Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,7,Mod(53,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.53");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.d (of order \(6\), 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: | \(37.2687615464\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 485774x^{12} + 87183614355x^{8} + 6839940225440174x^{4} + 198392288899684017121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{36} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 53.5 | ||
Root | \(-12.7063 - 11.9992i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.53 |
Dual form | 162.7.d.g.107.5 |
$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.89898 | − | 2.82843i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000 | − | 27.7128i | 0.250000 | − | 0.433013i | ||||
\(5\) | −148.146 | − | 85.5319i | −1.18516 | − | 0.684255i | −0.227961 | − | 0.973670i | \(-0.573206\pi\) |
−0.957204 | + | 0.289415i | \(0.906539\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −280.419 | − | 485.701i | −0.817549 | − | 1.41604i | −0.907483 | − | 0.420089i | \(-0.861999\pi\) |
0.0899339 | − | 0.995948i | \(-0.471334\pi\) | |||||||
\(8\) | − | 181.019i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −967.683 | −0.967683 | ||||||||
\(11\) | −190.829 | + | 110.175i | −0.143373 | + | 0.0827764i | −0.569971 | − | 0.821665i | \(-0.693045\pi\) |
0.426598 | + | 0.904442i | \(0.359712\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1890.50 | + | 3274.44i | −0.860491 | + | 1.49041i | 0.0109657 | + | 0.999940i | \(0.496509\pi\) |
−0.871456 | + | 0.490473i | \(0.836824\pi\) | |||||||
\(14\) | −2747.54 | − | 1586.29i | −1.00129 | − | 0.578094i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −512.000 | − | 886.810i | −0.125000 | − | 0.216506i | ||||
\(17\) | − | 2662.46i | − | 0.541922i | −0.962590 | − | 0.270961i | \(-0.912659\pi\) | ||
0.962590 | − | 0.270961i | \(-0.0873415\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10334.0 | 1.50663 | 0.753317 | − | 0.657658i | \(-0.228453\pi\) | ||||
0.753317 | + | 0.657658i | \(0.228453\pi\) | |||||||
\(20\) | −4740.66 | + | 2737.02i | −0.592582 | + | 0.342127i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −623.246 | + | 1079.49i | −0.0585317 | + | 0.101380i | ||||
\(23\) | 12804.8 | + | 7392.86i | 1.05242 | + | 0.607615i | 0.923326 | − | 0.384017i | \(-0.125460\pi\) |
0.129095 | + | 0.991632i | \(0.458793\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6818.90 | + | 11810.7i | 0.436410 | + | 0.755884i | ||||
\(26\) | 21388.5i | 1.21692i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −17946.8 | −0.817549 | ||||||||
\(29\) | −12880.3 | + | 7436.43i | −0.528118 | + | 0.304909i | −0.740250 | − | 0.672332i | \(-0.765293\pi\) |
0.212132 | + | 0.977241i | \(0.431959\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7915.51 | + | 13710.1i | −0.265701 | + | 0.460208i | −0.967747 | − | 0.251923i | \(-0.918937\pi\) |
0.702046 | + | 0.712132i | \(0.252270\pi\) | |||||||
\(32\) | −5016.55 | − | 2896.31i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7530.58 | − | 13043.4i | −0.191598 | − | 0.331858i | ||||
\(35\) | 95939.2i | 2.23765i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 26550.4 | 0.524162 | 0.262081 | − | 0.965046i | \(-0.415591\pi\) | ||||
0.262081 | + | 0.965046i | \(0.415591\pi\) | |||||||
\(38\) | 50626.0 | − | 29229.0i | 0.922621 | − | 0.532675i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −15482.9 | + | 26817.2i | −0.241921 | + | 0.419019i | ||||
\(41\) | −98677.0 | − | 56971.2i | −1.43174 | − | 0.826616i | −0.434487 | − | 0.900678i | \(-0.643070\pi\) |
−0.997254 | + | 0.0740621i | \(0.976404\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 26049.5 | + | 45119.0i | 0.327637 | + | 0.567485i | 0.982043 | − | 0.188660i | \(-0.0604143\pi\) |
−0.654405 | + | 0.756144i | \(0.727081\pi\) | |||||||
\(44\) | 7051.22i | 0.0827764i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 83640.6 | 0.859298 | ||||||||
\(47\) | −10009.8 | + | 5779.19i | −0.0964126 | + | 0.0556639i | −0.547431 | − | 0.836851i | \(-0.684394\pi\) |
0.451018 | + | 0.892515i | \(0.351061\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −98445.5 | + | 170513.i | −0.836773 | + | 1.44933i | ||||
\(50\) | 66811.3 | + | 38573.5i | 0.534490 | + | 0.308588i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 60495.9 | + | 104782.i | 0.430245 | + | 0.745207i | ||||
\(53\) | − | 137651.i | − | 0.924595i | −0.886725 | − | 0.462298i | \(-0.847025\pi\) | ||
0.886725 | − | 0.462298i | \(-0.152975\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 37694.0 | 0.226561 | ||||||||
\(56\) | −87921.2 | + | 50761.3i | −0.500645 | + | 0.289047i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −42066.8 | + | 72861.8i | −0.215603 | + | 0.373436i | ||||
\(59\) | −252344. | − | 145691.i | −1.22868 | − | 0.709377i | −0.261923 | − | 0.965089i | \(-0.584357\pi\) |
−0.966753 | + | 0.255712i | \(0.917690\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 141109. | + | 244408.i | 0.621678 | + | 1.07678i | 0.989173 | + | 0.146752i | \(0.0468821\pi\) |
−0.367495 | + | 0.930025i | \(0.619785\pi\) | |||||||
\(62\) | 89553.8i | 0.375759i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32768.0 | −0.125000 | ||||||||
\(65\) | 560138. | − | 323396.i | 2.03965 | − | 1.17759i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −188957. | + | 327283.i | −0.628258 | + | 1.08818i | 0.359643 | + | 0.933090i | \(0.382899\pi\) |
−0.987901 | + | 0.155085i | \(0.950435\pi\) | |||||||
\(68\) | −73784.4 | − | 42599.4i | −0.234659 | − | 0.135481i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 271357. | + | 470004.i | 0.791128 | + | 1.37027i | ||||
\(71\) | 521287.i | 1.45647i | 0.685328 | + | 0.728235i | \(0.259659\pi\) | ||||
−0.685328 | + | 0.728235i | \(0.740341\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −611614. | −1.57221 | −0.786103 | − | 0.618096i | \(-0.787904\pi\) | ||||
−0.786103 | + | 0.618096i | \(0.787904\pi\) | |||||||
\(74\) | 130070. | − | 75095.8i | 0.320982 | − | 0.185319i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 165344. | − | 286384.i | 0.376658 | − | 0.652391i | ||||
\(77\) | 107024. | + | 61790.6i | 0.234429 | + | 0.135348i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 87787.4 | + | 152052.i | 0.178054 | + | 0.308398i | 0.941214 | − | 0.337811i | \(-0.109687\pi\) |
−0.763160 | + | 0.646209i | \(0.776353\pi\) | |||||||
\(80\) | 175169.i | 0.342127i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −644556. | −1.16901 | ||||||||
\(83\) | 314364. | − | 181498.i | 0.549792 | − | 0.317422i | −0.199246 | − | 0.979949i | \(-0.563849\pi\) |
0.749038 | + | 0.662527i | \(0.230516\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −227725. | + | 394432.i | −0.370813 | + | 0.642267i | ||||
\(86\) | 255232. | + | 147358.i | 0.401272 | + | 0.231675i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 19943.9 | + | 34543.8i | 0.0292659 | + | 0.0506900i | ||||
\(89\) | − | 1.23323e6i | − | 1.74934i | −0.484719 | − | 0.874670i | \(-0.661078\pi\) | ||
0.484719 | − | 0.874670i | \(-0.338922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.12053e6 | 2.81397 | ||||||||
\(92\) | 409754. | − | 236571.i | 0.526210 | − | 0.303808i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −32692.0 | + | 56624.3i | −0.0393603 | + | 0.0681740i | ||||
\(95\) | −1.53094e6 | − | 883886.i | −1.78561 | − | 1.03092i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 624144. | + | 1.08105e6i | 0.683863 | + | 1.18449i | 0.973793 | + | 0.227438i | \(0.0730349\pi\) |
−0.289929 | + | 0.957048i | \(0.593632\pi\) | |||||||
\(98\) | 1.11378e6i | 1.18338i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 436410. | 0.436410 | ||||||||
\(101\) | −915242. | + | 528415.i | −0.888324 | + | 0.512874i | −0.873394 | − | 0.487014i | \(-0.838086\pi\) |
−0.0149303 | + | 0.999889i | \(0.504753\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 144795. | − | 250792.i | 0.132508 | − | 0.229511i | −0.792135 | − | 0.610346i | \(-0.791030\pi\) |
0.924643 | + | 0.380836i | \(0.124364\pi\) | |||||||
\(104\) | 592737. | + | 342217.i | 0.526941 | + | 0.304229i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −389336. | − | 674349.i | −0.326894 | − | 0.566197i | ||||
\(107\) | − | 811508.i | − | 0.662432i | −0.943555 | − | 0.331216i | \(-0.892541\pi\) | ||
0.943555 | − | 0.331216i | \(-0.107459\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −595882. | −0.460130 | −0.230065 | − | 0.973175i | \(-0.573894\pi\) | ||||
−0.230065 | + | 0.973175i | \(0.573894\pi\) | |||||||
\(110\) | 184662. | − | 106615.i | 0.138739 | − | 0.0801013i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −287149. | + | 497357.i | −0.204387 | + | 0.354009i | ||||
\(113\) | −557538. | − | 321895.i | −0.386402 | − | 0.223089i | 0.294198 | − | 0.955745i | \(-0.404948\pi\) |
−0.680600 | + | 0.732655i | \(0.738281\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.26465e6 | − | 2.19044e6i | −0.831528 | − | 1.44025i | ||||
\(116\) | 475931.i | 0.304909i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.64831e6 | −1.00321 | ||||||||
\(119\) | −1.29316e6 | + | 746606.i | −0.767382 | + | 0.443048i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −861503. | + | 1.49217e6i | −0.486296 | + | 0.842290i | ||||
\(122\) | 1.38258e6 | + | 798234.i | 0.761397 | + | 0.439593i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 253296. | + | 438722.i | 0.132851 | + | 0.230104i | ||||
\(125\) | 339938.i | 0.174048i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −53251.0 | −0.0259966 | −0.0129983 | − | 0.999916i | \(-0.504138\pi\) | ||||
−0.0129983 | + | 0.999916i | \(0.504138\pi\) | |||||||
\(128\) | −160530. | + | 92681.9i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.82940e6 | − | 3.16862e6i | 0.832682 | − | 1.44225i | ||||
\(131\) | 1.50264e6 | + | 867552.i | 0.668409 | + | 0.385906i | 0.795474 | − | 0.605988i | \(-0.207222\pi\) |
−0.127064 | + | 0.991894i | \(0.540556\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.89785e6 | − | 5.01923e6i | −1.23175 | − | 2.13345i | ||||
\(134\) | 2.13780e6i | 0.888491i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −481957. | −0.191598 | ||||||||
\(137\) | −1.84002e6 | + | 1.06233e6i | −0.715583 | + | 0.413142i | −0.813125 | − | 0.582089i | \(-0.802235\pi\) |
0.0975419 | + | 0.995231i | \(0.468902\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.49299e6 | − | 2.58593e6i | 0.555918 | − | 0.962879i | −0.441913 | − | 0.897058i | \(-0.645700\pi\) |
0.997831 | − | 0.0658211i | \(-0.0209667\pi\) | |||||||
\(140\) | 2.65874e6 | + | 1.53503e6i | 0.968930 | + | 0.559412i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.47442e6 | + | 2.55377e6i | 0.514940 | + | 0.891902i | ||||
\(143\) | − | 833145.i | − | 0.284913i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.54421e6 | 0.834542 | ||||||||
\(146\) | −2.99629e6 | + | 1.72991e6i | −0.962775 | + | 0.555858i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 424806. | − | 735786.i | 0.131041 | − | 0.226969i | ||||
\(149\) | 1.37292e6 | + | 792654.i | 0.415036 | + | 0.239621i | 0.692951 | − | 0.720985i | \(-0.256310\pi\) |
−0.277915 | + | 0.960606i | \(0.589643\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −100324. | − | 173767.i | −0.0291390 | − | 0.0504703i | 0.851088 | − | 0.525023i | \(-0.175943\pi\) |
−0.880227 | + | 0.474553i | \(0.842610\pi\) | |||||||
\(152\) | − | 1.87065e6i | − | 0.532675i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 699081. | 0.191410 | ||||||||
\(155\) | 2.34530e6 | − | 1.35406e6i | 0.629800 | − | 0.363615i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −525225. | + | 909716.i | −0.135721 | + | 0.235075i | −0.925873 | − | 0.377836i | \(-0.876668\pi\) |
0.790152 | + | 0.612911i | \(0.210002\pi\) | |||||||
\(158\) | 860137. | + | 496600.i | 0.218070 | + | 0.125903i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 495453. | + | 858151.i | 0.120960 | + | 0.209509i | ||||
\(161\) | − | 8.29240e6i | − | 1.98702i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.04370e6 | −0.471905 | −0.235953 | − | 0.971765i | \(-0.575821\pi\) | ||||
−0.235953 | + | 0.971765i | \(0.575821\pi\) | |||||||
\(164\) | −3.15766e6 | + | 1.82308e6i | −0.715870 | + | 0.413308i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.02671e6 | − | 1.77831e6i | 0.224451 | − | 0.388761i | ||||
\(167\) | −5.92645e6 | − | 3.42164e6i | −1.27246 | − | 0.734657i | −0.297012 | − | 0.954874i | \(-0.595990\pi\) |
−0.975451 | + | 0.220217i | \(0.929323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.73456e6 | − | 8.20050e6i | −0.980888 | − | 1.69895i | ||||
\(170\) | 2.57642e6i | 0.524409i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.66717e6 | 0.327637 | ||||||||
\(173\) | −1.08913e6 | + | 628810.i | −0.210350 | + | 0.121445i | −0.601474 | − | 0.798892i | \(-0.705420\pi\) |
0.391124 | + | 0.920338i | \(0.372086\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.82430e6 | − | 6.62389e6i | 0.713573 | − | 1.23594i | ||||
\(176\) | 195409. | + | 112820.i | 0.0358432 | + | 0.0206941i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.48810e6 | − | 6.04157e6i | −0.618485 | − | 1.07125i | ||||
\(179\) | − | 8.25586e6i | − | 1.43947i | −0.694248 | − | 0.719736i | \(-0.744263\pi\) | ||
0.694248 | − | 0.719736i | \(-0.255737\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.62711e6 | 0.443040 | 0.221520 | − | 0.975156i | \(-0.428898\pi\) | ||||
0.221520 | + | 0.975156i | \(0.428898\pi\) | |||||||
\(182\) | 1.03884e7 | − | 5.99776e6i | 1.72320 | − | 0.994890i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.33825e6 | − | 2.31792e6i | 0.214825 | − | 0.372087i | ||||
\(185\) | −3.93332e6 | − | 2.27090e6i | −0.621218 | − | 0.358661i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 293338. | + | 508076.i | 0.0448584 | + | 0.0776970i | ||||
\(188\) | 369868.i | 0.0556639i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.00000e7 | −1.45794 | ||||||||
\(191\) | −1.27253e6 | + | 734698.i | −0.182629 | + | 0.105441i | −0.588527 | − | 0.808477i | \(-0.700292\pi\) |
0.405898 | + | 0.913918i | \(0.366959\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 81598.8 | − | 141333.i | 0.0113504 | − | 0.0196595i | −0.860294 | − | 0.509798i | \(-0.829720\pi\) |
0.871645 | + | 0.490138i | \(0.163054\pi\) | |||||||
\(194\) | 6.11533e6 | + | 3.53069e6i | 0.837558 | + | 0.483564i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.15026e6 | + | 5.45640e6i | 0.418386 | + | 0.724667i | ||||
\(197\) | 1.03528e7i | 1.35413i | 0.735923 | + | 0.677065i | \(0.236748\pi\) | ||||
−0.735923 | + | 0.677065i | \(0.763252\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.96701e6 | −0.884071 | −0.442035 | − | 0.896998i | \(-0.645743\pi\) | ||||
−0.442035 | + | 0.896998i | \(0.645743\pi\) | |||||||
\(200\) | 2.13796e6 | − | 1.23435e6i | 0.267245 | − | 0.154294i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.98917e6 | + | 5.17739e6i | −0.362657 | + | 0.628140i | ||||
\(203\) | 7.22375e6 | + | 4.17064e6i | 0.863525 | + | 0.498556i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.74571e6 | + | 1.68801e7i | 1.13123 | + | 1.95935i | ||||
\(206\) | − | 1.63817e6i | − | 0.187395i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.87174e6 | 0.430245 | ||||||||
\(209\) | −1.97203e6 | + | 1.13855e6i | −0.216010 | + | 0.124714i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.08632e6 | + | 1.05418e7i | −0.647900 | + | 1.12220i | 0.335724 | + | 0.941960i | \(0.391019\pi\) |
−0.983624 | + | 0.180235i | \(0.942314\pi\) | |||||||
\(212\) | −3.81470e6 | − | 2.20242e6i | −0.400362 | − | 0.231149i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.29529e6 | − | 3.97556e6i | −0.234205 | − | 0.405655i | ||||
\(215\) | − | 8.91224e6i | − | 0.896750i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.87865e6 | 0.868896 | ||||||||
\(218\) | −2.91921e6 | + | 1.68541e6i | −0.281771 | + | 0.162681i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 603104. | − | 1.04461e6i | 0.0566401 | − | 0.0981036i | ||||
\(221\) | 8.71807e6 | + | 5.03338e6i | 0.807688 | + | 0.466319i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.85859e6 | + | 1.36115e7i | 0.708647 | + | 1.22741i | 0.965359 | + | 0.260925i | \(0.0840274\pi\) |
−0.256712 | + | 0.966488i | \(0.582639\pi\) | |||||||
\(224\) | 3.24872e6i | 0.289047i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.64183e6 | −0.315496 | ||||||||
\(227\) | −130354. | + | 75259.9i | −0.0111441 | + | 0.00643407i | −0.505562 | − | 0.862790i | \(-0.668715\pi\) |
0.494418 | + | 0.869225i | \(0.335381\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.30714e6 | − | 1.09243e7i | 0.525201 | − | 0.909675i | −0.474368 | − | 0.880327i | \(-0.657323\pi\) |
0.999569 | − | 0.0293486i | \(-0.00934330\pi\) | |||||||
\(230\) | −1.23910e7 | − | 7.15394e6i | −1.01841 | − | 0.587979i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.34614e6 | + | 2.33158e6i | 0.107802 | + | 0.186718i | ||||
\(233\) | 1.73833e7i | 1.37425i | 0.726542 | + | 0.687123i | \(0.241126\pi\) | ||||
−0.726542 | + | 0.687123i | \(0.758874\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.97722e6 | 0.152353 | ||||||||
\(236\) | −8.07502e6 | + | 4.66211e6i | −0.614338 | + | 0.354688i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.22344e6 | + | 7.31522e6i | −0.313282 | + | 0.542621i | ||||
\(239\) | −1.09822e7 | − | 6.34059e6i | −0.804445 | − | 0.464447i | 0.0405780 | − | 0.999176i | \(-0.487080\pi\) |
−0.845023 | + | 0.534730i | \(0.820413\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.99488e6 | − | 8.65139e6i | −0.356840 | − | 0.618066i | 0.630591 | − | 0.776116i | \(-0.282813\pi\) |
−0.987431 | + | 0.158050i | \(0.949479\pi\) | |||||||
\(242\) | 9.74680e6i | 0.687727i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.03098e6 | 0.621678 | ||||||||
\(245\) | 2.91685e7 | − | 1.68405e7i | 1.98343 | − | 1.14513i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.95364e7 | + | 3.38380e7i | −1.29644 | + | 2.24551i | ||||
\(248\) | 2.48179e6 | + | 1.43286e6i | 0.162708 | + | 0.0939396i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 961489. | + | 1.66535e6i | 0.0615353 | + | 0.106582i | ||||
\(251\) | 1.92884e7i | 1.21976i | 0.792493 | + | 0.609881i | \(0.208783\pi\) | ||||
−0.792493 | + | 0.609881i | \(0.791217\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.25804e6 | −0.201185 | ||||||||
\(254\) | −260876. | + | 150617.i | −0.0159196 | + | 0.00919119i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −524288. | + | 908093.i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −1.32457e7 | − | 7.64740e6i | −0.780324 | − | 0.450520i | 0.0562210 | − | 0.998418i | \(-0.482095\pi\) |
−0.836545 | + | 0.547898i | \(0.815428\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.44524e6 | − | 1.28955e7i | −0.428528 | − | 0.742233i | ||||
\(260\) | − | 2.06973e7i | − | 1.17759i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.81523e6 | 0.545754 | ||||||||
\(263\) | −1.90796e7 | + | 1.10156e7i | −1.04882 | + | 0.605537i | −0.922319 | − | 0.386429i | \(-0.873708\pi\) |
−0.126502 | + | 0.991966i | \(0.540375\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.17735e7 | + | 2.03924e7i | −0.632659 | + | 1.09580i | ||||
\(266\) | −2.83930e7 | − | 1.63927e7i | −1.50858 | − | 0.870976i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.04662e6 | + | 1.04731e7i | 0.314129 | + | 0.544088i | ||||
\(269\) | 1.44503e7i | 0.742368i | 0.928559 | + | 0.371184i | \(0.121048\pi\) | ||||
−0.928559 | + | 0.371184i | \(0.878952\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.83074e6 | −0.443700 | −0.221850 | − | 0.975081i | \(-0.571209\pi\) | ||||
−0.221850 | + | 0.975081i | \(0.571209\pi\) | |||||||
\(272\) | −2.36110e6 | + | 1.36318e6i | −0.117330 | + | 0.0677403i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00947e6 | + | 1.04087e7i | −0.292135 | + | 0.505994i | ||||
\(275\) | −2.60249e6 | − | 1.50255e6i | −0.125139 | − | 0.0722488i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.22908e7 | + | 2.12883e7i | 0.578283 | + | 1.00162i | 0.995676 | + | 0.0928895i | \(0.0296103\pi\) |
−0.417394 | + | 0.908726i | \(0.637056\pi\) | |||||||
\(278\) | − | 1.68912e7i | − | 0.786187i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.73668e7 | 0.791128 | ||||||||
\(281\) | 2.87160e7 | − | 1.65792e7i | 1.29421 | − | 0.747213i | 0.314813 | − | 0.949154i | \(-0.398058\pi\) |
0.979398 | + | 0.201940i | \(0.0647247\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.90735e7 | − | 3.30363e7i | 0.841533 | − | 1.45758i | −0.0470661 | − | 0.998892i | \(-0.514987\pi\) |
0.888599 | − | 0.458685i | \(-0.151680\pi\) | |||||||
\(284\) | 1.44463e7 | + | 8.34059e6i | 0.630670 | + | 0.364117i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.35649e6 | − | 4.08156e6i | −0.100732 | − | 0.174473i | ||||
\(287\) | 6.39033e7i | 2.70320i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.70489e7 | 0.706320 | ||||||||
\(290\) | 1.24640e7 | − | 7.19610e6i | 0.511051 | − | 0.295055i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.78583e6 | + | 1.69496e7i | −0.393051 | + | 0.680785i | ||||
\(293\) | 3.00232e7 | + | 1.73339e7i | 1.19359 | + | 0.689118i | 0.959118 | − | 0.283005i | \(-0.0913313\pi\) |
0.234470 | + | 0.972123i | \(0.424665\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.49225e7 | + | 4.31670e7i | 0.970789 | + | 1.68146i | ||||
\(296\) | − | 4.80613e6i | − | 0.185319i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.96786e6 | 0.338875 | ||||||||
\(299\) | −4.84149e7 | + | 2.79524e7i | −1.81120 | + | 1.04569i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.46095e7 | − | 2.53045e7i | 0.535719 | − | 0.927893i | ||||
\(302\) | −982972. | − | 567519.i | −0.0356879 | − | 0.0206044i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.29101e6 | − | 9.16429e6i | −0.188329 | − | 0.326196i | ||||
\(305\) | − | 4.82773e7i | − | 1.70154i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.85387e7 | −1.67754 | −0.838770 | − | 0.544486i | \(-0.816725\pi\) | ||||
−0.838770 | + | 0.544486i | \(0.816725\pi\) | |||||||
\(308\) | 3.42478e6 | − | 1.97730e6i | 0.117214 | − | 0.0676738i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.65970e6 | − | 1.32670e7i | 0.257115 | − | 0.445336i | ||||
\(311\) | 2.67899e7 | + | 1.54672e7i | 0.890616 | + | 0.514197i | 0.874144 | − | 0.485667i | \(-0.161423\pi\) |
0.0164719 | + | 0.999864i | \(0.494757\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −359747. | − | 623100.i | −0.0117318 | − | 0.0203201i | 0.860100 | − | 0.510126i | \(-0.170401\pi\) |
−0.871832 | + | 0.489806i | \(0.837068\pi\) | |||||||
\(314\) | 5.94224e6i | 0.191938i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.61839e6 | 0.178054 | ||||||||
\(317\) | 6.46139e6 | − | 3.73049e6i | 0.202838 | − | 0.117108i | −0.395141 | − | 0.918621i | \(-0.629304\pi\) |
0.597978 | + | 0.801512i | \(0.295971\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.63862e6 | − | 2.83818e6i | 0.0504785 | − | 0.0874314i | ||||
\(320\) | 4.85443e6 | + | 2.80271e6i | 0.148146 | + | 0.0855319i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.34544e7 | − | 4.06243e7i | −0.702518 | − | 1.21680i | ||||
\(323\) | − | 2.75139e7i | − | 0.816478i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.15645e7 | −1.50211 | ||||||||
\(326\) | −1.00121e7 | + | 5.78046e6i | −0.288982 | + | 0.166844i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.03129e7 | + | 1.78624e7i | −0.292253 | + | 0.506197i | ||||
\(329\) | 5.61391e6 | + | 3.24119e6i | 0.157644 | + | 0.0910159i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −742285. | − | 1.28568e6i | −0.0204685 | − | 0.0354525i | 0.855610 | − | 0.517622i | \(-0.173182\pi\) |
−0.876078 | + | 0.482169i | \(0.839849\pi\) | |||||||
\(332\) | − | 1.16159e7i | − | 0.317422i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.87114e7 | −1.03896 | ||||||||
\(335\) | 5.59862e7 | − | 3.23237e7i | 1.48918 | − | 0.859778i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.93257e6 | + | 6.81142e6i | −0.102751 | + | 0.177970i | −0.912817 | − | 0.408368i | \(-0.866098\pi\) |
0.810066 | + | 0.586339i | \(0.199431\pi\) | |||||||
\(338\) | −4.63890e7 | − | 2.67827e7i | −1.20134 | − | 0.693592i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.28722e6 | + | 1.26218e7i | 0.185406 | + | 0.321133i | ||||
\(341\) | − | 3.48838e6i | − | 0.0879752i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.44420e7 | 1.10131 | ||||||||
\(344\) | 8.16741e6 | − | 4.71546e6i | 0.200636 | − | 0.115837i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.55709e6 | + | 6.16105e6i | −0.0858749 | + | 0.148740i | ||||
\(347\) | −1.58793e7 | − | 9.16793e6i | −0.380052 | − | 0.219423i | 0.297789 | − | 0.954632i | \(-0.403751\pi\) |
−0.677841 | + | 0.735208i | \(0.737084\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.21650e7 | − | 5.57114e7i | −0.756672 | − | 1.31059i | −0.944539 | − | 0.328399i | \(-0.893491\pi\) |
0.187867 | − | 0.982194i | \(-0.439842\pi\) | |||||||
\(350\) | − | 4.32670e7i | − | 1.00914i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.27641e6 | 0.0292659 | ||||||||
\(353\) | −2.06487e7 | + | 1.19216e7i | −0.469429 | + | 0.271025i | −0.716000 | − | 0.698100i | \(-0.754029\pi\) |
0.246572 | + | 0.969124i | \(0.420696\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.45866e7 | − | 7.72263e7i | 0.996597 | − | 1.72616i | ||||
\(356\) | −3.41763e7 | − | 1.97317e7i | −0.757486 | − | 0.437335i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.33511e7 | − | 4.04453e7i | −0.508930 | − | 0.881493i | ||||
\(359\) | − | 1.50510e7i | − | 0.325298i | −0.986684 | − | 0.162649i | \(-0.947996\pi\) | ||
0.986684 | − | 0.162649i | \(-0.0520038\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.97456e7 | 1.26994 | ||||||||
\(362\) | 1.28702e7 | − | 7.43059e6i | 0.271305 | − | 0.156638i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.39285e7 | − | 5.87658e7i | 0.703493 | − | 1.21849i | ||||
\(365\) | 9.06080e7 | + | 5.23125e7i | 1.86332 | + | 1.07579i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.97392e6 | − | 1.55433e7i | −0.181545 | − | 0.314445i | 0.760862 | − | 0.648914i | \(-0.224776\pi\) |
−0.942407 | + | 0.334469i | \(0.891443\pi\) | |||||||
\(368\) | − | 1.51406e7i | − | 0.303808i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.56923e7 | −0.507223 | ||||||||
\(371\) | −6.68572e7 | + | 3.86000e7i | −1.30926 | + | 0.755902i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.33400e6 | − | 7.50671e6i | 0.0835147 | − | 0.144652i | −0.821243 | − | 0.570579i | \(-0.806719\pi\) |
0.904757 | + | 0.425927i | \(0.140052\pi\) | |||||||
\(374\) | 2.87411e6 | + | 1.65937e6i | 0.0549400 | + | 0.0317197i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.04614e6 | + | 1.81198e6i | 0.0196801 | + | 0.0340870i | ||||
\(377\) | − | 5.62342e7i | − | 1.04949i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.03648e7 | −0.190390 | −0.0951950 | − | 0.995459i | \(-0.530347\pi\) | ||||
−0.0951950 | + | 0.995459i | \(0.530347\pi\) | |||||||
\(380\) | −4.89899e7 | + | 2.82844e7i | −0.892804 | + | 0.515461i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.15608e6 | + | 7.19854e6i | −0.0745579 | + | 0.129138i | ||||
\(383\) | −2.16952e6 | − | 1.25257e6i | −0.0386160 | − | 0.0222950i | 0.480568 | − | 0.876958i | \(-0.340431\pi\) |
−0.519184 | + | 0.854663i | \(0.673764\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.05701e7 | − | 1.83080e7i | −0.185224 | − | 0.320818i | ||||
\(386\) | − | 923185.i | − | 0.0160519i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.99452e7 | 0.683863 | ||||||||
\(389\) | 2.13002e6 | − | 1.22977e6i | 0.0361855 | − | 0.0208917i | −0.481798 | − | 0.876282i | \(-0.660016\pi\) |
0.517984 | + | 0.855391i | \(0.326683\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.96832e7 | − | 3.40923e7i | 0.329280 | − | 0.570330i | ||||
\(392\) | 3.08661e7 | + | 1.78205e7i | 0.512417 | + | 0.295844i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.92822e7 | + | 5.07183e7i | 0.478757 | + | 0.829232i | ||||
\(395\) | − | 3.00345e7i | − | 0.487336i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.17180e6 | 0.0187275 | 0.00936376 | − | 0.999956i | \(-0.497019\pi\) | ||||
0.00936376 | + | 0.999956i | \(0.497019\pi\) | |||||||
\(398\) | −3.41312e7 | + | 1.97057e7i | −0.541380 | + | 0.312566i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.98255e6 | − | 1.20941e7i | 0.109102 | − | 0.188971i | ||||
\(401\) | 1.52455e7 | + | 8.80198e6i | 0.236433 | + | 0.136505i | 0.613536 | − | 0.789667i | \(-0.289746\pi\) |
−0.377103 | + | 0.926171i | \(0.623080\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.99285e7 | − | 5.18377e7i | −0.457267 | − | 0.792010i | ||||
\(404\) | 3.38186e7i | 0.512874i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.71854e7 | 0.705065 | ||||||||
\(407\) | −5.06659e6 | + | 2.92520e6i | −0.0751507 | + | 0.0433883i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.22649e7 | + | 5.58844e7i | −0.471585 | + | 0.816809i | −0.999472 | − | 0.0325057i | \(-0.989651\pi\) |
0.527887 | + | 0.849315i | \(0.322985\pi\) | |||||||
\(410\) | 9.54880e7 | + | 5.51300e7i | 1.38547 | + | 0.799902i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.63344e6 | − | 8.02536e6i | −0.0662540 | − | 0.114755i | ||||
\(413\) | 1.63418e8i | 2.31980i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.20954e7 | −0.868791 | ||||||||
\(416\) | 1.89676e7 | − | 1.09509e7i | 0.263470 | − | 0.152115i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.44062e6 | + | 1.11555e7i | −0.0881859 | + | 0.152742i | ||||
\(419\) | −9.58989e7 | − | 5.53672e7i | −1.30368 | − | 0.752681i | −0.322648 | − | 0.946519i | \(-0.604573\pi\) |
−0.981033 | + | 0.193838i | \(0.937906\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.58451e7 | − | 2.74445e7i | −0.212348 | − | 0.367798i | 0.740101 | − | 0.672496i | \(-0.234778\pi\) |
−0.952449 | + | 0.304698i | \(0.901444\pi\) | |||||||
\(422\) | 6.88589e7i | 0.916268i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.49175e7 | −0.326894 | ||||||||
\(425\) | 3.14455e7 | − | 1.81551e7i | 0.409630 | − | 0.236500i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.91394e7 | − | 1.37074e8i | 1.01650 | − | 1.76064i | ||||
\(428\) | −2.24892e7 | − | 1.29841e7i | −0.286841 | − | 0.165608i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.52076e7 | − | 4.36609e7i | −0.317049 | − | 0.549145i | ||||
\(431\) | 9.48759e6i | 0.118502i | 0.998243 | + | 0.0592508i | \(0.0188712\pi\) | ||||
−0.998243 | + | 0.0592508i | \(0.981129\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.03139e8 | −1.27045 | −0.635225 | − | 0.772327i | \(-0.719092\pi\) | ||||
−0.635225 | + | 0.772327i | \(0.719092\pi\) | |||||||
\(434\) | 4.34963e7 | − | 2.51126e7i | 0.532088 | − | 0.307201i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.53411e6 | + | 1.65136e7i | −0.115033 | + | 0.199242i | ||||
\(437\) | 1.32325e8 | + | 7.63978e7i | 1.58561 | + | 0.915454i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.31397e7 | + | 4.00791e7i | 0.273504 | + | 0.473723i | 0.969757 | − | 0.244074i | \(-0.0784839\pi\) |
−0.696252 | + | 0.717797i | \(0.745151\pi\) | |||||||
\(440\) | − | 6.82335e6i | − | 0.0801013i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.69462e7 | 0.659475 | ||||||||
\(443\) | −6.29030e7 | + | 3.63171e7i | −0.723536 | + | 0.417734i | −0.816053 | − | 0.577977i | \(-0.803842\pi\) |
0.0925165 | + | 0.995711i | \(0.470509\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.05480e8 | + | 1.82698e8i | −1.19699 | + | 2.07325i | ||||
\(446\) | 7.69981e7 | + | 4.44549e7i | 0.867912 | + | 0.501089i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.18878e6 | + | 1.59154e7i | 0.102194 | + | 0.177005i | ||||
\(449\) | − | 1.26263e7i | − | 0.139488i | −0.997565 | − | 0.0697439i | \(-0.977782\pi\) | ||
0.997565 | − | 0.0697439i | \(-0.0222182\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.51073e7 | 0.273697 | ||||||||
\(452\) | −1.78412e7 | + | 1.03006e7i | −0.193201 | + | 0.111545i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −425734. | + | 737393.i | −0.00454957 | + | 0.00788009i | ||||
\(455\) | −3.14147e8 | − | 1.81373e8i | −3.33502 | − | 1.92547i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.41175e7 | − | 1.28375e8i | −0.776555 | − | 1.34503i | −0.933916 | − | 0.357492i | \(-0.883632\pi\) |
0.157361 | − | 0.987541i | \(-0.449701\pi\) | |||||||
\(458\) | − | 7.13571e7i | − | 0.742747i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.09376e7 | −0.831528 | ||||||||
\(461\) | −1.04144e8 | + | 6.01278e7i | −1.06300 | + | 0.613723i | −0.926260 | − | 0.376884i | \(-0.876995\pi\) |
−0.136739 | + | 0.990607i | \(0.543662\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.27212e7 | + | 1.08636e8i | −0.631934 | + | 1.09454i | 0.355222 | + | 0.934782i | \(0.384405\pi\) |
−0.987156 | + | 0.159760i | \(0.948928\pi\) | |||||||
\(464\) | 1.31894e7 | + | 7.61490e6i | 0.132029 | + | 0.0762273i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.91674e7 | + | 8.51604e7i | 0.485869 | + | 0.841550i | ||||
\(467\) | − | 7.20089e7i | − | 0.707027i | −0.935429 | − | 0.353513i | \(-0.884987\pi\) | ||
0.935429 | − | 0.353513i | \(-0.115013\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.11949e8 | 2.05453 | ||||||||
\(470\) | 9.68636e6 | − | 5.59242e6i | 0.0932968 | − | 0.0538649i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.63729e7 | + | 4.56792e7i | −0.250803 | + | 0.434403i | ||||
\(473\) | −9.94200e6 | − | 5.74002e6i | −0.0939486 | − | 0.0542413i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.04665e7 | + | 1.22052e8i | 0.657509 | + | 1.13884i | ||||
\(476\) | 4.77828e7i | 0.443048i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.17356e7 | −0.656827 | ||||||||
\(479\) | 3.68659e7 | − | 2.12845e7i | 0.335443 | − | 0.193668i | −0.322812 | − | 0.946463i | \(-0.604628\pi\) |
0.658255 | + | 0.752795i | \(0.271295\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.01934e7 | + | 8.69376e7i | −0.451037 | + | 0.781218i | ||||
\(482\) | −4.89396e7 | − | 2.82553e7i | −0.437038 | − | 0.252324i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.75681e7 | + | 4.77494e7i | 0.243148 | + | 0.421145i | ||||
\(485\) | − | 2.13537e8i | − | 1.87175i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.50256e7 | 0.822723 | 0.411362 | − | 0.911472i | \(-0.365053\pi\) | ||||
0.411362 | + | 0.911472i | \(0.365053\pi\) | |||||||
\(488\) | 4.42426e7 | − | 2.55435e7i | 0.380698 | − | 0.219796i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.52640e7 | − | 1.65002e8i | 0.809731 | − | 1.40249i | ||||
\(491\) | 1.16209e8 | + | 6.70932e7i | 0.981735 | + | 0.566805i | 0.902794 | − | 0.430074i | \(-0.141513\pi\) |
0.0789417 | + | 0.996879i | \(0.474846\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.97992e7 | + | 3.42932e7i | 0.165237 | + | 0.286199i | ||||
\(494\) | 2.21029e8i | 1.83345i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.62110e7 | 0.132851 | ||||||||
\(497\) | 2.53189e8 | − | 1.46179e8i | 2.06241 | − | 1.19074i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.53110e6 | + | 2.65195e6i | −0.0123226 | + | 0.0213434i | −0.872121 | − | 0.489290i | \(-0.837256\pi\) |
0.859798 | + | 0.510634i | \(0.170589\pi\) | |||||||
\(500\) | 9.42063e6 | + | 5.43901e6i | 0.0753651 | + | 0.0435120i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.45559e7 | + | 9.44936e7i | 0.431251 | + | 0.746949i | ||||
\(503\) | 6.21612e7i | 0.488445i | 0.969719 | + | 0.244223i | \(0.0785327\pi\) | ||||
−0.969719 | + | 0.244223i | \(0.921467\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.80785e8 | 1.40375 | ||||||||
\(506\) | −1.59611e7 | + | 9.21514e6i | −0.123200 | + | 0.0711296i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −852016. | + | 1.47574e6i | −0.00649915 | + | 0.0112569i | ||||
\(509\) | −2.24463e8 | − | 1.29594e8i | −1.70212 | − | 0.982721i | −0.943608 | − | 0.331064i | \(-0.892592\pi\) |
−0.758514 | − | 0.651657i | \(-0.774074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.71509e8 | + | 2.97061e8i | 1.28535 | + | 2.22630i | ||||
\(512\) | 5.93164e6i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.65204e7 | −0.637132 | ||||||||
\(515\) | −4.29015e7 | + | 2.47692e7i | −0.314088 | + | 0.181339i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.27345e6 | − | 2.20568e6i | 0.00921531 | − | 0.0159614i | ||||
\(518\) | −7.29482e7 | − | 4.21167e7i | −0.524838 | − | 0.303015i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.85409e7 | − | 1.01396e8i | −0.416341 | − | 0.721123i | ||||
\(521\) | 6.34248e7i | 0.448483i | 0.974534 | + | 0.224241i | \(0.0719904\pi\) | ||||
−0.974534 | + | 0.224241i | \(0.928010\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.12228e8 | −1.48353 | −0.741766 | − | 0.670659i | \(-0.766011\pi\) | ||||
−0.741766 | + | 0.670659i | \(0.766011\pi\) | |||||||
\(524\) | 4.80846e7 | − | 2.77617e7i | 0.334205 | − | 0.192953i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.23136e7 | + | 1.07930e8i | −0.428179 | + | 0.741629i | ||||
\(527\) | 3.65026e7 | + | 2.10748e7i | 0.249397 | + | 0.143990i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.52907e7 | + | 6.11253e7i | 0.238393 | + | 0.412909i | ||||
\(530\) | 1.33202e8i | 0.894715i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.85463e8 | −1.23175 | ||||||||
\(533\) | 3.73097e8 | − | 2.15408e8i | 2.46400 | − | 1.42259i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.94098e7 | + | 1.20221e8i | −0.453272 | + | 0.785091i | ||||
\(536\) | 5.92445e7 | + | 3.42048e7i | 0.384728 | + | 0.222123i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.08716e7 | + | 7.07916e7i | 0.262467 | + | 0.454606i | ||||
\(539\) | − | 4.33851e7i | − | 0.277060i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 960703. | 0.00606733 | 0.00303366 | − | 0.999995i | \(-0.499034\pi\) | ||||
0.00303366 | + | 0.999995i | \(0.499034\pi\) | |||||||
\(542\) | −4.32616e7 | + | 2.49771e7i | −0.271710 | + | 0.156872i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.71132e6 | + | 1.33564e7i | −0.0478996 | + | 0.0829646i | ||||
\(545\) | 8.82772e7 | + | 5.09669e7i | 0.545330 | + | 0.314846i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.28973e8 | − | 2.23388e8i | −0.788021 | − | 1.36489i | −0.927178 | − | 0.374622i | \(-0.877773\pi\) |
0.139157 | − | 0.990270i | \(-0.455561\pi\) | |||||||
\(548\) | 6.79894e7i | 0.413142i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.69994e7 | −0.102175 | ||||||||
\(551\) | −1.33105e8 | + | 7.68480e7i | −0.795680 | + | 0.459386i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.92346e7 | − | 8.52767e7i | 0.291135 | − | 0.504261i | ||||
\(554\) | 1.20425e8 | + | 6.95272e7i | 0.708249 | + | 0.408908i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.77755e7 | − | 8.27496e7i | −0.277959 | − | 0.481440i | ||||
\(557\) | − | 7.25922e7i | − | 0.420073i | −0.977694 | − | 0.210036i | \(-0.932642\pi\) | ||
0.977694 | − | 0.210036i | \(-0.0673583\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.96986e8 | −1.12772 | ||||||||
\(560\) | 8.50798e7 | − | 4.91208e7i | 0.484465 | − | 0.279706i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.37861e7 | − | 1.62442e8i | 0.528360 | − | 0.915146i | ||||
\(563\) | −1.40634e8 | − | 8.11948e7i | −0.788068 | − | 0.454991i | 0.0512139 | − | 0.998688i | \(-0.483691\pi\) |
−0.839282 | + | 0.543696i | \(0.817024\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.50646e7 | + | 9.53746e7i | 0.305300 | + | 0.528795i | ||||
\(566\) | − | 2.15792e8i | − | 1.19011i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.43629e7 | 0.514940 | ||||||||
\(569\) | −1.35419e8 | + | 7.81841e7i | −0.735093 | + | 0.424406i | −0.820282 | − | 0.571959i | \(-0.806184\pi\) |
0.0851898 | + | 0.996365i | \(0.472850\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.72913e6 | + | 1.33872e7i | −0.0415166 | + | 0.0719089i | −0.886037 | − | 0.463614i | \(-0.846552\pi\) |
0.844520 | + | 0.535523i | \(0.179886\pi\) | |||||||
\(572\) | −2.30888e7 | − | 1.33303e7i | −0.123371 | − | 0.0712283i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.80746e8 | + | 3.13061e8i | 0.955724 | + | 1.65536i | ||||
\(575\) | 2.01645e8i | 1.06068i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.55108e7 | 0.445137 | 0.222568 | − | 0.974917i | \(-0.428556\pi\) | ||||
0.222568 | + | 0.974917i | \(0.428556\pi\) | |||||||
\(578\) | 8.35220e7 | − | 4.82214e7i | 0.432531 | − | 0.249722i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.07073e7 | − | 7.05071e7i | 0.208636 | − | 0.361367i | ||||
\(581\) | −1.76307e8 | − | 1.01791e8i | −0.898963 | − | 0.519017i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.51657e7 | + | 2.62678e7i | 0.0765347 | + | 0.132562i | ||||
\(584\) | 1.10714e8i | 0.555858i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.96111e8 | 0.974561 | ||||||||
\(587\) | −2.77326e8 | + | 1.60114e8i | −1.37112 | + | 0.791617i | −0.991069 | − | 0.133349i | \(-0.957427\pi\) |
−0.380051 | + | 0.924965i | \(0.624094\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.17989e7 | + | 1.41680e8i | −0.400315 | + | 0.693365i | ||||
\(590\) | 2.44189e8 | + | 1.40983e8i | 1.18897 | + | 0.686451i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.35938e7 | − | 2.35452e7i | −0.0655203 | − | 0.113484i | ||||
\(593\) | − | 2.07242e8i | − | 0.993832i | −0.867799 | − | 0.496916i | \(-0.834466\pi\) | ||
0.867799 | − | 0.496916i | \(-0.165534\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.55435e8 | 1.21263 | ||||||||
\(596\) | 4.39333e7 | − | 2.53649e7i | 0.207518 | − | 0.119810i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.58122e8 | + | 2.73876e8i | −0.739418 | + | 1.28071i | ||||
\(599\) | −2.43794e8 | − | 1.40755e8i | −1.13434 | − | 0.654911i | −0.189317 | − | 0.981916i | \(-0.560627\pi\) |
−0.945023 | + | 0.327005i | \(0.893961\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.57960e7 | − | 7.93211e7i | −0.210962 | − | 0.365397i | 0.741054 | − | 0.671446i | \(-0.234326\pi\) |
−0.952016 | + | 0.306049i | \(0.900993\pi\) | |||||||
\(602\) | − | 1.65288e8i | − | 0.757621i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.42075e6 | −0.0291390 | ||||||||
\(605\) | 2.55256e8 | − | 1.47372e8i | 1.15268 | − | 0.665501i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.45204e7 | + | 1.11753e8i | −0.288490 | + | 0.499680i | −0.973450 | − | 0.228902i | \(-0.926487\pi\) |
0.684959 | + | 0.728581i | \(0.259820\pi\) | |||||||
\(608\) | −5.18411e7 | − | 2.99305e7i | −0.230655 | − | 0.133169i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.36549e8 | − | 2.36509e8i | −0.601587 | − | 1.04198i | ||||
\(611\) | − | 4.37022e7i | − | 0.191593i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.34072e7 | −0.145030 | −0.0725151 | − | 0.997367i | \(-0.523103\pi\) | ||||
−0.0725151 | + | 0.997367i | \(0.523103\pi\) | |||||||
\(614\) | −2.37790e8 | + | 1.37288e8i | −1.02728 | + | 0.593100i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.11853e7 | − | 1.93735e7i | 0.0478526 | − | 0.0828831i | ||||
\(617\) | 3.57455e8 | + | 2.06377e8i | 1.52183 | + | 0.878628i | 0.999668 | + | 0.0257801i | \(0.00820697\pi\) |
0.522160 | + | 0.852848i | \(0.325126\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.96903e7 | − | 3.41046e7i | −0.0830196 | − | 0.143794i | 0.821526 | − | 0.570171i | \(-0.193123\pi\) |
−0.904546 | + | 0.426377i | \(0.859790\pi\) | |||||||
\(620\) | − | 8.66596e7i | − | 0.363615i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.74991e8 | 0.727185 | ||||||||
\(623\) | −5.98981e8 | + | 3.45822e8i | −2.47713 | + | 1.43017i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.35621e8 | − | 2.34902e8i | 0.555503 | − | 0.962159i | ||||
\(626\) | −3.52479e6 | − | 2.03504e6i | −0.0143685 | − | 0.00829563i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.68072e7 | + | 2.91109e7i | 0.0678603 | + | 0.117538i | ||||
\(629\) | − | 7.06894e7i | − | 0.284055i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.58330e8 | −1.42625 | −0.713124 | − | 0.701038i | \(-0.752720\pi\) | ||||
−0.713124 | + | 0.701038i | \(0.752720\pi\) | |||||||
\(632\) | 2.75244e7 | − | 1.58912e7i | 0.109035 | − | 0.0629515i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.11028e7 | − | 3.65511e7i | 0.0828081 | − | 0.143428i | ||||
\(635\) | 7.88890e6 | + | 4.55466e6i | 0.0308103 | + | 0.0177883i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.72222e8 | − | 6.44707e8i | −1.44007 | − | 2.49428i | ||||
\(638\) | − | 1.85389e7i | − | 0.0713874i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.17090e7 | 0.120960 | ||||||||
\(641\) | 2.56183e8 | − | 1.47908e8i | 0.972696 | − | 0.561586i | 0.0726388 | − | 0.997358i | \(-0.476858\pi\) |
0.900057 | + | 0.435772i | \(0.143525\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.45261e7 | − | 5.98010e7i | 0.129872 | − | 0.224945i | −0.793755 | − | 0.608238i | \(-0.791877\pi\) |
0.923627 | + | 0.383293i | \(0.125210\pi\) | |||||||
\(644\) | −2.29806e8 | − | 1.32678e8i | −0.860406 | − | 0.496755i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.78210e7 | − | 1.34790e8i | −0.288669 | − | 0.499989i | ||||
\(647\) | − | 7.16195e7i | − | 0.264435i | −0.991221 | − | 0.132217i | \(-0.957790\pi\) | ||
0.991221 | − | 0.132217i | \(-0.0422097\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.42063e7 | 0.234879 | ||||||||
\(650\) | −2.52613e8 | + | 1.45846e8i | −0.919848 | + | 0.531074i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.26992e7 | + | 5.66367e7i | −0.117976 | + | 0.204341i | ||||
\(653\) | 4.34310e8 | + | 2.50749e8i | 1.55977 | + | 0.900533i | 0.997278 | + | 0.0737286i | \(0.0234899\pi\) |
0.562490 | + | 0.826804i | \(0.309843\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.48407e8 | − | 2.57048e8i | −0.528116 | − | 0.914724i | ||||
\(656\) | 1.16677e8i | 0.413308i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.66699e7 | 0.128716 | ||||||||
\(659\) | 3.11452e8 | − | 1.79817e8i | 1.08827 | − | 0.628310i | 0.155151 | − | 0.987891i | \(-0.450414\pi\) |
0.933114 | + | 0.359581i | \(0.117080\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.95636e8 | − | 3.38851e8i | 0.677398 | − | 1.17329i | −0.298364 | − | 0.954452i | \(-0.596441\pi\) |
0.975762 | − | 0.218835i | \(-0.0702257\pi\) | |||||||
\(662\) | −7.27288e6 | − | 4.19900e6i | −0.0250687 | − | 0.0144734i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.28546e7 | − | 5.69059e7i | −0.112226 | − | 0.194381i | ||||
\(665\) | 9.91435e8i | 3.37131i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.19906e8 | −0.741070 | ||||||||
\(668\) | −1.89646e8 | + | 1.09492e8i | −0.636231 | + | 0.367328i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.82850e8 | − | 3.16706e8i | 0.607955 | − | 1.05301i | ||||
\(671\) | −5.38555e7 | − | 3.10935e7i | −0.178264 | − | 0.102921i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.50865e8 | + | 2.61306e8i | 0.494929 | + | 0.857242i | 0.999983 | − | 0.00584556i | \(-0.00186071\pi\) |
−0.505054 | + | 0.863088i | \(0.668527\pi\) | |||||||
\(674\) | 4.44920e7i | 0.145312i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.03012e8 | −0.980888 | ||||||||
\(677\) | −4.86730e7 | + | 2.81013e7i | −0.156863 | + | 0.0905652i | −0.576377 | − | 0.817184i | \(-0.695534\pi\) |
0.419514 | + | 0.907749i | \(0.362201\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.50044e8 | − | 6.06294e8i | 1.11818 | − | 1.93675i | ||||
\(680\) | 7.13998e7 | + | 4.12227e7i | 0.227076 | + | 0.131102i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.86662e6 | − | 1.70895e7i | −0.0311039 | − | 0.0538736i | ||||
\(683\) | − | 1.47922e8i | − | 0.464270i | −0.972684 | − | 0.232135i | \(-0.925429\pi\) | ||
0.972684 | − | 0.232135i | \(-0.0745711\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.63454e8 | 1.13078 | ||||||||
\(686\) | 2.17720e8 | − | 1.25701e8i | 0.674414 | − | 0.389373i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.66746e7 | − | 4.62018e7i | 0.0819093 | − | 0.141871i | ||||
\(689\) | 4.50730e8 | + | 2.60229e8i | 1.37803 | + | 0.795606i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.13616e7 | + | 1.96789e7i | 0.0344355 | + | 0.0596441i | 0.882730 | − | 0.469881i | \(-0.155703\pi\) |
−0.848294 | + | 0.529526i | \(0.822370\pi\) | |||||||
\(692\) | 4.02438e7i | 0.121445i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.03723e8 | −0.310311 | ||||||||
\(695\) | −4.42358e8 | + | 2.55396e8i | −1.31771 | + | 0.760780i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.51684e8 | + | 2.62724e8i | −0.447962 | + | 0.775892i | ||||
\(698\) | −3.15151e8 | − | 1.81953e8i | −0.926730 | − | 0.535048i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.22378e8 | − | 2.11964e8i | −0.356786 | − | 0.617972i | ||||
\(701\) | − | 5.55648e8i | − | 1.61304i | −0.591205 | − | 0.806521i | \(-0.701348\pi\) | ||
0.591205 | − | 0.806521i | \(-0.298652\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.74372e8 | 0.789720 | ||||||||
\(704\) | 6.25310e6 | − | 3.61023e6i | 0.0179216 | − | 0.0103470i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.74385e7 | + | 1.16807e8i | −0.191643 | + | 0.331936i | ||||
\(707\) | 5.13303e8 | + | 2.96356e8i | 1.45250 | + | 0.838600i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.40215e7 | + | 5.89270e7i | 0.0954585 | + | 0.165339i | 0.909800 | − | 0.415047i | \(-0.136235\pi\) |
−0.814341 | + | 0.580386i | \(0.802902\pi\) | |||||||
\(710\) | − | 5.04440e8i | − | 1.40940i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.23239e8 | −0.618485 | ||||||||
\(713\) | −2.02713e8 | + | 1.17036e8i | −0.559259 | + | 0.322889i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.12605e7 | + | 1.23427e8i | −0.194953 | + | 0.337669i | ||||
\(716\) | −2.28793e8 | − | 1.32094e8i | −0.623310 | − | 0.359868i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.25706e7 | − | 7.37344e7i | −0.115010 | − | 0.199203i | ||||
\(719\) | − | 1.29526e8i | − | 0.348474i | −0.984704 | − | 0.174237i | \(-0.944254\pi\) | ||
0.984704 | − | 0.174237i | \(-0.0557459\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.62413e8 | −0.433327 | ||||||||
\(722\) | 2.92692e8 | − | 1.68986e8i | 0.777678 | − | 0.448993i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.20338e7 | − | 7.28046e7i | 0.110760 | − | 0.191842i | ||||
\(725\) | −1.75659e8 | − | 1.01417e8i | −0.460952 | − | 0.266130i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.05350e8 | + | 5.28882e8i | 0.794684 | + | 1.37643i | 0.923039 | + | 0.384705i | \(0.125697\pi\) |
−0.128355 | + | 0.991728i | \(0.540970\pi\) | |||||||
\(728\) | − | 3.83857e8i | − | 0.994890i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.91849e8 | 1.52140 | ||||||||
\(731\) | 1.20128e8 | − | 6.93557e7i | 0.307532 | − | 0.177554i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.49347e7 | − | 9.51497e7i | 0.139487 | − | 0.241599i | −0.787815 | − | 0.615911i | \(-0.788788\pi\) |
0.927303 | + | 0.374312i | \(0.122121\pi\) | |||||||
\(734\) | −8.79261e7 | − | 5.07642e7i | −0.222346 | − | 0.128372i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.28240e7 | − | 7.41733e7i | −0.107412 | − | 0.186043i | ||||
\(737\) | − | 8.32736e7i | − | 0.208020i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.13732e8 | −0.777366 | −0.388683 | − | 0.921372i | \(-0.627070\pi\) | ||||
−0.388683 | + | 0.921372i | \(0.627070\pi\) | |||||||
\(740\) | −1.25866e8 | + | 7.26689e7i | −0.310609 | + | 0.179330i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.18355e8 | + | 3.78201e8i | −0.534504 | + | 0.925787i | ||||
\(743\) | 2.69001e8 | + | 1.55308e8i | 0.655824 | + | 0.378640i | 0.790684 | − | 0.612225i | \(-0.209725\pi\) |
−0.134860 | + | 0.990865i | \(0.543059\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.35594e8 | − | 2.34856e8i | −0.327924 | − | 0.567981i | ||||
\(746\) | − | 4.90336e7i | − | 0.118108i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.87736e7 | 0.0448584 | ||||||||
\(749\) | −3.94150e8 | + | 2.27562e8i | −0.938028 | + | 0.541571i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.78681e8 | − | 4.82690e8i | 0.657942 | − | 1.13959i | −0.323206 | − | 0.946329i | \(-0.604761\pi\) |
0.981148 | − | 0.193260i | \(-0.0619061\pi\) | |||||||
\(752\) | 1.02501e7 | + | 5.91789e6i | 0.0241032 | + | 0.0139160i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.59054e8 | − | 2.75490e8i | −0.371049 | − | 0.642676i | ||||
\(755\) | 3.43237e7i | 0.0797541i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.72743e7 | 0.0398210 | 0.0199105 | − | 0.999802i | \(-0.493662\pi\) | ||||
0.0199105 | + | 0.999802i | \(0.493662\pi\) | |||||||
\(758\) | −5.07770e7 | + | 2.93161e7i | −0.116590 | + | 0.0673130i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.60000e8 | + | 2.77129e8i | −0.364486 | + | 0.631308i | ||||
\(761\) | −3.28749e7 | − | 1.89803e7i | −0.0745951 | − | 0.0430675i | 0.462239 | − | 0.886756i | \(-0.347046\pi\) |
−0.536834 | + | 0.843688i | \(0.680380\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.67097e8 | + | 2.89420e8i | 0.376179 | + | 0.651561i | ||||
\(764\) | 4.70206e7i | 0.105441i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.41713e7 | −0.0315299 | ||||||||
\(767\) | 9.54113e8 | − | 5.50857e8i | 2.11453 | − | 1.22082i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.19828e7 | − | 1.24678e8i | 0.158289 | − | 0.274164i | −0.775963 | − | 0.630778i | \(-0.782736\pi\) |
0.934252 | + | 0.356614i | \(0.116069\pi\) | |||||||
\(770\) | −1.03566e8 | − | 5.97937e7i | −0.226853 | − | 0.130973i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.61116e6 | − | 4.52267e6i | −0.00567521 | − | 0.00982975i | ||||
\(773\) | − | 2.81284e8i | − | 0.608984i | −0.952515 | − | 0.304492i | \(-0.901513\pi\) | ||
0.952515 | − | 0.304492i | \(-0.0984867\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.15900e8 | −0.463819 | ||||||||
\(776\) | 1.95691e8 | − | 1.12982e8i | 0.418779 | − | 0.241782i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.95662e6 | − | 1.20492e7i | 0.0147727 | − | 0.0255870i | ||||
\(779\) | −1.01973e9 | − | 5.88740e8i | −2.15711 | − | 1.24541i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.74329e7 | − | 9.94768e7i | −0.120561 | − | 0.208818i | ||||
\(782\) | − | 2.22690e8i | − | 0.465673i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.01616e8 | 0.418386 | ||||||||
\(785\) | 1.55619e8 | − | 8.98469e7i | 0.321703 | − | 0.185735i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.40890e8 | − | 2.44028e8i | 0.289038 | − | 0.500628i | −0.684542 | − | 0.728973i | \(-0.739998\pi\) |
0.973580 | + | 0.228345i | \(0.0733313\pi\) | |||||||
\(788\) | 2.86906e8 | + | 1.65645e8i | 0.586355 | + | 0.338532i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.49503e7 | − | 1.47138e8i | −0.172299 | − | 0.298431i | ||||
\(791\) | 3.61062e8i | 0.729546i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.06707e9 | −2.13979 | ||||||||
\(794\) | 5.74060e6 | − | 3.31434e6i | 0.0114682 | − | 0.00662118i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.11472e8 | + | 1.93075e8i | −0.221018 | + | 0.382814i | ||||
\(797\) | −1.66240e8 | − | 9.59787e7i | −0.328368 | − | 0.189583i | 0.326748 | − | 0.945111i | \(-0.394047\pi\) |
−0.655116 | + | 0.755528i | \(0.727380\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.53869e7 | + | 2.66509e7i | 0.0301655 | + | 0.0522481i | ||||
\(800\) | − | 7.89986e7i | − | 0.154294i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.95830e7 | 0.193047 | ||||||||
\(803\) | 1.16714e8 | − | 6.73849e7i | 0.225412 | − | 0.130141i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.09264e8 | + | 1.22848e9i | −1.35963 | + | 2.35495i | ||||
\(806\) | −2.93238e8 | − | 1.69301e8i | −0.560036 | − | 0.323337i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.56533e7 | + | 1.65676e8i | 0.181328 | + | 0.314070i | ||||
\(809\) | 3.02304e8i | 0.570950i | 0.958386 | + | 0.285475i | \(0.0921513\pi\) | ||||
−0.958386 | + | 0.285475i | \(0.907849\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.85058e8 | −0.909351 | −0.454675 | − | 0.890657i | \(-0.650245\pi\) | ||||
−0.454675 | + | 0.890657i | \(0.650245\pi\) | |||||||
\(812\) | 2.31160e8 | − | 1.33460e8i | 0.431762 | − | 0.249278i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.65474e7 | + | 2.86610e7i | −0.0306801 | + | 0.0531395i | ||||
\(815\) | 3.02765e8 | + | 1.74802e8i | 0.559285 | + | 0.322903i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.69195e8 | + | 4.66260e8i | 0.493629 | + | 0.854991i | ||||
\(818\) | 3.65035e8i | 0.666922i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.23725e8 | 1.13123 | ||||||||
\(821\) | −7.89614e7 | + | 4.55884e7i | −0.142687 | + | 0.0823806i | −0.569644 | − | 0.821891i | \(-0.692919\pi\) |
0.426957 | + | 0.904272i | \(0.359586\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.68746e7 | + | 8.11892e7i | −0.0840888 | + | 0.145646i | −0.905003 | − | 0.425406i | \(-0.860131\pi\) |
0.820914 | + | 0.571052i | \(0.193465\pi\) | |||||||
\(824\) | −4.53983e7 | − | 2.62107e7i | −0.0811443 | − | 0.0468487i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.62217e8 | + | 8.00583e8i | 0.820173 | + | 1.42058i | ||||
\(827\) | 7.81578e8i | 1.38183i | 0.722934 | + | 0.690917i | \(0.242793\pi\) | ||||
−0.722934 | + | 0.690917i | \(0.757207\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.47882e8 | 0.961663 | 0.480832 | − | 0.876813i | \(-0.340335\pi\) | ||||
0.480832 | + | 0.876813i | \(0.340335\pi\) | |||||||
\(830\) | −3.04204e8 | + | 1.75632e8i | −0.532024 | + | 0.307164i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.19478e7 | − | 1.07297e8i | 0.107561 | − | 0.186302i | ||||
\(833\) | 4.53984e8 | + | 2.62108e8i | 0.785426 | + | 0.453466i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.85318e8 | + | 1.01380e9i | 1.00538 | + | 1.74138i | ||||
\(836\) | 7.28673e7i | 0.124714i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.26409e8 | −1.06445 | ||||||||
\(839\) | 4.63674e7 | − | 2.67702e7i | 0.0785103 | − | 0.0453279i | −0.460231 | − | 0.887799i | \(-0.652233\pi\) |
0.538741 | + | 0.842471i | \(0.318900\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.86811e8 | + | 3.23566e8i | −0.314061 | + | 0.543969i | ||||
\(842\) | −1.55250e8 | − | 8.96334e7i | −0.260073 | − | 0.150153i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.94762e8 | + | 3.37338e8i | 0.323950 | + | 0.561098i | ||||
\(845\) | 1.61982e9i | 2.68471i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.66329e8 | 1.59028 | ||||||||
\(848\) | −1.22070e8 | + | 7.04773e7i | −0.200181 | + | 0.115574i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.02701e8 | − | 1.77883e8i | 0.167231 | − | 0.289652i | ||||
\(851\) | 3.39973e8 | + | 1.96283e8i | 0.551639 | + | 0.318489i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.29396e8 | + | 2.24121e8i | 0.208485 | + | 0.361107i | 0.951238 | − | 0.308459i | \(-0.0998134\pi\) |
−0.742752 | + | 0.669566i | \(0.766480\pi\) | |||||||
\(854\) | − | 8.95360e8i | − | 1.43755i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.46899e8 | −0.234205 | ||||||||
\(857\) | 5.78169e8 | − | 3.33806e8i | 0.918571 | − | 0.530337i | 0.0353918 | − | 0.999374i | \(-0.488732\pi\) |
0.883179 | + | 0.469037i | \(0.155399\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.71527e8 | − | 9.89914e8i | 0.901690 | − | 1.56177i | 0.0763913 | − | 0.997078i | \(-0.475660\pi\) |
0.825299 | − | 0.564696i | \(-0.191006\pi\) | |||||||
\(860\) | −2.46983e8 | − | 1.42596e8i | −0.388304 | − | 0.224187i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.68350e7 | + | 4.64795e7i | 0.0418966 | + | 0.0725671i | ||||
\(863\) | 1.78293e8i | 0.277396i | 0.990335 | + | 0.138698i | \(0.0442918\pi\) | ||||
−0.990335 | + | 0.138698i | \(0.955708\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.15133e8 | 0.332398 | ||||||||
\(866\) | −5.05274e8 | + | 2.91720e8i | −0.777988 | + | 0.449172i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.42058e8 | − | 2.46052e8i | 0.217224 | − | 0.376243i | ||||
\(869\) | −3.35048e7 | − | 1.93440e7i | −0.0510561 | − | 0.0294773i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.14445e8 | − | 1.23745e9i | −1.08122 | − | 1.87273i | ||||
\(872\) | 1.07866e8i | 0.162681i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.64342e8 | 1.29465 | ||||||||
\(875\) | 1.65108e8 | − | 9.53251e7i | 0.246459 | − | 0.142293i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.64920e8 | + | 8.05265e8i | −0.689254 | + | 1.19382i | 0.282825 | + | 0.959172i | \(0.408728\pi\) |
−0.972079 | + | 0.234652i | \(0.924605\pi\) | |||||||
\(878\) | 2.26722e8 | + | 1.30898e8i | 0.334973 | + | 0.193397i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.92993e7 | − | 3.34274e7i | −0.0283201 | − | 0.0490518i | ||||
\(881\) | − | 5.01442e8i | − | 0.733319i | −0.930355 | − | 0.366660i | \(-0.880501\pi\) | ||
0.930355 | − | 0.366660i | \(-0.119499\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.14295e8 | 1.18277 | 0.591384 | − | 0.806390i | \(-0.298582\pi\) | ||||
0.591384 | + | 0.806390i | \(0.298582\pi\) | |||||||
\(884\) | 2.78978e8 | − | 1.61068e8i | 0.403844 | − | 0.233159i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.05440e8 | + | 3.55833e8i | −0.295382 | + | 0.511617i | ||||
\(887\) | −3.43598e8 | − | 1.98377e8i | −0.492357 | − | 0.284262i | 0.233195 | − | 0.972430i | \(-0.425082\pi\) |
−0.725552 | + | 0.688168i | \(0.758415\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.49326e7 | + | 2.58641e7i | 0.0212535 | + | 0.0368122i | ||||
\(890\) | 1.19338e9i | 1.69281i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.02950e8 | 0.708647 | ||||||||
\(893\) | −1.03442e8 | + | 5.97221e7i | −0.145258 | + | 0.0838650i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.06139e8 | + | 1.22307e9i | −0.984966 | + | 1.70601i | ||||
\(896\) | 9.00313e7 | + | 5.19796e7i | 0.125161 | + | 0.0722618i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.57125e7 | − | 6.18559e7i | −0.0493164 | − | 0.0854185i | ||||
\(899\) | − | 2.35453e8i | − | 0.324059i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.66491e8 | −0.501059 | ||||||||
\(902\) | 1.23000e8 | − | 7.10141e7i | 0.167605 | − | 0.0967665i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.82692e7 | + | 1.00925e8i | −0.0788740 | + | 0.136614i | ||||
\(905\) | −3.89195e8 | − | 2.24702e8i | −0.525075 | − | 0.303152i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.40034e8 | + | 7.62161e8i | 0.589745 | + | 1.02147i | 0.994266 | + | 0.106939i | \(0.0341051\pi\) |
−0.404520 | + | 0.914529i | \(0.632562\pi\) | |||||||
\(908\) | 4.81663e6i | 0.00643407i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.05200e9 | −2.72303 | ||||||||
\(911\) | −4.37526e8 | + | 2.52606e8i | −0.578693 | + | 0.334109i | −0.760614 | − | 0.649205i | \(-0.775102\pi\) |
0.181921 | + | 0.983313i | \(0.441769\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.99932e7 | + | 6.92703e7i | −0.0525501 | + | 0.0910195i | ||||
\(914\) | −7.26200e8 | − | 4.19272e8i | −0.951082 | − | 0.549107i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.01828e8 | − | 3.49577e8i | −0.262601 | − | 0.454838i | ||||
\(917\) | − | 9.73114e8i | − | 1.26199i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.68525e8 | −0.345969 | −0.172985 | − | 0.984925i | \(-0.555341\pi\) | ||||
−0.172985 | + | 0.984925i | \(0.555341\pi\) | |||||||
\(920\) | −3.96512e8 | + | 2.28926e8i | −0.509205 | + | 0.293989i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.40134e8 | + | 5.89129e8i | −0.433968 | + | 0.751654i | ||||
\(923\) | −1.70692e9 | − | 9.85491e8i | −2.17074 | − | 1.25328i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.81044e8 | + | 3.13578e8i | 0.228749 | + | 0.396206i | ||||
\(926\) | 7.09610e8i | 0.893690i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.61528e7 | 0.107802 | ||||||||
\(929\) | −6.07506e8 | + | 3.50744e8i | −0.757711 | + | 0.437465i | −0.828473 | − | 0.560029i | \(-0.810790\pi\) |
0.0707624 | + | 0.997493i | \(0.477457\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.01734e9 | + | 1.76208e9i | −1.26071 | + | 2.18361i | ||||
\(932\) | 4.81740e8 | + | 2.78133e8i | 0.595066 | + | 0.343561i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.03672e8 | − | 3.52770e8i | −0.249972 | − | 0.432964i | ||||
\(935\) | − | 1.00359e8i | − | 0.122778i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.16722e8 | 0.628114 | 0.314057 | − | 0.949404i | \(-0.398312\pi\) | ||||
0.314057 | + | 0.949404i | \(0.398312\pi\) | |||||||
\(938\) | 1.03833e9 | − | 5.99481e8i | 1.25814 | − | 0.726385i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.16355e7 | − | 5.47943e7i | 0.0380883 | − | 0.0659708i | ||||
\(941\) | −7.16202e7 | − | 4.13499e7i | −0.0859541 | − | 0.0496256i | 0.456407 | − | 0.889771i | \(-0.349136\pi\) |
−0.542361 | + | 0.840146i | \(0.682469\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.42360e8 | − | 1.45901e9i | −1.00453 | − | 1.73990i | ||||
\(944\) | 2.98375e8i | 0.354688i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.49409e7 | −0.0767087 | ||||||||
\(947\) | 4.08951e8 | − | 2.36108e8i | 0.481527 | − | 0.278010i | −0.239525 | − | 0.970890i | \(-0.576992\pi\) |
0.721053 | + | 0.692880i | \(0.243659\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.15626e9 | − | 2.00269e9i | 1.35287 | − | 2.34324i | ||||
\(950\) | 6.90428e8 | + | 3.98619e8i | 0.805281 | + | 0.464929i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.35150e8 | + | 2.34087e8i | 0.156641 | + | 0.271310i | ||||
\(953\) | − | 9.55129e8i | − | 1.10353i | −0.834000 | − | 0.551764i | \(-0.813955\pi\) | ||
0.834000 | − | 0.551764i | \(-0.186045\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.51360e8 | 0.288593 | ||||||||
\(956\) | −3.51431e8 | + | 2.02899e8i | −0.402223 | + | 0.232223i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.20404e8 | − | 2.08545e8i | 0.136944 | − | 0.237194i | ||||
\(959\) | 1.03195e9 | + | 5.95798e8i | 1.17005 | + | 0.675528i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.18441e8 | + | 5.51556e8i | 0.358805 | + | 0.621469i | ||||
\(962\) | 5.67874e8i | 0.637862i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.19672e8 | −0.356840 | ||||||||
\(965\) | −2.41770e7 | + | 1.39586e7i | −0.0269042 | + | 0.0155332i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.56862e7 | + | 7.91307e7i | −0.0505249 | + | 0.0875116i | −0.890182 | − | 0.455606i | \(-0.849423\pi\) |
0.839657 | + | 0.543117i | \(0.182756\pi\) | |||||||
\(968\) | 2.70111e8 | + | 1.55949e8i | 0.297794 | + | 0.171932i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.03973e8 | − | 1.04611e9i | −0.661763 | − | 1.14621i | ||||
\(971\) | 1.09426e8i | 0.119526i | 0.998213 | + | 0.0597630i | \(0.0190345\pi\) | ||||
−0.998213 | + | 0.0597630i | \(0.980966\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.67465e9 | −1.81796 | ||||||||
\(974\) | 4.65529e8 | − | 2.68773e8i | 0.503813 | − | 0.290877i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.44496e8 | − | 2.50274e8i | 0.155419 | − | 0.269194i | ||||
\(977\) | −5.11653e8 | − | 2.95403e8i | −0.548645 | − | 0.316760i | 0.199930 | − | 0.979810i | \(-0.435928\pi\) |
−0.748575 | + | 0.663050i | \(0.769262\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.35872e8 | + | 2.35337e8i | 0.144804 | + | 0.250808i | ||||
\(980\) | − | 1.07779e9i | − | 1.14513i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.59072e8 | 0.801584 | ||||||||
\(983\) | −1.34739e9 | + | 7.77917e8i | −1.41851 | + | 0.818978i | −0.996168 | − | 0.0874573i | \(-0.972126\pi\) |
−0.422344 | + | 0.906436i | \(0.638793\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.85497e8 | − | 1.53373e9i | 0.926570 | − | 1.60487i | ||||
\(986\) | 1.93992e8 | + | 1.12001e8i | 0.202373 | + | 0.116840i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.25165e8 | + | 1.08282e9i | 0.648222 | + | 1.12275i | ||||
\(989\) | 7.70320e8i | 0.796310i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.71185e9 | 1.75891 | 0.879456 | − | 0.475979i | \(-0.157906\pi\) | ||||
0.879456 | + | 0.475979i | \(0.157906\pi\) | |||||||
\(992\) | 7.94172e7 | − | 4.58515e7i | 0.0813541 | − | 0.0469698i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.26912e8 | − | 1.43225e9i | 0.841977 | − | 1.45835i | ||||
\(995\) | 1.03213e9 | + | 5.95901e8i | 1.04777 | + | 0.604930i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.57012e8 | + | 6.18363e8i | 0.360244 | + | 0.623961i | 0.988001 | − | 0.154448i | \(-0.0493600\pi\) |
−0.627757 | + | 0.778410i | \(0.716027\pi\) | |||||||
\(998\) | 1.73225e7i | 0.0174268i | ||||||||
\(999\) | 0 | 0 |
(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 | 162.7.d.g.53.5 | 16 | ||
3.2 | odd | 2 | inner | 162.7.d.g.53.4 | 16 | ||
9.2 | odd | 6 | inner | 162.7.d.g.107.5 | 16 | ||
9.4 | even | 3 | 162.7.b.b.161.8 | yes | 8 | ||
9.5 | odd | 6 | 162.7.b.b.161.1 | ✓ | 8 | ||
9.7 | even | 3 | inner | 162.7.d.g.107.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
162.7.b.b.161.1 | ✓ | 8 | 9.5 | odd | 6 | ||
162.7.b.b.161.8 | yes | 8 | 9.4 | even | 3 | ||
162.7.d.g.53.4 | 16 | 3.2 | odd | 2 | inner | ||
162.7.d.g.53.5 | 16 | 1.1 | even | 1 | trivial | ||
162.7.d.g.107.4 | 16 | 9.7 | even | 3 | inner | ||
162.7.d.g.107.5 | 16 | 9.2 | odd | 6 | inner |