Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,11,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (of order \(2\), degree \(1\), 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: | \(27.3203618650\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.21 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.11.b.b.42.14 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.6799i | 0.521245i | 0.965441 | + | 0.260623i | \(0.0839279\pi\) | ||||
−0.965441 | + | 0.260623i | \(0.916072\pi\) | |||||||
\(3\) | − | 405.855i | − | 1.67019i | −0.550108 | − | 0.835093i | \(-0.685414\pi\) | ||
0.550108 | − | 0.835093i | \(-0.314586\pi\) | |||||||
\(4\) | 745.782 | 0.728303 | ||||||||
\(5\) | 2509.28i | 0.802969i | 0.915866 | + | 0.401485i | \(0.131506\pi\) | ||||
−0.915866 | + | 0.401485i | \(0.868494\pi\) | |||||||
\(6\) | 6769.61 | 0.870577 | ||||||||
\(7\) | 11110.8i | 0.661080i | 0.943792 | + | 0.330540i | \(0.107231\pi\) | ||||
−0.943792 | + | 0.330540i | \(0.892769\pi\) | |||||||
\(8\) | 29519.7i | 0.900870i | ||||||||
\(9\) | −105670. | −1.78952 | ||||||||
\(10\) | −41854.4 | −0.418544 | ||||||||
\(11\) | 76827.0 | 0.477035 | 0.238518 | − | 0.971138i | \(-0.423339\pi\) | ||||
0.238518 | + | 0.971138i | \(0.423339\pi\) | |||||||
\(12\) | − | 302680.i | − | 1.21640i | ||||||
\(13\) | −613775. | −1.65307 | −0.826537 | − | 0.562882i | \(-0.809693\pi\) | ||||
−0.826537 | + | 0.562882i | \(0.809693\pi\) | |||||||
\(14\) | −185326. | −0.344585 | ||||||||
\(15\) | 1.01840e6 | 1.34111 | ||||||||
\(16\) | 271297. | 0.258729 | ||||||||
\(17\) | −2.69195e6 | −1.89593 | −0.947967 | − | 0.318370i | \(-0.896865\pi\) | ||||
−0.947967 | + | 0.318370i | \(0.896865\pi\) | |||||||
\(18\) | − | 1.76255e6i | − | 0.932781i | ||||||
\(19\) | 2.92835e6i | 1.18265i | 0.806435 | + | 0.591323i | \(0.201394\pi\) | ||||
−0.806435 | + | 0.591323i | \(0.798606\pi\) | |||||||
\(20\) | 1.87138e6i | 0.584805i | ||||||||
\(21\) | 4.50936e6 | 1.10413 | ||||||||
\(22\) | 1.28146e6i | 0.248652i | ||||||||
\(23\) | 2.15323e6 | 0.334543 | 0.167272 | − | 0.985911i | \(-0.446504\pi\) | ||||
0.167272 | + | 0.985911i | \(0.446504\pi\) | |||||||
\(24\) | 1.19807e7 | 1.50462 | ||||||||
\(25\) | 3.46914e6 | 0.355240 | ||||||||
\(26\) | − | 1.02377e7i | − | 0.861658i | ||||||
\(27\) | 1.89212e7i | 1.31865i | ||||||||
\(28\) | 8.28622e6i | 0.481467i | ||||||||
\(29\) | 3.40359e7i | 1.65938i | 0.558221 | + | 0.829692i | \(0.311484\pi\) | ||||
−0.558221 | + | 0.829692i | \(0.688516\pi\) | |||||||
\(30\) | 1.69868e7i | 0.699047i | ||||||||
\(31\) | −3.94514e7 | −1.37801 | −0.689007 | − | 0.724755i | \(-0.741953\pi\) | ||||
−0.689007 | + | 0.724755i | \(0.741953\pi\) | |||||||
\(32\) | 3.47534e7i | 1.03573i | ||||||||
\(33\) | − | 3.11807e7i | − | 0.796738i | ||||||
\(34\) | − | 4.49014e7i | − | 0.988247i | ||||||
\(35\) | −2.78800e7 | −0.530827 | ||||||||
\(36\) | −7.88065e7 | −1.30332 | ||||||||
\(37\) | − | 1.06797e8i | − | 1.54010i | −0.637981 | − | 0.770052i | \(-0.720230\pi\) | ||
0.637981 | − | 0.770052i | \(-0.279770\pi\) | |||||||
\(38\) | −4.88444e7 | −0.616449 | ||||||||
\(39\) | 2.49104e8i | 2.76094i | ||||||||
\(40\) | −7.40732e7 | −0.723371 | ||||||||
\(41\) | −6.32205e7 | −0.545680 | −0.272840 | − | 0.962059i | \(-0.587963\pi\) | ||||
−0.272840 | + | 0.962059i | \(0.587963\pi\) | |||||||
\(42\) | 7.52156e7i | 0.575521i | ||||||||
\(43\) | 6.01836e7 | + | 1.34125e8i | 0.409389 | + | 0.912360i | ||||
\(44\) | 5.72962e7 | 0.347426 | ||||||||
\(45\) | − | 2.65154e8i | − | 1.43693i | ||||||
\(46\) | 3.59156e7i | 0.174379i | ||||||||
\(47\) | −7.95596e7 | −0.346899 | −0.173450 | − | 0.984843i | \(-0.555491\pi\) | ||||
−0.173450 | + | 0.984843i | \(0.555491\pi\) | |||||||
\(48\) | − | 1.10107e8i | − | 0.432125i | ||||||
\(49\) | 1.59026e8 | 0.562973 | ||||||||
\(50\) | 5.78648e7i | 0.185167i | ||||||||
\(51\) | 1.09254e9i | 3.16656i | ||||||||
\(52\) | −4.57743e8 | −1.20394 | ||||||||
\(53\) | 5.81476e8 | 1.39044 | 0.695220 | − | 0.718797i | \(-0.255307\pi\) | ||||
0.695220 | + | 0.718797i | \(0.255307\pi\) | |||||||
\(54\) | −3.15603e8 | −0.687341 | ||||||||
\(55\) | 1.92780e8i | 0.383045i | ||||||||
\(56\) | −3.27987e8 | −0.595547 | ||||||||
\(57\) | 1.18849e9 | 1.97524 | ||||||||
\(58\) | −5.67714e8 | −0.864947 | ||||||||
\(59\) | 6.19231e8 | 0.866149 | 0.433075 | − | 0.901358i | \(-0.357429\pi\) | ||||
0.433075 | + | 0.901358i | \(0.357429\pi\) | |||||||
\(60\) | 7.59508e8 | 0.976734 | ||||||||
\(61\) | 7.79189e8i | 0.922558i | 0.887255 | + | 0.461279i | \(0.152609\pi\) | ||||
−0.887255 | + | 0.461279i | \(0.847391\pi\) | |||||||
\(62\) | − | 6.58043e8i | − | 0.718283i | ||||||
\(63\) | − | 1.17407e9i | − | 1.18302i | ||||||
\(64\) | −3.01874e8 | −0.281142 | ||||||||
\(65\) | − | 1.54013e9i | − | 1.32737i | ||||||
\(66\) | 5.20089e8 | 0.415296 | ||||||||
\(67\) | −6.11549e8 | −0.452958 | −0.226479 | − | 0.974016i | \(-0.572721\pi\) | ||||
−0.226479 | + | 0.974016i | \(0.572721\pi\) | |||||||
\(68\) | −2.00761e9 | −1.38081 | ||||||||
\(69\) | − | 8.73901e8i | − | 0.558749i | ||||||
\(70\) | − | 4.65035e8i | − | 0.276691i | ||||||
\(71\) | 7.76085e8i | 0.430148i | 0.976598 | + | 0.215074i | \(0.0689992\pi\) | ||||
−0.976598 | + | 0.215074i | \(0.931001\pi\) | |||||||
\(72\) | − | 3.11934e9i | − | 1.61213i | ||||||
\(73\) | − | 2.33701e8i | − | 0.112732i | −0.998410 | − | 0.0563660i | \(-0.982049\pi\) | ||
0.998410 | − | 0.0563660i | \(-0.0179514\pi\) | |||||||
\(74\) | 1.78136e9 | 0.802773 | ||||||||
\(75\) | − | 1.40797e9i | − | 0.593317i | ||||||
\(76\) | 2.18391e9i | 0.861325i | ||||||||
\(77\) | 8.53607e8i | 0.315358i | ||||||||
\(78\) | −4.15502e9 | −1.43913 | ||||||||
\(79\) | −2.30142e9 | −0.747931 | −0.373965 | − | 0.927443i | \(-0.622002\pi\) | ||||
−0.373965 | + | 0.927443i | \(0.622002\pi\) | |||||||
\(80\) | 6.80759e8i | 0.207751i | ||||||||
\(81\) | 1.43959e9 | 0.412871 | ||||||||
\(82\) | − | 1.05451e9i | − | 0.284433i | ||||||
\(83\) | 9.15067e8 | 0.232307 | 0.116154 | − | 0.993231i | \(-0.462944\pi\) | ||||
0.116154 | + | 0.993231i | \(0.462944\pi\) | |||||||
\(84\) | 3.36301e9 | 0.804139 | ||||||||
\(85\) | − | 6.75486e9i | − | 1.52238i | ||||||
\(86\) | −2.23718e9 | + | 1.00385e9i | −0.475564 | + | 0.213392i | ||||
\(87\) | 1.38136e10 | 2.77148 | ||||||||
\(88\) | 2.26791e9i | 0.429747i | ||||||||
\(89\) | − | 4.73920e9i | − | 0.848702i | −0.905498 | − | 0.424351i | \(-0.860502\pi\) | ||
0.905498 | − | 0.424351i | \(-0.139498\pi\) | |||||||
\(90\) | 4.42274e9 | 0.748995 | ||||||||
\(91\) | − | 6.81951e9i | − | 1.09281i | ||||||
\(92\) | 1.60584e9 | 0.243649 | ||||||||
\(93\) | 1.60115e10i | 2.30154i | ||||||||
\(94\) | − | 1.32704e9i | − | 0.180820i | ||||||
\(95\) | −7.34805e9 | −0.949629 | ||||||||
\(96\) | 1.41048e10 | 1.72986 | ||||||||
\(97\) | −1.01973e10 | −1.18748 | −0.593741 | − | 0.804656i | \(-0.702350\pi\) | ||||
−0.593741 | + | 0.804656i | \(0.702350\pi\) | |||||||
\(98\) | 2.65253e9i | 0.293447i | ||||||||
\(99\) | −8.11828e9 | −0.853666 | ||||||||
\(100\) | 2.58723e9 | 0.258723 | ||||||||
\(101\) | 1.77471e8 | 0.0168858 | 0.00844289 | − | 0.999964i | \(-0.497313\pi\) | ||||
0.00844289 | + | 0.999964i | \(0.497313\pi\) | |||||||
\(102\) | −1.82235e10 | −1.65056 | ||||||||
\(103\) | −1.35777e9 | −0.117122 | −0.0585610 | − | 0.998284i | \(-0.518651\pi\) | ||||
−0.0585610 | + | 0.998284i | \(0.518651\pi\) | |||||||
\(104\) | − | 1.81185e10i | − | 1.48921i | ||||||
\(105\) | 1.13153e10i | 0.886580i | ||||||||
\(106\) | 9.69893e9i | 0.724760i | ||||||||
\(107\) | 1.66408e10 | 1.18646 | 0.593232 | − | 0.805031i | \(-0.297852\pi\) | ||||
0.593232 | + | 0.805031i | \(0.297852\pi\) | |||||||
\(108\) | 1.41111e10i | 0.960378i | ||||||||
\(109\) | −1.12385e10 | −0.730423 | −0.365211 | − | 0.930925i | \(-0.619003\pi\) | ||||
−0.365211 | + | 0.930925i | \(0.619003\pi\) | |||||||
\(110\) | −3.21555e9 | −0.199660 | ||||||||
\(111\) | −4.33441e10 | −2.57226 | ||||||||
\(112\) | 3.01431e9i | 0.171040i | ||||||||
\(113\) | − | 3.46564e10i | − | 1.88101i | −0.339782 | − | 0.940504i | \(-0.610353\pi\) | ||
0.339782 | − | 0.940504i | \(-0.389647\pi\) | |||||||
\(114\) | 1.98238e10i | 1.02959i | ||||||||
\(115\) | 5.40306e9i | 0.268628i | ||||||||
\(116\) | 2.53834e10i | 1.20854i | ||||||||
\(117\) | 6.48574e10 | 2.95822 | ||||||||
\(118\) | 1.03287e10i | 0.451476i | ||||||||
\(119\) | − | 2.99097e10i | − | 1.25336i | ||||||
\(120\) | 3.00630e10i | 1.20816i | ||||||||
\(121\) | −2.00350e10 | −0.772437 | ||||||||
\(122\) | −1.29968e10 | −0.480879 | ||||||||
\(123\) | 2.56584e10i | 0.911388i | ||||||||
\(124\) | −2.94221e10 | −1.00361 | ||||||||
\(125\) | 3.32097e10i | 1.08822i | ||||||||
\(126\) | 1.95833e10 | 0.616643 | ||||||||
\(127\) | −2.00849e9 | −0.0607928 | −0.0303964 | − | 0.999538i | \(-0.509677\pi\) | ||||
−0.0303964 | + | 0.999538i | \(0.509677\pi\) | |||||||
\(128\) | 3.05523e10i | 0.889188i | ||||||||
\(129\) | 5.44352e10 | − | 2.44258e10i | 1.52381 | − | 0.683756i | ||||
\(130\) | 2.56892e10 | 0.691885 | ||||||||
\(131\) | − | 1.87042e10i | − | 0.484822i | −0.970174 | − | 0.242411i | \(-0.922062\pi\) | ||
0.970174 | − | 0.242411i | \(-0.0779383\pi\) | |||||||
\(132\) | − | 2.32540e10i | − | 0.580267i | ||||||
\(133\) | −3.25362e10 | −0.781824 | ||||||||
\(134\) | − | 1.02006e10i | − | 0.236102i | ||||||
\(135\) | −4.74786e10 | −1.05884 | ||||||||
\(136\) | − | 7.94657e10i | − | 1.70799i | ||||||
\(137\) | 2.95801e10i | 0.612910i | 0.951885 | + | 0.306455i | \(0.0991428\pi\) | ||||
−0.951885 | + | 0.306455i | \(0.900857\pi\) | |||||||
\(138\) | 1.45765e10 | 0.291246 | ||||||||
\(139\) | 7.84492e10 | 1.51187 | 0.755935 | − | 0.654647i | \(-0.227183\pi\) | ||||
0.755935 | + | 0.654647i | \(0.227183\pi\) | |||||||
\(140\) | −2.07924e10 | −0.386603 | ||||||||
\(141\) | 3.22897e10i | 0.579386i | ||||||||
\(142\) | −1.29450e10 | −0.224213 | ||||||||
\(143\) | −4.71545e10 | −0.788575 | ||||||||
\(144\) | −2.86678e10 | −0.463001 | ||||||||
\(145\) | −8.54055e10 | −1.33244 | ||||||||
\(146\) | 3.89811e9 | 0.0587610 | ||||||||
\(147\) | − | 6.45416e10i | − | 0.940271i | ||||||
\(148\) | − | 7.96473e10i | − | 1.12166i | ||||||
\(149\) | − | 2.73820e10i | − | 0.372849i | −0.982469 | − | 0.186425i | \(-0.940310\pi\) | ||
0.982469 | − | 0.186425i | \(-0.0596900\pi\) | |||||||
\(150\) | 2.34847e10 | 0.309264 | ||||||||
\(151\) | 5.86731e10i | 0.747402i | 0.927549 | + | 0.373701i | \(0.121911\pi\) | ||||
−0.927549 | + | 0.373701i | \(0.878089\pi\) | |||||||
\(152\) | −8.64440e10 | −1.06541 | ||||||||
\(153\) | 2.84458e11 | 3.39282 | ||||||||
\(154\) | −1.42380e10 | −0.164379 | ||||||||
\(155\) | − | 9.89945e10i | − | 1.10650i | ||||||
\(156\) | 1.85777e11i | 2.01080i | ||||||||
\(157\) | 4.25794e10i | 0.446377i | 0.974775 | + | 0.223188i | \(0.0716465\pi\) | ||||
−0.974775 | + | 0.223188i | \(0.928353\pi\) | |||||||
\(158\) | − | 3.83874e10i | − | 0.389855i | ||||||
\(159\) | − | 2.35995e11i | − | 2.32229i | ||||||
\(160\) | −8.72059e10 | −0.831661 | ||||||||
\(161\) | 2.39241e10i | 0.221160i | ||||||||
\(162\) | 2.40122e10i | 0.215207i | ||||||||
\(163\) | − | 1.20452e11i | − | 1.04683i | −0.852077 | − | 0.523416i | \(-0.824658\pi\) | ||
0.852077 | − | 0.523416i | \(-0.175342\pi\) | |||||||
\(164\) | −4.71487e10 | −0.397421 | ||||||||
\(165\) | 7.82410e10 | 0.639756 | ||||||||
\(166\) | 1.52632e10i | 0.121089i | ||||||||
\(167\) | −1.41144e11 | −1.08662 | −0.543312 | − | 0.839531i | \(-0.682830\pi\) | ||||
−0.543312 | + | 0.839531i | \(0.682830\pi\) | |||||||
\(168\) | 1.33115e11i | 0.994675i | ||||||||
\(169\) | 2.38861e11 | 1.73266 | ||||||||
\(170\) | 1.12670e11 | 0.793532 | ||||||||
\(171\) | − | 3.09437e11i | − | 2.11637i | ||||||
\(172\) | 4.48839e10 | + | 1.00028e11i | 0.298159 | + | 0.664475i | ||||
\(173\) | 1.24656e11 | 0.804419 | 0.402210 | − | 0.915548i | \(-0.368242\pi\) | ||||
0.402210 | + | 0.915548i | \(0.368242\pi\) | |||||||
\(174\) | 2.30410e11i | 1.44462i | ||||||||
\(175\) | 3.85448e10i | 0.234842i | ||||||||
\(176\) | 2.08429e10 | 0.123423 | ||||||||
\(177\) | − | 2.51318e11i | − | 1.44663i | ||||||
\(178\) | 7.90492e10 | 0.442382 | ||||||||
\(179\) | 2.61895e11i | 1.42515i | 0.701595 | + | 0.712576i | \(0.252472\pi\) | ||||
−0.701595 | + | 0.712576i | \(0.747528\pi\) | |||||||
\(180\) | − | 1.97748e11i | − | 1.04652i | ||||||
\(181\) | −3.23826e11 | −1.66694 | −0.833468 | − | 0.552568i | \(-0.813648\pi\) | ||||
−0.833468 | + | 0.552568i | \(0.813648\pi\) | |||||||
\(182\) | 1.13749e11 | 0.569625 | ||||||||
\(183\) | 3.16238e11 | 1.54084 | ||||||||
\(184\) | 6.35628e10i | 0.301380i | ||||||||
\(185\) | 2.67983e11 | 1.23666 | ||||||||
\(186\) | −2.67070e11 | −1.19967 | ||||||||
\(187\) | −2.06815e11 | −0.904427 | ||||||||
\(188\) | −5.93342e10 | −0.252648 | ||||||||
\(189\) | −2.10229e11 | −0.871734 | ||||||||
\(190\) | − | 1.22564e11i | − | 0.494990i | ||||||
\(191\) | 1.60403e11i | 0.631024i | 0.948922 | + | 0.315512i | \(0.102176\pi\) | ||||
−0.948922 | + | 0.315512i | \(0.897824\pi\) | |||||||
\(192\) | 1.22517e11i | 0.469559i | ||||||||
\(193\) | −1.46793e11 | −0.548176 | −0.274088 | − | 0.961705i | \(-0.588376\pi\) | ||||
−0.274088 | + | 0.961705i | \(0.588376\pi\) | |||||||
\(194\) | − | 1.70090e11i | − | 0.618969i | ||||||
\(195\) | −6.25071e11 | −2.21695 | ||||||||
\(196\) | 1.18599e11 | 0.410015 | ||||||||
\(197\) | 1.50878e11 | 0.508505 | 0.254253 | − | 0.967138i | \(-0.418171\pi\) | ||||
0.254253 | + | 0.967138i | \(0.418171\pi\) | |||||||
\(198\) | − | 1.35412e11i | − | 0.444969i | ||||||
\(199\) | 2.23559e11i | 0.716352i | 0.933654 | + | 0.358176i | \(0.116601\pi\) | ||||
−0.933654 | + | 0.358176i | \(0.883399\pi\) | |||||||
\(200\) | 1.02408e11i | 0.320025i | ||||||||
\(201\) | 2.48201e11i | 0.756524i | ||||||||
\(202\) | 2.96019e9i | 0.00880164i | ||||||||
\(203\) | −3.78165e11 | −1.09699 | ||||||||
\(204\) | 8.14800e11i | 2.30622i | ||||||||
\(205\) | − | 1.58638e11i | − | 0.438165i | ||||||
\(206\) | − | 2.26473e10i | − | 0.0610493i | ||||||
\(207\) | −2.27531e11 | −0.598673 | ||||||||
\(208\) | −1.66515e11 | −0.427698 | ||||||||
\(209\) | 2.24976e11i | 0.564164i | ||||||||
\(210\) | −1.88737e11 | −0.462126 | ||||||||
\(211\) | − | 2.74080e11i | − | 0.655337i | −0.944793 | − | 0.327668i | \(-0.893737\pi\) | ||
0.944793 | − | 0.327668i | \(-0.106263\pi\) | |||||||
\(212\) | 4.33654e11 | 1.01266 | ||||||||
\(213\) | 3.14978e11 | 0.718427 | ||||||||
\(214\) | 2.77566e11i | 0.618439i | ||||||||
\(215\) | −3.36556e11 | + | 1.51018e11i | −0.732597 | + | 0.328727i | ||||
\(216\) | −5.58549e11 | −1.18793 | ||||||||
\(217\) | − | 4.38335e11i | − | 0.910977i | ||||||
\(218\) | − | 1.87456e11i | − | 0.380730i | ||||||
\(219\) | −9.48490e10 | −0.188283 | ||||||||
\(220\) | 1.43772e11i | 0.278973i | ||||||||
\(221\) | 1.65225e12 | 3.13412 | ||||||||
\(222\) | − | 7.22974e11i | − | 1.34078i | ||||||
\(223\) | 2.54207e11i | 0.460960i | 0.973077 | + | 0.230480i | \(0.0740296\pi\) | ||||
−0.973077 | + | 0.230480i | \(0.925970\pi\) | |||||||
\(224\) | −3.86137e11 | −0.684701 | ||||||||
\(225\) | −3.66583e11 | −0.635711 | ||||||||
\(226\) | 5.78063e11 | 0.980467 | ||||||||
\(227\) | − | 9.29507e10i | − | 0.154214i | −0.997023 | − | 0.0771070i | \(-0.975432\pi\) | ||
0.997023 | − | 0.0771070i | \(-0.0245683\pi\) | |||||||
\(228\) | 8.86352e11 | 1.43857 | ||||||||
\(229\) | −1.73944e11 | −0.276206 | −0.138103 | − | 0.990418i | \(-0.544100\pi\) | ||||
−0.138103 | + | 0.990418i | \(0.544100\pi\) | |||||||
\(230\) | −9.01223e10 | −0.140021 | ||||||||
\(231\) | 3.46441e11 | 0.526707 | ||||||||
\(232\) | −1.00473e12 | −1.49489 | ||||||||
\(233\) | − | 2.89273e11i | − | 0.421238i | −0.977568 | − | 0.210619i | \(-0.932452\pi\) | ||
0.977568 | − | 0.210619i | \(-0.0675479\pi\) | |||||||
\(234\) | 1.08181e12i | 1.54196i | ||||||||
\(235\) | − | 1.99637e11i | − | 0.278549i | ||||||
\(236\) | 4.61812e11 | 0.630819 | ||||||||
\(237\) | 9.34045e11i | 1.24918i | ||||||||
\(238\) | 4.98889e11 | 0.653310 | ||||||||
\(239\) | 9.33811e11 | 1.19748 | 0.598742 | − | 0.800942i | \(-0.295668\pi\) | ||||
0.598742 | + | 0.800942i | \(0.295668\pi\) | |||||||
\(240\) | 2.76290e11 | 0.346983 | ||||||||
\(241\) | 1.41097e12i | 1.73553i | 0.496974 | + | 0.867765i | \(0.334444\pi\) | ||||
−0.496974 | + | 0.867765i | \(0.665556\pi\) | |||||||
\(242\) | − | 3.34181e11i | − | 0.402629i | ||||||
\(243\) | 5.33013e11i | 0.629080i | ||||||||
\(244\) | 5.81105e11i | 0.671902i | ||||||||
\(245\) | 3.99041e11i | 0.452050i | ||||||||
\(246\) | −4.27978e11 | −0.475057 | ||||||||
\(247\) | − | 1.79735e12i | − | 1.95500i | ||||||
\(248\) | − | 1.16459e12i | − | 1.24141i | ||||||
\(249\) | − | 3.71385e11i | − | 0.387996i | ||||||
\(250\) | −5.53933e11 | −0.567228 | ||||||||
\(251\) | 5.56452e11 | 0.558546 | 0.279273 | − | 0.960212i | \(-0.409906\pi\) | ||||
0.279273 | + | 0.960212i | \(0.409906\pi\) | |||||||
\(252\) | − | 8.75601e11i | − | 0.861596i | ||||||
\(253\) | 1.65427e11 | 0.159589 | ||||||||
\(254\) | − | 3.35014e10i | − | 0.0316879i | ||||||
\(255\) | −2.74150e12 | −2.54265 | ||||||||
\(256\) | −8.18726e11 | −0.744627 | ||||||||
\(257\) | − | 1.29683e12i | − | 1.15669i | −0.815792 | − | 0.578345i | \(-0.803699\pi\) | ||
0.815792 | − | 0.578345i | \(-0.196301\pi\) | |||||||
\(258\) | 4.07420e11 | + | 9.07971e11i | 0.356405 | + | 0.794280i | ||||
\(259\) | 1.18660e12 | 1.01813 | ||||||||
\(260\) | − | 1.14860e12i | − | 0.966727i | ||||||
\(261\) | − | 3.59656e12i | − | 2.96951i | ||||||
\(262\) | 3.11983e11 | 0.252711 | ||||||||
\(263\) | − | 1.45763e12i | − | 1.15843i | −0.815175 | − | 0.579215i | \(-0.803359\pi\) | ||
0.815175 | − | 0.579215i | \(-0.196641\pi\) | |||||||
\(264\) | 9.20444e11 | 0.717758 | ||||||||
\(265\) | 1.45908e12i | 1.11648i | ||||||||
\(266\) | − | 5.42699e11i | − | 0.407522i | ||||||
\(267\) | −1.92343e12 | −1.41749 | ||||||||
\(268\) | −4.56083e11 | −0.329890 | ||||||||
\(269\) | −6.65425e11 | −0.472430 | −0.236215 | − | 0.971701i | \(-0.575907\pi\) | ||||
−0.236215 | + | 0.971701i | \(0.575907\pi\) | |||||||
\(270\) | − | 7.91936e11i | − | 0.551914i | ||||||
\(271\) | 4.95618e11 | 0.339079 | 0.169539 | − | 0.985523i | \(-0.445772\pi\) | ||||
0.169539 | + | 0.985523i | \(0.445772\pi\) | |||||||
\(272\) | −7.30318e11 | −0.490532 | ||||||||
\(273\) | −2.76774e12 | −1.82520 | ||||||||
\(274\) | −4.93391e11 | −0.319476 | ||||||||
\(275\) | 2.66524e11 | 0.169462 | ||||||||
\(276\) | − | 6.51740e11i | − | 0.406939i | ||||||
\(277\) | 2.78269e12i | 1.70634i | 0.521632 | + | 0.853170i | \(0.325323\pi\) | ||||
−0.521632 | + | 0.853170i | \(0.674677\pi\) | |||||||
\(278\) | 1.30852e12i | 0.788055i | ||||||||
\(279\) | 4.16881e12 | 2.46599 | ||||||||
\(280\) | − | 8.23010e11i | − | 0.478206i | ||||||
\(281\) | −5.43758e11 | −0.310366 | −0.155183 | − | 0.987886i | \(-0.549597\pi\) | ||||
−0.155183 | + | 0.987886i | \(0.549597\pi\) | |||||||
\(282\) | −5.38587e11 | −0.302003 | ||||||||
\(283\) | 1.78970e12 | 0.985933 | 0.492966 | − | 0.870048i | \(-0.335913\pi\) | ||||
0.492966 | + | 0.870048i | \(0.335913\pi\) | |||||||
\(284\) | 5.78791e11i | 0.313278i | ||||||||
\(285\) | 2.98224e12i | 1.58606i | ||||||||
\(286\) | − | 7.86530e11i | − | 0.411041i | ||||||
\(287\) | − | 7.02428e11i | − | 0.360738i | ||||||
\(288\) | − | 3.67237e12i | − | 1.85347i | ||||||
\(289\) | 5.23062e12 | 2.59456 | ||||||||
\(290\) | − | 1.42455e12i | − | 0.694526i | ||||||
\(291\) | 4.13863e12i | 1.98332i | ||||||||
\(292\) | − | 1.74290e11i | − | 0.0821030i | ||||||
\(293\) | 1.63092e12 | 0.755257 | 0.377628 | − | 0.925957i | \(-0.376740\pi\) | ||||
0.377628 | + | 0.925957i | \(0.376740\pi\) | |||||||
\(294\) | 1.07654e12 | 0.490112 | ||||||||
\(295\) | 1.55382e12i | 0.695491i | ||||||||
\(296\) | 3.15262e12 | 1.38743 | ||||||||
\(297\) | 1.45366e12i | 0.629043i | ||||||||
\(298\) | 4.56727e11 | 0.194346 | ||||||||
\(299\) | −1.32160e12 | −0.553025 | ||||||||
\(300\) | − | 1.05004e12i | − | 0.432115i | ||||||
\(301\) | −1.49023e12 | + | 6.68686e11i | −0.603143 | + | 0.270639i | ||||
\(302\) | −9.78658e11 | −0.389580 | ||||||||
\(303\) | − | 7.20276e10i | − | 0.0282024i | ||||||
\(304\) | 7.94451e11i | 0.305984i | ||||||||
\(305\) | −1.95520e12 | −0.740786 | ||||||||
\(306\) | 4.74471e12i | 1.76849i | ||||||||
\(307\) | −4.22741e12 | −1.55018 | −0.775091 | − | 0.631850i | \(-0.782296\pi\) | ||||
−0.775091 | + | 0.631850i | \(0.782296\pi\) | |||||||
\(308\) | 6.36605e11i | 0.229677i | ||||||||
\(309\) | 5.51056e11i | 0.195616i | ||||||||
\(310\) | 1.65121e12 | 0.576760 | ||||||||
\(311\) | −2.41955e12 | −0.831635 | −0.415817 | − | 0.909448i | \(-0.636504\pi\) | ||||
−0.415817 | + | 0.909448i | \(0.636504\pi\) | |||||||
\(312\) | −7.35348e12 | −2.48725 | ||||||||
\(313\) | 3.43794e12i | 1.14440i | 0.820116 | + | 0.572198i | \(0.193909\pi\) | ||||
−0.820116 | + | 0.572198i | \(0.806091\pi\) | |||||||
\(314\) | −7.10219e11 | −0.232672 | ||||||||
\(315\) | 2.94607e12 | 0.949927 | ||||||||
\(316\) | −1.71636e12 | −0.544720 | ||||||||
\(317\) | 3.70850e11 | 0.115852 | 0.0579258 | − | 0.998321i | \(-0.481551\pi\) | ||||
0.0579258 | + | 0.998321i | \(0.481551\pi\) | |||||||
\(318\) | 3.93636e12 | 1.21049 | ||||||||
\(319\) | 2.61488e12i | 0.791585i | ||||||||
\(320\) | − | 7.57485e11i | − | 0.225748i | ||||||
\(321\) | − | 6.75375e12i | − | 1.98162i | ||||||
\(322\) | −3.99050e11 | −0.115278 | ||||||||
\(323\) | − | 7.88298e12i | − | 2.24222i | ||||||
\(324\) | 1.07362e12 | 0.300695 | ||||||||
\(325\) | −2.12927e12 | −0.587239 | ||||||||
\(326\) | 2.00913e12 | 0.545656 | ||||||||
\(327\) | 4.56119e12i | 1.21994i | ||||||||
\(328\) | − | 1.86625e12i | − | 0.491587i | ||||||
\(329\) | − | 8.83968e11i | − | 0.229328i | ||||||
\(330\) | 1.30505e12i | 0.333470i | ||||||||
\(331\) | 1.08567e11i | 0.0273247i | 0.999907 | + | 0.0136624i | \(0.00434900\pi\) | ||||
−0.999907 | + | 0.0136624i | \(0.995651\pi\) | |||||||
\(332\) | 6.82441e11 | 0.169190 | ||||||||
\(333\) | 1.12852e13i | 2.75605i | ||||||||
\(334\) | − | 2.35426e12i | − | 0.566398i | ||||||
\(335\) | − | 1.53455e12i | − | 0.363711i | ||||||
\(336\) | 1.22338e12 | 0.285669 | ||||||||
\(337\) | −4.77947e12 | −1.09959 | −0.549795 | − | 0.835300i | \(-0.685294\pi\) | ||||
−0.549795 | + | 0.835300i | \(0.685294\pi\) | |||||||
\(338\) | 3.98417e12i | 0.903140i | ||||||||
\(339\) | −1.40655e13 | −3.14164 | ||||||||
\(340\) | − | 5.03766e12i | − | 1.10875i | ||||||
\(341\) | −3.03093e12 | −0.657361 | ||||||||
\(342\) | 5.16137e12 | 1.10315 | ||||||||
\(343\) | 4.90542e12i | 1.03325i | ||||||||
\(344\) | −3.95932e12 | + | 1.77660e12i | −0.821918 | + | 0.368806i | ||||
\(345\) | 2.19286e12 | 0.448659 | ||||||||
\(346\) | 2.07924e12i | 0.419300i | ||||||||
\(347\) | − | 1.41224e12i | − | 0.280713i | −0.990101 | − | 0.140357i | \(-0.955175\pi\) | ||
0.990101 | − | 0.140357i | \(-0.0448249\pi\) | |||||||
\(348\) | 1.03020e13 | 2.01848 | ||||||||
\(349\) | − | 1.72628e12i | − | 0.333414i | −0.986006 | − | 0.166707i | \(-0.946687\pi\) | ||
0.986006 | − | 0.166707i | \(-0.0533134\pi\) | |||||||
\(350\) | −6.42922e11 | −0.122410 | ||||||||
\(351\) | − | 1.16134e13i | − | 2.17983i | ||||||
\(352\) | 2.67000e12i | 0.494080i | ||||||||
\(353\) | 6.27311e12 | 1.14448 | 0.572241 | − | 0.820085i | \(-0.306074\pi\) | ||||
0.572241 | + | 0.820085i | \(0.306074\pi\) | |||||||
\(354\) | 4.19195e12 | 0.754050 | ||||||||
\(355\) | −1.94741e12 | −0.345396 | ||||||||
\(356\) | − | 3.53441e12i | − | 0.618112i | ||||||
\(357\) | −1.21390e13 | −2.09335 | ||||||||
\(358\) | −4.36836e12 | −0.742854 | ||||||||
\(359\) | 6.17964e12 | 1.03631 | 0.518156 | − | 0.855286i | \(-0.326619\pi\) | ||||
0.518156 | + | 0.855286i | \(0.326619\pi\) | |||||||
\(360\) | 7.82728e12 | 1.29449 | ||||||||
\(361\) | −2.44416e12 | −0.398653 | ||||||||
\(362\) | − | 5.40137e12i | − | 0.868883i | ||||||
\(363\) | 8.13133e12i | 1.29011i | ||||||||
\(364\) | − | 5.08587e12i | − | 0.795900i | ||||||
\(365\) | 5.86422e11 | 0.0905203 | ||||||||
\(366\) | 5.27480e12i | 0.803158i | ||||||||
\(367\) | 2.58037e12 | 0.387571 | 0.193785 | − | 0.981044i | \(-0.437923\pi\) | ||||
0.193785 | + | 0.981044i | \(0.437923\pi\) | |||||||
\(368\) | 5.84165e11 | 0.0865559 | ||||||||
\(369\) | 6.68048e12 | 0.976508 | ||||||||
\(370\) | 4.46992e12i | 0.644602i | ||||||||
\(371\) | 6.46064e12i | 0.919192i | ||||||||
\(372\) | 1.19411e13i | 1.67622i | ||||||||
\(373\) | − | 3.98350e12i | − | 0.551722i | −0.961198 | − | 0.275861i | \(-0.911037\pi\) | ||
0.961198 | − | 0.275861i | \(-0.0889630\pi\) | |||||||
\(374\) | − | 3.44964e12i | − | 0.471428i | ||||||
\(375\) | 1.34783e13 | 1.81752 | ||||||||
\(376\) | − | 2.34858e12i | − | 0.312511i | ||||||
\(377\) | − | 2.08904e13i | − | 2.74309i | ||||||
\(378\) | − | 3.50659e12i | − | 0.454387i | ||||||
\(379\) | 5.15467e12 | 0.659181 | 0.329591 | − | 0.944124i | \(-0.393089\pi\) | ||||
0.329591 | + | 0.944124i | \(0.393089\pi\) | |||||||
\(380\) | −5.48004e12 | −0.691618 | ||||||||
\(381\) | 8.15158e11i | 0.101535i | ||||||||
\(382\) | −2.67550e12 | −0.328918 | ||||||||
\(383\) | 5.06981e11i | 0.0615174i | 0.999527 | + | 0.0307587i | \(0.00979234\pi\) | ||||
−0.999527 | + | 0.0307587i | \(0.990208\pi\) | |||||||
\(384\) | 1.23998e13 | 1.48511 | ||||||||
\(385\) | −2.14194e12 | −0.253223 | ||||||||
\(386\) | − | 2.44849e12i | − | 0.285734i | ||||||
\(387\) | −6.35958e12 | − | 1.41729e13i | −0.732611 | − | 1.63269i | ||||
\(388\) | −7.60497e12 | −0.864847 | ||||||||
\(389\) | 5.06187e12i | 0.568280i | 0.958783 | + | 0.284140i | \(0.0917081\pi\) | ||||
−0.958783 | + | 0.284140i | \(0.908292\pi\) | |||||||
\(390\) | − | 1.04261e13i | − | 1.15558i | ||||||
\(391\) | −5.79641e12 | −0.634271 | ||||||||
\(392\) | 4.69440e12i | 0.507166i | ||||||||
\(393\) | −7.59120e12 | −0.809744 | ||||||||
\(394\) | 2.51663e12i | 0.265056i | ||||||||
\(395\) | − | 5.77492e12i | − | 0.600565i | ||||||
\(396\) | −6.05447e12 | −0.621728 | ||||||||
\(397\) | 6.66168e12 | 0.675509 | 0.337755 | − | 0.941234i | \(-0.390333\pi\) | ||||
0.337755 | + | 0.941234i | \(0.390333\pi\) | |||||||
\(398\) | −3.72893e12 | −0.373395 | ||||||||
\(399\) | 1.32050e13i | 1.30579i | ||||||||
\(400\) | 9.41167e11 | 0.0919108 | ||||||||
\(401\) | 8.84283e12 | 0.852844 | 0.426422 | − | 0.904524i | \(-0.359774\pi\) | ||||
0.426422 | + | 0.904524i | \(0.359774\pi\) | |||||||
\(402\) | −4.13995e12 | −0.394335 | ||||||||
\(403\) | 2.42143e13 | 2.27796 | ||||||||
\(404\) | 1.32355e11 | 0.0122980 | ||||||||
\(405\) | 3.61234e12i | 0.331522i | ||||||||
\(406\) | − | 6.30774e12i | − | 0.571799i | ||||||
\(407\) | − | 8.20489e12i | − | 0.734684i | ||||||
\(408\) | −3.22516e13 | −2.85266 | ||||||||
\(409\) | − | 1.85041e12i | − | 0.161678i | −0.996727 | − | 0.0808391i | \(-0.974240\pi\) | ||
0.996727 | − | 0.0808391i | \(-0.0257600\pi\) | |||||||
\(410\) | 2.64606e12 | 0.228391 | ||||||||
\(411\) | 1.20052e13 | 1.02367 | ||||||||
\(412\) | −1.01260e12 | −0.0853004 | ||||||||
\(413\) | 6.88013e12i | 0.572594i | ||||||||
\(414\) | − | 3.79519e12i | − | 0.312055i | ||||||
\(415\) | 2.29616e12i | 0.186536i | ||||||||
\(416\) | − | 2.13308e13i | − | 1.71214i | ||||||
\(417\) | − | 3.18390e13i | − | 2.52511i | ||||||
\(418\) | −3.75257e12 | −0.294068 | ||||||||
\(419\) | − | 4.49945e12i | − | 0.348409i | −0.984709 | − | 0.174204i | \(-0.944265\pi\) | ||
0.984709 | − | 0.174204i | \(-0.0557354\pi\) | |||||||
\(420\) | 8.43872e12i | 0.645699i | ||||||||
\(421\) | 1.73413e13i | 1.31121i | 0.755105 | + | 0.655604i | \(0.227586\pi\) | ||||
−0.755105 | + | 0.655604i | \(0.772414\pi\) | |||||||
\(422\) | 4.57161e12 | 0.341591 | ||||||||
\(423\) | 8.40703e12 | 0.620784 | ||||||||
\(424\) | 1.71650e13i | 1.25261i | ||||||||
\(425\) | −9.33877e12 | −0.673512 | ||||||||
\(426\) | 5.25379e12i | 0.374477i | ||||||||
\(427\) | −8.65739e12 | −0.609884 | ||||||||
\(428\) | 1.24104e13 | 0.864106 | ||||||||
\(429\) | 1.91379e13i | 1.31707i | ||||||||
\(430\) | −2.51895e12 | − | 5.61371e12i | −0.171347 | − | 0.381863i | ||||
\(431\) | −1.53852e13 | −1.03447 | −0.517234 | − | 0.855844i | \(-0.673038\pi\) | ||||
−0.517234 | + | 0.855844i | \(0.673038\pi\) | |||||||
\(432\) | 5.13326e12i | 0.341173i | ||||||||
\(433\) | 8.11708e12i | 0.533286i | 0.963795 | + | 0.266643i | \(0.0859144\pi\) | ||||
−0.963795 | + | 0.266643i | \(0.914086\pi\) | |||||||
\(434\) | 7.31136e12 | 0.474843 | ||||||||
\(435\) | 3.46623e13i | 2.22542i | ||||||||
\(436\) | −8.38144e12 | −0.531969 | ||||||||
\(437\) | 6.30542e12i | 0.395646i | ||||||||
\(438\) | − | 1.58207e12i | − | 0.0981419i | ||||||
\(439\) | 1.67646e13 | 1.02819 | 0.514093 | − | 0.857734i | \(-0.328129\pi\) | ||||
0.514093 | + | 0.857734i | \(0.328129\pi\) | |||||||
\(440\) | −5.69082e12 | −0.345074 | ||||||||
\(441\) | −1.68042e13 | −1.00745 | ||||||||
\(442\) | 2.75594e13i | 1.63365i | ||||||||
\(443\) | 2.29764e13 | 1.34668 | 0.673338 | − | 0.739335i | \(-0.264860\pi\) | ||||
0.673338 | + | 0.739335i | \(0.264860\pi\) | |||||||
\(444\) | −3.23253e13 | −1.87339 | ||||||||
\(445\) | 1.18920e13 | 0.681481 | ||||||||
\(446\) | −4.24013e12 | −0.240273 | ||||||||
\(447\) | −1.11131e13 | −0.622728 | ||||||||
\(448\) | − | 3.35405e12i | − | 0.185857i | ||||||
\(449\) | 1.16891e13i | 0.640546i | 0.947325 | + | 0.320273i | \(0.103775\pi\) | ||||
−0.947325 | + | 0.320273i | \(0.896225\pi\) | |||||||
\(450\) | − | 6.11455e12i | − | 0.331361i | ||||||
\(451\) | −4.85704e12 | −0.260309 | ||||||||
\(452\) | − | 2.58461e13i | − | 1.36994i | ||||||
\(453\) | 2.38128e13 | 1.24830 | ||||||||
\(454\) | 1.55041e12 | 0.0803833 | ||||||||
\(455\) | 1.71121e13 | 0.877497 | ||||||||
\(456\) | 3.50838e13i | 1.77944i | ||||||||
\(457\) | − | 1.33810e13i | − | 0.671286i | −0.941989 | − | 0.335643i | \(-0.891046\pi\) | ||
0.941989 | − | 0.335643i | \(-0.108954\pi\) | |||||||
\(458\) | − | 2.90136e12i | − | 0.143971i | ||||||
\(459\) | − | 5.09350e13i | − | 2.50007i | ||||||
\(460\) | 4.02951e12i | 0.195642i | ||||||||
\(461\) | −1.17208e13 | −0.562927 | −0.281464 | − | 0.959572i | \(-0.590820\pi\) | ||||
−0.281464 | + | 0.959572i | \(0.590820\pi\) | |||||||
\(462\) | 5.77859e12i | 0.274544i | ||||||||
\(463\) | − | 2.52630e13i | − | 1.18735i | −0.804704 | − | 0.593676i | \(-0.797676\pi\) | ||
0.804704 | − | 0.593676i | \(-0.202324\pi\) | |||||||
\(464\) | 9.23382e12i | 0.429330i | ||||||||
\(465\) | −4.01774e13 | −1.84807 | ||||||||
\(466\) | 4.82502e12 | 0.219568 | ||||||||
\(467\) | 4.89076e10i | 0.00220187i | 0.999999 | + | 0.00110093i | \(0.000350438\pi\) | ||||
−0.999999 | + | 0.00110093i | \(0.999650\pi\) | |||||||
\(468\) | 4.83695e13 | 2.15448 | ||||||||
\(469\) | − | 6.79478e12i | − | 0.299441i | ||||||
\(470\) | 3.32992e12 | 0.145193 | ||||||||
\(471\) | 1.72811e13 | 0.745533 | ||||||||
\(472\) | 1.82795e13i | 0.780288i | ||||||||
\(473\) | 4.62373e12 | + | 1.03044e13i | 0.195293 | + | 0.435228i | ||||
\(474\) | −1.55797e13 | −0.651131 | ||||||||
\(475\) | 1.01589e13i | 0.420124i | ||||||||
\(476\) | − | 2.23061e13i | − | 0.912828i | ||||||
\(477\) | −6.14443e13 | −2.48822 | ||||||||
\(478\) | 1.55758e13i | 0.624183i | ||||||||
\(479\) | 3.88075e13 | 1.53900 | 0.769499 | − | 0.638648i | \(-0.220506\pi\) | ||||
0.769499 | + | 0.638648i | \(0.220506\pi\) | |||||||
\(480\) | 3.53930e13i | 1.38903i | ||||||||
\(481\) | 6.55493e13i | 2.54591i | ||||||||
\(482\) | −2.35348e13 | −0.904637 | ||||||||
\(483\) | 9.70972e12 | 0.369378 | ||||||||
\(484\) | −1.49418e13 | −0.562569 | ||||||||
\(485\) | − | 2.55879e13i | − | 0.953511i | ||||||
\(486\) | −8.89057e12 | −0.327905 | ||||||||
\(487\) | 5.88432e11 | 0.0214808 | 0.0107404 | − | 0.999942i | \(-0.496581\pi\) | ||||
0.0107404 | + | 0.999942i | \(0.496581\pi\) | |||||||
\(488\) | −2.30014e13 | −0.831105 | ||||||||
\(489\) | −4.88862e13 | −1.74840 | ||||||||
\(490\) | −6.65594e12 | −0.235629 | ||||||||
\(491\) | − | 5.31550e13i | − | 1.86267i | −0.364158 | − | 0.931337i | \(-0.618643\pi\) | ||
0.364158 | − | 0.931337i | \(-0.381357\pi\) | |||||||
\(492\) | 1.91356e13i | 0.663767i | ||||||||
\(493\) | − | 9.16230e13i | − | 3.14608i | ||||||
\(494\) | 2.99795e13 | 1.01904 | ||||||||
\(495\) | − | 2.03710e13i | − | 0.685468i | ||||||
\(496\) | −1.07030e13 | −0.356532 | ||||||||
\(497\) | −8.62290e12 | −0.284362 | ||||||||
\(498\) | 6.19465e12 | 0.202241 | ||||||||
\(499\) | 3.18268e13i | 1.02870i | 0.857579 | + | 0.514352i | \(0.171967\pi\) | ||||
−0.857579 | + | 0.514352i | \(0.828033\pi\) | |||||||
\(500\) | 2.47672e13i | 0.792551i | ||||||||
\(501\) | 5.72839e13i | 1.81486i | ||||||||
\(502\) | 9.28154e12i | 0.291140i | ||||||||
\(503\) | 4.15805e13i | 1.29137i | 0.763605 | + | 0.645684i | \(0.223428\pi\) | ||||
−0.763605 | + | 0.645684i | \(0.776572\pi\) | |||||||
\(504\) | 3.46582e13 | 1.06575 | ||||||||
\(505\) | 4.45325e11i | 0.0135588i | ||||||||
\(506\) | 2.75929e12i | 0.0831850i | ||||||||
\(507\) | − | 9.69432e13i | − | 2.89386i | ||||||
\(508\) | −1.49790e12 | −0.0442756 | ||||||||
\(509\) | 6.77543e13 | 1.98312 | 0.991558 | − | 0.129662i | \(-0.0413892\pi\) | ||||
0.991558 | + | 0.129662i | \(0.0413892\pi\) | |||||||
\(510\) | − | 4.57278e13i | − | 1.32535i | ||||||
\(511\) | 2.59660e12 | 0.0745248 | ||||||||
\(512\) | 1.76293e13i | 0.501054i | ||||||||
\(513\) | −5.54079e13 | −1.55950 | ||||||||
\(514\) | 2.16309e13 | 0.602920 | ||||||||
\(515\) | − | 3.40701e12i | − | 0.0940454i | ||||||
\(516\) | 4.05968e13 | − | 1.82164e13i | 1.10980 | − | 0.497982i | ||||
\(517\) | −6.11233e12 | −0.165483 | ||||||||
\(518\) | 1.97923e13i | 0.530697i | ||||||||
\(519\) | − | 5.05923e13i | − | 1.34353i | ||||||
\(520\) | 4.54643e13 | 1.19579 | ||||||||
\(521\) | 2.87429e13i | 0.748758i | 0.927276 | + | 0.374379i | \(0.122144\pi\) | ||||
−0.927276 | + | 0.374379i | \(0.877856\pi\) | |||||||
\(522\) | 5.99901e13 | 1.54784 | ||||||||
\(523\) | 3.41560e12i | 0.0872888i | 0.999047 | + | 0.0436444i | \(0.0138969\pi\) | ||||
−0.999047 | + | 0.0436444i | \(0.986103\pi\) | |||||||
\(524\) | − | 1.39493e13i | − | 0.353098i | ||||||
\(525\) | 1.56436e13 | 0.392230 | ||||||||
\(526\) | 2.43131e13 | 0.603826 | ||||||||
\(527\) | 1.06201e14 | 2.61262 | ||||||||
\(528\) | − | 8.45921e12i | − | 0.206139i | ||||||
\(529\) | −3.67901e13 | −0.888081 | ||||||||
\(530\) | −2.43373e13 | −0.581960 | ||||||||
\(531\) | −6.54339e13 | −1.54999 | ||||||||
\(532\) | −2.42649e13 | −0.569405 | ||||||||
\(533\) | 3.88031e13 | 0.902051 | ||||||||
\(534\) | − | 3.20825e13i | − | 0.738860i | ||||||
\(535\) | 4.17564e13i | 0.952694i | ||||||||
\(536\) | − | 1.80528e13i | − | 0.408056i | ||||||
\(537\) | 1.06291e14 | 2.38027 | ||||||||
\(538\) | − | 1.10992e13i | − | 0.246252i | ||||||
\(539\) | 1.22175e13 | 0.268558 | ||||||||
\(540\) | −3.54087e13 | −0.771154 | ||||||||
\(541\) | −8.41281e13 | −1.81533 | −0.907664 | − | 0.419698i | \(-0.862136\pi\) | ||||
−0.907664 | + | 0.419698i | \(0.862136\pi\) | |||||||
\(542\) | 8.26683e12i | 0.176743i | ||||||||
\(543\) | 1.31427e14i | 2.78409i | ||||||||
\(544\) | − | 9.35545e13i | − | 1.96368i | ||||||
\(545\) | − | 2.82004e13i | − | 0.586507i | ||||||
\(546\) | − | 4.61654e13i | − | 0.951379i | ||||||
\(547\) | −6.17362e13 | −1.26067 | −0.630337 | − | 0.776321i | \(-0.717083\pi\) | ||||
−0.630337 | + | 0.776321i | \(0.717083\pi\) | |||||||
\(548\) | 2.20603e13i | 0.446384i | ||||||||
\(549\) | − | 8.23366e13i | − | 1.65094i | ||||||
\(550\) | 4.44558e12i | 0.0883314i | ||||||||
\(551\) | −9.96690e13 | −1.96247 | ||||||||
\(552\) | 2.57973e13 | 0.503361 | ||||||||
\(553\) | − | 2.55706e13i | − | 0.494442i | ||||||
\(554\) | −4.64148e13 | −0.889422 | ||||||||
\(555\) | − | 1.08763e14i | − | 2.06545i | ||||||
\(556\) | 5.85060e13 | 1.10110 | ||||||||
\(557\) | −1.78793e12 | −0.0333483 | −0.0166742 | − | 0.999861i | \(-0.505308\pi\) | ||||
−0.0166742 | + | 0.999861i | \(0.505308\pi\) | |||||||
\(558\) | 6.95351e13i | 1.28539i | ||||||||
\(559\) | −3.69392e13 | − | 8.23224e13i | −0.676751 | − | 1.50820i | ||||
\(560\) | −7.56376e12 | −0.137340 | ||||||||
\(561\) | 8.39369e13i | 1.51056i | ||||||||
\(562\) | − | 9.06980e12i | − | 0.161777i | ||||||
\(563\) | −9.07777e13 | −1.60486 | −0.802430 | − | 0.596747i | \(-0.796460\pi\) | ||||
−0.802430 | + | 0.596747i | \(0.796460\pi\) | |||||||
\(564\) | 2.40811e13i | 0.421969i | ||||||||
\(565\) | 8.69625e13 | 1.51039 | ||||||||
\(566\) | 2.98519e13i | 0.513913i | ||||||||
\(567\) | 1.59950e13i | 0.272940i | ||||||||
\(568\) | −2.29098e13 | −0.387507 | ||||||||
\(569\) | −3.84255e13 | −0.644255 | −0.322128 | − | 0.946696i | \(-0.604398\pi\) | ||||
−0.322128 | + | 0.946696i | \(0.604398\pi\) | |||||||
\(570\) | −4.97434e13 | −0.826725 | ||||||||
\(571\) | − | 3.72579e13i | − | 0.613816i | −0.951739 | − | 0.306908i | \(-0.900706\pi\) | ||
0.951739 | − | 0.306908i | \(-0.0992943\pi\) | |||||||
\(572\) | −3.51670e13 | −0.574322 | ||||||||
\(573\) | 6.51005e13 | 1.05393 | ||||||||
\(574\) | 1.17164e13 | 0.188033 | ||||||||
\(575\) | 7.46987e12 | 0.118843 | ||||||||
\(576\) | 3.18988e13 | 0.503110 | ||||||||
\(577\) | 1.11966e13i | 0.175068i | 0.996162 | + | 0.0875338i | \(0.0278986\pi\) | ||||
−0.996162 | + | 0.0875338i | \(0.972101\pi\) | |||||||
\(578\) | 8.72460e13i | 1.35240i | ||||||||
\(579\) | 5.95768e13i | 0.915556i | ||||||||
\(580\) | −6.36940e13 | −0.970417 | ||||||||
\(581\) | 1.01671e13i | 0.153574i | ||||||||
\(582\) | −6.90318e13 | −1.03379 | ||||||||
\(583\) | 4.46730e13 | 0.663289 | ||||||||
\(584\) | 6.89880e12 | 0.101557 | ||||||||
\(585\) | 1.62745e14i | 2.37536i | ||||||||
\(586\) | 2.72035e13i | 0.393674i | ||||||||
\(587\) | 1.88182e13i | 0.270014i | 0.990845 | + | 0.135007i | \(0.0431057\pi\) | ||||
−0.990845 | + | 0.135007i | \(0.956894\pi\) | |||||||
\(588\) | − | 4.81340e13i | − | 0.684802i | ||||||
\(589\) | − | 1.15527e14i | − | 1.62970i | ||||||
\(590\) | −2.59176e13 | −0.362522 | ||||||||
\(591\) | − | 6.12347e13i | − | 0.849299i | ||||||
\(592\) | − | 2.89737e13i | − | 0.398469i | ||||||
\(593\) | 4.85616e13i | 0.662246i | 0.943588 | + | 0.331123i | \(0.107428\pi\) | ||||
−0.943588 | + | 0.331123i | \(0.892572\pi\) | |||||||
\(594\) | −2.42468e13 | −0.327886 | ||||||||
\(595\) | 7.50517e13 | 1.00641 | ||||||||
\(596\) | − | 2.04210e13i | − | 0.271547i | ||||||
\(597\) | 9.07326e13 | 1.19644 | ||||||||
\(598\) | − | 2.20441e13i | − | 0.288262i | ||||||
\(599\) | 4.38950e12 | 0.0569222 | 0.0284611 | − | 0.999595i | \(-0.490939\pi\) | ||||
0.0284611 | + | 0.999595i | \(0.490939\pi\) | |||||||
\(600\) | 4.15629e13 | 0.534502 | ||||||||
\(601\) | 1.15896e14i | 1.47808i | 0.673664 | + | 0.739038i | \(0.264720\pi\) | ||||
−0.673664 | + | 0.739038i | \(0.735280\pi\) | |||||||
\(602\) | −1.11536e13 | − | 2.48568e13i | −0.141069 | − | 0.314385i | ||||
\(603\) | 6.46222e13 | 0.810578 | ||||||||
\(604\) | 4.37574e13i | 0.544335i | ||||||||
\(605\) | − | 5.02735e13i | − | 0.620243i | ||||||
\(606\) | 1.20141e12 | 0.0147004 | ||||||||
\(607\) | 1.57153e14i | 1.90712i | 0.301200 | + | 0.953561i | \(0.402613\pi\) | ||||
−0.301200 | + | 0.953561i | \(0.597387\pi\) | |||||||
\(608\) | −1.01770e14 | −1.22490 | ||||||||
\(609\) | 1.53480e14i | 1.83217i | ||||||||
\(610\) | − | 3.26125e13i | − | 0.386131i | ||||||
\(611\) | 4.88317e13 | 0.573450 | ||||||||
\(612\) | 2.12143e14 | 2.47100 | ||||||||
\(613\) | 3.49249e13 | 0.403490 | 0.201745 | − | 0.979438i | \(-0.435339\pi\) | ||||
0.201745 | + | 0.979438i | \(0.435339\pi\) | |||||||
\(614\) | − | 7.05126e13i | − | 0.808025i | ||||||
\(615\) | −6.43840e13 | −0.731817 | ||||||||
\(616\) | −2.51982e13 | −0.284097 | ||||||||
\(617\) | 7.37831e13 | 0.825147 | 0.412573 | − | 0.910924i | \(-0.364630\pi\) | ||||
0.412573 | + | 0.910924i | \(0.364630\pi\) | |||||||
\(618\) | −9.19154e12 | −0.101964 | ||||||||
\(619\) | −1.02207e14 | −1.12467 | −0.562337 | − | 0.826908i | \(-0.690098\pi\) | ||||
−0.562337 | + | 0.826908i | \(0.690098\pi\) | |||||||
\(620\) | − | 7.38283e13i | − | 0.805869i | ||||||
\(621\) | 4.07418e13i | 0.441146i | ||||||||
\(622\) | − | 4.03578e13i | − | 0.433486i | ||||||
\(623\) | 5.26562e13 | 0.561059 | ||||||||
\(624\) | 6.75811e13i | 0.714335i | ||||||||
\(625\) | −4.94541e13 | −0.518564 | ||||||||
\(626\) | −5.73443e13 | −0.596511 | ||||||||
\(627\) | 9.13079e13 | 0.942259 | ||||||||
\(628\) | 3.17550e13i | 0.325098i | ||||||||
\(629\) | 2.87493e14i | 2.91994i | ||||||||
\(630\) | 4.91400e13i | 0.495145i | ||||||||
\(631\) | − | 1.28225e14i | − | 1.28182i | −0.767618 | − | 0.640908i | \(-0.778558\pi\) | ||
0.767618 | − | 0.640908i | \(-0.221442\pi\) | |||||||
\(632\) | − | 6.79374e13i | − | 0.673788i | ||||||
\(633\) | −1.11237e14 | −1.09454 | ||||||||
\(634\) | 6.18572e12i | 0.0603871i | ||||||||
\(635\) | − | 5.03987e12i | − | 0.0488147i | ||||||
\(636\) | − | 1.76001e14i | − | 1.69133i | ||||||
\(637\) | −9.76063e13 | −0.930637 | ||||||||
\(638\) | −4.36157e13 | −0.412610 | ||||||||
\(639\) | − | 8.20086e13i | − | 0.769760i | ||||||
\(640\) | −7.66641e13 | −0.713990 | ||||||||
\(641\) | 8.53595e13i | 0.788791i | 0.918941 | + | 0.394395i | \(0.129046\pi\) | ||||
−0.918941 | + | 0.394395i | \(0.870954\pi\) | |||||||
\(642\) | 1.12652e14 | 1.03291 | ||||||||
\(643\) | −1.93404e14 | −1.75959 | −0.879795 | − | 0.475354i | \(-0.842320\pi\) | ||||
−0.879795 | + | 0.475354i | \(0.842320\pi\) | |||||||
\(644\) | 1.78422e13i | 0.161071i | ||||||||
\(645\) | 6.12913e13 | + | 1.36593e14i | 0.549035 | + | 1.22357i | ||||
\(646\) | 1.31487e14 | 1.16875 | ||||||||
\(647\) | 7.73921e12i | 0.0682614i | 0.999417 | + | 0.0341307i | \(0.0108663\pi\) | ||||
−0.999417 | + | 0.0341307i | \(0.989134\pi\) | |||||||
\(648\) | 4.24963e13i | 0.371943i | ||||||||
\(649\) | 4.75737e13 | 0.413184 | ||||||||
\(650\) | − | 3.55160e13i | − | 0.306096i | ||||||
\(651\) | −1.77901e14 | −1.52150 | ||||||||
\(652\) | − | 8.98311e13i | − | 0.762411i | ||||||
\(653\) | 1.09094e14i | 0.918832i | 0.888221 | + | 0.459416i | \(0.151941\pi\) | ||||
−0.888221 | + | 0.459416i | \(0.848059\pi\) | |||||||
\(654\) | −7.60800e13 | −0.635889 | ||||||||
\(655\) | 4.69341e13 | 0.389298 | ||||||||
\(656\) | −1.71515e13 | −0.141183 | ||||||||
\(657\) | 2.46951e13i | 0.201736i | ||||||||
\(658\) | 1.47445e13 | 0.119536 | ||||||||
\(659\) | −1.90131e14 | −1.52977 | −0.764885 | − | 0.644167i | \(-0.777204\pi\) | ||||
−0.764885 | + | 0.644167i | \(0.777204\pi\) | |||||||
\(660\) | 5.83507e13 | 0.465936 | ||||||||
\(661\) | 1.49707e14 | 1.18641 | 0.593205 | − | 0.805052i | \(-0.297863\pi\) | ||||
0.593205 | + | 0.805052i | \(0.297863\pi\) | |||||||
\(662\) | −1.81087e12 | −0.0142429 | ||||||||
\(663\) | − | 6.70576e14i | − | 5.23456i | ||||||
\(664\) | 2.70125e13i | 0.209279i | ||||||||
\(665\) | − | 8.16424e13i | − | 0.627780i | ||||||
\(666\) | −1.88235e14 | −1.43658 | ||||||||
\(667\) | 7.32872e13i | 0.555136i | ||||||||
\(668\) | −1.05263e14 | −0.791392 | ||||||||
\(669\) | 1.03171e14 | 0.769889 | ||||||||
\(670\) | 2.55960e13 | 0.189583 | ||||||||
\(671\) | 5.98628e13i | 0.440093i | ||||||||
\(672\) | 1.56716e14i | 1.14358i | ||||||||
\(673\) | − | 9.38323e13i | − | 0.679637i | −0.940491 | − | 0.339819i | \(-0.889634\pi\) | ||
0.940491 | − | 0.339819i | \(-0.110366\pi\) | |||||||
\(674\) | − | 7.97209e13i | − | 0.573156i | ||||||
\(675\) | 6.56404e13i | 0.468438i | ||||||||
\(676\) | 1.78139e14 | 1.26190 | ||||||||
\(677\) | 1.72758e14i | 1.21477i | 0.794408 | + | 0.607385i | \(0.207781\pi\) | ||||
−0.794408 | + | 0.607385i | \(0.792219\pi\) | |||||||
\(678\) | − | 2.34610e14i | − | 1.63756i | ||||||
\(679\) | − | 1.13300e14i | − | 0.785020i | ||||||
\(680\) | 1.99402e14 | 1.37146 | ||||||||
\(681\) | −3.77246e13 | −0.257566 | ||||||||
\(682\) | − | 5.05555e13i | − | 0.342647i | ||||||
\(683\) | 5.54255e12 | 0.0372912 | 0.0186456 | − | 0.999826i | \(-0.494065\pi\) | ||||
0.0186456 | + | 0.999826i | \(0.494065\pi\) | |||||||
\(684\) | − | 2.30773e14i | − | 1.54136i | ||||||
\(685\) | −7.42247e13 | −0.492148 | ||||||||
\(686\) | −8.18217e13 | −0.538577 | ||||||||
\(687\) | 7.05962e13i | 0.461315i | ||||||||
\(688\) | 1.63276e13 | + | 3.63876e13i | 0.105921 | + | 0.236054i | ||||
\(689\) | −3.56895e14 | −2.29850 | ||||||||
\(690\) | 3.65766e13i | 0.233861i | ||||||||
\(691\) | − | 1.88483e14i | − | 1.19642i | −0.801341 | − | 0.598208i | \(-0.795879\pi\) | ||
0.801341 | − | 0.598208i | \(-0.204121\pi\) | |||||||
\(692\) | 9.29662e13 | 0.585861 | ||||||||
\(693\) | − | 9.02003e13i | − | 0.564341i | ||||||
\(694\) | 2.35560e13 | 0.146320 | ||||||||
\(695\) | 1.96851e14i | 1.21399i | ||||||||
\(696\) | 4.07775e14i | 2.49675i | ||||||||
\(697\) | 1.70187e14 | 1.03457 | ||||||||
\(698\) | 2.87941e13 | 0.173791 | ||||||||
\(699\) | −1.17403e14 | −0.703546 | ||||||||
\(700\) | 2.87461e13i | 0.171036i | ||||||||
\(701\) | 2.13063e14 | 1.25869 | 0.629345 | − | 0.777126i | \(-0.283323\pi\) | ||||
0.629345 | + | 0.777126i | \(0.283323\pi\) | |||||||
\(702\) | 1.93709e14 | 1.13623 | ||||||||
\(703\) | 3.12739e14 | 1.82140 | ||||||||
\(704\) | −2.31920e13 | −0.134114 | ||||||||
\(705\) | −8.10239e13 | −0.465230 | ||||||||
\(706\) | 1.04635e14i | 0.596556i | ||||||||
\(707\) | 1.97184e12i | 0.0111628i | ||||||||
\(708\) | − | 1.87429e14i | − | 1.05359i | ||||||
\(709\) | −2.23426e14 | −1.24710 | −0.623551 | − | 0.781782i | \(-0.714311\pi\) | ||||
−0.623551 | + | 0.781782i | \(0.714311\pi\) | |||||||
\(710\) | − | 3.24826e13i | − | 0.180036i | ||||||
\(711\) | 2.43191e14 | 1.33844 | ||||||||
\(712\) | 1.39900e14 | 0.764570 | ||||||||
\(713\) | −8.49480e13 | −0.461005 | ||||||||
\(714\) | − | 2.02477e14i | − | 1.09115i | ||||||
\(715\) | − | 1.18324e14i | − | 0.633202i | ||||||
\(716\) | 1.95316e14i | 1.03794i | ||||||||
\(717\) | − | 3.78992e14i | − | 2.00002i | ||||||
\(718\) | 1.03075e14i | 0.540173i | ||||||||
\(719\) | 1.59686e13 | 0.0831039 | 0.0415519 | − | 0.999136i | \(-0.486770\pi\) | ||||
0.0415519 | + | 0.999136i | \(0.486770\pi\) | |||||||
\(720\) | − | 7.19355e13i | − | 0.371776i | ||||||
\(721\) | − | 1.50858e13i | − | 0.0774270i | ||||||
\(722\) | − | 4.07683e13i | − | 0.207796i | ||||||
\(723\) | 5.72649e14 | 2.89866 | ||||||||
\(724\) | −2.41504e14 | −1.21403 | ||||||||
\(725\) | 1.18075e14i | 0.589480i | ||||||||
\(726\) | −1.35629e14 | −0.672466 | ||||||||
\(727\) | − | 1.71498e14i | − | 0.844478i | −0.906485 | − | 0.422239i | \(-0.861244\pi\) | ||
0.906485 | − | 0.422239i | \(-0.138756\pi\) | |||||||
\(728\) | 2.01310e14 | 0.984484 | ||||||||
\(729\) | 3.01332e14 | 1.46355 | ||||||||
\(730\) | 9.78143e12i | 0.0471833i | ||||||||
\(731\) | −1.62012e14 | − | 3.61057e14i | −0.776174 | − | 1.72977i | ||||
\(732\) | 2.35845e14 | 1.12220 | ||||||||
\(733\) | 2.82615e14i | 1.33560i | 0.744342 | + | 0.667799i | \(0.232763\pi\) | ||||
−0.744342 | + | 0.667799i | \(0.767237\pi\) | |||||||
\(734\) | 4.30401e13i | 0.202019i | ||||||||
\(735\) | 1.61953e14 | 0.755009 | ||||||||
\(736\) | 7.48321e13i | 0.346497i | ||||||||
\(737\) | −4.69835e13 | −0.216077 | ||||||||
\(738\) | 1.11429e14i | 0.509000i | ||||||||
\(739\) | 2.45807e14i | 1.11525i | 0.830093 | + | 0.557625i | \(0.188287\pi\) | ||||
−0.830093 | + | 0.557625i | \(0.811713\pi\) | |||||||
\(740\) | 1.99857e14 | 0.900661 | ||||||||
\(741\) | −7.29463e14 | −3.26522 | ||||||||
\(742\) | −1.07763e14 | −0.479124 | ||||||||
\(743\) | 1.73003e14i | 0.764030i | 0.924156 | + | 0.382015i | \(0.124770\pi\) | ||||
−0.924156 | + | 0.382015i | \(0.875230\pi\) | |||||||
\(744\) | −4.72656e14 | −2.07339 | ||||||||
\(745\) | 6.87090e13 | 0.299387 | ||||||||
\(746\) | 6.64442e13 | 0.287583 | ||||||||
\(747\) | −9.66948e13 | −0.415719 | ||||||||
\(748\) | −1.54239e14 | −0.658697 | ||||||||
\(749\) | 1.84892e14i | 0.784348i | ||||||||
\(750\) | 2.24817e14i | 0.947376i | ||||||||
\(751\) | 1.68192e14i | 0.704054i | 0.935990 | + | 0.352027i | \(0.114507\pi\) | ||||
−0.935990 | + | 0.352027i | \(0.885493\pi\) | |||||||
\(752\) | −2.15843e13 | −0.0897528 | ||||||||
\(753\) | − | 2.25839e14i | − | 0.932877i | ||||||
\(754\) | 3.48449e14 | 1.42982 | ||||||||
\(755\) | −1.47227e14 | −0.600141 | ||||||||
\(756\) | −1.56785e14 | −0.634887 | ||||||||
\(757\) | 1.98344e14i | 0.797883i | 0.916976 | + | 0.398942i | \(0.130622\pi\) | ||||
−0.916976 | + | 0.398942i | \(0.869378\pi\) | |||||||
\(758\) | 8.59791e13i | 0.343595i | ||||||||
\(759\) | − | 6.71392e13i | − | 0.266543i | ||||||
\(760\) | − | 2.16912e14i | − | 0.855492i | ||||||
\(761\) | − | 2.64042e14i | − | 1.03455i | −0.855820 | − | 0.517273i | \(-0.826947\pi\) | ||
0.855820 | − | 0.517273i | \(-0.173053\pi\) | |||||||
\(762\) | −1.35967e13 | −0.0529248 | ||||||||
\(763\) | − | 1.24868e14i | − | 0.482868i | ||||||
\(764\) | 1.19626e14i | 0.459577i | ||||||||
\(765\) | 7.13784e14i | 2.72433i | ||||||||
\(766\) | −8.45637e12 | −0.0320657 | ||||||||
\(767\) | −3.80069e14 | −1.43181 | ||||||||
\(768\) | 3.32284e14i | 1.24367i | ||||||||
\(769\) | 4.16117e14 | 1.54733 | 0.773667 | − | 0.633592i | \(-0.218420\pi\) | ||||
0.773667 | + | 0.633592i | \(0.218420\pi\) | |||||||
\(770\) | − | 3.57272e13i | − | 0.131991i | ||||||
\(771\) | −5.26325e14 | −1.93189 | ||||||||
\(772\) | −1.09476e14 | −0.399238 | ||||||||
\(773\) | 8.38066e13i | 0.303655i | 0.988407 | + | 0.151828i | \(0.0485158\pi\) | ||||
−0.988407 | + | 0.151828i | \(0.951484\pi\) | |||||||
\(774\) | 2.36402e14 | − | 1.06077e14i | 0.851032 | − | 0.381870i | ||||
\(775\) | −1.36862e14 | −0.489526 | ||||||||
\(776\) | − | 3.01022e14i | − | 1.06977i | ||||||
\(777\) | − | 4.81587e14i | − | 1.70047i | ||||||
\(778\) | −8.44312e13 | −0.296214 | ||||||||
\(779\) | − | 1.85132e14i | − | 0.645347i | ||||||
\(780\) | −4.66167e14 | −1.61461 | ||||||||
\(781\) | 5.96243e13i | 0.205196i | ||||||||
\(782\) | − | 9.66832e13i | − | 0.330611i | ||||||
\(783\) | −6.44000e14 | −2.18815 | ||||||||
\(784\) | 4.31432e13 | 0.145657 | ||||||||
\(785\) | −1.06844e14 | −0.358427 | ||||||||
\(786\) | − | 1.26620e14i | − | 0.422075i | ||||||
\(787\) | 4.02270e14 | 1.33243 | 0.666215 | − | 0.745760i | \(-0.267913\pi\) | ||||
0.666215 | + | 0.745760i | \(0.267913\pi\) | |||||||
\(788\) | 1.12522e14 | 0.370346 | ||||||||
\(789\) | −5.91589e14 | −1.93479 | ||||||||
\(790\) | 9.63248e13 | 0.313042 | ||||||||
\(791\) | 3.85059e14 | 1.24350 | ||||||||
\(792\) | − | 2.39649e14i | − | 0.769042i | ||||||
\(793\) | − | 4.78247e14i | − | 1.52506i | ||||||
\(794\) | 1.11116e14i | 0.352106i | ||||||||
\(795\) | 5.92177e14 | 1.86473 | ||||||||
\(796\) | 1.66726e14i | 0.521722i | ||||||||
\(797\) | −2.47975e12 | −0.00771109 | −0.00385555 | − | 0.999993i | \(-0.501227\pi\) | ||||
−0.00385555 | + | 0.999993i | \(0.501227\pi\) | |||||||
\(798\) | −2.20257e14 | −0.680638 | ||||||||
\(799\) | 2.14171e14 | 0.657698 | ||||||||
\(800\) | 1.20564e14i | 0.367933i | ||||||||
\(801\) | 5.00789e14i | 1.51877i | ||||||||
\(802\) | 1.47497e14i | 0.444541i | ||||||||
\(803\) | − | 1.79546e13i | − | 0.0537771i | ||||||
\(804\) | 1.85104e14i | 0.550979i | ||||||||
\(805\) | −6.00322e13 | −0.177584 | ||||||||
\(806\) | 4.03890e14i | 1.18738i | ||||||||
\(807\) | 2.70066e14i | 0.789046i | ||||||||
\(808\) | 5.23890e12i | 0.0152119i | ||||||||
\(809\) | 3.81321e14 | 1.10039 | 0.550197 | − | 0.835035i | \(-0.314553\pi\) | ||||
0.550197 | + | 0.835035i | \(0.314553\pi\) | |||||||
\(810\) | −6.02532e13 | −0.172805 | ||||||||
\(811\) | − | 3.74301e13i | − | 0.106688i | −0.998576 | − | 0.0533442i | \(-0.983012\pi\) | ||
0.998576 | − | 0.0533442i | \(-0.0169880\pi\) | |||||||
\(812\) | −2.82029e14 | −0.798938 | ||||||||
\(813\) | − | 2.01149e14i | − | 0.566324i | ||||||
\(814\) | 1.36856e14 | 0.382951 | ||||||||
\(815\) | 3.02248e14 | 0.840573 | ||||||||
\(816\) | 2.96403e14i | 0.819280i | ||||||||
\(817\) | −3.92764e14 | + | 1.76239e14i | −1.07900 | + | 0.484162i | ||||
\(818\) | 3.08646e13 | 0.0842740 | ||||||||
\(819\) | 7.20615e14i | 1.95562i | ||||||||
\(820\) | − | 1.18309e14i | − | 0.319117i | ||||||
\(821\) | 2.48957e14 | 0.667434 | 0.333717 | − | 0.942673i | \(-0.391697\pi\) | ||||
0.333717 | + | 0.942673i | \(0.391697\pi\) | |||||||
\(822\) | 2.00246e14i | 0.533585i | ||||||||
\(823\) | 7.28643e14 | 1.92981 | 0.964907 | − | 0.262590i | \(-0.0845768\pi\) | ||||
0.964907 | + | 0.262590i | \(0.0845768\pi\) | |||||||
\(824\) | − | 4.00809e13i | − | 0.105512i | ||||||
\(825\) | − | 1.08170e14i | − | 0.283033i | ||||||
\(826\) | −1.14760e14 | −0.298462 | ||||||||
\(827\) | −1.70887e14 | −0.441755 | −0.220878 | − | 0.975302i | \(-0.570892\pi\) | ||||
−0.220878 | + | 0.975302i | \(0.570892\pi\) | |||||||
\(828\) | −1.69689e14 | −0.436015 | ||||||||
\(829\) | − | 4.73101e14i | − | 1.20832i | −0.796864 | − | 0.604159i | \(-0.793509\pi\) | ||
0.796864 | − | 0.604159i | \(-0.206491\pi\) | |||||||
\(830\) | −3.82996e13 | −0.0972308 | ||||||||
\(831\) | 1.12937e15 | 2.84991 | ||||||||
\(832\) | 1.85282e14 | 0.464748 | ||||||||
\(833\) | −4.28091e14 | −1.06736 | ||||||||
\(834\) | 5.31070e14 | 1.31620 | ||||||||
\(835\) | − | 3.54169e14i | − | 0.872526i | ||||||
\(836\) | 1.67783e14i | 0.410882i | ||||||||
\(837\) | − | 7.46467e14i | − | 1.81712i | ||||||
\(838\) | 7.50502e13 | 0.181607 | ||||||||
\(839\) | 6.55885e14i | 1.57768i | 0.614601 | + | 0.788838i | \(0.289317\pi\) | ||||
−0.614601 | + | 0.788838i | \(0.710683\pi\) | |||||||
\(840\) | −3.34023e14 | −0.798693 | ||||||||
\(841\) | −7.37734e14 | −1.75356 | ||||||||
\(842\) | −2.89251e14 | −0.683461 | ||||||||
\(843\) | 2.20687e14i | 0.518369i | ||||||||
\(844\) | − | 2.04404e14i | − | 0.477284i | ||||||
\(845\) | 5.99370e14i | 1.39127i | ||||||||
\(846\) | 1.40228e14i | 0.323581i | ||||||||
\(847\) | − | 2.22605e14i | − | 0.510643i | ||||||
\(848\) | 1.57752e14 | 0.359747 | ||||||||
\(849\) | − | 7.26358e14i | − | 1.64669i | ||||||
\(850\) | − | 1.55769e14i | − | 0.351065i | ||||||
\(851\) | − | 2.29959e14i | − | 0.515231i | ||||||
\(852\) | 2.34905e14 | 0.523233 | ||||||||
\(853\) | −1.94723e14 | −0.431194 | −0.215597 | − | 0.976482i | \(-0.569170\pi\) | ||||
−0.215597 | + | 0.976482i | \(0.569170\pi\) | |||||||
\(854\) | − | 1.44404e14i | − | 0.317899i | ||||||
\(855\) | 7.76465e14 | 1.69938 | ||||||||
\(856\) | 4.91231e14i | 1.06885i | ||||||||
\(857\) | 3.78101e14 | 0.817906 | 0.408953 | − | 0.912555i | \(-0.365894\pi\) | ||||
0.408953 | + | 0.912555i | \(0.365894\pi\) | |||||||
\(858\) | −3.19218e14 | −0.686516 | ||||||||
\(859\) | 4.26496e13i | 0.0911903i | 0.998960 | + | 0.0455952i | \(0.0145184\pi\) | ||||
−0.998960 | + | 0.0455952i | \(0.985482\pi\) | |||||||
\(860\) | −2.50998e14 | + | 1.12626e14i | −0.533553 | + | 0.239413i | ||||
\(861\) | −2.85084e14 | −0.602500 | ||||||||
\(862\) | − | 2.56623e14i | − | 0.539212i | ||||||
\(863\) | 8.81338e14i | 1.84115i | 0.390569 | + | 0.920574i | \(0.372278\pi\) | ||||
−0.390569 | + | 0.920574i | \(0.627722\pi\) | |||||||
\(864\) | −6.57576e14 | −1.36577 | ||||||||
\(865\) | 3.12797e14i | 0.645924i | ||||||||
\(866\) | −1.35392e14 | −0.277973 | ||||||||
\(867\) | − | 2.12288e15i | − | 4.33340i | ||||||
\(868\) | − | 3.26903e14i | − | 0.663467i | ||||||
\(869\) | −1.76812e14 | −0.356789 | ||||||||
\(870\) | −5.78162e14 | −1.15999 | ||||||||
\(871\) | 3.75354e14 | 0.748773 | ||||||||
\(872\) | − | 3.31756e14i | − | 0.658016i | ||||||
\(873\) | 1.07755e15 | 2.12503 | ||||||||
\(874\) | −1.05174e14 | −0.206229 | ||||||||
\(875\) | −3.68986e14 | −0.719398 | ||||||||
\(876\) | −7.07367e13 | −0.137127 | ||||||||
\(877\) | −3.78193e14 | −0.728979 | −0.364489 | − | 0.931208i | \(-0.618756\pi\) | ||||
−0.364489 | + | 0.931208i | \(0.618756\pi\) | |||||||
\(878\) | 2.79632e14i | 0.535937i | ||||||||
\(879\) | − | 6.61918e14i | − | 1.26142i | ||||||
\(880\) | 5.23007e13i | 0.0991046i | ||||||||
\(881\) | 3.65860e14 | 0.689343 | 0.344672 | − | 0.938723i | \(-0.387990\pi\) | ||||
0.344672 | + | 0.938723i | \(0.387990\pi\) | |||||||
\(882\) | − | 2.80292e14i | − | 0.525131i | ||||||
\(883\) | −5.91275e14 | −1.10150 | −0.550752 | − | 0.834669i | \(-0.685659\pi\) | ||||
−0.550752 | + | 0.834669i | \(0.685659\pi\) | |||||||
\(884\) | 1.23222e15 | 2.28259 | ||||||||
\(885\) | 6.30628e14 | 1.16160 | ||||||||
\(886\) | 3.83243e14i | 0.701949i | ||||||||
\(887\) | − | 3.37843e14i | − | 0.615314i | −0.951497 | − | 0.307657i | \(-0.900455\pi\) | ||
0.951497 | − | 0.307657i | \(-0.0995450\pi\) | |||||||
\(888\) | − | 1.27951e15i | − | 2.31727i | ||||||
\(889\) | − | 2.23159e13i | − | 0.0401889i | ||||||
\(890\) | 1.98356e14i | 0.355219i | ||||||||
\(891\) | 1.10599e14 | 0.196954 | ||||||||
\(892\) | 1.89583e14i | 0.335718i | ||||||||
\(893\) | − | 2.32978e14i | − | 0.410259i | ||||||
\(894\) | − | 1.85365e14i | − | 0.324594i | ||||||
\(895\) | −6.57167e14 | −1.14435 | ||||||||
\(896\) | −3.39459e14 | −0.587824 | ||||||||
\(897\) | 5.36379e14i | 0.923654i | ||||||||
\(898\) | −1.94973e14 | −0.333882 | ||||||||
\(899\) | − | 1.34276e15i | − | 2.28665i | ||||||
\(900\) | −2.73391e14 | −0.462990 | ||||||||
\(901\) | −1.56531e15 | −2.63618 | ||||||||
\(902\) | − | 8.10147e13i | − | 0.135685i | ||||||
\(903\) | 2.71390e14 | + | 6.04817e14i | 0.452017 | + | 1.00736i | ||||
\(904\) | 1.02305e15 | 1.69454 | ||||||||
\(905\) | − | 8.12570e14i | − | 1.33850i | ||||||
\(906\) | 3.97194e14i | 0.650671i | ||||||||
\(907\) | −3.21598e14 | −0.523934 | −0.261967 | − | 0.965077i | \(-0.584371\pi\) | ||||
−0.261967 | + | 0.965077i | \(0.584371\pi\) | |||||||
\(908\) | − | 6.93210e13i | − | 0.112314i | ||||||
\(909\) | −1.87533e13 | −0.0302175 | ||||||||
\(910\) | 2.85427e14i | 0.457391i | ||||||||
\(911\) | 7.13693e14i | 1.13742i | 0.822539 | + | 0.568708i | \(0.192557\pi\) | ||||
−0.822539 | + | 0.568708i | \(0.807443\pi\) | |||||||
\(912\) | 3.22432e14 | 0.511051 | ||||||||
\(913\) | 7.03019e13 | 0.110819 | ||||||||
\(914\) | 2.23193e14 | 0.349905 | ||||||||
\(915\) | 7.93529e14i | 1.23725i | ||||||||
\(916\) | −1.29724e14 | −0.201161 | ||||||||
\(917\) | 2.07818e14 | 0.320506 | ||||||||
\(918\) | 8.49589e14 | 1.30315 | ||||||||
\(919\) | 8.00764e14 | 1.22159 | 0.610797 | − | 0.791787i | \(-0.290849\pi\) | ||||
0.610797 | + | 0.791787i | \(0.290849\pi\) | |||||||
\(920\) | −1.59497e14 | −0.241999 | ||||||||
\(921\) | 1.71572e15i | 2.58909i | ||||||||
\(922\) | − | 1.95501e14i | − | 0.293423i | ||||||
\(923\) | − | 4.76342e14i | − | 0.711067i | ||||||
\(924\) | 2.58370e14 | 0.383603 | ||||||||
\(925\) | − | 3.70494e14i | − | 0.547107i | ||||||
\(926\) | 4.21383e14 | 0.618902 | ||||||||
\(927\) | 1.43475e14 | 0.209593 | ||||||||
\(928\) | −1.18286e15 | −1.71868 | ||||||||
\(929\) | − | 1.55500e14i | − | 0.224725i | −0.993667 | − | 0.112362i | \(-0.964158\pi\) | ||
0.993667 | − | 0.112362i | \(-0.0358417\pi\) | |||||||
\(930\) | − | 6.70154e14i | − | 0.963296i | ||||||
\(931\) | 4.65684e14i | 0.665799i | ||||||||
\(932\) | − | 2.15734e14i | − | 0.306789i | ||||||
\(933\) | 9.81988e14i | 1.38899i | ||||||||
\(934\) | −8.15771e11 | −0.00114771 | ||||||||
\(935\) | − | 5.18956e14i | − | 0.726227i | ||||||
\(936\) | 1.91457e15i | 2.66497i | ||||||||
\(937\) | − | 6.33075e14i | − | 0.876511i | −0.898851 | − | 0.438255i | \(-0.855597\pi\) | ||
0.898851 | − | 0.438255i | \(-0.144403\pi\) | |||||||
\(938\) | 1.13336e14 | 0.156082 | ||||||||
\(939\) | 1.39530e15 | 1.91135 | ||||||||
\(940\) | − | 1.48886e14i | − | 0.202868i | ||||||
\(941\) | −4.12314e14 | −0.558830 | −0.279415 | − | 0.960170i | \(-0.590141\pi\) | ||||
−0.279415 | + | 0.960170i | \(0.590141\pi\) | |||||||
\(942\) | 2.88246e14i | 0.388606i | ||||||||
\(943\) | −1.36128e14 | −0.182554 | ||||||||
\(944\) | 1.67995e14 | 0.224098 | ||||||||
\(945\) | − | 5.27524e14i | − | 0.699976i | ||||||
\(946\) | −1.71876e14 | + | 7.71231e13i | −0.226861 | + | 0.101796i | ||||
\(947\) | −1.02096e15 | −1.34048 | −0.670241 | − | 0.742144i | \(-0.733809\pi\) | ||||
−0.670241 | + | 0.742144i | \(0.733809\pi\) | |||||||
\(948\) | 6.96595e14i | 0.909784i | ||||||||
\(949\) | 1.43440e14i | 0.186354i | ||||||||
\(950\) | −1.69448e14 | −0.218988 | ||||||||
\(951\) | − | 1.50511e14i | − | 0.193494i | ||||||
\(952\) | 8.82925e14 | 1.12912 | ||||||||
\(953\) | − | 1.10496e14i | − | 0.140566i | −0.997527 | − | 0.0702831i | \(-0.977610\pi\) | ||
0.997527 | − | 0.0702831i | \(-0.0223903\pi\) | |||||||
\(954\) | − | 1.02488e15i | − | 1.29698i | ||||||
\(955\) | −4.02496e14 | −0.506693 | ||||||||
\(956\) | 6.96420e14 | 0.872131 | ||||||||
\(957\) | 1.06126e15 | 1.32209 | ||||||||
\(958\) | 6.47304e14i | 0.802196i | ||||||||
\(959\) | −3.28657e14 | −0.405182 | ||||||||
\(960\) | −3.07429e14 | −0.377041 | ||||||||
\(961\) | 7.36782e14 | 0.898922 | ||||||||
\(962\) | −1.09335e15 | −1.32704 | ||||||||
\(963\) | −1.75842e15 | −2.12321 | ||||||||
\(964\) | 1.05228e15i | 1.26399i | ||||||||
\(965\) | − | 3.68345e14i | − | 0.440168i | ||||||
\(966\) | 1.61957e14i | 0.192537i | ||||||||
\(967\) | 3.60545e14 | 0.426410 | 0.213205 | − | 0.977007i | \(-0.431610\pi\) | ||||
0.213205 | + | 0.977007i | \(0.431610\pi\) | |||||||
\(968\) | − | 5.91429e14i | − | 0.695866i | ||||||
\(969\) | −3.19935e15 | −3.74492 | ||||||||
\(970\) | 4.26802e14 | 0.497014 | ||||||||
\(971\) | −7.24583e14 | −0.839444 | −0.419722 | − | 0.907653i | \(-0.637872\pi\) | ||||
−0.419722 | + | 0.907653i | \(0.637872\pi\) | |||||||
\(972\) | 3.97511e14i | 0.458161i | ||||||||
\(973\) | 8.71631e14i | 0.999467i | ||||||||
\(974\) | 9.81496e12i | 0.0111968i | ||||||||
\(975\) | 8.64177e14i | 0.980798i | ||||||||
\(976\) | 2.11391e14i | 0.238692i | ||||||||
\(977\) | −1.62182e14 | −0.182192 | −0.0910960 | − | 0.995842i | \(-0.529037\pi\) | ||||
−0.0910960 | + | 0.995842i | \(0.529037\pi\) | |||||||
\(978\) | − | 8.15414e14i | − | 0.911348i | ||||||
\(979\) | − | 3.64099e14i | − | 0.404861i | ||||||
\(980\) | 2.97598e14i | 0.329230i | ||||||||
\(981\) | 1.18756e15 | 1.30711 | ||||||||
\(982\) | 8.86618e14 | 0.970911 | ||||||||
\(983\) | − | 4.56618e13i | − | 0.0497491i | −0.999691 | − | 0.0248745i | \(-0.992081\pi\) | ||
0.999691 | − | 0.0248745i | \(-0.00791863\pi\) | |||||||
\(984\) | −7.57428e14 | −0.821042 | ||||||||
\(985\) | 3.78596e14i | 0.408314i | ||||||||
\(986\) | 1.52826e15 | 1.63988 | ||||||||
\(987\) | −3.58763e14 | −0.383021 | ||||||||
\(988\) | − | 1.34043e15i | − | 1.42383i | ||||||
\(989\) | 1.29589e14 | + | 2.88802e14i | 0.136958 | + | 0.305224i | ||||
\(990\) | 3.39786e14 | 0.357297 | ||||||||
\(991\) | 6.28779e14i | 0.657855i | 0.944355 | + | 0.328927i | \(0.106687\pi\) | ||||
−0.944355 | + | 0.328927i | \(0.893313\pi\) | |||||||
\(992\) | − | 1.37107e15i | − | 1.42725i | ||||||
\(993\) | 4.40623e13 | 0.0456374 | ||||||||
\(994\) | − | 1.43829e14i | − | 0.148222i | ||||||
\(995\) | −5.60972e14 | −0.575209 | ||||||||
\(996\) | − | 2.76972e14i | − | 0.282579i | ||||||
\(997\) | − | 1.75740e15i | − | 1.78400i | −0.452031 | − | 0.892002i | \(-0.649300\pi\) | ||
0.452031 | − | 0.892002i | \(-0.350700\pi\) | |||||||
\(998\) | −5.30866e14 | −0.536207 | ||||||||
\(999\) | 2.02073e15 | 2.03086 |
(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 | 43.11.b.b.42.21 | yes | 34 | |
43.42 | odd | 2 | inner | 43.11.b.b.42.14 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.11.b.b.42.14 | ✓ | 34 | 43.42 | odd | 2 | inner | |
43.11.b.b.42.21 | yes | 34 | 1.1 | even | 1 | trivial |