Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,110,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, 110, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 110);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 110 \) |
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: | \(75.2394221917\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2 x^{7} + \cdots + 46\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{118}\cdot 3^{40}\cdot 5^{14}\cdot 7^{6}\cdot 11^{3}\cdot 13 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.47185e14\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.71735e16 | −1.85167 | −0.925835 | − | 0.377928i | \(-0.876637\pi\) | ||||
−0.925835 | + | 0.377928i | \(0.876637\pi\) | |||||||
\(3\) | −1.38575e26 | −1.37586 | −0.687932 | − | 0.725775i | \(-0.741481\pi\) | ||||
−0.687932 | + | 0.725775i | \(0.741481\pi\) | |||||||
\(4\) | 1.57631e33 | 2.42868 | ||||||||
\(5\) | −1.39304e38 | −1.12227 | −0.561137 | − | 0.827723i | \(-0.689636\pi\) | ||||
−0.561137 | + | 0.827723i | \(0.689636\pi\) | |||||||
\(6\) | 6.53705e42 | 2.54765 | ||||||||
\(7\) | 1.59904e46 | 1.39964 | 0.699821 | − | 0.714318i | \(-0.253263\pi\) | ||||
0.699821 | + | 0.714318i | \(0.253263\pi\) | |||||||
\(8\) | −4.37425e49 | −2.64545 | ||||||||
\(9\) | 9.05875e51 | 0.893000 | ||||||||
\(10\) | 6.57147e54 | 2.07808 | ||||||||
\(11\) | −5.93232e56 | −1.04069 | −0.520347 | − | 0.853955i | \(-0.674198\pi\) | ||||
−0.520347 | + | 0.853955i | \(0.674198\pi\) | |||||||
\(12\) | −2.18436e59 | −3.34154 | ||||||||
\(13\) | 1.89568e60 | 0.369703 | 0.184851 | − | 0.982766i | \(-0.440820\pi\) | ||||
0.184851 | + | 0.982766i | \(0.440820\pi\) | |||||||
\(14\) | −7.54325e62 | −2.59167 | ||||||||
\(15\) | 1.93040e64 | 1.54410 | ||||||||
\(16\) | 1.04041e66 | 2.46982 | ||||||||
\(17\) | −1.15719e67 | −1.00911 | −0.504553 | − | 0.863381i | \(-0.668343\pi\) | ||||
−0.504553 | + | 0.863381i | \(0.668343\pi\) | |||||||
\(18\) | −4.27333e68 | −1.65354 | ||||||||
\(19\) | −3.88309e69 | −0.789053 | −0.394527 | − | 0.918885i | \(-0.629091\pi\) | ||||
−0.394527 | + | 0.918885i | \(0.629091\pi\) | |||||||
\(20\) | −2.19586e71 | −2.72565 | ||||||||
\(21\) | −2.21587e72 | −1.92572 | ||||||||
\(22\) | 2.79849e73 | 1.92702 | ||||||||
\(23\) | −1.96493e74 | −1.20000 | −0.599998 | − | 0.800001i | \(-0.704832\pi\) | ||||
−0.599998 | + | 0.800001i | \(0.704832\pi\) | |||||||
\(24\) | 6.06160e75 | 3.63978 | ||||||||
\(25\) | 3.99823e75 | 0.259500 | ||||||||
\(26\) | −8.94260e76 | −0.684567 | ||||||||
\(27\) | 1.50412e77 | 0.147217 | ||||||||
\(28\) | 2.52058e79 | 3.39929 | ||||||||
\(29\) | 5.20249e79 | 1.03638 | 0.518191 | − | 0.855265i | \(-0.326605\pi\) | ||||
0.518191 | + | 0.855265i | \(0.326605\pi\) | |||||||
\(30\) | −9.10639e80 | −2.85916 | ||||||||
\(31\) | 8.91312e80 | 0.468616 | 0.234308 | − | 0.972162i | \(-0.424718\pi\) | ||||
0.234308 | + | 0.972162i | \(0.424718\pi\) | |||||||
\(32\) | −2.06892e82 | −1.92784 | ||||||||
\(33\) | 8.22069e82 | 1.43185 | ||||||||
\(34\) | 5.45885e83 | 1.86853 | ||||||||
\(35\) | −2.22753e84 | −1.57078 | ||||||||
\(36\) | 1.42794e85 | 2.16881 | ||||||||
\(37\) | 1.37849e85 | 0.470336 | 0.235168 | − | 0.971955i | \(-0.424436\pi\) | ||||
0.235168 | + | 0.971955i | \(0.424436\pi\) | |||||||
\(38\) | 1.83179e86 | 1.46107 | ||||||||
\(39\) | −2.62693e86 | −0.508660 | ||||||||
\(40\) | 6.09352e87 | 2.96892 | ||||||||
\(41\) | 8.15104e87 | 1.03393 | 0.516967 | − | 0.856005i | \(-0.327061\pi\) | ||||
0.516967 | + | 0.856005i | \(0.327061\pi\) | |||||||
\(42\) | 1.04530e89 | 3.56579 | ||||||||
\(43\) | 3.10377e88 | 0.293670 | 0.146835 | − | 0.989161i | \(-0.453091\pi\) | ||||
0.146835 | + | 0.989161i | \(0.453091\pi\) | |||||||
\(44\) | −9.35115e89 | −2.52752 | ||||||||
\(45\) | −1.26192e90 | −1.00219 | ||||||||
\(46\) | 9.26927e90 | 2.22200 | ||||||||
\(47\) | −1.80658e91 | −1.34129 | −0.670647 | − | 0.741776i | \(-0.733984\pi\) | ||||
−0.670647 | + | 0.741776i | \(0.733984\pi\) | |||||||
\(48\) | −1.44174e92 | −3.39813 | ||||||||
\(49\) | 1.25171e92 | 0.958997 | ||||||||
\(50\) | −1.88610e92 | −0.480508 | ||||||||
\(51\) | 1.60356e93 | 1.38839 | ||||||||
\(52\) | 2.98817e93 | 0.897890 | ||||||||
\(53\) | 1.31683e94 | 1.40118 | 0.700592 | − | 0.713562i | \(-0.252919\pi\) | ||||
0.700592 | + | 0.713562i | \(0.252919\pi\) | |||||||
\(54\) | −7.09548e93 | −0.272598 | ||||||||
\(55\) | 8.26397e94 | 1.16794 | ||||||||
\(56\) | −6.99461e95 | −3.70268 | ||||||||
\(57\) | 5.38098e95 | 1.08563 | ||||||||
\(58\) | −2.45420e96 | −1.91904 | ||||||||
\(59\) | −5.81637e95 | −0.179150 | −0.0895751 | − | 0.995980i | \(-0.528551\pi\) | ||||
−0.0895751 | + | 0.995980i | \(0.528551\pi\) | |||||||
\(60\) | 3.04290e97 | 3.75012 | ||||||||
\(61\) | −2.73879e97 | −1.37114 | −0.685572 | − | 0.728005i | \(-0.740448\pi\) | ||||
−0.685572 | + | 0.728005i | \(0.740448\pi\) | |||||||
\(62\) | −4.20463e97 | −0.867723 | ||||||||
\(63\) | 1.44853e98 | 1.24988 | ||||||||
\(64\) | 3.00720e98 | 1.09990 | ||||||||
\(65\) | −2.64076e98 | −0.414908 | ||||||||
\(66\) | −3.87799e99 | −2.65132 | ||||||||
\(67\) | 1.37350e99 | 0.413763 | 0.206881 | − | 0.978366i | \(-0.433669\pi\) | ||||
0.206881 | + | 0.978366i | \(0.433669\pi\) | |||||||
\(68\) | −1.82408e100 | −2.45080 | ||||||||
\(69\) | 2.72289e100 | 1.65103 | ||||||||
\(70\) | 1.05081e101 | 2.90857 | ||||||||
\(71\) | −9.18618e99 | −0.117369 | −0.0586847 | − | 0.998277i | \(-0.518691\pi\) | ||||
−0.0586847 | + | 0.998277i | \(0.518691\pi\) | |||||||
\(72\) | −3.96252e101 | −2.36239 | ||||||||
\(73\) | −1.17575e101 | −0.330535 | −0.165267 | − | 0.986249i | \(-0.552849\pi\) | ||||
−0.165267 | + | 0.986249i | \(0.552849\pi\) | |||||||
\(74\) | −6.50281e101 | −0.870908 | ||||||||
\(75\) | −5.54053e101 | −0.357036 | ||||||||
\(76\) | −6.12094e102 | −1.91636 | ||||||||
\(77\) | −9.48603e102 | −1.45660 | ||||||||
\(78\) | 1.23922e103 | 0.941871 | ||||||||
\(79\) | 4.74076e103 | 1.79958 | 0.899792 | − | 0.436320i | \(-0.143718\pi\) | ||||
0.899792 | + | 0.436320i | \(0.143718\pi\) | |||||||
\(80\) | −1.44933e104 | −2.77181 | ||||||||
\(81\) | −1.12737e104 | −1.09555 | ||||||||
\(82\) | −3.84513e104 | −1.91450 | ||||||||
\(83\) | 7.42464e104 | 1.90950 | 0.954749 | − | 0.297412i | \(-0.0961235\pi\) | ||||
0.954749 | + | 0.297412i | \(0.0961235\pi\) | |||||||
\(84\) | −3.49288e105 | −4.67695 | ||||||||
\(85\) | 1.61201e105 | 1.13249 | ||||||||
\(86\) | −1.46416e105 | −0.543780 | ||||||||
\(87\) | −7.20933e105 | −1.42592 | ||||||||
\(88\) | 2.59495e106 | 2.75310 | ||||||||
\(89\) | −1.07483e106 | −0.616004 | −0.308002 | − | 0.951386i | \(-0.599660\pi\) | ||||
−0.308002 | + | 0.951386i | \(0.599660\pi\) | |||||||
\(90\) | 5.95293e106 | 1.85573 | ||||||||
\(91\) | 3.03128e106 | 0.517451 | ||||||||
\(92\) | −3.09733e107 | −2.91441 | ||||||||
\(93\) | −1.23513e107 | −0.644752 | ||||||||
\(94\) | 8.52228e107 | 2.48364 | ||||||||
\(95\) | 5.40931e107 | 0.885534 | ||||||||
\(96\) | 2.86700e108 | 2.65244 | ||||||||
\(97\) | 2.33996e108 | 1.23069 | 0.615344 | − | 0.788259i | \(-0.289017\pi\) | ||||
0.615344 | + | 0.788259i | \(0.289017\pi\) | |||||||
\(98\) | −5.90475e108 | −1.77575 | ||||||||
\(99\) | −5.37394e108 | −0.929340 | ||||||||
\(100\) | 6.30242e108 | 0.630242 | ||||||||
\(101\) | 9.45240e108 | 0.549575 | 0.274788 | − | 0.961505i | \(-0.411392\pi\) | ||||
0.274788 | + | 0.961505i | \(0.411392\pi\) | |||||||
\(102\) | −7.56458e109 | −2.57084 | ||||||||
\(103\) | −1.41845e109 | −0.283261 | −0.141630 | − | 0.989920i | \(-0.545234\pi\) | ||||
−0.141630 | + | 0.989920i | \(0.545234\pi\) | |||||||
\(104\) | −8.29218e109 | −0.978030 | ||||||||
\(105\) | 3.08680e110 | 2.16118 | ||||||||
\(106\) | −6.21195e110 | −2.59453 | ||||||||
\(107\) | 5.22090e110 | 1.30716 | 0.653581 | − | 0.756856i | \(-0.273266\pi\) | ||||
0.653581 | + | 0.756856i | \(0.273266\pi\) | |||||||
\(108\) | 2.37096e110 | 0.357544 | ||||||||
\(109\) | −5.92760e110 | −0.540922 | −0.270461 | − | 0.962731i | \(-0.587176\pi\) | ||||
−0.270461 | + | 0.962731i | \(0.587176\pi\) | |||||||
\(110\) | −3.89841e111 | −2.16265 | ||||||||
\(111\) | −1.91023e111 | −0.647118 | ||||||||
\(112\) | 1.66366e112 | 3.45686 | ||||||||
\(113\) | 7.64888e111 | 0.979090 | 0.489545 | − | 0.871978i | \(-0.337163\pi\) | ||||
0.489545 | + | 0.871978i | \(0.337163\pi\) | |||||||
\(114\) | −2.53840e112 | −2.01023 | ||||||||
\(115\) | 2.73723e112 | 1.34673 | ||||||||
\(116\) | 8.20071e112 | 2.51704 | ||||||||
\(117\) | 1.71725e112 | 0.330145 | ||||||||
\(118\) | 2.74379e112 | 0.331727 | ||||||||
\(119\) | −1.85039e113 | −1.41239 | ||||||||
\(120\) | −8.44407e113 | −4.08483 | ||||||||
\(121\) | 2.69847e112 | 0.0830453 | ||||||||
\(122\) | 1.29198e114 | 2.53891 | ||||||||
\(123\) | −1.12953e114 | −1.42255 | ||||||||
\(124\) | 1.40498e114 | 1.13812 | ||||||||
\(125\) | 1.58935e114 | 0.831044 | ||||||||
\(126\) | −6.83324e114 | −2.31437 | ||||||||
\(127\) | −1.46989e114 | −0.323580 | −0.161790 | − | 0.986825i | \(-0.551727\pi\) | ||||
−0.161790 | + | 0.986825i | \(0.551727\pi\) | |||||||
\(128\) | −7.57951e113 | −0.108817 | ||||||||
\(129\) | −4.30104e114 | −0.404049 | ||||||||
\(130\) | 1.24574e115 | 0.768273 | ||||||||
\(131\) | 4.52763e114 | 0.183902 | 0.0919508 | − | 0.995764i | \(-0.470690\pi\) | ||||
0.0919508 | + | 0.995764i | \(0.470690\pi\) | |||||||
\(132\) | 1.29583e116 | 3.47752 | ||||||||
\(133\) | −6.20923e115 | −1.10439 | ||||||||
\(134\) | −6.47927e115 | −0.766152 | ||||||||
\(135\) | −2.09531e115 | −0.165218 | ||||||||
\(136\) | 5.06182e116 | 2.66954 | ||||||||
\(137\) | 9.68902e115 | 0.342775 | 0.171387 | − | 0.985204i | \(-0.445175\pi\) | ||||
0.171387 | + | 0.985204i | \(0.445175\pi\) | |||||||
\(138\) | −1.28449e117 | −3.05717 | ||||||||
\(139\) | 1.81881e116 | 0.292066 | 0.146033 | − | 0.989280i | \(-0.453349\pi\) | ||||
0.146033 | + | 0.989280i | \(0.453349\pi\) | |||||||
\(140\) | −3.51127e117 | −3.81493 | ||||||||
\(141\) | 2.50346e117 | 1.84544 | ||||||||
\(142\) | 4.33344e116 | 0.217329 | ||||||||
\(143\) | −1.12458e117 | −0.384748 | ||||||||
\(144\) | 9.42480e117 | 2.20555 | ||||||||
\(145\) | −7.24729e117 | −1.16311 | ||||||||
\(146\) | 5.54641e117 | 0.612042 | ||||||||
\(147\) | −1.73455e118 | −1.31945 | ||||||||
\(148\) | 2.17291e118 | 1.14230 | ||||||||
\(149\) | −6.34226e117 | −0.230990 | −0.115495 | − | 0.993308i | \(-0.536845\pi\) | ||||
−0.115495 | + | 0.993308i | \(0.536845\pi\) | |||||||
\(150\) | 2.61366e118 | 0.661113 | ||||||||
\(151\) | −6.83251e118 | −1.20320 | −0.601598 | − | 0.798799i | \(-0.705469\pi\) | ||||
−0.601598 | + | 0.798799i | \(0.705469\pi\) | |||||||
\(152\) | 1.69856e119 | 2.08740 | ||||||||
\(153\) | −1.04827e119 | −0.901132 | ||||||||
\(154\) | 4.47490e119 | 2.69714 | ||||||||
\(155\) | −1.24163e119 | −0.525916 | ||||||||
\(156\) | −4.14085e119 | −1.23537 | ||||||||
\(157\) | 1.79026e119 | 0.377037 | 0.188519 | − | 0.982070i | \(-0.439631\pi\) | ||||
0.188519 | + | 0.982070i | \(0.439631\pi\) | |||||||
\(158\) | −2.23639e120 | −3.33223 | ||||||||
\(159\) | −1.82479e120 | −1.92784 | ||||||||
\(160\) | 2.88209e120 | 2.16356 | ||||||||
\(161\) | −3.14201e120 | −1.67957 | ||||||||
\(162\) | 5.31820e120 | 2.02860 | ||||||||
\(163\) | 4.13047e120 | 1.12661 | 0.563306 | − | 0.826248i | \(-0.309529\pi\) | ||||
0.563306 | + | 0.826248i | \(0.309529\pi\) | |||||||
\(164\) | 1.28485e121 | 2.51110 | ||||||||
\(165\) | −1.14518e121 | −1.60693 | ||||||||
\(166\) | −3.50246e121 | −3.53576 | ||||||||
\(167\) | 1.26735e121 | 0.922250 | 0.461125 | − | 0.887335i | \(-0.347446\pi\) | ||||
0.461125 | + | 0.887335i | \(0.347446\pi\) | |||||||
\(168\) | 9.69276e121 | 5.09438 | ||||||||
\(169\) | −2.26985e121 | −0.863320 | ||||||||
\(170\) | −7.60441e121 | −2.09700 | ||||||||
\(171\) | −3.51759e121 | −0.704625 | ||||||||
\(172\) | 4.89249e121 | 0.713231 | ||||||||
\(173\) | −1.71087e122 | −1.81846 | −0.909231 | − | 0.416292i | \(-0.863330\pi\) | ||||
−0.909231 | + | 0.416292i | \(0.863330\pi\) | |||||||
\(174\) | 3.40089e122 | 2.64034 | ||||||||
\(175\) | 6.39333e121 | 0.363207 | ||||||||
\(176\) | −6.17203e122 | −2.57032 | ||||||||
\(177\) | 8.06001e121 | 0.246486 | ||||||||
\(178\) | 5.07035e122 | 1.14064 | ||||||||
\(179\) | −4.41932e122 | −0.732598 | −0.366299 | − | 0.930497i | \(-0.619375\pi\) | ||||
−0.366299 | + | 0.930497i | \(0.619375\pi\) | |||||||
\(180\) | −1.98917e123 | −2.43400 | ||||||||
\(181\) | 6.21437e122 | 0.562231 | 0.281115 | − | 0.959674i | \(-0.409296\pi\) | ||||
0.281115 | + | 0.959674i | \(0.409296\pi\) | |||||||
\(182\) | −1.42996e123 | −0.958149 | ||||||||
\(183\) | 3.79527e123 | 1.88651 | ||||||||
\(184\) | 8.59510e123 | 3.17453 | ||||||||
\(185\) | −1.92029e123 | −0.527846 | ||||||||
\(186\) | 5.82655e123 | 1.19387 | ||||||||
\(187\) | 6.86479e123 | 1.05017 | ||||||||
\(188\) | −2.84772e124 | −3.25758 | ||||||||
\(189\) | 2.40516e123 | 0.206051 | ||||||||
\(190\) | −2.55176e124 | −1.63972 | ||||||||
\(191\) | 3.71768e124 | 1.79454 | 0.897271 | − | 0.441481i | \(-0.145547\pi\) | ||||
0.897271 | + | 0.441481i | \(0.145547\pi\) | |||||||
\(192\) | −4.16721e124 | −1.51331 | ||||||||
\(193\) | 1.92715e124 | 0.527280 | 0.263640 | − | 0.964621i | \(-0.415077\pi\) | ||||
0.263640 | + | 0.964621i | \(0.415077\pi\) | |||||||
\(194\) | −1.10384e125 | −2.27883 | ||||||||
\(195\) | 3.65943e124 | 0.570857 | ||||||||
\(196\) | 1.97308e125 | 2.32910 | ||||||||
\(197\) | −7.39002e124 | −0.661053 | −0.330526 | − | 0.943797i | \(-0.607226\pi\) | ||||
−0.330526 | + | 0.943797i | \(0.607226\pi\) | |||||||
\(198\) | 2.53508e125 | 1.72083 | ||||||||
\(199\) | −2.88558e125 | −1.48847 | −0.744235 | − | 0.667918i | \(-0.767186\pi\) | ||||
−0.744235 | + | 0.667918i | \(0.767186\pi\) | |||||||
\(200\) | −1.74892e125 | −0.686493 | ||||||||
\(201\) | −1.90332e125 | −0.569281 | ||||||||
\(202\) | −4.45903e125 | −1.01763 | ||||||||
\(203\) | 8.31900e125 | 1.45056 | ||||||||
\(204\) | 2.52771e126 | 3.37196 | ||||||||
\(205\) | −1.13547e126 | −1.16036 | ||||||||
\(206\) | 6.69135e125 | 0.524506 | ||||||||
\(207\) | −1.77998e126 | −1.07160 | ||||||||
\(208\) | 1.97228e126 | 0.913098 | ||||||||
\(209\) | 2.30357e126 | 0.821163 | ||||||||
\(210\) | −1.45615e127 | −4.00180 | ||||||||
\(211\) | −6.69610e126 | −1.42046 | −0.710229 | − | 0.703971i | \(-0.751408\pi\) | ||||
−0.710229 | + | 0.703971i | \(0.751408\pi\) | |||||||
\(212\) | 2.07573e127 | 3.40303 | ||||||||
\(213\) | 1.27297e126 | 0.161484 | ||||||||
\(214\) | −2.46288e127 | −2.42043 | ||||||||
\(215\) | −4.32369e126 | −0.329578 | ||||||||
\(216\) | −6.57942e126 | −0.389456 | ||||||||
\(217\) | 1.42525e127 | 0.655895 | ||||||||
\(218\) | 2.79626e127 | 1.00161 | ||||||||
\(219\) | 1.62928e127 | 0.454771 | ||||||||
\(220\) | 1.30265e128 | 2.83657 | ||||||||
\(221\) | −2.19365e127 | −0.373069 | ||||||||
\(222\) | 9.01124e127 | 1.19825 | ||||||||
\(223\) | −1.21785e128 | −1.26759 | −0.633794 | − | 0.773502i | \(-0.718503\pi\) | ||||
−0.633794 | + | 0.773502i | \(0.718503\pi\) | |||||||
\(224\) | −3.30829e128 | −2.69828 | ||||||||
\(225\) | 3.62189e127 | 0.231733 | ||||||||
\(226\) | −3.60825e128 | −1.81295 | ||||||||
\(227\) | 1.34197e128 | 0.530071 | 0.265036 | − | 0.964239i | \(-0.414616\pi\) | ||||
0.265036 | + | 0.964239i | \(0.414616\pi\) | |||||||
\(228\) | 8.48206e128 | 2.63665 | ||||||||
\(229\) | 4.19421e128 | 1.02711 | 0.513555 | − | 0.858057i | \(-0.328328\pi\) | ||||
0.513555 | + | 0.858057i | \(0.328328\pi\) | |||||||
\(230\) | −1.29125e129 | −2.49369 | ||||||||
\(231\) | 1.31452e129 | 2.00408 | ||||||||
\(232\) | −2.27570e129 | −2.74170 | ||||||||
\(233\) | 2.65404e128 | 0.252935 | 0.126468 | − | 0.991971i | \(-0.459636\pi\) | ||||
0.126468 | + | 0.991971i | \(0.459636\pi\) | |||||||
\(234\) | −8.10088e128 | −0.611319 | ||||||||
\(235\) | 2.51664e129 | 1.50530 | ||||||||
\(236\) | −9.16837e128 | −0.435099 | ||||||||
\(237\) | −6.56950e129 | −2.47598 | ||||||||
\(238\) | 8.72894e129 | 2.61527 | ||||||||
\(239\) | −5.27383e129 | −1.25731 | −0.628653 | − | 0.777686i | \(-0.716393\pi\) | ||||
−0.628653 | + | 0.777686i | \(0.716393\pi\) | |||||||
\(240\) | 2.00841e130 | 3.81363 | ||||||||
\(241\) | 3.26287e128 | 0.0493936 | 0.0246968 | − | 0.999695i | \(-0.492138\pi\) | ||||
0.0246968 | + | 0.999695i | \(0.492138\pi\) | |||||||
\(242\) | −1.27296e129 | −0.153773 | ||||||||
\(243\) | 1.40967e130 | 1.36011 | ||||||||
\(244\) | −4.31717e130 | −3.33007 | ||||||||
\(245\) | −1.74368e130 | −1.07626 | ||||||||
\(246\) | 5.32838e130 | 2.63410 | ||||||||
\(247\) | −7.36110e129 | −0.291715 | ||||||||
\(248\) | −3.89882e130 | −1.23970 | ||||||||
\(249\) | −1.02887e131 | −2.62721 | ||||||||
\(250\) | −7.49753e130 | −1.53882 | ||||||||
\(251\) | 4.44276e130 | 0.733558 | 0.366779 | − | 0.930308i | \(-0.380460\pi\) | ||||
0.366779 | + | 0.930308i | \(0.380460\pi\) | |||||||
\(252\) | 2.28333e131 | 3.03556 | ||||||||
\(253\) | 1.16566e131 | 1.24883 | ||||||||
\(254\) | 6.93398e130 | 0.599163 | ||||||||
\(255\) | −2.23383e131 | −1.55816 | ||||||||
\(256\) | −1.59423e131 | −0.898407 | ||||||||
\(257\) | 1.62556e131 | 0.740709 | 0.370354 | − | 0.928891i | \(-0.379236\pi\) | ||||
0.370354 | + | 0.928891i | \(0.379236\pi\) | |||||||
\(258\) | 2.02895e131 | 0.748166 | ||||||||
\(259\) | 2.20426e131 | 0.658302 | ||||||||
\(260\) | −4.16265e131 | −1.00768 | ||||||||
\(261\) | 4.71280e131 | 0.925490 | ||||||||
\(262\) | −2.13584e131 | −0.340525 | ||||||||
\(263\) | 1.49206e132 | 1.93285 | 0.966425 | − | 0.256949i | \(-0.0827171\pi\) | ||||
0.966425 | + | 0.256949i | \(0.0827171\pi\) | |||||||
\(264\) | −3.59594e132 | −3.78790 | ||||||||
\(265\) | −1.83440e132 | −1.57251 | ||||||||
\(266\) | 2.92911e132 | 2.04497 | ||||||||
\(267\) | 1.48944e132 | 0.847538 | ||||||||
\(268\) | 2.16505e132 | 1.00490 | ||||||||
\(269\) | −2.00465e132 | −0.759520 | −0.379760 | − | 0.925085i | \(-0.623993\pi\) | ||||
−0.379760 | + | 0.925085i | \(0.623993\pi\) | |||||||
\(270\) | 9.88431e131 | 0.305929 | ||||||||
\(271\) | −8.97234e131 | −0.227028 | −0.113514 | − | 0.993536i | \(-0.536211\pi\) | ||||
−0.113514 | + | 0.993536i | \(0.536211\pi\) | |||||||
\(272\) | −1.20394e133 | −2.49231 | ||||||||
\(273\) | −4.20058e132 | −0.711942 | ||||||||
\(274\) | −4.57065e132 | −0.634706 | ||||||||
\(275\) | −2.37188e132 | −0.270060 | ||||||||
\(276\) | 4.29211e133 | 4.00983 | ||||||||
\(277\) | 7.68228e132 | 0.589309 | 0.294654 | − | 0.955604i | \(-0.404795\pi\) | ||||
0.294654 | + | 0.955604i | \(0.404795\pi\) | |||||||
\(278\) | −8.57998e132 | −0.540810 | ||||||||
\(279\) | 8.07417e132 | 0.418474 | ||||||||
\(280\) | 9.74379e133 | 4.15542 | ||||||||
\(281\) | −2.42903e133 | −0.852978 | −0.426489 | − | 0.904493i | \(-0.640250\pi\) | ||||
−0.426489 | + | 0.904493i | \(0.640250\pi\) | |||||||
\(282\) | −1.18097e134 | −3.41714 | ||||||||
\(283\) | −5.67399e133 | −1.35372 | −0.676859 | − | 0.736113i | \(-0.736659\pi\) | ||||
−0.676859 | + | 0.736113i | \(0.736659\pi\) | |||||||
\(284\) | −1.44802e133 | −0.285053 | ||||||||
\(285\) | −7.49593e133 | −1.21837 | ||||||||
\(286\) | 5.30504e133 | 0.712426 | ||||||||
\(287\) | 1.30339e134 | 1.44714 | ||||||||
\(288\) | −1.87418e134 | −1.72156 | ||||||||
\(289\) | 2.40573e132 | 0.0182943 | ||||||||
\(290\) | 3.41880e134 | 2.15369 | ||||||||
\(291\) | −3.24258e134 | −1.69326 | ||||||||
\(292\) | −1.85333e134 | −0.802764 | ||||||||
\(293\) | 2.19518e134 | 0.789195 | 0.394597 | − | 0.918854i | \(-0.370884\pi\) | ||||
0.394597 | + | 0.918854i | \(0.370884\pi\) | |||||||
\(294\) | 8.18249e134 | 2.44318 | ||||||||
\(295\) | 8.10245e133 | 0.201056 | ||||||||
\(296\) | −6.02984e134 | −1.24425 | ||||||||
\(297\) | −8.92295e133 | −0.153208 | ||||||||
\(298\) | 2.99187e134 | 0.427717 | ||||||||
\(299\) | −3.72488e134 | −0.443642 | ||||||||
\(300\) | −8.73356e134 | −0.867128 | ||||||||
\(301\) | 4.96307e134 | 0.411032 | ||||||||
\(302\) | 3.22314e135 | 2.22792 | ||||||||
\(303\) | −1.30986e135 | −0.756141 | ||||||||
\(304\) | −4.04000e135 | −1.94882 | ||||||||
\(305\) | 3.81525e135 | 1.53880 | ||||||||
\(306\) | 4.94504e135 | 1.66860 | ||||||||
\(307\) | −3.90972e135 | −1.10434 | −0.552172 | − | 0.833730i | \(-0.686201\pi\) | ||||
−0.552172 | + | 0.833730i | \(0.686201\pi\) | |||||||
\(308\) | −1.49529e136 | −3.53762 | ||||||||
\(309\) | 1.96562e135 | 0.389728 | ||||||||
\(310\) | 5.85723e135 | 0.973823 | ||||||||
\(311\) | −3.06682e135 | −0.427806 | −0.213903 | − | 0.976855i | \(-0.568618\pi\) | ||||
−0.213903 | + | 0.976855i | \(0.568618\pi\) | |||||||
\(312\) | 1.14909e136 | 1.34564 | ||||||||
\(313\) | −1.43759e136 | −1.41406 | −0.707029 | − | 0.707184i | \(-0.749965\pi\) | ||||
−0.707029 | + | 0.707184i | \(0.749965\pi\) | |||||||
\(314\) | −8.44527e135 | −0.698149 | ||||||||
\(315\) | −2.01787e136 | −1.40271 | ||||||||
\(316\) | 7.47289e136 | 4.37062 | ||||||||
\(317\) | −2.09847e136 | −1.03317 | −0.516585 | − | 0.856236i | \(-0.672797\pi\) | ||||
−0.516585 | + | 0.856236i | \(0.672797\pi\) | |||||||
\(318\) | 8.60819e136 | 3.56972 | ||||||||
\(319\) | −3.08628e136 | −1.07856 | ||||||||
\(320\) | −4.18915e136 | −1.23439 | ||||||||
\(321\) | −7.23484e136 | −1.79848 | ||||||||
\(322\) | 1.48220e137 | 3.11000 | ||||||||
\(323\) | 4.49345e136 | 0.796238 | ||||||||
\(324\) | −1.77708e137 | −2.66075 | ||||||||
\(325\) | 7.57936e135 | 0.0959377 | ||||||||
\(326\) | −1.94849e137 | −2.08612 | ||||||||
\(327\) | 8.21414e136 | 0.744234 | ||||||||
\(328\) | −3.56547e137 | −2.73522 | ||||||||
\(329\) | −2.88880e137 | −1.87733 | ||||||||
\(330\) | 5.40220e137 | 2.97551 | ||||||||
\(331\) | 1.86462e137 | 0.870895 | 0.435447 | − | 0.900214i | \(-0.356590\pi\) | ||||
0.435447 | + | 0.900214i | \(0.356590\pi\) | |||||||
\(332\) | 1.17035e138 | 4.63757 | ||||||||
\(333\) | 1.24874e137 | 0.420010 | ||||||||
\(334\) | −5.97853e137 | −1.70770 | ||||||||
\(335\) | −1.91334e137 | −0.464355 | ||||||||
\(336\) | −2.30541e138 | −4.75616 | ||||||||
\(337\) | 7.88367e137 | 1.38324 | 0.691622 | − | 0.722260i | \(-0.256896\pi\) | ||||
0.691622 | + | 0.722260i | \(0.256896\pi\) | |||||||
\(338\) | 1.07077e138 | 1.59858 | ||||||||
\(339\) | −1.05994e138 | −1.34709 | ||||||||
\(340\) | 2.54102e138 | 2.75047 | ||||||||
\(341\) | −5.28755e137 | −0.487686 | ||||||||
\(342\) | 1.65937e138 | 1.30473 | ||||||||
\(343\) | −8.55787e136 | −0.0573900 | ||||||||
\(344\) | −1.35767e138 | −0.776888 | ||||||||
\(345\) | −3.79311e138 | −1.85291 | ||||||||
\(346\) | 8.07078e138 | 3.36719 | ||||||||
\(347\) | −2.10832e138 | −0.751588 | −0.375794 | − | 0.926703i | \(-0.622630\pi\) | ||||
−0.375794 | + | 0.926703i | \(0.622630\pi\) | |||||||
\(348\) | −1.13641e139 | −3.46311 | ||||||||
\(349\) | 2.35789e138 | 0.614522 | 0.307261 | − | 0.951625i | \(-0.400588\pi\) | ||||
0.307261 | + | 0.951625i | \(0.400588\pi\) | |||||||
\(350\) | −3.01596e138 | −0.672539 | ||||||||
\(351\) | 2.85134e137 | 0.0544266 | ||||||||
\(352\) | 1.22735e139 | 2.00629 | ||||||||
\(353\) | −9.68777e138 | −1.35676 | −0.678379 | − | 0.734712i | \(-0.737317\pi\) | ||||
−0.678379 | + | 0.734712i | \(0.737317\pi\) | |||||||
\(354\) | −3.80219e138 | −0.456411 | ||||||||
\(355\) | 1.27967e138 | 0.131721 | ||||||||
\(356\) | −1.69426e139 | −1.49608 | ||||||||
\(357\) | 2.56417e139 | 1.94325 | ||||||||
\(358\) | 2.08475e139 | 1.35653 | ||||||||
\(359\) | −6.41840e138 | −0.358740 | −0.179370 | − | 0.983782i | \(-0.557406\pi\) | ||||
−0.179370 | + | 0.983782i | \(0.557406\pi\) | |||||||
\(360\) | 5.51996e139 | 2.65125 | ||||||||
\(361\) | −9.13984e138 | −0.377395 | ||||||||
\(362\) | −2.93154e139 | −1.04107 | ||||||||
\(363\) | −3.73940e138 | −0.114259 | ||||||||
\(364\) | 4.77821e139 | 1.25672 | ||||||||
\(365\) | 1.63786e139 | 0.370951 | ||||||||
\(366\) | −1.79036e140 | −3.49319 | ||||||||
\(367\) | 1.74773e139 | 0.293883 | 0.146942 | − | 0.989145i | \(-0.453057\pi\) | ||||
0.146942 | + | 0.989145i | \(0.453057\pi\) | |||||||
\(368\) | −2.04433e140 | −2.96377 | ||||||||
\(369\) | 7.38382e139 | 0.923303 | ||||||||
\(370\) | 9.05868e139 | 0.977397 | ||||||||
\(371\) | 2.10567e140 | 1.96115 | ||||||||
\(372\) | −1.94694e140 | −1.56590 | ||||||||
\(373\) | 1.93532e140 | 1.34469 | 0.672344 | − | 0.740239i | \(-0.265288\pi\) | ||||
0.672344 | + | 0.740239i | \(0.265288\pi\) | |||||||
\(374\) | −3.23837e140 | −1.94457 | ||||||||
\(375\) | −2.20244e140 | −1.14340 | ||||||||
\(376\) | 7.90244e140 | 3.54833 | ||||||||
\(377\) | 9.86226e139 | 0.383154 | ||||||||
\(378\) | −1.13460e140 | −0.381539 | ||||||||
\(379\) | −4.29785e140 | −1.25145 | −0.625727 | − | 0.780042i | \(-0.715198\pi\) | ||||
−0.625727 | + | 0.780042i | \(0.715198\pi\) | |||||||
\(380\) | 8.52672e140 | 2.15068 | ||||||||
\(381\) | 2.03689e140 | 0.445202 | ||||||||
\(382\) | −1.75376e141 | −3.32290 | ||||||||
\(383\) | −2.42666e139 | −0.0398727 | −0.0199363 | − | 0.999801i | \(-0.506346\pi\) | ||||
−0.0199363 | + | 0.999801i | \(0.506346\pi\) | |||||||
\(384\) | 1.05033e140 | 0.149718 | ||||||||
\(385\) | 1.32144e141 | 1.63470 | ||||||||
\(386\) | −9.09103e140 | −0.976349 | ||||||||
\(387\) | 2.81163e140 | 0.262247 | ||||||||
\(388\) | 3.68848e141 | 2.98895 | ||||||||
\(389\) | −1.36551e141 | −0.961704 | −0.480852 | − | 0.876802i | \(-0.659672\pi\) | ||||
−0.480852 | + | 0.876802i | \(0.659672\pi\) | |||||||
\(390\) | −1.72628e141 | −1.05704 | ||||||||
\(391\) | 2.27379e141 | 1.21092 | ||||||||
\(392\) | −5.47529e141 | −2.53698 | ||||||||
\(393\) | −6.27415e140 | −0.253023 | ||||||||
\(394\) | 3.48613e141 | 1.22405 | ||||||||
\(395\) | −6.60408e141 | −2.01963 | ||||||||
\(396\) | −8.47097e141 | −2.25707 | ||||||||
\(397\) | −5.30890e141 | −1.23288 | −0.616442 | − | 0.787400i | \(-0.711426\pi\) | ||||
−0.616442 | + | 0.787400i | \(0.711426\pi\) | |||||||
\(398\) | 1.36123e142 | 2.75616 | ||||||||
\(399\) | 8.60441e141 | 1.51949 | ||||||||
\(400\) | 4.15979e141 | 0.640917 | ||||||||
\(401\) | 4.22919e141 | 0.568708 | 0.284354 | − | 0.958719i | \(-0.408221\pi\) | ||||
0.284354 | + | 0.958719i | \(0.408221\pi\) | |||||||
\(402\) | 8.97863e141 | 1.05412 | ||||||||
\(403\) | 1.68964e141 | 0.173249 | ||||||||
\(404\) | 1.48999e142 | 1.33474 | ||||||||
\(405\) | 1.57047e142 | 1.22951 | ||||||||
\(406\) | −3.92437e142 | −2.68597 | ||||||||
\(407\) | −8.17762e141 | −0.489476 | ||||||||
\(408\) | −7.01440e142 | −3.67292 | ||||||||
\(409\) | 2.87320e142 | 1.31657 | 0.658286 | − | 0.752768i | \(-0.271282\pi\) | ||||
0.658286 | + | 0.752768i | \(0.271282\pi\) | |||||||
\(410\) | 5.35643e142 | 2.14860 | ||||||||
\(411\) | −1.34265e142 | −0.471611 | ||||||||
\(412\) | −2.23592e142 | −0.687950 | ||||||||
\(413\) | −9.30062e141 | −0.250746 | ||||||||
\(414\) | 8.39680e142 | 1.98424 | ||||||||
\(415\) | −1.03428e143 | −2.14298 | ||||||||
\(416\) | −3.92202e142 | −0.712726 | ||||||||
\(417\) | −2.52041e142 | −0.401843 | ||||||||
\(418\) | −1.08668e143 | −1.52052 | ||||||||
\(419\) | −1.40826e143 | −1.72990 | −0.864948 | − | 0.501862i | \(-0.832648\pi\) | ||||
−0.864948 | + | 0.501862i | \(0.832648\pi\) | |||||||
\(420\) | 4.86573e143 | 5.24882 | ||||||||
\(421\) | 1.82884e143 | 1.73301 | 0.866505 | − | 0.499169i | \(-0.166361\pi\) | ||||
0.866505 | + | 0.499169i | \(0.166361\pi\) | |||||||
\(422\) | 3.15879e143 | 2.63022 | ||||||||
\(423\) | −1.63654e143 | −1.19778 | ||||||||
\(424\) | −5.76015e143 | −3.70676 | ||||||||
\(425\) | −4.62669e142 | −0.261863 | ||||||||
\(426\) | −6.00505e142 | −0.299016 | ||||||||
\(427\) | −4.37944e143 | −1.91911 | ||||||||
\(428\) | 8.22973e143 | 3.17468 | ||||||||
\(429\) | 1.55838e143 | 0.529360 | ||||||||
\(430\) | 2.03964e143 | 0.610270 | ||||||||
\(431\) | −4.53523e143 | −1.19561 | −0.597803 | − | 0.801643i | \(-0.703960\pi\) | ||||
−0.597803 | + | 0.801643i | \(0.703960\pi\) | |||||||
\(432\) | 1.56490e143 | 0.363599 | ||||||||
\(433\) | 2.56699e143 | 0.525817 | 0.262908 | − | 0.964821i | \(-0.415318\pi\) | ||||
0.262908 | + | 0.964821i | \(0.415318\pi\) | |||||||
\(434\) | −6.72339e143 | −1.21450 | ||||||||
\(435\) | 1.00429e144 | 1.60027 | ||||||||
\(436\) | −9.34370e143 | −1.31373 | ||||||||
\(437\) | 7.63000e143 | 0.946861 | ||||||||
\(438\) | −7.68591e143 | −0.842086 | ||||||||
\(439\) | −4.56420e143 | −0.441620 | −0.220810 | − | 0.975317i | \(-0.570870\pi\) | ||||
−0.220810 | + | 0.975317i | \(0.570870\pi\) | |||||||
\(440\) | −3.61487e144 | −3.08974 | ||||||||
\(441\) | 1.13389e144 | 0.856384 | ||||||||
\(442\) | 1.03482e144 | 0.690801 | ||||||||
\(443\) | 5.83986e143 | 0.344667 | 0.172333 | − | 0.985039i | \(-0.444869\pi\) | ||||
0.172333 | + | 0.985039i | \(0.444869\pi\) | |||||||
\(444\) | −3.01111e144 | −1.57165 | ||||||||
\(445\) | 1.49728e144 | 0.691326 | ||||||||
\(446\) | 5.74502e144 | 2.34716 | ||||||||
\(447\) | 8.78876e143 | 0.317810 | ||||||||
\(448\) | 4.80864e144 | 1.53947 | ||||||||
\(449\) | −1.68497e144 | −0.477713 | −0.238857 | − | 0.971055i | \(-0.576773\pi\) | ||||
−0.238857 | + | 0.971055i | \(0.576773\pi\) | |||||||
\(450\) | −1.70858e144 | −0.429094 | ||||||||
\(451\) | −4.83546e144 | −1.07601 | ||||||||
\(452\) | 1.20570e145 | 2.37790 | ||||||||
\(453\) | 9.46812e144 | 1.65543 | ||||||||
\(454\) | −6.33056e144 | −0.981517 | ||||||||
\(455\) | −4.22269e144 | −0.580722 | ||||||||
\(456\) | −2.35377e145 | −2.87198 | ||||||||
\(457\) | −1.39230e145 | −1.50765 | −0.753823 | − | 0.657078i | \(-0.771792\pi\) | ||||
−0.753823 | + | 0.657078i | \(0.771792\pi\) | |||||||
\(458\) | −1.97856e145 | −1.90187 | ||||||||
\(459\) | −1.74055e144 | −0.148558 | ||||||||
\(460\) | 4.31471e145 | 3.27077 | ||||||||
\(461\) | 1.55703e145 | 1.04857 | 0.524283 | − | 0.851544i | \(-0.324333\pi\) | ||||
0.524283 | + | 0.851544i | \(0.324333\pi\) | |||||||
\(462\) | −6.20107e145 | −3.71090 | ||||||||
\(463\) | 2.93745e145 | 1.56245 | 0.781226 | − | 0.624249i | \(-0.214595\pi\) | ||||
0.781226 | + | 0.624249i | \(0.214595\pi\) | |||||||
\(464\) | 5.41271e145 | 2.55968 | ||||||||
\(465\) | 1.72059e145 | 0.723589 | ||||||||
\(466\) | −1.25200e145 | −0.468352 | ||||||||
\(467\) | −3.05255e145 | −1.01600 | −0.507999 | − | 0.861358i | \(-0.669615\pi\) | ||||
−0.507999 | + | 0.861358i | \(0.669615\pi\) | |||||||
\(468\) | 2.70691e145 | 0.801816 | ||||||||
\(469\) | 2.19628e145 | 0.579119 | ||||||||
\(470\) | −1.18719e146 | −2.78732 | ||||||||
\(471\) | −2.48084e145 | −0.518752 | ||||||||
\(472\) | 2.54423e145 | 0.473933 | ||||||||
\(473\) | −1.84126e145 | −0.305621 | ||||||||
\(474\) | 3.09906e146 | 4.58470 | ||||||||
\(475\) | −1.55255e145 | −0.204759 | ||||||||
\(476\) | −2.91678e146 | −3.43024 | ||||||||
\(477\) | 1.19288e146 | 1.25126 | ||||||||
\(478\) | 2.48785e146 | 2.32811 | ||||||||
\(479\) | −1.12113e146 | −0.936200 | −0.468100 | − | 0.883675i | \(-0.655061\pi\) | ||||
−0.468100 | + | 0.883675i | \(0.655061\pi\) | |||||||
\(480\) | −3.99385e146 | −2.97676 | ||||||||
\(481\) | 2.61317e145 | 0.173885 | ||||||||
\(482\) | −1.53921e145 | −0.0914607 | ||||||||
\(483\) | 4.35402e146 | 2.31085 | ||||||||
\(484\) | 4.25362e145 | 0.201691 | ||||||||
\(485\) | −3.25966e146 | −1.38117 | ||||||||
\(486\) | −6.64989e146 | −2.51848 | ||||||||
\(487\) | −3.19882e146 | −1.08308 | −0.541541 | − | 0.840674i | \(-0.682159\pi\) | ||||
−0.541541 | + | 0.840674i | \(0.682159\pi\) | |||||||
\(488\) | 1.19802e147 | 3.62729 | ||||||||
\(489\) | −5.72378e146 | −1.55007 | ||||||||
\(490\) | 8.22557e146 | 1.99287 | ||||||||
\(491\) | 4.41373e146 | 0.956895 | 0.478448 | − | 0.878116i | \(-0.341200\pi\) | ||||
0.478448 | + | 0.878116i | \(0.341200\pi\) | |||||||
\(492\) | −1.78048e147 | −3.45493 | ||||||||
\(493\) | −6.02024e146 | −1.04582 | ||||||||
\(494\) | 3.47249e146 | 0.540160 | ||||||||
\(495\) | 7.48613e146 | 1.04297 | ||||||||
\(496\) | 9.27328e146 | 1.15740 | ||||||||
\(497\) | −1.46891e146 | −0.164275 | ||||||||
\(498\) | 4.85353e147 | 4.86472 | ||||||||
\(499\) | −2.11151e147 | −1.89720 | −0.948598 | − | 0.316482i | \(-0.897498\pi\) | ||||
−0.948598 | + | 0.316482i | \(0.897498\pi\) | |||||||
\(500\) | 2.50530e147 | 2.01834 | ||||||||
\(501\) | −1.75622e147 | −1.26889 | ||||||||
\(502\) | −2.09580e147 | −1.35831 | ||||||||
\(503\) | 1.05113e147 | 0.611227 | 0.305613 | − | 0.952156i | \(-0.401139\pi\) | ||||
0.305613 | + | 0.952156i | \(0.401139\pi\) | |||||||
\(504\) | −6.33625e147 | −3.30649 | ||||||||
\(505\) | −1.31676e147 | −0.616774 | ||||||||
\(506\) | −5.49883e147 | −2.31242 | ||||||||
\(507\) | 3.14544e147 | 1.18781 | ||||||||
\(508\) | −2.31699e147 | −0.785873 | ||||||||
\(509\) | 3.24831e146 | 0.0989780 | 0.0494890 | − | 0.998775i | \(-0.484241\pi\) | ||||
0.0494890 | + | 0.998775i | \(0.484241\pi\) | |||||||
\(510\) | 1.05378e148 | 2.88519 | ||||||||
\(511\) | −1.88007e147 | −0.462630 | ||||||||
\(512\) | 8.01249e147 | 1.77237 | ||||||||
\(513\) | −5.84065e146 | −0.116162 | ||||||||
\(514\) | −7.66834e147 | −1.37155 | ||||||||
\(515\) | 1.97597e147 | 0.317896 | ||||||||
\(516\) | −6.77976e147 | −0.981308 | ||||||||
\(517\) | 1.07172e148 | 1.39588 | ||||||||
\(518\) | −1.03983e148 | −1.21896 | ||||||||
\(519\) | 2.37083e148 | 2.50196 | ||||||||
\(520\) | 1.15514e148 | 1.09762 | ||||||||
\(521\) | −1.91111e148 | −1.63542 | −0.817709 | − | 0.575632i | \(-0.804756\pi\) | ||||
−0.817709 | + | 0.575632i | \(0.804756\pi\) | |||||||
\(522\) | −2.22320e148 | −1.71370 | ||||||||
\(523\) | 2.11342e148 | 1.46772 | 0.733862 | − | 0.679299i | \(-0.237716\pi\) | ||||
0.733862 | + | 0.679299i | \(0.237716\pi\) | |||||||
\(524\) | 7.13693e147 | 0.446638 | ||||||||
\(525\) | −8.85954e147 | −0.499723 | ||||||||
\(526\) | −7.03858e148 | −3.57900 | ||||||||
\(527\) | −1.03141e148 | −0.472883 | ||||||||
\(528\) | 8.55287e148 | 3.53642 | ||||||||
\(529\) | 1.17972e148 | 0.439992 | ||||||||
\(530\) | 8.65351e148 | 2.91177 | ||||||||
\(531\) | −5.26890e147 | −0.159981 | ||||||||
\(532\) | −9.78764e148 | −2.68222 | ||||||||
\(533\) | 1.54518e148 | 0.382248 | ||||||||
\(534\) | −7.02621e148 | −1.56936 | ||||||||
\(535\) | −7.27294e148 | −1.46699 | ||||||||
\(536\) | −6.00802e148 | −1.09459 | ||||||||
\(537\) | 6.12406e148 | 1.00795 | ||||||||
\(538\) | 9.45664e148 | 1.40638 | ||||||||
\(539\) | −7.42554e148 | −0.998023 | ||||||||
\(540\) | −3.30285e148 | −0.401262 | ||||||||
\(541\) | 4.73993e148 | 0.520620 | 0.260310 | − | 0.965525i | \(-0.416175\pi\) | ||||
0.260310 | + | 0.965525i | \(0.416175\pi\) | |||||||
\(542\) | 4.23257e148 | 0.420381 | ||||||||
\(543\) | −8.61154e148 | −0.773553 | ||||||||
\(544\) | 2.39413e149 | 1.94539 | ||||||||
\(545\) | 8.25739e148 | 0.607063 | ||||||||
\(546\) | 1.98156e149 | 1.31828 | ||||||||
\(547\) | 8.52224e148 | 0.513150 | 0.256575 | − | 0.966524i | \(-0.417406\pi\) | ||||
0.256575 | + | 0.966524i | \(0.417406\pi\) | |||||||
\(548\) | 1.52729e149 | 0.832491 | ||||||||
\(549\) | −2.48100e149 | −1.22443 | ||||||||
\(550\) | 1.11890e149 | 0.500062 | ||||||||
\(551\) | −2.02017e149 | −0.817761 | ||||||||
\(552\) | −1.19106e150 | −4.36772 | ||||||||
\(553\) | 7.58068e149 | 2.51877 | ||||||||
\(554\) | −3.62400e149 | −1.09121 | ||||||||
\(555\) | 2.66103e149 | 0.726244 | ||||||||
\(556\) | 2.86700e149 | 0.709336 | ||||||||
\(557\) | 4.63517e149 | 1.03982 | 0.519910 | − | 0.854221i | \(-0.325966\pi\) | ||||
0.519910 | + | 0.854221i | \(0.325966\pi\) | |||||||
\(558\) | −3.80887e149 | −0.774877 | ||||||||
\(559\) | 5.88377e148 | 0.108570 | ||||||||
\(560\) | −2.31754e150 | −3.87954 | ||||||||
\(561\) | −9.51286e149 | −1.44489 | ||||||||
\(562\) | 1.14586e150 | 1.57943 | ||||||||
\(563\) | −8.04877e149 | −1.00698 | −0.503492 | − | 0.864000i | \(-0.667952\pi\) | ||||
−0.503492 | + | 0.864000i | \(0.667952\pi\) | |||||||
\(564\) | 3.94622e150 | 4.48198 | ||||||||
\(565\) | −1.06552e150 | −1.09881 | ||||||||
\(566\) | 2.67662e150 | 2.50664 | ||||||||
\(567\) | −1.80271e150 | −1.53338 | ||||||||
\(568\) | 4.01826e149 | 0.310495 | ||||||||
\(569\) | −2.27486e149 | −0.159712 | −0.0798558 | − | 0.996806i | \(-0.525446\pi\) | ||||
−0.0798558 | + | 0.996806i | \(0.525446\pi\) | |||||||
\(570\) | 3.53609e150 | 2.25603 | ||||||||
\(571\) | 2.35542e150 | 1.36584 | 0.682920 | − | 0.730493i | \(-0.260710\pi\) | ||||
0.682920 | + | 0.730493i | \(0.260710\pi\) | |||||||
\(572\) | −1.77268e150 | −0.934430 | ||||||||
\(573\) | −5.15176e150 | −2.46904 | ||||||||
\(574\) | −6.14853e150 | −2.67962 | ||||||||
\(575\) | −7.85623e149 | −0.311399 | ||||||||
\(576\) | 2.72415e150 | 0.982212 | ||||||||
\(577\) | 5.43843e150 | 1.78399 | 0.891994 | − | 0.452048i | \(-0.149306\pi\) | ||||
0.891994 | + | 0.452048i | \(0.149306\pi\) | |||||||
\(578\) | −1.13487e149 | −0.0338749 | ||||||||
\(579\) | −2.67054e150 | −0.725466 | ||||||||
\(580\) | −1.14239e151 | −2.82481 | ||||||||
\(581\) | 1.18723e151 | 2.67261 | ||||||||
\(582\) | 1.52964e151 | 3.13536 | ||||||||
\(583\) | −7.81186e150 | −1.45820 | ||||||||
\(584\) | 5.14300e150 | 0.874413 | ||||||||
\(585\) | −2.39220e150 | −0.370513 | ||||||||
\(586\) | −1.03554e151 | −1.46133 | ||||||||
\(587\) | 3.72559e150 | 0.479092 | 0.239546 | − | 0.970885i | \(-0.423001\pi\) | ||||
0.239546 | + | 0.970885i | \(0.423001\pi\) | |||||||
\(588\) | −2.73418e151 | −3.20452 | ||||||||
\(589\) | −3.46104e150 | −0.369763 | ||||||||
\(590\) | −3.82221e150 | −0.372289 | ||||||||
\(591\) | 1.02407e151 | 0.909519 | ||||||||
\(592\) | 1.43419e151 | 1.16164 | ||||||||
\(593\) | −8.99967e150 | −0.664884 | −0.332442 | − | 0.943124i | \(-0.607873\pi\) | ||||
−0.332442 | + | 0.943124i | \(0.607873\pi\) | |||||||
\(594\) | 4.20927e150 | 0.283691 | ||||||||
\(595\) | 2.57767e151 | 1.58508 | ||||||||
\(596\) | −9.99734e150 | −0.561000 | ||||||||
\(597\) | 3.99868e151 | 2.04793 | ||||||||
\(598\) | 1.75716e151 | 0.821479 | ||||||||
\(599\) | −1.00935e151 | −0.430806 | −0.215403 | − | 0.976525i | \(-0.569106\pi\) | ||||
−0.215403 | + | 0.976525i | \(0.569106\pi\) | |||||||
\(600\) | 2.42357e151 | 0.944521 | ||||||||
\(601\) | −1.51618e151 | −0.539624 | −0.269812 | − | 0.962913i | \(-0.586962\pi\) | ||||
−0.269812 | + | 0.962913i | \(0.586962\pi\) | |||||||
\(602\) | −2.34125e151 | −0.761096 | ||||||||
\(603\) | 1.24422e151 | 0.369490 | ||||||||
\(604\) | −1.07701e152 | −2.92218 | ||||||||
\(605\) | −3.75909e150 | −0.0931997 | ||||||||
\(606\) | 6.17909e151 | 1.40012 | ||||||||
\(607\) | 4.50398e151 | 0.932851 | 0.466426 | − | 0.884560i | \(-0.345541\pi\) | ||||
0.466426 | + | 0.884560i | \(0.345541\pi\) | |||||||
\(608\) | 8.03381e151 | 1.52117 | ||||||||
\(609\) | −1.15280e152 | −1.99578 | ||||||||
\(610\) | −1.79979e152 | −2.84935 | ||||||||
\(611\) | −3.42470e151 | −0.495880 | ||||||||
\(612\) | −1.65239e152 | −2.18856 | ||||||||
\(613\) | −7.27362e151 | −0.881362 | −0.440681 | − | 0.897664i | \(-0.645263\pi\) | ||||
−0.440681 | + | 0.897664i | \(0.645263\pi\) | |||||||
\(614\) | 1.84435e152 | 2.04488 | ||||||||
\(615\) | 1.57348e152 | 1.59649 | ||||||||
\(616\) | 4.14943e152 | 3.85336 | ||||||||
\(617\) | −4.88189e151 | −0.414999 | −0.207499 | − | 0.978235i | \(-0.566533\pi\) | ||||
−0.207499 | + | 0.978235i | \(0.566533\pi\) | |||||||
\(618\) | −9.27251e151 | −0.721648 | ||||||||
\(619\) | 2.26844e152 | 1.61654 | 0.808270 | − | 0.588812i | \(-0.200404\pi\) | ||||
0.808270 | + | 0.588812i | \(0.200404\pi\) | |||||||
\(620\) | −1.95720e152 | −1.27728 | ||||||||
\(621\) | −2.95550e151 | −0.176660 | ||||||||
\(622\) | 1.44673e152 | 0.792155 | ||||||||
\(623\) | −1.71870e152 | −0.862185 | ||||||||
\(624\) | −2.73308e152 | −1.25630 | ||||||||
\(625\) | −2.83006e152 | −1.19216 | ||||||||
\(626\) | 6.78160e152 | 2.61837 | ||||||||
\(627\) | −3.19217e152 | −1.12981 | ||||||||
\(628\) | 2.82199e152 | 0.915704 | ||||||||
\(629\) | −1.59516e152 | −0.474619 | ||||||||
\(630\) | 9.51899e152 | 2.59735 | ||||||||
\(631\) | −3.38724e152 | −0.847706 | −0.423853 | − | 0.905731i | \(-0.639323\pi\) | ||||
−0.423853 | + | 0.905731i | \(0.639323\pi\) | |||||||
\(632\) | −2.07373e153 | −4.76070 | ||||||||
\(633\) | 9.27909e152 | 1.95435 | ||||||||
\(634\) | 9.89920e152 | 1.91309 | ||||||||
\(635\) | 2.04762e152 | 0.363145 | ||||||||
\(636\) | −2.87643e153 | −4.68210 | ||||||||
\(637\) | 2.37284e152 | 0.354544 | ||||||||
\(638\) | 1.45591e153 | 1.99713 | ||||||||
\(639\) | −8.32153e151 | −0.104811 | ||||||||
\(640\) | 1.05586e152 | 0.122123 | ||||||||
\(641\) | 1.73006e152 | 0.183780 | 0.0918900 | − | 0.995769i | \(-0.470709\pi\) | ||||
0.0918900 | + | 0.995769i | \(0.470709\pi\) | |||||||
\(642\) | 3.41293e153 | 3.33019 | ||||||||
\(643\) | 6.90756e151 | 0.0619194 | 0.0309597 | − | 0.999521i | \(-0.490144\pi\) | ||||
0.0309597 | + | 0.999521i | \(0.490144\pi\) | |||||||
\(644\) | −4.95276e153 | −4.07913 | ||||||||
\(645\) | 5.99153e152 | 0.453454 | ||||||||
\(646\) | −2.11972e153 | −1.47437 | ||||||||
\(647\) | −1.40129e153 | −0.895867 | −0.447933 | − | 0.894067i | \(-0.647840\pi\) | ||||
−0.447933 | + | 0.894067i | \(0.647840\pi\) | |||||||
\(648\) | 4.93139e153 | 2.89822 | ||||||||
\(649\) | 3.45046e152 | 0.186441 | ||||||||
\(650\) | −3.57545e152 | −0.177645 | ||||||||
\(651\) | −1.97503e153 | −0.902422 | ||||||||
\(652\) | 6.51088e153 | 2.73619 | ||||||||
\(653\) | −8.18554e152 | −0.316431 | −0.158215 | − | 0.987405i | \(-0.550574\pi\) | ||||
−0.158215 | + | 0.987405i | \(0.550574\pi\) | |||||||
\(654\) | −3.87490e153 | −1.37808 | ||||||||
\(655\) | −6.30718e152 | −0.206388 | ||||||||
\(656\) | 8.48040e153 | 2.55363 | ||||||||
\(657\) | −1.06508e153 | −0.295168 | ||||||||
\(658\) | 1.36275e154 | 3.47620 | ||||||||
\(659\) | −2.28669e153 | −0.536972 | −0.268486 | − | 0.963284i | \(-0.586523\pi\) | ||||
−0.268486 | + | 0.963284i | \(0.586523\pi\) | |||||||
\(660\) | −1.80515e154 | −3.90273 | ||||||||
\(661\) | 1.69864e153 | 0.338159 | 0.169079 | − | 0.985602i | \(-0.445921\pi\) | ||||
0.169079 | + | 0.985602i | \(0.445921\pi\) | |||||||
\(662\) | −8.79609e153 | −1.61261 | ||||||||
\(663\) | 3.03985e153 | 0.513292 | ||||||||
\(664\) | −3.24772e154 | −5.05148 | ||||||||
\(665\) | 8.64972e153 | 1.23943 | ||||||||
\(666\) | −5.89073e153 | −0.777721 | ||||||||
\(667\) | −1.02225e154 | −1.24366 | ||||||||
\(668\) | 1.99773e154 | 2.23985 | ||||||||
\(669\) | 1.68763e154 | 1.74403 | ||||||||
\(670\) | 9.02590e153 | 0.859833 | ||||||||
\(671\) | 1.62474e154 | 1.42694 | ||||||||
\(672\) | 4.58446e154 | 3.71246 | ||||||||
\(673\) | −1.56625e154 | −1.16960 | −0.584802 | − | 0.811176i | \(-0.698828\pi\) | ||||
−0.584802 | + | 0.811176i | \(0.698828\pi\) | |||||||
\(674\) | −3.71900e154 | −2.56131 | ||||||||
\(675\) | 6.01383e152 | 0.0382028 | ||||||||
\(676\) | −3.57798e154 | −2.09673 | ||||||||
\(677\) | 1.72855e154 | 0.934541 | 0.467270 | − | 0.884114i | \(-0.345237\pi\) | ||||
0.467270 | + | 0.884114i | \(0.345237\pi\) | |||||||
\(678\) | 5.00012e154 | 2.49437 | ||||||||
\(679\) | 3.74169e154 | 1.72252 | ||||||||
\(680\) | −7.05133e154 | −2.99595 | ||||||||
\(681\) | −1.85963e154 | −0.729306 | ||||||||
\(682\) | 2.49432e154 | 0.903034 | ||||||||
\(683\) | 1.75638e154 | 0.587070 | 0.293535 | − | 0.955948i | \(-0.405168\pi\) | ||||
0.293535 | + | 0.955948i | \(0.405168\pi\) | |||||||
\(684\) | −5.54480e154 | −1.71131 | ||||||||
\(685\) | −1.34972e154 | −0.384687 | ||||||||
\(686\) | 4.03705e153 | 0.106267 | ||||||||
\(687\) | −5.81212e154 | −1.41316 | ||||||||
\(688\) | 3.22919e154 | 0.725310 | ||||||||
\(689\) | 2.49629e154 | 0.518021 | ||||||||
\(690\) | 1.78934e155 | 3.43098 | ||||||||
\(691\) | −1.02056e154 | −0.180836 | −0.0904179 | − | 0.995904i | \(-0.528820\pi\) | ||||
−0.0904179 | + | 0.995904i | \(0.528820\pi\) | |||||||
\(692\) | −2.69685e155 | −4.41647 | ||||||||
\(693\) | −8.59316e154 | −1.30074 | ||||||||
\(694\) | 9.94568e154 | 1.39169 | ||||||||
\(695\) | −2.53368e154 | −0.327778 | ||||||||
\(696\) | 3.15354e155 | 3.77220 | ||||||||
\(697\) | −9.43226e154 | −1.04335 | ||||||||
\(698\) | −1.11230e155 | −1.13789 | ||||||||
\(699\) | −3.67782e154 | −0.348004 | ||||||||
\(700\) | 1.00778e155 | 0.882114 | ||||||||
\(701\) | 5.12780e154 | 0.415240 | 0.207620 | − | 0.978210i | \(-0.433428\pi\) | ||||
0.207620 | + | 0.978210i | \(0.433428\pi\) | |||||||
\(702\) | −1.34508e154 | −0.100780 | ||||||||
\(703\) | −5.35279e154 | −0.371120 | ||||||||
\(704\) | −1.78397e155 | −1.14466 | ||||||||
\(705\) | −3.48743e155 | −2.07109 | ||||||||
\(706\) | 4.57006e155 | 2.51227 | ||||||||
\(707\) | 1.51148e155 | 0.769208 | ||||||||
\(708\) | 1.27050e155 | 0.598637 | ||||||||
\(709\) | 1.33999e155 | 0.584631 | 0.292315 | − | 0.956322i | \(-0.405574\pi\) | ||||
0.292315 | + | 0.956322i | \(0.405574\pi\) | |||||||
\(710\) | −6.03667e154 | −0.243903 | ||||||||
\(711\) | 4.29454e155 | 1.60703 | ||||||||
\(712\) | 4.70157e155 | 1.62961 | ||||||||
\(713\) | −1.75137e155 | −0.562338 | ||||||||
\(714\) | −1.20961e156 | −3.59826 | ||||||||
\(715\) | 1.56659e155 | 0.431792 | ||||||||
\(716\) | −6.96620e155 | −1.77925 | ||||||||
\(717\) | 7.30819e155 | 1.72988 | ||||||||
\(718\) | 3.02779e155 | 0.664268 | ||||||||
\(719\) | −5.33416e155 | −1.08478 | −0.542390 | − | 0.840127i | \(-0.682481\pi\) | ||||
−0.542390 | + | 0.840127i | \(0.682481\pi\) | |||||||
\(720\) | −1.31291e156 | −2.47523 | ||||||||
\(721\) | −2.26817e155 | −0.396464 | ||||||||
\(722\) | 4.31159e155 | 0.698811 | ||||||||
\(723\) | −4.52151e154 | −0.0679589 | ||||||||
\(724\) | 9.79574e155 | 1.36548 | ||||||||
\(725\) | 2.08007e155 | 0.268941 | ||||||||
\(726\) | 1.76401e155 | 0.211570 | ||||||||
\(727\) | 2.56000e155 | 0.284849 | 0.142424 | − | 0.989806i | \(-0.454510\pi\) | ||||
0.142424 | + | 0.989806i | \(0.454510\pi\) | |||||||
\(728\) | −1.32596e156 | −1.36889 | ||||||||
\(729\) | −8.09817e155 | −0.775776 | ||||||||
\(730\) | −7.72638e155 | −0.686879 | ||||||||
\(731\) | −3.59164e155 | −0.296344 | ||||||||
\(732\) | 5.98250e156 | 4.58173 | ||||||||
\(733\) | 9.76773e155 | 0.694428 | 0.347214 | − | 0.937786i | \(-0.387128\pi\) | ||||
0.347214 | + | 0.937786i | \(0.387128\pi\) | |||||||
\(734\) | −8.24467e155 | −0.544174 | ||||||||
\(735\) | 2.41630e156 | 1.48078 | ||||||||
\(736\) | 4.06529e156 | 2.31340 | ||||||||
\(737\) | −8.14803e155 | −0.430601 | ||||||||
\(738\) | −3.48321e156 | −1.70965 | ||||||||
\(739\) | −2.09989e156 | −0.957360 | −0.478680 | − | 0.877989i | \(-0.658885\pi\) | ||||
−0.478680 | + | 0.877989i | \(0.658885\pi\) | |||||||
\(740\) | −3.02696e156 | −1.28197 | ||||||||
\(741\) | 1.02006e156 | 0.401360 | ||||||||
\(742\) | −9.93318e156 | −3.63141 | ||||||||
\(743\) | −5.65572e156 | −1.92131 | −0.960655 | − | 0.277744i | \(-0.910413\pi\) | ||||
−0.960655 | + | 0.277744i | \(0.910413\pi\) | |||||||
\(744\) | 5.40278e156 | 1.70566 | ||||||||
\(745\) | 8.83504e155 | 0.259234 | ||||||||
\(746\) | −9.12959e156 | −2.48992 | ||||||||
\(747\) | 6.72579e156 | 1.70518 | ||||||||
\(748\) | 1.08210e157 | 2.55053 | ||||||||
\(749\) | 8.34844e156 | 1.82956 | ||||||||
\(750\) | 1.03897e157 | 2.11721 | ||||||||
\(751\) | −1.67403e156 | −0.317239 | −0.158619 | − | 0.987340i | \(-0.550704\pi\) | ||||
−0.158619 | + | 0.987340i | \(0.550704\pi\) | |||||||
\(752\) | −1.87958e157 | −3.31275 | ||||||||
\(753\) | −6.15653e156 | −1.00928 | ||||||||
\(754\) | −4.65238e156 | −0.709474 | ||||||||
\(755\) | 9.51797e156 | 1.35032 | ||||||||
\(756\) | 3.79126e156 | 0.500433 | ||||||||
\(757\) | 1.10892e156 | 0.136200 | 0.0680998 | − | 0.997679i | \(-0.478306\pi\) | ||||
0.0680998 | + | 0.997679i | \(0.478306\pi\) | |||||||
\(758\) | 2.02745e157 | 2.31728 | ||||||||
\(759\) | −1.61531e157 | −1.71822 | ||||||||
\(760\) | −2.36617e157 | −2.34264 | ||||||||
\(761\) | −4.72490e156 | −0.435441 | −0.217720 | − | 0.976011i | \(-0.569862\pi\) | ||||
−0.217720 | + | 0.976011i | \(0.569862\pi\) | |||||||
\(762\) | −9.60874e156 | −0.824367 | ||||||||
\(763\) | −9.47848e156 | −0.757097 | ||||||||
\(764\) | 5.86020e157 | 4.35837 | ||||||||
\(765\) | 1.46028e157 | 1.01132 | ||||||||
\(766\) | 1.14474e156 | 0.0738311 | ||||||||
\(767\) | −1.10260e156 | −0.0662323 | ||||||||
\(768\) | 2.20920e157 | 1.23609 | ||||||||
\(769\) | 1.40771e157 | 0.733715 | 0.366857 | − | 0.930277i | \(-0.380434\pi\) | ||||
0.366857 | + | 0.930277i | \(0.380434\pi\) | |||||||
\(770\) | −6.23372e157 | −3.02693 | ||||||||
\(771\) | −2.25261e157 | −1.01911 | ||||||||
\(772\) | 3.03777e157 | 1.28060 | ||||||||
\(773\) | 2.08791e157 | 0.820218 | 0.410109 | − | 0.912037i | \(-0.365491\pi\) | ||||
0.410109 | + | 0.912037i | \(0.365491\pi\) | |||||||
\(774\) | −1.32635e157 | −0.485595 | ||||||||
\(775\) | 3.56367e156 | 0.121606 | ||||||||
\(776\) | −1.02355e158 | −3.25572 | ||||||||
\(777\) | −3.05454e157 | −0.905734 | ||||||||
\(778\) | 6.44159e157 | 1.78076 | ||||||||
\(779\) | −3.16512e157 | −0.815829 | ||||||||
\(780\) | 5.76838e157 | 1.38643 | ||||||||
\(781\) | 5.44954e156 | 0.122146 | ||||||||
\(782\) | −1.07263e158 | −2.24223 | ||||||||
\(783\) | 7.82519e156 | 0.152573 | ||||||||
\(784\) | 1.30229e158 | 2.36855 | ||||||||
\(785\) | −2.49390e157 | −0.423139 | ||||||||
\(786\) | 2.95974e157 | 0.468516 | ||||||||
\(787\) | −4.20264e157 | −0.620725 | −0.310363 | − | 0.950618i | \(-0.600450\pi\) | ||||
−0.310363 | + | 0.950618i | \(0.600450\pi\) | |||||||
\(788\) | −1.16489e158 | −1.60549 | ||||||||
\(789\) | −2.06762e158 | −2.65934 | ||||||||
\(790\) | 3.11538e158 | 3.73968 | ||||||||
\(791\) | 1.22309e158 | 1.37038 | ||||||||
\(792\) | 2.35070e158 | 2.45852 | ||||||||
\(793\) | −5.19188e157 | −0.506916 | ||||||||
\(794\) | 2.50440e158 | 2.28289 | ||||||||
\(795\) | 2.54201e158 | 2.16356 | ||||||||
\(796\) | −4.54855e158 | −3.61502 | ||||||||
\(797\) | −1.23123e158 | −0.913819 | −0.456910 | − | 0.889513i | \(-0.651044\pi\) | ||||
−0.456910 | + | 0.889513i | \(0.651044\pi\) | |||||||
\(798\) | −4.05901e158 | −2.81360 | ||||||||
\(799\) | 2.09055e158 | 1.35351 | ||||||||
\(800\) | −8.27202e157 | −0.500273 | ||||||||
\(801\) | −9.73660e157 | −0.550092 | ||||||||
\(802\) | −1.99506e158 | −1.05306 | ||||||||
\(803\) | 6.97490e157 | 0.343986 | ||||||||
\(804\) | −3.00021e158 | −1.38260 | ||||||||
\(805\) | 4.37695e158 | 1.88493 | ||||||||
\(806\) | −7.97064e157 | −0.320799 | ||||||||
\(807\) | 2.77794e158 | 1.04500 | ||||||||
\(808\) | −4.13472e158 | −1.45387 | ||||||||
\(809\) | 1.65763e158 | 0.544870 | 0.272435 | − | 0.962174i | \(-0.412171\pi\) | ||||
0.272435 | + | 0.962174i | \(0.412171\pi\) | |||||||
\(810\) | −7.40847e158 | −2.27664 | ||||||||
\(811\) | −2.95648e158 | −0.849450 | −0.424725 | − | 0.905322i | \(-0.639629\pi\) | ||||
−0.424725 | + | 0.905322i | \(0.639629\pi\) | |||||||
\(812\) | 1.31133e159 | 3.52296 | ||||||||
\(813\) | 1.24334e158 | 0.312360 | ||||||||
\(814\) | 3.85767e158 | 0.906349 | ||||||||
\(815\) | −5.75391e158 | −1.26437 | ||||||||
\(816\) | 1.66836e159 | 3.42907 | ||||||||
\(817\) | −1.20522e158 | −0.231721 | ||||||||
\(818\) | −1.35539e159 | −2.43786 | ||||||||
\(819\) | 2.74596e158 | 0.462084 | ||||||||
\(820\) | −1.78985e159 | −2.81814 | ||||||||
\(821\) | 1.08754e159 | 1.60230 | 0.801149 | − | 0.598464i | \(-0.204222\pi\) | ||||
0.801149 | + | 0.598464i | \(0.204222\pi\) | |||||||
\(822\) | 6.33377e158 | 0.873269 | ||||||||
\(823\) | −2.47121e158 | −0.318874 | −0.159437 | − | 0.987208i | \(-0.550968\pi\) | ||||
−0.159437 | + | 0.987208i | \(0.550968\pi\) | |||||||
\(824\) | 6.20467e158 | 0.749352 | ||||||||
\(825\) | 3.28682e158 | 0.371566 | ||||||||
\(826\) | 4.38743e158 | 0.464299 | ||||||||
\(827\) | −7.41827e158 | −0.734941 | −0.367470 | − | 0.930035i | \(-0.619776\pi\) | ||||
−0.367470 | + | 0.930035i | \(0.619776\pi\) | |||||||
\(828\) | −2.80579e159 | −2.60257 | ||||||||
\(829\) | −1.38484e159 | −1.20276 | −0.601378 | − | 0.798964i | \(-0.705382\pi\) | ||||
−0.601378 | + | 0.798964i | \(0.705382\pi\) | |||||||
\(830\) | 4.87908e159 | 3.96809 | ||||||||
\(831\) | −1.06457e159 | −0.810808 | ||||||||
\(832\) | 5.70069e158 | 0.406636 | ||||||||
\(833\) | −1.44846e159 | −0.967729 | ||||||||
\(834\) | 1.18897e159 | 0.744081 | ||||||||
\(835\) | −1.76547e159 | −1.03502 | ||||||||
\(836\) | 3.63114e159 | 1.99435 | ||||||||
\(837\) | 1.34064e158 | 0.0689884 | ||||||||
\(838\) | 6.64328e159 | 3.20320 | ||||||||
\(839\) | −5.53168e158 | −0.249937 | −0.124968 | − | 0.992161i | \(-0.539883\pi\) | ||||
−0.124968 | + | 0.992161i | \(0.539883\pi\) | |||||||
\(840\) | −1.35024e160 | −5.71729 | ||||||||
\(841\) | 1.86697e158 | 0.0740893 | ||||||||
\(842\) | −8.62727e159 | −3.20896 | ||||||||
\(843\) | 3.36602e159 | 1.17358 | ||||||||
\(844\) | −1.05551e160 | −3.44984 | ||||||||
\(845\) | 3.16200e159 | 0.968882 | ||||||||
\(846\) | 7.72012e159 | 2.21789 | ||||||||
\(847\) | 4.31497e158 | 0.116234 | ||||||||
\(848\) | 1.37004e160 | 3.46067 | ||||||||
\(849\) | 7.86272e159 | 1.86253 | ||||||||
\(850\) | 2.18257e159 | 0.484883 | ||||||||
\(851\) | −2.70863e159 | −0.564402 | ||||||||
\(852\) | 2.00659e159 | 0.392194 | ||||||||
\(853\) | −7.81502e159 | −1.43287 | −0.716437 | − | 0.697652i | \(-0.754228\pi\) | ||||
−0.716437 | + | 0.697652i | \(0.754228\pi\) | |||||||
\(854\) | 2.06594e160 | 3.55356 | ||||||||
\(855\) | 4.90016e159 | 0.790782 | ||||||||
\(856\) | −2.28375e160 | −3.45803 | ||||||||
\(857\) | 2.15979e159 | 0.306872 | 0.153436 | − | 0.988159i | \(-0.450966\pi\) | ||||
0.153436 | + | 0.988159i | \(0.450966\pi\) | |||||||
\(858\) | −7.35143e159 | −0.980200 | ||||||||
\(859\) | −5.21993e159 | −0.653187 | −0.326593 | − | 0.945165i | \(-0.605901\pi\) | ||||
−0.326593 | + | 0.945165i | \(0.605901\pi\) | |||||||
\(860\) | −6.81545e159 | −0.800440 | ||||||||
\(861\) | −1.80616e160 | −1.99106 | ||||||||
\(862\) | 2.13943e160 | 2.21387 | ||||||||
\(863\) | −9.18916e159 | −0.892663 | −0.446331 | − | 0.894868i | \(-0.647270\pi\) | ||||
−0.446331 | + | 0.894868i | \(0.647270\pi\) | |||||||
\(864\) | −3.11191e159 | −0.283811 | ||||||||
\(865\) | 2.38331e160 | 2.04081 | ||||||||
\(866\) | −1.21094e160 | −0.973639 | ||||||||
\(867\) | −3.33373e158 | −0.0251704 | ||||||||
\(868\) | 2.24662e160 | 1.59296 | ||||||||
\(869\) | −2.81237e160 | −1.87282 | ||||||||
\(870\) | −4.73759e160 | −2.96318 | ||||||||
\(871\) | 2.60371e159 | 0.152969 | ||||||||
\(872\) | 2.59288e160 | 1.43098 | ||||||||
\(873\) | 2.11971e160 | 1.09900 | ||||||||
\(874\) | −3.59934e160 | −1.75327 | ||||||||
\(875\) | 2.54144e160 | 1.16316 | ||||||||
\(876\) | 2.56825e160 | 1.10449 | ||||||||
\(877\) | 2.00367e160 | 0.809744 | 0.404872 | − | 0.914373i | \(-0.367316\pi\) | ||||
0.404872 | + | 0.914373i | \(0.367316\pi\) | |||||||
\(878\) | 2.15310e160 | 0.817735 | ||||||||
\(879\) | −3.04196e160 | −1.08582 | ||||||||
\(880\) | 8.59790e160 | 2.88461 | ||||||||
\(881\) | −2.34895e160 | −0.740775 | −0.370387 | − | 0.928877i | \(-0.620775\pi\) | ||||
−0.370387 | + | 0.928877i | \(0.620775\pi\) | |||||||
\(882\) | −5.34897e160 | −1.58574 | ||||||||
\(883\) | 2.56121e160 | 0.713817 | 0.356909 | − | 0.934139i | \(-0.383831\pi\) | ||||
0.356909 | + | 0.934139i | \(0.383831\pi\) | |||||||
\(884\) | −3.45787e160 | −0.906066 | ||||||||
\(885\) | −1.12279e160 | −0.276625 | ||||||||
\(886\) | −2.75487e160 | −0.638209 | ||||||||
\(887\) | 1.55464e160 | 0.338682 | 0.169341 | − | 0.985558i | \(-0.445836\pi\) | ||||
0.169341 | + | 0.985558i | \(0.445836\pi\) | |||||||
\(888\) | 8.35583e160 | 1.71192 | ||||||||
\(889\) | −2.35041e160 | −0.452896 | ||||||||
\(890\) | −7.06321e160 | −1.28011 | ||||||||
\(891\) | 6.68791e160 | 1.14013 | ||||||||
\(892\) | −1.91970e161 | −3.07857 | ||||||||
\(893\) | 7.01512e160 | 1.05835 | ||||||||
\(894\) | −4.14597e160 | −0.588480 | ||||||||
\(895\) | 6.15630e160 | 0.822175 | ||||||||
\(896\) | −1.21200e160 | −0.152305 | ||||||||
\(897\) | 5.16174e160 | 0.610391 | ||||||||
\(898\) | 7.94861e160 | 0.884567 | ||||||||
\(899\) | 4.63704e160 | 0.485666 | ||||||||
\(900\) | 5.70921e160 | 0.562807 | ||||||||
\(901\) | −1.52382e161 | −1.41394 | ||||||||
\(902\) | 2.28106e161 | 1.99241 | ||||||||
\(903\) | −6.87755e160 | −0.565524 | ||||||||
\(904\) | −3.34581e161 | −2.59013 | ||||||||
\(905\) | −8.65688e160 | −0.630977 | ||||||||
\(906\) | −4.46645e161 | −3.06532 | ||||||||
\(907\) | 1.22079e161 | 0.788937 | 0.394469 | − | 0.918909i | \(-0.370929\pi\) | ||||
0.394469 | + | 0.918909i | \(0.370929\pi\) | |||||||
\(908\) | 2.11536e161 | 1.28738 | ||||||||
\(909\) | 8.56269e160 | 0.490771 | ||||||||
\(910\) | 1.99199e161 | 1.07531 | ||||||||
\(911\) | −1.61893e161 | −0.823145 | −0.411572 | − | 0.911377i | \(-0.635020\pi\) | ||||
−0.411572 | + | 0.911377i | \(0.635020\pi\) | |||||||
\(912\) | 5.59841e161 | 2.68131 | ||||||||
\(913\) | −4.40453e161 | −1.98720 | ||||||||
\(914\) | 6.56796e161 | 2.79166 | ||||||||
\(915\) | −5.28697e161 | −2.11718 | ||||||||
\(916\) | 6.61136e161 | 2.49452 | ||||||||
\(917\) | 7.23987e160 | 0.257396 | ||||||||
\(918\) | 8.21079e160 | 0.275080 | ||||||||
\(919\) | 2.86737e161 | 0.905292 | 0.452646 | − | 0.891690i | \(-0.350480\pi\) | ||||
0.452646 | + | 0.891690i | \(0.350480\pi\) | |||||||
\(920\) | −1.19733e162 | −3.56269 | ||||||||
\(921\) | 5.41788e161 | 1.51943 | ||||||||
\(922\) | −7.34505e161 | −1.94160 | ||||||||
\(923\) | −1.74141e160 | −0.0433918 | ||||||||
\(924\) | 2.07209e162 | 4.86728 | ||||||||
\(925\) | 5.51150e160 | 0.122052 | ||||||||
\(926\) | −1.38570e162 | −2.89314 | ||||||||
\(927\) | −1.28494e161 | −0.252952 | ||||||||
\(928\) | −1.07635e162 | −1.99798 | ||||||||
\(929\) | −8.62702e161 | −1.51009 | −0.755047 | − | 0.655670i | \(-0.772386\pi\) | ||||
−0.755047 | + | 0.655670i | \(0.772386\pi\) | |||||||
\(930\) | −8.11664e161 | −1.33985 | ||||||||
\(931\) | −4.86050e161 | −0.756699 | ||||||||
\(932\) | 4.18357e161 | 0.614299 | ||||||||
\(933\) | 4.24983e161 | 0.588602 | ||||||||
\(934\) | 1.44000e162 | 1.88129 | ||||||||
\(935\) | −9.56295e161 | −1.17858 | ||||||||
\(936\) | −7.51168e161 | −0.873381 | ||||||||
\(937\) | 8.30813e161 | 0.911371 | 0.455686 | − | 0.890141i | \(-0.349394\pi\) | ||||
0.455686 | + | 0.890141i | \(0.349394\pi\) | |||||||
\(938\) | −1.03606e162 | −1.07234 | ||||||||
\(939\) | 1.99213e162 | 1.94555 | ||||||||
\(940\) | 3.96700e162 | 3.65590 | ||||||||
\(941\) | 1.18361e162 | 1.02937 | 0.514687 | − | 0.857378i | \(-0.327908\pi\) | ||||
0.514687 | + | 0.857378i | \(0.327908\pi\) | |||||||
\(942\) | 1.17030e162 | 0.960557 | ||||||||
\(943\) | −1.60162e162 | −1.24072 | ||||||||
\(944\) | −6.05140e161 | −0.442468 | ||||||||
\(945\) | −3.35049e161 | −0.231246 | ||||||||
\(946\) | 8.68587e161 | 0.565908 | ||||||||
\(947\) | 2.65712e161 | 0.163432 | 0.0817160 | − | 0.996656i | \(-0.473960\pi\) | ||||
0.0817160 | + | 0.996656i | \(0.473960\pi\) | |||||||
\(948\) | −1.03555e163 | −6.01337 | ||||||||
\(949\) | −2.22884e161 | −0.122200 | ||||||||
\(950\) | 7.32392e161 | 0.379146 | ||||||||
\(951\) | 2.90794e162 | 1.42150 | ||||||||
\(952\) | 8.09406e162 | 3.73640 | ||||||||
\(953\) | 3.16901e162 | 1.38153 | 0.690766 | − | 0.723078i | \(-0.257273\pi\) | ||||
0.690766 | + | 0.723078i | \(0.257273\pi\) | |||||||
\(954\) | −5.62725e162 | −2.31692 | ||||||||
\(955\) | −5.17889e162 | −2.01397 | ||||||||
\(956\) | −8.31317e162 | −3.05360 | ||||||||
\(957\) | 4.27680e162 | 1.48395 | ||||||||
\(958\) | 5.28875e162 | 1.73353 | ||||||||
\(959\) | 1.54932e162 | 0.479762 | ||||||||
\(960\) | 5.80511e162 | 1.69835 | ||||||||
\(961\) | −2.82320e162 | −0.780399 | ||||||||
\(962\) | −1.23272e162 | −0.321977 | ||||||||
\(963\) | 4.72948e162 | 1.16730 | ||||||||
\(964\) | 5.14328e161 | 0.119961 | ||||||||
\(965\) | −2.68460e162 | −0.591753 | ||||||||
\(966\) | −2.05395e163 | −4.27894 | ||||||||
\(967\) | −3.42547e162 | −0.674492 | −0.337246 | − | 0.941417i | \(-0.609495\pi\) | ||||
−0.337246 | + | 0.941417i | \(0.609495\pi\) | |||||||
\(968\) | −1.18038e162 | −0.219692 | ||||||||
\(969\) | −6.22679e162 | −1.09551 | ||||||||
\(970\) | 1.53769e163 | 2.55747 | ||||||||
\(971\) | −4.29278e161 | −0.0674980 | −0.0337490 | − | 0.999430i | \(-0.510745\pi\) | ||||
−0.0337490 | + | 0.999430i | \(0.510745\pi\) | |||||||
\(972\) | 2.22206e163 | 3.30328 | ||||||||
\(973\) | 2.90836e162 | 0.408788 | ||||||||
\(974\) | 1.50900e163 | 2.00551 | ||||||||
\(975\) | −1.05031e162 | −0.131997 | ||||||||
\(976\) | −2.84946e163 | −3.38647 | ||||||||
\(977\) | −1.19615e163 | −1.34441 | −0.672205 | − | 0.740365i | \(-0.734653\pi\) | ||||
−0.672205 | + | 0.740365i | \(0.734653\pi\) | |||||||
\(978\) | 2.70011e163 | 2.87021 | ||||||||
\(979\) | 6.37623e162 | 0.641072 | ||||||||
\(980\) | −2.74858e163 | −2.61389 | ||||||||
\(981\) | −5.36966e162 | −0.483043 | ||||||||
\(982\) | −2.08211e163 | −1.77185 | ||||||||
\(983\) | −1.25172e163 | −1.00772 | −0.503860 | − | 0.863785i | \(-0.668087\pi\) | ||||
−0.503860 | + | 0.863785i | \(0.668087\pi\) | |||||||
\(984\) | 4.94083e163 | 3.76329 | ||||||||
\(985\) | 1.02946e163 | 0.741883 | ||||||||
\(986\) | 2.83996e163 | 1.93651 | ||||||||
\(987\) | 4.00314e163 | 2.58295 | ||||||||
\(988\) | −1.16033e163 | −0.708483 | ||||||||
\(989\) | −6.09870e162 | −0.352403 | ||||||||
\(990\) | −3.53147e163 | −1.93125 | ||||||||
\(991\) | −1.45616e163 | −0.753691 | −0.376846 | − | 0.926276i | \(-0.622991\pi\) | ||||
−0.376846 | + | 0.926276i | \(0.622991\pi\) | |||||||
\(992\) | −1.84405e163 | −0.903415 | ||||||||
\(993\) | −2.58390e163 | −1.19823 | ||||||||
\(994\) | 6.92936e162 | 0.304183 | ||||||||
\(995\) | 4.01973e163 | 1.67047 | ||||||||
\(996\) | −1.62181e164 | −6.38066 | ||||||||
\(997\) | −4.04544e162 | −0.150688 | −0.0753441 | − | 0.997158i | \(-0.524006\pi\) | ||||
−0.0753441 | + | 0.997158i | \(0.524006\pi\) | |||||||
\(998\) | 9.96072e163 | 3.51298 | ||||||||
\(999\) | 2.07341e162 | 0.0692416 |
(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 | 1.110.a.a.1.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.110.a.a.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial |