Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,118,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, 118, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 118);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 118 \) |
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: | \(86.6887159558\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4 x^{8} + \cdots - 93\!\cdots\!48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{151}\cdot 3^{56}\cdot 5^{18}\cdot 7^{7}\cdot 11^{4}\cdot 13^{4}\cdot 17^{2}\cdot 19\cdot 23\cdot 29^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-7.00565e14\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.06254e17 | 0.505996 | 0.252998 | − | 0.967467i | \(-0.418583\pi\) | ||||
0.252998 | + | 0.967467i | \(0.418583\pi\) | |||||||
\(3\) | −1.02253e28 | −1.25338 | −0.626689 | − | 0.779270i | \(-0.715590\pi\) | ||||
−0.626689 | + | 0.779270i | \(0.715590\pi\) | |||||||
\(4\) | −1.23613e35 | −0.743968 | ||||||||
\(5\) | −6.31988e40 | −0.814637 | −0.407318 | − | 0.913286i | \(-0.633536\pi\) | ||||
−0.407318 | + | 0.913286i | \(0.633536\pi\) | |||||||
\(6\) | −2.10900e45 | −0.634204 | ||||||||
\(7\) | 1.11715e49 | 0.407264 | 0.203632 | − | 0.979047i | \(-0.434725\pi\) | ||||
0.203632 | + | 0.979047i | \(0.434725\pi\) | |||||||
\(8\) | −5.97654e52 | −0.882441 | ||||||||
\(9\) | 3.80005e55 | 0.570956 | ||||||||
\(10\) | −1.30350e58 | −0.412203 | ||||||||
\(11\) | 2.60121e60 | 0.311676 | 0.155838 | − | 0.987783i | \(-0.450192\pi\) | ||||
0.155838 | + | 0.987783i | \(0.450192\pi\) | |||||||
\(12\) | 1.26398e63 | 0.932473 | ||||||||
\(13\) | −1.57235e65 | −1.07365 | −0.536826 | − | 0.843693i | \(-0.680377\pi\) | ||||
−0.536826 | + | 0.843693i | \(0.680377\pi\) | |||||||
\(14\) | 2.30416e66 | 0.206074 | ||||||||
\(15\) | 6.46226e68 | 1.02105 | ||||||||
\(16\) | 8.21190e69 | 0.297457 | ||||||||
\(17\) | 3.00946e71 | 0.314215 | 0.157108 | − | 0.987581i | \(-0.449783\pi\) | ||||
0.157108 | + | 0.987581i | \(0.449783\pi\) | |||||||
\(18\) | 7.83774e72 | 0.288901 | ||||||||
\(19\) | 5.05945e74 | 0.788893 | 0.394446 | − | 0.918919i | \(-0.370936\pi\) | ||||
0.394446 | + | 0.918919i | \(0.370936\pi\) | |||||||
\(20\) | 7.81220e75 | 0.606064 | ||||||||
\(21\) | −1.14232e77 | −0.510456 | ||||||||
\(22\) | 5.36510e77 | 0.157707 | ||||||||
\(23\) | 4.56056e79 | 0.995266 | 0.497633 | − | 0.867388i | \(-0.334203\pi\) | ||||
0.497633 | + | 0.867388i | \(0.334203\pi\) | |||||||
\(24\) | 6.11118e80 | 1.10603 | ||||||||
\(25\) | −2.02444e81 | −0.336367 | ||||||||
\(26\) | −3.24303e82 | −0.543263 | ||||||||
\(27\) | 2.91988e83 | 0.537755 | ||||||||
\(28\) | −1.38094e84 | −0.302992 | ||||||||
\(29\) | 6.67232e85 | 1.87929 | 0.939646 | − | 0.342149i | \(-0.111155\pi\) | ||||
0.939646 | + | 0.342149i | \(0.111155\pi\) | |||||||
\(30\) | 1.33286e86 | 0.516646 | ||||||||
\(31\) | 2.24272e87 | 1.27678 | 0.638389 | − | 0.769714i | \(-0.279601\pi\) | ||||
0.638389 | + | 0.769714i | \(0.279601\pi\) | |||||||
\(32\) | 1.16240e88 | 1.03295 | ||||||||
\(33\) | −2.65981e88 | −0.390648 | ||||||||
\(34\) | 6.20713e88 | 0.158992 | ||||||||
\(35\) | −7.06026e89 | −0.331772 | ||||||||
\(36\) | −4.69735e90 | −0.424773 | ||||||||
\(37\) | −8.85763e91 | −1.61256 | −0.806281 | − | 0.591532i | \(-0.798523\pi\) | ||||
−0.806281 | + | 0.591532i | \(0.798523\pi\) | |||||||
\(38\) | 1.04353e92 | 0.399176 | ||||||||
\(39\) | 1.60777e93 | 1.34569 | ||||||||
\(40\) | 3.77710e93 | 0.718868 | ||||||||
\(41\) | −2.18111e94 | −0.979088 | −0.489544 | − | 0.871979i | \(-0.662837\pi\) | ||||
−0.489544 | + | 0.871979i | \(0.662837\pi\) | |||||||
\(42\) | −2.35607e94 | −0.258288 | ||||||||
\(43\) | −3.81160e95 | −1.05488 | −0.527440 | − | 0.849592i | \(-0.676848\pi\) | ||||
−0.527440 | + | 0.849592i | \(0.676848\pi\) | |||||||
\(44\) | −3.21544e95 | −0.231877 | ||||||||
\(45\) | −2.40159e96 | −0.465121 | ||||||||
\(46\) | 9.40631e96 | 0.503601 | ||||||||
\(47\) | −2.67847e97 | −0.407532 | −0.203766 | − | 0.979020i | \(-0.565318\pi\) | ||||
−0.203766 | + | 0.979020i | \(0.565318\pi\) | |||||||
\(48\) | −8.39690e97 | −0.372826 | ||||||||
\(49\) | −6.27636e98 | −0.834136 | ||||||||
\(50\) | −4.17547e98 | −0.170200 | ||||||||
\(51\) | −3.07726e99 | −0.393830 | ||||||||
\(52\) | 1.94363e100 | 0.798763 | ||||||||
\(53\) | 8.42877e100 | 1.13665 | 0.568324 | − | 0.822805i | \(-0.307592\pi\) | ||||
0.568324 | + | 0.822805i | \(0.307592\pi\) | |||||||
\(54\) | 6.02235e100 | 0.272102 | ||||||||
\(55\) | −1.64394e101 | −0.253903 | ||||||||
\(56\) | −6.67669e101 | −0.359386 | ||||||||
\(57\) | −5.17343e102 | −0.988780 | ||||||||
\(58\) | 1.37619e103 | 0.950913 | ||||||||
\(59\) | 3.41944e103 | 0.869184 | 0.434592 | − | 0.900627i | \(-0.356893\pi\) | ||||
0.434592 | + | 0.900627i | \(0.356893\pi\) | |||||||
\(60\) | −7.98819e103 | −0.759627 | ||||||||
\(61\) | −4.30059e104 | −1.55501 | −0.777505 | − | 0.628877i | \(-0.783515\pi\) | ||||
−0.777505 | + | 0.628877i | \(0.783515\pi\) | |||||||
\(62\) | 4.62569e104 | 0.646045 | ||||||||
\(63\) | 4.24522e104 | 0.232530 | ||||||||
\(64\) | 1.03305e105 | 0.225212 | ||||||||
\(65\) | 9.93708e105 | 0.874636 | ||||||||
\(66\) | −5.48596e105 | −0.197666 | ||||||||
\(67\) | 7.34075e105 | 0.109740 | 0.0548700 | − | 0.998494i | \(-0.482526\pi\) | ||||
0.0548700 | + | 0.998494i | \(0.482526\pi\) | |||||||
\(68\) | −3.72009e106 | −0.233766 | ||||||||
\(69\) | −4.66330e107 | −1.24744 | ||||||||
\(70\) | −1.45620e107 | −0.167875 | ||||||||
\(71\) | 2.49365e108 | 1.25378 | 0.626890 | − | 0.779108i | \(-0.284327\pi\) | ||||
0.626890 | + | 0.779108i | \(0.284327\pi\) | |||||||
\(72\) | −2.27111e108 | −0.503834 | ||||||||
\(73\) | 7.67304e108 | 0.759591 | 0.379796 | − | 0.925070i | \(-0.375994\pi\) | ||||
0.379796 | + | 0.925070i | \(0.375994\pi\) | |||||||
\(74\) | −1.82692e109 | −0.815950 | ||||||||
\(75\) | 2.07004e109 | 0.421595 | ||||||||
\(76\) | −6.25414e109 | −0.586911 | ||||||||
\(77\) | 2.90595e109 | 0.126935 | ||||||||
\(78\) | 3.31609e110 | 0.680914 | ||||||||
\(79\) | −6.74284e110 | −0.657140 | −0.328570 | − | 0.944480i | \(-0.606567\pi\) | ||||
−0.328570 | + | 0.944480i | \(0.606567\pi\) | |||||||
\(80\) | −5.18982e110 | −0.242320 | ||||||||
\(81\) | −5.51481e111 | −1.24497 | ||||||||
\(82\) | −4.49862e111 | −0.495414 | ||||||||
\(83\) | 1.43081e112 | 0.775377 | 0.387689 | − | 0.921790i | \(-0.373274\pi\) | ||||
0.387689 | + | 0.921790i | \(0.373274\pi\) | |||||||
\(84\) | 1.41205e112 | 0.379763 | ||||||||
\(85\) | −1.90195e112 | −0.255971 | ||||||||
\(86\) | −7.86157e112 | −0.533764 | ||||||||
\(87\) | −6.82264e113 | −2.35546 | ||||||||
\(88\) | −1.55463e113 | −0.275036 | ||||||||
\(89\) | −1.04979e114 | −0.958928 | −0.479464 | − | 0.877562i | \(-0.659169\pi\) | ||||
−0.479464 | + | 0.877562i | \(0.659169\pi\) | |||||||
\(90\) | −4.95336e113 | −0.235349 | ||||||||
\(91\) | −1.75655e114 | −0.437260 | ||||||||
\(92\) | −5.63744e114 | −0.740447 | ||||||||
\(93\) | −2.29324e115 | −1.60029 | ||||||||
\(94\) | −5.52444e114 | −0.206209 | ||||||||
\(95\) | −3.19752e115 | −0.642661 | ||||||||
\(96\) | −1.18858e116 | −1.29468 | ||||||||
\(97\) | −1.36089e116 | −0.808492 | −0.404246 | − | 0.914650i | \(-0.632466\pi\) | ||||
−0.404246 | + | 0.914650i | \(0.632466\pi\) | |||||||
\(98\) | −1.29452e116 | −0.422069 | ||||||||
\(99\) | 9.88474e115 | 0.177953 | ||||||||
\(100\) | 2.50247e116 | 0.250247 | ||||||||
\(101\) | −2.33869e117 | −1.30669 | −0.653346 | − | 0.757060i | \(-0.726635\pi\) | ||||
−0.653346 | + | 0.757060i | \(0.726635\pi\) | |||||||
\(102\) | −6.34696e116 | −0.199276 | ||||||||
\(103\) | 8.81025e117 | 1.56319 | 0.781593 | − | 0.623789i | \(-0.214408\pi\) | ||||
0.781593 | + | 0.623789i | \(0.214408\pi\) | |||||||
\(104\) | 9.39722e117 | 0.947434 | ||||||||
\(105\) | 7.21931e117 | 0.415836 | ||||||||
\(106\) | 1.73846e118 | 0.575139 | ||||||||
\(107\) | 1.43168e118 | 0.273461 | 0.136731 | − | 0.990608i | \(-0.456341\pi\) | ||||
0.136731 | + | 0.990608i | \(0.456341\pi\) | |||||||
\(108\) | −3.60934e118 | −0.400072 | ||||||||
\(109\) | 1.62351e119 | 1.04955 | 0.524777 | − | 0.851240i | \(-0.324149\pi\) | ||||
0.524777 | + | 0.851240i | \(0.324149\pi\) | |||||||
\(110\) | −3.39068e118 | −0.128474 | ||||||||
\(111\) | 9.05718e119 | 2.02115 | ||||||||
\(112\) | 9.17392e118 | 0.121144 | ||||||||
\(113\) | 1.94627e119 | 0.152797 | 0.0763983 | − | 0.997077i | \(-0.475658\pi\) | ||||
0.0763983 | + | 0.997077i | \(0.475658\pi\) | |||||||
\(114\) | −1.06704e120 | −0.500319 | ||||||||
\(115\) | −2.88222e120 | −0.810780 | ||||||||
\(116\) | −8.24785e120 | −1.39813 | ||||||||
\(117\) | −5.97501e120 | −0.613008 | ||||||||
\(118\) | 7.05271e120 | 0.439803 | ||||||||
\(119\) | 3.36202e120 | 0.127969 | ||||||||
\(120\) | −3.86219e121 | −0.901013 | ||||||||
\(121\) | −6.28874e121 | −0.902858 | ||||||||
\(122\) | −8.87013e121 | −0.786828 | ||||||||
\(123\) | 2.23025e122 | 1.22717 | ||||||||
\(124\) | −2.77229e122 | −0.949883 | ||||||||
\(125\) | 5.08306e122 | 1.08865 | ||||||||
\(126\) | 8.75593e121 | 0.117659 | ||||||||
\(127\) | 1.11458e123 | 0.943180 | 0.471590 | − | 0.881818i | \(-0.343680\pi\) | ||||
0.471590 | + | 0.881818i | \(0.343680\pi\) | |||||||
\(128\) | −1.71829e123 | −0.918996 | ||||||||
\(129\) | 3.89747e123 | 1.32216 | ||||||||
\(130\) | 2.04956e123 | 0.442562 | ||||||||
\(131\) | 3.81645e123 | 0.526368 | 0.263184 | − | 0.964746i | \(-0.415227\pi\) | ||||
0.263184 | + | 0.964746i | \(0.415227\pi\) | |||||||
\(132\) | 3.28788e123 | 0.290630 | ||||||||
\(133\) | 5.65217e123 | 0.321288 | ||||||||
\(134\) | 1.51406e123 | 0.0555279 | ||||||||
\(135\) | −1.84533e124 | −0.438075 | ||||||||
\(136\) | −1.79862e124 | −0.277276 | ||||||||
\(137\) | −1.23314e125 | −1.23839 | −0.619196 | − | 0.785236i | \(-0.712541\pi\) | ||||
−0.619196 | + | 0.785236i | \(0.712541\pi\) | |||||||
\(138\) | −9.61822e124 | −0.631202 | ||||||||
\(139\) | −2.80964e125 | −1.20860 | −0.604302 | − | 0.796755i | \(-0.706548\pi\) | ||||
−0.604302 | + | 0.796755i | \(0.706548\pi\) | |||||||
\(140\) | 8.72739e124 | 0.246828 | ||||||||
\(141\) | 2.73881e125 | 0.510791 | ||||||||
\(142\) | 5.14324e125 | 0.634408 | ||||||||
\(143\) | −4.09002e125 | −0.334632 | ||||||||
\(144\) | 3.12056e125 | 0.169835 | ||||||||
\(145\) | −4.21683e126 | −1.53094 | ||||||||
\(146\) | 1.58259e126 | 0.384350 | ||||||||
\(147\) | 6.41775e126 | 1.04549 | ||||||||
\(148\) | 1.09492e127 | 1.19970 | ||||||||
\(149\) | 8.13026e126 | 0.600769 | 0.300385 | − | 0.953818i | \(-0.402885\pi\) | ||||
0.300385 | + | 0.953818i | \(0.402885\pi\) | |||||||
\(150\) | 4.26954e126 | 0.213325 | ||||||||
\(151\) | 1.66189e127 | 0.562924 | 0.281462 | − | 0.959572i | \(-0.409181\pi\) | ||||
0.281462 | + | 0.959572i | \(0.409181\pi\) | |||||||
\(152\) | −3.02380e127 | −0.696151 | ||||||||
\(153\) | 1.14361e127 | 0.179403 | ||||||||
\(154\) | 5.99362e126 | 0.0642284 | ||||||||
\(155\) | −1.41737e128 | −1.04011 | ||||||||
\(156\) | −1.98742e128 | −1.00115 | ||||||||
\(157\) | 3.29730e128 | 1.14296 | 0.571478 | − | 0.820618i | \(-0.306370\pi\) | ||||
0.571478 | + | 0.820618i | \(0.306370\pi\) | |||||||
\(158\) | −1.39073e128 | −0.332510 | ||||||||
\(159\) | −8.61866e128 | −1.42465 | ||||||||
\(160\) | −7.34621e128 | −0.841481 | ||||||||
\(161\) | 5.09482e128 | 0.405336 | ||||||||
\(162\) | −1.13745e129 | −0.629947 | ||||||||
\(163\) | 3.57156e129 | 1.38001 | 0.690006 | − | 0.723804i | \(-0.257608\pi\) | ||||
0.690006 | + | 0.723804i | \(0.257608\pi\) | |||||||
\(164\) | 2.69613e129 | 0.728410 | ||||||||
\(165\) | 1.68097e129 | 0.318236 | ||||||||
\(166\) | 2.95109e129 | 0.392338 | ||||||||
\(167\) | −5.12749e129 | −0.479724 | −0.239862 | − | 0.970807i | \(-0.577102\pi\) | ||||
−0.239862 | + | 0.970807i | \(0.577102\pi\) | |||||||
\(168\) | 6.82710e129 | 0.450447 | ||||||||
\(169\) | 3.27560e129 | 0.152728 | ||||||||
\(170\) | −3.92283e129 | −0.129520 | ||||||||
\(171\) | 1.92262e130 | 0.450423 | ||||||||
\(172\) | 4.71163e130 | 0.784797 | ||||||||
\(173\) | −9.87059e129 | −0.117124 | −0.0585620 | − | 0.998284i | \(-0.518652\pi\) | ||||
−0.0585620 | + | 0.998284i | \(0.518652\pi\) | |||||||
\(174\) | −1.40719e131 | −1.19185 | ||||||||
\(175\) | −2.26160e130 | −0.136990 | ||||||||
\(176\) | 2.13609e130 | 0.0927104 | ||||||||
\(177\) | −3.49647e131 | −1.08942 | ||||||||
\(178\) | −2.16523e131 | −0.485214 | ||||||||
\(179\) | −9.05305e131 | −1.46182 | −0.730908 | − | 0.682476i | \(-0.760903\pi\) | ||||
−0.730908 | + | 0.682476i | \(0.760903\pi\) | |||||||
\(180\) | 2.96867e131 | 0.346036 | ||||||||
\(181\) | 1.41858e132 | 1.19580 | 0.597899 | − | 0.801571i | \(-0.296002\pi\) | ||||
0.597899 | + | 0.801571i | \(0.296002\pi\) | |||||||
\(182\) | −3.62295e131 | −0.221252 | ||||||||
\(183\) | 4.39748e132 | 1.94901 | ||||||||
\(184\) | −2.72563e132 | −0.878263 | ||||||||
\(185\) | 5.59792e132 | 1.31365 | ||||||||
\(186\) | −4.72990e132 | −0.809738 | ||||||||
\(187\) | 7.82826e131 | 0.0979335 | ||||||||
\(188\) | 3.31093e132 | 0.303191 | ||||||||
\(189\) | 3.26194e132 | 0.219008 | ||||||||
\(190\) | −6.59499e132 | −0.325184 | ||||||||
\(191\) | 4.37164e133 | 1.58560 | 0.792798 | − | 0.609485i | \(-0.208624\pi\) | ||||
0.792798 | + | 0.609485i | \(0.208624\pi\) | |||||||
\(192\) | −1.05632e133 | −0.282276 | ||||||||
\(193\) | −9.31937e133 | −1.83774 | −0.918870 | − | 0.394562i | \(-0.870896\pi\) | ||||
−0.918870 | + | 0.394562i | \(0.870896\pi\) | |||||||
\(194\) | −2.80688e133 | −0.409094 | ||||||||
\(195\) | −1.01609e134 | −1.09625 | ||||||||
\(196\) | 7.75839e133 | 0.620571 | ||||||||
\(197\) | −8.84922e132 | −0.0525570 | −0.0262785 | − | 0.999655i | \(-0.508366\pi\) | ||||
−0.0262785 | + | 0.999655i | \(0.508366\pi\) | |||||||
\(198\) | 2.03876e133 | 0.0900437 | ||||||||
\(199\) | −3.89716e133 | −0.128187 | −0.0640934 | − | 0.997944i | \(-0.520416\pi\) | ||||
−0.0640934 | + | 0.997944i | \(0.520416\pi\) | |||||||
\(200\) | 1.20991e134 | 0.296824 | ||||||||
\(201\) | −7.50613e133 | −0.137546 | ||||||||
\(202\) | −4.82364e134 | −0.661180 | ||||||||
\(203\) | 7.45398e134 | 0.765368 | ||||||||
\(204\) | 3.80389e134 | 0.292997 | ||||||||
\(205\) | 1.37844e135 | 0.797601 | ||||||||
\(206\) | 1.81715e135 | 0.790965 | ||||||||
\(207\) | 1.73303e135 | 0.568253 | ||||||||
\(208\) | −1.29120e135 | −0.319365 | ||||||||
\(209\) | 1.31607e135 | 0.245879 | ||||||||
\(210\) | 1.48901e135 | 0.210411 | ||||||||
\(211\) | −1.06499e136 | −1.13978 | −0.569892 | − | 0.821720i | \(-0.693015\pi\) | ||||
−0.569892 | + | 0.821720i | \(0.693015\pi\) | |||||||
\(212\) | −1.04191e136 | −0.845630 | ||||||||
\(213\) | −2.54982e136 | −1.57146 | ||||||||
\(214\) | 2.95290e135 | 0.138370 | ||||||||
\(215\) | 2.40889e136 | 0.859343 | ||||||||
\(216\) | −1.74507e136 | −0.474536 | ||||||||
\(217\) | 2.50545e136 | 0.519986 | ||||||||
\(218\) | 3.34855e136 | 0.531070 | ||||||||
\(219\) | −7.84590e136 | −0.952055 | ||||||||
\(220\) | 2.03212e136 | 0.188896 | ||||||||
\(221\) | −4.73193e136 | −0.337358 | ||||||||
\(222\) | 1.86808e137 | 1.02269 | ||||||||
\(223\) | 8.11659e136 | 0.341617 | 0.170808 | − | 0.985304i | \(-0.445362\pi\) | ||||
0.170808 | + | 0.985304i | \(0.445362\pi\) | |||||||
\(224\) | 1.29857e137 | 0.420684 | ||||||||
\(225\) | −7.69296e136 | −0.192051 | ||||||||
\(226\) | 4.01425e136 | 0.0773144 | ||||||||
\(227\) | 4.44026e137 | 0.660536 | 0.330268 | − | 0.943887i | \(-0.392861\pi\) | ||||
0.330268 | + | 0.943887i | \(0.392861\pi\) | |||||||
\(228\) | 6.39503e137 | 0.735621 | ||||||||
\(229\) | −4.74332e137 | −0.422383 | −0.211192 | − | 0.977445i | \(-0.567734\pi\) | ||||
−0.211192 | + | 0.977445i | \(0.567734\pi\) | |||||||
\(230\) | −5.94468e137 | −0.410251 | ||||||||
\(231\) | −2.97141e137 | −0.159097 | ||||||||
\(232\) | −3.98774e138 | −1.65836 | ||||||||
\(233\) | −5.00182e137 | −0.161736 | −0.0808680 | − | 0.996725i | \(-0.525769\pi\) | ||||
−0.0808680 | + | 0.996725i | \(0.525769\pi\) | |||||||
\(234\) | −1.23237e138 | −0.310179 | ||||||||
\(235\) | 1.69276e138 | 0.331990 | ||||||||
\(236\) | −4.22687e138 | −0.646645 | ||||||||
\(237\) | 6.89474e138 | 0.823644 | ||||||||
\(238\) | 6.93429e137 | 0.0647515 | ||||||||
\(239\) | −5.26866e138 | −0.384966 | −0.192483 | − | 0.981300i | \(-0.561654\pi\) | ||||
−0.192483 | + | 0.981300i | \(0.561654\pi\) | |||||||
\(240\) | 5.30674e138 | 0.303718 | ||||||||
\(241\) | 6.24703e138 | 0.280334 | 0.140167 | − | 0.990128i | \(-0.455236\pi\) | ||||
0.140167 | + | 0.990128i | \(0.455236\pi\) | |||||||
\(242\) | −1.29708e139 | −0.456842 | ||||||||
\(243\) | 3.69570e139 | 1.02266 | ||||||||
\(244\) | 5.31609e139 | 1.15688 | ||||||||
\(245\) | 3.96658e139 | 0.679518 | ||||||||
\(246\) | 4.59996e139 | 0.620941 | ||||||||
\(247\) | −7.95524e139 | −0.846996 | ||||||||
\(248\) | −1.34037e140 | −1.12668 | ||||||||
\(249\) | −1.46304e140 | −0.971841 | ||||||||
\(250\) | 1.04840e140 | 0.550854 | ||||||||
\(251\) | −2.35375e140 | −0.979145 | −0.489572 | − | 0.871963i | \(-0.662847\pi\) | ||||
−0.489572 | + | 0.871963i | \(0.662847\pi\) | |||||||
\(252\) | −5.24765e139 | −0.172995 | ||||||||
\(253\) | 1.18630e140 | 0.310201 | ||||||||
\(254\) | 2.29887e140 | 0.477245 | ||||||||
\(255\) | 1.94479e140 | 0.320829 | ||||||||
\(256\) | −5.26049e140 | −0.690220 | ||||||||
\(257\) | −6.06950e140 | −0.633965 | −0.316982 | − | 0.948431i | \(-0.602670\pi\) | ||||
−0.316982 | + | 0.948431i | \(0.602670\pi\) | |||||||
\(258\) | 8.03867e140 | 0.669009 | ||||||||
\(259\) | −9.89530e140 | −0.656739 | ||||||||
\(260\) | −1.22835e141 | −0.650701 | ||||||||
\(261\) | 2.53551e141 | 1.07299 | ||||||||
\(262\) | 7.87157e140 | 0.266340 | ||||||||
\(263\) | 6.71043e141 | 1.81693 | 0.908466 | − | 0.417958i | \(-0.137254\pi\) | ||||
0.908466 | + | 0.417958i | \(0.137254\pi\) | |||||||
\(264\) | 1.58965e141 | 0.344724 | ||||||||
\(265\) | −5.32689e141 | −0.925955 | ||||||||
\(266\) | 1.16578e141 | 0.162570 | ||||||||
\(267\) | 1.07344e142 | 1.20190 | ||||||||
\(268\) | −9.07412e140 | −0.0816430 | ||||||||
\(269\) | −1.79907e142 | −1.30178 | −0.650892 | − | 0.759170i | \(-0.725605\pi\) | ||||
−0.650892 | + | 0.759170i | \(0.725605\pi\) | |||||||
\(270\) | −3.80606e141 | −0.221664 | ||||||||
\(271\) | −3.65599e142 | −1.71515 | −0.857575 | − | 0.514360i | \(-0.828030\pi\) | ||||
−0.857575 | + | 0.514360i | \(0.828030\pi\) | |||||||
\(272\) | 2.47134e141 | 0.0934656 | ||||||||
\(273\) | 1.79612e142 | 0.548052 | ||||||||
\(274\) | −2.54339e142 | −0.626621 | ||||||||
\(275\) | −5.26599e141 | −0.104838 | ||||||||
\(276\) | 5.76444e142 | 0.928059 | ||||||||
\(277\) | −3.51238e142 | −0.457652 | −0.228826 | − | 0.973467i | \(-0.573489\pi\) | ||||
−0.228826 | + | 0.973467i | \(0.573489\pi\) | |||||||
\(278\) | −5.79498e142 | −0.611549 | ||||||||
\(279\) | 8.52244e142 | 0.728984 | ||||||||
\(280\) | 4.21959e142 | 0.292769 | ||||||||
\(281\) | 2.99440e142 | 0.168651 | 0.0843257 | − | 0.996438i | \(-0.473126\pi\) | ||||
0.0843257 | + | 0.996438i | \(0.473126\pi\) | |||||||
\(282\) | 5.64889e142 | 0.258458 | ||||||||
\(283\) | 3.94255e143 | 1.46646 | 0.733231 | − | 0.679979i | \(-0.238011\pi\) | ||||
0.733231 | + | 0.679979i | \(0.238011\pi\) | |||||||
\(284\) | −3.08247e143 | −0.932773 | ||||||||
\(285\) | 3.26955e143 | 0.805497 | ||||||||
\(286\) | −8.43582e142 | −0.169322 | ||||||||
\(287\) | −2.43662e143 | −0.398747 | ||||||||
\(288\) | 4.41716e143 | 0.589770 | ||||||||
\(289\) | −8.26758e143 | −0.901269 | ||||||||
\(290\) | −8.69737e143 | −0.774649 | ||||||||
\(291\) | 1.39155e144 | 1.01335 | ||||||||
\(292\) | −9.48487e143 | −0.565112 | ||||||||
\(293\) | −3.46158e144 | −1.68857 | −0.844285 | − | 0.535895i | \(-0.819974\pi\) | ||||
−0.844285 | + | 0.535895i | \(0.819974\pi\) | |||||||
\(294\) | 1.32368e144 | 0.529012 | ||||||||
\(295\) | −2.16104e144 | −0.708069 | ||||||||
\(296\) | 5.29380e144 | 1.42299 | ||||||||
\(297\) | 7.59522e143 | 0.167605 | ||||||||
\(298\) | 1.67690e144 | 0.303987 | ||||||||
\(299\) | −7.17080e144 | −1.06857 | ||||||||
\(300\) | −2.55884e144 | −0.313654 | ||||||||
\(301\) | −4.25813e144 | −0.429614 | ||||||||
\(302\) | 3.42770e144 | 0.284837 | ||||||||
\(303\) | 2.39138e145 | 1.63778 | ||||||||
\(304\) | 4.15477e144 | 0.234662 | ||||||||
\(305\) | 2.71793e145 | 1.26677 | ||||||||
\(306\) | 2.35874e144 | 0.0907771 | ||||||||
\(307\) | 2.43352e145 | 0.773821 | 0.386910 | − | 0.922117i | \(-0.373542\pi\) | ||||
0.386910 | + | 0.922117i | \(0.373542\pi\) | |||||||
\(308\) | −3.59212e144 | −0.0944353 | ||||||||
\(309\) | −9.00873e145 | −1.95926 | ||||||||
\(310\) | −2.92338e145 | −0.526292 | ||||||||
\(311\) | −5.29296e144 | −0.0789252 | −0.0394626 | − | 0.999221i | \(-0.512565\pi\) | ||||
−0.0394626 | + | 0.999221i | \(0.512565\pi\) | |||||||
\(312\) | −9.60892e145 | −1.18749 | ||||||||
\(313\) | −4.02666e145 | −0.412669 | −0.206334 | − | 0.978482i | \(-0.566153\pi\) | ||||
−0.206334 | + | 0.978482i | \(0.566153\pi\) | |||||||
\(314\) | 6.80081e145 | 0.578331 | ||||||||
\(315\) | −2.68293e145 | −0.189427 | ||||||||
\(316\) | 8.33502e145 | 0.488891 | ||||||||
\(317\) | 1.18600e146 | 0.578253 | 0.289126 | − | 0.957291i | \(-0.406635\pi\) | ||||
0.289126 | + | 0.957291i | \(0.406635\pi\) | |||||||
\(318\) | −1.77763e146 | −0.720866 | ||||||||
\(319\) | 1.73561e146 | 0.585731 | ||||||||
\(320\) | −6.52875e145 | −0.183466 | ||||||||
\(321\) | −1.46394e146 | −0.342750 | ||||||||
\(322\) | 1.05083e146 | 0.205098 | ||||||||
\(323\) | 1.52262e146 | 0.247882 | ||||||||
\(324\) | 6.81702e146 | 0.926215 | ||||||||
\(325\) | 3.18313e146 | 0.361141 | ||||||||
\(326\) | 7.36647e146 | 0.698280 | ||||||||
\(327\) | −1.66008e147 | −1.31549 | ||||||||
\(328\) | 1.30355e147 | 0.863987 | ||||||||
\(329\) | −2.99225e146 | −0.165973 | ||||||||
\(330\) | 3.46707e146 | 0.161026 | ||||||||
\(331\) | −2.45081e146 | −0.0953614 | −0.0476807 | − | 0.998863i | \(-0.515183\pi\) | ||||
−0.0476807 | + | 0.998863i | \(0.515183\pi\) | |||||||
\(332\) | −1.76866e147 | −0.576856 | ||||||||
\(333\) | −3.36594e147 | −0.920702 | ||||||||
\(334\) | −1.05756e147 | −0.242738 | ||||||||
\(335\) | −4.63927e146 | −0.0893982 | ||||||||
\(336\) | −9.38059e146 | −0.151839 | ||||||||
\(337\) | −1.19796e147 | −0.162964 | −0.0814822 | − | 0.996675i | \(-0.525965\pi\) | ||||
−0.0814822 | + | 0.996675i | \(0.525965\pi\) | |||||||
\(338\) | 6.75605e146 | 0.0772798 | ||||||||
\(339\) | −1.99011e147 | −0.191512 | ||||||||
\(340\) | 2.35105e147 | 0.190434 | ||||||||
\(341\) | 5.83379e147 | 0.397942 | ||||||||
\(342\) | 3.96547e147 | 0.227912 | ||||||||
\(343\) | −1.54175e148 | −0.746978 | ||||||||
\(344\) | 2.27802e148 | 0.930868 | ||||||||
\(345\) | 2.94715e148 | 1.01621 | ||||||||
\(346\) | −2.03584e147 | −0.0592642 | ||||||||
\(347\) | −4.41566e148 | −1.08573 | −0.542864 | − | 0.839820i | \(-0.682660\pi\) | ||||
−0.542864 | + | 0.839820i | \(0.682660\pi\) | |||||||
\(348\) | 8.43366e148 | 1.75239 | ||||||||
\(349\) | 3.55967e148 | 0.625349 | 0.312675 | − | 0.949860i | \(-0.398775\pi\) | ||||
0.312675 | + | 0.949860i | \(0.398775\pi\) | |||||||
\(350\) | −4.66463e147 | −0.0693165 | ||||||||
\(351\) | −4.59107e148 | −0.577361 | ||||||||
\(352\) | 3.02364e148 | 0.321947 | ||||||||
\(353\) | −1.87564e149 | −1.69172 | −0.845860 | − | 0.533406i | \(-0.820912\pi\) | ||||
−0.845860 | + | 0.533406i | \(0.820912\pi\) | |||||||
\(354\) | −7.21160e148 | −0.551240 | ||||||||
\(355\) | −1.57596e149 | −1.02138 | ||||||||
\(356\) | 1.29767e149 | 0.713412 | ||||||||
\(357\) | −3.43776e148 | −0.160393 | ||||||||
\(358\) | −1.86723e149 | −0.739673 | ||||||||
\(359\) | 1.17918e149 | 0.396784 | 0.198392 | − | 0.980123i | \(-0.436428\pi\) | ||||
0.198392 | + | 0.980123i | \(0.436428\pi\) | |||||||
\(360\) | 1.43532e149 | 0.410442 | ||||||||
\(361\) | −1.55331e149 | −0.377648 | ||||||||
\(362\) | 2.92588e149 | 0.605069 | ||||||||
\(363\) | 6.43041e149 | 1.13162 | ||||||||
\(364\) | 2.17133e149 | 0.325307 | ||||||||
\(365\) | −4.84927e149 | −0.618791 | ||||||||
\(366\) | 9.06996e149 | 0.986193 | ||||||||
\(367\) | −1.64912e150 | −1.52858 | −0.764289 | − | 0.644874i | \(-0.776910\pi\) | ||||
−0.764289 | + | 0.644874i | \(0.776910\pi\) | |||||||
\(368\) | 3.74508e149 | 0.296049 | ||||||||
\(369\) | −8.28832e149 | −0.559016 | ||||||||
\(370\) | 1.15459e150 | 0.664703 | ||||||||
\(371\) | 9.41620e149 | 0.462916 | ||||||||
\(372\) | 2.83475e150 | 1.19056 | ||||||||
\(373\) | 1.25728e150 | 0.451302 | 0.225651 | − | 0.974208i | \(-0.427549\pi\) | ||||
0.225651 | + | 0.974208i | \(0.427549\pi\) | |||||||
\(374\) | 1.61461e149 | 0.0495539 | ||||||||
\(375\) | −5.19758e150 | −1.36449 | ||||||||
\(376\) | 1.60080e150 | 0.359623 | ||||||||
\(377\) | −1.04912e151 | −2.01770 | ||||||||
\(378\) | 6.72787e149 | 0.110817 | ||||||||
\(379\) | −7.82834e150 | −1.10478 | −0.552390 | − | 0.833586i | \(-0.686284\pi\) | ||||
−0.552390 | + | 0.833586i | \(0.686284\pi\) | |||||||
\(380\) | 3.95254e150 | 0.478119 | ||||||||
\(381\) | −1.13969e151 | −1.18216 | ||||||||
\(382\) | 9.01667e150 | 0.802305 | ||||||||
\(383\) | 1.36028e151 | 1.03872 | 0.519360 | − | 0.854555i | \(-0.326170\pi\) | ||||
0.519360 | + | 0.854555i | \(0.326170\pi\) | |||||||
\(384\) | 1.75700e151 | 1.15185 | ||||||||
\(385\) | −1.83652e150 | −0.103406 | ||||||||
\(386\) | −1.92215e151 | −0.929888 | ||||||||
\(387\) | −1.44843e151 | −0.602289 | ||||||||
\(388\) | 1.68223e151 | 0.601493 | ||||||||
\(389\) | 5.70014e151 | 1.75321 | 0.876605 | − | 0.481211i | \(-0.159803\pi\) | ||||
0.876605 | + | 0.481211i | \(0.159803\pi\) | |||||||
\(390\) | −2.09573e151 | −0.554697 | ||||||||
\(391\) | 1.37248e151 | 0.312728 | ||||||||
\(392\) | 3.75109e151 | 0.736075 | ||||||||
\(393\) | −3.90243e151 | −0.659737 | ||||||||
\(394\) | −1.82518e150 | −0.0265936 | ||||||||
\(395\) | 4.26140e151 | 0.535330 | ||||||||
\(396\) | −1.22188e151 | −0.132392 | ||||||||
\(397\) | −1.28954e152 | −1.20557 | −0.602783 | − | 0.797905i | \(-0.705941\pi\) | ||||
−0.602783 | + | 0.797905i | \(0.705941\pi\) | |||||||
\(398\) | −8.03803e150 | −0.0648619 | ||||||||
\(399\) | −5.77950e151 | −0.402695 | ||||||||
\(400\) | −1.66245e151 | −0.100055 | ||||||||
\(401\) | −1.35206e152 | −0.703151 | −0.351576 | − | 0.936159i | \(-0.614354\pi\) | ||||
−0.351576 | + | 0.936159i | \(0.614354\pi\) | |||||||
\(402\) | −1.54817e151 | −0.0695975 | ||||||||
\(403\) | −3.52634e152 | −1.37082 | ||||||||
\(404\) | 2.89093e152 | 0.972137 | ||||||||
\(405\) | 3.48530e152 | 1.01419 | ||||||||
\(406\) | 1.53741e152 | 0.387273 | ||||||||
\(407\) | −2.30406e152 | −0.502598 | ||||||||
\(408\) | 1.83914e152 | 0.347532 | ||||||||
\(409\) | −3.83225e151 | −0.0627539 | −0.0313769 | − | 0.999508i | \(-0.509989\pi\) | ||||
−0.0313769 | + | 0.999508i | \(0.509989\pi\) | |||||||
\(410\) | 2.84307e152 | 0.403583 | ||||||||
\(411\) | 1.26092e153 | 1.55217 | ||||||||
\(412\) | −1.08906e153 | −1.16296 | ||||||||
\(413\) | 3.82002e152 | 0.353987 | ||||||||
\(414\) | 3.57444e152 | 0.287534 | ||||||||
\(415\) | −9.04255e152 | −0.631651 | ||||||||
\(416\) | −1.82769e153 | −1.10903 | ||||||||
\(417\) | 2.87293e153 | 1.51484 | ||||||||
\(418\) | 2.71445e152 | 0.124414 | ||||||||
\(419\) | −1.20496e152 | −0.0480232 | −0.0240116 | − | 0.999712i | \(-0.507644\pi\) | ||||
−0.0240116 | + | 0.999712i | \(0.507644\pi\) | |||||||
\(420\) | −8.92401e152 | −0.309369 | ||||||||
\(421\) | 2.08475e153 | 0.628855 | 0.314428 | − | 0.949281i | \(-0.398187\pi\) | ||||
0.314428 | + | 0.949281i | \(0.398187\pi\) | |||||||
\(422\) | −2.19658e153 | −0.576726 | ||||||||
\(423\) | −1.01783e153 | −0.232683 | ||||||||
\(424\) | −5.03749e153 | −1.00302 | ||||||||
\(425\) | −6.09247e152 | −0.105692 | ||||||||
\(426\) | −5.25911e153 | −0.795152 | ||||||||
\(427\) | −4.80441e153 | −0.633299 | ||||||||
\(428\) | −1.76975e153 | −0.203447 | ||||||||
\(429\) | 4.18216e153 | 0.419420 | ||||||||
\(430\) | 4.96842e153 | 0.434824 | ||||||||
\(431\) | 1.44213e154 | 1.10175 | 0.550877 | − | 0.834586i | \(-0.314293\pi\) | ||||
0.550877 | + | 0.834586i | \(0.314293\pi\) | |||||||
\(432\) | 2.39777e153 | 0.159959 | ||||||||
\(433\) | 3.21884e153 | 0.187568 | 0.0937838 | − | 0.995593i | \(-0.470104\pi\) | ||||
0.0937838 | + | 0.995593i | \(0.470104\pi\) | |||||||
\(434\) | 5.16759e153 | 0.263111 | ||||||||
\(435\) | 4.31183e154 | 1.91885 | ||||||||
\(436\) | −2.00687e154 | −0.780835 | ||||||||
\(437\) | 2.30739e154 | 0.785158 | ||||||||
\(438\) | −1.61824e154 | −0.481736 | ||||||||
\(439\) | −4.91798e154 | −1.28119 | −0.640593 | − | 0.767881i | \(-0.721311\pi\) | ||||
−0.640593 | + | 0.767881i | \(0.721311\pi\) | |||||||
\(440\) | 9.82505e153 | 0.224054 | ||||||||
\(441\) | −2.38505e154 | −0.476255 | ||||||||
\(442\) | −9.75978e153 | −0.170702 | ||||||||
\(443\) | 5.06151e154 | 0.775644 | 0.387822 | − | 0.921734i | \(-0.373228\pi\) | ||||
0.387822 | + | 0.921734i | \(0.373228\pi\) | |||||||
\(444\) | −1.11958e155 | −1.50367 | ||||||||
\(445\) | 6.63454e154 | 0.781178 | ||||||||
\(446\) | 1.67408e154 | 0.172857 | ||||||||
\(447\) | −8.31342e154 | −0.752991 | ||||||||
\(448\) | 1.15407e154 | 0.0917209 | ||||||||
\(449\) | −3.80471e154 | −0.265406 | −0.132703 | − | 0.991156i | \(-0.542366\pi\) | ||||
−0.132703 | + | 0.991156i | \(0.542366\pi\) | |||||||
\(450\) | −1.58670e154 | −0.0971769 | ||||||||
\(451\) | −5.67353e154 | −0.305159 | ||||||||
\(452\) | −2.40584e154 | −0.113676 | ||||||||
\(453\) | −1.69933e155 | −0.705557 | ||||||||
\(454\) | 9.15821e154 | 0.334228 | ||||||||
\(455\) | 1.11012e155 | 0.356208 | ||||||||
\(456\) | 3.09192e155 | 0.872540 | ||||||||
\(457\) | 7.92549e155 | 1.96756 | 0.983781 | − | 0.179373i | \(-0.0574067\pi\) | ||||
0.983781 | + | 0.179373i | \(0.0574067\pi\) | |||||||
\(458\) | −9.78326e154 | −0.213724 | ||||||||
\(459\) | 8.78726e154 | 0.168971 | ||||||||
\(460\) | 3.56280e155 | 0.603195 | ||||||||
\(461\) | −8.52437e155 | −1.27104 | −0.635518 | − | 0.772086i | \(-0.719214\pi\) | ||||
−0.635518 | + | 0.772086i | \(0.719214\pi\) | |||||||
\(462\) | −6.12864e154 | −0.0805024 | ||||||||
\(463\) | −1.49464e156 | −1.73001 | −0.865007 | − | 0.501760i | \(-0.832686\pi\) | ||||
−0.865007 | + | 0.501760i | \(0.832686\pi\) | |||||||
\(464\) | 5.47924e155 | 0.559009 | ||||||||
\(465\) | 1.44930e156 | 1.30365 | ||||||||
\(466\) | −1.03164e155 | −0.0818378 | ||||||||
\(467\) | −8.02419e155 | −0.561518 | −0.280759 | − | 0.959778i | \(-0.590586\pi\) | ||||
−0.280759 | + | 0.959778i | \(0.590586\pi\) | |||||||
\(468\) | 7.38589e155 | 0.456058 | ||||||||
\(469\) | 8.20072e154 | 0.0446931 | ||||||||
\(470\) | 3.49138e155 | 0.167986 | ||||||||
\(471\) | −3.37159e156 | −1.43255 | ||||||||
\(472\) | −2.04364e156 | −0.767003 | ||||||||
\(473\) | −9.91479e155 | −0.328781 | ||||||||
\(474\) | 1.42207e156 | 0.416761 | ||||||||
\(475\) | −1.02425e156 | −0.265358 | ||||||||
\(476\) | −4.15589e155 | −0.0952045 | ||||||||
\(477\) | 3.20297e156 | 0.648975 | ||||||||
\(478\) | −1.08668e156 | −0.194791 | ||||||||
\(479\) | −5.47633e156 | −0.868684 | −0.434342 | − | 0.900748i | \(-0.643019\pi\) | ||||
−0.434342 | + | 0.900748i | \(0.643019\pi\) | |||||||
\(480\) | 7.51171e156 | 1.05469 | ||||||||
\(481\) | 1.39273e157 | 1.73133 | ||||||||
\(482\) | 1.28847e156 | 0.141848 | ||||||||
\(483\) | −5.20960e156 | −0.508039 | ||||||||
\(484\) | 7.77369e156 | 0.671698 | ||||||||
\(485\) | 8.60065e156 | 0.658627 | ||||||||
\(486\) | 7.62252e156 | 0.517460 | ||||||||
\(487\) | −2.05161e157 | −1.23495 | −0.617477 | − | 0.786589i | \(-0.711845\pi\) | ||||
−0.617477 | + | 0.786589i | \(0.711845\pi\) | |||||||
\(488\) | 2.57027e157 | 1.37220 | ||||||||
\(489\) | −3.65202e157 | −1.72968 | ||||||||
\(490\) | 8.18122e156 | 0.343833 | ||||||||
\(491\) | −4.10785e157 | −1.53231 | −0.766156 | − | 0.642654i | \(-0.777833\pi\) | ||||
−0.766156 | + | 0.642654i | \(0.777833\pi\) | |||||||
\(492\) | −2.75687e157 | −0.912973 | ||||||||
\(493\) | 2.00801e157 | 0.590502 | ||||||||
\(494\) | −1.64080e157 | −0.428576 | ||||||||
\(495\) | −6.24704e156 | −0.144967 | ||||||||
\(496\) | 1.84170e157 | 0.379787 | ||||||||
\(497\) | 2.78578e157 | 0.510620 | ||||||||
\(498\) | −3.01758e157 | −0.491747 | ||||||||
\(499\) | 7.09122e157 | 1.02764 | 0.513818 | − | 0.857899i | \(-0.328231\pi\) | ||||
0.513818 | + | 0.857899i | \(0.328231\pi\) | |||||||
\(500\) | −6.28332e157 | −0.809924 | ||||||||
\(501\) | 5.24301e157 | 0.601275 | ||||||||
\(502\) | −4.85469e157 | −0.495443 | ||||||||
\(503\) | −1.50629e157 | −0.136830 | −0.0684152 | − | 0.997657i | \(-0.521794\pi\) | ||||
−0.0684152 | + | 0.997657i | \(0.521794\pi\) | |||||||
\(504\) | −2.53717e157 | −0.205194 | ||||||||
\(505\) | 1.47803e158 | 1.06448 | ||||||||
\(506\) | 2.44678e157 | 0.156960 | ||||||||
\(507\) | −3.34940e157 | −0.191426 | ||||||||
\(508\) | −1.37777e158 | −0.701696 | ||||||||
\(509\) | 3.20519e158 | 1.45500 | 0.727502 | − | 0.686106i | \(-0.240681\pi\) | ||||
0.727502 | + | 0.686106i | \(0.240681\pi\) | |||||||
\(510\) | 4.01121e157 | 0.162338 | ||||||||
\(511\) | 8.57193e157 | 0.309354 | ||||||||
\(512\) | 1.77001e158 | 0.569747 | ||||||||
\(513\) | 1.47730e158 | 0.424231 | ||||||||
\(514\) | −1.25186e158 | −0.320783 | ||||||||
\(515\) | −5.56797e158 | −1.27343 | ||||||||
\(516\) | −4.81778e158 | −0.983647 | ||||||||
\(517\) | −6.96727e157 | −0.127018 | ||||||||
\(518\) | −2.04094e158 | −0.332307 | ||||||||
\(519\) | 1.00930e158 | 0.146801 | ||||||||
\(520\) | −5.93893e158 | −0.771814 | ||||||||
\(521\) | 5.48692e158 | 0.637267 | 0.318634 | − | 0.947878i | \(-0.396776\pi\) | ||||
0.318634 | + | 0.947878i | \(0.396776\pi\) | |||||||
\(522\) | 5.22959e158 | 0.542929 | ||||||||
\(523\) | −1.11172e159 | −1.03193 | −0.515963 | − | 0.856611i | \(-0.672566\pi\) | ||||
−0.515963 | + | 0.856611i | \(0.672566\pi\) | |||||||
\(524\) | −4.71763e158 | −0.391601 | ||||||||
\(525\) | 2.31255e158 | 0.171701 | ||||||||
\(526\) | 1.38405e159 | 0.919360 | ||||||||
\(527\) | 6.74938e158 | 0.401183 | ||||||||
\(528\) | −2.18421e158 | −0.116201 | ||||||||
\(529\) | −1.98311e157 | −0.00944473 | ||||||||
\(530\) | −1.09869e159 | −0.468529 | ||||||||
\(531\) | 1.29940e159 | 0.496266 | ||||||||
\(532\) | −6.98681e158 | −0.239028 | ||||||||
\(533\) | 3.42947e159 | 1.05120 | ||||||||
\(534\) | 2.21400e159 | 0.608156 | ||||||||
\(535\) | −9.04807e158 | −0.222772 | ||||||||
\(536\) | −4.38723e158 | −0.0968390 | ||||||||
\(537\) | 9.25700e159 | 1.83221 | ||||||||
\(538\) | −3.71064e159 | −0.658697 | ||||||||
\(539\) | −1.63261e159 | −0.259981 | ||||||||
\(540\) | 2.28106e159 | 0.325914 | ||||||||
\(541\) | −1.13734e160 | −1.45832 | −0.729159 | − | 0.684345i | \(-0.760088\pi\) | ||||
−0.729159 | + | 0.684345i | \(0.760088\pi\) | |||||||
\(542\) | −7.54062e159 | −0.867858 | ||||||||
\(543\) | −1.45054e160 | −1.49879 | ||||||||
\(544\) | 3.49819e159 | 0.324569 | ||||||||
\(545\) | −1.02604e160 | −0.855005 | ||||||||
\(546\) | 3.70457e159 | 0.277312 | ||||||||
\(547\) | 7.37062e159 | 0.495730 | 0.247865 | − | 0.968795i | \(-0.420271\pi\) | ||||
0.247865 | + | 0.968795i | \(0.420271\pi\) | |||||||
\(548\) | 1.52432e160 | 0.921324 | ||||||||
\(549\) | −1.63425e160 | −0.887842 | ||||||||
\(550\) | −1.08613e159 | −0.0530475 | ||||||||
\(551\) | 3.37583e160 | 1.48256 | ||||||||
\(552\) | 2.78704e160 | 1.10080 | ||||||||
\(553\) | −7.53276e159 | −0.267629 | ||||||||
\(554\) | −7.24441e159 | −0.231570 | ||||||||
\(555\) | −5.72403e160 | −1.64650 | ||||||||
\(556\) | 3.47307e160 | 0.899164 | ||||||||
\(557\) | −1.61276e160 | −0.375872 | −0.187936 | − | 0.982181i | \(-0.560180\pi\) | ||||
−0.187936 | + | 0.982181i | \(0.560180\pi\) | |||||||
\(558\) | 1.75778e160 | 0.368863 | ||||||||
\(559\) | 5.99318e160 | 1.13257 | ||||||||
\(560\) | −5.79781e159 | −0.0986880 | ||||||||
\(561\) | −8.00461e159 | −0.122748 | ||||||||
\(562\) | 6.17606e159 | 0.0853369 | ||||||||
\(563\) | 3.35018e160 | 0.417184 | 0.208592 | − | 0.978003i | \(-0.433112\pi\) | ||||
0.208592 | + | 0.978003i | \(0.433112\pi\) | |||||||
\(564\) | −3.38552e160 | −0.380013 | ||||||||
\(565\) | −1.23002e160 | −0.124474 | ||||||||
\(566\) | 8.13166e160 | 0.742024 | ||||||||
\(567\) | −6.16087e160 | −0.507030 | ||||||||
\(568\) | −1.49034e161 | −1.10639 | ||||||||
\(569\) | −1.22970e161 | −0.823626 | −0.411813 | − | 0.911268i | \(-0.635104\pi\) | ||||
−0.411813 | + | 0.911268i | \(0.635104\pi\) | |||||||
\(570\) | 6.74357e160 | 0.407578 | ||||||||
\(571\) | 1.76853e161 | 0.964718 | 0.482359 | − | 0.875974i | \(-0.339780\pi\) | ||||
0.482359 | + | 0.875974i | \(0.339780\pi\) | |||||||
\(572\) | 5.05580e160 | 0.248956 | ||||||||
\(573\) | −4.47013e161 | −1.98735 | ||||||||
\(574\) | −5.02563e160 | −0.201764 | ||||||||
\(575\) | −9.23256e160 | −0.334775 | ||||||||
\(576\) | 3.92564e160 | 0.128586 | ||||||||
\(577\) | −2.79681e161 | −0.827708 | −0.413854 | − | 0.910343i | \(-0.635818\pi\) | ||||
−0.413854 | + | 0.910343i | \(0.635818\pi\) | |||||||
\(578\) | −1.70522e161 | −0.456038 | ||||||||
\(579\) | 9.52932e161 | 2.30338 | ||||||||
\(580\) | 5.21255e161 | 1.13897 | ||||||||
\(581\) | 1.59843e161 | 0.315783 | ||||||||
\(582\) | 2.87011e161 | 0.512749 | ||||||||
\(583\) | 2.19250e161 | 0.354266 | ||||||||
\(584\) | −4.58582e161 | −0.670294 | ||||||||
\(585\) | 3.77614e161 | 0.499378 | ||||||||
\(586\) | −7.13964e161 | −0.854409 | ||||||||
\(587\) | 3.81473e161 | 0.413176 | 0.206588 | − | 0.978428i | \(-0.433764\pi\) | ||||
0.206588 | + | 0.978428i | \(0.433764\pi\) | |||||||
\(588\) | −7.93317e161 | −0.777810 | ||||||||
\(589\) | 1.13469e162 | 1.00724 | ||||||||
\(590\) | −4.45723e161 | −0.358280 | ||||||||
\(591\) | 9.04857e160 | 0.0658738 | ||||||||
\(592\) | −7.27379e161 | −0.479668 | ||||||||
\(593\) | −4.84288e161 | −0.289337 | −0.144669 | − | 0.989480i | \(-0.546212\pi\) | ||||
−0.144669 | + | 0.989480i | \(0.546212\pi\) | |||||||
\(594\) | 1.56654e161 | 0.0848076 | ||||||||
\(595\) | −2.12476e161 | −0.104248 | ||||||||
\(596\) | −1.00501e162 | −0.446953 | ||||||||
\(597\) | 3.98495e161 | 0.160666 | ||||||||
\(598\) | −1.47900e162 | −0.540692 | ||||||||
\(599\) | −2.82842e162 | −0.937725 | −0.468862 | − | 0.883271i | \(-0.655336\pi\) | ||||
−0.468862 | + | 0.883271i | \(0.655336\pi\) | |||||||
\(600\) | −1.23717e162 | −0.372033 | ||||||||
\(601\) | 2.49792e162 | 0.681432 | 0.340716 | − | 0.940166i | \(-0.389331\pi\) | ||||
0.340716 | + | 0.940166i | \(0.389331\pi\) | |||||||
\(602\) | −8.78255e161 | −0.217383 | ||||||||
\(603\) | 2.78952e161 | 0.0626566 | ||||||||
\(604\) | −2.05431e162 | −0.418798 | ||||||||
\(605\) | 3.97441e162 | 0.735501 | ||||||||
\(606\) | 4.93231e162 | 0.828708 | ||||||||
\(607\) | 6.61731e162 | 1.00958 | 0.504792 | − | 0.863241i | \(-0.331569\pi\) | ||||
0.504792 | + | 0.863241i | \(0.331569\pi\) | |||||||
\(608\) | 5.88109e162 | 0.814889 | ||||||||
\(609\) | −7.62191e162 | −0.959295 | ||||||||
\(610\) | 5.60582e162 | 0.640979 | ||||||||
\(611\) | 4.21149e162 | 0.437547 | ||||||||
\(612\) | −1.41365e162 | −0.133470 | ||||||||
\(613\) | −8.03381e162 | −0.689420 | −0.344710 | − | 0.938709i | \(-0.612023\pi\) | ||||
−0.344710 | + | 0.938709i | \(0.612023\pi\) | |||||||
\(614\) | 5.01923e162 | 0.391550 | ||||||||
\(615\) | −1.40949e163 | −0.999695 | ||||||||
\(616\) | −1.73675e162 | −0.112012 | ||||||||
\(617\) | 8.99712e162 | 0.527742 | 0.263871 | − | 0.964558i | \(-0.415001\pi\) | ||||
0.263871 | + | 0.964558i | \(0.415001\pi\) | |||||||
\(618\) | −1.85808e163 | −0.991378 | ||||||||
\(619\) | −7.73941e162 | −0.375669 | −0.187834 | − | 0.982201i | \(-0.560147\pi\) | ||||
−0.187834 | + | 0.982201i | \(0.560147\pi\) | |||||||
\(620\) | 1.75206e163 | 0.773809 | ||||||||
\(621\) | 1.33163e163 | 0.535209 | ||||||||
\(622\) | −1.09169e162 | −0.0399358 | ||||||||
\(623\) | −1.17277e163 | −0.390537 | ||||||||
\(624\) | 1.32029e163 | 0.400286 | ||||||||
\(625\) | −1.99402e163 | −0.550490 | ||||||||
\(626\) | −8.30514e162 | −0.208809 | ||||||||
\(627\) | −1.34572e163 | −0.308180 | ||||||||
\(628\) | −4.07589e163 | −0.850323 | ||||||||
\(629\) | −2.66567e163 | −0.506692 | ||||||||
\(630\) | −5.53365e162 | −0.0958494 | ||||||||
\(631\) | −2.94001e163 | −0.464121 | −0.232061 | − | 0.972701i | \(-0.574547\pi\) | ||||
−0.232061 | + | 0.972701i | \(0.574547\pi\) | |||||||
\(632\) | 4.02988e163 | 0.579887 | ||||||||
\(633\) | 1.08898e164 | 1.42858 | ||||||||
\(634\) | 2.44617e163 | 0.292593 | ||||||||
\(635\) | −7.04403e163 | −0.768349 | ||||||||
\(636\) | 1.06538e164 | 1.05989 | ||||||||
\(637\) | 9.86864e163 | 0.895572 | ||||||||
\(638\) | 3.57977e163 | 0.296377 | ||||||||
\(639\) | 9.47598e163 | 0.715853 | ||||||||
\(640\) | 1.08594e164 | 0.748648 | ||||||||
\(641\) | −8.78740e163 | −0.552924 | −0.276462 | − | 0.961025i | \(-0.589162\pi\) | ||||
−0.276462 | + | 0.961025i | \(0.589162\pi\) | |||||||
\(642\) | −3.01942e163 | −0.173430 | ||||||||
\(643\) | −1.70500e164 | −0.894094 | −0.447047 | − | 0.894510i | \(-0.647524\pi\) | ||||
−0.447047 | + | 0.894510i | \(0.647524\pi\) | |||||||
\(644\) | −6.29786e163 | −0.301557 | ||||||||
\(645\) | −2.46316e164 | −1.07708 | ||||||||
\(646\) | 3.14047e163 | 0.125427 | ||||||||
\(647\) | −3.89635e164 | −1.42154 | −0.710768 | − | 0.703426i | \(-0.751653\pi\) | ||||
−0.710768 | + | 0.703426i | \(0.751653\pi\) | |||||||
\(648\) | 3.29595e164 | 1.09861 | ||||||||
\(649\) | 8.89468e163 | 0.270904 | ||||||||
\(650\) | 6.56531e163 | 0.182736 | ||||||||
\(651\) | −2.56190e164 | −0.651739 | ||||||||
\(652\) | −4.41491e164 | −1.02668 | ||||||||
\(653\) | 6.09081e164 | 1.29495 | 0.647477 | − | 0.762085i | \(-0.275824\pi\) | ||||
0.647477 | + | 0.762085i | \(0.275824\pi\) | |||||||
\(654\) | −3.42398e164 | −0.665631 | ||||||||
\(655\) | −2.41195e164 | −0.428798 | ||||||||
\(656\) | −1.79110e164 | −0.291237 | ||||||||
\(657\) | 2.91579e164 | 0.433693 | ||||||||
\(658\) | −6.17162e163 | −0.0839817 | ||||||||
\(659\) | 9.84938e164 | 1.22634 | 0.613172 | − | 0.789950i | \(-0.289893\pi\) | ||||
0.613172 | + | 0.789950i | \(0.289893\pi\) | |||||||
\(660\) | −2.07790e164 | −0.236758 | ||||||||
\(661\) | 9.16804e164 | 0.956073 | 0.478036 | − | 0.878340i | \(-0.341349\pi\) | ||||
0.478036 | + | 0.878340i | \(0.341349\pi\) | |||||||
\(662\) | −5.05489e163 | −0.0482525 | ||||||||
\(663\) | 4.83854e164 | 0.422837 | ||||||||
\(664\) | −8.55128e164 | −0.684224 | ||||||||
\(665\) | −3.57210e164 | −0.261733 | ||||||||
\(666\) | −6.94238e164 | −0.465871 | ||||||||
\(667\) | 3.04295e165 | 1.87040 | ||||||||
\(668\) | 6.33824e164 | 0.356899 | ||||||||
\(669\) | −8.29944e164 | −0.428175 | ||||||||
\(670\) | −9.56867e163 | −0.0452351 | ||||||||
\(671\) | −1.11868e165 | −0.484660 | ||||||||
\(672\) | −1.32783e165 | −0.527276 | ||||||||
\(673\) | 1.96629e165 | 0.715758 | 0.357879 | − | 0.933768i | \(-0.383500\pi\) | ||||
0.357879 | + | 0.933768i | \(0.383500\pi\) | |||||||
\(674\) | −2.47083e164 | −0.0824593 | ||||||||
\(675\) | −5.91110e164 | −0.180883 | ||||||||
\(676\) | −4.04907e164 | −0.113625 | ||||||||
\(677\) | −6.54449e165 | −1.68437 | −0.842187 | − | 0.539186i | \(-0.818732\pi\) | ||||
−0.842187 | + | 0.539186i | \(0.818732\pi\) | |||||||
\(678\) | −4.10468e164 | −0.0969041 | ||||||||
\(679\) | −1.52032e165 | −0.329270 | ||||||||
\(680\) | 1.13671e165 | 0.225879 | ||||||||
\(681\) | −4.54030e165 | −0.827900 | ||||||||
\(682\) | 1.20324e165 | 0.201357 | ||||||||
\(683\) | 9.66733e165 | 1.48489 | 0.742447 | − | 0.669905i | \(-0.233665\pi\) | ||||
0.742447 | + | 0.669905i | \(0.233665\pi\) | |||||||
\(684\) | −2.37660e165 | −0.335100 | ||||||||
\(685\) | 7.79328e165 | 1.00884 | ||||||||
\(686\) | −3.17991e165 | −0.377967 | ||||||||
\(687\) | 4.85018e165 | 0.529406 | ||||||||
\(688\) | −3.13005e165 | −0.313781 | ||||||||
\(689\) | −1.32530e166 | −1.22036 | ||||||||
\(690\) | 6.07860e165 | 0.514200 | ||||||||
\(691\) | 2.25132e165 | 0.174973 | 0.0874866 | − | 0.996166i | \(-0.472117\pi\) | ||||
0.0874866 | + | 0.996166i | \(0.472117\pi\) | |||||||
\(692\) | 1.22013e165 | 0.0871365 | ||||||||
\(693\) | 1.10427e165 | 0.0724740 | ||||||||
\(694\) | −9.10746e165 | −0.549374 | ||||||||
\(695\) | 1.77566e166 | 0.984573 | ||||||||
\(696\) | 4.07758e166 | 2.07855 | ||||||||
\(697\) | −6.56396e165 | −0.307644 | ||||||||
\(698\) | 7.34195e165 | 0.316424 | ||||||||
\(699\) | 5.11450e165 | 0.202716 | ||||||||
\(700\) | 2.79563e165 | 0.101916 | ||||||||
\(701\) | −3.61920e166 | −1.21369 | −0.606846 | − | 0.794819i | \(-0.707566\pi\) | ||||
−0.606846 | + | 0.794819i | \(0.707566\pi\) | |||||||
\(702\) | −9.46925e165 | −0.292142 | ||||||||
\(703\) | −4.48148e166 | −1.27214 | ||||||||
\(704\) | 2.68718e165 | 0.0701934 | ||||||||
\(705\) | −1.73090e166 | −0.416109 | ||||||||
\(706\) | −3.86857e166 | −0.856003 | ||||||||
\(707\) | −2.61267e166 | −0.532168 | ||||||||
\(708\) | 4.32209e166 | 0.810491 | ||||||||
\(709\) | −3.87666e166 | −0.669349 | −0.334674 | − | 0.942334i | \(-0.608626\pi\) | ||||
−0.334674 | + | 0.942334i | \(0.608626\pi\) | |||||||
\(710\) | −3.25047e166 | −0.516812 | ||||||||
\(711\) | −2.56231e166 | −0.375198 | ||||||||
\(712\) | 6.27410e166 | 0.846197 | ||||||||
\(713\) | 1.02280e167 | 1.27074 | ||||||||
\(714\) | −7.09051e165 | −0.0811581 | ||||||||
\(715\) | 2.58485e166 | 0.272603 | ||||||||
\(716\) | 1.11907e167 | 1.08754 | ||||||||
\(717\) | 5.38735e166 | 0.482508 | ||||||||
\(718\) | 2.43210e166 | 0.200771 | ||||||||
\(719\) | −8.96599e166 | −0.682273 | −0.341137 | − | 0.940014i | \(-0.610812\pi\) | ||||
−0.341137 | + | 0.940014i | \(0.610812\pi\) | |||||||
\(720\) | −1.97216e166 | −0.138354 | ||||||||
\(721\) | 9.84236e166 | 0.636629 | ||||||||
\(722\) | −3.20376e166 | −0.191088 | ||||||||
\(723\) | −6.38776e166 | −0.351365 | ||||||||
\(724\) | −1.75355e167 | −0.889636 | ||||||||
\(725\) | −1.35077e167 | −0.632132 | ||||||||
\(726\) | 1.32630e167 | 0.572596 | ||||||||
\(727\) | 3.81141e167 | 1.51818 | 0.759089 | − | 0.650987i | \(-0.225645\pi\) | ||||
0.759089 | + | 0.650987i | \(0.225645\pi\) | |||||||
\(728\) | 1.04981e167 | 0.385856 | ||||||||
\(729\) | −1.08525e166 | −0.0368103 | ||||||||
\(730\) | −1.00018e167 | −0.313106 | ||||||||
\(731\) | −1.14709e167 | −0.331459 | ||||||||
\(732\) | −5.43585e167 | −1.45000 | ||||||||
\(733\) | 3.88613e167 | 0.957051 | 0.478525 | − | 0.878074i | \(-0.341171\pi\) | ||||
0.478525 | + | 0.878074i | \(0.341171\pi\) | |||||||
\(734\) | −3.40137e167 | −0.773454 | ||||||||
\(735\) | −4.05594e167 | −0.851692 | ||||||||
\(736\) | 5.30117e167 | 1.02806 | ||||||||
\(737\) | 1.90949e166 | 0.0342033 | ||||||||
\(738\) | −1.70950e167 | −0.282860 | ||||||||
\(739\) | −1.02588e168 | −1.56819 | −0.784095 | − | 0.620640i | \(-0.786873\pi\) | ||||
−0.784095 | + | 0.620640i | \(0.786873\pi\) | |||||||
\(740\) | −6.91975e167 | −0.977316 | ||||||||
\(741\) | 8.13445e167 | 1.06161 | ||||||||
\(742\) | 1.94213e167 | 0.234233 | ||||||||
\(743\) | 4.99109e167 | 0.556352 | 0.278176 | − | 0.960530i | \(-0.410270\pi\) | ||||
0.278176 | + | 0.960530i | \(0.410270\pi\) | |||||||
\(744\) | 1.37057e168 | 1.41216 | ||||||||
\(745\) | −5.13823e167 | −0.489408 | ||||||||
\(746\) | 2.59320e167 | 0.228357 | ||||||||
\(747\) | 5.43714e167 | 0.442706 | ||||||||
\(748\) | −9.67674e166 | −0.0728594 | ||||||||
\(749\) | 1.59940e167 | 0.111371 | ||||||||
\(750\) | −1.07202e168 | −0.690428 | ||||||||
\(751\) | 1.86758e168 | 1.11261 | 0.556305 | − | 0.830978i | \(-0.312218\pi\) | ||||
0.556305 | + | 0.830978i | \(0.312218\pi\) | |||||||
\(752\) | −2.19953e167 | −0.121223 | ||||||||
\(753\) | 2.40677e168 | 1.22724 | ||||||||
\(754\) | −2.16385e168 | −1.02095 | ||||||||
\(755\) | −1.05029e168 | −0.458579 | ||||||||
\(756\) | −4.03218e167 | −0.162935 | ||||||||
\(757\) | 3.18804e168 | 1.19238 | 0.596190 | − | 0.802843i | \(-0.296680\pi\) | ||||
0.596190 | + | 0.802843i | \(0.296680\pi\) | |||||||
\(758\) | −1.61462e168 | −0.559014 | ||||||||
\(759\) | −1.21302e168 | −0.388799 | ||||||||
\(760\) | 1.91101e168 | 0.567110 | ||||||||
\(761\) | −3.17720e168 | −0.873057 | −0.436528 | − | 0.899690i | \(-0.643792\pi\) | ||||
−0.436528 | + | 0.899690i | \(0.643792\pi\) | |||||||
\(762\) | −2.35066e168 | −0.598168 | ||||||||
\(763\) | 1.81370e168 | 0.427446 | ||||||||
\(764\) | −5.40391e168 | −1.17963 | ||||||||
\(765\) | −7.22749e167 | −0.146148 | ||||||||
\(766\) | 2.80562e168 | 0.525588 | ||||||||
\(767\) | −5.37655e168 | −0.933201 | ||||||||
\(768\) | 5.37900e168 | 0.865107 | ||||||||
\(769\) | −1.13101e169 | −1.68568 | −0.842841 | − | 0.538163i | \(-0.819119\pi\) | ||||
−0.842841 | + | 0.538163i | \(0.819119\pi\) | |||||||
\(770\) | −3.78790e167 | −0.0523228 | ||||||||
\(771\) | 6.20623e168 | 0.794597 | ||||||||
\(772\) | 1.15199e169 | 1.36722 | ||||||||
\(773\) | −1.88326e168 | −0.207209 | −0.103605 | − | 0.994619i | \(-0.533038\pi\) | ||||
−0.103605 | + | 0.994619i | \(0.533038\pi\) | |||||||
\(774\) | −2.98743e168 | −0.304756 | ||||||||
\(775\) | −4.54024e168 | −0.429467 | ||||||||
\(776\) | 8.13340e168 | 0.713446 | ||||||||
\(777\) | 1.01182e169 | 0.823142 | ||||||||
\(778\) | 1.17567e169 | 0.887116 | ||||||||
\(779\) | −1.10352e169 | −0.772395 | ||||||||
\(780\) | 1.25602e169 | 0.815575 | ||||||||
\(781\) | 6.48651e168 | 0.390774 | ||||||||
\(782\) | 2.83079e168 | 0.158239 | ||||||||
\(783\) | 1.94823e169 | 1.01060 | ||||||||
\(784\) | −5.15408e168 | −0.248120 | ||||||||
\(785\) | −2.08386e169 | −0.931093 | ||||||||
\(786\) | −8.04891e168 | −0.333824 | ||||||||
\(787\) | −2.71141e169 | −1.04393 | −0.521967 | − | 0.852966i | \(-0.674802\pi\) | ||||
−0.521967 | + | 0.852966i | \(0.674802\pi\) | |||||||
\(788\) | 1.09388e168 | 0.0391007 | ||||||||
\(789\) | −6.86160e169 | −2.27730 | ||||||||
\(790\) | 8.78928e168 | 0.270875 | ||||||||
\(791\) | 2.17427e168 | 0.0622285 | ||||||||
\(792\) | −5.90765e168 | −0.157033 | ||||||||
\(793\) | 6.76204e169 | 1.66954 | ||||||||
\(794\) | −2.65973e169 | −0.610011 | ||||||||
\(795\) | 5.44689e169 | 1.16057 | ||||||||
\(796\) | 4.81739e168 | 0.0953669 | ||||||||
\(797\) | −1.79020e169 | −0.329298 | −0.164649 | − | 0.986352i | \(-0.552649\pi\) | ||||
−0.164649 | + | 0.986352i | \(0.552649\pi\) | |||||||
\(798\) | −1.19204e169 | −0.203762 | ||||||||
\(799\) | −8.06075e168 | −0.128053 | ||||||||
\(800\) | −2.35320e169 | −0.347451 | ||||||||
\(801\) | −3.98924e169 | −0.547505 | ||||||||
\(802\) | −2.78866e169 | −0.355792 | ||||||||
\(803\) | 1.99592e169 | 0.236747 | ||||||||
\(804\) | 9.27855e168 | 0.102330 | ||||||||
\(805\) | −3.21987e169 | −0.330202 | ||||||||
\(806\) | −7.27321e169 | −0.693627 | ||||||||
\(807\) | 1.83960e170 | 1.63163 | ||||||||
\(808\) | 1.39773e170 | 1.15308 | ||||||||
\(809\) | −1.04540e170 | −0.802225 | −0.401112 | − | 0.916029i | \(-0.631376\pi\) | ||||
−0.401112 | + | 0.916029i | \(0.631376\pi\) | |||||||
\(810\) | 7.18855e169 | 0.513178 | ||||||||
\(811\) | 1.67747e170 | 1.11413 | 0.557064 | − | 0.830470i | \(-0.311928\pi\) | ||||
0.557064 | + | 0.830470i | \(0.311928\pi\) | |||||||
\(812\) | −9.21409e169 | −0.569409 | ||||||||
\(813\) | 3.73836e170 | 2.14973 | ||||||||
\(814\) | −4.75221e169 | −0.254312 | ||||||||
\(815\) | −2.25718e170 | −1.12421 | ||||||||
\(816\) | −2.52702e169 | −0.117148 | ||||||||
\(817\) | −1.92846e170 | −0.832187 | ||||||||
\(818\) | −7.90416e168 | −0.0317532 | ||||||||
\(819\) | −6.67498e169 | −0.249656 | ||||||||
\(820\) | −1.70392e170 | −0.593390 | ||||||||
\(821\) | −3.20975e170 | −1.04087 | −0.520434 | − | 0.853902i | \(-0.674230\pi\) | ||||
−0.520434 | + | 0.853902i | \(0.674230\pi\) | |||||||
\(822\) | 2.60069e170 | 0.785393 | ||||||||
\(823\) | 1.90558e170 | 0.535965 | 0.267982 | − | 0.963424i | \(-0.413643\pi\) | ||||
0.267982 | + | 0.963424i | \(0.413643\pi\) | |||||||
\(824\) | −5.26548e170 | −1.37942 | ||||||||
\(825\) | 5.38463e169 | 0.131401 | ||||||||
\(826\) | 7.87893e169 | 0.179116 | ||||||||
\(827\) | −6.00446e170 | −1.27175 | −0.635875 | − | 0.771792i | \(-0.719360\pi\) | ||||
−0.635875 | + | 0.771792i | \(0.719360\pi\) | |||||||
\(828\) | −2.14225e170 | −0.422762 | ||||||||
\(829\) | 9.94678e170 | 1.82912 | 0.914560 | − | 0.404450i | \(-0.132537\pi\) | ||||
0.914560 | + | 0.404450i | \(0.132537\pi\) | |||||||
\(830\) | −1.86506e170 | −0.319613 | ||||||||
\(831\) | 3.59151e170 | 0.573610 | ||||||||
\(832\) | −1.62432e170 | −0.241800 | ||||||||
\(833\) | −1.88885e170 | −0.262098 | ||||||||
\(834\) | 5.92553e170 | 0.766502 | ||||||||
\(835\) | 3.24052e170 | 0.390801 | ||||||||
\(836\) | −1.62684e170 | −0.182926 | ||||||||
\(837\) | 6.54846e170 | 0.686594 | ||||||||
\(838\) | −2.48527e169 | −0.0242995 | ||||||||
\(839\) | −1.66290e171 | −1.51632 | −0.758159 | − | 0.652070i | \(-0.773901\pi\) | ||||
−0.758159 | + | 0.652070i | \(0.773901\pi\) | |||||||
\(840\) | −4.31465e170 | −0.366950 | ||||||||
\(841\) | 3.19142e171 | 2.53174 | ||||||||
\(842\) | 4.29987e170 | 0.318198 | ||||||||
\(843\) | −3.06186e170 | −0.211384 | ||||||||
\(844\) | 1.31647e171 | 0.847963 | ||||||||
\(845\) | −2.07014e170 | −0.124418 | ||||||||
\(846\) | −2.09931e170 | −0.117736 | ||||||||
\(847\) | −7.02546e170 | −0.367702 | ||||||||
\(848\) | 6.92162e170 | 0.338104 | ||||||||
\(849\) | −4.03137e171 | −1.83803 | ||||||||
\(850\) | −1.25659e170 | −0.0534795 | ||||||||
\(851\) | −4.03957e171 | −1.60493 | ||||||||
\(852\) | 3.15191e171 | 1.16912 | ||||||||
\(853\) | −1.09954e171 | −0.380797 | −0.190399 | − | 0.981707i | \(-0.560978\pi\) | ||||
−0.190399 | + | 0.981707i | \(0.560978\pi\) | |||||||
\(854\) | −9.90926e170 | −0.320447 | ||||||||
\(855\) | −1.21507e171 | −0.366931 | ||||||||
\(856\) | −8.55651e170 | −0.241313 | ||||||||
\(857\) | −5.62118e170 | −0.148064 | −0.0740320 | − | 0.997256i | \(-0.523587\pi\) | ||||
−0.0740320 | + | 0.997256i | \(0.523587\pi\) | |||||||
\(858\) | 8.62586e170 | 0.212225 | ||||||||
\(859\) | 5.39313e171 | 1.23948 | 0.619742 | − | 0.784805i | \(-0.287237\pi\) | ||||
0.619742 | + | 0.784805i | \(0.287237\pi\) | |||||||
\(860\) | −2.97770e171 | −0.639324 | ||||||||
\(861\) | 2.49152e171 | 0.499781 | ||||||||
\(862\) | 2.97445e171 | 0.557483 | ||||||||
\(863\) | −6.37689e171 | −1.11681 | −0.558403 | − | 0.829570i | \(-0.688586\pi\) | ||||
−0.558403 | + | 0.829570i | \(0.688586\pi\) | |||||||
\(864\) | 3.39405e171 | 0.555475 | ||||||||
\(865\) | 6.23810e170 | 0.0954135 | ||||||||
\(866\) | 6.63898e170 | 0.0949084 | ||||||||
\(867\) | 8.45383e171 | 1.12963 | ||||||||
\(868\) | −3.09706e171 | −0.386853 | ||||||||
\(869\) | −1.75396e171 | −0.204815 | ||||||||
\(870\) | 8.89330e171 | 0.970927 | ||||||||
\(871\) | −1.15422e171 | −0.117822 | ||||||||
\(872\) | −9.70297e171 | −0.926169 | ||||||||
\(873\) | −5.17144e171 | −0.461613 | ||||||||
\(874\) | 4.75908e171 | 0.397287 | ||||||||
\(875\) | 5.67854e171 | 0.443369 | ||||||||
\(876\) | 9.69855e171 | 0.708299 | ||||||||
\(877\) | −6.87419e171 | −0.469619 | −0.234809 | − | 0.972041i | \(-0.575447\pi\) | ||||
−0.234809 | + | 0.972041i | \(0.575447\pi\) | |||||||
\(878\) | −1.01435e172 | −0.648274 | ||||||||
\(879\) | 3.53957e172 | 2.11642 | ||||||||
\(880\) | −1.34998e171 | −0.0755253 | ||||||||
\(881\) | −3.04162e172 | −1.59226 | −0.796131 | − | 0.605125i | \(-0.793123\pi\) | ||||
−0.796131 | + | 0.605125i | \(0.793123\pi\) | |||||||
\(882\) | −4.91924e171 | −0.240983 | ||||||||
\(883\) | −1.53410e172 | −0.703322 | −0.351661 | − | 0.936128i | \(-0.614383\pi\) | ||||
−0.351661 | + | 0.936128i | \(0.614383\pi\) | |||||||
\(884\) | 5.84928e171 | 0.250983 | ||||||||
\(885\) | 2.20973e172 | 0.887478 | ||||||||
\(886\) | 1.04396e172 | 0.392472 | ||||||||
\(887\) | −4.39366e172 | −1.54630 | −0.773152 | − | 0.634220i | \(-0.781321\pi\) | ||||
−0.773152 | + | 0.634220i | \(0.781321\pi\) | |||||||
\(888\) | −5.41306e172 | −1.78355 | ||||||||
\(889\) | 1.24516e172 | 0.384123 | ||||||||
\(890\) | 1.36840e172 | 0.395273 | ||||||||
\(891\) | −1.43452e172 | −0.388026 | ||||||||
\(892\) | −1.00332e172 | −0.254152 | ||||||||
\(893\) | −1.35516e172 | −0.321499 | ||||||||
\(894\) | −1.71467e172 | −0.381010 | ||||||||
\(895\) | 5.72143e172 | 1.19085 | ||||||||
\(896\) | −1.91959e172 | −0.374274 | ||||||||
\(897\) | 7.33234e172 | 1.33932 | ||||||||
\(898\) | −7.84734e171 | −0.134294 | ||||||||
\(899\) | 1.49641e173 | 2.39944 | ||||||||
\(900\) | 9.50949e171 | 0.142880 | ||||||||
\(901\) | 2.53661e172 | 0.357152 | ||||||||
\(902\) | −1.17019e172 | −0.154409 | ||||||||
\(903\) | 4.35406e172 | 0.538469 | ||||||||
\(904\) | −1.16319e172 | −0.134834 | ||||||||
\(905\) | −8.96528e172 | −0.974141 | ||||||||
\(906\) | −3.50492e172 | −0.357009 | ||||||||
\(907\) | −3.61788e172 | −0.345484 | −0.172742 | − | 0.984967i | \(-0.555263\pi\) | ||||
−0.172742 | + | 0.984967i | \(0.555263\pi\) | |||||||
\(908\) | −5.48874e172 | −0.491418 | ||||||||
\(909\) | −8.88715e172 | −0.746063 | ||||||||
\(910\) | 2.28966e172 | 0.180240 | ||||||||
\(911\) | 4.18676e172 | 0.309067 | 0.154534 | − | 0.987988i | \(-0.450613\pi\) | ||||
0.154534 | + | 0.987988i | \(0.450613\pi\) | |||||||
\(912\) | −4.24837e172 | −0.294120 | ||||||||
\(913\) | 3.72184e172 | 0.241667 | ||||||||
\(914\) | 1.63466e173 | 0.995578 | ||||||||
\(915\) | −2.77916e173 | −1.58774 | ||||||||
\(916\) | 5.86335e172 | 0.314240 | ||||||||
\(917\) | 4.26355e172 | 0.214371 | ||||||||
\(918\) | 1.81240e172 | 0.0854984 | ||||||||
\(919\) | −7.07915e172 | −0.313345 | −0.156673 | − | 0.987651i | \(-0.550077\pi\) | ||||
−0.156673 | + | 0.987651i | \(0.550077\pi\) | |||||||
\(920\) | 1.72257e173 | 0.715465 | ||||||||
\(921\) | −2.48835e173 | −0.969890 | ||||||||
\(922\) | −1.75818e173 | −0.643139 | ||||||||
\(923\) | −3.92089e173 | −1.34612 | ||||||||
\(924\) | 3.67305e172 | 0.118363 | ||||||||
\(925\) | 1.79317e173 | 0.542413 | ||||||||
\(926\) | −3.08275e173 | −0.875379 | ||||||||
\(927\) | 3.34794e173 | 0.892509 | ||||||||
\(928\) | 7.75588e173 | 1.94122 | ||||||||
\(929\) | 3.48959e173 | 0.820077 | 0.410039 | − | 0.912068i | \(-0.365515\pi\) | ||||
0.410039 | + | 0.912068i | \(0.365515\pi\) | |||||||
\(930\) | 2.98924e173 | 0.659642 | ||||||||
\(931\) | −3.17549e173 | −0.658044 | ||||||||
\(932\) | 6.18290e172 | 0.120327 | ||||||||
\(933\) | 5.41220e172 | 0.0989231 | ||||||||
\(934\) | −1.65502e173 | −0.284126 | ||||||||
\(935\) | −4.94737e172 | −0.0797802 | ||||||||
\(936\) | 3.57099e173 | 0.540943 | ||||||||
\(937\) | −2.76839e173 | −0.393969 | −0.196984 | − | 0.980407i | \(-0.563115\pi\) | ||||
−0.196984 | + | 0.980407i | \(0.563115\pi\) | |||||||
\(938\) | 1.69143e172 | 0.0226145 | ||||||||
\(939\) | 4.11738e173 | 0.517230 | ||||||||
\(940\) | −2.09247e173 | −0.246990 | ||||||||
\(941\) | 1.65023e173 | 0.183043 | 0.0915213 | − | 0.995803i | \(-0.470827\pi\) | ||||
0.0915213 | + | 0.995803i | \(0.470827\pi\) | |||||||
\(942\) | −6.95402e173 | −0.724867 | ||||||||
\(943\) | −9.94707e173 | −0.974453 | ||||||||
\(944\) | 2.80801e173 | 0.258545 | ||||||||
\(945\) | −2.06151e173 | −0.178412 | ||||||||
\(946\) | −2.04496e173 | −0.166362 | ||||||||
\(947\) | 1.71987e174 | 1.31529 | 0.657647 | − | 0.753326i | \(-0.271552\pi\) | ||||
0.657647 | + | 0.753326i | \(0.271552\pi\) | |||||||
\(948\) | −8.52279e173 | −0.612765 | ||||||||
\(949\) | −1.20647e174 | −0.815537 | ||||||||
\(950\) | −2.11256e173 | −0.134270 | ||||||||
\(951\) | −1.21272e174 | −0.724769 | ||||||||
\(952\) | −2.00932e173 | −0.112925 | ||||||||
\(953\) | 3.14844e174 | 1.66403 | 0.832013 | − | 0.554756i | \(-0.187188\pi\) | ||||
0.832013 | + | 0.554756i | \(0.187188\pi\) | |||||||
\(954\) | 6.60625e173 | 0.328379 | ||||||||
\(955\) | −2.76283e174 | −1.29168 | ||||||||
\(956\) | 6.51274e173 | 0.286403 | ||||||||
\(957\) | −1.77471e174 | −0.734142 | ||||||||
\(958\) | −1.12951e174 | −0.439550 | ||||||||
\(959\) | −1.37760e174 | −0.504353 | ||||||||
\(960\) | 6.67583e173 | 0.229952 | ||||||||
\(961\) | 1.94434e174 | 0.630164 | ||||||||
\(962\) | 2.87256e174 | 0.876046 | ||||||||
\(963\) | 5.44047e173 | 0.156134 | ||||||||
\(964\) | −7.72214e173 | −0.208560 | ||||||||
\(965\) | 5.88973e174 | 1.49709 | ||||||||
\(966\) | −1.07450e174 | −0.257066 | ||||||||
\(967\) | 6.89859e173 | 0.155350 | 0.0776750 | − | 0.996979i | \(-0.475250\pi\) | ||||
0.0776750 | + | 0.996979i | \(0.475250\pi\) | |||||||
\(968\) | 3.75849e174 | 0.796718 | ||||||||
\(969\) | −1.55693e174 | −0.310690 | ||||||||
\(970\) | 1.77392e174 | 0.333263 | ||||||||
\(971\) | 1.00197e175 | 1.77227 | 0.886135 | − | 0.463426i | \(-0.153380\pi\) | ||||
0.886135 | + | 0.463426i | \(0.153380\pi\) | |||||||
\(972\) | −4.56837e174 | −0.760825 | ||||||||
\(973\) | −3.13878e174 | −0.492221 | ||||||||
\(974\) | −4.23152e174 | −0.624881 | ||||||||
\(975\) | −3.25484e174 | −0.452647 | ||||||||
\(976\) | −3.53160e174 | −0.462549 | ||||||||
\(977\) | −5.22761e174 | −0.644869 | −0.322435 | − | 0.946592i | \(-0.604501\pi\) | ||||
−0.322435 | + | 0.946592i | \(0.604501\pi\) | |||||||
\(978\) | −7.53242e174 | −0.875208 | ||||||||
\(979\) | −2.73072e174 | −0.298875 | ||||||||
\(980\) | −4.90321e174 | −0.505540 | ||||||||
\(981\) | 6.16942e174 | 0.599249 | ||||||||
\(982\) | −8.47259e174 | −0.775344 | ||||||||
\(983\) | 1.49888e175 | 1.29237 | 0.646184 | − | 0.763182i | \(-0.276364\pi\) | ||||
0.646184 | + | 0.763182i | \(0.276364\pi\) | |||||||
\(984\) | −1.33291e175 | −1.08290 | ||||||||
\(985\) | 5.59260e173 | 0.0428148 | ||||||||
\(986\) | 4.14159e174 | 0.298791 | ||||||||
\(987\) | 3.05966e174 | 0.208027 | ||||||||
\(988\) | 9.83370e174 | 0.630138 | ||||||||
\(989\) | −1.73830e175 | −1.04989 | ||||||||
\(990\) | −1.28847e174 | −0.0733529 | ||||||||
\(991\) | 8.39333e174 | 0.450428 | 0.225214 | − | 0.974309i | \(-0.427692\pi\) | ||||
0.225214 | + | 0.974309i | \(0.427692\pi\) | |||||||
\(992\) | 2.60693e175 | 1.31885 | ||||||||
\(993\) | 2.50603e174 | 0.119524 | ||||||||
\(994\) | 5.74577e174 | 0.258371 | ||||||||
\(995\) | 2.46296e174 | 0.104426 | ||||||||
\(996\) | 1.80851e175 | 0.723019 | ||||||||
\(997\) | −1.23005e175 | −0.463718 | −0.231859 | − | 0.972749i | \(-0.574481\pi\) | ||||
−0.231859 | + | 0.972749i | \(0.574481\pi\) | |||||||
\(998\) | 1.46259e175 | 0.519979 | ||||||||
\(999\) | −2.58632e175 | −0.867163 |
(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 | 1.118.a.a.1.6 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.118.a.a.1.6 | ✓ | 9 | 1.1 | even | 1 | trivial |