Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,6,Mod(49,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.i (of order \(3\), degree \(2\), not 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: | \(23.0952700531\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 175x^{8} + 8800x^{6} + 124623x^{4} + 498609x^{2} + 442368 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{10} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 97.4 | ||
Root | \(7.64342i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.97 |
Dual form | 144.6.i.d.49.4 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 11.7655 | + | 10.2260i | 0.754760 | + | 0.656001i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.88422 | + | 8.45972i | 0.0873716 | + | 0.151332i | 0.906399 | − | 0.422422i | \(-0.138820\pi\) |
−0.819028 | + | 0.573754i | \(0.805487\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 68.3340 | − | 118.358i | 0.527099 | − | 0.912962i | −0.472403 | − | 0.881383i | \(-0.656613\pi\) |
0.999501 | − | 0.0315789i | \(-0.0100535\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 33.8560 | + | 240.630i | 0.139325 | + | 0.990247i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 326.660 | − | 565.792i | 0.813982 | − | 1.40986i | −0.0960745 | − | 0.995374i | \(-0.530629\pi\) |
0.910057 | − | 0.414484i | \(-0.136038\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −125.247 | − | 216.934i | −0.205546 | − | 0.356016i | 0.744761 | − | 0.667332i | \(-0.232564\pi\) |
−0.950307 | + | 0.311316i | \(0.899230\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −29.0440 | + | 149.479i | −0.0333294 | + | 0.171535i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 249.768 | 0.209611 | 0.104806 | − | 0.994493i | \(-0.466578\pi\) | ||||
0.104806 | + | 0.994493i | \(0.466578\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1754.03 | 1.11469 | 0.557343 | − | 0.830282i | \(-0.311821\pi\) | ||||
0.557343 | + | 0.830282i | \(0.311821\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2014.32 | − | 693.759i | 0.996737 | − | 0.343290i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −827.440 | − | 1433.17i | −0.326150 | − | 0.564908i | 0.655595 | − | 0.755113i | \(-0.272418\pi\) |
−0.981744 | + | 0.190205i | \(0.939085\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1514.79 | − | 2623.69i | 0.484732 | − | 0.839581i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2062.36 | + | 3177.35i | −0.544446 | + | 0.838796i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2123.96 | + | 3678.81i | −0.468977 | + | 0.812292i | −0.999371 | − | 0.0354595i | \(-0.988711\pi\) |
0.530394 | + | 0.847751i | \(0.322044\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4493.72 | + | 7783.34i | 0.839849 | + | 1.45466i | 0.890020 | + | 0.455921i | \(0.150690\pi\) |
−0.0501712 | + | 0.998741i | \(0.515977\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9629.16 | − | 3316.41i | 1.53923 | − | 0.530131i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1335.03 | 0.184214 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6000.33 | −0.720561 | −0.360280 | − | 0.932844i | \(-0.617319\pi\) | ||||
−0.360280 | + | 0.932844i | \(0.617319\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 744.779 | − | 3833.13i | 0.0784090 | − | 0.403545i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5372.59 | + | 9305.61i | 0.499142 | + | 0.864540i | 1.00000 | 0.000990010i | \(-0.000315130\pi\) | |
−0.500857 | + | 0.865530i | \(0.666982\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5023.30 | − | 8700.62i | 0.414303 | − | 0.717594i | −0.581052 | − | 0.813867i | \(-0.697359\pi\) |
0.995355 | + | 0.0962724i | \(0.0306920\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1870.30 | + | 1461.70i | −0.137683 | + | 0.107604i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11743.3 | − | 20340.0i | 0.775435 | − | 1.34309i | −0.159114 | − | 0.987260i | \(-0.550864\pi\) |
0.934550 | − | 0.355833i | \(-0.115803\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −935.582 | − | 1620.48i | −0.0556662 | − | 0.0964167i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2938.66 | + | 2554.14i | 0.158206 | + | 0.137505i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9411.34 | 0.460216 | 0.230108 | − | 0.973165i | \(-0.426092\pi\) | ||||
0.230108 | + | 0.973165i | \(0.426092\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6381.93 | 0.284476 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 20637.1 | + | 17936.8i | 0.841320 | + | 0.731235i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 22083.4 | + | 38249.5i | 0.825915 | + | 1.43053i | 0.901218 | + | 0.433366i | \(0.142674\pi\) |
−0.0753026 | + | 0.997161i | \(0.523992\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11202.4 | − | 19403.2i | 0.385467 | − | 0.667649i | −0.606366 | − | 0.795185i | \(-0.707374\pi\) |
0.991834 | + | 0.127536i | \(0.0407069\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 30794.0 | + | 12436.1i | 0.977496 | + | 0.394759i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1223.47 | − | 2119.11i | 0.0359177 | − | 0.0622113i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −18001.5 | − | 31179.5i | −0.489916 | − | 0.848560i | 0.510016 | − | 0.860165i | \(-0.329639\pi\) |
−0.999933 | + | 0.0116049i | \(0.996306\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4920.36 | − | 25323.4i | 0.124415 | − | 0.640325i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −78538.5 | −1.84900 | −0.924499 | − | 0.381184i | \(-0.875517\pi\) | ||||
−0.924499 | + | 0.381184i | \(0.875517\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 61305.5 | 1.34646 | 0.673229 | − | 0.739434i | \(-0.264907\pi\) | ||||
0.673229 | + | 0.739434i | \(0.264907\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 44652.3 | − | 15378.9i | 0.916623 | − | 0.315697i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −44644.1 | − | 77325.8i | −0.858098 | − | 1.48627i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13745.0 | − | 23807.1i | 0.247787 | − | 0.429180i | −0.715125 | − | 0.698997i | \(-0.753630\pi\) |
0.962911 | + | 0.269817i | \(0.0869634\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −56756.5 | + | 16293.5i | −0.961177 | + | 0.275932i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −32403.2 | + | 56124.0i | −0.516289 | + | 0.894238i | 0.483533 | + | 0.875326i | \(0.339353\pi\) |
−0.999821 | + | 0.0189117i | \(0.993980\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1219.92 | + | 2112.97i | 0.0183141 | + | 0.0317209i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −62609.2 | + | 21563.4i | −0.886829 | + | 0.305436i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −34652.4 | −0.463722 | −0.231861 | − | 0.972749i | \(-0.574482\pi\) | ||||
−0.231861 | + | 0.972749i | \(0.574482\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −34234.5 | −0.433372 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −26721.8 | + | 137528.i | −0.320375 | + | 1.64886i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8567.06 | + | 14838.6i | 0.0973919 | + | 0.168688i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8056.14 | + | 13953.6i | −0.0869356 | + | 0.150577i | −0.906214 | − | 0.422819i | \(-0.861041\pi\) |
0.819279 | + | 0.573395i | \(0.194374\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 147206. | + | 59448.8i | 1.50952 | + | 0.609614i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −93469.6 | + | 161894.i | −0.911731 | + | 1.57916i | −0.100113 | + | 0.994976i | \(0.531921\pi\) |
−0.811618 | + | 0.584189i | \(0.801413\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −84293.8 | − | 146001.i | −0.782893 | − | 1.35601i | −0.930250 | − | 0.366927i | \(-0.880410\pi\) |
0.147357 | − | 0.989083i | \(-0.452923\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 15707.4 | + | 13652.1i | 0.139037 | + | 0.120844i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −155131. | −1.30991 | −0.654953 | − | 0.755669i | \(-0.727312\pi\) | ||||
−0.654953 | + | 0.755669i | \(0.727312\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −115289. | −0.929439 | −0.464720 | − | 0.885458i | \(-0.653845\pi\) | ||||
−0.464720 | + | 0.885458i | \(0.653845\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −70597.1 | − | 61359.6i | −0.543850 | − | 0.472689i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −62693.8 | − | 108589.i | −0.461880 | − | 0.799999i | 0.537175 | − | 0.843471i | \(-0.319491\pi\) |
−0.999055 | + | 0.0434719i | \(0.986158\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8082.80 | − | 13999.8i | 0.0569924 | − | 0.0987138i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 47960.5 | − | 37482.7i | 0.323906 | − | 0.253143i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17067.7 | − | 29562.1i | 0.110486 | − | 0.191367i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −132889. | − | 230170.i | −0.825134 | − | 1.42917i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −31948.1 | + | 164426.i | −0.190407 | + | 0.979958i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 60120.6 | 0.344151 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17459.4 | −0.0960548 | −0.0480274 | − | 0.998846i | \(-0.515293\pi\) | ||||
−0.0480274 | + | 0.998846i | \(0.515293\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 148075. | − | 50998.9i | 0.783442 | − | 0.269828i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14464.0 | − | 25052.4i | −0.0736395 | − | 0.127547i | 0.826854 | − | 0.562416i | \(-0.190128\pi\) |
−0.900494 | + | 0.434869i | \(0.856795\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 119860. | − | 207603.i | 0.587549 | − | 1.01767i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −36952.5 | − | 1928.07i | −0.174506 | − | 0.00910518i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −204277. | + | 353818.i | −0.929862 | + | 1.61057i | −0.146312 | + | 0.989239i | \(0.546740\pi\) |
−0.783550 | + | 0.621329i | \(0.786593\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 144577. | + | 250415.i | 0.634693 | + | 1.09932i | 0.986580 | + | 0.163278i | \(0.0522066\pi\) |
−0.351888 | + | 0.936042i | \(0.614460\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 346164. | − | 119224.i | 1.46634 | − | 0.505027i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −163653. | −0.669243 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −41495.6 | −0.163901 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5563.42 | − | 28633.1i | 0.0212348 | − | 0.109289i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 169.673 | + | 293.882i | 0.000626104 | + | 0.00108444i | 0.866338 | − | 0.499458i | \(-0.166467\pi\) |
−0.865712 | + | 0.500542i | \(0.833134\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 178737. | − | 309581.i | 0.637928 | − | 1.10492i | −0.347958 | − | 0.937510i | \(-0.613125\pi\) |
0.985887 | − | 0.167414i | \(-0.0535417\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8456.15 | + | 60101.7i | 0.0292041 | + | 0.207567i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −43896.6 | + | 76031.1i | −0.146758 | + | 0.254192i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 376.310 | + | 651.789i | 0.00121842 | + | 0.00211037i | 0.866634 | − | 0.498944i | \(-0.166279\pi\) |
−0.865416 | + | 0.501055i | \(0.832945\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 110730. | + | 96240.8i | 0.347353 | + | 0.301902i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −226169. | −0.687653 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 358488. | 1.05683 | 0.528416 | − | 0.848986i | \(-0.322786\pi\) | ||||
0.528416 | + | 0.848986i | \(0.322786\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 75086.8 | + | 65261.9i | 0.214711 | + | 0.186616i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −246875. | − | 427601.i | −0.684994 | − | 1.18644i | −0.973439 | − | 0.228948i | \(-0.926472\pi\) |
0.288445 | − | 0.957496i | \(-0.406862\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 154273. | − | 267209.i | 0.415502 | − | 0.719670i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 59384.4 | + | 422072.i | 0.155304 | + | 1.10381i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −83924.6 | + | 145362.i | −0.213193 | + | 0.369262i | −0.952712 | − | 0.303874i | \(-0.901720\pi\) |
0.739519 | + | 0.673136i | \(0.235053\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −207023. | − | 358575.i | −0.511004 | − | 0.885084i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −131319. | + | 675852.i | −0.315060 | + | 1.62151i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 483862. | 1.12873 | 0.564364 | − | 0.825526i | \(-0.309122\pi\) | ||||
0.564364 | + | 0.825526i | \(0.309122\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 74732.3 | 0.169555 | 0.0847777 | − | 0.996400i | \(-0.472982\pi\) | ||||
0.0847777 | + | 0.996400i | \(0.472982\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 330221. | − | 113732.i | 0.728914 | − | 0.251048i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −29306.9 | − | 50761.1i | −0.0629565 | − | 0.109044i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 81589.4 | − | 141317.i | 0.170620 | − | 0.295522i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 235136. | + | 461218.i | 0.478812 | + | 0.939187i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −297130. | + | 514645.i | −0.589337 | + | 1.02076i | 0.404983 | + | 0.914324i | \(0.367277\pi\) |
−0.994319 | + | 0.106437i | \(0.966056\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 44949.8 | + | 77855.4i | 0.0868630 | + | 0.150451i | 0.906184 | − | 0.422885i | \(-0.138982\pi\) |
−0.819321 | + | 0.573336i | \(0.805649\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 36064.8 | − | 12421.2i | 0.0679200 | − | 0.0233926i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 425161. | 0.780527 | 0.390263 | − | 0.920703i | \(-0.372384\pi\) | ||||
0.390263 | + | 0.920703i | \(0.372384\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −374339. | −0.670089 | −0.335044 | − | 0.942202i | \(-0.608751\pi\) | ||||
−0.335044 | + | 0.942202i | \(0.608751\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 107046. | − | 550928.i | 0.186887 | − | 0.961844i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 290278. | + | 502775.i | 0.494394 | + | 0.856316i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −52481.9 | + | 90901.3i | −0.0872217 | + | 0.151072i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 316849. | − | 247628.i | 0.513957 | − | 0.401675i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 572971. | − | 992416.i | 0.907334 | − | 1.57155i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −82302.7 | − | 142552.i | −0.127265 | − | 0.220429i | 0.795351 | − | 0.606149i | \(-0.207286\pi\) |
−0.922616 | + | 0.385720i | \(0.873953\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −924048. | − | 803138.i | −1.39555 | − | 1.21295i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 98139.7 | 0.144793 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.22829e6 | 1.77073 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 721293. | + | 626913.i | 1.01625 | + | 0.883278i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −31282.7 | − | 54183.2i | −0.0430848 | − | 0.0746250i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −162339. | + | 281179.i | −0.218605 | + | 0.378635i | −0.954382 | − | 0.298589i | \(-0.903484\pi\) |
0.735777 | + | 0.677224i | \(0.236817\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 682623. | + | 275676.i | 0.898928 | + | 0.363030i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −354884. | + | 614677.i | −0.457111 | + | 0.791739i | −0.998807 | − | 0.0488351i | \(-0.984449\pi\) |
0.541696 | + | 0.840575i | \(0.317782\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 126953. | + | 219889.i | 0.159976 | + | 0.277086i | 0.934860 | − | 0.355017i | \(-0.115525\pi\) |
−0.774884 | + | 0.632104i | \(0.782192\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 265475. | − | 1.36631e6i | 0.327336 | − | 1.68469i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −557666. | −0.672952 | −0.336476 | − | 0.941692i | \(-0.609235\pi\) | ||||
−0.336476 | + | 0.941692i | \(0.609235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 229427. | 0.271004 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 405171. | − | 139546.i | 0.468562 | − | 0.161379i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −266147. | − | 460981.i | −0.301389 | − | 0.522021i | 0.675062 | − | 0.737761i | \(-0.264117\pi\) |
−0.976451 | + | 0.215740i | \(0.930784\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −332544. | + | 575984.i | −0.368814 | + | 0.638804i | −0.989380 | − | 0.145350i | \(-0.953569\pi\) |
0.620567 | + | 0.784154i | \(0.286903\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −834390. | − | 388693.i | −0.906470 | − | 0.422270i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9139.17 | − | 15829.5i | 0.00972729 | − | 0.0168482i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −219687. | − | 380508.i | −0.229119 | − | 0.396846i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −955167. | + | 328972.i | −0.976295 | + | 0.336249i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 906446. | 0.908150 | 0.454075 | − | 0.890963i | \(-0.349970\pi\) | ||||
0.454075 | + | 0.890963i | \(0.349970\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.08117e6 | −1.06192 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7254.26 | + | 37335.2i | −0.00698622 | + | 0.0359557i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 362420. | + | 627731.i | 0.342279 | + | 0.592844i | 0.984855 | − | 0.173377i | \(-0.0554680\pi\) |
−0.642577 | + | 0.766221i | \(0.722135\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −410027. | + | 710187.i | −0.379807 | + | 0.657844i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −957140. | − | 386539.i | −0.869709 | − | 0.351230i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 126262. | − | 218692.i | 0.112560 | − | 0.194959i | −0.804242 | − | 0.594302i | \(-0.797428\pi\) |
0.916802 | + | 0.399343i | \(0.130762\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 45967.1 | + | 79617.3i | 0.0402098 | + | 0.0696455i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −407704. | − | 354357.i | −0.349999 | − | 0.304202i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −191107. | −0.161026 | −0.0805131 | − | 0.996754i | \(-0.525656\pi\) | ||||
−0.0805131 | + | 0.996754i | \(0.525656\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −86694.8 | −0.0717084 | −0.0358542 | − | 0.999357i | \(-0.511415\pi\) | ||||
−0.0358542 | + | 0.999357i | \(0.511415\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −402788. | − | 350084.i | −0.327092 | − | 0.284292i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −989643. | − | 1.71411e6i | −0.789127 | − | 1.36681i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −635239. | + | 1.10027e6i | −0.497437 | + | 0.861586i | −0.999996 | − | 0.00295734i | \(-0.999059\pi\) |
0.502559 | + | 0.864543i | \(0.332392\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.72077e6 | + | 1.34484e6i | −1.32346 | + | 1.03433i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28414.8 | − | 49215.9i | 0.0214674 | − | 0.0371826i | −0.855092 | − | 0.518476i | \(-0.826500\pi\) |
0.876560 | + | 0.481293i | \(0.159833\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 676798. | + | 1.17225e6i | 0.502335 | + | 0.870069i | 0.999996 | + | 0.00269796i | \(0.000858787\pi\) |
−0.497662 | + | 0.867371i | \(0.665808\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −50943.9 | + | 262191.i | −0.0371518 | + | 0.191208i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.46852e6 | 1.05239 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.35747e6 | −0.956063 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −237475. | + | 81789.7i | −0.164394 | + | 0.0566195i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 263851. | + | 457003.i | 0.179552 | + | 0.310993i | 0.941727 | − | 0.336378i | \(-0.109202\pi\) |
−0.762175 | + | 0.647371i | \(0.775869\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −215720. | + | 373638.i | −0.144323 | + | 0.249975i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.12403e6 | + | 2.20478e6i | 0.739414 | + | 1.45036i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −207269. | + | 359000.i | −0.134077 | + | 0.232229i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −686525. | − | 1.18910e6i | −0.436757 | − | 0.756486i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.75526e6 | + | 948947.i | −1.72407 | + | 0.593794i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 218861. | 0.134716 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.15348e6 | −0.698497 | −0.349249 | − | 0.937030i | \(-0.613563\pi\) | ||||
−0.349249 | + | 0.937030i | \(0.613563\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 501252. | − | 2.57977e6i | 0.298648 | − | 1.53704i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −758833. | − | 1.31434e6i | −0.444883 | − | 0.770559i | 0.553161 | − | 0.833074i | \(-0.313421\pi\) |
−0.998044 | + | 0.0625148i | \(0.980088\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 979958. | − | 1.69734e6i | 0.565388 | − | 0.979281i | −0.431625 | − | 0.902053i | \(-0.642060\pi\) |
0.997013 | − | 0.0772280i | \(-0.0246069\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 45198.9 | + | 321249.i | 0.0256656 | + | 0.182417i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −916140. | + | 1.58680e6i | −0.512052 | + | 0.886899i | 0.487851 | + | 0.872927i | \(0.337781\pi\) |
−0.999902 | + | 0.0139724i | \(0.995552\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.38763e6 | + | 2.40344e6i | 0.763477 | + | 1.32238i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.82521e6 | − | 1.58638e6i | −0.988665 | − | 0.859300i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 438100. | 0.233651 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −758891. | −0.398539 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.35644e6 | − | 1.17895e6i | −0.701503 | − | 0.609713i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.60493e6 | − | 2.77983e6i | −0.817462 | − | 1.41589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −360056. | + | 623635.i | −0.180634 | + | 0.312868i | −0.942097 | − | 0.335341i | \(-0.891148\pi\) |
0.761462 | + | 0.648209i | \(0.224482\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −203147. | − | 1.44386e6i | −0.100392 | − | 0.713533i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 175847. | − | 304575.i | 0.0856095 | − | 0.148280i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.55433e6 | + | 2.69218e6i | 0.745537 | + | 1.29131i | 0.949943 | + | 0.312422i | \(0.101140\pi\) |
−0.204406 | + | 0.978886i | \(0.565526\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 372808. | − | 1.91872e6i | 0.176192 | − | 0.906801i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.87168e6 | 2.73449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.04125e6 | 0.936831 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 238261. | − | 82060.4i | 0.107772 | − | 0.0371181i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 136034. | + | 235618.i | 0.0606490 | + | 0.105047i | 0.894756 | − | 0.446556i | \(-0.147350\pi\) |
−0.834107 | + | 0.551603i | \(0.814016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.51024e6 | + | 2.61582e6i | −0.663718 | + | 1.14959i | 0.315913 | + | 0.948788i | \(0.397689\pi\) |
−0.979631 | + | 0.200805i | \(0.935644\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 947581. | + | 49441.8i | 0.410533 | + | 0.0214204i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −526944. | + | 912695.i | −0.225075 | + | 0.389842i | −0.956342 | − | 0.292250i | \(-0.905596\pi\) |
0.731267 | + | 0.682092i | \(0.238930\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −383599. | − | 664413.i | −0.161550 | − | 0.279813i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 503114. | − | 173279.i | 0.208927 | − | 0.0719574i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.26085e6 | 1.74486 | 0.872430 | − | 0.488739i | \(-0.162543\pi\) | ||||
0.872430 | + | 0.488739i | \(0.162543\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 600514. | 0.242524 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 790220. | − | 4.06700e6i | 0.314762 | − | 1.61997i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 299430. | + | 518628.i | 0.117642 | + | 0.203762i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −155650. | + | 269594.i | −0.0603231 | + | 0.104483i | −0.894610 | − | 0.446848i | \(-0.852546\pi\) |
0.834287 | + | 0.551331i | \(0.185880\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.05731e6 | + | 1.60786e6i | −0.786565 | + | 0.614726i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 643115. | − | 1.11391e6i | 0.242579 | − | 0.420160i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.13768e6 | + | 1.97052e6i | 0.423397 | + | 0.733345i | 0.996269 | − | 0.0862997i | \(-0.0275043\pi\) |
−0.572872 | + | 0.819645i | \(0.694171\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 707352. | + | 614796.i | 0.259751 | + | 0.225763i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.06408e6 | 0.385585 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.28710e6 | −1.17548 | −0.587739 | − | 0.809050i | \(-0.699982\pi\) | ||||
−0.587739 | + | 0.809050i | \(0.699982\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −205419. | − | 178540.i | −0.0724983 | − | 0.0630121i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.12336e6 | + | 1.94572e6i | 0.391311 | + | 0.677770i | 0.992623 | − | 0.121244i | \(-0.0386885\pi\) |
−0.601312 | + | 0.799014i | \(0.705355\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 436103. | − | 755352.i | 0.149947 | − | 0.259715i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.26370e6 | + | 914189.i | 0.768318 | + | 0.310283i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 683723. | − | 1.18424e6i | 0.229090 | − | 0.396796i | −0.728449 | − | 0.685100i | \(-0.759758\pi\) |
0.957539 | + | 0.288305i | \(0.0930916\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −206668. | − | 357960.i | −0.0683647 | − | 0.118411i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 86010.2 | − | 442665.i | 0.0280911 | − | 0.144575i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 268535. | 0.0865982 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.52652e6 | 0.486099 | 0.243050 | − | 0.970014i | \(-0.421852\pi\) | ||||
0.243050 | + | 0.970014i | \(0.421852\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.53318e6 | − | 1.21687e6i | 1.11105 | − | 0.382660i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.36998e6 | − | 4.10493e6i | −0.736011 | − | 1.27481i | −0.954278 | − | 0.298920i | \(-0.903374\pi\) |
0.218267 | − | 0.975889i | \(-0.429960\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.12565e6 | − | 1.94968e6i | 0.345255 | − | 0.597999i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −415050. | − | 400563.i | −0.125737 | − | 0.121348i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.96007e6 | + | 3.39494e6i | −0.586523 | + | 1.01589i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −478468. | − | 828731.i | −0.141431 | − | 0.244966i | 0.786605 | − | 0.617457i | \(-0.211837\pi\) |
−0.928036 | + | 0.372491i | \(0.878504\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.02159e6 | + | 2.07392e6i | −1.75836 | + | 0.605602i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.03619e6 | 1.74136 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −633057. | −0.180436 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −859728. | + | 4.42473e6i | −0.242114 | + | 1.24608i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 885418. | + | 1.53359e6i | 0.246384 | + | 0.426750i | 0.962520 | − | 0.271211i | \(-0.0874241\pi\) |
−0.716135 | + | 0.697961i | \(0.754091\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.54265e6 | + | 2.67194e6i | −0.424190 | + | 0.734719i | −0.996344 | − | 0.0854269i | \(-0.972775\pi\) |
0.572154 | + | 0.820146i | \(0.306108\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.29199e6 | + | 2.13716e6i | 1.43803 | + | 0.580746i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 378346. | − | 655315.i | 0.101605 | − | 0.175986i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.53101e6 | − | 2.65180e6i | −0.406359 | − | 0.703834i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.92547e6 | − | 1.67352e6i | −0.505117 | − | 0.439024i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.16873e6 | −0.562356 | −0.281178 | − | 0.959656i | \(-0.590725\pi\) | ||||
−0.281178 | + | 0.959656i | \(0.590725\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.69677e6 | 1.71651 | 0.858253 | − | 0.513226i | \(-0.171550\pi\) | ||||
0.858253 | + | 0.513226i | \(0.171550\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −488218. | − | 424335.i | −0.123706 | − | 0.107519i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.45135e6 | − | 2.51382e6i | −0.363554 | − | 0.629695i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.23130e6 | + | 5.59677e6i | −0.800231 | + | 1.38604i | 0.119232 | + | 0.992866i | \(0.461957\pi\) |
−0.919464 | + | 0.393175i | \(0.871377\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 358260. | − | 279992.i | 0.0877206 | − | 0.0685565i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 877362. | − | 1.51964e6i | 0.212407 | − | 0.367900i | −0.740060 | − | 0.672541i | \(-0.765203\pi\) |
0.952467 | + | 0.304640i | \(0.0985363\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −169250. | − | 293149.i | −0.0405162 | − | 0.0701761i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1008.96 | + | 5192.76i | −0.000238838 | + | 0.00122922i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −515131. | −0.120587 | −0.0602937 | − | 0.998181i | \(-0.519204\pi\) | ||||
−0.0602937 | + | 0.998181i | \(0.519204\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.02006e6 | 1.62517 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.26873e6 | − | 1.81462e6i | 1.20631 | − | 0.415471i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −167209. | − | 289614.i | −0.0378644 | − | 0.0655830i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.46694e6 | − | 4.27287e6i | 0.552546 | − | 0.957038i | −0.445543 | − | 0.895260i | \(-0.646990\pi\) |
0.998090 | − | 0.0617782i | \(-0.0196771\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −515112. | + | 793602.i | −0.114122 | + | 0.175821i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.12932e6 | + | 7.15219e6i | −0.904953 | + | 1.56742i | −0.0839718 | + | 0.996468i | \(0.526761\pi\) |
−0.820981 | + | 0.570956i | \(0.806573\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.09543e6 | + | 1.89734e6i | 0.237482 | + | 0.411331i | 0.959991 | − | 0.280030i | \(-0.0903445\pi\) |
−0.722509 | + | 0.691362i | \(0.757011\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.29396e6 | + | 445659.i | −0.277517 | + | 0.0955807i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.29374e6 | −0.486691 | −0.243345 | − | 0.969940i | \(-0.578245\pi\) | ||||
−0.243345 | + | 0.969940i | \(0.578245\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.92046e6 | −1.03294 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2237.73 | + | 11516.8i | −0.000464788 | + | 0.00239210i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.28183e6 | − | 5.68429e6i | −0.674471 | − | 1.16822i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.65698e6 | − | 4.60203e6i | 0.540324 | − | 0.935869i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 318630. | + | 2.26465e6i | 0.0641197 | + | 0.455728i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 46443.2 | − | 80442.0i | 0.00924876 | − | 0.0160193i | −0.861364 | − | 0.507988i | \(-0.830389\pi\) |
0.870613 | + | 0.491969i | \(0.163723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 751522. | + | 1.30168e6i | 0.148108 | + | 0.256531i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.66101e6 | − | 2.31282e6i | −0.519013 | − | 0.451101i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −157392. | −0.0303828 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.13899e6 | 0.217620 | 0.108810 | − | 0.994063i | \(-0.465296\pi\) | ||||
0.108810 | + | 0.994063i | \(0.465296\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.21781e6 | + | 3.66592e6i | 0.797654 | + | 0.693283i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.36473e6 | − | 7.55993e6i | −0.817060 | − | 1.41519i | −0.907840 | − | 0.419318i | \(-0.862269\pi\) |
0.0907800 | − | 0.995871i | \(-0.471064\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −530498. | + | 918849.i | −0.0983029 | + | 0.170266i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 216066. | + | 1.53568e6i | 0.0396346 | + | 0.281701i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.36685e6 | + | 9.29566e6i | −0.974605 | + | 1.68807i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −738810. | − | 1.27966e6i | −0.132825 | − | 0.230061i | 0.791939 | − | 0.610600i | \(-0.209072\pi\) |
−0.924765 | + | 0.380539i | \(0.875738\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.46804e6 | − | 7.55551e6i | 0.261303 | − | 1.34484i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 743514. | 0.131029 | 0.0655147 | − | 0.997852i | \(-0.479131\pi\) | ||||
0.0655147 | + | 0.997852i | \(0.479131\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.82610e6 | −0.318638 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.54759e6 | − | 1.56625e6i | 0.785709 | − | 0.270609i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.43560e6 | + | 7.68269e6i | 0.758854 | + | 1.31437i | 0.943435 | + | 0.331556i | \(0.107574\pi\) |
−0.184582 | + | 0.982817i | \(0.559093\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.18926e6 | − | 7.25600e6i | 0.709716 | − | 1.22926i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.61743e6 | + | 5.57317e6i | −0.606886 | + | 0.934994i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 823419. | − | 1.42620e6i | 0.136805 | − | 0.236954i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.67214e6 | − | 1.32885e7i | −1.26238 | − | 2.18651i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.47389e6 | + | 852042.i | −0.403146 | + | 0.138849i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.00935e6 | −0.324311 | −0.162155 | − | 0.986765i | \(-0.551845\pi\) | ||||
−0.162155 | + | 0.986765i | \(0.551845\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.39895e6 | −1.02295 | −0.511475 | − | 0.859298i | \(-0.670901\pi\) | ||||
−0.511475 | + | 0.859298i | \(0.670901\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.23106e6 | − | 6.33586e6i | 0.194931 | − | 1.00325i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.12239e6 | + | 1.94403e6i | 0.176042 | + | 0.304914i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.84886e6 | − | 3.20231e6i | 0.287253 | − | 0.497536i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.45633e6 | + | 6.60890e6i | −1.30150 | + | 1.01717i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.34580e6 | − | 2.33100e6i | 0.205193 | − | 0.355405i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −757696. | − | 1.31237e6i | −0.114449 | − | 0.198231i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.69290e6 | + | 4.94800e6i | 0.851918 | + | 0.740447i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.22247e6 | −0.181245 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.26335e7 | −1.85580 | −0.927899 | − | 0.372832i | \(-0.878387\pi\) | ||||
−0.927899 | + | 0.372832i | \(0.878387\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 879266. | + | 764216.i | 0.127974 | + | 0.111229i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −563096. | − | 975311.i | −0.0812066 | − | 0.140654i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.51776e6 | + | 9.55704e6i | −0.788487 | + | 1.36570i | 0.138407 | + | 0.990375i | \(0.455802\pi\) |
−0.926894 | + | 0.375323i | \(0.877532\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.04826e6 | + | 2.03873e6i | 0.714843 | + | 0.288688i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.72548e6 | + | 6.45273e6i | −0.522762 | + | 0.905450i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.87851e6 | − | 3.25367e6i | −0.261216 | − | 0.452440i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 174273. | − | 896925.i | 0.0240159 | − | 0.123602i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.08374e7 | −1.48009 | −0.740046 | − | 0.672557i | \(-0.765196\pi\) | ||||
−0.740046 | + | 0.672557i | \(0.765196\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.51661e6 | −0.340633 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.40506e6 | − | 828334.i | 0.322640 | − | 0.111122i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.65688e6 | − | 2.86981e6i | −0.220303 | − | 0.381577i | 0.734597 | − | 0.678504i | \(-0.237371\pi\) |
−0.954900 | + | 0.296927i | \(0.904038\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 612421. | − | 1.06074e6i | 0.0807103 | − | 0.139794i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.94993e6 | + | 7.83100e6i | −0.254719 | + | 1.02296i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 774757. | − | 1.34192e6i | 0.100319 | − | 0.173758i | −0.811497 | − | 0.584357i | \(-0.801347\pi\) |
0.911816 | + | 0.410599i | \(0.134680\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.59557e6 | + | 2.76361e6i | 0.204798 | + | 0.354720i | 0.950068 | − | 0.312042i | \(-0.101013\pi\) |
−0.745271 | + | 0.666762i | \(0.767680\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.75868e6 | + | 3.01661e6i | −1.11443 | + | 0.383824i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.01359e6 | −0.632381 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.55234e6 | 1.19446 | 0.597228 | − | 0.802072i | \(-0.296269\pi\) | ||||
0.597228 | + | 0.802072i | \(0.296269\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −267293. | + | 1.37567e6i | −0.0331354 | + | 0.170537i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.42848e6 | + | 7.67035e6i | 0.544270 | + | 0.942704i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.07431e6 | − | 5.32487e6i | 0.374608 | − | 0.648840i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 551342. | + | 222658.i | 0.0666088 | + | 0.0268998i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.64410e6 | + | 9.77587e6i | −0.676083 | + | 1.17101i | 0.300069 | + | 0.953918i | \(0.402990\pi\) |
−0.976151 | + | 0.217092i | \(0.930343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.88210e6 | + | 1.36522e7i | 0.936168 | + | 1.62149i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.00225e6 | + | 4.34771e6i | 0.589110 | + | 0.512026i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.91815e6 | −0.924671 | −0.462336 | − | 0.886705i | \(-0.652988\pi\) | ||||
−0.462336 | + | 0.886705i | \(0.652988\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 333449. | 0.0386133 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.40430e6 | − | 3.82801e6i | −0.505756 | − | 0.439579i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.60914e6 | − | 2.78711e6i | −0.183242 | − | 0.317385i | 0.759740 | − | 0.650227i | \(-0.225326\pi\) |
−0.942983 | + | 0.332841i | \(0.891993\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.74304e6 | − | 6.48314e6i | 0.422706 | − | 0.732149i | −0.573497 | − | 0.819208i | \(-0.694414\pi\) |
0.996203 | + | 0.0870589i | \(0.0277468\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.89327e6 | − | 5.38731e6i | 0.772026 | − | 0.603364i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.29811e6 | − | 2.24840e6i | 0.144186 | − | 0.249738i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.06061e6 | − | 8.76524e6i | −0.557483 | − | 0.965588i | −0.997706 | − | 0.0676999i | \(-0.978434\pi\) |
0.440223 | − | 0.897888i | \(-0.354899\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.72613e6 | + | 8.88382e6i | −0.188595 | + | 0.970636i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.88325e6 | −0.637550 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.34715e6 | −0.467254 | −0.233627 | − | 0.972326i | \(-0.575059\pi\) | ||||
−0.233627 | + | 0.972326i | \(0.575059\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.54704e6 | + | 532821.i | −0.164935 | + | 0.0568059i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.29590e6 | − | 1.61010e7i | −0.983056 | − | 1.70270i | −0.650275 | − | 0.759699i | \(-0.725346\pi\) |
−0.332781 | − | 0.943004i | \(-0.607987\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.83014e6 | − | 1.18301e7i | 0.716478 | − | 1.24098i | −0.245909 | − | 0.969293i | \(-0.579086\pi\) |
0.962387 | − | 0.271683i | \(-0.0875802\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.26016e6 | + | 326636.i | 0.651413 | + | 0.0339887i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.36794e6 | + | 4.10139e6i | −0.244428 | + | 0.423361i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.44007e6 | − | 7.69043e6i | −0.454663 | − | 0.787500i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.68898e7 | − | 5.81708e6i | 1.71576 | − | 0.590930i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.49869e6 | −0.151038 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.33121e6 | 0.333065 | 0.166532 | − | 0.986036i | \(-0.446743\pi\) | ||||
0.166532 | + | 0.986036i | \(0.446743\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 489412. | − | 2.51884e6i | 0.0485473 | − | 0.249857i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −85275.4 | − | 147701.i | −0.00839246 | − | 0.0145362i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −234358. | + | 405919.i | −0.0228839 | + | 0.0396361i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.65900e6 | − | 1.88987e7i | −0.257612 | − | 1.83096i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.14477e6 | + | 1.98280e6i | −0.110046 | + | 0.190604i | −0.915788 | − | 0.401661i | \(-0.868433\pi\) |
0.805743 | + | 0.592266i | \(0.201766\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.40519e6 | − | 5.89797e6i | −0.324799 | − | 0.562568i | 0.656673 | − | 0.754176i | \(-0.271963\pi\) |
−0.981472 | + | 0.191608i | \(0.938630\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.15467e6 | + | 1.00358e6i | 0.109284 | + | 0.0949846i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.48250e7 | 1.39231 | 0.696153 | − | 0.717894i | \(-0.254894\pi\) | ||||
0.696153 | + | 0.717894i | \(0.254894\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.88551e7 | 2.68912 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.44516e7 | + | 1.25606e7i | 1.33648 | + | 1.16160i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.06356e6 | + | 7.03829e6i | 0.372927 | + | 0.645928i | 0.990014 | − | 0.140966i | \(-0.0450209\pi\) |
−0.617088 | + | 0.786894i | \(0.711688\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 141291. | − | 244723.i | 0.0128680 | − | 0.0222880i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.07556e6 | + | 1.47520e7i | 0.187595 | + | 1.33332i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.07616e6 | + | 7.06011e6i | −0.365626 | + | 0.633283i | −0.988876 | − | 0.148739i | \(-0.952478\pi\) |
0.623250 | + | 0.782023i | \(0.285812\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.37958e6 | + | 7.58565e6i | 0.389878 | + | 0.675288i | 0.992433 | − | 0.122789i | \(-0.0391839\pi\) |
−0.602555 | + | 0.798077i | \(0.705851\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 186022. | − | 957394.i | 0.0164354 | − | 0.0845876i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.34169e6 | 0.205341 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.02980e6 | 0.611827 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.78536e6 | + | 1.64814e6i | −0.413380 | + | 0.142374i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.31878e6 | − | 1.26765e7i | −0.627527 | − | 1.08691i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.26745e6 | + | 7.39143e6i | −0.363187 | + | 0.629058i | −0.988483 | − | 0.151329i | \(-0.951645\pi\) |
0.625296 | + | 0.780387i | \(0.284978\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.21236e6 | + | 1.02240e7i | 0.440327 | + | 0.863698i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.58162e6 | − | 1.31317e7i | 0.635755 | − | 1.10116i | −0.350599 | − | 0.936526i | \(-0.614022\pi\) |
0.986355 | − | 0.164635i | \(-0.0526447\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.10102e6 | + | 1.90702e6i | 0.0916473 | + | 0.158738i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.04611e7 | + | 3.60295e6i | −0.864391 | + | 0.297708i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.33221e7 | 1.09275 | 0.546376 | − | 0.837540i | \(-0.316007\pi\) | ||||
0.546376 | + | 0.837540i | \(0.316007\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.99094e6 | −0.324974 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −754925. | + | 3.88535e6i | −0.0610256 | + | 0.314078i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.17874e6 | − | 2.04164e6i | −0.0945956 | − | 0.163844i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −981739. | + | 1.70042e6i | −0.0782169 | + | 0.135476i | −0.902481 | − | 0.430730i | \(-0.858256\pi\) |
0.824264 | + | 0.566206i | \(0.191589\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.70954e7 | − | 1.33606e7i | 1.35222 | − | 1.05680i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.41230e6 | + | 2.44617e6i | −0.110908 | + | 0.192099i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.34190e6 | + | 2.32425e6i | 0.104626 | + | 0.181217i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.56124e6 | − | 5.70271e6i | −0.507917 | − | 0.441457i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.36605e7 | 1.81856 | 0.909282 | − | 0.416180i | \(-0.136631\pi\) | ||||
0.909282 | + | 0.416180i | \(0.136631\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.05247e7 | −0.803199 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.69934e6 | + | 2.34614e6i | 0.204543 | + | 0.177779i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.27743e7 | + | 2.21257e7i | 0.961145 | + | 1.66475i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.39194e6 | − | 1.45353e7i | 0.626970 | − | 1.08594i | −0.361186 | − | 0.932494i | \(-0.617628\pi\) |
0.988156 | − | 0.153451i | \(-0.0490386\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.19406e6 | + | 2.50146e6i | 0.459517 | + | 0.185575i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.43656e6 | − | 1.28805e7i | 0.547833 | − | 0.948875i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −799317. | − | 1.38446e6i | −0.0584728 | − | 0.101278i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.58264e6 | − | 8.14532e6i | 0.114970 | − | 0.591712i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.89621e6 | 0.425355 | 0.212677 | − | 0.977123i | \(-0.431782\pi\) | ||||
0.212677 | + | 0.977123i | \(0.431782\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.30405e7 | −1.65065 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.80260e6 | + | 3.37615e6i | −0.697422 | + | 0.240201i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.43470e6 | + | 1.11452e7i | 0.454656 | + | 0.787488i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.15459e6 | + | 8.92800e6i | −0.361708 | + | 0.626496i | −0.988242 | − | 0.152898i | \(-0.951139\pi\) |
0.626534 | + | 0.779394i | \(0.284473\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.84226e6 | − | 1.31057e7i | −0.407157 | − | 0.913358i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.25466e6 | − | 2.17314e6i | 0.0868427 | − | 0.150416i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.66868e6 | − | 1.32825e7i | −0.527182 | − | 0.913106i | −0.999498 | − | 0.0316768i | \(-0.989915\pi\) |
0.472316 | − | 0.881429i | \(-0.343418\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 269401. | − | 92785.2i | 0.0183942 | − | 0.00633520i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.35215e7 | −1.59513 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.97929e6 | 0.133321 | 0.0666606 | − | 0.997776i | \(-0.478766\pi\) | ||||
0.0666606 | + | 0.997776i | \(0.478766\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.30636e6 | − | 6.72341e6i | 0.0874014 | − | 0.449826i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.44874e7 | − | 2.50929e7i | −0.962758 | − | 1.66755i | −0.715520 | − | 0.698592i | \(-0.753810\pi\) |
−0.247238 | − | 0.968955i | \(-0.579523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1657.44 | + | 2870.77i | −0.000109407 | + | 0.000189499i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.46021e7 | − | 5.89704e6i | −0.957448 | − | 0.386663i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.06008e7 | + | 1.83611e7i | −0.690450 | + | 1.19589i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.21827e6 | + | 9.03831e6i | 0.337619 | + | 0.584773i | 0.983984 | − | 0.178255i | \(-0.0570452\pi\) |
−0.646366 | + | 0.763028i | \(0.723712\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.06648e7 | + | 9.26936e6i | 0.685436 | + | 0.595748i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.49196e6 | 0.222947 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.51464e7 | 0.960661 | 0.480331 | − | 0.877087i | \(-0.340517\pi\) | ||||
0.480331 | + | 0.877087i | \(0.340517\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.27205e7 | − | 1.10561e7i | −0.801495 | − | 0.696621i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.10900e7 | + | 1.92084e7i | 0.694176 | + | 1.20235i | 0.970458 | + | 0.241271i | \(0.0775642\pi\) |
−0.276282 | + | 0.961077i | \(0.589102\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.87815e6 | + | 1.36454e7i | −0.489906 | + | 0.848542i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −467142. | + | 365087.i | −0.0288599 | + | 0.0225550i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.53175e6 | − | 9.58127e6i | 0.339527 | − | 0.588078i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.21191e6 | + | 5.56319e6i | 0.195861 | + | 0.339241i | 0.947182 | − | 0.320695i | \(-0.103917\pi\) |
−0.751322 | + | 0.659936i | \(0.770583\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.15513e6 | + | 1.10917e7i | −0.130568 | + | 0.671990i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.34346e6 | 0.141062 | 0.0705308 | − | 0.997510i | \(-0.477531\pi\) | ||||
0.0705308 | + | 0.997510i | \(0.477531\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.72281e7 | 1.62841 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.20866e7 | + | 4.16278e6i | −0.718209 | + | 0.247361i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.42368e6 | + | 1.63223e7i | 0.556387 | + | 0.963690i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.56554e7 | + | 4.44365e7i | −1.50505 | + | 2.60683i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.30851e6 | − | 1.43356e7i | −0.426014 | − | 0.835625i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3675.97 | + | 6366.96i | −0.000212911 | + | 0.000368772i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.42540e7 | + | 2.46887e7i | 0.820354 | + | 1.42089i | 0.905419 | + | 0.424519i | \(0.139557\pi\) |
−0.0850650 | + | 0.996375i | \(0.527110\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.72189e6 | − | 1.28187e6i | 0.212849 | − | 0.0733079i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.71365e7 | −0.973824 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.61228e6 | −0.316925 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −273343. | + | 1.40680e6i | −0.0153387 | + | 0.0789433i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.77498e6 | − | 6.53845e6i | −0.210508 | − | 0.364611i | 0.741366 | − | 0.671101i | \(-0.234178\pi\) |
−0.951874 | + | 0.306491i | \(0.900845\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.93310e6 | − | 5.08028e6i | 0.162540 | − | 0.281528i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.17319e6 | − | 8.33840e6i | −0.0646082 | − | 0.459200i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.00261e7 | − | 3.46862e7i | 1.09599 | − | 1.89831i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.10466e6 | − | 1.91333e6i | −0.0600813 | − | 0.104064i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.24848e6 | − | 1.95427e6i | −0.121536 | − | 0.105633i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.98225e6 | 0.321361 | 0.160680 | − | 0.987006i | \(-0.448631\pi\) | ||||
0.160680 | + | 0.987006i | \(0.448631\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.22339e6 | −0.492423 | −0.246212 | − | 0.969216i | \(-0.579186\pi\) | ||||
−0.246212 | + | 0.969216i | \(0.579186\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.02001e6 | − | 886545.i | −0.0541226 | − | 0.0470408i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.75093e6 | + | 3.03271e6i | 0.0923370 | + | 0.159932i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.81101e6 | − | 1.52611e7i | 0.461818 | − | 0.799892i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.15904e6 | − | 8.23785e6i | −0.0603796 | − | 0.429145i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.48011e6 | + | 1.12239e7i | −0.335525 | + | 0.581146i | −0.983585 | − | 0.180443i | \(-0.942247\pi\) |
0.648061 | + | 0.761589i | \(0.275580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.76675e6 | − | 6.52421e6i | −0.193851 | − | 0.335759i | 0.752672 | − | 0.658395i | \(-0.228764\pi\) |
−0.946523 | + | 0.322636i | \(0.895431\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.88490e6 | − | 3.02876e7i | 0.301026 | − | 1.54928i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.59694e7 | −0.811942 | −0.405971 | − | 0.913886i | \(-0.633067\pi\) | ||||
−0.405971 | + | 0.913886i | \(0.633067\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.71049e7 | −1.36981 | −0.684907 | − | 0.728631i | \(-0.740157\pi\) | ||||
−0.684907 | + | 0.728631i | \(0.740157\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.87253e7 | + | 6.44925e6i | −0.940646 | + | 0.323971i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −233679. | − | 404743.i | −0.0116683 | − | 0.0202100i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.41159e6 | − | 4.17699e6i | 0.119698 | − | 0.207323i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.39981e7 | − | 1.77392e6i | −1.67742 | − | 0.0875224i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.38138e7 | − | 2.39261e7i | 0.677497 | − | 1.17346i | −0.298236 | − | 0.954492i | \(-0.596398\pi\) |
0.975732 | − | 0.218967i | \(-0.0702686\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.23316e6 | + | 2.13590e6i | 0.0601216 | + | 0.104134i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 837600. | − | 288481.i | 0.0405946 | − | 0.0139813i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.01401e6 | 0.145212 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.63233e7 | −1.73971 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.02457e6 | + | 2.07131e7i | −0.191624 | + | 0.986225i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.96491e6 | + | 8.59948e6i | 0.235011 | + | 0.407050i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.66982e6 | − | 1.67486e7i | 0.455036 | − | 0.788145i | −0.543654 | − | 0.839309i | \(-0.682960\pi\) |
0.998690 | + | 0.0511638i | \(0.0162931\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.28056e6 | + | 2.56387e6i | −0.153473 | + | 0.119944i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.37449e7 | − | 2.38068e7i | 0.639277 | − | 1.10726i | −0.346315 | − | 0.938118i | \(-0.612567\pi\) |
0.985592 | − | 0.169142i | \(-0.0540995\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.33195e6 | + | 4.03905e6i | 0.107829 | + | 0.186765i | 0.914891 | − | 0.403702i | \(-0.132277\pi\) |
−0.807061 | + | 0.590467i | \(0.798943\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.72780e7 | + | 1.50172e7i | 0.794301 | + | 0.690369i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.10059e6 | 0.141716 | 0.0708578 | − | 0.997486i | \(-0.477426\pi\) | ||||
0.0708578 | + | 0.997486i | \(0.477426\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.63962e6 | −0.0745082 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.59714e7 | − | 1.38816e7i | −0.721598 | − | 0.627178i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.97993e6 | − | 1.55537e7i | −0.403388 | − | 0.698689i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.50927e6 | + | 7.81028e6i | −0.201400 | + | 0.348836i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.63041e6 | − | 1.46613e6i | −0.161221 | − | 0.0651086i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.10829e6 | − | 7.11576e6i | 0.181401 | − | 0.314196i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.22715e6 | + | 1.42498e7i | 0.361202 | + | 0.625621i | 0.988159 | − | 0.153433i | \(-0.0490330\pi\) |
−0.626957 | + | 0.779054i | \(0.715700\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.56899e6 | + | 8.07504e6i | −0.0684931 | + | 0.352511i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.06332e6 | 0.0895626 | 0.0447813 | − | 0.998997i | \(-0.485741\pi\) | ||||
0.0447813 | + | 0.998997i | \(0.485741\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.00336e7 | 0.864683 | 0.432342 | − | 0.901710i | \(-0.357687\pi\) | ||||
0.432342 | + | 0.901710i | \(0.357687\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.35891e6 | + | 2.19009e6i | −0.272913 | + | 0.0939949i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.41621e7 | + | 2.45295e7i | 0.604393 | + | 1.04684i | 0.992147 | + | 0.125077i | \(0.0399177\pi\) |
−0.387754 | + | 0.921763i | \(0.626749\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.19307e6 | + | 2.06646e6i | −0.0506304 | + | 0.0876944i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.32136e6 | + | 3.74349e7i | −0.393355 | + | 1.57973i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.05981e7 | − | 3.56769e7i | 0.864366 | − | 1.49713i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.36329e6 | + | 4.09334e6i | 0.0986187 | + | 0.170813i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.10978e6 | + | 2.10429e6i | −0.253539 | + | 0.0873222i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.81779e7 | −1.57548 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.35066e6 | 0.0964666 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.08241e6 | − | 2.10108e7i | 0.166609 | − | 0.857479i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 365009. | + | 632214.i | 0.0148143 | + | 0.0256592i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.40375e7 | + | 2.43137e7i | −0.566593 | + | 0.981369i | 0.430306 | + | 0.902683i | \(0.358406\pi\) |
−0.996899 | + | 0.0786856i | \(0.974928\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.21211e7 | − | 1.70105e7i | −1.69079 | − | 0.682822i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.35864e7 | + | 2.35324e7i | −0.542387 | + | 0.939443i | 0.456379 | + | 0.889786i | \(0.349146\pi\) |
−0.998766 | + | 0.0496571i | \(0.984187\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.11697e7 | + | 3.66670e7i | 0.840499 | + | 1.45579i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.57501e6 | + | 2.23808e6i | 0.101678 | + | 0.0883736i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.95354e6 | −0.155261 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.48360e7 | −1.75121 | −0.875604 | − | 0.483029i | \(-0.839536\pi\) | ||||
−0.875604 | + | 0.483029i | \(0.839536\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.35713e7 | − | 1.17956e7i | −0.527198 | − | 0.458215i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.83670e6 | + | 1.70377e7i | 0.380054 | + | 0.658273i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.08923e6 | + | 1.57430e7i | −0.349279 | + | 0.604969i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.22784e7 | − | 2.52266e7i | 1.23371 | − | 0.964183i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 786592. | − | 1.36242e6i | 0.0299027 | − | 0.0517930i | −0.850687 | − | 0.525673i | \(-0.823814\pi\) |
0.880589 | + | 0.473880i | \(0.157147\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.64104e6 | − | 2.84236e6i | −0.0620503 | − | 0.107474i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.51239e6 | − | 2.32238e7i | 0.169708 | − | 0.873431i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.59400e6 | 0.0596293 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.08278e6 | 0.0774986 | 0.0387493 | − | 0.999249i | \(-0.487663\pi\) | ||||
0.0387493 | + | 0.999249i | \(0.487663\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.88868e7 | − | 9.94900e6i | 1.06914 | − | 0.368227i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.15451e6 | + | 7.19583e6i | 0.152949 | + | 0.264915i | 0.932310 | − | 0.361659i | \(-0.117790\pi\) |
−0.779361 | + | 0.626575i | \(0.784456\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.89100e6 | − | 1.53997e7i | 0.325590 | − | 0.563939i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.75332e6 | + | 4.24188e6i | −0.100294 | + | 0.154518i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.34570e7 | − | 4.06287e7i | 0.849958 | − | 1.47217i | −0.0312875 | − | 0.999510i | \(-0.509961\pi\) |
0.881245 | − | 0.472659i | \(-0.156706\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.67833e6 | − | 1.32993e7i | −0.276759 | − | 0.479360i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.70056e7 | + | 9.30109e6i | −0.968283 | + | 0.333490i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.19875e7 | 0.427559 | 0.213779 | − | 0.976882i | \(-0.431423\pi\) | ||||
0.213779 | + | 0.976882i | \(0.431423\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.80500e6 | −0.205965 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.25151e6 | + | 4.24677e7i | −0.291242 | + | 1.49892i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.79182e7 | + | 4.83557e7i | 0.980258 | + | 1.69786i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.60724e7 | + | 4.51587e7i | −0.910693 | + | 1.57737i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.25213e6 | − | 3.73293e7i | −0.182503 | − | 1.29713i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −439090. | + | 760525.i | −0.0151787 | + | 0.0262903i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.44190e7 | − | 2.49745e7i | −0.495872 | − | 0.858876i | 0.504116 | − | 0.863636i | \(-0.331818\pi\) |
−0.999989 | + | 0.00475965i | \(0.998485\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.15449e6 | + | 4.48004e6i | 0.176350 | + | 0.153275i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.30199e7 | −0.443158 | −0.221579 | − | 0.975142i | \(-0.571121\pi\) | ||||
−0.221579 | + | 0.975142i | \(0.571121\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.95182e7 | 1.33818 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.92876e6 | − | 7.76045e6i | −0.300801 | − | 0.261442i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.14539e6 | + | 1.58403e7i | 0.306525 | + | 0.530917i | 0.977600 | − | 0.210473i | \(-0.0675003\pi\) |
−0.671075 | + | 0.741390i | \(0.734167\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.13196e7 | + | 1.96061e7i | −0.377462 | + | 0.653783i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.90322e6 | − | 2.77419e7i | −0.129494 | − | 0.920374i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 484901. | − | 839872.i | 0.0160055 | − | 0.0277223i | −0.857912 | − | 0.513797i | \(-0.828238\pi\) |
0.873917 | + | 0.486075i | \(0.161572\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.07658e6 | + | 3.59674e6i | 0.0681959 | + | 0.118119i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.54372e6 | − | 4.91183e7i | 0.311835 | − | 1.60491i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.66259e7 | −0.540500 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.04589e7 | 1.63213 | 0.816063 | − | 0.577962i | \(-0.196152\pi\) | ||||
0.816063 | + | 0.577962i | \(0.196152\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.06136e7 | + | 3.65546e6i | −0.341577 | + | 0.117644i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.82835e6 | − | 3.16680e6i | −0.0585467 | − | 0.101406i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.90625e6 | + | 1.54261e7i | −0.283764 | + | 0.491493i | −0.972309 | − | 0.233700i | \(-0.924917\pi\) |
0.688545 | + | 0.725194i | \(0.258250\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.23748e7 | − | 1.90652e7i | 0.392306 | − | 0.604403i |
(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 | 144.6.i.d.97.4 | 10 | ||
3.2 | odd | 2 | 432.6.i.d.289.3 | 10 | |||
4.3 | odd | 2 | 36.6.e.a.25.2 | yes | 10 | ||
9.4 | even | 3 | inner | 144.6.i.d.49.4 | 10 | ||
9.5 | odd | 6 | 432.6.i.d.145.3 | 10 | |||
12.11 | even | 2 | 108.6.e.a.73.3 | 10 | |||
36.7 | odd | 6 | 324.6.a.e.1.3 | 5 | |||
36.11 | even | 6 | 324.6.a.d.1.3 | 5 | |||
36.23 | even | 6 | 108.6.e.a.37.3 | 10 | |||
36.31 | odd | 6 | 36.6.e.a.13.2 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.e.a.13.2 | ✓ | 10 | 36.31 | odd | 6 | ||
36.6.e.a.25.2 | yes | 10 | 4.3 | odd | 2 | ||
108.6.e.a.37.3 | 10 | 36.23 | even | 6 | |||
108.6.e.a.73.3 | 10 | 12.11 | even | 2 | |||
144.6.i.d.49.4 | 10 | 9.4 | even | 3 | inner | ||
144.6.i.d.97.4 | 10 | 1.1 | even | 1 | trivial | ||
324.6.a.d.1.3 | 5 | 36.11 | even | 6 | |||
324.6.a.e.1.3 | 5 | 36.7 | odd | 6 | |||
432.6.i.d.145.3 | 10 | 9.5 | odd | 6 | |||
432.6.i.d.289.3 | 10 | 3.2 | odd | 2 |