Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,104,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 104, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 104);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 104 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(67.1843880807\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3 x^{7} + \cdots + 10\!\cdots\!50 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{104}\cdot 3^{40}\cdot 5^{12}\cdot 7^{8}\cdot 11\cdot 13^{3}\cdot 17^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.05899e14\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.09018e15 | 0.970375 | 0.485187 | − | 0.874410i | \(-0.338751\pi\) | ||||
0.485187 | + | 0.874410i | \(0.338751\pi\) | |||||||
\(3\) | −9.30646e23 | −0.249482 | −0.124741 | − | 0.992189i | \(-0.539810\pi\) | ||||
−0.124741 | + | 0.992189i | \(0.539810\pi\) | |||||||
\(4\) | −5.91967e29 | −0.0583725 | ||||||||
\(5\) | −7.61227e35 | −0.766583 | −0.383292 | − | 0.923627i | \(-0.625210\pi\) | ||||
−0.383292 | + | 0.923627i | \(0.625210\pi\) | |||||||
\(6\) | −2.87587e39 | −0.242091 | ||||||||
\(7\) | −3.39343e43 | −1.01880 | −0.509401 | − | 0.860529i | \(-0.670133\pi\) | ||||
−0.509401 | + | 0.860529i | \(0.670133\pi\) | |||||||
\(8\) | −3.31675e46 | −1.02702 | ||||||||
\(9\) | −1.30491e49 | −0.937759 | ||||||||
\(10\) | −2.35233e51 | −0.743873 | ||||||||
\(11\) | −1.54885e53 | −0.361647 | −0.180824 | − | 0.983516i | \(-0.557876\pi\) | ||||
−0.180824 | + | 0.983516i | \(0.557876\pi\) | |||||||
\(12\) | 5.50912e53 | 0.0145629 | ||||||||
\(13\) | −6.78771e56 | −0.290831 | −0.145415 | − | 0.989371i | \(-0.546452\pi\) | ||||
−0.145415 | + | 0.989371i | \(0.546452\pi\) | |||||||
\(14\) | −1.04863e59 | −0.988620 | ||||||||
\(15\) | 7.08433e59 | 0.191249 | ||||||||
\(16\) | −9.64903e61 | −0.938220 | ||||||||
\(17\) | 3.47857e63 | 1.49033 | 0.745163 | − | 0.666883i | \(-0.232372\pi\) | ||||
0.745163 | + | 0.666883i | \(0.232372\pi\) | |||||||
\(18\) | −4.03241e64 | −0.909977 | ||||||||
\(19\) | −3.44755e64 | −0.0480507 | −0.0240254 | − | 0.999711i | \(-0.507648\pi\) | ||||
−0.0240254 | + | 0.999711i | \(0.507648\pi\) | |||||||
\(20\) | 4.50622e65 | 0.0447474 | ||||||||
\(21\) | 3.15808e67 | 0.254173 | ||||||||
\(22\) | −4.78622e68 | −0.350933 | ||||||||
\(23\) | −5.84642e69 | −0.434416 | −0.217208 | − | 0.976125i | \(-0.569695\pi\) | ||||
−0.217208 | + | 0.976125i | \(0.569695\pi\) | |||||||
\(24\) | 3.08672e70 | 0.256223 | ||||||||
\(25\) | −4.06609e71 | −0.412350 | ||||||||
\(26\) | −2.09753e72 | −0.282215 | ||||||||
\(27\) | 2.50942e73 | 0.483437 | ||||||||
\(28\) | 2.00880e73 | 0.0594700 | ||||||||
\(29\) | 3.50391e73 | 0.0170238 | 0.00851190 | − | 0.999964i | \(-0.497291\pi\) | ||||
0.00851190 | + | 0.999964i | \(0.497291\pi\) | |||||||
\(30\) | 2.18919e75 | 0.185583 | ||||||||
\(31\) | 1.38875e76 | 0.217519 | 0.108759 | − | 0.994068i | \(-0.465312\pi\) | ||||
0.108759 | + | 0.994068i | \(0.465312\pi\) | |||||||
\(32\) | 3.81852e76 | 0.116593 | ||||||||
\(33\) | 1.44143e77 | 0.0902246 | ||||||||
\(34\) | 1.07494e79 | 1.44617 | ||||||||
\(35\) | 2.58317e79 | 0.780997 | ||||||||
\(36\) | 7.72464e78 | 0.0547393 | ||||||||
\(37\) | 1.03572e81 | 1.79000 | 0.895000 | − | 0.446066i | \(-0.147175\pi\) | ||||
0.895000 | + | 0.446066i | \(0.147175\pi\) | |||||||
\(38\) | −1.06536e80 | −0.0466272 | ||||||||
\(39\) | 6.31696e80 | 0.0725572 | ||||||||
\(40\) | 2.52480e82 | 0.787295 | ||||||||
\(41\) | −1.61257e83 | −1.40978 | −0.704889 | − | 0.709317i | \(-0.749003\pi\) | ||||
−0.704889 | + | 0.709317i | \(0.749003\pi\) | |||||||
\(42\) | 9.75906e82 | 0.246643 | ||||||||
\(43\) | −2.10970e84 | −1.58707 | −0.793533 | − | 0.608527i | \(-0.791761\pi\) | ||||
−0.793533 | + | 0.608527i | \(0.791761\pi\) | |||||||
\(44\) | 9.16867e82 | 0.0211103 | ||||||||
\(45\) | 9.93333e84 | 0.718870 | ||||||||
\(46\) | −1.80665e85 | −0.421547 | ||||||||
\(47\) | 1.62802e86 | 1.25493 | 0.627465 | − | 0.778645i | \(-0.284093\pi\) | ||||
0.627465 | + | 0.778645i | \(0.284093\pi\) | |||||||
\(48\) | 8.97984e85 | 0.234069 | ||||||||
\(49\) | 4.21120e85 | 0.0379584 | ||||||||
\(50\) | −1.25650e87 | −0.400135 | ||||||||
\(51\) | −3.23732e87 | −0.371810 | ||||||||
\(52\) | 4.01810e86 | 0.0169765 | ||||||||
\(53\) | −6.47734e88 | −1.02610 | −0.513049 | − | 0.858359i | \(-0.671484\pi\) | ||||
−0.513049 | + | 0.858359i | \(0.671484\pi\) | |||||||
\(54\) | 7.75457e88 | 0.469115 | ||||||||
\(55\) | 1.17902e89 | 0.277233 | ||||||||
\(56\) | 1.12552e90 | 1.04633 | ||||||||
\(57\) | 3.20845e88 | 0.0119878 | ||||||||
\(58\) | 1.08277e89 | 0.0165195 | ||||||||
\(59\) | −7.57677e90 | −0.479298 | −0.239649 | − | 0.970860i | \(-0.577032\pi\) | ||||
−0.239649 | + | 0.970860i | \(0.577032\pi\) | |||||||
\(60\) | −4.19369e89 | −0.0111637 | ||||||||
\(61\) | −4.94411e91 | −0.561826 | −0.280913 | − | 0.959733i | \(-0.590637\pi\) | ||||
−0.280913 | + | 0.959733i | \(0.590637\pi\) | |||||||
\(62\) | 4.29149e91 | 0.211075 | ||||||||
\(63\) | 4.42812e92 | 0.955391 | ||||||||
\(64\) | 1.09653e93 | 1.05136 | ||||||||
\(65\) | 5.16699e92 | 0.222946 | ||||||||
\(66\) | 4.45428e92 | 0.0875517 | ||||||||
\(67\) | 1.38891e94 | 1.25841 | 0.629205 | − | 0.777239i | \(-0.283380\pi\) | ||||
0.629205 | + | 0.777239i | \(0.283380\pi\) | |||||||
\(68\) | −2.05920e93 | −0.0869940 | ||||||||
\(69\) | 5.44094e93 | 0.108379 | ||||||||
\(70\) | 7.98248e94 | 0.757860 | ||||||||
\(71\) | 3.57169e95 | 1.63331 | 0.816656 | − | 0.577124i | \(-0.195825\pi\) | ||||
0.816656 | + | 0.577124i | \(0.195825\pi\) | |||||||
\(72\) | 4.32805e95 | 0.963095 | ||||||||
\(73\) | 8.65911e95 | 0.946992 | 0.473496 | − | 0.880796i | \(-0.342992\pi\) | ||||
0.473496 | + | 0.880796i | \(0.342992\pi\) | |||||||
\(74\) | 3.20056e96 | 1.73697 | ||||||||
\(75\) | 3.78409e95 | 0.102874 | ||||||||
\(76\) | 2.04084e94 | 0.00280484 | ||||||||
\(77\) | 5.25590e96 | 0.368447 | ||||||||
\(78\) | 1.95206e96 | 0.0704077 | ||||||||
\(79\) | −9.98014e96 | −0.186785 | −0.0933924 | − | 0.995629i | \(-0.529771\pi\) | ||||
−0.0933924 | + | 0.995629i | \(0.529771\pi\) | |||||||
\(80\) | 7.34511e97 | 0.719224 | ||||||||
\(81\) | 1.58227e98 | 0.817150 | ||||||||
\(82\) | −4.98315e98 | −1.36801 | ||||||||
\(83\) | −8.18903e98 | −1.20423 | −0.602117 | − | 0.798408i | \(-0.705676\pi\) | ||||
−0.602117 | + | 0.798408i | \(0.705676\pi\) | |||||||
\(84\) | −1.86948e97 | −0.0148367 | ||||||||
\(85\) | −2.64798e99 | −1.14246 | ||||||||
\(86\) | −6.51936e99 | −1.54005 | ||||||||
\(87\) | −3.26090e97 | −0.00424714 | ||||||||
\(88\) | 5.13713e99 | 0.371418 | ||||||||
\(89\) | −7.53893e99 | −0.304596 | −0.152298 | − | 0.988335i | \(-0.548667\pi\) | ||||
−0.152298 | + | 0.988335i | \(0.548667\pi\) | |||||||
\(90\) | 3.06958e100 | 0.697573 | ||||||||
\(91\) | 2.30336e100 | 0.296299 | ||||||||
\(92\) | 3.46089e99 | 0.0253580 | ||||||||
\(93\) | −1.29243e100 | −0.0542671 | ||||||||
\(94\) | 5.03087e101 | 1.21775 | ||||||||
\(95\) | 2.62437e100 | 0.0368349 | ||||||||
\(96\) | −3.55370e100 | −0.0290879 | ||||||||
\(97\) | 3.33364e102 | 1.60020 | 0.800100 | − | 0.599867i | \(-0.204780\pi\) | ||||
0.800100 | + | 0.599867i | \(0.204780\pi\) | |||||||
\(98\) | 1.30134e101 | 0.0368339 | ||||||||
\(99\) | 2.02110e102 | 0.339138 | ||||||||
\(100\) | 2.40699e101 | 0.0240699 | ||||||||
\(101\) | −3.07503e103 | −1.84204 | −0.921020 | − | 0.389515i | \(-0.872643\pi\) | ||||
−0.921020 | + | 0.389515i | \(0.872643\pi\) | |||||||
\(102\) | −1.00039e103 | −0.360795 | ||||||||
\(103\) | −5.88557e103 | −1.28431 | −0.642157 | − | 0.766573i | \(-0.721960\pi\) | ||||
−0.642157 | + | 0.766573i | \(0.721960\pi\) | |||||||
\(104\) | 2.25131e103 | 0.298689 | ||||||||
\(105\) | −2.40402e103 | −0.194845 | ||||||||
\(106\) | −2.00162e104 | −0.995700 | ||||||||
\(107\) | 4.99845e104 | 1.53310 | 0.766551 | − | 0.642184i | \(-0.221971\pi\) | ||||
0.766551 | + | 0.642184i | \(0.221971\pi\) | |||||||
\(108\) | −1.48549e103 | −0.0282194 | ||||||||
\(109\) | −9.22156e103 | −0.108978 | −0.0544891 | − | 0.998514i | \(-0.517353\pi\) | ||||
−0.0544891 | + | 0.998514i | \(0.517353\pi\) | |||||||
\(110\) | 3.64340e104 | 0.269020 | ||||||||
\(111\) | −9.63888e104 | −0.446574 | ||||||||
\(112\) | 3.27433e105 | 0.955861 | ||||||||
\(113\) | 5.74183e105 | 1.06050 | 0.530249 | − | 0.847842i | \(-0.322098\pi\) | ||||
0.530249 | + | 0.847842i | \(0.322098\pi\) | |||||||
\(114\) | 9.91469e103 | 0.0116327 | ||||||||
\(115\) | 4.45045e105 | 0.333016 | ||||||||
\(116\) | −2.07420e103 | −0.000993721 0 | ||||||||
\(117\) | 8.85735e105 | 0.272729 | ||||||||
\(118\) | −2.34136e106 | −0.465098 | ||||||||
\(119\) | −1.18043e107 | −1.51835 | ||||||||
\(120\) | −2.34969e106 | −0.196416 | ||||||||
\(121\) | −1.59431e107 | −0.869211 | ||||||||
\(122\) | −1.52782e107 | −0.545181 | ||||||||
\(123\) | 1.50073e107 | 0.351715 | ||||||||
\(124\) | −8.22094e105 | −0.0126971 | ||||||||
\(125\) | 1.06015e108 | 1.08268 | ||||||||
\(126\) | 1.36837e108 | 0.927087 | ||||||||
\(127\) | −2.37665e108 | −1.07170 | −0.535851 | − | 0.844313i | \(-0.680009\pi\) | ||||
−0.535851 | + | 0.844313i | \(0.680009\pi\) | |||||||
\(128\) | 3.00123e108 | 0.903620 | ||||||||
\(129\) | 1.96338e108 | 0.395945 | ||||||||
\(130\) | 1.59670e108 | 0.216341 | ||||||||
\(131\) | −3.88226e108 | −0.354498 | −0.177249 | − | 0.984166i | \(-0.556720\pi\) | ||||
−0.177249 | + | 0.984166i | \(0.556720\pi\) | |||||||
\(132\) | −8.53278e106 | −0.00526664 | ||||||||
\(133\) | 1.16990e108 | 0.0489542 | ||||||||
\(134\) | 4.29199e109 | 1.22113 | ||||||||
\(135\) | −1.91024e109 | −0.370594 | ||||||||
\(136\) | −1.15375e110 | −1.53059 | ||||||||
\(137\) | −1.01353e110 | −0.921991 | −0.460995 | − | 0.887403i | \(-0.652508\pi\) | ||||
−0.460995 | + | 0.887403i | \(0.652508\pi\) | |||||||
\(138\) | 1.68135e109 | 0.105168 | ||||||||
\(139\) | −1.76086e110 | −0.759385 | −0.379692 | − | 0.925113i | \(-0.623970\pi\) | ||||
−0.379692 | + | 0.925113i | \(0.623970\pi\) | |||||||
\(140\) | −1.52915e109 | −0.0455887 | ||||||||
\(141\) | −1.51511e110 | −0.313083 | ||||||||
\(142\) | 1.10372e111 | 1.58493 | ||||||||
\(143\) | 1.05131e110 | 0.105178 | ||||||||
\(144\) | 1.25911e111 | 0.879824 | ||||||||
\(145\) | −2.66727e109 | −0.0130501 | ||||||||
\(146\) | 2.67583e111 | 0.918937 | ||||||||
\(147\) | −3.91914e109 | −0.00946996 | ||||||||
\(148\) | −6.13112e110 | −0.104487 | ||||||||
\(149\) | −1.09933e112 | −1.32445 | −0.662226 | − | 0.749304i | \(-0.730388\pi\) | ||||
−0.662226 | + | 0.749304i | \(0.730388\pi\) | |||||||
\(150\) | 1.16935e111 | 0.0998265 | ||||||||
\(151\) | 6.03159e111 | 0.365695 | 0.182848 | − | 0.983141i | \(-0.441469\pi\) | ||||
0.182848 | + | 0.983141i | \(0.441469\pi\) | |||||||
\(152\) | 1.14346e111 | 0.0493490 | ||||||||
\(153\) | −4.53922e112 | −1.39757 | ||||||||
\(154\) | 1.62417e112 | 0.357532 | ||||||||
\(155\) | −1.05715e112 | −0.166746 | ||||||||
\(156\) | −3.73943e110 | −0.00423535 | ||||||||
\(157\) | −3.47276e112 | −0.283037 | −0.141518 | − | 0.989936i | \(-0.545198\pi\) | ||||
−0.141518 | + | 0.989936i | \(0.545198\pi\) | |||||||
\(158\) | −3.08405e112 | −0.181251 | ||||||||
\(159\) | 6.02811e112 | 0.255994 | ||||||||
\(160\) | −2.90677e112 | −0.0893781 | ||||||||
\(161\) | 1.98394e113 | 0.442584 | ||||||||
\(162\) | 4.88950e113 | 0.792941 | ||||||||
\(163\) | 1.33487e114 | 1.57680 | 0.788402 | − | 0.615160i | \(-0.210909\pi\) | ||||
0.788402 | + | 0.615160i | \(0.210909\pi\) | |||||||
\(164\) | 9.54591e112 | 0.0822923 | ||||||||
\(165\) | −1.09725e113 | −0.0691647 | ||||||||
\(166\) | −2.53056e114 | −1.16856 | ||||||||
\(167\) | 2.11932e113 | 0.0718289 | 0.0359144 | − | 0.999355i | \(-0.488566\pi\) | ||||
0.0359144 | + | 0.999355i | \(0.488566\pi\) | |||||||
\(168\) | −1.04746e114 | −0.261041 | ||||||||
\(169\) | −4.98637e114 | −0.915417 | ||||||||
\(170\) | −8.18275e114 | −1.10861 | ||||||||
\(171\) | 4.49874e113 | 0.0450600 | ||||||||
\(172\) | 1.24887e114 | 0.0926410 | ||||||||
\(173\) | 1.25212e115 | 0.689081 | 0.344540 | − | 0.938772i | \(-0.388035\pi\) | ||||
0.344540 | + | 0.938772i | \(0.388035\pi\) | |||||||
\(174\) | −1.00768e113 | −0.00412131 | ||||||||
\(175\) | 1.37980e115 | 0.420104 | ||||||||
\(176\) | 1.49449e115 | 0.339305 | ||||||||
\(177\) | 7.05129e114 | 0.119576 | ||||||||
\(178\) | −2.32967e115 | −0.295572 | ||||||||
\(179\) | 6.23982e115 | 0.593255 | 0.296627 | − | 0.954993i | \(-0.404138\pi\) | ||||
0.296627 | + | 0.954993i | \(0.404138\pi\) | |||||||
\(180\) | −5.88020e114 | −0.0419622 | ||||||||
\(181\) | 3.59924e115 | 0.193092 | 0.0965460 | − | 0.995329i | \(-0.469221\pi\) | ||||
0.0965460 | + | 0.995329i | \(0.469221\pi\) | |||||||
\(182\) | 7.11782e115 | 0.287521 | ||||||||
\(183\) | 4.60121e115 | 0.140166 | ||||||||
\(184\) | 1.93911e116 | 0.446153 | ||||||||
\(185\) | −7.88418e116 | −1.37218 | ||||||||
\(186\) | −3.99386e115 | −0.0526594 | ||||||||
\(187\) | −5.38777e116 | −0.538972 | ||||||||
\(188\) | −9.63733e115 | −0.0732534 | ||||||||
\(189\) | −8.51555e116 | −0.492526 | ||||||||
\(190\) | 8.10978e115 | 0.0357436 | ||||||||
\(191\) | −3.05068e117 | −1.02607 | −0.513037 | − | 0.858367i | \(-0.671480\pi\) | ||||
−0.513037 | + | 0.858367i | \(0.671480\pi\) | |||||||
\(192\) | −1.02048e117 | −0.262296 | ||||||||
\(193\) | 8.06071e117 | 1.58552 | 0.792760 | − | 0.609534i | \(-0.208643\pi\) | ||||
0.792760 | + | 0.609534i | \(0.208643\pi\) | |||||||
\(194\) | 1.03016e118 | 1.55279 | ||||||||
\(195\) | −4.80864e116 | −0.0556211 | ||||||||
\(196\) | −2.49290e115 | −0.00221573 | ||||||||
\(197\) | 8.16653e117 | 0.558505 | 0.279252 | − | 0.960218i | \(-0.409913\pi\) | ||||
0.279252 | + | 0.960218i | \(0.409913\pi\) | |||||||
\(198\) | 6.24558e117 | 0.329091 | ||||||||
\(199\) | −2.29387e118 | −0.932470 | −0.466235 | − | 0.884661i | \(-0.654390\pi\) | ||||
−0.466235 | + | 0.884661i | \(0.654390\pi\) | |||||||
\(200\) | 1.34862e118 | 0.423491 | ||||||||
\(201\) | −1.29259e118 | −0.313951 | ||||||||
\(202\) | −9.50242e118 | −1.78747 | ||||||||
\(203\) | −1.18903e117 | −0.0173439 | ||||||||
\(204\) | 1.91639e117 | 0.0217035 | ||||||||
\(205\) | 1.22754e119 | 1.08071 | ||||||||
\(206\) | −1.81875e119 | −1.24627 | ||||||||
\(207\) | 7.62904e118 | 0.407378 | ||||||||
\(208\) | 6.54949e118 | 0.272863 | ||||||||
\(209\) | 5.33972e117 | 0.0173774 | ||||||||
\(210\) | −7.42886e118 | −0.189073 | ||||||||
\(211\) | 1.64335e118 | 0.0327478 | 0.0163739 | − | 0.999866i | \(-0.494788\pi\) | ||||
0.0163739 | + | 0.999866i | \(0.494788\pi\) | |||||||
\(212\) | 3.83437e118 | 0.0598959 | ||||||||
\(213\) | −3.32398e119 | −0.407483 | ||||||||
\(214\) | 1.54461e120 | 1.48768 | ||||||||
\(215\) | 1.60596e120 | 1.21662 | ||||||||
\(216\) | −8.32311e119 | −0.496498 | ||||||||
\(217\) | −4.71262e119 | −0.221608 | ||||||||
\(218\) | −2.84963e119 | −0.105750 | ||||||||
\(219\) | −8.05857e119 | −0.236258 | ||||||||
\(220\) | −6.97944e118 | −0.0161828 | ||||||||
\(221\) | −2.36115e120 | −0.433433 | ||||||||
\(222\) | −2.97859e120 | −0.433344 | ||||||||
\(223\) | −1.63017e121 | −1.88163 | −0.940813 | − | 0.338927i | \(-0.889936\pi\) | ||||
−0.940813 | + | 0.338927i | \(0.889936\pi\) | |||||||
\(224\) | −1.29579e120 | −0.118785 | ||||||||
\(225\) | 5.30588e120 | 0.386685 | ||||||||
\(226\) | 1.77433e121 | 1.02908 | ||||||||
\(227\) | −2.48101e120 | −0.114630 | −0.0573149 | − | 0.998356i | \(-0.518254\pi\) | ||||
−0.0573149 | + | 0.998356i | \(0.518254\pi\) | |||||||
\(228\) | −1.89930e118 | −0.000699758 0 | ||||||||
\(229\) | 4.69922e121 | 1.38197 | 0.690984 | − | 0.722870i | \(-0.257177\pi\) | ||||
0.690984 | + | 0.722870i | \(0.257177\pi\) | |||||||
\(230\) | 1.37527e121 | 0.323151 | ||||||||
\(231\) | −4.89139e120 | −0.0919211 | ||||||||
\(232\) | −1.16216e120 | −0.0174837 | ||||||||
\(233\) | 3.18301e121 | 0.383715 | 0.191857 | − | 0.981423i | \(-0.438549\pi\) | ||||
0.191857 | + | 0.981423i | \(0.438549\pi\) | |||||||
\(234\) | 2.73708e121 | 0.264650 | ||||||||
\(235\) | −1.23929e122 | −0.962008 | ||||||||
\(236\) | 4.48520e120 | 0.0279778 | ||||||||
\(237\) | 9.28798e120 | 0.0465995 | ||||||||
\(238\) | −3.64774e122 | −1.47337 | ||||||||
\(239\) | 1.30194e122 | 0.423738 | 0.211869 | − | 0.977298i | \(-0.432045\pi\) | ||||
0.211869 | + | 0.977298i | \(0.432045\pi\) | |||||||
\(240\) | −6.83570e121 | −0.179434 | ||||||||
\(241\) | 5.92699e122 | 1.25590 | 0.627952 | − | 0.778252i | \(-0.283893\pi\) | ||||
0.627952 | + | 0.778252i | \(0.283893\pi\) | |||||||
\(242\) | −4.92670e122 | −0.843461 | ||||||||
\(243\) | −4.96444e122 | −0.687301 | ||||||||
\(244\) | 2.92675e121 | 0.0327952 | ||||||||
\(245\) | −3.20568e121 | −0.0290983 | ||||||||
\(246\) | 4.63755e122 | 0.341295 | ||||||||
\(247\) | 2.34010e121 | 0.0139746 | ||||||||
\(248\) | −4.60613e122 | −0.223396 | ||||||||
\(249\) | 7.62109e122 | 0.300435 | ||||||||
\(250\) | 3.27606e123 | 1.05061 | ||||||||
\(251\) | 4.58935e123 | 1.19827 | 0.599134 | − | 0.800648i | \(-0.295512\pi\) | ||||
0.599134 | + | 0.800648i | \(0.295512\pi\) | |||||||
\(252\) | −2.62130e122 | −0.0557685 | ||||||||
\(253\) | 9.05520e122 | 0.157105 | ||||||||
\(254\) | −7.34429e123 | −1.03995 | ||||||||
\(255\) | 2.46433e123 | 0.285023 | ||||||||
\(256\) | −1.84577e123 | −0.174509 | ||||||||
\(257\) | −1.50678e124 | −1.16545 | −0.582725 | − | 0.812670i | \(-0.698013\pi\) | ||||
−0.582725 | + | 0.812670i | \(0.698013\pi\) | |||||||
\(258\) | 6.06721e123 | 0.384215 | ||||||||
\(259\) | −3.51464e124 | −1.82366 | ||||||||
\(260\) | −3.05869e122 | −0.0130139 | ||||||||
\(261\) | −4.57229e122 | −0.0159642 | ||||||||
\(262\) | −1.19969e124 | −0.343996 | ||||||||
\(263\) | 7.65944e124 | 1.80499 | 0.902497 | − | 0.430696i | \(-0.141732\pi\) | ||||
0.902497 | + | 0.430696i | \(0.141732\pi\) | |||||||
\(264\) | −4.78085e123 | −0.0926623 | ||||||||
\(265\) | 4.93073e124 | 0.786590 | ||||||||
\(266\) | 3.61521e123 | 0.0475039 | ||||||||
\(267\) | 7.01607e123 | 0.0759913 | ||||||||
\(268\) | −8.22191e123 | −0.0734566 | ||||||||
\(269\) | 2.10976e124 | 0.155593 | 0.0777965 | − | 0.996969i | \(-0.475212\pi\) | ||||
0.0777965 | + | 0.996969i | \(0.475212\pi\) | |||||||
\(270\) | −5.90299e124 | −0.359615 | ||||||||
\(271\) | 3.54564e125 | 1.78557 | 0.892784 | − | 0.450485i | \(-0.148749\pi\) | ||||
0.892784 | + | 0.450485i | \(0.148749\pi\) | |||||||
\(272\) | −3.35648e125 | −1.39825 | ||||||||
\(273\) | −2.14362e124 | −0.0739215 | ||||||||
\(274\) | −3.13199e125 | −0.894677 | ||||||||
\(275\) | 6.29775e124 | 0.149125 | ||||||||
\(276\) | −3.22086e123 | −0.00632637 | ||||||||
\(277\) | 4.60382e125 | 0.750603 | 0.375302 | − | 0.926903i | \(-0.377539\pi\) | ||||
0.375302 | + | 0.926903i | \(0.377539\pi\) | |||||||
\(278\) | −5.44137e125 | −0.736888 | ||||||||
\(279\) | −1.81219e125 | −0.203980 | ||||||||
\(280\) | −8.56773e125 | −0.802098 | ||||||||
\(281\) | 4.92394e125 | 0.383652 | 0.191826 | − | 0.981429i | \(-0.438559\pi\) | ||||
0.191826 | + | 0.981429i | \(0.438559\pi\) | |||||||
\(282\) | −4.68196e125 | −0.303808 | ||||||||
\(283\) | 5.29101e125 | 0.286113 | 0.143056 | − | 0.989715i | \(-0.454307\pi\) | ||||
0.143056 | + | 0.989715i | \(0.454307\pi\) | |||||||
\(284\) | −2.11433e125 | −0.0953405 | ||||||||
\(285\) | −2.44236e124 | −0.00918965 | ||||||||
\(286\) | 3.24875e125 | 0.102062 | ||||||||
\(287\) | 5.47216e126 | 1.43629 | ||||||||
\(288\) | −4.98283e125 | −0.109336 | ||||||||
\(289\) | 6.65242e126 | 1.22107 | ||||||||
\(290\) | −8.24237e124 | −0.0126635 | ||||||||
\(291\) | −3.10244e126 | −0.399222 | ||||||||
\(292\) | −5.12591e125 | −0.0552783 | ||||||||
\(293\) | −6.26659e126 | −0.566694 | −0.283347 | − | 0.959017i | \(-0.591445\pi\) | ||||
−0.283347 | + | 0.959017i | \(0.591445\pi\) | |||||||
\(294\) | −1.21109e125 | −0.00918941 | ||||||||
\(295\) | 5.76764e126 | 0.367421 | ||||||||
\(296\) | −3.43522e127 | −1.83836 | ||||||||
\(297\) | −3.88671e126 | −0.174834 | ||||||||
\(298\) | −3.39714e127 | −1.28522 | ||||||||
\(299\) | 3.96838e126 | 0.126342 | ||||||||
\(300\) | −2.24006e125 | −0.00600502 | ||||||||
\(301\) | 7.15912e127 | 1.61691 | ||||||||
\(302\) | 1.86387e127 | 0.354861 | ||||||||
\(303\) | 2.86177e127 | 0.459557 | ||||||||
\(304\) | 3.32655e126 | 0.0450822 | ||||||||
\(305\) | 3.76359e127 | 0.430686 | ||||||||
\(306\) | −1.40270e128 | −1.35616 | ||||||||
\(307\) | 1.74147e128 | 1.42328 | 0.711640 | − | 0.702544i | \(-0.247953\pi\) | ||||
0.711640 | + | 0.702544i | \(0.247953\pi\) | |||||||
\(308\) | −3.11132e126 | −0.0215072 | ||||||||
\(309\) | 5.47738e127 | 0.320414 | ||||||||
\(310\) | −3.26680e127 | −0.161806 | ||||||||
\(311\) | −2.61176e128 | −1.09590 | −0.547952 | − | 0.836510i | \(-0.684592\pi\) | ||||
−0.547952 | + | 0.836510i | \(0.684592\pi\) | |||||||
\(312\) | −2.09517e127 | −0.0745176 | ||||||||
\(313\) | 3.82086e128 | 1.15246 | 0.576232 | − | 0.817286i | \(-0.304522\pi\) | ||||
0.576232 | + | 0.817286i | \(0.304522\pi\) | |||||||
\(314\) | −1.07315e128 | −0.274652 | ||||||||
\(315\) | −3.37081e128 | −0.732386 | ||||||||
\(316\) | 5.90792e126 | 0.0109031 | ||||||||
\(317\) | −3.08293e128 | −0.483516 | −0.241758 | − | 0.970337i | \(-0.577724\pi\) | ||||
−0.241758 | + | 0.970337i | \(0.577724\pi\) | |||||||
\(318\) | 1.86280e128 | 0.248410 | ||||||||
\(319\) | −5.42702e126 | −0.00615661 | ||||||||
\(320\) | −8.34707e128 | −0.805954 | ||||||||
\(321\) | −4.65179e128 | −0.382482 | ||||||||
\(322\) | 6.13074e128 | 0.429473 | ||||||||
\(323\) | −1.19925e128 | −0.0716112 | ||||||||
\(324\) | −9.36651e127 | −0.0476991 | ||||||||
\(325\) | 2.75994e128 | 0.119924 | ||||||||
\(326\) | 4.12500e129 | 1.53009 | ||||||||
\(327\) | 8.58201e127 | 0.0271881 | ||||||||
\(328\) | 5.34850e129 | 1.44787 | ||||||||
\(329\) | −5.52457e129 | −1.27853 | ||||||||
\(330\) | −3.39072e128 | −0.0671157 | ||||||||
\(331\) | 8.63187e129 | 1.46205 | 0.731027 | − | 0.682349i | \(-0.239042\pi\) | ||||
0.731027 | + | 0.682349i | \(0.239042\pi\) | |||||||
\(332\) | 4.84764e128 | 0.0702941 | ||||||||
\(333\) | −1.35152e130 | −1.67859 | ||||||||
\(334\) | 6.54910e128 | 0.0697009 | ||||||||
\(335\) | −1.05728e130 | −0.964676 | ||||||||
\(336\) | −3.04725e129 | −0.238471 | ||||||||
\(337\) | 2.49506e129 | 0.167549 | 0.0837744 | − | 0.996485i | \(-0.473302\pi\) | ||||
0.0837744 | + | 0.996485i | \(0.473302\pi\) | |||||||
\(338\) | −1.54088e130 | −0.888298 | ||||||||
\(339\) | −5.34361e129 | −0.264576 | ||||||||
\(340\) | 1.56752e129 | 0.0666881 | ||||||||
\(341\) | −2.15096e129 | −0.0786650 | ||||||||
\(342\) | 1.39019e129 | 0.0437251 | ||||||||
\(343\) | 3.62185e130 | 0.980130 | ||||||||
\(344\) | 6.99734e130 | 1.62995 | ||||||||
\(345\) | −4.14180e129 | −0.0830817 | ||||||||
\(346\) | 3.86927e130 | 0.668667 | ||||||||
\(347\) | −1.05028e131 | −1.56436 | −0.782181 | − | 0.623051i | \(-0.785893\pi\) | ||||
−0.782181 | + | 0.623051i | \(0.785893\pi\) | |||||||
\(348\) | 1.93035e127 | 0.000247916 0 | ||||||||
\(349\) | 3.77219e130 | 0.417911 | 0.208956 | − | 0.977925i | \(-0.432994\pi\) | ||||
0.208956 | + | 0.977925i | \(0.432994\pi\) | |||||||
\(350\) | 4.26383e130 | 0.407658 | ||||||||
\(351\) | −1.70332e130 | −0.140598 | ||||||||
\(352\) | −5.91431e129 | −0.0421655 | ||||||||
\(353\) | −5.95150e129 | −0.0366631 | −0.0183315 | − | 0.999832i | \(-0.505835\pi\) | ||||
−0.0183315 | + | 0.999832i | \(0.505835\pi\) | |||||||
\(354\) | 2.17898e130 | 0.116034 | ||||||||
\(355\) | −2.71887e131 | −1.25207 | ||||||||
\(356\) | 4.46280e129 | 0.0177800 | ||||||||
\(357\) | 1.09856e131 | 0.378801 | ||||||||
\(358\) | 1.92822e131 | 0.575680 | ||||||||
\(359\) | −5.18908e130 | −0.134192 | −0.0670959 | − | 0.997747i | \(-0.521373\pi\) | ||||
−0.0670959 | + | 0.997747i | \(0.521373\pi\) | |||||||
\(360\) | −3.29463e131 | −0.738292 | ||||||||
\(361\) | −5.13591e131 | −0.997691 | ||||||||
\(362\) | 1.11223e131 | 0.187372 | ||||||||
\(363\) | 1.48374e131 | 0.216853 | ||||||||
\(364\) | −1.36352e130 | −0.0172957 | ||||||||
\(365\) | −6.59156e131 | −0.725948 | ||||||||
\(366\) | 1.42186e131 | 0.136013 | ||||||||
\(367\) | 2.04929e132 | 1.70334 | 0.851670 | − | 0.524079i | \(-0.175590\pi\) | ||||
0.851670 | + | 0.524079i | \(0.175590\pi\) | |||||||
\(368\) | 5.64123e131 | 0.407578 | ||||||||
\(369\) | 2.10426e132 | 1.32203 | ||||||||
\(370\) | −2.43636e132 | −1.33153 | ||||||||
\(371\) | 2.19804e132 | 1.04539 | ||||||||
\(372\) | 7.65078e129 | 0.00316770 | ||||||||
\(373\) | 8.75779e131 | 0.315784 | 0.157892 | − | 0.987456i | \(-0.449530\pi\) | ||||
0.157892 | + | 0.987456i | \(0.449530\pi\) | |||||||
\(374\) | −1.66492e132 | −0.523005 | ||||||||
\(375\) | −9.86624e131 | −0.270111 | ||||||||
\(376\) | −5.39972e132 | −1.28884 | ||||||||
\(377\) | −2.37835e130 | −0.00495105 | ||||||||
\(378\) | −2.63146e132 | −0.477935 | ||||||||
\(379\) | −2.47269e132 | −0.391967 | −0.195984 | − | 0.980607i | \(-0.562790\pi\) | ||||
−0.195984 | + | 0.980607i | \(0.562790\pi\) | |||||||
\(380\) | −1.55354e130 | −0.00215014 | ||||||||
\(381\) | 2.21182e132 | 0.267371 | ||||||||
\(382\) | −9.42717e132 | −0.995676 | ||||||||
\(383\) | 6.52492e132 | 0.602335 | 0.301168 | − | 0.953571i | \(-0.402624\pi\) | ||||
0.301168 | + | 0.953571i | \(0.402624\pi\) | |||||||
\(384\) | −2.79308e132 | −0.225437 | ||||||||
\(385\) | −4.00094e132 | −0.282445 | ||||||||
\(386\) | 2.49091e133 | 1.53855 | ||||||||
\(387\) | 2.75296e133 | 1.48828 | ||||||||
\(388\) | −1.97341e132 | −0.0934076 | ||||||||
\(389\) | −5.81266e132 | −0.240974 | −0.120487 | − | 0.992715i | \(-0.538446\pi\) | ||||
−0.120487 | + | 0.992715i | \(0.538446\pi\) | |||||||
\(390\) | −1.48596e132 | −0.0539733 | ||||||||
\(391\) | −2.03372e133 | −0.647422 | ||||||||
\(392\) | −1.39675e132 | −0.0389840 | ||||||||
\(393\) | 3.61301e132 | 0.0884409 | ||||||||
\(394\) | 2.52361e133 | 0.541959 | ||||||||
\(395\) | 7.59716e132 | 0.143186 | ||||||||
\(396\) | −1.19643e132 | −0.0197963 | ||||||||
\(397\) | −4.10497e133 | −0.596485 | −0.298242 | − | 0.954490i | \(-0.596400\pi\) | ||||
−0.298242 | + | 0.954490i | \(0.596400\pi\) | |||||||
\(398\) | −7.08847e133 | −0.904845 | ||||||||
\(399\) | −1.08876e132 | −0.0122132 | ||||||||
\(400\) | 3.92338e133 | 0.386875 | ||||||||
\(401\) | 1.48258e133 | 0.128553 | 0.0642767 | − | 0.997932i | \(-0.479526\pi\) | ||||
0.0642767 | + | 0.997932i | \(0.479526\pi\) | |||||||
\(402\) | −3.99433e133 | −0.304651 | ||||||||
\(403\) | −9.42642e132 | −0.0632611 | ||||||||
\(404\) | 1.82032e133 | 0.107524 | ||||||||
\(405\) | −1.20447e134 | −0.626413 | ||||||||
\(406\) | −3.67432e132 | −0.0168301 | ||||||||
\(407\) | −1.60417e134 | −0.647349 | ||||||||
\(408\) | 1.07374e134 | 0.381856 | ||||||||
\(409\) | −1.69483e133 | −0.0531345 | −0.0265672 | − | 0.999647i | \(-0.508458\pi\) | ||||
−0.0265672 | + | 0.999647i | \(0.508458\pi\) | |||||||
\(410\) | 3.79331e134 | 1.04870 | ||||||||
\(411\) | 9.43236e133 | 0.230020 | ||||||||
\(412\) | 3.48406e133 | 0.0749686 | ||||||||
\(413\) | 2.57112e134 | 0.488310 | ||||||||
\(414\) | 2.35751e134 | 0.395309 | ||||||||
\(415\) | 6.23372e134 | 0.923145 | ||||||||
\(416\) | −2.59190e133 | −0.0339088 | ||||||||
\(417\) | 1.63873e134 | 0.189453 | ||||||||
\(418\) | 1.65007e133 | 0.0168626 | ||||||||
\(419\) | −1.96923e135 | −1.77940 | −0.889700 | − | 0.456546i | \(-0.849086\pi\) | ||||
−0.889700 | + | 0.456546i | \(0.849086\pi\) | |||||||
\(420\) | 1.42310e133 | 0.0113736 | ||||||||
\(421\) | −1.41262e135 | −0.998841 | −0.499420 | − | 0.866360i | \(-0.666454\pi\) | ||||
−0.499420 | + | 0.866360i | \(0.666454\pi\) | |||||||
\(422\) | 5.07824e133 | 0.0317777 | ||||||||
\(423\) | −2.12442e135 | −1.17682 | ||||||||
\(424\) | 2.14837e135 | 1.05382 | ||||||||
\(425\) | −1.41442e135 | −0.614536 | ||||||||
\(426\) | −1.02717e135 | −0.395411 | ||||||||
\(427\) | 1.67775e135 | 0.572389 | ||||||||
\(428\) | −2.95892e134 | −0.0894909 | ||||||||
\(429\) | −9.78400e133 | −0.0262401 | ||||||||
\(430\) | 4.96271e135 | 1.18058 | ||||||||
\(431\) | 3.87417e135 | 0.817709 | 0.408855 | − | 0.912600i | \(-0.365928\pi\) | ||||
0.408855 | + | 0.912600i | \(0.365928\pi\) | |||||||
\(432\) | −2.42135e135 | −0.453570 | ||||||||
\(433\) | 5.39175e135 | 0.896610 | 0.448305 | − | 0.893881i | \(-0.352028\pi\) | ||||
0.448305 | + | 0.893881i | \(0.352028\pi\) | |||||||
\(434\) | −1.45629e135 | −0.215043 | ||||||||
\(435\) | 2.48229e133 | 0.00325578 | ||||||||
\(436\) | 5.45886e133 | 0.00636133 | ||||||||
\(437\) | 2.01558e134 | 0.0208740 | ||||||||
\(438\) | −2.49025e135 | −0.229259 | ||||||||
\(439\) | −3.84644e135 | −0.314873 | −0.157437 | − | 0.987529i | \(-0.550323\pi\) | ||||
−0.157437 | + | 0.987529i | \(0.550323\pi\) | |||||||
\(440\) | −3.91053e135 | −0.284723 | ||||||||
\(441\) | −5.49524e134 | −0.0355958 | ||||||||
\(442\) | −7.29639e135 | −0.420592 | ||||||||
\(443\) | 1.84814e136 | 0.948293 | 0.474146 | − | 0.880446i | \(-0.342757\pi\) | ||||
0.474146 | + | 0.880446i | \(0.342757\pi\) | |||||||
\(444\) | 5.70590e134 | 0.0260676 | ||||||||
\(445\) | 5.73884e135 | 0.233498 | ||||||||
\(446\) | −5.03753e136 | −1.82588 | ||||||||
\(447\) | 1.02309e136 | 0.330427 | ||||||||
\(448\) | −3.72099e136 | −1.07113 | ||||||||
\(449\) | 2.03484e136 | 0.522209 | 0.261105 | − | 0.965310i | \(-0.415913\pi\) | ||||
0.261105 | + | 0.965310i | \(0.415913\pi\) | |||||||
\(450\) | 1.63961e136 | 0.375230 | ||||||||
\(451\) | 2.49763e136 | 0.509842 | ||||||||
\(452\) | −3.39897e135 | −0.0619040 | ||||||||
\(453\) | −5.61328e135 | −0.0912345 | ||||||||
\(454\) | −7.66679e135 | −0.111234 | ||||||||
\(455\) | −1.75338e136 | −0.227138 | ||||||||
\(456\) | −1.06416e135 | −0.0123117 | ||||||||
\(457\) | −1.04378e136 | −0.107876 | −0.0539379 | − | 0.998544i | \(-0.517177\pi\) | ||||
−0.0539379 | + | 0.998544i | \(0.517177\pi\) | |||||||
\(458\) | 1.45214e137 | 1.34103 | ||||||||
\(459\) | 8.72919e136 | 0.720478 | ||||||||
\(460\) | −2.63452e135 | −0.0194390 | ||||||||
\(461\) | 2.02664e137 | 1.33715 | 0.668574 | − | 0.743645i | \(-0.266905\pi\) | ||||
0.668574 | + | 0.743645i | \(0.266905\pi\) | |||||||
\(462\) | −1.51153e136 | −0.0891979 | ||||||||
\(463\) | −3.03753e137 | −1.60361 | −0.801806 | − | 0.597584i | \(-0.796128\pi\) | ||||
−0.801806 | + | 0.597584i | \(0.796128\pi\) | |||||||
\(464\) | −3.38094e135 | −0.0159721 | ||||||||
\(465\) | 9.83836e135 | 0.0416002 | ||||||||
\(466\) | 9.83609e136 | 0.372347 | ||||||||
\(467\) | −3.51688e137 | −1.19217 | −0.596085 | − | 0.802921i | \(-0.703278\pi\) | ||||
−0.596085 | + | 0.802921i | \(0.703278\pi\) | |||||||
\(468\) | −5.24326e135 | −0.0159199 | ||||||||
\(469\) | −4.71318e137 | −1.28207 | ||||||||
\(470\) | −3.82964e137 | −0.933508 | ||||||||
\(471\) | 3.23191e136 | 0.0706127 | ||||||||
\(472\) | 2.51302e137 | 0.492247 | ||||||||
\(473\) | 3.26760e137 | 0.573958 | ||||||||
\(474\) | 2.87016e136 | 0.0452190 | ||||||||
\(475\) | 1.40180e136 | 0.0198137 | ||||||||
\(476\) | 6.98775e136 | 0.0886297 | ||||||||
\(477\) | 8.45233e137 | 0.962233 | ||||||||
\(478\) | 4.02322e137 | 0.411185 | ||||||||
\(479\) | 6.63006e137 | 0.608469 | 0.304235 | − | 0.952597i | \(-0.401599\pi\) | ||||
0.304235 | + | 0.952597i | \(0.401599\pi\) | |||||||
\(480\) | 2.70517e136 | 0.0222983 | ||||||||
\(481\) | −7.03016e137 | −0.520587 | ||||||||
\(482\) | 1.83155e138 | 1.21870 | ||||||||
\(483\) | −1.84635e137 | −0.110417 | ||||||||
\(484\) | 9.43778e136 | 0.0507380 | ||||||||
\(485\) | −2.53766e138 | −1.22669 | ||||||||
\(486\) | −1.53410e138 | −0.666940 | ||||||||
\(487\) | −6.31224e137 | −0.246855 | −0.123427 | − | 0.992354i | \(-0.539389\pi\) | ||||
−0.123427 | + | 0.992354i | \(0.539389\pi\) | |||||||
\(488\) | 1.63984e138 | 0.577005 | ||||||||
\(489\) | −1.24229e138 | −0.393385 | ||||||||
\(490\) | −9.90616e136 | −0.0282363 | ||||||||
\(491\) | 1.20288e138 | 0.308692 | 0.154346 | − | 0.988017i | \(-0.450673\pi\) | ||||
0.154346 | + | 0.988017i | \(0.450673\pi\) | |||||||
\(492\) | −8.88386e136 | −0.0205305 | ||||||||
\(493\) | 1.21886e137 | 0.0253710 | ||||||||
\(494\) | 7.23133e136 | 0.0135606 | ||||||||
\(495\) | −1.53852e138 | −0.259977 | ||||||||
\(496\) | −1.34001e138 | −0.204080 | ||||||||
\(497\) | −1.21203e139 | −1.66402 | ||||||||
\(498\) | 2.35506e138 | 0.291535 | ||||||||
\(499\) | 1.17929e139 | 1.31656 | 0.658281 | − | 0.752772i | \(-0.271284\pi\) | ||||
0.658281 | + | 0.752772i | \(0.271284\pi\) | |||||||
\(500\) | −6.27574e137 | −0.0631990 | ||||||||
\(501\) | −1.97234e137 | −0.0179200 | ||||||||
\(502\) | 1.41819e139 | 1.16277 | ||||||||
\(503\) | −9.85276e138 | −0.729133 | −0.364566 | − | 0.931177i | \(-0.618783\pi\) | ||||
−0.364566 | + | 0.931177i | \(0.618783\pi\) | |||||||
\(504\) | −1.46870e139 | −0.981204 | ||||||||
\(505\) | 2.34080e139 | 1.41208 | ||||||||
\(506\) | 2.79822e138 | 0.152451 | ||||||||
\(507\) | 4.64054e138 | 0.228381 | ||||||||
\(508\) | 1.40690e138 | 0.0625579 | ||||||||
\(509\) | 3.90438e139 | 1.56887 | 0.784434 | − | 0.620213i | \(-0.212954\pi\) | ||||
0.784434 | + | 0.620213i | \(0.212954\pi\) | |||||||
\(510\) | 7.61524e138 | 0.276579 | ||||||||
\(511\) | −2.93841e139 | −0.964797 | ||||||||
\(512\) | −3.61398e139 | −1.07296 | ||||||||
\(513\) | −8.65135e137 | −0.0232295 | ||||||||
\(514\) | −4.65622e139 | −1.13092 | ||||||||
\(515\) | 4.48026e139 | 0.984534 | ||||||||
\(516\) | −1.16226e138 | −0.0231123 | ||||||||
\(517\) | −2.52155e139 | −0.453842 | ||||||||
\(518\) | −1.08609e140 | −1.76963 | ||||||||
\(519\) | −1.16528e139 | −0.171913 | ||||||||
\(520\) | −1.71376e139 | −0.228970 | ||||||||
\(521\) | 5.34960e139 | 0.647408 | 0.323704 | − | 0.946158i | \(-0.395072\pi\) | ||||
0.323704 | + | 0.946158i | \(0.395072\pi\) | |||||||
\(522\) | −1.41292e138 | −0.0154913 | ||||||||
\(523\) | 7.87355e139 | 0.782228 | 0.391114 | − | 0.920342i | \(-0.372090\pi\) | ||||
0.391114 | + | 0.920342i | \(0.372090\pi\) | |||||||
\(524\) | 2.29817e138 | 0.0206929 | ||||||||
\(525\) | −1.28410e139 | −0.104808 | ||||||||
\(526\) | 2.36691e140 | 1.75152 | ||||||||
\(527\) | 4.83086e139 | 0.324173 | ||||||||
\(528\) | −1.39084e139 | −0.0846506 | ||||||||
\(529\) | −1.46940e140 | −0.811282 | ||||||||
\(530\) | 1.52368e140 | 0.763287 | ||||||||
\(531\) | 9.88699e139 | 0.449465 | ||||||||
\(532\) | −6.92544e137 | −0.00285758 | ||||||||
\(533\) | 1.09457e140 | 0.410007 | ||||||||
\(534\) | 2.16810e139 | 0.0737401 | ||||||||
\(535\) | −3.80496e140 | −1.17525 | ||||||||
\(536\) | −4.60667e140 | −1.29241 | ||||||||
\(537\) | −5.80707e139 | −0.148007 | ||||||||
\(538\) | 6.51954e139 | 0.150983 | ||||||||
\(539\) | −6.52251e138 | −0.0137276 | ||||||||
\(540\) | 1.13080e139 | 0.0216325 | ||||||||
\(541\) | −7.84823e140 | −1.36494 | −0.682468 | − | 0.730915i | \(-0.739093\pi\) | ||||
−0.682468 | + | 0.730915i | \(0.739093\pi\) | |||||||
\(542\) | 1.09567e141 | 1.73267 | ||||||||
\(543\) | −3.34962e139 | −0.0481730 | ||||||||
\(544\) | 1.32830e140 | 0.173761 | ||||||||
\(545\) | 7.01970e139 | 0.0835408 | ||||||||
\(546\) | −6.62417e139 | −0.0717315 | ||||||||
\(547\) | −1.20441e141 | −1.18693 | −0.593466 | − | 0.804859i | \(-0.702241\pi\) | ||||
−0.593466 | + | 0.804859i | \(0.702241\pi\) | |||||||
\(548\) | 5.99976e139 | 0.0538189 | ||||||||
\(549\) | 6.45161e140 | 0.526857 | ||||||||
\(550\) | 1.94612e140 | 0.144708 | ||||||||
\(551\) | −1.20799e138 | −0.000818005 0 | ||||||||
\(552\) | −1.80462e140 | −0.111307 | ||||||||
\(553\) | 3.38669e140 | 0.190297 | ||||||||
\(554\) | 1.42267e141 | 0.728367 | ||||||||
\(555\) | 7.33738e140 | 0.342336 | ||||||||
\(556\) | 1.04237e140 | 0.0443272 | ||||||||
\(557\) | 1.34802e141 | 0.522580 | 0.261290 | − | 0.965260i | \(-0.415852\pi\) | ||||
0.261290 | + | 0.965260i | \(0.415852\pi\) | |||||||
\(558\) | −5.60000e140 | −0.197937 | ||||||||
\(559\) | 1.43200e141 | 0.461568 | ||||||||
\(560\) | −2.49251e141 | −0.732747 | ||||||||
\(561\) | 5.01411e140 | 0.134464 | ||||||||
\(562\) | 1.52159e141 | 0.372286 | ||||||||
\(563\) | −1.30404e141 | −0.291144 | −0.145572 | − | 0.989348i | \(-0.546502\pi\) | ||||
−0.145572 | + | 0.989348i | \(0.546502\pi\) | |||||||
\(564\) | 8.96895e139 | 0.0182754 | ||||||||
\(565\) | −4.37084e141 | −0.812960 | ||||||||
\(566\) | 1.63502e141 | 0.277637 | ||||||||
\(567\) | −5.36932e141 | −0.832514 | ||||||||
\(568\) | −1.18464e142 | −1.67744 | ||||||||
\(569\) | −4.65743e141 | −0.602372 | −0.301186 | − | 0.953565i | \(-0.597383\pi\) | ||||
−0.301186 | + | 0.953565i | \(0.597383\pi\) | |||||||
\(570\) | −7.54734e139 | −0.00891741 | ||||||||
\(571\) | 9.58062e141 | 1.03427 | 0.517135 | − | 0.855904i | \(-0.326998\pi\) | ||||
0.517135 | + | 0.855904i | \(0.326998\pi\) | |||||||
\(572\) | −6.22343e139 | −0.00613951 | ||||||||
\(573\) | 2.83910e141 | 0.255987 | ||||||||
\(574\) | 1.69100e142 | 1.39374 | ||||||||
\(575\) | 2.37720e141 | 0.179132 | ||||||||
\(576\) | −1.43087e142 | −0.985921 | ||||||||
\(577\) | 1.26876e142 | 0.799514 | 0.399757 | − | 0.916621i | \(-0.369095\pi\) | ||||
0.399757 | + | 0.916621i | \(0.369095\pi\) | |||||||
\(578\) | 2.05572e142 | 1.18490 | ||||||||
\(579\) | −7.50167e141 | −0.395559 | ||||||||
\(580\) | 1.57894e139 | 0.000761770 0 | ||||||||
\(581\) | 2.77889e142 | 1.22688 | ||||||||
\(582\) | −9.58710e141 | −0.387395 | ||||||||
\(583\) | 1.00324e142 | 0.371086 | ||||||||
\(584\) | −2.87201e142 | −0.972578 | ||||||||
\(585\) | −6.74245e141 | −0.209070 | ||||||||
\(586\) | −1.93649e142 | −0.549906 | ||||||||
\(587\) | −1.60821e142 | −0.418294 | −0.209147 | − | 0.977884i | \(-0.567069\pi\) | ||||
−0.209147 | + | 0.977884i | \(0.567069\pi\) | |||||||
\(588\) | 2.32000e139 | 0.000552785 0 | ||||||||
\(589\) | −4.78778e140 | −0.0104519 | ||||||||
\(590\) | 1.78231e142 | 0.356537 | ||||||||
\(591\) | −7.60015e141 | −0.139337 | ||||||||
\(592\) | −9.99369e142 | −1.67941 | ||||||||
\(593\) | −1.19977e142 | −0.184834 | −0.0924169 | − | 0.995720i | \(-0.529459\pi\) | ||||
−0.0924169 | + | 0.995720i | \(0.529459\pi\) | |||||||
\(594\) | −1.20106e142 | −0.169654 | ||||||||
\(595\) | 8.98574e142 | 1.16394 | ||||||||
\(596\) | 6.50769e141 | 0.0773116 | ||||||||
\(597\) | 2.13478e142 | 0.232635 | ||||||||
\(598\) | 1.22630e142 | 0.122599 | ||||||||
\(599\) | 1.21247e143 | 1.11222 | 0.556108 | − | 0.831110i | \(-0.312294\pi\) | ||||
0.556108 | + | 0.831110i | \(0.312294\pi\) | |||||||
\(600\) | −1.25509e142 | −0.105654 | ||||||||
\(601\) | −2.28866e143 | −1.76826 | −0.884131 | − | 0.467239i | \(-0.845249\pi\) | ||||
−0.884131 | + | 0.467239i | \(0.845249\pi\) | |||||||
\(602\) | 2.21230e143 | 1.56901 | ||||||||
\(603\) | −1.81240e143 | −1.18009 | ||||||||
\(604\) | −3.57051e141 | −0.0213465 | ||||||||
\(605\) | 1.21363e143 | 0.666323 | ||||||||
\(606\) | 8.84339e142 | 0.445942 | ||||||||
\(607\) | 1.17644e143 | 0.544945 | 0.272473 | − | 0.962164i | \(-0.412159\pi\) | ||||
0.272473 | + | 0.962164i | \(0.412159\pi\) | |||||||
\(608\) | −1.31645e141 | −0.00560237 | ||||||||
\(609\) | 1.10656e141 | 0.00432699 | ||||||||
\(610\) | 1.16302e143 | 0.417927 | ||||||||
\(611\) | −1.10505e143 | −0.364972 | ||||||||
\(612\) | 2.68707e142 | 0.0815794 | ||||||||
\(613\) | −4.43772e143 | −1.23864 | −0.619320 | − | 0.785139i | \(-0.712592\pi\) | ||||
−0.619320 | + | 0.785139i | \(0.712592\pi\) | |||||||
\(614\) | 5.38147e143 | 1.38112 | ||||||||
\(615\) | −1.14240e143 | −0.269619 | ||||||||
\(616\) | −1.74325e143 | −0.378402 | ||||||||
\(617\) | −3.29116e142 | −0.0657147 | −0.0328574 | − | 0.999460i | \(-0.510461\pi\) | ||||
−0.0328574 | + | 0.999460i | \(0.510461\pi\) | |||||||
\(618\) | 1.69261e143 | 0.310922 | ||||||||
\(619\) | −9.92293e143 | −1.67715 | −0.838574 | − | 0.544788i | \(-0.816610\pi\) | ||||
−0.838574 | + | 0.544788i | \(0.816610\pi\) | |||||||
\(620\) | 6.25800e141 | 0.00973338 | ||||||||
\(621\) | −1.46711e143 | −0.210013 | ||||||||
\(622\) | −8.07081e143 | −1.06344 | ||||||||
\(623\) | 2.55828e143 | 0.310323 | ||||||||
\(624\) | −6.09525e142 | −0.0680746 | ||||||||
\(625\) | −4.06068e143 | −0.417617 | ||||||||
\(626\) | 1.18072e144 | 1.11832 | ||||||||
\(627\) | −4.96939e141 | −0.00433536 | ||||||||
\(628\) | 2.05576e142 | 0.0165216 | ||||||||
\(629\) | 3.60282e144 | 2.66768 | ||||||||
\(630\) | −1.04164e144 | −0.710689 | ||||||||
\(631\) | 8.95555e143 | 0.563093 | 0.281547 | − | 0.959548i | \(-0.409153\pi\) | ||||
0.281547 | + | 0.959548i | \(0.409153\pi\) | |||||||
\(632\) | 3.31016e143 | 0.191831 | ||||||||
\(633\) | −1.52937e142 | −0.00817001 | ||||||||
\(634\) | −9.52681e143 | −0.469192 | ||||||||
\(635\) | 1.80917e144 | 0.821549 | ||||||||
\(636\) | −3.56844e142 | −0.0149430 | ||||||||
\(637\) | −2.85844e142 | −0.0110395 | ||||||||
\(638\) | −1.67705e142 | −0.00597422 | ||||||||
\(639\) | −4.66074e144 | −1.53165 | ||||||||
\(640\) | −2.28462e144 | −0.692699 | ||||||||
\(641\) | −1.80207e144 | −0.504178 | −0.252089 | − | 0.967704i | \(-0.581118\pi\) | ||||
−0.252089 | + | 0.967704i | \(0.581118\pi\) | |||||||
\(642\) | −1.43749e144 | −0.371151 | ||||||||
\(643\) | 3.33669e144 | 0.795152 | 0.397576 | − | 0.917569i | \(-0.369851\pi\) | ||||
0.397576 | + | 0.917569i | \(0.369851\pi\) | |||||||
\(644\) | −1.17443e143 | −0.0258348 | ||||||||
\(645\) | −1.49458e144 | −0.303525 | ||||||||
\(646\) | −3.70591e143 | −0.0694897 | ||||||||
\(647\) | 1.92009e144 | 0.332469 | 0.166235 | − | 0.986086i | \(-0.446839\pi\) | ||||
0.166235 | + | 0.986086i | \(0.446839\pi\) | |||||||
\(648\) | −5.24798e144 | −0.839227 | ||||||||
\(649\) | 1.17352e144 | 0.173337 | ||||||||
\(650\) | 8.52873e143 | 0.116372 | ||||||||
\(651\) | 4.38578e143 | 0.0552874 | ||||||||
\(652\) | −7.90200e143 | −0.0920420 | ||||||||
\(653\) | 1.26374e145 | 1.36029 | 0.680143 | − | 0.733079i | \(-0.261918\pi\) | ||||
0.680143 | + | 0.733079i | \(0.261918\pi\) | |||||||
\(654\) | 2.65200e143 | 0.0263827 | ||||||||
\(655\) | 2.95529e144 | 0.271752 | ||||||||
\(656\) | 1.55598e145 | 1.32268 | ||||||||
\(657\) | −1.12994e145 | −0.888050 | ||||||||
\(658\) | −1.70719e145 | −1.24065 | ||||||||
\(659\) | 1.69140e144 | 0.113671 | 0.0568353 | − | 0.998384i | \(-0.481899\pi\) | ||||
0.0568353 | + | 0.998384i | \(0.481899\pi\) | |||||||
\(660\) | 6.49539e142 | 0.00403731 | ||||||||
\(661\) | −9.69697e144 | −0.557521 | −0.278760 | − | 0.960361i | \(-0.589924\pi\) | ||||
−0.278760 | + | 0.960361i | \(0.589924\pi\) | |||||||
\(662\) | 2.66741e145 | 1.41874 | ||||||||
\(663\) | 2.19740e144 | 0.108134 | ||||||||
\(664\) | 2.71610e145 | 1.23677 | ||||||||
\(665\) | −8.90561e143 | −0.0375275 | ||||||||
\(666\) | −4.17644e145 | −1.62886 | ||||||||
\(667\) | −2.04853e143 | −0.00739541 | ||||||||
\(668\) | −1.25457e143 | −0.00419283 | ||||||||
\(669\) | 1.51711e145 | 0.469432 | ||||||||
\(670\) | −3.26718e145 | −0.936098 | ||||||||
\(671\) | 7.65767e144 | 0.203183 | ||||||||
\(672\) | 1.20592e144 | 0.0296348 | ||||||||
\(673\) | −5.58858e145 | −1.27211 | −0.636057 | − | 0.771642i | \(-0.719436\pi\) | ||||
−0.636057 | + | 0.771642i | \(0.719436\pi\) | |||||||
\(674\) | 7.71020e144 | 0.162585 | ||||||||
\(675\) | −1.02035e145 | −0.199345 | ||||||||
\(676\) | 2.95177e144 | 0.0534352 | ||||||||
\(677\) | 3.97647e145 | 0.667086 | 0.333543 | − | 0.942735i | \(-0.391756\pi\) | ||||
0.333543 | + | 0.942735i | \(0.391756\pi\) | |||||||
\(678\) | −1.65127e145 | −0.256738 | ||||||||
\(679\) | −1.13125e146 | −1.63029 | ||||||||
\(680\) | 8.78269e145 | 1.17333 | ||||||||
\(681\) | 2.30895e144 | 0.0285981 | ||||||||
\(682\) | −6.64686e144 | −0.0763345 | ||||||||
\(683\) | 6.61264e145 | 0.704220 | 0.352110 | − | 0.935959i | \(-0.385464\pi\) | ||||
0.352110 | + | 0.935959i | \(0.385464\pi\) | |||||||
\(684\) | −2.66311e143 | −0.00263026 | ||||||||
\(685\) | 7.71525e145 | 0.706782 | ||||||||
\(686\) | 1.11922e146 | 0.951094 | ||||||||
\(687\) | −4.37331e145 | −0.344777 | ||||||||
\(688\) | 2.03566e146 | 1.48902 | ||||||||
\(689\) | 4.39663e145 | 0.298421 | ||||||||
\(690\) | −1.27989e145 | −0.0806204 | ||||||||
\(691\) | −1.17807e146 | −0.688733 | −0.344366 | − | 0.938835i | \(-0.611906\pi\) | ||||
−0.344366 | + | 0.938835i | \(0.611906\pi\) | |||||||
\(692\) | −7.41211e144 | −0.0402234 | ||||||||
\(693\) | −6.85848e145 | −0.345514 | ||||||||
\(694\) | −3.24556e146 | −1.51802 | ||||||||
\(695\) | 1.34041e146 | 0.582131 | ||||||||
\(696\) | 1.08156e144 | 0.00436189 | ||||||||
\(697\) | −5.60945e146 | −2.10103 | ||||||||
\(698\) | 1.16568e146 | 0.405531 | ||||||||
\(699\) | −2.96226e145 | −0.0957300 | ||||||||
\(700\) | −8.16796e144 | −0.0245225 | ||||||||
\(701\) | 7.11768e145 | 0.198546 | 0.0992728 | − | 0.995060i | \(-0.468348\pi\) | ||||
0.0992728 | + | 0.995060i | \(0.468348\pi\) | |||||||
\(702\) | −5.26358e145 | −0.136433 | ||||||||
\(703\) | −3.57069e145 | −0.0860108 | ||||||||
\(704\) | −1.69835e146 | −0.380221 | ||||||||
\(705\) | 1.15334e146 | 0.240004 | ||||||||
\(706\) | −1.83912e145 | −0.0355769 | ||||||||
\(707\) | 1.04349e147 | 1.87668 | ||||||||
\(708\) | −4.17413e144 | −0.00697997 | ||||||||
\(709\) | 6.25496e146 | 0.972620 | 0.486310 | − | 0.873786i | \(-0.338343\pi\) | ||||
0.486310 | + | 0.873786i | \(0.338343\pi\) | |||||||
\(710\) | −8.40181e146 | −1.21498 | ||||||||
\(711\) | 1.30232e146 | 0.175159 | ||||||||
\(712\) | 2.50047e146 | 0.312826 | ||||||||
\(713\) | −8.11920e145 | −0.0944936 | ||||||||
\(714\) | 3.39476e146 | 0.367579 | ||||||||
\(715\) | −8.00288e145 | −0.0806278 | ||||||||
\(716\) | −3.69377e145 | −0.0346298 | ||||||||
\(717\) | −1.21164e146 | −0.105715 | ||||||||
\(718\) | −1.60352e146 | −0.130216 | ||||||||
\(719\) | 1.25794e146 | 0.0950876 | 0.0475438 | − | 0.998869i | \(-0.484861\pi\) | ||||
0.0475438 | + | 0.998869i | \(0.484861\pi\) | |||||||
\(720\) | −9.58470e146 | −0.674458 | ||||||||
\(721\) | 1.99723e147 | 1.30846 | ||||||||
\(722\) | −1.58709e147 | −0.968134 | ||||||||
\(723\) | −5.51593e146 | −0.313326 | ||||||||
\(724\) | −2.13063e145 | −0.0112713 | ||||||||
\(725\) | −1.42472e145 | −0.00701977 | ||||||||
\(726\) | 4.58502e146 | 0.210429 | ||||||||
\(727\) | 2.64267e147 | 1.12985 | 0.564926 | − | 0.825142i | \(-0.308905\pi\) | ||||
0.564926 | + | 0.825142i | \(0.308905\pi\) | |||||||
\(728\) | −7.63967e146 | −0.304305 | ||||||||
\(729\) | −1.73974e147 | −0.645680 | ||||||||
\(730\) | −2.03691e147 | −0.704442 | ||||||||
\(731\) | −7.33873e147 | −2.36524 | ||||||||
\(732\) | −2.72377e145 | −0.00818181 | ||||||||
\(733\) | 1.86567e147 | 0.522372 | 0.261186 | − | 0.965289i | \(-0.415886\pi\) | ||||
0.261186 | + | 0.965289i | \(0.415886\pi\) | |||||||
\(734\) | 6.33269e147 | 1.65288 | ||||||||
\(735\) | 2.98336e145 | 0.00725951 | ||||||||
\(736\) | −2.23247e146 | −0.0506498 | ||||||||
\(737\) | −2.15121e147 | −0.455101 | ||||||||
\(738\) | 6.50256e147 | 1.28287 | ||||||||
\(739\) | −3.72257e147 | −0.684943 | −0.342472 | − | 0.939528i | \(-0.611264\pi\) | ||||
−0.342472 | + | 0.939528i | \(0.611264\pi\) | |||||||
\(740\) | 4.66717e146 | 0.0800978 | ||||||||
\(741\) | −2.17780e145 | −0.00348643 | ||||||||
\(742\) | 6.79235e147 | 1.01442 | ||||||||
\(743\) | −1.87751e147 | −0.261612 | −0.130806 | − | 0.991408i | \(-0.541757\pi\) | ||||
−0.130806 | + | 0.991408i | \(0.541757\pi\) | |||||||
\(744\) | 4.28667e146 | 0.0557332 | ||||||||
\(745\) | 8.36842e147 | 1.01530 | ||||||||
\(746\) | 2.70632e147 | 0.306429 | ||||||||
\(747\) | 1.06859e148 | 1.12928 | ||||||||
\(748\) | 3.18938e146 | 0.0314611 | ||||||||
\(749\) | −1.69619e148 | −1.56193 | ||||||||
\(750\) | −3.04885e147 | −0.262109 | ||||||||
\(751\) | 9.93437e146 | 0.0797413 | 0.0398707 | − | 0.999205i | \(-0.487305\pi\) | ||||
0.0398707 | + | 0.999205i | \(0.487305\pi\) | |||||||
\(752\) | −1.57088e148 | −1.17740 | ||||||||
\(753\) | −4.27106e147 | −0.298947 | ||||||||
\(754\) | −7.34955e145 | −0.00480437 | ||||||||
\(755\) | −4.59141e147 | −0.280336 | ||||||||
\(756\) | 5.04092e146 | 0.0287500 | ||||||||
\(757\) | −1.88500e148 | −1.00432 | −0.502161 | − | 0.864774i | \(-0.667461\pi\) | ||||
−0.502161 | + | 0.864774i | \(0.667461\pi\) | |||||||
\(758\) | −7.64106e147 | −0.380355 | ||||||||
\(759\) | −8.42719e146 | −0.0391951 | ||||||||
\(760\) | −8.70437e146 | −0.0378301 | ||||||||
\(761\) | 1.09839e148 | 0.446116 | 0.223058 | − | 0.974805i | \(-0.428396\pi\) | ||||
0.223058 | + | 0.974805i | \(0.428396\pi\) | |||||||
\(762\) | 6.83494e147 | 0.259450 | ||||||||
\(763\) | 3.12927e147 | 0.111027 | ||||||||
\(764\) | 1.80590e147 | 0.0598945 | ||||||||
\(765\) | 3.45538e148 | 1.07135 | ||||||||
\(766\) | 2.01632e148 | 0.584491 | ||||||||
\(767\) | 5.14289e147 | 0.139395 | ||||||||
\(768\) | 1.71775e147 | 0.0435370 | ||||||||
\(769\) | 2.13006e148 | 0.504876 | 0.252438 | − | 0.967613i | \(-0.418768\pi\) | ||||
0.252438 | + | 0.967613i | \(0.418768\pi\) | |||||||
\(770\) | −1.23636e148 | −0.274078 | ||||||||
\(771\) | 1.40228e148 | 0.290759 | ||||||||
\(772\) | −4.77168e147 | −0.0925508 | ||||||||
\(773\) | −3.96679e148 | −0.719772 | −0.359886 | − | 0.932996i | \(-0.617184\pi\) | ||||
−0.359886 | + | 0.932996i | \(0.617184\pi\) | |||||||
\(774\) | 8.50717e148 | 1.44419 | ||||||||
\(775\) | −5.64677e147 | −0.0896939 | ||||||||
\(776\) | −1.10568e149 | −1.64343 | ||||||||
\(777\) | 3.27089e148 | 0.454970 | ||||||||
\(778\) | −1.79622e148 | −0.233835 | ||||||||
\(779\) | 5.55942e147 | 0.0677409 | ||||||||
\(780\) | 2.84656e146 | 0.00324674 | ||||||||
\(781\) | −5.53201e148 | −0.590683 | ||||||||
\(782\) | −6.28456e148 | −0.628242 | ||||||||
\(783\) | 8.79279e146 | 0.00822992 | ||||||||
\(784\) | −4.06341e147 | −0.0356134 | ||||||||
\(785\) | 2.64356e148 | 0.216971 | ||||||||
\(786\) | 1.11649e148 | 0.0858209 | ||||||||
\(787\) | 1.51510e149 | 1.09079 | 0.545396 | − | 0.838178i | \(-0.316379\pi\) | ||||
0.545396 | + | 0.838178i | \(0.316379\pi\) | |||||||
\(788\) | −4.83432e147 | −0.0326013 | ||||||||
\(789\) | −7.12823e148 | −0.450314 | ||||||||
\(790\) | 2.34766e148 | 0.138944 | ||||||||
\(791\) | −1.94845e149 | −1.08044 | ||||||||
\(792\) | −6.70349e148 | −0.348301 | ||||||||
\(793\) | 3.35592e148 | 0.163396 | ||||||||
\(794\) | −1.26851e149 | −0.578814 | ||||||||
\(795\) | −4.58876e148 | −0.196240 | ||||||||
\(796\) | 1.35789e148 | 0.0544306 | ||||||||
\(797\) | 2.69553e149 | 1.01284 | 0.506419 | − | 0.862288i | \(-0.330969\pi\) | ||||
0.506419 | + | 0.862288i | \(0.330969\pi\) | |||||||
\(798\) | −3.36448e147 | −0.0118514 | ||||||||
\(799\) | 5.66317e149 | 1.87025 | ||||||||
\(800\) | −1.55265e148 | −0.0480771 | ||||||||
\(801\) | 9.83761e148 | 0.285637 | ||||||||
\(802\) | 4.58145e148 | 0.124745 | ||||||||
\(803\) | −1.34116e149 | −0.342477 | ||||||||
\(804\) | 7.65168e147 | 0.0183261 | ||||||||
\(805\) | −1.51023e149 | −0.339278 | ||||||||
\(806\) | −2.91294e148 | −0.0613870 | ||||||||
\(807\) | −1.96344e148 | −0.0388177 | ||||||||
\(808\) | 1.01991e150 | 1.89181 | ||||||||
\(809\) | −1.21477e149 | −0.211420 | −0.105710 | − | 0.994397i | \(-0.533712\pi\) | ||||
−0.105710 | + | 0.994397i | \(0.533712\pi\) | |||||||
\(810\) | −3.72202e149 | −0.607855 | ||||||||
\(811\) | −9.32412e149 | −1.42900 | −0.714502 | − | 0.699633i | \(-0.753347\pi\) | ||||
−0.714502 | + | 0.699633i | \(0.753347\pi\) | |||||||
\(812\) | 7.03866e146 | 0.00101241 | ||||||||
\(813\) | −3.29974e149 | −0.445468 | ||||||||
\(814\) | −4.95718e149 | −0.628171 | ||||||||
\(815\) | −1.01614e150 | −1.20875 | ||||||||
\(816\) | 3.12370e149 | 0.348840 | ||||||||
\(817\) | 7.27329e148 | 0.0762597 | ||||||||
\(818\) | −5.23734e148 | −0.0515603 | ||||||||
\(819\) | −3.00568e149 | −0.277857 | ||||||||
\(820\) | −7.26661e148 | −0.0630839 | ||||||||
\(821\) | 3.43581e149 | 0.280128 | 0.140064 | − | 0.990142i | \(-0.455269\pi\) | ||||
0.140064 | + | 0.990142i | \(0.455269\pi\) | |||||||
\(822\) | 2.91477e149 | 0.223206 | ||||||||
\(823\) | −3.27566e149 | −0.235617 | −0.117809 | − | 0.993036i | \(-0.537587\pi\) | ||||
−0.117809 | + | 0.993036i | \(0.537587\pi\) | |||||||
\(824\) | 1.95209e150 | 1.31901 | ||||||||
\(825\) | −5.86098e148 | −0.0372042 | ||||||||
\(826\) | 7.94524e149 | 0.473843 | ||||||||
\(827\) | 2.51231e150 | 1.40779 | 0.703897 | − | 0.710302i | \(-0.251442\pi\) | ||||
0.703897 | + | 0.710302i | \(0.251442\pi\) | |||||||
\(828\) | −4.51614e148 | −0.0237796 | ||||||||
\(829\) | −1.69501e150 | −0.838715 | −0.419357 | − | 0.907821i | \(-0.637745\pi\) | ||||
−0.419357 | + | 0.907821i | \(0.637745\pi\) | |||||||
\(830\) | 1.92633e150 | 0.895797 | ||||||||
\(831\) | −4.28453e149 | −0.187262 | ||||||||
\(832\) | −7.44291e149 | −0.305768 | ||||||||
\(833\) | 1.46490e149 | 0.0565704 | ||||||||
\(834\) | 5.06399e149 | 0.183841 | ||||||||
\(835\) | −1.61329e149 | −0.0550628 | ||||||||
\(836\) | −3.16094e147 | −0.00101436 | ||||||||
\(837\) | 3.48495e149 | 0.105156 | ||||||||
\(838\) | −6.08527e150 | −1.72668 | ||||||||
\(839\) | 3.72041e150 | 0.992773 | 0.496387 | − | 0.868102i | \(-0.334660\pi\) | ||||
0.496387 | + | 0.868102i | \(0.334660\pi\) | |||||||
\(840\) | 7.97353e149 | 0.200109 | ||||||||
\(841\) | −4.23514e150 | −0.999710 | ||||||||
\(842\) | −4.36524e150 | −0.969250 | ||||||||
\(843\) | −4.58244e149 | −0.0957144 | ||||||||
\(844\) | −9.72807e147 | −0.00191157 | ||||||||
\(845\) | 3.79576e150 | 0.701743 | ||||||||
\(846\) | −6.56483e150 | −1.14196 | ||||||||
\(847\) | 5.41017e150 | 0.885555 | ||||||||
\(848\) | 6.25000e150 | 0.962706 | ||||||||
\(849\) | −4.92406e149 | −0.0713801 | ||||||||
\(850\) | −4.37081e150 | −0.596331 | ||||||||
\(851\) | −6.05524e150 | −0.777605 | ||||||||
\(852\) | 1.96769e149 | 0.0237858 | ||||||||
\(853\) | 1.00654e151 | 1.14539 | 0.572697 | − | 0.819767i | \(-0.305897\pi\) | ||||
0.572697 | + | 0.819767i | \(0.305897\pi\) | |||||||
\(854\) | 5.18455e150 | 0.555432 | ||||||||
\(855\) | −3.42456e149 | −0.0345422 | ||||||||
\(856\) | −1.65786e151 | −1.57452 | ||||||||
\(857\) | 1.71589e151 | 1.53453 | 0.767267 | − | 0.641328i | \(-0.221616\pi\) | ||||
0.767267 | + | 0.641328i | \(0.221616\pi\) | |||||||
\(858\) | −3.02344e149 | −0.0254628 | ||||||||
\(859\) | −1.00890e151 | −0.800204 | −0.400102 | − | 0.916471i | \(-0.631025\pi\) | ||||
−0.400102 | + | 0.916471i | \(0.631025\pi\) | |||||||
\(860\) | −9.50676e149 | −0.0710170 | ||||||||
\(861\) | −5.09264e150 | −0.358328 | ||||||||
\(862\) | 1.19719e151 | 0.793485 | ||||||||
\(863\) | 2.30280e151 | 1.43780 | 0.718902 | − | 0.695111i | \(-0.244645\pi\) | ||||
0.718902 | + | 0.695111i | \(0.244645\pi\) | |||||||
\(864\) | 9.58228e149 | 0.0563652 | ||||||||
\(865\) | −9.53145e150 | −0.528238 | ||||||||
\(866\) | 1.66615e151 | 0.870048 | ||||||||
\(867\) | −6.19104e150 | −0.304635 | ||||||||
\(868\) | 2.78972e149 | 0.0129358 | ||||||||
\(869\) | 1.54577e150 | 0.0675502 | ||||||||
\(870\) | 7.67073e148 | 0.00315933 | ||||||||
\(871\) | −9.42753e150 | −0.365985 | ||||||||
\(872\) | 3.05856e150 | 0.111923 | ||||||||
\(873\) | −4.35010e151 | −1.50060 | ||||||||
\(874\) | 6.22851e149 | 0.0202556 | ||||||||
\(875\) | −3.59755e151 | −1.10304 | ||||||||
\(876\) | 4.77041e149 | 0.0137910 | ||||||||
\(877\) | 3.15300e151 | 0.859497 | 0.429749 | − | 0.902949i | \(-0.358602\pi\) | ||||
0.429749 | + | 0.902949i | \(0.358602\pi\) | |||||||
\(878\) | −1.18862e151 | −0.305545 | ||||||||
\(879\) | 5.83198e150 | 0.141380 | ||||||||
\(880\) | −1.13764e151 | −0.260105 | ||||||||
\(881\) | −7.29314e151 | −1.57273 | −0.786367 | − | 0.617760i | \(-0.788040\pi\) | ||||
−0.786367 | + | 0.617760i | \(0.788040\pi\) | |||||||
\(882\) | −1.69813e150 | −0.0345413 | ||||||||
\(883\) | 1.46757e151 | 0.281593 | 0.140796 | − | 0.990039i | \(-0.455034\pi\) | ||||
0.140796 | + | 0.990039i | \(0.455034\pi\) | |||||||
\(884\) | 1.39772e150 | 0.0253006 | ||||||||
\(885\) | −5.36763e150 | −0.0916652 | ||||||||
\(886\) | 5.71108e151 | 0.920199 | ||||||||
\(887\) | 1.03249e152 | 1.56972 | 0.784858 | − | 0.619676i | \(-0.212736\pi\) | ||||
0.784858 | + | 0.619676i | \(0.212736\pi\) | |||||||
\(888\) | 3.19697e151 | 0.458639 | ||||||||
\(889\) | 8.06501e151 | 1.09185 | ||||||||
\(890\) | 1.77341e151 | 0.226581 | ||||||||
\(891\) | −2.45069e151 | −0.295520 | ||||||||
\(892\) | 9.65009e150 | 0.109835 | ||||||||
\(893\) | −5.61267e150 | −0.0603003 | ||||||||
\(894\) | 3.16153e151 | 0.320639 | ||||||||
\(895\) | −4.74993e151 | −0.454779 | ||||||||
\(896\) | −1.01845e152 | −0.920610 | ||||||||
\(897\) | −3.69316e150 | −0.0315200 | ||||||||
\(898\) | 6.28804e151 | 0.506739 | ||||||||
\(899\) | 4.86605e149 | 0.00370299 | ||||||||
\(900\) | −3.14091e150 | −0.0225718 | ||||||||
\(901\) | −2.25319e152 | −1.52922 | ||||||||
\(902\) | 7.71813e151 | 0.494738 | ||||||||
\(903\) | −6.66260e151 | −0.403390 | ||||||||
\(904\) | −1.90442e152 | −1.08915 | ||||||||
\(905\) | −2.73984e151 | −0.148021 | ||||||||
\(906\) | −1.73461e151 | −0.0885317 | ||||||||
\(907\) | 5.53998e151 | 0.267136 | 0.133568 | − | 0.991040i | \(-0.457356\pi\) | ||||
0.133568 | + | 0.991040i | \(0.457356\pi\) | |||||||
\(908\) | 1.46868e150 | 0.00669123 | ||||||||
\(909\) | 4.01264e152 | 1.72739 | ||||||||
\(910\) | −5.41828e151 | −0.220409 | ||||||||
\(911\) | −3.31225e152 | −1.27329 | −0.636643 | − | 0.771159i | \(-0.719678\pi\) | ||||
−0.636643 | + | 0.771159i | \(0.719678\pi\) | |||||||
\(912\) | −3.09584e150 | −0.0112472 | ||||||||
\(913\) | 1.26836e152 | 0.435508 | ||||||||
\(914\) | −3.22547e151 | −0.104680 | ||||||||
\(915\) | −3.50257e151 | −0.107449 | ||||||||
\(916\) | −2.78178e151 | −0.0806689 | ||||||||
\(917\) | 1.31742e152 | 0.361163 | ||||||||
\(918\) | 2.69748e152 | 0.699134 | ||||||||
\(919\) | 3.61151e152 | 0.884992 | 0.442496 | − | 0.896770i | \(-0.354093\pi\) | ||||
0.442496 | + | 0.896770i | \(0.354093\pi\) | |||||||
\(920\) | −1.47610e152 | −0.342014 | ||||||||
\(921\) | −1.62070e152 | −0.355084 | ||||||||
\(922\) | 6.26270e152 | 1.29754 | ||||||||
\(923\) | −2.42436e152 | −0.475018 | ||||||||
\(924\) | 2.89554e150 | 0.00536566 | ||||||||
\(925\) | −4.21132e152 | −0.738107 | ||||||||
\(926\) | −9.38653e152 | −1.55611 | ||||||||
\(927\) | 7.68013e152 | 1.20438 | ||||||||
\(928\) | 1.33798e150 | 0.00198485 | ||||||||
\(929\) | 8.45797e152 | 1.18702 | 0.593508 | − | 0.804828i | \(-0.297742\pi\) | ||||
0.593508 | + | 0.804828i | \(0.297742\pi\) | |||||||
\(930\) | 3.04023e151 | 0.0403678 | ||||||||
\(931\) | −1.45183e150 | −0.00182393 | ||||||||
\(932\) | −1.88424e151 | −0.0223984 | ||||||||
\(933\) | 2.43062e152 | 0.273409 | ||||||||
\(934\) | −1.08678e153 | −1.15685 | ||||||||
\(935\) | 4.10132e152 | 0.413167 | ||||||||
\(936\) | −2.93776e152 | −0.280098 | ||||||||
\(937\) | 4.31161e152 | 0.389091 | 0.194545 | − | 0.980894i | \(-0.437677\pi\) | ||||
0.194545 | + | 0.980894i | \(0.437677\pi\) | |||||||
\(938\) | −1.45646e153 | −1.24409 | ||||||||
\(939\) | −3.55587e152 | −0.287520 | ||||||||
\(940\) | 7.33620e151 | 0.0561548 | ||||||||
\(941\) | −2.36826e153 | −1.71618 | −0.858092 | − | 0.513496i | \(-0.828350\pi\) | ||||
−0.858092 | + | 0.513496i | \(0.828350\pi\) | |||||||
\(942\) | 9.98720e151 | 0.0685208 | ||||||||
\(943\) | 9.42777e152 | 0.612431 | ||||||||
\(944\) | 7.31085e152 | 0.449687 | ||||||||
\(945\) | 6.48227e152 | 0.377562 | ||||||||
\(946\) | 1.00975e153 | 0.556954 | ||||||||
\(947\) | −1.66395e153 | −0.869193 | −0.434596 | − | 0.900625i | \(-0.643109\pi\) | ||||
−0.434596 | + | 0.900625i | \(0.643109\pi\) | |||||||
\(948\) | −5.49818e150 | −0.00272013 | ||||||||
\(949\) | −5.87756e152 | −0.275415 | ||||||||
\(950\) | 4.33183e151 | 0.0192268 | ||||||||
\(951\) | 2.86911e152 | 0.120629 | ||||||||
\(952\) | 3.91518e153 | 1.55937 | ||||||||
\(953\) | −1.09805e153 | −0.414322 | −0.207161 | − | 0.978307i | \(-0.566422\pi\) | ||||
−0.207161 | + | 0.978307i | \(0.566422\pi\) | |||||||
\(954\) | 2.61193e153 | 0.933727 | ||||||||
\(955\) | 2.32226e153 | 0.786570 | ||||||||
\(956\) | −7.70703e151 | −0.0247347 | ||||||||
\(957\) | 5.05064e150 | 0.00153597 | ||||||||
\(958\) | 2.04881e153 | 0.590443 | ||||||||
\(959\) | 3.43934e153 | 0.939326 | ||||||||
\(960\) | 7.76817e152 | 0.201071 | ||||||||
\(961\) | −3.88333e153 | −0.952686 | ||||||||
\(962\) | −2.17245e153 | −0.505165 | ||||||||
\(963\) | −6.52252e153 | −1.43768 | ||||||||
\(964\) | −3.50859e152 | −0.0733103 | ||||||||
\(965\) | −6.13603e153 | −1.21543 | ||||||||
\(966\) | −5.70555e152 | −0.107146 | ||||||||
\(967\) | −6.60714e151 | −0.0117639 | −0.00588193 | − | 0.999983i | \(-0.501872\pi\) | ||||
−0.00588193 | + | 0.999983i | \(0.501872\pi\) | |||||||
\(968\) | 5.28791e153 | 0.892696 | ||||||||
\(969\) | 1.11608e152 | 0.0178657 | ||||||||
\(970\) | −7.84183e153 | −1.19035 | ||||||||
\(971\) | −7.08512e153 | −1.01990 | −0.509949 | − | 0.860205i | \(-0.670336\pi\) | ||||
−0.509949 | + | 0.860205i | \(0.670336\pi\) | |||||||
\(972\) | 2.93879e152 | 0.0401195 | ||||||||
\(973\) | 5.97535e153 | 0.773663 | ||||||||
\(974\) | −1.95060e153 | −0.239542 | ||||||||
\(975\) | −2.56853e152 | −0.0299190 | ||||||||
\(976\) | 4.77059e153 | 0.527116 | ||||||||
\(977\) | 1.38503e154 | 1.45174 | 0.725868 | − | 0.687834i | \(-0.241438\pi\) | ||||
0.725868 | + | 0.687834i | \(0.241438\pi\) | |||||||
\(978\) | −3.83891e153 | −0.381731 | ||||||||
\(979\) | 1.16766e153 | 0.110156 | ||||||||
\(980\) | 1.89766e151 | 0.00169854 | ||||||||
\(981\) | 1.20333e153 | 0.102195 | ||||||||
\(982\) | 3.71712e153 | 0.299547 | ||||||||
\(983\) | 8.88217e153 | 0.679224 | 0.339612 | − | 0.940566i | \(-0.389704\pi\) | ||||
0.339612 | + | 0.940566i | \(0.389704\pi\) | |||||||
\(984\) | −4.97756e153 | −0.361218 | ||||||||
\(985\) | −6.21658e153 | −0.428140 | ||||||||
\(986\) | 3.76650e152 | 0.0246194 | ||||||||
\(987\) | 5.14142e153 | 0.318970 | ||||||||
\(988\) | −1.38526e151 | −0.000815734 0 | ||||||||
\(989\) | 1.23342e154 | 0.689447 | ||||||||
\(990\) | −4.75431e153 | −0.252275 | ||||||||
\(991\) | 4.72938e153 | 0.238238 | 0.119119 | − | 0.992880i | \(-0.461993\pi\) | ||||
0.119119 | + | 0.992880i | \(0.461993\pi\) | |||||||
\(992\) | 5.30297e152 | 0.0253611 | ||||||||
\(993\) | −8.03321e153 | −0.364757 | ||||||||
\(994\) | −3.74540e154 | −1.61473 | ||||||||
\(995\) | 1.74615e154 | 0.714815 | ||||||||
\(996\) | −4.51144e152 | −0.0175371 | ||||||||
\(997\) | −1.51373e154 | −0.558788 | −0.279394 | − | 0.960177i | \(-0.590134\pi\) | ||||
−0.279394 | + | 0.960177i | \(0.590134\pi\) | |||||||
\(998\) | 3.64421e154 | 1.27756 | ||||||||
\(999\) | 2.59905e154 | 0.865352 |
(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 | 1.104.a.a.1.6 | ✓ | 8 | |
3.2 | odd | 2 | 9.104.a.a.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.104.a.a.1.6 | ✓ | 8 | 1.1 | even | 1 | trivial | |
9.104.a.a.1.3 | 8 | 3.2 | odd | 2 |