Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,6,Mod(5,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 16]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.5");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.i (of order \(9\), degree \(6\), 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: | \(12.1891703058\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 5.5 | ||
Character | \(\chi\) | \(=\) | 76.5 |
Dual form | 76.6.i.a.61.5 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{8}{9}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50126 | − | 8.51408i | 0.0963059 | − | 0.546178i | −0.898033 | − | 0.439927i | \(-0.855004\pi\) |
0.994339 | − | 0.106251i | \(-0.0338847\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.90022 | − | 7.46817i | −0.159212 | − | 0.133595i | 0.559701 | − | 0.828694i | \(-0.310916\pi\) |
−0.718913 | + | 0.695100i | \(0.755360\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 70.8987 | + | 122.800i | 0.546882 | + | 0.947227i | 0.998486 | + | 0.0550084i | \(0.0175186\pi\) |
−0.451604 | + | 0.892218i | \(0.649148\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 158.110 | + | 57.5472i | 0.650657 | + | 0.236820i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 194.817 | − | 337.433i | 0.485450 | − | 0.840825i | −0.514410 | − | 0.857544i | \(-0.671989\pi\) |
0.999860 | + | 0.0167197i | \(0.00532230\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −114.779 | − | 650.941i | −0.188366 | − | 1.06828i | −0.921554 | − | 0.388250i | \(-0.873080\pi\) |
0.733188 | − | 0.680026i | \(-0.238032\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −76.9461 | + | 64.5655i | −0.0882996 | + | 0.0740921i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 368.551 | − | 134.142i | 0.309297 | − | 0.112575i | −0.182708 | − | 0.983167i | \(-0.558486\pi\) |
0.492005 | + | 0.870592i | \(0.336264\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1147.26 | − | 1076.98i | 0.729087 | − | 0.684421i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1151.97 | − | 419.282i | 0.570023 | − | 0.207471i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −396.668 | + | 332.844i | −0.156353 | + | 0.131196i | −0.717608 | − | 0.696447i | \(-0.754763\pi\) |
0.561255 | + | 0.827643i | \(0.310319\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −519.210 | − | 2944.59i | −0.166147 | − | 0.942268i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1777.74 | − | 3079.14i | 0.469310 | − | 0.812868i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6195.96 | + | 2255.15i | 1.36809 | + | 0.497943i | 0.918545 | − | 0.395316i | \(-0.129365\pi\) |
0.449542 | + | 0.893259i | \(0.351587\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −306.669 | − | 531.166i | −0.0573146 | − | 0.0992718i | 0.835945 | − | 0.548814i | \(-0.184920\pi\) |
−0.893259 | + | 0.449542i | \(0.851587\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2580.46 | − | 2165.26i | −0.412488 | − | 0.346119i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 286.079 | − | 1622.43i | 0.0394744 | − | 0.223870i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9518.19 | 1.14301 | 0.571505 | − | 0.820598i | \(-0.306360\pi\) | ||||
0.571505 | + | 0.820598i | \(0.306360\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5714.48 | −0.601610 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2681.23 | + | 15206.0i | −0.249100 | + | 1.41272i | 0.561674 | + | 0.827359i | \(0.310158\pi\) |
−0.810774 | + | 0.585359i | \(0.800953\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 779.136 | + | 653.773i | 0.0642602 | + | 0.0539207i | 0.674352 | − | 0.738410i | \(-0.264423\pi\) |
−0.610092 | + | 0.792331i | \(0.708867\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −977.438 | − | 1692.97i | −0.0719545 | − | 0.124629i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −15932.9 | − | 5799.09i | −1.05208 | − | 0.382926i | −0.242633 | − | 0.970118i | \(-0.578011\pi\) |
−0.809448 | + | 0.587192i | \(0.800233\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1649.76 | + | 2857.46i | −0.0981590 | + | 0.170016i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −588.800 | − | 3339.25i | −0.0316988 | − | 0.179773i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −20338.2 | + | 17065.8i | −0.994543 | + | 0.834521i | −0.986219 | − | 0.165445i | \(-0.947094\pi\) |
−0.00832396 | + | 0.999965i | \(0.502650\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4253.92 | + | 1548.30i | −0.189619 | + | 0.0690158i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7447.15 | − | 11384.7i | −0.303601 | − | 0.464125i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 18836.8 | − | 6856.03i | 0.704493 | − | 0.256414i | 0.0351650 | − | 0.999382i | \(-0.488804\pi\) |
0.669328 | + | 0.742967i | \(0.266582\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −38667.8 | + | 32446.1i | −1.33053 | + | 1.11645i | −0.346575 | + | 0.938022i | \(0.612655\pi\) |
−0.983954 | + | 0.178424i | \(0.942900\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4142.96 | + | 23495.9i | 0.131510 | + | 0.745832i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3839.79 | + | 6650.71i | −0.112726 | + | 0.195247i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 33834.2 | + | 12314.7i | 0.920809 | + | 0.335147i | 0.758560 | − | 0.651603i | \(-0.225903\pi\) |
0.162248 | + | 0.986750i | \(0.448125\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2238.36 | + | 3876.95i | 0.0565987 | + | 0.0980318i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −19090.6 | − | 16018.9i | −0.449442 | − | 0.377127i | 0.389787 | − | 0.920905i | \(-0.372549\pi\) |
−0.839229 | + | 0.543779i | \(0.816993\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5135.69 | + | 29125.9i | −0.112795 | + | 0.639695i | 0.875023 | + | 0.484082i | \(0.160846\pi\) |
−0.987818 | + | 0.155613i | \(0.950265\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −25849.9 | −0.530647 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 55249.1 | 1.06194 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5030.54 | − | 28529.6i | 0.0906873 | − | 0.514313i | −0.905297 | − | 0.424780i | \(-0.860351\pi\) |
0.995984 | − | 0.0895331i | \(-0.0285375\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7773.60 | + | 6522.83i | 0.131647 | + | 0.110465i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −36878.7 | − | 63875.8i | −0.587599 | − | 1.01775i | −0.994546 | − | 0.104299i | \(-0.966740\pi\) |
0.406947 | − | 0.913452i | \(-0.366593\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4281.98 | − | 1558.51i | −0.0642831 | − | 0.0233971i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 28502.2 | − | 49367.3i | 0.403720 | − | 0.699264i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4801.09 | + | 27228.3i | 0.0642487 | + | 0.364373i | 0.999933 | + | 0.0115355i | \(0.00367193\pi\) |
−0.935685 | + | 0.352837i | \(0.885217\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 71798.1 | − | 60245.7i | 0.908886 | − | 0.762646i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4982.78 | + | 1813.58i | −0.0597398 | + | 0.0217435i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18254.0 | + | 1017.40i | −0.207514 | + | 0.0115660i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13600.4 | − | 4950.16i | 0.146765 | − | 0.0534182i | −0.267593 | − | 0.963532i | \(-0.586228\pi\) |
0.414358 | + | 0.910114i | \(0.364006\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 50220.7 | − | 42140.2i | 0.514986 | − | 0.432124i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17060.8 | + | 96756.9i | 0.166417 | + | 0.943796i | 0.947592 | + | 0.319484i | \(0.103510\pi\) |
−0.781175 | + | 0.624312i | \(0.785379\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 52648.8 | − | 91190.3i | 0.488985 | − | 0.846946i | −0.510935 | − | 0.859619i | \(-0.670701\pi\) |
0.999920 | + | 0.0126732i | \(0.00403411\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13384.0 | − | 4871.39i | −0.118471 | − | 0.0431201i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −31764.1 | − | 55017.0i | −0.268211 | − | 0.464555i | 0.700189 | − | 0.713958i | \(-0.253099\pi\) |
−0.968400 | + | 0.249402i | \(0.919766\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10028.1 | − | 8414.60i | −0.0808451 | − | 0.0678371i | 0.601470 | − | 0.798896i | \(-0.294582\pi\) |
−0.682315 | + | 0.731059i | \(0.739027\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14289.3 | − | 81038.6i | 0.110079 | − | 0.624287i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 43980.7 | 0.324016 | 0.162008 | − | 0.986789i | \(-0.448203\pi\) | ||||
0.162008 | + | 0.986789i | \(0.448203\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6016.17 | 0.0424205 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 19312.3 | − | 109525.i | 0.130427 | − | 0.739690i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 42602.4 | + | 35747.6i | 0.275782 | + | 0.231409i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4618.27 | + | 7999.08i | 0.0286758 | + | 0.0496680i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 125440. | + | 45656.4i | 0.747606 | + | 0.272106i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −35523.4 | + | 61528.3i | −0.203348 | + | 0.352208i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 42814.2 | + | 242811.i | 0.235548 | + | 1.33586i | 0.841457 | + | 0.540323i | \(0.181698\pi\) |
−0.605910 | + | 0.795533i | \(0.707191\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6735.96 | − | 5652.14i | 0.0356390 | − | 0.0299047i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −277294. | + | 100927.i | −1.41176 | + | 0.513840i | −0.931647 | − | 0.363365i | \(-0.881628\pi\) |
−0.480117 | + | 0.877205i | \(0.659406\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 213593. | + | 64527.7i | 1.04703 | + | 0.316313i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −38817.9 | + | 14128.5i | −0.183315 | + | 0.0667211i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −221298. | + | 185691.i | −1.00734 | + | 0.845257i | −0.987984 | − | 0.154556i | \(-0.950605\pi\) |
−0.0193539 | + | 0.999813i | \(0.506161\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −67554.3 | − | 383120.i | −0.296562 | − | 1.68189i | −0.660784 | − | 0.750576i | \(-0.729776\pi\) |
0.364221 | − | 0.931312i | \(-0.381335\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −73293.2 | + | 126948.i | −0.310467 | + | 0.537745i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −242010. | − | 88084.4i | −0.989675 | − | 0.360212i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −38303.6 | − | 66343.8i | −0.151293 | − | 0.262048i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21851.9 | + | 18336.0i | 0.0834059 | + | 0.0699859i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18638.0 | + | 105701.i | −0.0687753 | + | 0.390044i | 0.930917 | + | 0.365231i | \(0.119010\pi\) |
−0.999692 | + | 0.0248128i | \(0.992101\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −164771. | −0.588082 | −0.294041 | − | 0.955793i | \(-0.595000\pi\) | ||||
−0.294041 | + | 0.955793i | \(0.595000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 65990.9 | 0.227906 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1237.42 | + | 7017.75i | −0.00413702 | + | 0.0234622i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2382.87 | − | 1999.46i | −0.00771527 | − | 0.00647388i | 0.638922 | − | 0.769272i | \(-0.279381\pi\) |
−0.646637 | + | 0.762798i | \(0.723825\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 114767. | + | 198781.i | 0.360017 | + | 0.623567i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −68996.6 | − | 25112.7i | −0.209779 | − | 0.0763534i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −235705. | + | 408254.i | −0.694865 | + | 1.20354i | 0.275361 | + | 0.961341i | \(0.411203\pi\) |
−0.970226 | + | 0.242201i | \(0.922131\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6796.10 | + | 38542.6i | 0.0194334 | + | 0.110213i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −277637. | + | 232965.i | −0.770346 | + | 0.646397i | −0.940797 | − | 0.338969i | \(-0.889922\pi\) |
0.170452 | + | 0.985366i | \(0.445477\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −61649.4 | + | 22438.6i | −0.166040 | + | 0.0604336i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 243371. | − | 104259.i | 0.636470 | − | 0.272661i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −464197. | + | 168954.i | −1.17920 | + | 0.429193i | −0.855919 | − | 0.517110i | \(-0.827008\pi\) |
−0.323280 | + | 0.946303i | \(0.604786\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 324785. | − | 272527.i | 0.801679 | − | 0.672688i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −30093.8 | − | 170670.i | −0.0722011 | − | 0.409473i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 146354. | − | 253492.i | 0.341406 | − | 0.591333i | −0.643288 | − | 0.765624i | \(-0.722430\pi\) |
0.984694 | + | 0.174291i | \(0.0557635\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 358542. | + | 130499.i | 0.813475 | + | 0.296081i | 0.715058 | − | 0.699065i | \(-0.246400\pi\) |
0.0984165 | + | 0.995145i | \(0.468622\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 218198. | + | 377930.i | 0.481641 | + | 0.834226i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −84714.0 | − | 71083.5i | −0.181981 | − | 0.152700i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 26536.2 | − | 150494.i | 0.0554925 | − | 0.314714i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 504159. | 1.02663 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 107928. | 0.214067 | 0.107033 | − | 0.994255i | \(-0.465865\pi\) | ||||
0.107033 | + | 0.994255i | \(0.465865\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 126314. | − | 716364.i | 0.244095 | − | 1.38433i | −0.578490 | − | 0.815690i | \(-0.696358\pi\) |
0.822585 | − | 0.568643i | \(-0.192531\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 50860.1 | + | 42676.7i | 0.0957835 | + | 0.0803719i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −244831. | − | 424060.i | −0.449470 | − | 0.778505i | 0.548881 | − | 0.835900i | \(-0.315054\pi\) |
−0.998352 | + | 0.0573952i | \(0.981720\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −354815. | − | 129142.i | −0.635140 | − | 0.231172i | 0.00432687 | − | 0.999991i | \(-0.498623\pi\) |
−0.639467 | + | 0.768819i | \(0.720845\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 155642. | − | 269580.i | 0.271729 | − | 0.470649i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 162353. | + | 920752.i | 0.276517 | + | 1.56820i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 137425. | − | 115313.i | 0.228391 | − | 0.191643i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −81871.3 | + | 29798.7i | −0.132802 | + | 0.0483361i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −139902. | − | 596938.i | −0.221543 | − | 0.945287i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 627262. | − | 228305.i | 0.969936 | − | 0.353028i | 0.192016 | − | 0.981392i | \(-0.438497\pi\) |
0.777920 | + | 0.628364i | \(0.216275\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −165046. | + | 138490.i | −0.249262 | + | 0.209156i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2052.00 | − | 11637.4i | −0.00302747 | − | 0.0171697i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 43484.8 | − | 75317.9i | 0.0626886 | − | 0.108580i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 240270. | + | 87451.3i | 0.338524 | + | 0.123213i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −129620. | − | 224508.i | −0.178522 | − | 0.309209i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 433966. | + | 364140.i | 0.584377 | + | 0.490350i | 0.886381 | − | 0.462956i | \(-0.153211\pi\) |
−0.302004 | + | 0.953307i | \(0.597656\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 87360.6 | − | 495447.i | 0.115043 | − | 0.652440i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −468869. | −0.603930 | −0.301965 | − | 0.953319i | \(-0.597643\pi\) | ||||
−0.301965 | + | 0.953319i | \(0.597643\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 937113. | 1.18087 | 0.590437 | − | 0.807084i | \(-0.298956\pi\) | ||||
0.590437 | + | 0.807084i | \(0.298956\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 82943.3 | − | 470395.i | 0.102271 | − | 0.580006i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −448581. | − | 376404.i | −0.541317 | − | 0.454219i | 0.330671 | − | 0.943746i | \(-0.392725\pi\) |
−0.871988 | + | 0.489527i | \(0.837169\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 98497.4 | + | 170602.i | 0.116347 | + | 0.201519i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −235351. | − | 85660.7i | −0.272173 | − | 0.0990629i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 118788. | − | 205746.i | 0.134517 | − | 0.232990i | −0.790896 | − | 0.611951i | \(-0.790385\pi\) |
0.925413 | + | 0.378961i | \(0.123718\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2934.13 | − | 16640.3i | −0.00325415 | − | 0.0184552i | 0.983137 | − | 0.182868i | \(-0.0585381\pi\) |
−0.986392 | + | 0.164413i | \(0.947427\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 729056. | − | 611750.i | 0.792036 | − | 0.664597i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 36023.2 | − | 13111.4i | 0.0383414 | − | 0.0139551i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −832732. | − | 623187.i | −0.868486 | − | 0.649944i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −599208. | + | 218094.i | −0.612462 | + | 0.222918i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.37034e6 | + | 1.14985e6i | −1.37292 | + | 1.15201i | −0.401166 | + | 0.916005i | \(0.631395\pi\) |
−0.971751 | + | 0.236009i | \(0.924161\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 35034.8 | + | 198692.i | 0.0344111 | + | 0.195155i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19697.6 | + | 34117.3i | −0.0189699 | + | 0.0328567i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 326623. | + | 118881.i | 0.308470 | + | 0.112274i | 0.491617 | − | 0.870812i | \(-0.336406\pi\) |
−0.183146 | + | 0.983086i | \(0.558628\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 674828. | + | 1.16884e6i | 0.625091 | + | 1.08269i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 849864. | + | 713120.i | 0.772232 | + | 0.647980i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −222265. | + | 1.26053e6i | −0.198144 | + | 1.12373i | 0.709725 | + | 0.704479i | \(0.248819\pi\) |
−0.907869 | + | 0.419253i | \(0.862292\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 308465. | 0.269831 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 239032. | 0.205200 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −269600. | + | 1.52898e6i | −0.227164 | + | 1.28831i | 0.631342 | + | 0.775504i | \(0.282504\pi\) |
−0.858506 | + | 0.512804i | \(0.828607\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 355499. | + | 298299.i | 0.294046 | + | 0.246734i | 0.777861 | − | 0.628436i | \(-0.216305\pi\) |
−0.483815 | + | 0.875170i | \(0.660749\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −405149. | − | 701739.i | −0.329009 | − | 0.569861i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.09475e6 | − | 398457.i | −0.872939 | − | 0.317724i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 856730. | − | 1.48390e6i | 0.670880 | − | 1.16200i | −0.306776 | − | 0.951782i | \(-0.599250\pi\) |
0.977655 | − | 0.210216i | \(-0.0674166\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17920.2 | − | 101630.i | −0.0137826 | − | 0.0781651i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −183817. | + | 154240.i | −0.138873 | + | 0.116529i | −0.709578 | − | 0.704627i | \(-0.751114\pi\) |
0.570705 | + | 0.821155i | \(0.306670\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.97635e6 | + | 719332.i | −1.46689 | + | 0.533904i | −0.947254 | − | 0.320484i | \(-0.896154\pi\) |
−0.519635 | + | 0.854388i | \(0.673932\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18741.8 | + | 156943.i | −0.0136678 | + | 0.114454i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.05740e6 | + | 748831.i | −1.47439 | + | 0.536635i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −969838. | + | 813791.i | −0.683053 | + | 0.573150i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21728.2 | − | 123227.i | −0.0150415 | − | 0.0853045i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 442562. | − | 766539.i | 0.301165 | − | 0.521633i | −0.675235 | − | 0.737603i | \(-0.735958\pi\) |
0.976400 | + | 0.215969i | \(0.0692911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −218853. | − | 79656.2i | −0.146419 | − | 0.0532923i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −692669. | − | 1.19974e6i | −0.455653 | − | 0.789215i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 262191. | + | 220004.i | 0.169605 | + | 0.142316i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25043.7 | + | 142030.i | −0.0159324 | + | 0.0903573i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 849408. | 0.531508 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 586465. | 0.360987 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −40981.2 | + | 232416.i | −0.0248164 | + | 0.140741i | −0.994699 | − | 0.102834i | \(-0.967209\pi\) |
0.969882 | + | 0.243575i | \(0.0783201\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −697362. | − | 585156.i | −0.415491 | − | 0.348639i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.05972e6 | + | 1.83549e6i | 0.621284 | + | 1.07610i | 0.989247 | + | 0.146255i | \(0.0467221\pi\) |
−0.367963 | + | 0.929841i | \(0.619945\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.93620e6 | − | 704720.i | −1.11709 | − | 0.406589i | −0.283504 | − | 0.958971i | \(-0.591497\pi\) |
−0.833591 | + | 0.552382i | \(0.813719\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 138598. | − | 240059.i | 0.0787012 | − | 0.136314i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 569321. | + | 3.22878e6i | 0.318207 | + | 1.80464i | 0.553648 | + | 0.832751i | \(0.313235\pi\) |
−0.235442 | + | 0.971888i | \(0.575654\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.96804e6 | − | 1.65138e6i | 1.08282 | − | 0.908595i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −516105. | + | 187847.i | −0.279560 | + | 0.101752i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 278357. | − | 550817.i | 0.148455 | − | 0.293766i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.85716e6 | + | 675951.i | −0.975306 | + | 0.354982i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −86697.4 | + | 72747.7i | −0.0448370 | + | 0.0376227i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −417490. | − | 2.36771e6i | −0.212646 | − | 1.20597i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.09997e6 | − | 1.90521e6i | 0.551838 | − | 0.955811i | −0.446304 | − | 0.894881i | \(-0.647260\pi\) |
0.998142 | − | 0.0609297i | \(-0.0194065\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.50492e6 | + | 547745.i | 0.743708 | + | 0.270687i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −209164. | − | 362283.i | −0.101830 | − | 0.176375i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.38586e6 | + | 1.16288e6i | 0.664730 | + | 0.557775i | 0.911500 | − | 0.411299i | \(-0.134925\pi\) |
−0.246770 | + | 0.969074i | \(0.579369\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 66026.5 | − | 374455.i | 0.0312046 | − | 0.176970i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −238977. | −0.111294 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.91533e6 | 0.879038 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9031.84 | − | 51222.1i | 0.00408534 | − | 0.0231691i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −571789. | − | 479788.i | −0.254925 | − | 0.213907i | 0.506365 | − | 0.862319i | \(-0.330989\pi\) |
−0.761289 | + | 0.648412i | \(0.775433\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.10644e6 | + | 3.64847e6i | 0.925734 | + | 1.60342i | 0.790377 | + | 0.612621i | \(0.209885\pi\) |
0.135357 | + | 0.990797i | \(0.456782\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.20839e6 | − | 803787.i | −0.956770 | − | 0.348236i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.41425e6 | − | 2.44955e6i | 0.604071 | − | 1.04628i | −0.388126 | − | 0.921606i | \(-0.626877\pi\) |
0.992197 | − | 0.124676i | \(-0.0397892\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 50278.5 | + | 285144.i | 0.0211744 | + | 0.120086i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 368315. | − | 309053.i | 0.152950 | − | 0.128340i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.10605e6 | − | 1.49448e6i | 1.68147 | − | 0.612004i | 0.687957 | − | 0.725751i | \(-0.258508\pi\) |
0.993510 | + | 0.113748i | \(0.0362856\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 156328. | − | 2.47116e6i | 0.0631348 | − | 0.998005i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 75038.0 | − | 27311.6i | 0.0298892 | − | 0.0108788i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 263226. | − | 220873.i | 0.103418 | − | 0.0867782i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −712246. | − | 4.03935e6i | −0.276035 | − | 1.56547i | −0.735654 | − | 0.677358i | \(-0.763125\pi\) |
0.459618 | − | 0.888116i | \(-0.347986\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.29899e6 | + | 2.24992e6i | −0.496638 | + | 0.860203i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.53764e6 | − | 1.28760e6i | −1.33438 | − | 0.485674i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.48064e6 | + | 4.29659e6i | 0.923190 | + | 1.59901i | 0.794447 | + | 0.607334i | \(0.207761\pi\) |
0.128743 | + | 0.991678i | \(0.458906\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 470527. | + | 394819.i | 0.172785 | + | 0.144984i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 756804. | − | 4.29205e6i | 0.274240 | − | 1.55529i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 867337. | 0.310163 | 0.155081 | − | 0.987902i | \(-0.450436\pi\) | ||||
0.155081 | + | 0.987902i | \(0.450436\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.13159e6 | 0.752300 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 281973. | − | 1.59915e6i | 0.0982223 | − | 0.557046i | −0.895490 | − | 0.445082i | \(-0.853175\pi\) |
0.993712 | − | 0.111964i | \(-0.0357143\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −491729. | − | 412610.i | −0.169073 | − | 0.141869i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 85566.1 | + | 148205.i | 0.0290419 | + | 0.0503020i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 475214. | + | 172964.i | 0.159226 | + | 0.0579537i | 0.420404 | − | 0.907337i | \(-0.361888\pi\) |
−0.261177 | + | 0.965291i | \(0.584111\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −101544. | + | 175880.i | −0.0335902 | + | 0.0581800i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 443007. | + | 2.51242e6i | 0.144687 | + | 0.820560i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −257837. | + | 216351.i | −0.0831480 | + | 0.0697695i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.13354e6 | + | 1.14052e6i | −0.997837 | + | 0.363183i | −0.788750 | − | 0.614714i | \(-0.789271\pi\) |
−0.209087 | + | 0.977897i | \(0.567049\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 870052. | − | 1.72167e6i | 0.273598 | − | 0.541400i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.77310e6 | + | 2.10124e6i | −1.79287 | + | 0.652550i | −0.793855 | + | 0.608107i | \(0.791929\pi\) |
−0.999012 | + | 0.0444431i | \(0.985849\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −310559. | + | 260590.i | −0.0952536 | + | 0.0799272i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20473.2 | − | 116109.i | −0.00620223 | − | 0.0351746i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.85430e6 | − | 3.21175e6i | 0.554875 | − | 0.961071i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −732420. | − | 266579.i | −0.216497 | − | 0.0787985i | 0.231495 | − | 0.972836i | \(-0.425638\pi\) |
−0.447992 | + | 0.894038i | \(0.647861\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.24876e6 | + | 2.16291e6i | 0.364648 | + | 0.631589i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.17743e6 | + | 1.82708e6i | 0.628157 | + | 0.527086i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −148807. | + | 843926.i | −0.0424134 | + | 0.240538i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.36333e6 | −0.947172 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.32803e6 | 1.76089 | 0.880447 | − | 0.474144i | \(-0.157242\pi\) | ||||
0.880447 | + | 0.474144i | \(0.157242\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 458810. | − | 2.60204e6i | 0.126162 | − | 0.715498i | −0.854449 | − | 0.519534i | \(-0.826105\pi\) |
0.980611 | − | 0.195964i | \(-0.0627835\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.18542e6 | − | 1.83378e6i | −0.593859 | − | 0.498307i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −586347. | − | 1.01558e6i | −0.157464 | − | 0.272736i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.72588e6 | − | 2.44802e6i | −1.78517 | − | 0.649749i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.11328e6 | + | 1.92825e6i | −0.292052 | + | 0.505849i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.09334e6 | + | 6.20062e6i | 0.283505 | + | 1.60784i | 0.710578 | + | 0.703619i | \(0.248434\pi\) |
−0.427073 | + | 0.904217i | \(0.640455\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 191609. | − | 160779.i | 0.0491129 | − | 0.0412106i | −0.617901 | − | 0.786256i | \(-0.712017\pi\) |
0.667014 | + | 0.745045i | \(0.267572\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −622360. | + | 226520.i | −0.157695 | + | 0.0573963i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −96616.5 | + | 809063.i | −0.0242018 | + | 0.202665i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.11989e6 | + | 1.86349e6i | −1.26794 | + | 0.461493i | −0.886427 | − | 0.462869i | \(-0.846820\pi\) |
−0.381516 | + | 0.924362i | \(0.624598\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −425282. | + | 356854.i | −0.104131 | + | 0.0873763i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −129202. | − | 732739.i | −0.0312794 | − | 0.177395i | 0.965166 | − | 0.261640i | \(-0.0842632\pi\) |
−0.996445 | + | 0.0842452i | \(0.973152\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 160615. | − | 278193.i | 0.0384491 | − | 0.0665958i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 871967. | + | 317370.i | 0.206410 | + | 0.0751271i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.70632e6 | + | 6.41953e6i | 0.867614 | + | 1.50275i | 0.864428 | + | 0.502757i | \(0.167681\pi\) |
0.00318678 | + | 0.999995i | \(0.498986\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.60866e6 | + | 3.86712e6i | 1.06692 | + | 0.895254i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −247364. | + | 1.40287e6i | −0.0566358 | + | 0.321197i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.08894e6 | −0.246591 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.14993e6 | −1.15348 | −0.576741 | − | 0.816927i | \(-0.695676\pi\) | ||||
−0.576741 | + | 0.816927i | \(0.695676\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 242148. | − | 1.37329e6i | 0.0536475 | − | 0.304250i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.22701e6 | + | 1.02959e6i | 0.268904 | + | 0.225637i | 0.767262 | − | 0.641334i | \(-0.221619\pi\) |
−0.498357 | + | 0.866972i | \(0.666063\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 434748. | + | 753006.i | 0.0942509 | + | 0.163247i | 0.909296 | − | 0.416151i | \(-0.136621\pi\) |
−0.815045 | + | 0.579398i | \(0.803288\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 57891.9 | + | 21070.9i | 0.0124161 | + | 0.00451910i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.60301e6 | − | 2.77649e6i | 0.340129 | − | 0.589121i | −0.644327 | − | 0.764750i | \(-0.722863\pi\) |
0.984456 | + | 0.175629i | \(0.0561959\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 886562. | + | 5.02794e6i | 0.186113 | + | 1.05550i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20600.9 | + | 17286.2i | −0.00427892 | + | 0.00359044i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 372393. | − | 135540.i | 0.0765331 | − | 0.0278558i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.76693e6 | − | 2.81904e6i | −0.766044 | − | 0.573280i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.19776e6 | + | 1.52786e6i | −0.844737 | + | 0.307459i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.71800e6 | + | 5.63707e6i | −1.33783 | + | 1.12257i | −0.355652 | + | 0.934618i | \(0.615741\pi\) |
−0.982178 | + | 0.187954i | \(0.939814\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.09248e6 | − | 6.19579e6i | −0.215304 | − | 1.22105i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −317393. | + | 549741.i | −0.0619056 | + | 0.107224i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −158016. | − | 57512.9i | −0.0305032 | − | 0.0111023i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.14673e6 | − | 3.71825e6i | −0.410162 | − | 0.710422i | 0.584745 | − | 0.811217i | \(-0.301195\pi\) |
−0.994907 | + | 0.100795i | \(0.967861\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.12205e6 | + | 2.61971e6i | 0.590429 | + | 0.495428i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 846598. | − | 4.80129e6i | 0.158480 | − | 0.898783i | −0.797056 | − | 0.603906i | \(-0.793610\pi\) |
0.955535 | − | 0.294877i | \(-0.0952786\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.58603e6 | 0.479200 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −761686. | −0.139721 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 613627. | − | 3.48005e6i | 0.111433 | − | 0.631967i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.13120e6 | + | 1.78829e6i | 0.383153 | + | 0.321504i | 0.813939 | − | 0.580951i | \(-0.197319\pi\) |
−0.430786 | + | 0.902454i | \(0.641763\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.56667e6 | + | 2.71356e6i | 0.278859 | + | 0.482998i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.71225e6 | − | 987179.i | −0.477980 | − | 0.173971i | 0.0917837 | − | 0.995779i | \(-0.470743\pi\) |
−0.569764 | + | 0.821808i | \(0.692965\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 570752. | − | 988571.i | 0.0995907 | − | 0.172496i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 98491.7 | + | 558574.i | 0.0170169 | + | 0.0965074i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.43422e6 | − | 5.39895e6i | 1.10078 | − | 0.923666i | 0.103305 | − | 0.994650i | \(-0.467058\pi\) |
0.997477 | + | 0.0709840i | \(0.0226139\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.94078e6 | + | 1.43433e6i | −0.667622 | + | 0.242994i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.27663e6 | − | 5.44718e6i | −0.214177 | − | 0.913857i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.14961e6 | + | 418424.i | −0.191000 | + | 0.0695182i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.06079e6 | + | 4.24651e6i | −0.832707 | + | 0.698724i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 741605. | + | 4.20585e6i | 0.120852 | + | 0.685387i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.29254e6 | − | 9.16695e6i | 0.854220 | − | 1.47955i | −0.0231464 | − | 0.999732i | \(-0.507368\pi\) |
0.877367 | − | 0.479821i | \(-0.159298\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.98548e6 | + | 1.81457e6i | 0.796990 | + | 0.290081i | 0.708239 | − | 0.705973i | \(-0.249490\pi\) |
0.0887515 | + | 0.996054i | \(0.471712\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.83273e6 | − | 3.17437e6i | −0.290201 | − | 0.502643i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −184274. | − | 154625.i | −0.0289027 | − | 0.0242522i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.07110e6 | + | 6.07450e6i | −0.166414 | + | 0.943782i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.37282e6 | 0.519107 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.02060e7 | 1.55610 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −128169. | + | 726883.i | −0.0193597 | + | 0.109794i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.93854e6 | − | 1.62663e6i | −0.290094 | − | 0.243418i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 642801. | + | 1.11336e6i | 0.0953026 | + | 0.165069i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 135462. | + | 49304.3i | 0.0198988 | + | 0.00724255i | 0.351950 | − | 0.936019i | \(-0.385519\pi\) |
−0.332052 | + | 0.943261i | \(0.607741\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.64934e6 | − | 2.85675e6i | 0.240055 | − | 0.415788i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26410.9 | + | 149784.i | 0.00380883 | + | 0.0216009i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.83552e6 | − | 3.21838e6i | 0.548095 | − | 0.459907i | −0.326200 | − | 0.945301i | \(-0.605768\pi\) |
0.874295 | + | 0.485394i | \(0.161324\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.98093e6 | + | 2.90482e6i | −1.13011 | + | 0.411328i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.53714e6 | − | 4.08568e6i | 1.33826 | − | 0.573304i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.86010e6 | − | 1.40496e6i | 0.536767 | − | 0.195367i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −732388. | + | 614547.i | −0.100927 | + | 0.0846881i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.37928e6 | − | 7.82228e6i | −0.188371 | − | 1.06831i | −0.921547 | − | 0.388266i | \(-0.873074\pi\) |
0.733176 | − | 0.680039i | \(-0.238037\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 336140. | − | 582211.i | 0.0454978 | − | 0.0788045i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.24148e6 | − | 451862.i | −0.166545 | − | 0.0606176i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.88834e6 | − | 3.27070e6i | −0.251078 | − | 0.434880i | 0.712745 | − | 0.701423i | \(-0.247452\pi\) |
−0.963823 | + | 0.266543i | \(0.914118\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −391438. | − | 328455.i | −0.0515872 | − | 0.0432868i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −249866. | + | 1.41706e6i | −0.0326399 | + | 0.185110i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.06210e7 | 1.37526 | 0.687630 | − | 0.726061i | \(-0.258651\pi\) | ||||
0.687630 | + | 0.726061i | \(0.258651\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.71674e6 | 0.990476 | 0.495238 | − | 0.868757i | \(-0.335081\pi\) | ||||
0.495238 | + | 0.868757i | \(0.335081\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 162028. | − | 918904.i | 0.0206159 | − | 0.116919i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.18604e6 | + | 995208.i | 0.149600 | + | 0.125529i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.76850e6 | − | 8.25928e6i | −0.596269 | − | 1.03277i | −0.993366 | − | 0.114991i | \(-0.963316\pi\) |
0.397098 | − | 0.917776i | \(-0.370017\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.90955e6 | − | 2.15090e6i | −0.732584 | − | 0.266639i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.22931e6 | − | 9.05743e6i | 0.642694 | − | 1.11318i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.79633e6 | + | 1.01875e7i | 0.218884 | + | 1.24135i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −989837. | + | 830572.i | −0.119584 | + | 0.100343i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.87713e6 | + | 1.41116e6i | −0.464424 | + | 0.169037i | −0.563625 | − | 0.826031i | \(-0.690594\pi\) |
0.0992006 | + | 0.995067i | \(0.468371\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −923885. | − | 279111.i | −0.109731 | − | 0.0331504i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.97803e6 | + | 1.44788e6i | −0.468489 | + | 0.170516i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.15399e6 | + | 1.80742e6i | −0.251540 | + | 0.211068i | −0.759835 | − | 0.650116i | \(-0.774720\pi\) |
0.508295 | + | 0.861183i | \(0.330276\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −112201. | − | 636324.i | −0.0129929 | − | 0.0736861i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.63220e6 | + | 2.82705e6i | −0.187429 | + | 0.324636i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.17608e7 | + | 4.28056e6i | 1.33927 | + | 0.487454i | 0.909582 | − | 0.415524i | \(-0.136402\pi\) |
0.429687 | + | 0.902978i | \(0.358624\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.49522e6 | + | 6.05389e6i | 0.394719 | + | 0.683673i | 0.993065 | − | 0.117565i | \(-0.0375087\pi\) |
−0.598346 | + | 0.801237i | \(0.704175\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.64084e6 | + | 3.89413e6i | 0.519761 | + | 0.436131i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18634.9 | − | 105684.i | 0.00206985 | − | 0.0117387i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.20698e6 | −0.793929 | −0.396964 | − | 0.917834i | \(-0.629936\pi\) | ||||
−0.396964 | + | 0.917834i | \(0.629936\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.08309e6 | 0.883149 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.94612e6 | + | 1.10370e7i | −0.210895 | + | 1.19604i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.57240e6 | − | 8.03220e6i | −1.02889 | − | 0.863343i | −0.0381730 | − | 0.999271i | \(-0.512154\pi\) |
−0.990719 | + | 0.135929i | \(0.956598\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −775473. | − | 1.34316e6i | −0.0826759 | − | 0.143199i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.32473e7 | − | 4.82164e6i | −1.40093 | − | 0.509896i | −0.472475 | − | 0.881344i | \(-0.656639\pi\) |
−0.928454 | + | 0.371448i | \(0.878861\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.00321e6 | + | 5.20170e6i | −0.315035 | + | 0.545656i | −0.979445 | − | 0.201712i | \(-0.935349\pi\) |
0.664410 | + | 0.747368i | \(0.268683\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 319700. | + | 1.81311e6i | 0.0332670 | + | 0.188666i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.00325e6 | + | 2.52003e6i | −0.310007 | + | 0.260127i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.00462e6 | + | 2.91344e6i | −0.819673 | + | 0.298337i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.29241e6 | + | 294976.i | −0.537631 | + | 0.0299652i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.50794e6 | − | 1.27678e6i | 0.353529 | − | 0.128674i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28000.5 | − | 23495.2i | 0.00279957 | − | 0.00234912i | −0.641387 | − | 0.767218i | \(-0.721641\pi\) |
0.644186 | + | 0.764869i | \(0.277196\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.00212e6 | − | 5.68330e6i | −0.0994055 | − | 0.563757i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.43230e6 | − | 2.48082e6i | 0.140961 | − | 0.244152i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.04940e6 | + | 745920.i | 0.200114 | + | 0.0728356i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.09656e6 | − | 3.63135e6i | −0.203121 | − | 0.351817i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.17087e7 | − | 9.82481e6i | −1.12555 | − | 0.944450i | −0.126680 | − | 0.991944i | \(-0.540432\pi\) |
−0.998872 | + | 0.0474937i | \(0.984877\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 123239. | − | 698923.i | 0.0117549 | − | 0.0666656i | −0.978366 | − | 0.206881i | \(-0.933669\pi\) |
0.990121 | + | 0.140216i | \(0.0447797\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −102163. | −0.00966926 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 774794. | 0.0727655 | 0.0363827 | − | 0.999338i | \(-0.488416\pi\) | ||||
0.0363827 | + | 0.999338i | \(0.488416\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.35627e6 | − | 7.69182e6i | 0.126397 | − | 0.716832i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −575981. | − | 483305.i | −0.0532666 | − | 0.0446960i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.68597e6 | + | 1.15804e7i | 0.613595 | + | 1.06278i | 0.990629 | + | 0.136578i | \(0.0436104\pi\) |
−0.377035 | + | 0.926199i | \(0.623056\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.22171e6 | + | 1.17261e6i | 0.293416 | + | 0.106795i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.48812e6 | + | 4.30955e6i | −0.224883 | + | 0.389509i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.32818e6 | + | 1.32038e7i | 0.208835 | + | 1.18436i | 0.891290 | + | 0.453433i | \(0.149801\pi\) |
−0.682455 | + | 0.730927i | \(0.739088\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.81984e6 | + | 4.04432e6i | −0.429071 | + | 0.360033i | −0.831601 | − | 0.555374i | \(-0.812575\pi\) |
0.402530 | + | 0.915407i | \(0.368131\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.10608e6 | + | 766549.i | −0.186076 | + | 0.0677261i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.41912e6 | − | 2.16946e6i | −0.124441 | − | 0.190238i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.20835e6 | + | 1.16774e6i | −0.279233 | + | 0.101633i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.75181e6 | − | 3.14815e6i | 0.324098 | − | 0.271950i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.41524e6 | + | 1.93688e7i | 0.292830 | + | 1.66072i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.18441e6 | + | 1.41758e7i | −0.696545 | + | 1.20645i | 0.273111 | + | 0.961982i | \(0.411947\pi\) |
−0.969657 | + | 0.244470i | \(0.921386\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.98982e6 | − | 3.63600e6i | −0.843914 | − | 0.307160i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −696613. | − | 1.20657e6i | −0.0584144 | − | 0.101177i | 0.835339 | − | 0.549735i | \(-0.185271\pi\) |
−0.893754 | + | 0.448558i | \(0.851938\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.57213e6 | + | 1.31918e6i | 0.130862 | + | 0.109807i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −703895. | + | 3.99199e6i | −0.0581621 | + | 0.329854i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.26107e7 | −1.03440 | −0.517198 | − | 0.855866i | \(-0.673025\pi\) | ||||
−0.517198 | + | 0.855866i | \(0.673025\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.35637e6 | 0.273302 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.40685e6 | − | 7.97865e6i | 0.113725 | − | 0.644967i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.34432e7 | + | 1.12802e7i | 1.07884 | + | 0.905251i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.72975e6 | − | 2.99601e6i | −0.137812 | − | 0.238698i | 0.788856 | − | 0.614578i | \(-0.210674\pi\) |
−0.926668 | + | 0.375880i | \(0.877340\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.73541e6 | + | 3.17943e6i | 0.690956 | + | 0.251487i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.25995e6 | + | 3.91436e6i | −0.177475 | + | 0.307396i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.05159e6 | + | 5.96385e6i | 0.0819905 | + | 0.464991i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.87817e6 | + | 3.25417e6i | −0.300216 | + | 0.251911i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.75018e6 | + | 2.45686e6i | −0.518824 | + | 0.188837i | −0.588141 | − | 0.808758i | \(-0.700140\pi\) |
0.0693173 | + | 0.997595i | \(0.477918\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.09199e7 | − | 1.02509e7i | 0.833354 | − | 0.782301i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.60039e6 | − | 582495.i | 0.121270 | − | 0.0441387i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.06722e7 | + | 8.95501e6i | −0.802979 | + | 0.673779i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.71457e6 | − | 9.72378e6i | −0.128097 | − | 0.726473i | −0.979420 | − | 0.201832i | \(-0.935311\pi\) |
0.851323 | − | 0.524641i | \(-0.175801\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.43717e6 | − | 4.22131e6i | 0.180806 | − | 0.313165i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 298441. | + | 108624.i | 0.0219854 | + | 0.00800204i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.49611e6 | + | 2.59134e6i | 0.109446 | + | 0.189566i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.57341e6 | − | 1.32025e6i | −0.114299 | − | 0.0959085i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.80846e6 | − | 1.02563e7i | 0.130463 | − | 0.739892i | −0.847449 | − | 0.530876i | \(-0.821863\pi\) |
0.977912 | − | 0.209016i | \(-0.0670260\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.49309e7 | 1.06967 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −146082. | −0.0103932 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.42347e6 | − | 1.94154e7i | 0.241892 | − | 1.37184i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.38410e6 | − | 4.51780e6i | −0.377813 | − | 0.317023i | 0.434030 | − | 0.900898i | \(-0.357091\pi\) |
−0.811843 | + | 0.583875i | \(0.801536\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.88104e6 | − | 4.99010e6i | −0.200784 | − | 0.347769i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 374849. | + | 136434.i | 0.0259456 | + | 0.00944342i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.45753e6 | + | 5.98862e6i | −0.237687 | + | 0.411686i | −0.960050 | − | 0.279828i | \(-0.909723\pi\) |
0.722363 | + | 0.691514i | \(0.243056\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −57551.0 | − | 326388.i | −0.00392948 | − | 0.0222852i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.07468e7 | − | 9.01768e6i | 0.728807 | − | 0.611542i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.97366e7 | − | 7.18353e6i | 1.32942 | − | 0.483868i | 0.422953 | − | 0.906152i | \(-0.360994\pi\) |
0.906464 | + | 0.422284i | \(0.138771\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.55601e6 | + | 6.15438e6i | −0.438626 | + | 0.411755i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.79122e6 | + | 2.10783e6i | −0.384856 | + | 0.140076i | −0.527200 | − | 0.849741i | \(-0.676758\pi\) |
0.142344 | + | 0.989817i | \(0.454536\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 955276. | − | 801571.i | 0.0630577 | − | 0.0529117i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.15501e6 | − | 1.22217e7i | −0.141302 | − | 0.801361i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.50407e6 | − | 7.80127e6i | 0.293360 | − | 0.508114i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.83002e6 | − | 3.21386e6i | −0.571297 | − | 0.207935i | 0.0401867 | − | 0.999192i | \(-0.487205\pi\) |
−0.611484 | + | 0.791257i | \(0.709427\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.73269e6 | + | 1.33934e7i | 0.496985 | + | 0.860803i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.46650e6 | + | 1.23054e6i | 0.0936297 | + | 0.0785646i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45805.4 | + | 259775.i | −0.00290521 | + | 0.0164762i | −0.986226 | − | 0.165404i | \(-0.947107\pi\) |
0.983321 | + | 0.181880i | \(0.0582183\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.74428e6 | 0.109903 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.46615e7 | −1.54368 | −0.771841 | − | 0.635815i | \(-0.780664\pi\) | ||||
−0.771841 | + | 0.635815i | \(0.780664\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 322333. | − | 1.82804e6i | 0.0200444 | − | 0.113677i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −587333. | − | 492831.i | −0.0362853 | − | 0.0304470i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.62493e6 | − | 1.14747e7i | −0.406624 | − | 0.704293i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.43176e6 | + | 3.43288e6i | 0.575144 | + | 0.209335i | 0.613183 | − | 0.789941i | \(-0.289889\pi\) |
−0.0380388 | + | 0.999276i | \(0.512111\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.50251e6 | − | 2.60242e6i | 0.0910292 | − | 0.157667i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.40728e6 | − | 1.93236e7i | −0.205097 | − | 1.16316i | −0.897287 | − | 0.441447i | \(-0.854465\pi\) |
0.692191 | − | 0.721715i | \(-0.256646\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.40484e6 | + | 1.17880e6i | −0.0840180 | + | 0.0704994i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.09646e7 | − | 3.99081e6i | 0.651542 | − | 0.237142i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.33005e7 | + | 2.03329e7i | 0.785279 | + | 1.20048i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.12448e6 | + | 3.32104e6i | −0.535279 | + | 0.194826i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.79587e7 | − | 1.50692e7i | 1.04682 | − | 0.878385i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6275.72 | + | 35591.4i | 0.000363487 | + | 0.00206144i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.45243e7 | − | 2.51569e7i | 0.835910 | − | 1.44784i | −0.0573777 | − | 0.998353i | \(-0.518274\pi\) |
0.893288 | − | 0.449486i | \(-0.148393\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.03985e7 | + | 3.78476e6i | 0.594675 | + | 0.216444i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.11817e6 | + | 5.40084e6i | 0.177198 | + | 0.306916i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.55587e7 | + | 2.14463e7i | 1.44330 | + | 1.21107i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 463087. | − | 2.62630e6i | 0.0259863 | − | 0.147376i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.83010e7 | −1.02054 | −0.510269 | − | 0.860015i | \(-0.670454\pi\) | ||||
−0.510269 | + | 0.860015i | \(0.670454\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.64997e6 | −0.368513 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −807815. | + | 4.58135e6i | −0.0444868 | + | 0.252297i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.82752e6 | + | 7.40717e6i | 0.483114 | + | 0.405381i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 426539. | + | 738787.i | 0.0231990 | + | 0.0401818i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.26131e7 | + | 4.59078e6i | 0.681769 | + | 0.248144i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.86634e6 | + | 3.23260e6i | −0.100258 | + | 0.173653i | −0.911791 | − | 0.410654i | \(-0.865300\pi\) |
0.811533 | + | 0.584307i | \(0.198634\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.06242e6 | − | 2.30391e7i | −0.216887 | − | 1.23003i | −0.877602 | − | 0.479390i | \(-0.840858\pi\) |
0.660715 | − | 0.750636i | \(-0.270253\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.07344e6 | − | 2.57892e6i | 0.163079 | − | 0.136840i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.14674e6 | − | 1.87326e6i | 0.271418 | − | 0.0987879i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.59798e6 | − | 89064.2i | 0.0837558 | − | 0.00466819i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.48189e7 | − | 5.39365e6i | 0.771982 | − | 0.280979i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.78767e6 | + | 1.50003e6i | −0.0925611 | + | 0.0776680i | −0.687894 | − | 0.725811i | \(-0.741465\pi\) |
0.595333 | + | 0.803479i | \(0.297020\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12536.8 | + | 71099.6i | 0.000645188 | + | 0.00365904i | 0.985129 | − | 0.171818i | \(-0.0549642\pi\) |
−0.984483 | + | 0.175477i | \(0.943853\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.03600e6 | + | 8.72261e6i | −0.257603 | + | 0.446181i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.63894e7 | − | 9.60494e6i | −1.34173 | − | 0.488350i | −0.431373 | − | 0.902174i | \(-0.641971\pi\) |
−0.910357 | + | 0.413824i | \(0.864193\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.65912e7 | − | 2.87368e7i | −0.838478 | − | 1.45229i | −0.891167 | − | 0.453675i | \(-0.850113\pi\) |
0.0526892 | − | 0.998611i | \(-0.483221\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.13479e7 | − | 9.52198e6i | −0.570048 | − | 0.478327i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −224715. | + | 1.27442e6i | −0.0112207 | + | 0.0636357i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.21085e6 | 0.209003 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.18071e6 | −0.107593 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.87283e6 | + | 1.06213e7i | −0.0918530 | + | 0.520924i | 0.903813 | + | 0.427927i | \(0.140756\pi\) |
−0.995666 | + | 0.0929975i | \(0.970355\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.75918e7 | + | 1.47613e7i | 0.857670 | + | 0.719670i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.03726e6 | + | 1.79658e6i | 0.0502710 | + | 0.0870720i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 716268. | + | 260700.i | 0.0345091 | + | 0.0125603i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −654859. | + | 1.13425e6i | −0.0313646 | + | 0.0543250i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.15743e6 | + | 1.79067e7i | 0.150337 | + | 0.852601i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.77556e6 | + | 3.16807e6i | −0.178714 | + | 0.149959i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.18539e7 | + | 4.31448e6i | −0.557815 | + | 0.203028i | −0.605515 | − | 0.795834i | \(-0.707033\pi\) |
0.0477006 | + | 0.998862i | \(0.484811\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.94468e6 | − | 889604.i | −0.137760 | − | 0.0416180i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.54596e6 | − | 3.47444e6i | 0.443984 | − | 0.161597i | −0.110347 | − | 0.993893i | \(-0.535196\pi\) |
0.554331 | + | 0.832296i | \(0.312974\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.22368e6 | − | 1.02679e6i | 0.0565828 | − | 0.0474786i | −0.614058 | − | 0.789261i | \(-0.710464\pi\) |
0.670640 | + | 0.741783i | \(0.266019\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.28691e6 | + | 1.86410e7i | 0.151106 | + | 0.856962i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.13172e7 | + | 1.96020e7i | −0.517265 | + | 0.895929i | 0.482534 | + | 0.875877i | \(0.339717\pi\) |
−0.999799 | + | 0.0200520i | \(0.993617\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.39323e6 | + | 1.96298e6i | 0.245081 | + | 0.0892020i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.47269e6 | + | 9.47898e6i | 0.247260 | + | 0.428266i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.64678e6 | − | 7.25551e6i | −0.388423 | − | 0.325926i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.13268e6 | − | 2.34376e7i | 0.184581 | − | 1.04681i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.43523e6 | 0.108144 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00742e7 | −0.444828 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.63706e6 | + | 2.62981e7i | −0.203584 | + | 1.15458i | 0.696069 | + | 0.717975i | \(0.254931\pi\) |
−0.899652 | + | 0.436607i | \(0.856180\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.86197e6 | − | 4.91878e6i | −0.255901 | − | 0.214726i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.98917e6 | + | 1.38377e7i | 0.346786 | + | 0.600652i | 0.985677 | − | 0.168646i | \(-0.0539396\pi\) |
−0.638890 | + | 0.769298i | \(0.720606\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.36914e7 | + | 4.98325e6i | 0.590942 | + | 0.215085i | 0.620144 | − | 0.784488i | \(-0.287074\pi\) |
−0.0292017 | + | 0.999574i | \(0.509297\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.00675e6 | + | 1.74375e6i | −0.0432081 | + | 0.0748387i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.44258e6 | − | 1.95239e7i | −0.146918 | − | 0.833214i | −0.965807 | − | 0.259262i | \(-0.916521\pi\) |
0.818889 | − | 0.573952i | \(-0.194590\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.67818e7 | + | 2.24726e7i | −1.13654 | + | 0.953672i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.71544e6 | − | 1.35231e6i | 0.156789 | − | 0.0570666i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.45247e7 | + | 1.05063e7i | −1.02914 | + | 0.440880i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.19571e6 | + | 1.16314e6i | −0.133355 | + | 0.0485372i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.26675e6 | − | 1.90203e6i | 0.0940638 | − | 0.0789289i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −702251. | − | 3.98266e6i | −0.0289797 | − | 0.164352i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.20644e6 | + | 9.01782e6i | −0.213663 | + | 0.370075i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.17166e6 | + | 426448.i | 0.0478168 | + | 0.0174039i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.21652e6 | − | 3.83912e6i | −0.0899601 | − | 0.155816i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.66921e7 | − | 2.23973e7i | −1.07737 | − | 0.904019i | −0.0816678 | − | 0.996660i | \(-0.526025\pi\) |
−0.995700 | + | 0.0926410i | \(0.970469\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.87060e6 | + | 1.62800e7i | −0.115229 | + | 0.653498i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.94250e7 | −0.775471 | −0.387735 | − | 0.921771i | \(-0.626743\pi\) | ||||
−0.387735 | + | 0.921771i | \(0.626743\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.87384e7 | −1.14100 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 880436. | − | 4.99320e6i | 0.0347652 | − | 0.197163i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.20536e7 | − | 2.68962e7i | −1.25879 | − | 1.05625i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.36621e7 | + | 2.36634e7i | 0.533614 | + | 0.924247i | 0.999229 | + | 0.0392595i | \(0.0124999\pi\) |
−0.465615 | + | 0.884988i | \(0.654167\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.91729e6 | + | 697835.i | 0.0744797 | + | 0.0271084i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.23618e6 | + | 1.42655e7i | −0.318216 | + | 0.551166i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.94194e6 | − | 2.80271e7i | −0.189908 | − | 1.07702i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.35720e7 | − | 1.13883e7i | 0.518735 | − | 0.435270i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.70740e7 | − | 6.21442e6i | 0.649075 | − | 0.236244i | 0.00356274 | − | 0.999994i | \(-0.498866\pi\) |
0.645513 | + | 0.763749i | \(0.276644\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.18472e6 | + | 5.05502e6i | 0.0447964 | + | 0.191139i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.72184e7 | − | 6.26699e6i | 0.647574 | − | 0.235697i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.36009e6 | + | 1.14125e6i | −0.0508791 | + | 0.0426927i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.97107e6 | + | 4.52062e7i | 0.296597 | + | 1.68209i | 0.660638 | + | 0.750705i | \(0.270286\pi\) |
−0.364041 | + | 0.931383i | \(0.618603\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.90679e6 | + | 1.54270e7i | −0.329653 | + | 0.570976i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.87085e6 | + | 1.40887e6i | 0.142506 | + | 0.0518679i | 0.412288 | − | 0.911053i | \(-0.364730\pi\) |
−0.269783 | + | 0.962921i | \(0.586952\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.99767e6 | − | 6.92417e6i | −0.146396 | − | 0.253564i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.48713e6 | − | 3.76515e6i | −0.163451 | − | 0.137152i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.28310e6 | + | 4.13045e7i | −0.263901 | + | 1.49666i | 0.508245 | + | 0.861213i | \(0.330295\pi\) |
−0.772146 | + | 0.635445i | \(0.780817\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.95487e7 | 0.704617 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.83448e7 | 1.01630 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.14225e6 | + | 4.61770e7i | −0.290410 | + | 1.64700i | 0.394883 | + | 0.918731i | \(0.370785\pi\) |
−0.685294 | + | 0.728267i | \(0.740326\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −960580. | − | 806022.i | −0.0340820 | − | 0.0285982i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.11054e7 | − | 1.92352e7i | −0.391972 | − | 0.678916i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.84926e7 | − | 1.40101e7i | −1.35154 | − | 0.491922i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.41265e7 | − | 2.44678e7i | 0.493430 | − | 0.854646i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.85613e6 | − | 1.05267e7i | −0.0644976 | − | 0.365784i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.47415e6 | + | 5.43246e6i | −0.223802 | + | 0.187792i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.76089e7 | − | 1.73282e7i | 1.63728 | − | 0.595920i | 0.650717 | − | 0.759320i | \(-0.274468\pi\) |
0.986560 | + | 0.163400i | \(0.0522460\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.27181e6 | − | 3.19687e6i | −0.146151 | − | 0.109375i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.54102e7 | − | 9.24856e6i | 0.864889 | − | 0.314794i | 0.128793 | − | 0.991671i | \(-0.458890\pi\) |
0.736095 | + | 0.676878i | \(0.236667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.22576e7 | − | 3.54584e7i | 1.43095 | − | 1.20071i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.96702e6 | + | 1.68268e7i | 0.0999559 | + | 0.566878i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.21791e7 | + | 3.84154e7i | −0.743375 | + | 1.28756i | 0.207575 | + | 0.978219i | \(0.433443\pi\) |
−0.950950 | + | 0.309345i | \(0.899890\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.01231e7 | + | 3.68449e6i | 0.337563 | + | 0.122863i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.10131e6 | − | 1.90752e6i | −0.0365372 | − | 0.0632844i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.92569e7 | − | 1.61584e7i | −0.635626 | − | 0.533354i | 0.267045 | − | 0.963684i | \(-0.413953\pi\) |
−0.902672 | + | 0.430330i | \(0.858397\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −987901. | + | 5.60266e6i | −0.0324431 | + | 0.183994i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.07856e7 | −0.679156 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −526663. | −0.0171215 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.93327e6 | + | 2.79780e7i | −0.159570 | + | 0.904965i | 0.794918 | + | 0.606716i | \(0.207514\pi\) |
−0.954488 | + | 0.298249i | \(0.903597\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.45697e7 | − | 1.22255e7i | −0.468898 | − | 0.393452i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.19348e6 | + | 3.79921e6i | 0.0702385 | + | 0.121657i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.88890e7 | + | 1.05147e7i | 0.920437 | + | 0.335012i | 0.758412 | − | 0.651775i | \(-0.225975\pi\) |
0.162025 | + | 0.986787i | \(0.448198\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.69209e7 | − | 2.93079e7i | 0.536426 | − | 0.929117i |
(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 | 76.6.i.a.5.5 | ✓ | 48 | |
19.4 | even | 9 | inner | 76.6.i.a.61.5 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.i.a.5.5 | ✓ | 48 | 1.1 | even | 1 | trivial | |
76.6.i.a.61.5 | yes | 48 | 19.4 | even | 9 | inner |