Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,10,Mod(1,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(19.0563259381\) |
Analytic rank: | \(1\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 6 x^{12} - 4637 x^{11} + 28852 x^{10} + 8006690 x^{9} - 52024972 x^{8} - 6415977160 x^{7} + \cdots - 99\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-36.3196\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 37.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 34.3196 | 1.51673 | 0.758364 | − | 0.651832i | \(-0.225999\pi\) | ||||
0.758364 | + | 0.651832i | \(0.225999\pi\) | |||||||
\(3\) | −129.318 | −0.921748 | −0.460874 | − | 0.887466i | \(-0.652464\pi\) | ||||
−0.460874 | + | 0.887466i | \(0.652464\pi\) | |||||||
\(4\) | 665.837 | 1.30046 | ||||||||
\(5\) | −1076.40 | −0.770209 | −0.385104 | − | 0.922873i | \(-0.625835\pi\) | ||||
−0.385104 | + | 0.922873i | \(0.625835\pi\) | |||||||
\(6\) | −4438.14 | −1.39804 | ||||||||
\(7\) | 9336.44 | 1.46974 | 0.734869 | − | 0.678209i | \(-0.237243\pi\) | ||||
0.734869 | + | 0.678209i | \(0.237243\pi\) | |||||||
\(8\) | 5279.62 | 0.455720 | ||||||||
\(9\) | −2959.93 | −0.150380 | ||||||||
\(10\) | −36941.6 | −1.16820 | ||||||||
\(11\) | −58047.3 | −1.19540 | −0.597702 | − | 0.801718i | \(-0.703919\pi\) | ||||
−0.597702 | + | 0.801718i | \(0.703919\pi\) | |||||||
\(12\) | −86104.5 | −1.19870 | ||||||||
\(13\) | −108005. | −1.04882 | −0.524409 | − | 0.851467i | \(-0.675714\pi\) | ||||
−0.524409 | + | 0.851467i | \(0.675714\pi\) | |||||||
\(14\) | 320423. | 2.22919 | ||||||||
\(15\) | 139197. | 0.709938 | ||||||||
\(16\) | −159714. | −0.609260 | ||||||||
\(17\) | −668634. | −1.94164 | −0.970819 | − | 0.239814i | \(-0.922914\pi\) | ||||
−0.970819 | + | 0.239814i | \(0.922914\pi\) | |||||||
\(18\) | −101584. | −0.228086 | ||||||||
\(19\) | −243278. | −0.428265 | −0.214132 | − | 0.976805i | \(-0.568692\pi\) | ||||
−0.214132 | + | 0.976805i | \(0.568692\pi\) | |||||||
\(20\) | −716706. | −1.00163 | ||||||||
\(21\) | −1.20737e6 | −1.35473 | ||||||||
\(22\) | −1.99216e6 | −1.81310 | ||||||||
\(23\) | 2.32530e6 | 1.73262 | 0.866311 | − | 0.499505i | \(-0.166485\pi\) | ||||
0.866311 | + | 0.499505i | \(0.166485\pi\) | |||||||
\(24\) | −682749. | −0.420059 | ||||||||
\(25\) | −794490. | −0.406779 | ||||||||
\(26\) | −3.70670e6 | −1.59077 | ||||||||
\(27\) | 2.92813e6 | 1.06036 | ||||||||
\(28\) | 6.21655e6 | 1.91134 | ||||||||
\(29\) | 2.01991e6 | 0.530323 | 0.265161 | − | 0.964204i | \(-0.414575\pi\) | ||||
0.265161 | + | 0.964204i | \(0.414575\pi\) | |||||||
\(30\) | 4.77721e6 | 1.07678 | ||||||||
\(31\) | 8.33762e6 | 1.62149 | 0.810745 | − | 0.585399i | \(-0.199062\pi\) | ||||
0.810745 | + | 0.585399i | \(0.199062\pi\) | |||||||
\(32\) | −8.18448e6 | −1.37980 | ||||||||
\(33\) | 7.50654e6 | 1.10186 | ||||||||
\(34\) | −2.29473e7 | −2.94494 | ||||||||
\(35\) | −1.00497e7 | −1.13201 | ||||||||
\(36\) | −1.97083e6 | −0.195564 | ||||||||
\(37\) | −1.87416e6 | −0.164399 | ||||||||
\(38\) | −8.34923e6 | −0.649561 | ||||||||
\(39\) | 1.39670e7 | 0.966746 | ||||||||
\(40\) | −5.68298e6 | −0.351000 | ||||||||
\(41\) | −7.34580e6 | −0.405987 | −0.202993 | − | 0.979180i | \(-0.565067\pi\) | ||||
−0.202993 | + | 0.979180i | \(0.565067\pi\) | |||||||
\(42\) | −4.14364e7 | −2.05476 | ||||||||
\(43\) | −8.69984e6 | −0.388064 | −0.194032 | − | 0.980995i | \(-0.562157\pi\) | ||||
−0.194032 | + | 0.980995i | \(0.562157\pi\) | |||||||
\(44\) | −3.86500e7 | −1.55458 | ||||||||
\(45\) | 3.18607e6 | 0.115824 | ||||||||
\(46\) | 7.98035e7 | 2.62792 | ||||||||
\(47\) | −4.36777e7 | −1.30563 | −0.652814 | − | 0.757518i | \(-0.726412\pi\) | ||||
−0.652814 | + | 0.757518i | \(0.726412\pi\) | |||||||
\(48\) | 2.06538e7 | 0.561584 | ||||||||
\(49\) | 4.68155e7 | 1.16013 | ||||||||
\(50\) | −2.72666e7 | −0.616972 | ||||||||
\(51\) | 8.64662e7 | 1.78970 | ||||||||
\(52\) | −7.19139e7 | −1.36395 | ||||||||
\(53\) | −2.04504e7 | −0.356009 | −0.178004 | − | 0.984030i | \(-0.556964\pi\) | ||||
−0.178004 | + | 0.984030i | \(0.556964\pi\) | |||||||
\(54\) | 1.00492e8 | 1.60828 | ||||||||
\(55\) | 6.24820e7 | 0.920710 | ||||||||
\(56\) | 4.92929e7 | 0.669789 | ||||||||
\(57\) | 3.14602e7 | 0.394752 | ||||||||
\(58\) | 6.93225e7 | 0.804355 | ||||||||
\(59\) | −1.49555e7 | −0.160682 | −0.0803408 | − | 0.996767i | \(-0.525601\pi\) | ||||
−0.0803408 | + | 0.996767i | \(0.525601\pi\) | |||||||
\(60\) | 9.26828e7 | 0.923248 | ||||||||
\(61\) | −1.03469e8 | −0.956807 | −0.478403 | − | 0.878140i | \(-0.658784\pi\) | ||||
−0.478403 | + | 0.878140i | \(0.658784\pi\) | |||||||
\(62\) | 2.86144e8 | 2.45936 | ||||||||
\(63\) | −2.76352e7 | −0.221020 | ||||||||
\(64\) | −1.99115e8 | −1.48352 | ||||||||
\(65\) | 1.16257e8 | 0.807808 | ||||||||
\(66\) | 2.57622e8 | 1.67122 | ||||||||
\(67\) | 1.75352e8 | 1.06310 | 0.531549 | − | 0.847028i | \(-0.321610\pi\) | ||||
0.531549 | + | 0.847028i | \(0.321610\pi\) | |||||||
\(68\) | −4.45201e8 | −2.52503 | ||||||||
\(69\) | −3.00703e8 | −1.59704 | ||||||||
\(70\) | −3.44903e8 | −1.71694 | ||||||||
\(71\) | 6.24089e7 | 0.291464 | 0.145732 | − | 0.989324i | \(-0.453446\pi\) | ||||
0.145732 | + | 0.989324i | \(0.453446\pi\) | |||||||
\(72\) | −1.56273e7 | −0.0685313 | ||||||||
\(73\) | 4.17335e8 | 1.72001 | 0.860007 | − | 0.510282i | \(-0.170459\pi\) | ||||
0.860007 | + | 0.510282i | \(0.170459\pi\) | |||||||
\(74\) | −6.43205e7 | −0.249348 | ||||||||
\(75\) | 1.02742e8 | 0.374947 | ||||||||
\(76\) | −1.61984e8 | −0.556943 | ||||||||
\(77\) | −5.41955e8 | −1.75693 | ||||||||
\(78\) | 4.79342e8 | 1.46629 | ||||||||
\(79\) | 2.96492e8 | 0.856427 | 0.428214 | − | 0.903677i | \(-0.359143\pi\) | ||||
0.428214 | + | 0.903677i | \(0.359143\pi\) | |||||||
\(80\) | 1.71916e8 | 0.469257 | ||||||||
\(81\) | −3.20399e8 | −0.827006 | ||||||||
\(82\) | −2.52105e8 | −0.615771 | ||||||||
\(83\) | −8.94658e7 | −0.206921 | −0.103461 | − | 0.994634i | \(-0.532992\pi\) | ||||
−0.103461 | + | 0.994634i | \(0.532992\pi\) | |||||||
\(84\) | −8.03910e8 | −1.76177 | ||||||||
\(85\) | 7.19717e8 | 1.49547 | ||||||||
\(86\) | −2.98575e8 | −0.588587 | ||||||||
\(87\) | −2.61210e8 | −0.488824 | ||||||||
\(88\) | −3.06468e8 | −0.544770 | ||||||||
\(89\) | −9.24749e8 | −1.56232 | −0.781158 | − | 0.624333i | \(-0.785371\pi\) | ||||
−0.781158 | + | 0.624333i | \(0.785371\pi\) | |||||||
\(90\) | 1.09345e8 | 0.175674 | ||||||||
\(91\) | −1.00838e9 | −1.54149 | ||||||||
\(92\) | 1.54827e9 | 2.25321 | ||||||||
\(93\) | −1.07820e9 | −1.49461 | ||||||||
\(94\) | −1.49900e9 | −1.98028 | ||||||||
\(95\) | 2.61865e8 | 0.329853 | ||||||||
\(96\) | 1.05840e9 | 1.27183 | ||||||||
\(97\) | −6.81238e8 | −0.781315 | −0.390658 | − | 0.920536i | \(-0.627752\pi\) | ||||
−0.390658 | + | 0.920536i | \(0.627752\pi\) | |||||||
\(98\) | 1.60669e9 | 1.75960 | ||||||||
\(99\) | 1.71816e8 | 0.179765 | ||||||||
\(100\) | −5.29000e8 | −0.529000 | ||||||||
\(101\) | −8.72358e8 | −0.834159 | −0.417079 | − | 0.908870i | \(-0.636946\pi\) | ||||
−0.417079 | + | 0.908870i | \(0.636946\pi\) | |||||||
\(102\) | 2.96749e9 | 2.71449 | ||||||||
\(103\) | −8.48087e7 | −0.0742460 | −0.0371230 | − | 0.999311i | \(-0.511819\pi\) | ||||
−0.0371230 | + | 0.999311i | \(0.511819\pi\) | |||||||
\(104\) | −5.70227e8 | −0.477967 | ||||||||
\(105\) | 1.29961e9 | 1.04342 | ||||||||
\(106\) | −7.01850e8 | −0.539968 | ||||||||
\(107\) | 1.53011e9 | 1.12849 | 0.564243 | − | 0.825609i | \(-0.309168\pi\) | ||||
0.564243 | + | 0.825609i | \(0.309168\pi\) | |||||||
\(108\) | 1.94966e9 | 1.37896 | ||||||||
\(109\) | −9.84674e8 | −0.668149 | −0.334074 | − | 0.942547i | \(-0.608424\pi\) | ||||
−0.334074 | + | 0.942547i | \(0.608424\pi\) | |||||||
\(110\) | 2.14436e9 | 1.39647 | ||||||||
\(111\) | 2.42362e8 | 0.151534 | ||||||||
\(112\) | −1.49116e9 | −0.895452 | ||||||||
\(113\) | 4.23223e8 | 0.244183 | 0.122092 | − | 0.992519i | \(-0.461040\pi\) | ||||
0.122092 | + | 0.992519i | \(0.461040\pi\) | |||||||
\(114\) | 1.07970e9 | 0.598732 | ||||||||
\(115\) | −2.50295e9 | −1.33448 | ||||||||
\(116\) | 1.34493e9 | 0.689665 | ||||||||
\(117\) | 3.19688e8 | 0.157721 | ||||||||
\(118\) | −5.13267e8 | −0.243710 | ||||||||
\(119\) | −6.24266e9 | −2.85370 | ||||||||
\(120\) | 7.34910e8 | 0.323533 | ||||||||
\(121\) | 1.01154e9 | 0.428991 | ||||||||
\(122\) | −3.55100e9 | −1.45121 | ||||||||
\(123\) | 9.49942e8 | 0.374217 | ||||||||
\(124\) | 5.55149e9 | 2.10869 | ||||||||
\(125\) | 2.95753e9 | 1.08351 | ||||||||
\(126\) | −9.48431e8 | −0.335227 | ||||||||
\(127\) | −2.35378e9 | −0.802876 | −0.401438 | − | 0.915886i | \(-0.631489\pi\) | ||||
−0.401438 | + | 0.915886i | \(0.631489\pi\) | |||||||
\(128\) | −2.64310e9 | −0.870299 | ||||||||
\(129\) | 1.12504e9 | 0.357697 | ||||||||
\(130\) | 3.98989e9 | 1.22522 | ||||||||
\(131\) | −3.81437e8 | −0.113162 | −0.0565812 | − | 0.998398i | \(-0.518020\pi\) | ||||
−0.0565812 | + | 0.998398i | \(0.518020\pi\) | |||||||
\(132\) | 4.99813e9 | 1.43293 | ||||||||
\(133\) | −2.27136e9 | −0.629438 | ||||||||
\(134\) | 6.01800e9 | 1.61243 | ||||||||
\(135\) | −3.15184e9 | −0.816699 | ||||||||
\(136\) | −3.53014e9 | −0.884843 | ||||||||
\(137\) | 5.95543e9 | 1.44434 | 0.722172 | − | 0.691714i | \(-0.243144\pi\) | ||||
0.722172 | + | 0.691714i | \(0.243144\pi\) | |||||||
\(138\) | −1.03200e10 | −2.42228 | ||||||||
\(139\) | −5.54132e9 | −1.25906 | −0.629530 | − | 0.776976i | \(-0.716753\pi\) | ||||
−0.629530 | + | 0.776976i | \(0.716753\pi\) | |||||||
\(140\) | −6.69149e9 | −1.47213 | ||||||||
\(141\) | 5.64830e9 | 1.20346 | ||||||||
\(142\) | 2.14185e9 | 0.442071 | ||||||||
\(143\) | 6.26941e9 | 1.25376 | ||||||||
\(144\) | 4.72742e8 | 0.0916205 | ||||||||
\(145\) | −2.17423e9 | −0.408459 | ||||||||
\(146\) | 1.43228e10 | 2.60879 | ||||||||
\(147\) | −6.05408e9 | −1.06935 | ||||||||
\(148\) | −1.24789e9 | −0.213795 | ||||||||
\(149\) | −1.13376e10 | −1.88445 | −0.942223 | − | 0.334986i | \(-0.891268\pi\) | ||||
−0.942223 | + | 0.334986i | \(0.891268\pi\) | |||||||
\(150\) | 3.52605e9 | 0.568693 | ||||||||
\(151\) | 2.20689e9 | 0.345450 | 0.172725 | − | 0.984970i | \(-0.444743\pi\) | ||||
0.172725 | + | 0.984970i | \(0.444743\pi\) | |||||||
\(152\) | −1.28442e9 | −0.195169 | ||||||||
\(153\) | 1.97911e9 | 0.291984 | ||||||||
\(154\) | −1.85997e10 | −2.66479 | ||||||||
\(155\) | −8.97461e9 | −1.24889 | ||||||||
\(156\) | 9.29974e9 | 1.25722 | ||||||||
\(157\) | 6.67257e8 | 0.0876485 | 0.0438243 | − | 0.999039i | \(-0.486046\pi\) | ||||
0.0438243 | + | 0.999039i | \(0.486046\pi\) | |||||||
\(158\) | 1.01755e10 | 1.29897 | ||||||||
\(159\) | 2.64460e9 | 0.328150 | ||||||||
\(160\) | 8.80977e9 | 1.06273 | ||||||||
\(161\) | 2.17100e10 | 2.54650 | ||||||||
\(162\) | −1.09960e10 | −1.25434 | ||||||||
\(163\) | 4.54691e9 | 0.504513 | 0.252256 | − | 0.967660i | \(-0.418827\pi\) | ||||
0.252256 | + | 0.967660i | \(0.418827\pi\) | |||||||
\(164\) | −4.89110e9 | −0.527970 | ||||||||
\(165\) | −8.08003e9 | −0.848663 | ||||||||
\(166\) | −3.07043e9 | −0.313843 | ||||||||
\(167\) | −1.23916e10 | −1.23283 | −0.616413 | − | 0.787423i | \(-0.711415\pi\) | ||||
−0.616413 | + | 0.787423i | \(0.711415\pi\) | |||||||
\(168\) | −6.37445e9 | −0.617377 | ||||||||
\(169\) | 1.06064e9 | 0.100018 | ||||||||
\(170\) | 2.47004e10 | 2.26822 | ||||||||
\(171\) | 7.20088e8 | 0.0644026 | ||||||||
\(172\) | −5.79267e9 | −0.504662 | ||||||||
\(173\) | −1.67206e10 | −1.41920 | −0.709602 | − | 0.704603i | \(-0.751125\pi\) | ||||
−0.709602 | + | 0.704603i | \(0.751125\pi\) | |||||||
\(174\) | −8.96462e9 | −0.741413 | ||||||||
\(175\) | −7.41770e9 | −0.597858 | ||||||||
\(176\) | 9.27095e9 | 0.728311 | ||||||||
\(177\) | 1.93401e9 | 0.148108 | ||||||||
\(178\) | −3.17371e10 | −2.36961 | ||||||||
\(179\) | −9.43404e9 | −0.686846 | −0.343423 | − | 0.939181i | \(-0.611586\pi\) | ||||
−0.343423 | + | 0.939181i | \(0.611586\pi\) | |||||||
\(180\) | 2.12140e9 | 0.150625 | ||||||||
\(181\) | 9.43961e9 | 0.653733 | 0.326867 | − | 0.945070i | \(-0.394007\pi\) | ||||
0.326867 | + | 0.945070i | \(0.394007\pi\) | |||||||
\(182\) | −3.46074e10 | −2.33802 | ||||||||
\(183\) | 1.33803e10 | 0.881935 | ||||||||
\(184\) | 1.22767e10 | 0.789591 | ||||||||
\(185\) | 2.01735e9 | 0.126622 | ||||||||
\(186\) | −3.70035e10 | −2.26691 | ||||||||
\(187\) | 3.88124e10 | 2.32104 | ||||||||
\(188\) | −2.90822e10 | −1.69792 | ||||||||
\(189\) | 2.73383e10 | 1.55845 | ||||||||
\(190\) | 8.98710e9 | 0.500298 | ||||||||
\(191\) | 1.33064e10 | 0.723453 | 0.361726 | − | 0.932284i | \(-0.382187\pi\) | ||||
0.361726 | + | 0.932284i | \(0.382187\pi\) | |||||||
\(192\) | 2.57491e10 | 1.36743 | ||||||||
\(193\) | 1.05626e10 | 0.547976 | 0.273988 | − | 0.961733i | \(-0.411657\pi\) | ||||
0.273988 | + | 0.961733i | \(0.411657\pi\) | |||||||
\(194\) | −2.33798e10 | −1.18504 | ||||||||
\(195\) | −1.50341e10 | −0.744596 | ||||||||
\(196\) | 3.11715e10 | 1.50871 | ||||||||
\(197\) | −3.02661e10 | −1.43172 | −0.715861 | − | 0.698243i | \(-0.753966\pi\) | ||||
−0.715861 | + | 0.698243i | \(0.753966\pi\) | |||||||
\(198\) | 5.89666e9 | 0.272655 | ||||||||
\(199\) | 1.30242e10 | 0.588726 | 0.294363 | − | 0.955694i | \(-0.404892\pi\) | ||||
0.294363 | + | 0.955694i | \(0.404892\pi\) | |||||||
\(200\) | −4.19461e9 | −0.185377 | ||||||||
\(201\) | −2.26761e10 | −0.979909 | ||||||||
\(202\) | −2.99390e10 | −1.26519 | ||||||||
\(203\) | 1.88587e10 | 0.779436 | ||||||||
\(204\) | 5.75724e10 | 2.32744 | ||||||||
\(205\) | 7.90701e9 | 0.312694 | ||||||||
\(206\) | −2.91060e9 | −0.112611 | ||||||||
\(207\) | −6.88273e9 | −0.260552 | ||||||||
\(208\) | 1.72499e10 | 0.639002 | ||||||||
\(209\) | 1.41217e10 | 0.511950 | ||||||||
\(210\) | 4.46021e10 | 1.58259 | ||||||||
\(211\) | −1.86716e10 | −0.648502 | −0.324251 | − | 0.945971i | \(-0.605112\pi\) | ||||
−0.324251 | + | 0.945971i | \(0.605112\pi\) | |||||||
\(212\) | −1.36166e10 | −0.462976 | ||||||||
\(213\) | −8.07058e9 | −0.268656 | ||||||||
\(214\) | 5.25129e10 | 1.71161 | ||||||||
\(215\) | 9.36450e9 | 0.298890 | ||||||||
\(216\) | 1.54594e10 | 0.483228 | ||||||||
\(217\) | 7.78437e10 | 2.38317 | ||||||||
\(218\) | −3.37936e10 | −1.01340 | ||||||||
\(219\) | −5.39688e10 | −1.58542 | ||||||||
\(220\) | 4.16028e10 | 1.19735 | ||||||||
\(221\) | 7.22160e10 | 2.03642 | ||||||||
\(222\) | 8.31778e9 | 0.229837 | ||||||||
\(223\) | −1.12955e10 | −0.305868 | −0.152934 | − | 0.988236i | \(-0.548872\pi\) | ||||
−0.152934 | + | 0.988236i | \(0.548872\pi\) | |||||||
\(224\) | −7.64139e10 | −2.02795 | ||||||||
\(225\) | 2.35164e9 | 0.0611714 | ||||||||
\(226\) | 1.45249e10 | 0.370360 | ||||||||
\(227\) | −2.45410e10 | −0.613445 | −0.306723 | − | 0.951799i | \(-0.599232\pi\) | ||||
−0.306723 | + | 0.951799i | \(0.599232\pi\) | |||||||
\(228\) | 2.09474e10 | 0.513361 | ||||||||
\(229\) | 3.55035e10 | 0.853123 | 0.426561 | − | 0.904459i | \(-0.359725\pi\) | ||||
0.426561 | + | 0.904459i | \(0.359725\pi\) | |||||||
\(230\) | −8.59004e10 | −2.02404 | ||||||||
\(231\) | 7.00844e10 | 1.61945 | ||||||||
\(232\) | 1.06644e10 | 0.241679 | ||||||||
\(233\) | 1.97421e10 | 0.438825 | 0.219413 | − | 0.975632i | \(-0.429586\pi\) | ||||
0.219413 | + | 0.975632i | \(0.429586\pi\) | |||||||
\(234\) | 1.09716e10 | 0.239220 | ||||||||
\(235\) | 4.70147e10 | 1.00561 | ||||||||
\(236\) | −9.95791e9 | −0.208961 | ||||||||
\(237\) | −3.83416e10 | −0.789410 | ||||||||
\(238\) | −2.14246e11 | −4.32829 | ||||||||
\(239\) | −2.47767e10 | −0.491194 | −0.245597 | − | 0.969372i | \(-0.578984\pi\) | ||||
−0.245597 | + | 0.969372i | \(0.578984\pi\) | |||||||
\(240\) | −2.22317e10 | −0.432537 | ||||||||
\(241\) | −1.01590e11 | −1.93988 | −0.969940 | − | 0.243343i | \(-0.921756\pi\) | ||||
−0.969940 | + | 0.243343i | \(0.921756\pi\) | |||||||
\(242\) | 3.47156e10 | 0.650662 | ||||||||
\(243\) | −1.62012e10 | −0.298070 | ||||||||
\(244\) | −6.88932e10 | −1.24429 | ||||||||
\(245\) | −5.03922e10 | −0.893544 | ||||||||
\(246\) | 3.26017e10 | 0.567586 | ||||||||
\(247\) | 2.62754e10 | 0.449172 | ||||||||
\(248\) | 4.40195e10 | 0.738946 | ||||||||
\(249\) | 1.15695e10 | 0.190729 | ||||||||
\(250\) | 1.01501e11 | 1.64339 | ||||||||
\(251\) | −1.06726e11 | −1.69722 | −0.848612 | − | 0.529016i | \(-0.822561\pi\) | ||||
−0.848612 | + | 0.529016i | \(0.822561\pi\) | |||||||
\(252\) | −1.84006e10 | −0.287428 | ||||||||
\(253\) | −1.34977e11 | −2.07118 | ||||||||
\(254\) | −8.07807e10 | −1.21774 | ||||||||
\(255\) | −9.30722e10 | −1.37844 | ||||||||
\(256\) | 1.12368e10 | 0.163516 | ||||||||
\(257\) | 1.58787e10 | 0.227047 | 0.113524 | − | 0.993535i | \(-0.463786\pi\) | ||||
0.113524 | + | 0.993535i | \(0.463786\pi\) | |||||||
\(258\) | 3.86111e10 | 0.542529 | ||||||||
\(259\) | −1.74980e10 | −0.241624 | ||||||||
\(260\) | 7.74081e10 | 1.05052 | ||||||||
\(261\) | −5.97879e9 | −0.0797500 | ||||||||
\(262\) | −1.30908e10 | −0.171637 | ||||||||
\(263\) | −6.87094e10 | −0.885554 | −0.442777 | − | 0.896632i | \(-0.646007\pi\) | ||||
−0.442777 | + | 0.896632i | \(0.646007\pi\) | |||||||
\(264\) | 3.96317e10 | 0.502140 | ||||||||
\(265\) | 2.20128e10 | 0.274201 | ||||||||
\(266\) | −7.79521e10 | −0.954685 | ||||||||
\(267\) | 1.19586e11 | 1.44006 | ||||||||
\(268\) | 1.16756e11 | 1.38252 | ||||||||
\(269\) | −2.57655e10 | −0.300022 | −0.150011 | − | 0.988684i | \(-0.547931\pi\) | ||||
−0.150011 | + | 0.988684i | \(0.547931\pi\) | |||||||
\(270\) | −1.08170e11 | −1.23871 | ||||||||
\(271\) | 9.41053e10 | 1.05987 | 0.529934 | − | 0.848039i | \(-0.322217\pi\) | ||||
0.529934 | + | 0.848039i | \(0.322217\pi\) | |||||||
\(272\) | 1.06790e11 | 1.18296 | ||||||||
\(273\) | 1.30402e11 | 1.42086 | ||||||||
\(274\) | 2.04388e11 | 2.19068 | ||||||||
\(275\) | 4.61179e10 | 0.486265 | ||||||||
\(276\) | −2.00219e11 | −2.07689 | ||||||||
\(277\) | −2.17075e10 | −0.221540 | −0.110770 | − | 0.993846i | \(-0.535332\pi\) | ||||
−0.110770 | + | 0.993846i | \(0.535332\pi\) | |||||||
\(278\) | −1.90176e11 | −1.90965 | ||||||||
\(279\) | −2.46788e10 | −0.243840 | ||||||||
\(280\) | −5.30589e10 | −0.515878 | ||||||||
\(281\) | 6.38970e10 | 0.611367 | 0.305684 | − | 0.952133i | \(-0.401115\pi\) | ||||
0.305684 | + | 0.952133i | \(0.401115\pi\) | |||||||
\(282\) | 1.93848e11 | 1.82532 | ||||||||
\(283\) | 9.07777e10 | 0.841280 | 0.420640 | − | 0.907228i | \(-0.361806\pi\) | ||||
0.420640 | + | 0.907228i | \(0.361806\pi\) | |||||||
\(284\) | 4.15542e10 | 0.379037 | ||||||||
\(285\) | −3.38638e10 | −0.304042 | ||||||||
\(286\) | 2.15164e11 | 1.90161 | ||||||||
\(287\) | −6.85836e10 | −0.596694 | ||||||||
\(288\) | 2.42255e10 | 0.207495 | ||||||||
\(289\) | 3.28483e11 | 2.76996 | ||||||||
\(290\) | −7.46186e10 | −0.619521 | ||||||||
\(291\) | 8.80962e10 | 0.720176 | ||||||||
\(292\) | 2.77877e11 | 2.23681 | ||||||||
\(293\) | −7.63723e10 | −0.605385 | −0.302692 | − | 0.953088i | \(-0.597885\pi\) | ||||
−0.302692 | + | 0.953088i | \(0.597885\pi\) | |||||||
\(294\) | −2.07774e11 | −1.62191 | ||||||||
\(295\) | 1.60981e10 | 0.123758 | ||||||||
\(296\) | −9.89487e9 | −0.0749199 | ||||||||
\(297\) | −1.69970e11 | −1.26756 | ||||||||
\(298\) | −3.89103e11 | −2.85819 | ||||||||
\(299\) | −2.51145e11 | −1.81720 | ||||||||
\(300\) | 6.84091e10 | 0.487605 | ||||||||
\(301\) | −8.12255e10 | −0.570352 | ||||||||
\(302\) | 7.57398e10 | 0.523953 | ||||||||
\(303\) | 1.12811e11 | 0.768884 | ||||||||
\(304\) | 3.88549e10 | 0.260924 | ||||||||
\(305\) | 1.11373e11 | 0.736941 | ||||||||
\(306\) | 6.79224e10 | 0.442860 | ||||||||
\(307\) | −3.03562e11 | −1.95041 | −0.975203 | − | 0.221312i | \(-0.928966\pi\) | ||||
−0.975203 | + | 0.221312i | \(0.928966\pi\) | |||||||
\(308\) | −3.60854e11 | −2.28482 | ||||||||
\(309\) | 1.09673e10 | 0.0684361 | ||||||||
\(310\) | −3.08005e11 | −1.89422 | ||||||||
\(311\) | 2.97890e11 | 1.80565 | 0.902827 | − | 0.430004i | \(-0.141488\pi\) | ||||
0.902827 | + | 0.430004i | \(0.141488\pi\) | |||||||
\(312\) | 7.37405e10 | 0.440565 | ||||||||
\(313\) | −2.16129e10 | −0.127281 | −0.0636406 | − | 0.997973i | \(-0.520271\pi\) | ||||
−0.0636406 | + | 0.997973i | \(0.520271\pi\) | |||||||
\(314\) | 2.29000e10 | 0.132939 | ||||||||
\(315\) | 2.97466e10 | 0.170231 | ||||||||
\(316\) | 1.97415e11 | 1.11375 | ||||||||
\(317\) | 2.26531e11 | 1.25997 | 0.629986 | − | 0.776607i | \(-0.283061\pi\) | ||||
0.629986 | + | 0.776607i | \(0.283061\pi\) | |||||||
\(318\) | 9.07617e10 | 0.497715 | ||||||||
\(319\) | −1.17250e11 | −0.633950 | ||||||||
\(320\) | 2.14327e11 | 1.14262 | ||||||||
\(321\) | −1.97871e11 | −1.04018 | ||||||||
\(322\) | 7.45080e11 | 3.86235 | ||||||||
\(323\) | 1.62664e11 | 0.831535 | ||||||||
\(324\) | −2.13333e11 | −1.07549 | ||||||||
\(325\) | 8.58091e10 | 0.426636 | ||||||||
\(326\) | 1.56048e11 | 0.765208 | ||||||||
\(327\) | 1.27336e11 | 0.615865 | ||||||||
\(328\) | −3.87831e10 | −0.185016 | ||||||||
\(329\) | −4.07795e11 | −1.91893 | ||||||||
\(330\) | −2.77304e11 | −1.28719 | ||||||||
\(331\) | 1.24181e11 | 0.568631 | 0.284316 | − | 0.958731i | \(-0.408234\pi\) | ||||
0.284316 | + | 0.958731i | \(0.408234\pi\) | |||||||
\(332\) | −5.95696e10 | −0.269094 | ||||||||
\(333\) | 5.54739e9 | 0.0247223 | ||||||||
\(334\) | −4.25274e11 | −1.86986 | ||||||||
\(335\) | −1.88748e11 | −0.818807 | ||||||||
\(336\) | 1.92833e11 | 0.825382 | ||||||||
\(337\) | 1.42832e11 | 0.603240 | 0.301620 | − | 0.953428i | \(-0.402473\pi\) | ||||
0.301620 | + | 0.953428i | \(0.402473\pi\) | |||||||
\(338\) | 3.64007e10 | 0.151700 | ||||||||
\(339\) | −5.47302e10 | −0.225076 | ||||||||
\(340\) | 4.79214e11 | 1.94480 | ||||||||
\(341\) | −4.83976e11 | −1.93834 | ||||||||
\(342\) | 2.47132e10 | 0.0976811 | ||||||||
\(343\) | 6.03313e10 | 0.235353 | ||||||||
\(344\) | −4.59319e10 | −0.176848 | ||||||||
\(345\) | 3.23676e11 | 1.23006 | ||||||||
\(346\) | −5.73845e11 | −2.15255 | ||||||||
\(347\) | 3.42139e11 | 1.26683 | 0.633417 | − | 0.773810i | \(-0.281652\pi\) | ||||
0.633417 | + | 0.773810i | \(0.281652\pi\) | |||||||
\(348\) | −1.73923e11 | −0.635698 | ||||||||
\(349\) | −2.29495e10 | −0.0828055 | −0.0414028 | − | 0.999143i | \(-0.513183\pi\) | ||||
−0.0414028 | + | 0.999143i | \(0.513183\pi\) | |||||||
\(350\) | −2.54573e11 | −0.906788 | ||||||||
\(351\) | −3.16254e11 | −1.11212 | ||||||||
\(352\) | 4.75087e11 | 1.64942 | ||||||||
\(353\) | −7.47849e9 | −0.0256347 | −0.0128173 | − | 0.999918i | \(-0.504080\pi\) | ||||
−0.0128173 | + | 0.999918i | \(0.504080\pi\) | |||||||
\(354\) | 6.63744e10 | 0.224640 | ||||||||
\(355\) | −6.71769e10 | −0.224488 | ||||||||
\(356\) | −6.15732e11 | −2.03173 | ||||||||
\(357\) | 8.07287e11 | 2.63039 | ||||||||
\(358\) | −3.23773e11 | −1.04176 | ||||||||
\(359\) | 2.61976e10 | 0.0832409 | 0.0416204 | − | 0.999133i | \(-0.486748\pi\) | ||||
0.0416204 | + | 0.999133i | \(0.486748\pi\) | |||||||
\(360\) | 1.68213e10 | 0.0527834 | ||||||||
\(361\) | −2.63503e11 | −0.816589 | ||||||||
\(362\) | 3.23964e11 | 0.991535 | ||||||||
\(363\) | −1.30810e11 | −0.395421 | ||||||||
\(364\) | −6.71420e11 | −2.00465 | ||||||||
\(365\) | −4.49219e11 | −1.32477 | ||||||||
\(366\) | 4.59207e11 | 1.33765 | ||||||||
\(367\) | −2.23555e11 | −0.643260 | −0.321630 | − | 0.946865i | \(-0.604231\pi\) | ||||
−0.321630 | + | 0.946865i | \(0.604231\pi\) | |||||||
\(368\) | −3.71382e11 | −1.05562 | ||||||||
\(369\) | 2.17431e10 | 0.0610523 | ||||||||
\(370\) | 6.92346e10 | 0.192050 | ||||||||
\(371\) | −1.90934e11 | −0.523240 | ||||||||
\(372\) | −7.17906e11 | −1.94368 | ||||||||
\(373\) | 4.30341e11 | 1.15113 | 0.575563 | − | 0.817757i | \(-0.304783\pi\) | ||||
0.575563 | + | 0.817757i | \(0.304783\pi\) | |||||||
\(374\) | 1.33203e12 | 3.52039 | ||||||||
\(375\) | −3.82461e11 | −0.998726 | ||||||||
\(376\) | −2.30602e11 | −0.595001 | ||||||||
\(377\) | −2.18161e11 | −0.556212 | ||||||||
\(378\) | 9.38241e11 | 2.36375 | ||||||||
\(379\) | 2.25490e11 | 0.561373 | 0.280687 | − | 0.959799i | \(-0.409438\pi\) | ||||
0.280687 | + | 0.959799i | \(0.409438\pi\) | |||||||
\(380\) | 1.74359e11 | 0.428962 | ||||||||
\(381\) | 3.04385e11 | 0.740050 | ||||||||
\(382\) | 4.56671e11 | 1.09728 | ||||||||
\(383\) | 4.20977e11 | 0.999687 | 0.499843 | − | 0.866116i | \(-0.333391\pi\) | ||||
0.499843 | + | 0.866116i | \(0.333391\pi\) | |||||||
\(384\) | 3.41799e11 | 0.802196 | ||||||||
\(385\) | 5.83360e11 | 1.35320 | ||||||||
\(386\) | 3.62503e11 | 0.831130 | ||||||||
\(387\) | 2.57509e10 | 0.0583571 | ||||||||
\(388\) | −4.53594e11 | −1.01607 | ||||||||
\(389\) | −6.16332e11 | −1.36471 | −0.682357 | − | 0.731019i | \(-0.739045\pi\) | ||||
−0.682357 | + | 0.731019i | \(0.739045\pi\) | |||||||
\(390\) | −5.15963e11 | −1.12935 | ||||||||
\(391\) | −1.55477e12 | −3.36412 | ||||||||
\(392\) | 2.47168e11 | 0.528696 | ||||||||
\(393\) | 4.93266e10 | 0.104307 | ||||||||
\(394\) | −1.03872e12 | −2.17153 | ||||||||
\(395\) | −3.19143e11 | −0.659628 | ||||||||
\(396\) | 1.14401e11 | 0.233778 | ||||||||
\(397\) | −2.35545e10 | −0.0475900 | −0.0237950 | − | 0.999717i | \(-0.507575\pi\) | ||||
−0.0237950 | + | 0.999717i | \(0.507575\pi\) | |||||||
\(398\) | 4.46987e11 | 0.892937 | ||||||||
\(399\) | 2.93726e11 | 0.580183 | ||||||||
\(400\) | 1.26891e11 | 0.247834 | ||||||||
\(401\) | −1.46531e11 | −0.282995 | −0.141497 | − | 0.989939i | \(-0.545192\pi\) | ||||
−0.141497 | + | 0.989939i | \(0.545192\pi\) | |||||||
\(402\) | −7.78234e11 | −1.48625 | ||||||||
\(403\) | −9.00507e11 | −1.70065 | ||||||||
\(404\) | −5.80848e11 | −1.08479 | ||||||||
\(405\) | 3.44877e11 | 0.636967 | ||||||||
\(406\) | 6.47225e11 | 1.18219 | ||||||||
\(407\) | 1.08790e11 | 0.196523 | ||||||||
\(408\) | 4.56509e11 | 0.815603 | ||||||||
\(409\) | 1.24646e11 | 0.220253 | 0.110127 | − | 0.993918i | \(-0.464874\pi\) | ||||
0.110127 | + | 0.993918i | \(0.464874\pi\) | |||||||
\(410\) | 2.71366e11 | 0.474272 | ||||||||
\(411\) | −7.70143e11 | −1.33132 | ||||||||
\(412\) | −5.64688e10 | −0.0965541 | ||||||||
\(413\) | −1.39631e11 | −0.236160 | ||||||||
\(414\) | −2.36213e11 | −0.395186 | ||||||||
\(415\) | 9.63009e10 | 0.159373 | ||||||||
\(416\) | 8.83967e11 | 1.44716 | ||||||||
\(417\) | 7.16591e11 | 1.16054 | ||||||||
\(418\) | 4.84650e11 | 0.776488 | ||||||||
\(419\) | −1.86536e11 | −0.295664 | −0.147832 | − | 0.989012i | \(-0.547230\pi\) | ||||
−0.147832 | + | 0.989012i | \(0.547230\pi\) | |||||||
\(420\) | 8.65328e11 | 1.35693 | ||||||||
\(421\) | 4.32115e11 | 0.670394 | 0.335197 | − | 0.942148i | \(-0.391197\pi\) | ||||
0.335197 | + | 0.942148i | \(0.391197\pi\) | |||||||
\(422\) | −6.40803e11 | −0.983600 | ||||||||
\(423\) | 1.29283e11 | 0.196341 | ||||||||
\(424\) | −1.07970e11 | −0.162240 | ||||||||
\(425\) | 5.31223e11 | 0.789817 | ||||||||
\(426\) | −2.76979e11 | −0.407478 | ||||||||
\(427\) | −9.66028e11 | −1.40626 | ||||||||
\(428\) | 1.01880e12 | 1.46755 | ||||||||
\(429\) | −8.10746e11 | −1.15565 | ||||||||
\(430\) | 3.21386e11 | 0.453335 | ||||||||
\(431\) | 4.77460e11 | 0.666483 | 0.333241 | − | 0.942842i | \(-0.391858\pi\) | ||||
0.333241 | + | 0.942842i | \(0.391858\pi\) | |||||||
\(432\) | −4.67663e11 | −0.646035 | ||||||||
\(433\) | 9.38153e10 | 0.128256 | 0.0641281 | − | 0.997942i | \(-0.479573\pi\) | ||||
0.0641281 | + | 0.997942i | \(0.479573\pi\) | |||||||
\(434\) | 2.67157e12 | 3.61462 | ||||||||
\(435\) | 2.81166e11 | 0.376497 | ||||||||
\(436\) | −6.55632e11 | −0.868902 | ||||||||
\(437\) | −5.65696e11 | −0.742021 | ||||||||
\(438\) | −1.85219e12 | −2.40465 | ||||||||
\(439\) | −9.23783e11 | −1.18708 | −0.593540 | − | 0.804805i | \(-0.702270\pi\) | ||||
−0.593540 | + | 0.804805i | \(0.702270\pi\) | |||||||
\(440\) | 3.29882e11 | 0.419586 | ||||||||
\(441\) | −1.38571e11 | −0.174461 | ||||||||
\(442\) | 2.47843e12 | 3.08870 | ||||||||
\(443\) | −3.26798e11 | −0.403146 | −0.201573 | − | 0.979473i | \(-0.564605\pi\) | ||||
−0.201573 | + | 0.979473i | \(0.564605\pi\) | |||||||
\(444\) | 1.61374e11 | 0.197065 | ||||||||
\(445\) | 9.95400e11 | 1.20331 | ||||||||
\(446\) | −3.87658e11 | −0.463919 | ||||||||
\(447\) | 1.46615e12 | 1.73698 | ||||||||
\(448\) | −1.85903e12 | −2.18039 | ||||||||
\(449\) | 3.50572e11 | 0.407070 | 0.203535 | − | 0.979068i | \(-0.434757\pi\) | ||||
0.203535 | + | 0.979068i | \(0.434757\pi\) | |||||||
\(450\) | 8.07073e10 | 0.0927804 | ||||||||
\(451\) | 4.26404e11 | 0.485318 | ||||||||
\(452\) | 2.81797e11 | 0.317552 | ||||||||
\(453\) | −2.85390e11 | −0.318418 | ||||||||
\(454\) | −8.42238e11 | −0.930430 | ||||||||
\(455\) | 1.08542e12 | 1.18727 | ||||||||
\(456\) | 1.66098e11 | 0.179897 | ||||||||
\(457\) | 5.37992e11 | 0.576970 | 0.288485 | − | 0.957484i | \(-0.406848\pi\) | ||||
0.288485 | + | 0.957484i | \(0.406848\pi\) | |||||||
\(458\) | 1.21847e12 | 1.29396 | ||||||||
\(459\) | −1.95785e12 | −2.05884 | ||||||||
\(460\) | −1.66656e12 | −1.73544 | ||||||||
\(461\) | 2.24837e11 | 0.231853 | 0.115927 | − | 0.993258i | \(-0.463016\pi\) | ||||
0.115927 | + | 0.993258i | \(0.463016\pi\) | |||||||
\(462\) | 2.40527e12 | 2.45626 | ||||||||
\(463\) | 5.19651e11 | 0.525530 | 0.262765 | − | 0.964860i | \(-0.415366\pi\) | ||||
0.262765 | + | 0.964860i | \(0.415366\pi\) | |||||||
\(464\) | −3.22607e11 | −0.323104 | ||||||||
\(465\) | 1.16058e12 | 1.15116 | ||||||||
\(466\) | 6.77542e11 | 0.665579 | ||||||||
\(467\) | −1.05163e12 | −1.02314 | −0.511571 | − | 0.859241i | \(-0.670936\pi\) | ||||
−0.511571 | + | 0.859241i | \(0.670936\pi\) | |||||||
\(468\) | 2.12860e11 | 0.205111 | ||||||||
\(469\) | 1.63716e12 | 1.56248 | ||||||||
\(470\) | 1.61353e12 | 1.52523 | ||||||||
\(471\) | −8.62881e10 | −0.0807899 | ||||||||
\(472\) | −7.89593e10 | −0.0732259 | ||||||||
\(473\) | 5.05002e11 | 0.463893 | ||||||||
\(474\) | −1.31587e12 | −1.19732 | ||||||||
\(475\) | 1.93282e11 | 0.174209 | ||||||||
\(476\) | −4.15659e12 | −3.71113 | ||||||||
\(477\) | 6.05318e10 | 0.0535366 | ||||||||
\(478\) | −8.50327e11 | −0.745008 | ||||||||
\(479\) | 1.27153e12 | 1.10361 | 0.551807 | − | 0.833972i | \(-0.313939\pi\) | ||||
0.551807 | + | 0.833972i | \(0.313939\pi\) | |||||||
\(480\) | −1.13926e12 | −0.979574 | ||||||||
\(481\) | 2.02419e11 | 0.172425 | ||||||||
\(482\) | −3.48654e12 | −2.94227 | ||||||||
\(483\) | −2.80749e12 | −2.34723 | ||||||||
\(484\) | 6.73519e11 | 0.557886 | ||||||||
\(485\) | 7.33284e11 | 0.601776 | ||||||||
\(486\) | −5.56018e11 | −0.452091 | ||||||||
\(487\) | −1.94977e12 | −1.57074 | −0.785369 | − | 0.619027i | \(-0.787527\pi\) | ||||
−0.785369 | + | 0.619027i | \(0.787527\pi\) | |||||||
\(488\) | −5.46275e11 | −0.436036 | ||||||||
\(489\) | −5.87996e11 | −0.465034 | ||||||||
\(490\) | −1.72944e12 | −1.35526 | ||||||||
\(491\) | 4.08089e11 | 0.316875 | 0.158438 | − | 0.987369i | \(-0.449354\pi\) | ||||
0.158438 | + | 0.987369i | \(0.449354\pi\) | |||||||
\(492\) | 6.32506e11 | 0.486656 | ||||||||
\(493\) | −1.35058e12 | −1.02969 | ||||||||
\(494\) | 9.01761e11 | 0.681271 | ||||||||
\(495\) | −1.84943e11 | −0.138457 | ||||||||
\(496\) | −1.33163e12 | −0.987908 | ||||||||
\(497\) | 5.82677e11 | 0.428375 | ||||||||
\(498\) | 3.97061e11 | 0.289285 | ||||||||
\(499\) | 1.98112e12 | 1.43040 | 0.715201 | − | 0.698919i | \(-0.246335\pi\) | ||||
0.715201 | + | 0.698919i | \(0.246335\pi\) | |||||||
\(500\) | 1.96923e12 | 1.40907 | ||||||||
\(501\) | 1.60245e12 | 1.13636 | ||||||||
\(502\) | −3.66280e12 | −2.57423 | ||||||||
\(503\) | 8.23536e11 | 0.573623 | 0.286811 | − | 0.957987i | \(-0.407405\pi\) | ||||
0.286811 | + | 0.957987i | \(0.407405\pi\) | |||||||
\(504\) | −1.45904e11 | −0.100723 | ||||||||
\(505\) | 9.39006e11 | 0.642476 | ||||||||
\(506\) | −4.63237e12 | −3.14142 | ||||||||
\(507\) | −1.37159e11 | −0.0921912 | ||||||||
\(508\) | −1.56723e12 | −1.04411 | ||||||||
\(509\) | −8.61412e11 | −0.568828 | −0.284414 | − | 0.958702i | \(-0.591799\pi\) | ||||
−0.284414 | + | 0.958702i | \(0.591799\pi\) | |||||||
\(510\) | −3.19420e12 | −2.09072 | ||||||||
\(511\) | 3.89642e12 | 2.52797 | ||||||||
\(512\) | 1.73891e12 | 1.11831 | ||||||||
\(513\) | −7.12352e11 | −0.454115 | ||||||||
\(514\) | 5.44952e11 | 0.344369 | ||||||||
\(515\) | 9.12880e10 | 0.0571849 | ||||||||
\(516\) | 7.49095e11 | 0.465172 | ||||||||
\(517\) | 2.53537e12 | 1.56075 | ||||||||
\(518\) | −6.00525e11 | −0.366477 | ||||||||
\(519\) | 2.16227e12 | 1.30815 | ||||||||
\(520\) | 6.13792e11 | 0.368134 | ||||||||
\(521\) | 2.18788e12 | 1.30093 | 0.650463 | − | 0.759538i | \(-0.274575\pi\) | ||||
0.650463 | + | 0.759538i | \(0.274575\pi\) | |||||||
\(522\) | −2.05190e11 | −0.120959 | ||||||||
\(523\) | −1.08120e11 | −0.0631901 | −0.0315951 | − | 0.999501i | \(-0.510059\pi\) | ||||
−0.0315951 | + | 0.999501i | \(0.510059\pi\) | |||||||
\(524\) | −2.53975e11 | −0.147164 | ||||||||
\(525\) | 9.59240e11 | 0.551075 | ||||||||
\(526\) | −2.35808e12 | −1.34314 | ||||||||
\(527\) | −5.57481e12 | −3.14835 | ||||||||
\(528\) | −1.19890e12 | −0.671320 | ||||||||
\(529\) | 3.60587e12 | 2.00198 | ||||||||
\(530\) | 7.55471e11 | 0.415888 | ||||||||
\(531\) | 4.42672e10 | 0.0241633 | ||||||||
\(532\) | −1.51235e12 | −0.818560 | ||||||||
\(533\) | 7.93385e11 | 0.425806 | ||||||||
\(534\) | 4.10416e12 | 2.18418 | ||||||||
\(535\) | −1.64701e12 | −0.869170 | ||||||||
\(536\) | 9.25791e11 | 0.484475 | ||||||||
\(537\) | 1.21999e12 | 0.633099 | ||||||||
\(538\) | −8.84263e11 | −0.455052 | ||||||||
\(539\) | −2.71751e12 | −1.38683 | ||||||||
\(540\) | −2.09861e12 | −1.06209 | ||||||||
\(541\) | −4.50335e11 | −0.226021 | −0.113010 | − | 0.993594i | \(-0.536049\pi\) | ||||
−0.113010 | + | 0.993594i | \(0.536049\pi\) | |||||||
\(542\) | 3.22966e12 | 1.60753 | ||||||||
\(543\) | −1.22071e12 | −0.602577 | ||||||||
\(544\) | 5.47242e12 | 2.67907 | ||||||||
\(545\) | 1.05990e12 | 0.514614 | ||||||||
\(546\) | 4.47535e12 | 2.15506 | ||||||||
\(547\) | −2.31775e12 | −1.10694 | −0.553469 | − | 0.832870i | \(-0.686696\pi\) | ||||
−0.553469 | + | 0.832870i | \(0.686696\pi\) | |||||||
\(548\) | 3.96535e12 | 1.87832 | ||||||||
\(549\) | 3.06260e11 | 0.143885 | ||||||||
\(550\) | 1.58275e12 | 0.737531 | ||||||||
\(551\) | −4.91400e11 | −0.227119 | ||||||||
\(552\) | −1.58760e12 | −0.727804 | ||||||||
\(553\) | 2.76818e12 | 1.25872 | ||||||||
\(554\) | −7.44994e11 | −0.336015 | ||||||||
\(555\) | −2.60878e11 | −0.116713 | ||||||||
\(556\) | −3.68962e12 | −1.63736 | ||||||||
\(557\) | −1.99632e12 | −0.878782 | −0.439391 | − | 0.898296i | \(-0.644806\pi\) | ||||
−0.439391 | + | 0.898296i | \(0.644806\pi\) | |||||||
\(558\) | −8.46967e11 | −0.369839 | ||||||||
\(559\) | 9.39628e11 | 0.407008 | ||||||||
\(560\) | 1.60508e12 | 0.689685 | ||||||||
\(561\) | −5.01913e12 | −2.13942 | ||||||||
\(562\) | 2.19292e12 | 0.927277 | ||||||||
\(563\) | 3.59948e12 | 1.50991 | 0.754957 | − | 0.655774i | \(-0.227658\pi\) | ||||
0.754957 | + | 0.655774i | \(0.227658\pi\) | |||||||
\(564\) | 3.76085e12 | 1.56506 | ||||||||
\(565\) | −4.55557e11 | −0.188072 | ||||||||
\(566\) | 3.11546e12 | 1.27599 | ||||||||
\(567\) | −2.99139e12 | −1.21548 | ||||||||
\(568\) | 3.29496e11 | 0.132826 | ||||||||
\(569\) | −3.76278e12 | −1.50489 | −0.752443 | − | 0.658658i | \(-0.771125\pi\) | ||||
−0.752443 | + | 0.658658i | \(0.771125\pi\) | |||||||
\(570\) | −1.16219e12 | −0.461149 | ||||||||
\(571\) | 2.22709e12 | 0.876751 | 0.438375 | − | 0.898792i | \(-0.355554\pi\) | ||||
0.438375 | + | 0.898792i | \(0.355554\pi\) | |||||||
\(572\) | 4.17440e12 | 1.63047 | ||||||||
\(573\) | −1.72075e12 | −0.666842 | ||||||||
\(574\) | −2.35376e12 | −0.905023 | ||||||||
\(575\) | −1.84743e12 | −0.704794 | ||||||||
\(576\) | 5.89367e11 | 0.223092 | ||||||||
\(577\) | 2.46554e12 | 0.926021 | 0.463011 | − | 0.886353i | \(-0.346769\pi\) | ||||
0.463011 | + | 0.886353i | \(0.346769\pi\) | |||||||
\(578\) | 1.12734e13 | 4.20127 | ||||||||
\(579\) | −1.36593e12 | −0.505096 | ||||||||
\(580\) | −1.44768e12 | −0.531186 | ||||||||
\(581\) | −8.35292e11 | −0.304121 | ||||||||
\(582\) | 3.02343e12 | 1.09231 | ||||||||
\(583\) | 1.18709e12 | 0.425574 | ||||||||
\(584\) | 2.20337e12 | 0.783845 | ||||||||
\(585\) | −3.44112e11 | −0.121478 | ||||||||
\(586\) | −2.62107e12 | −0.918204 | ||||||||
\(587\) | 1.80230e12 | 0.626550 | 0.313275 | − | 0.949662i | \(-0.398574\pi\) | ||||
0.313275 | + | 0.949662i | \(0.398574\pi\) | |||||||
\(588\) | −4.03103e12 | −1.39065 | ||||||||
\(589\) | −2.02836e12 | −0.694427 | ||||||||
\(590\) | 5.52480e11 | 0.187708 | ||||||||
\(591\) | 3.91395e12 | 1.31969 | ||||||||
\(592\) | 2.99329e11 | 0.100162 | ||||||||
\(593\) | −2.92045e12 | −0.969848 | −0.484924 | − | 0.874556i | \(-0.661153\pi\) | ||||
−0.484924 | + | 0.874556i | \(0.661153\pi\) | |||||||
\(594\) | −5.83331e12 | −1.92254 | ||||||||
\(595\) | 6.71960e12 | 2.19795 | ||||||||
\(596\) | −7.54901e12 | −2.45065 | ||||||||
\(597\) | −1.68426e12 | −0.542657 | ||||||||
\(598\) | −8.61919e12 | −2.75620 | ||||||||
\(599\) | −4.02964e12 | −1.27893 | −0.639463 | − | 0.768822i | \(-0.720843\pi\) | ||||
−0.639463 | + | 0.768822i | \(0.720843\pi\) | |||||||
\(600\) | 5.42437e11 | 0.170871 | ||||||||
\(601\) | −3.81051e12 | −1.19137 | −0.595686 | − | 0.803217i | \(-0.703120\pi\) | ||||
−0.595686 | + | 0.803217i | \(0.703120\pi\) | |||||||
\(602\) | −2.78763e12 | −0.865069 | ||||||||
\(603\) | −5.19029e11 | −0.159869 | ||||||||
\(604\) | 1.46943e12 | 0.449245 | ||||||||
\(605\) | −1.08882e12 | −0.330412 | ||||||||
\(606\) | 3.87164e12 | 1.16619 | ||||||||
\(607\) | −5.59887e12 | −1.67398 | −0.836991 | − | 0.547216i | \(-0.815687\pi\) | ||||
−0.836991 | + | 0.547216i | \(0.815687\pi\) | |||||||
\(608\) | 1.99111e12 | 0.590920 | ||||||||
\(609\) | −2.43877e12 | −0.718444 | ||||||||
\(610\) | 3.82230e12 | 1.11774 | ||||||||
\(611\) | 4.71743e12 | 1.36937 | ||||||||
\(612\) | 1.31777e12 | 0.379714 | ||||||||
\(613\) | 1.65775e12 | 0.474185 | 0.237093 | − | 0.971487i | \(-0.423806\pi\) | ||||
0.237093 | + | 0.971487i | \(0.423806\pi\) | |||||||
\(614\) | −1.04181e13 | −2.95824 | ||||||||
\(615\) | −1.02252e12 | −0.288226 | ||||||||
\(616\) | −2.86132e12 | −0.800669 | ||||||||
\(617\) | −6.21572e12 | −1.72666 | −0.863332 | − | 0.504636i | \(-0.831627\pi\) | ||||
−0.863332 | + | 0.504636i | \(0.831627\pi\) | |||||||
\(618\) | 3.76393e11 | 0.103799 | ||||||||
\(619\) | 4.17471e12 | 1.14293 | 0.571464 | − | 0.820627i | \(-0.306376\pi\) | ||||
0.571464 | + | 0.820627i | \(0.306376\pi\) | |||||||
\(620\) | −5.97562e12 | −1.62413 | ||||||||
\(621\) | 6.80879e12 | 1.83720 | ||||||||
\(622\) | 1.02235e13 | 2.73869 | ||||||||
\(623\) | −8.63387e12 | −2.29620 | ||||||||
\(624\) | −2.23072e12 | −0.588999 | ||||||||
\(625\) | −1.63175e12 | −0.427753 | ||||||||
\(626\) | −7.41748e11 | −0.193051 | ||||||||
\(627\) | −1.82618e12 | −0.471889 | ||||||||
\(628\) | 4.44284e11 | 0.113984 | ||||||||
\(629\) | 1.25313e12 | 0.319203 | ||||||||
\(630\) | 1.02089e12 | 0.258194 | ||||||||
\(631\) | 5.75695e12 | 1.44564 | 0.722820 | − | 0.691036i | \(-0.242845\pi\) | ||||
0.722820 | + | 0.691036i | \(0.242845\pi\) | |||||||
\(632\) | 1.56536e12 | 0.390291 | ||||||||
\(633\) | 2.41457e12 | 0.597755 | ||||||||
\(634\) | 7.77446e12 | 1.91103 | ||||||||
\(635\) | 2.53360e12 | 0.618382 | ||||||||
\(636\) | 1.76087e12 | 0.426747 | ||||||||
\(637\) | −5.05632e12 | −1.21677 | ||||||||
\(638\) | −4.02398e12 | −0.961530 | ||||||||
\(639\) | −1.84726e11 | −0.0438303 | ||||||||
\(640\) | 2.84503e12 | 0.670312 | ||||||||
\(641\) | 3.35199e12 | 0.784225 | 0.392113 | − | 0.919917i | \(-0.371744\pi\) | ||||
0.392113 | + | 0.919917i | \(0.371744\pi\) | |||||||
\(642\) | −6.79084e12 | −1.57767 | ||||||||
\(643\) | 1.74616e12 | 0.402842 | 0.201421 | − | 0.979505i | \(-0.435444\pi\) | ||||
0.201421 | + | 0.979505i | \(0.435444\pi\) | |||||||
\(644\) | 1.44553e13 | 3.31163 | ||||||||
\(645\) | −1.21100e12 | −0.275501 | ||||||||
\(646\) | 5.58258e12 | 1.26121 | ||||||||
\(647\) | 3.68639e11 | 0.0827050 | 0.0413525 | − | 0.999145i | \(-0.486833\pi\) | ||||
0.0413525 | + | 0.999145i | \(0.486833\pi\) | |||||||
\(648\) | −1.69159e12 | −0.376883 | ||||||||
\(649\) | 8.68125e11 | 0.192080 | ||||||||
\(650\) | 2.94493e12 | 0.647091 | ||||||||
\(651\) | −1.00666e13 | −2.19668 | ||||||||
\(652\) | 3.02750e12 | 0.656100 | ||||||||
\(653\) | 3.37602e12 | 0.726601 | 0.363301 | − | 0.931672i | \(-0.381650\pi\) | ||||
0.363301 | + | 0.931672i | \(0.381650\pi\) | |||||||
\(654\) | 4.37011e12 | 0.934099 | ||||||||
\(655\) | 4.10579e11 | 0.0871587 | ||||||||
\(656\) | 1.17323e12 | 0.247351 | ||||||||
\(657\) | −1.23528e12 | −0.258656 | ||||||||
\(658\) | −1.39954e13 | −2.91050 | ||||||||
\(659\) | −9.07216e11 | −0.187381 | −0.0936906 | − | 0.995601i | \(-0.529866\pi\) | ||||
−0.0936906 | + | 0.995601i | \(0.529866\pi\) | |||||||
\(660\) | −5.37998e12 | −1.10365 | ||||||||
\(661\) | −3.66823e12 | −0.747394 | −0.373697 | − | 0.927551i | \(-0.621910\pi\) | ||||
−0.373697 | + | 0.927551i | \(0.621910\pi\) | |||||||
\(662\) | 4.26186e12 | 0.862458 | ||||||||
\(663\) | −9.33880e12 | −1.87707 | ||||||||
\(664\) | −4.72346e11 | −0.0942983 | ||||||||
\(665\) | 2.44489e12 | 0.484798 | ||||||||
\(666\) | 1.90384e11 | 0.0374971 | ||||||||
\(667\) | 4.69689e12 | 0.918849 | ||||||||
\(668\) | −8.25076e12 | −1.60325 | ||||||||
\(669\) | 1.46071e12 | 0.281934 | ||||||||
\(670\) | −6.47778e12 | −1.24191 | ||||||||
\(671\) | 6.00607e12 | 1.14377 | ||||||||
\(672\) | 9.88168e12 | 1.86926 | ||||||||
\(673\) | 6.92489e12 | 1.30120 | 0.650601 | − | 0.759419i | \(-0.274517\pi\) | ||||
0.650601 | + | 0.759419i | \(0.274517\pi\) | |||||||
\(674\) | 4.90193e12 | 0.914950 | ||||||||
\(675\) | −2.32637e12 | −0.431332 | ||||||||
\(676\) | 7.06212e11 | 0.130069 | ||||||||
\(677\) | 2.22502e12 | 0.407085 | 0.203542 | − | 0.979066i | \(-0.434754\pi\) | ||||
0.203542 | + | 0.979066i | \(0.434754\pi\) | |||||||
\(678\) | −1.87832e12 | −0.341379 | ||||||||
\(679\) | −6.36034e12 | −1.14833 | ||||||||
\(680\) | 3.79984e12 | 0.681514 | ||||||||
\(681\) | 3.17359e12 | 0.565442 | ||||||||
\(682\) | −1.66099e13 | −2.93993 | ||||||||
\(683\) | −7.53860e12 | −1.32555 | −0.662777 | − | 0.748817i | \(-0.730622\pi\) | ||||
−0.662777 | + | 0.748817i | \(0.730622\pi\) | |||||||
\(684\) | 4.79461e11 | 0.0837531 | ||||||||
\(685\) | −6.41042e12 | −1.11245 | ||||||||
\(686\) | 2.07055e12 | 0.356966 | ||||||||
\(687\) | −4.59123e12 | −0.786365 | ||||||||
\(688\) | 1.38948e12 | 0.236432 | ||||||||
\(689\) | 2.20875e12 | 0.373388 | ||||||||
\(690\) | 1.11084e13 | 1.86566 | ||||||||
\(691\) | −2.77605e11 | −0.0463208 | −0.0231604 | − | 0.999732i | \(-0.507373\pi\) | ||||
−0.0231604 | + | 0.999732i | \(0.507373\pi\) | |||||||
\(692\) | −1.11332e13 | −1.84562 | ||||||||
\(693\) | 1.60415e12 | 0.264208 | ||||||||
\(694\) | 1.17421e13 | 1.92144 | ||||||||
\(695\) | 5.96467e12 | 0.969740 | ||||||||
\(696\) | −1.37909e12 | −0.222767 | ||||||||
\(697\) | 4.91165e12 | 0.788279 | ||||||||
\(698\) | −7.87619e11 | −0.125593 | ||||||||
\(699\) | −2.55300e12 | −0.404487 | ||||||||
\(700\) | −4.93898e12 | −0.777492 | ||||||||
\(701\) | −8.90286e12 | −1.39251 | −0.696255 | − | 0.717794i | \(-0.745152\pi\) | ||||
−0.696255 | + | 0.717794i | \(0.745152\pi\) | |||||||
\(702\) | −1.08537e13 | −1.68679 | ||||||||
\(703\) | 4.55943e11 | 0.0704063 | ||||||||
\(704\) | 1.15581e13 | 1.77341 | ||||||||
\(705\) | −6.07983e12 | −0.926916 | ||||||||
\(706\) | −2.56659e11 | −0.0388808 | ||||||||
\(707\) | −8.14472e12 | −1.22600 | ||||||||
\(708\) | 1.28773e12 | 0.192609 | ||||||||
\(709\) | −3.06048e12 | −0.454864 | −0.227432 | − | 0.973794i | \(-0.573033\pi\) | ||||
−0.227432 | + | 0.973794i | \(0.573033\pi\) | |||||||
\(710\) | −2.30549e12 | −0.340487 | ||||||||
\(711\) | −8.77595e11 | −0.128790 | ||||||||
\(712\) | −4.88233e12 | −0.711979 | ||||||||
\(713\) | 1.93875e13 | 2.80943 | ||||||||
\(714\) | 2.77058e13 | 3.98959 | ||||||||
\(715\) | −6.74839e12 | −0.965657 | ||||||||
\(716\) | −6.28153e12 | −0.893217 | ||||||||
\(717\) | 3.20407e12 | 0.452757 | ||||||||
\(718\) | 8.99092e11 | 0.126254 | ||||||||
\(719\) | 1.18782e13 | 1.65756 | 0.828782 | − | 0.559572i | \(-0.189034\pi\) | ||||
0.828782 | + | 0.559572i | \(0.189034\pi\) | |||||||
\(720\) | −5.08859e11 | −0.0705669 | ||||||||
\(721\) | −7.91812e11 | −0.109122 | ||||||||
\(722\) | −9.04333e12 | −1.23854 | ||||||||
\(723\) | 1.31374e13 | 1.78808 | ||||||||
\(724\) | 6.28524e12 | 0.850156 | ||||||||
\(725\) | −1.60479e12 | −0.215724 | ||||||||
\(726\) | −4.48934e12 | −0.599747 | ||||||||
\(727\) | 3.88538e12 | 0.515857 | 0.257928 | − | 0.966164i | \(-0.416960\pi\) | ||||
0.257928 | + | 0.966164i | \(0.416960\pi\) | |||||||
\(728\) | −5.32389e12 | −0.702487 | ||||||||
\(729\) | 8.40151e12 | 1.10175 | ||||||||
\(730\) | −1.54170e13 | −2.00932 | ||||||||
\(731\) | 5.81701e12 | 0.753479 | ||||||||
\(732\) | 8.90911e12 | 1.14692 | ||||||||
\(733\) | −1.42676e13 | −1.82550 | −0.912752 | − | 0.408513i | \(-0.866047\pi\) | ||||
−0.912752 | + | 0.408513i | \(0.866047\pi\) | |||||||
\(734\) | −7.67231e12 | −0.975650 | ||||||||
\(735\) | 6.51660e12 | 0.823623 | ||||||||
\(736\) | −1.90314e13 | −2.39067 | ||||||||
\(737\) | −1.01787e13 | −1.27083 | ||||||||
\(738\) | 7.46214e11 | 0.0925998 | ||||||||
\(739\) | 1.15651e13 | 1.42643 | 0.713216 | − | 0.700945i | \(-0.247238\pi\) | ||||
0.713216 | + | 0.700945i | \(0.247238\pi\) | |||||||
\(740\) | 1.34322e12 | 0.164667 | ||||||||
\(741\) | −3.39787e12 | −0.414023 | ||||||||
\(742\) | −6.55278e12 | −0.793612 | ||||||||
\(743\) | −3.25689e12 | −0.392061 | −0.196031 | − | 0.980598i | \(-0.562805\pi\) | ||||
−0.196031 | + | 0.980598i | \(0.562805\pi\) | |||||||
\(744\) | −5.69250e12 | −0.681122 | ||||||||
\(745\) | 1.22038e13 | 1.45142 | ||||||||
\(746\) | 1.47691e13 | 1.74595 | ||||||||
\(747\) | 2.64813e11 | 0.0311169 | ||||||||
\(748\) | 2.58427e13 | 3.01843 | ||||||||
\(749\) | 1.42858e13 | 1.65858 | ||||||||
\(750\) | −1.31259e13 | −1.51480 | ||||||||
\(751\) | −1.38050e13 | −1.58365 | −0.791823 | − | 0.610751i | \(-0.790868\pi\) | ||||
−0.791823 | + | 0.610751i | \(0.790868\pi\) | |||||||
\(752\) | 6.97593e12 | 0.795467 | ||||||||
\(753\) | 1.38016e13 | 1.56441 | ||||||||
\(754\) | −7.48719e12 | −0.843622 | ||||||||
\(755\) | −2.37550e12 | −0.266069 | ||||||||
\(756\) | 1.82029e13 | 2.02671 | ||||||||
\(757\) | 2.07544e12 | 0.229709 | 0.114855 | − | 0.993382i | \(-0.463360\pi\) | ||||
0.114855 | + | 0.993382i | \(0.463360\pi\) | |||||||
\(758\) | 7.73875e12 | 0.851450 | ||||||||
\(759\) | 1.74550e13 | 1.90911 | ||||||||
\(760\) | 1.38255e12 | 0.150321 | ||||||||
\(761\) | −1.05770e13 | −1.14323 | −0.571614 | − | 0.820523i | \(-0.693683\pi\) | ||||
−0.571614 | + | 0.820523i | \(0.693683\pi\) | |||||||
\(762\) | 1.04464e13 | 1.12245 | ||||||||
\(763\) | −9.19335e12 | −0.982004 | ||||||||
\(764\) | 8.85989e12 | 0.940824 | ||||||||
\(765\) | −2.13031e12 | −0.224888 | ||||||||
\(766\) | 1.44478e13 | 1.51625 | ||||||||
\(767\) | 1.61527e12 | 0.168526 | ||||||||
\(768\) | −1.45311e12 | −0.150721 | ||||||||
\(769\) | −1.75639e13 | −1.81114 | −0.905571 | − | 0.424194i | \(-0.860557\pi\) | ||||
−0.905571 | + | 0.424194i | \(0.860557\pi\) | |||||||
\(770\) | 2.00207e13 | 2.05244 | ||||||||
\(771\) | −2.05340e12 | −0.209280 | ||||||||
\(772\) | 7.03295e12 | 0.712622 | ||||||||
\(773\) | −1.89617e13 | −1.91016 | −0.955082 | − | 0.296342i | \(-0.904233\pi\) | ||||
−0.955082 | + | 0.296342i | \(0.904233\pi\) | |||||||
\(774\) | 8.83763e11 | 0.0885118 | ||||||||
\(775\) | −6.62415e12 | −0.659588 | ||||||||
\(776\) | −3.59668e12 | −0.356061 | ||||||||
\(777\) | 2.26280e12 | 0.222716 | ||||||||
\(778\) | −2.11523e13 | −2.06990 | ||||||||
\(779\) | 1.78708e12 | 0.173870 | ||||||||
\(780\) | −1.00102e13 | −0.968319 | ||||||||
\(781\) | −3.62267e12 | −0.348417 | ||||||||
\(782\) | −5.33593e13 | −5.10246 | ||||||||
\(783\) | 5.91455e12 | 0.562334 | ||||||||
\(784\) | −7.47708e12 | −0.706822 | ||||||||
\(785\) | −7.18235e11 | −0.0675076 | ||||||||
\(786\) | 1.69287e12 | 0.158206 | ||||||||
\(787\) | 1.53039e13 | 1.42205 | 0.711027 | − | 0.703165i | \(-0.248230\pi\) | ||||
0.711027 | + | 0.703165i | \(0.248230\pi\) | |||||||
\(788\) | −2.01523e13 | −1.86190 | ||||||||
\(789\) | 8.88534e12 | 0.816258 | ||||||||
\(790\) | −1.09529e13 | −1.00048 | ||||||||
\(791\) | 3.95140e12 | 0.358886 | ||||||||
\(792\) | 9.07124e11 | 0.0819225 | ||||||||
\(793\) | 1.11751e13 | 1.00352 | ||||||||
\(794\) | −8.08381e11 | −0.0721811 | ||||||||
\(795\) | −2.84665e12 | −0.252744 | ||||||||
\(796\) | 8.67202e12 | 0.765617 | ||||||||
\(797\) | 3.76037e11 | 0.0330117 | 0.0165059 | − | 0.999864i | \(-0.494746\pi\) | ||||
0.0165059 | + | 0.999864i | \(0.494746\pi\) | |||||||
\(798\) | 1.00806e13 | 0.879980 | ||||||||
\(799\) | 2.92044e13 | 2.53506 | ||||||||
\(800\) | 6.50249e12 | 0.561273 | ||||||||
\(801\) | 2.73720e12 | 0.234941 | ||||||||
\(802\) | −5.02887e12 | −0.429226 | ||||||||
\(803\) | −2.42252e13 | −2.05611 | ||||||||
\(804\) | −1.50986e13 | −1.27433 | ||||||||
\(805\) | −2.33687e13 | −1.96134 | ||||||||
\(806\) | −3.09051e13 | −2.57942 | ||||||||
\(807\) | 3.33194e12 | 0.276545 | ||||||||
\(808\) | −4.60572e12 | −0.380143 | ||||||||
\(809\) | 8.16350e12 | 0.670051 | 0.335026 | − | 0.942209i | \(-0.391255\pi\) | ||||
0.335026 | + | 0.942209i | \(0.391255\pi\) | |||||||
\(810\) | 1.18361e13 | 0.966105 | ||||||||
\(811\) | 7.26498e11 | 0.0589713 | 0.0294856 | − | 0.999565i | \(-0.490613\pi\) | ||||
0.0294856 | + | 0.999565i | \(0.490613\pi\) | |||||||
\(812\) | 1.25568e13 | 1.01363 | ||||||||
\(813\) | −1.21695e13 | −0.976932 | ||||||||
\(814\) | 3.73363e12 | 0.298072 | ||||||||
\(815\) | −4.89429e12 | −0.388580 | ||||||||
\(816\) | −1.38098e13 | −1.09039 | ||||||||
\(817\) | 2.11648e12 | 0.166194 | ||||||||
\(818\) | 4.27780e12 | 0.334064 | ||||||||
\(819\) | 2.98475e12 | 0.231809 | ||||||||
\(820\) | 5.26478e12 | 0.406647 | ||||||||
\(821\) | −2.03191e13 | −1.56084 | −0.780422 | − | 0.625253i | \(-0.784996\pi\) | ||||
−0.780422 | + | 0.625253i | \(0.784996\pi\) | |||||||
\(822\) | −2.64310e13 | −2.01925 | ||||||||
\(823\) | 1.08873e13 | 0.827220 | 0.413610 | − | 0.910454i | \(-0.364268\pi\) | ||||
0.413610 | + | 0.910454i | \(0.364268\pi\) | |||||||
\(824\) | −4.47758e11 | −0.0338354 | ||||||||
\(825\) | −5.96387e12 | −0.448214 | ||||||||
\(826\) | −4.79208e12 | −0.358191 | ||||||||
\(827\) | −9.13590e11 | −0.0679167 | −0.0339583 | − | 0.999423i | \(-0.510811\pi\) | ||||
−0.0339583 | + | 0.999423i | \(0.510811\pi\) | |||||||
\(828\) | −4.58278e12 | −0.338838 | ||||||||
\(829\) | 1.57245e13 | 1.15633 | 0.578163 | − | 0.815921i | \(-0.303770\pi\) | ||||
0.578163 | + | 0.815921i | \(0.303770\pi\) | |||||||
\(830\) | 3.30501e12 | 0.241725 | ||||||||
\(831\) | 2.80717e12 | 0.204204 | ||||||||
\(832\) | 2.15055e13 | 1.55594 | ||||||||
\(833\) | −3.13024e13 | −2.25256 | ||||||||
\(834\) | 2.45931e13 | 1.76022 | ||||||||
\(835\) | 1.33383e13 | 0.949534 | ||||||||
\(836\) | 9.40272e12 | 0.665771 | ||||||||
\(837\) | 2.44136e13 | 1.71936 | ||||||||
\(838\) | −6.40183e12 | −0.448442 | ||||||||
\(839\) | −3.47812e12 | −0.242335 | −0.121167 | − | 0.992632i | \(-0.538664\pi\) | ||||
−0.121167 | + | 0.992632i | \(0.538664\pi\) | |||||||
\(840\) | 6.86145e12 | 0.475509 | ||||||||
\(841\) | −1.04271e13 | −0.718758 | ||||||||
\(842\) | 1.48300e13 | 1.01681 | ||||||||
\(843\) | −8.26301e12 | −0.563527 | ||||||||
\(844\) | −1.24323e13 | −0.843352 | ||||||||
\(845\) | −1.14167e12 | −0.0770346 | ||||||||
\(846\) | 4.43695e12 | 0.297795 | ||||||||
\(847\) | 9.44416e12 | 0.630504 | ||||||||
\(848\) | 3.26621e12 | 0.216902 | ||||||||
\(849\) | −1.17392e13 | −0.775448 | ||||||||
\(850\) | 1.82314e13 | 1.19794 | ||||||||
\(851\) | −4.35799e12 | −0.284841 | ||||||||
\(852\) | −5.37369e12 | −0.349377 | ||||||||
\(853\) | 1.17204e13 | 0.758006 | 0.379003 | − | 0.925395i | \(-0.376267\pi\) | ||||
0.379003 | + | 0.925395i | \(0.376267\pi\) | |||||||
\(854\) | −3.31537e13 | −2.13291 | ||||||||
\(855\) | −7.75102e11 | −0.0496034 | ||||||||
\(856\) | 8.07842e12 | 0.514274 | ||||||||
\(857\) | −1.27242e13 | −0.805783 | −0.402891 | − | 0.915248i | \(-0.631995\pi\) | ||||
−0.402891 | + | 0.915248i | \(0.631995\pi\) | |||||||
\(858\) | −2.78245e13 | −1.75281 | ||||||||
\(859\) | 2.65726e13 | 1.66519 | 0.832597 | − | 0.553879i | \(-0.186853\pi\) | ||||
0.832597 | + | 0.553879i | \(0.186853\pi\) | |||||||
\(860\) | 6.23523e12 | 0.388695 | ||||||||
\(861\) | 8.86908e12 | 0.550002 | ||||||||
\(862\) | 1.63862e13 | 1.01087 | ||||||||
\(863\) | 6.65761e12 | 0.408573 | 0.204287 | − | 0.978911i | \(-0.434513\pi\) | ||||
0.204287 | + | 0.978911i | \(0.434513\pi\) | |||||||
\(864\) | −2.39652e13 | −1.46309 | ||||||||
\(865\) | 1.79981e13 | 1.09308 | ||||||||
\(866\) | 3.21971e12 | 0.194530 | ||||||||
\(867\) | −4.24787e13 | −2.55320 | ||||||||
\(868\) | 5.18312e13 | 3.09922 | ||||||||
\(869\) | −1.72105e13 | −1.02378 | ||||||||
\(870\) | 9.64951e12 | 0.571043 | ||||||||
\(871\) | −1.89389e13 | −1.11500 | ||||||||
\(872\) | −5.19871e12 | −0.304489 | ||||||||
\(873\) | 2.01642e12 | 0.117494 | ||||||||
\(874\) | −1.94145e13 | −1.12544 | ||||||||
\(875\) | 2.76128e13 | 1.59248 | ||||||||
\(876\) | −3.59344e13 | −2.06178 | ||||||||
\(877\) | −1.19094e13 | −0.679819 | −0.339909 | − | 0.940458i | \(-0.610396\pi\) | ||||
−0.339909 | + | 0.940458i | \(0.610396\pi\) | |||||||
\(878\) | −3.17039e13 | −1.80048 | ||||||||
\(879\) | 9.87629e12 | 0.558012 | ||||||||
\(880\) | −9.97924e12 | −0.560952 | ||||||||
\(881\) | 1.24700e13 | 0.697391 | 0.348696 | − | 0.937236i | \(-0.386625\pi\) | ||||
0.348696 | + | 0.937236i | \(0.386625\pi\) | |||||||
\(882\) | −4.75570e12 | −0.264610 | ||||||||
\(883\) | 3.32785e12 | 0.184222 | 0.0921108 | − | 0.995749i | \(-0.470639\pi\) | ||||
0.0921108 | + | 0.995749i | \(0.470639\pi\) | |||||||
\(884\) | 4.80841e13 | 2.64829 | ||||||||
\(885\) | −2.08177e12 | −0.114074 | ||||||||
\(886\) | −1.12156e13 | −0.611463 | ||||||||
\(887\) | −5.24337e12 | −0.284416 | −0.142208 | − | 0.989837i | \(-0.545420\pi\) | ||||
−0.142208 | + | 0.989837i | \(0.545420\pi\) | |||||||
\(888\) | 1.27958e12 | 0.0690573 | ||||||||
\(889\) | −2.19759e13 | −1.18002 | ||||||||
\(890\) | 3.41617e13 | 1.82509 | ||||||||
\(891\) | 1.85983e13 | 0.988606 | ||||||||
\(892\) | −7.52098e12 | −0.397770 | ||||||||
\(893\) | 1.06259e13 | 0.559155 | ||||||||
\(894\) | 5.03179e13 | 2.63453 | ||||||||
\(895\) | 1.01548e13 | 0.529014 | ||||||||
\(896\) | −2.46771e13 | −1.27911 | ||||||||
\(897\) | 3.24775e13 | 1.67500 | ||||||||
\(898\) | 1.20315e13 | 0.617414 | ||||||||
\(899\) | 1.68412e13 | 0.859913 | ||||||||
\(900\) | 1.56581e12 | 0.0795512 | ||||||||
\(901\) | 1.36738e13 | 0.691240 | ||||||||
\(902\) | 1.46340e13 | 0.736095 | ||||||||
\(903\) | 1.05039e13 | 0.525721 | ||||||||
\(904\) | 2.23446e12 | 0.111279 | ||||||||
\(905\) | −1.01608e13 | −0.503511 | ||||||||
\(906\) | −9.79449e12 | −0.482953 | ||||||||
\(907\) | 2.17234e13 | 1.06585 | 0.532923 | − | 0.846164i | \(-0.321094\pi\) | ||||
0.532923 | + | 0.846164i | \(0.321094\pi\) | |||||||
\(908\) | −1.63403e13 | −0.797763 | ||||||||
\(909\) | 2.58212e12 | 0.125441 | ||||||||
\(910\) | 3.72514e13 | 1.80076 | ||||||||
\(911\) | 8.39548e12 | 0.403843 | 0.201922 | − | 0.979402i | \(-0.435281\pi\) | ||||
0.201922 | + | 0.979402i | \(0.435281\pi\) | |||||||
\(912\) | −5.02463e12 | −0.240507 | ||||||||
\(913\) | 5.19324e12 | 0.247355 | ||||||||
\(914\) | 1.84637e13 | 0.875106 | ||||||||
\(915\) | −1.44026e13 | −0.679274 | ||||||||
\(916\) | 2.36395e13 | 1.10945 | ||||||||
\(917\) | −3.56127e12 | −0.166319 | ||||||||
\(918\) | −6.71926e13 | −3.12269 | ||||||||
\(919\) | −4.20773e13 | −1.94593 | −0.972967 | − | 0.230945i | \(-0.925818\pi\) | ||||
−0.972967 | + | 0.230945i | \(0.925818\pi\) | |||||||
\(920\) | −1.32146e13 | −0.608150 | ||||||||
\(921\) | 3.92560e13 | 1.79778 | ||||||||
\(922\) | 7.71631e12 | 0.351658 | ||||||||
\(923\) | −6.74049e12 | −0.305692 | ||||||||
\(924\) | 4.66648e13 | 2.10603 | ||||||||
\(925\) | 1.48900e12 | 0.0668740 | ||||||||
\(926\) | 1.78342e13 | 0.797085 | ||||||||
\(927\) | 2.51028e11 | 0.0111651 | ||||||||
\(928\) | −1.65319e13 | −0.731740 | ||||||||
\(929\) | 2.25599e13 | 0.993727 | 0.496863 | − | 0.867829i | \(-0.334485\pi\) | ||||
0.496863 | + | 0.867829i | \(0.334485\pi\) | |||||||
\(930\) | 3.98305e13 | 1.74599 | ||||||||
\(931\) | −1.13892e13 | −0.496844 | ||||||||
\(932\) | 1.31450e13 | 0.570676 | ||||||||
\(933\) | −3.85225e13 | −1.66436 | ||||||||
\(934\) | −3.60915e13 | −1.55183 | ||||||||
\(935\) | −4.17776e13 | −1.78769 | ||||||||
\(936\) | 1.68783e12 | 0.0718768 | ||||||||
\(937\) | −3.05601e13 | −1.29517 | −0.647585 | − | 0.761993i | \(-0.724221\pi\) | ||||
−0.647585 | + | 0.761993i | \(0.724221\pi\) | |||||||
\(938\) | 5.61867e13 | 2.36985 | ||||||||
\(939\) | 2.79494e12 | 0.117321 | ||||||||
\(940\) | 3.13041e13 | 1.30775 | ||||||||
\(941\) | 3.36609e13 | 1.39950 | 0.699750 | − | 0.714388i | \(-0.253295\pi\) | ||||
0.699750 | + | 0.714388i | \(0.253295\pi\) | |||||||
\(942\) | −2.96138e12 | −0.122536 | ||||||||
\(943\) | −1.70812e13 | −0.703421 | ||||||||
\(944\) | 2.38860e12 | 0.0978968 | ||||||||
\(945\) | −2.94270e13 | −1.20033 | ||||||||
\(946\) | 1.73315e13 | 0.703599 | ||||||||
\(947\) | −2.11821e13 | −0.855843 | −0.427921 | − | 0.903816i | \(-0.640754\pi\) | ||||
−0.427921 | + | 0.903816i | \(0.640754\pi\) | |||||||
\(948\) | −2.55293e13 | −1.02660 | ||||||||
\(949\) | −4.50744e13 | −1.80398 | ||||||||
\(950\) | 6.63337e12 | 0.264228 | ||||||||
\(951\) | −2.92945e13 | −1.16138 | ||||||||
\(952\) | −3.29589e13 | −1.30049 | ||||||||
\(953\) | −1.54910e13 | −0.608362 | −0.304181 | − | 0.952614i | \(-0.598383\pi\) | ||||
−0.304181 | + | 0.952614i | \(0.598383\pi\) | |||||||
\(954\) | 2.07743e12 | 0.0812005 | ||||||||
\(955\) | −1.43230e13 | −0.557210 | ||||||||
\(956\) | −1.64972e13 | −0.638780 | ||||||||
\(957\) | 1.51625e13 | 0.584342 | ||||||||
\(958\) | 4.36384e13 | 1.67388 | ||||||||
\(959\) | 5.56025e13 | 2.12281 | ||||||||
\(960\) | −2.77163e13 | −1.05321 | ||||||||
\(961\) | 4.30762e13 | 1.62923 | ||||||||
\(962\) | 6.94695e12 | 0.261521 | ||||||||
\(963\) | −4.52903e12 | −0.169702 | ||||||||
\(964\) | −6.76425e13 | −2.52274 | ||||||||
\(965\) | −1.13695e13 | −0.422056 | ||||||||
\(966\) | −9.63521e13 | −3.56011 | ||||||||
\(967\) | −3.03489e12 | −0.111615 | −0.0558077 | − | 0.998442i | \(-0.517773\pi\) | ||||
−0.0558077 | + | 0.998442i | \(0.517773\pi\) | |||||||
\(968\) | 5.34054e12 | 0.195500 | ||||||||
\(969\) | −2.10354e13 | −0.766466 | ||||||||
\(970\) | 2.51660e13 | 0.912730 | ||||||||
\(971\) | −1.48960e13 | −0.537755 | −0.268877 | − | 0.963174i | \(-0.586653\pi\) | ||||
−0.268877 | + | 0.963174i | \(0.586653\pi\) | |||||||
\(972\) | −1.07873e13 | −0.387629 | ||||||||
\(973\) | −5.17362e13 | −1.85049 | ||||||||
\(974\) | −6.69155e13 | −2.38238 | ||||||||
\(975\) | −1.10966e13 | −0.393251 | ||||||||
\(976\) | 1.65253e13 | 0.582943 | ||||||||
\(977\) | −5.30931e12 | −0.186429 | −0.0932144 | − | 0.995646i | \(-0.529714\pi\) | ||||
−0.0932144 | + | 0.995646i | \(0.529714\pi\) | |||||||
\(978\) | −2.01798e13 | −0.705329 | ||||||||
\(979\) | 5.36792e13 | 1.86760 | ||||||||
\(980\) | −3.35530e13 | −1.16202 | ||||||||
\(981\) | 2.91457e12 | 0.100476 | ||||||||
\(982\) | 1.40055e13 | 0.480614 | ||||||||
\(983\) | −2.98890e13 | −1.02099 | −0.510495 | − | 0.859881i | \(-0.670538\pi\) | ||||
−0.510495 | + | 0.859881i | \(0.670538\pi\) | |||||||
\(984\) | 5.01534e12 | 0.170538 | ||||||||
\(985\) | 3.25784e13 | 1.10273 | ||||||||
\(986\) | −4.63513e13 | −1.56177 | ||||||||
\(987\) | 5.27351e13 | 1.76877 | ||||||||
\(988\) | 1.74951e13 | 0.584131 | ||||||||
\(989\) | −2.02297e13 | −0.672368 | ||||||||
\(990\) | −6.34716e12 | −0.210001 | ||||||||
\(991\) | 5.09698e13 | 1.67873 | 0.839367 | − | 0.543565i | \(-0.182926\pi\) | ||||
0.839367 | + | 0.543565i | \(0.182926\pi\) | |||||||
\(992\) | −6.82391e13 | −2.23733 | ||||||||
\(993\) | −1.60589e13 | −0.524135 | ||||||||
\(994\) | 1.99973e13 | 0.649729 | ||||||||
\(995\) | −1.40193e13 | −0.453442 | ||||||||
\(996\) | 7.70341e12 | 0.248037 | ||||||||
\(997\) | −1.83136e12 | −0.0587009 | −0.0293505 | − | 0.999569i | \(-0.509344\pi\) | ||||
−0.0293505 | + | 0.999569i | \(0.509344\pi\) | |||||||
\(998\) | 6.79913e13 | 2.16953 | ||||||||
\(999\) | −5.48779e12 | −0.174322 |
(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 | 37.10.a.a.1.12 | ✓ | 13 | |
3.2 | odd | 2 | 333.10.a.c.1.2 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.10.a.a.1.12 | ✓ | 13 | 1.1 | even | 1 | trivial | |
333.10.a.c.1.2 | 13 | 3.2 | odd | 2 |