Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,8,Mod(1,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.a (trivial) |
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: | yes |
Analytic conductor: | \(21.5545667584\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 466x^{4} + 540x^{3} + 48973x^{2} - 77282x - 1061812 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-4.35108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.35108 | 0.296196 | 0.148098 | − | 0.988973i | \(-0.452685\pi\) | ||||
0.148098 | + | 0.988973i | \(0.452685\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | −116.770 | −0.912268 | ||||||||
\(5\) | 0.849066 | 0.00303771 | 0.00151886 | − | 0.999999i | \(-0.499517\pi\) | ||||
0.00151886 | + | 0.999999i | \(0.499517\pi\) | |||||||
\(6\) | 90.4791 | 0.171009 | ||||||||
\(7\) | 405.736 | 0.447095 | 0.223548 | − | 0.974693i | \(-0.428236\pi\) | ||||
0.223548 | + | 0.974693i | \(0.428236\pi\) | |||||||
\(8\) | −820.245 | −0.566407 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 2.84529 | 0.000899759 0 | ||||||||
\(11\) | 2663.62 | 0.603389 | 0.301695 | − | 0.953405i | \(-0.402448\pi\) | ||||
0.301695 | + | 0.953405i | \(0.402448\pi\) | |||||||
\(12\) | −3152.80 | −0.526698 | ||||||||
\(13\) | −9506.50 | −1.20010 | −0.600052 | − | 0.799961i | \(-0.704854\pi\) | ||||
−0.600052 | + | 0.799961i | \(0.704854\pi\) | |||||||
\(14\) | 1359.65 | 0.132428 | ||||||||
\(15\) | 22.9248 | 0.00175382 | ||||||||
\(16\) | 12197.9 | 0.744500 | ||||||||
\(17\) | −36191.1 | −1.78661 | −0.893306 | − | 0.449448i | \(-0.851621\pi\) | ||||
−0.893306 | + | 0.449448i | \(0.851621\pi\) | |||||||
\(18\) | 2442.94 | 0.0987321 | ||||||||
\(19\) | −35806.9 | −1.19765 | −0.598824 | − | 0.800881i | \(-0.704365\pi\) | ||||
−0.598824 | + | 0.800881i | \(0.704365\pi\) | |||||||
\(20\) | −99.1457 | −0.00277121 | ||||||||
\(21\) | 10954.9 | 0.258131 | ||||||||
\(22\) | 8925.99 | 0.178722 | ||||||||
\(23\) | −12167.0 | −0.208514 | ||||||||
\(24\) | −22146.6 | −0.327015 | ||||||||
\(25\) | −78124.3 | −0.999991 | ||||||||
\(26\) | −31857.0 | −0.355467 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | −47377.9 | −0.407871 | ||||||||
\(29\) | 128430. | 0.977855 | 0.488927 | − | 0.872325i | \(-0.337388\pi\) | ||||
0.488927 | + | 0.872325i | \(0.337388\pi\) | |||||||
\(30\) | 76.8228 | 0.000519476 0 | ||||||||
\(31\) | −32645.9 | −0.196817 | −0.0984085 | − | 0.995146i | \(-0.531375\pi\) | ||||
−0.0984085 | + | 0.995146i | \(0.531375\pi\) | |||||||
\(32\) | 145867. | 0.786925 | ||||||||
\(33\) | 71917.7 | 0.348367 | ||||||||
\(34\) | −121279. | −0.529188 | ||||||||
\(35\) | 344.497 | 0.00135815 | ||||||||
\(36\) | −85125.5 | −0.304089 | ||||||||
\(37\) | −583405. | −1.89349 | −0.946747 | − | 0.321978i | \(-0.895652\pi\) | ||||
−0.946747 | + | 0.321978i | \(0.895652\pi\) | |||||||
\(38\) | −119992. | −0.354739 | ||||||||
\(39\) | −256676. | −0.692881 | ||||||||
\(40\) | −696.442 | −0.00172058 | ||||||||
\(41\) | −756639. | −1.71453 | −0.857266 | − | 0.514874i | \(-0.827839\pi\) | ||||
−0.857266 | + | 0.514874i | \(0.827839\pi\) | |||||||
\(42\) | 36710.6 | 0.0764573 | ||||||||
\(43\) | 769827. | 1.47657 | 0.738284 | − | 0.674490i | \(-0.235636\pi\) | ||||
0.738284 | + | 0.674490i | \(0.235636\pi\) | |||||||
\(44\) | −311031. | −0.550452 | ||||||||
\(45\) | 618.969 | 0.00101257 | ||||||||
\(46\) | −40772.6 | −0.0617612 | ||||||||
\(47\) | −84751.0 | −0.119070 | −0.0595350 | − | 0.998226i | \(-0.518962\pi\) | ||||
−0.0595350 | + | 0.998226i | \(0.518962\pi\) | |||||||
\(48\) | 329343. | 0.429837 | ||||||||
\(49\) | −658922. | −0.800106 | ||||||||
\(50\) | −261801. | −0.296194 | ||||||||
\(51\) | −977159. | −1.03150 | ||||||||
\(52\) | 1.11008e6 | 1.09482 | ||||||||
\(53\) | −52581.8 | −0.0485143 | −0.0242572 | − | 0.999706i | \(-0.507722\pi\) | ||||
−0.0242572 | + | 0.999706i | \(0.507722\pi\) | |||||||
\(54\) | 65959.3 | 0.0570030 | ||||||||
\(55\) | 2261.59 | 0.00183292 | ||||||||
\(56\) | −332803. | −0.253238 | ||||||||
\(57\) | −966787. | −0.691462 | ||||||||
\(58\) | 430380. | 0.289637 | ||||||||
\(59\) | 2.26778e6 | 1.43753 | 0.718767 | − | 0.695251i | \(-0.244707\pi\) | ||||
0.718767 | + | 0.695251i | \(0.244707\pi\) | |||||||
\(60\) | −2676.93 | −0.00159996 | ||||||||
\(61\) | 1.62312e6 | 0.915578 | 0.457789 | − | 0.889061i | \(-0.348642\pi\) | ||||
0.457789 | + | 0.889061i | \(0.348642\pi\) | |||||||
\(62\) | −109399. | −0.0582965 | ||||||||
\(63\) | 295781. | 0.149032 | ||||||||
\(64\) | −1.07252e6 | −0.511416 | ||||||||
\(65\) | −8071.65 | −0.00364557 | ||||||||
\(66\) | 241002. | 0.103185 | ||||||||
\(67\) | 2.11923e6 | 0.860827 | 0.430414 | − | 0.902632i | \(-0.358368\pi\) | ||||
0.430414 | + | 0.902632i | \(0.358368\pi\) | |||||||
\(68\) | 4.22604e6 | 1.62987 | ||||||||
\(69\) | −328509. | −0.120386 | ||||||||
\(70\) | 1154.44 | 0.000402278 0 | ||||||||
\(71\) | −4.91652e6 | −1.63025 | −0.815124 | − | 0.579286i | \(-0.803331\pi\) | ||||
−0.815124 | + | 0.579286i | \(0.803331\pi\) | |||||||
\(72\) | −597958. | −0.188802 | ||||||||
\(73\) | 3.45746e6 | 1.04022 | 0.520112 | − | 0.854098i | \(-0.325890\pi\) | ||||
0.520112 | + | 0.854098i | \(0.325890\pi\) | |||||||
\(74\) | −1.95504e6 | −0.560846 | ||||||||
\(75\) | −2.10936e6 | −0.577345 | ||||||||
\(76\) | 4.18118e6 | 1.09258 | ||||||||
\(77\) | 1.08072e6 | 0.269772 | ||||||||
\(78\) | −860140. | −0.205229 | ||||||||
\(79\) | 2.91026e6 | 0.664106 | 0.332053 | − | 0.943261i | \(-0.392259\pi\) | ||||
0.332053 | + | 0.943261i | \(0.392259\pi\) | |||||||
\(80\) | 10356.8 | 0.00226158 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −2.53556e6 | −0.507838 | ||||||||
\(83\) | 1.88250e6 | 0.361379 | 0.180689 | − | 0.983540i | \(-0.442167\pi\) | ||||
0.180689 | + | 0.983540i | \(0.442167\pi\) | |||||||
\(84\) | −1.27920e6 | −0.235484 | ||||||||
\(85\) | −30728.6 | −0.00542721 | ||||||||
\(86\) | 2.57975e6 | 0.437354 | ||||||||
\(87\) | 3.46762e6 | 0.564565 | ||||||||
\(88\) | −2.18482e6 | −0.341764 | ||||||||
\(89\) | −234356. | −0.0352380 | −0.0176190 | − | 0.999845i | \(-0.505609\pi\) | ||||
−0.0176190 | + | 0.999845i | \(0.505609\pi\) | |||||||
\(90\) | 2074.22 | 0.000299920 0 | ||||||||
\(91\) | −3.85713e6 | −0.536561 | ||||||||
\(92\) | 1.42074e6 | 0.190221 | ||||||||
\(93\) | −881439. | −0.113632 | ||||||||
\(94\) | −284007. | −0.0352681 | ||||||||
\(95\) | −30402.4 | −0.00363811 | ||||||||
\(96\) | 3.93842e6 | 0.454331 | ||||||||
\(97\) | 1.52882e7 | 1.70081 | 0.850405 | − | 0.526128i | \(-0.176357\pi\) | ||||
0.850405 | + | 0.526128i | \(0.176357\pi\) | |||||||
\(98\) | −2.20810e6 | −0.236988 | ||||||||
\(99\) | 1.94178e6 | 0.201130 | ||||||||
\(100\) | 9.12259e6 | 0.912259 | ||||||||
\(101\) | −1.36904e7 | −1.32218 | −0.661090 | − | 0.750307i | \(-0.729906\pi\) | ||||
−0.661090 | + | 0.750307i | \(0.729906\pi\) | |||||||
\(102\) | −3.27454e6 | −0.305527 | ||||||||
\(103\) | 5.79120e6 | 0.522202 | 0.261101 | − | 0.965311i | \(-0.415914\pi\) | ||||
0.261101 | + | 0.965311i | \(0.415914\pi\) | |||||||
\(104\) | 7.79766e6 | 0.679747 | ||||||||
\(105\) | 9301.41 | 0.000784126 0 | ||||||||
\(106\) | −176206. | −0.0143698 | ||||||||
\(107\) | 7.59691e6 | 0.599506 | 0.299753 | − | 0.954017i | \(-0.403096\pi\) | ||||
0.299753 | + | 0.954017i | \(0.403096\pi\) | |||||||
\(108\) | −2.29839e6 | −0.175566 | ||||||||
\(109\) | 6.28572e6 | 0.464903 | 0.232452 | − | 0.972608i | \(-0.425325\pi\) | ||||
0.232452 | + | 0.972608i | \(0.425325\pi\) | |||||||
\(110\) | 7578.76 | 0.000542905 0 | ||||||||
\(111\) | −1.57519e7 | −1.09321 | ||||||||
\(112\) | 4.94912e6 | 0.332862 | ||||||||
\(113\) | −2.80396e7 | −1.82809 | −0.914044 | − | 0.405615i | \(-0.867057\pi\) | ||||
−0.914044 | + | 0.405615i | \(0.867057\pi\) | |||||||
\(114\) | −3.23978e6 | −0.204809 | ||||||||
\(115\) | −10330.6 | −0.000633407 0 | ||||||||
\(116\) | −1.49968e7 | −0.892065 | ||||||||
\(117\) | −6.93024e6 | −0.400035 | ||||||||
\(118\) | 7.59950e6 | 0.425792 | ||||||||
\(119\) | −1.46840e7 | −0.798786 | ||||||||
\(120\) | −18803.9 | −0.000993378 0 | ||||||||
\(121\) | −1.23923e7 | −0.635922 | ||||||||
\(122\) | 5.43919e6 | 0.271191 | ||||||||
\(123\) | −2.04293e7 | −0.989885 | ||||||||
\(124\) | 3.81207e6 | 0.179550 | ||||||||
\(125\) | −132666. | −0.00607540 | ||||||||
\(126\) | 991187. | 0.0441427 | ||||||||
\(127\) | −3.71325e7 | −1.60858 | −0.804288 | − | 0.594239i | \(-0.797453\pi\) | ||||
−0.804288 | + | 0.594239i | \(0.797453\pi\) | |||||||
\(128\) | −2.22651e7 | −0.938404 | ||||||||
\(129\) | 2.07853e7 | 0.852497 | ||||||||
\(130\) | −27048.7 | −0.00107981 | ||||||||
\(131\) | 4.87971e6 | 0.189646 | 0.0948232 | − | 0.995494i | \(-0.469771\pi\) | ||||
0.0948232 | + | 0.995494i | \(0.469771\pi\) | |||||||
\(132\) | −8.39785e6 | −0.317804 | ||||||||
\(133\) | −1.45281e7 | −0.535463 | ||||||||
\(134\) | 7.10170e6 | 0.254974 | ||||||||
\(135\) | 16712.2 | 0.000584608 0 | ||||||||
\(136\) | 2.96855e7 | 1.01195 | ||||||||
\(137\) | −3.10114e7 | −1.03038 | −0.515192 | − | 0.857075i | \(-0.672279\pi\) | ||||
−0.515192 | + | 0.857075i | \(0.672279\pi\) | |||||||
\(138\) | −1.10086e6 | −0.0356579 | ||||||||
\(139\) | 4.11634e7 | 1.30005 | 0.650024 | − | 0.759914i | \(-0.274759\pi\) | ||||
0.650024 | + | 0.759914i | \(0.274759\pi\) | |||||||
\(140\) | −40227.0 | −0.00123899 | ||||||||
\(141\) | −2.28828e6 | −0.0687451 | ||||||||
\(142\) | −1.64757e7 | −0.482874 | ||||||||
\(143\) | −2.53217e7 | −0.724130 | ||||||||
\(144\) | 8.89226e6 | 0.248167 | ||||||||
\(145\) | 109046. | 0.00297044 | ||||||||
\(146\) | 1.15862e7 | 0.308110 | ||||||||
\(147\) | −1.77909e7 | −0.461941 | ||||||||
\(148\) | 6.81243e7 | 1.72737 | ||||||||
\(149\) | −5.31056e7 | −1.31519 | −0.657594 | − | 0.753372i | \(-0.728426\pi\) | ||||
−0.657594 | + | 0.753372i | \(0.728426\pi\) | |||||||
\(150\) | −7.06862e6 | −0.171007 | ||||||||
\(151\) | 4.43931e7 | 1.04929 | 0.524646 | − | 0.851320i | \(-0.324198\pi\) | ||||
0.524646 | + | 0.851320i | \(0.324198\pi\) | |||||||
\(152\) | 2.93704e7 | 0.678356 | ||||||||
\(153\) | −2.63833e7 | −0.595538 | ||||||||
\(154\) | 3.62159e6 | 0.0799056 | ||||||||
\(155\) | −27718.5 | −0.000597873 0 | ||||||||
\(156\) | 2.99721e7 | 0.632093 | ||||||||
\(157\) | −8.18134e7 | −1.68723 | −0.843617 | − | 0.536945i | \(-0.819578\pi\) | ||||
−0.843617 | + | 0.536945i | \(0.819578\pi\) | |||||||
\(158\) | 9.75252e6 | 0.196706 | ||||||||
\(159\) | −1.41971e6 | −0.0280098 | ||||||||
\(160\) | 123851. | 0.00239045 | ||||||||
\(161\) | −4.93659e6 | −0.0932258 | ||||||||
\(162\) | 1.78090e6 | 0.0329107 | ||||||||
\(163\) | 8.21430e7 | 1.48564 | 0.742820 | − | 0.669491i | \(-0.233488\pi\) | ||||
0.742820 | + | 0.669491i | \(0.233488\pi\) | |||||||
\(164\) | 8.83530e7 | 1.56411 | ||||||||
\(165\) | 61062.9 | 0.00105824 | ||||||||
\(166\) | 6.30842e6 | 0.107039 | ||||||||
\(167\) | 7.89460e7 | 1.31166 | 0.655831 | − | 0.754907i | \(-0.272318\pi\) | ||||
0.655831 | + | 0.754907i | \(0.272318\pi\) | |||||||
\(168\) | −8.98567e6 | −0.146207 | ||||||||
\(169\) | 2.76251e7 | 0.440251 | ||||||||
\(170\) | −102974. | −0.00160752 | ||||||||
\(171\) | −2.61032e7 | −0.399216 | ||||||||
\(172\) | −8.98929e7 | −1.34703 | ||||||||
\(173\) | 9.10823e7 | 1.33744 | 0.668718 | − | 0.743517i | \(-0.266844\pi\) | ||||
0.668718 | + | 0.743517i | \(0.266844\pi\) | |||||||
\(174\) | 1.16203e7 | 0.167222 | ||||||||
\(175\) | −3.16978e7 | −0.447091 | ||||||||
\(176\) | 3.24905e7 | 0.449223 | ||||||||
\(177\) | 6.12300e7 | 0.829961 | ||||||||
\(178\) | −785346. | −0.0104374 | ||||||||
\(179\) | −1.15252e8 | −1.50197 | −0.750985 | − | 0.660319i | \(-0.770421\pi\) | ||||
−0.750985 | + | 0.660319i | \(0.770421\pi\) | |||||||
\(180\) | −72277.2 | −0.000923736 0 | ||||||||
\(181\) | 4.18769e6 | 0.0524927 | 0.0262464 | − | 0.999656i | \(-0.491645\pi\) | ||||
0.0262464 | + | 0.999656i | \(0.491645\pi\) | |||||||
\(182\) | −1.29255e7 | −0.158927 | ||||||||
\(183\) | 4.38241e7 | 0.528609 | ||||||||
\(184\) | 9.97992e6 | 0.118104 | ||||||||
\(185\) | −495349. | −0.00575189 | ||||||||
\(186\) | −2.95377e6 | −0.0336575 | ||||||||
\(187\) | −9.63992e7 | −1.07802 | ||||||||
\(188\) | 9.89639e6 | 0.108624 | ||||||||
\(189\) | 7.98610e6 | 0.0860435 | ||||||||
\(190\) | −101881. | −0.00107759 | ||||||||
\(191\) | −1.27500e7 | −0.132402 | −0.0662010 | − | 0.997806i | \(-0.521088\pi\) | ||||
−0.0662010 | + | 0.997806i | \(0.521088\pi\) | |||||||
\(192\) | −2.89579e7 | −0.295266 | ||||||||
\(193\) | −3.88747e7 | −0.389240 | −0.194620 | − | 0.980879i | \(-0.562347\pi\) | ||||
−0.194620 | + | 0.980879i | \(0.562347\pi\) | |||||||
\(194\) | 5.12321e7 | 0.503774 | ||||||||
\(195\) | −217935. | −0.00210477 | ||||||||
\(196\) | 7.69424e7 | 0.729911 | ||||||||
\(197\) | 7.01957e7 | 0.654152 | 0.327076 | − | 0.944998i | \(-0.393937\pi\) | ||||
0.327076 | + | 0.944998i | \(0.393937\pi\) | |||||||
\(198\) | 6.50705e6 | 0.0595739 | ||||||||
\(199\) | 1.64934e7 | 0.148362 | 0.0741811 | − | 0.997245i | \(-0.476366\pi\) | ||||
0.0741811 | + | 0.997245i | \(0.476366\pi\) | |||||||
\(200\) | 6.40810e7 | 0.566402 | ||||||||
\(201\) | 5.72192e7 | 0.496999 | ||||||||
\(202\) | −4.58775e7 | −0.391625 | ||||||||
\(203\) | 5.21087e7 | 0.437194 | ||||||||
\(204\) | 1.14103e8 | 0.941005 | ||||||||
\(205\) | −642437. | −0.00520825 | ||||||||
\(206\) | 1.94068e7 | 0.154674 | ||||||||
\(207\) | −8.86974e6 | −0.0695048 | ||||||||
\(208\) | −1.15959e8 | −0.893478 | ||||||||
\(209\) | −9.53759e7 | −0.722648 | ||||||||
\(210\) | 31169.8 | 0.000232255 0 | ||||||||
\(211\) | −1.48167e8 | −1.08583 | −0.542917 | − | 0.839787i | \(-0.682680\pi\) | ||||
−0.542917 | + | 0.839787i | \(0.682680\pi\) | |||||||
\(212\) | 6.13999e6 | 0.0442581 | ||||||||
\(213\) | −1.32746e8 | −0.941224 | ||||||||
\(214\) | 2.54578e7 | 0.177571 | ||||||||
\(215\) | 653634. | 0.00448539 | ||||||||
\(216\) | −1.61449e7 | −0.109005 | ||||||||
\(217\) | −1.32456e7 | −0.0879959 | ||||||||
\(218\) | 2.10640e7 | 0.137703 | ||||||||
\(219\) | 9.33513e7 | 0.600573 | ||||||||
\(220\) | −264086. | −0.00167212 | ||||||||
\(221\) | 3.44051e8 | 2.14412 | ||||||||
\(222\) | −5.27860e7 | −0.323805 | ||||||||
\(223\) | 1.24032e8 | 0.748972 | 0.374486 | − | 0.927233i | \(-0.377819\pi\) | ||||
0.374486 | + | 0.927233i | \(0.377819\pi\) | |||||||
\(224\) | 5.91836e7 | 0.351830 | ||||||||
\(225\) | −5.69526e7 | −0.333330 | ||||||||
\(226\) | −9.39629e7 | −0.541473 | ||||||||
\(227\) | −3.44311e8 | −1.95371 | −0.976855 | − | 0.213902i | \(-0.931383\pi\) | ||||
−0.976855 | + | 0.213902i | \(0.931383\pi\) | |||||||
\(228\) | 1.12892e8 | 0.630799 | ||||||||
\(229\) | −1.13249e8 | −0.623177 | −0.311589 | − | 0.950217i | \(-0.600861\pi\) | ||||
−0.311589 | + | 0.950217i | \(0.600861\pi\) | |||||||
\(230\) | −34618.6 | −0.000187613 0 | ||||||||
\(231\) | 2.91796e7 | 0.155753 | ||||||||
\(232\) | −1.05344e8 | −0.553863 | ||||||||
\(233\) | −1.91098e8 | −0.989717 | −0.494859 | − | 0.868973i | \(-0.664780\pi\) | ||||
−0.494859 | + | 0.868973i | \(0.664780\pi\) | |||||||
\(234\) | −2.32238e7 | −0.118489 | ||||||||
\(235\) | −71959.2 | −0.000361700 0 | ||||||||
\(236\) | −2.64809e8 | −1.31142 | ||||||||
\(237\) | 7.85771e7 | 0.383422 | ||||||||
\(238\) | −4.92073e7 | −0.236598 | ||||||||
\(239\) | 3.38240e7 | 0.160263 | 0.0801313 | − | 0.996784i | \(-0.474466\pi\) | ||||
0.0801313 | + | 0.996784i | \(0.474466\pi\) | |||||||
\(240\) | 279634. | 0.00130572 | ||||||||
\(241\) | −1.53606e8 | −0.706883 | −0.353441 | − | 0.935457i | \(-0.614989\pi\) | ||||
−0.353441 | + | 0.935457i | \(0.614989\pi\) | |||||||
\(242\) | −4.15276e7 | −0.188358 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | −1.89532e8 | −0.835252 | ||||||||
\(245\) | −559468. | −0.00243049 | ||||||||
\(246\) | −6.84601e7 | −0.293200 | ||||||||
\(247\) | 3.40398e8 | 1.43730 | ||||||||
\(248\) | 2.67776e7 | 0.111478 | ||||||||
\(249\) | 5.08276e7 | 0.208642 | ||||||||
\(250\) | −444574. | −0.00179951 | ||||||||
\(251\) | 1.31841e8 | 0.526250 | 0.263125 | − | 0.964762i | \(-0.415247\pi\) | ||||
0.263125 | + | 0.964762i | \(0.415247\pi\) | |||||||
\(252\) | −3.45385e7 | −0.135957 | ||||||||
\(253\) | −3.24082e7 | −0.125815 | ||||||||
\(254\) | −1.24434e8 | −0.476454 | ||||||||
\(255\) | −829673. | −0.00313340 | ||||||||
\(256\) | 6.26700e7 | 0.233464 | ||||||||
\(257\) | 1.01425e8 | 0.372718 | 0.186359 | − | 0.982482i | \(-0.440331\pi\) | ||||
0.186359 | + | 0.982482i | \(0.440331\pi\) | |||||||
\(258\) | 6.96533e7 | 0.252507 | ||||||||
\(259\) | −2.36708e8 | −0.846572 | ||||||||
\(260\) | 942529. | 0.00332574 | ||||||||
\(261\) | 9.36256e7 | 0.325952 | ||||||||
\(262\) | 1.63523e7 | 0.0561726 | ||||||||
\(263\) | 3.14970e8 | 1.06764 | 0.533819 | − | 0.845599i | \(-0.320756\pi\) | ||||
0.533819 | + | 0.845599i | \(0.320756\pi\) | |||||||
\(264\) | −5.89901e7 | −0.197317 | ||||||||
\(265\) | −44645.5 | −0.000147373 0 | ||||||||
\(266\) | −4.86850e7 | −0.158602 | ||||||||
\(267\) | −6.32761e6 | −0.0203447 | ||||||||
\(268\) | −2.47463e8 | −0.785305 | ||||||||
\(269\) | 2.25334e8 | 0.705819 | 0.352909 | − | 0.935657i | \(-0.385192\pi\) | ||||
0.352909 | + | 0.935657i | \(0.385192\pi\) | |||||||
\(270\) | 56003.8 | 0.000173159 0 | ||||||||
\(271\) | 3.42841e7 | 0.104641 | 0.0523204 | − | 0.998630i | \(-0.483338\pi\) | ||||
0.0523204 | + | 0.998630i | \(0.483338\pi\) | |||||||
\(272\) | −4.41455e8 | −1.33013 | ||||||||
\(273\) | −1.04142e8 | −0.309784 | ||||||||
\(274\) | −1.03922e8 | −0.305196 | ||||||||
\(275\) | −2.08093e8 | −0.603384 | ||||||||
\(276\) | 3.83601e7 | 0.109824 | ||||||||
\(277\) | −3.88720e8 | −1.09890 | −0.549449 | − | 0.835527i | \(-0.685162\pi\) | ||||
−0.549449 | + | 0.835527i | \(0.685162\pi\) | |||||||
\(278\) | 1.37942e8 | 0.385070 | ||||||||
\(279\) | −2.37988e7 | −0.0656056 | ||||||||
\(280\) | −282571. | −0.000769263 0 | ||||||||
\(281\) | −2.65787e8 | −0.714597 | −0.357299 | − | 0.933990i | \(-0.616302\pi\) | ||||
−0.357299 | + | 0.933990i | \(0.616302\pi\) | |||||||
\(282\) | −7.66820e6 | −0.0203620 | ||||||||
\(283\) | 9.51931e7 | 0.249662 | 0.124831 | − | 0.992178i | \(-0.460161\pi\) | ||||
0.124831 | + | 0.992178i | \(0.460161\pi\) | |||||||
\(284\) | 5.74104e8 | 1.48722 | ||||||||
\(285\) | −820866. | −0.00210046 | ||||||||
\(286\) | −8.48550e7 | −0.214485 | ||||||||
\(287\) | −3.06996e8 | −0.766559 | ||||||||
\(288\) | 1.06337e8 | 0.262308 | ||||||||
\(289\) | 8.99456e8 | 2.19198 | ||||||||
\(290\) | 365421. | 0.000879834 0 | ||||||||
\(291\) | 4.12782e8 | 0.981964 | ||||||||
\(292\) | −4.03728e8 | −0.948962 | ||||||||
\(293\) | −2.36355e8 | −0.548944 | −0.274472 | − | 0.961595i | \(-0.588503\pi\) | ||||
−0.274472 | + | 0.961595i | \(0.588503\pi\) | |||||||
\(294\) | −5.96187e7 | −0.136825 | ||||||||
\(295\) | 1.92549e6 | 0.00436682 | ||||||||
\(296\) | 4.78535e8 | 1.07249 | ||||||||
\(297\) | 5.24280e7 | 0.116122 | ||||||||
\(298\) | −1.77961e8 | −0.389554 | ||||||||
\(299\) | 1.15666e8 | 0.250239 | ||||||||
\(300\) | 2.46310e8 | 0.526693 | ||||||||
\(301\) | 3.12346e8 | 0.660167 | ||||||||
\(302\) | 1.48765e8 | 0.310797 | ||||||||
\(303\) | −3.69640e8 | −0.763360 | ||||||||
\(304\) | −4.36769e8 | −0.891649 | ||||||||
\(305\) | 1.37813e6 | 0.00278126 | ||||||||
\(306\) | −8.84125e7 | −0.176396 | ||||||||
\(307\) | −4.36850e8 | −0.861684 | −0.430842 | − | 0.902427i | \(-0.641783\pi\) | ||||
−0.430842 | + | 0.902427i | \(0.641783\pi\) | |||||||
\(308\) | −1.26197e8 | −0.246105 | ||||||||
\(309\) | 1.56363e8 | 0.301493 | ||||||||
\(310\) | −92886.9 | −0.000177088 0 | ||||||||
\(311\) | −1.43706e8 | −0.270904 | −0.135452 | − | 0.990784i | \(-0.543249\pi\) | ||||
−0.135452 | + | 0.990784i | \(0.543249\pi\) | |||||||
\(312\) | 2.10537e8 | 0.392452 | ||||||||
\(313\) | 7.98141e8 | 1.47121 | 0.735605 | − | 0.677411i | \(-0.236898\pi\) | ||||
0.735605 | + | 0.677411i | \(0.236898\pi\) | |||||||
\(314\) | −2.74163e8 | −0.499753 | ||||||||
\(315\) | 251138. | 0.000452716 0 | ||||||||
\(316\) | −3.39832e8 | −0.605842 | ||||||||
\(317\) | 1.58206e8 | 0.278943 | 0.139472 | − | 0.990226i | \(-0.455460\pi\) | ||||
0.139472 | + | 0.990226i | \(0.455460\pi\) | |||||||
\(318\) | −4.75756e6 | −0.00829639 | ||||||||
\(319\) | 3.42089e8 | 0.590027 | ||||||||
\(320\) | −910638. | −0.00155353 | ||||||||
\(321\) | 2.05116e8 | 0.346125 | ||||||||
\(322\) | −1.65429e7 | −0.0276131 | ||||||||
\(323\) | 1.29589e9 | 2.13973 | ||||||||
\(324\) | −6.20565e7 | −0.101363 | ||||||||
\(325\) | 7.42689e8 | 1.20009 | ||||||||
\(326\) | 2.75268e8 | 0.440041 | ||||||||
\(327\) | 1.69714e8 | 0.268412 | ||||||||
\(328\) | 6.20629e8 | 0.971122 | ||||||||
\(329\) | −3.43865e7 | −0.0532356 | ||||||||
\(330\) | 204627. | 0.000313446 0 | ||||||||
\(331\) | 5.55118e8 | 0.841370 | 0.420685 | − | 0.907207i | \(-0.361790\pi\) | ||||
0.420685 | + | 0.907207i | \(0.361790\pi\) | |||||||
\(332\) | −2.19821e8 | −0.329674 | ||||||||
\(333\) | −4.25302e8 | −0.631165 | ||||||||
\(334\) | 2.64554e8 | 0.388510 | ||||||||
\(335\) | 1.79937e6 | 0.00261495 | ||||||||
\(336\) | 1.33626e8 | 0.192178 | ||||||||
\(337\) | −2.24145e8 | −0.319025 | −0.159512 | − | 0.987196i | \(-0.550992\pi\) | ||||
−0.159512 | + | 0.987196i | \(0.550992\pi\) | |||||||
\(338\) | 9.25738e7 | 0.130401 | ||||||||
\(339\) | −7.57069e8 | −1.05545 | ||||||||
\(340\) | 3.58819e6 | 0.00495107 | ||||||||
\(341\) | −8.69561e7 | −0.118757 | ||||||||
\(342\) | −8.74740e7 | −0.118246 | ||||||||
\(343\) | −6.01489e8 | −0.804819 | ||||||||
\(344\) | −6.31447e8 | −0.836339 | ||||||||
\(345\) | −278926. | −0.000365698 0 | ||||||||
\(346\) | 3.05224e8 | 0.396143 | ||||||||
\(347\) | 3.33457e7 | 0.0428437 | 0.0214219 | − | 0.999771i | \(-0.493181\pi\) | ||||
0.0214219 | + | 0.999771i | \(0.493181\pi\) | |||||||
\(348\) | −4.04915e8 | −0.515034 | ||||||||
\(349\) | 9.08225e8 | 1.14368 | 0.571840 | − | 0.820365i | \(-0.306230\pi\) | ||||
0.571840 | + | 0.820365i | \(0.306230\pi\) | |||||||
\(350\) | −1.06222e8 | −0.132427 | ||||||||
\(351\) | −1.87116e8 | −0.230960 | ||||||||
\(352\) | 3.88535e8 | 0.474822 | ||||||||
\(353\) | 3.91774e8 | 0.474051 | 0.237025 | − | 0.971503i | \(-0.423828\pi\) | ||||
0.237025 | + | 0.971503i | \(0.423828\pi\) | |||||||
\(354\) | 2.05186e8 | 0.245831 | ||||||||
\(355\) | −4.17445e6 | −0.00495222 | ||||||||
\(356\) | 2.73658e7 | 0.0321465 | ||||||||
\(357\) | −3.96468e8 | −0.461179 | ||||||||
\(358\) | −3.86217e8 | −0.444878 | ||||||||
\(359\) | −1.07880e9 | −1.23058 | −0.615288 | − | 0.788302i | \(-0.710960\pi\) | ||||
−0.615288 | + | 0.788302i | \(0.710960\pi\) | |||||||
\(360\) | −507706. | −0.000573527 0 | ||||||||
\(361\) | 3.88263e8 | 0.434361 | ||||||||
\(362\) | 1.40333e7 | 0.0155482 | ||||||||
\(363\) | −3.34592e8 | −0.367149 | ||||||||
\(364\) | 4.50398e8 | 0.489487 | ||||||||
\(365\) | 2.93561e6 | 0.00315990 | ||||||||
\(366\) | 1.46858e8 | 0.156572 | ||||||||
\(367\) | 1.24645e9 | 1.31626 | 0.658131 | − | 0.752903i | \(-0.271347\pi\) | ||||
0.658131 | + | 0.752903i | \(0.271347\pi\) | |||||||
\(368\) | −1.48412e8 | −0.155239 | ||||||||
\(369\) | −5.51590e8 | −0.571510 | ||||||||
\(370\) | −1.65996e6 | −0.00170369 | ||||||||
\(371\) | −2.13343e7 | −0.0216905 | ||||||||
\(372\) | 1.02926e8 | 0.103663 | ||||||||
\(373\) | 4.12114e8 | 0.411184 | 0.205592 | − | 0.978638i | \(-0.434088\pi\) | ||||
0.205592 | + | 0.978638i | \(0.434088\pi\) | |||||||
\(374\) | −3.23041e8 | −0.319306 | ||||||||
\(375\) | −3.58198e6 | −0.00350763 | ||||||||
\(376\) | 6.95165e7 | 0.0674420 | ||||||||
\(377\) | −1.22092e9 | −1.17353 | ||||||||
\(378\) | 2.67620e7 | 0.0254858 | ||||||||
\(379\) | −1.27834e9 | −1.20617 | −0.603085 | − | 0.797677i | \(-0.706062\pi\) | ||||
−0.603085 | + | 0.797677i | \(0.706062\pi\) | |||||||
\(380\) | 3.55010e6 | 0.00331893 | ||||||||
\(381\) | −1.00258e9 | −0.928712 | ||||||||
\(382\) | −4.27264e7 | −0.0392170 | ||||||||
\(383\) | −9.34297e8 | −0.849746 | −0.424873 | − | 0.905253i | \(-0.639681\pi\) | ||||
−0.424873 | + | 0.905253i | \(0.639681\pi\) | |||||||
\(384\) | −6.01158e8 | −0.541788 | ||||||||
\(385\) | 917607. | 0.000819491 0 | ||||||||
\(386\) | −1.30272e8 | −0.115291 | ||||||||
\(387\) | 5.61204e8 | 0.492190 | ||||||||
\(388\) | −1.78521e9 | −1.55159 | ||||||||
\(389\) | 3.03608e8 | 0.261511 | 0.130755 | − | 0.991415i | \(-0.458260\pi\) | ||||
0.130755 | + | 0.991415i | \(0.458260\pi\) | |||||||
\(390\) | −730316. | −0.000623426 0 | ||||||||
\(391\) | 4.40337e8 | 0.372534 | ||||||||
\(392\) | 5.40477e8 | 0.453185 | ||||||||
\(393\) | 1.31752e8 | 0.109492 | ||||||||
\(394\) | 2.35231e8 | 0.193757 | ||||||||
\(395\) | 2.47100e6 | 0.00201736 | ||||||||
\(396\) | −2.26742e8 | −0.183484 | ||||||||
\(397\) | −4.05735e8 | −0.325443 | −0.162722 | − | 0.986672i | \(-0.552027\pi\) | ||||
−0.162722 | + | 0.986672i | \(0.552027\pi\) | |||||||
\(398\) | 5.52706e7 | 0.0439444 | ||||||||
\(399\) | −3.92260e8 | −0.309150 | ||||||||
\(400\) | −9.52951e8 | −0.744493 | ||||||||
\(401\) | −8.42816e8 | −0.652721 | −0.326360 | − | 0.945245i | \(-0.605822\pi\) | ||||
−0.326360 | + | 0.945245i | \(0.605822\pi\) | |||||||
\(402\) | 1.91746e8 | 0.147209 | ||||||||
\(403\) | 3.10348e8 | 0.236201 | ||||||||
\(404\) | 1.59863e9 | 1.20618 | ||||||||
\(405\) | 451229. | 0.000337524 0 | ||||||||
\(406\) | 1.74621e8 | 0.129495 | ||||||||
\(407\) | −1.55397e9 | −1.14251 | ||||||||
\(408\) | 8.01510e8 | 0.584249 | ||||||||
\(409\) | 9.52820e8 | 0.688619 | 0.344310 | − | 0.938856i | \(-0.388113\pi\) | ||||
0.344310 | + | 0.938856i | \(0.388113\pi\) | |||||||
\(410\) | −2.15286e6 | −0.00154267 | ||||||||
\(411\) | −8.37308e8 | −0.594893 | ||||||||
\(412\) | −6.76240e8 | −0.476388 | ||||||||
\(413\) | 9.20118e8 | 0.642715 | ||||||||
\(414\) | −2.97232e7 | −0.0205871 | ||||||||
\(415\) | 1.59837e6 | 0.00109776 | ||||||||
\(416\) | −1.38669e9 | −0.944392 | ||||||||
\(417\) | 1.11141e9 | 0.750583 | ||||||||
\(418\) | −3.19612e8 | −0.214046 | ||||||||
\(419\) | −1.41758e9 | −0.941454 | −0.470727 | − | 0.882279i | \(-0.656008\pi\) | ||||
−0.470727 | + | 0.882279i | \(0.656008\pi\) | |||||||
\(420\) | −1.08613e6 | −0.000715333 0 | ||||||||
\(421\) | 1.59148e9 | 1.03948 | 0.519738 | − | 0.854326i | \(-0.326030\pi\) | ||||
0.519738 | + | 0.854326i | \(0.326030\pi\) | |||||||
\(422\) | −4.96520e8 | −0.321620 | ||||||||
\(423\) | −6.17835e7 | −0.0396900 | ||||||||
\(424\) | 4.31300e7 | 0.0274788 | ||||||||
\(425\) | 2.82740e9 | 1.78660 | ||||||||
\(426\) | −4.44843e8 | −0.278787 | ||||||||
\(427\) | 6.58556e8 | 0.409351 | ||||||||
\(428\) | −8.87093e8 | −0.546910 | ||||||||
\(429\) | −6.83686e8 | −0.418077 | ||||||||
\(430\) | 2.19038e6 | 0.00132856 | ||||||||
\(431\) | −2.04772e9 | −1.23197 | −0.615984 | − | 0.787759i | \(-0.711241\pi\) | ||||
−0.615984 | + | 0.787759i | \(0.711241\pi\) | |||||||
\(432\) | 2.40091e8 | 0.143279 | ||||||||
\(433\) | 1.15795e9 | 0.685458 | 0.342729 | − | 0.939434i | \(-0.388649\pi\) | ||||
0.342729 | + | 0.939434i | \(0.388649\pi\) | |||||||
\(434\) | −4.43870e7 | −0.0260641 | ||||||||
\(435\) | 2.94424e6 | 0.00171498 | ||||||||
\(436\) | −7.33985e8 | −0.424116 | ||||||||
\(437\) | 4.35663e8 | 0.249727 | ||||||||
\(438\) | 3.12828e8 | 0.177888 | ||||||||
\(439\) | 1.71302e8 | 0.0966356 | 0.0483178 | − | 0.998832i | \(-0.484614\pi\) | ||||
0.0483178 | + | 0.998832i | \(0.484614\pi\) | |||||||
\(440\) | −1.85506e6 | −0.00103818 | ||||||||
\(441\) | −4.80354e8 | −0.266702 | ||||||||
\(442\) | 1.15294e9 | 0.635081 | ||||||||
\(443\) | −2.01064e9 | −1.09881 | −0.549404 | − | 0.835557i | \(-0.685145\pi\) | ||||
−0.549404 | + | 0.835557i | \(0.685145\pi\) | |||||||
\(444\) | 1.83936e9 | 0.997300 | ||||||||
\(445\) | −198984. | −0.000107043 0 | ||||||||
\(446\) | 4.15640e8 | 0.221843 | ||||||||
\(447\) | −1.43385e9 | −0.759324 | ||||||||
\(448\) | −4.35158e8 | −0.228652 | ||||||||
\(449\) | 1.66574e9 | 0.868451 | 0.434225 | − | 0.900804i | \(-0.357022\pi\) | ||||
0.434225 | + | 0.900804i | \(0.357022\pi\) | |||||||
\(450\) | −1.90853e8 | −0.0987312 | ||||||||
\(451\) | −2.01540e9 | −1.03453 | ||||||||
\(452\) | 3.27419e9 | 1.66771 | ||||||||
\(453\) | 1.19861e9 | 0.605809 | ||||||||
\(454\) | −1.15381e9 | −0.578682 | ||||||||
\(455\) | −3.27496e6 | −0.00162992 | ||||||||
\(456\) | 7.93001e8 | 0.391649 | ||||||||
\(457\) | −1.76044e9 | −0.862811 | −0.431405 | − | 0.902158i | \(-0.641982\pi\) | ||||
−0.431405 | + | 0.902158i | \(0.641982\pi\) | |||||||
\(458\) | −3.79508e8 | −0.184583 | ||||||||
\(459\) | −7.12349e8 | −0.343834 | ||||||||
\(460\) | 1.20631e6 | 0.000577837 0 | ||||||||
\(461\) | −2.02454e9 | −0.962440 | −0.481220 | − | 0.876600i | \(-0.659806\pi\) | ||||
−0.481220 | + | 0.876600i | \(0.659806\pi\) | |||||||
\(462\) | 9.77831e7 | 0.0461335 | ||||||||
\(463\) | −2.65240e9 | −1.24196 | −0.620978 | − | 0.783828i | \(-0.713264\pi\) | ||||
−0.620978 | + | 0.783828i | \(0.713264\pi\) | |||||||
\(464\) | 1.56658e9 | 0.728013 | ||||||||
\(465\) | −748400. | −0.000345182 0 | ||||||||
\(466\) | −6.40386e8 | −0.293151 | ||||||||
\(467\) | 2.57500e9 | 1.16995 | 0.584977 | − | 0.811050i | \(-0.301103\pi\) | ||||
0.584977 | + | 0.811050i | \(0.301103\pi\) | |||||||
\(468\) | 8.09246e8 | 0.364939 | ||||||||
\(469\) | 8.59847e8 | 0.384872 | ||||||||
\(470\) | −241141. | −0.000107134 0 | ||||||||
\(471\) | −2.20896e9 | −0.974125 | ||||||||
\(472\) | −1.86013e9 | −0.814229 | ||||||||
\(473\) | 2.05053e9 | 0.890946 | ||||||||
\(474\) | 2.63318e8 | 0.113568 | ||||||||
\(475\) | 2.79739e9 | 1.19764 | ||||||||
\(476\) | 1.71466e9 | 0.728707 | ||||||||
\(477\) | −3.83321e7 | −0.0161714 | ||||||||
\(478\) | 1.13347e8 | 0.0474692 | ||||||||
\(479\) | −8.23862e8 | −0.342515 | −0.171258 | − | 0.985226i | \(-0.554783\pi\) | ||||
−0.171258 | + | 0.985226i | \(0.554783\pi\) | |||||||
\(480\) | 3.34398e6 | 0.00138013 | ||||||||
\(481\) | 5.54614e9 | 2.27239 | ||||||||
\(482\) | −5.14745e8 | −0.209376 | ||||||||
\(483\) | −1.33288e8 | −0.0538239 | ||||||||
\(484\) | 1.44705e9 | 0.580131 | ||||||||
\(485\) | 1.29807e7 | 0.00516657 | ||||||||
\(486\) | 4.80843e7 | 0.0190010 | ||||||||
\(487\) | 2.67396e9 | 1.04907 | 0.524533 | − | 0.851390i | \(-0.324240\pi\) | ||||
0.524533 | + | 0.851390i | \(0.324240\pi\) | |||||||
\(488\) | −1.33135e9 | −0.518589 | ||||||||
\(489\) | 2.21786e9 | 0.857735 | ||||||||
\(490\) | −1.87482e6 | −0.000719903 0 | ||||||||
\(491\) | −1.23865e9 | −0.472239 | −0.236120 | − | 0.971724i | \(-0.575876\pi\) | ||||
−0.236120 | + | 0.971724i | \(0.575876\pi\) | |||||||
\(492\) | 2.38553e9 | 0.903040 | ||||||||
\(493\) | −4.64803e9 | −1.74705 | ||||||||
\(494\) | 1.14070e9 | 0.425724 | ||||||||
\(495\) | 1.64870e6 | 0.000610974 0 | ||||||||
\(496\) | −3.98211e8 | −0.146530 | ||||||||
\(497\) | −1.99481e9 | −0.728876 | ||||||||
\(498\) | 1.70327e8 | 0.0617990 | ||||||||
\(499\) | −2.12672e9 | −0.766229 | −0.383115 | − | 0.923701i | \(-0.625149\pi\) | ||||
−0.383115 | + | 0.923701i | \(0.625149\pi\) | |||||||
\(500\) | 1.54914e7 | 0.00554239 | ||||||||
\(501\) | 2.13154e9 | 0.757289 | ||||||||
\(502\) | 4.41809e8 | 0.155873 | ||||||||
\(503\) | 2.18140e8 | 0.0764271 | 0.0382135 | − | 0.999270i | \(-0.487833\pi\) | ||||
0.0382135 | + | 0.999270i | \(0.487833\pi\) | |||||||
\(504\) | −2.42613e8 | −0.0844126 | ||||||||
\(505\) | −1.16240e7 | −0.00401640 | ||||||||
\(506\) | −1.08603e8 | −0.0372660 | ||||||||
\(507\) | 7.45877e8 | 0.254179 | ||||||||
\(508\) | 4.33598e9 | 1.46745 | ||||||||
\(509\) | 2.84720e9 | 0.956985 | 0.478492 | − | 0.878092i | \(-0.341183\pi\) | ||||
0.478492 | + | 0.878092i | \(0.341183\pi\) | |||||||
\(510\) | −2.78030e6 | −0.000928103 0 | ||||||||
\(511\) | 1.40281e9 | 0.465079 | ||||||||
\(512\) | 3.05995e9 | 1.00756 | ||||||||
\(513\) | −7.04787e8 | −0.230487 | ||||||||
\(514\) | 3.39884e8 | 0.110398 | ||||||||
\(515\) | 4.91712e6 | 0.00158630 | ||||||||
\(516\) | −2.42711e9 | −0.777706 | ||||||||
\(517\) | −2.25744e8 | −0.0718455 | ||||||||
\(518\) | −7.93228e8 | −0.250752 | ||||||||
\(519\) | 2.45922e9 | 0.772169 | ||||||||
\(520\) | 6.62073e6 | 0.00206488 | ||||||||
\(521\) | −3.03891e9 | −0.941426 | −0.470713 | − | 0.882286i | \(-0.656003\pi\) | ||||
−0.470713 | + | 0.882286i | \(0.656003\pi\) | |||||||
\(522\) | 3.13747e8 | 0.0965457 | ||||||||
\(523\) | −3.95904e8 | −0.121013 | −0.0605067 | − | 0.998168i | \(-0.519272\pi\) | ||||
−0.0605067 | + | 0.998168i | \(0.519272\pi\) | |||||||
\(524\) | −5.69805e8 | −0.173008 | ||||||||
\(525\) | −8.55841e8 | −0.258128 | ||||||||
\(526\) | 1.05549e9 | 0.316230 | ||||||||
\(527\) | 1.18149e9 | 0.351636 | ||||||||
\(528\) | 8.77244e8 | 0.259359 | ||||||||
\(529\) | 1.48036e8 | 0.0434783 | ||||||||
\(530\) | −149610. | −4.36512e−5 0 | ||||||||
\(531\) | 1.65321e9 | 0.479178 | ||||||||
\(532\) | 1.69645e9 | 0.488485 | ||||||||
\(533\) | 7.19299e9 | 2.05762 | ||||||||
\(534\) | −2.12043e7 | −0.00602601 | ||||||||
\(535\) | 6.45028e6 | 0.00182113 | ||||||||
\(536\) | −1.73829e9 | −0.487578 | ||||||||
\(537\) | −3.11179e9 | −0.867163 | ||||||||
\(538\) | 7.55111e8 | 0.209061 | ||||||||
\(539\) | −1.75512e9 | −0.482775 | ||||||||
\(540\) | −1.95148e6 | −0.000533319 0 | ||||||||
\(541\) | −5.18940e9 | −1.40905 | −0.704525 | − | 0.709679i | \(-0.748840\pi\) | ||||
−0.704525 | + | 0.709679i | \(0.748840\pi\) | |||||||
\(542\) | 1.14889e8 | 0.0309942 | ||||||||
\(543\) | 1.13068e8 | 0.0303067 | ||||||||
\(544\) | −5.27910e9 | −1.40593 | ||||||||
\(545\) | 5.33700e6 | 0.00141224 | ||||||||
\(546\) | −3.48990e8 | −0.0917568 | ||||||||
\(547\) | −7.01245e9 | −1.83195 | −0.915976 | − | 0.401232i | \(-0.868582\pi\) | ||||
−0.915976 | + | 0.401232i | \(0.868582\pi\) | |||||||
\(548\) | 3.62121e9 | 0.939987 | ||||||||
\(549\) | 1.18325e9 | 0.305193 | ||||||||
\(550\) | −6.97337e8 | −0.178720 | ||||||||
\(551\) | −4.59869e9 | −1.17113 | ||||||||
\(552\) | 2.69458e8 | 0.0681874 | ||||||||
\(553\) | 1.18080e9 | 0.296919 | ||||||||
\(554\) | −1.30263e9 | −0.325490 | ||||||||
\(555\) | −1.33744e7 | −0.00332086 | ||||||||
\(556\) | −4.80666e9 | −1.18599 | ||||||||
\(557\) | −2.56612e9 | −0.629193 | −0.314597 | − | 0.949225i | \(-0.601869\pi\) | ||||
−0.314597 | + | 0.949225i | \(0.601869\pi\) | |||||||
\(558\) | −7.97518e7 | −0.0194322 | ||||||||
\(559\) | −7.31836e9 | −1.77204 | ||||||||
\(560\) | 4.20213e6 | 0.00101114 | ||||||||
\(561\) | −2.60278e9 | −0.622397 | ||||||||
\(562\) | −8.90673e8 | −0.211661 | ||||||||
\(563\) | −8.98840e8 | −0.212277 | −0.106139 | − | 0.994351i | \(-0.533849\pi\) | ||||
−0.106139 | + | 0.994351i | \(0.533849\pi\) | |||||||
\(564\) | 2.67203e8 | 0.0627139 | ||||||||
\(565\) | −2.38075e7 | −0.00555320 | ||||||||
\(566\) | 3.18999e8 | 0.0739490 | ||||||||
\(567\) | 2.15625e8 | 0.0496773 | ||||||||
\(568\) | 4.03275e9 | 0.923384 | ||||||||
\(569\) | −3.86463e9 | −0.879458 | −0.439729 | − | 0.898130i | \(-0.644926\pi\) | ||||
−0.439729 | + | 0.898130i | \(0.644926\pi\) | |||||||
\(570\) | −2.75079e6 | −0.000622150 0 | ||||||||
\(571\) | 4.00586e9 | 0.900471 | 0.450235 | − | 0.892910i | \(-0.351340\pi\) | ||||
0.450235 | + | 0.892910i | \(0.351340\pi\) | |||||||
\(572\) | 2.95682e9 | 0.660600 | ||||||||
\(573\) | −3.44251e8 | −0.0764424 | ||||||||
\(574\) | −1.02877e9 | −0.227052 | ||||||||
\(575\) | 9.50538e8 | 0.208512 | ||||||||
\(576\) | −7.81865e8 | −0.170472 | ||||||||
\(577\) | −5.38283e9 | −1.16653 | −0.583264 | − | 0.812282i | \(-0.698225\pi\) | ||||
−0.583264 | + | 0.812282i | \(0.698225\pi\) | |||||||
\(578\) | 3.01415e9 | 0.649258 | ||||||||
\(579\) | −1.04962e9 | −0.224728 | ||||||||
\(580\) | −1.27333e7 | −0.00270984 | ||||||||
\(581\) | 7.63799e8 | 0.161571 | ||||||||
\(582\) | 1.38327e9 | 0.290854 | ||||||||
\(583\) | −1.40058e8 | −0.0292730 | ||||||||
\(584\) | −2.83596e9 | −0.589190 | ||||||||
\(585\) | −5.88423e6 | −0.00121519 | ||||||||
\(586\) | −7.92044e8 | −0.162595 | ||||||||
\(587\) | 4.39683e9 | 0.897234 | 0.448617 | − | 0.893724i | \(-0.351917\pi\) | ||||
0.448617 | + | 0.893724i | \(0.351917\pi\) | |||||||
\(588\) | 2.07745e9 | 0.421414 | ||||||||
\(589\) | 1.16895e9 | 0.235717 | ||||||||
\(590\) | 6.45248e6 | 0.00129343 | ||||||||
\(591\) | 1.89528e9 | 0.377675 | ||||||||
\(592\) | −7.11631e9 | −1.40971 | ||||||||
\(593\) | −1.78104e9 | −0.350737 | −0.175368 | − | 0.984503i | \(-0.556112\pi\) | ||||
−0.175368 | + | 0.984503i | \(0.556112\pi\) | |||||||
\(594\) | 1.75690e8 | 0.0343950 | ||||||||
\(595\) | −1.24677e7 | −0.00242648 | ||||||||
\(596\) | 6.20115e9 | 1.19980 | ||||||||
\(597\) | 4.45321e8 | 0.0856570 | ||||||||
\(598\) | 3.87605e8 | 0.0741199 | ||||||||
\(599\) | −3.87905e9 | −0.737449 | −0.368724 | − | 0.929539i | \(-0.620205\pi\) | ||||
−0.368724 | + | 0.929539i | \(0.620205\pi\) | |||||||
\(600\) | 1.73019e9 | 0.327012 | ||||||||
\(601\) | 3.87683e9 | 0.728478 | 0.364239 | − | 0.931305i | \(-0.381329\pi\) | ||||
0.364239 | + | 0.931305i | \(0.381329\pi\) | |||||||
\(602\) | 1.04670e9 | 0.195539 | ||||||||
\(603\) | 1.54492e9 | 0.286942 | ||||||||
\(604\) | −5.18380e9 | −0.957236 | ||||||||
\(605\) | −1.05219e7 | −0.00193175 | ||||||||
\(606\) | −1.23869e9 | −0.226105 | ||||||||
\(607\) | −6.73366e9 | −1.22205 | −0.611027 | − | 0.791610i | \(-0.709243\pi\) | ||||
−0.611027 | + | 0.791610i | \(0.709243\pi\) | |||||||
\(608\) | −5.22306e9 | −0.942459 | ||||||||
\(609\) | 1.40694e9 | 0.252414 | ||||||||
\(610\) | 4.61824e6 | 0.000823800 0 | ||||||||
\(611\) | 8.05685e8 | 0.142896 | ||||||||
\(612\) | 3.08079e9 | 0.543290 | ||||||||
\(613\) | 6.28531e9 | 1.10208 | 0.551042 | − | 0.834477i | \(-0.314230\pi\) | ||||
0.551042 | + | 0.834477i | \(0.314230\pi\) | |||||||
\(614\) | −1.46392e9 | −0.255228 | ||||||||
\(615\) | −1.73458e7 | −0.00300699 | ||||||||
\(616\) | −8.86459e8 | −0.152801 | ||||||||
\(617\) | −6.71956e9 | −1.15171 | −0.575854 | − | 0.817552i | \(-0.695330\pi\) | ||||
−0.575854 | + | 0.817552i | \(0.695330\pi\) | |||||||
\(618\) | 5.23983e8 | 0.0893013 | ||||||||
\(619\) | 1.62081e9 | 0.274672 | 0.137336 | − | 0.990525i | \(-0.456146\pi\) | ||||
0.137336 | + | 0.990525i | \(0.456146\pi\) | |||||||
\(620\) | 3.23670e6 | 0.000545420 0 | ||||||||
\(621\) | −2.39483e8 | −0.0401286 | ||||||||
\(622\) | −4.81572e8 | −0.0802407 | ||||||||
\(623\) | −9.50866e7 | −0.0157547 | ||||||||
\(624\) | −3.13090e9 | −0.515850 | ||||||||
\(625\) | 6.10335e9 | 0.999972 | ||||||||
\(626\) | 2.67463e9 | 0.435767 | ||||||||
\(627\) | −2.57515e9 | −0.417221 | ||||||||
\(628\) | 9.55337e9 | 1.53921 | ||||||||
\(629\) | 2.11141e10 | 3.38294 | ||||||||
\(630\) | 841583. | 0.000134093 0 | ||||||||
\(631\) | −8.43752e9 | −1.33694 | −0.668470 | − | 0.743739i | \(-0.733051\pi\) | ||||
−0.668470 | + | 0.743739i | \(0.733051\pi\) | |||||||
\(632\) | −2.38713e9 | −0.376154 | ||||||||
\(633\) | −4.00051e9 | −0.626906 | ||||||||
\(634\) | 5.30162e8 | 0.0826220 | ||||||||
\(635\) | −3.15280e7 | −0.00488639 | ||||||||
\(636\) | 1.65780e8 | 0.0255524 | ||||||||
\(637\) | 6.26404e9 | 0.960211 | ||||||||
\(638\) | 1.14637e9 | 0.174764 | ||||||||
\(639\) | −3.58414e9 | −0.543416 | ||||||||
\(640\) | −1.89046e7 | −0.00285060 | ||||||||
\(641\) | −1.15180e10 | −1.72733 | −0.863663 | − | 0.504069i | \(-0.831836\pi\) | ||||
−0.863663 | + | 0.504069i | \(0.831836\pi\) | |||||||
\(642\) | 6.87362e8 | 0.102521 | ||||||||
\(643\) | −1.06978e10 | −1.58692 | −0.793461 | − | 0.608621i | \(-0.791723\pi\) | ||||
−0.793461 | + | 0.608621i | \(0.791723\pi\) | |||||||
\(644\) | 5.76447e8 | 0.0850469 | ||||||||
\(645\) | 1.76481e7 | 0.00258964 | ||||||||
\(646\) | 4.34263e9 | 0.633781 | ||||||||
\(647\) | 1.28732e10 | 1.86862 | 0.934311 | − | 0.356459i | \(-0.116016\pi\) | ||||
0.934311 | + | 0.356459i | \(0.116016\pi\) | |||||||
\(648\) | −4.35912e8 | −0.0629341 | ||||||||
\(649\) | 6.04049e9 | 0.867393 | ||||||||
\(650\) | 2.48881e9 | 0.355463 | ||||||||
\(651\) | −3.57631e8 | −0.0508045 | ||||||||
\(652\) | −9.59186e9 | −1.35530 | ||||||||
\(653\) | −4.92927e9 | −0.692765 | −0.346383 | − | 0.938093i | \(-0.612590\pi\) | ||||
−0.346383 | + | 0.938093i | \(0.612590\pi\) | |||||||
\(654\) | 5.68727e8 | 0.0795026 | ||||||||
\(655\) | 4.14320e6 | 0.000576091 0 | ||||||||
\(656\) | −9.22940e9 | −1.27647 | ||||||||
\(657\) | 2.52049e9 | 0.346741 | ||||||||
\(658\) | −1.15232e8 | −0.0157682 | ||||||||
\(659\) | −7.40103e9 | −1.00738 | −0.503690 | − | 0.863885i | \(-0.668024\pi\) | ||||
−0.503690 | + | 0.863885i | \(0.668024\pi\) | |||||||
\(660\) | −7.13033e6 | −0.000965397 0 | ||||||||
\(661\) | 2.57426e9 | 0.346695 | 0.173348 | − | 0.984861i | \(-0.444542\pi\) | ||||
0.173348 | + | 0.984861i | \(0.444542\pi\) | |||||||
\(662\) | 1.86024e9 | 0.249211 | ||||||||
\(663\) | 9.28937e9 | 1.23791 | ||||||||
\(664\) | −1.54411e9 | −0.204687 | ||||||||
\(665\) | −1.23354e7 | −0.00162658 | ||||||||
\(666\) | −1.42522e9 | −0.186949 | ||||||||
\(667\) | −1.56261e9 | −0.203897 | ||||||||
\(668\) | −9.21854e9 | −1.19659 | ||||||||
\(669\) | 3.34886e9 | 0.432419 | ||||||||
\(670\) | 6.02982e6 | 0.000774537 0 | ||||||||
\(671\) | 4.32336e9 | 0.552450 | ||||||||
\(672\) | 1.59796e9 | 0.203129 | ||||||||
\(673\) | 1.33767e9 | 0.169159 | 0.0845795 | − | 0.996417i | \(-0.473045\pi\) | ||||
0.0845795 | + | 0.996417i | \(0.473045\pi\) | |||||||
\(674\) | −7.51127e8 | −0.0944939 | ||||||||
\(675\) | −1.53772e9 | −0.192448 | ||||||||
\(676\) | −3.22579e9 | −0.401626 | ||||||||
\(677\) | 5.47938e9 | 0.678689 | 0.339345 | − | 0.940662i | \(-0.389795\pi\) | ||||
0.339345 | + | 0.940662i | \(0.389795\pi\) | |||||||
\(678\) | −2.53700e9 | −0.312620 | ||||||||
\(679\) | 6.20298e9 | 0.760425 | ||||||||
\(680\) | 2.52050e7 | 0.00307401 | ||||||||
\(681\) | −9.29639e9 | −1.12798 | ||||||||
\(682\) | −2.91397e8 | −0.0351754 | ||||||||
\(683\) | 9.90832e9 | 1.18995 | 0.594973 | − | 0.803745i | \(-0.297163\pi\) | ||||
0.594973 | + | 0.803745i | \(0.297163\pi\) | |||||||
\(684\) | 3.04808e9 | 0.364192 | ||||||||
\(685\) | −2.63307e7 | −0.00313001 | ||||||||
\(686\) | −2.01564e9 | −0.238384 | ||||||||
\(687\) | −3.05773e9 | −0.359792 | ||||||||
\(688\) | 9.39027e9 | 1.09931 | ||||||||
\(689\) | 4.99869e8 | 0.0582223 | ||||||||
\(690\) | −934703. | −0.000108318 0 | ||||||||
\(691\) | −9.22230e9 | −1.06332 | −0.531662 | − | 0.846956i | \(-0.678432\pi\) | ||||
−0.531662 | + | 0.846956i | \(0.678432\pi\) | |||||||
\(692\) | −1.06357e10 | −1.22010 | ||||||||
\(693\) | 7.87848e8 | 0.0899241 | ||||||||
\(694\) | 1.11744e8 | 0.0126902 | ||||||||
\(695\) | 3.49505e7 | 0.00394917 | ||||||||
\(696\) | −2.84429e9 | −0.319773 | ||||||||
\(697\) | 2.73836e10 | 3.06320 | ||||||||
\(698\) | 3.04353e9 | 0.338754 | ||||||||
\(699\) | −5.15966e9 | −0.571414 | ||||||||
\(700\) | 3.70136e9 | 0.407867 | ||||||||
\(701\) | 1.26162e9 | 0.138329 | 0.0691646 | − | 0.997605i | \(-0.477967\pi\) | ||||
0.0691646 | + | 0.997605i | \(0.477967\pi\) | |||||||
\(702\) | −6.27042e8 | −0.0684096 | ||||||||
\(703\) | 2.08899e10 | 2.26774 | ||||||||
\(704\) | −2.85677e9 | −0.308583 | ||||||||
\(705\) | −1.94290e6 | −0.000208828 0 | ||||||||
\(706\) | 1.31287e9 | 0.140412 | ||||||||
\(707\) | −5.55467e9 | −0.591140 | ||||||||
\(708\) | −7.14984e9 | −0.757146 | ||||||||
\(709\) | 5.11962e9 | 0.539481 | 0.269740 | − | 0.962933i | \(-0.413062\pi\) | ||||
0.269740 | + | 0.962933i | \(0.413062\pi\) | |||||||
\(710\) | −1.39889e7 | −0.00146683 | ||||||||
\(711\) | 2.12158e9 | 0.221369 | ||||||||
\(712\) | 1.92229e8 | 0.0199590 | ||||||||
\(713\) | 3.97202e8 | 0.0410392 | ||||||||
\(714\) | −1.32860e9 | −0.136600 | ||||||||
\(715\) | −2.14998e7 | −0.00219970 | ||||||||
\(716\) | 1.34580e10 | 1.37020 | ||||||||
\(717\) | 9.13248e8 | 0.0925277 | ||||||||
\(718\) | −3.61513e9 | −0.364492 | ||||||||
\(719\) | 3.58731e9 | 0.359930 | 0.179965 | − | 0.983673i | \(-0.442402\pi\) | ||||
0.179965 | + | 0.983673i | \(0.442402\pi\) | |||||||
\(720\) | 7.55012e6 | 0.000753859 0 | ||||||||
\(721\) | 2.34970e9 | 0.233474 | ||||||||
\(722\) | 1.30110e9 | 0.128656 | ||||||||
\(723\) | −4.14735e9 | −0.408119 | ||||||||
\(724\) | −4.88997e8 | −0.0478874 | ||||||||
\(725\) | −1.00335e10 | −0.977846 | ||||||||
\(726\) | −1.12125e9 | −0.108748 | ||||||||
\(727\) | 1.00951e10 | 0.974406 | 0.487203 | − | 0.873289i | \(-0.338017\pi\) | ||||
0.487203 | + | 0.873289i | \(0.338017\pi\) | |||||||
\(728\) | 3.16379e9 | 0.303912 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 9.83746e6 | 0.000935951 0 | ||||||||
\(731\) | −2.78609e10 | −2.63806 | ||||||||
\(732\) | −5.11736e9 | −0.482233 | ||||||||
\(733\) | 5.17030e9 | 0.484900 | 0.242450 | − | 0.970164i | \(-0.422049\pi\) | ||||
0.242450 | + | 0.970164i | \(0.422049\pi\) | |||||||
\(734\) | 4.17694e9 | 0.389872 | ||||||||
\(735\) | −1.51056e7 | −0.00140324 | ||||||||
\(736\) | −1.77477e9 | −0.164085 | ||||||||
\(737\) | 5.64482e9 | 0.519414 | ||||||||
\(738\) | −1.84842e9 | −0.169279 | ||||||||
\(739\) | 1.13371e10 | 1.03335 | 0.516675 | − | 0.856182i | \(-0.327170\pi\) | ||||
0.516675 | + | 0.856182i | \(0.327170\pi\) | |||||||
\(740\) | 5.78421e7 | 0.00524726 | ||||||||
\(741\) | 9.19076e9 | 0.829827 | ||||||||
\(742\) | −7.14930e7 | −0.00642466 | ||||||||
\(743\) | 7.35179e9 | 0.657555 | 0.328778 | − | 0.944407i | \(-0.393363\pi\) | ||||
0.328778 | + | 0.944407i | \(0.393363\pi\) | |||||||
\(744\) | 7.22995e8 | 0.0643621 | ||||||||
\(745\) | −4.50901e7 | −0.00399516 | ||||||||
\(746\) | 1.38103e9 | 0.121791 | ||||||||
\(747\) | 1.37235e9 | 0.120460 | ||||||||
\(748\) | 1.12566e10 | 0.983445 | ||||||||
\(749\) | 3.08234e9 | 0.268036 | ||||||||
\(750\) | −1.20035e7 | −0.00103895 | ||||||||
\(751\) | 2.57204e8 | 0.0221584 | 0.0110792 | − | 0.999939i | \(-0.496473\pi\) | ||||
0.0110792 | + | 0.999939i | \(0.496473\pi\) | |||||||
\(752\) | −1.03378e9 | −0.0886476 | ||||||||
\(753\) | 3.55970e9 | 0.303830 | ||||||||
\(754\) | −4.09141e9 | −0.347595 | ||||||||
\(755\) | 3.76927e7 | 0.00318745 | ||||||||
\(756\) | −9.32539e8 | −0.0784947 | ||||||||
\(757\) | 2.62859e9 | 0.220236 | 0.110118 | − | 0.993919i | \(-0.464877\pi\) | ||||
0.110118 | + | 0.993919i | \(0.464877\pi\) | |||||||
\(758\) | −4.28381e9 | −0.357263 | ||||||||
\(759\) | −8.75022e8 | −0.0726395 | ||||||||
\(760\) | 2.49374e7 | 0.00206065 | ||||||||
\(761\) | −3.73461e9 | −0.307184 | −0.153592 | − | 0.988134i | \(-0.549084\pi\) | ||||
−0.153592 | + | 0.988134i | \(0.549084\pi\) | |||||||
\(762\) | −3.35972e9 | −0.275081 | ||||||||
\(763\) | 2.55034e9 | 0.207856 | ||||||||
\(764\) | 1.48883e9 | 0.120786 | ||||||||
\(765\) | −2.24012e7 | −0.00180907 | ||||||||
\(766\) | −3.13090e9 | −0.251692 | ||||||||
\(767\) | −2.15586e10 | −1.72519 | ||||||||
\(768\) | 1.69209e9 | 0.134790 | ||||||||
\(769\) | −1.96580e10 | −1.55882 | −0.779412 | − | 0.626512i | \(-0.784482\pi\) | ||||
−0.779412 | + | 0.626512i | \(0.784482\pi\) | |||||||
\(770\) | 3.07497e6 | 0.000242730 0 | ||||||||
\(771\) | 2.73848e9 | 0.215189 | ||||||||
\(772\) | 4.53941e9 | 0.355091 | ||||||||
\(773\) | 1.22575e9 | 0.0954497 | 0.0477248 | − | 0.998861i | \(-0.484803\pi\) | ||||
0.0477248 | + | 0.998861i | \(0.484803\pi\) | |||||||
\(774\) | 1.88064e9 | 0.145785 | ||||||||
\(775\) | 2.55044e9 | 0.196815 | ||||||||
\(776\) | −1.25401e10 | −0.963351 | ||||||||
\(777\) | −6.39112e9 | −0.488769 | ||||||||
\(778\) | 1.01741e9 | 0.0774585 | ||||||||
\(779\) | 2.70929e10 | 2.05341 | ||||||||
\(780\) | 2.54483e7 | 0.00192012 | ||||||||
\(781\) | −1.30957e10 | −0.983674 | ||||||||
\(782\) | 1.47560e9 | 0.110343 | ||||||||
\(783\) | 2.52789e9 | 0.188188 | ||||||||
\(784\) | −8.03745e9 | −0.595679 | ||||||||
\(785\) | −6.94650e7 | −0.00512533 | ||||||||
\(786\) | 4.41512e8 | 0.0324312 | ||||||||
\(787\) | −1.08127e10 | −0.790721 | −0.395361 | − | 0.918526i | \(-0.629380\pi\) | ||||
−0.395361 | + | 0.918526i | \(0.629380\pi\) | |||||||
\(788\) | −8.19677e9 | −0.596762 | ||||||||
\(789\) | 8.50419e9 | 0.616401 | ||||||||
\(790\) | 8.28053e6 | 0.000597535 0 | ||||||||
\(791\) | −1.13767e10 | −0.817329 | ||||||||
\(792\) | −1.59273e9 | −0.113921 | ||||||||
\(793\) | −1.54302e10 | −1.09879 | ||||||||
\(794\) | −1.35965e9 | −0.0963951 | ||||||||
\(795\) | −1.20543e6 | −8.50856e−5 0 | ||||||||
\(796\) | −1.92593e9 | −0.135346 | ||||||||
\(797\) | −1.95009e10 | −1.36443 | −0.682215 | − | 0.731151i | \(-0.738983\pi\) | ||||
−0.682215 | + | 0.731151i | \(0.738983\pi\) | |||||||
\(798\) | −1.31449e9 | −0.0915690 | ||||||||
\(799\) | 3.06723e9 | 0.212732 | ||||||||
\(800\) | −1.13958e10 | −0.786918 | ||||||||
\(801\) | −1.70846e8 | −0.0117460 | ||||||||
\(802\) | −2.82434e9 | −0.193333 | ||||||||
\(803\) | 9.20934e9 | 0.627660 | ||||||||
\(804\) | −6.68150e9 | −0.453396 | ||||||||
\(805\) | −4.19149e6 | −0.000283193 0 | ||||||||
\(806\) | 1.04000e9 | 0.0699618 | ||||||||
\(807\) | 6.08401e9 | 0.407505 | ||||||||
\(808\) | 1.12294e10 | 0.748891 | ||||||||
\(809\) | 2.59821e10 | 1.72526 | 0.862631 | − | 0.505833i | \(-0.168815\pi\) | ||||
0.862631 | + | 0.505833i | \(0.168815\pi\) | |||||||
\(810\) | 1.51210e6 | 9.99733e−5 0 | ||||||||
\(811\) | 2.97565e9 | 0.195888 | 0.0979441 | − | 0.995192i | \(-0.468773\pi\) | ||||
0.0979441 | + | 0.995192i | \(0.468773\pi\) | |||||||
\(812\) | −6.08475e9 | −0.398838 | ||||||||
\(813\) | 9.25672e8 | 0.0604144 | ||||||||
\(814\) | −5.20747e9 | −0.338408 | ||||||||
\(815\) | 6.97448e7 | 0.00451295 | ||||||||
\(816\) | −1.19193e10 | −0.767953 | ||||||||
\(817\) | −2.75651e10 | −1.76841 | ||||||||
\(818\) | 3.19297e9 | 0.203966 | ||||||||
\(819\) | −2.81185e9 | −0.178854 | ||||||||
\(820\) | 7.50175e7 | 0.00475132 | ||||||||
\(821\) | 3.94381e9 | 0.248722 | 0.124361 | − | 0.992237i | \(-0.460312\pi\) | ||||
0.124361 | + | 0.992237i | \(0.460312\pi\) | |||||||
\(822\) | −2.80588e9 | −0.176205 | ||||||||
\(823\) | −1.36446e10 | −0.853218 | −0.426609 | − | 0.904436i | \(-0.640292\pi\) | ||||
−0.426609 | + | 0.904436i | \(0.640292\pi\) | |||||||
\(824\) | −4.75020e9 | −0.295779 | ||||||||
\(825\) | −5.61852e9 | −0.348364 | ||||||||
\(826\) | 3.08339e9 | 0.190370 | ||||||||
\(827\) | −2.13778e10 | −1.31430 | −0.657149 | − | 0.753760i | \(-0.728238\pi\) | ||||
−0.657149 | + | 0.753760i | \(0.728238\pi\) | |||||||
\(828\) | 1.03572e9 | 0.0634070 | ||||||||
\(829\) | 1.14474e10 | 0.697856 | 0.348928 | − | 0.937150i | \(-0.386546\pi\) | ||||
0.348928 | + | 0.937150i | \(0.386546\pi\) | |||||||
\(830\) | 5.35627e6 | 0.000325154 0 | ||||||||
\(831\) | −1.04954e10 | −0.634449 | ||||||||
\(832\) | 1.01959e10 | 0.613752 | ||||||||
\(833\) | 2.38471e10 | 1.42948 | ||||||||
\(834\) | 3.72443e9 | 0.222320 | ||||||||
\(835\) | 6.70304e7 | 0.00398445 | ||||||||
\(836\) | 1.11371e10 | 0.659248 | ||||||||
\(837\) | −6.42569e8 | −0.0378774 | ||||||||
\(838\) | −4.75043e9 | −0.278855 | ||||||||
\(839\) | −3.27466e10 | −1.91426 | −0.957128 | − | 0.289665i | \(-0.906456\pi\) | ||||
−0.957128 | + | 0.289665i | \(0.906456\pi\) | |||||||
\(840\) | −7.62943e6 | −0.000444134 0 | ||||||||
\(841\) | −7.55549e8 | −0.0438003 | ||||||||
\(842\) | 5.33318e9 | 0.307889 | ||||||||
\(843\) | −7.17625e9 | −0.412573 | ||||||||
\(844\) | 1.73015e10 | 0.990571 | ||||||||
\(845\) | 2.34555e7 | 0.00133735 | ||||||||
\(846\) | −2.07041e8 | −0.0117560 | ||||||||
\(847\) | −5.02800e9 | −0.284318 | ||||||||
\(848\) | −6.41387e8 | −0.0361189 | ||||||||
\(849\) | 2.57021e9 | 0.144143 | ||||||||
\(850\) | 9.47485e9 | 0.529183 | ||||||||
\(851\) | 7.09829e9 | 0.394821 | ||||||||
\(852\) | 1.55008e10 | 0.858649 | ||||||||
\(853\) | 1.38359e10 | 0.763281 | 0.381641 | − | 0.924311i | \(-0.375359\pi\) | ||||
0.381641 | + | 0.924311i | \(0.375359\pi\) | |||||||
\(854\) | 2.20687e9 | 0.121248 | ||||||||
\(855\) | −2.21634e7 | −0.00121270 | ||||||||
\(856\) | −6.23132e9 | −0.339564 | ||||||||
\(857\) | −1.99079e10 | −1.08042 | −0.540209 | − | 0.841531i | \(-0.681655\pi\) | ||||
−0.540209 | + | 0.841531i | \(0.681655\pi\) | |||||||
\(858\) | −2.29108e9 | −0.123833 | ||||||||
\(859\) | −2.25943e10 | −1.21625 | −0.608124 | − | 0.793842i | \(-0.708078\pi\) | ||||
−0.608124 | + | 0.793842i | \(0.708078\pi\) | |||||||
\(860\) | −7.63251e7 | −0.00409188 | ||||||||
\(861\) | −8.28888e9 | −0.442573 | ||||||||
\(862\) | −6.86206e9 | −0.364904 | ||||||||
\(863\) | 2.03862e10 | 1.07969 | 0.539844 | − | 0.841765i | \(-0.318483\pi\) | ||||
0.539844 | + | 0.841765i | \(0.318483\pi\) | |||||||
\(864\) | 2.87111e9 | 0.151444 | ||||||||
\(865\) | 7.73349e7 | 0.00406274 | ||||||||
\(866\) | 3.88037e9 | 0.203030 | ||||||||
\(867\) | 2.42853e10 | 1.26554 | ||||||||
\(868\) | 1.54669e9 | 0.0802758 | ||||||||
\(869\) | 7.75182e9 | 0.400714 | ||||||||
\(870\) | 9.86637e6 | 0.000507972 0 | ||||||||
\(871\) | −2.01465e10 | −1.03308 | ||||||||
\(872\) | −5.15583e9 | −0.263324 | ||||||||
\(873\) | 1.11451e10 | 0.566937 | ||||||||
\(874\) | 1.45994e9 | 0.0739682 | ||||||||
\(875\) | −5.38273e7 | −0.00271628 | ||||||||
\(876\) | −1.09007e10 | −0.547884 | ||||||||
\(877\) | −5.24578e8 | −0.0262610 | −0.0131305 | − | 0.999914i | \(-0.504180\pi\) | ||||
−0.0131305 | + | 0.999914i | \(0.504180\pi\) | |||||||
\(878\) | 5.74047e8 | 0.0286231 | ||||||||
\(879\) | −6.38158e9 | −0.316933 | ||||||||
\(880\) | 2.75866e7 | 0.00136461 | ||||||||
\(881\) | 3.10939e10 | 1.53200 | 0.766000 | − | 0.642840i | \(-0.222244\pi\) | ||||
0.766000 | + | 0.642840i | \(0.222244\pi\) | |||||||
\(882\) | −1.60970e9 | −0.0789961 | ||||||||
\(883\) | 2.38047e10 | 1.16359 | 0.581794 | − | 0.813336i | \(-0.302351\pi\) | ||||
0.581794 | + | 0.813336i | \(0.302351\pi\) | |||||||
\(884\) | −4.01749e10 | −1.95601 | ||||||||
\(885\) | 5.19883e7 | 0.00252118 | ||||||||
\(886\) | −6.73782e9 | −0.325463 | ||||||||
\(887\) | 3.21183e10 | 1.54533 | 0.772663 | − | 0.634817i | \(-0.218925\pi\) | ||||
0.772663 | + | 0.634817i | \(0.218925\pi\) | |||||||
\(888\) | 1.29204e10 | 0.619201 | ||||||||
\(889\) | −1.50660e10 | −0.719187 | ||||||||
\(890\) | −666810. | −3.17057e−5 0 | ||||||||
\(891\) | 1.41556e9 | 0.0670432 | ||||||||
\(892\) | −1.44832e10 | −0.683263 | ||||||||
\(893\) | 3.03467e9 | 0.142604 | ||||||||
\(894\) | −4.80494e9 | −0.224909 | ||||||||
\(895\) | −9.78562e7 | −0.00456255 | ||||||||
\(896\) | −9.03375e9 | −0.419556 | ||||||||
\(897\) | 3.12297e9 | 0.144476 | ||||||||
\(898\) | 5.58203e9 | 0.257232 | ||||||||
\(899\) | −4.19272e9 | −0.192458 | ||||||||
\(900\) | 6.65037e9 | 0.304086 | ||||||||
\(901\) | 1.90299e9 | 0.0866763 | ||||||||
\(902\) | −6.75376e9 | −0.306424 | ||||||||
\(903\) | 8.43335e9 | 0.381148 | ||||||||
\(904\) | 2.29993e10 | 1.03544 | ||||||||
\(905\) | 3.55562e6 | 0.000159458 0 | ||||||||
\(906\) | 4.01665e9 | 0.179439 | ||||||||
\(907\) | −4.96459e9 | −0.220931 | −0.110466 | − | 0.993880i | \(-0.535234\pi\) | ||||
−0.110466 | + | 0.993880i | \(0.535234\pi\) | |||||||
\(908\) | 4.02053e10 | 1.78231 | ||||||||
\(909\) | −9.98028e9 | −0.440726 | ||||||||
\(910\) | −1.09746e7 | −0.000482776 0 | ||||||||
\(911\) | −2.58578e10 | −1.13312 | −0.566562 | − | 0.824019i | \(-0.691727\pi\) | ||||
−0.566562 | + | 0.824019i | \(0.691727\pi\) | |||||||
\(912\) | −1.17928e10 | −0.514794 | ||||||||
\(913\) | 5.01427e9 | 0.218052 | ||||||||
\(914\) | −5.89939e9 | −0.255561 | ||||||||
\(915\) | 3.72096e7 | 0.00160576 | ||||||||
\(916\) | 1.32242e10 | 0.568505 | ||||||||
\(917\) | 1.97987e9 | 0.0847900 | ||||||||
\(918\) | −2.38714e9 | −0.101842 | ||||||||
\(919\) | −4.44902e10 | −1.89087 | −0.945433 | − | 0.325818i | \(-0.894360\pi\) | ||||
−0.945433 | + | 0.325818i | \(0.894360\pi\) | |||||||
\(920\) | 8.47361e6 | 0.000358766 0 | ||||||||
\(921\) | −1.17949e10 | −0.497493 | ||||||||
\(922\) | −6.78440e9 | −0.285071 | ||||||||
\(923\) | 4.67389e10 | 1.95647 | ||||||||
\(924\) | −3.40731e9 | −0.142089 | ||||||||
\(925\) | 4.55781e10 | 1.89348 | ||||||||
\(926\) | −8.88841e9 | −0.367863 | ||||||||
\(927\) | 4.22179e9 | 0.174067 | ||||||||
\(928\) | 1.87338e10 | 0.769498 | ||||||||
\(929\) | 1.94659e9 | 0.0796562 | 0.0398281 | − | 0.999207i | \(-0.487319\pi\) | ||||
0.0398281 | + | 0.999207i | \(0.487319\pi\) | |||||||
\(930\) | −2.50795e6 | −0.000102242 0 | ||||||||
\(931\) | 2.35939e10 | 0.958245 | ||||||||
\(932\) | 2.23146e10 | 0.902887 | ||||||||
\(933\) | −3.88007e9 | −0.156406 | ||||||||
\(934\) | 8.62905e9 | 0.346536 | ||||||||
\(935\) | −8.18493e7 | −0.00327472 | ||||||||
\(936\) | 5.68449e9 | 0.226582 | ||||||||
\(937\) | −3.37108e10 | −1.33869 | −0.669346 | − | 0.742951i | \(-0.733426\pi\) | ||||
−0.669346 | + | 0.742951i | \(0.733426\pi\) | |||||||
\(938\) | 2.88141e9 | 0.113998 | ||||||||
\(939\) | 2.15498e10 | 0.849403 | ||||||||
\(940\) | 8.40269e6 | 0.000329967 0 | ||||||||
\(941\) | 1.04003e10 | 0.406895 | 0.203448 | − | 0.979086i | \(-0.434785\pi\) | ||||
0.203448 | + | 0.979086i | \(0.434785\pi\) | |||||||
\(942\) | −7.40240e9 | −0.288532 | ||||||||
\(943\) | 9.20603e9 | 0.357504 | ||||||||
\(944\) | 2.76621e10 | 1.07024 | ||||||||
\(945\) | 6.78073e6 | 0.000261375 0 | ||||||||
\(946\) | 6.87147e9 | 0.263895 | ||||||||
\(947\) | −1.40028e10 | −0.535783 | −0.267892 | − | 0.963449i | \(-0.586327\pi\) | ||||
−0.267892 | + | 0.963449i | \(0.586327\pi\) | |||||||
\(948\) | −9.17546e9 | −0.349783 | ||||||||
\(949\) | −3.28683e10 | −1.24838 | ||||||||
\(950\) | 9.37427e9 | 0.354736 | ||||||||
\(951\) | 4.27157e9 | 0.161048 | ||||||||
\(952\) | 1.20445e10 | 0.452438 | ||||||||
\(953\) | 4.94805e9 | 0.185186 | 0.0925931 | − | 0.995704i | \(-0.470484\pi\) | ||||
0.0925931 | + | 0.995704i | \(0.470484\pi\) | |||||||
\(954\) | −1.28454e8 | −0.00478992 | ||||||||
\(955\) | −1.08256e7 | −0.000402199 0 | ||||||||
\(956\) | −3.94964e9 | −0.146202 | ||||||||
\(957\) | 9.23640e9 | 0.340652 | ||||||||
\(958\) | −2.76083e9 | −0.101452 | ||||||||
\(959\) | −1.25824e10 | −0.460680 | ||||||||
\(960\) | −2.45872e7 | −0.000896933 0 | ||||||||
\(961\) | −2.64469e10 | −0.961263 | ||||||||
\(962\) | 1.85856e10 | 0.673074 | ||||||||
\(963\) | 5.53814e9 | 0.199835 | ||||||||
\(964\) | 1.79366e10 | 0.644866 | ||||||||
\(965\) | −3.30072e7 | −0.00118240 | ||||||||
\(966\) | −4.46658e8 | −0.0159425 | ||||||||
\(967\) | −1.79902e10 | −0.639798 | −0.319899 | − | 0.947452i | \(-0.603649\pi\) | ||||
−0.319899 | + | 0.947452i | \(0.603649\pi\) | |||||||
\(968\) | 1.01647e10 | 0.360190 | ||||||||
\(969\) | 3.49891e10 | 1.23538 | ||||||||
\(970\) | 4.34994e7 | 0.00153032 | ||||||||
\(971\) | −1.54029e10 | −0.539929 | −0.269964 | − | 0.962870i | \(-0.587012\pi\) | ||||
−0.269964 | + | 0.962870i | \(0.587012\pi\) | |||||||
\(972\) | −1.67553e9 | −0.0585220 | ||||||||
\(973\) | 1.67015e10 | 0.581245 | ||||||||
\(974\) | 8.96064e9 | 0.310730 | ||||||||
\(975\) | 2.00526e10 | 0.692874 | ||||||||
\(976\) | 1.97986e10 | 0.681648 | ||||||||
\(977\) | −1.43057e10 | −0.490769 | −0.245384 | − | 0.969426i | \(-0.578914\pi\) | ||||
−0.245384 | + | 0.969426i | \(0.578914\pi\) | |||||||
\(978\) | 7.43223e9 | 0.254058 | ||||||||
\(979\) | −6.24235e8 | −0.0212622 | ||||||||
\(980\) | 6.53292e7 | 0.00221726 | ||||||||
\(981\) | 4.58229e9 | 0.154968 | ||||||||
\(982\) | −4.15080e9 | −0.139876 | ||||||||
\(983\) | 1.72656e10 | 0.579756 | 0.289878 | − | 0.957064i | \(-0.406385\pi\) | ||||
0.289878 | + | 0.957064i | \(0.406385\pi\) | |||||||
\(984\) | 1.67570e10 | 0.560678 | ||||||||
\(985\) | 5.96008e7 | 0.00198712 | ||||||||
\(986\) | −1.55759e10 | −0.517469 | ||||||||
\(987\) | −9.28435e8 | −0.0307356 | ||||||||
\(988\) | −3.97484e10 | −1.31120 | ||||||||
\(989\) | −9.36649e9 | −0.307886 | ||||||||
\(990\) | 5.52492e6 | 0.000180968 0 | ||||||||
\(991\) | −1.25900e10 | −0.410929 | −0.205464 | − | 0.978665i | \(-0.565870\pi\) | ||||
−0.205464 | + | 0.978665i | \(0.565870\pi\) | |||||||
\(992\) | −4.76197e9 | −0.154880 | ||||||||
\(993\) | 1.49882e10 | 0.485765 | ||||||||
\(994\) | −6.68476e9 | −0.215891 | ||||||||
\(995\) | 1.40040e7 | 0.000450682 0 | ||||||||
\(996\) | −5.93515e9 | −0.190337 | ||||||||
\(997\) | −2.34721e10 | −0.750100 | −0.375050 | − | 0.927005i | \(-0.622374\pi\) | ||||
−0.375050 | + | 0.927005i | \(0.622374\pi\) | |||||||
\(998\) | −7.12681e9 | −0.226954 | ||||||||
\(999\) | −1.14832e10 | −0.364403 |
(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 | 69.8.a.b.1.4 | ✓ | 6 | |
3.2 | odd | 2 | 207.8.a.c.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.8.a.b.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial | |
207.8.a.c.1.3 | 6 | 3.2 | odd | 2 |