Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,98,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, 98, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 98);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 98 \) |
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: | \(59.5852992940\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} + \cdots - 60\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{83}\cdot 3^{30}\cdot 5^{10}\cdot 7^{8}\cdot 11^{2}\cdot 19 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.16497e13\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.56799e14 | 1.39876 | 0.699380 | − | 0.714750i | \(-0.253459\pi\) | ||||
0.699380 | + | 0.714750i | \(0.253459\pi\) | |||||||
\(3\) | −1.35917e23 | −0.983766 | −0.491883 | − | 0.870661i | \(-0.663691\pi\) | ||||
−0.491883 | + | 0.870661i | \(0.663691\pi\) | |||||||
\(4\) | 1.51568e29 | 0.956531 | ||||||||
\(5\) | 4.66064e33 | 0.586679 | 0.293340 | − | 0.956008i | \(-0.405233\pi\) | ||||
0.293340 | + | 0.956008i | \(0.405233\pi\) | |||||||
\(6\) | −7.56782e37 | −1.37605 | ||||||||
\(7\) | 2.73237e40 | 0.281374 | 0.140687 | − | 0.990054i | \(-0.455069\pi\) | ||||
0.140687 | + | 0.990054i | \(0.455069\pi\) | |||||||
\(8\) | −3.83521e42 | −0.0608030 | ||||||||
\(9\) | −6.14732e44 | −0.0322050 | ||||||||
\(10\) | 2.59504e48 | 0.820624 | ||||||||
\(11\) | 3.91912e50 | 1.21799 | 0.608995 | − | 0.793174i | \(-0.291573\pi\) | ||||
0.608995 | + | 0.793174i | \(0.291573\pi\) | |||||||
\(12\) | −2.06007e52 | −0.941002 | ||||||||
\(13\) | −1.22584e54 | −1.15393 | −0.576967 | − | 0.816767i | \(-0.695764\pi\) | ||||
−0.576967 | + | 0.816767i | \(0.695764\pi\) | |||||||
\(14\) | 1.52138e55 | 0.393575 | ||||||||
\(15\) | −6.33459e56 | −0.577155 | ||||||||
\(16\) | −2.61524e58 | −1.04158 | ||||||||
\(17\) | −1.30833e59 | −0.275387 | −0.137694 | − | 0.990475i | \(-0.543969\pi\) | ||||
−0.137694 | + | 0.990475i | \(0.543969\pi\) | |||||||
\(18\) | −3.42282e59 | −0.0450471 | ||||||||
\(19\) | 1.63455e62 | 1.56260 | 0.781299 | − | 0.624157i | \(-0.214557\pi\) | ||||
0.781299 | + | 0.624157i | \(0.214557\pi\) | |||||||
\(20\) | 7.06406e62 | 0.561177 | ||||||||
\(21\) | −3.71374e63 | −0.276806 | ||||||||
\(22\) | 2.18216e65 | 1.70368 | ||||||||
\(23\) | 5.04020e64 | 0.0455667 | 0.0227833 | − | 0.999740i | \(-0.492747\pi\) | ||||
0.0227833 | + | 0.999740i | \(0.492747\pi\) | |||||||
\(24\) | 5.21269e65 | 0.0598159 | ||||||||
\(25\) | −4.13873e67 | −0.655808 | ||||||||
\(26\) | −6.82546e68 | −1.61408 | ||||||||
\(27\) | 2.67794e69 | 1.01545 | ||||||||
\(28\) | 4.14140e69 | 0.269143 | ||||||||
\(29\) | −9.43257e70 | −1.11771 | −0.558853 | − | 0.829267i | \(-0.688758\pi\) | ||||
−0.558853 | + | 0.829267i | \(0.688758\pi\) | |||||||
\(30\) | −3.52709e71 | −0.807301 | ||||||||
\(31\) | −3.22328e72 | −1.50403 | −0.752015 | − | 0.659146i | \(-0.770918\pi\) | ||||
−0.752015 | + | 0.659146i | \(0.770918\pi\) | |||||||
\(32\) | −1.39539e73 | −1.39612 | ||||||||
\(33\) | −5.32674e73 | −1.19822 | ||||||||
\(34\) | −7.28475e73 | −0.385201 | ||||||||
\(35\) | 1.27346e74 | 0.165076 | ||||||||
\(36\) | −9.31739e73 | −0.0308051 | ||||||||
\(37\) | −5.50816e75 | −0.482195 | −0.241098 | − | 0.970501i | \(-0.577507\pi\) | ||||
−0.241098 | + | 0.970501i | \(0.577507\pi\) | |||||||
\(38\) | 9.10113e76 | 2.18570 | ||||||||
\(39\) | 1.66612e77 | 1.13520 | ||||||||
\(40\) | −1.78746e76 | −0.0356719 | ||||||||
\(41\) | −2.31752e78 | −1.39639 | −0.698196 | − | 0.715907i | \(-0.746014\pi\) | ||||
−0.698196 | + | 0.715907i | \(0.746014\pi\) | |||||||
\(42\) | −2.06780e78 | −0.387185 | ||||||||
\(43\) | −2.39827e79 | −1.43442 | −0.717212 | − | 0.696856i | \(-0.754582\pi\) | ||||
−0.717212 | + | 0.696856i | \(0.754582\pi\) | |||||||
\(44\) | 5.94015e79 | 1.16505 | ||||||||
\(45\) | −2.86505e78 | −0.0188940 | ||||||||
\(46\) | 2.80637e79 | 0.0637369 | ||||||||
\(47\) | 8.89362e80 | 0.711758 | 0.355879 | − | 0.934532i | \(-0.384181\pi\) | ||||
0.355879 | + | 0.934532i | \(0.384181\pi\) | |||||||
\(48\) | 3.55455e81 | 1.02467 | ||||||||
\(49\) | −8.68338e81 | −0.920829 | ||||||||
\(50\) | −2.30444e82 | −0.917318 | ||||||||
\(51\) | 1.77823e82 | 0.270916 | ||||||||
\(52\) | −1.85798e83 | −1.10377 | ||||||||
\(53\) | −1.93323e83 | −0.455936 | −0.227968 | − | 0.973669i | \(-0.573208\pi\) | ||||
−0.227968 | + | 0.973669i | \(0.573208\pi\) | |||||||
\(54\) | 1.49107e84 | 1.42037 | ||||||||
\(55\) | 1.82656e84 | 0.714570 | ||||||||
\(56\) | −1.04792e83 | −0.0171084 | ||||||||
\(57\) | −2.22162e85 | −1.53723 | ||||||||
\(58\) | −5.25204e85 | −1.56340 | ||||||||
\(59\) | −4.61663e85 | −0.599795 | −0.299898 | − | 0.953971i | \(-0.596952\pi\) | ||||
−0.299898 | + | 0.953971i | \(0.596952\pi\) | |||||||
\(60\) | −9.60123e85 | −0.552066 | ||||||||
\(61\) | 3.65079e86 | 0.941652 | 0.470826 | − | 0.882226i | \(-0.343956\pi\) | ||||
0.470826 | + | 0.882226i | \(0.343956\pi\) | |||||||
\(62\) | −1.79472e87 | −2.10378 | ||||||||
\(63\) | −1.67967e85 | −0.00906166 | ||||||||
\(64\) | −3.62550e87 | −0.911254 | ||||||||
\(65\) | −5.71320e87 | −0.676989 | ||||||||
\(66\) | −2.96592e88 | −1.67602 | ||||||||
\(67\) | −6.07665e88 | −1.65591 | −0.827955 | − | 0.560795i | \(-0.810496\pi\) | ||||
−0.827955 | + | 0.560795i | \(0.810496\pi\) | |||||||
\(68\) | −1.98301e88 | −0.263416 | ||||||||
\(69\) | −6.85047e87 | −0.0448269 | ||||||||
\(70\) | 7.09060e88 | 0.230902 | ||||||||
\(71\) | 6.82951e89 | 1.11779 | 0.558894 | − | 0.829239i | \(-0.311226\pi\) | ||||
0.558894 | + | 0.829239i | \(0.311226\pi\) | |||||||
\(72\) | 2.35763e87 | 0.00195816 | ||||||||
\(73\) | −2.98123e89 | −0.126834 | −0.0634171 | − | 0.997987i | \(-0.520200\pi\) | ||||
−0.0634171 | + | 0.997987i | \(0.520200\pi\) | |||||||
\(74\) | −3.06694e90 | −0.674476 | ||||||||
\(75\) | 5.62522e90 | 0.645161 | ||||||||
\(76\) | 2.47745e91 | 1.49467 | ||||||||
\(77\) | 1.07085e91 | 0.342711 | ||||||||
\(78\) | 9.27693e91 | 1.58787 | ||||||||
\(79\) | 1.13407e92 | 1.04647 | 0.523236 | − | 0.852188i | \(-0.324725\pi\) | ||||
0.523236 | + | 0.852188i | \(0.324725\pi\) | |||||||
\(80\) | −1.21887e92 | −0.611073 | ||||||||
\(81\) | −3.52242e92 | −0.966758 | ||||||||
\(82\) | −1.29039e93 | −1.95322 | ||||||||
\(83\) | 1.13702e93 | 0.956054 | 0.478027 | − | 0.878345i | \(-0.341352\pi\) | ||||
0.478027 | + | 0.878345i | \(0.341352\pi\) | |||||||
\(84\) | −5.62885e92 | −0.264774 | ||||||||
\(85\) | −6.09765e92 | −0.161564 | ||||||||
\(86\) | −1.33535e94 | −2.00641 | ||||||||
\(87\) | 1.28204e94 | 1.09956 | ||||||||
\(88\) | −1.50307e93 | −0.0740575 | ||||||||
\(89\) | −9.49289e93 | −0.270385 | −0.135193 | − | 0.990819i | \(-0.543165\pi\) | ||||
−0.135193 | + | 0.990819i | \(0.543165\pi\) | |||||||
\(90\) | −1.59525e93 | −0.0264282 | ||||||||
\(91\) | −3.34944e94 | −0.324687 | ||||||||
\(92\) | 7.63934e93 | 0.0435859 | ||||||||
\(93\) | 4.38098e95 | 1.47961 | ||||||||
\(94\) | 4.95196e95 | 0.995579 | ||||||||
\(95\) | 7.61803e95 | 0.916744 | ||||||||
\(96\) | 1.89657e96 | 1.37345 | ||||||||
\(97\) | −4.30104e96 | −1.88427 | −0.942137 | − | 0.335228i | \(-0.891187\pi\) | ||||
−0.942137 | + | 0.335228i | \(0.891187\pi\) | |||||||
\(98\) | −4.83489e96 | −1.28802 | ||||||||
\(99\) | −2.40921e95 | −0.0392254 | ||||||||
\(100\) | −6.27300e96 | −0.627300 | ||||||||
\(101\) | −6.37462e96 | −0.393430 | −0.196715 | − | 0.980461i | \(-0.563027\pi\) | ||||
−0.196715 | + | 0.980461i | \(0.563027\pi\) | |||||||
\(102\) | 9.90118e96 | 0.378947 | ||||||||
\(103\) | 6.76626e94 | 0.00161340 | 0.000806702 | − | 1.00000i | \(-0.499743\pi\) | ||||
0.000806702 | 1.00000i | \(0.499743\pi\) | ||||||||
\(104\) | 4.70135e96 | 0.0701627 | ||||||||
\(105\) | −1.73084e97 | −0.162396 | ||||||||
\(106\) | −1.07642e98 | −0.637746 | ||||||||
\(107\) | −9.38861e97 | −0.352767 | −0.176384 | − | 0.984321i | \(-0.556440\pi\) | ||||
−0.176384 | + | 0.984321i | \(0.556440\pi\) | |||||||
\(108\) | 4.05890e98 | 0.971307 | ||||||||
\(109\) | 5.07226e98 | 0.776276 | 0.388138 | − | 0.921601i | \(-0.373118\pi\) | ||||
0.388138 | + | 0.921601i | \(0.373118\pi\) | |||||||
\(110\) | 1.01703e99 | 0.999512 | ||||||||
\(111\) | 7.48650e98 | 0.474367 | ||||||||
\(112\) | −7.14579e98 | −0.293073 | ||||||||
\(113\) | 4.60425e99 | 1.22703 | 0.613514 | − | 0.789684i | \(-0.289755\pi\) | ||||
0.613514 | + | 0.789684i | \(0.289755\pi\) | |||||||
\(114\) | −1.23699e100 | −2.15022 | ||||||||
\(115\) | 2.34906e98 | 0.0267330 | ||||||||
\(116\) | −1.42968e100 | −1.06912 | ||||||||
\(117\) | 7.53562e98 | 0.0371625 | ||||||||
\(118\) | −2.57054e100 | −0.838970 | ||||||||
\(119\) | −3.57483e99 | −0.0774868 | ||||||||
\(120\) | 2.42945e99 | 0.0350928 | ||||||||
\(121\) | 5.00596e100 | 0.483500 | ||||||||
\(122\) | 2.03276e101 | 1.31715 | ||||||||
\(123\) | 3.14990e101 | 1.37372 | ||||||||
\(124\) | −4.88548e101 | −1.43865 | ||||||||
\(125\) | −4.87019e101 | −0.971428 | ||||||||
\(126\) | −9.35239e99 | −0.0126751 | ||||||||
\(127\) | 1.73469e102 | 1.60229 | 0.801146 | − | 0.598469i | \(-0.204224\pi\) | ||||
0.801146 | + | 0.598469i | \(0.204224\pi\) | |||||||
\(128\) | 1.92410e101 | 0.121491 | ||||||||
\(129\) | 3.25964e102 | 1.41114 | ||||||||
\(130\) | −3.18110e102 | −0.946945 | ||||||||
\(131\) | −4.26262e102 | −0.875022 | −0.437511 | − | 0.899213i | \(-0.644140\pi\) | ||||
−0.437511 | + | 0.899213i | \(0.644140\pi\) | |||||||
\(132\) | −8.07365e102 | −1.14613 | ||||||||
\(133\) | 4.46618e102 | 0.439674 | ||||||||
\(134\) | −3.38347e103 | −2.31622 | ||||||||
\(135\) | 1.24809e103 | 0.595742 | ||||||||
\(136\) | 5.01771e101 | 0.0167444 | ||||||||
\(137\) | 6.31336e103 | 1.47677 | 0.738386 | − | 0.674379i | \(-0.235588\pi\) | ||||
0.738386 | + | 0.674379i | \(0.235588\pi\) | |||||||
\(138\) | −3.81433e102 | −0.0627022 | ||||||||
\(139\) | 1.17407e104 | 1.35981 | 0.679904 | − | 0.733301i | \(-0.262021\pi\) | ||||
0.679904 | + | 0.733301i | \(0.262021\pi\) | |||||||
\(140\) | 1.93016e103 | 0.157901 | ||||||||
\(141\) | −1.20879e104 | −0.700203 | ||||||||
\(142\) | 3.80266e104 | 1.56352 | ||||||||
\(143\) | −4.80422e104 | −1.40548 | ||||||||
\(144\) | 1.60767e103 | 0.0335441 | ||||||||
\(145\) | −4.39619e104 | −0.655734 | ||||||||
\(146\) | −1.65994e104 | −0.177411 | ||||||||
\(147\) | 1.18022e105 | 0.905880 | ||||||||
\(148\) | −8.34863e104 | −0.461235 | ||||||||
\(149\) | −3.69564e105 | −1.47284 | −0.736421 | − | 0.676524i | \(-0.763486\pi\) | ||||
−0.736421 | + | 0.676524i | \(0.763486\pi\) | |||||||
\(150\) | 3.13211e105 | 0.902426 | ||||||||
\(151\) | −1.91877e105 | −0.400536 | −0.200268 | − | 0.979741i | \(-0.564181\pi\) | ||||
−0.200268 | + | 0.979741i | \(0.564181\pi\) | |||||||
\(152\) | −6.26883e104 | −0.0950107 | ||||||||
\(153\) | 8.04270e103 | 0.00886886 | ||||||||
\(154\) | 5.96247e105 | 0.479370 | ||||||||
\(155\) | −1.50226e106 | −0.882383 | ||||||||
\(156\) | 2.52531e106 | 1.08585 | ||||||||
\(157\) | 2.05563e106 | 0.648355 | 0.324177 | − | 0.945996i | \(-0.394913\pi\) | ||||
0.324177 | + | 0.945996i | \(0.394913\pi\) | |||||||
\(158\) | 6.31451e106 | 1.46376 | ||||||||
\(159\) | 2.62758e106 | 0.448535 | ||||||||
\(160\) | −6.50342e106 | −0.819073 | ||||||||
\(161\) | 1.37717e105 | 0.0128213 | ||||||||
\(162\) | −1.96128e107 | −1.35226 | ||||||||
\(163\) | −1.65361e107 | −0.845932 | −0.422966 | − | 0.906146i | \(-0.639011\pi\) | ||||
−0.422966 | + | 0.906146i | \(0.639011\pi\) | |||||||
\(164\) | −3.51263e107 | −1.33569 | ||||||||
\(165\) | −2.48260e107 | −0.702969 | ||||||||
\(166\) | 6.33094e107 | 1.33729 | ||||||||
\(167\) | 8.88372e107 | 1.40232 | 0.701158 | − | 0.713006i | \(-0.252667\pi\) | ||||
0.701158 | + | 0.713006i | \(0.252667\pi\) | |||||||
\(168\) | 1.42430e106 | 0.0168306 | ||||||||
\(169\) | 3.74173e107 | 0.331564 | ||||||||
\(170\) | −3.39516e107 | −0.225989 | ||||||||
\(171\) | −1.00481e107 | −0.0503235 | ||||||||
\(172\) | −3.63501e108 | −1.37207 | ||||||||
\(173\) | 4.51855e108 | 1.28755 | 0.643773 | − | 0.765216i | \(-0.277368\pi\) | ||||
0.643773 | + | 0.765216i | \(0.277368\pi\) | |||||||
\(174\) | 7.13840e108 | 1.53802 | ||||||||
\(175\) | −1.13085e108 | −0.184527 | ||||||||
\(176\) | −1.02495e109 | −1.26863 | ||||||||
\(177\) | 6.27477e108 | 0.590058 | ||||||||
\(178\) | −5.28563e108 | −0.378204 | ||||||||
\(179\) | 3.66503e108 | 0.199851 | 0.0999254 | − | 0.994995i | \(-0.468140\pi\) | ||||
0.0999254 | + | 0.994995i | \(0.468140\pi\) | |||||||
\(180\) | −4.34250e107 | −0.0180727 | ||||||||
\(181\) | −2.82368e109 | −0.898265 | −0.449132 | − | 0.893465i | \(-0.648267\pi\) | ||||
−0.449132 | + | 0.893465i | \(0.648267\pi\) | |||||||
\(182\) | −1.86496e109 | −0.454159 | ||||||||
\(183\) | −4.96203e109 | −0.926365 | ||||||||
\(184\) | −1.93302e107 | −0.00277059 | ||||||||
\(185\) | −2.56716e109 | −0.282894 | ||||||||
\(186\) | 2.43932e110 | 2.06962 | ||||||||
\(187\) | −5.12750e109 | −0.335419 | ||||||||
\(188\) | 1.34799e110 | 0.680819 | ||||||||
\(189\) | 7.31710e109 | 0.285721 | ||||||||
\(190\) | 4.24171e110 | 1.28231 | ||||||||
\(191\) | −3.19030e110 | −0.747675 | −0.373837 | − | 0.927494i | \(-0.621958\pi\) | ||||
−0.373837 | + | 0.927494i | \(0.621958\pi\) | |||||||
\(192\) | 4.92766e110 | 0.896461 | ||||||||
\(193\) | −2.94804e110 | −0.416873 | −0.208436 | − | 0.978036i | \(-0.566837\pi\) | ||||
−0.208436 | + | 0.978036i | \(0.566837\pi\) | |||||||
\(194\) | −2.39481e111 | −2.63565 | ||||||||
\(195\) | 7.76519e110 | 0.665999 | ||||||||
\(196\) | −1.31613e111 | −0.880801 | ||||||||
\(197\) | 2.89772e110 | 0.151511 | 0.0757554 | − | 0.997126i | \(-0.475863\pi\) | ||||
0.0757554 | + | 0.997126i | \(0.475863\pi\) | |||||||
\(198\) | −1.34144e110 | −0.0548670 | ||||||||
\(199\) | 4.51636e110 | 0.144682 | 0.0723409 | − | 0.997380i | \(-0.476953\pi\) | ||||
0.0723409 | + | 0.997380i | \(0.476953\pi\) | |||||||
\(200\) | 1.58729e110 | 0.0398751 | ||||||||
\(201\) | 8.25918e111 | 1.62903 | ||||||||
\(202\) | −3.54938e111 | −0.550315 | ||||||||
\(203\) | −2.57732e111 | −0.314493 | ||||||||
\(204\) | 2.69524e111 | 0.259140 | ||||||||
\(205\) | −1.08012e112 | −0.819234 | ||||||||
\(206\) | 3.76744e109 | 0.00225677 | ||||||||
\(207\) | −3.09837e109 | −0.00146748 | ||||||||
\(208\) | 3.20586e112 | 1.20191 | ||||||||
\(209\) | 6.40599e112 | 1.90323 | ||||||||
\(210\) | −9.63730e111 | −0.227154 | ||||||||
\(211\) | −4.76566e112 | −0.892122 | −0.446061 | − | 0.895003i | \(-0.647174\pi\) | ||||
−0.446061 | + | 0.895003i | \(0.647174\pi\) | |||||||
\(212\) | −2.93017e112 | −0.436117 | ||||||||
\(213\) | −9.28244e112 | −1.09964 | ||||||||
\(214\) | −5.22757e112 | −0.493437 | ||||||||
\(215\) | −1.11775e113 | −0.841546 | ||||||||
\(216\) | −1.02705e112 | −0.0617423 | ||||||||
\(217\) | −8.80719e112 | −0.423195 | ||||||||
\(218\) | 2.82423e113 | 1.08582 | ||||||||
\(219\) | 4.05198e112 | 0.124775 | ||||||||
\(220\) | 2.76849e113 | 0.683508 | ||||||||
\(221\) | 1.60380e113 | 0.317779 | ||||||||
\(222\) | 4.16848e113 | 0.663526 | ||||||||
\(223\) | 1.96663e113 | 0.251731 | 0.125865 | − | 0.992047i | \(-0.459829\pi\) | ||||
0.125865 | + | 0.992047i | \(0.459829\pi\) | |||||||
\(224\) | −3.81272e113 | −0.392831 | ||||||||
\(225\) | 2.54421e112 | 0.0211203 | ||||||||
\(226\) | 2.56364e114 | 1.71632 | ||||||||
\(227\) | −1.82708e114 | −0.987423 | −0.493712 | − | 0.869626i | \(-0.664360\pi\) | ||||
−0.493712 | + | 0.869626i | \(0.664360\pi\) | |||||||
\(228\) | −3.36727e114 | −1.47041 | ||||||||
\(229\) | −2.36794e114 | −0.836277 | −0.418138 | − | 0.908383i | \(-0.637317\pi\) | ||||
−0.418138 | + | 0.908383i | \(0.637317\pi\) | |||||||
\(230\) | 1.30795e113 | 0.0373931 | ||||||||
\(231\) | −1.45546e114 | −0.337147 | ||||||||
\(232\) | 3.61759e113 | 0.0679598 | ||||||||
\(233\) | 6.68027e114 | 1.01867 | 0.509333 | − | 0.860570i | \(-0.329892\pi\) | ||||
0.509333 | + | 0.860570i | \(0.329892\pi\) | |||||||
\(234\) | 4.19582e113 | 0.0519814 | ||||||||
\(235\) | 4.14500e114 | 0.417574 | ||||||||
\(236\) | −6.99736e114 | −0.573722 | ||||||||
\(237\) | −1.54139e115 | −1.02948 | ||||||||
\(238\) | −1.99046e114 | −0.108385 | ||||||||
\(239\) | 2.80228e115 | 1.24513 | 0.622563 | − | 0.782570i | \(-0.286091\pi\) | ||||
0.622563 | + | 0.782570i | \(0.286091\pi\) | |||||||
\(240\) | 1.65665e115 | 0.601153 | ||||||||
\(241\) | −2.46032e115 | −0.729735 | −0.364868 | − | 0.931059i | \(-0.618886\pi\) | ||||
−0.364868 | + | 0.931059i | \(0.618886\pi\) | |||||||
\(242\) | 2.78731e115 | 0.676301 | ||||||||
\(243\) | −3.24106e114 | −0.0643848 | ||||||||
\(244\) | 5.53345e115 | 0.900719 | ||||||||
\(245\) | −4.04701e115 | −0.540231 | ||||||||
\(246\) | 1.75386e116 | 1.92151 | ||||||||
\(247\) | −2.00369e116 | −1.80314 | ||||||||
\(248\) | 1.23620e115 | 0.0914495 | ||||||||
\(249\) | −1.54541e116 | −0.940533 | ||||||||
\(250\) | −2.71172e116 | −1.35879 | ||||||||
\(251\) | −3.13517e116 | −1.29445 | −0.647225 | − | 0.762299i | \(-0.724070\pi\) | ||||
−0.647225 | + | 0.762299i | \(0.724070\pi\) | |||||||
\(252\) | −2.54585e114 | −0.00866776 | ||||||||
\(253\) | 1.97532e115 | 0.0554998 | ||||||||
\(254\) | 9.65873e116 | 2.24122 | ||||||||
\(255\) | 8.28772e115 | 0.158941 | ||||||||
\(256\) | 6.81618e116 | 1.08119 | ||||||||
\(257\) | −8.27239e116 | −1.08611 | −0.543056 | − | 0.839697i | \(-0.682733\pi\) | ||||
−0.543056 | + | 0.839697i | \(0.682733\pi\) | |||||||
\(258\) | 1.81496e117 | 1.97384 | ||||||||
\(259\) | −1.50503e116 | −0.135677 | ||||||||
\(260\) | −8.65940e116 | −0.647561 | ||||||||
\(261\) | 5.79850e115 | 0.0359957 | ||||||||
\(262\) | −2.37342e117 | −1.22395 | ||||||||
\(263\) | 3.71022e116 | 0.159055 | 0.0795273 | − | 0.996833i | \(-0.474659\pi\) | ||||
0.0795273 | + | 0.996833i | \(0.474659\pi\) | |||||||
\(264\) | 2.04292e116 | 0.0728552 | ||||||||
\(265\) | −9.01010e116 | −0.267488 | ||||||||
\(266\) | 2.48676e117 | 0.614999 | ||||||||
\(267\) | 1.29024e117 | 0.265996 | ||||||||
\(268\) | −9.21029e117 | −1.58393 | ||||||||
\(269\) | 1.31056e117 | 0.188135 | 0.0940676 | − | 0.995566i | \(-0.470013\pi\) | ||||
0.0940676 | + | 0.995566i | \(0.470013\pi\) | |||||||
\(270\) | 6.94935e117 | 0.833301 | ||||||||
\(271\) | −1.76170e118 | −1.76571 | −0.882857 | − | 0.469643i | \(-0.844383\pi\) | ||||
−0.882857 | + | 0.469643i | \(0.844383\pi\) | |||||||
\(272\) | 3.42159e117 | 0.286838 | ||||||||
\(273\) | 4.55245e117 | 0.319416 | ||||||||
\(274\) | 3.51527e118 | 2.06565 | ||||||||
\(275\) | −1.62202e118 | −0.798767 | ||||||||
\(276\) | −1.03831e117 | −0.0428784 | ||||||||
\(277\) | −4.94686e118 | −1.71420 | −0.857099 | − | 0.515152i | \(-0.827736\pi\) | ||||
−0.857099 | + | 0.515152i | \(0.827736\pi\) | |||||||
\(278\) | 6.53723e118 | 1.90205 | ||||||||
\(279\) | 1.98145e117 | 0.0484373 | ||||||||
\(280\) | −4.88398e116 | −0.0100371 | ||||||||
\(281\) | 1.08158e119 | 1.86983 | 0.934914 | − | 0.354874i | \(-0.115476\pi\) | ||||
0.934914 | + | 0.354874i | \(0.115476\pi\) | |||||||
\(282\) | −6.73053e118 | −0.979417 | ||||||||
\(283\) | −3.09182e118 | −0.378941 | −0.189471 | − | 0.981886i | \(-0.560677\pi\) | ||||
−0.189471 | + | 0.981886i | \(0.560677\pi\) | |||||||
\(284\) | 1.03514e119 | 1.06920 | ||||||||
\(285\) | −1.03542e119 | −0.901861 | ||||||||
\(286\) | −2.67498e119 | −1.96593 | ||||||||
\(287\) | −6.33232e118 | −0.392908 | ||||||||
\(288\) | 8.57791e117 | 0.0449620 | ||||||||
\(289\) | −2.08590e119 | −0.924162 | ||||||||
\(290\) | −2.44779e119 | −0.917215 | ||||||||
\(291\) | 5.84582e119 | 1.85368 | ||||||||
\(292\) | −4.51860e118 | −0.121321 | ||||||||
\(293\) | 6.68329e119 | 1.52023 | 0.760117 | − | 0.649786i | \(-0.225141\pi\) | ||||
0.760117 | + | 0.649786i | \(0.225141\pi\) | |||||||
\(294\) | 6.57142e119 | 1.26711 | ||||||||
\(295\) | −2.15165e119 | −0.351887 | ||||||||
\(296\) | 2.11250e118 | 0.0293189 | ||||||||
\(297\) | 1.04952e120 | 1.23681 | ||||||||
\(298\) | −2.05773e120 | −2.06015 | ||||||||
\(299\) | −6.17847e118 | −0.0525810 | ||||||||
\(300\) | 8.52605e119 | 0.617116 | ||||||||
\(301\) | −6.55294e119 | −0.403609 | ||||||||
\(302\) | −1.06837e120 | −0.560253 | ||||||||
\(303\) | 8.66417e119 | 0.387043 | ||||||||
\(304\) | −4.27473e120 | −1.62757 | ||||||||
\(305\) | 1.70150e120 | 0.552447 | ||||||||
\(306\) | 4.47817e118 | 0.0124054 | ||||||||
\(307\) | 4.55957e120 | 1.07823 | 0.539117 | − | 0.842231i | \(-0.318758\pi\) | ||||
0.539117 | + | 0.842231i | \(0.318758\pi\) | |||||||
\(308\) | 1.62307e120 | 0.327813 | ||||||||
\(309\) | −9.19647e117 | −0.00158721 | ||||||||
\(310\) | −8.36455e120 | −1.23424 | ||||||||
\(311\) | −4.75642e120 | −0.600346 | −0.300173 | − | 0.953885i | \(-0.597044\pi\) | ||||
−0.300173 | + | 0.953885i | \(0.597044\pi\) | |||||||
\(312\) | −6.38992e119 | −0.0690236 | ||||||||
\(313\) | −4.80816e120 | −0.444712 | −0.222356 | − | 0.974966i | \(-0.571375\pi\) | ||||
−0.222356 | + | 0.974966i | \(0.571375\pi\) | |||||||
\(314\) | 1.14457e121 | 0.906893 | ||||||||
\(315\) | −7.82835e118 | −0.00531629 | ||||||||
\(316\) | 1.71890e121 | 1.00098 | ||||||||
\(317\) | 3.46333e121 | 1.73029 | 0.865145 | − | 0.501521i | \(-0.167226\pi\) | ||||
0.865145 | + | 0.501521i | \(0.167226\pi\) | |||||||
\(318\) | 1.46303e121 | 0.627392 | ||||||||
\(319\) | −3.69674e121 | −1.36135 | ||||||||
\(320\) | −1.68972e121 | −0.534614 | ||||||||
\(321\) | 1.27607e121 | 0.347040 | ||||||||
\(322\) | 7.66804e119 | 0.0179339 | ||||||||
\(323\) | −2.13852e121 | −0.430320 | ||||||||
\(324\) | −5.33887e121 | −0.924734 | ||||||||
\(325\) | 5.07341e121 | 0.756759 | ||||||||
\(326\) | −9.20730e121 | −1.18326 | ||||||||
\(327\) | −6.89404e121 | −0.763674 | ||||||||
\(328\) | 8.88820e120 | 0.0849048 | ||||||||
\(329\) | 2.43006e121 | 0.200270 | ||||||||
\(330\) | −1.38231e122 | −0.983285 | ||||||||
\(331\) | 1.29740e122 | 0.796924 | 0.398462 | − | 0.917185i | \(-0.369544\pi\) | ||||
0.398462 | + | 0.917185i | \(0.369544\pi\) | |||||||
\(332\) | 1.72337e122 | 0.914495 | ||||||||
\(333\) | 3.38604e120 | 0.0155291 | ||||||||
\(334\) | 4.94644e122 | 1.96150 | ||||||||
\(335\) | −2.83211e122 | −0.971488 | ||||||||
\(336\) | 9.71232e121 | 0.288316 | ||||||||
\(337\) | 5.17092e122 | 1.32898 | 0.664489 | − | 0.747298i | \(-0.268649\pi\) | ||||
0.664489 | + | 0.747298i | \(0.268649\pi\) | |||||||
\(338\) | 2.08339e122 | 0.463778 | ||||||||
\(339\) | −6.25794e122 | −1.20711 | ||||||||
\(340\) | −9.24210e121 | −0.154541 | ||||||||
\(341\) | −1.26324e123 | −1.83189 | ||||||||
\(342\) | −5.59475e121 | −0.0703906 | ||||||||
\(343\) | −4.94923e122 | −0.540471 | ||||||||
\(344\) | 9.19786e121 | 0.0872172 | ||||||||
\(345\) | −3.19276e121 | −0.0262990 | ||||||||
\(346\) | 2.51592e123 | 1.80097 | ||||||||
\(347\) | −1.84097e123 | −1.14569 | −0.572845 | − | 0.819664i | \(-0.694160\pi\) | ||||
−0.572845 | + | 0.819664i | \(0.694160\pi\) | |||||||
\(348\) | 1.94317e123 | 1.05176 | ||||||||
\(349\) | 3.57643e122 | 0.168429 | 0.0842145 | − | 0.996448i | \(-0.473162\pi\) | ||||
0.0842145 | + | 0.996448i | \(0.473162\pi\) | |||||||
\(350\) | −6.29657e122 | −0.258109 | ||||||||
\(351\) | −3.28272e123 | −1.17176 | ||||||||
\(352\) | −5.46871e123 | −1.70046 | ||||||||
\(353\) | 4.06742e123 | 1.10216 | 0.551081 | − | 0.834452i | \(-0.314216\pi\) | ||||
0.551081 | + | 0.834452i | \(0.314216\pi\) | |||||||
\(354\) | 3.49378e123 | 0.825349 | ||||||||
\(355\) | 3.18299e123 | 0.655783 | ||||||||
\(356\) | −1.43882e123 | −0.258632 | ||||||||
\(357\) | 4.85879e122 | 0.0762288 | ||||||||
\(358\) | 2.04068e123 | 0.279543 | ||||||||
\(359\) | 8.70448e123 | 1.04151 | 0.520754 | − | 0.853707i | \(-0.325651\pi\) | ||||
0.520754 | + | 0.853707i | \(0.325651\pi\) | |||||||
\(360\) | 1.09881e121 | 0.00114881 | ||||||||
\(361\) | 1.57753e124 | 1.44171 | ||||||||
\(362\) | −1.57222e124 | −1.25646 | ||||||||
\(363\) | −6.80393e123 | −0.475651 | ||||||||
\(364\) | −5.07669e123 | −0.310573 | ||||||||
\(365\) | −1.38944e123 | −0.0744110 | ||||||||
\(366\) | −2.76285e124 | −1.29576 | ||||||||
\(367\) | −2.33190e124 | −0.958089 | −0.479045 | − | 0.877791i | \(-0.659017\pi\) | ||||
−0.479045 | + | 0.877791i | \(0.659017\pi\) | |||||||
\(368\) | −1.31813e123 | −0.0474613 | ||||||||
\(369\) | 1.42466e123 | 0.0449709 | ||||||||
\(370\) | −1.42939e124 | −0.395701 | ||||||||
\(371\) | −5.28230e123 | −0.128289 | ||||||||
\(372\) | 6.64018e124 | 1.41530 | ||||||||
\(373\) | 4.36469e124 | 0.816724 | 0.408362 | − | 0.912820i | \(-0.366100\pi\) | ||||
0.408362 | + | 0.912820i | \(0.366100\pi\) | |||||||
\(374\) | −2.85498e124 | −0.469171 | ||||||||
\(375\) | 6.61940e124 | 0.955657 | ||||||||
\(376\) | −3.41089e123 | −0.0432770 | ||||||||
\(377\) | 1.15628e125 | 1.28976 | ||||||||
\(378\) | 4.07415e124 | 0.399655 | ||||||||
\(379\) | −1.60339e125 | −1.38368 | −0.691842 | − | 0.722049i | \(-0.743201\pi\) | ||||
−0.691842 | + | 0.722049i | \(0.743201\pi\) | |||||||
\(380\) | 1.15465e125 | 0.876894 | ||||||||
\(381\) | −2.35773e125 | −1.57628 | ||||||||
\(382\) | −1.77635e125 | −1.04582 | ||||||||
\(383\) | 2.86390e125 | 1.48531 | 0.742654 | − | 0.669675i | \(-0.233567\pi\) | ||||
0.742654 | + | 0.669675i | \(0.233567\pi\) | |||||||
\(384\) | −2.61517e124 | −0.119519 | ||||||||
\(385\) | 4.99084e124 | 0.201061 | ||||||||
\(386\) | −1.64146e125 | −0.583105 | ||||||||
\(387\) | 1.47429e124 | 0.0461957 | ||||||||
\(388\) | −6.51901e125 | −1.80237 | ||||||||
\(389\) | −3.30470e124 | −0.0806448 | −0.0403224 | − | 0.999187i | \(-0.512838\pi\) | ||||
−0.0403224 | + | 0.999187i | \(0.512838\pi\) | |||||||
\(390\) | 4.32365e125 | 0.931572 | ||||||||
\(391\) | −6.59423e123 | −0.0125485 | ||||||||
\(392\) | 3.33026e124 | 0.0559892 | ||||||||
\(393\) | 5.79361e125 | 0.860817 | ||||||||
\(394\) | 1.61344e125 | 0.211927 | ||||||||
\(395\) | 5.28551e125 | 0.613943 | ||||||||
\(396\) | −3.65160e124 | −0.0375203 | ||||||||
\(397\) | −1.73042e126 | −1.57330 | −0.786649 | − | 0.617400i | \(-0.788186\pi\) | ||||
−0.786649 | + | 0.617400i | \(0.788186\pi\) | |||||||
\(398\) | 2.51470e125 | 0.202375 | ||||||||
\(399\) | −6.07027e125 | −0.432537 | ||||||||
\(400\) | 1.08238e126 | 0.683076 | ||||||||
\(401\) | −1.93417e126 | −1.08142 | −0.540708 | − | 0.841210i | \(-0.681844\pi\) | ||||
−0.540708 | + | 0.841210i | \(0.681844\pi\) | |||||||
\(402\) | 4.59870e126 | 2.27862 | ||||||||
\(403\) | 3.95123e126 | 1.73555 | ||||||||
\(404\) | −9.66191e125 | −0.376328 | ||||||||
\(405\) | −1.64167e126 | −0.567177 | ||||||||
\(406\) | −1.43505e126 | −0.439900 | ||||||||
\(407\) | −2.15872e126 | −0.587309 | ||||||||
\(408\) | −6.81991e124 | −0.0164725 | ||||||||
\(409\) | −1.45137e126 | −0.311313 | −0.155656 | − | 0.987811i | \(-0.549749\pi\) | ||||
−0.155656 | + | 0.987811i | \(0.549749\pi\) | |||||||
\(410\) | −6.01407e126 | −1.14591 | ||||||||
\(411\) | −8.58091e126 | −1.45280 | ||||||||
\(412\) | 1.02555e124 | 0.00154327 | ||||||||
\(413\) | −1.26143e126 | −0.168767 | ||||||||
\(414\) | −1.72517e124 | −0.00205265 | ||||||||
\(415\) | 5.29927e126 | 0.560897 | ||||||||
\(416\) | 1.71052e127 | 1.61103 | ||||||||
\(417\) | −1.59576e127 | −1.33773 | ||||||||
\(418\) | 3.56684e127 | 2.66216 | ||||||||
\(419\) | 1.52094e127 | 1.01095 | 0.505477 | − | 0.862840i | \(-0.331316\pi\) | ||||
0.505477 | + | 0.862840i | \(0.331316\pi\) | |||||||
\(420\) | −2.62341e126 | −0.155337 | ||||||||
\(421\) | 4.18467e126 | 0.220790 | 0.110395 | − | 0.993888i | \(-0.464788\pi\) | ||||
0.110395 | + | 0.993888i | \(0.464788\pi\) | |||||||
\(422\) | −2.65351e127 | −1.24786 | ||||||||
\(423\) | −5.46719e125 | −0.0229222 | ||||||||
\(424\) | 7.41435e125 | 0.0277223 | ||||||||
\(425\) | 5.41481e126 | 0.180601 | ||||||||
\(426\) | −5.16845e127 | −1.53814 | ||||||||
\(427\) | 9.97530e126 | 0.264956 | ||||||||
\(428\) | −1.42302e127 | −0.337433 | ||||||||
\(429\) | 6.52973e127 | 1.38266 | ||||||||
\(430\) | −6.22360e127 | −1.17712 | ||||||||
\(431\) | −1.47635e127 | −0.249484 | −0.124742 | − | 0.992189i | \(-0.539810\pi\) | ||||
−0.124742 | + | 0.992189i | \(0.539810\pi\) | |||||||
\(432\) | −7.00345e127 | −1.05767 | ||||||||
\(433\) | 6.61951e127 | 0.893641 | 0.446821 | − | 0.894624i | \(-0.352556\pi\) | ||||
0.446821 | + | 0.894624i | \(0.352556\pi\) | |||||||
\(434\) | −4.90383e127 | −0.591948 | ||||||||
\(435\) | 5.97515e127 | 0.645089 | ||||||||
\(436\) | 7.68794e127 | 0.742532 | ||||||||
\(437\) | 8.23843e126 | 0.0712024 | ||||||||
\(438\) | 2.25614e127 | 0.174531 | ||||||||
\(439\) | −1.19115e128 | −0.824965 | −0.412483 | − | 0.910965i | \(-0.635338\pi\) | ||||
−0.412483 | + | 0.910965i | \(0.635338\pi\) | |||||||
\(440\) | −7.00526e126 | −0.0434480 | ||||||||
\(441\) | 5.33795e126 | 0.0296553 | ||||||||
\(442\) | 8.92993e127 | 0.444496 | ||||||||
\(443\) | −1.78349e127 | −0.0795590 | −0.0397795 | − | 0.999208i | \(-0.512666\pi\) | ||||
−0.0397795 | + | 0.999208i | \(0.512666\pi\) | |||||||
\(444\) | 1.13472e128 | 0.453747 | ||||||||
\(445\) | −4.42430e127 | −0.158629 | ||||||||
\(446\) | 1.09502e128 | 0.352111 | ||||||||
\(447\) | 5.02299e128 | 1.44893 | ||||||||
\(448\) | −9.90620e127 | −0.256403 | ||||||||
\(449\) | −2.61967e128 | −0.608555 | −0.304277 | − | 0.952583i | \(-0.598415\pi\) | ||||
−0.304277 | + | 0.952583i | \(0.598415\pi\) | |||||||
\(450\) | 1.41661e127 | 0.0295423 | ||||||||
\(451\) | −9.08267e128 | −1.70079 | ||||||||
\(452\) | 6.97859e128 | 1.17369 | ||||||||
\(453\) | 2.60793e128 | 0.394033 | ||||||||
\(454\) | −1.01732e129 | −1.38117 | ||||||||
\(455\) | −1.56106e128 | −0.190487 | ||||||||
\(456\) | 8.52038e127 | 0.0934683 | ||||||||
\(457\) | −2.50980e128 | −0.247573 | −0.123787 | − | 0.992309i | \(-0.539504\pi\) | ||||
−0.123787 | + | 0.992309i | \(0.539504\pi\) | |||||||
\(458\) | −1.31847e129 | −1.16975 | ||||||||
\(459\) | −3.50362e128 | −0.279641 | ||||||||
\(460\) | 3.56043e127 | 0.0255710 | ||||||||
\(461\) | 2.49750e129 | 1.61440 | 0.807198 | − | 0.590280i | \(-0.200983\pi\) | ||||
0.807198 | + | 0.590280i | \(0.200983\pi\) | |||||||
\(462\) | −8.10398e128 | −0.471588 | ||||||||
\(463\) | −8.35396e128 | −0.437738 | −0.218869 | − | 0.975754i | \(-0.570237\pi\) | ||||
−0.218869 | + | 0.975754i | \(0.570237\pi\) | |||||||
\(464\) | 2.46684e129 | 1.16418 | ||||||||
\(465\) | 2.04182e129 | 0.868058 | ||||||||
\(466\) | 3.71956e129 | 1.42487 | ||||||||
\(467\) | 6.68430e128 | 0.230774 | 0.115387 | − | 0.993321i | \(-0.463189\pi\) | ||||
0.115387 | + | 0.993321i | \(0.463189\pi\) | |||||||
\(468\) | 1.14216e128 | 0.0355471 | ||||||||
\(469\) | −1.66036e129 | −0.465930 | ||||||||
\(470\) | 2.30793e129 | 0.584086 | ||||||||
\(471\) | −2.79395e129 | −0.637829 | ||||||||
\(472\) | 1.77058e128 | 0.0364693 | ||||||||
\(473\) | −9.39910e129 | −1.74711 | ||||||||
\(474\) | −8.58246e129 | −1.44000 | ||||||||
\(475\) | −6.76494e129 | −1.02476 | ||||||||
\(476\) | −5.41831e128 | −0.0741185 | ||||||||
\(477\) | 1.18842e128 | 0.0146834 | ||||||||
\(478\) | 1.56031e130 | 1.74163 | ||||||||
\(479\) | 3.95123e129 | 0.398529 | 0.199265 | − | 0.979946i | \(-0.436145\pi\) | ||||
0.199265 | + | 0.979946i | \(0.436145\pi\) | |||||||
\(480\) | 8.83923e129 | 0.805776 | ||||||||
\(481\) | 6.75212e129 | 0.556422 | ||||||||
\(482\) | −1.36990e130 | −1.02072 | ||||||||
\(483\) | −1.87180e128 | −0.0126131 | ||||||||
\(484\) | 7.58745e129 | 0.462483 | ||||||||
\(485\) | −2.00456e130 | −1.10546 | ||||||||
\(486\) | −1.80462e129 | −0.0900589 | ||||||||
\(487\) | 3.95586e129 | 0.178684 | 0.0893420 | − | 0.996001i | \(-0.471524\pi\) | ||||
0.0893420 | + | 0.996001i | \(0.471524\pi\) | |||||||
\(488\) | −1.40016e129 | −0.0572553 | ||||||||
\(489\) | 2.24754e130 | 0.832199 | ||||||||
\(490\) | −2.25337e130 | −0.755654 | ||||||||
\(491\) | 3.72426e130 | 1.13133 | 0.565663 | − | 0.824637i | \(-0.308620\pi\) | ||||
0.565663 | + | 0.824637i | \(0.308620\pi\) | |||||||
\(492\) | 4.77425e130 | 1.31401 | ||||||||
\(493\) | 1.23409e130 | 0.307802 | ||||||||
\(494\) | −1.11565e131 | −2.52215 | ||||||||
\(495\) | −1.12285e129 | −0.0230127 | ||||||||
\(496\) | 8.42966e130 | 1.56657 | ||||||||
\(497\) | 1.86607e130 | 0.314517 | ||||||||
\(498\) | −8.60479e130 | −1.31558 | ||||||||
\(499\) | 1.22476e131 | 1.69893 | 0.849463 | − | 0.527648i | \(-0.176926\pi\) | ||||
0.849463 | + | 0.527648i | \(0.176926\pi\) | |||||||
\(500\) | −7.38167e130 | −0.929201 | ||||||||
\(501\) | −1.20744e131 | −1.37955 | ||||||||
\(502\) | −1.74566e131 | −1.81062 | ||||||||
\(503\) | 1.00764e131 | 0.948980 | 0.474490 | − | 0.880261i | \(-0.342632\pi\) | ||||
0.474490 | + | 0.880261i | \(0.342632\pi\) | |||||||
\(504\) | 6.44190e127 | 0.000550976 0 | ||||||||
\(505\) | −2.97098e130 | −0.230817 | ||||||||
\(506\) | 1.09985e130 | 0.0776309 | ||||||||
\(507\) | −5.08563e130 | −0.326181 | ||||||||
\(508\) | 2.62924e131 | 1.53264 | ||||||||
\(509\) | −1.64486e131 | −0.871598 | −0.435799 | − | 0.900044i | \(-0.643534\pi\) | ||||
−0.435799 | + | 0.900044i | \(0.643534\pi\) | |||||||
\(510\) | 4.61459e130 | 0.222320 | ||||||||
\(511\) | −8.14581e129 | −0.0356879 | ||||||||
\(512\) | 3.49035e131 | 1.39084 | ||||||||
\(513\) | 4.37721e131 | 1.58674 | ||||||||
\(514\) | −4.60606e131 | −1.51921 | ||||||||
\(515\) | 3.15351e128 | 0.000946551 0 | ||||||||
\(516\) | 4.94059e131 | 1.34980 | ||||||||
\(517\) | 3.48552e131 | 0.866915 | ||||||||
\(518\) | −8.37999e130 | −0.189780 | ||||||||
\(519\) | −6.14146e131 | −1.26664 | ||||||||
\(520\) | 2.19113e130 | 0.0411630 | ||||||||
\(521\) | −9.86220e131 | −1.68789 | −0.843945 | − | 0.536430i | \(-0.819773\pi\) | ||||
−0.843945 | + | 0.536430i | \(0.819773\pi\) | |||||||
\(522\) | 3.22860e130 | 0.0503494 | ||||||||
\(523\) | −6.15255e131 | −0.874426 | −0.437213 | − | 0.899358i | \(-0.644034\pi\) | ||||
−0.437213 | + | 0.899358i | \(0.644034\pi\) | |||||||
\(524\) | −6.46078e131 | −0.836985 | ||||||||
\(525\) | 1.53702e131 | 0.181531 | ||||||||
\(526\) | 2.06585e131 | 0.222479 | ||||||||
\(527\) | 4.21711e131 | 0.414191 | ||||||||
\(528\) | 1.39307e132 | 1.24804 | ||||||||
\(529\) | −1.22095e132 | −0.997924 | ||||||||
\(530\) | −5.01681e131 | −0.374152 | ||||||||
\(531\) | 2.83799e130 | 0.0193164 | ||||||||
\(532\) | 6.76931e131 | 0.420562 | ||||||||
\(533\) | 2.84091e132 | 1.61134 | ||||||||
\(534\) | 7.18405e131 | 0.372064 | ||||||||
\(535\) | −4.37570e131 | −0.206961 | ||||||||
\(536\) | 2.33053e131 | 0.100684 | ||||||||
\(537\) | −4.98139e131 | −0.196606 | ||||||||
\(538\) | 7.29716e131 | 0.263156 | ||||||||
\(539\) | −3.40312e132 | −1.12156 | ||||||||
\(540\) | 1.89171e132 | 0.569846 | ||||||||
\(541\) | 1.62318e132 | 0.446992 | 0.223496 | − | 0.974705i | \(-0.428253\pi\) | ||||
0.223496 | + | 0.974705i | \(0.428253\pi\) | |||||||
\(542\) | −9.80909e132 | −2.46981 | ||||||||
\(543\) | 3.83785e132 | 0.883682 | ||||||||
\(544\) | 1.82563e132 | 0.384473 | ||||||||
\(545\) | 2.36400e132 | 0.455425 | ||||||||
\(546\) | 2.53480e132 | 0.446786 | ||||||||
\(547\) | −8.11601e130 | −0.0130905 | −0.00654526 | − | 0.999979i | \(-0.502083\pi\) | ||||
−0.00654526 | + | 0.999979i | \(0.502083\pi\) | |||||||
\(548\) | 9.56906e132 | 1.41258 | ||||||||
\(549\) | −2.24426e131 | −0.0303259 | ||||||||
\(550\) | −9.03138e132 | −1.11728 | ||||||||
\(551\) | −1.54180e133 | −1.74652 | ||||||||
\(552\) | 2.62730e130 | 0.00272561 | ||||||||
\(553\) | 3.09870e132 | 0.294450 | ||||||||
\(554\) | −2.75441e133 | −2.39775 | ||||||||
\(555\) | 3.48919e132 | 0.278301 | ||||||||
\(556\) | 1.77952e133 | 1.30070 | ||||||||
\(557\) | −1.26292e133 | −0.846054 | −0.423027 | − | 0.906117i | \(-0.639033\pi\) | ||||
−0.423027 | + | 0.906117i | \(0.639033\pi\) | |||||||
\(558\) | 1.10327e132 | 0.0677522 | ||||||||
\(559\) | 2.93989e133 | 1.65523 | ||||||||
\(560\) | −3.33040e132 | −0.171940 | ||||||||
\(561\) | 6.96912e132 | 0.329974 | ||||||||
\(562\) | 6.02222e133 | 2.61544 | ||||||||
\(563\) | 3.25814e130 | 0.00129811 | 0.000649056 | − | 1.00000i | \(-0.499793\pi\) | ||||
0.000649056 | 1.00000i | \(0.499793\pi\) | ||||||||
\(564\) | −1.83214e133 | −0.669766 | ||||||||
\(565\) | 2.14588e133 | 0.719872 | ||||||||
\(566\) | −1.72152e133 | −0.530048 | ||||||||
\(567\) | −9.62454e132 | −0.272020 | ||||||||
\(568\) | −2.61926e132 | −0.0679649 | ||||||||
\(569\) | −3.87831e133 | −0.924054 | −0.462027 | − | 0.886866i | \(-0.652878\pi\) | ||||
−0.462027 | + | 0.886866i | \(0.652878\pi\) | |||||||
\(570\) | −5.76519e133 | −1.26149 | ||||||||
\(571\) | 5.41263e133 | 1.08782 | 0.543910 | − | 0.839144i | \(-0.316943\pi\) | ||||
0.543910 | + | 0.839144i | \(0.316943\pi\) | |||||||
\(572\) | −7.28167e133 | −1.34439 | ||||||||
\(573\) | 4.33614e133 | 0.735537 | ||||||||
\(574\) | −3.52583e133 | −0.549585 | ||||||||
\(575\) | −2.08600e132 | −0.0298830 | ||||||||
\(576\) | 2.22871e132 | 0.0293470 | ||||||||
\(577\) | 1.44687e132 | 0.0175147 | 0.00875734 | − | 0.999962i | \(-0.497212\pi\) | ||||
0.00875734 | + | 0.999962i | \(0.497212\pi\) | |||||||
\(578\) | −1.16143e134 | −1.29268 | ||||||||
\(579\) | 4.00687e133 | 0.410105 | ||||||||
\(580\) | −6.66323e133 | −0.627230 | ||||||||
\(581\) | 3.10677e133 | 0.269009 | ||||||||
\(582\) | 3.25495e134 | 2.59286 | ||||||||
\(583\) | −7.57657e133 | −0.555326 | ||||||||
\(584\) | 1.14336e132 | 0.00771190 | ||||||||
\(585\) | 3.51208e132 | 0.0218025 | ||||||||
\(586\) | 3.72125e134 | 2.12644 | ||||||||
\(587\) | −7.76480e133 | −0.408491 | −0.204245 | − | 0.978920i | \(-0.565474\pi\) | ||||
−0.204245 | + | 0.978920i | \(0.565474\pi\) | |||||||
\(588\) | 1.78883e134 | 0.866502 | ||||||||
\(589\) | −5.26860e134 | −2.35019 | ||||||||
\(590\) | −1.19803e134 | −0.492206 | ||||||||
\(591\) | −3.93848e133 | −0.149051 | ||||||||
\(592\) | 1.44052e134 | 0.502245 | ||||||||
\(593\) | −2.11462e134 | −0.679330 | −0.339665 | − | 0.940547i | \(-0.610314\pi\) | ||||
−0.339665 | + | 0.940547i | \(0.610314\pi\) | |||||||
\(594\) | 5.84369e134 | 1.72999 | ||||||||
\(595\) | −1.66610e133 | −0.0454599 | ||||||||
\(596\) | −5.60143e134 | −1.40882 | ||||||||
\(597\) | −6.13848e133 | −0.142333 | ||||||||
\(598\) | −3.44016e133 | −0.0735482 | ||||||||
\(599\) | 2.23758e134 | 0.441141 | 0.220571 | − | 0.975371i | \(-0.429208\pi\) | ||||
0.220571 | + | 0.975371i | \(0.429208\pi\) | |||||||
\(600\) | −2.15739e133 | −0.0392277 | ||||||||
\(601\) | 1.32563e134 | 0.222337 | 0.111168 | − | 0.993802i | \(-0.464541\pi\) | ||||
0.111168 | + | 0.993802i | \(0.464541\pi\) | |||||||
\(602\) | −3.64867e134 | −0.564553 | ||||||||
\(603\) | 3.73551e133 | 0.0533286 | ||||||||
\(604\) | −2.90825e134 | −0.383125 | ||||||||
\(605\) | 2.33310e134 | 0.283660 | ||||||||
\(606\) | 4.82420e134 | 0.541381 | ||||||||
\(607\) | −1.06946e133 | −0.0110793 | −0.00553964 | − | 0.999985i | \(-0.501763\pi\) | ||||
−0.00553964 | + | 0.999985i | \(0.501763\pi\) | |||||||
\(608\) | −2.28083e135 | −2.18157 | ||||||||
\(609\) | 3.50301e134 | 0.309388 | ||||||||
\(610\) | 9.47396e134 | 0.772742 | ||||||||
\(611\) | −1.09021e135 | −0.821322 | ||||||||
\(612\) | 1.21902e133 | 0.00848333 | ||||||||
\(613\) | 2.12784e135 | 1.36806 | 0.684032 | − | 0.729452i | \(-0.260225\pi\) | ||||
0.684032 | + | 0.729452i | \(0.260225\pi\) | |||||||
\(614\) | 2.53876e135 | 1.50819 | ||||||||
\(615\) | 1.46806e135 | 0.805934 | ||||||||
\(616\) | −4.10693e133 | −0.0208378 | ||||||||
\(617\) | −2.66046e134 | −0.124774 | −0.0623872 | − | 0.998052i | \(-0.519871\pi\) | ||||
−0.0623872 | + | 0.998052i | \(0.519871\pi\) | |||||||
\(618\) | −5.12058e132 | −0.00222013 | ||||||||
\(619\) | 2.14756e135 | 0.860892 | 0.430446 | − | 0.902616i | \(-0.358356\pi\) | ||||
0.430446 | + | 0.902616i | \(0.358356\pi\) | |||||||
\(620\) | −2.27695e135 | −0.844026 | ||||||||
\(621\) | 1.34973e134 | 0.0462706 | ||||||||
\(622\) | −2.64837e135 | −0.839740 | ||||||||
\(623\) | −2.59380e134 | −0.0760794 | ||||||||
\(624\) | −4.35730e135 | −1.18240 | ||||||||
\(625\) | 3.42081e134 | 0.0858910 | ||||||||
\(626\) | −2.67718e135 | −0.622046 | ||||||||
\(627\) | −8.70680e135 | −1.87233 | ||||||||
\(628\) | 3.11569e135 | 0.620171 | ||||||||
\(629\) | 7.20648e134 | 0.132790 | ||||||||
\(630\) | −4.35882e133 | −0.00743621 | ||||||||
\(631\) | −4.79344e135 | −0.757222 | −0.378611 | − | 0.925556i | \(-0.623598\pi\) | ||||
−0.378611 | + | 0.925556i | \(0.623598\pi\) | |||||||
\(632\) | −4.34941e134 | −0.0636286 | ||||||||
\(633\) | 6.47733e135 | 0.877639 | ||||||||
\(634\) | 1.92837e136 | 2.42026 | ||||||||
\(635\) | 8.08477e135 | 0.940031 | ||||||||
\(636\) | 3.98258e135 | 0.429037 | ||||||||
\(637\) | 1.06444e136 | 1.06258 | ||||||||
\(638\) | −2.05834e136 | −1.90421 | ||||||||
\(639\) | −4.19832e134 | −0.0359984 | ||||||||
\(640\) | 8.96755e134 | 0.0712763 | ||||||||
\(641\) | −1.80663e136 | −1.33124 | −0.665619 | − | 0.746291i | \(-0.731833\pi\) | ||||
−0.665619 | + | 0.746291i | \(0.731833\pi\) | |||||||
\(642\) | 7.10513e135 | 0.485426 | ||||||||
\(643\) | −3.51510e135 | −0.222693 | −0.111346 | − | 0.993782i | \(-0.535516\pi\) | ||||
−0.111346 | + | 0.993782i | \(0.535516\pi\) | |||||||
\(644\) | 2.08735e134 | 0.0122639 | ||||||||
\(645\) | 1.51920e136 | 0.827884 | ||||||||
\(646\) | −1.19073e136 | −0.601914 | ||||||||
\(647\) | 4.19654e135 | 0.196804 | 0.0984019 | − | 0.995147i | \(-0.468627\pi\) | ||||
0.0984019 | + | 0.995147i | \(0.468627\pi\) | |||||||
\(648\) | 1.35092e135 | 0.0587818 | ||||||||
\(649\) | −1.80932e136 | −0.730544 | ||||||||
\(650\) | 2.82487e136 | 1.05852 | ||||||||
\(651\) | 1.19704e136 | 0.416324 | ||||||||
\(652\) | −2.50636e136 | −0.809160 | ||||||||
\(653\) | −3.81194e136 | −1.14250 | −0.571250 | − | 0.820776i | \(-0.693541\pi\) | ||||
−0.571250 | + | 0.820776i | \(0.693541\pi\) | |||||||
\(654\) | −3.83859e136 | −1.06820 | ||||||||
\(655\) | −1.98666e136 | −0.513357 | ||||||||
\(656\) | 6.06088e136 | 1.45445 | ||||||||
\(657\) | 1.83266e134 | 0.00408470 | ||||||||
\(658\) | 1.35306e136 | 0.280130 | ||||||||
\(659\) | 5.46387e136 | 1.05089 | 0.525445 | − | 0.850827i | \(-0.323899\pi\) | ||||
0.525445 | + | 0.850827i | \(0.323899\pi\) | |||||||
\(660\) | −3.76284e136 | −0.672411 | ||||||||
\(661\) | −6.27330e136 | −1.04166 | −0.520830 | − | 0.853661i | \(-0.674377\pi\) | ||||
−0.520830 | + | 0.853661i | \(0.674377\pi\) | |||||||
\(662\) | 7.22392e136 | 1.11471 | ||||||||
\(663\) | −2.17983e136 | −0.312620 | ||||||||
\(664\) | −4.36073e135 | −0.0581310 | ||||||||
\(665\) | 2.08153e136 | 0.257948 | ||||||||
\(666\) | 1.88534e135 | 0.0217215 | ||||||||
\(667\) | −4.75420e135 | −0.0509301 | ||||||||
\(668\) | 1.34649e137 | 1.34136 | ||||||||
\(669\) | −2.67298e136 | −0.247644 | ||||||||
\(670\) | −1.57692e137 | −1.35888 | ||||||||
\(671\) | 1.43079e137 | 1.14692 | ||||||||
\(672\) | 5.18212e136 | 0.386454 | ||||||||
\(673\) | −1.67353e136 | −0.116119 | −0.0580594 | − | 0.998313i | \(-0.518491\pi\) | ||||
−0.0580594 | + | 0.998313i | \(0.518491\pi\) | |||||||
\(674\) | 2.87916e137 | 1.85892 | ||||||||
\(675\) | −1.10832e137 | −0.665938 | ||||||||
\(676\) | 5.67127e136 | 0.317151 | ||||||||
\(677\) | −1.69999e137 | −0.884901 | −0.442451 | − | 0.896793i | \(-0.645891\pi\) | ||||
−0.442451 | + | 0.896793i | \(0.645891\pi\) | |||||||
\(678\) | −3.48441e137 | −1.68846 | ||||||||
\(679\) | −1.17520e137 | −0.530186 | ||||||||
\(680\) | 2.33858e135 | 0.00982358 | ||||||||
\(681\) | 2.48330e137 | 0.971393 | ||||||||
\(682\) | −7.03373e137 | −2.56238 | ||||||||
\(683\) | −2.06049e137 | −0.699143 | −0.349572 | − | 0.936910i | \(-0.613673\pi\) | ||||
−0.349572 | + | 0.936910i | \(0.613673\pi\) | |||||||
\(684\) | −1.52297e136 | −0.0481360 | ||||||||
\(685\) | 2.94243e137 | 0.866391 | ||||||||
\(686\) | −2.75572e137 | −0.755990 | ||||||||
\(687\) | 3.21843e137 | 0.822701 | ||||||||
\(688\) | 6.27204e137 | 1.49407 | ||||||||
\(689\) | 2.36983e137 | 0.526120 | ||||||||
\(690\) | −1.77772e136 | −0.0367861 | ||||||||
\(691\) | 5.67605e137 | 1.09487 | 0.547433 | − | 0.836850i | \(-0.315605\pi\) | ||||
0.547433 | + | 0.836850i | \(0.315605\pi\) | |||||||
\(692\) | 6.84869e137 | 1.23158 | ||||||||
\(693\) | −6.58284e135 | −0.0110370 | ||||||||
\(694\) | −1.02505e138 | −1.60255 | ||||||||
\(695\) | 5.47194e137 | 0.797771 | ||||||||
\(696\) | −4.91691e136 | −0.0668566 | ||||||||
\(697\) | 3.03208e137 | 0.384548 | ||||||||
\(698\) | 1.99135e137 | 0.235592 | ||||||||
\(699\) | −9.07959e137 | −1.00213 | ||||||||
\(700\) | −1.71401e137 | −0.176506 | ||||||||
\(701\) | 7.43944e137 | 0.714852 | 0.357426 | − | 0.933941i | \(-0.383654\pi\) | ||||
0.357426 | + | 0.933941i | \(0.383654\pi\) | |||||||
\(702\) | −1.82781e138 | −1.63901 | ||||||||
\(703\) | −9.00334e137 | −0.753478 | ||||||||
\(704\) | −1.42088e138 | −1.10990 | ||||||||
\(705\) | −5.63374e137 | −0.410795 | ||||||||
\(706\) | 2.26473e138 | 1.54166 | ||||||||
\(707\) | −1.74178e137 | −0.110701 | ||||||||
\(708\) | 9.51057e137 | 0.564408 | ||||||||
\(709\) | −4.02698e137 | −0.223171 | −0.111585 | − | 0.993755i | \(-0.535593\pi\) | ||||
−0.111585 | + | 0.993755i | \(0.535593\pi\) | |||||||
\(710\) | 1.77229e138 | 0.917284 | ||||||||
\(711\) | −6.97151e136 | −0.0337017 | ||||||||
\(712\) | 3.64073e136 | 0.0164402 | ||||||||
\(713\) | −1.62460e137 | −0.0685337 | ||||||||
\(714\) | 2.70537e137 | 0.106626 | ||||||||
\(715\) | −2.23907e138 | −0.824566 | ||||||||
\(716\) | 5.55503e137 | 0.191163 | ||||||||
\(717\) | −3.80877e138 | −1.22491 | ||||||||
\(718\) | 4.84664e138 | 1.45682 | ||||||||
\(719\) | −4.27047e138 | −1.19984 | −0.599921 | − | 0.800059i | \(-0.704801\pi\) | ||||
−0.599921 | + | 0.800059i | \(0.704801\pi\) | |||||||
\(720\) | 7.49278e136 | 0.0196796 | ||||||||
\(721\) | 1.84879e135 | 0.000453970 0 | ||||||||
\(722\) | 8.78368e138 | 2.01661 | ||||||||
\(723\) | 3.34399e138 | 0.717888 | ||||||||
\(724\) | −4.27980e138 | −0.859218 | ||||||||
\(725\) | 3.90388e138 | 0.732999 | ||||||||
\(726\) | −3.78842e138 | −0.665322 | ||||||||
\(727\) | 5.97013e137 | 0.0980765 | 0.0490383 | − | 0.998797i | \(-0.484384\pi\) | ||||
0.0490383 | + | 0.998797i | \(0.484384\pi\) | |||||||
\(728\) | 1.28458e137 | 0.0197419 | ||||||||
\(729\) | 7.16413e138 | 1.03010 | ||||||||
\(730\) | −7.73641e137 | −0.104083 | ||||||||
\(731\) | 3.13772e138 | 0.395022 | ||||||||
\(732\) | −7.52087e138 | −0.886096 | ||||||||
\(733\) | −3.84503e138 | −0.423992 | −0.211996 | − | 0.977271i | \(-0.567996\pi\) | ||||
−0.211996 | + | 0.977271i | \(0.567996\pi\) | |||||||
\(734\) | −1.29840e139 | −1.34014 | ||||||||
\(735\) | 5.50056e138 | 0.531461 | ||||||||
\(736\) | −7.03305e137 | −0.0636164 | ||||||||
\(737\) | −2.38152e139 | −2.01688 | ||||||||
\(738\) | 7.93246e137 | 0.0629035 | ||||||||
\(739\) | −6.16139e138 | −0.457534 | −0.228767 | − | 0.973481i | \(-0.573469\pi\) | ||||
−0.228767 | + | 0.973481i | \(0.573469\pi\) | |||||||
\(740\) | −3.89100e138 | −0.270597 | ||||||||
\(741\) | 2.72335e139 | 1.77386 | ||||||||
\(742\) | −2.94117e138 | −0.179445 | ||||||||
\(743\) | 1.66865e139 | 0.953691 | 0.476846 | − | 0.878987i | \(-0.341780\pi\) | ||||
0.476846 | + | 0.878987i | \(0.341780\pi\) | |||||||
\(744\) | −1.68020e138 | −0.0899649 | ||||||||
\(745\) | −1.72241e139 | −0.864086 | ||||||||
\(746\) | 2.43025e139 | 1.14240 | ||||||||
\(747\) | −6.98965e137 | −0.0307898 | ||||||||
\(748\) | −7.77166e138 | −0.320839 | ||||||||
\(749\) | −2.56531e138 | −0.0992595 | ||||||||
\(750\) | 3.68567e139 | 1.33674 | ||||||||
\(751\) | 3.06018e138 | 0.104042 | 0.0520211 | − | 0.998646i | \(-0.483434\pi\) | ||||
0.0520211 | + | 0.998646i | \(0.483434\pi\) | |||||||
\(752\) | −2.32590e139 | −0.741353 | ||||||||
\(753\) | 4.26121e139 | 1.27344 | ||||||||
\(754\) | 6.43816e139 | 1.80406 | ||||||||
\(755\) | −8.94271e138 | −0.234986 | ||||||||
\(756\) | 1.10904e139 | 0.273301 | ||||||||
\(757\) | −4.50908e139 | −1.04217 | −0.521084 | − | 0.853505i | \(-0.674472\pi\) | ||||
−0.521084 | + | 0.853505i | \(0.674472\pi\) | |||||||
\(758\) | −8.92764e139 | −1.93544 | ||||||||
\(759\) | −2.68478e138 | −0.0545988 | ||||||||
\(760\) | −2.92168e138 | −0.0557408 | ||||||||
\(761\) | −3.68505e139 | −0.659610 | −0.329805 | − | 0.944049i | \(-0.606983\pi\) | ||||
−0.329805 | + | 0.944049i | \(0.606983\pi\) | |||||||
\(762\) | −1.31278e140 | −2.20484 | ||||||||
\(763\) | 1.38593e139 | 0.218424 | ||||||||
\(764\) | −4.83548e139 | −0.715174 | ||||||||
\(765\) | 3.74842e137 | 0.00520317 | ||||||||
\(766\) | 1.59461e140 | 2.07759 | ||||||||
\(767\) | 5.65925e139 | 0.692124 | ||||||||
\(768\) | −9.26432e139 | −1.06364 | ||||||||
\(769\) | 1.27976e140 | 1.37943 | 0.689715 | − | 0.724081i | \(-0.257736\pi\) | ||||
0.689715 | + | 0.724081i | \(0.257736\pi\) | |||||||
\(770\) | 2.77889e139 | 0.281237 | ||||||||
\(771\) | 1.12436e140 | 1.06848 | ||||||||
\(772\) | −4.46829e139 | −0.398752 | ||||||||
\(773\) | −1.66967e140 | −1.39935 | −0.699674 | − | 0.714462i | \(-0.746671\pi\) | ||||
−0.699674 | + | 0.714462i | \(0.746671\pi\) | |||||||
\(774\) | 8.20883e138 | 0.0646167 | ||||||||
\(775\) | 1.33403e140 | 0.986354 | ||||||||
\(776\) | 1.64954e139 | 0.114570 | ||||||||
\(777\) | 2.04559e139 | 0.133475 | ||||||||
\(778\) | −1.84005e139 | −0.112803 | ||||||||
\(779\) | −3.78810e140 | −2.18200 | ||||||||
\(780\) | 1.17696e140 | 0.637048 | ||||||||
\(781\) | 2.67657e140 | 1.36146 | ||||||||
\(782\) | −3.67166e138 | −0.0175523 | ||||||||
\(783\) | −2.52598e140 | −1.13497 | ||||||||
\(784\) | 2.27091e140 | 0.959116 | ||||||||
\(785\) | 9.58058e139 | 0.380376 | ||||||||
\(786\) | 3.22587e140 | 1.20408 | ||||||||
\(787\) | −3.94973e140 | −1.38609 | −0.693047 | − | 0.720893i | \(-0.743732\pi\) | ||||
−0.693047 | + | 0.720893i | \(0.743732\pi\) | |||||||
\(788\) | 4.39202e139 | 0.144925 | ||||||||
\(789\) | −5.04281e139 | −0.156472 | ||||||||
\(790\) | 2.94297e140 | 0.858759 | ||||||||
\(791\) | 1.25805e140 | 0.345254 | ||||||||
\(792\) | 9.23983e137 | 0.00238502 | ||||||||
\(793\) | −4.47529e140 | −1.08660 | ||||||||
\(794\) | −9.63494e140 | −2.20067 | ||||||||
\(795\) | 1.22462e140 | 0.263146 | ||||||||
\(796\) | 6.84537e139 | 0.138393 | ||||||||
\(797\) | −1.74076e139 | −0.0331140 | −0.0165570 | − | 0.999863i | \(-0.505270\pi\) | ||||
−0.0165570 | + | 0.999863i | \(0.505270\pi\) | |||||||
\(798\) | −3.37992e140 | −0.605015 | ||||||||
\(799\) | −1.16358e140 | −0.196009 | ||||||||
\(800\) | 5.77514e140 | 0.915584 | ||||||||
\(801\) | 5.83558e138 | 0.00870777 | ||||||||
\(802\) | −1.07694e141 | −1.51264 | ||||||||
\(803\) | −1.16838e140 | −0.154483 | ||||||||
\(804\) | 1.25183e141 | 1.55821 | ||||||||
\(805\) | 6.41848e138 | 0.00752198 | ||||||||
\(806\) | 2.20004e141 | 2.42762 | ||||||||
\(807\) | −1.78126e140 | −0.185081 | ||||||||
\(808\) | 2.44480e139 | 0.0239217 | ||||||||
\(809\) | 9.54940e140 | 0.879980 | 0.439990 | − | 0.898003i | \(-0.354982\pi\) | ||||
0.439990 | + | 0.898003i | \(0.354982\pi\) | |||||||
\(810\) | −9.14082e140 | −0.793344 | ||||||||
\(811\) | 9.09885e140 | 0.743832 | 0.371916 | − | 0.928266i | \(-0.378701\pi\) | ||||
0.371916 | + | 0.928266i | \(0.378701\pi\) | |||||||
\(812\) | −3.90641e140 | −0.300822 | ||||||||
\(813\) | 2.39444e141 | 1.73705 | ||||||||
\(814\) | −1.20197e141 | −0.821505 | ||||||||
\(815\) | −7.70691e140 | −0.496291 | ||||||||
\(816\) | −4.65051e140 | −0.282181 | ||||||||
\(817\) | −3.92007e141 | −2.24143 | ||||||||
\(818\) | −8.08119e140 | −0.435452 | ||||||||
\(819\) | 2.05901e139 | 0.0104566 | ||||||||
\(820\) | −1.63711e141 | −0.783623 | ||||||||
\(821\) | 2.89041e141 | 1.30412 | 0.652059 | − | 0.758168i | \(-0.273905\pi\) | ||||
0.652059 | + | 0.758168i | \(0.273905\pi\) | |||||||
\(822\) | −4.77784e141 | −2.03212 | ||||||||
\(823\) | 3.60875e141 | 1.44699 | 0.723495 | − | 0.690330i | \(-0.242535\pi\) | ||||
0.723495 | + | 0.690330i | \(0.242535\pi\) | |||||||
\(824\) | −2.59501e137 | −9.80999e−5 0 | ||||||||
\(825\) | 2.20459e141 | 0.785800 | ||||||||
\(826\) | −7.02364e140 | −0.236064 | ||||||||
\(827\) | −2.12752e141 | −0.674305 | −0.337153 | − | 0.941450i | \(-0.609464\pi\) | ||||
−0.337153 | + | 0.941450i | \(0.609464\pi\) | |||||||
\(828\) | −4.69615e138 | −0.00140369 | ||||||||
\(829\) | −6.01564e141 | −1.69585 | −0.847925 | − | 0.530116i | \(-0.822148\pi\) | ||||
−0.847925 | + | 0.530116i | \(0.822148\pi\) | |||||||
\(830\) | 2.95062e141 | 0.784560 | ||||||||
\(831\) | 6.72361e141 | 1.68637 | ||||||||
\(832\) | 4.44428e141 | 1.05153 | ||||||||
\(833\) | 1.13607e141 | 0.253584 | ||||||||
\(834\) | −8.88518e141 | −1.87117 | ||||||||
\(835\) | 4.14038e141 | 0.822710 | ||||||||
\(836\) | 9.70945e141 | 1.82050 | ||||||||
\(837\) | −8.63175e141 | −1.52726 | ||||||||
\(838\) | 8.46857e141 | 1.41408 | ||||||||
\(839\) | −1.64061e141 | −0.258553 | −0.129277 | − | 0.991609i | \(-0.541266\pi\) | ||||
−0.129277 | + | 0.991609i | \(0.541266\pi\) | |||||||
\(840\) | 6.63815e139 | 0.00987419 | ||||||||
\(841\) | 1.77528e141 | 0.249265 | ||||||||
\(842\) | 2.33002e141 | 0.308833 | ||||||||
\(843\) | −1.47005e142 | −1.83947 | ||||||||
\(844\) | −7.22323e141 | −0.853342 | ||||||||
\(845\) | 1.74388e141 | 0.194521 | ||||||||
\(846\) | −3.04412e140 | −0.0320627 | ||||||||
\(847\) | 1.36781e141 | 0.136044 | ||||||||
\(848\) | 5.05587e141 | 0.474894 | ||||||||
\(849\) | 4.20229e141 | 0.372789 | ||||||||
\(850\) | 3.01496e141 | 0.252618 | ||||||||
\(851\) | −2.77622e140 | −0.0219720 | ||||||||
\(852\) | −1.40692e142 | −1.05184 | ||||||||
\(853\) | −5.34434e141 | −0.377456 | −0.188728 | − | 0.982029i | \(-0.560436\pi\) | ||||
−0.188728 | + | 0.982029i | \(0.560436\pi\) | |||||||
\(854\) | 5.55424e141 | 0.370610 | ||||||||
\(855\) | −4.68305e140 | −0.0295238 | ||||||||
\(856\) | 3.60073e140 | 0.0214493 | ||||||||
\(857\) | 4.63866e140 | 0.0261109 | 0.0130555 | − | 0.999915i | \(-0.495844\pi\) | ||||
0.0130555 | + | 0.999915i | \(0.495844\pi\) | |||||||
\(858\) | 3.63574e142 | 1.93401 | ||||||||
\(859\) | −3.09056e142 | −1.55370 | −0.776852 | − | 0.629683i | \(-0.783185\pi\) | ||||
−0.776852 | + | 0.629683i | \(0.783185\pi\) | |||||||
\(860\) | −1.69415e142 | −0.804965 | ||||||||
\(861\) | 8.60668e141 | 0.386530 | ||||||||
\(862\) | −8.22031e141 | −0.348968 | ||||||||
\(863\) | −3.22288e142 | −1.29336 | −0.646681 | − | 0.762760i | \(-0.723844\pi\) | ||||
−0.646681 | + | 0.762760i | \(0.723844\pi\) | |||||||
\(864\) | −3.73677e142 | −1.41768 | ||||||||
\(865\) | 2.10593e142 | 0.755377 | ||||||||
\(866\) | 3.68574e142 | 1.24999 | ||||||||
\(867\) | 2.83508e142 | 0.909159 | ||||||||
\(868\) | −1.33489e142 | −0.404799 | ||||||||
\(869\) | 4.44458e142 | 1.27459 | ||||||||
\(870\) | 3.32695e142 | 0.902325 | ||||||||
\(871\) | 7.44900e142 | 1.91081 | ||||||||
\(872\) | −1.94532e141 | −0.0471999 | ||||||||
\(873\) | 2.64398e141 | 0.0606831 | ||||||||
\(874\) | 4.58715e141 | 0.0995951 | ||||||||
\(875\) | −1.33071e142 | −0.273334 | ||||||||
\(876\) | 6.14153e141 | 0.119351 | ||||||||
\(877\) | −6.11498e142 | −1.12438 | −0.562192 | − | 0.827007i | \(-0.690042\pi\) | ||||
−0.562192 | + | 0.827007i | \(0.690042\pi\) | |||||||
\(878\) | −6.63228e142 | −1.15393 | ||||||||
\(879\) | −9.08370e142 | −1.49555 | ||||||||
\(880\) | −4.77690e142 | −0.744281 | ||||||||
\(881\) | −4.39442e141 | −0.0647992 | −0.0323996 | − | 0.999475i | \(-0.510315\pi\) | ||||
−0.0323996 | + | 0.999475i | \(0.510315\pi\) | |||||||
\(882\) | 2.97216e141 | 0.0414807 | ||||||||
\(883\) | −4.34742e142 | −0.574298 | −0.287149 | − | 0.957886i | \(-0.592707\pi\) | ||||
−0.287149 | + | 0.957886i | \(0.592707\pi\) | |||||||
\(884\) | 2.43085e142 | 0.303965 | ||||||||
\(885\) | 2.92445e142 | 0.346175 | ||||||||
\(886\) | −9.93043e141 | −0.111284 | ||||||||
\(887\) | 2.29243e142 | 0.243221 | 0.121610 | − | 0.992578i | \(-0.461194\pi\) | ||||
0.121610 | + | 0.992578i | \(0.461194\pi\) | |||||||
\(888\) | −2.87123e141 | −0.0288430 | ||||||||
\(889\) | 4.73981e142 | 0.450843 | ||||||||
\(890\) | −2.46344e142 | −0.221885 | ||||||||
\(891\) | −1.38048e143 | −1.17750 | ||||||||
\(892\) | 2.98079e142 | 0.240788 | ||||||||
\(893\) | 1.45370e143 | 1.11219 | ||||||||
\(894\) | 2.79680e143 | 2.02671 | ||||||||
\(895\) | 1.70814e142 | 0.117248 | ||||||||
\(896\) | 5.25735e141 | 0.0341844 | ||||||||
\(897\) | 8.39757e141 | 0.0517273 | ||||||||
\(898\) | −1.45863e143 | −0.851222 | ||||||||
\(899\) | 3.04039e143 | 1.68106 | ||||||||
\(900\) | 3.85621e141 | 0.0202022 | ||||||||
\(901\) | 2.52930e142 | 0.125559 | ||||||||
\(902\) | −5.05722e143 | −2.37900 | ||||||||
\(903\) | 8.90653e142 | 0.397057 | ||||||||
\(904\) | −1.76583e142 | −0.0746070 | ||||||||
\(905\) | −1.31602e143 | −0.526993 | ||||||||
\(906\) | 1.45209e143 | 0.551158 | ||||||||
\(907\) | 2.02374e143 | 0.728117 | 0.364058 | − | 0.931376i | \(-0.381391\pi\) | ||||
0.364058 | + | 0.931376i | \(0.381391\pi\) | |||||||
\(908\) | −2.76927e143 | −0.944501 | ||||||||
\(909\) | 3.91868e141 | 0.0126704 | ||||||||
\(910\) | −8.69193e142 | −0.266446 | ||||||||
\(911\) | −5.57500e143 | −1.62033 | −0.810166 | − | 0.586201i | \(-0.800623\pi\) | ||||
−0.810166 | + | 0.586201i | \(0.800623\pi\) | |||||||
\(912\) | 5.81007e143 | 1.60115 | ||||||||
\(913\) | 4.45614e143 | 1.16446 | ||||||||
\(914\) | −1.39745e143 | −0.346296 | ||||||||
\(915\) | −2.31263e143 | −0.543479 | ||||||||
\(916\) | −3.58905e143 | −0.799925 | ||||||||
\(917\) | −1.16470e143 | −0.246208 | ||||||||
\(918\) | −1.95081e143 | −0.391151 | ||||||||
\(919\) | 4.43056e143 | 0.842669 | 0.421334 | − | 0.906905i | \(-0.361562\pi\) | ||||
0.421334 | + | 0.906905i | \(0.361562\pi\) | |||||||
\(920\) | −9.00913e140 | −0.00162545 | ||||||||
\(921\) | −6.19721e143 | −1.06073 | ||||||||
\(922\) | 1.39060e144 | 2.25815 | ||||||||
\(923\) | −8.37188e143 | −1.28985 | ||||||||
\(924\) | −2.20602e143 | −0.322492 | ||||||||
\(925\) | 2.27968e143 | 0.316227 | ||||||||
\(926\) | −4.65147e143 | −0.612291 | ||||||||
\(927\) | −4.15943e139 | −5.19598e−5 0 | ||||||||
\(928\) | 1.31621e144 | 1.56045 | ||||||||
\(929\) | −5.20440e143 | −0.585610 | −0.292805 | − | 0.956172i | \(-0.594589\pi\) | ||||
−0.292805 | + | 0.956172i | \(0.594589\pi\) | |||||||
\(930\) | 1.13688e144 | 1.21421 | ||||||||
\(931\) | −1.41934e144 | −1.43889 | ||||||||
\(932\) | 1.01252e144 | 0.974385 | ||||||||
\(933\) | 6.46477e143 | 0.590599 | ||||||||
\(934\) | 3.72181e143 | 0.322798 | ||||||||
\(935\) | −2.38974e143 | −0.196783 | ||||||||
\(936\) | −2.89007e141 | −0.00225959 | ||||||||
\(937\) | 1.99216e143 | 0.147895 | 0.0739477 | − | 0.997262i | \(-0.476440\pi\) | ||||
0.0739477 | + | 0.997262i | \(0.476440\pi\) | |||||||
\(938\) | −9.24489e143 | −0.651724 | ||||||||
\(939\) | 6.53509e143 | 0.437493 | ||||||||
\(940\) | 6.28251e143 | 0.399422 | ||||||||
\(941\) | −1.36308e143 | −0.0823049 | −0.0411524 | − | 0.999153i | \(-0.513103\pi\) | ||||
−0.0411524 | + | 0.999153i | \(0.513103\pi\) | |||||||
\(942\) | −1.55567e144 | −0.892170 | ||||||||
\(943\) | −1.16808e143 | −0.0636290 | ||||||||
\(944\) | 1.20736e144 | 0.624734 | ||||||||
\(945\) | 3.41024e143 | 0.167626 | ||||||||
\(946\) | −5.23341e144 | −2.44379 | ||||||||
\(947\) | 2.79634e144 | 1.24055 | 0.620277 | − | 0.784383i | \(-0.287020\pi\) | ||||
0.620277 | + | 0.784383i | \(0.287020\pi\) | |||||||
\(948\) | −2.33627e144 | −0.984732 | ||||||||
\(949\) | 3.65451e143 | 0.146358 | ||||||||
\(950\) | −3.76671e144 | −1.43340 | ||||||||
\(951\) | −4.70723e144 | −1.70220 | ||||||||
\(952\) | 1.37102e142 | 0.00471143 | ||||||||
\(953\) | 4.62054e144 | 1.50899 | 0.754496 | − | 0.656305i | \(-0.227882\pi\) | ||||
0.754496 | + | 0.656305i | \(0.227882\pi\) | |||||||
\(954\) | 6.61710e142 | 0.0205386 | ||||||||
\(955\) | −1.48688e144 | −0.438645 | ||||||||
\(956\) | 4.24737e144 | 1.19100 | ||||||||
\(957\) | 5.02449e144 | 1.33925 | ||||||||
\(958\) | 2.20004e144 | 0.557447 | ||||||||
\(959\) | 1.72504e144 | 0.415525 | ||||||||
\(960\) | 2.29661e144 | 0.525935 | ||||||||
\(961\) | 5.79669e144 | 1.26211 | ||||||||
\(962\) | 3.75957e144 | 0.778300 | ||||||||
\(963\) | 5.77148e142 | 0.0113609 | ||||||||
\(964\) | −3.72907e144 | −0.698014 | ||||||||
\(965\) | −1.37398e144 | −0.244571 | ||||||||
\(966\) | −1.04221e143 | −0.0176428 | ||||||||
\(967\) | −1.02299e145 | −1.64697 | −0.823487 | − | 0.567335i | \(-0.807974\pi\) | ||||
−0.823487 | + | 0.567335i | \(0.807974\pi\) | |||||||
\(968\) | −1.91989e143 | −0.0293983 | ||||||||
\(969\) | 2.90660e144 | 0.423334 | ||||||||
\(970\) | −1.11614e145 | −1.54628 | ||||||||
\(971\) | −4.08826e144 | −0.538773 | −0.269386 | − | 0.963032i | \(-0.586821\pi\) | ||||
−0.269386 | + | 0.963032i | \(0.586821\pi\) | |||||||
\(972\) | −4.91242e143 | −0.0615860 | ||||||||
\(973\) | 3.20800e144 | 0.382614 | ||||||||
\(974\) | 2.20261e144 | 0.249936 | ||||||||
\(975\) | −6.89561e144 | −0.744473 | ||||||||
\(976\) | −9.54770e144 | −0.980805 | ||||||||
\(977\) | 1.04203e145 | 1.01858 | 0.509288 | − | 0.860596i | \(-0.329909\pi\) | ||||
0.509288 | + | 0.860596i | \(0.329909\pi\) | |||||||
\(978\) | 1.25143e145 | 1.16405 | ||||||||
\(979\) | −3.72038e144 | −0.329327 | ||||||||
\(980\) | −6.13399e144 | −0.516748 | ||||||||
\(981\) | −3.11808e143 | −0.0250000 | ||||||||
\(982\) | 2.07366e145 | 1.58245 | ||||||||
\(983\) | −8.25221e144 | −0.599411 | −0.299706 | − | 0.954032i | \(-0.596888\pi\) | ||||
−0.299706 | + | 0.954032i | \(0.596888\pi\) | |||||||
\(984\) | −1.20805e144 | −0.0835265 | ||||||||
\(985\) | 1.35052e144 | 0.0888883 | ||||||||
\(986\) | 6.87139e144 | 0.430541 | ||||||||
\(987\) | −3.30286e144 | −0.197019 | ||||||||
\(988\) | −3.03696e145 | −1.72475 | ||||||||
\(989\) | −1.20877e144 | −0.0653619 | ||||||||
\(990\) | −6.25200e143 | −0.0321893 | ||||||||
\(991\) | −5.52515e144 | −0.270877 | −0.135438 | − | 0.990786i | \(-0.543244\pi\) | ||||
−0.135438 | + | 0.990786i | \(0.543244\pi\) | |||||||
\(992\) | 4.49774e145 | 2.09980 | ||||||||
\(993\) | −1.76339e145 | −0.783987 | ||||||||
\(994\) | 1.03903e145 | 0.439933 | ||||||||
\(995\) | 2.10491e144 | 0.0848818 | ||||||||
\(996\) | −2.34234e145 | −0.899649 | ||||||||
\(997\) | 3.50363e145 | 1.28175 | 0.640875 | − | 0.767645i | \(-0.278571\pi\) | ||||
0.640875 | + | 0.767645i | \(0.278571\pi\) | |||||||
\(998\) | 6.81945e145 | 2.37639 | ||||||||
\(999\) | −1.47505e145 | −0.489644 |
(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 | 1.98.a.a.1.6 | ✓ | 7 | |
3.2 | odd | 2 | 9.98.a.a.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.98.a.a.1.6 | ✓ | 7 | 1.1 | even | 1 | trivial | |
9.98.a.a.1.2 | 7 | 3.2 | odd | 2 |