Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,12,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(22.2819522362\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 15790 x^{9} + 14666 x^{8} + 87206462 x^{7} - 14008334 x^{6} - 203974096304 x^{5} + \cdots - 75\!\cdots\!58 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{13}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-18.9987\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −21.9987 | −0.486107 | −0.243054 | − | 0.970013i | \(-0.578149\pi\) | ||||
−0.243054 | + | 0.970013i | \(0.578149\pi\) | |||||||
\(3\) | 310.394 | 0.737474 | 0.368737 | − | 0.929534i | \(-0.379790\pi\) | ||||
0.368737 | + | 0.929534i | \(0.379790\pi\) | |||||||
\(4\) | −1564.06 | −0.763700 | ||||||||
\(5\) | −886.321 | −0.126840 | −0.0634200 | − | 0.997987i | \(-0.520201\pi\) | ||||
−0.0634200 | + | 0.997987i | \(0.520201\pi\) | |||||||
\(6\) | −6828.28 | −0.358492 | ||||||||
\(7\) | 44263.6 | 0.995422 | 0.497711 | − | 0.867343i | \(-0.334174\pi\) | ||||
0.497711 | + | 0.867343i | \(0.334174\pi\) | |||||||
\(8\) | 79460.6 | 0.857348 | ||||||||
\(9\) | −80802.4 | −0.456132 | ||||||||
\(10\) | 19497.9 | 0.0616579 | ||||||||
\(11\) | −480464. | −0.899500 | −0.449750 | − | 0.893154i | \(-0.648487\pi\) | ||||
−0.449750 | + | 0.893154i | \(0.648487\pi\) | |||||||
\(12\) | −485474. | −0.563209 | ||||||||
\(13\) | 729102. | 0.544627 | 0.272314 | − | 0.962209i | \(-0.412211\pi\) | ||||
0.272314 | + | 0.962209i | \(0.412211\pi\) | |||||||
\(14\) | −973741. | −0.483882 | ||||||||
\(15\) | −275109. | −0.0935412 | ||||||||
\(16\) | 1.45516e6 | 0.346936 | ||||||||
\(17\) | 6.80915e6 | 1.16312 | 0.581559 | − | 0.813504i | \(-0.302443\pi\) | ||||
0.581559 | + | 0.813504i | \(0.302443\pi\) | |||||||
\(18\) | 1.77755e6 | 0.221729 | ||||||||
\(19\) | −1.56192e7 | −1.44715 | −0.723574 | − | 0.690246i | \(-0.757502\pi\) | ||||
−0.723574 | + | 0.690246i | \(0.757502\pi\) | |||||||
\(20\) | 1.38626e6 | 0.0968676 | ||||||||
\(21\) | 1.37392e7 | 0.734098 | ||||||||
\(22\) | 1.05696e7 | 0.437254 | ||||||||
\(23\) | −3.18252e7 | −1.03102 | −0.515511 | − | 0.856883i | \(-0.672398\pi\) | ||||
−0.515511 | + | 0.856883i | \(0.672398\pi\) | |||||||
\(24\) | 2.46641e7 | 0.632272 | ||||||||
\(25\) | −4.80426e7 | −0.983912 | ||||||||
\(26\) | −1.60393e7 | −0.264748 | ||||||||
\(27\) | −8.00660e7 | −1.07386 | ||||||||
\(28\) | −6.92307e7 | −0.760203 | ||||||||
\(29\) | 2.05111e7 | 0.185695 | ||||||||
\(30\) | 6.05205e6 | 0.0454711 | ||||||||
\(31\) | −3.08016e8 | −1.93234 | −0.966172 | − | 0.257898i | \(-0.916970\pi\) | ||||
−0.966172 | + | 0.257898i | \(0.916970\pi\) | |||||||
\(32\) | −1.94747e8 | −1.02600 | ||||||||
\(33\) | −1.49133e8 | −0.663358 | ||||||||
\(34\) | −1.49793e8 | −0.565401 | ||||||||
\(35\) | −3.92317e7 | −0.126259 | ||||||||
\(36\) | 1.26379e8 | 0.348348 | ||||||||
\(37\) | 4.28251e8 | 1.01529 | 0.507643 | − | 0.861567i | \(-0.330517\pi\) | ||||
0.507643 | + | 0.861567i | \(0.330517\pi\) | |||||||
\(38\) | 3.43602e8 | 0.703470 | ||||||||
\(39\) | 2.26309e8 | 0.401649 | ||||||||
\(40\) | −7.04276e7 | −0.108746 | ||||||||
\(41\) | −1.00915e9 | −1.36033 | −0.680163 | − | 0.733061i | \(-0.738091\pi\) | ||||
−0.680163 | + | 0.733061i | \(0.738091\pi\) | |||||||
\(42\) | −3.02244e8 | −0.356850 | ||||||||
\(43\) | 3.53819e8 | 0.367033 | 0.183516 | − | 0.983017i | \(-0.441252\pi\) | ||||
0.183516 | + | 0.983017i | \(0.441252\pi\) | |||||||
\(44\) | 7.51473e8 | 0.686948 | ||||||||
\(45\) | 7.16169e7 | 0.0578557 | ||||||||
\(46\) | 7.00114e8 | 0.501188 | ||||||||
\(47\) | −2.87373e9 | −1.82772 | −0.913858 | − | 0.406035i | \(-0.866911\pi\) | ||||
−0.913858 | + | 0.406035i | \(0.866911\pi\) | |||||||
\(48\) | 4.51672e8 | 0.255857 | ||||||||
\(49\) | −1.80646e7 | −0.00913589 | ||||||||
\(50\) | 1.05687e9 | 0.478287 | ||||||||
\(51\) | 2.11352e9 | 0.857770 | ||||||||
\(52\) | −1.14036e9 | −0.415932 | ||||||||
\(53\) | −1.08796e9 | −0.357353 | −0.178676 | − | 0.983908i | \(-0.557182\pi\) | ||||
−0.178676 | + | 0.983908i | \(0.557182\pi\) | |||||||
\(54\) | 1.76135e9 | 0.522011 | ||||||||
\(55\) | 4.25846e8 | 0.114093 | ||||||||
\(56\) | 3.51721e9 | 0.853422 | ||||||||
\(57\) | −4.84810e9 | −1.06724 | ||||||||
\(58\) | −4.51219e8 | −0.0902679 | ||||||||
\(59\) | 9.69237e9 | 1.76500 | 0.882499 | − | 0.470315i | \(-0.155860\pi\) | ||||
0.882499 | + | 0.470315i | \(0.155860\pi\) | |||||||
\(60\) | 4.30286e8 | 0.0714374 | ||||||||
\(61\) | 2.73036e9 | 0.413910 | 0.206955 | − | 0.978350i | \(-0.433645\pi\) | ||||
0.206955 | + | 0.978350i | \(0.433645\pi\) | |||||||
\(62\) | 6.77597e9 | 0.939327 | ||||||||
\(63\) | −3.57660e9 | −0.454043 | ||||||||
\(64\) | 1.30402e9 | 0.151808 | ||||||||
\(65\) | −6.46218e8 | −0.0690805 | ||||||||
\(66\) | 3.28074e9 | 0.322463 | ||||||||
\(67\) | 5.53037e9 | 0.500429 | 0.250215 | − | 0.968190i | \(-0.419499\pi\) | ||||
0.250215 | + | 0.968190i | \(0.419499\pi\) | |||||||
\(68\) | −1.06499e10 | −0.888273 | ||||||||
\(69\) | −9.87837e9 | −0.760353 | ||||||||
\(70\) | 8.63048e8 | 0.0613756 | ||||||||
\(71\) | 1.51715e10 | 0.997949 | 0.498974 | − | 0.866617i | \(-0.333710\pi\) | ||||
0.498974 | + | 0.866617i | \(0.333710\pi\) | |||||||
\(72\) | −6.42060e9 | −0.391063 | ||||||||
\(73\) | 2.05445e10 | 1.15990 | 0.579949 | − | 0.814653i | \(-0.303072\pi\) | ||||
0.579949 | + | 0.814653i | \(0.303072\pi\) | |||||||
\(74\) | −9.42097e9 | −0.493538 | ||||||||
\(75\) | −1.49121e10 | −0.725610 | ||||||||
\(76\) | 2.44293e10 | 1.10519 | ||||||||
\(77\) | −2.12671e10 | −0.895382 | ||||||||
\(78\) | −4.97851e9 | −0.195244 | ||||||||
\(79\) | −2.27864e10 | −0.833158 | −0.416579 | − | 0.909100i | \(-0.636771\pi\) | ||||
−0.416579 | + | 0.909100i | \(0.636771\pi\) | |||||||
\(80\) | −1.28974e9 | −0.0440054 | ||||||||
\(81\) | −1.05381e10 | −0.335812 | ||||||||
\(82\) | 2.21999e10 | 0.661265 | ||||||||
\(83\) | −6.37446e9 | −0.177629 | −0.0888144 | − | 0.996048i | \(-0.528308\pi\) | ||||
−0.0888144 | + | 0.996048i | \(0.528308\pi\) | |||||||
\(84\) | −2.14888e10 | −0.560630 | ||||||||
\(85\) | −6.03510e9 | −0.147530 | ||||||||
\(86\) | −7.78357e9 | −0.178417 | ||||||||
\(87\) | 6.36654e9 | 0.136946 | ||||||||
\(88\) | −3.81780e10 | −0.771184 | ||||||||
\(89\) | −2.92283e10 | −0.554828 | −0.277414 | − | 0.960751i | \(-0.589477\pi\) | ||||
−0.277414 | + | 0.960751i | \(0.589477\pi\) | |||||||
\(90\) | −1.57548e9 | −0.0281241 | ||||||||
\(91\) | 3.22726e10 | 0.542134 | ||||||||
\(92\) | 4.97764e10 | 0.787392 | ||||||||
\(93\) | −9.56066e10 | −1.42505 | ||||||||
\(94\) | 6.32185e10 | 0.888466 | ||||||||
\(95\) | 1.38436e10 | 0.183556 | ||||||||
\(96\) | −6.04483e10 | −0.756646 | ||||||||
\(97\) | −1.24338e11 | −1.47014 | −0.735069 | − | 0.677992i | \(-0.762850\pi\) | ||||
−0.735069 | + | 0.677992i | \(0.762850\pi\) | |||||||
\(98\) | 3.97399e8 | 0.00444103 | ||||||||
\(99\) | 3.88226e10 | 0.410291 | ||||||||
\(100\) | 7.51413e10 | 0.751413 | ||||||||
\(101\) | −2.60286e10 | −0.246424 | −0.123212 | − | 0.992380i | \(-0.539320\pi\) | ||||
−0.123212 | + | 0.992380i | \(0.539320\pi\) | |||||||
\(102\) | −4.64948e10 | −0.416968 | ||||||||
\(103\) | −1.19818e11 | −1.01840 | −0.509200 | − | 0.860648i | \(-0.670059\pi\) | ||||
−0.509200 | + | 0.860648i | \(0.670059\pi\) | |||||||
\(104\) | 5.79348e10 | 0.466935 | ||||||||
\(105\) | −1.21773e10 | −0.0931130 | ||||||||
\(106\) | 2.39338e10 | 0.173712 | ||||||||
\(107\) | −1.11393e11 | −0.767795 | −0.383897 | − | 0.923376i | \(-0.625418\pi\) | ||||
−0.383897 | + | 0.923376i | \(0.625418\pi\) | |||||||
\(108\) | 1.25228e11 | 0.820106 | ||||||||
\(109\) | 1.17465e11 | 0.731247 | 0.365624 | − | 0.930763i | \(-0.380856\pi\) | ||||
0.365624 | + | 0.930763i | \(0.380856\pi\) | |||||||
\(110\) | −9.36806e9 | −0.0554613 | ||||||||
\(111\) | 1.32927e11 | 0.748748 | ||||||||
\(112\) | 6.44104e10 | 0.345348 | ||||||||
\(113\) | 3.69905e11 | 1.88868 | 0.944340 | − | 0.328972i | \(-0.106702\pi\) | ||||
0.944340 | + | 0.328972i | \(0.106702\pi\) | |||||||
\(114\) | 1.06652e11 | 0.518791 | ||||||||
\(115\) | 2.82074e10 | 0.130775 | ||||||||
\(116\) | −3.20806e10 | −0.141815 | ||||||||
\(117\) | −5.89131e10 | −0.248422 | ||||||||
\(118\) | −2.13220e11 | −0.857978 | ||||||||
\(119\) | 3.01397e11 | 1.15779 | ||||||||
\(120\) | −2.18603e10 | −0.0801973 | ||||||||
\(121\) | −5.44658e10 | −0.190899 | ||||||||
\(122\) | −6.00645e10 | −0.201205 | ||||||||
\(123\) | −3.13233e11 | −1.00321 | ||||||||
\(124\) | 4.81755e11 | 1.47573 | ||||||||
\(125\) | 8.58586e10 | 0.251639 | ||||||||
\(126\) | 7.86806e10 | 0.220714 | ||||||||
\(127\) | −5.07350e11 | −1.36266 | −0.681329 | − | 0.731977i | \(-0.738598\pi\) | ||||
−0.681329 | + | 0.731977i | \(0.738598\pi\) | |||||||
\(128\) | 3.70155e11 | 0.952201 | ||||||||
\(129\) | 1.09823e11 | 0.270677 | ||||||||
\(130\) | 1.42160e10 | 0.0335806 | ||||||||
\(131\) | 3.44791e11 | 0.780843 | 0.390422 | − | 0.920636i | \(-0.372329\pi\) | ||||
0.390422 | + | 0.920636i | \(0.372329\pi\) | |||||||
\(132\) | 2.33253e11 | 0.506606 | ||||||||
\(133\) | −6.91360e11 | −1.44052 | ||||||||
\(134\) | −1.21661e11 | −0.243262 | ||||||||
\(135\) | 7.09642e10 | 0.136208 | ||||||||
\(136\) | 5.41059e11 | 0.997197 | ||||||||
\(137\) | 5.50954e11 | 0.975332 | 0.487666 | − | 0.873030i | \(-0.337848\pi\) | ||||
0.487666 | + | 0.873030i | \(0.337848\pi\) | |||||||
\(138\) | 2.17311e11 | 0.369613 | ||||||||
\(139\) | −9.76916e11 | −1.59689 | −0.798447 | − | 0.602065i | \(-0.794345\pi\) | ||||
−0.798447 | + | 0.602065i | \(0.794345\pi\) | |||||||
\(140\) | 6.13606e10 | 0.0964241 | ||||||||
\(141\) | −8.91991e11 | −1.34789 | ||||||||
\(142\) | −3.33754e11 | −0.485110 | ||||||||
\(143\) | −3.50307e11 | −0.489893 | ||||||||
\(144\) | −1.17580e11 | −0.158249 | ||||||||
\(145\) | −1.81795e10 | −0.0235536 | ||||||||
\(146\) | −4.51953e11 | −0.563835 | ||||||||
\(147\) | −5.60716e9 | −0.00673749 | ||||||||
\(148\) | −6.69808e11 | −0.775374 | ||||||||
\(149\) | −5.22457e9 | −0.00582809 | −0.00291404 | − | 0.999996i | \(-0.500928\pi\) | ||||
−0.00291404 | + | 0.999996i | \(0.500928\pi\) | |||||||
\(150\) | 3.28048e11 | 0.352724 | ||||||||
\(151\) | 2.71454e11 | 0.281400 | 0.140700 | − | 0.990052i | \(-0.455065\pi\) | ||||
0.140700 | + | 0.990052i | \(0.455065\pi\) | |||||||
\(152\) | −1.24111e12 | −1.24071 | ||||||||
\(153\) | −5.50195e11 | −0.530535 | ||||||||
\(154\) | 4.67848e11 | 0.435252 | ||||||||
\(155\) | 2.73002e11 | 0.245099 | ||||||||
\(156\) | −3.53960e11 | −0.306739 | ||||||||
\(157\) | −8.51389e11 | −0.712328 | −0.356164 | − | 0.934424i | \(-0.615915\pi\) | ||||
−0.356164 | + | 0.934424i | \(0.615915\pi\) | |||||||
\(158\) | 5.01272e11 | 0.405004 | ||||||||
\(159\) | −3.37698e11 | −0.263539 | ||||||||
\(160\) | 1.72608e11 | 0.130137 | ||||||||
\(161\) | −1.40870e12 | −1.02630 | ||||||||
\(162\) | 2.31826e11 | 0.163241 | ||||||||
\(163\) | 1.66971e12 | 1.13661 | 0.568304 | − | 0.822819i | \(-0.307600\pi\) | ||||
0.568304 | + | 0.822819i | \(0.307600\pi\) | |||||||
\(164\) | 1.57836e12 | 1.03888 | ||||||||
\(165\) | 1.32180e11 | 0.0841403 | ||||||||
\(166\) | 1.40230e11 | 0.0863467 | ||||||||
\(167\) | 1.10002e12 | 0.655328 | 0.327664 | − | 0.944794i | \(-0.393739\pi\) | ||||
0.327664 | + | 0.944794i | \(0.393739\pi\) | |||||||
\(168\) | 1.09172e12 | 0.629377 | ||||||||
\(169\) | −1.26057e12 | −0.703381 | ||||||||
\(170\) | 1.32764e11 | 0.0717154 | ||||||||
\(171\) | 1.26207e12 | 0.660090 | ||||||||
\(172\) | −5.53393e11 | −0.280303 | ||||||||
\(173\) | −1.93882e12 | −0.951225 | −0.475612 | − | 0.879655i | \(-0.657774\pi\) | ||||
−0.475612 | + | 0.879655i | \(0.657774\pi\) | |||||||
\(174\) | −1.40056e11 | −0.0665703 | ||||||||
\(175\) | −2.12653e12 | −0.979407 | ||||||||
\(176\) | −6.99151e11 | −0.312069 | ||||||||
\(177\) | 3.00846e12 | 1.30164 | ||||||||
\(178\) | 6.42984e11 | 0.269706 | ||||||||
\(179\) | 9.66841e11 | 0.393245 | 0.196623 | − | 0.980479i | \(-0.437003\pi\) | ||||
0.196623 | + | 0.980479i | \(0.437003\pi\) | |||||||
\(180\) | −1.12013e11 | −0.0441844 | ||||||||
\(181\) | 3.06155e12 | 1.17141 | 0.585705 | − | 0.810524i | \(-0.300818\pi\) | ||||
0.585705 | + | 0.810524i | \(0.300818\pi\) | |||||||
\(182\) | −7.09956e11 | −0.263535 | ||||||||
\(183\) | 8.47489e11 | 0.305248 | ||||||||
\(184\) | −2.52885e12 | −0.883945 | ||||||||
\(185\) | −3.79568e11 | −0.128779 | ||||||||
\(186\) | 2.10322e12 | 0.692730 | ||||||||
\(187\) | −3.27155e12 | −1.04623 | ||||||||
\(188\) | 4.49468e12 | 1.39583 | ||||||||
\(189\) | −3.54401e12 | −1.06894 | ||||||||
\(190\) | −3.04542e11 | −0.0892281 | ||||||||
\(191\) | 1.59095e12 | 0.452869 | 0.226435 | − | 0.974026i | \(-0.427293\pi\) | ||||
0.226435 | + | 0.974026i | \(0.427293\pi\) | |||||||
\(192\) | 4.04760e11 | 0.111954 | ||||||||
\(193\) | −2.02014e12 | −0.543021 | −0.271511 | − | 0.962435i | \(-0.587523\pi\) | ||||
−0.271511 | + | 0.962435i | \(0.587523\pi\) | |||||||
\(194\) | 2.73527e12 | 0.714645 | ||||||||
\(195\) | −2.00582e11 | −0.0509451 | ||||||||
\(196\) | 2.82541e10 | 0.00697708 | ||||||||
\(197\) | −1.30724e12 | −0.313901 | −0.156950 | − | 0.987607i | \(-0.550166\pi\) | ||||
−0.156950 | + | 0.987607i | \(0.550166\pi\) | |||||||
\(198\) | −8.54048e11 | −0.199445 | ||||||||
\(199\) | 2.91409e12 | 0.661928 | 0.330964 | − | 0.943643i | \(-0.392626\pi\) | ||||
0.330964 | + | 0.943643i | \(0.392626\pi\) | |||||||
\(200\) | −3.81749e12 | −0.843554 | ||||||||
\(201\) | 1.71659e12 | 0.369054 | ||||||||
\(202\) | 5.72595e11 | 0.119789 | ||||||||
\(203\) | 9.07896e11 | 0.184845 | ||||||||
\(204\) | −3.30567e12 | −0.655078 | ||||||||
\(205\) | 8.94428e11 | 0.172544 | ||||||||
\(206\) | 2.63585e12 | 0.495052 | ||||||||
\(207\) | 2.57155e12 | 0.470282 | ||||||||
\(208\) | 1.06096e12 | 0.188951 | ||||||||
\(209\) | 7.50445e12 | 1.30171 | ||||||||
\(210\) | 2.67885e11 | 0.0452629 | ||||||||
\(211\) | 7.99404e12 | 1.31587 | 0.657935 | − | 0.753075i | \(-0.271430\pi\) | ||||
0.657935 | + | 0.753075i | \(0.271430\pi\) | |||||||
\(212\) | 1.70164e12 | 0.272910 | ||||||||
\(213\) | 4.70915e12 | 0.735961 | ||||||||
\(214\) | 2.45049e12 | 0.373231 | ||||||||
\(215\) | −3.13597e11 | −0.0465544 | ||||||||
\(216\) | −6.36209e12 | −0.920671 | ||||||||
\(217\) | −1.36339e13 | −1.92350 | ||||||||
\(218\) | −2.58409e12 | −0.355465 | ||||||||
\(219\) | 6.37690e12 | 0.855395 | ||||||||
\(220\) | −6.66047e11 | −0.0871325 | ||||||||
\(221\) | 4.96456e12 | 0.633466 | ||||||||
\(222\) | −2.92421e12 | −0.363972 | ||||||||
\(223\) | −8.85549e12 | −1.07532 | −0.537658 | − | 0.843163i | \(-0.680691\pi\) | ||||
−0.537658 | + | 0.843163i | \(0.680691\pi\) | |||||||
\(224\) | −8.62019e12 | −1.02130 | ||||||||
\(225\) | 3.88195e12 | 0.448793 | ||||||||
\(226\) | −8.13743e12 | −0.918101 | ||||||||
\(227\) | −9.57786e12 | −1.05469 | −0.527347 | − | 0.849650i | \(-0.676813\pi\) | ||||
−0.527347 | + | 0.849650i | \(0.676813\pi\) | |||||||
\(228\) | 7.58271e12 | 0.815047 | ||||||||
\(229\) | −1.53613e13 | −1.61188 | −0.805940 | − | 0.591998i | \(-0.798339\pi\) | ||||
−0.805940 | + | 0.591998i | \(0.798339\pi\) | |||||||
\(230\) | −6.20526e11 | −0.0635707 | ||||||||
\(231\) | −6.60117e12 | −0.660321 | ||||||||
\(232\) | 1.62983e12 | 0.159205 | ||||||||
\(233\) | 1.29012e13 | 1.23076 | 0.615379 | − | 0.788231i | \(-0.289003\pi\) | ||||
0.615379 | + | 0.788231i | \(0.289003\pi\) | |||||||
\(234\) | 1.29601e12 | 0.120760 | ||||||||
\(235\) | 2.54705e12 | 0.231827 | ||||||||
\(236\) | −1.51594e13 | −1.34793 | ||||||||
\(237\) | −7.07278e12 | −0.614432 | ||||||||
\(238\) | −6.63035e12 | −0.562812 | ||||||||
\(239\) | −6.63263e12 | −0.550170 | −0.275085 | − | 0.961420i | \(-0.588706\pi\) | ||||
−0.275085 | + | 0.961420i | \(0.588706\pi\) | |||||||
\(240\) | −4.00327e11 | −0.0324529 | ||||||||
\(241\) | 1.46207e13 | 1.15845 | 0.579223 | − | 0.815169i | \(-0.303356\pi\) | ||||
0.579223 | + | 0.815169i | \(0.303356\pi\) | |||||||
\(242\) | 1.19818e12 | 0.0927976 | ||||||||
\(243\) | 1.09125e13 | 0.826207 | ||||||||
\(244\) | −4.27044e12 | −0.316103 | ||||||||
\(245\) | 1.60111e10 | 0.00115880 | ||||||||
\(246\) | 6.89073e12 | 0.487666 | ||||||||
\(247\) | −1.13880e13 | −0.788157 | ||||||||
\(248\) | −2.44752e13 | −1.65669 | ||||||||
\(249\) | −1.97859e12 | −0.130997 | ||||||||
\(250\) | −1.88878e12 | −0.122324 | ||||||||
\(251\) | 9.17406e12 | 0.581241 | 0.290620 | − | 0.956838i | \(-0.406138\pi\) | ||||
0.290620 | + | 0.956838i | \(0.406138\pi\) | |||||||
\(252\) | 5.59400e12 | 0.346753 | ||||||||
\(253\) | 1.52909e13 | 0.927405 | ||||||||
\(254\) | 1.11610e13 | 0.662399 | ||||||||
\(255\) | −1.87326e12 | −0.108800 | ||||||||
\(256\) | −1.08136e13 | −0.614680 | ||||||||
\(257\) | 1.33408e13 | 0.742249 | 0.371125 | − | 0.928583i | \(-0.378972\pi\) | ||||
0.371125 | + | 0.928583i | \(0.378972\pi\) | |||||||
\(258\) | −2.41597e12 | −0.131578 | ||||||||
\(259\) | 1.89559e13 | 1.01064 | ||||||||
\(260\) | 1.01072e12 | 0.0527568 | ||||||||
\(261\) | −1.65735e12 | −0.0847015 | ||||||||
\(262\) | −7.58496e12 | −0.379574 | ||||||||
\(263\) | 1.17880e13 | 0.577677 | 0.288838 | − | 0.957378i | \(-0.406731\pi\) | ||||
0.288838 | + | 0.957378i | \(0.406731\pi\) | |||||||
\(264\) | −1.18502e13 | −0.568729 | ||||||||
\(265\) | 9.64286e11 | 0.0453266 | ||||||||
\(266\) | 1.52090e13 | 0.700249 | ||||||||
\(267\) | −9.07229e12 | −0.409171 | ||||||||
\(268\) | −8.64981e12 | −0.382177 | ||||||||
\(269\) | 4.69213e12 | 0.203111 | 0.101555 | − | 0.994830i | \(-0.467618\pi\) | ||||
0.101555 | + | 0.994830i | \(0.467618\pi\) | |||||||
\(270\) | −1.56112e12 | −0.0662119 | ||||||||
\(271\) | 2.00690e13 | 0.834056 | 0.417028 | − | 0.908894i | \(-0.363072\pi\) | ||||
0.417028 | + | 0.908894i | \(0.363072\pi\) | |||||||
\(272\) | 9.90838e12 | 0.403528 | ||||||||
\(273\) | 1.00172e13 | 0.399810 | ||||||||
\(274\) | −1.21203e13 | −0.474116 | ||||||||
\(275\) | 2.30827e13 | 0.885029 | ||||||||
\(276\) | 1.54503e13 | 0.580681 | ||||||||
\(277\) | −3.83151e13 | −1.41166 | −0.705832 | − | 0.708379i | \(-0.749427\pi\) | ||||
−0.705832 | + | 0.708379i | \(0.749427\pi\) | |||||||
\(278\) | 2.14909e13 | 0.776262 | ||||||||
\(279\) | 2.48885e13 | 0.881404 | ||||||||
\(280\) | −3.11738e12 | −0.108248 | ||||||||
\(281\) | 2.14260e13 | 0.729552 | 0.364776 | − | 0.931095i | \(-0.381146\pi\) | ||||
0.364776 | + | 0.931095i | \(0.381146\pi\) | |||||||
\(282\) | 1.96227e13 | 0.655221 | ||||||||
\(283\) | −1.96008e13 | −0.641873 | −0.320936 | − | 0.947101i | \(-0.603998\pi\) | ||||
−0.320936 | + | 0.947101i | \(0.603998\pi\) | |||||||
\(284\) | −2.37291e13 | −0.762133 | ||||||||
\(285\) | 4.29698e12 | 0.135368 | ||||||||
\(286\) | 7.70631e12 | 0.238140 | ||||||||
\(287\) | −4.46684e13 | −1.35410 | ||||||||
\(288\) | 1.57360e13 | 0.467989 | ||||||||
\(289\) | 1.20926e13 | 0.352844 | ||||||||
\(290\) | 3.99925e11 | 0.0114496 | ||||||||
\(291\) | −3.85937e13 | −1.08419 | ||||||||
\(292\) | −3.21328e13 | −0.885814 | ||||||||
\(293\) | 5.83139e13 | 1.57761 | 0.788807 | − | 0.614642i | \(-0.210699\pi\) | ||||
0.788807 | + | 0.614642i | \(0.210699\pi\) | |||||||
\(294\) | 1.23350e11 | 0.00327514 | ||||||||
\(295\) | −8.59056e12 | −0.223872 | ||||||||
\(296\) | 3.40291e13 | 0.870453 | ||||||||
\(297\) | 3.84689e13 | 0.965937 | ||||||||
\(298\) | 1.14934e11 | 0.00283308 | ||||||||
\(299\) | −2.32038e13 | −0.561523 | ||||||||
\(300\) | 2.33234e13 | 0.554148 | ||||||||
\(301\) | 1.56613e13 | 0.365352 | ||||||||
\(302\) | −5.97165e12 | −0.136790 | ||||||||
\(303\) | −8.07912e12 | −0.181731 | ||||||||
\(304\) | −2.27283e13 | −0.502069 | ||||||||
\(305\) | −2.41998e12 | −0.0525004 | ||||||||
\(306\) | 1.21036e13 | 0.257897 | ||||||||
\(307\) | −8.69471e13 | −1.81968 | −0.909838 | − | 0.414964i | \(-0.863794\pi\) | ||||
−0.909838 | + | 0.414964i | \(0.863794\pi\) | |||||||
\(308\) | 3.32629e13 | 0.683803 | ||||||||
\(309\) | −3.71909e13 | −0.751044 | ||||||||
\(310\) | −6.00568e12 | −0.119144 | ||||||||
\(311\) | 2.77778e13 | 0.541398 | 0.270699 | − | 0.962664i | \(-0.412745\pi\) | ||||
0.270699 | + | 0.962664i | \(0.412745\pi\) | |||||||
\(312\) | 1.79826e13 | 0.344353 | ||||||||
\(313\) | −1.13541e13 | −0.213629 | −0.106814 | − | 0.994279i | \(-0.534065\pi\) | ||||
−0.106814 | + | 0.994279i | \(0.534065\pi\) | |||||||
\(314\) | 1.87295e13 | 0.346268 | ||||||||
\(315\) | 3.17002e12 | 0.0575908 | ||||||||
\(316\) | 3.56393e13 | 0.636282 | ||||||||
\(317\) | −3.72872e13 | −0.654236 | −0.327118 | − | 0.944984i | \(-0.606077\pi\) | ||||
−0.327118 | + | 0.944984i | \(0.606077\pi\) | |||||||
\(318\) | 7.42892e12 | 0.128108 | ||||||||
\(319\) | −9.85487e12 | −0.167033 | ||||||||
\(320\) | −1.15578e12 | −0.0192553 | ||||||||
\(321\) | −3.45756e13 | −0.566229 | ||||||||
\(322\) | 3.09895e13 | 0.498893 | ||||||||
\(323\) | −1.06353e14 | −1.68321 | ||||||||
\(324\) | 1.64823e13 | 0.256460 | ||||||||
\(325\) | −3.50279e13 | −0.535865 | ||||||||
\(326\) | −3.67316e13 | −0.552513 | ||||||||
\(327\) | 3.64606e13 | 0.539276 | ||||||||
\(328\) | −8.01874e13 | −1.16627 | ||||||||
\(329\) | −1.27202e14 | −1.81935 | ||||||||
\(330\) | −2.90779e12 | −0.0409013 | ||||||||
\(331\) | −1.28189e14 | −1.77336 | −0.886678 | − | 0.462388i | \(-0.846993\pi\) | ||||
−0.886678 | + | 0.462388i | \(0.846993\pi\) | |||||||
\(332\) | 9.97001e12 | 0.135655 | ||||||||
\(333\) | −3.46037e13 | −0.463104 | ||||||||
\(334\) | −2.41989e13 | −0.318560 | ||||||||
\(335\) | −4.90168e12 | −0.0634744 | ||||||||
\(336\) | 1.99926e13 | 0.254685 | ||||||||
\(337\) | 6.54934e13 | 0.820792 | 0.410396 | − | 0.911907i | \(-0.365390\pi\) | ||||
0.410396 | + | 0.911907i | \(0.365390\pi\) | |||||||
\(338\) | 2.77309e13 | 0.341919 | ||||||||
\(339\) | 1.14816e14 | 1.39285 | ||||||||
\(340\) | 9.43923e12 | 0.112669 | ||||||||
\(341\) | 1.47991e14 | 1.73814 | ||||||||
\(342\) | −2.77638e13 | −0.320875 | ||||||||
\(343\) | −8.83231e13 | −1.00452 | ||||||||
\(344\) | 2.81147e13 | 0.314675 | ||||||||
\(345\) | 8.75541e12 | 0.0964431 | ||||||||
\(346\) | 4.26515e13 | 0.462398 | ||||||||
\(347\) | 8.39610e13 | 0.895912 | 0.447956 | − | 0.894056i | \(-0.352152\pi\) | ||||
0.447956 | + | 0.894056i | \(0.352152\pi\) | |||||||
\(348\) | −9.95764e12 | −0.104585 | ||||||||
\(349\) | −1.07463e13 | −0.111102 | −0.0555509 | − | 0.998456i | \(-0.517691\pi\) | ||||
−0.0555509 | + | 0.998456i | \(0.517691\pi\) | |||||||
\(350\) | 4.67810e13 | 0.476097 | ||||||||
\(351\) | −5.83763e13 | −0.584853 | ||||||||
\(352\) | 9.35689e13 | 0.922884 | ||||||||
\(353\) | −1.25603e13 | −0.121966 | −0.0609832 | − | 0.998139i | \(-0.519424\pi\) | ||||
−0.0609832 | + | 0.998139i | \(0.519424\pi\) | |||||||
\(354\) | −6.61822e13 | −0.632737 | ||||||||
\(355\) | −1.34468e13 | −0.126580 | ||||||||
\(356\) | 4.57147e13 | 0.423722 | ||||||||
\(357\) | 9.35520e13 | 0.853843 | ||||||||
\(358\) | −2.12693e13 | −0.191159 | ||||||||
\(359\) | −1.38150e14 | −1.22273 | −0.611365 | − | 0.791349i | \(-0.709379\pi\) | ||||
−0.611365 | + | 0.791349i | \(0.709379\pi\) | |||||||
\(360\) | 5.69072e12 | 0.0496025 | ||||||||
\(361\) | 1.27468e14 | 1.09424 | ||||||||
\(362\) | −6.73502e13 | −0.569432 | ||||||||
\(363\) | −1.69059e13 | −0.140783 | ||||||||
\(364\) | −5.04762e13 | −0.414027 | ||||||||
\(365\) | −1.82090e13 | −0.147121 | ||||||||
\(366\) | −1.86437e13 | −0.148383 | ||||||||
\(367\) | 2.02429e14 | 1.58712 | 0.793559 | − | 0.608494i | \(-0.208226\pi\) | ||||
0.793559 | + | 0.608494i | \(0.208226\pi\) | |||||||
\(368\) | −4.63107e13 | −0.357699 | ||||||||
\(369\) | 8.15414e13 | 0.620488 | ||||||||
\(370\) | 8.35000e12 | 0.0626004 | ||||||||
\(371\) | −4.81572e13 | −0.355717 | ||||||||
\(372\) | 1.49534e14 | 1.08831 | ||||||||
\(373\) | 2.52372e13 | 0.180985 | 0.0904927 | − | 0.995897i | \(-0.471156\pi\) | ||||
0.0904927 | + | 0.995897i | \(0.471156\pi\) | |||||||
\(374\) | 7.19700e13 | 0.508578 | ||||||||
\(375\) | 2.66500e13 | 0.185578 | ||||||||
\(376\) | −2.28349e14 | −1.56699 | ||||||||
\(377\) | 1.49547e13 | 0.101135 | ||||||||
\(378\) | 7.79636e13 | 0.519621 | ||||||||
\(379\) | −5.31941e13 | −0.349420 | −0.174710 | − | 0.984620i | \(-0.555899\pi\) | ||||
−0.174710 | + | 0.984620i | \(0.555899\pi\) | |||||||
\(380\) | −2.16522e13 | −0.140182 | ||||||||
\(381\) | −1.57479e14 | −1.00493 | ||||||||
\(382\) | −3.49988e13 | −0.220143 | ||||||||
\(383\) | 3.19109e14 | 1.97854 | 0.989272 | − | 0.146084i | \(-0.0466669\pi\) | ||||
0.989272 | + | 0.146084i | \(0.0466669\pi\) | |||||||
\(384\) | 1.14894e14 | 0.702224 | ||||||||
\(385\) | 1.88494e13 | 0.113570 | ||||||||
\(386\) | 4.44405e13 | 0.263967 | ||||||||
\(387\) | −2.85894e13 | −0.167415 | ||||||||
\(388\) | 1.94471e14 | 1.12274 | ||||||||
\(389\) | −7.65689e13 | −0.435842 | −0.217921 | − | 0.975966i | \(-0.569928\pi\) | ||||
−0.217921 | + | 0.975966i | \(0.569928\pi\) | |||||||
\(390\) | 4.41256e12 | 0.0247648 | ||||||||
\(391\) | −2.16703e14 | −1.19920 | ||||||||
\(392\) | −1.43543e12 | −0.00783264 | ||||||||
\(393\) | 1.07021e14 | 0.575852 | ||||||||
\(394\) | 2.87577e13 | 0.152589 | ||||||||
\(395\) | 2.01961e13 | 0.105678 | ||||||||
\(396\) | −6.07208e13 | −0.313339 | ||||||||
\(397\) | −3.97244e13 | −0.202166 | −0.101083 | − | 0.994878i | \(-0.532231\pi\) | ||||
−0.101083 | + | 0.994878i | \(0.532231\pi\) | |||||||
\(398\) | −6.41062e13 | −0.321768 | ||||||||
\(399\) | −2.14594e14 | −1.06235 | ||||||||
\(400\) | −6.99095e13 | −0.341355 | ||||||||
\(401\) | 3.19615e14 | 1.53934 | 0.769668 | − | 0.638444i | \(-0.220422\pi\) | ||||
0.769668 | + | 0.638444i | \(0.220422\pi\) | |||||||
\(402\) | −3.77629e13 | −0.179400 | ||||||||
\(403\) | −2.24575e14 | −1.05241 | ||||||||
\(404\) | 4.07102e13 | 0.188194 | ||||||||
\(405\) | 9.34018e12 | 0.0425944 | ||||||||
\(406\) | −1.99726e13 | −0.0898546 | ||||||||
\(407\) | −2.05759e14 | −0.913250 | ||||||||
\(408\) | 1.67942e14 | 0.735407 | ||||||||
\(409\) | −1.92549e14 | −0.831885 | −0.415942 | − | 0.909391i | \(-0.636548\pi\) | ||||
−0.415942 | + | 0.909391i | \(0.636548\pi\) | |||||||
\(410\) | −1.96763e13 | −0.0838748 | ||||||||
\(411\) | 1.71013e14 | 0.719282 | ||||||||
\(412\) | 1.87403e14 | 0.777752 | ||||||||
\(413\) | 4.29019e14 | 1.75692 | ||||||||
\(414\) | −5.65709e13 | −0.228608 | ||||||||
\(415\) | 5.64982e12 | 0.0225304 | ||||||||
\(416\) | −1.41990e14 | −0.558786 | ||||||||
\(417\) | −3.03229e14 | −1.17767 | ||||||||
\(418\) | −1.65088e14 | −0.632771 | ||||||||
\(419\) | −4.17916e13 | −0.158093 | −0.0790464 | − | 0.996871i | \(-0.525188\pi\) | ||||
−0.0790464 | + | 0.996871i | \(0.525188\pi\) | |||||||
\(420\) | 1.90460e13 | 0.0711103 | ||||||||
\(421\) | 2.60522e14 | 0.960048 | 0.480024 | − | 0.877255i | \(-0.340628\pi\) | ||||
0.480024 | + | 0.877255i | \(0.340628\pi\) | |||||||
\(422\) | −1.75859e14 | −0.639654 | ||||||||
\(423\) | 2.32205e14 | 0.833679 | ||||||||
\(424\) | −8.64503e13 | −0.306376 | ||||||||
\(425\) | −3.27129e14 | −1.14441 | ||||||||
\(426\) | −1.03595e14 | −0.357756 | ||||||||
\(427\) | 1.20856e14 | 0.412015 | ||||||||
\(428\) | 1.74224e14 | 0.586365 | ||||||||
\(429\) | −1.08733e14 | −0.361283 | ||||||||
\(430\) | 6.89874e12 | 0.0226305 | ||||||||
\(431\) | −1.31690e14 | −0.426508 | −0.213254 | − | 0.976997i | \(-0.568406\pi\) | ||||
−0.213254 | + | 0.976997i | \(0.568406\pi\) | |||||||
\(432\) | −1.16509e14 | −0.372561 | ||||||||
\(433\) | −1.19097e13 | −0.0376026 | −0.0188013 | − | 0.999823i | \(-0.505985\pi\) | ||||
−0.0188013 | + | 0.999823i | \(0.505985\pi\) | |||||||
\(434\) | 2.99928e14 | 0.935027 | ||||||||
\(435\) | −5.64280e12 | −0.0173702 | ||||||||
\(436\) | −1.83723e14 | −0.558453 | ||||||||
\(437\) | 4.97084e14 | 1.49204 | ||||||||
\(438\) | −1.40284e14 | −0.415814 | ||||||||
\(439\) | −5.65097e14 | −1.65413 | −0.827063 | − | 0.562110i | \(-0.809990\pi\) | ||||
−0.827063 | + | 0.562110i | \(0.809990\pi\) | |||||||
\(440\) | 3.38380e13 | 0.0978170 | ||||||||
\(441\) | 1.45967e12 | 0.00416717 | ||||||||
\(442\) | −1.09214e14 | −0.307933 | ||||||||
\(443\) | −1.77548e14 | −0.494419 | −0.247210 | − | 0.968962i | \(-0.579514\pi\) | ||||
−0.247210 | + | 0.968962i | \(0.579514\pi\) | |||||||
\(444\) | −2.07905e14 | −0.571818 | ||||||||
\(445\) | 2.59056e13 | 0.0703743 | ||||||||
\(446\) | 1.94809e14 | 0.522719 | ||||||||
\(447\) | −1.62168e12 | −0.00429806 | ||||||||
\(448\) | 5.77206e13 | 0.151113 | ||||||||
\(449\) | −7.83747e13 | −0.202685 | −0.101342 | − | 0.994852i | \(-0.532314\pi\) | ||||
−0.101342 | + | 0.994852i | \(0.532314\pi\) | |||||||
\(450\) | −8.53980e13 | −0.218162 | ||||||||
\(451\) | 4.84859e14 | 1.22361 | ||||||||
\(452\) | −5.78552e14 | −1.44238 | ||||||||
\(453\) | 8.42579e13 | 0.207525 | ||||||||
\(454\) | 2.10701e14 | 0.512694 | ||||||||
\(455\) | −2.86039e13 | −0.0687643 | ||||||||
\(456\) | −3.85233e14 | −0.914991 | ||||||||
\(457\) | −4.40497e14 | −1.03372 | −0.516861 | − | 0.856069i | \(-0.672900\pi\) | ||||
−0.516861 | + | 0.856069i | \(0.672900\pi\) | |||||||
\(458\) | 3.37929e14 | 0.783547 | ||||||||
\(459\) | −5.45182e14 | −1.24903 | ||||||||
\(460\) | −4.41179e13 | −0.0998727 | ||||||||
\(461\) | 2.97082e14 | 0.664541 | 0.332270 | − | 0.943184i | \(-0.392185\pi\) | ||||
0.332270 | + | 0.943184i | \(0.392185\pi\) | |||||||
\(462\) | 1.45217e14 | 0.320987 | ||||||||
\(463\) | 1.07028e14 | 0.233776 | 0.116888 | − | 0.993145i | \(-0.462708\pi\) | ||||
0.116888 | + | 0.993145i | \(0.462708\pi\) | |||||||
\(464\) | 2.98469e13 | 0.0644245 | ||||||||
\(465\) | 8.47381e13 | 0.180754 | ||||||||
\(466\) | −2.83810e14 | −0.598281 | ||||||||
\(467\) | −2.59277e14 | −0.540158 | −0.270079 | − | 0.962838i | \(-0.587050\pi\) | ||||
−0.270079 | + | 0.962838i | \(0.587050\pi\) | |||||||
\(468\) | 9.21435e13 | 0.189720 | ||||||||
\(469\) | 2.44794e14 | 0.498138 | ||||||||
\(470\) | −5.60319e13 | −0.112693 | ||||||||
\(471\) | −2.64266e14 | −0.525323 | ||||||||
\(472\) | 7.70162e14 | 1.51322 | ||||||||
\(473\) | −1.69997e14 | −0.330146 | ||||||||
\(474\) | 1.55592e14 | 0.298680 | ||||||||
\(475\) | 7.50385e14 | 1.42387 | ||||||||
\(476\) | −4.71402e14 | −0.884206 | ||||||||
\(477\) | 8.79101e13 | 0.163000 | ||||||||
\(478\) | 1.45909e14 | 0.267442 | ||||||||
\(479\) | −9.69340e13 | −0.175643 | −0.0878215 | − | 0.996136i | \(-0.527991\pi\) | ||||
−0.0878215 | + | 0.996136i | \(0.527991\pi\) | |||||||
\(480\) | 5.35766e13 | 0.0959729 | ||||||||
\(481\) | 3.12238e14 | 0.552953 | ||||||||
\(482\) | −3.21637e14 | −0.563129 | ||||||||
\(483\) | −4.37252e14 | −0.756872 | ||||||||
\(484\) | 8.51876e13 | 0.145790 | ||||||||
\(485\) | 1.10203e14 | 0.186472 | ||||||||
\(486\) | −2.40060e14 | −0.401625 | ||||||||
\(487\) | 4.95544e14 | 0.819735 | 0.409867 | − | 0.912145i | \(-0.365575\pi\) | ||||
0.409867 | + | 0.912145i | \(0.365575\pi\) | |||||||
\(488\) | 2.16956e14 | 0.354865 | ||||||||
\(489\) | 5.18270e14 | 0.838219 | ||||||||
\(490\) | −3.52223e11 | −0.000563300 0 | ||||||||
\(491\) | −9.75658e14 | −1.54294 | −0.771471 | − | 0.636264i | \(-0.780479\pi\) | ||||
−0.771471 | + | 0.636264i | \(0.780479\pi\) | |||||||
\(492\) | 4.89915e14 | 0.766147 | ||||||||
\(493\) | 1.39664e14 | 0.215986 | ||||||||
\(494\) | 2.50521e14 | 0.383129 | ||||||||
\(495\) | −3.44093e13 | −0.0520412 | ||||||||
\(496\) | −4.48212e14 | −0.670401 | ||||||||
\(497\) | 6.71545e14 | 0.993380 | ||||||||
\(498\) | 4.35265e13 | 0.0636785 | ||||||||
\(499\) | 1.26831e15 | 1.83516 | 0.917579 | − | 0.397554i | \(-0.130141\pi\) | ||||
0.917579 | + | 0.397554i | \(0.130141\pi\) | |||||||
\(500\) | −1.34288e14 | −0.192177 | ||||||||
\(501\) | 3.41439e14 | 0.483287 | ||||||||
\(502\) | −2.01817e14 | −0.282545 | ||||||||
\(503\) | 7.13091e14 | 0.987463 | 0.493732 | − | 0.869614i | \(-0.335632\pi\) | ||||
0.493732 | + | 0.869614i | \(0.335632\pi\) | |||||||
\(504\) | −2.84199e14 | −0.389273 | ||||||||
\(505\) | 2.30697e13 | 0.0312564 | ||||||||
\(506\) | −3.36380e14 | −0.450819 | ||||||||
\(507\) | −3.91274e14 | −0.518725 | ||||||||
\(508\) | 7.93524e14 | 1.04066 | ||||||||
\(509\) | −1.47779e14 | −0.191719 | −0.0958597 | − | 0.995395i | \(-0.530560\pi\) | ||||
−0.0958597 | + | 0.995395i | \(0.530560\pi\) | |||||||
\(510\) | 4.12093e13 | 0.0528883 | ||||||||
\(511\) | 9.09373e14 | 1.15459 | ||||||||
\(512\) | −5.20193e14 | −0.653400 | ||||||||
\(513\) | 1.25056e15 | 1.55403 | ||||||||
\(514\) | −2.93480e14 | −0.360813 | ||||||||
\(515\) | 1.06198e14 | 0.129174 | ||||||||
\(516\) | −1.71770e14 | −0.206716 | ||||||||
\(517\) | 1.38073e15 | 1.64403 | ||||||||
\(518\) | −4.17005e14 | −0.491279 | ||||||||
\(519\) | −6.01798e14 | −0.701504 | ||||||||
\(520\) | −5.13489e13 | −0.0592260 | ||||||||
\(521\) | 2.60928e14 | 0.297792 | 0.148896 | − | 0.988853i | \(-0.452428\pi\) | ||||
0.148896 | + | 0.988853i | \(0.452428\pi\) | |||||||
\(522\) | 3.64596e13 | 0.0411740 | ||||||||
\(523\) | 7.01208e14 | 0.783587 | 0.391794 | − | 0.920053i | \(-0.371855\pi\) | ||||
0.391794 | + | 0.920053i | \(0.371855\pi\) | |||||||
\(524\) | −5.39273e14 | −0.596330 | ||||||||
\(525\) | −6.60064e14 | −0.722287 | ||||||||
\(526\) | −2.59322e14 | −0.280813 | ||||||||
\(527\) | −2.09733e15 | −2.24755 | ||||||||
\(528\) | −2.17012e14 | −0.230143 | ||||||||
\(529\) | 6.00349e13 | 0.0630082 | ||||||||
\(530\) | −2.12130e13 | −0.0220336 | ||||||||
\(531\) | −7.83166e14 | −0.805071 | ||||||||
\(532\) | 1.08133e15 | 1.10013 | ||||||||
\(533\) | −7.35770e14 | −0.740871 | ||||||||
\(534\) | 1.99579e14 | 0.198901 | ||||||||
\(535\) | 9.87296e13 | 0.0973871 | ||||||||
\(536\) | 4.39446e14 | 0.429042 | ||||||||
\(537\) | 3.00102e14 | 0.290008 | ||||||||
\(538\) | −1.03221e14 | −0.0987336 | ||||||||
\(539\) | 8.67942e12 | 0.00821774 | ||||||||
\(540\) | −1.10992e14 | −0.104022 | ||||||||
\(541\) | −1.43669e15 | −1.33284 | −0.666419 | − | 0.745578i | \(-0.732174\pi\) | ||||
−0.666419 | + | 0.745578i | \(0.732174\pi\) | |||||||
\(542\) | −4.41493e14 | −0.405441 | ||||||||
\(543\) | 9.50288e14 | 0.863885 | ||||||||
\(544\) | −1.32606e15 | −1.19335 | ||||||||
\(545\) | −1.04112e14 | −0.0927514 | ||||||||
\(546\) | −2.20366e14 | −0.194351 | ||||||||
\(547\) | −9.61440e14 | −0.839444 | −0.419722 | − | 0.907653i | \(-0.637872\pi\) | ||||
−0.419722 | + | 0.907653i | \(0.637872\pi\) | |||||||
\(548\) | −8.61724e14 | −0.744861 | ||||||||
\(549\) | −2.20620e14 | −0.188798 | ||||||||
\(550\) | −5.07790e14 | −0.430219 | ||||||||
\(551\) | −3.20367e14 | −0.268729 | ||||||||
\(552\) | −7.84941e14 | −0.651887 | ||||||||
\(553\) | −1.00861e15 | −0.829343 | ||||||||
\(554\) | 8.42884e14 | 0.686221 | ||||||||
\(555\) | −1.17816e14 | −0.0949711 | ||||||||
\(556\) | 1.52795e15 | 1.21955 | ||||||||
\(557\) | −2.91552e14 | −0.230416 | −0.115208 | − | 0.993341i | \(-0.536753\pi\) | ||||
−0.115208 | + | 0.993341i | \(0.536753\pi\) | |||||||
\(558\) | −5.47514e14 | −0.428457 | ||||||||
\(559\) | 2.57970e14 | 0.199896 | ||||||||
\(560\) | −5.70883e13 | −0.0438039 | ||||||||
\(561\) | −1.01547e15 | −0.771564 | ||||||||
\(562\) | −4.71344e14 | −0.354641 | ||||||||
\(563\) | −6.42960e14 | −0.479057 | −0.239529 | − | 0.970889i | \(-0.576993\pi\) | ||||
−0.239529 | + | 0.970889i | \(0.576993\pi\) | |||||||
\(564\) | 1.39512e15 | 1.02939 | ||||||||
\(565\) | −3.27854e14 | −0.239560 | ||||||||
\(566\) | 4.31193e14 | 0.312019 | ||||||||
\(567\) | −4.66456e14 | −0.334275 | ||||||||
\(568\) | 1.20554e15 | 0.855589 | ||||||||
\(569\) | 4.54572e14 | 0.319511 | 0.159755 | − | 0.987157i | \(-0.448929\pi\) | ||||
0.159755 | + | 0.987157i | \(0.448929\pi\) | |||||||
\(570\) | −9.45280e13 | −0.0658034 | ||||||||
\(571\) | −1.61565e15 | −1.11391 | −0.556955 | − | 0.830543i | \(-0.688030\pi\) | ||||
−0.556955 | + | 0.830543i | \(0.688030\pi\) | |||||||
\(572\) | 5.47900e14 | 0.374131 | ||||||||
\(573\) | 4.93822e14 | 0.333979 | ||||||||
\(574\) | 9.82647e14 | 0.658237 | ||||||||
\(575\) | 1.52897e15 | 1.01444 | ||||||||
\(576\) | −1.05368e14 | −0.0692444 | ||||||||
\(577\) | −3.96128e14 | −0.257851 | −0.128926 | − | 0.991654i | \(-0.541153\pi\) | ||||
−0.128926 | + | 0.991654i | \(0.541153\pi\) | |||||||
\(578\) | −2.66022e14 | −0.171520 | ||||||||
\(579\) | −6.27041e14 | −0.400464 | ||||||||
\(580\) | 2.84337e13 | 0.0179879 | ||||||||
\(581\) | −2.82156e14 | −0.176816 | ||||||||
\(582\) | 8.49012e14 | 0.527033 | ||||||||
\(583\) | 5.22728e14 | 0.321439 | ||||||||
\(584\) | 1.63248e15 | 0.994436 | ||||||||
\(585\) | 5.22160e13 | 0.0315098 | ||||||||
\(586\) | −1.28283e15 | −0.766890 | ||||||||
\(587\) | −6.16212e14 | −0.364939 | −0.182470 | − | 0.983211i | \(-0.558409\pi\) | ||||
−0.182470 | + | 0.983211i | \(0.558409\pi\) | |||||||
\(588\) | 8.76992e12 | 0.00514542 | ||||||||
\(589\) | 4.81096e15 | 2.79639 | ||||||||
\(590\) | 1.88981e14 | 0.108826 | ||||||||
\(591\) | −4.05761e14 | −0.231494 | ||||||||
\(592\) | 6.23172e14 | 0.352240 | ||||||||
\(593\) | −1.04704e15 | −0.586360 | −0.293180 | − | 0.956057i | \(-0.594714\pi\) | ||||
−0.293180 | + | 0.956057i | \(0.594714\pi\) | |||||||
\(594\) | −8.46265e14 | −0.469549 | ||||||||
\(595\) | −2.67135e14 | −0.146854 | ||||||||
\(596\) | 8.17152e12 | 0.00445091 | ||||||||
\(597\) | 9.04516e14 | 0.488155 | ||||||||
\(598\) | 5.10454e14 | 0.272961 | ||||||||
\(599\) | −3.29250e15 | −1.74453 | −0.872265 | − | 0.489033i | \(-0.837350\pi\) | ||||
−0.872265 | + | 0.489033i | \(0.837350\pi\) | |||||||
\(600\) | −1.18493e15 | −0.622100 | ||||||||
\(601\) | −2.47950e14 | −0.128990 | −0.0644949 | − | 0.997918i | \(-0.520544\pi\) | ||||
−0.0644949 | + | 0.997918i | \(0.520544\pi\) | |||||||
\(602\) | −3.44528e14 | −0.177600 | ||||||||
\(603\) | −4.46867e14 | −0.228262 | ||||||||
\(604\) | −4.24570e14 | −0.214905 | ||||||||
\(605\) | 4.82742e13 | 0.0242137 | ||||||||
\(606\) | 1.77730e14 | 0.0883410 | ||||||||
\(607\) | −2.44547e15 | −1.20455 | −0.602274 | − | 0.798290i | \(-0.705738\pi\) | ||||
−0.602274 | + | 0.798290i | \(0.705738\pi\) | |||||||
\(608\) | 3.04179e15 | 1.48477 | ||||||||
\(609\) | 2.81806e14 | 0.136319 | ||||||||
\(610\) | 5.32364e13 | 0.0255208 | ||||||||
\(611\) | −2.09524e15 | −0.995424 | ||||||||
\(612\) | 8.60537e14 | 0.405169 | ||||||||
\(613\) | 2.10077e15 | 0.980270 | 0.490135 | − | 0.871646i | \(-0.336947\pi\) | ||||
0.490135 | + | 0.871646i | \(0.336947\pi\) | |||||||
\(614\) | 1.91272e15 | 0.884558 | ||||||||
\(615\) | 2.77625e14 | 0.127247 | ||||||||
\(616\) | −1.68989e15 | −0.767653 | ||||||||
\(617\) | −2.30636e14 | −0.103839 | −0.0519194 | − | 0.998651i | \(-0.516534\pi\) | ||||
−0.0519194 | + | 0.998651i | \(0.516534\pi\) | |||||||
\(618\) | 8.18152e14 | 0.365088 | ||||||||
\(619\) | −1.04593e15 | −0.462599 | −0.231300 | − | 0.972883i | \(-0.574298\pi\) | ||||
−0.231300 | + | 0.972883i | \(0.574298\pi\) | |||||||
\(620\) | −4.26990e14 | −0.187182 | ||||||||
\(621\) | 2.54812e15 | 1.10717 | ||||||||
\(622\) | −6.11077e14 | −0.263177 | ||||||||
\(623\) | −1.29375e15 | −0.552287 | ||||||||
\(624\) | 3.29315e14 | 0.139347 | ||||||||
\(625\) | 2.26973e15 | 0.951994 | ||||||||
\(626\) | 2.49776e14 | 0.103846 | ||||||||
\(627\) | 2.32934e15 | 0.959978 | ||||||||
\(628\) | 1.33162e15 | 0.544004 | ||||||||
\(629\) | 2.91602e15 | 1.18090 | ||||||||
\(630\) | −6.97363e13 | −0.0279953 | ||||||||
\(631\) | 8.37986e14 | 0.333484 | 0.166742 | − | 0.986001i | \(-0.446675\pi\) | ||||
0.166742 | + | 0.986001i | \(0.446675\pi\) | |||||||
\(632\) | −1.81062e15 | −0.714306 | ||||||||
\(633\) | 2.48130e15 | 0.970420 | ||||||||
\(634\) | 8.20271e14 | 0.318029 | ||||||||
\(635\) | 4.49675e14 | 0.172840 | ||||||||
\(636\) | 5.28179e14 | 0.201264 | ||||||||
\(637\) | −1.31710e13 | −0.00497566 | ||||||||
\(638\) | 2.16795e14 | 0.0811960 | ||||||||
\(639\) | −1.22589e15 | −0.455196 | ||||||||
\(640\) | −3.28076e14 | −0.120777 | ||||||||
\(641\) | −4.90090e15 | −1.78878 | −0.894390 | − | 0.447288i | \(-0.852390\pi\) | ||||
−0.894390 | + | 0.447288i | \(0.852390\pi\) | |||||||
\(642\) | 7.60619e14 | 0.275248 | ||||||||
\(643\) | 1.71965e15 | 0.616991 | 0.308496 | − | 0.951226i | \(-0.400174\pi\) | ||||
0.308496 | + | 0.951226i | \(0.400174\pi\) | |||||||
\(644\) | 2.20328e15 | 0.783787 | ||||||||
\(645\) | −9.73389e13 | −0.0343327 | ||||||||
\(646\) | 2.33964e15 | 0.818219 | ||||||||
\(647\) | 8.99014e14 | 0.311740 | 0.155870 | − | 0.987778i | \(-0.450182\pi\) | ||||
0.155870 | + | 0.987778i | \(0.450182\pi\) | |||||||
\(648\) | −8.37367e14 | −0.287908 | ||||||||
\(649\) | −4.65684e15 | −1.58762 | ||||||||
\(650\) | 7.70569e14 | 0.260488 | ||||||||
\(651\) | −4.23189e15 | −1.41853 | ||||||||
\(652\) | −2.61153e15 | −0.868026 | ||||||||
\(653\) | 1.85055e15 | 0.609927 | 0.304964 | − | 0.952364i | \(-0.401356\pi\) | ||||
0.304964 | + | 0.952364i | \(0.401356\pi\) | |||||||
\(654\) | −8.02086e14 | −0.262146 | ||||||||
\(655\) | −3.05596e14 | −0.0990421 | ||||||||
\(656\) | −1.46847e15 | −0.471947 | ||||||||
\(657\) | −1.66004e15 | −0.529066 | ||||||||
\(658\) | 2.79827e15 | 0.884398 | ||||||||
\(659\) | −8.51169e14 | −0.266776 | −0.133388 | − | 0.991064i | \(-0.542586\pi\) | ||||
−0.133388 | + | 0.991064i | \(0.542586\pi\) | |||||||
\(660\) | −2.06737e14 | −0.0642579 | ||||||||
\(661\) | 5.25610e15 | 1.62015 | 0.810075 | − | 0.586326i | \(-0.199426\pi\) | ||||
0.810075 | + | 0.586326i | \(0.199426\pi\) | |||||||
\(662\) | 2.81999e15 | 0.862042 | ||||||||
\(663\) | 1.54097e15 | 0.467165 | ||||||||
\(664\) | −5.06518e14 | −0.152290 | ||||||||
\(665\) | 6.12767e14 | 0.182716 | ||||||||
\(666\) | 7.61236e14 | 0.225119 | ||||||||
\(667\) | −6.52772e14 | −0.191456 | ||||||||
\(668\) | −1.72049e15 | −0.500473 | ||||||||
\(669\) | −2.74869e15 | −0.793017 | ||||||||
\(670\) | 1.07831e14 | 0.0308554 | ||||||||
\(671\) | −1.31184e15 | −0.372313 | ||||||||
\(672\) | −2.67566e15 | −0.753181 | ||||||||
\(673\) | 6.49345e14 | 0.181298 | 0.0906490 | − | 0.995883i | \(-0.471106\pi\) | ||||
0.0906490 | + | 0.995883i | \(0.471106\pi\) | |||||||
\(674\) | −1.44077e15 | −0.398993 | ||||||||
\(675\) | 3.84658e15 | 1.05658 | ||||||||
\(676\) | 1.97160e15 | 0.537172 | ||||||||
\(677\) | 4.60763e15 | 1.24520 | 0.622601 | − | 0.782540i | \(-0.286076\pi\) | ||||
0.622601 | + | 0.782540i | \(0.286076\pi\) | |||||||
\(678\) | −2.52581e15 | −0.677076 | ||||||||
\(679\) | −5.50363e15 | −1.46341 | ||||||||
\(680\) | −4.79552e14 | −0.126484 | ||||||||
\(681\) | −2.97291e15 | −0.777809 | ||||||||
\(682\) | −3.25561e15 | −0.844925 | ||||||||
\(683\) | −1.97762e15 | −0.509131 | −0.254566 | − | 0.967056i | \(-0.581932\pi\) | ||||
−0.254566 | + | 0.967056i | \(0.581932\pi\) | |||||||
\(684\) | −1.97394e15 | −0.504111 | ||||||||
\(685\) | −4.88323e14 | −0.123711 | ||||||||
\(686\) | 1.94299e15 | 0.488303 | ||||||||
\(687\) | −4.76806e15 | −1.18872 | ||||||||
\(688\) | 5.14862e14 | 0.127337 | ||||||||
\(689\) | −7.93236e14 | −0.194624 | ||||||||
\(690\) | −1.92608e14 | −0.0468817 | ||||||||
\(691\) | −5.65502e15 | −1.36554 | −0.682770 | − | 0.730633i | \(-0.739225\pi\) | ||||
−0.682770 | + | 0.730633i | \(0.739225\pi\) | |||||||
\(692\) | 3.03242e15 | 0.726450 | ||||||||
\(693\) | 1.71843e15 | 0.408412 | ||||||||
\(694\) | −1.84703e15 | −0.435510 | ||||||||
\(695\) | 8.65862e14 | 0.202550 | ||||||||
\(696\) | 5.05889e14 | 0.117410 | ||||||||
\(697\) | −6.87143e15 | −1.58222 | ||||||||
\(698\) | 2.36406e14 | 0.0540074 | ||||||||
\(699\) | 4.00446e15 | 0.907653 | ||||||||
\(700\) | 3.32602e15 | 0.747973 | ||||||||
\(701\) | 6.37840e15 | 1.42319 | 0.711595 | − | 0.702590i | \(-0.247973\pi\) | ||||
0.711595 | + | 0.702590i | \(0.247973\pi\) | |||||||
\(702\) | 1.28420e15 | 0.284302 | ||||||||
\(703\) | −6.68892e15 | −1.46927 | ||||||||
\(704\) | −6.26535e14 | −0.136551 | ||||||||
\(705\) | 7.90591e14 | 0.170967 | ||||||||
\(706\) | 2.76311e14 | 0.0592887 | ||||||||
\(707\) | −1.15212e15 | −0.245296 | ||||||||
\(708\) | −4.70540e15 | −0.994062 | ||||||||
\(709\) | −1.82210e15 | −0.381961 | −0.190980 | − | 0.981594i | \(-0.561167\pi\) | ||||
−0.190980 | + | 0.981594i | \(0.561167\pi\) | |||||||
\(710\) | 2.95813e14 | 0.0615314 | ||||||||
\(711\) | 1.84120e15 | 0.380030 | ||||||||
\(712\) | −2.32250e15 | −0.475680 | ||||||||
\(713\) | 9.80269e15 | 1.99229 | ||||||||
\(714\) | −2.05802e15 | −0.415059 | ||||||||
\(715\) | 3.10485e14 | 0.0621380 | ||||||||
\(716\) | −1.51219e15 | −0.300321 | ||||||||
\(717\) | −2.05873e15 | −0.405736 | ||||||||
\(718\) | 3.03912e15 | 0.594378 | ||||||||
\(719\) | 4.72441e15 | 0.916935 | 0.458467 | − | 0.888711i | \(-0.348399\pi\) | ||||
0.458467 | + | 0.888711i | \(0.348399\pi\) | |||||||
\(720\) | 1.04214e14 | 0.0200723 | ||||||||
\(721\) | −5.30358e15 | −1.01374 | ||||||||
\(722\) | −2.80414e15 | −0.531918 | ||||||||
\(723\) | 4.53819e15 | 0.854324 | ||||||||
\(724\) | −4.78844e15 | −0.894606 | ||||||||
\(725\) | −9.85408e14 | −0.182708 | ||||||||
\(726\) | 3.71908e14 | 0.0684359 | ||||||||
\(727\) | 9.76903e15 | 1.78407 | 0.892035 | − | 0.451966i | \(-0.149277\pi\) | ||||
0.892035 | + | 0.451966i | \(0.149277\pi\) | |||||||
\(728\) | 2.56440e15 | 0.464797 | ||||||||
\(729\) | 5.25397e15 | 0.945118 | ||||||||
\(730\) | 4.00575e14 | 0.0715169 | ||||||||
\(731\) | 2.40921e15 | 0.426902 | ||||||||
\(732\) | −1.32552e15 | −0.233118 | ||||||||
\(733\) | −2.30118e15 | −0.401678 | −0.200839 | − | 0.979624i | \(-0.564367\pi\) | ||||
−0.200839 | + | 0.979624i | \(0.564367\pi\) | |||||||
\(734\) | −4.45317e15 | −0.771510 | ||||||||
\(735\) | 4.96975e12 | 0.000854583 0 | ||||||||
\(736\) | 6.19786e15 | 1.05783 | ||||||||
\(737\) | −2.65714e15 | −0.450136 | ||||||||
\(738\) | −1.79381e15 | −0.301624 | ||||||||
\(739\) | 7.78978e15 | 1.30011 | 0.650056 | − | 0.759886i | \(-0.274745\pi\) | ||||
0.650056 | + | 0.759886i | \(0.274745\pi\) | |||||||
\(740\) | 5.93665e14 | 0.0983484 | ||||||||
\(741\) | −3.53476e15 | −0.581246 | ||||||||
\(742\) | 1.05940e15 | 0.172917 | ||||||||
\(743\) | −7.50411e14 | −0.121580 | −0.0607898 | − | 0.998151i | \(-0.519362\pi\) | ||||
−0.0607898 | + | 0.998151i | \(0.519362\pi\) | |||||||
\(744\) | −7.59695e15 | −1.22177 | ||||||||
\(745\) | 4.63065e12 | 0.000739234 0 | ||||||||
\(746\) | −5.55187e14 | −0.0879783 | ||||||||
\(747\) | 5.15071e14 | 0.0810222 | ||||||||
\(748\) | 5.11689e15 | 0.799002 | ||||||||
\(749\) | −4.93063e15 | −0.764280 | ||||||||
\(750\) | −5.86266e14 | −0.0902106 | ||||||||
\(751\) | −8.59656e15 | −1.31312 | −0.656561 | − | 0.754273i | \(-0.727989\pi\) | ||||
−0.656561 | + | 0.754273i | \(0.727989\pi\) | |||||||
\(752\) | −4.18174e15 | −0.634101 | ||||||||
\(753\) | 2.84757e15 | 0.428650 | ||||||||
\(754\) | −3.28984e14 | −0.0491624 | ||||||||
\(755\) | −2.40596e14 | −0.0356927 | ||||||||
\(756\) | 5.54303e15 | 0.816351 | ||||||||
\(757\) | −5.23719e15 | −0.765722 | −0.382861 | − | 0.923806i | \(-0.625061\pi\) | ||||
−0.382861 | + | 0.923806i | \(0.625061\pi\) | |||||||
\(758\) | 1.17020e15 | 0.169856 | ||||||||
\(759\) | 4.74620e15 | 0.683938 | ||||||||
\(760\) | 1.10002e15 | 0.157372 | ||||||||
\(761\) | −5.40274e15 | −0.767358 | −0.383679 | − | 0.923466i | \(-0.625343\pi\) | ||||
−0.383679 | + | 0.923466i | \(0.625343\pi\) | |||||||
\(762\) | 3.46432e15 | 0.488502 | ||||||||
\(763\) | 5.19944e15 | 0.727899 | ||||||||
\(764\) | −2.48834e15 | −0.345856 | ||||||||
\(765\) | 4.87650e14 | 0.0672931 | ||||||||
\(766\) | −7.01999e15 | −0.961785 | ||||||||
\(767\) | 7.06672e15 | 0.961266 | ||||||||
\(768\) | −3.35647e15 | −0.453311 | ||||||||
\(769\) | 1.68378e15 | 0.225783 | 0.112891 | − | 0.993607i | \(-0.463989\pi\) | ||||
0.112891 | + | 0.993607i | \(0.463989\pi\) | |||||||
\(770\) | −4.14663e14 | −0.0552073 | ||||||||
\(771\) | 4.14091e15 | 0.547390 | ||||||||
\(772\) | 3.15962e15 | 0.414705 | ||||||||
\(773\) | −6.91163e14 | −0.0900727 | −0.0450363 | − | 0.998985i | \(-0.514340\pi\) | ||||
−0.0450363 | + | 0.998985i | \(0.514340\pi\) | |||||||
\(774\) | 6.28930e14 | 0.0813818 | ||||||||
\(775\) | 1.47979e16 | 1.90126 | ||||||||
\(776\) | −9.87995e15 | −1.26042 | ||||||||
\(777\) | 5.88380e15 | 0.745320 | ||||||||
\(778\) | 1.68442e15 | 0.211866 | ||||||||
\(779\) | 1.57620e16 | 1.96859 | ||||||||
\(780\) | 3.13722e14 | 0.0389068 | ||||||||
\(781\) | −7.28937e15 | −0.897655 | ||||||||
\(782\) | 4.76718e15 | 0.582941 | ||||||||
\(783\) | −1.64225e15 | −0.199411 | ||||||||
\(784\) | −2.62869e13 | −0.00316957 | ||||||||
\(785\) | 7.54604e14 | 0.0903516 | ||||||||
\(786\) | −2.35433e15 | −0.279926 | ||||||||
\(787\) | −8.76844e15 | −1.03529 | −0.517644 | − | 0.855596i | \(-0.673191\pi\) | ||||
−0.517644 | + | 0.855596i | \(0.673191\pi\) | |||||||
\(788\) | 2.04460e15 | 0.239726 | ||||||||
\(789\) | 3.65894e15 | 0.426022 | ||||||||
\(790\) | −4.44288e14 | −0.0513707 | ||||||||
\(791\) | 1.63733e16 | 1.88003 | ||||||||
\(792\) | 3.08487e15 | 0.351762 | ||||||||
\(793\) | 1.99071e15 | 0.225427 | ||||||||
\(794\) | 8.73885e14 | 0.0982746 | ||||||||
\(795\) | 2.99309e14 | 0.0334272 | ||||||||
\(796\) | −4.55780e15 | −0.505514 | ||||||||
\(797\) | −9.97692e15 | −1.09894 | −0.549472 | − | 0.835512i | \(-0.685171\pi\) | ||||
−0.549472 | + | 0.835512i | \(0.685171\pi\) | |||||||
\(798\) | 4.72080e15 | 0.516416 | ||||||||
\(799\) | −1.95677e16 | −2.12585 | ||||||||
\(800\) | 9.35614e15 | 1.00949 | ||||||||
\(801\) | 2.36171e15 | 0.253074 | ||||||||
\(802\) | −7.03113e15 | −0.748283 | ||||||||
\(803\) | −9.87090e15 | −1.04333 | ||||||||
\(804\) | −2.68485e15 | −0.281846 | ||||||||
\(805\) | 1.24856e15 | 0.130176 | ||||||||
\(806\) | 4.94037e15 | 0.511583 | ||||||||
\(807\) | 1.45641e15 | 0.149789 | ||||||||
\(808\) | −2.06825e15 | −0.211271 | ||||||||
\(809\) | 1.81464e16 | 1.84108 | 0.920540 | − | 0.390648i | \(-0.127749\pi\) | ||||
0.920540 | + | 0.390648i | \(0.127749\pi\) | |||||||
\(810\) | −2.05472e14 | −0.0207055 | ||||||||
\(811\) | 1.48265e16 | 1.48397 | 0.741984 | − | 0.670418i | \(-0.233885\pi\) | ||||
0.741984 | + | 0.670418i | \(0.233885\pi\) | |||||||
\(812\) | −1.42000e15 | −0.141166 | ||||||||
\(813\) | 6.22931e15 | 0.615095 | ||||||||
\(814\) | 4.52644e15 | 0.443938 | ||||||||
\(815\) | −1.47990e15 | −0.144167 | ||||||||
\(816\) | 3.07551e15 | 0.297592 | ||||||||
\(817\) | −5.52636e15 | −0.531151 | ||||||||
\(818\) | 4.23583e15 | 0.404385 | ||||||||
\(819\) | −2.60770e15 | −0.247284 | ||||||||
\(820\) | −1.39894e15 | −0.131772 | ||||||||
\(821\) | −1.98325e16 | −1.85562 | −0.927812 | − | 0.373048i | \(-0.878313\pi\) | ||||
−0.927812 | + | 0.373048i | \(0.878313\pi\) | |||||||
\(822\) | −3.76207e15 | −0.349649 | ||||||||
\(823\) | −4.07918e15 | −0.376594 | −0.188297 | − | 0.982112i | \(-0.560297\pi\) | ||||
−0.188297 | + | 0.982112i | \(0.560297\pi\) | |||||||
\(824\) | −9.52083e15 | −0.873123 | ||||||||
\(825\) | 7.16475e15 | 0.652686 | ||||||||
\(826\) | −9.43786e15 | −0.854050 | ||||||||
\(827\) | −1.50273e16 | −1.35083 | −0.675417 | − | 0.737436i | \(-0.736036\pi\) | ||||
−0.675417 | + | 0.737436i | \(0.736036\pi\) | |||||||
\(828\) | −4.02205e15 | −0.359154 | ||||||||
\(829\) | 1.78355e15 | 0.158211 | 0.0791054 | − | 0.996866i | \(-0.474794\pi\) | ||||
0.0791054 | + | 0.996866i | \(0.474794\pi\) | |||||||
\(830\) | −1.24289e14 | −0.0109522 | ||||||||
\(831\) | −1.18928e16 | −1.04107 | ||||||||
\(832\) | 9.50763e14 | 0.0826787 | ||||||||
\(833\) | −1.23005e14 | −0.0106261 | ||||||||
\(834\) | 6.67065e15 | 0.572473 | ||||||||
\(835\) | −9.74968e14 | −0.0831217 | ||||||||
\(836\) | −1.17374e16 | −0.994116 | ||||||||
\(837\) | 2.46616e16 | 2.07507 | ||||||||
\(838\) | 9.19362e14 | 0.0768501 | ||||||||
\(839\) | 2.08273e16 | 1.72959 | 0.864794 | − | 0.502126i | \(-0.167449\pi\) | ||||
0.864794 | + | 0.502126i | \(0.167449\pi\) | |||||||
\(840\) | −9.67616e14 | −0.0798302 | ||||||||
\(841\) | 4.20707e14 | 0.0344828 | ||||||||
\(842\) | −5.73115e15 | −0.466686 | ||||||||
\(843\) | 6.65050e15 | 0.538026 | ||||||||
\(844\) | −1.25031e16 | −1.00493 | ||||||||
\(845\) | 1.11727e15 | 0.0892168 | ||||||||
\(846\) | −5.10820e15 | −0.405257 | ||||||||
\(847\) | −2.41085e15 | −0.190025 | ||||||||
\(848\) | −1.58316e15 | −0.123979 | ||||||||
\(849\) | −6.08399e15 | −0.473365 | ||||||||
\(850\) | 7.19642e15 | 0.556304 | ||||||||
\(851\) | −1.36292e16 | −1.04678 | ||||||||
\(852\) | −7.36538e15 | −0.562053 | ||||||||
\(853\) | −2.58806e16 | −1.96225 | −0.981126 | − | 0.193370i | \(-0.938058\pi\) | ||||
−0.981126 | + | 0.193370i | \(0.938058\pi\) | |||||||
\(854\) | −2.65867e15 | −0.200284 | ||||||||
\(855\) | −1.11860e15 | −0.0837259 | ||||||||
\(856\) | −8.85132e15 | −0.658267 | ||||||||
\(857\) | −1.86002e16 | −1.37443 | −0.687215 | − | 0.726454i | \(-0.741167\pi\) | ||||
−0.687215 | + | 0.726454i | \(0.741167\pi\) | |||||||
\(858\) | 2.39199e15 | 0.175622 | ||||||||
\(859\) | −1.99564e16 | −1.45586 | −0.727931 | − | 0.685650i | \(-0.759518\pi\) | ||||
−0.727931 | + | 0.685650i | \(0.759518\pi\) | |||||||
\(860\) | 4.90484e14 | 0.0355536 | ||||||||
\(861\) | −1.38648e16 | −0.998612 | ||||||||
\(862\) | 2.89701e15 | 0.207329 | ||||||||
\(863\) | 5.86095e14 | 0.0416782 | 0.0208391 | − | 0.999783i | \(-0.493366\pi\) | ||||
0.0208391 | + | 0.999783i | \(0.493366\pi\) | |||||||
\(864\) | 1.55926e16 | 1.10178 | ||||||||
\(865\) | 1.71841e15 | 0.120653 | ||||||||
\(866\) | 2.61998e14 | 0.0182789 | ||||||||
\(867\) | 3.75349e15 | 0.260213 | ||||||||
\(868\) | 2.13242e16 | 1.46897 | ||||||||
\(869\) | 1.09481e16 | 0.749425 | ||||||||
\(870\) | 1.24134e14 | 0.00844377 | ||||||||
\(871\) | 4.03220e15 | 0.272547 | ||||||||
\(872\) | 9.33387e15 | 0.626933 | ||||||||
\(873\) | 1.00468e16 | 0.670577 | ||||||||
\(874\) | −1.09352e16 | −0.725294 | ||||||||
\(875\) | 3.80040e15 | 0.250487 | ||||||||
\(876\) | −9.97383e15 | −0.653265 | ||||||||
\(877\) | −2.50479e16 | −1.63032 | −0.815162 | − | 0.579232i | \(-0.803352\pi\) | ||||
−0.815162 | + | 0.579232i | \(0.803352\pi\) | |||||||
\(878\) | 1.24314e16 | 0.804083 | ||||||||
\(879\) | 1.81003e16 | 1.16345 | ||||||||
\(880\) | 6.19672e14 | 0.0395829 | ||||||||
\(881\) | −2.71552e16 | −1.72379 | −0.861896 | − | 0.507085i | \(-0.830723\pi\) | ||||
−0.861896 | + | 0.507085i | \(0.830723\pi\) | |||||||
\(882\) | −3.21108e13 | −0.00202569 | ||||||||
\(883\) | −6.82561e14 | −0.0427915 | −0.0213958 | − | 0.999771i | \(-0.506811\pi\) | ||||
−0.0213958 | + | 0.999771i | \(0.506811\pi\) | |||||||
\(884\) | −7.76486e15 | −0.483778 | ||||||||
\(885\) | −2.66646e15 | −0.165100 | ||||||||
\(886\) | 3.90583e15 | 0.240341 | ||||||||
\(887\) | 1.46682e16 | 0.897008 | 0.448504 | − | 0.893781i | \(-0.351957\pi\) | ||||
0.448504 | + | 0.893781i | \(0.351957\pi\) | |||||||
\(888\) | 1.05624e16 | 0.641937 | ||||||||
\(889\) | −2.24571e16 | −1.35642 | ||||||||
\(890\) | −5.69891e14 | −0.0342095 | ||||||||
\(891\) | 5.06320e15 | 0.302063 | ||||||||
\(892\) | 1.38505e16 | 0.821218 | ||||||||
\(893\) | 4.48854e16 | 2.64498 | ||||||||
\(894\) | 3.56748e13 | 0.00208932 | ||||||||
\(895\) | −8.56932e14 | −0.0498792 | ||||||||
\(896\) | 1.63844e16 | 0.947841 | ||||||||
\(897\) | −7.20233e15 | −0.414109 | ||||||||
\(898\) | 1.72414e15 | 0.0985266 | ||||||||
\(899\) | −6.31777e15 | −0.358827 | ||||||||
\(900\) | −6.07159e15 | −0.342743 | ||||||||
\(901\) | −7.40811e15 | −0.415644 | ||||||||
\(902\) | −1.06663e16 | −0.594808 | ||||||||
\(903\) | 4.86118e15 | 0.269438 | ||||||||
\(904\) | 2.93928e16 | 1.61925 | ||||||||
\(905\) | −2.71352e15 | −0.148582 | ||||||||
\(906\) | −1.85356e15 | −0.100879 | ||||||||
\(907\) | 1.65196e16 | 0.893634 | 0.446817 | − | 0.894625i | \(-0.352558\pi\) | ||||
0.446817 | + | 0.894625i | \(0.352558\pi\) | |||||||
\(908\) | 1.49803e16 | 0.805469 | ||||||||
\(909\) | 2.10317e15 | 0.112402 | ||||||||
\(910\) | 6.29249e14 | 0.0334268 | ||||||||
\(911\) | −2.65587e16 | −1.40235 | −0.701173 | − | 0.712991i | \(-0.747340\pi\) | ||||
−0.701173 | + | 0.712991i | \(0.747340\pi\) | |||||||
\(912\) | −7.05475e15 | −0.370263 | ||||||||
\(913\) | 3.06270e15 | 0.159777 | ||||||||
\(914\) | 9.69037e15 | 0.502500 | ||||||||
\(915\) | −7.51148e14 | −0.0387177 | ||||||||
\(916\) | 2.40259e16 | 1.23099 | ||||||||
\(917\) | 1.52617e16 | 0.777268 | ||||||||
\(918\) | 1.19933e16 | 0.607161 | ||||||||
\(919\) | 1.23677e16 | 0.622378 | 0.311189 | − | 0.950348i | \(-0.399273\pi\) | ||||
0.311189 | + | 0.950348i | \(0.399273\pi\) | |||||||
\(920\) | 2.24137e15 | 0.112120 | ||||||||
\(921\) | −2.69879e16 | −1.34196 | ||||||||
\(922\) | −6.53543e15 | −0.323038 | ||||||||
\(923\) | 1.10616e16 | 0.543510 | ||||||||
\(924\) | 1.03246e16 | 0.504287 | ||||||||
\(925\) | −2.05743e16 | −0.998952 | ||||||||
\(926\) | −2.35447e15 | −0.113640 | ||||||||
\(927\) | 9.68160e15 | 0.464525 | ||||||||
\(928\) | −3.99448e15 | −0.190523 | ||||||||
\(929\) | −2.12065e16 | −1.00550 | −0.502751 | − | 0.864432i | \(-0.667679\pi\) | ||||
−0.502751 | + | 0.864432i | \(0.667679\pi\) | |||||||
\(930\) | −1.86413e15 | −0.0878658 | ||||||||
\(931\) | 2.82155e14 | 0.0132210 | ||||||||
\(932\) | −2.01782e16 | −0.939929 | ||||||||
\(933\) | 8.62208e15 | 0.399267 | ||||||||
\(934\) | 5.70376e15 | 0.262575 | ||||||||
\(935\) | 2.89965e15 | 0.132703 | ||||||||
\(936\) | −4.68127e15 | −0.212984 | ||||||||
\(937\) | 4.75067e15 | 0.214876 | 0.107438 | − | 0.994212i | \(-0.465735\pi\) | ||||
0.107438 | + | 0.994212i | \(0.465735\pi\) | |||||||
\(938\) | −5.38515e15 | −0.242149 | ||||||||
\(939\) | −3.52425e15 | −0.157546 | ||||||||
\(940\) | −3.98373e15 | −0.177046 | ||||||||
\(941\) | 1.38698e16 | 0.612813 | 0.306406 | − | 0.951901i | \(-0.400873\pi\) | ||||
0.306406 | + | 0.951901i | \(0.400873\pi\) | |||||||
\(942\) | 5.81352e15 | 0.255364 | ||||||||
\(943\) | 3.21163e16 | 1.40253 | ||||||||
\(944\) | 1.41039e16 | 0.612342 | ||||||||
\(945\) | 3.14113e15 | 0.135585 | ||||||||
\(946\) | 3.73972e15 | 0.160486 | ||||||||
\(947\) | −5.40709e15 | −0.230695 | −0.115348 | − | 0.993325i | \(-0.536798\pi\) | ||||
−0.115348 | + | 0.993325i | \(0.536798\pi\) | |||||||
\(948\) | 1.10622e16 | 0.469242 | ||||||||
\(949\) | 1.49790e16 | 0.631713 | ||||||||
\(950\) | −1.65075e16 | −0.692152 | ||||||||
\(951\) | −1.15737e16 | −0.482482 | ||||||||
\(952\) | 2.39492e16 | 0.992631 | ||||||||
\(953\) | −2.32910e16 | −0.959793 | −0.479896 | − | 0.877325i | \(-0.659326\pi\) | ||||
−0.479896 | + | 0.877325i | \(0.659326\pi\) | |||||||
\(954\) | −1.93391e15 | −0.0792355 | ||||||||
\(955\) | −1.41009e15 | −0.0574419 | ||||||||
\(956\) | 1.03738e16 | 0.420165 | ||||||||
\(957\) | −3.05890e15 | −0.123183 | ||||||||
\(958\) | 2.13242e15 | 0.0853814 | ||||||||
\(959\) | 2.43872e16 | 0.970867 | ||||||||
\(960\) | −3.58748e14 | −0.0142003 | ||||||||
\(961\) | 6.94656e16 | 2.73396 | ||||||||
\(962\) | −6.86884e15 | −0.268795 | ||||||||
\(963\) | 9.00078e15 | 0.350216 | ||||||||
\(964\) | −2.28677e16 | −0.884704 | ||||||||
\(965\) | 1.79050e15 | 0.0688768 | ||||||||
\(966\) | 9.61897e15 | 0.367921 | ||||||||
\(967\) | −4.20715e16 | −1.60008 | −0.800042 | − | 0.599944i | \(-0.795189\pi\) | ||||
−0.800042 | + | 0.599944i | \(0.795189\pi\) | |||||||
\(968\) | −4.32789e15 | −0.163667 | ||||||||
\(969\) | −3.30115e16 | −1.24132 | ||||||||
\(970\) | −2.42433e15 | −0.0906456 | ||||||||
\(971\) | −4.86896e16 | −1.81022 | −0.905108 | − | 0.425181i | \(-0.860210\pi\) | ||||
−0.905108 | + | 0.425181i | \(0.860210\pi\) | |||||||
\(972\) | −1.70677e16 | −0.630974 | ||||||||
\(973\) | −4.32418e16 | −1.58958 | ||||||||
\(974\) | −1.09013e16 | −0.398479 | ||||||||
\(975\) | −1.08725e16 | −0.395187 | ||||||||
\(976\) | 3.97311e15 | 0.143601 | ||||||||
\(977\) | −3.15141e15 | −0.113262 | −0.0566311 | − | 0.998395i | \(-0.518036\pi\) | ||||
−0.0566311 | + | 0.998395i | \(0.518036\pi\) | |||||||
\(978\) | −1.14013e16 | −0.407464 | ||||||||
\(979\) | 1.40431e16 | 0.499068 | ||||||||
\(980\) | −2.50422e13 | −0.000884972 0 | ||||||||
\(981\) | −9.49148e15 | −0.333545 | ||||||||
\(982\) | 2.14632e16 | 0.750036 | ||||||||
\(983\) | 1.18477e16 | 0.411709 | 0.205855 | − | 0.978583i | \(-0.434003\pi\) | ||||
0.205855 | + | 0.978583i | \(0.434003\pi\) | |||||||
\(984\) | −2.48897e16 | −0.860096 | ||||||||
\(985\) | 1.15864e15 | 0.0398151 | ||||||||
\(986\) | −3.07242e15 | −0.104992 | ||||||||
\(987\) | −3.94827e16 | −1.34172 | ||||||||
\(988\) | 1.78114e16 | 0.601915 | ||||||||
\(989\) | −1.12604e16 | −0.378419 | ||||||||
\(990\) | 7.56961e14 | 0.0252976 | ||||||||
\(991\) | 3.30955e16 | 1.09993 | 0.549963 | − | 0.835189i | \(-0.314642\pi\) | ||||
0.549963 | + | 0.835189i | \(0.314642\pi\) | |||||||
\(992\) | 5.99852e16 | 1.98258 | ||||||||
\(993\) | −3.97891e16 | −1.30780 | ||||||||
\(994\) | −1.47731e16 | −0.482889 | ||||||||
\(995\) | −2.58282e15 | −0.0839589 | ||||||||
\(996\) | 3.09463e15 | 0.100042 | ||||||||
\(997\) | 1.17372e15 | 0.0377346 | 0.0188673 | − | 0.999822i | \(-0.493994\pi\) | ||||
0.0188673 | + | 0.999822i | \(0.493994\pi\) | |||||||
\(998\) | −2.79013e16 | −0.892084 | ||||||||
\(999\) | −3.42883e16 | −1.09028 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 29.12.a.a.1.6 | ✓ | 11 | |
3.2 | odd | 2 | 261.12.a.a.1.6 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.12.a.a.1.6 | ✓ | 11 | 1.1 | even | 1 | trivial | |
261.12.a.a.1.6 | 11 | 3.2 | odd | 2 |