Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,7,Mod(41,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.41");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.m (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.5638940206\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.13 | ||
Character | \(\chi\) | \(=\) | 72.65 |
Dual form | 72.7.m.a.41.13 |
$q$-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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 16.4370 | + | 21.4202i | 0.608778 | + | 0.793340i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −124.675 | + | 71.9811i | −0.997400 | + | 0.575849i | −0.907478 | − | 0.420100i | \(-0.861995\pi\) |
−0.0899218 | + | 0.995949i | \(0.528662\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 53.2895 | − | 92.3001i | 0.155363 | − | 0.269097i | −0.777828 | − | 0.628477i | \(-0.783679\pi\) |
0.933191 | + | 0.359380i | \(0.117012\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −188.649 | + | 704.168i | −0.258777 | + | 0.965937i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1739.76 | − | 1004.45i | −1.30711 | − | 0.754659i | −0.325495 | − | 0.945544i | \(-0.605531\pi\) |
−0.981612 | + | 0.190885i | \(0.938864\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 48.1438 | + | 83.3874i | 0.0219134 | + | 0.0379551i | 0.876774 | − | 0.480902i | \(-0.159691\pi\) |
−0.854861 | + | 0.518858i | \(0.826358\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3591.13 | − | 1487.41i | −1.06404 | − | 0.440713i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4372.29i | − | 0.889942i | −0.895545 | − | 0.444971i | \(-0.853214\pi\) | ||
0.895545 | − | 0.444971i | \(-0.146786\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2326.88 | 0.339245 | 0.169623 | − | 0.985509i | \(-0.445745\pi\) | ||||
0.169623 | + | 0.985509i | \(0.445745\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2853.01 | − | 375.668i | 0.308067 | − | 0.0405645i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1354.63 | + | 782.094i | −0.111336 | + | 0.0642799i | −0.554634 | − | 0.832094i | \(-0.687142\pi\) |
0.443298 | + | 0.896374i | \(0.353808\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2550.06 | − | 4416.84i | 0.163204 | − | 0.282678i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −18184.2 | + | 7533.53i | −0.923855 | + | 0.382743i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −28838.4 | − | 16649.9i | −1.18243 | − | 0.682679i | −0.225858 | − | 0.974160i | \(-0.572519\pi\) |
−0.956577 | + | 0.291481i | \(0.905852\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −15212.2 | − | 26348.4i | −0.510632 | − | 0.884441i | −0.999924 | − | 0.0123209i | \(-0.996078\pi\) |
0.489292 | − | 0.872120i | \(-0.337255\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7080.94 | − | 53776.1i | −0.197038 | − | 1.49640i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 15343.4i | 0.357863i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −41378.1 | −0.816894 | −0.408447 | − | 0.912782i | \(-0.633929\pi\) | ||||
−0.408447 | + | 0.912782i | \(0.633929\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −994.835 | + | 2401.89i | −0.0167709 | + | 0.0404911i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −80787.0 | + | 46642.4i | −1.17217 | + | 0.676751i | −0.954190 | − | 0.299203i | \(-0.903279\pi\) |
−0.217978 | + | 0.975954i | \(0.569946\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −33877.9 | + | 58678.2i | −0.426099 | + | 0.738026i | −0.996522 | − | 0.0833254i | \(-0.973446\pi\) |
0.570423 | + | 0.821351i | \(0.306779\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −27167.0 | − | 101371.i | −0.298129 | − | 1.11244i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 141018. | + | 81416.9i | 1.35826 | + | 0.784190i | 0.989389 | − | 0.145292i | \(-0.0464123\pi\) |
0.368868 | + | 0.929482i | \(0.379746\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 53145.0 | + | 92049.8i | 0.451725 | + | 0.782410i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 93655.2 | − | 71867.4i | 0.706027 | − | 0.541778i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 156182.i | − | 1.04906i | −0.851391 | − | 0.524532i | \(-0.824240\pi\) | ||
0.851391 | − | 0.524532i | \(-0.175760\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 289206. | 1.73828 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 38247.0 | + | 49842.3i | 0.206525 | + | 0.269137i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −320776. | + | 185200.i | −1.56187 | + | 0.901749i | −0.564807 | + | 0.825223i | \(0.691049\pi\) |
−0.997068 | + | 0.0765256i | \(0.975617\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 134449. | − | 232872.i | 0.592336 | − | 1.02596i | −0.401581 | − | 0.915823i | \(-0.631539\pi\) |
0.993917 | − | 0.110132i | \(-0.0351274\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 54941.8 | + | 54937.1i | 0.219726 | + | 0.219707i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12004.6 | − | 6930.88i | −0.0437129 | − | 0.0252376i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 266314. | + | 461270.i | 0.885462 | + | 1.53367i | 0.845183 | + | 0.534477i | \(0.179491\pi\) |
0.0402793 | + | 0.999188i | \(0.487175\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −39018.6 | − | 16161.1i | −0.118775 | − | 0.0491952i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 279389.i | 0.780612i | 0.920685 | + | 0.390306i | \(0.127631\pi\) | ||||
−0.920685 | + | 0.390306i | \(0.872369\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 506606. | 1.30227 | 0.651136 | − | 0.758961i | \(-0.274293\pi\) | ||||
0.651136 | + | 0.758961i | \(0.274293\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 136525. | − | 17976.8i | 0.323615 | − | 0.0426118i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −185422. | + | 107053.i | −0.406152 | + | 0.234492i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −181815. | + | 314913.i | −0.368764 | + | 0.638718i | −0.989373 | − | 0.145403i | \(-0.953552\pi\) |
0.620609 | + | 0.784120i | \(0.286886\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −460264. | − | 265681.i | −0.866068 | − | 0.499925i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −198892. | − | 114830.i | −0.347843 | − | 0.200827i | 0.315892 | − | 0.948795i | \(-0.397696\pi\) |
−0.663735 | + | 0.747968i | \(0.731030\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 314722. | + | 545115.i | 0.512472 | + | 0.887628i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −117374. | − | 891398.i | −0.178244 | − | 1.35367i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 822140.i | 1.16621i | 0.812398 | + | 0.583104i | \(0.198162\pi\) | ||||
−0.812398 | + | 0.583104i | \(0.801838\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10262.2 | 0.0136181 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 314343. | − | 758938.i | 0.390801 | − | 0.943534i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −290104. | + | 167492.i | −0.338363 | + | 0.195354i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 370018. | − | 640891.i | 0.405423 | − | 0.702213i | −0.588948 | − | 0.808171i | \(-0.700458\pi\) |
0.994371 | + | 0.105958i | \(0.0337910\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.03551e6 | − | 1.03559e6i | 1.06720 | − | 1.06729i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.44645e6 | − | 835106.i | −1.40391 | − | 0.810545i | −0.409115 | − | 0.912483i | \(-0.634162\pi\) |
−0.994791 | + | 0.101938i | \(0.967496\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −107611. | − | 186388.i | −0.0984795 | − | 0.170571i | 0.812576 | − | 0.582855i | \(-0.198065\pi\) |
−0.911055 | + | 0.412284i | \(0.864731\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −328658. | + | 252199.i | −0.283907 | + | 0.217859i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.19727e6i | 0.977330i | 0.872472 | + | 0.488665i | \(0.162516\pi\) | ||||
−0.872472 | + | 0.488665i | \(0.837484\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −268991. | −0.207710 | −0.103855 | − | 0.994592i | \(-0.533118\pi\) | ||||
−0.103855 | + | 0.994592i | \(0.533118\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −680133. | − | 886327.i | −0.497307 | − | 0.648075i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −836647. | + | 483038.i | −0.579838 | + | 0.334770i | −0.761069 | − | 0.648671i | \(-0.775325\pi\) |
0.181231 | + | 0.983441i | \(0.441992\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 112592. | − | 195015.i | 0.0740311 | − | 0.128226i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −67801.0 | + | 18170.4i | −0.0423330 | + | 0.0113450i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −403563. | − | 232997.i | −0.239481 | − | 0.138264i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.13206e6 | + | 1.96079e6i | 0.639019 | + | 1.10681i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.32698e6 | − | 963810.i | −1.25048 | − | 0.517936i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.51518e6i | − | 0.775774i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.16272e6 | −0.567626 | −0.283813 | − | 0.958880i | \(-0.591599\pi\) | ||||
−0.283813 | + | 0.958880i | \(0.591599\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.81375e6 | + | 238824.i | −0.844905 | + | 0.111252i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −437330. | + | 252492.i | −0.194534 | + | 0.112314i | −0.594103 | − | 0.804389i | \(-0.702493\pi\) |
0.399569 | + | 0.916703i | \(0.369160\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 123998. | − | 214772.i | 0.0527062 | − | 0.0912898i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.72485e6 | − | 2.24816e6i | 0.701050 | − | 0.913749i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.23139e6 | − | 710942.i | −0.478887 | − | 0.276486i | 0.241065 | − | 0.970509i | \(-0.422503\pi\) |
−0.719953 | + | 0.694023i | \(0.755837\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.40705e6 | − | 2.43709e6i | −0.523921 | − | 0.907458i | −0.999612 | − | 0.0278457i | \(-0.991135\pi\) |
0.475691 | − | 0.879612i | \(-0.342198\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 573954. | + | 4.35889e6i | 0.204748 | + | 1.55496i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 193432.i | − | 0.0661486i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.79390e6 | 1.57248 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.09818e6 | + | 2.65140e6i | −0.345717 | + | 0.834686i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 998781. | − | 576646.i | 0.301933 | − | 0.174321i | −0.341378 | − | 0.939926i | \(-0.610894\pi\) |
0.643311 | + | 0.765605i | \(0.277560\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 785975. | − | 1.36135e6i | 0.228285 | − | 0.395402i | −0.729015 | − | 0.684498i | \(-0.760021\pi\) |
0.957300 | + | 0.289096i | \(0.0933547\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.07882e6 | + | 824827.i | 0.859628 | + | 0.230297i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.79317e6 | + | 2.18999e6i | 1.01861 | + | 0.588094i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.42652e6 | + | 5.93490e6i | 0.885429 | + | 1.53361i | 0.845221 | + | 0.534417i | \(0.179469\pi\) |
0.0402080 | + | 0.999191i | \(0.487198\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.34544e6 | − | 2.56716e6i | 0.832265 | − | 0.638648i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 166710.i | 0.0399469i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.22428e6 | −1.66814 | −0.834069 | − | 0.551660i | \(-0.813994\pi\) | ||||
−0.834069 | + | 0.551660i | \(0.813994\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.75368e6 | + | 6.19485e6i | 1.05823 | + | 1.37905i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.78931e6 | − | 2.76511e6i | 1.02831 | − | 0.593694i | 0.111809 | − | 0.993730i | \(-0.464335\pi\) |
0.916500 | + | 0.400035i | \(0.131002\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.40877e6 | − | 4.17211e6i | 0.499040 | − | 0.864362i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −438964. | + | 1.63852e6i | −0.0877890 | + | 0.327690i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.70821e6 | + | 986236.i | 0.329916 | + | 0.190477i | 0.655804 | − | 0.754931i | \(-0.272330\pi\) |
−0.325888 | + | 0.945408i | \(0.605663\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −271783. | − | 470743.i | −0.0507118 | − | 0.0878354i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.23963e6 | − | 3.82695e6i | −1.66623 | − | 0.690133i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.13469e6i | 0.895271i | 0.894216 | + | 0.447636i | \(0.147734\pi\) | ||||
−0.894216 | + | 0.447636i | \(0.852266\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.46001e6 | −1.59535 | −0.797675 | − | 0.603088i | \(-0.793937\pi\) | ||||
−0.797675 | + | 0.603088i | \(0.793937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.19811e6 | − | 947807.i | 1.17453 | − | 0.154656i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.15881e6 | − | 2.97844e6i | 0.814769 | − | 0.470407i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.39175e6 | + | 7.60673e6i | −0.671603 | + | 1.16325i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −273683. | + | 2.07987e6i | −0.0405380 | + | 0.308070i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.03548e6 | + | 4.63929e6i | 1.15322 | + | 0.665811i | 0.949670 | − | 0.313253i | \(-0.101419\pi\) |
0.203549 | + | 0.979065i | \(0.434752\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.84018e6 | − | 8.38344e6i | −0.673271 | − | 1.16614i | −0.976971 | − | 0.213372i | \(-0.931555\pi\) |
0.303700 | − | 0.952768i | \(-0.401778\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −48859.7 | − | 371065.i | −0.00658942 | − | 0.0500433i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.09301e7i | − | 1.42963i | −0.699313 | − | 0.714816i | \(-0.746511\pi\) | ||
0.699313 | − | 0.714816i | \(-0.253489\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.81142e6 | −1.24501 | −0.622505 | − | 0.782616i | \(-0.713885\pi\) | ||||
−0.622505 | + | 0.782616i | \(0.713885\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.50307e6 | + | 1.32864e7i | −0.677668 | + | 1.63614i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.07357e6 | + | 1.77453e6i | −0.367413 | + | 0.212126i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.71474e6 | − | 1.16303e7i | 0.779413 | − | 1.34998i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −295177. | − | 1.10143e6i | −0.0332791 | − | 0.124178i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.04822e6 | − | 2.33724e6i | −0.443430 | − | 0.256014i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.24898e6 | + | 7.35946e6i | 0.452312 | + | 0.783427i | 0.998529 | − | 0.0542165i | \(-0.0172661\pi\) |
−0.546217 | + | 0.837643i | \(0.683933\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.98457e6 | + | 4.59233e6i | −0.619291 | + | 0.475220i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 9.75427e6i | − | 0.981475i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.24261e6 | −0.317333 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.32709e6 | + | 1.08516e7i | 0.792795 | + | 1.03315i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 364594. | − | 210498.i | 0.0337779 | − | 0.0195017i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.38221e6 | − | 1.62505e7i | 0.846040 | − | 1.46538i | −0.0386755 | − | 0.999252i | \(-0.512314\pi\) |
0.884715 | − | 0.466132i | \(-0.154353\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.62913e6 | + | 2.62891e6i | 0.230815 | + | 0.230796i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.93422e6 | + | 1.69407e6i | 0.250851 | + | 0.144829i | 0.620154 | − | 0.784480i | \(-0.287070\pi\) |
−0.369303 | + | 0.929309i | \(0.620404\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.78200e6 | − | 3.08652e6i | −0.148389 | − | 0.257018i | 0.782243 | − | 0.622973i | \(-0.214076\pi\) |
−0.930632 | + | 0.365956i | \(0.880742\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.34089e6 | − | 2.21213e6i | −0.433289 | − | 0.179463i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.98835e7i | − | 1.57190i | −0.618291 | − | 0.785949i | \(-0.712175\pi\) | ||
0.618291 | − | 0.785949i | \(-0.287825\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.34419e7 | −1.80630 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.73398e6 | + | 1.28172e6i | −0.731216 | + | 0.0962824i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.82336e6 | − | 1.05272e6i | 0.133561 | − | 0.0771113i | −0.431731 | − | 0.902002i | \(-0.642097\pi\) |
0.565292 | + | 0.824891i | \(0.308764\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.31473e6 | + | 2.27719e6i | −0.0939262 | + | 0.162685i | −0.909160 | − | 0.416447i | \(-0.863275\pi\) |
0.815234 | + | 0.579132i | \(0.196608\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.87444e6 | − | 1.42259e7i | −0.130633 | − | 0.991431i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.32517e7 | − | 7.65087e6i | −0.901100 | − | 0.520250i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 112025. | + | 194033.i | 0.00743402 | + | 0.0128761i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −809505. | − | 6.14778e6i | −0.0524350 | − | 0.398217i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.87341e6i | 0.434661i | 0.976098 | + | 0.217331i | \(0.0697350\pi\) | ||||
−0.976098 | + | 0.217331i | \(0.930265\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.14230e6 | 0.194038 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.50337e6 | + | 1.57015e7i | −0.392209 | + | 0.946934i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.58920e6 | − | 2.64958e6i | 0.270357 | − | 0.156091i | −0.358693 | − | 0.933456i | \(-0.616777\pi\) |
0.629050 | + | 0.777365i | \(0.283444\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.20502e6 | + | 3.81921e6i | −0.126915 | + | 0.219823i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.71646e7 | − | 1.71661e7i | 0.965412 | − | 0.965495i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.60550e7 | + | 9.26938e6i | 0.882560 | + | 0.509546i | 0.871502 | − | 0.490393i | \(-0.163147\pi\) |
0.0110583 | + | 0.999939i | \(0.496480\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.12421e7 | + | 1.94719e7i | 0.604102 | + | 1.04634i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.76104e7 | + | 1.35135e7i | −0.925199 | + | 0.709962i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.87621e7i | 1.47762i | 0.673912 | + | 0.738811i | \(0.264613\pi\) | ||||
−0.673912 | + | 0.738811i | \(0.735387\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.12312e7 | −1.06676 | −0.533380 | − | 0.845875i | \(-0.679079\pi\) | ||||
−0.533380 | + | 0.845875i | \(0.679079\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 168680. | + | 219819.i | 0.00829043 | + | 0.0108038i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.87300e6 | + | 5.12283e6i | −0.426651 | + | 0.246327i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.36611e6 | − | 4.09821e6i | 0.111326 | − | 0.192821i | −0.804979 | − | 0.593303i | \(-0.797824\pi\) |
0.916305 | + | 0.400481i | \(0.131157\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.14235e7 | − | 5.74139e6i | 0.986454 | − | 0.264365i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.99752e6 | − | 3.46267e6i | −0.270304 | − | 0.156060i | 0.358722 | − | 0.933445i | \(-0.383213\pi\) |
−0.629026 | + | 0.777384i | \(0.716546\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.09878e6 | + | 1.57595e7i | 0.401443 | + | 0.695320i | 0.993900 | − | 0.110282i | \(-0.0351755\pi\) |
−0.592457 | + | 0.805602i | \(0.701842\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.35615e6 | − | 3.46102e6i | −0.360970 | − | 0.149510i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.94220e6i | 0.420568i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.02068e6 | 0.208003 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.98100e7 | − | 2.60847e6i | 0.803906 | − | 0.105854i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.52950e6 | − | 2.03776e6i | 0.140317 | − | 0.0810120i | −0.428198 | − | 0.903685i | \(-0.640851\pi\) |
0.568515 | + | 0.822673i | \(0.307518\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.66618e7 | − | 4.61797e7i | 1.03854 | − | 1.79881i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.92033e7 | + | 5.15863e6i | 1.49642 | + | 0.196909i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −130434. | − | 75305.9i | −0.00487951 | − | 0.00281718i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.61067e6 | + | 6.25387e6i | 0.132400 | + | 0.229324i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.88713e6 | − | 4.47098e7i | −0.211629 | − | 1.60722i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.87111e7i | 1.36438i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.09672e7 | 1.41586 | 0.707931 | − | 0.706282i | \(-0.249629\pi\) | ||||
0.707931 | + | 0.706282i | \(0.249629\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.22366e6 | − | 5.36871e6i | 0.0753690 | − | 0.181968i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.12927e6 | − | 2.96139e6i | 0.170520 | − | 0.0984496i | −0.412311 | − | 0.911043i | \(-0.635278\pi\) |
0.582831 | + | 0.812593i | \(0.301945\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.50612e7 | + | 2.60868e7i | −0.491164 | + | 0.850721i | −0.999948 | − | 0.0101728i | \(-0.996762\pi\) |
0.508784 | + | 0.860894i | \(0.330095\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.08043e7 | − | 2.89451e6i | −0.345673 | − | 0.0926068i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.20152e6 | + | 693697.i | 0.0377183 | + | 0.0217767i | 0.518741 | − | 0.854932i | \(-0.326401\pi\) |
−0.481022 | + | 0.876708i | \(0.659734\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.34479e7 | + | 5.79335e7i | 1.03038 | + | 1.78467i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.56458e7 | + | 1.96796e7i | −0.775355 | + | 0.594977i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.01738e7i | − | 0.301909i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 491079. | 0.0143054 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.42141e6 | − | 5.76183e6i | −0.126450 | − | 0.164785i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.50296e7 | − | 8.67734e6i | 0.422046 | − | 0.243668i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.36146e6 | + | 4.09016e6i | −0.0651172 | + | 0.112786i | −0.896746 | − | 0.442546i | \(-0.854075\pi\) |
0.831629 | + | 0.555332i | \(0.187409\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.80593e6 | − | 2.91371e7i | 0.211394 | − | 0.789068i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.64054e7 | − | 3.83392e7i | −1.76632 | − | 1.01979i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.08625e7 | + | 5.34554e7i | 0.806383 | + | 1.39670i | 0.915354 | + | 0.402651i | \(0.131911\pi\) |
−0.108971 | + | 0.994045i | \(0.534756\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.40988e7 | − | 9.98142e6i | −0.618579 | − | 0.256208i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.11198e7i | 1.54141i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.38672e7 | 0.591451 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.02794e6 | − | 793725.i | 0.146795 | − | 0.0193291i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.43027e7 | + | 3.13517e7i | −1.29967 | + | 0.750365i | −0.980347 | − | 0.197282i | \(-0.936789\pi\) |
−0.319323 | + | 0.947646i | \(0.603455\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.44844e7 | − | 5.97287e7i | 0.811233 | − | 1.40510i | −0.100768 | − | 0.994910i | \(-0.532130\pi\) |
0.912001 | − | 0.410188i | \(-0.134537\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.50366e6 | − | 1.15364e6i | −0.0347719 | − | 0.0266778i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.84347e7 | − | 1.06433e7i | −0.419095 | − | 0.241965i | 0.275595 | − | 0.961274i | \(-0.411125\pi\) |
−0.694690 | + | 0.719309i | \(0.744458\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.01108e7 | − | 3.48329e7i | −0.449514 | − | 0.778582i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.64253e6 | − | 1.24742e7i | −0.0361001 | − | 0.274162i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 8.45699e7i | − | 1.82782i | −0.405921 | − | 0.913908i | \(-0.633049\pi\) | ||
0.405921 | − | 0.913908i | \(-0.366951\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.16315e7 | −0.884913 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.33927e7 | + | 5.64785e7i | −0.489059 | + | 1.18076i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.31611e7 | + | 3.64661e7i | −1.29889 | + | 0.749912i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.64119e6 | + | 1.15029e7i | −0.134353 | + | 0.232706i | −0.925350 | − | 0.379114i | \(-0.876229\pi\) |
0.790997 | + | 0.611820i | \(0.209562\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.76037e7 | − | 6.56866e7i | −0.350368 | − | 1.30737i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.44156e7 | − | 8.32284e6i | −0.282300 | − | 0.162986i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.29319e6 | − | 3.97192e6i | −0.0441889 | − | 0.0765374i | 0.843085 | − | 0.537780i | \(-0.180737\pi\) |
−0.887274 | + | 0.461243i | \(0.847404\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.24555e7 | − | 2.49051e7i | 0.615453 | − | 0.472275i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.20635e6i | − | 0.0598393i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.45824e7 | 0.267863 | 0.133931 | − | 0.990991i | \(-0.457240\pi\) | ||||
0.133931 | + | 0.990991i | \(0.457240\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.91116e7 | − | 2.49056e7i | −0.345558 | − | 0.450321i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.27308e7 | + | 3.62176e7i | −1.11657 | + | 0.644650i | −0.940522 | − | 0.339732i | \(-0.889663\pi\) |
−0.176044 | + | 0.984382i | \(0.556330\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.54116e7 | − | 2.66938e7i | 0.270064 | − | 0.467765i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.49283e7 | − | 3.49253e7i | −0.602621 | − | 0.602569i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.81934e7 | + | 4.51450e7i | 1.32838 | + | 0.766939i | 0.985049 | − | 0.172276i | \(-0.0551121\pi\) |
0.343329 | + | 0.939215i | \(0.388445\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.41954e6 | + | 5.92281e6i | 0.0572054 | + | 0.0990827i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.25968e7 | − | 5.21746e6i | −0.207531 | − | 0.0859570i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 5.23490e7i | − | 0.849409i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.64278e7 | −1.22146 | −0.610731 | − | 0.791838i | \(-0.709124\pi\) | ||||
−0.610731 | + | 0.791838i | \(0.709124\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.63862e6 | − | 874136.i | 0.104510 | − | 0.0137613i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.62663e7 | − | 3.82589e7i | 1.02768 | − | 0.593334i | 0.111364 | − | 0.993780i | \(-0.464478\pi\) |
0.916320 | + | 0.400446i | \(0.131145\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.46475e6 | − | 2.53702e6i | 0.0223794 | − | 0.0387622i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.65074e7 | − | 6582.02i | 1.15170 | − | 9.90819e-5i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.19880e7 | + | 4.15623e7i | 1.06777 | + | 0.616476i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.34137e6 | + | 1.44477e7i | 0.121918 | + | 0.211168i | 0.920524 | − | 0.390686i | \(-0.127762\pi\) |
−0.798606 | + | 0.601854i | \(0.794429\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.01184e6 | − | 3.80623e7i | −0.0721890 | − | 0.548239i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.94769e7i | 0.560394i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.30625e7 | 0.462585 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.90751e7 | − | 7.01978e7i | 0.400971 | − | 0.968089i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.62457e6 | − | 2.09265e6i | 0.0492736 | − | 0.0284481i | −0.475161 | − | 0.879899i | \(-0.657610\pi\) |
0.524434 | + | 0.851451i | \(0.324277\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.24928e7 | + | 7.35996e7i | −0.569467 | + | 0.986346i | 0.427151 | + | 0.904180i | \(0.359517\pi\) |
−0.996619 | + | 0.0821661i | \(0.973816\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.39341e7 | + | 8.39413e7i | −1.10896 | + | 1.10906i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.93117e7 | − | 1.11496e7i | −0.251567 | − | 0.145242i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.43294e7 | − | 2.48193e7i | −0.184054 | − | 0.318791i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.14335e6 | − | 3.17945e6i | 0.0524783 | − | 0.0402698i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.01870e6i | 0.100155i | 0.998745 | + | 0.0500774i | \(0.0159468\pi\) | ||||
−0.998745 | + | 0.0500774i | \(0.984053\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.34153e8 | −1.65248 | −0.826242 | − | 0.563316i | \(-0.809526\pi\) | ||||
−0.826242 | + | 0.563316i | \(0.809526\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.87975e7 | + | 1.02686e8i | 0.957292 | + | 1.24751i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.15206e6 | + | 1.81984e6i | −0.0377702 | + | 0.0218067i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.27209e6 | + | 1.08636e7i | −0.0741343 | + | 0.128404i | −0.900709 | − | 0.434422i | \(-0.856953\pi\) |
0.826575 | + | 0.562826i | \(0.190286\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.48442e7 | + | 2.00579e7i | −0.872655 | + | 0.233867i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.17519e7 | + | 1.83319e7i | 0.365223 | + | 0.210861i | 0.671369 | − | 0.741123i | \(-0.265706\pi\) |
−0.306147 | + | 0.951984i | \(0.599040\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.91786e7 | − | 1.02500e8i | −0.671559 | − | 1.16317i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.87688e7 | + | 1.19157e7i | 0.322107 | + | 0.133413i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.40589e7i | − | 0.597212i | −0.954376 | − | 0.298606i | \(-0.903478\pi\) | ||
0.954376 | − | 0.298606i | \(-0.0965216\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.87400e8 | 2.04286 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.20794e7 | − | 5.54078e6i | 0.452663 | − | 0.0596042i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.27944e6 | + | 738687.i | −0.0135827 | + | 0.00784199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.39420e7 | − | 4.14688e7i | 0.250849 | − | 0.434483i | −0.712911 | − | 0.701255i | \(-0.752624\pi\) |
0.963760 | + | 0.266772i | \(0.0859569\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.29388e7 | + | 7.95067e7i | 0.340619 | + | 0.822178i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.07133e8 | − | 6.18534e7i | −1.09351 | − | 0.631337i | −0.158999 | − | 0.987279i | \(-0.550827\pi\) |
−0.934508 | + | 0.355942i | \(0.884160\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.61569e7 | + | 4.53052e7i | 0.263538 | + | 0.456462i | 0.967180 | − | 0.254093i | \(-0.0817771\pi\) |
−0.703641 | + | 0.710555i | \(0.748444\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.54385e7 | + | 1.17247e8i | 0.153548 | + | 1.16612i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 6.71249e7i | − | 0.659072i | −0.944143 | − | 0.329536i | \(-0.893108\pi\) | ||
0.944143 | − | 0.329536i | \(-0.106892\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.67670e7 | 0.550272 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.08049e7 | + | 1.70949e8i | −0.677643 | + | 1.63607i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.17879e8 | − | 6.80573e7i | 1.11391 | − | 0.643119i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.93370e6 | − | 1.02775e7i | 0.0553662 | − | 0.0958971i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.09978e8 | + | 2.94635e7i | 1.01333 | + | 0.271474i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.44028e7 | + | 5.45035e7i | 0.858971 | + | 0.495927i | 0.863668 | − | 0.504062i | \(-0.168162\pi\) |
−0.00469653 | + | 0.999989i | \(0.501495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.99210e6 | − | 3.45041e6i | −0.0179009 | − | 0.0310053i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.57095e6 | + | 2.74021e6i | −0.0316915 | + | 0.0243188i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.06537e8i | 0.933849i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.79097e8 | −1.55061 | −0.775303 | − | 0.631590i | \(-0.782403\pi\) | ||||
−0.775303 | + | 0.631590i | \(0.782403\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.18746e8 | − | 1.54745e8i | −1.01553 | − | 1.32340i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.99035e8 | − | 1.14913e8i | 1.68146 | − | 0.970790i | 0.720762 | − | 0.693183i | \(-0.243792\pi\) |
0.960695 | − | 0.277607i | \(-0.0895413\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.27980e7 | + | 1.26090e8i | −0.607545 | + | 1.05230i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.45584e7 | + | 2.03650e8i | −0.449827 | + | 1.67907i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.57877e7 | + | 1.48885e7i | 0.210060 | + | 0.121278i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −458787. | − | 794643.i | −0.00369241 | − | 0.00639544i | 0.864173 | − | 0.503194i | \(-0.167842\pi\) |
−0.867866 | + | 0.496799i | \(0.834509\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.37951e8 | + | 5.71378e7i | 1.09701 | + | 0.454371i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.59072e6i | − | 0.0124994i | −0.999980 | − | 0.00624970i | \(-0.998011\pi\) | ||
0.999980 | − | 0.00624970i | \(-0.00198935\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.40447e8 | 1.86701 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.28960e8 | − | 1.69808e7i | 0.989538 | − | 0.130297i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.71008e8 | − | 9.87317e7i | 1.29677 | − | 0.748692i | 0.316927 | − | 0.948450i | \(-0.397349\pi\) |
0.979845 | + | 0.199758i | \(0.0640156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.69968e7 | − | 4.67598e7i | 0.202325 | − | 0.350437i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.23126e7 | + | 1.75296e7i | −0.313413 | + | 0.129844i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.68328e7 | + | 1.54919e7i | 0.196447 | + | 0.113419i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.63559e8 | − | 2.83292e8i | −1.18359 | − | 2.05004i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.95253e6 | + | 5.28010e7i | 0.0497326 | + | 0.377694i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.39765e7i | 0.381673i | 0.981622 | + | 0.190836i | \(0.0611200\pi\) | ||||
−0.981622 | + | 0.190836i | \(0.938880\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.09281e8 | −0.763909 | −0.381954 | − | 0.924181i | \(-0.624749\pi\) | ||||
−0.381954 | + | 0.924181i | \(0.624749\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.61609e6 | − | 1.35593e7i | 0.0388111 | − | 0.0937040i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.15203e8 | + | 6.65123e7i | −0.787102 | + | 0.454433i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.27946e7 | + | 1.26084e8i | −0.491736 | + | 0.851712i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.98980e7 | − | 2.60818e8i | −0.466854 | − | 1.74202i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.77878e6 | − | 4.49108e6i | −0.0513724 | − | 0.0296599i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.61809e7 | − | 1.49270e8i | −0.562794 | − | 0.974788i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.09986e8 | + | 8.43989e7i | −0.710255 | + | 0.545022i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 2.13526e8i | − | 1.36359i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.57746e8 | −1.62780 | −0.813900 | − | 0.581005i | \(-0.802660\pi\) | ||||
−0.813900 | + | 0.581005i | \(0.802660\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.55494e8 | − | 2.02635e8i | −0.971214 | − | 1.26565i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.35364e7 | − | 1.93623e7i | 0.207170 | − | 0.119610i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.06280e7 | + | 1.05011e8i | −0.370434 | + | 0.641611i | −0.989632 | − | 0.143624i | \(-0.954124\pi\) |
0.619198 | + | 0.785235i | \(0.287458\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.38618e8 | + | 1.38606e8i | 0.837725 | + | 0.837653i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.71036e7 | − | 3.87423e7i | −0.401135 | − | 0.231596i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.93777e7 | + | 3.35631e7i | 0.114585 | + | 0.198466i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.48594e8 | + | 6.15460e7i | 0.869207 | + | 0.360015i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.95457e7i | 0.344576i | 0.985047 | + | 0.172288i | \(0.0551160\pi\) | ||||
−0.985047 | + | 0.172288i | \(0.944884\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.52403e6 | −0.0373492 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.35125e8 | + | 3.09599e7i | −1.33171 | + | 0.175352i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.44627e8 | + | 1.41236e8i | −1.37082 | + | 0.791442i | −0.991031 | − | 0.133632i | \(-0.957336\pi\) |
−0.379787 | + | 0.925074i | \(0.624003\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.95393e7 | − | 1.20446e8i | 0.385554 | − | 0.667799i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.90496e7 | + | 2.83245e7i | −0.269083 | + | 0.155386i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.40407e7 | + | 8.10640e6i | 0.0762170 | + | 0.0440039i | 0.537624 | − | 0.843185i | \(-0.319322\pi\) |
−0.461407 | + | 0.887188i | \(0.652655\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.40346e8 | − | 2.43086e8i | −0.753860 | − | 1.30572i | −0.945939 | − | 0.324345i | \(-0.894856\pi\) |
0.192079 | − | 0.981380i | \(-0.438477\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.27050e7 | + | 2.48378e8i | 0.173840 | + | 1.32023i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.97756e6i | 0.0419630i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.67978e8 | 0.874429 | 0.437214 | − | 0.899357i | \(-0.355965\pi\) | ||||
0.437214 | + | 0.899357i | \(0.355965\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.00017e8 | − | 2.41476e8i | 0.515273 | − | 1.24405i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.11977e7 | + | 1.22385e7i | −0.108084 | + | 0.0624023i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.56877e8 | + | 2.71718e8i | −0.791685 | + | 1.37124i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.14517e6 | − | 7.14578e6i | 0.0356899 | − | 0.0356929i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.47664e7 | + | 2.58459e7i | 0.221329 | + | 0.127784i | 0.606565 | − | 0.795034i | \(-0.292547\pi\) |
−0.385237 | + | 0.922818i | \(0.625880\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.53971e7 | − | 6.13096e7i | −0.173230 | − | 0.300042i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.34124e8 | − | 1.79658e8i | 1.13418 | − | 0.870329i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 4.84333e7i | − | 0.232263i | −0.993234 | − | 0.116132i | \(-0.962951\pi\) | ||
0.993234 | − | 0.116132i | \(-0.0370494\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.70856e7 | 0.318477 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.61271e8 | − | 2.10162e8i | −0.757935 | − | 0.987716i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.53845e6 | − | 2.04292e6i | 0.0164639 | − | 0.00950543i | −0.491745 | − | 0.870739i | \(-0.663641\pi\) |
0.508209 | + | 0.861234i | \(0.330308\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.90601e7 | + | 6.76540e7i | −0.179932 | + | 0.311652i | −0.941857 | − | 0.336013i | \(-0.890921\pi\) |
0.761925 | + | 0.647666i | \(0.224255\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.75051e8 | + | 1.00512e8i | −1.71056 | + | 0.458423i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.82279e8 | − | 1.62974e8i | −1.27472 | − | 0.735957i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.03843e7 | + | 1.21909e8i | 0.314709 | + | 0.545093i | 0.979376 | − | 0.202048i | \(-0.0647596\pi\) |
−0.664666 | + | 0.747140i | \(0.731426\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.85310e7 | − | 3.66685e7i | −0.391962 | − | 0.162346i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.56789e7i | 0.0687371i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.44586e8 | 1.06182 | 0.530910 | − | 0.847428i | \(-0.321850\pi\) | ||||
0.530910 | + | 0.847428i | \(0.321850\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.59493e8 | − | 4.73360e7i | 1.54549 | − | 0.203501i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.23709e8 | − | 1.29159e8i | 0.952421 | − | 0.549880i | 0.0585887 | − | 0.998282i | \(-0.481340\pi\) |
0.893832 | + | 0.448402i | \(0.148007\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.28102e7 | − | 1.60752e8i | 0.391312 | − | 0.677773i | −0.601310 | − | 0.799015i | \(-0.705355\pi\) |
0.992623 | + | 0.121242i | \(0.0386878\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.87409e7 | − | 2.44269e7i | 0.0782557 | − | 0.101998i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.58836e7 | + | 4.38114e7i | 0.313822 | + | 0.181185i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.48909e8 | + | 2.57919e8i | 0.609933 | + | 1.05643i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.64765e7 | − | 1.25131e8i | −0.0668441 | − | 0.507647i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.80917e8i | 0.726988i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.23326e8 | 0.490871 | 0.245435 | − | 0.969413i | \(-0.421069\pi\) | ||||
0.245435 | + | 0.969413i | \(0.421069\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.78003e7 | + | 2.11982e8i | −0.346166 | + | 0.835771i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.44961e8 | − | 8.36936e7i | 0.566150 | − | 0.326867i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.11720e6 | + | 8.86324e6i | −0.0197977 | + | 0.0342905i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.96737e8 | − | 5.27065e7i | −0.754022 | − | 0.202005i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.58563e8 | − | 1.49281e8i | −0.981729 | − | 0.566802i | −0.0789374 | − | 0.996880i | \(-0.525153\pi\) |
−0.902792 | + | 0.430078i | \(0.858486\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.66786e7 | − | 6.35293e7i | −0.137969 | − | 0.238969i | 0.788759 | − | 0.614703i | \(-0.210724\pi\) |
−0.926728 | + | 0.375734i | \(0.877391\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.08938e8 | − | 1.60331e8i | 0.778644 | − | 0.597501i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1.17069e7i | − | 0.0432245i | −0.999766 | − | 0.0216123i | \(-0.993120\pi\) | ||
0.999766 | − | 0.0216123i | \(-0.00687993\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.44098e8 | 2.72205 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.32989e7 | − | 6.94574e7i | −0.193186 | − | 0.251753i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.40473e8 | + | 2.54307e8i | −1.58190 | + | 0.913311i | −0.587319 | + | 0.809356i | \(0.699817\pi\) |
−0.994582 | + | 0.103955i | \(0.966850\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.63494e7 | − | 6.29590e7i | 0.129352 | − | 0.224044i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.55706e7 | + | 3.56736e8i | −0.336999 | + | 1.25791i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.81850e8 | + | 1.62726e8i | 0.984830 | + | 0.568592i | 0.903725 | − | 0.428114i | \(-0.140822\pi\) |
0.0811048 | + | 0.996706i | \(0.474155\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.06288e7 | + | 8.76917e7i | 0.175305 | + | 0.303637i | 0.940267 | − | 0.340439i | \(-0.110576\pi\) |
−0.764962 | + | 0.644075i | \(0.777242\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.05018e7 | + | 4.34970e6i | 0.0360347 | + | 0.0149252i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.57022e7i | 0.121403i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.20870e7 | 0.175530 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.02304e8 | − | 6.61405e7i | 1.67760 | − | 0.220897i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.67818e8 | + | 2.70095e8i | −1.54849 | + | 0.894022i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.80186e8 | + | 3.12091e8i | −0.591120 | + | 1.02385i | 0.402962 | + | 0.915217i | \(0.367981\pi\) |
−0.994082 | + | 0.108633i | \(0.965353\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.30966e7 | + | 9.95279e7i | −0.0425839 | + | 0.323619i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.21214e8 | − | 6.99830e7i | −0.390649 | − | 0.225542i | 0.291792 | − | 0.956482i | \(-0.405748\pi\) |
−0.682441 | + | 0.730940i | \(0.739082\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.94362e7 | − | 6.83055e7i | −0.125975 | − | 0.218196i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.19425e7 | + | 9.06971e7i | 0.0378141 | + | 0.287179i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.34089e8i | 1.04858i | 0.851541 | + | 0.524288i | \(0.175669\pi\) | ||||
−0.851541 | + | 0.524288i | \(0.824331\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.04698e8 | 0.636856 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.68231e7 | − | 8.89041e7i | 0.113566 | − | 0.274190i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.30236e7 | − | 7.51917e6i | 0.0398174 | − | 0.0229886i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.54192e8 | + | 2.67069e8i | −0.467335 | + | 0.809447i | −0.999303 | − | 0.0373166i | \(-0.988119\pi\) |
0.531969 | + | 0.846764i | \(0.321452\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.04040e7 | − | 1.50764e8i | −0.121402 | − | 0.452999i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.50848e8 | + | 2.02562e8i | 1.04512 | + | 0.603399i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.03934e8 | + | 3.53224e8i | 0.602270 | + | 1.04316i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.25908e8 | − | 3.26825e8i | 1.24705 | − | 0.956938i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.82604e8i | 0.530099i | 0.964235 | + | 0.265049i | \(0.0853882\pi\) | ||||
−0.964235 | + | 0.265049i | \(0.914612\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.62820e7 | −0.277127 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.85315e8 | − | 5.02130e8i | −1.09964 | − | 1.43301i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.54161e8 | + | 8.90047e7i | −0.436230 | + | 0.251858i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.64587e8 | − | 2.85073e8i | 0.461803 | − | 0.799865i | −0.537248 | − | 0.843424i | \(-0.680536\pi\) |
0.999051 | + | 0.0435587i | \(0.0138695\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.87452e8 | − | 1.87436e8i | −0.521533 | − | 0.521488i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.12138e7 | + | 2.37948e7i | 0.113704 | + | 0.0656468i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.39235e7 | + | 2.41161e7i | 0.0380916 | + | 0.0659766i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.25200e7 | + | 2.17532e7i | 0.142484 | + | 0.0590154i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.01542e7i | 0.0273188i | 0.999907 | + | 0.0136594i | \(0.00434805\pi\) | ||||
−0.999907 | + | 0.0136594i | \(0.995652\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.29382e7 | −0.0612003 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.03880e7 | + | 9.26830e6i | −0.186245 | + | 0.0245237i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.47080e8 | + | 8.49164e7i | −0.385956 | + | 0.222832i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.20302e8 | + | 3.81574e8i | −0.573344 | + | 0.993061i | 0.422875 | + | 0.906188i | \(0.361021\pi\) |
−0.996219 | + | 0.0868730i | \(0.972313\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.73912e8 | − | 2.73983e8i | 0.707016 | − | 0.707198i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.56558e8 | + | 1.48124e8i | 0.656800 | + | 0.379204i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.13230e8 | − | 3.69324e8i | −0.541422 | − | 0.937770i | −0.998823 | − | 0.0485091i | \(-0.984553\pi\) |
0.457401 | − | 0.889260i | \(-0.348780\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.39353e7 | − | 4.09611e8i | −0.135835 | − | 1.03160i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.07000e9i | − | 2.67289i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.16367e8 | 0.783895 | 0.391947 | − | 0.919988i | \(-0.371801\pi\) | ||||
0.391947 | + | 0.919988i | \(0.371801\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.31486e6 | + | 5.58892e6i | −0.00568946 | + | 0.0137364i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.94589e8 | + | 1.12346e8i | −0.474409 | + | 0.273900i | −0.718084 | − | 0.695957i | \(-0.754980\pi\) |
0.243675 | + | 0.969857i | \(0.421647\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.30153e7 | + | 1.43787e8i | −0.200766 | + | 0.347736i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.18381e8 | − | 1.18391e8i | 0.284001 | − | 0.284025i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.10508e8 | + | 6.38020e7i | 0.262996 | + | 0.151841i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.67156e8 | + | 2.89522e8i | 0.394641 | + | 0.683538i | 0.993055 | − | 0.117649i | \(-0.0375358\pi\) |
−0.598415 | + | 0.801187i | \(0.704202\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.47230e8 | + | 1.12978e8i | −0.344834 | + | 0.264613i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.26302e8i | 0.525832i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.61999e7 | 0.0834488 | 0.0417244 | − | 0.999129i | \(-0.486715\pi\) | ||||
0.0417244 | + | 0.999129i | \(0.486715\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.16500e7 | + | 6.73086e7i | 0.118126 | + | 0.153938i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.36281e8 | − | 1.36417e8i | 0.536135 | − | 0.309538i | −0.207376 | − | 0.978261i | \(-0.566492\pi\) |
0.743511 | + | 0.668724i | \(0.233159\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.43344e7 | + | 2.48279e7i | −0.0322705 | + | 0.0558941i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.43224e8 | + | 1.18782e8i | −0.990009 | + | 0.265318i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.08867e7 | − | 1.78325e7i | −0.0684520 | − | 0.0395208i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.68022e8 | − | 4.64227e8i | −0.589374 | − | 1.02083i | −0.994315 | − | 0.106483i | \(-0.966041\pi\) |
0.404940 | − | 0.914343i | \(-0.367292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.32187e8 | + | 5.47504e7i | 0.288421 | + | 0.119460i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.46060e8i | 1.39873i | 0.714764 | + | 0.699366i | \(0.246534\pi\) | ||||
−0.714764 | + | 0.699366i | \(0.753466\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.55169e8 | −0.333349 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.18052e8 | + | 1.55444e7i | −0.251658 | + | 0.0331369i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.87982e8 | + | 1.08531e8i | −0.397652 | + | 0.229585i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.80633e8 | − | 4.86070e8i | 0.589095 | − | 1.02034i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.49837e8 | + | 8.55099e7i | 1.35369 | + | 0.178128i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.54401e8 | − | 4.93289e8i | −1.76625 | − | 1.01975i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.33267e7 | + | 7.50441e7i | 0.0888857 | + | 0.153954i | 0.907040 | − | 0.421044i | \(-0.138336\pi\) |
−0.818155 | + | 0.574998i | \(0.805003\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.53451e7 | + | 4.96263e8i | 0.133040 | + | 1.01037i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.02964e8i | 0.208043i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.58915e7 | 0.0519204 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.32305e8 | + | 5.60869e8i | −0.462336 | + | 1.11625i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.67720e8 | + | 1.54568e8i | −0.528818 | + | 0.305313i | −0.740535 | − | 0.672018i | \(-0.765428\pi\) |
0.211717 | + | 0.977331i | \(0.432095\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.55978e8 | − | 6.16572e8i | 0.697884 | − | 1.20877i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.78925e8 | − | 1.55096e8i | −1.12648 | − | 0.301788i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.81373e8 | − | 5.08861e8i | −1.70221 | − | 0.982771i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.19999e7 | − | 2.07845e7i | −0.0230034 | − | 0.0398430i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.16089e8 | + | 4.72763e8i | −1.17226 | + | 0.899545i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 7.10498e8i | − | 1.34189i | −0.741507 | − | 0.670945i | \(-0.765888\pi\) | ||
0.741507 | − | 0.670945i | \(-0.234112\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.80207e8 | −0.712784 | −0.356392 | − | 0.934337i | \(-0.615993\pi\) | ||||
−0.356392 | + | 0.934337i | \(0.615993\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.48978e8 | − | 4.54777e8i | −0.649421 | − | 0.846304i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.00687e8 | − | 5.20012e8i | 1.66380 | − | 0.960595i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.88299e7 | + | 1.36537e8i | −0.144552 | + | 0.250372i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.93596e6 | + | 7.22634e6i | −0.00352407 | + | 0.0131543i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.30301e7 | + | 1.90700e7i | 0.0596872 | + | 0.0344604i | 0.529547 | − | 0.848281i | \(-0.322362\pi\) |
−0.469859 | + | 0.882741i | \(0.655695\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.47622e8 | − | 6.02100e8i | −0.623603 | − | 1.08011i | −0.988809 | − | 0.149185i | \(-0.952335\pi\) |
0.365206 | − | 0.930927i | \(-0.380998\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.55578e8 | − | 1.05857e8i | −0.455157 | − | 0.188521i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 4.10947e8i | − | 0.726556i | −0.931681 | − | 0.363278i | \(-0.881658\pi\) | ||
0.931681 | − | 0.363278i | \(-0.118342\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.04443e9 | −1.83322 | −0.916611 | − | 0.399780i | \(-0.869087\pi\) | ||||
−0.916611 | + | 0.399780i | \(0.869087\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.26676e8 | − | 1.66800e7i | 0.220746 | − | 0.0290665i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.02468e8 | − | 2.32365e8i | 0.696300 | − | 0.402009i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.98071e8 | + | 6.89480e8i | −0.683757 | + | 1.18430i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.75119e8 | + | 3.64523e8i | 0.810264 | + | 0.621654i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.63528e8 | + | 1.52148e8i | 0.446212 | + | 0.257621i | 0.706229 | − | 0.707983i | \(-0.250395\pi\) |
−0.260017 | + | 0.965604i | \(0.583728\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.57024e8 | + | 4.45179e8i | 0.432101 | + | 0.748422i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.44103e7 | − | 1.85384e8i | −0.0407466 | − | 0.309449i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.93544e8i | 1.14949i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.41308e8 | 0.397120 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.88016e8 | + | 4.53938e8i | −0.307235 | + | 0.741776i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.60519e7 | − | 3.23616e7i | 0.0909497 | − | 0.0525099i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.49067e8 | − | 6.04602e8i | 0.562421 | − | 0.974142i | −0.434863 | − | 0.900497i | \(-0.643203\pi\) |
0.997284 | − | 0.0736458i | \(-0.0234634\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.32145e7 | − | 2.35879e8i | −0.101139 | − | 0.377391i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.22145e8 | + | 4.16931e8i | 1.14731 | + | 0.662402i | 0.948231 | − | 0.317581i | \(-0.102871\pi\) |
0.199082 | + | 0.979983i | \(0.436204\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.45038e8 | + | 4.24419e8i | 0.386594 | + | 0.669600i | 0.991989 | − | 0.126325i | \(-0.0403183\pi\) |
−0.605395 | + | 0.795925i | \(0.706985\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.12964e8 | + | 1.63420e8i | −0.333654 | + | 0.256033i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 5.57427e8i | − | 0.867272i | −0.901088 | − | 0.433636i | \(-0.857230\pi\) | ||
0.901088 | − | 0.433636i | \(-0.142770\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.83961e8 | −0.438744 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.25249e7 | + | 1.07544e8i | 0.126627 | + | 0.165017i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.32629e8 | − | 3.65248e8i | 0.964028 | − | 0.556582i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.56427e7 | + | 4.44145e7i | −0.0388070 | + | 0.0672157i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.81491e8 | + | 3.81458e8i | 0.573379 | + | 0.573330i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.39852e8 | − | 8.07434e7i | −0.208758 | − | 0.120527i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.76013e7 | − | 4.78069e7i | −0.0409196 | − | 0.0708748i | 0.844840 | − | 0.535019i | \(-0.179695\pi\) |
−0.885760 | + | 0.464144i | \(0.846362\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.01663e8 | + | 4.21078e7i | 0.149692 | + | 0.0620006i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.32288e8i | 1.21715i | 0.793495 | + | 0.608577i | \(0.208259\pi\) | ||||
−0.793495 | + | 0.608577i | \(0.791741\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.04504e8 | −1.16855 | −0.584273 | − | 0.811557i | \(-0.698620\pi\) | ||||
−0.584273 | + | 0.811557i | \(0.698620\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.42742e9 | − | 1.87954e8i | 2.05931 | − | 0.271158i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.50775e8 | − | 3.17990e8i | 0.789230 | − | 0.455662i | −0.0504616 | − | 0.998726i | \(-0.516069\pi\) |
0.839691 | + | 0.543064i | \(0.182736\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.19605e7 | + | 1.07319e8i | −0.0881881 | + | 0.152746i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.33886e8 | + | 9.24534e8i | 0.754771 | + | 1.30704i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.28133e8 | + | 1.89448e8i | 0.460782 | + | 0.266033i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.69600e8 | − | 6.40167e8i | −0.515541 | − | 0.892943i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −530874. | − | 4.03172e6i | −0.000735553 | − | 0.00558615i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.01313e9i | 1.39439i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.82870e8 | −0.933607 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.46103e7 | + | 1.80136e8i | −0.101329 | + | 0.244646i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.17943e9 | − | 6.80942e8i | 1.59120 | − | 0.918680i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.39576e8 | − | 7.61369e8i | 0.589132 | − | 1.02041i | −0.405215 | − | 0.914222i | \(-0.632803\pi\) |
0.994346 | − | 0.106185i | \(-0.0338635\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.60925e8 | − | 8.60999e8i | 1.14623 | − | 1.14633i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.25800e7 | − | 3.03571e7i | −0.0695449 | − | 0.0401518i | 0.464824 | − | 0.885403i | \(-0.346117\pi\) |
−0.534369 | + | 0.845251i | \(0.679451\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.30683e8 | + | 3.99555e8i | 0.303112 | + | 0.525006i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.29200e8 | + | 6.36296e8i | −1.08242 | + | 0.830607i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.38208e7i | 0.0697978i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.30423e9 | 1.68038 | 0.840190 | − | 0.542292i | \(-0.182443\pi\) | ||||
0.840190 | + | 0.542292i | \(0.182443\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.73378e8 | + | 8.77524e8i | 0.861946 | + | 1.12326i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.32976e7 | + | 1.34509e7i | −0.0296282 | + | 0.0171059i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.05517e8 | + | 1.82761e8i | −0.133320 | + | 0.230918i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.51549e8 | − | 4.06145e7i | 0.190246 | − | 0.0509849i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.30422e8 | + | 4.21709e8i | 0.911017 | + | 0.525976i | 0.880758 | − | 0.473566i | \(-0.157034\pi\) |
0.0302588 | + | 0.999542i | \(0.490367\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.23662e8 | + | 2.14189e8i | 0.153245 | + | 0.265429i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.47743e8 | + | 6.11936e7i | 0.181913 | + | 0.0753462i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1.26449e9i | − | 1.54697i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.31817e9 | −1.60233 | −0.801165 | − | 0.598443i | \(-0.795786\pi\) | ||||
−0.801165 | + | 0.598443i | \(0.795786\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.06345e8 | + | 1.06175e8i | −0.973922 | + | 0.128241i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.10670e9 | + | 6.38955e8i | −1.32820 | + | 0.766835i | −0.985021 | − | 0.172437i | \(-0.944836\pi\) |
−0.343176 | + | 0.939271i | \(0.611503\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.29574e7 | − | 1.26366e8i | 0.0870030 | − | 0.150694i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.15590e8 | − | 2.79007e8i | −0.136969 | − | 0.330613i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.28443e8 | + | 1.89627e8i | 0.386732 | + | 0.223280i | 0.680743 | − | 0.732522i | \(-0.261657\pi\) |
−0.294011 | + | 0.955802i | \(0.594990\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.43899e7 | + | 4.22446e7i | 0.0285372 | + | 0.0494279i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.89026e6 | + | 3.71390e7i | 0.00568578 | + | 0.0431806i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 7.90215e8i | − | 0.912992i | −0.889726 | − | 0.456496i | \(-0.849104\pi\) | ||
0.889726 | − | 0.456496i | \(-0.150896\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.33576e9 | −1.53363 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.91162e8 | + | 1.66871e9i | −0.788577 | + | 1.90391i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.31240e8 | + | 7.57715e7i | −0.148803 | + | 0.0859113i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.90731e7 | + | 3.30355e7i | −0.0214907 | + | 0.0372230i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.43080e8 | − | 2.25864e8i | −0.944039 | − | 0.252911i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.20690e9 | + | 6.96804e8i | 1.34304 | + | 0.775405i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.38801e8 | − | 5.86820e8i | −0.374684 | − | 0.648971i | 0.615596 | − | 0.788062i | \(-0.288915\pi\) |
−0.990280 | + | 0.139091i | \(0.955582\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.17925e8 | − | 1.67227e8i | 0.239516 | − | 0.183796i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 6.48713e8i | − | 0.708590i | −0.935134 | − | 0.354295i | \(-0.884721\pi\) | ||
0.935134 | − | 0.354295i | \(-0.115279\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.99925e8 | −0.325592 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.07187e6 | + | 1.05190e7i | 0.00870884 | + | 0.0113491i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.54202e8 | + | 5.50909e8i | −1.02319 | + | 0.590739i | −0.915027 | − | 0.403394i | \(-0.867831\pi\) |
−0.108164 | + | 0.994133i | \(0.534497\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.25799e8 | − | 1.43033e9i | 0.880088 | − | 1.52436i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.07448e7 | − | 1.89415e8i | 0.0537507 | − | 0.200635i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.68969e8 | − | 2.13024e8i | −0.388445 | − | 0.224269i | 0.293041 | − | 0.956100i | \(-0.405333\pi\) |
−0.681486 | + | 0.731831i | \(0.738666\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.86758e8 | + | 1.36271e9i | 0.823252 | + | 1.42591i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.32912e8 | + | 1.79307e8i | 0.450244 | + | 0.186486i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.05983e8i | − | 0.109559i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.57667e8 | 0.367500 | 0.183750 | − | 0.982973i | \(-0.441176\pi\) | ||||
0.183750 | + | 0.982973i | \(0.441176\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.26427e8 | + | 1.66472e7i | −0.129120 | + | 0.0170018i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.22324e9 | − | 7.06237e8i | 1.24177 | − | 0.716937i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.84916e8 | + | 1.01310e9i | −0.590212 | + | 1.02228i | 0.403991 | + | 0.914763i | \(0.367623\pi\) |
−0.994204 | + | 0.107515i | \(0.965711\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.52429e8 | − | 3.11723e8i | 0.754691 | − | 0.312660i |
(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 | 72.7.m.a.65.13 | yes | 36 | |
3.2 | odd | 2 | 216.7.m.a.89.16 | 36 | |||
4.3 | odd | 2 | 144.7.q.d.65.6 | 36 | |||
9.2 | odd | 6 | 648.7.e.c.161.30 | 36 | |||
9.4 | even | 3 | 216.7.m.a.17.16 | 36 | |||
9.5 | odd | 6 | inner | 72.7.m.a.41.13 | ✓ | 36 | |
9.7 | even | 3 | 648.7.e.c.161.7 | 36 | |||
12.11 | even | 2 | 432.7.q.d.305.16 | 36 | |||
36.23 | even | 6 | 144.7.q.d.113.6 | 36 | |||
36.31 | odd | 6 | 432.7.q.d.17.16 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.7.m.a.41.13 | ✓ | 36 | 9.5 | odd | 6 | inner | |
72.7.m.a.65.13 | yes | 36 | 1.1 | even | 1 | trivial | |
144.7.q.d.65.6 | 36 | 4.3 | odd | 2 | |||
144.7.q.d.113.6 | 36 | 36.23 | even | 6 | |||
216.7.m.a.17.16 | 36 | 9.4 | even | 3 | |||
216.7.m.a.89.16 | 36 | 3.2 | odd | 2 | |||
432.7.q.d.17.16 | 36 | 36.31 | odd | 6 | |||
432.7.q.d.305.16 | 36 | 12.11 | even | 2 | |||
648.7.e.c.161.7 | 36 | 9.7 | even | 3 | |||
648.7.e.c.161.30 | 36 | 9.2 | odd | 6 |