Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,28,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 28, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 28);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 28 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(46.1855574838\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{711649}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 177912 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(422.296\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8192.00 | 0.707107 | ||||||||
\(3\) | −5.48964e6 | −1.98796 | −0.993979 | − | 0.109571i | \(-0.965052\pi\) | ||||
−0.993979 | + | 0.109571i | \(0.965052\pi\) | |||||||
\(4\) | 6.71089e7 | 0.500000 | ||||||||
\(5\) | −1.22070e9 | −0.447214 | ||||||||
\(6\) | −4.49712e10 | −1.40570 | ||||||||
\(7\) | −8.15752e10 | −0.318225 | −0.159113 | − | 0.987260i | \(-0.550863\pi\) | ||||
−0.159113 | + | 0.987260i | \(0.550863\pi\) | |||||||
\(8\) | 5.49756e11 | 0.353553 | ||||||||
\(9\) | 2.25106e13 | 2.95198 | ||||||||
\(10\) | −1.00000e13 | −0.316228 | ||||||||
\(11\) | 1.33950e13 | 0.116988 | 0.0584939 | − | 0.998288i | \(-0.481370\pi\) | ||||
0.0584939 | + | 0.998288i | \(0.481370\pi\) | |||||||
\(12\) | −3.68404e14 | −0.993979 | ||||||||
\(13\) | 5.64686e14 | 0.517096 | 0.258548 | − | 0.965998i | \(-0.416756\pi\) | ||||
0.258548 | + | 0.965998i | \(0.416756\pi\) | |||||||
\(14\) | −6.68264e14 | −0.225019 | ||||||||
\(15\) | 6.70123e15 | 0.889042 | ||||||||
\(16\) | 4.50360e15 | 0.250000 | ||||||||
\(17\) | −1.28911e16 | −0.315668 | −0.157834 | − | 0.987466i | \(-0.550451\pi\) | ||||
−0.157834 | + | 0.987466i | \(0.550451\pi\) | |||||||
\(18\) | 1.84407e17 | 2.08736 | ||||||||
\(19\) | 3.07151e17 | 1.67563 | 0.837816 | − | 0.545952i | \(-0.183832\pi\) | ||||
0.837816 | + | 0.545952i | \(0.183832\pi\) | |||||||
\(20\) | −8.19200e16 | −0.223607 | ||||||||
\(21\) | 4.47819e17 | 0.632618 | ||||||||
\(22\) | 1.09732e17 | 0.0827229 | ||||||||
\(23\) | −1.99871e18 | −0.826843 | −0.413422 | − | 0.910540i | \(-0.635666\pi\) | ||||
−0.413422 | + | 0.910540i | \(0.635666\pi\) | |||||||
\(24\) | −3.01796e18 | −0.702849 | ||||||||
\(25\) | 1.49012e18 | 0.200000 | ||||||||
\(26\) | 4.62590e18 | 0.365642 | ||||||||
\(27\) | −8.17133e19 | −3.88045 | ||||||||
\(28\) | −5.47442e18 | −0.159113 | ||||||||
\(29\) | −8.80094e19 | −1.59278 | −0.796390 | − | 0.604783i | \(-0.793260\pi\) | ||||
−0.796390 | + | 0.604783i | \(0.793260\pi\) | |||||||
\(30\) | 5.48964e19 | 0.628648 | ||||||||
\(31\) | 2.22760e20 | 1.63853 | 0.819265 | − | 0.573415i | \(-0.194382\pi\) | ||||
0.819265 | + | 0.573415i | \(0.194382\pi\) | |||||||
\(32\) | 3.68935e19 | 0.176777 | ||||||||
\(33\) | −7.35337e19 | −0.232567 | ||||||||
\(34\) | −1.05604e20 | −0.223211 | ||||||||
\(35\) | 9.95791e19 | 0.142315 | ||||||||
\(36\) | 1.51066e21 | 1.47599 | ||||||||
\(37\) | −1.61882e21 | −1.09264 | −0.546319 | − | 0.837577i | \(-0.683971\pi\) | ||||
−0.546319 | + | 0.837577i | \(0.683971\pi\) | |||||||
\(38\) | 2.51618e21 | 1.18485 | ||||||||
\(39\) | −3.09992e21 | −1.02797 | ||||||||
\(40\) | −6.71089e20 | −0.158114 | ||||||||
\(41\) | −9.68899e21 | −1.63567 | −0.817837 | − | 0.575450i | \(-0.804827\pi\) | ||||
−0.817837 | + | 0.575450i | \(0.804827\pi\) | |||||||
\(42\) | 3.66853e21 | 0.447329 | ||||||||
\(43\) | 9.33483e21 | 0.828481 | 0.414240 | − | 0.910167i | \(-0.364047\pi\) | ||||
0.414240 | + | 0.910167i | \(0.364047\pi\) | |||||||
\(44\) | 8.98922e20 | 0.0584939 | ||||||||
\(45\) | −2.74787e22 | −1.32016 | ||||||||
\(46\) | −1.63734e22 | −0.584667 | ||||||||
\(47\) | 1.20564e22 | 0.322031 | 0.161016 | − | 0.986952i | \(-0.448523\pi\) | ||||
0.161016 | + | 0.986952i | \(0.448523\pi\) | |||||||
\(48\) | −2.47232e22 | −0.496990 | ||||||||
\(49\) | −5.90579e22 | −0.898733 | ||||||||
\(50\) | 1.22070e22 | 0.141421 | ||||||||
\(51\) | 7.07676e22 | 0.627534 | ||||||||
\(52\) | 3.78954e22 | 0.258548 | ||||||||
\(53\) | −8.75697e21 | −0.0461987 | −0.0230993 | − | 0.999733i | \(-0.507353\pi\) | ||||
−0.0230993 | + | 0.999733i | \(0.507353\pi\) | |||||||
\(54\) | −6.69395e23 | −2.74389 | ||||||||
\(55\) | −1.63513e22 | −0.0523186 | ||||||||
\(56\) | −4.48464e22 | −0.112510 | ||||||||
\(57\) | −1.68615e24 | −3.33109 | ||||||||
\(58\) | −7.20973e23 | −1.12627 | ||||||||
\(59\) | 3.03895e23 | 0.376896 | 0.188448 | − | 0.982083i | \(-0.439654\pi\) | ||||
0.188448 | + | 0.982083i | \(0.439654\pi\) | |||||||
\(60\) | 4.49712e23 | 0.444521 | ||||||||
\(61\) | 1.15214e24 | 0.911070 | 0.455535 | − | 0.890218i | \(-0.349448\pi\) | ||||
0.455535 | + | 0.890218i | \(0.349448\pi\) | |||||||
\(62\) | 1.82485e24 | 1.15862 | ||||||||
\(63\) | −1.83631e24 | −0.939393 | ||||||||
\(64\) | 3.02231e23 | 0.125000 | ||||||||
\(65\) | −6.89313e23 | −0.231253 | ||||||||
\(66\) | −6.02388e23 | −0.164450 | ||||||||
\(67\) | −1.86933e24 | −0.416559 | −0.208280 | − | 0.978069i | \(-0.566786\pi\) | ||||
−0.208280 | + | 0.978069i | \(0.566786\pi\) | |||||||
\(68\) | −8.65108e23 | −0.157834 | ||||||||
\(69\) | 1.09722e25 | 1.64373 | ||||||||
\(70\) | 8.15752e23 | 0.100632 | ||||||||
\(71\) | −8.93880e24 | −0.910524 | −0.455262 | − | 0.890357i | \(-0.650454\pi\) | ||||
−0.455262 | + | 0.890357i | \(0.650454\pi\) | |||||||
\(72\) | 1.23753e25 | 1.04368 | ||||||||
\(73\) | −2.18673e25 | −1.53086 | −0.765432 | − | 0.643517i | \(-0.777475\pi\) | ||||
−0.765432 | + | 0.643517i | \(0.777475\pi\) | |||||||
\(74\) | −1.32614e25 | −0.772612 | ||||||||
\(75\) | −8.18021e24 | −0.397592 | ||||||||
\(76\) | 2.06126e25 | 0.837816 | ||||||||
\(77\) | −1.09270e24 | −0.0372285 | ||||||||
\(78\) | −2.53946e25 | −0.726882 | ||||||||
\(79\) | 1.05795e25 | 0.254975 | 0.127488 | − | 0.991840i | \(-0.459309\pi\) | ||||
0.127488 | + | 0.991840i | \(0.459309\pi\) | |||||||
\(80\) | −5.49756e24 | −0.111803 | ||||||||
\(81\) | 2.76920e26 | 4.76219 | ||||||||
\(82\) | −7.93722e25 | −1.15660 | ||||||||
\(83\) | 2.25868e25 | 0.279448 | 0.139724 | − | 0.990190i | \(-0.455378\pi\) | ||||
0.139724 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(84\) | 3.00526e25 | 0.316309 | ||||||||
\(85\) | 1.57362e25 | 0.141171 | ||||||||
\(86\) | 7.64710e25 | 0.585824 | ||||||||
\(87\) | 4.83140e26 | 3.16638 | ||||||||
\(88\) | 7.36397e24 | 0.0413615 | ||||||||
\(89\) | −1.78891e26 | −0.862626 | −0.431313 | − | 0.902202i | \(-0.641950\pi\) | ||||
−0.431313 | + | 0.902202i | \(0.641950\pi\) | |||||||
\(90\) | −2.25106e26 | −0.933497 | ||||||||
\(91\) | −4.60643e25 | −0.164553 | ||||||||
\(92\) | −1.34131e26 | −0.413422 | ||||||||
\(93\) | −1.22287e27 | −3.25733 | ||||||||
\(94\) | 9.87663e25 | 0.227710 | ||||||||
\(95\) | −3.74941e26 | −0.749366 | ||||||||
\(96\) | −2.02532e26 | −0.351425 | ||||||||
\(97\) | 8.87997e26 | 1.33966 | 0.669828 | − | 0.742517i | \(-0.266368\pi\) | ||||
0.669828 | + | 0.742517i | \(0.266368\pi\) | |||||||
\(98\) | −4.83802e26 | −0.635500 | ||||||||
\(99\) | 3.01529e26 | 0.345346 | ||||||||
\(100\) | 1.00000e26 | 0.100000 | ||||||||
\(101\) | 5.69733e26 | 0.498119 | 0.249059 | − | 0.968488i | \(-0.419879\pi\) | ||||
0.249059 | + | 0.968488i | \(0.419879\pi\) | |||||||
\(102\) | 5.79728e26 | 0.443733 | ||||||||
\(103\) | −1.77162e27 | −1.18869 | −0.594343 | − | 0.804212i | \(-0.702588\pi\) | ||||
−0.594343 | + | 0.804212i | \(0.702588\pi\) | |||||||
\(104\) | 3.10439e26 | 0.182821 | ||||||||
\(105\) | −5.46654e26 | −0.282915 | ||||||||
\(106\) | −7.17371e25 | −0.0326674 | ||||||||
\(107\) | −2.46061e27 | −0.987102 | −0.493551 | − | 0.869717i | \(-0.664301\pi\) | ||||
−0.493551 | + | 0.869717i | \(0.664301\pi\) | |||||||
\(108\) | −5.48369e27 | −1.94022 | ||||||||
\(109\) | 3.19335e27 | 0.997674 | 0.498837 | − | 0.866696i | \(-0.333761\pi\) | ||||
0.498837 | + | 0.866696i | \(0.333761\pi\) | |||||||
\(110\) | −1.33950e26 | −0.0369948 | ||||||||
\(111\) | 8.88677e27 | 2.17212 | ||||||||
\(112\) | −3.67382e26 | −0.0795563 | ||||||||
\(113\) | −7.75073e26 | −0.148862 | −0.0744310 | − | 0.997226i | \(-0.523714\pi\) | ||||
−0.0744310 | + | 0.997226i | \(0.523714\pi\) | |||||||
\(114\) | −1.38130e28 | −2.35543 | ||||||||
\(115\) | 2.43983e27 | 0.369776 | ||||||||
\(116\) | −5.90621e27 | −0.796390 | ||||||||
\(117\) | 1.27114e28 | 1.52646 | ||||||||
\(118\) | 2.48951e27 | 0.266506 | ||||||||
\(119\) | 1.05159e27 | 0.100453 | ||||||||
\(120\) | 3.68404e27 | 0.314324 | ||||||||
\(121\) | −1.29306e28 | −0.986314 | ||||||||
\(122\) | 9.43831e27 | 0.644224 | ||||||||
\(123\) | 5.31891e28 | 3.25165 | ||||||||
\(124\) | 1.49492e28 | 0.819265 | ||||||||
\(125\) | −1.81899e27 | −0.0894427 | ||||||||
\(126\) | −1.50430e28 | −0.664251 | ||||||||
\(127\) | 1.11798e28 | 0.443695 | 0.221848 | − | 0.975081i | \(-0.428791\pi\) | ||||
0.221848 | + | 0.975081i | \(0.428791\pi\) | |||||||
\(128\) | 2.47588e27 | 0.0883883 | ||||||||
\(129\) | −5.12449e28 | −1.64699 | ||||||||
\(130\) | −5.64686e27 | −0.163520 | ||||||||
\(131\) | 8.48344e27 | 0.221518 | 0.110759 | − | 0.993847i | \(-0.464672\pi\) | ||||
0.110759 | + | 0.993847i | \(0.464672\pi\) | |||||||
\(132\) | −4.93476e27 | −0.116283 | ||||||||
\(133\) | −2.50559e28 | −0.533228 | ||||||||
\(134\) | −1.53136e28 | −0.294552 | ||||||||
\(135\) | 9.97477e28 | 1.73539 | ||||||||
\(136\) | −7.08696e27 | −0.111605 | ||||||||
\(137\) | −8.14420e28 | −1.16177 | −0.580886 | − | 0.813985i | \(-0.697294\pi\) | ||||
−0.580886 | + | 0.813985i | \(0.697294\pi\) | |||||||
\(138\) | 8.98842e28 | 1.16229 | ||||||||
\(139\) | −4.14318e28 | −0.485997 | −0.242999 | − | 0.970027i | \(-0.578131\pi\) | ||||
−0.242999 | + | 0.970027i | \(0.578131\pi\) | |||||||
\(140\) | 6.68264e27 | 0.0711573 | ||||||||
\(141\) | −6.61855e28 | −0.640184 | ||||||||
\(142\) | −7.32267e28 | −0.643838 | ||||||||
\(143\) | 7.56395e27 | 0.0604940 | ||||||||
\(144\) | 1.01379e29 | 0.737994 | ||||||||
\(145\) | 1.07433e29 | 0.712313 | ||||||||
\(146\) | −1.79137e29 | −1.08248 | ||||||||
\(147\) | 3.24207e29 | 1.78664 | ||||||||
\(148\) | −1.08637e29 | −0.546319 | ||||||||
\(149\) | −2.60623e29 | −1.19674 | −0.598368 | − | 0.801221i | \(-0.704184\pi\) | ||||
−0.598368 | + | 0.801221i | \(0.704184\pi\) | |||||||
\(150\) | −6.70123e28 | −0.281140 | ||||||||
\(151\) | −2.46658e29 | −0.946034 | −0.473017 | − | 0.881053i | \(-0.656835\pi\) | ||||
−0.473017 | + | 0.881053i | \(0.656835\pi\) | |||||||
\(152\) | 1.68858e29 | 0.592426 | ||||||||
\(153\) | −2.90187e29 | −0.931843 | ||||||||
\(154\) | −8.95138e27 | −0.0263245 | ||||||||
\(155\) | −2.71924e29 | −0.732773 | ||||||||
\(156\) | −2.08032e29 | −0.513983 | ||||||||
\(157\) | −6.53188e29 | −1.48045 | −0.740223 | − | 0.672361i | \(-0.765280\pi\) | ||||
−0.740223 | + | 0.672361i | \(0.765280\pi\) | |||||||
\(158\) | 8.66671e28 | 0.180295 | ||||||||
\(159\) | 4.80726e28 | 0.0918410 | ||||||||
\(160\) | −4.50360e28 | −0.0790569 | ||||||||
\(161\) | 1.63045e29 | 0.263122 | ||||||||
\(162\) | 2.26853e30 | 3.36738 | ||||||||
\(163\) | −4.95480e29 | −0.676851 | −0.338426 | − | 0.940993i | \(-0.609894\pi\) | ||||
−0.338426 | + | 0.940993i | \(0.609894\pi\) | |||||||
\(164\) | −6.50217e29 | −0.817837 | ||||||||
\(165\) | 8.97628e28 | 0.104007 | ||||||||
\(166\) | 1.85031e29 | 0.197600 | ||||||||
\(167\) | −3.99121e29 | −0.393036 | −0.196518 | − | 0.980500i | \(-0.562963\pi\) | ||||
−0.196518 | + | 0.980500i | \(0.562963\pi\) | |||||||
\(168\) | 2.46191e29 | 0.223664 | ||||||||
\(169\) | −8.73663e29 | −0.732611 | ||||||||
\(170\) | 1.28911e29 | 0.0998228 | ||||||||
\(171\) | 6.91416e30 | 4.94643 | ||||||||
\(172\) | 6.26450e29 | 0.414240 | ||||||||
\(173\) | −1.45903e30 | −0.892160 | −0.446080 | − | 0.894993i | \(-0.647180\pi\) | ||||
−0.446080 | + | 0.894993i | \(0.647180\pi\) | |||||||
\(174\) | 3.95788e30 | 2.23897 | ||||||||
\(175\) | −1.21556e29 | −0.0636450 | ||||||||
\(176\) | 6.03256e28 | 0.0292470 | ||||||||
\(177\) | −1.66828e30 | −0.749254 | ||||||||
\(178\) | −1.46547e30 | −0.609969 | ||||||||
\(179\) | 3.95662e29 | 0.152689 | 0.0763446 | − | 0.997081i | \(-0.475675\pi\) | ||||
0.0763446 | + | 0.997081i | \(0.475675\pi\) | |||||||
\(180\) | −1.84407e30 | −0.660082 | ||||||||
\(181\) | −1.52183e30 | −0.505481 | −0.252740 | − | 0.967534i | \(-0.581332\pi\) | ||||
−0.252740 | + | 0.967534i | \(0.581332\pi\) | |||||||
\(182\) | −3.77359e29 | −0.116357 | ||||||||
\(183\) | −6.32483e30 | −1.81117 | ||||||||
\(184\) | −1.09880e30 | −0.292333 | ||||||||
\(185\) | 1.97610e30 | 0.488643 | ||||||||
\(186\) | −1.00178e31 | −2.30328 | ||||||||
\(187\) | −1.72676e29 | −0.0369293 | ||||||||
\(188\) | 8.09094e29 | 0.161016 | ||||||||
\(189\) | 6.66578e30 | 1.23486 | ||||||||
\(190\) | −3.07151e30 | −0.529882 | ||||||||
\(191\) | 2.06556e29 | 0.0331961 | 0.0165980 | − | 0.999862i | \(-0.494716\pi\) | ||||
0.0165980 | + | 0.999862i | \(0.494716\pi\) | |||||||
\(192\) | −1.65914e30 | −0.248495 | ||||||||
\(193\) | 8.12733e30 | 1.13481 | 0.567407 | − | 0.823438i | \(-0.307947\pi\) | ||||
0.567407 | + | 0.823438i | \(0.307947\pi\) | |||||||
\(194\) | 7.27447e30 | 0.947279 | ||||||||
\(195\) | 3.78409e30 | 0.459720 | ||||||||
\(196\) | −3.96331e30 | −0.449366 | ||||||||
\(197\) | −1.15879e31 | −1.22662 | −0.613311 | − | 0.789841i | \(-0.710163\pi\) | ||||
−0.613311 | + | 0.789841i | \(0.710163\pi\) | |||||||
\(198\) | 2.47012e30 | 0.244196 | ||||||||
\(199\) | −1.61914e31 | −1.49543 | −0.747717 | − | 0.664018i | \(-0.768850\pi\) | ||||
−0.747717 | + | 0.664018i | \(0.768850\pi\) | |||||||
\(200\) | 8.19200e29 | 0.0707107 | ||||||||
\(201\) | 1.02620e31 | 0.828103 | ||||||||
\(202\) | 4.66725e30 | 0.352223 | ||||||||
\(203\) | 7.17938e30 | 0.506863 | ||||||||
\(204\) | 4.74913e30 | 0.313767 | ||||||||
\(205\) | 1.18274e31 | 0.731495 | ||||||||
\(206\) | −1.45131e31 | −0.840528 | ||||||||
\(207\) | −4.49921e31 | −2.44082 | ||||||||
\(208\) | 2.54312e30 | 0.129274 | ||||||||
\(209\) | 4.11429e30 | 0.196029 | ||||||||
\(210\) | −4.47819e30 | −0.200051 | ||||||||
\(211\) | −8.13808e30 | −0.340964 | −0.170482 | − | 0.985361i | \(-0.554532\pi\) | ||||
−0.170482 | + | 0.985361i | \(0.554532\pi\) | |||||||
\(212\) | −5.87670e29 | −0.0230993 | ||||||||
\(213\) | 4.90708e31 | 1.81008 | ||||||||
\(214\) | −2.01573e31 | −0.697986 | ||||||||
\(215\) | −1.13951e31 | −0.370508 | ||||||||
\(216\) | −4.49224e31 | −1.37195 | ||||||||
\(217\) | −1.81717e31 | −0.521422 | ||||||||
\(218\) | 2.61599e31 | 0.705462 | ||||||||
\(219\) | 1.20044e32 | 3.04329 | ||||||||
\(220\) | −1.09732e30 | −0.0261593 | ||||||||
\(221\) | −7.27943e30 | −0.163231 | ||||||||
\(222\) | 7.28004e31 | 1.53592 | ||||||||
\(223\) | −4.12421e31 | −0.818890 | −0.409445 | − | 0.912335i | \(-0.634278\pi\) | ||||
−0.409445 | + | 0.912335i | \(0.634278\pi\) | |||||||
\(224\) | −3.00959e30 | −0.0562548 | ||||||||
\(225\) | 3.35434e31 | 0.590395 | ||||||||
\(226\) | −6.34940e30 | −0.105261 | ||||||||
\(227\) | 8.27912e31 | 1.29311 | 0.646555 | − | 0.762868i | \(-0.276209\pi\) | ||||
0.646555 | + | 0.762868i | \(0.276209\pi\) | |||||||
\(228\) | −1.13156e32 | −1.66554 | ||||||||
\(229\) | 9.00491e31 | 1.24940 | 0.624698 | − | 0.780866i | \(-0.285222\pi\) | ||||
0.624698 | + | 0.780866i | \(0.285222\pi\) | |||||||
\(230\) | 1.99871e31 | 0.261471 | ||||||||
\(231\) | 5.99852e30 | 0.0740087 | ||||||||
\(232\) | −4.83837e31 | −0.563133 | ||||||||
\(233\) | 3.39840e31 | 0.373224 | 0.186612 | − | 0.982434i | \(-0.440249\pi\) | ||||
0.186612 | + | 0.982434i | \(0.440249\pi\) | |||||||
\(234\) | 1.04132e32 | 1.07937 | ||||||||
\(235\) | −1.47173e31 | −0.144017 | ||||||||
\(236\) | 2.03941e31 | 0.188448 | ||||||||
\(237\) | −5.80775e31 | −0.506880 | ||||||||
\(238\) | 8.61467e30 | 0.0710313 | ||||||||
\(239\) | −1.37775e32 | −1.07349 | −0.536747 | − | 0.843743i | \(-0.680347\pi\) | ||||
−0.536747 | + | 0.843743i | \(0.680347\pi\) | |||||||
\(240\) | 3.01796e31 | 0.222260 | ||||||||
\(241\) | −8.67658e31 | −0.604114 | −0.302057 | − | 0.953290i | \(-0.597673\pi\) | ||||
−0.302057 | + | 0.953290i | \(0.597673\pi\) | |||||||
\(242\) | −1.05927e32 | −0.697429 | ||||||||
\(243\) | −8.97081e32 | −5.58659 | ||||||||
\(244\) | 7.73187e31 | 0.455535 | ||||||||
\(245\) | 7.20921e31 | 0.401926 | ||||||||
\(246\) | 4.35725e32 | 2.29926 | ||||||||
\(247\) | 1.73444e32 | 0.866464 | ||||||||
\(248\) | 1.22464e32 | 0.579308 | ||||||||
\(249\) | −1.23994e32 | −0.555531 | ||||||||
\(250\) | −1.49012e31 | −0.0632456 | ||||||||
\(251\) | 4.76708e32 | 1.91716 | 0.958578 | − | 0.284829i | \(-0.0919367\pi\) | ||||
0.958578 | + | 0.284829i | \(0.0919367\pi\) | |||||||
\(252\) | −1.23232e32 | −0.469697 | ||||||||
\(253\) | −2.67726e31 | −0.0967307 | ||||||||
\(254\) | 9.15852e31 | 0.313740 | ||||||||
\(255\) | −8.63862e31 | −0.280642 | ||||||||
\(256\) | 2.02824e31 | 0.0625000 | ||||||||
\(257\) | 3.36363e32 | 0.983357 | 0.491678 | − | 0.870777i | \(-0.336384\pi\) | ||||
0.491678 | + | 0.870777i | \(0.336384\pi\) | |||||||
\(258\) | −4.19798e32 | −1.16459 | ||||||||
\(259\) | 1.32056e32 | 0.347705 | ||||||||
\(260\) | −4.62590e31 | −0.115626 | ||||||||
\(261\) | −1.98114e33 | −4.70185 | ||||||||
\(262\) | 6.94964e31 | 0.156637 | ||||||||
\(263\) | −1.96857e32 | −0.421453 | −0.210726 | − | 0.977545i | \(-0.567583\pi\) | ||||
−0.210726 | + | 0.977545i | \(0.567583\pi\) | |||||||
\(264\) | −4.04256e31 | −0.0822248 | ||||||||
\(265\) | 1.06897e31 | 0.0206607 | ||||||||
\(266\) | −2.05258e32 | −0.377049 | ||||||||
\(267\) | 9.82046e32 | 1.71486 | ||||||||
\(268\) | −1.25449e32 | −0.208280 | ||||||||
\(269\) | 9.12489e32 | 1.44069 | 0.720347 | − | 0.693613i | \(-0.243982\pi\) | ||||
0.720347 | + | 0.693613i | \(0.243982\pi\) | |||||||
\(270\) | 8.17133e32 | 1.22711 | ||||||||
\(271\) | 3.57579e32 | 0.510841 | 0.255421 | − | 0.966830i | \(-0.417786\pi\) | ||||
0.255421 | + | 0.966830i | \(0.417786\pi\) | |||||||
\(272\) | −5.80564e31 | −0.0789169 | ||||||||
\(273\) | 2.52877e32 | 0.327125 | ||||||||
\(274\) | −6.67173e32 | −0.821496 | ||||||||
\(275\) | 1.99601e31 | 0.0233976 | ||||||||
\(276\) | 7.36331e32 | 0.821865 | ||||||||
\(277\) | −1.49389e33 | −1.58797 | −0.793986 | − | 0.607936i | \(-0.791998\pi\) | ||||
−0.793986 | + | 0.607936i | \(0.791998\pi\) | |||||||
\(278\) | −3.39409e32 | −0.343652 | ||||||||
\(279\) | 5.01446e33 | 4.83690 | ||||||||
\(280\) | 5.47442e31 | 0.0503158 | ||||||||
\(281\) | −6.43291e32 | −0.563472 | −0.281736 | − | 0.959492i | \(-0.590910\pi\) | ||||
−0.281736 | + | 0.959492i | \(0.590910\pi\) | |||||||
\(282\) | −5.42192e32 | −0.452679 | ||||||||
\(283\) | 4.79228e32 | 0.381439 | 0.190720 | − | 0.981645i | \(-0.438918\pi\) | ||||
0.190720 | + | 0.981645i | \(0.438918\pi\) | |||||||
\(284\) | −5.99873e32 | −0.455262 | ||||||||
\(285\) | 2.05829e33 | 1.48971 | ||||||||
\(286\) | 6.19639e31 | 0.0427757 | ||||||||
\(287\) | 7.90381e32 | 0.520512 | ||||||||
\(288\) | 8.30494e32 | 0.521841 | ||||||||
\(289\) | −1.50153e33 | −0.900354 | ||||||||
\(290\) | 8.80094e32 | 0.503682 | ||||||||
\(291\) | −4.87479e33 | −2.66318 | ||||||||
\(292\) | −1.46749e33 | −0.765432 | ||||||||
\(293\) | −3.27376e32 | −0.163055 | −0.0815275 | − | 0.996671i | \(-0.525980\pi\) | ||||
−0.0815275 | + | 0.996671i | \(0.525980\pi\) | |||||||
\(294\) | 2.65590e33 | 1.26335 | ||||||||
\(295\) | −3.70966e32 | −0.168553 | ||||||||
\(296\) | −8.89958e32 | −0.386306 | ||||||||
\(297\) | −1.09455e33 | −0.453965 | ||||||||
\(298\) | −2.13503e33 | −0.846221 | ||||||||
\(299\) | −1.12864e33 | −0.427558 | ||||||||
\(300\) | −5.48964e32 | −0.198796 | ||||||||
\(301\) | −7.61491e32 | −0.263643 | ||||||||
\(302\) | −2.02062e33 | −0.668947 | ||||||||
\(303\) | −3.12763e33 | −0.990239 | ||||||||
\(304\) | 1.38329e33 | 0.418908 | ||||||||
\(305\) | −1.40642e33 | −0.407443 | ||||||||
\(306\) | −2.37721e33 | −0.658913 | ||||||||
\(307\) | 8.73502e32 | 0.231684 | 0.115842 | − | 0.993268i | \(-0.463043\pi\) | ||||
0.115842 | + | 0.993268i | \(0.463043\pi\) | |||||||
\(308\) | −7.33297e31 | −0.0186142 | ||||||||
\(309\) | 9.72554e33 | 2.36306 | ||||||||
\(310\) | −2.22760e33 | −0.518149 | ||||||||
\(311\) | 3.78077e33 | 0.842005 | 0.421002 | − | 0.907059i | \(-0.361678\pi\) | ||||
0.421002 | + | 0.907059i | \(0.361678\pi\) | |||||||
\(312\) | −1.70420e33 | −0.363441 | ||||||||
\(313\) | −1.46656e33 | −0.299537 | −0.149769 | − | 0.988721i | \(-0.547853\pi\) | ||||
−0.149769 | + | 0.988721i | \(0.547853\pi\) | |||||||
\(314\) | −5.35091e33 | −1.04683 | ||||||||
\(315\) | 2.24158e33 | 0.420110 | ||||||||
\(316\) | 7.09976e32 | 0.127488 | ||||||||
\(317\) | −7.26388e31 | −0.0124988 | −0.00624940 | − | 0.999980i | \(-0.501989\pi\) | ||||
−0.00624940 | + | 0.999980i | \(0.501989\pi\) | |||||||
\(318\) | 3.93811e32 | 0.0649414 | ||||||||
\(319\) | −1.17888e33 | −0.186336 | ||||||||
\(320\) | −3.68935e32 | −0.0559017 | ||||||||
\(321\) | 1.35079e34 | 1.96232 | ||||||||
\(322\) | 1.33566e33 | 0.186056 | ||||||||
\(323\) | −3.95952e33 | −0.528943 | ||||||||
\(324\) | 1.85838e34 | 2.38110 | ||||||||
\(325\) | 8.41447e32 | 0.103419 | ||||||||
\(326\) | −4.05897e33 | −0.478606 | ||||||||
\(327\) | −1.75303e34 | −1.98333 | ||||||||
\(328\) | −5.32658e33 | −0.578298 | ||||||||
\(329\) | −9.83506e32 | −0.102478 | ||||||||
\(330\) | 7.35337e32 | 0.0735441 | ||||||||
\(331\) | 1.22753e34 | 1.17857 | 0.589284 | − | 0.807926i | \(-0.299410\pi\) | ||||
0.589284 | + | 0.807926i | \(0.299410\pi\) | |||||||
\(332\) | 1.51578e33 | 0.139724 | ||||||||
\(333\) | −3.64407e34 | −3.22544 | ||||||||
\(334\) | −3.26960e33 | −0.277918 | ||||||||
\(335\) | 2.28190e33 | 0.186291 | ||||||||
\(336\) | 2.01680e33 | 0.158155 | ||||||||
\(337\) | 3.74086e33 | 0.281817 | 0.140909 | − | 0.990023i | \(-0.454998\pi\) | ||||
0.140909 | + | 0.990023i | \(0.454998\pi\) | |||||||
\(338\) | −7.15705e33 | −0.518034 | ||||||||
\(339\) | 4.25487e33 | 0.295931 | ||||||||
\(340\) | 1.05604e33 | 0.0705854 | ||||||||
\(341\) | 2.98387e33 | 0.191688 | ||||||||
\(342\) | 5.66408e34 | 3.49765 | ||||||||
\(343\) | 1.01782e34 | 0.604225 | ||||||||
\(344\) | 5.13188e33 | 0.292912 | ||||||||
\(345\) | −1.33938e34 | −0.735098 | ||||||||
\(346\) | −1.19524e34 | −0.630852 | ||||||||
\(347\) | −5.08016e33 | −0.257887 | −0.128943 | − | 0.991652i | \(-0.541159\pi\) | ||||
−0.128943 | + | 0.991652i | \(0.541159\pi\) | |||||||
\(348\) | 3.24230e34 | 1.58319 | ||||||||
\(349\) | 3.72143e34 | 1.74810 | 0.874050 | − | 0.485835i | \(-0.161485\pi\) | ||||
0.874050 | + | 0.485835i | \(0.161485\pi\) | |||||||
\(350\) | −9.95791e32 | −0.0450038 | ||||||||
\(351\) | −4.61423e34 | −2.00657 | ||||||||
\(352\) | 4.94188e32 | 0.0206807 | ||||||||
\(353\) | 1.32758e34 | 0.534690 | 0.267345 | − | 0.963601i | \(-0.413854\pi\) | ||||
0.267345 | + | 0.963601i | \(0.413854\pi\) | |||||||
\(354\) | −1.36665e34 | −0.529803 | ||||||||
\(355\) | 1.09116e34 | 0.407199 | ||||||||
\(356\) | −1.20052e34 | −0.431313 | ||||||||
\(357\) | −5.77288e33 | −0.199697 | ||||||||
\(358\) | 3.24126e33 | 0.107968 | ||||||||
\(359\) | −4.06074e34 | −1.30266 | −0.651329 | − | 0.758795i | \(-0.725788\pi\) | ||||
−0.651329 | + | 0.758795i | \(0.725788\pi\) | |||||||
\(360\) | −1.51066e34 | −0.466749 | ||||||||
\(361\) | 6.07413e34 | 1.80774 | ||||||||
\(362\) | −1.24668e34 | −0.357429 | ||||||||
\(363\) | 7.09842e34 | 1.96075 | ||||||||
\(364\) | −3.09132e33 | −0.0822765 | ||||||||
\(365\) | 2.66935e34 | 0.684623 | ||||||||
\(366\) | −5.18130e34 | −1.28069 | ||||||||
\(367\) | 4.81487e33 | 0.114708 | 0.0573539 | − | 0.998354i | \(-0.481734\pi\) | ||||
0.0573539 | + | 0.998354i | \(0.481734\pi\) | |||||||
\(368\) | −9.00137e33 | −0.206711 | ||||||||
\(369\) | −2.18105e35 | −4.82847 | ||||||||
\(370\) | 1.61882e34 | 0.345523 | ||||||||
\(371\) | 7.14351e32 | 0.0147016 | ||||||||
\(372\) | −8.20657e34 | −1.62866 | ||||||||
\(373\) | −2.48819e34 | −0.476228 | −0.238114 | − | 0.971237i | \(-0.576529\pi\) | ||||
−0.238114 | + | 0.971237i | \(0.576529\pi\) | |||||||
\(374\) | −1.41456e33 | −0.0261129 | ||||||||
\(375\) | 9.98560e33 | 0.177808 | ||||||||
\(376\) | 6.62810e33 | 0.113855 | ||||||||
\(377\) | −4.96976e34 | −0.823621 | ||||||||
\(378\) | 5.46061e34 | 0.873175 | ||||||||
\(379\) | 2.13394e34 | 0.329270 | 0.164635 | − | 0.986355i | \(-0.447355\pi\) | ||||
0.164635 | + | 0.986355i | \(0.447355\pi\) | |||||||
\(380\) | −2.51618e34 | −0.374683 | ||||||||
\(381\) | −6.13733e34 | −0.882048 | ||||||||
\(382\) | 1.69210e33 | 0.0234732 | ||||||||
\(383\) | 9.26670e34 | 1.24091 | 0.620457 | − | 0.784241i | \(-0.286947\pi\) | ||||
0.620457 | + | 0.784241i | \(0.286947\pi\) | |||||||
\(384\) | −1.35917e34 | −0.175712 | ||||||||
\(385\) | 1.33386e33 | 0.0166491 | ||||||||
\(386\) | 6.65791e34 | 0.802434 | ||||||||
\(387\) | 2.10133e35 | 2.44566 | ||||||||
\(388\) | 5.95925e34 | 0.669828 | ||||||||
\(389\) | 2.66544e34 | 0.289368 | 0.144684 | − | 0.989478i | \(-0.453784\pi\) | ||||
0.144684 | + | 0.989478i | \(0.453784\pi\) | |||||||
\(390\) | 3.09992e34 | 0.325071 | ||||||||
\(391\) | 2.57656e34 | 0.261008 | ||||||||
\(392\) | −3.24674e34 | −0.317750 | ||||||||
\(393\) | −4.65711e34 | −0.440369 | ||||||||
\(394\) | −9.49281e34 | −0.867353 | ||||||||
\(395\) | −1.29144e34 | −0.114028 | ||||||||
\(396\) | 2.02353e34 | 0.172673 | ||||||||
\(397\) | 6.20560e34 | 0.511814 | 0.255907 | − | 0.966701i | \(-0.417626\pi\) | ||||
0.255907 | + | 0.966701i | \(0.417626\pi\) | |||||||
\(398\) | −1.32640e35 | −1.05743 | ||||||||
\(399\) | 1.37548e35 | 1.06004 | ||||||||
\(400\) | 6.71089e33 | 0.0500000 | ||||||||
\(401\) | −3.83625e34 | −0.276349 | −0.138174 | − | 0.990408i | \(-0.544123\pi\) | ||||
−0.138174 | + | 0.990408i | \(0.544123\pi\) | |||||||
\(402\) | 8.40661e34 | 0.585557 | ||||||||
\(403\) | 1.25789e35 | 0.847278 | ||||||||
\(404\) | 3.82341e34 | 0.249059 | ||||||||
\(405\) | −3.38037e35 | −2.12972 | ||||||||
\(406\) | 5.88135e34 | 0.358406 | ||||||||
\(407\) | −2.16841e34 | −0.127825 | ||||||||
\(408\) | 3.89049e34 | 0.221867 | ||||||||
\(409\) | 6.77841e33 | 0.0373993 | 0.0186996 | − | 0.999825i | \(-0.494047\pi\) | ||||
0.0186996 | + | 0.999825i | \(0.494047\pi\) | |||||||
\(410\) | 9.68899e34 | 0.517245 | ||||||||
\(411\) | 4.47087e35 | 2.30955 | ||||||||
\(412\) | −1.18891e35 | −0.594343 | ||||||||
\(413\) | −2.47903e34 | −0.119938 | ||||||||
\(414\) | −3.68575e35 | −1.72592 | ||||||||
\(415\) | −2.75718e34 | −0.124973 | ||||||||
\(416\) | 2.08332e34 | 0.0914106 | ||||||||
\(417\) | 2.27446e35 | 0.966142 | ||||||||
\(418\) | 3.37042e34 | 0.138613 | ||||||||
\(419\) | −1.94310e35 | −0.773760 | −0.386880 | − | 0.922130i | \(-0.626447\pi\) | ||||
−0.386880 | + | 0.922130i | \(0.626447\pi\) | |||||||
\(420\) | −3.66853e34 | −0.141458 | ||||||||
\(421\) | 1.96151e35 | 0.732457 | 0.366229 | − | 0.930525i | \(-0.380649\pi\) | ||||
0.366229 | + | 0.930525i | \(0.380649\pi\) | |||||||
\(422\) | −6.66671e34 | −0.241098 | ||||||||
\(423\) | 2.71397e35 | 0.950629 | ||||||||
\(424\) | −4.81419e33 | −0.0163337 | ||||||||
\(425\) | −1.92093e34 | −0.0631335 | ||||||||
\(426\) | 4.01988e35 | 1.27992 | ||||||||
\(427\) | −9.39859e34 | −0.289925 | ||||||||
\(428\) | −1.65129e35 | −0.493551 | ||||||||
\(429\) | −4.15234e34 | −0.120260 | ||||||||
\(430\) | −9.33483e34 | −0.261989 | ||||||||
\(431\) | −4.47018e33 | −0.0121585 | −0.00607927 | − | 0.999982i | \(-0.501935\pi\) | ||||
−0.00607927 | + | 0.999982i | \(0.501935\pi\) | |||||||
\(432\) | −3.68004e35 | −0.970112 | ||||||||
\(433\) | −3.75519e35 | −0.959501 | −0.479751 | − | 0.877405i | \(-0.659273\pi\) | ||||
−0.479751 | + | 0.877405i | \(0.659273\pi\) | |||||||
\(434\) | −1.48863e35 | −0.368701 | ||||||||
\(435\) | −5.89771e35 | −1.41605 | ||||||||
\(436\) | 2.14302e35 | 0.498837 | ||||||||
\(437\) | −6.13905e35 | −1.38549 | ||||||||
\(438\) | 9.83398e35 | 2.15193 | ||||||||
\(439\) | −2.32360e35 | −0.493050 | −0.246525 | − | 0.969136i | \(-0.579289\pi\) | ||||
−0.246525 | + | 0.969136i | \(0.579289\pi\) | |||||||
\(440\) | −8.98922e33 | −0.0184974 | ||||||||
\(441\) | −1.32943e36 | −2.65304 | ||||||||
\(442\) | −5.96331e34 | −0.115421 | ||||||||
\(443\) | −9.07441e35 | −1.70360 | −0.851801 | − | 0.523865i | \(-0.824490\pi\) | ||||
−0.851801 | + | 0.523865i | \(0.824490\pi\) | |||||||
\(444\) | 5.96381e35 | 1.08606 | ||||||||
\(445\) | 2.18372e35 | 0.385778 | ||||||||
\(446\) | −3.37855e35 | −0.579042 | ||||||||
\(447\) | 1.43073e36 | 2.37906 | ||||||||
\(448\) | −2.46546e34 | −0.0397781 | ||||||||
\(449\) | −7.86327e35 | −1.23106 | −0.615528 | − | 0.788115i | \(-0.711057\pi\) | ||||
−0.615528 | + | 0.788115i | \(0.711057\pi\) | |||||||
\(450\) | 2.74787e35 | 0.417473 | ||||||||
\(451\) | −1.29784e35 | −0.191354 | ||||||||
\(452\) | −5.20143e34 | −0.0744310 | ||||||||
\(453\) | 1.35407e36 | 1.88068 | ||||||||
\(454\) | 6.78226e35 | 0.914366 | ||||||||
\(455\) | 5.62309e34 | 0.0735904 | ||||||||
\(456\) | −9.26972e35 | −1.17772 | ||||||||
\(457\) | −7.49955e35 | −0.925053 | −0.462526 | − | 0.886606i | \(-0.653057\pi\) | ||||
−0.462526 | + | 0.886606i | \(0.653057\pi\) | |||||||
\(458\) | 7.37682e35 | 0.883457 | ||||||||
\(459\) | 1.05338e36 | 1.22493 | ||||||||
\(460\) | 1.63734e35 | 0.184888 | ||||||||
\(461\) | −1.56743e35 | −0.171880 | −0.0859399 | − | 0.996300i | \(-0.527389\pi\) | ||||
−0.0859399 | + | 0.996300i | \(0.527389\pi\) | |||||||
\(462\) | 4.91399e34 | 0.0523320 | ||||||||
\(463\) | −5.52219e35 | −0.571173 | −0.285587 | − | 0.958353i | \(-0.592188\pi\) | ||||
−0.285587 | + | 0.958353i | \(0.592188\pi\) | |||||||
\(464\) | −3.96359e35 | −0.398195 | ||||||||
\(465\) | 1.49277e36 | 1.45672 | ||||||||
\(466\) | 2.78397e35 | 0.263909 | ||||||||
\(467\) | −1.27404e36 | −1.17329 | −0.586643 | − | 0.809845i | \(-0.699551\pi\) | ||||
−0.586643 | + | 0.809845i | \(0.699551\pi\) | |||||||
\(468\) | 8.53048e35 | 0.763228 | ||||||||
\(469\) | 1.52491e35 | 0.132560 | ||||||||
\(470\) | −1.20564e35 | −0.101835 | ||||||||
\(471\) | 3.58577e36 | 2.94306 | ||||||||
\(472\) | 1.67068e35 | 0.133253 | ||||||||
\(473\) | 1.25040e35 | 0.0969222 | ||||||||
\(474\) | −4.75771e35 | −0.358419 | ||||||||
\(475\) | 4.57691e35 | 0.335127 | ||||||||
\(476\) | 7.05713e34 | 0.0502267 | ||||||||
\(477\) | −1.97125e35 | −0.136377 | ||||||||
\(478\) | −1.12866e36 | −0.759076 | ||||||||
\(479\) | −9.37975e35 | −0.613285 | −0.306642 | − | 0.951825i | \(-0.599206\pi\) | ||||
−0.306642 | + | 0.951825i | \(0.599206\pi\) | |||||||
\(480\) | 2.47232e35 | 0.157162 | ||||||||
\(481\) | −9.14127e35 | −0.564999 | ||||||||
\(482\) | −7.10786e35 | −0.427173 | ||||||||
\(483\) | −8.95058e35 | −0.523076 | ||||||||
\(484\) | −8.67756e35 | −0.493157 | ||||||||
\(485\) | −1.08398e36 | −0.599112 | ||||||||
\(486\) | −7.34888e36 | −3.95032 | ||||||||
\(487\) | 1.24632e35 | 0.0651610 | 0.0325805 | − | 0.999469i | \(-0.489627\pi\) | ||||
0.0325805 | + | 0.999469i | \(0.489627\pi\) | |||||||
\(488\) | 6.33395e35 | 0.322112 | ||||||||
\(489\) | 2.72001e36 | 1.34555 | ||||||||
\(490\) | 5.90579e35 | 0.284204 | ||||||||
\(491\) | 2.13166e36 | 0.997972 | 0.498986 | − | 0.866610i | \(-0.333706\pi\) | ||||
0.498986 | + | 0.866610i | \(0.333706\pi\) | |||||||
\(492\) | 3.56946e36 | 1.62583 | ||||||||
\(493\) | 1.13454e36 | 0.502789 | ||||||||
\(494\) | 1.42085e36 | 0.612682 | ||||||||
\(495\) | −3.68077e35 | −0.154443 | ||||||||
\(496\) | 1.00322e36 | 0.409633 | ||||||||
\(497\) | 7.29184e35 | 0.289752 | ||||||||
\(498\) | −1.01576e36 | −0.392820 | ||||||||
\(499\) | 1.17967e36 | 0.444020 | 0.222010 | − | 0.975044i | \(-0.428738\pi\) | ||||
0.222010 | + | 0.975044i | \(0.428738\pi\) | |||||||
\(500\) | −1.22070e35 | −0.0447214 | ||||||||
\(501\) | 2.19103e36 | 0.781338 | ||||||||
\(502\) | 3.90520e36 | 1.35563 | ||||||||
\(503\) | −4.40912e36 | −1.48999 | −0.744996 | − | 0.667069i | \(-0.767548\pi\) | ||||
−0.744996 | + | 0.667069i | \(0.767548\pi\) | |||||||
\(504\) | −1.00952e36 | −0.332126 | ||||||||
\(505\) | −6.95475e35 | −0.222765 | ||||||||
\(506\) | −2.19321e35 | −0.0683989 | ||||||||
\(507\) | 4.79610e36 | 1.45640 | ||||||||
\(508\) | 7.50266e35 | 0.221848 | ||||||||
\(509\) | −1.66203e36 | −0.478574 | −0.239287 | − | 0.970949i | \(-0.576914\pi\) | ||||
−0.239287 | + | 0.970949i | \(0.576914\pi\) | |||||||
\(510\) | −7.07676e35 | −0.198444 | ||||||||
\(511\) | 1.78383e36 | 0.487160 | ||||||||
\(512\) | 1.66153e35 | 0.0441942 | ||||||||
\(513\) | −2.50984e37 | −6.50221 | ||||||||
\(514\) | 2.75549e36 | 0.695338 | ||||||||
\(515\) | 2.16262e36 | 0.531596 | ||||||||
\(516\) | −3.43899e36 | −0.823493 | ||||||||
\(517\) | 1.61496e35 | 0.0376737 | ||||||||
\(518\) | 1.08180e36 | 0.245865 | ||||||||
\(519\) | 8.00957e36 | 1.77358 | ||||||||
\(520\) | −3.78954e35 | −0.0817601 | ||||||||
\(521\) | −1.69142e36 | −0.355583 | −0.177792 | − | 0.984068i | \(-0.556895\pi\) | ||||
−0.177792 | + | 0.984068i | \(0.556895\pi\) | |||||||
\(522\) | −1.62295e37 | −3.32471 | ||||||||
\(523\) | 4.63272e36 | 0.924832 | 0.462416 | − | 0.886663i | \(-0.346983\pi\) | ||||
0.462416 | + | 0.886663i | \(0.346983\pi\) | |||||||
\(524\) | 5.69314e35 | 0.110759 | ||||||||
\(525\) | 6.67302e35 | 0.126524 | ||||||||
\(526\) | −1.61265e36 | −0.298012 | ||||||||
\(527\) | −2.87163e36 | −0.517231 | ||||||||
\(528\) | −3.31166e35 | −0.0581417 | ||||||||
\(529\) | −1.84838e36 | −0.316330 | ||||||||
\(530\) | 8.75697e34 | 0.0146093 | ||||||||
\(531\) | 6.84086e36 | 1.11259 | ||||||||
\(532\) | −1.68147e36 | −0.266614 | ||||||||
\(533\) | −5.47124e36 | −0.845801 | ||||||||
\(534\) | 8.04492e36 | 1.21259 | ||||||||
\(535\) | 3.00368e36 | 0.441445 | ||||||||
\(536\) | −1.02768e36 | −0.147276 | ||||||||
\(537\) | −2.17204e36 | −0.303540 | ||||||||
\(538\) | 7.47511e36 | 1.01873 | ||||||||
\(539\) | −7.91079e35 | −0.105141 | ||||||||
\(540\) | 6.69395e36 | 0.867695 | ||||||||
\(541\) | 1.22619e37 | 1.55022 | 0.775112 | − | 0.631823i | \(-0.217693\pi\) | ||||
0.775112 | + | 0.631823i | \(0.217693\pi\) | |||||||
\(542\) | 2.92928e36 | 0.361219 | ||||||||
\(543\) | 8.35429e36 | 1.00487 | ||||||||
\(544\) | −4.75598e35 | −0.0558027 | ||||||||
\(545\) | −3.89813e36 | −0.446173 | ||||||||
\(546\) | 2.07157e36 | 0.231312 | ||||||||
\(547\) | 1.26741e37 | 1.38066 | 0.690330 | − | 0.723494i | \(-0.257465\pi\) | ||||
0.690330 | + | 0.723494i | \(0.257465\pi\) | |||||||
\(548\) | −5.46548e36 | −0.580886 | ||||||||
\(549\) | 2.59353e37 | 2.68946 | ||||||||
\(550\) | 1.63513e35 | 0.0165446 | ||||||||
\(551\) | −2.70322e37 | −2.66892 | ||||||||
\(552\) | 6.03202e36 | 0.581146 | ||||||||
\(553\) | −8.63023e35 | −0.0811396 | ||||||||
\(554\) | −1.22380e37 | −1.12287 | ||||||||
\(555\) | −1.08481e37 | −0.971401 | ||||||||
\(556\) | −2.78044e36 | −0.242999 | ||||||||
\(557\) | −5.14205e36 | −0.438623 | −0.219312 | − | 0.975655i | \(-0.570381\pi\) | ||||
−0.219312 | + | 0.975655i | \(0.570381\pi\) | |||||||
\(558\) | 4.10785e37 | 3.42021 | ||||||||
\(559\) | 5.27125e36 | 0.428404 | ||||||||
\(560\) | 4.48464e35 | 0.0355787 | ||||||||
\(561\) | 9.47931e35 | 0.0734139 | ||||||||
\(562\) | −5.26984e36 | −0.398435 | ||||||||
\(563\) | 1.08130e37 | 0.798147 | 0.399074 | − | 0.916919i | \(-0.369332\pi\) | ||||
0.399074 | + | 0.916919i | \(0.369332\pi\) | |||||||
\(564\) | −4.44164e36 | −0.320092 | ||||||||
\(565\) | 9.46134e35 | 0.0665731 | ||||||||
\(566\) | 3.92583e36 | 0.269718 | ||||||||
\(567\) | −2.25898e37 | −1.51545 | ||||||||
\(568\) | −4.91416e36 | −0.321919 | ||||||||
\(569\) | −1.71706e37 | −1.09843 | −0.549213 | − | 0.835682i | \(-0.685073\pi\) | ||||
−0.549213 | + | 0.835682i | \(0.685073\pi\) | |||||||
\(570\) | 1.68615e37 | 1.05338 | ||||||||
\(571\) | −2.73444e37 | −1.66833 | −0.834163 | − | 0.551518i | \(-0.814049\pi\) | ||||
−0.834163 | + | 0.551518i | \(0.814049\pi\) | |||||||
\(572\) | 5.07608e35 | 0.0302470 | ||||||||
\(573\) | −1.13392e36 | −0.0659924 | ||||||||
\(574\) | 6.47480e36 | 0.368058 | ||||||||
\(575\) | −2.97831e36 | −0.165369 | ||||||||
\(576\) | 6.80341e36 | 0.368997 | ||||||||
\(577\) | −3.20240e36 | −0.169669 | −0.0848345 | − | 0.996395i | \(-0.527036\pi\) | ||||
−0.0848345 | + | 0.996395i | \(0.527036\pi\) | |||||||
\(578\) | −1.23005e37 | −0.636646 | ||||||||
\(579\) | −4.46162e37 | −2.25596 | ||||||||
\(580\) | 7.20973e36 | 0.356157 | ||||||||
\(581\) | −1.84253e36 | −0.0889275 | ||||||||
\(582\) | −3.99343e37 | −1.88315 | ||||||||
\(583\) | −1.17299e35 | −0.00540469 | ||||||||
\(584\) | −1.20217e37 | −0.541242 | ||||||||
\(585\) | −1.55169e37 | −0.682652 | ||||||||
\(586\) | −2.68186e36 | −0.115297 | ||||||||
\(587\) | −5.30209e36 | −0.222758 | −0.111379 | − | 0.993778i | \(-0.535527\pi\) | ||||
−0.111379 | + | 0.993778i | \(0.535527\pi\) | |||||||
\(588\) | 2.17571e37 | 0.893321 | ||||||||
\(589\) | 6.84211e37 | 2.74558 | ||||||||
\(590\) | −3.03895e36 | −0.119185 | ||||||||
\(591\) | 6.36135e37 | 2.43847 | ||||||||
\(592\) | −7.29054e36 | −0.273160 | ||||||||
\(593\) | −1.26381e37 | −0.462855 | −0.231428 | − | 0.972852i | \(-0.574340\pi\) | ||||
−0.231428 | + | 0.972852i | \(0.574340\pi\) | |||||||
\(594\) | −8.96654e36 | −0.321002 | ||||||||
\(595\) | −1.28369e36 | −0.0449241 | ||||||||
\(596\) | −1.74901e37 | −0.598368 | ||||||||
\(597\) | 8.88849e37 | 2.97286 | ||||||||
\(598\) | −9.24583e36 | −0.302329 | ||||||||
\(599\) | −2.17161e37 | −0.694255 | −0.347128 | − | 0.937818i | \(-0.612843\pi\) | ||||
−0.347128 | + | 0.937818i | \(0.612843\pi\) | |||||||
\(600\) | −4.49712e36 | −0.140570 | ||||||||
\(601\) | −2.82821e37 | −0.864382 | −0.432191 | − | 0.901782i | \(-0.642259\pi\) | ||||
−0.432191 | + | 0.901782i | \(0.642259\pi\) | |||||||
\(602\) | −6.23813e36 | −0.186424 | ||||||||
\(603\) | −4.20798e37 | −1.22967 | ||||||||
\(604\) | −1.65529e37 | −0.473017 | ||||||||
\(605\) | 1.57844e37 | 0.441093 | ||||||||
\(606\) | −2.56215e37 | −0.700204 | ||||||||
\(607\) | 4.82470e37 | 1.28951 | 0.644753 | − | 0.764391i | \(-0.276960\pi\) | ||||
0.644753 | + | 0.764391i | \(0.276960\pi\) | |||||||
\(608\) | 1.13319e37 | 0.296213 | ||||||||
\(609\) | −3.94122e37 | −1.00762 | ||||||||
\(610\) | −1.15214e37 | −0.288106 | ||||||||
\(611\) | 6.80810e36 | 0.166521 | ||||||||
\(612\) | −1.94741e37 | −0.465922 | ||||||||
\(613\) | −4.26300e37 | −0.997698 | −0.498849 | − | 0.866689i | \(-0.666244\pi\) | ||||
−0.498849 | + | 0.866689i | \(0.666244\pi\) | |||||||
\(614\) | 7.15573e36 | 0.163825 | ||||||||
\(615\) | −6.49281e37 | −1.45418 | ||||||||
\(616\) | −6.00717e35 | −0.0131623 | ||||||||
\(617\) | 7.03658e37 | 1.50838 | 0.754192 | − | 0.656655i | \(-0.228029\pi\) | ||||
0.754192 | + | 0.656655i | \(0.228029\pi\) | |||||||
\(618\) | 7.96716e37 | 1.67093 | ||||||||
\(619\) | −6.05562e37 | −1.24261 | −0.621305 | − | 0.783569i | \(-0.713397\pi\) | ||||
−0.621305 | + | 0.783569i | \(0.713397\pi\) | |||||||
\(620\) | −1.82485e37 | −0.366387 | ||||||||
\(621\) | 1.63321e38 | 3.20852 | ||||||||
\(622\) | 3.09720e37 | 0.595387 | ||||||||
\(623\) | 1.45930e37 | 0.274509 | ||||||||
\(624\) | −1.39608e37 | −0.256991 | ||||||||
\(625\) | 2.22045e36 | 0.0400000 | ||||||||
\(626\) | −1.20140e37 | −0.211805 | ||||||||
\(627\) | −2.25860e37 | −0.389697 | ||||||||
\(628\) | −4.38347e37 | −0.740223 | ||||||||
\(629\) | 2.08684e37 | 0.344910 | ||||||||
\(630\) | 1.83631e37 | 0.297062 | ||||||||
\(631\) | 9.89033e37 | 1.56608 | 0.783041 | − | 0.621970i | \(-0.213668\pi\) | ||||
0.783041 | + | 0.621970i | \(0.213668\pi\) | |||||||
\(632\) | 5.81613e36 | 0.0901474 | ||||||||
\(633\) | 4.46751e37 | 0.677822 | ||||||||
\(634\) | −5.95057e35 | −0.00883799 | ||||||||
\(635\) | −1.36473e37 | −0.198427 | ||||||||
\(636\) | 3.22610e36 | 0.0459205 | ||||||||
\(637\) | −3.33491e37 | −0.464731 | ||||||||
\(638\) | −9.65742e36 | −0.131759 | ||||||||
\(639\) | −2.01218e38 | −2.68785 | ||||||||
\(640\) | −3.02231e36 | −0.0395285 | ||||||||
\(641\) | 5.95420e37 | 0.762500 | 0.381250 | − | 0.924472i | \(-0.375494\pi\) | ||||
0.381250 | + | 0.924472i | \(0.375494\pi\) | |||||||
\(642\) | 1.10657e38 | 1.38757 | ||||||||
\(643\) | 2.01207e36 | 0.0247056 | 0.0123528 | − | 0.999924i | \(-0.496068\pi\) | ||||
0.0123528 | + | 0.999924i | \(0.496068\pi\) | |||||||
\(644\) | 1.09418e37 | 0.131561 | ||||||||
\(645\) | 6.25548e37 | 0.736554 | ||||||||
\(646\) | −3.24364e37 | −0.374019 | ||||||||
\(647\) | 3.99414e37 | 0.451040 | 0.225520 | − | 0.974239i | \(-0.427592\pi\) | ||||
0.225520 | + | 0.974239i | \(0.427592\pi\) | |||||||
\(648\) | 1.52238e38 | 1.68369 | ||||||||
\(649\) | 4.07067e36 | 0.0440923 | ||||||||
\(650\) | 6.89313e36 | 0.0731285 | ||||||||
\(651\) | 9.97561e37 | 1.03656 | ||||||||
\(652\) | −3.32511e37 | −0.338426 | ||||||||
\(653\) | 1.78987e37 | 0.178440 | 0.0892201 | − | 0.996012i | \(-0.471563\pi\) | ||||
0.0892201 | + | 0.996012i | \(0.471563\pi\) | |||||||
\(654\) | −1.43609e38 | −1.40243 | ||||||||
\(655\) | −1.03558e37 | −0.0990660 | ||||||||
\(656\) | −4.36353e37 | −0.408918 | ||||||||
\(657\) | −4.92246e38 | −4.51908 | ||||||||
\(658\) | −8.05688e36 | −0.0724632 | ||||||||
\(659\) | −5.06340e36 | −0.0446159 | −0.0223079 | − | 0.999751i | \(-0.507101\pi\) | ||||
−0.0223079 | + | 0.999751i | \(0.507101\pi\) | |||||||
\(660\) | 6.02388e36 | 0.0520036 | ||||||||
\(661\) | −2.02410e38 | −1.71203 | −0.856016 | − | 0.516949i | \(-0.827068\pi\) | ||||
−0.856016 | + | 0.516949i | \(0.827068\pi\) | |||||||
\(662\) | 1.00559e38 | 0.833373 | ||||||||
\(663\) | 3.99615e37 | 0.324495 | ||||||||
\(664\) | 1.24173e37 | 0.0987999 | ||||||||
\(665\) | 3.05858e37 | 0.238467 | ||||||||
\(666\) | −2.98522e38 | −2.28073 | ||||||||
\(667\) | 1.75905e38 | 1.31698 | ||||||||
\(668\) | −2.67845e37 | −0.196518 | ||||||||
\(669\) | 2.26405e38 | 1.62792 | ||||||||
\(670\) | 1.86933e37 | 0.131728 | ||||||||
\(671\) | 1.54329e37 | 0.106584 | ||||||||
\(672\) | 1.65216e37 | 0.111832 | ||||||||
\(673\) | 7.53924e36 | 0.0500178 | 0.0250089 | − | 0.999687i | \(-0.492039\pi\) | ||||
0.0250089 | + | 0.999687i | \(0.492039\pi\) | |||||||
\(674\) | 3.06451e37 | 0.199275 | ||||||||
\(675\) | −1.21762e38 | −0.776090 | ||||||||
\(676\) | −5.86306e37 | −0.366306 | ||||||||
\(677\) | 1.83489e38 | 1.12373 | 0.561866 | − | 0.827228i | \(-0.310084\pi\) | ||||
0.561866 | + | 0.827228i | \(0.310084\pi\) | |||||||
\(678\) | 3.48559e37 | 0.209255 | ||||||||
\(679\) | −7.24385e37 | −0.426312 | ||||||||
\(680\) | 8.65108e36 | 0.0499114 | ||||||||
\(681\) | −4.54494e38 | −2.57065 | ||||||||
\(682\) | 2.44438e37 | 0.135544 | ||||||||
\(683\) | 2.34491e38 | 1.27481 | 0.637407 | − | 0.770527i | \(-0.280007\pi\) | ||||
0.637407 | + | 0.770527i | \(0.280007\pi\) | |||||||
\(684\) | 4.64001e38 | 2.47321 | ||||||||
\(685\) | 9.94165e37 | 0.519560 | ||||||||
\(686\) | 8.33794e37 | 0.427251 | ||||||||
\(687\) | −4.94337e38 | −2.48375 | ||||||||
\(688\) | 4.20404e37 | 0.207120 | ||||||||
\(689\) | −4.94493e36 | −0.0238892 | ||||||||
\(690\) | −1.09722e38 | −0.519793 | ||||||||
\(691\) | 6.34902e37 | 0.294953 | 0.147477 | − | 0.989066i | \(-0.452885\pi\) | ||||
0.147477 | + | 0.989066i | \(0.452885\pi\) | |||||||
\(692\) | −9.79141e37 | −0.446080 | ||||||||
\(693\) | −2.45973e37 | −0.109898 | ||||||||
\(694\) | −4.16166e37 | −0.182354 | ||||||||
\(695\) | 5.05759e37 | 0.217345 | ||||||||
\(696\) | 2.65609e38 | 1.11948 | ||||||||
\(697\) | 1.24902e38 | 0.516329 | ||||||||
\(698\) | 3.04859e38 | 1.23609 | ||||||||
\(699\) | −1.86560e38 | −0.741953 | ||||||||
\(700\) | −8.15752e36 | −0.0318225 | ||||||||
\(701\) | 2.26958e38 | 0.868465 | 0.434233 | − | 0.900801i | \(-0.357020\pi\) | ||||
0.434233 | + | 0.900801i | \(0.357020\pi\) | |||||||
\(702\) | −3.77998e38 | −1.41886 | ||||||||
\(703\) | −4.97224e38 | −1.83086 | ||||||||
\(704\) | 4.04838e36 | 0.0146235 | ||||||||
\(705\) | 8.07929e37 | 0.286299 | ||||||||
\(706\) | 1.08755e38 | 0.378083 | ||||||||
\(707\) | −4.64761e37 | −0.158514 | ||||||||
\(708\) | −1.11956e38 | −0.374627 | ||||||||
\(709\) | −4.92739e37 | −0.161768 | −0.0808840 | − | 0.996724i | \(-0.525774\pi\) | ||||
−0.0808840 | + | 0.996724i | \(0.525774\pi\) | |||||||
\(710\) | 8.93880e37 | 0.287933 | ||||||||
\(711\) | 2.38150e38 | 0.752682 | ||||||||
\(712\) | −9.83462e37 | −0.304984 | ||||||||
\(713\) | −4.45232e38 | −1.35481 | ||||||||
\(714\) | −4.72914e37 | −0.141207 | ||||||||
\(715\) | −9.23334e36 | −0.0270537 | ||||||||
\(716\) | 2.65524e37 | 0.0763446 | ||||||||
\(717\) | 7.56338e38 | 2.13406 | ||||||||
\(718\) | −3.32656e38 | −0.921118 | ||||||||
\(719\) | −1.73047e38 | −0.470246 | −0.235123 | − | 0.971966i | \(-0.575549\pi\) | ||||
−0.235123 | + | 0.971966i | \(0.575549\pi\) | |||||||
\(720\) | −1.23753e38 | −0.330041 | ||||||||
\(721\) | 1.44520e38 | 0.378270 | ||||||||
\(722\) | 4.97593e38 | 1.27827 | ||||||||
\(723\) | 4.76314e38 | 1.20095 | ||||||||
\(724\) | −1.02128e38 | −0.252740 | ||||||||
\(725\) | −1.31144e38 | −0.318556 | ||||||||
\(726\) | 5.81503e38 | 1.38646 | ||||||||
\(727\) | 7.52465e37 | 0.176105 | 0.0880525 | − | 0.996116i | \(-0.471936\pi\) | ||||
0.0880525 | + | 0.996116i | \(0.471936\pi\) | |||||||
\(728\) | −2.53241e37 | −0.0581783 | ||||||||
\(729\) | 2.81297e39 | 6.34371 | ||||||||
\(730\) | 2.18673e38 | 0.484102 | ||||||||
\(731\) | −1.20336e38 | −0.261525 | ||||||||
\(732\) | −4.24452e38 | −0.905584 | ||||||||
\(733\) | −5.84393e37 | −0.122406 | −0.0612028 | − | 0.998125i | \(-0.519494\pi\) | ||||
−0.0612028 | + | 0.998125i | \(0.519494\pi\) | |||||||
\(734\) | 3.94434e37 | 0.0811106 | ||||||||
\(735\) | −3.95760e38 | −0.799011 | ||||||||
\(736\) | −7.37393e37 | −0.146167 | ||||||||
\(737\) | −2.50397e37 | −0.0487324 | ||||||||
\(738\) | −1.78672e39 | −3.41424 | ||||||||
\(739\) | −2.75465e38 | −0.516851 | −0.258426 | − | 0.966031i | \(-0.583204\pi\) | ||||
−0.258426 | + | 0.966031i | \(0.583204\pi\) | |||||||
\(740\) | 1.32614e38 | 0.244321 | ||||||||
\(741\) | −9.52145e38 | −1.72249 | ||||||||
\(742\) | 5.85197e36 | 0.0103956 | ||||||||
\(743\) | 6.91625e38 | 1.20648 | 0.603242 | − | 0.797558i | \(-0.293875\pi\) | ||||
0.603242 | + | 0.797558i | \(0.293875\pi\) | |||||||
\(744\) | −6.72282e38 | −1.15164 | ||||||||
\(745\) | 3.18144e38 | 0.535197 | ||||||||
\(746\) | −2.03833e38 | −0.336744 | ||||||||
\(747\) | 5.08443e38 | 0.824925 | ||||||||
\(748\) | −1.15881e37 | −0.0184646 | ||||||||
\(749\) | 2.00725e38 | 0.314121 | ||||||||
\(750\) | 8.18021e37 | 0.125730 | ||||||||
\(751\) | −9.44712e38 | −1.42613 | −0.713067 | − | 0.701096i | \(-0.752694\pi\) | ||||
−0.713067 | + | 0.701096i | \(0.752694\pi\) | |||||||
\(752\) | 5.42974e37 | 0.0805078 | ||||||||
\(753\) | −2.61696e39 | −3.81123 | ||||||||
\(754\) | −4.07123e38 | −0.582388 | ||||||||
\(755\) | 3.01096e38 | 0.423079 | ||||||||
\(756\) | 4.47333e38 | 0.617428 | ||||||||
\(757\) | −1.05837e39 | −1.43497 | −0.717484 | − | 0.696575i | \(-0.754706\pi\) | ||||
−0.717484 | + | 0.696575i | \(0.754706\pi\) | |||||||
\(758\) | 1.74812e38 | 0.232829 | ||||||||
\(759\) | 1.46972e38 | 0.192296 | ||||||||
\(760\) | −2.06126e38 | −0.264941 | ||||||||
\(761\) | 6.48621e38 | 0.819026 | 0.409513 | − | 0.912304i | \(-0.365699\pi\) | ||||
0.409513 | + | 0.912304i | \(0.365699\pi\) | |||||||
\(762\) | −5.02770e38 | −0.623702 | ||||||||
\(763\) | −2.60498e38 | −0.317485 | ||||||||
\(764\) | 1.38617e37 | 0.0165980 | ||||||||
\(765\) | 3.54232e38 | 0.416733 | ||||||||
\(766\) | 7.59128e38 | 0.877458 | ||||||||
\(767\) | 1.71605e38 | 0.194892 | ||||||||
\(768\) | −1.11343e38 | −0.124247 | ||||||||
\(769\) | −5.73159e38 | −0.628449 | −0.314224 | − | 0.949349i | \(-0.601744\pi\) | ||||
−0.314224 | + | 0.949349i | \(0.601744\pi\) | |||||||
\(770\) | 1.09270e37 | 0.0117727 | ||||||||
\(771\) | −1.84651e39 | −1.95487 | ||||||||
\(772\) | 5.45416e38 | 0.567407 | ||||||||
\(773\) | −7.89580e38 | −0.807185 | −0.403592 | − | 0.914939i | \(-0.632239\pi\) | ||||
−0.403592 | + | 0.914939i | \(0.632239\pi\) | |||||||
\(774\) | 1.72141e39 | 1.72934 | ||||||||
\(775\) | 3.31938e38 | 0.327706 | ||||||||
\(776\) | 4.88181e38 | 0.473640 | ||||||||
\(777\) | −7.24940e38 | −0.691223 | ||||||||
\(778\) | 2.18353e38 | 0.204614 | ||||||||
\(779\) | −2.97599e39 | −2.74079 | ||||||||
\(780\) | 2.53946e38 | 0.229860 | ||||||||
\(781\) | −1.19735e38 | −0.106520 | ||||||||
\(782\) | 2.11071e38 | 0.184560 | ||||||||
\(783\) | 7.19154e39 | 6.18070 | ||||||||
\(784\) | −2.65973e38 | −0.224683 | ||||||||
\(785\) | 7.97348e38 | 0.662076 | ||||||||
\(786\) | −3.81510e38 | −0.311388 | ||||||||
\(787\) | 1.73852e39 | 1.39483 | 0.697414 | − | 0.716668i | \(-0.254334\pi\) | ||||
0.697414 | + | 0.716668i | \(0.254334\pi\) | |||||||
\(788\) | −7.77651e38 | −0.613311 | ||||||||
\(789\) | 1.08068e39 | 0.837830 | ||||||||
\(790\) | −1.05795e38 | −0.0806303 | ||||||||
\(791\) | 6.32267e37 | 0.0473716 | ||||||||
\(792\) | 1.65767e38 | 0.122098 | ||||||||
\(793\) | 6.50596e38 | 0.471111 | ||||||||
\(794\) | 5.08363e38 | 0.361907 | ||||||||
\(795\) | −5.86824e37 | −0.0410726 | ||||||||
\(796\) | −1.08658e39 | −0.747717 | ||||||||
\(797\) | 1.88301e39 | 1.27399 | 0.636994 | − | 0.770869i | \(-0.280178\pi\) | ||||
0.636994 | + | 0.770869i | \(0.280178\pi\) | |||||||
\(798\) | 1.12679e39 | 0.749559 | ||||||||
\(799\) | −1.55421e38 | −0.101655 | ||||||||
\(800\) | 5.49756e37 | 0.0353553 | ||||||||
\(801\) | −4.02693e39 | −2.54645 | ||||||||
\(802\) | −3.14265e38 | −0.195408 | ||||||||
\(803\) | −2.92912e38 | −0.179093 | ||||||||
\(804\) | 6.88669e38 | 0.414051 | ||||||||
\(805\) | −1.99029e38 | −0.117672 | ||||||||
\(806\) | 1.03047e39 | 0.599116 | ||||||||
\(807\) | −5.00924e39 | −2.86404 | ||||||||
\(808\) | 3.13214e38 | 0.176111 | ||||||||
\(809\) | −1.60495e38 | −0.0887474 | −0.0443737 | − | 0.999015i | \(-0.514129\pi\) | ||||
−0.0443737 | + | 0.999015i | \(0.514129\pi\) | |||||||
\(810\) | −2.76920e39 | −1.50594 | ||||||||
\(811\) | 2.12672e39 | 1.13744 | 0.568721 | − | 0.822531i | \(-0.307439\pi\) | ||||
0.568721 | + | 0.822531i | \(0.307439\pi\) | |||||||
\(812\) | 4.81800e38 | 0.253431 | ||||||||
\(813\) | −1.96298e39 | −1.01553 | ||||||||
\(814\) | −1.77636e38 | −0.0903862 | ||||||||
\(815\) | 6.04834e38 | 0.302697 | ||||||||
\(816\) | 3.18709e38 | 0.156883 | ||||||||
\(817\) | 2.86721e39 | 1.38823 | ||||||||
\(818\) | 5.55287e37 | 0.0264453 | ||||||||
\(819\) | −1.03694e39 | −0.485757 | ||||||||
\(820\) | 7.93722e38 | 0.365748 | ||||||||
\(821\) | −2.13403e39 | −0.967317 | −0.483658 | − | 0.875257i | \(-0.660692\pi\) | ||||
−0.483658 | + | 0.875257i | \(0.660692\pi\) | |||||||
\(822\) | 3.66254e39 | 1.63310 | ||||||||
\(823\) | 1.46819e39 | 0.643997 | 0.321998 | − | 0.946740i | \(-0.395645\pi\) | ||||
0.321998 | + | 0.946740i | \(0.395645\pi\) | |||||||
\(824\) | −9.73956e38 | −0.420264 | ||||||||
\(825\) | −1.09574e38 | −0.0465134 | ||||||||
\(826\) | −2.03082e38 | −0.0848089 | ||||||||
\(827\) | 1.74523e39 | 0.717016 | 0.358508 | − | 0.933527i | \(-0.383286\pi\) | ||||
0.358508 | + | 0.933527i | \(0.383286\pi\) | |||||||
\(828\) | −3.01937e39 | −1.22041 | ||||||||
\(829\) | −1.03362e39 | −0.411031 | −0.205515 | − | 0.978654i | \(-0.565887\pi\) | ||||
−0.205515 | + | 0.978654i | \(0.565887\pi\) | |||||||
\(830\) | −2.25868e38 | −0.0883693 | ||||||||
\(831\) | 8.20094e39 | 3.15682 | ||||||||
\(832\) | 1.70666e38 | 0.0646370 | ||||||||
\(833\) | 7.61321e38 | 0.283701 | ||||||||
\(834\) | 1.86323e39 | 0.683165 | ||||||||
\(835\) | 4.87208e38 | 0.175771 | ||||||||
\(836\) | 2.76105e38 | 0.0980144 | ||||||||
\(837\) | −1.82025e40 | −6.35823 | ||||||||
\(838\) | −1.59179e39 | −0.547131 | ||||||||
\(839\) | 1.58461e39 | 0.535966 | 0.267983 | − | 0.963424i | \(-0.413643\pi\) | ||||
0.267983 | + | 0.963424i | \(0.413643\pi\) | |||||||
\(840\) | −3.00526e38 | −0.100026 | ||||||||
\(841\) | 4.69252e39 | 1.53695 | ||||||||
\(842\) | 1.60687e39 | 0.517926 | ||||||||
\(843\) | 3.53144e39 | 1.12016 | ||||||||
\(844\) | −5.46137e38 | −0.170482 | ||||||||
\(845\) | 1.06648e39 | 0.327634 | ||||||||
\(846\) | 2.22329e39 | 0.672196 | ||||||||
\(847\) | 1.05481e39 | 0.313870 | ||||||||
\(848\) | −3.94379e37 | −0.0115497 | ||||||||
\(849\) | −2.63079e39 | −0.758285 | ||||||||
\(850\) | −1.57362e38 | −0.0446421 | ||||||||
\(851\) | 3.23556e39 | 0.903441 | ||||||||
\(852\) | 3.29309e39 | 0.905042 | ||||||||
\(853\) | −4.84028e39 | −1.30936 | −0.654679 | − | 0.755907i | \(-0.727196\pi\) | ||||
−0.654679 | + | 0.755907i | \(0.727196\pi\) | |||||||
\(854\) | −7.69932e38 | −0.205008 | ||||||||
\(855\) | −8.44013e39 | −2.21211 | ||||||||
\(856\) | −1.35274e39 | −0.348993 | ||||||||
\(857\) | 1.36798e38 | 0.0347406 | 0.0173703 | − | 0.999849i | \(-0.494471\pi\) | ||||
0.0173703 | + | 0.999849i | \(0.494471\pi\) | |||||||
\(858\) | −3.40160e38 | −0.0850363 | ||||||||
\(859\) | −4.42921e39 | −1.08998 | −0.544990 | − | 0.838442i | \(-0.683467\pi\) | ||||
−0.544990 | + | 0.838442i | \(0.683467\pi\) | |||||||
\(860\) | −7.64710e38 | −0.185254 | ||||||||
\(861\) | −4.33891e39 | −1.03476 | ||||||||
\(862\) | −3.66197e37 | −0.00859739 | ||||||||
\(863\) | −7.25613e39 | −1.67710 | −0.838550 | − | 0.544824i | \(-0.816596\pi\) | ||||
−0.838550 | + | 0.544824i | \(0.816596\pi\) | |||||||
\(864\) | −3.01469e39 | −0.685973 | ||||||||
\(865\) | 1.78105e39 | 0.398986 | ||||||||
\(866\) | −3.07625e39 | −0.678470 | ||||||||
\(867\) | 8.24287e39 | 1.78987 | ||||||||
\(868\) | −1.21948e39 | −0.260711 | ||||||||
\(869\) | 1.41712e38 | 0.0298290 | ||||||||
\(870\) | −4.83140e39 | −1.00130 | ||||||||
\(871\) | −1.05559e39 | −0.215401 | ||||||||
\(872\) | 1.75556e39 | 0.352731 | ||||||||
\(873\) | 1.99893e40 | 3.95463 | ||||||||
\(874\) | −5.02911e39 | −0.979686 | ||||||||
\(875\) | 1.48384e38 | 0.0284629 | ||||||||
\(876\) | 8.05600e39 | 1.52165 | ||||||||
\(877\) | 7.76731e39 | 1.44470 | 0.722348 | − | 0.691530i | \(-0.243063\pi\) | ||||
0.722348 | + | 0.691530i | \(0.243063\pi\) | |||||||
\(878\) | −1.90350e39 | −0.348639 | ||||||||
\(879\) | 1.79718e39 | 0.324146 | ||||||||
\(880\) | −7.36397e37 | −0.0130796 | ||||||||
\(881\) | −3.34645e39 | −0.585341 | −0.292671 | − | 0.956213i | \(-0.594544\pi\) | ||||
−0.292671 | + | 0.956213i | \(0.594544\pi\) | |||||||
\(882\) | −1.08907e40 | −1.87598 | ||||||||
\(883\) | 5.35163e39 | 0.907856 | 0.453928 | − | 0.891038i | \(-0.350022\pi\) | ||||
0.453928 | + | 0.891038i | \(0.350022\pi\) | |||||||
\(884\) | −4.88514e38 | −0.0816153 | ||||||||
\(885\) | 2.03647e39 | 0.335077 | ||||||||
\(886\) | −7.43376e39 | −1.20463 | ||||||||
\(887\) | 9.27354e38 | 0.148005 | 0.0740026 | − | 0.997258i | \(-0.476423\pi\) | ||||
0.0740026 | + | 0.997258i | \(0.476423\pi\) | |||||||
\(888\) | 4.88555e39 | 0.767960 | ||||||||
\(889\) | −9.11997e38 | −0.141195 | ||||||||
\(890\) | 1.78891e39 | 0.272786 | ||||||||
\(891\) | 3.70934e39 | 0.557119 | ||||||||
\(892\) | −2.76771e39 | −0.409445 | ||||||||
\(893\) | 3.70315e39 | 0.539606 | ||||||||
\(894\) | 1.17205e40 | 1.68225 | ||||||||
\(895\) | −4.82986e38 | −0.0682847 | ||||||||
\(896\) | −2.01970e38 | −0.0281274 | ||||||||
\(897\) | 6.19584e39 | 0.849967 | ||||||||
\(898\) | −6.44159e39 | −0.870488 | ||||||||
\(899\) | −1.96050e40 | −2.60982 | ||||||||
\(900\) | 2.25106e39 | 0.295198 | ||||||||
\(901\) | 1.12887e38 | 0.0145834 | ||||||||
\(902\) | −1.06319e39 | −0.135308 | ||||||||
\(903\) | 4.18031e39 | 0.524112 | ||||||||
\(904\) | −4.26101e38 | −0.0526306 | ||||||||
\(905\) | 1.85770e39 | 0.226058 | ||||||||
\(906\) | 1.10925e40 | 1.32984 | ||||||||
\(907\) | 1.06013e40 | 1.25217 | 0.626083 | − | 0.779756i | \(-0.284657\pi\) | ||||
0.626083 | + | 0.779756i | \(0.284657\pi\) | |||||||
\(908\) | 5.55602e39 | 0.646555 | ||||||||
\(909\) | 1.28250e40 | 1.47043 | ||||||||
\(910\) | 4.60643e38 | 0.0520362 | ||||||||
\(911\) | −1.34212e40 | −1.49381 | −0.746903 | − | 0.664933i | \(-0.768460\pi\) | ||||
−0.746903 | + | 0.664933i | \(0.768460\pi\) | |||||||
\(912\) | −7.59375e39 | −0.832772 | ||||||||
\(913\) | 3.02550e38 | 0.0326921 | ||||||||
\(914\) | −6.14363e39 | −0.654111 | ||||||||
\(915\) | 7.72074e39 | 0.809979 | ||||||||
\(916\) | 6.04309e39 | 0.624698 | ||||||||
\(917\) | −6.92038e38 | −0.0704927 | ||||||||
\(918\) | 8.62925e39 | 0.866158 | ||||||||
\(919\) | 6.48496e39 | 0.641428 | 0.320714 | − | 0.947176i | \(-0.396077\pi\) | ||||
0.320714 | + | 0.947176i | \(0.396077\pi\) | |||||||
\(920\) | 1.34131e39 | 0.130735 | ||||||||
\(921\) | −4.79521e39 | −0.460578 | ||||||||
\(922\) | −1.28404e39 | −0.121537 | ||||||||
\(923\) | −5.04761e39 | −0.470829 | ||||||||
\(924\) | 4.02554e38 | 0.0370043 | ||||||||
\(925\) | −2.41224e39 | −0.218528 | ||||||||
\(926\) | −4.52378e39 | −0.403881 | ||||||||
\(927\) | −3.98801e40 | −3.50897 | ||||||||
\(928\) | −3.24697e39 | −0.281567 | ||||||||
\(929\) | 4.31118e39 | 0.368454 | 0.184227 | − | 0.982884i | \(-0.441022\pi\) | ||||
0.184227 | + | 0.982884i | \(0.441022\pi\) | |||||||
\(930\) | 1.22287e40 | 1.03006 | ||||||||
\(931\) | −1.81397e40 | −1.50595 | ||||||||
\(932\) | 2.28063e39 | 0.186612 | ||||||||
\(933\) | −2.07551e40 | −1.67387 | ||||||||
\(934\) | −1.04369e40 | −0.829639 | ||||||||
\(935\) | 2.10786e38 | 0.0165153 | ||||||||
\(936\) | 6.98817e39 | 0.539684 | ||||||||
\(937\) | 1.66692e40 | 1.26891 | 0.634453 | − | 0.772962i | \(-0.281226\pi\) | ||||
0.634453 | + | 0.772962i | \(0.281226\pi\) | |||||||
\(938\) | 1.24921e39 | 0.0937339 | ||||||||
\(939\) | 8.05088e39 | 0.595467 | ||||||||
\(940\) | −9.87663e38 | −0.0720084 | ||||||||
\(941\) | −2.51285e40 | −1.80596 | −0.902978 | − | 0.429687i | \(-0.858624\pi\) | ||||
−0.902978 | + | 0.429687i | \(0.858624\pi\) | |||||||
\(942\) | 2.93746e40 | 2.08106 | ||||||||
\(943\) | 1.93655e40 | 1.35245 | ||||||||
\(944\) | 1.36862e39 | 0.0942241 | ||||||||
\(945\) | −8.13694e39 | −0.552245 | ||||||||
\(946\) | 1.02433e39 | 0.0685344 | ||||||||
\(947\) | 1.74731e40 | 1.15251 | 0.576257 | − | 0.817268i | \(-0.304513\pi\) | ||||
0.576257 | + | 0.817268i | \(0.304513\pi\) | |||||||
\(948\) | −3.89752e39 | −0.253440 | ||||||||
\(949\) | −1.23482e40 | −0.791604 | ||||||||
\(950\) | 3.74941e39 | 0.236970 | ||||||||
\(951\) | 3.98761e38 | 0.0248471 | ||||||||
\(952\) | 5.78120e38 | 0.0355156 | ||||||||
\(953\) | −1.34477e40 | −0.814504 | −0.407252 | − | 0.913316i | \(-0.633513\pi\) | ||||
−0.407252 | + | 0.913316i | \(0.633513\pi\) | |||||||
\(954\) | −1.61484e39 | −0.0964334 | ||||||||
\(955\) | −2.52143e38 | −0.0148457 | ||||||||
\(956\) | −9.24595e39 | −0.536747 | ||||||||
\(957\) | 6.47165e39 | 0.370428 | ||||||||
\(958\) | −7.68389e39 | −0.433658 | ||||||||
\(959\) | 6.64365e39 | 0.369705 | ||||||||
\(960\) | 2.02532e39 | 0.111130 | ||||||||
\(961\) | 3.11393e40 | 1.68478 | ||||||||
\(962\) | −7.48853e39 | −0.399515 | ||||||||
\(963\) | −5.53898e40 | −2.91390 | ||||||||
\(964\) | −5.82276e39 | −0.302057 | ||||||||
\(965\) | −9.92106e39 | −0.507504 | ||||||||
\(966\) | −7.33232e39 | −0.369871 | ||||||||
\(967\) | −6.46684e38 | −0.0321688 | −0.0160844 | − | 0.999871i | \(-0.505120\pi\) | ||||
−0.0160844 | + | 0.999871i | \(0.505120\pi\) | |||||||
\(968\) | −7.10866e39 | −0.348715 | ||||||||
\(969\) | 2.17364e40 | 1.05152 | ||||||||
\(970\) | −8.87997e39 | −0.423636 | ||||||||
\(971\) | 9.04161e38 | 0.0425389 | 0.0212694 | − | 0.999774i | \(-0.493229\pi\) | ||||
0.0212694 | + | 0.999774i | \(0.493229\pi\) | |||||||
\(972\) | −6.02021e40 | −2.79329 | ||||||||
\(973\) | 3.37980e39 | 0.154657 | ||||||||
\(974\) | 1.02098e39 | 0.0460758 | ||||||||
\(975\) | −4.61924e39 | −0.205593 | ||||||||
\(976\) | 5.18877e39 | 0.227767 | ||||||||
\(977\) | −2.22532e40 | −0.963420 | −0.481710 | − | 0.876331i | \(-0.659984\pi\) | ||||
−0.481710 | + | 0.876331i | \(0.659984\pi\) | |||||||
\(978\) | 2.22823e40 | 0.951449 | ||||||||
\(979\) | −2.39624e39 | −0.100917 | ||||||||
\(980\) | 4.83802e39 | 0.200963 | ||||||||
\(981\) | 7.18842e40 | 2.94511 | ||||||||
\(982\) | 1.74626e40 | 0.705673 | ||||||||
\(983\) | −2.74028e40 | −1.09225 | −0.546126 | − | 0.837703i | \(-0.683898\pi\) | ||||
−0.546126 | + | 0.837703i | \(0.683898\pi\) | |||||||
\(984\) | 2.92410e40 | 1.14963 | ||||||||
\(985\) | 1.41454e40 | 0.548562 | ||||||||
\(986\) | 9.29414e39 | 0.355526 | ||||||||
\(987\) | 5.39910e39 | 0.203723 | ||||||||
\(988\) | 1.16396e40 | 0.433232 | ||||||||
\(989\) | −1.86576e40 | −0.685024 | ||||||||
\(990\) | −3.01529e39 | −0.109208 | ||||||||
\(991\) | 1.63958e40 | 0.585786 | 0.292893 | − | 0.956145i | \(-0.405382\pi\) | ||||
0.292893 | + | 0.956145i | \(0.405382\pi\) | |||||||
\(992\) | 8.21840e39 | 0.289654 | ||||||||
\(993\) | −6.73871e40 | −2.34294 | ||||||||
\(994\) | 5.97348e39 | 0.204885 | ||||||||
\(995\) | 1.97649e40 | 0.668778 | ||||||||
\(996\) | −8.32108e39 | −0.277766 | ||||||||
\(997\) | 3.56689e40 | 1.17464 | 0.587320 | − | 0.809355i | \(-0.300183\pi\) | ||||
0.587320 | + | 0.809355i | \(0.300183\pi\) | |||||||
\(998\) | 9.66385e39 | 0.313970 | ||||||||
\(999\) | 1.32279e41 | 4.23993 |
(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 | 10.28.a.c.1.1 | ✓ | 2 | |
5.2 | odd | 4 | 50.28.b.c.49.4 | 4 | |||
5.3 | odd | 4 | 50.28.b.c.49.1 | 4 | |||
5.4 | even | 2 | 50.28.a.c.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.28.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.28.a.c.1.2 | 2 | 5.4 | even | 2 | |||
50.28.b.c.49.1 | 4 | 5.3 | odd | 4 | |||
50.28.b.c.49.4 | 4 | 5.2 | odd | 4 |