Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,124,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, 124, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 124);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 124 \) |
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: | \(95.8076224914\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 5 x^{9} + \cdots - 30\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{178}\cdot 3^{70}\cdot 5^{22}\cdot 7^{9}\cdot 11^{6}\cdot 13^{2}\cdot 17\cdot 31^{2}\cdot 41^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.24732e16\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.83831e18 | 0.563734 | 0.281867 | − | 0.959454i | \(-0.409046\pi\) | ||||
0.281867 | + | 0.959454i | \(0.409046\pi\) | |||||||
\(3\) | 1.91755e29 | 0.870543 | 0.435271 | − | 0.900299i | \(-0.356652\pi\) | ||||
0.435271 | + | 0.900299i | \(0.356652\pi\) | |||||||
\(4\) | −7.25444e36 | −0.682204 | ||||||||
\(5\) | −8.31906e42 | −0.857865 | −0.428933 | − | 0.903336i | \(-0.641110\pi\) | ||||
−0.428933 | + | 0.903336i | \(0.641110\pi\) | |||||||
\(6\) | 3.52506e47 | 0.490754 | ||||||||
\(7\) | −1.53178e52 | −1.62805 | −0.814023 | − | 0.580832i | \(-0.802727\pi\) | ||||
−0.814023 | + | 0.580832i | \(0.802727\pi\) | |||||||
\(8\) | −3.28842e55 | −0.948315 | ||||||||
\(9\) | −1.17492e58 | −0.242156 | ||||||||
\(10\) | −1.52930e61 | −0.483608 | ||||||||
\(11\) | −3.64877e63 | −0.328470 | −0.164235 | − | 0.986421i | \(-0.552516\pi\) | ||||
−0.164235 | + | 0.986421i | \(0.552516\pi\) | |||||||
\(12\) | −1.39108e66 | −0.593888 | ||||||||
\(13\) | −3.93413e68 | −1.22274 | −0.611368 | − | 0.791346i | \(-0.709381\pi\) | ||||
−0.611368 | + | 0.791346i | \(0.709381\pi\) | |||||||
\(14\) | −2.81589e70 | −0.917785 | ||||||||
\(15\) | −1.59522e72 | −0.746808 | ||||||||
\(16\) | 1.66911e73 | 0.147607 | ||||||||
\(17\) | 6.26916e75 | 1.33230 | 0.666148 | − | 0.745819i | \(-0.267942\pi\) | ||||
0.666148 | + | 0.745819i | \(0.267942\pi\) | |||||||
\(18\) | −2.15987e76 | −0.136511 | ||||||||
\(19\) | −7.77701e78 | −1.76794 | −0.883968 | − | 0.467548i | \(-0.845138\pi\) | ||||
−0.883968 | + | 0.467548i | \(0.845138\pi\) | |||||||
\(20\) | 6.03501e79 | 0.585239 | ||||||||
\(21\) | −2.93727e81 | −1.41728 | ||||||||
\(22\) | −6.70757e81 | −0.185170 | ||||||||
\(23\) | 4.70089e83 | 0.843176 | 0.421588 | − | 0.906788i | \(-0.361473\pi\) | ||||
0.421588 | + | 0.906788i | \(0.361473\pi\) | |||||||
\(24\) | −6.30571e84 | −0.825549 | ||||||||
\(25\) | −2.48327e85 | −0.264067 | ||||||||
\(26\) | −7.23216e86 | −0.689298 | ||||||||
\(27\) | −1.15568e88 | −1.08135 | ||||||||
\(28\) | 1.11122e89 | 1.11066 | ||||||||
\(29\) | 6.71958e89 | 0.776007 | 0.388003 | − | 0.921658i | \(-0.373165\pi\) | ||||
0.388003 | + | 0.921658i | \(0.373165\pi\) | |||||||
\(30\) | −2.93252e90 | −0.421001 | ||||||||
\(31\) | 2.07270e91 | 0.396088 | 0.198044 | − | 0.980193i | \(-0.436541\pi\) | ||||
0.198044 | + | 0.980193i | \(0.436541\pi\) | |||||||
\(32\) | 3.80368e92 | 1.03153 | ||||||||
\(33\) | −6.99671e92 | −0.285948 | ||||||||
\(34\) | 1.15247e94 | 0.751061 | ||||||||
\(35\) | 1.27430e95 | 1.39664 | ||||||||
\(36\) | 8.52340e94 | 0.165200 | ||||||||
\(37\) | 8.83217e95 | 0.317440 | 0.158720 | − | 0.987324i | \(-0.449263\pi\) | ||||
0.158720 | + | 0.987324i | \(0.449263\pi\) | |||||||
\(38\) | −1.42966e97 | −0.996645 | ||||||||
\(39\) | −7.54391e97 | −1.06444 | ||||||||
\(40\) | 2.73566e98 | 0.813527 | ||||||||
\(41\) | −6.43781e97 | −0.0419306 | −0.0209653 | − | 0.999780i | \(-0.506674\pi\) | ||||
−0.0209653 | + | 0.999780i | \(0.506674\pi\) | |||||||
\(42\) | −5.39961e99 | −0.798971 | ||||||||
\(43\) | 3.49211e100 | 1.21557 | 0.607783 | − | 0.794103i | \(-0.292059\pi\) | ||||
0.607783 | + | 0.794103i | \(0.292059\pi\) | |||||||
\(44\) | 2.64698e100 | 0.224084 | ||||||||
\(45\) | 9.77424e100 | 0.207737 | ||||||||
\(46\) | 8.64169e101 | 0.475327 | ||||||||
\(47\) | −8.32956e102 | −1.22068 | −0.610342 | − | 0.792138i | \(-0.708968\pi\) | ||||
−0.610342 | + | 0.792138i | \(0.708968\pi\) | |||||||
\(48\) | 3.20061e102 | 0.128498 | ||||||||
\(49\) | 1.46111e104 | 1.65054 | ||||||||
\(50\) | −4.56503e103 | −0.148863 | ||||||||
\(51\) | 1.20214e105 | 1.15982 | ||||||||
\(52\) | 2.85399e105 | 0.834156 | ||||||||
\(53\) | −4.35998e105 | −0.394928 | −0.197464 | − | 0.980310i | \(-0.563271\pi\) | ||||
−0.197464 | + | 0.980310i | \(0.563271\pi\) | |||||||
\(54\) | −2.12450e106 | −0.609593 | ||||||||
\(55\) | 3.03543e106 | 0.281783 | ||||||||
\(56\) | 5.03713e107 | 1.54390 | ||||||||
\(57\) | −1.49128e108 | −1.53906 | ||||||||
\(58\) | 1.23527e108 | 0.437461 | ||||||||
\(59\) | −8.62805e108 | −1.06786 | −0.533930 | − | 0.845529i | \(-0.679285\pi\) | ||||
−0.533930 | + | 0.845529i | \(0.679285\pi\) | |||||||
\(60\) | 1.15725e109 | 0.509476 | ||||||||
\(61\) | −7.55451e109 | −1.20343 | −0.601716 | − | 0.798710i | \(-0.705516\pi\) | ||||
−0.601716 | + | 0.798710i | \(0.705516\pi\) | |||||||
\(62\) | 3.81026e109 | 0.223288 | ||||||||
\(63\) | 1.79972e110 | 0.394241 | ||||||||
\(64\) | 5.21744e110 | 0.433899 | ||||||||
\(65\) | 3.27283e111 | 1.04894 | ||||||||
\(66\) | −1.28621e111 | −0.161198 | ||||||||
\(67\) | −1.06990e112 | −0.531793 | −0.265896 | − | 0.964002i | \(-0.585668\pi\) | ||||
−0.265896 | + | 0.964002i | \(0.585668\pi\) | |||||||
\(68\) | −4.54793e112 | −0.908898 | ||||||||
\(69\) | 9.01420e112 | 0.734021 | ||||||||
\(70\) | 2.34255e113 | 0.787336 | ||||||||
\(71\) | −9.58273e113 | −1.34617 | −0.673087 | − | 0.739564i | \(-0.735032\pi\) | ||||
−0.673087 | + | 0.739564i | \(0.735032\pi\) | |||||||
\(72\) | 3.86363e113 | 0.229640 | ||||||||
\(73\) | −1.40162e114 | −0.356675 | −0.178338 | − | 0.983969i | \(-0.557072\pi\) | ||||
−0.178338 | + | 0.983969i | \(0.557072\pi\) | |||||||
\(74\) | 1.62363e114 | 0.178952 | ||||||||
\(75\) | −4.76181e114 | −0.229881 | ||||||||
\(76\) | 5.64179e115 | 1.20609 | ||||||||
\(77\) | 5.58911e115 | 0.534765 | ||||||||
\(78\) | −1.38680e116 | −0.600063 | ||||||||
\(79\) | −1.66329e116 | −0.328777 | −0.164389 | − | 0.986396i | \(-0.552565\pi\) | ||||
−0.164389 | + | 0.986396i | \(0.552565\pi\) | |||||||
\(80\) | −1.38854e116 | −0.126627 | ||||||||
\(81\) | −1.64601e117 | −0.699205 | ||||||||
\(82\) | −1.18347e116 | −0.0236377 | ||||||||
\(83\) | 6.67836e117 | 0.632946 | 0.316473 | − | 0.948601i | \(-0.397501\pi\) | ||||
0.316473 | + | 0.948601i | \(0.397501\pi\) | |||||||
\(84\) | 2.13082e118 | 0.966877 | ||||||||
\(85\) | −5.21536e118 | −1.14293 | ||||||||
\(86\) | 6.41959e118 | 0.685255 | ||||||||
\(87\) | 1.28852e119 | 0.675547 | ||||||||
\(88\) | 1.19987e119 | 0.311494 | ||||||||
\(89\) | −1.04169e120 | −1.34974 | −0.674872 | − | 0.737934i | \(-0.735801\pi\) | ||||
−0.674872 | + | 0.737934i | \(0.735801\pi\) | |||||||
\(90\) | 1.79681e119 | 0.117108 | ||||||||
\(91\) | 6.02623e120 | 1.99067 | ||||||||
\(92\) | −3.41023e120 | −0.575218 | ||||||||
\(93\) | 3.97450e120 | 0.344811 | ||||||||
\(94\) | −1.53123e121 | −0.688141 | ||||||||
\(95\) | 6.46975e121 | 1.51665 | ||||||||
\(96\) | 7.29376e121 | 0.897988 | ||||||||
\(97\) | 1.90065e122 | 1.23720 | 0.618602 | − | 0.785704i | \(-0.287699\pi\) | ||||
0.618602 | + | 0.785704i | \(0.287699\pi\) | |||||||
\(98\) | 2.68598e122 | 0.930463 | ||||||||
\(99\) | 4.28702e121 | 0.0795410 | ||||||||
\(100\) | 1.80148e122 | 0.180148 | ||||||||
\(101\) | 7.23189e122 | 0.392182 | 0.196091 | − | 0.980586i | \(-0.437175\pi\) | ||||
0.196091 | + | 0.980586i | \(0.437175\pi\) | |||||||
\(102\) | 2.20992e123 | 0.653830 | ||||||||
\(103\) | 1.07903e124 | 1.75204 | 0.876021 | − | 0.482274i | \(-0.160189\pi\) | ||||
0.876021 | + | 0.482274i | \(0.160189\pi\) | |||||||
\(104\) | 1.29371e124 | 1.15954 | ||||||||
\(105\) | 2.44353e124 | 1.21584 | ||||||||
\(106\) | −8.01499e123 | −0.222634 | ||||||||
\(107\) | 6.45004e124 | 1.00568 | 0.502840 | − | 0.864379i | \(-0.332288\pi\) | ||||
0.502840 | + | 0.864379i | \(0.332288\pi\) | |||||||
\(108\) | 8.38381e124 | 0.737701 | ||||||||
\(109\) | −1.22678e125 | −0.612400 | −0.306200 | − | 0.951967i | \(-0.599058\pi\) | ||||
−0.306200 | + | 0.951967i | \(0.599058\pi\) | |||||||
\(110\) | 5.58007e124 | 0.158851 | ||||||||
\(111\) | 1.69361e125 | 0.276345 | ||||||||
\(112\) | −2.55671e125 | −0.240311 | ||||||||
\(113\) | 4.82188e125 | 0.262357 | 0.131178 | − | 0.991359i | \(-0.458124\pi\) | ||||
0.131178 | + | 0.991359i | \(0.458124\pi\) | |||||||
\(114\) | −2.74144e126 | −0.867622 | ||||||||
\(115\) | −3.91070e126 | −0.723332 | ||||||||
\(116\) | −4.87468e126 | −0.529395 | ||||||||
\(117\) | 4.62230e126 | 0.296093 | ||||||||
\(118\) | −1.58610e127 | −0.601988 | ||||||||
\(119\) | −9.60298e127 | −2.16904 | ||||||||
\(120\) | 5.24576e127 | 0.708210 | ||||||||
\(121\) | −1.10082e128 | −0.892107 | ||||||||
\(122\) | −1.38875e128 | −0.678415 | ||||||||
\(123\) | −1.23448e127 | −0.0365024 | ||||||||
\(124\) | −1.50362e128 | −0.270213 | ||||||||
\(125\) | 9.88906e128 | 1.08440 | ||||||||
\(126\) | 3.30844e128 | 0.222247 | ||||||||
\(127\) | 4.11989e129 | 1.70199 | 0.850995 | − | 0.525173i | \(-0.175999\pi\) | ||||
0.850995 | + | 0.525173i | \(0.175999\pi\) | |||||||
\(128\) | −3.08564e129 | −0.786923 | ||||||||
\(129\) | 6.69631e129 | 1.05820 | ||||||||
\(130\) | 6.01648e129 | 0.591325 | ||||||||
\(131\) | −2.42268e130 | −1.48631 | −0.743157 | − | 0.669117i | \(-0.766672\pi\) | ||||
−0.743157 | + | 0.669117i | \(0.766672\pi\) | |||||||
\(132\) | 5.07572e129 | 0.195075 | ||||||||
\(133\) | 1.19127e131 | 2.87828 | ||||||||
\(134\) | −1.96681e130 | −0.299790 | ||||||||
\(135\) | 9.61417e130 | 0.927652 | ||||||||
\(136\) | −2.06156e131 | −1.26344 | ||||||||
\(137\) | −3.96219e131 | −1.54746 | −0.773732 | − | 0.633514i | \(-0.781612\pi\) | ||||
−0.773732 | + | 0.633514i | \(0.781612\pi\) | |||||||
\(138\) | 1.65709e131 | 0.413792 | ||||||||
\(139\) | 1.50811e131 | 0.241558 | 0.120779 | − | 0.992679i | \(-0.461461\pi\) | ||||
0.120779 | + | 0.992679i | \(0.461461\pi\) | |||||||
\(140\) | −9.24431e131 | −0.952797 | ||||||||
\(141\) | −1.59724e132 | −1.06266 | ||||||||
\(142\) | −1.76160e132 | −0.758883 | ||||||||
\(143\) | 1.43548e132 | 0.401633 | ||||||||
\(144\) | −1.96107e131 | −0.0357438 | ||||||||
\(145\) | −5.59006e132 | −0.665709 | ||||||||
\(146\) | −2.57661e132 | −0.201070 | ||||||||
\(147\) | 2.80176e133 | 1.43686 | ||||||||
\(148\) | −6.40724e132 | −0.216559 | ||||||||
\(149\) | 5.69247e133 | 1.27158 | 0.635792 | − | 0.771860i | \(-0.280673\pi\) | ||||
0.635792 | + | 0.771860i | \(0.280673\pi\) | |||||||
\(150\) | −8.75368e132 | −0.129592 | ||||||||
\(151\) | −5.66160e133 | −0.557002 | −0.278501 | − | 0.960436i | \(-0.589838\pi\) | ||||
−0.278501 | + | 0.960436i | \(0.589838\pi\) | |||||||
\(152\) | 2.55741e134 | 1.67656 | ||||||||
\(153\) | −7.36577e133 | −0.322623 | ||||||||
\(154\) | 1.02745e134 | 0.301465 | ||||||||
\(155\) | −1.72429e134 | −0.339790 | ||||||||
\(156\) | 5.47268e134 | 0.726169 | ||||||||
\(157\) | 2.23778e134 | 0.200442 | 0.100221 | − | 0.994965i | \(-0.468045\pi\) | ||||
0.100221 | + | 0.994965i | \(0.468045\pi\) | |||||||
\(158\) | −3.05764e134 | −0.185343 | ||||||||
\(159\) | −8.36048e134 | −0.343802 | ||||||||
\(160\) | −3.16431e135 | −0.884911 | ||||||||
\(161\) | −7.20073e135 | −1.37273 | ||||||||
\(162\) | −3.02588e135 | −0.394166 | ||||||||
\(163\) | −5.59907e135 | −0.499549 | −0.249775 | − | 0.968304i | \(-0.580357\pi\) | ||||
−0.249775 | + | 0.968304i | \(0.580357\pi\) | |||||||
\(164\) | 4.67027e134 | 0.0286052 | ||||||||
\(165\) | 5.82060e135 | 0.245305 | ||||||||
\(166\) | 1.22769e136 | 0.356813 | ||||||||
\(167\) | −7.56334e135 | −0.151933 | −0.0759663 | − | 0.997110i | \(-0.524204\pi\) | ||||
−0.0759663 | + | 0.997110i | \(0.524204\pi\) | |||||||
\(168\) | 9.65896e136 | 1.34403 | ||||||||
\(169\) | 5.12522e136 | 0.495086 | ||||||||
\(170\) | −9.58744e136 | −0.644309 | ||||||||
\(171\) | 9.13738e136 | 0.428115 | ||||||||
\(172\) | −2.53333e137 | −0.829264 | ||||||||
\(173\) | 7.60124e137 | 1.74200 | 0.871002 | − | 0.491279i | \(-0.163470\pi\) | ||||
0.871002 | + | 0.491279i | \(0.163470\pi\) | |||||||
\(174\) | 2.36869e137 | 0.380829 | ||||||||
\(175\) | 3.80383e137 | 0.429913 | ||||||||
\(176\) | −6.09020e136 | −0.0484845 | ||||||||
\(177\) | −1.65447e138 | −0.929617 | ||||||||
\(178\) | −1.91494e138 | −0.760897 | ||||||||
\(179\) | 2.84392e137 | 0.0800674 | 0.0400337 | − | 0.999198i | \(-0.487253\pi\) | ||||
0.0400337 | + | 0.999198i | \(0.487253\pi\) | |||||||
\(180\) | −7.09067e137 | −0.141719 | ||||||||
\(181\) | −7.36733e138 | −1.04732 | −0.523658 | − | 0.851929i | \(-0.675433\pi\) | ||||
−0.523658 | + | 0.851929i | \(0.675433\pi\) | |||||||
\(182\) | 1.10781e139 | 1.12221 | ||||||||
\(183\) | −1.44862e139 | −1.04764 | ||||||||
\(184\) | −1.54585e139 | −0.799597 | ||||||||
\(185\) | −7.34754e138 | −0.272321 | ||||||||
\(186\) | 7.30637e138 | 0.194382 | ||||||||
\(187\) | −2.28747e139 | −0.437620 | ||||||||
\(188\) | 6.04263e139 | 0.832756 | ||||||||
\(189\) | 1.77025e140 | 1.76049 | ||||||||
\(190\) | 1.18934e140 | 0.854987 | ||||||||
\(191\) | −1.02618e140 | −0.534160 | −0.267080 | − | 0.963674i | \(-0.586059\pi\) | ||||
−0.267080 | + | 0.963674i | \(0.586059\pi\) | |||||||
\(192\) | 1.00047e140 | 0.377728 | ||||||||
\(193\) | −1.92038e140 | −0.526761 | −0.263381 | − | 0.964692i | \(-0.584837\pi\) | ||||
−0.263381 | + | 0.964692i | \(0.584837\pi\) | |||||||
\(194\) | 3.49399e140 | 0.697454 | ||||||||
\(195\) | 6.27583e140 | 0.913150 | ||||||||
\(196\) | −1.05996e141 | −1.12600 | ||||||||
\(197\) | −1.93333e141 | −1.50188 | −0.750938 | − | 0.660373i | \(-0.770398\pi\) | ||||
−0.750938 | + | 0.660373i | \(0.770398\pi\) | |||||||
\(198\) | 7.88087e139 | 0.0448399 | ||||||||
\(199\) | 1.15580e141 | 0.482411 | 0.241205 | − | 0.970474i | \(-0.422457\pi\) | ||||
0.241205 | + | 0.970474i | \(0.422457\pi\) | |||||||
\(200\) | 8.16604e140 | 0.250419 | ||||||||
\(201\) | −2.05159e141 | −0.462948 | ||||||||
\(202\) | 1.32945e141 | 0.221086 | ||||||||
\(203\) | −1.02929e142 | −1.26338 | ||||||||
\(204\) | −8.72089e141 | −0.791235 | ||||||||
\(205\) | 5.35565e140 | 0.0359708 | ||||||||
\(206\) | 1.98359e142 | 0.987685 | ||||||||
\(207\) | −5.52318e141 | −0.204180 | ||||||||
\(208\) | −6.56651e141 | −0.180484 | ||||||||
\(209\) | 2.83765e142 | 0.580715 | ||||||||
\(210\) | 4.49197e142 | 0.685410 | ||||||||
\(211\) | 1.57848e143 | 1.79832 | 0.899160 | − | 0.437620i | \(-0.144179\pi\) | ||||
0.899160 | + | 0.437620i | \(0.144179\pi\) | |||||||
\(212\) | 3.16292e142 | 0.269422 | ||||||||
\(213\) | −1.83754e143 | −1.17190 | ||||||||
\(214\) | 1.18572e143 | 0.566936 | ||||||||
\(215\) | −2.90511e143 | −1.04279 | ||||||||
\(216\) | 3.80036e143 | 1.02546 | ||||||||
\(217\) | −3.17491e143 | −0.644849 | ||||||||
\(218\) | −2.25519e143 | −0.345231 | ||||||||
\(219\) | −2.68767e143 | −0.310501 | ||||||||
\(220\) | −2.20204e143 | −0.192234 | ||||||||
\(221\) | −2.46637e144 | −1.62905 | ||||||||
\(222\) | 3.11339e143 | 0.155785 | ||||||||
\(223\) | 3.64941e144 | 1.38507 | 0.692537 | − | 0.721382i | \(-0.256493\pi\) | ||||
0.692537 | + | 0.721382i | \(0.256493\pi\) | |||||||
\(224\) | −5.82640e144 | −1.67937 | ||||||||
\(225\) | 2.91765e143 | 0.0639453 | ||||||||
\(226\) | 8.86412e143 | 0.147899 | ||||||||
\(227\) | 1.15604e145 | 1.47022 | 0.735110 | − | 0.677948i | \(-0.237131\pi\) | ||||
0.735110 | + | 0.677948i | \(0.237131\pi\) | |||||||
\(228\) | 1.08184e145 | 1.04996 | ||||||||
\(229\) | −4.59197e144 | −0.340500 | −0.170250 | − | 0.985401i | \(-0.554457\pi\) | ||||
−0.170250 | + | 0.985401i | \(0.554457\pi\) | |||||||
\(230\) | −7.18908e144 | −0.407766 | ||||||||
\(231\) | 1.07174e145 | 0.465536 | ||||||||
\(232\) | −2.20968e145 | −0.735899 | ||||||||
\(233\) | 1.33984e145 | 0.342502 | 0.171251 | − | 0.985227i | \(-0.445219\pi\) | ||||
0.171251 | + | 0.985227i | \(0.445219\pi\) | |||||||
\(234\) | 8.49722e144 | 0.166917 | ||||||||
\(235\) | 6.92941e145 | 1.04718 | ||||||||
\(236\) | 6.25917e145 | 0.728498 | ||||||||
\(237\) | −3.18944e145 | −0.286214 | ||||||||
\(238\) | −1.76533e146 | −1.22276 | ||||||||
\(239\) | −1.38760e146 | −0.742668 | −0.371334 | − | 0.928499i | \(-0.621100\pi\) | ||||
−0.371334 | + | 0.928499i | \(0.621100\pi\) | |||||||
\(240\) | −2.66261e145 | −0.110234 | ||||||||
\(241\) | −3.78427e146 | −1.21320 | −0.606602 | − | 0.795006i | \(-0.707468\pi\) | ||||
−0.606602 | + | 0.795006i | \(0.707468\pi\) | |||||||
\(242\) | −2.02365e146 | −0.502911 | ||||||||
\(243\) | 2.45096e146 | 0.472661 | ||||||||
\(244\) | 5.48037e146 | 0.820986 | ||||||||
\(245\) | −1.21551e147 | −1.41594 | ||||||||
\(246\) | −2.26936e145 | −0.0205776 | ||||||||
\(247\) | 3.05958e147 | 2.16172 | ||||||||
\(248\) | −6.81589e146 | −0.375616 | ||||||||
\(249\) | 1.28061e147 | 0.551007 | ||||||||
\(250\) | 1.81792e147 | 0.611313 | ||||||||
\(251\) | 1.31467e147 | 0.345847 | 0.172923 | − | 0.984935i | \(-0.444679\pi\) | ||||
0.172923 | + | 0.984935i | \(0.444679\pi\) | |||||||
\(252\) | −1.30560e147 | −0.268953 | ||||||||
\(253\) | −1.71525e147 | −0.276958 | ||||||||
\(254\) | 7.57364e147 | 0.959470 | ||||||||
\(255\) | −1.00007e148 | −0.994970 | ||||||||
\(256\) | −1.12205e148 | −0.877514 | ||||||||
\(257\) | 1.10486e148 | 0.679859 | 0.339929 | − | 0.940451i | \(-0.389597\pi\) | ||||
0.339929 | + | 0.940451i | \(0.389597\pi\) | |||||||
\(258\) | 1.23099e148 | 0.596544 | ||||||||
\(259\) | −1.35289e148 | −0.516807 | ||||||||
\(260\) | −2.37426e148 | −0.715594 | ||||||||
\(261\) | −7.89498e147 | −0.187914 | ||||||||
\(262\) | −4.45363e148 | −0.837885 | ||||||||
\(263\) | −4.79340e148 | −0.713452 | −0.356726 | − | 0.934209i | \(-0.616107\pi\) | ||||
−0.356726 | + | 0.934209i | \(0.616107\pi\) | |||||||
\(264\) | 2.30081e148 | 0.271168 | ||||||||
\(265\) | 3.62709e148 | 0.338795 | ||||||||
\(266\) | 2.18992e149 | 1.62258 | ||||||||
\(267\) | −1.99749e149 | −1.17501 | ||||||||
\(268\) | 7.76152e148 | 0.362791 | ||||||||
\(269\) | −2.68638e148 | −0.0998625 | −0.0499313 | − | 0.998753i | \(-0.515900\pi\) | ||||
−0.0499313 | + | 0.998753i | \(0.515900\pi\) | |||||||
\(270\) | 1.76738e149 | 0.522949 | ||||||||
\(271\) | 6.66346e148 | 0.157068 | 0.0785341 | − | 0.996911i | \(-0.474976\pi\) | ||||
0.0785341 | + | 0.996911i | \(0.474976\pi\) | |||||||
\(272\) | 1.04639e149 | 0.196656 | ||||||||
\(273\) | 1.15556e150 | 1.73297 | ||||||||
\(274\) | −7.28373e149 | −0.872357 | ||||||||
\(275\) | 9.06089e148 | 0.0867382 | ||||||||
\(276\) | −6.53930e149 | −0.500752 | ||||||||
\(277\) | 9.02775e149 | 0.553444 | 0.276722 | − | 0.960950i | \(-0.410752\pi\) | ||||
0.276722 | + | 0.960950i | \(0.410752\pi\) | |||||||
\(278\) | 2.77237e149 | 0.136175 | ||||||||
\(279\) | −2.43525e149 | −0.0959149 | ||||||||
\(280\) | −4.19042e150 | −1.32446 | ||||||||
\(281\) | −5.60846e150 | −1.42366 | −0.711828 | − | 0.702354i | \(-0.752132\pi\) | ||||
−0.711828 | + | 0.702354i | \(0.752132\pi\) | |||||||
\(282\) | −2.93621e150 | −0.599056 | ||||||||
\(283\) | −4.73677e150 | −0.777349 | −0.388675 | − | 0.921375i | \(-0.627067\pi\) | ||||
−0.388675 | + | 0.921375i | \(0.627067\pi\) | |||||||
\(284\) | 6.95174e150 | 0.918365 | ||||||||
\(285\) | 1.24061e151 | 1.32031 | ||||||||
\(286\) | 2.63885e150 | 0.226414 | ||||||||
\(287\) | 9.86130e149 | 0.0682649 | ||||||||
\(288\) | −4.46902e150 | −0.249790 | ||||||||
\(289\) | 1.71604e151 | 0.775015 | ||||||||
\(290\) | −1.02763e151 | −0.375283 | ||||||||
\(291\) | 3.64460e151 | 1.07704 | ||||||||
\(292\) | 1.01679e151 | 0.243325 | ||||||||
\(293\) | −9.51924e151 | −1.84605 | −0.923026 | − | 0.384738i | \(-0.874292\pi\) | ||||
−0.923026 | + | 0.384738i | \(0.874292\pi\) | |||||||
\(294\) | 5.15051e151 | 0.810008 | ||||||||
\(295\) | 7.17773e151 | 0.916079 | ||||||||
\(296\) | −2.90439e151 | −0.301033 | ||||||||
\(297\) | 4.21681e151 | 0.355191 | ||||||||
\(298\) | 1.04645e152 | 0.716835 | ||||||||
\(299\) | −1.84939e152 | −1.03098 | ||||||||
\(300\) | 3.45442e151 | 0.156826 | ||||||||
\(301\) | −5.34915e152 | −1.97900 | ||||||||
\(302\) | −1.04078e152 | −0.314001 | ||||||||
\(303\) | 1.38675e152 | 0.341411 | ||||||||
\(304\) | −1.29807e152 | −0.260959 | ||||||||
\(305\) | 6.28465e152 | 1.03238 | ||||||||
\(306\) | −1.35406e152 | −0.181874 | ||||||||
\(307\) | −1.37302e153 | −1.50892 | −0.754459 | − | 0.656347i | \(-0.772101\pi\) | ||||
−0.754459 | + | 0.656347i | \(0.772101\pi\) | |||||||
\(308\) | −4.05459e152 | −0.364819 | ||||||||
\(309\) | 2.06910e153 | 1.52523 | ||||||||
\(310\) | −3.16978e152 | −0.191551 | ||||||||
\(311\) | 1.97533e153 | 0.979210 | 0.489605 | − | 0.871944i | \(-0.337141\pi\) | ||||
0.489605 | + | 0.871944i | \(0.337141\pi\) | |||||||
\(312\) | 2.48075e153 | 1.00943 | ||||||||
\(313\) | 2.29332e152 | 0.0766456 | 0.0383228 | − | 0.999265i | \(-0.487798\pi\) | ||||
0.0383228 | + | 0.999265i | \(0.487798\pi\) | |||||||
\(314\) | 4.11373e152 | 0.112996 | ||||||||
\(315\) | −1.49720e153 | −0.338205 | ||||||||
\(316\) | 1.20662e153 | 0.224293 | ||||||||
\(317\) | 1.61583e152 | 0.0247315 | 0.0123658 | − | 0.999924i | \(-0.496064\pi\) | ||||
0.0123658 | + | 0.999924i | \(0.496064\pi\) | |||||||
\(318\) | −1.53692e153 | −0.193813 | ||||||||
\(319\) | −2.45182e153 | −0.254895 | ||||||||
\(320\) | −4.34042e153 | −0.372227 | ||||||||
\(321\) | 1.23683e154 | 0.875488 | ||||||||
\(322\) | −1.32372e154 | −0.773854 | ||||||||
\(323\) | −4.87554e154 | −2.35541 | ||||||||
\(324\) | 1.19409e154 | 0.477001 | ||||||||
\(325\) | 9.76953e153 | 0.322884 | ||||||||
\(326\) | −1.02928e154 | −0.281613 | ||||||||
\(327\) | −2.35241e154 | −0.533121 | ||||||||
\(328\) | 2.11702e153 | 0.0397634 | ||||||||
\(329\) | 1.27590e155 | 1.98733 | ||||||||
\(330\) | 1.07001e154 | 0.138286 | ||||||||
\(331\) | 3.52184e154 | 0.377875 | 0.188937 | − | 0.981989i | \(-0.439496\pi\) | ||||
0.188937 | + | 0.981989i | \(0.439496\pi\) | |||||||
\(332\) | −4.84477e154 | −0.431799 | ||||||||
\(333\) | −1.03771e154 | −0.0768698 | ||||||||
\(334\) | −1.39038e154 | −0.0856495 | ||||||||
\(335\) | 8.90056e154 | 0.456207 | ||||||||
\(336\) | −4.90263e154 | −0.209201 | ||||||||
\(337\) | −1.28842e153 | −0.00457952 | −0.00228976 | − | 0.999997i | \(-0.500729\pi\) | ||||
−0.00228976 | + | 0.999997i | \(0.500729\pi\) | |||||||
\(338\) | 9.42175e154 | 0.279097 | ||||||||
\(339\) | 9.24622e154 | 0.228393 | ||||||||
\(340\) | 3.78345e155 | 0.779713 | ||||||||
\(341\) | −7.56279e154 | −0.130103 | ||||||||
\(342\) | 1.67973e155 | 0.241343 | ||||||||
\(343\) | −8.82118e155 | −1.05910 | ||||||||
\(344\) | −1.14835e156 | −1.15274 | ||||||||
\(345\) | −7.49897e155 | −0.629691 | ||||||||
\(346\) | 1.39734e156 | 0.982027 | ||||||||
\(347\) | −1.68942e156 | −0.994205 | −0.497102 | − | 0.867692i | \(-0.665603\pi\) | ||||
−0.497102 | + | 0.867692i | \(0.665603\pi\) | |||||||
\(348\) | −9.34746e155 | −0.460861 | ||||||||
\(349\) | −1.85162e156 | −0.765221 | −0.382611 | − | 0.923910i | \(-0.624975\pi\) | ||||
−0.382611 | + | 0.923910i | \(0.624975\pi\) | |||||||
\(350\) | 6.99262e155 | 0.242357 | ||||||||
\(351\) | 4.54660e156 | 1.32221 | ||||||||
\(352\) | −1.38788e156 | −0.338826 | ||||||||
\(353\) | 8.44770e156 | 1.73218 | 0.866092 | − | 0.499884i | \(-0.166624\pi\) | ||||
0.866092 | + | 0.499884i | \(0.166624\pi\) | |||||||
\(354\) | −3.04144e156 | −0.524056 | ||||||||
\(355\) | 7.97194e156 | 1.15484 | ||||||||
\(356\) | 7.55685e156 | 0.920802 | ||||||||
\(357\) | −1.84142e157 | −1.88824 | ||||||||
\(358\) | 5.22800e155 | 0.0451367 | ||||||||
\(359\) | 2.59815e156 | 0.188954 | 0.0944770 | − | 0.995527i | \(-0.469882\pi\) | ||||
0.0944770 | + | 0.995527i | \(0.469882\pi\) | |||||||
\(360\) | −3.21418e156 | −0.197000 | ||||||||
\(361\) | 4.11314e157 | 2.12560 | ||||||||
\(362\) | −1.35434e157 | −0.590407 | ||||||||
\(363\) | −2.11088e157 | −0.776617 | ||||||||
\(364\) | −4.37169e157 | −1.35805 | ||||||||
\(365\) | 1.16601e157 | 0.305979 | ||||||||
\(366\) | −2.66301e157 | −0.590589 | ||||||||
\(367\) | −3.01128e157 | −0.564661 | −0.282331 | − | 0.959317i | \(-0.591107\pi\) | ||||
−0.282331 | + | 0.959317i | \(0.591107\pi\) | |||||||
\(368\) | 7.84631e156 | 0.124459 | ||||||||
\(369\) | 7.56392e155 | 0.0101537 | ||||||||
\(370\) | −1.35071e157 | −0.153516 | ||||||||
\(371\) | 6.67852e157 | 0.642962 | ||||||||
\(372\) | −2.88328e157 | −0.235232 | ||||||||
\(373\) | −2.77145e157 | −0.191696 | −0.0958481 | − | 0.995396i | \(-0.530556\pi\) | ||||
−0.0958481 | + | 0.995396i | \(0.530556\pi\) | |||||||
\(374\) | −4.20509e157 | −0.246701 | ||||||||
\(375\) | 1.89628e158 | 0.944016 | ||||||||
\(376\) | 2.73911e158 | 1.15759 | ||||||||
\(377\) | −2.64357e158 | −0.948852 | ||||||||
\(378\) | 3.25426e158 | 0.992446 | ||||||||
\(379\) | −1.70323e158 | −0.441532 | −0.220766 | − | 0.975327i | \(-0.570856\pi\) | ||||
−0.220766 | + | 0.975327i | \(0.570856\pi\) | |||||||
\(380\) | −4.69344e158 | −1.03467 | ||||||||
\(381\) | 7.90011e158 | 1.48166 | ||||||||
\(382\) | −1.88644e158 | −0.301124 | ||||||||
\(383\) | 1.09260e159 | 1.48504 | 0.742519 | − | 0.669825i | \(-0.233631\pi\) | ||||
0.742519 | + | 0.669825i | \(0.233631\pi\) | |||||||
\(384\) | −5.91687e158 | −0.685050 | ||||||||
\(385\) | −4.64962e158 | −0.458757 | ||||||||
\(386\) | −3.53026e158 | −0.296953 | ||||||||
\(387\) | −4.10296e158 | −0.294356 | ||||||||
\(388\) | −1.37882e159 | −0.844026 | ||||||||
\(389\) | −3.77080e158 | −0.197030 | −0.0985150 | − | 0.995136i | \(-0.531409\pi\) | ||||
−0.0985150 | + | 0.995136i | \(0.531409\pi\) | |||||||
\(390\) | 1.15369e159 | 0.514774 | ||||||||
\(391\) | 2.94707e159 | 1.12336 | ||||||||
\(392\) | −4.80475e159 | −1.56523 | ||||||||
\(393\) | −4.64561e159 | −1.29390 | ||||||||
\(394\) | −3.55407e159 | −0.846658 | ||||||||
\(395\) | 1.38370e159 | 0.282046 | ||||||||
\(396\) | −3.10999e158 | −0.0542632 | ||||||||
\(397\) | 1.04375e160 | 1.55949 | 0.779744 | − | 0.626098i | \(-0.215349\pi\) | ||||
0.779744 | + | 0.626098i | \(0.215349\pi\) | |||||||
\(398\) | 2.12471e159 | 0.271951 | ||||||||
\(399\) | 2.28432e160 | 2.50567 | ||||||||
\(400\) | −4.14486e158 | −0.0389781 | ||||||||
\(401\) | −1.66506e159 | −0.134293 | −0.0671463 | − | 0.997743i | \(-0.521389\pi\) | ||||
−0.0671463 | + | 0.997743i | \(0.521389\pi\) | |||||||
\(402\) | −3.77146e159 | −0.260980 | ||||||||
\(403\) | −8.15427e159 | −0.484311 | ||||||||
\(404\) | −5.24633e159 | −0.267548 | ||||||||
\(405\) | 1.36933e160 | 0.599824 | ||||||||
\(406\) | −1.89216e160 | −0.712207 | ||||||||
\(407\) | −3.22266e159 | −0.104270 | ||||||||
\(408\) | −3.95315e160 | −1.09988 | ||||||||
\(409\) | 6.84012e160 | 1.63712 | 0.818560 | − | 0.574421i | \(-0.194773\pi\) | ||||
0.818560 | + | 0.574421i | \(0.194773\pi\) | |||||||
\(410\) | 9.84535e158 | 0.0202780 | ||||||||
\(411\) | −7.59770e160 | −1.34713 | ||||||||
\(412\) | −7.82776e160 | −1.19525 | ||||||||
\(413\) | 1.32163e161 | 1.73852 | ||||||||
\(414\) | −1.01533e160 | −0.115103 | ||||||||
\(415\) | −5.55577e160 | −0.542983 | ||||||||
\(416\) | −1.49642e161 | −1.26129 | ||||||||
\(417\) | 2.89188e160 | 0.210287 | ||||||||
\(418\) | 5.21649e160 | 0.327368 | ||||||||
\(419\) | 1.24603e161 | 0.675097 | 0.337549 | − | 0.941308i | \(-0.390402\pi\) | ||||
0.337549 | + | 0.941308i | \(0.390402\pi\) | |||||||
\(420\) | −1.77265e161 | −0.829450 | ||||||||
\(421\) | 1.44201e161 | 0.582932 | 0.291466 | − | 0.956581i | \(-0.405857\pi\) | ||||
0.291466 | + | 0.956581i | \(0.405857\pi\) | |||||||
\(422\) | 2.90173e161 | 1.01377 | ||||||||
\(423\) | 9.78657e160 | 0.295596 | ||||||||
\(424\) | 1.43374e161 | 0.374516 | ||||||||
\(425\) | −1.55680e161 | −0.351815 | ||||||||
\(426\) | −3.37797e161 | −0.660640 | ||||||||
\(427\) | 1.15718e162 | 1.95924 | ||||||||
\(428\) | −4.67914e161 | −0.686080 | ||||||||
\(429\) | 2.75260e161 | 0.349639 | ||||||||
\(430\) | −5.34049e161 | −0.587857 | ||||||||
\(431\) | −7.35947e161 | −0.702254 | −0.351127 | − | 0.936328i | \(-0.614201\pi\) | ||||
−0.351127 | + | 0.936328i | \(0.614201\pi\) | |||||||
\(432\) | −1.92896e161 | −0.159615 | ||||||||
\(433\) | 1.20458e162 | 0.864632 | 0.432316 | − | 0.901722i | \(-0.357697\pi\) | ||||
0.432316 | + | 0.901722i | \(0.357697\pi\) | |||||||
\(434\) | −5.83648e161 | −0.363523 | ||||||||
\(435\) | −1.07192e162 | −0.579528 | ||||||||
\(436\) | 8.89957e161 | 0.417782 | ||||||||
\(437\) | −3.65589e162 | −1.49068 | ||||||||
\(438\) | −4.94077e161 | −0.175040 | ||||||||
\(439\) | 4.62284e161 | 0.142345 | 0.0711723 | − | 0.997464i | \(-0.477326\pi\) | ||||
0.0711723 | + | 0.997464i | \(0.477326\pi\) | |||||||
\(440\) | −9.98178e161 | −0.267220 | ||||||||
\(441\) | −1.71669e162 | −0.399686 | ||||||||
\(442\) | −4.53396e162 | −0.918350 | ||||||||
\(443\) | 9.37803e162 | 1.65304 | 0.826518 | − | 0.562910i | \(-0.190318\pi\) | ||||
0.826518 | + | 0.562910i | \(0.190318\pi\) | |||||||
\(444\) | −1.22862e162 | −0.188524 | ||||||||
\(445\) | 8.66586e162 | 1.15790 | ||||||||
\(446\) | 6.70874e162 | 0.780813 | ||||||||
\(447\) | 1.09156e163 | 1.10697 | ||||||||
\(448\) | −7.99197e162 | −0.706409 | ||||||||
\(449\) | 1.36044e162 | 0.104841 | 0.0524203 | − | 0.998625i | \(-0.483306\pi\) | ||||
0.0524203 | + | 0.998625i | \(0.483306\pi\) | |||||||
\(450\) | 5.36355e161 | 0.0360481 | ||||||||
\(451\) | 2.34901e161 | 0.0137730 | ||||||||
\(452\) | −3.49801e162 | −0.178981 | ||||||||
\(453\) | −1.08564e163 | −0.484894 | ||||||||
\(454\) | 2.12516e163 | 0.828812 | ||||||||
\(455\) | −5.01326e163 | −1.70773 | ||||||||
\(456\) | 4.90396e163 | 1.45952 | ||||||||
\(457\) | −4.60761e163 | −1.19848 | −0.599238 | − | 0.800571i | \(-0.704530\pi\) | ||||
−0.599238 | + | 0.800571i | \(0.704530\pi\) | |||||||
\(458\) | −8.44146e162 | −0.191951 | ||||||||
\(459\) | −7.24515e163 | −1.44068 | ||||||||
\(460\) | 2.83699e163 | 0.493460 | ||||||||
\(461\) | −6.94769e161 | −0.0105739 | −0.00528693 | − | 0.999986i | \(-0.501683\pi\) | ||||
−0.00528693 | + | 0.999986i | \(0.501683\pi\) | |||||||
\(462\) | 1.97019e163 | 0.262438 | ||||||||
\(463\) | 8.10358e163 | 0.945031 | 0.472515 | − | 0.881322i | \(-0.343346\pi\) | ||||
0.472515 | + | 0.881322i | \(0.343346\pi\) | |||||||
\(464\) | 1.12157e163 | 0.114544 | ||||||||
\(465\) | −3.30641e163 | −0.295802 | ||||||||
\(466\) | 2.46304e163 | 0.193080 | ||||||||
\(467\) | −2.43027e164 | −1.66981 | −0.834905 | − | 0.550394i | \(-0.814478\pi\) | ||||
−0.834905 | + | 0.550394i | \(0.814478\pi\) | |||||||
\(468\) | −3.35322e163 | −0.201996 | ||||||||
\(469\) | 1.63885e164 | 0.865784 | ||||||||
\(470\) | 1.27384e164 | 0.590333 | ||||||||
\(471\) | 4.29106e163 | 0.174493 | ||||||||
\(472\) | 2.83726e164 | 1.01267 | ||||||||
\(473\) | −1.27419e164 | −0.399277 | ||||||||
\(474\) | −5.86319e163 | −0.161349 | ||||||||
\(475\) | 1.93125e164 | 0.466853 | ||||||||
\(476\) | 6.96642e164 | 1.47973 | ||||||||
\(477\) | 5.12263e163 | 0.0956341 | ||||||||
\(478\) | −2.55085e164 | −0.418667 | ||||||||
\(479\) | −2.17864e164 | −0.314450 | −0.157225 | − | 0.987563i | \(-0.550255\pi\) | ||||
−0.157225 | + | 0.987563i | \(0.550255\pi\) | |||||||
\(480\) | −6.06772e164 | −0.770353 | ||||||||
\(481\) | −3.47469e164 | −0.388145 | ||||||||
\(482\) | −6.95666e164 | −0.683924 | ||||||||
\(483\) | −1.38078e165 | −1.19502 | ||||||||
\(484\) | 7.98585e164 | 0.608599 | ||||||||
\(485\) | −1.58117e165 | −1.06136 | ||||||||
\(486\) | 4.50562e164 | 0.266455 | ||||||||
\(487\) | 1.99967e165 | 1.04214 | 0.521072 | − | 0.853513i | \(-0.325532\pi\) | ||||
0.521072 | + | 0.853513i | \(0.325532\pi\) | |||||||
\(488\) | 2.48424e165 | 1.14123 | ||||||||
\(489\) | −1.07365e165 | −0.434879 | ||||||||
\(490\) | −2.23448e165 | −0.798212 | ||||||||
\(491\) | −5.00204e165 | −1.57629 | −0.788143 | − | 0.615492i | \(-0.788957\pi\) | ||||
−0.788143 | + | 0.615492i | \(0.788957\pi\) | |||||||
\(492\) | 8.95549e163 | 0.0249021 | ||||||||
\(493\) | 4.21262e165 | 1.03387 | ||||||||
\(494\) | 5.62446e165 | 1.21863 | ||||||||
\(495\) | −3.56640e164 | −0.0682354 | ||||||||
\(496\) | 3.45956e164 | 0.0584653 | ||||||||
\(497\) | 1.46786e166 | 2.19163 | ||||||||
\(498\) | 2.35416e165 | 0.310621 | ||||||||
\(499\) | −6.80979e165 | −0.794237 | −0.397119 | − | 0.917767i | \(-0.629990\pi\) | ||||
−0.397119 | + | 0.917767i | \(0.629990\pi\) | |||||||
\(500\) | −7.17396e165 | −0.739782 | ||||||||
\(501\) | −1.45031e165 | −0.132264 | ||||||||
\(502\) | 2.41678e165 | 0.194965 | ||||||||
\(503\) | −7.94197e164 | −0.0566888 | −0.0283444 | − | 0.999598i | \(-0.509024\pi\) | ||||
−0.0283444 | + | 0.999598i | \(0.509024\pi\) | |||||||
\(504\) | −5.91823e165 | −0.373864 | ||||||||
\(505\) | −6.01626e165 | −0.336439 | ||||||||
\(506\) | −3.15316e165 | −0.156131 | ||||||||
\(507\) | 9.82788e165 | 0.430993 | ||||||||
\(508\) | −2.98875e166 | −1.16111 | ||||||||
\(509\) | −2.81399e166 | −0.968675 | −0.484338 | − | 0.874881i | \(-0.660939\pi\) | ||||
−0.484338 | + | 0.874881i | \(0.660939\pi\) | |||||||
\(510\) | −1.83844e166 | −0.560898 | ||||||||
\(511\) | 2.14697e166 | 0.580684 | ||||||||
\(512\) | 1.21854e166 | 0.292238 | ||||||||
\(513\) | 8.98774e166 | 1.91176 | ||||||||
\(514\) | 2.03107e166 | 0.383259 | ||||||||
\(515\) | −8.97652e166 | −1.50302 | ||||||||
\(516\) | −4.85780e166 | −0.721909 | ||||||||
\(517\) | 3.03926e166 | 0.400959 | ||||||||
\(518\) | −2.48704e166 | −0.291341 | ||||||||
\(519\) | 1.45758e167 | 1.51649 | ||||||||
\(520\) | −1.07624e167 | −0.994730 | ||||||||
\(521\) | 5.82912e166 | 0.478722 | 0.239361 | − | 0.970931i | \(-0.423062\pi\) | ||||
0.239361 | + | 0.970931i | \(0.423062\pi\) | |||||||
\(522\) | −1.45134e166 | −0.105934 | ||||||||
\(523\) | 4.42302e166 | 0.286989 | 0.143494 | − | 0.989651i | \(-0.454166\pi\) | ||||
0.143494 | + | 0.989651i | \(0.454166\pi\) | |||||||
\(524\) | 1.75752e167 | 1.01397 | ||||||||
\(525\) | 7.29404e166 | 0.374258 | ||||||||
\(526\) | −8.81175e166 | −0.402197 | ||||||||
\(527\) | 1.29941e167 | 0.527706 | ||||||||
\(528\) | −1.16783e166 | −0.0422078 | ||||||||
\(529\) | −8.98469e166 | −0.289054 | ||||||||
\(530\) | 6.66772e166 | 0.190990 | ||||||||
\(531\) | 1.01373e167 | 0.258588 | ||||||||
\(532\) | −8.64198e167 | −1.96358 | ||||||||
\(533\) | 2.53272e166 | 0.0512701 | ||||||||
\(534\) | −3.67200e167 | −0.662393 | ||||||||
\(535\) | −5.36583e167 | −0.862739 | ||||||||
\(536\) | 3.51828e167 | 0.504307 | ||||||||
\(537\) | 5.45336e166 | 0.0697021 | ||||||||
\(538\) | −4.93840e166 | −0.0562959 | ||||||||
\(539\) | −5.33127e167 | −0.542152 | ||||||||
\(540\) | −6.97454e167 | −0.632848 | ||||||||
\(541\) | 2.24152e168 | 1.81514 | 0.907570 | − | 0.419901i | \(-0.137935\pi\) | ||||
0.907570 | + | 0.419901i | \(0.137935\pi\) | |||||||
\(542\) | 1.22495e167 | 0.0885446 | ||||||||
\(543\) | −1.41272e168 | −0.911733 | ||||||||
\(544\) | 2.38459e168 | 1.37430 | ||||||||
\(545\) | 1.02056e168 | 0.525357 | ||||||||
\(546\) | 2.12428e168 | 0.976931 | ||||||||
\(547\) | −2.42945e168 | −0.998360 | −0.499180 | − | 0.866498i | \(-0.666365\pi\) | ||||
−0.499180 | + | 0.866498i | \(0.666365\pi\) | |||||||
\(548\) | 2.87435e168 | 1.05569 | ||||||||
\(549\) | 8.87596e167 | 0.291418 | ||||||||
\(550\) | 1.66567e167 | 0.0488972 | ||||||||
\(551\) | −5.22583e168 | −1.37193 | ||||||||
\(552\) | −2.96425e168 | −0.696083 | ||||||||
\(553\) | 2.54779e168 | 0.535264 | ||||||||
\(554\) | 1.65958e168 | 0.311995 | ||||||||
\(555\) | −1.40893e168 | −0.237067 | ||||||||
\(556\) | −1.09405e168 | −0.164792 | ||||||||
\(557\) | 6.38649e168 | 0.861326 | 0.430663 | − | 0.902513i | \(-0.358280\pi\) | ||||
0.430663 | + | 0.902513i | \(0.358280\pi\) | |||||||
\(558\) | −4.47675e167 | −0.0540704 | ||||||||
\(559\) | −1.37384e169 | −1.48632 | ||||||||
\(560\) | 2.12694e168 | 0.206154 | ||||||||
\(561\) | −4.38635e168 | −0.380967 | ||||||||
\(562\) | −1.03101e169 | −0.802563 | ||||||||
\(563\) | −9.62259e168 | −0.671469 | −0.335734 | − | 0.941957i | \(-0.608984\pi\) | ||||
−0.335734 | + | 0.941957i | \(0.608984\pi\) | |||||||
\(564\) | 1.15870e169 | 0.724950 | ||||||||
\(565\) | −4.01136e168 | −0.225067 | ||||||||
\(566\) | −8.70765e168 | −0.438218 | ||||||||
\(567\) | 2.52133e169 | 1.13834 | ||||||||
\(568\) | 3.15120e169 | 1.27660 | ||||||||
\(569\) | −1.66824e169 | −0.606531 | −0.303266 | − | 0.952906i | \(-0.598077\pi\) | ||||
−0.303266 | + | 0.952906i | \(0.598077\pi\) | |||||||
\(570\) | 2.28062e169 | 0.744303 | ||||||||
\(571\) | 1.32112e169 | 0.387098 | 0.193549 | − | 0.981091i | \(-0.438000\pi\) | ||||
0.193549 | + | 0.981091i | \(0.438000\pi\) | |||||||
\(572\) | −1.04136e169 | −0.273996 | ||||||||
\(573\) | −1.96775e169 | −0.465009 | ||||||||
\(574\) | 1.81281e168 | 0.0384833 | ||||||||
\(575\) | −1.16736e169 | −0.222655 | ||||||||
\(576\) | −6.13008e168 | −0.105071 | ||||||||
\(577\) | 6.60626e169 | 1.01775 | 0.508877 | − | 0.860839i | \(-0.330061\pi\) | ||||
0.508877 | + | 0.860839i | \(0.330061\pi\) | |||||||
\(578\) | 3.15461e169 | 0.436902 | ||||||||
\(579\) | −3.68244e169 | −0.458568 | ||||||||
\(580\) | 4.05528e169 | 0.454150 | ||||||||
\(581\) | −1.02298e170 | −1.03047 | ||||||||
\(582\) | 6.69991e169 | 0.607163 | ||||||||
\(583\) | 1.59085e169 | 0.129722 | ||||||||
\(584\) | 4.60910e169 | 0.338241 | ||||||||
\(585\) | −3.84532e169 | −0.254008 | ||||||||
\(586\) | −1.74993e170 | −1.04068 | ||||||||
\(587\) | −1.10122e170 | −0.589700 | −0.294850 | − | 0.955544i | \(-0.595270\pi\) | ||||
−0.294850 | + | 0.955544i | \(0.595270\pi\) | |||||||
\(588\) | −2.03252e170 | −0.980233 | ||||||||
\(589\) | −1.61194e170 | −0.700258 | ||||||||
\(590\) | 1.31949e170 | 0.516425 | ||||||||
\(591\) | −3.70727e170 | −1.30745 | ||||||||
\(592\) | 1.47419e169 | 0.0468563 | ||||||||
\(593\) | 5.95213e170 | 1.70533 | 0.852665 | − | 0.522458i | \(-0.174985\pi\) | ||||
0.852665 | + | 0.522458i | \(0.174985\pi\) | |||||||
\(594\) | 7.75180e169 | 0.200233 | ||||||||
\(595\) | 7.98878e170 | 1.86075 | ||||||||
\(596\) | −4.12957e170 | −0.867481 | ||||||||
\(597\) | 2.21630e170 | 0.419959 | ||||||||
\(598\) | −3.39976e170 | −0.581200 | ||||||||
\(599\) | 5.03707e170 | 0.777013 | 0.388507 | − | 0.921446i | \(-0.372991\pi\) | ||||
0.388507 | + | 0.921446i | \(0.372991\pi\) | |||||||
\(600\) | 1.56588e170 | 0.218000 | ||||||||
\(601\) | 9.98664e170 | 1.25499 | 0.627494 | − | 0.778622i | \(-0.284081\pi\) | ||||
0.627494 | + | 0.778622i | \(0.284081\pi\) | |||||||
\(602\) | −9.83339e170 | −1.11563 | ||||||||
\(603\) | 1.25705e170 | 0.128777 | ||||||||
\(604\) | 4.10717e170 | 0.379989 | ||||||||
\(605\) | 9.15781e170 | 0.765308 | ||||||||
\(606\) | 2.54928e170 | 0.192465 | ||||||||
\(607\) | −2.29593e171 | −1.56622 | −0.783112 | − | 0.621881i | \(-0.786369\pi\) | ||||
−0.783112 | + | 0.621881i | \(0.786369\pi\) | |||||||
\(608\) | −2.95813e171 | −1.82367 | ||||||||
\(609\) | −1.97372e171 | −1.09982 | ||||||||
\(610\) | 1.15531e171 | 0.581989 | ||||||||
\(611\) | 3.27696e171 | 1.49258 | ||||||||
\(612\) | 5.34346e170 | 0.220095 | ||||||||
\(613\) | 1.19254e171 | 0.444278 | 0.222139 | − | 0.975015i | \(-0.428696\pi\) | ||||
0.222139 | + | 0.975015i | \(0.428696\pi\) | |||||||
\(614\) | −2.52403e171 | −0.850628 | ||||||||
\(615\) | 1.02697e170 | 0.0313141 | ||||||||
\(616\) | −1.83793e171 | −0.507126 | ||||||||
\(617\) | −4.58978e171 | −1.14618 | −0.573091 | − | 0.819491i | \(-0.694256\pi\) | ||||
−0.573091 | + | 0.819491i | \(0.694256\pi\) | |||||||
\(618\) | 3.80364e171 | 0.859822 | ||||||||
\(619\) | −1.36892e171 | −0.280157 | −0.140079 | − | 0.990140i | \(-0.544736\pi\) | ||||
−0.140079 | + | 0.990140i | \(0.544736\pi\) | |||||||
\(620\) | 1.25088e171 | 0.231806 | ||||||||
\(621\) | −5.43272e171 | −0.911768 | ||||||||
\(622\) | 3.63127e171 | 0.552014 | ||||||||
\(623\) | 1.59563e172 | 2.19745 | ||||||||
\(624\) | −1.25916e171 | −0.157119 | ||||||||
\(625\) | −5.89151e171 | −0.666202 | ||||||||
\(626\) | 4.21583e170 | 0.0432077 | ||||||||
\(627\) | 5.44135e171 | 0.505537 | ||||||||
\(628\) | −1.62338e171 | −0.136742 | ||||||||
\(629\) | 5.53703e171 | 0.422924 | ||||||||
\(630\) | −2.75232e171 | −0.190658 | ||||||||
\(631\) | −1.66513e171 | −0.104627 | −0.0523133 | − | 0.998631i | \(-0.516659\pi\) | ||||
−0.0523133 | + | 0.998631i | \(0.516659\pi\) | |||||||
\(632\) | 5.46959e171 | 0.311784 | ||||||||
\(633\) | 3.02681e172 | 1.56551 | ||||||||
\(634\) | 2.97039e170 | 0.0139420 | ||||||||
\(635\) | −3.42737e172 | −1.46008 | ||||||||
\(636\) | 6.06506e171 | 0.234543 | ||||||||
\(637\) | −5.74822e172 | −2.01817 | ||||||||
\(638\) | −4.50721e171 | −0.143693 | ||||||||
\(639\) | 1.12590e172 | 0.325983 | ||||||||
\(640\) | 2.56696e172 | 0.675074 | ||||||||
\(641\) | −5.07748e172 | −1.21305 | −0.606526 | − | 0.795064i | \(-0.707437\pi\) | ||||
−0.606526 | + | 0.795064i | \(0.707437\pi\) | |||||||
\(642\) | 2.27368e172 | 0.493542 | ||||||||
\(643\) | −2.14595e172 | −0.423297 | −0.211648 | − | 0.977346i | \(-0.567883\pi\) | ||||
−0.211648 | + | 0.977346i | \(0.567883\pi\) | |||||||
\(644\) | 5.22373e172 | 0.936482 | ||||||||
\(645\) | −5.57070e172 | −0.907794 | ||||||||
\(646\) | −8.96275e172 | −1.32783 | ||||||||
\(647\) | 6.10334e172 | 0.822156 | 0.411078 | − | 0.911600i | \(-0.365152\pi\) | ||||
0.411078 | + | 0.911600i | \(0.365152\pi\) | |||||||
\(648\) | 5.41278e172 | 0.663067 | ||||||||
\(649\) | 3.14818e172 | 0.350760 | ||||||||
\(650\) | 1.79594e172 | 0.182021 | ||||||||
\(651\) | −6.08806e172 | −0.561369 | ||||||||
\(652\) | 4.06181e172 | 0.340795 | ||||||||
\(653\) | 1.03044e173 | 0.786797 | 0.393399 | − | 0.919368i | \(-0.371299\pi\) | ||||
0.393399 | + | 0.919368i | \(0.371299\pi\) | |||||||
\(654\) | −4.32445e172 | −0.300538 | ||||||||
\(655\) | 2.01544e173 | 1.27506 | ||||||||
\(656\) | −1.07454e171 | −0.00618924 | ||||||||
\(657\) | 1.64679e172 | 0.0863709 | ||||||||
\(658\) | 2.34551e173 | 1.12033 | ||||||||
\(659\) | −3.11673e171 | −0.0135596 | −0.00677979 | − | 0.999977i | \(-0.502158\pi\) | ||||
−0.00677979 | + | 0.999977i | \(0.502158\pi\) | |||||||
\(660\) | −4.22252e172 | −0.167348 | ||||||||
\(661\) | −9.08000e172 | −0.327866 | −0.163933 | − | 0.986471i | \(-0.552418\pi\) | ||||
−0.163933 | + | 0.986471i | \(0.552418\pi\) | |||||||
\(662\) | 6.47424e172 | 0.213021 | ||||||||
\(663\) | −4.72940e173 | −1.41816 | ||||||||
\(664\) | −2.19612e173 | −0.600233 | ||||||||
\(665\) | −9.91023e173 | −2.46918 | ||||||||
\(666\) | −1.90763e172 | −0.0433341 | ||||||||
\(667\) | 3.15880e173 | 0.654310 | ||||||||
\(668\) | 5.48678e172 | 0.103649 | ||||||||
\(669\) | 6.99793e173 | 1.20577 | ||||||||
\(670\) | 1.63620e173 | 0.257179 | ||||||||
\(671\) | 2.75647e173 | 0.395292 | ||||||||
\(672\) | −1.11724e174 | −1.46197 | ||||||||
\(673\) | 7.84062e173 | 0.936320 | 0.468160 | − | 0.883644i | \(-0.344917\pi\) | ||||
0.468160 | + | 0.883644i | \(0.344917\pi\) | |||||||
\(674\) | −2.36852e171 | −0.00258163 | ||||||||
\(675\) | 2.86987e173 | 0.285549 | ||||||||
\(676\) | −3.71806e173 | −0.337750 | ||||||||
\(677\) | 3.25468e173 | 0.269964 | 0.134982 | − | 0.990848i | \(-0.456902\pi\) | ||||
0.134982 | + | 0.990848i | \(0.456902\pi\) | |||||||
\(678\) | 1.69974e173 | 0.128753 | ||||||||
\(679\) | −2.91138e174 | −2.01423 | ||||||||
\(680\) | 1.71503e174 | 1.08386 | ||||||||
\(681\) | 2.21676e174 | 1.27989 | ||||||||
\(682\) | −1.39028e173 | −0.0733435 | ||||||||
\(683\) | 8.08437e173 | 0.389738 | 0.194869 | − | 0.980829i | \(-0.437572\pi\) | ||||
0.194869 | + | 0.980829i | \(0.437572\pi\) | |||||||
\(684\) | −6.62866e173 | −0.292062 | ||||||||
\(685\) | 3.29617e174 | 1.32752 | ||||||||
\(686\) | −1.62161e174 | −0.597052 | ||||||||
\(687\) | −8.80534e173 | −0.296419 | ||||||||
\(688\) | 5.82873e173 | 0.179426 | ||||||||
\(689\) | 1.71527e174 | 0.482893 | ||||||||
\(690\) | −1.37854e174 | −0.354978 | ||||||||
\(691\) | 3.33428e174 | 0.785421 | 0.392710 | − | 0.919662i | \(-0.371537\pi\) | ||||
0.392710 | + | 0.919662i | \(0.371537\pi\) | |||||||
\(692\) | −5.51428e174 | −1.18840 | ||||||||
\(693\) | −6.56677e173 | −0.129496 | ||||||||
\(694\) | −3.10568e174 | −0.560467 | ||||||||
\(695\) | −1.25460e174 | −0.207225 | ||||||||
\(696\) | −4.23718e174 | −0.640632 | ||||||||
\(697\) | −4.03597e173 | −0.0558640 | ||||||||
\(698\) | −3.40384e174 | −0.431381 | ||||||||
\(699\) | 2.56921e174 | 0.298163 | ||||||||
\(700\) | −2.75946e174 | −0.293289 | ||||||||
\(701\) | −5.23508e174 | −0.509642 | −0.254821 | − | 0.966988i | \(-0.582017\pi\) | ||||
−0.254821 | + | 0.966988i | \(0.582017\pi\) | |||||||
\(702\) | 8.35806e174 | 0.745372 | ||||||||
\(703\) | −6.86879e174 | −0.561213 | ||||||||
\(704\) | −1.90372e174 | −0.142523 | ||||||||
\(705\) | 1.32875e175 | 0.911618 | ||||||||
\(706\) | 1.55295e175 | 0.976491 | ||||||||
\(707\) | −1.10777e175 | −0.638491 | ||||||||
\(708\) | 1.20023e175 | 0.634188 | ||||||||
\(709\) | −2.46995e174 | −0.119659 | −0.0598294 | − | 0.998209i | \(-0.519056\pi\) | ||||
−0.0598294 | + | 0.998209i | \(0.519056\pi\) | |||||||
\(710\) | 1.46549e175 | 0.651020 | ||||||||
\(711\) | 1.95423e174 | 0.0796152 | ||||||||
\(712\) | 3.42550e175 | 1.27998 | ||||||||
\(713\) | 9.74352e174 | 0.333972 | ||||||||
\(714\) | −3.38510e175 | −1.06447 | ||||||||
\(715\) | −1.19418e175 | −0.344547 | ||||||||
\(716\) | −2.06310e174 | −0.0546223 | ||||||||
\(717\) | −2.66080e175 | −0.646524 | ||||||||
\(718\) | 4.77621e174 | 0.106520 | ||||||||
\(719\) | 8.28565e175 | 1.69629 | 0.848145 | − | 0.529765i | \(-0.177720\pi\) | ||||
0.848145 | + | 0.529765i | \(0.177720\pi\) | |||||||
\(720\) | 1.63143e174 | 0.0306634 | ||||||||
\(721\) | −1.65284e176 | −2.85240 | ||||||||
\(722\) | 7.56123e175 | 1.19827 | ||||||||
\(723\) | −7.25653e175 | −1.05615 | ||||||||
\(724\) | 5.34458e175 | 0.714483 | ||||||||
\(725\) | −1.66866e175 | −0.204918 | ||||||||
\(726\) | −3.88046e175 | −0.437805 | ||||||||
\(727\) | −1.03615e176 | −1.07413 | −0.537065 | − | 0.843541i | \(-0.680467\pi\) | ||||
−0.537065 | + | 0.843541i | \(0.680467\pi\) | |||||||
\(728\) | −1.98168e176 | −1.88779 | ||||||||
\(729\) | 1.26862e176 | 1.11068 | ||||||||
\(730\) | 2.14349e175 | 0.172491 | ||||||||
\(731\) | 2.18926e176 | 1.61949 | ||||||||
\(732\) | 1.05089e176 | 0.714704 | ||||||||
\(733\) | 1.23434e176 | 0.771863 | 0.385931 | − | 0.922528i | \(-0.373880\pi\) | ||||
0.385931 | + | 0.922528i | \(0.373880\pi\) | |||||||
\(734\) | −5.53566e175 | −0.318319 | ||||||||
\(735\) | −2.33080e176 | −1.23263 | ||||||||
\(736\) | 1.78807e176 | 0.869758 | ||||||||
\(737\) | 3.90382e175 | 0.174678 | ||||||||
\(738\) | 1.39048e174 | 0.00572400 | ||||||||
\(739\) | −2.31018e176 | −0.875010 | −0.437505 | − | 0.899216i | \(-0.644138\pi\) | ||||
−0.437505 | + | 0.899216i | \(0.644138\pi\) | |||||||
\(740\) | 5.33023e175 | 0.185778 | ||||||||
\(741\) | 5.86691e176 | 1.88187 | ||||||||
\(742\) | 1.22772e176 | 0.362459 | ||||||||
\(743\) | −2.17632e175 | −0.0591441 | −0.0295720 | − | 0.999563i | \(-0.509414\pi\) | ||||
−0.0295720 | + | 0.999563i | \(0.509414\pi\) | |||||||
\(744\) | −1.30698e176 | −0.326990 | ||||||||
\(745\) | −4.73560e176 | −1.09085 | ||||||||
\(746\) | −5.09478e175 | −0.108066 | ||||||||
\(747\) | −7.84654e175 | −0.153271 | ||||||||
\(748\) | 1.65943e176 | 0.298546 | ||||||||
\(749\) | −9.88004e176 | −1.63730 | ||||||||
\(750\) | 3.48595e176 | 0.532174 | ||||||||
\(751\) | 1.27682e177 | 1.79587 | 0.897933 | − | 0.440133i | \(-0.145069\pi\) | ||||
0.897933 | + | 0.440133i | \(0.145069\pi\) | |||||||
\(752\) | −1.39030e176 | −0.180181 | ||||||||
\(753\) | 2.52095e176 | 0.301074 | ||||||||
\(754\) | −4.85971e176 | −0.534900 | ||||||||
\(755\) | 4.70992e176 | 0.477833 | ||||||||
\(756\) | −1.28421e177 | −1.20101 | ||||||||
\(757\) | −1.48488e177 | −1.28025 | −0.640123 | − | 0.768272i | \(-0.721117\pi\) | ||||
−0.640123 | + | 0.768272i | \(0.721117\pi\) | |||||||
\(758\) | −3.13106e176 | −0.248906 | ||||||||
\(759\) | −3.28908e176 | −0.241104 | ||||||||
\(760\) | −2.12752e177 | −1.43826 | ||||||||
\(761\) | 1.35393e176 | 0.0844189 | 0.0422095 | − | 0.999109i | \(-0.486560\pi\) | ||||
0.0422095 | + | 0.999109i | \(0.486560\pi\) | |||||||
\(762\) | 1.45229e177 | 0.835259 | ||||||||
\(763\) | 1.87915e177 | 0.997017 | ||||||||
\(764\) | 7.44435e176 | 0.364406 | ||||||||
\(765\) | 6.12763e176 | 0.276767 | ||||||||
\(766\) | 2.00854e177 | 0.837167 | ||||||||
\(767\) | 3.39439e177 | 1.30571 | ||||||||
\(768\) | −2.15159e177 | −0.763914 | ||||||||
\(769\) | 1.92276e177 | 0.630168 | 0.315084 | − | 0.949064i | \(-0.397967\pi\) | ||||
0.315084 | + | 0.949064i | \(0.397967\pi\) | |||||||
\(770\) | −8.54744e176 | −0.258617 | ||||||||
\(771\) | 2.11862e177 | 0.591846 | ||||||||
\(772\) | 1.39313e177 | 0.359359 | ||||||||
\(773\) | −5.45552e176 | −0.129956 | −0.0649782 | − | 0.997887i | \(-0.520698\pi\) | ||||
−0.0649782 | + | 0.997887i | \(0.520698\pi\) | |||||||
\(774\) | −7.54251e176 | −0.165938 | ||||||||
\(775\) | −5.14707e176 | −0.104594 | ||||||||
\(776\) | −6.25015e177 | −1.17326 | ||||||||
\(777\) | −2.59424e177 | −0.449902 | ||||||||
\(778\) | −6.93189e176 | −0.111072 | ||||||||
\(779\) | 5.00669e176 | 0.0741306 | ||||||||
\(780\) | −4.55276e177 | −0.622955 | ||||||||
\(781\) | 3.49652e177 | 0.442178 | ||||||||
\(782\) | 5.41762e177 | 0.633276 | ||||||||
\(783\) | −7.76569e177 | −0.839134 | ||||||||
\(784\) | 2.43876e177 | 0.243630 | ||||||||
\(785\) | −1.86162e177 | −0.171952 | ||||||||
\(786\) | −8.54007e177 | −0.729415 | ||||||||
\(787\) | −1.22207e178 | −0.965275 | −0.482637 | − | 0.875820i | \(-0.660321\pi\) | ||||
−0.482637 | + | 0.875820i | \(0.660321\pi\) | |||||||
\(788\) | 1.40253e178 | 1.02459 | ||||||||
\(789\) | −9.19159e177 | −0.621091 | ||||||||
\(790\) | 2.54367e177 | 0.158999 | ||||||||
\(791\) | −7.38606e177 | −0.427129 | ||||||||
\(792\) | −1.40975e177 | −0.0754299 | ||||||||
\(793\) | 2.97205e178 | 1.47148 | ||||||||
\(794\) | 1.91874e178 | 0.879136 | ||||||||
\(795\) | 6.95514e177 | 0.294936 | ||||||||
\(796\) | −8.38465e177 | −0.329102 | ||||||||
\(797\) | 7.22875e177 | 0.262649 | 0.131325 | − | 0.991339i | \(-0.458077\pi\) | ||||
0.131325 | + | 0.991339i | \(0.458077\pi\) | |||||||
\(798\) | 4.19928e178 | 1.41253 | ||||||||
\(799\) | −5.22193e178 | −1.62631 | ||||||||
\(800\) | −9.44558e177 | −0.272392 | ||||||||
\(801\) | 1.22390e178 | 0.326848 | ||||||||
\(802\) | −3.06090e177 | −0.0757053 | ||||||||
\(803\) | 5.11417e177 | 0.117157 | ||||||||
\(804\) | 1.48831e178 | 0.315825 | ||||||||
\(805\) | 5.99033e178 | 1.17762 | ||||||||
\(806\) | −1.49901e178 | −0.273023 | ||||||||
\(807\) | −5.15128e177 | −0.0869346 | ||||||||
\(808\) | −2.37815e178 | −0.371912 | ||||||||
\(809\) | −1.16706e179 | −1.69145 | −0.845723 | − | 0.533622i | \(-0.820830\pi\) | ||||
−0.845723 | + | 0.533622i | \(0.820830\pi\) | |||||||
\(810\) | 2.51725e178 | 0.338141 | ||||||||
\(811\) | −9.72451e178 | −1.21084 | −0.605418 | − | 0.795908i | \(-0.706994\pi\) | ||||
−0.605418 | + | 0.795908i | \(0.706994\pi\) | |||||||
\(812\) | 7.46694e178 | 0.861880 | ||||||||
\(813\) | 1.27775e178 | 0.136735 | ||||||||
\(814\) | −5.92424e177 | −0.0587803 | ||||||||
\(815\) | 4.65790e178 | 0.428546 | ||||||||
\(816\) | 2.00651e178 | 0.171197 | ||||||||
\(817\) | −2.71582e179 | −2.14904 | ||||||||
\(818\) | 1.25743e179 | 0.922900 | ||||||||
\(819\) | −7.08034e178 | −0.482053 | ||||||||
\(820\) | −3.88523e177 | −0.0245394 | ||||||||
\(821\) | 2.77613e179 | 1.62680 | 0.813402 | − | 0.581702i | \(-0.197613\pi\) | ||||
0.813402 | + | 0.581702i | \(0.197613\pi\) | |||||||
\(822\) | −1.39669e179 | −0.759424 | ||||||||
\(823\) | 6.66809e178 | 0.336443 | 0.168222 | − | 0.985749i | \(-0.446198\pi\) | ||||
0.168222 | + | 0.985749i | \(0.446198\pi\) | |||||||
\(824\) | −3.54830e179 | −1.66149 | ||||||||
\(825\) | 1.73747e178 | 0.0755093 | ||||||||
\(826\) | 2.42956e179 | 0.980065 | ||||||||
\(827\) | 3.43479e179 | 1.28621 | 0.643104 | − | 0.765779i | \(-0.277646\pi\) | ||||
0.643104 | + | 0.765779i | \(0.277646\pi\) | |||||||
\(828\) | 4.00675e178 | 0.139292 | ||||||||
\(829\) | −5.56651e178 | −0.179672 | −0.0898359 | − | 0.995957i | \(-0.528634\pi\) | ||||
−0.0898359 | + | 0.995957i | \(0.528634\pi\) | |||||||
\(830\) | −1.02132e179 | −0.306098 | ||||||||
\(831\) | 1.73112e179 | 0.481796 | ||||||||
\(832\) | −2.05261e179 | −0.530545 | ||||||||
\(833\) | 9.15996e179 | 2.19900 | ||||||||
\(834\) | 5.31617e178 | 0.118546 | ||||||||
\(835\) | 6.29199e178 | 0.130338 | ||||||||
\(836\) | −2.05856e179 | −0.396166 | ||||||||
\(837\) | −2.39537e179 | −0.428309 | ||||||||
\(838\) | 2.29059e179 | 0.380575 | ||||||||
\(839\) | −3.00269e179 | −0.463608 | −0.231804 | − | 0.972763i | \(-0.574463\pi\) | ||||
−0.231804 | + | 0.972763i | \(0.574463\pi\) | |||||||
\(840\) | −8.03535e179 | −1.15300 | ||||||||
\(841\) | −2.98286e179 | −0.397813 | ||||||||
\(842\) | 2.65085e179 | 0.328619 | ||||||||
\(843\) | −1.07545e180 | −1.23935 | ||||||||
\(844\) | −1.14510e180 | −1.22682 | ||||||||
\(845\) | −4.26371e179 | −0.424717 | ||||||||
\(846\) | 1.79908e179 | 0.166637 | ||||||||
\(847\) | 1.68622e180 | 1.45239 | ||||||||
\(848\) | −7.27729e178 | −0.0582941 | ||||||||
\(849\) | −9.08300e179 | −0.676716 | ||||||||
\(850\) | −2.86189e179 | −0.198330 | ||||||||
\(851\) | 4.15191e179 | 0.267658 | ||||||||
\(852\) | 1.33303e180 | 0.799476 | ||||||||
\(853\) | 1.48180e180 | 0.826848 | 0.413424 | − | 0.910539i | \(-0.364333\pi\) | ||||
0.413424 | + | 0.910539i | \(0.364333\pi\) | |||||||
\(854\) | 2.12726e180 | 1.10449 | ||||||||
\(855\) | −7.60144e179 | −0.367265 | ||||||||
\(856\) | −2.12104e180 | −0.953703 | ||||||||
\(857\) | −3.01163e179 | −0.126032 | −0.0630160 | − | 0.998013i | \(-0.520072\pi\) | ||||
−0.0630160 | + | 0.998013i | \(0.520072\pi\) | |||||||
\(858\) | 5.06013e179 | 0.197103 | ||||||||
\(859\) | 1.79804e180 | 0.651957 | 0.325978 | − | 0.945377i | \(-0.394306\pi\) | ||||
0.325978 | + | 0.945377i | \(0.394306\pi\) | |||||||
\(860\) | 2.10750e180 | 0.711397 | ||||||||
\(861\) | 1.89096e179 | 0.0594275 | ||||||||
\(862\) | −1.35290e180 | −0.395884 | ||||||||
\(863\) | 3.52886e180 | 0.961548 | 0.480774 | − | 0.876845i | \(-0.340356\pi\) | ||||
0.480774 | + | 0.876845i | \(0.340356\pi\) | |||||||
\(864\) | −4.39584e180 | −1.11544 | ||||||||
\(865\) | −6.32352e180 | −1.49441 | ||||||||
\(866\) | 2.21440e180 | 0.487422 | ||||||||
\(867\) | 3.29060e180 | 0.674683 | ||||||||
\(868\) | 2.30322e180 | 0.439919 | ||||||||
\(869\) | 6.06896e179 | 0.107994 | ||||||||
\(870\) | −1.97053e180 | −0.326700 | ||||||||
\(871\) | 4.20913e180 | 0.650243 | ||||||||
\(872\) | 4.03415e180 | 0.580749 | ||||||||
\(873\) | −2.23312e180 | −0.299596 | ||||||||
\(874\) | −6.72066e180 | −0.840347 | ||||||||
\(875\) | −1.51479e181 | −1.76545 | ||||||||
\(876\) | 1.94976e180 | 0.211825 | ||||||||
\(877\) | −2.94272e180 | −0.298039 | −0.149020 | − | 0.988834i | \(-0.547612\pi\) | ||||
−0.149020 | + | 0.988834i | \(0.547612\pi\) | |||||||
\(878\) | 8.49822e179 | 0.0802445 | ||||||||
\(879\) | −1.82536e181 | −1.60707 | ||||||||
\(880\) | 5.06648e179 | 0.0415932 | ||||||||
\(881\) | 1.22554e181 | 0.938228 | 0.469114 | − | 0.883138i | \(-0.344573\pi\) | ||||
0.469114 | + | 0.883138i | \(0.344573\pi\) | |||||||
\(882\) | −3.15581e180 | −0.225317 | ||||||||
\(883\) | 4.21674e180 | 0.280798 | 0.140399 | − | 0.990095i | \(-0.455162\pi\) | ||||
0.140399 | + | 0.990095i | \(0.455162\pi\) | |||||||
\(884\) | 1.78922e181 | 1.11134 | ||||||||
\(885\) | 1.37637e181 | 0.797486 | ||||||||
\(886\) | 1.72397e181 | 0.931872 | ||||||||
\(887\) | 6.09390e180 | 0.307321 | 0.153661 | − | 0.988124i | \(-0.450894\pi\) | ||||
0.153661 | + | 0.988124i | \(0.450894\pi\) | |||||||
\(888\) | −5.56931e180 | −0.262062 | ||||||||
\(889\) | −6.31077e181 | −2.77092 | ||||||||
\(890\) | 1.59305e181 | 0.652747 | ||||||||
\(891\) | 6.00592e180 | 0.229668 | ||||||||
\(892\) | −2.64744e181 | −0.944904 | ||||||||
\(893\) | 6.47791e181 | 2.15809 | ||||||||
\(894\) | 2.00663e181 | 0.624036 | ||||||||
\(895\) | −2.36587e180 | −0.0686870 | ||||||||
\(896\) | 4.72652e181 | 1.28115 | ||||||||
\(897\) | −3.54631e181 | −0.897514 | ||||||||
\(898\) | 2.50091e180 | 0.0591022 | ||||||||
\(899\) | 1.39277e181 | 0.307367 | ||||||||
\(900\) | −2.11659e180 | −0.0436237 | ||||||||
\(901\) | −2.73334e181 | −0.526162 | ||||||||
\(902\) | 4.31821e179 | 0.00776428 | ||||||||
\(903\) | −1.02573e182 | −1.72280 | ||||||||
\(904\) | −1.58564e181 | −0.248797 | ||||||||
\(905\) | 6.12893e181 | 0.898456 | ||||||||
\(906\) | −1.99575e181 | −0.273351 | ||||||||
\(907\) | 6.03501e180 | 0.0772378 | 0.0386189 | − | 0.999254i | \(-0.487704\pi\) | ||||
0.0386189 | + | 0.999254i | \(0.487704\pi\) | |||||||
\(908\) | −8.38641e181 | −1.00299 | ||||||||
\(909\) | −8.49691e180 | −0.0949690 | ||||||||
\(910\) | −9.21592e181 | −0.962705 | ||||||||
\(911\) | 3.46381e181 | 0.338200 | 0.169100 | − | 0.985599i | \(-0.445914\pi\) | ||||
0.169100 | + | 0.985599i | \(0.445914\pi\) | |||||||
\(912\) | −2.48912e181 | −0.227176 | ||||||||
\(913\) | −2.43678e181 | −0.207904 | ||||||||
\(914\) | −8.47021e181 | −0.675621 | ||||||||
\(915\) | 1.20511e182 | 0.898733 | ||||||||
\(916\) | 3.33122e181 | 0.232290 | ||||||||
\(917\) | 3.71100e182 | 2.41979 | ||||||||
\(918\) | −1.33188e182 | −0.812159 | ||||||||
\(919\) | 8.27431e181 | 0.471876 | 0.235938 | − | 0.971768i | \(-0.424184\pi\) | ||||
0.235938 | + | 0.971768i | \(0.424184\pi\) | |||||||
\(920\) | 1.28600e182 | 0.685946 | ||||||||
\(921\) | −2.63283e182 | −1.31358 | ||||||||
\(922\) | −1.27720e180 | −0.00596084 | ||||||||
\(923\) | 3.76998e182 | 1.64602 | ||||||||
\(924\) | −7.77488e181 | −0.317591 | ||||||||
\(925\) | −2.19327e181 | −0.0838253 | ||||||||
\(926\) | 1.48969e182 | 0.532746 | ||||||||
\(927\) | −1.26778e182 | −0.424267 | ||||||||
\(928\) | 2.55591e182 | 0.800471 | ||||||||
\(929\) | 2.49107e182 | 0.730163 | 0.365082 | − | 0.930976i | \(-0.381041\pi\) | ||||
0.365082 | + | 0.930976i | \(0.381041\pi\) | |||||||
\(930\) | −6.07821e181 | −0.166753 | ||||||||
\(931\) | −1.13631e183 | −2.91804 | ||||||||
\(932\) | −9.71977e181 | −0.233656 | ||||||||
\(933\) | 3.78780e182 | 0.852444 | ||||||||
\(934\) | −4.46760e182 | −0.941329 | ||||||||
\(935\) | 1.90296e182 | 0.375419 | ||||||||
\(936\) | −1.52000e182 | −0.280789 | ||||||||
\(937\) | −2.72308e182 | −0.471059 | −0.235529 | − | 0.971867i | \(-0.575682\pi\) | ||||
−0.235529 | + | 0.971867i | \(0.575682\pi\) | |||||||
\(938\) | 3.01272e182 | 0.488072 | ||||||||
\(939\) | 4.39755e181 | 0.0667233 | ||||||||
\(940\) | −5.02690e182 | −0.714393 | ||||||||
\(941\) | 1.39301e183 | 1.85436 | 0.927179 | − | 0.374620i | \(-0.122227\pi\) | ||||
0.927179 | + | 0.374620i | \(0.122227\pi\) | |||||||
\(942\) | 7.88829e181 | 0.0983677 | ||||||||
\(943\) | −3.02634e181 | −0.0353549 | ||||||||
\(944\) | −1.44012e182 | −0.157623 | ||||||||
\(945\) | −1.47268e183 | −1.51026 | ||||||||
\(946\) | −2.34236e182 | −0.225086 | ||||||||
\(947\) | −1.09472e183 | −0.985782 | −0.492891 | − | 0.870091i | \(-0.664060\pi\) | ||||
−0.492891 | + | 0.870091i | \(0.664060\pi\) | |||||||
\(948\) | 2.31376e182 | 0.195257 | ||||||||
\(949\) | 5.51415e182 | 0.436120 | ||||||||
\(950\) | 3.55023e182 | 0.263181 | ||||||||
\(951\) | 3.09843e181 | 0.0215298 | ||||||||
\(952\) | 3.15786e183 | 2.05694 | ||||||||
\(953\) | −1.95172e183 | −1.19180 | −0.595900 | − | 0.803058i | \(-0.703205\pi\) | ||||
−0.595900 | + | 0.803058i | \(0.703205\pi\) | |||||||
\(954\) | 9.41698e181 | 0.0539121 | ||||||||
\(955\) | 8.53685e182 | 0.458237 | ||||||||
\(956\) | 1.00663e183 | 0.506651 | ||||||||
\(957\) | −4.70150e182 | −0.221897 | ||||||||
\(958\) | −4.00502e182 | −0.177266 | ||||||||
\(959\) | 6.06920e183 | 2.51934 | ||||||||
\(960\) | −8.32298e182 | −0.324040 | ||||||||
\(961\) | −2.30874e183 | −0.843114 | ||||||||
\(962\) | −6.38757e182 | −0.218811 | ||||||||
\(963\) | −7.57829e182 | −0.243531 | ||||||||
\(964\) | 2.74527e183 | 0.827653 | ||||||||
\(965\) | 1.59758e183 | 0.451890 | ||||||||
\(966\) | −2.53830e183 | −0.673673 | ||||||||
\(967\) | −6.70395e183 | −1.66956 | −0.834782 | − | 0.550581i | \(-0.814406\pi\) | ||||
−0.834782 | + | 0.550581i | \(0.814406\pi\) | |||||||
\(968\) | 3.61996e183 | 0.845999 | ||||||||
\(969\) | −9.34910e183 | −2.05049 | ||||||||
\(970\) | −2.90667e183 | −0.598322 | ||||||||
\(971\) | 5.25177e183 | 1.01467 | 0.507333 | − | 0.861750i | \(-0.330631\pi\) | ||||
0.507333 | + | 0.861750i | \(0.330631\pi\) | |||||||
\(972\) | −1.77803e183 | −0.322452 | ||||||||
\(973\) | −2.31009e183 | −0.393268 | ||||||||
\(974\) | 3.67602e183 | 0.587492 | ||||||||
\(975\) | 1.87336e183 | 0.281085 | ||||||||
\(976\) | −1.26093e183 | −0.177635 | ||||||||
\(977\) | −5.07777e183 | −0.671673 | −0.335836 | − | 0.941920i | \(-0.609019\pi\) | ||||
−0.335836 | + | 0.941920i | \(0.609019\pi\) | |||||||
\(978\) | −1.97370e183 | −0.245156 | ||||||||
\(979\) | 3.80088e183 | 0.443351 | ||||||||
\(980\) | 8.81784e183 | 0.965959 | ||||||||
\(981\) | 1.44136e183 | 0.148296 | ||||||||
\(982\) | −9.19530e183 | −0.888606 | ||||||||
\(983\) | −7.90467e183 | −0.717534 | −0.358767 | − | 0.933427i | \(-0.616803\pi\) | ||||
−0.358767 | + | 0.933427i | \(0.616803\pi\) | |||||||
\(984\) | 4.05950e182 | 0.0346157 | ||||||||
\(985\) | 1.60835e184 | 1.28841 | ||||||||
\(986\) | 7.74410e183 | 0.582828 | ||||||||
\(987\) | 2.44661e184 | 1.73006 | ||||||||
\(988\) | −2.21956e184 | −1.47473 | ||||||||
\(989\) | 1.64160e184 | 1.02494 | ||||||||
\(990\) | −6.55614e182 | −0.0384666 | ||||||||
\(991\) | −1.75082e184 | −0.965411 | −0.482706 | − | 0.875783i | \(-0.660346\pi\) | ||||
−0.482706 | + | 0.875783i | \(0.660346\pi\) | |||||||
\(992\) | 7.88387e183 | 0.408575 | ||||||||
\(993\) | 6.75331e183 | 0.328956 | ||||||||
\(994\) | 2.69839e184 | 1.23550 | ||||||||
\(995\) | −9.61514e183 | −0.413843 | ||||||||
\(996\) | −9.29011e183 | −0.375899 | ||||||||
\(997\) | 1.12976e184 | 0.429767 | 0.214883 | − | 0.976640i | \(-0.431063\pi\) | ||||
0.214883 | + | 0.976640i | \(0.431063\pi\) | |||||||
\(998\) | −1.25185e184 | −0.447738 | ||||||||
\(999\) | −1.02072e184 | −0.343263 |
(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 | 1.124.a.a.1.6 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.124.a.a.1.6 | ✓ | 10 | 1.1 | even | 1 | trivial |