Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,10,Mod(28,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.28");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(14.9360392488\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 28.20 | ||
Character | \(\chi\) | \(=\) | 29.28 |
Dual form | 29.10.b.a.28.3 |
$q$-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 \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 37.8978i | 1.67486i | 0.546543 | + | 0.837431i | \(0.315944\pi\) | ||||
−0.546543 | + | 0.837431i | \(0.684056\pi\) | |||||||
\(3\) | 104.304i | 0.743455i | 0.928342 | + | 0.371727i | \(0.121234\pi\) | ||||
−0.928342 | + | 0.371727i | \(0.878766\pi\) | |||||||
\(4\) | −924.245 | −1.80517 | ||||||||
\(5\) | −2682.94 | −1.91976 | −0.959879 | − | 0.280413i | \(-0.909528\pi\) | ||||
−0.959879 | + | 0.280413i | \(0.909528\pi\) | |||||||
\(6\) | −3952.89 | −1.24518 | ||||||||
\(7\) | 4793.67 | 0.754618 | 0.377309 | − | 0.926087i | \(-0.376850\pi\) | ||||
0.377309 | + | 0.926087i | \(0.376850\pi\) | |||||||
\(8\) | − | 15623.2i | − | 1.34854i | ||||||
\(9\) | 8803.72 | 0.447275 | ||||||||
\(10\) | − | 101678.i | − | 3.21533i | ||||||
\(11\) | 53533.4i | 1.10245i | 0.834357 | + | 0.551224i | \(0.185839\pi\) | ||||
−0.834357 | + | 0.551224i | \(0.814161\pi\) | |||||||
\(12\) | − | 96402.2i | − | 1.34206i | ||||||
\(13\) | −65912.0 | −0.640058 | −0.320029 | − | 0.947408i | \(-0.603693\pi\) | ||||
−0.320029 | + | 0.947408i | \(0.603693\pi\) | |||||||
\(14\) | 181670.i | 1.26388i | ||||||||
\(15\) | − | 279841.i | − | 1.42725i | ||||||
\(16\) | 118871. | 0.453456 | ||||||||
\(17\) | 91109.1i | 0.264571i | 0.991212 | + | 0.132285i | \(0.0422315\pi\) | ||||
−0.991212 | + | 0.132285i | \(0.957769\pi\) | |||||||
\(18\) | 333642.i | 0.749125i | ||||||||
\(19\) | − | 562353.i | − | 0.989961i | −0.868904 | − | 0.494980i | \(-0.835175\pi\) | ||
0.868904 | − | 0.494980i | \(-0.164825\pi\) | |||||||
\(20\) | 2.47970e6 | 3.46548 | ||||||||
\(21\) | 499998.i | 0.561024i | ||||||||
\(22\) | −2.02880e6 | −1.84645 | ||||||||
\(23\) | −22800.0 | −0.0169886 | −0.00849432 | − | 0.999964i | \(-0.502704\pi\) | ||||
−0.00849432 | + | 0.999964i | \(0.502704\pi\) | |||||||
\(24\) | 1.62956e6 | 1.00258 | ||||||||
\(25\) | 5.24507e6 | 2.68547 | ||||||||
\(26\) | − | 2.49792e6i | − | 1.07201i | ||||||
\(27\) | 2.97127e6i | 1.07598i | ||||||||
\(28\) | −4.43052e6 | −1.36221 | ||||||||
\(29\) | −3.34566e6 | − | 1.82036e6i | −0.878397 | − | 0.477932i | ||||
\(30\) | 1.06054e7 | 2.39045 | ||||||||
\(31\) | − | 771940.i | − | 0.150126i | −0.997179 | − | 0.0750630i | \(-0.976084\pi\) | ||
0.997179 | − | 0.0750630i | \(-0.0239158\pi\) | |||||||
\(32\) | − | 3.49412e6i | − | 0.589065i | ||||||
\(33\) | −5.58374e6 | −0.819620 | ||||||||
\(34\) | −3.45283e6 | −0.443119 | ||||||||
\(35\) | −1.28612e7 | −1.44868 | ||||||||
\(36\) | −8.13679e6 | −0.807406 | ||||||||
\(37\) | − | 1.39331e7i | − | 1.22220i | −0.791555 | − | 0.611098i | \(-0.790728\pi\) | ||
0.791555 | − | 0.611098i | \(-0.209272\pi\) | |||||||
\(38\) | 2.13120e7 | 1.65805 | ||||||||
\(39\) | − | 6.87487e6i | − | 0.475854i | ||||||
\(40\) | 4.19161e7i | 2.58887i | ||||||||
\(41\) | − | 1.80833e7i | − | 0.999426i | −0.866191 | − | 0.499713i | \(-0.833439\pi\) | ||
0.866191 | − | 0.499713i | \(-0.166561\pi\) | |||||||
\(42\) | −1.89488e7 | −0.939638 | ||||||||
\(43\) | 1.71895e7i | 0.766754i | 0.923592 | + | 0.383377i | \(0.125239\pi\) | ||||
−0.923592 | + | 0.383377i | \(0.874761\pi\) | |||||||
\(44\) | − | 4.94780e7i | − | 1.99010i | ||||||
\(45\) | −2.36199e7 | −0.858661 | ||||||||
\(46\) | − | 864068.i | − | 0.0284536i | ||||||
\(47\) | 4.69934e7i | 1.40474i | 0.711812 | + | 0.702371i | \(0.247875\pi\) | ||||
−0.711812 | + | 0.702371i | \(0.752125\pi\) | |||||||
\(48\) | 1.23987e7i | 0.337124i | ||||||||
\(49\) | −1.73743e7 | −0.430552 | ||||||||
\(50\) | 1.98777e8i | 4.49780i | ||||||||
\(51\) | −9.50302e6 | −0.196696 | ||||||||
\(52\) | 6.09188e7 | 1.15541 | ||||||||
\(53\) | 4.76701e7 | 0.829859 | 0.414930 | − | 0.909854i | \(-0.363806\pi\) | ||||
0.414930 | + | 0.909854i | \(0.363806\pi\) | |||||||
\(54\) | −1.12605e8 | −1.80212 | ||||||||
\(55\) | − | 1.43627e8i | − | 2.11643i | ||||||
\(56\) | − | 7.48923e7i | − | 1.01763i | ||||||
\(57\) | 5.86556e7 | 0.735991 | ||||||||
\(58\) | 6.89877e7 | − | 1.26793e8i | 0.800471 | − | 1.47119i | ||||
\(59\) | −1.64817e8 | −1.77080 | −0.885399 | − | 0.464832i | \(-0.846115\pi\) | ||||
−0.885399 | + | 0.464832i | \(0.846115\pi\) | |||||||
\(60\) | 2.58642e8i | 2.57643i | ||||||||
\(61\) | − | 1.71039e8i | − | 1.58165i | −0.612043 | − | 0.790825i | \(-0.709652\pi\) | ||
0.612043 | − | 0.790825i | \(-0.290348\pi\) | |||||||
\(62\) | 2.92548e7 | 0.251440 | ||||||||
\(63\) | 4.22021e7 | 0.337522 | ||||||||
\(64\) | 1.93281e8 | 1.44006 | ||||||||
\(65\) | 1.76838e8 | 1.22876 | ||||||||
\(66\) | − | 2.11612e8i | − | 1.37275i | ||||||
\(67\) | −3.13045e8 | −1.89788 | −0.948942 | − | 0.315450i | \(-0.897845\pi\) | ||||
−0.948942 | + | 0.315450i | \(0.897845\pi\) | |||||||
\(68\) | − | 8.42071e7i | − | 0.477593i | ||||||
\(69\) | − | 2.37812e6i | − | 0.0126303i | ||||||
\(70\) | − | 4.87410e8i | − | 2.42635i | ||||||
\(71\) | −1.66663e8 | −0.778355 | −0.389178 | − | 0.921163i | \(-0.627241\pi\) | ||||
−0.389178 | + | 0.921163i | \(0.627241\pi\) | |||||||
\(72\) | − | 1.37542e8i | − | 0.603169i | ||||||
\(73\) | 2.67257e7i | 0.110148i | 0.998482 | + | 0.0550739i | \(0.0175395\pi\) | ||||
−0.998482 | + | 0.0550739i | \(0.982461\pi\) | |||||||
\(74\) | 5.28035e8 | 2.04701 | ||||||||
\(75\) | 5.47080e8i | 1.99653i | ||||||||
\(76\) | 5.19752e8i | 1.78704i | ||||||||
\(77\) | 2.56622e8i | 0.831927i | ||||||||
\(78\) | 2.60543e8 | 0.796990 | ||||||||
\(79\) | 5.08030e8i | 1.46746i | 0.679440 | + | 0.733731i | \(0.262223\pi\) | ||||
−0.679440 | + | 0.733731i | \(0.737777\pi\) | |||||||
\(80\) | −3.18924e8 | −0.870526 | ||||||||
\(81\) | −1.36631e8 | −0.352669 | ||||||||
\(82\) | 6.85318e8 | 1.67390 | ||||||||
\(83\) | −4.73692e7 | −0.109558 | −0.0547791 | − | 0.998498i | \(-0.517445\pi\) | ||||
−0.0547791 | + | 0.998498i | \(0.517445\pi\) | |||||||
\(84\) | − | 4.62120e8i | − | 1.01274i | ||||||
\(85\) | − | 2.44441e8i | − | 0.507912i | ||||||
\(86\) | −6.51446e8 | −1.28421 | ||||||||
\(87\) | 1.89870e8 | − | 3.48965e8i | 0.355321 | − | 0.653048i | ||||
\(88\) | 8.36362e8 | 1.48670 | ||||||||
\(89\) | 8.92144e8i | 1.50723i | 0.657316 | + | 0.753615i | \(0.271692\pi\) | ||||
−0.657316 | + | 0.753615i | \(0.728308\pi\) | |||||||
\(90\) | − | 8.95142e8i | − | 1.43814i | ||||||
\(91\) | −3.15960e8 | −0.482999 | ||||||||
\(92\) | 2.10727e7 | 0.0306673 | ||||||||
\(93\) | 8.05163e7 | 0.111612 | ||||||||
\(94\) | −1.78095e9 | −2.35275 | ||||||||
\(95\) | 1.50876e9i | 1.90049i | ||||||||
\(96\) | 3.64450e8 | 0.437943 | ||||||||
\(97\) | − | 6.96072e8i | − | 0.798328i | −0.916880 | − | 0.399164i | \(-0.869300\pi\) | ||
0.916880 | − | 0.399164i | \(-0.130700\pi\) | |||||||
\(98\) | − | 6.58449e8i | − | 0.721116i | ||||||
\(99\) | 4.71293e8i | 0.493098i | ||||||||
\(100\) | −4.84772e9 | −4.84772 | ||||||||
\(101\) | − | 1.06718e9i | − | 1.02045i | −0.860040 | − | 0.510227i | \(-0.829561\pi\) | ||
0.860040 | − | 0.510227i | \(-0.170439\pi\) | |||||||
\(102\) | − | 3.60144e8i | − | 0.329439i | ||||||
\(103\) | −7.55529e8 | −0.661429 | −0.330715 | − | 0.943731i | \(-0.607290\pi\) | ||||
−0.330715 | + | 0.943731i | \(0.607290\pi\) | |||||||
\(104\) | 1.02975e9i | 0.863145i | ||||||||
\(105\) | − | 1.34147e9i | − | 1.07703i | ||||||
\(106\) | 1.80659e9i | 1.38990i | ||||||||
\(107\) | 8.63192e8 | 0.636621 | 0.318310 | − | 0.947987i | \(-0.396885\pi\) | ||||
0.318310 | + | 0.947987i | \(0.396885\pi\) | |||||||
\(108\) | − | 2.74618e9i | − | 1.94233i | ||||||
\(109\) | −4.28219e7 | −0.0290567 | −0.0145284 | − | 0.999894i | \(-0.504625\pi\) | ||||
−0.0145284 | + | 0.999894i | \(0.504625\pi\) | |||||||
\(110\) | 5.44316e9 | 3.54474 | ||||||||
\(111\) | 1.45328e9 | 0.908647 | ||||||||
\(112\) | 5.69827e8 | 0.342186 | ||||||||
\(113\) | 3.33207e9i | 1.92248i | 0.275714 | + | 0.961240i | \(0.411086\pi\) | ||||
−0.275714 | + | 0.961240i | \(0.588914\pi\) | |||||||
\(114\) | 2.22292e9i | 1.23268i | ||||||||
\(115\) | 6.11710e7 | 0.0326141 | ||||||||
\(116\) | 3.09221e9 | + | 1.68246e9i | 1.58565 | + | 0.862746i | ||||
\(117\) | −5.80271e8 | −0.286282 | ||||||||
\(118\) | − | 6.24622e9i | − | 2.96584i | ||||||
\(119\) | 4.36747e8i | 0.199650i | ||||||||
\(120\) | −4.37201e9 | −1.92471 | ||||||||
\(121\) | −5.07881e8 | −0.215391 | ||||||||
\(122\) | 6.48199e9 | 2.64905 | ||||||||
\(123\) | 1.88616e9 | 0.743028 | ||||||||
\(124\) | 7.13461e8i | 0.271002i | ||||||||
\(125\) | −8.83209e9 | −3.23570 | ||||||||
\(126\) | 1.59937e9i | 0.565303i | ||||||||
\(127\) | − | 2.30665e8i | − | 0.0786802i | −0.999226 | − | 0.0393401i | \(-0.987474\pi\) | ||
0.999226 | − | 0.0393401i | \(-0.0125256\pi\) | |||||||
\(128\) | 5.53595e9i | 1.82284i | ||||||||
\(129\) | −1.79293e9 | −0.570047 | ||||||||
\(130\) | 6.70178e9i | 2.05800i | ||||||||
\(131\) | 8.68012e7i | 0.0257516i | 0.999917 | + | 0.0128758i | \(0.00409861\pi\) | ||||
−0.999917 | + | 0.0128758i | \(0.995901\pi\) | |||||||
\(132\) | 5.16074e9 | 1.47955 | ||||||||
\(133\) | − | 2.69574e9i | − | 0.747042i | ||||||
\(134\) | − | 1.18637e10i | − | 3.17870i | ||||||
\(135\) | − | 7.97176e9i | − | 2.06563i | ||||||
\(136\) | 1.42341e9 | 0.356784 | ||||||||
\(137\) | − | 1.78653e9i | − | 0.433279i | −0.976252 | − | 0.216640i | \(-0.930490\pi\) | ||
0.976252 | − | 0.216640i | \(-0.0695096\pi\) | |||||||
\(138\) | 9.01256e7 | 0.0211540 | ||||||||
\(139\) | −2.25449e9 | −0.512249 | −0.256124 | − | 0.966644i | \(-0.582446\pi\) | ||||
−0.256124 | + | 0.966644i | \(0.582446\pi\) | |||||||
\(140\) | 1.18868e10 | 2.61511 | ||||||||
\(141\) | −4.90159e9 | −1.04436 | ||||||||
\(142\) | − | 6.31618e9i | − | 1.30364i | ||||||
\(143\) | − | 3.52850e9i | − | 0.705631i | ||||||
\(144\) | 1.04650e9 | 0.202820 | ||||||||
\(145\) | 8.97622e9 | + | 4.88392e9i | 1.68631 | + | 0.917514i | ||||
\(146\) | −1.01285e9 | −0.184483 | ||||||||
\(147\) | − | 1.81221e9i | − | 0.320096i | ||||||
\(148\) | 1.28776e10i | 2.20627i | ||||||||
\(149\) | 2.47169e9 | 0.410823 | 0.205412 | − | 0.978676i | \(-0.434147\pi\) | ||||
0.205412 | + | 0.978676i | \(0.434147\pi\) | |||||||
\(150\) | −2.07331e10 | −3.34391 | ||||||||
\(151\) | 5.04614e9 | 0.789884 | 0.394942 | − | 0.918706i | \(-0.370765\pi\) | ||||
0.394942 | + | 0.918706i | \(0.370765\pi\) | |||||||
\(152\) | −8.78574e9 | −1.33500 | ||||||||
\(153\) | 8.02099e8i | 0.118336i | ||||||||
\(154\) | −9.72540e9 | −1.39336 | ||||||||
\(155\) | 2.07107e9i | 0.288206i | ||||||||
\(156\) | 6.35406e9i | 0.858995i | ||||||||
\(157\) | − | 9.57722e9i | − | 1.25803i | −0.777393 | − | 0.629015i | \(-0.783458\pi\) | ||
0.777393 | − | 0.629015i | \(-0.216542\pi\) | |||||||
\(158\) | −1.92532e10 | −2.45780 | ||||||||
\(159\) | 4.97217e9i | 0.616963i | ||||||||
\(160\) | 9.37453e9i | 1.13086i | ||||||||
\(161\) | −1.09295e8 | −0.0128199 | ||||||||
\(162\) | − | 5.17803e9i | − | 0.590673i | ||||||
\(163\) | 9.89194e9i | 1.09758i | 0.835960 | + | 0.548791i | \(0.184912\pi\) | ||||
−0.835960 | + | 0.548791i | \(0.815088\pi\) | |||||||
\(164\) | 1.67134e10i | 1.80413i | ||||||||
\(165\) | 1.49809e10 | 1.57347 | ||||||||
\(166\) | − | 1.79519e9i | − | 0.183495i | ||||||
\(167\) | 9.15965e9 | 0.911286 | 0.455643 | − | 0.890163i | \(-0.349409\pi\) | ||||
0.455643 | + | 0.890163i | \(0.349409\pi\) | |||||||
\(168\) | 7.81155e9 | 0.756564 | ||||||||
\(169\) | −6.26011e9 | −0.590326 | ||||||||
\(170\) | 9.26376e9 | 0.850682 | ||||||||
\(171\) | − | 4.95080e9i | − | 0.442785i | ||||||
\(172\) | − | 1.58873e10i | − | 1.38412i | ||||||
\(173\) | −1.28288e10 | −1.08888 | −0.544440 | − | 0.838800i | \(-0.683258\pi\) | ||||
−0.544440 | + | 0.838800i | \(0.683258\pi\) | |||||||
\(174\) | 1.32250e10 | + | 7.19567e9i | 1.09377 | + | 0.595114i | ||||
\(175\) | 2.51431e10 | 2.02651 | ||||||||
\(176\) | 6.36356e9i | 0.499911i | ||||||||
\(177\) | − | 1.71911e10i | − | 1.31651i | ||||||
\(178\) | −3.38103e10 | −2.52440 | ||||||||
\(179\) | −1.86413e10 | −1.35718 | −0.678588 | − | 0.734519i | \(-0.737408\pi\) | ||||
−0.678588 | + | 0.734519i | \(0.737408\pi\) | |||||||
\(180\) | 2.18306e10 | 1.55002 | ||||||||
\(181\) | −2.69935e9 | −0.186942 | −0.0934708 | − | 0.995622i | \(-0.529796\pi\) | ||||
−0.0934708 | + | 0.995622i | \(0.529796\pi\) | |||||||
\(182\) | − | 1.19742e10i | − | 0.808957i | ||||||
\(183\) | 1.78400e10 | 1.17588 | ||||||||
\(184\) | 3.56207e8i | 0.0229099i | ||||||||
\(185\) | 3.73818e10i | 2.34632i | ||||||||
\(186\) | 3.05139e9i | 0.186935i | ||||||||
\(187\) | −4.87738e9 | −0.291675 | ||||||||
\(188\) | − | 4.34334e10i | − | 2.53579i | ||||||
\(189\) | 1.42433e10i | 0.811956i | ||||||||
\(190\) | −5.71788e10 | −3.18305 | ||||||||
\(191\) | − | 2.46163e9i | − | 0.133836i | −0.997758 | − | 0.0669181i | \(-0.978683\pi\) | ||
0.997758 | − | 0.0669181i | \(-0.0213166\pi\) | |||||||
\(192\) | 2.01600e10i | 1.07062i | ||||||||
\(193\) | − | 1.82202e10i | − | 0.945246i | −0.881265 | − | 0.472623i | \(-0.843307\pi\) | ||
0.881265 | − | 0.472623i | \(-0.156693\pi\) | |||||||
\(194\) | 2.63796e10 | 1.33709 | ||||||||
\(195\) | 1.84449e10i | 0.913525i | ||||||||
\(196\) | 1.60581e10 | 0.777218 | ||||||||
\(197\) | 1.14606e10 | 0.542135 | 0.271068 | − | 0.962560i | \(-0.412623\pi\) | ||||
0.271068 | + | 0.962560i | \(0.412623\pi\) | |||||||
\(198\) | −1.78610e10 | −0.825871 | ||||||||
\(199\) | 3.12553e9 | 0.141281 | 0.0706406 | − | 0.997502i | \(-0.477496\pi\) | ||||
0.0706406 | + | 0.997502i | \(0.477496\pi\) | |||||||
\(200\) | − | 8.19445e10i | − | 3.62147i | ||||||
\(201\) | − | 3.26518e10i | − | 1.41099i | ||||||
\(202\) | 4.04440e10 | 1.70912 | ||||||||
\(203\) | −1.60380e10 | − | 8.72620e9i | −0.662854 | − | 0.360656i | ||||
\(204\) | 8.78312e9 | 0.355069 | ||||||||
\(205\) | 4.85165e10i | 1.91866i | ||||||||
\(206\) | − | 2.86329e10i | − | 1.10780i | ||||||
\(207\) | −2.00724e8 | −0.00759860 | ||||||||
\(208\) | −7.83501e9 | −0.290238 | ||||||||
\(209\) | 3.01047e10 | 1.09138 | ||||||||
\(210\) | 5.08387e10 | 1.80388 | ||||||||
\(211\) | 2.09832e10i | 0.728789i | 0.931245 | + | 0.364394i | \(0.118724\pi\) | ||||
−0.931245 | + | 0.364394i | \(0.881276\pi\) | |||||||
\(212\) | −4.40588e10 | −1.49803 | ||||||||
\(213\) | − | 1.73836e10i | − | 0.578672i | ||||||
\(214\) | 3.27131e10i | 1.06625i | ||||||||
\(215\) | − | 4.61186e10i | − | 1.47198i | ||||||
\(216\) | 4.64207e10 | 1.45101 | ||||||||
\(217\) | − | 3.70043e9i | − | 0.113288i | ||||||
\(218\) | − | 1.62286e9i | − | 0.0486660i | ||||||
\(219\) | −2.78759e9 | −0.0818899 | ||||||||
\(220\) | 1.32747e11i | 3.82051i | ||||||||
\(221\) | − | 6.00518e9i | − | 0.169341i | ||||||
\(222\) | 5.50761e10i | 1.52186i | ||||||||
\(223\) | −4.21485e9 | −0.114133 | −0.0570664 | − | 0.998370i | \(-0.518175\pi\) | ||||
−0.0570664 | + | 0.998370i | \(0.518175\pi\) | |||||||
\(224\) | − | 1.67497e10i | − | 0.444519i | ||||||
\(225\) | 4.61761e10 | 1.20115 | ||||||||
\(226\) | −1.26278e11 | −3.21989 | ||||||||
\(227\) | 2.42992e10 | 0.607402 | 0.303701 | − | 0.952767i | \(-0.401778\pi\) | ||||
0.303701 | + | 0.952767i | \(0.401778\pi\) | |||||||
\(228\) | −5.42121e10 | −1.32859 | ||||||||
\(229\) | 4.53493e10i | 1.08971i | 0.838530 | + | 0.544855i | \(0.183415\pi\) | ||||
−0.838530 | + | 0.544855i | \(0.816585\pi\) | |||||||
\(230\) | 2.31825e9i | 0.0546241i | ||||||||
\(231\) | −2.67666e10 | −0.618500 | ||||||||
\(232\) | −2.84398e10 | + | 5.22698e10i | −0.644511 | + | 1.18455i | ||||
\(233\) | −1.18024e10 | −0.262344 | −0.131172 | − | 0.991360i | \(-0.541874\pi\) | ||||
−0.131172 | + | 0.991360i | \(0.541874\pi\) | |||||||
\(234\) | − | 2.19910e10i | − | 0.479483i | ||||||
\(235\) | − | 1.26081e11i | − | 2.69676i | ||||||
\(236\) | 1.52332e11 | 3.19658 | ||||||||
\(237\) | −5.29894e10 | −1.09099 | ||||||||
\(238\) | −1.65518e10 | −0.334386 | ||||||||
\(239\) | −2.03587e10 | −0.403607 | −0.201804 | − | 0.979426i | \(-0.564680\pi\) | ||||
−0.201804 | + | 0.979426i | \(0.564680\pi\) | |||||||
\(240\) | − | 3.32649e10i | − | 0.647196i | ||||||
\(241\) | −4.91678e10 | −0.938867 | −0.469434 | − | 0.882968i | \(-0.655542\pi\) | ||||
−0.469434 | + | 0.882968i | \(0.655542\pi\) | |||||||
\(242\) | − | 1.92476e10i | − | 0.360751i | ||||||
\(243\) | 4.42324e10i | 0.813790i | ||||||||
\(244\) | 1.58082e11i | 2.85514i | ||||||||
\(245\) | 4.66144e10 | 0.826556 | ||||||||
\(246\) | 7.14813e10i | 1.24447i | ||||||||
\(247\) | 3.70658e10i | 0.633633i | ||||||||
\(248\) | −1.20601e10 | −0.202451 | ||||||||
\(249\) | − | 4.94079e9i | − | 0.0814516i | ||||||
\(250\) | − | 3.34717e11i | − | 5.41936i | ||||||
\(251\) | 1.81902e9i | 0.0289272i | 0.999895 | + | 0.0144636i | \(0.00460407\pi\) | ||||
−0.999895 | + | 0.0144636i | \(0.995396\pi\) | |||||||
\(252\) | −3.90051e10 | −0.609283 | ||||||||
\(253\) | − | 1.22056e9i | − | 0.0187291i | ||||||
\(254\) | 8.74171e9 | 0.131779 | ||||||||
\(255\) | 2.54961e10 | 0.377609 | ||||||||
\(256\) | −1.10840e11 | −1.61294 | ||||||||
\(257\) | −1.75025e10 | −0.250266 | −0.125133 | − | 0.992140i | \(-0.539936\pi\) | ||||
−0.125133 | + | 0.992140i | \(0.539936\pi\) | |||||||
\(258\) | − | 6.79483e10i | − | 0.954751i | ||||||
\(259\) | − | 6.67908e10i | − | 0.922291i | ||||||
\(260\) | −1.63442e11 | −2.21811 | ||||||||
\(261\) | −2.94542e10 | − | 1.60259e10i | −0.392885 | − | 0.213767i | ||||
\(262\) | −3.28958e9 | −0.0431304 | ||||||||
\(263\) | − | 6.19778e10i | − | 0.798795i | −0.916778 | − | 0.399398i | \(-0.869219\pi\) | ||
0.916778 | − | 0.399398i | \(-0.130781\pi\) | |||||||
\(264\) | 8.72357e10i | 1.10529i | ||||||||
\(265\) | −1.27896e11 | −1.59313 | ||||||||
\(266\) | 1.02163e11 | 1.25119 | ||||||||
\(267\) | −9.30540e10 | −1.12056 | ||||||||
\(268\) | 2.89330e11 | 3.42599 | ||||||||
\(269\) | 1.49608e11i | 1.74208i | 0.491211 | + | 0.871040i | \(0.336554\pi\) | ||||
−0.491211 | + | 0.871040i | \(0.663446\pi\) | |||||||
\(270\) | 3.02112e11 | 3.45964 | ||||||||
\(271\) | − | 5.16998e10i | − | 0.582274i | −0.956681 | − | 0.291137i | \(-0.905966\pi\) | ||
0.956681 | − | 0.291137i | \(-0.0940335\pi\) | |||||||
\(272\) | 1.08302e10i | 0.119971i | ||||||||
\(273\) | − | 3.29559e10i | − | 0.359088i | ||||||
\(274\) | 6.77056e10 | 0.725683 | ||||||||
\(275\) | 2.80786e11i | 2.96059i | ||||||||
\(276\) | 2.19797e9i | 0.0227997i | ||||||||
\(277\) | −5.77205e10 | −0.589076 | −0.294538 | − | 0.955640i | \(-0.595166\pi\) | ||||
−0.294538 | + | 0.955640i | \(0.595166\pi\) | |||||||
\(278\) | − | 8.54401e10i | − | 0.857946i | ||||||
\(279\) | − | 6.79594e9i | − | 0.0671476i | ||||||
\(280\) | 2.00932e11i | 1.95361i | ||||||||
\(281\) | 7.15486e10 | 0.684577 | 0.342289 | − | 0.939595i | \(-0.388798\pi\) | ||||
0.342289 | + | 0.939595i | \(0.388798\pi\) | |||||||
\(282\) | − | 1.85759e11i | − | 1.74916i | ||||||
\(283\) | −1.28813e11 | −1.19377 | −0.596884 | − | 0.802328i | \(-0.703595\pi\) | ||||
−0.596884 | + | 0.802328i | \(0.703595\pi\) | |||||||
\(284\) | 1.54038e11 | 1.40506 | ||||||||
\(285\) | −1.57370e11 | −1.41293 | ||||||||
\(286\) | 1.33722e11 | 1.18183 | ||||||||
\(287\) | − | 8.66855e10i | − | 0.754185i | ||||||
\(288\) | − | 3.07613e10i | − | 0.263474i | ||||||
\(289\) | 1.10287e11 | 0.930002 | ||||||||
\(290\) | −1.85090e11 | + | 3.40179e11i | −1.53671 | + | 2.82434i | ||||
\(291\) | 7.26029e10 | 0.593520 | ||||||||
\(292\) | − | 2.47011e10i | − | 0.198835i | ||||||
\(293\) | − | 1.84976e11i | − | 1.46626i | −0.680090 | − | 0.733128i | \(-0.738059\pi\) | ||
0.680090 | − | 0.733128i | \(-0.261941\pi\) | |||||||
\(294\) | 6.86788e10 | 0.536117 | ||||||||
\(295\) | 4.42196e11 | 3.39950 | ||||||||
\(296\) | −2.17680e11 | −1.64818 | ||||||||
\(297\) | −1.59062e11 | −1.18622 | ||||||||
\(298\) | 9.36715e10i | 0.688072i | ||||||||
\(299\) | 1.50279e9 | 0.0108737 | ||||||||
\(300\) | − | 5.05636e11i | − | 3.60406i | ||||||
\(301\) | 8.24010e10i | 0.578606i | ||||||||
\(302\) | 1.91238e11i | 1.32295i | ||||||||
\(303\) | 1.11311e11 | 0.758661 | ||||||||
\(304\) | − | 6.68473e10i | − | 0.448904i | ||||||
\(305\) | 4.58887e11i | 3.03639i | ||||||||
\(306\) | −3.03978e10 | −0.198196 | ||||||||
\(307\) | − | 9.05584e10i | − | 0.581843i | −0.956747 | − | 0.290922i | \(-0.906038\pi\) | ||
0.956747 | − | 0.290922i | \(-0.0939619\pi\) | |||||||
\(308\) | − | 2.37181e11i | − | 1.50176i | ||||||
\(309\) | − | 7.88045e10i | − | 0.491743i | ||||||
\(310\) | −7.84891e10 | −0.482705 | ||||||||
\(311\) | − | 1.41145e11i | − | 0.855545i | −0.903886 | − | 0.427773i | \(-0.859298\pi\) | ||
0.903886 | − | 0.427773i | \(-0.140702\pi\) | |||||||
\(312\) | −1.07407e11 | −0.641709 | ||||||||
\(313\) | −7.41145e10 | −0.436470 | −0.218235 | − | 0.975896i | \(-0.570030\pi\) | ||||
−0.218235 | + | 0.975896i | \(0.570030\pi\) | |||||||
\(314\) | 3.62956e11 | 2.10703 | ||||||||
\(315\) | −1.13226e11 | −0.647961 | ||||||||
\(316\) | − | 4.69543e11i | − | 2.64901i | ||||||
\(317\) | − | 3.77794e10i | − | 0.210130i | −0.994465 | − | 0.105065i | \(-0.966495\pi\) | ||
0.994465 | − | 0.105065i | \(-0.0335051\pi\) | |||||||
\(318\) | −1.88434e11 | −1.03333 | ||||||||
\(319\) | 9.74501e10 | − | 1.79105e11i | 0.526895 | − | 0.968387i | ||||
\(320\) | −5.18563e11 | −2.76456 | ||||||||
\(321\) | 9.00342e10i | 0.473298i | ||||||||
\(322\) | − | 4.14206e9i | − | 0.0214716i | ||||||
\(323\) | 5.12355e10 | 0.261915 | ||||||||
\(324\) | 1.26281e11 | 0.636627 | ||||||||
\(325\) | −3.45713e11 | −1.71886 | ||||||||
\(326\) | −3.74883e11 | −1.83830 | ||||||||
\(327\) | − | 4.46648e9i | − | 0.0216023i | ||||||
\(328\) | −2.82519e11 | −1.34777 | ||||||||
\(329\) | 2.25271e11i | 1.06004i | ||||||||
\(330\) | 5.67742e11i | 2.63535i | ||||||||
\(331\) | 1.62074e11i | 0.742143i | 0.928604 | + | 0.371071i | \(0.121009\pi\) | ||||
−0.928604 | + | 0.371071i | \(0.878991\pi\) | |||||||
\(332\) | 4.37808e10 | 0.197771 | ||||||||
\(333\) | − | 1.22663e11i | − | 0.546658i | ||||||
\(334\) | 3.47131e11i | 1.52628i | ||||||||
\(335\) | 8.39882e11 | 3.64348 | ||||||||
\(336\) | 5.94351e10i | 0.254400i | ||||||||
\(337\) | 8.78925e10i | 0.371208i | 0.982625 | + | 0.185604i | \(0.0594241\pi\) | ||||
−0.982625 | + | 0.185604i | \(0.940576\pi\) | |||||||
\(338\) | − | 2.37244e11i | − | 0.988714i | ||||||
\(339\) | −3.47548e11 | −1.42928 | ||||||||
\(340\) | 2.25923e11i | 0.916864i | ||||||||
\(341\) | 4.13246e10 | 0.165506 | ||||||||
\(342\) | 1.87625e11 | 0.741604 | ||||||||
\(343\) | −2.76729e11 | −1.07952 | ||||||||
\(344\) | 2.68555e11 | 1.03400 | ||||||||
\(345\) | 6.38037e9i | 0.0242471i | ||||||||
\(346\) | − | 4.86185e11i | − | 1.82372i | ||||||
\(347\) | 3.84875e10 | 0.142507 | 0.0712537 | − | 0.997458i | \(-0.477300\pi\) | ||||
0.0712537 | + | 0.997458i | \(0.477300\pi\) | |||||||
\(348\) | −1.75487e11 | + | 3.22529e11i | −0.641413 | + | 1.17886i | ||||
\(349\) | −2.89105e11 | −1.04314 | −0.521568 | − | 0.853210i | \(-0.674653\pi\) | ||||
−0.521568 | + | 0.853210i | \(0.674653\pi\) | |||||||
\(350\) | 9.52869e11i | 3.39412i | ||||||||
\(351\) | − | 1.95843e11i | − | 0.688692i | ||||||
\(352\) | 1.87052e11 | 0.649413 | ||||||||
\(353\) | −2.17749e11 | −0.746398 | −0.373199 | − | 0.927751i | \(-0.621739\pi\) | ||||
−0.373199 | + | 0.927751i | \(0.621739\pi\) | |||||||
\(354\) | 6.51504e11 | 2.20497 | ||||||||
\(355\) | 4.47149e11 | 1.49425 | ||||||||
\(356\) | − | 8.24559e11i | − | 2.72080i | ||||||
\(357\) | −4.55544e10 | −0.148430 | ||||||||
\(358\) | − | 7.06463e11i | − | 2.27308i | ||||||
\(359\) | 5.05244e11i | 1.60537i | 0.596401 | + | 0.802687i | \(0.296597\pi\) | ||||
−0.596401 | + | 0.802687i | \(0.703403\pi\) | |||||||
\(360\) | 3.69017e11i | 1.15794i | ||||||||
\(361\) | 6.44641e9 | 0.0199772 | ||||||||
\(362\) | − | 1.02300e11i | − | 0.313102i | ||||||
\(363\) | − | 5.29739e10i | − | 0.160134i | ||||||
\(364\) | 2.92025e11 | 0.871893 | ||||||||
\(365\) | − | 7.17035e10i | − | 0.211457i | ||||||
\(366\) | 6.76097e11i | 1.96945i | ||||||||
\(367\) | 3.17655e11i | 0.914027i | 0.889460 | + | 0.457013i | \(0.151081\pi\) | ||||
−0.889460 | + | 0.457013i | \(0.848919\pi\) | |||||||
\(368\) | −2.71025e9 | −0.00770360 | ||||||||
\(369\) | − | 1.59200e11i | − | 0.447019i | ||||||
\(370\) | −1.41669e12 | −3.92977 | ||||||||
\(371\) | 2.28515e11 | 0.626226 | ||||||||
\(372\) | −7.44167e10 | −0.201478 | ||||||||
\(373\) | 1.32100e11 | 0.353357 | 0.176678 | − | 0.984269i | \(-0.443465\pi\) | ||||
0.176678 | + | 0.984269i | \(0.443465\pi\) | |||||||
\(374\) | − | 1.84842e11i | − | 0.488516i | ||||||
\(375\) | − | 9.21221e11i | − | 2.40560i | ||||||
\(376\) | 7.34185e11 | 1.89435 | ||||||||
\(377\) | 2.20519e11 | + | 1.19984e11i | 0.562225 | + | 0.305904i | ||||
\(378\) | −5.39790e11 | −1.35992 | ||||||||
\(379\) | 4.95405e11i | 1.23334i | 0.787220 | + | 0.616672i | \(0.211519\pi\) | ||||
−0.787220 | + | 0.616672i | \(0.788481\pi\) | |||||||
\(380\) | − | 1.39447e12i | − | 3.43069i | ||||||
\(381\) | 2.40593e10 | 0.0584951 | ||||||||
\(382\) | 9.32906e10 | 0.224157 | ||||||||
\(383\) | 8.75133e10 | 0.207816 | 0.103908 | − | 0.994587i | \(-0.466865\pi\) | ||||
0.103908 | + | 0.994587i | \(0.466865\pi\) | |||||||
\(384\) | −5.77421e11 | −1.35520 | ||||||||
\(385\) | − | 6.88502e11i | − | 1.59710i | ||||||
\(386\) | 6.90505e11 | 1.58316 | ||||||||
\(387\) | 1.51332e11i | 0.342950i | ||||||||
\(388\) | 6.43340e11i | 1.44111i | ||||||||
\(389\) | 1.83451e10i | 0.0406207i | 0.999794 | + | 0.0203103i | \(0.00646542\pi\) | ||||
−0.999794 | + | 0.0203103i | \(0.993535\pi\) | |||||||
\(390\) | −6.99021e11 | −1.53003 | ||||||||
\(391\) | − | 2.07728e9i | − | 0.00449469i | ||||||
\(392\) | 2.71442e11i | 0.580617i | ||||||||
\(393\) | −9.05369e9 | −0.0191452 | ||||||||
\(394\) | 4.34330e11i | 0.908002i | ||||||||
\(395\) | − | 1.36301e12i | − | 2.81717i | ||||||
\(396\) | − | 4.35590e11i | − | 0.890123i | ||||||
\(397\) | 4.93659e11 | 0.997401 | 0.498701 | − | 0.866774i | \(-0.333811\pi\) | ||||
0.498701 | + | 0.866774i | \(0.333811\pi\) | |||||||
\(398\) | 1.18451e11i | 0.236627i | ||||||||
\(399\) | 2.81176e11 | 0.555392 | ||||||||
\(400\) | 6.23485e11 | 1.21774 | ||||||||
\(401\) | −7.77915e11 | −1.50239 | −0.751195 | − | 0.660080i | \(-0.770522\pi\) | ||||
−0.751195 | + | 0.660080i | \(0.770522\pi\) | |||||||
\(402\) | 1.23743e12 | 2.36322 | ||||||||
\(403\) | 5.08801e10i | 0.0960894i | ||||||||
\(404\) | 9.86340e11i | 1.84209i | ||||||||
\(405\) | 3.66574e11 | 0.677040 | ||||||||
\(406\) | 3.30704e11 | − | 6.07805e11i | 0.604049 | − | 1.11019i | ||||
\(407\) | 7.45888e11 | 1.34741 | ||||||||
\(408\) | 1.48467e11i | 0.265253i | ||||||||
\(409\) | − | 5.05154e11i | − | 0.892624i | −0.894877 | − | 0.446312i | \(-0.852737\pi\) | ||
0.894877 | − | 0.446312i | \(-0.147263\pi\) | |||||||
\(410\) | −1.83867e12 | −3.21349 | ||||||||
\(411\) | 1.86342e11 | 0.322123 | ||||||||
\(412\) | 6.98293e11 | 1.19399 | ||||||||
\(413\) | −7.90080e11 | −1.33628 | ||||||||
\(414\) | − | 7.60702e9i | − | 0.0127266i | ||||||
\(415\) | 1.27089e11 | 0.210325 | ||||||||
\(416\) | 2.30304e11i | 0.377036i | ||||||||
\(417\) | − | 2.35151e11i | − | 0.380834i | ||||||
\(418\) | 1.14090e12i | 1.82791i | ||||||||
\(419\) | −1.34849e11 | −0.213739 | −0.106870 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106870 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(420\) | 1.23984e12i | 1.94422i | ||||||||
\(421\) | − | 1.24371e11i | − | 0.192952i | −0.995335 | − | 0.0964762i | \(-0.969243\pi\) | ||
0.995335 | − | 0.0964762i | \(-0.0307572\pi\) | |||||||
\(422\) | −7.95219e11 | −1.22062 | ||||||||
\(423\) | 4.13717e11i | 0.628306i | ||||||||
\(424\) | − | 7.44758e11i | − | 1.11910i | ||||||
\(425\) | 4.77873e11i | 0.710497i | ||||||||
\(426\) | 6.58802e11 | 0.969196 | ||||||||
\(427\) | − | 8.19903e11i | − | 1.19354i | ||||||
\(428\) | −7.97801e11 | −1.14921 | ||||||||
\(429\) | 3.68035e11 | 0.524604 | ||||||||
\(430\) | 1.74779e12 | 2.46537 | ||||||||
\(431\) | −1.00132e12 | −1.39774 | −0.698869 | − | 0.715250i | \(-0.746313\pi\) | ||||
−0.698869 | + | 0.715250i | \(0.746313\pi\) | |||||||
\(432\) | 3.53197e11i | 0.487911i | ||||||||
\(433\) | 1.37571e12i | 1.88075i | 0.340135 | + | 0.940377i | \(0.389527\pi\) | ||||
−0.340135 | + | 0.940377i | \(0.610473\pi\) | |||||||
\(434\) | 1.40238e11 | 0.189741 | ||||||||
\(435\) | −5.09412e11 | + | 9.36254e11i | −0.682130 | + | 1.25369i | ||||
\(436\) | 3.95779e10 | 0.0524522 | ||||||||
\(437\) | 1.28216e10i | 0.0168181i | ||||||||
\(438\) | − | 1.05644e11i | − | 0.137154i | ||||||
\(439\) | −1.11975e12 | −1.43891 | −0.719453 | − | 0.694541i | \(-0.755607\pi\) | ||||
−0.719453 | + | 0.694541i | \(0.755607\pi\) | |||||||
\(440\) | −2.24391e12 | −2.85410 | ||||||||
\(441\) | −1.52959e11 | −0.192575 | ||||||||
\(442\) | 2.27583e11 | 0.283622 | ||||||||
\(443\) | 5.69596e11i | 0.702668i | 0.936250 | + | 0.351334i | \(0.114272\pi\) | ||||
−0.936250 | + | 0.351334i | \(0.885728\pi\) | |||||||
\(444\) | −1.34318e12 | −1.64026 | ||||||||
\(445\) | − | 2.39357e12i | − | 2.89352i | ||||||
\(446\) | − | 1.59734e11i | − | 0.191157i | ||||||
\(447\) | 2.57806e11i | 0.305428i | ||||||||
\(448\) | 9.26527e11 | 1.08669 | ||||||||
\(449\) | 1.09783e12i | 1.27476i | 0.770550 | + | 0.637379i | \(0.219982\pi\) | ||||
−0.770550 | + | 0.637379i | \(0.780018\pi\) | |||||||
\(450\) | 1.74997e12i | 2.01175i | ||||||||
\(451\) | 9.68062e11 | 1.10182 | ||||||||
\(452\) | − | 3.07965e12i | − | 3.47039i | ||||||
\(453\) | 5.26332e11i | 0.587243i | ||||||||
\(454\) | 9.20887e11i | 1.01731i | ||||||||
\(455\) | 8.47704e11 | 0.927242 | ||||||||
\(456\) | − | 9.16386e11i | − | 0.992514i | ||||||
\(457\) | 1.55960e12 | 1.67259 | 0.836297 | − | 0.548277i | \(-0.184716\pi\) | ||||
0.836297 | + | 0.548277i | \(0.184716\pi\) | |||||||
\(458\) | −1.71864e12 | −1.82512 | ||||||||
\(459\) | −2.70710e11 | −0.284674 | ||||||||
\(460\) | −5.65370e10 | −0.0588738 | ||||||||
\(461\) | − | 4.63879e11i | − | 0.478355i | −0.970976 | − | 0.239178i | \(-0.923122\pi\) | ||
0.970976 | − | 0.239178i | \(-0.0768778\pi\) | |||||||
\(462\) | − | 1.01440e12i | − | 1.03590i | ||||||
\(463\) | −9.44509e11 | −0.955194 | −0.477597 | − | 0.878579i | \(-0.658492\pi\) | ||||
−0.477597 | + | 0.878579i | \(0.658492\pi\) | |||||||
\(464\) | −3.97701e11 | − | 2.16387e11i | −0.398314 | − | 0.216721i | ||||
\(465\) | −2.16021e11 | −0.214268 | ||||||||
\(466\) | − | 4.47287e11i | − | 0.439389i | ||||||
\(467\) | 1.41202e12i | 1.37377i | 0.726766 | + | 0.686885i | \(0.241022\pi\) | ||||
−0.726766 | + | 0.686885i | \(0.758978\pi\) | |||||||
\(468\) | 5.36312e11 | 0.516787 | ||||||||
\(469\) | −1.50063e12 | −1.43218 | ||||||||
\(470\) | 4.77818e12 | 4.51671 | ||||||||
\(471\) | 9.98941e11 | 0.935289 | ||||||||
\(472\) | 2.57497e12i | 2.38799i | ||||||||
\(473\) | −9.20215e11 | −0.845307 | ||||||||
\(474\) | − | 2.00818e12i | − | 1.82726i | ||||||
\(475\) | − | 2.94958e12i | − | 2.65851i | ||||||
\(476\) | − | 4.03661e11i | − | 0.360400i | ||||||
\(477\) | 4.19674e11 | 0.371176 | ||||||||
\(478\) | − | 7.71550e11i | − | 0.675987i | ||||||
\(479\) | − | 5.22956e11i | − | 0.453895i | −0.973907 | − | 0.226948i | \(-0.927125\pi\) | ||
0.973907 | − | 0.226948i | \(-0.0728746\pi\) | |||||||
\(480\) | −9.77799e11 | −0.840745 | ||||||||
\(481\) | 9.18360e11i | 0.782276i | ||||||||
\(482\) | − | 1.86335e12i | − | 1.57247i | ||||||
\(483\) | − | 1.13999e10i | − | 0.00953104i | ||||||
\(484\) | 4.69406e11 | 0.388817 | ||||||||
\(485\) | 1.86752e12i | 1.53260i | ||||||||
\(486\) | −1.67631e12 | −1.36299 | ||||||||
\(487\) | 9.11397e11 | 0.734222 | 0.367111 | − | 0.930177i | \(-0.380347\pi\) | ||||
0.367111 | + | 0.930177i | \(0.380347\pi\) | |||||||
\(488\) | −2.67217e12 | −2.13292 | ||||||||
\(489\) | −1.03177e12 | −0.816002 | ||||||||
\(490\) | 1.76658e12i | 1.38437i | ||||||||
\(491\) | 1.70623e12i | 1.32486i | 0.749124 | + | 0.662430i | \(0.230475\pi\) | ||||
−0.749124 | + | 0.662430i | \(0.769525\pi\) | |||||||
\(492\) | −1.74327e12 | −1.34129 | ||||||||
\(493\) | 1.65851e11 | − | 3.04820e11i | 0.126447 | − | 0.232398i | ||||
\(494\) | −1.40471e12 | −1.06125 | ||||||||
\(495\) | − | 1.26445e12i | − | 0.946629i | ||||||
\(496\) | − | 9.17611e10i | − | 0.0680755i | ||||||
\(497\) | −7.98930e11 | −0.587361 | ||||||||
\(498\) | 1.87245e11 | 0.136420 | ||||||||
\(499\) | 6.76138e11 | 0.488183 | 0.244092 | − | 0.969752i | \(-0.421510\pi\) | ||||
0.244092 | + | 0.969752i | \(0.421510\pi\) | |||||||
\(500\) | 8.16301e12 | 5.84098 | ||||||||
\(501\) | 9.55386e11i | 0.677499i | ||||||||
\(502\) | −6.89370e10 | −0.0484491 | ||||||||
\(503\) | 4.87781e11i | 0.339758i | 0.985465 | + | 0.169879i | \(0.0543376\pi\) | ||||
−0.985465 | + | 0.169879i | \(0.945662\pi\) | |||||||
\(504\) | − | 6.59331e11i | − | 0.455162i | ||||||
\(505\) | 2.86320e12i | 1.95903i | ||||||||
\(506\) | 4.62566e10 | 0.0313687 | ||||||||
\(507\) | − | 6.52953e11i | − | 0.438880i | ||||||
\(508\) | 2.13191e11i | 0.142031i | ||||||||
\(509\) | −2.79337e11 | −0.184458 | −0.0922291 | − | 0.995738i | \(-0.529399\pi\) | ||||
−0.0922291 | + | 0.995738i | \(0.529399\pi\) | |||||||
\(510\) | 9.66246e11i | 0.632444i | ||||||||
\(511\) | 1.28114e11i | 0.0831195i | ||||||||
\(512\) | − | 1.36620e12i | − | 0.878619i | ||||||
\(513\) | 1.67091e12 | 1.06518 | ||||||||
\(514\) | − | 6.63308e11i | − | 0.419161i | ||||||
\(515\) | 2.02704e12 | 1.26978 | ||||||||
\(516\) | 1.65711e12 | 1.02903 | ||||||||
\(517\) | −2.51572e12 | −1.54865 | ||||||||
\(518\) | 2.53123e12 | 1.54471 | ||||||||
\(519\) | − | 1.33810e12i | − | 0.809533i | ||||||
\(520\) | − | 2.76277e12i | − | 1.65703i | ||||||
\(521\) | 1.16532e12 | 0.692905 | 0.346453 | − | 0.938067i | \(-0.387386\pi\) | ||||
0.346453 | + | 0.938067i | \(0.387386\pi\) | |||||||
\(522\) | 6.07348e11 | − | 1.11625e12i | 0.358031 | − | 0.658029i | ||||
\(523\) | 3.13918e12 | 1.83467 | 0.917337 | − | 0.398112i | \(-0.130335\pi\) | ||||
0.917337 | + | 0.398112i | \(0.130335\pi\) | |||||||
\(524\) | − | 8.02255e10i | − | 0.0464859i | ||||||
\(525\) | 2.62252e12i | 1.50662i | ||||||||
\(526\) | 2.34882e12 | 1.33787 | ||||||||
\(527\) | 7.03307e10 | 0.0397189 | ||||||||
\(528\) | −6.63743e11 | −0.371661 | ||||||||
\(529\) | −1.80063e12 | −0.999711 | ||||||||
\(530\) | − | 4.84699e12i | − | 2.66827i | ||||||
\(531\) | −1.45101e12 | −0.792034 | ||||||||
\(532\) | 2.49152e12i | 1.34853i | ||||||||
\(533\) | 1.19191e12i | 0.639691i | ||||||||
\(534\) | − | 3.52654e12i | − | 1.87678i | ||||||
\(535\) | −2.31590e12 | −1.22216 | ||||||||
\(536\) | 4.89075e12i | 2.55937i | ||||||||
\(537\) | − | 1.94435e12i | − | 1.00900i | ||||||
\(538\) | −5.66980e12 | −2.91775 | ||||||||
\(539\) | − | 9.30108e11i | − | 0.474661i | ||||||
\(540\) | 7.36786e12i | 3.72880i | ||||||||
\(541\) | 6.00049e11i | 0.301161i | 0.988598 | + | 0.150581i | \(0.0481143\pi\) | ||||
−0.988598 | + | 0.150581i | \(0.951886\pi\) | |||||||
\(542\) | 1.95931e12 | 0.975229 | ||||||||
\(543\) | − | 2.81553e11i | − | 0.138983i | ||||||
\(544\) | 3.18346e11 | 0.155849 | ||||||||
\(545\) | 1.14889e11 | 0.0557819 | ||||||||
\(546\) | 1.24896e12 | 0.601423 | ||||||||
\(547\) | −1.83298e12 | −0.875417 | −0.437709 | − | 0.899117i | \(-0.644210\pi\) | ||||
−0.437709 | + | 0.899117i | \(0.644210\pi\) | |||||||
\(548\) | 1.65119e12i | 0.782140i | ||||||||
\(549\) | − | 1.50578e12i | − | 0.707433i | ||||||
\(550\) | −1.06412e13 | −4.95859 | ||||||||
\(551\) | −1.02369e12 | + | 1.88144e12i | −0.473134 | + | 0.869579i | ||||
\(552\) | −3.71538e10 | −0.0170325 | ||||||||
\(553\) | 2.43533e12i | 1.10737i | ||||||||
\(554\) | − | 2.18748e12i | − | 0.986621i | ||||||
\(555\) | −3.89906e12 | −1.74438 | ||||||||
\(556\) | 2.08370e12 | 0.924694 | ||||||||
\(557\) | −3.46594e12 | −1.52571 | −0.762856 | − | 0.646568i | \(-0.776204\pi\) | ||||
−0.762856 | + | 0.646568i | \(0.776204\pi\) | |||||||
\(558\) | 2.57551e11 | 0.112463 | ||||||||
\(559\) | − | 1.13300e12i | − | 0.490767i | ||||||
\(560\) | −1.52881e12 | −0.656914 | ||||||||
\(561\) | − | 5.08729e11i | − | 0.216847i | ||||||
\(562\) | 2.71153e12i | 1.14657i | ||||||||
\(563\) | − | 3.56054e12i | − | 1.49358i | −0.665060 | − | 0.746790i | \(-0.731594\pi\) | ||
0.665060 | − | 0.746790i | \(-0.268406\pi\) | |||||||
\(564\) | 4.53026e12 | 1.88524 | ||||||||
\(565\) | − | 8.93977e12i | − | 3.69070i | ||||||
\(566\) | − | 4.88172e12i | − | 1.99940i | ||||||
\(567\) | −6.54966e11 | −0.266131 | ||||||||
\(568\) | 2.60381e12i | 1.04964i | ||||||||
\(569\) | 7.92923e11i | 0.317122i | 0.987349 | + | 0.158561i | \(0.0506854\pi\) | ||||
−0.987349 | + | 0.158561i | \(0.949315\pi\) | |||||||
\(570\) | − | 5.96397e12i | − | 2.36646i | ||||||
\(571\) | 3.84707e12 | 1.51449 | 0.757247 | − | 0.653129i | \(-0.226544\pi\) | ||||
0.757247 | + | 0.653129i | \(0.226544\pi\) | |||||||
\(572\) | 3.26119e12i | 1.27378i | ||||||||
\(573\) | 2.56758e11 | 0.0995011 | ||||||||
\(574\) | 3.28519e12 | 1.26316 | ||||||||
\(575\) | −1.19587e11 | −0.0456226 | ||||||||
\(576\) | 1.70159e12 | 0.644103 | ||||||||
\(577\) | − | 1.22383e12i | − | 0.459655i | −0.973231 | − | 0.229827i | \(-0.926184\pi\) | ||
0.973231 | − | 0.229827i | \(-0.0738161\pi\) | |||||||
\(578\) | 4.17964e12i | 1.55763i | ||||||||
\(579\) | 1.90043e12 | 0.702747 | ||||||||
\(580\) | −8.29622e12 | − | 4.51394e12i | −3.04407 | − | 1.65626i | ||||
\(581\) | −2.27072e11 | −0.0826746 | ||||||||
\(582\) | 2.75149e12i | 0.994065i | ||||||||
\(583\) | 2.55194e12i | 0.914876i | ||||||||
\(584\) | 4.17540e11 | 0.148539 | ||||||||
\(585\) | 1.55683e12 | 0.549593 | ||||||||
\(586\) | 7.01017e12 | 2.45578 | ||||||||
\(587\) | 2.75983e12 | 0.959424 | 0.479712 | − | 0.877426i | \(-0.340741\pi\) | ||||
0.479712 | + | 0.877426i | \(0.340741\pi\) | |||||||
\(588\) | 1.67492e12i | 0.577826i | ||||||||
\(589\) | −4.34103e11 | −0.148619 | ||||||||
\(590\) | 1.67583e13i | 5.69370i | ||||||||
\(591\) | 1.19538e12i | 0.403053i | ||||||||
\(592\) | − | 1.65624e12i | − | 0.554212i | ||||||
\(593\) | −1.24835e12 | −0.414563 | −0.207282 | − | 0.978281i | \(-0.566462\pi\) | ||||
−0.207282 | + | 0.978281i | \(0.566462\pi\) | |||||||
\(594\) | − | 6.02812e12i | − | 1.98675i | ||||||
\(595\) | − | 1.17177e12i | − | 0.383279i | ||||||
\(596\) | −2.28444e12 | −0.741604 | ||||||||
\(597\) | 3.26004e11i | 0.105036i | ||||||||
\(598\) | 5.69525e10i | 0.0182120i | ||||||||
\(599\) | − | 1.96318e11i | − | 0.0623074i | −0.999515 | − | 0.0311537i | \(-0.990082\pi\) | ||
0.999515 | − | 0.0311537i | \(-0.00991813\pi\) | |||||||
\(600\) | 8.54713e12 | 2.69240 | ||||||||
\(601\) | 3.14658e12i | 0.983793i | 0.870654 | + | 0.491896i | \(0.163696\pi\) | ||||
−0.870654 | + | 0.491896i | \(0.836304\pi\) | |||||||
\(602\) | −3.12282e12 | −0.969086 | ||||||||
\(603\) | −2.75596e12 | −0.848877 | ||||||||
\(604\) | −4.66387e12 | −1.42587 | ||||||||
\(605\) | 1.36262e12 | 0.413499 | ||||||||
\(606\) | 4.21846e12i | 1.27065i | ||||||||
\(607\) | 4.02375e12i | 1.20305i | 0.798856 | + | 0.601523i | \(0.205439\pi\) | ||||
−0.798856 | + | 0.601523i | \(0.794561\pi\) | |||||||
\(608\) | −1.96493e12 | −0.583151 | ||||||||
\(609\) | 9.10176e11 | − | 1.67282e12i | 0.268131 | − | 0.492802i | ||||
\(610\) | −1.73908e13 | −5.08553 | ||||||||
\(611\) | − | 3.09743e12i | − | 0.899116i | ||||||
\(612\) | − | 7.41335e11i | − | 0.213616i | ||||||
\(613\) | 5.36267e12 | 1.53394 | 0.766971 | − | 0.641681i | \(-0.221763\pi\) | ||||
0.766971 | + | 0.641681i | \(0.221763\pi\) | |||||||
\(614\) | 3.43197e12 | 0.974508 | ||||||||
\(615\) | −5.06046e12 | −1.42643 | ||||||||
\(616\) | 4.00924e12 | 1.12189 | ||||||||
\(617\) | − | 5.00018e12i | − | 1.38900i | −0.719492 | − | 0.694500i | \(-0.755625\pi\) | ||
0.719492 | − | 0.694500i | \(-0.244375\pi\) | |||||||
\(618\) | 2.98652e12 | 0.823601 | ||||||||
\(619\) | − | 8.35185e11i | − | 0.228652i | −0.993443 | − | 0.114326i | \(-0.963529\pi\) | ||
0.993443 | − | 0.114326i | \(-0.0364708\pi\) | |||||||
\(620\) | − | 1.91418e12i | − | 0.520259i | ||||||
\(621\) | − | 6.77449e10i | − | 0.0182795i | ||||||
\(622\) | 5.34908e12 | 1.43292 | ||||||||
\(623\) | 4.27664e12i | 1.13738i | ||||||||
\(624\) | − | 8.17221e11i | − | 0.215779i | ||||||
\(625\) | 1.34517e13 | 3.52629 | ||||||||
\(626\) | − | 2.80878e12i | − | 0.731027i | ||||||
\(627\) | 3.14003e12i | 0.811392i | ||||||||
\(628\) | 8.85170e12i | 2.27095i | ||||||||
\(629\) | 1.26943e12 | 0.323357 | ||||||||
\(630\) | − | 4.29102e12i | − | 1.08524i | ||||||
\(631\) | −4.91799e12 | −1.23497 | −0.617484 | − | 0.786583i | \(-0.711848\pi\) | ||||
−0.617484 | + | 0.786583i | \(0.711848\pi\) | |||||||
\(632\) | 7.93703e12 | 1.97893 | ||||||||
\(633\) | −2.18863e12 | −0.541821 | ||||||||
\(634\) | 1.43176e12 | 0.351939 | ||||||||
\(635\) | 6.18862e11i | 0.151047i | ||||||||
\(636\) | − | 4.59550e12i | − | 1.11372i | ||||||
\(637\) | 1.14518e12 | 0.275578 | ||||||||
\(638\) | 6.78767e12 | + | 3.69315e12i | 1.62191 | + | 0.882477i | ||||
\(639\) | −1.46726e12 | −0.348139 | ||||||||
\(640\) | − | 1.48526e13i | − | 3.49940i | ||||||
\(641\) | − | 4.70484e12i | − | 1.10074i | −0.834922 | − | 0.550369i | \(-0.814487\pi\) | ||
0.834922 | − | 0.550369i | \(-0.185513\pi\) | |||||||
\(642\) | −3.41210e12 | −0.792710 | ||||||||
\(643\) | −1.03747e12 | −0.239346 | −0.119673 | − | 0.992813i | \(-0.538185\pi\) | ||||
−0.119673 | + | 0.992813i | \(0.538185\pi\) | |||||||
\(644\) | 1.01016e11 | 0.0231421 | ||||||||
\(645\) | 4.81034e12 | 1.09435 | ||||||||
\(646\) | 1.94171e12i | 0.438671i | ||||||||
\(647\) | −5.53484e12 | −1.24175 | −0.620877 | − | 0.783908i | \(-0.713223\pi\) | ||||
−0.620877 | + | 0.783908i | \(0.713223\pi\) | |||||||
\(648\) | 2.13461e12i | 0.475589i | ||||||||
\(649\) | − | 8.82324e12i | − | 1.95221i | ||||||
\(650\) | − | 1.31018e13i | − | 2.87885i | ||||||
\(651\) | 3.85968e11 | 0.0842243 | ||||||||
\(652\) | − | 9.14257e12i | − | 1.98132i | ||||||
\(653\) | − | 1.66756e12i | − | 0.358898i | −0.983767 | − | 0.179449i | \(-0.942568\pi\) | ||
0.983767 | − | 0.179449i | \(-0.0574315\pi\) | |||||||
\(654\) | 1.69270e11 | 0.0361810 | ||||||||
\(655\) | − | 2.32883e11i | − | 0.0494369i | ||||||
\(656\) | − | 2.14958e12i | − | 0.453196i | ||||||
\(657\) | 2.35285e11i | 0.0492664i | ||||||||
\(658\) | −8.53727e12 | −1.77543 | ||||||||
\(659\) | 1.17342e12i | 0.242364i | 0.992630 | + | 0.121182i | \(0.0386685\pi\) | ||||
−0.992630 | + | 0.121182i | \(0.961332\pi\) | |||||||
\(660\) | −1.38460e13 | −2.84038 | ||||||||
\(661\) | 2.45865e12 | 0.500946 | 0.250473 | − | 0.968124i | \(-0.419414\pi\) | ||||
0.250473 | + | 0.968124i | \(0.419414\pi\) | |||||||
\(662\) | −6.14225e12 | −1.24299 | ||||||||
\(663\) | 6.26363e11 | 0.125897 | ||||||||
\(664\) | 7.40057e11i | 0.147744i | ||||||||
\(665\) | 7.23251e12i | 1.43414i | ||||||||
\(666\) | 4.64867e12 | 0.915577 | ||||||||
\(667\) | 7.62809e10 | + | 4.15041e10i | 0.0149228 | + | 0.00811942i | ||||
\(668\) | −8.46575e12 | −1.64502 | ||||||||
\(669\) | − | 4.39625e11i | − | 0.0848526i | ||||||
\(670\) | 3.18297e13i | 6.10233i | ||||||||
\(671\) | 9.15629e12 | 1.74369 | ||||||||
\(672\) | 1.74705e12 | 0.330479 | ||||||||
\(673\) | 3.83983e12 | 0.721513 | 0.360757 | − | 0.932660i | \(-0.382519\pi\) | ||||
0.360757 | + | 0.932660i | \(0.382519\pi\) | |||||||
\(674\) | −3.33093e12 | −0.621722 | ||||||||
\(675\) | 1.55845e13i | 2.88953i | ||||||||
\(676\) | 5.78587e12 | 1.06564 | ||||||||
\(677\) | 3.34063e12i | 0.611194i | 0.952161 | + | 0.305597i | \(0.0988561\pi\) | ||||
−0.952161 | + | 0.305597i | \(0.901144\pi\) | |||||||
\(678\) | − | 1.31713e13i | − | 2.39384i | ||||||
\(679\) | − | 3.33674e12i | − | 0.602432i | ||||||
\(680\) | −3.81894e12 | −0.684940 | ||||||||
\(681\) | 2.53450e12i | 0.451576i | ||||||||
\(682\) | 1.56611e12i | 0.277200i | ||||||||
\(683\) | −4.84375e11 | −0.0851703 | −0.0425851 | − | 0.999093i | \(-0.513559\pi\) | ||||
−0.0425851 | + | 0.999093i | \(0.513559\pi\) | |||||||
\(684\) | 4.57575e12i | 0.799300i | ||||||||
\(685\) | 4.79316e12i | 0.831791i | ||||||||
\(686\) | − | 1.04874e13i | − | 1.80805i | ||||||
\(687\) | −4.73011e12 | −0.810150 | ||||||||
\(688\) | 2.04333e12i | 0.347689i | ||||||||
\(689\) | −3.14203e12 | −0.531158 | ||||||||
\(690\) | −2.41802e11 | −0.0406106 | ||||||||
\(691\) | −6.75627e11 | −0.112734 | −0.0563671 | − | 0.998410i | \(-0.517952\pi\) | ||||
−0.0563671 | + | 0.998410i | \(0.517952\pi\) | |||||||
\(692\) | 1.18570e13 | 1.96561 | ||||||||
\(693\) | 2.25923e12i | 0.372100i | ||||||||
\(694\) | 1.45859e12i | 0.238680i | ||||||||
\(695\) | 6.04866e12 | 0.983394 | ||||||||
\(696\) | −5.45194e12 | − | 2.96638e12i | −0.880662 | − | 0.479165i | ||||
\(697\) | 1.64755e12 | 0.264419 | ||||||||
\(698\) | − | 1.09564e13i | − | 1.74711i | ||||||
\(699\) | − | 1.23104e12i | − | 0.195041i | ||||||
\(700\) | −2.32384e13 | −3.65818 | ||||||||
\(701\) | −2.03482e12 | −0.318270 | −0.159135 | − | 0.987257i | \(-0.550871\pi\) | ||||
−0.159135 | + | 0.987257i | \(0.550871\pi\) | |||||||
\(702\) | 7.42200e12 | 1.15346 | ||||||||
\(703\) | −7.83534e12 | −1.20993 | ||||||||
\(704\) | 1.03470e13i | 1.58759i | ||||||||
\(705\) | 1.31507e13 | 2.00492 | ||||||||
\(706\) | − | 8.25222e12i | − | 1.25011i | ||||||
\(707\) | − | 5.11573e12i | − | 0.770053i | ||||||
\(708\) | 1.58888e13i | 2.37651i | ||||||||
\(709\) | 5.16026e12 | 0.766943 | 0.383472 | − | 0.923553i | \(-0.374728\pi\) | ||||
0.383472 | + | 0.923553i | \(0.374728\pi\) | |||||||
\(710\) | 1.69460e13i | 2.50267i | ||||||||
\(711\) | 4.47255e12i | 0.656360i | ||||||||
\(712\) | 1.39381e13 | 2.03256 | ||||||||
\(713\) | 1.76002e10i | 0.00255044i | ||||||||
\(714\) | − | 1.72641e12i | − | 0.248601i | ||||||
\(715\) | 9.46676e12i | 1.35464i | ||||||||
\(716\) | 1.72291e13 | 2.44993 | ||||||||
\(717\) | − | 2.12349e12i | − | 0.300064i | ||||||
\(718\) | −1.91476e13 | −2.68878 | ||||||||
\(719\) | 8.19452e12 | 1.14352 | 0.571760 | − | 0.820421i | \(-0.306261\pi\) | ||||
0.571760 | + | 0.820421i | \(0.306261\pi\) | |||||||
\(720\) | −2.80771e12 | −0.389365 | ||||||||
\(721\) | −3.62176e12 | −0.499126 | ||||||||
\(722\) | 2.44305e11i | 0.0334591i | ||||||||
\(723\) | − | 5.12839e12i | − | 0.698005i | ||||||
\(724\) | 2.49486e12 | 0.337461 | ||||||||
\(725\) | −1.75482e13 | − | 9.54791e12i | −2.35891 | − | 1.28347i | ||||
\(726\) | 2.00760e12 | 0.268202 | ||||||||
\(727\) | − | 5.36300e12i | − | 0.712038i | −0.934479 | − | 0.356019i | \(-0.884134\pi\) | ||
0.934479 | − | 0.356019i | \(-0.115866\pi\) | |||||||
\(728\) | 4.93630e12i | 0.651344i | ||||||||
\(729\) | −7.30292e12 | −0.957685 | ||||||||
\(730\) | 2.71741e12 | 0.354162 | ||||||||
\(731\) | −1.56612e12 | −0.202861 | ||||||||
\(732\) | −1.64885e13 | −2.12267 | ||||||||
\(733\) | − | 2.69936e12i | − | 0.345377i | −0.984976 | − | 0.172688i | \(-0.944755\pi\) | ||
0.984976 | − | 0.172688i | \(-0.0552454\pi\) | |||||||
\(734\) | −1.20384e13 | −1.53087 | ||||||||
\(735\) | 4.86206e12i | 0.614507i | ||||||||
\(736\) | 7.96658e10i | 0.0100074i | ||||||||
\(737\) | − | 1.67584e13i | − | 2.09232i | ||||||
\(738\) | 6.03335e12 | 0.748695 | ||||||||
\(739\) | 1.34727e12i | 0.166171i | 0.996542 | + | 0.0830855i | \(0.0264775\pi\) | ||||
−0.996542 | + | 0.0830855i | \(0.973523\pi\) | |||||||
\(740\) | − | 3.45499e13i | − | 4.23550i | ||||||
\(741\) | −3.86611e12 | −0.471077 | ||||||||
\(742\) | 8.66021e12i | 1.04884i | ||||||||
\(743\) | − | 1.20853e13i | − | 1.45481i | −0.686207 | − | 0.727406i | \(-0.740726\pi\) | ||
0.686207 | − | 0.727406i | \(-0.259274\pi\) | |||||||
\(744\) | − | 1.25792e12i | − | 0.150513i | ||||||
\(745\) | −6.63139e12 | −0.788681 | ||||||||
\(746\) | 5.00631e12i | 0.591824i | ||||||||
\(747\) | −4.17025e11 | −0.0490027 | ||||||||
\(748\) | 4.50789e12 | 0.526522 | ||||||||
\(749\) | 4.13786e12 | 0.480405 | ||||||||
\(750\) | 3.49123e13 | 4.02905 | ||||||||
\(751\) | 1.34457e13i | 1.54242i | 0.636578 | + | 0.771212i | \(0.280349\pi\) | ||||
−0.636578 | + | 0.771212i | \(0.719651\pi\) | |||||||
\(752\) | 5.58614e12i | 0.636988i | ||||||||
\(753\) | −1.89731e11 | −0.0215061 | ||||||||
\(754\) | −4.54711e12 | + | 8.35719e12i | −0.512348 | + | 0.941650i | ||||
\(755\) | −1.35385e13 | −1.51639 | ||||||||
\(756\) | − | 1.31643e13i | − | 1.46571i | ||||||
\(757\) | − | 4.30724e12i | − | 0.476725i | −0.971176 | − | 0.238363i | \(-0.923389\pi\) | ||
0.971176 | − | 0.238363i | \(-0.0766106\pi\) | |||||||
\(758\) | −1.87748e13 | −2.06568 | ||||||||
\(759\) | 1.27309e11 | 0.0139242 | ||||||||
\(760\) | 2.35717e13 | 2.56288 | ||||||||
\(761\) | −4.18265e12 | −0.452086 | −0.226043 | − | 0.974117i | \(-0.572579\pi\) | ||||
−0.226043 | + | 0.974117i | \(0.572579\pi\) | |||||||
\(762\) | 9.11793e11i | 0.0979713i | ||||||||
\(763\) | −2.05274e11 | −0.0219267 | ||||||||
\(764\) | 2.27515e12i | 0.241596i | ||||||||
\(765\) | − | 2.15199e12i | − | 0.227176i | ||||||
\(766\) | 3.31656e12i | 0.348064i | ||||||||
\(767\) | 1.08634e13 | 1.13341 | ||||||||
\(768\) | − | 1.15611e13i | − | 1.19915i | ||||||
\(769\) | − | 8.62518e12i | − | 0.889405i | −0.895678 | − | 0.444702i | \(-0.853309\pi\) | ||
0.895678 | − | 0.444702i | \(-0.146691\pi\) | |||||||
\(770\) | 2.60927e13 | 2.67492 | ||||||||
\(771\) | − | 1.82558e12i | − | 0.186062i | ||||||
\(772\) | 1.68399e13i | 1.70632i | ||||||||
\(773\) | 6.76528e12i | 0.681519i | 0.940150 | + | 0.340760i | \(0.110684\pi\) | ||||
−0.940150 | + | 0.340760i | \(0.889316\pi\) | |||||||
\(774\) | −5.73515e12 | −0.574395 | ||||||||
\(775\) | − | 4.04888e12i | − | 0.403159i | ||||||
\(776\) | −1.08748e13 | −1.07658 | ||||||||
\(777\) | 6.96654e12 | 0.685681 | ||||||||
\(778\) | −6.95239e11 | −0.0680340 | ||||||||
\(779\) | −1.01692e13 | −0.989393 | ||||||||
\(780\) | − | 1.70476e13i | − | 1.64906i | ||||||
\(781\) | − | 8.92207e12i | − | 0.858096i | ||||||
\(782\) | 7.87245e10 | 0.00752800 | ||||||||
\(783\) | 5.40879e12 | − | 9.94087e12i | 0.514247 | − | 0.945140i | ||||
\(784\) | −2.06530e12 | −0.195236 | ||||||||
\(785\) | 2.56952e13i | 2.41512i | ||||||||
\(786\) | − | 3.43115e11i | − | 0.0320655i | ||||||
\(787\) | −6.60390e12 | −0.613640 | −0.306820 | − | 0.951767i | \(-0.599265\pi\) | ||||
−0.306820 | + | 0.951767i | \(0.599265\pi\) | |||||||
\(788\) | −1.05924e13 | −0.978643 | ||||||||
\(789\) | 6.46452e12 | 0.593868 | ||||||||
\(790\) | 5.16553e13 | 4.71838 | ||||||||
\(791\) | 1.59729e13i | 1.45074i | ||||||||
\(792\) | 7.36309e12 | 0.664962 | ||||||||
\(793\) | 1.12735e13i | 1.01235i | ||||||||
\(794\) | 1.87086e13i | 1.67051i | ||||||||
\(795\) | − | 1.33401e13i | − | 1.18442i | ||||||
\(796\) | −2.88875e12 | −0.255036 | ||||||||
\(797\) | − | 4.49942e12i | − | 0.394998i | −0.980303 | − | 0.197499i | \(-0.936718\pi\) | ||
0.980303 | − | 0.197499i | \(-0.0632819\pi\) | |||||||
\(798\) | 1.06559e13i | 0.930205i | ||||||||
\(799\) | −4.28152e12 | −0.371653 | ||||||||
\(800\) | − | 1.83269e13i | − | 1.58192i | ||||||
\(801\) | 7.85418e12i | 0.674147i | ||||||||
\(802\) | − | 2.94813e13i | − | 2.51630i | ||||||
\(803\) | −1.43072e12 | −0.121432 | ||||||||
\(804\) | 3.01782e13i | 2.54707i | ||||||||
\(805\) | 2.93234e11 | 0.0246112 | ||||||||
\(806\) | −1.92824e12 | −0.160936 | ||||||||
\(807\) | −1.56046e13 | −1.29516 | ||||||||
\(808\) | −1.66728e13 | −1.37612 | ||||||||
\(809\) | 1.50450e12i | 0.123487i | 0.998092 | + | 0.0617437i | \(0.0196661\pi\) | ||||
−0.998092 | + | 0.0617437i | \(0.980334\pi\) | |||||||
\(810\) | 1.38924e13i | 1.13395i | ||||||||
\(811\) | 1.47030e13 | 1.19347 | 0.596735 | − | 0.802438i | \(-0.296464\pi\) | ||||
0.596735 | + | 0.802438i | \(0.296464\pi\) | |||||||
\(812\) | 1.48230e13 | + | 8.06515e12i | 1.19656 | + | 0.651044i | ||||
\(813\) | 5.39249e12 | 0.432894 | ||||||||
\(814\) | 2.82675e13i | 2.25672i | ||||||||
\(815\) | − | 2.65395e13i | − | 2.10709i | ||||||
\(816\) | −1.12963e12 | −0.0891930 | ||||||||
\(817\) | 9.66660e12 | 0.759057 | ||||||||
\(818\) | 1.91442e13 | 1.49502 | ||||||||
\(819\) | −2.78163e12 | −0.216034 | ||||||||
\(820\) | − | 4.48411e13i | − | 3.46349i | ||||||
\(821\) | −9.51209e12 | −0.730687 | −0.365344 | − | 0.930873i | \(-0.619049\pi\) | ||||
−0.365344 | + | 0.930873i | \(0.619049\pi\) | |||||||
\(822\) | 7.06195e12i | 0.539512i | ||||||||
\(823\) | − | 4.52787e11i | − | 0.0344029i | −0.999852 | − | 0.0172014i | \(-0.994524\pi\) | ||
0.999852 | − | 0.0172014i | \(-0.00547565\pi\) | |||||||
\(824\) | 1.18038e13i | 0.891965i | ||||||||
\(825\) | −2.92871e13 | −2.20107 | ||||||||
\(826\) | − | 2.99423e13i | − | 2.23808i | ||||||
\(827\) | 1.84701e13i | 1.37308i | 0.727093 | + | 0.686539i | \(0.240871\pi\) | ||||
−0.727093 | + | 0.686539i | \(0.759129\pi\) | |||||||
\(828\) | 1.85518e11 | 0.0137167 | ||||||||
\(829\) | 1.74632e13i | 1.28419i | 0.766626 | + | 0.642093i | \(0.221934\pi\) | ||||
−0.766626 | + | 0.642093i | \(0.778066\pi\) | |||||||
\(830\) | 4.81640e12i | 0.352266i | ||||||||
\(831\) | − | 6.02047e12i | − | 0.437951i | ||||||
\(832\) | −1.27396e13 | −0.921721 | ||||||||
\(833\) | − | 1.58296e12i | − | 0.113911i | ||||||
\(834\) | 8.91173e12 | 0.637844 | ||||||||
\(835\) | −2.45748e13 | −1.74945 | ||||||||
\(836\) | −2.78241e13 | −1.97012 | ||||||||
\(837\) | 2.29364e12 | 0.161533 | ||||||||
\(838\) | − | 5.11048e12i | − | 0.357984i | ||||||
\(839\) | − | 6.33361e12i | − | 0.441288i | −0.975354 | − | 0.220644i | \(-0.929184\pi\) | ||
0.975354 | − | 0.220644i | \(-0.0708159\pi\) | |||||||
\(840\) | −2.09580e13 | −1.45242 | ||||||||
\(841\) | 7.87973e12 | + | 1.21806e13i | 0.543162 | + | 0.839628i | ||||
\(842\) | 4.71339e12 | 0.323169 | ||||||||
\(843\) | 7.46279e12i | 0.508952i | ||||||||
\(844\) | − | 1.93936e13i | − | 1.31558i | ||||||
\(845\) | 1.67955e13 | 1.13328 | ||||||||
\(846\) | −1.56790e13 | −1.05233 | ||||||||
\(847\) | −2.43461e12 | −0.162538 | ||||||||
\(848\) | 5.66658e12 | 0.376304 | ||||||||
\(849\) | − | 1.34357e13i | − | 0.887512i | ||||||
\(850\) | −1.81103e13 | −1.18999 | ||||||||
\(851\) | 3.17675e11i | 0.0207635i | ||||||||
\(852\) | 1.60667e13i | 1.04460i | ||||||||
\(853\) | − | 4.39884e12i | − | 0.284490i | −0.989831 | − | 0.142245i | \(-0.954568\pi\) | ||
0.989831 | − | 0.142245i | \(-0.0454322\pi\) | |||||||
\(854\) | 3.10725e13 | 1.99902 | ||||||||
\(855\) | 1.32827e13i | 0.850041i | ||||||||
\(856\) | − | 1.34858e13i | − | 0.858509i | ||||||
\(857\) | −1.76635e13 | −1.11857 | −0.559283 | − | 0.828976i | \(-0.688924\pi\) | ||||
−0.559283 | + | 0.828976i | \(0.688924\pi\) | |||||||
\(858\) | 1.39477e13i | 0.878640i | ||||||||
\(859\) | 1.02651e13i | 0.643274i | 0.946863 | + | 0.321637i | \(0.104233\pi\) | ||||
−0.946863 | + | 0.321637i | \(0.895767\pi\) | |||||||
\(860\) | 4.26249e13i | 2.65717i | ||||||||
\(861\) | 9.04162e12 | 0.560702 | ||||||||
\(862\) | − | 3.79479e13i | − | 2.34102i | ||||||
\(863\) | −9.67133e12 | −0.593523 | −0.296762 | − | 0.954952i | \(-0.595907\pi\) | ||||
−0.296762 | + | 0.954952i | \(0.595907\pi\) | |||||||
\(864\) | 1.03820e13 | 0.633824 | ||||||||
\(865\) | 3.44191e13 | 2.09039 | ||||||||
\(866\) | −5.21365e13 | −3.15000 | ||||||||
\(867\) | 1.15034e13i | 0.691415i | ||||||||
\(868\) | 3.42010e12i | 0.204503i | ||||||||
\(869\) | −2.71966e13 | −1.61780 | ||||||||
\(870\) | −3.54820e13 | − | 1.93056e13i | −2.09977 | − | 1.14247i | ||||
\(871\) | 2.06334e13 | 1.21476 | ||||||||
\(872\) | 6.69013e11i | 0.0391842i | ||||||||
\(873\) | − | 6.12802e12i | − | 0.357072i | ||||||
\(874\) | −4.85912e11 | −0.0281680 | ||||||||
\(875\) | −4.23381e13 | −2.44172 | ||||||||
\(876\) | 2.57642e12 | 0.147825 | ||||||||
\(877\) | 3.11553e13 | 1.77842 | 0.889209 | − | 0.457502i | \(-0.151256\pi\) | ||||
0.889209 | + | 0.457502i | \(0.151256\pi\) | |||||||
\(878\) | − | 4.24362e13i | − | 2.40997i | ||||||
\(879\) | 1.92936e13 | 1.09010 | ||||||||
\(880\) | − | 1.70731e13i | − | 0.959709i | ||||||
\(881\) | − | 1.27511e13i | − | 0.713109i | −0.934275 | − | 0.356554i | \(-0.883951\pi\) | ||
0.934275 | − | 0.356554i | \(-0.116049\pi\) | |||||||
\(882\) | − | 5.79680e12i | − | 0.322537i | ||||||
\(883\) | 6.02313e11 | 0.0333425 | 0.0166713 | − | 0.999861i | \(-0.494693\pi\) | ||||
0.0166713 | + | 0.999861i | \(0.494693\pi\) | |||||||
\(884\) | 5.55026e12i | 0.305688i | ||||||||
\(885\) | 4.61227e13i | 2.52738i | ||||||||
\(886\) | −2.15864e13 | −1.17687 | ||||||||
\(887\) | − | 1.27454e13i | − | 0.691348i | −0.938355 | − | 0.345674i | \(-0.887650\pi\) | ||
0.938355 | − | 0.345674i | \(-0.112350\pi\) | |||||||
\(888\) | − | 2.27048e13i | − | 1.22535i | ||||||
\(889\) | − | 1.10573e12i | − | 0.0593735i | ||||||
\(890\) | 9.07111e13 | 4.84625 | ||||||||
\(891\) | − | 7.31435e12i | − | 0.388800i | ||||||
\(892\) | 3.89556e12 | 0.206029 | ||||||||
\(893\) | 2.64269e13 | 1.39064 | ||||||||
\(894\) | −9.77029e12 | −0.511551 | ||||||||
\(895\) | 5.00134e13 | 2.60545 | ||||||||
\(896\) | 2.65375e13i | 1.37554i | ||||||||
\(897\) | 1.56747e11i | 0.00808412i | ||||||||
\(898\) | −4.16055e13 | −2.13505 | ||||||||
\(899\) | −1.40521e12 | + | 2.58265e12i | −0.0717500 | + | 0.131870i | ||||
\(900\) | −4.26780e13 | −2.16827 | ||||||||
\(901\) | 4.34318e12i | 0.219556i | ||||||||
\(902\) | 3.66874e13i | 1.84539i | ||||||||
\(903\) | −8.59474e12 | −0.430168 | ||||||||
\(904\) | 5.20576e13 | 2.59254 | ||||||||
\(905\) | 7.24221e12 | 0.358883 | ||||||||
\(906\) | −1.99468e13 | −0.983551 | ||||||||
\(907\) | 2.99982e13i | 1.47185i | 0.677064 | + | 0.735924i | \(0.263252\pi\) | ||||
−0.677064 | + | 0.735924i | \(0.736748\pi\) | |||||||
\(908\) | −2.24584e13 | −1.09646 | ||||||||
\(909\) | − | 9.39520e12i | − | 0.456424i | ||||||
\(910\) | 3.21261e13i | 1.55300i | ||||||||
\(911\) | 1.20731e13i | 0.580744i | 0.956914 | + | 0.290372i | \(0.0937790\pi\) | ||||
−0.956914 | + | 0.290372i | \(0.906221\pi\) | |||||||
\(912\) | 6.97243e12 | 0.333739 | ||||||||
\(913\) | − | 2.53584e12i | − | 0.120782i | ||||||
\(914\) | 5.91054e13i | 2.80136i | ||||||||
\(915\) | −4.78637e13 | −2.25741 | ||||||||
\(916\) | − | 4.19139e13i | − | 1.96711i | ||||||
\(917\) | 4.16096e11i | 0.0194326i | ||||||||
\(918\) | − | 1.02593e13i | − | 0.476789i | ||||||
\(919\) | 1.51682e13 | 0.701479 | 0.350739 | − | 0.936473i | \(-0.385930\pi\) | ||||
0.350739 | + | 0.936473i | \(0.385930\pi\) | |||||||
\(920\) | − | 9.55685e11i | − | 0.0439814i | ||||||
\(921\) | 9.44558e12 | 0.432574 | ||||||||
\(922\) | 1.75800e13 | 0.801179 | ||||||||
\(923\) | 1.09851e13 | 0.498193 | ||||||||
\(924\) | 2.47389e13 | 1.11649 | ||||||||
\(925\) | − | 7.30802e13i | − | 3.28217i | ||||||
\(926\) | − | 3.57948e13i | − | 1.59982i | ||||||
\(927\) | −6.65146e12 | −0.295841 | ||||||||
\(928\) | −6.36056e12 | + | 1.16901e13i | −0.281533 | + | 0.517433i | ||||
\(929\) | 1.66057e13 | 0.731451 | 0.365726 | − | 0.930723i | \(-0.380821\pi\) | ||||
0.365726 | + | 0.930723i | \(0.380821\pi\) | |||||||
\(930\) | − | 8.18671e12i | − | 0.358869i | ||||||
\(931\) | 9.77051e12i | 0.426230i | ||||||||
\(932\) | 1.09083e13 | 0.473573 | ||||||||
\(933\) | 1.47219e13 | 0.636059 | ||||||||
\(934\) | −5.35124e13 | −2.30088 | ||||||||
\(935\) | 1.30857e13 | 0.559946 | ||||||||
\(936\) | 9.06567e12i | 0.386063i | ||||||||
\(937\) | −2.74085e13 | −1.16160 | −0.580801 | − | 0.814045i | \(-0.697261\pi\) | ||||
−0.580801 | + | 0.814045i | \(0.697261\pi\) | |||||||
\(938\) | − | 5.68707e13i | − | 2.39870i | ||||||
\(939\) | − | 7.73043e12i | − | 0.324495i | ||||||
\(940\) | 1.16529e14i | 4.86810i | ||||||||
\(941\) | −1.92736e13 | −0.801328 | −0.400664 | − | 0.916225i | \(-0.631220\pi\) | ||||
−0.400664 | + | 0.916225i | \(0.631220\pi\) | |||||||
\(942\) | 3.78577e13i | 1.56648i | ||||||||
\(943\) | 4.12299e11i | 0.0169789i | ||||||||
\(944\) | −1.95920e13 | −0.802978 | ||||||||
\(945\) | − | 3.82140e13i | − | 1.55876i | ||||||
\(946\) | − | 3.48742e13i | − | 1.41577i | ||||||
\(947\) | − | 1.74559e13i | − | 0.705291i | −0.935757 | − | 0.352645i | \(-0.885282\pi\) | ||
0.935757 | − | 0.352645i | \(-0.114718\pi\) | |||||||
\(948\) | 4.89752e13 | 1.96942 | ||||||||
\(949\) | − | 1.76154e12i | − | 0.0705010i | ||||||
\(950\) | 1.11783e14 | 4.45265 | ||||||||
\(951\) | 3.94054e12 | 0.156222 | ||||||||
\(952\) | 6.82337e12 | 0.269236 | ||||||||
\(953\) | −4.68001e12 | −0.183793 | −0.0918964 | − | 0.995769i | \(-0.529293\pi\) | ||||
−0.0918964 | + | 0.995769i | \(0.529293\pi\) | |||||||
\(954\) | 1.59047e13i | 0.621668i | ||||||||
\(955\) | 6.60443e12i | 0.256933i | ||||||||
\(956\) | 1.88164e13 | 0.728578 | ||||||||
\(957\) | 1.86813e13 | + | 1.01644e13i | 0.719951 | + | 0.391723i | ||||
\(958\) | 1.98189e13 | 0.760212 | ||||||||
\(959\) | − | 8.56404e12i | − | 0.326960i | ||||||
\(960\) | − | 5.40881e13i | − | 2.05533i | ||||||
\(961\) | 2.58437e13 | 0.977462 | ||||||||
\(962\) | −3.48038e13 | −1.31021 | ||||||||
\(963\) | 7.59930e12 | 0.284745 | ||||||||
\(964\) | 4.54431e13 | 1.69481 | ||||||||
\(965\) | 4.88837e13i | 1.81464i | ||||||||
\(966\) | 4.32032e11 | 0.0159632 | ||||||||
\(967\) | − | 4.94429e13i | − | 1.81838i | −0.416380 | − | 0.909191i | \(-0.636701\pi\) | ||
0.416380 | − | 0.909191i | \(-0.363299\pi\) | |||||||
\(968\) | 7.93471e12i | 0.290464i | ||||||||
\(969\) | 5.34406e12i | 0.194722i | ||||||||
\(970\) | −7.07750e13 | −2.56689 | ||||||||
\(971\) | 1.82402e13i | 0.658482i | 0.944246 | + | 0.329241i | \(0.106793\pi\) | ||||
−0.944246 | + | 0.329241i | \(0.893207\pi\) | |||||||
\(972\) | − | 4.08815e13i | − | 1.46902i | ||||||
\(973\) | −1.08073e13 | −0.386552 | ||||||||
\(974\) | 3.45400e13i | 1.22972i | ||||||||
\(975\) | − | 3.60592e13i | − | 1.27789i | ||||||
\(976\) | − | 2.03315e13i | − | 0.717208i | ||||||
\(977\) | −3.89337e13 | −1.36710 | −0.683549 | − | 0.729904i | \(-0.739565\pi\) | ||||
−0.683549 | + | 0.729904i | \(0.739565\pi\) | |||||||
\(978\) | − | 3.91017e13i | − | 1.36669i | ||||||
\(979\) | −4.77595e13 | −1.66164 | ||||||||
\(980\) | −4.30831e13 | −1.49207 | ||||||||
\(981\) | −3.76992e11 | −0.0129964 | ||||||||
\(982\) | −6.46623e13 | −2.21896 | ||||||||
\(983\) | 1.37206e13i | 0.468686i | 0.972154 | + | 0.234343i | \(0.0752939\pi\) | ||||
−0.972154 | + | 0.234343i | \(0.924706\pi\) | |||||||
\(984\) | − | 2.94678e13i | − | 1.00200i | ||||||
\(985\) | −3.07480e13 | −1.04077 | ||||||||
\(986\) | 1.15520e13 | + | 6.28540e12i | 0.389235 | + | 0.211781i | ||||
\(987\) | −2.34966e13 | −0.788093 | ||||||||
\(988\) | − | 3.42579e13i | − | 1.14381i | ||||||
\(989\) | − | 3.91921e11i | − | 0.0130261i | ||||||
\(990\) | 4.79200e13 | 1.58547 | ||||||||
\(991\) | 3.31744e13 | 1.09263 | 0.546313 | − | 0.837581i | \(-0.316031\pi\) | ||||
0.546313 | + | 0.837581i | \(0.316031\pi\) | |||||||
\(992\) | −2.69725e12 | −0.0884339 | ||||||||
\(993\) | −1.69049e13 | −0.551749 | ||||||||
\(994\) | − | 3.02777e13i | − | 0.983748i | ||||||
\(995\) | −8.38561e12 | −0.271226 | ||||||||
\(996\) | 4.56650e12i | 0.147034i | ||||||||
\(997\) | − | 9.55727e12i | − | 0.306341i | −0.988200 | − | 0.153171i | \(-0.951052\pi\) | ||
0.988200 | − | 0.153171i | \(-0.0489484\pi\) | |||||||
\(998\) | 2.56242e13i | 0.817640i | ||||||||
\(999\) | 4.13991e13 | 1.31506 |
(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 | 29.10.b.a.28.20 | yes | 22 | |
29.28 | even | 2 | inner | 29.10.b.a.28.3 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.10.b.a.28.3 | ✓ | 22 | 29.28 | even | 2 | inner | |
29.10.b.a.28.20 | yes | 22 | 1.1 | even | 1 | trivial |