203691.i | 0.540299i | ||||||||
\(615\) | 197608. | − | 416997.i | 0.522461 | − | 1.10251i | ||||
\(616\) | −323966. | −0.853764 | ||||||||
\(617\) | 382747.i | 1.00541i | 0.864459 | + | 0.502703i | \(0.167661\pi\) | ||||
−0.864459 | + | 0.502703i | \(0.832339\pi\) | |||||||
\(618\) | −609308. | − | 288741.i | −1.59536 | − | 0.756016i | ||||
\(619\) | −514375. | −1.34245 | −0.671225 | − | 0.741253i | \(-0.734232\pi\) | ||||
−0.671225 | + | 0.741253i | \(0.734232\pi\) | |||||||
\(620\) | 396769.i | 1.03218i | ||||||||
\(621\) | 70506.9 | + | 284191.i | 0.182830 | + | 0.736932i | ||||
\(622\) | −10888.7 | −0.0281445 | ||||||||
\(623\) | − | 473579.i | − | 1.22016i | ||||||
\(624\) | 7556.32 | − | 15945.5i | 0.0194062 | − | 0.0409515i | ||||
\(625\) | −441649. | −1.13062 | ||||||||
\(626\) | 711128.i | 1.81468i | ||||||||
\(627\) | −236931. | − | 112277.i | −0.602679 | − | 0.285599i | ||||
\(628\) | 436114. | 1.10581 | ||||||||
\(629\) | − | 327366.i | − | 0.827432i | ||||||
\(630\) | −778337. | − | 951313.i | −1.96104 | − | 2.39686i | ||||
\(631\) | 683875. | 1.71758 | 0.858792 | − | 0.512324i | \(-0.171215\pi\) | ||||
0.858792 | + | 0.512324i | \(0.171215\pi\) | |||||||
\(632\) | 268304.i | 0.671726i | ||||||||
\(633\) | 156218. | − | 329656.i | 0.389874 | − | 0.822722i | ||||
\(634\) | 510315. | 1.26958 | ||||||||
\(635\) | − | 112342.i | − | 0.278610i | ||||||
\(636\) | 383823. | + | 181887.i | 0.948891 | + | 0.449663i | ||||
\(637\) | 33502.5 | 0.0825655 | ||||||||
\(638\) | − | 391588.i | − | 0.962029i | ||||||
\(639\) | 476029. | − | 389473.i | 1.16582 | − | 0.953841i | ||||
\(640\) | −524046. | −1.27941 | ||||||||
\(641\) | 218772.i | 0.532447i | 0.963911 | + | 0.266223i | \(0.0857759\pi\) | ||||
−0.963911 | + | 0.266223i | \(0.914224\pi\) | |||||||
\(642\) | −73387.5 | + | 154864.i | −0.178054 | + | 0.375735i | ||||
\(643\) | −187495. | −0.453490 | −0.226745 | − | 0.973954i | \(-0.572808\pi\) | ||||
−0.226745 | + | 0.973954i | \(0.572808\pi\) | |||||||
\(644\) | − | 337419.i | − | 0.813575i | ||||||
\(645\) | −340880. | − | 161537.i | −0.819373 | − | 0.388287i | ||||
\(646\) | −381102. | −0.913222 | ||||||||
\(647\) | 390577.i | 0.933035i | 0.884512 | + | 0.466518i | \(0.154492\pi\) | ||||
−0.884512 | + | 0.466518i | \(0.845508\pi\) | |||||||
\(648\) | −211286. | − | 42686.8i | −0.503177 | − | 0.101659i | ||||
\(649\) | −50498.5 | −0.119892 | ||||||||
\(650\) | − | 16462.0i | − | 0.0389634i | ||||||
\(651\) | −419727. | + | 885718.i | −0.990386 | + | 2.08994i | ||||
\(652\) | −237881. | −0.559583 | ||||||||
\(653\) | 801944.i | 1.88069i | 0.340219 | + | 0.940346i | \(0.389499\pi\) | ||||
−0.340219 | + | 0.940346i | \(0.610501\pi\) | |||||||
\(654\) | −734339. | − | 347991.i | −1.71688 | − | 0.813603i | ||||
\(655\) | −817027. | −1.90438 | ||||||||
\(656\) | 479730.i | 1.11478i | ||||||||
\(657\) | 244148. | + | 298407.i | 0.565617 | + | 0.691319i | ||||
\(658\) | 66571.9 | 0.153759 | ||||||||
\(659\) | 892.461i | 0.00205503i | 0.999999 | + | 0.00102752i | \(0.000327069\pi\) | ||||
−0.999999 | + | 0.00102752i | \(0.999673\pi\) | |||||||
\(660\) | 138461. | − | 292184.i | 0.317863 | − | 0.670762i | ||||
\(661\) | 610212. | 1.39662 | 0.698309 | − | 0.715796i | \(-0.253936\pi\) | ||||
0.698309 | + | 0.715796i | \(0.253936\pi\) | |||||||
\(662\) | 206808.i | 0.471902i | ||||||||
\(663\) | −14487.3 | − | 6865.27i | −0.0329579 | − | 0.0156182i | ||||
\(664\) | 258548. | 0.586416 | ||||||||
\(665\) | − | 785737.i | − | 1.77678i | ||||||
\(666\) | −358912. | + | 293651.i | −0.809169 | + | 0.662038i | ||||
\(667\) | −279558. | −0.628376 | ||||||||
\(668\) | − | 307704.i | − | 0.689573i | ||||||
\(669\) | −63054.1 | + | 133058.i | −0.140884 | + | 0.297297i | ||||
\(670\) | −1.31950e6 | −2.93941 | ||||||||
\(671\) | 285987.i | 0.635185i | ||||||||
\(672\) | 776417. | + | 367931.i | 1.71932 | + | 0.814756i | ||||
\(673\) | 385805. | 0.851801 | 0.425900 | − | 0.904770i | \(-0.359957\pi\) | ||||
0.425900 | + | 0.904770i | \(0.359957\pi\) | |||||||
\(674\) | − | 531538.i | − | 1.17008i | ||||||
\(675\) | −373901. | + | 92763.5i | −0.820632 | + | 0.203596i | ||||
\(676\) | 270770. | 0.592525 | ||||||||
\(677\) | − | 106731.i | − | 0.232871i | −0.993198 | − | 0.116435i | \(-0.962853\pi\) | ||
0.993198 | − | 0.116435i | \(-0.0371468\pi\) | |||||||
\(678\) | 46931.3 | − | 99035.7i | 0.102095 | − | 0.215443i | ||||
\(679\) | −706877. | −1.53322 | ||||||||
\(680\) | 322143.i | 0.696675i | ||||||||
\(681\) | −708127. | − | 335569.i | −1.52692 | − | 0.723582i | ||||
\(682\) | −692381. | −1.48859 | ||||||||
\(683\) | 115229.i | 0.247013i | 0.992344 | + | 0.123507i | \(0.0394140\pi\) | ||||
−0.992344 | + | 0.123507i | \(0.960586\pi\) | |||||||
\(684\) | 127298. | + | 155589.i | 0.272089 | + | 0.332558i | ||||
\(685\) | −532163. | −1.13413 | ||||||||
\(686\) | 1.35340e6i | 2.87594i | ||||||||
\(687\) | 64212.7 | − | 135503.i | 0.136053 | − | 0.287102i | ||||
\(688\) | 392162. | 0.828492 | ||||||||
\(689\) | 30672.3i | 0.0646112i | ||||||||
\(690\) | −560163. | − | 265452.i | −1.17657 | − | 0.557555i | ||||
\(691\) | −735740. | −1.54088 | −0.770439 | − | 0.637513i | \(-0.779963\pi\) | ||||
−0.770439 | + | 0.637513i | \(0.779963\pi\) | |||||||
\(692\) | 524876.i | 1.09609i | ||||||||
\(693\) | 618180. | − | 505777.i | 1.28721 | − | 1.05316i | ||||
\(694\) | 184922. | 0.383945 | ||||||||
\(695\) | − | 766777.i | − | 1.58745i | ||||||
\(696\) | 88131.0 | − | 185976.i | 0.181933 | − | 0.383919i | ||||
\(697\) | 435858. | 0.897179 | ||||||||
\(698\) | 60014.7i | 0.123182i | ||||||||
\(699\) | 214169. | + | 101491.i | 0.438332 | + | 0.207718i | ||||
\(700\) | 443931. | 0.905981 | ||||||||
\(701\) | 12876.8i | 0.0262043i | 0.999914 | + | 0.0131022i | \(0.00417067\pi\) | ||||
−0.999914 | + | 0.0131022i | \(0.995829\pi\) | |||||||
\(702\) | 5468.43 | + | 22041.5i | 0.0110966 | + | 0.0447267i | ||||
\(703\) | −296443. | −0.599833 | ||||||||
\(704\) | 40393.6i | 0.0815017i | ||||||||
\(705\) | 19502.5 | − | 41154.8i | 0.0392386 | − | 0.0828022i | ||||
\(706\) | 648745. | 1.30156 | ||||||||
\(707\) | 290038.i | 0.580251i | ||||||||
\(708\) | 34989.3 | + | 16580.8i | 0.0698022 | + | 0.0330781i | ||||
\(709\) | 495300. | 0.985316 | 0.492658 | − | 0.870223i | \(-0.336025\pi\) | ||||
0.492658 | + | 0.870223i | \(0.336025\pi\) | |||||||
\(710\) | 1.30208e6i | 2.58299i | ||||||||
\(711\) | −418877. | − | 511968.i | −0.828605 | − | 1.01275i | ||||
\(712\) | 175821. | 0.346825 | ||||||||
\(713\) | 494296.i | 0.972318i | ||||||||
\(714\) | 497170. | − | 1.04914e6i | 0.975234 | − | 2.05796i | ||||
\(715\) | 23349.2 | 0.0456731 | ||||||||
\(716\) | − | 161499.i | − | 0.315024i | ||||||
\(717\) | 540629. | + | 256195.i | 1.05163 | + | 0.498348i | ||||
\(718\) | −1.04595e6 | −2.02890 | ||||||||
\(719\) | − | 670622.i | − | 1.29724i | −0.761113 | − | 0.648619i | \(-0.775347\pi\) | ||
0.761113 | − | 0.648619i | \(-0.224653\pi\) | |||||||
\(720\) | 676576. | − | 553555.i | 1.30512 | − | 1.06781i | ||||
\(721\) | 1.31306e6 | 2.52589 | ||||||||
\(722\) | − | 312896.i | − | 0.600241i | ||||||
\(723\) | −61569.5 | + | 129926.i | −0.117785 | + | 0.248552i | ||||
\(724\) | −168160. | −0.320808 | ||||||||
\(725\) | − | 367804.i | − | 0.699747i | ||||||
\(726\) | −91344.5 | − | 43286.6i | −0.173304 | − | 0.0821259i | ||||
\(727\) | −191652. | −0.362614 | −0.181307 | − | 0.983427i | \(-0.558033\pi\) | ||||
−0.181307 | + | 0.983427i | \(0.558033\pi\) | |||||||
\(728\) | 17937.9i | 0.0338461i | ||||||||
\(729\) | 469812. | − | 248408.i | 0.884034 | − | 0.467423i | ||||
\(730\) | −816233. | −1.53168 | ||||||||
\(731\) | − | 356298.i | − | 0.666773i | ||||||
\(732\) | 93901.7 | − | 198154.i | 0.175247 | − | 0.369811i | ||||
\(733\) | −2889.84 | −0.00537856 | −0.00268928 | − | 0.999996i | \(-0.500856\pi\) | ||||
−0.00268928 | + | 0.999996i | \(0.500856\pi\) | |||||||
\(734\) | − | 621496.i | − | 1.15358i | ||||||
\(735\) | 1.49987e6 | + | 710763.i | 2.77638 | + | 1.31568i | ||||
\(736\) | 433298. | 0.799892 | ||||||||
\(737\) | − | 857435.i | − | 1.57858i | ||||||
\(738\) | −390969. | − | 477857.i | −0.717844 | − | 0.877376i | ||||
\(739\) | −779522. | −1.42738 | −0.713690 | − | 0.700462i | \(-0.752977\pi\) | ||||
−0.713690 | + | 0.700462i | \(0.752977\pi\) | |||||||
\(740\) | − | 365575.i | − | 0.667595i | ||||||
\(741\) | −6216.78 | + | 13118.8i | −0.0113221 | + | 0.0238923i | ||||
\(742\) | −2.22123e6 | −4.03447 | ||||||||
\(743\) | − | 341811.i | − | 0.619168i | −0.950872 | − | 0.309584i | \(-0.899810\pi\) | ||
0.950872 | − | 0.309584i | \(-0.100190\pi\) | |||||||
\(744\) | −328832. | − | 155828.i | −0.594056 | − | 0.281513i | ||||
\(745\) | 50457.7 | 0.0909106 | ||||||||
\(746\) | − | 1.08976e6i | − | 1.95818i | ||||||
\(747\) | −493353. | + | 403647.i | −0.884131 | + | 0.723371i | ||||
\(748\) | 305399. | 0.545839 | ||||||||
\(749\) | − | 333733.i | − | 0.594888i | ||||||
\(750\) | −63813.1 | + | 134660.i | −0.113446 | + | 0.239396i | ||||
\(751\) | 110915. | 0.196658 | 0.0983290 | − | 0.995154i | \(-0.468650\pi\) | ||||
0.0983290 | + | 0.995154i | \(0.468650\pi\) | |||||||
\(752\) | 47346.1i | 0.0837237i | ||||||||
\(753\) | 491024. | + | 232688.i | 0.865990 | + | 0.410378i | ||||
\(754\) | −21682.1 | −0.0381381 | ||||||||
\(755\) | 693199.i | 1.21609i | ||||||||
\(756\) | −594392. | + | 147467.i | −1.03999 | + | 0.258018i | ||||
\(757\) | −1.02325e6 | −1.78563 | −0.892813 | − | 0.450427i | \(-0.851272\pi\) | ||||
−0.892813 | + | 0.450427i | \(0.851272\pi\) | |||||||
\(758\) | 862966.i | 1.50195i | ||||||||
\(759\) | 172495. | − | 364004.i | 0.299429 | − | 0.631862i | ||||
\(760\) | 291713. | 0.505043 | ||||||||
\(761\) | 191598.i | 0.330842i | 0.986223 | + | 0.165421i | \(0.0528983\pi\) | ||||
−0.986223 | + | 0.165421i | \(0.947102\pi\) | |||||||
\(762\) | −135834. | − | 64369.3i | −0.233936 | − | 0.110858i | ||||
\(763\) | 1.58250e6 | 2.71829 | ||||||||
\(764\) | 461175.i | 0.790095i | ||||||||
\(765\) | −502931. | − | 614701.i | −0.859380 | − | 1.05037i | ||||
\(766\) | 207880. | 0.354286 | ||||||||
\(767\) | 2796.09i | 0.00475292i | ||||||||
\(768\) | −322619. | + | 680799.i | −0.546975 | + | 1.15424i | ||||
\(769\) | −423911. | −0.716839 | −0.358419 | − | 0.933561i | \(-0.616684\pi\) | ||||
−0.358419 | + | 0.933561i | \(0.616684\pi\) | |||||||
\(770\) | 1.69091e6i | 2.85193i | ||||||||
\(771\) | 346176. | + | 164047.i | 0.582355 | + | 0.275968i | ||||
\(772\) | −306823. | −0.514818 | ||||||||
\(773\) | − | 413018.i | − | 0.691210i | −0.938380 | − | 0.345605i | \(-0.887674\pi\) | ||
0.938380 | − | 0.345605i | \(-0.112326\pi\) | |||||||
\(774\) | −390631. | + | 319603.i | −0.652056 | + | 0.533493i | ||||
\(775\) | −650329. | −1.08275 | ||||||||
\(776\) | − | 262435.i | − | 0.435812i | ||||||
\(777\) | 386727. | − | 816082.i | 0.640565 | − | 1.35174i | ||||
\(778\) | 60553.3 | 0.100041 | ||||||||
\(779\) | − | 394686.i | − | 0.650395i | ||||||
\(780\) | −16178.2 | − | 7666.56i | −0.0265913 | − | 0.0126012i | ||||
\(781\) | −846116. | −1.38716 | ||||||||
\(782\) | − | 585499.i | − | 0.957442i | ||||||
\(783\) | 122179. | + | 492464.i | 0.199284 | + | 0.803251i | ||||
\(784\) | −1.72551e6 | −2.80728 | ||||||||
\(785\) | 1.56024e6i | 2.53194i | ||||||||
\(786\) | −468135. | + | 987871.i | −0.757751 | + | 1.59903i | ||||
\(787\) | 682596. | 1.10208 | 0.551041 | − | 0.834478i | \(-0.314231\pi\) | ||||
0.551041 | + | 0.834478i | \(0.314231\pi\) | |||||||
\(788\) | − | 228810.i | − | 0.368488i | ||||||
\(789\) | 616773. | + | 292278.i | 0.990767 | + | 0.469507i | ||||
\(790\) | 1.40038e6 | 2.24385 | ||||||||
\(791\) | 213422.i | 0.341104i | ||||||||
\(792\) | 187775. | + | 229506.i | 0.299355 | + | 0.365884i | ||||
\(793\) | 15835.0 | 0.0251809 | ||||||||
\(794\) | − | 331155.i | − | 0.525279i | ||||||
\(795\) | −650720. | + | 1.37317e6i | −1.02958 | + | 2.17264i | ||||
\(796\) | −400420. | −0.631960 | ||||||||
\(797\) | − | 753632.i | − | 1.18643i | −0.805043 | − | 0.593216i | \(-0.797858\pi\) | ||
0.805043 | − | 0.593216i | \(-0.202142\pi\) | |||||||
\(798\) | −950039. | − | 450207.i | −1.49189 | − | 0.706980i | ||||
\(799\) | 43016.2 | 0.0673811 | ||||||||
\(800\) | 570076.i | 0.890743i | ||||||||
\(801\) | −335496. | + | 274493.i | −0.522904 | + | 0.427825i | ||||
\(802\) | 784737. | 1.22004 | ||||||||
\(803\) | − | 530402.i | − | 0.822573i | ||||||
\(804\) | −281533. | + | 594098.i | −0.435529 | + | 0.919064i | ||||
\(805\) | 1.20715e6 | 1.86282 | ||||||||
\(806\) | 38337.0i | 0.0590130i | ||||||||
\(807\) | −874275. | − | 414304.i | −1.34246 | − | 0.636168i | ||||
\(808\) | −107680. | −0.164934 | ||||||||
\(809\) | 682052.i | 1.04213i | 0.853518 | + | 0.521063i | \(0.174464\pi\) | ||||
−0.853518 | + | 0.521063i | \(0.825536\pi\) | |||||||
\(810\) | −222800. | + | 1.10279e6i | −0.339582 | + | 1.68082i | ||||
\(811\) | 784718. | 1.19309 | 0.596543 | − | 0.802581i | \(-0.296541\pi\) | ||||
0.596543 | + | 0.802581i | \(0.296541\pi\) | |||||||
\(812\) | − | 584701.i | − | 0.886792i | ||||||
\(813\) | −50369.5 | + | 106291.i | −0.0762055 | + | 0.160811i | ||||
\(814\) | 637946. | 0.962798 | ||||||||
\(815\) | − | 851044.i | − | 1.28126i | ||||||
\(816\) | 746152. | + | 353589.i | 1.12059 | + | 0.531028i | ||||
\(817\) | −322642. | −0.483366 | ||||||||
\(818\) | − | 20697.6i | − | 0.0309324i | ||||||
\(819\) | −28004.8 | − | 34228.5i | −0.0417508 | − | 0.0510294i | ||||
\(820\) | 486729. | 0.723868 | ||||||||
\(821\) | 579986.i | 0.860461i | 0.902719 | + | 0.430231i | \(0.141568\pi\) | ||||
−0.902719 | + | 0.430231i | \(0.858432\pi\) | |||||||
\(822\) | −304916. | + | 643442.i | −0.451270 | + | 0.952282i | ||||
\(823\) | −1.12641e6 | −1.66302 | −0.831512 | − | 0.555507i | \(-0.812524\pi\) | ||||
−0.831512 | + | 0.555507i | \(0.812524\pi\) | |||||||
\(824\) | 487486.i | 0.717973i | ||||||||
\(825\) | 478907. | + | 226946.i | 0.703629 | + | 0.333438i | ||||
\(826\) | −202488. | −0.296783 | ||||||||
\(827\) | − | 380772.i | − | 0.556743i | −0.960474 | − | 0.278371i | \(-0.910205\pi\) | ||
0.960474 | − | 0.278371i | \(-0.0897946\pi\) | |||||||
\(828\) | −239036. | + | 195573.i | −0.348661 | + | 0.285264i | ||||
\(829\) | 292205. | 0.425186 | 0.212593 | − | 0.977141i | \(-0.431809\pi\) | ||||
0.212593 | + | 0.977141i | \(0.431809\pi\) | |||||||
\(830\) | − | 1.34947e6i | − | 1.95887i | ||||||
\(831\) | −141799. | + | 299228.i | −0.205339 | + | 0.433311i | ||||
\(832\) | 2236.58 | 0.00323101 | ||||||||
\(833\) | 1.56771e6i | 2.25931i | ||||||||
\(834\) | −927114. | − | 439344.i | −1.33291 | − | 0.631644i | ||||
\(835\) | 1.10084e6 | 1.57889 | ||||||||
\(836\) | − | 276551.i | − | 0.395697i | ||||||
\(837\) | 870744. | − | 216029.i | 1.24291 | − | 0.308362i | ||||
\(838\) | 66329.0 | 0.0944530 | ||||||||
\(839\) | 546728.i | 0.776689i | 0.921514 | + | 0.388344i | \(0.126953\pi\) | ||||
−0.921514 | + | 0.388344i | \(0.873047\pi\) | |||||||
\(840\) | −380557. | + | 803060.i | −0.539338 | + | 1.13812i | ||||
\(841\) | 222846. | 0.315074 | ||||||||
\(842\) | 440149.i | 0.620833i | ||||||||
\(843\) | 946889. | + | 448715.i | 1.33243 | + | 0.631415i | ||||
\(844\) | 384782. | 0.540169 | ||||||||
\(845\) | 968707.i | 1.35669i | ||||||||
\(846\) | −38586.0 | − | 47161.3i | −0.0539124 | − | 0.0658938i | ||||
\(847\) | 196848. | 0.274387 | ||||||||
\(848\) | − | 1.57975e6i | − | 2.19682i | ||||||
\(849\) | 291561. | − | 615260.i | 0.404496 | − | 0.853578i | ||||
\(850\) | 770321. | 1.06619 | ||||||||
\(851\) | − | 455434.i | − | 0.628879i | ||||||
\(852\) | 586255. | + | 277816.i | 0.807621 | + | 0.382718i | ||||
\(853\) | −474069. | −0.651543 | −0.325772 | − | 0.945449i | \(-0.605624\pi\) | ||||
−0.325772 | + | 0.945449i | \(0.605624\pi\) | |||||||
\(854\) | 1.14674e6i | 1.57235i | ||||||||
\(855\) | −556636. | + | 455424.i | −0.761446 | + | 0.622994i | ||||
\(856\) | 123902. | 0.169095 | ||||||||
\(857\) | − | 686889.i | − | 0.935245i | −0.883928 | − | 0.467622i | \(-0.845111\pi\) | ||
0.883928 | − | 0.467622i | \(-0.154889\pi\) | |||||||
\(858\) | 13378.5 | − | 28231.7i | 0.0181733 | − | 0.0383497i | ||||
\(859\) | −251544. | −0.340900 | −0.170450 | − | 0.985366i | \(-0.554522\pi\) | ||||
−0.170450 | + | 0.985366i | \(0.554522\pi\) | |||||||
\(860\) | − | 397883.i | − | 0.537971i | ||||||
\(861\) | 1.08654e6 | + | 514892.i | 1.46568 | + | 0.694560i | ||||
\(862\) | 165352. | 0.222533 | ||||||||
\(863\) | − | 779321.i | − | 1.04639i | −0.852212 | − | 0.523196i | \(-0.824740\pi\) | ||
0.852212 | − | 0.523196i | \(-0.175260\pi\) | |||||||
\(864\) | −189370. | − | 763291.i | −0.253679 | − | 1.02250i | ||||
\(865\) | −1.87780e6 | −2.50967 | ||||||||
\(866\) | − | 246.972i | − | 0.000329315i | ||||||
\(867\) | −646.240 | + | 1363.71i | −0.000859717 | + | 0.00181420i | ||||
\(868\) | −1.03383e6 | −1.37218 | ||||||||
\(869\) | 909995.i | 1.20503i | ||||||||
\(870\) | −970686. | − | 459991.i | −1.28245 | − | 0.607731i | ||||
\(871\) | −47476.0 | −0.0625803 | ||||||||
\(872\) | 587520.i | 0.772662i | ||||||||
\(873\) | 409715. | + | 500770.i | 0.537593 | + | 0.657067i | ||||
\(874\) | −530192. | −0.694082 | ||||||||
\(875\) | − | 290193.i | − | 0.379027i | ||||||
\(876\) | −174154. | + | 367504.i | −0.226947 | + | 0.478910i | ||||
\(877\) | −1.13477e6 | −1.47540 | −0.737698 | − | 0.675131i | \(-0.764087\pi\) | ||||
−0.737698 | + | 0.675131i | \(0.764087\pi\) | |||||||
\(878\) | − | 1.81749e6i | − | 2.35767i | ||||||
\(879\) | 1.11034e6 | + | 526170.i | 1.43707 | + | 0.681002i | ||||
\(880\) | −1.20258e6 | −1.55291 | ||||||||
\(881\) | − | 651746.i | − | 0.839705i | −0.907592 | − | 0.419853i | \(-0.862082\pi\) | ||
0.907592 | − | 0.419853i | \(-0.137918\pi\) | |||||||
\(882\) | 1.71878e6 | − | 1.40625e6i | 2.20944 | − | 1.80770i | ||||
\(883\) | −740498. | −0.949736 | −0.474868 | − | 0.880057i | \(-0.657504\pi\) | ||||
−0.474868 | + | 0.880057i | \(0.657504\pi\) | |||||||
\(884\) | − | 16909.9i | − | 0.0216390i | ||||||
\(885\) | −59319.7 | + | 125178.i | −0.0757378 | + | 0.159824i | ||||
\(886\) | 1.36955e6 | 1.74466 | ||||||||
\(887\) | 846445.i | 1.07585i | 0.842993 | + | 0.537925i | \(0.180792\pi\) | ||||
−0.842993 | + | 0.537925i | \(0.819208\pi\) | |||||||
\(888\) | 302979. | + | 143576.i | 0.384226 | + | 0.182078i | ||||
\(889\) | 292722. | 0.370384 | ||||||||
\(890\) | − | 917681.i | − | 1.15854i | ||||||
\(891\) | −716611. | − | 144779.i | −0.902668 | − | 0.182369i | ||||
\(892\) | −155309. | −0.195194 | ||||||||
\(893\) | − | 38952.9i | − | 0.0488468i | ||||||
\(894\) | 28911.0 | − | 61008.7i | 0.0361732 | − | 0.0763337i | ||||
\(895\) | 577779. | 0.721300 | ||||||||
\(896\) | − | 1.36547e6i | − | 1.70085i | ||||||
\(897\) | −20154.8 | − | 9551.02i | −0.0250492 | − | 0.0118704i | ||||
\(898\) | −61792.8 | −0.0766276 | ||||||||
\(899\) | 856548.i | 1.05982i | ||||||||
\(900\) | −257308. | − | 314492.i | −0.317664 | − | 0.388261i | ||||
\(901\) | −1.43527e6 | −1.76801 | ||||||||
\(902\) | 849366.i | 1.04395i | ||||||||
\(903\) | 420905. | − | 888204.i | 0.516189 | − | 1.08927i | ||||
\(904\) | −79235.1 | −0.0969573 | ||||||||
\(905\) | − | 601609.i | − | 0.734543i | ||||||
\(906\) | 838151. | + | 397185.i | 1.02109 | + | 0.483879i | ||||
\(907\) | −1.01416e6 | −1.23280 | −0.616402 | − | 0.787432i | \(-0.711410\pi\) | ||||
−0.616402 | + | 0.787432i | \(0.711410\pi\) | |||||||
\(908\) | − | 826543.i | − | 1.00252i | ||||||
\(909\) | 205470. | − | 168110.i | 0.248669 | − | 0.203454i | ||||
\(910\) | 93625.2 | 0.113060 | ||||||||
\(911\) | 353146.i | 0.425518i | 0.977105 | + | 0.212759i | \(0.0682449\pi\) | ||||
−0.977105 | + | 0.212759i | \(0.931755\pi\) | |||||||
\(912\) | 320188. | − | 675670.i | 0.384960 | − | 0.812353i | ||||
\(913\) | 876908. | 1.05199 | ||||||||
\(914\) | − | 1.84213e6i | − | 2.20510i | ||||||
\(915\) | 708916. | + | 335943.i | 0.846745 | + | 0.401258i | ||||
\(916\) | 158163. | 0.188501 | ||||||||
\(917\) | − | 2.12886e6i | − | 2.53168i | ||||||
\(918\) | −1.03141e6 | + | 255888.i | −1.22389 | + | 0.303644i | ||||
\(919\) | 571593. | 0.676793 | 0.338396 | − | 0.941004i | \(-0.390116\pi\) | ||||
0.338396 | + | 0.941004i | \(0.390116\pi\) | |||||||
\(920\) | 448167.i | 0.529498i | ||||||||
\(921\) | −155483. | + | 328104.i | −0.183301 | + | 0.386806i | ||||
\(922\) | 1.10966e6 | 1.30535 | ||||||||
\(923\) | 46849.3i | 0.0549920i | ||||||||
\(924\) | 761322. | + | 360777.i | 0.891711 | + | 0.422567i | ||||
\(925\) | 599200. | 0.700306 | ||||||||
\(926\) | 959750.i | 1.11927i | ||||||||
\(927\) | −761067. | − | 930204.i | −0.885652 | − | 1.08248i | ||||
\(928\) | 750847. | 0.871877 | ||||||||
\(929\) | 613192.i | 0.710502i | 0.934771 | + | 0.355251i | \(0.115605\pi\) | ||||
−0.934771 | + | 0.355251i | \(0.884395\pi\) | |||||||
\(930\) | −813328. | + | 1.71630e6i | −0.940372 | + | 1.98440i | ||||
\(931\) | 1.41962e6 | 1.63785 | ||||||||
\(932\) | 249984.i | 0.287793i | ||||||||
\(933\) | −17539.4 | − | 8311.63i | −0.0201489 | − | 0.00954823i | ||||
\(934\) | −2.16080e6 | −2.47697 | ||||||||
\(935\) | 1.09260e6i | 1.24979i | ||||||||
\(936\) | 12707.7 | − | 10397.1i | 0.0145049 | − | 0.0118675i | ||||
\(937\) | 1.14653e6 | 1.30589 | 0.652944 | − | 0.757406i | \(-0.273534\pi\) | ||||
0.652944 | + | 0.757406i | \(0.273534\pi\) | |||||||
\(938\) | − | 3.43812e6i | − | 3.90765i | ||||||
\(939\) | −542825. | + | 1.14548e6i | −0.615642 | + | 1.29914i | ||||
\(940\) | 48036.8 | 0.0543649 | ||||||||
\(941\) | 1.17604e6i | 1.32814i | 0.747670 | + | 0.664070i | \(0.231172\pi\) | ||||
−0.747670 | + | 0.664070i | \(0.768828\pi\) | |||||||
\(942\) | 1.88650e6 | + | 893981.i | 2.12596 | + | 1.00746i | ||||
\(943\) | 606369. | 0.681889 | ||||||||
\(944\) | − | 144010.i | − | 0.161602i | ||||||
\(945\) | −527578. | − | 2.12650e6i | −0.590776 | − | 2.38123i | ||||
\(946\) | 694325. | 0.775855 | ||||||||
\(947\) | 777766.i | 0.867259i | 0.901091 | + | 0.433629i | \(0.142767\pi\) | ||||
−0.901091 | + | 0.433629i | \(0.857233\pi\) | |||||||
\(948\) | 298790. | − | 630515.i | 0.332468 | − | 0.701583i | ||||
\(949\) | −29368.3 | −0.0326096 | ||||||||
\(950\) | − | 697556.i | − | 0.772915i | ||||||
\(951\) | 822014. | + | 389538.i | 0.908904 | + | 0.430714i | ||||
\(952\) | −839382. | −0.926160 | ||||||||
\(953\) | − | 1840.55i | − | 0.00202657i | −0.999999 | − | 0.00101329i | \(-0.999677\pi\) | ||
0.999999 | − | 0.00101329i | \(-0.000322539\pi\) | |||||||
\(954\) | 1.28746e6 | + | 1.57358e6i | 1.41461 | + | 1.72899i | ||||
\(955\) | −1.64990e6 | −1.80906 | ||||||||
\(956\) | 631036.i | 0.690459i | ||||||||
\(957\) | 298911. | − | 630769.i | 0.326375 | − | 0.688726i | ||||
\(958\) | 315151. | 0.343390 | ||||||||
\(959\) | − | 1.38662e6i | − | 1.50772i | ||||||
\(960\) | 100129. | + | 47449.6i | 0.108647 | + | 0.0514861i | ||||
\(961\) | 590972. | 0.639912 | ||||||||
\(962\) | − | 35322.9i | − | 0.0381686i | ||||||
\(963\) | −236425. | + | 193436.i | −0.254941 | + | 0.208586i | ||||
\(964\) | −151652. | −0.163190 | ||||||||
\(965\) | − | 1.09769e6i | − | 1.17876i | ||||||
\(966\) | 691667. | − | 1.45957e6i | 0.741213 | − | 1.56413i | ||||
\(967\) | 408089. | 0.436417 | 0.218209 | − | 0.975902i | \(-0.429979\pi\) | ||||
0.218209 | + | 0.975902i | \(0.429979\pi\) | |||||||
\(968\) | 73081.6i | 0.0779933i | ||||||||
\(969\) | −613878. | − | 290906.i | −0.653784 | − | 0.309817i | ||||
\(970\) | −1.36976e6 | −1.45579 | ||||||||
\(971\) | − | 109032.i | − | 0.115642i | −0.998327 | − | 0.0578209i | \(-0.981585\pi\) | ||
0.998327 | − | 0.0578209i | \(-0.0184152\pi\) | |||||||
\(972\) | 448987. | + | 335609.i | 0.475227 | + | 0.355223i | ||||
\(973\) | 1.99793e6 | 2.11035 | ||||||||
\(974\) | 2.36880e6i | 2.49696i | ||||||||
\(975\) | 12566.0 | − | 26517.0i | 0.0132186 | − | 0.0278943i | ||||
\(976\) | −815566. | −0.856168 | ||||||||
\(977\) | 874095.i | 0.915735i | 0.889020 | + | 0.457867i | \(0.151387\pi\) | ||||
−0.889020 | + | 0.457867i | \(0.848613\pi\) | |||||||
\(978\) | −1.02900e6 | − | 487627.i | −1.07582 | − | 0.509811i | ||||
\(979\) | 596325. | 0.622183 | ||||||||
\(980\) | 1.75069e6i | 1.82287i | ||||||||
\(981\) | −917239. | − | 1.12108e6i | −0.953114 | − | 1.16493i | ||||
\(982\) | −535665. | −0.555482 | ||||||||
\(983\) | 641128.i | 0.663495i | 0.943368 | + | 0.331747i | \(0.107638\pi\) | ||||
−0.943368 | + | 0.331747i | \(0.892362\pi\) | |||||||
\(984\) | −191159. | + | 403388.i | −0.197426 | + | 0.416613i | ||||
\(985\) | 818593. | 0.843715 | ||||||||
\(986\) | − | 1.01459e6i | − | 1.04361i | ||||||
\(987\) | 107234. | + | 50816.3i | 0.110077 | + | 0.0521637i | ||||
\(988\) | −15312.6 | −0.0156868 | ||||||||
\(989\) | − | 495684.i | − | 0.506772i | ||||||
\(990\) | 1.19788e6 | − | 980073.i | 1.22220 | − | 0.999972i | ||||
\(991\) | −290313. | −0.295610 | −0.147805 | − | 0.989017i | \(-0.547221\pi\) | ||||
−0.147805 | + | 0.989017i | \(0.547221\pi\) | |||||||
\(992\) | − | 1.32760e6i | − | 1.34910i | ||||||
\(993\) | −157863. | + | 333126.i | −0.160096 | + | 0.337839i | ||||
\(994\) | −3.39274e6 | −3.43382 | ||||||||
\(995\) | − | 1.43255e6i | − | 1.44698i | ||||||
\(996\) | −607590. | − | 287927.i | −0.612480 | − | 0.290244i | ||||
\(997\) | 996017. | 1.00202 | 0.501010 | − | 0.865442i | \(-0.332962\pi\) | ||||
0.501010 | + | 0.865442i | \(0.332962\pi\) | |||||||
\(998\) | − | 1.93928e6i | − | 1.94706i | ||||||
\(999\) | −802286. | + | 199045.i | −0.803893 | + | 0.199443i |
(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 | 177.5.b.a.119.61 | yes | 78 | |
3.2 | odd | 2 | inner | 177.5.b.a.119.18 | ✓ | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.b.a.119.18 | ✓ | 78 | 3.2 | odd | 2 | inner | |
177.5.b.a.119.61 | yes | 78 | 1.1 | even | 1 | trivial |