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 | 1.8 | ||
Root | \(-2.42126e14\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.67743e16 | 1.83600 | 0.917999 | − | 0.396582i | \(-0.129804\pi\) | ||||
0.917999 | + | 0.396582i | \(0.129804\pi\) | |||||||
\(3\) | 3.08304e25 | 0.306105 | 0.153053 | − | 0.988218i | \(-0.451090\pi\) | ||||
0.153053 | + | 0.988218i | \(0.451090\pi\) | |||||||
\(4\) | 1.53880e33 | 2.37089 | ||||||||
\(5\) | −1.66073e38 | −1.33793 | −0.668964 | − | 0.743295i | \(-0.733262\pi\) | ||||
−0.668964 | + | 0.743295i | \(0.733262\pi\) | |||||||
\(6\) | 1.44207e42 | 0.562009 | ||||||||
\(7\) | 8.52831e45 | 0.746483 | 0.373241 | − | 0.927734i | \(-0.378246\pi\) | ||||
0.373241 | + | 0.927734i | \(0.378246\pi\) | |||||||
\(8\) | 4.16178e49 | 2.51695 | ||||||||
\(9\) | −9.19366e51 | −0.906300 | ||||||||
\(10\) | −7.76792e54 | −2.45643 | ||||||||
\(11\) | −4.17646e56 | −0.732668 | −0.366334 | − | 0.930483i | \(-0.619387\pi\) | ||||
−0.366334 | + | 0.930483i | \(0.619387\pi\) | |||||||
\(12\) | 4.74417e58 | 0.725742 | ||||||||
\(13\) | −8.29806e60 | −1.61832 | −0.809159 | − | 0.587590i | \(-0.800077\pi\) | ||||
−0.809159 | + | 0.587590i | \(0.800077\pi\) | |||||||
\(14\) | 3.98905e62 | 1.37054 | ||||||||
\(15\) | −5.12008e63 | −0.409547 | ||||||||
\(16\) | 9.47907e65 | 2.25023 | ||||||||
\(17\) | −6.45752e65 | −0.0563118 | −0.0281559 | − | 0.999604i | \(-0.508963\pi\) | ||||
−0.0281559 | + | 0.999604i | \(0.508963\pi\) | |||||||
\(18\) | −4.30027e68 | −1.66396 | ||||||||
\(19\) | −6.23924e69 | −1.26783 | −0.633915 | − | 0.773403i | \(-0.718553\pi\) | ||||
−0.633915 | + | 0.773403i | \(0.718553\pi\) | |||||||
\(20\) | −2.55552e71 | −3.17208 | ||||||||
\(21\) | 2.62931e71 | 0.228502 | ||||||||
\(22\) | −1.95351e73 | −1.34518 | ||||||||
\(23\) | 2.48258e74 | 1.51613 | 0.758064 | − | 0.652180i | \(-0.226145\pi\) | ||||
0.758064 | + | 0.652180i | \(0.226145\pi\) | |||||||
\(24\) | 1.28309e75 | 0.770452 | ||||||||
\(25\) | 1.21727e76 | 0.790051 | ||||||||
\(26\) | −3.88135e77 | −2.97123 | ||||||||
\(27\) | −5.96193e77 | −0.583528 | ||||||||
\(28\) | 1.31233e79 | 1.76983 | ||||||||
\(29\) | 1.15567e79 | 0.230220 | 0.115110 | − | 0.993353i | \(-0.463278\pi\) | ||||
0.115110 | + | 0.993353i | \(0.463278\pi\) | |||||||
\(30\) | −2.39488e80 | −0.751927 | ||||||||
\(31\) | −2.19372e81 | −1.15337 | −0.576685 | − | 0.816967i | \(-0.695654\pi\) | ||||
−0.576685 | + | 0.816967i | \(0.695654\pi\) | |||||||
\(32\) | 1.73262e82 | 1.61446 | ||||||||
\(33\) | −1.28762e82 | −0.224273 | ||||||||
\(34\) | −3.02046e82 | −0.103388 | ||||||||
\(35\) | −1.41632e84 | −0.998740 | ||||||||
\(36\) | −1.41472e85 | −2.14874 | ||||||||
\(37\) | 5.13467e85 | 1.75194 | 0.875969 | − | 0.482367i | \(-0.160223\pi\) | ||||
0.875969 | + | 0.482367i | \(0.160223\pi\) | |||||||
\(38\) | −2.91836e86 | −2.32773 | ||||||||
\(39\) | −2.55832e86 | −0.495375 | ||||||||
\(40\) | −6.91157e87 | −3.36750 | ||||||||
\(41\) | −1.09454e88 | −1.38839 | −0.694197 | − | 0.719785i | \(-0.744240\pi\) | ||||
−0.694197 | + | 0.719785i | \(0.744240\pi\) | |||||||
\(42\) | 1.22984e88 | 0.419530 | ||||||||
\(43\) | −1.31384e89 | −1.24311 | −0.621556 | − | 0.783370i | \(-0.713499\pi\) | ||||
−0.621556 | + | 0.783370i | \(0.713499\pi\) | |||||||
\(44\) | −6.42672e89 | −1.73707 | ||||||||
\(45\) | 1.52682e90 | 1.21256 | ||||||||
\(46\) | 1.16121e91 | 2.78361 | ||||||||
\(47\) | 4.22488e89 | 0.0313676 | 0.0156838 | − | 0.999877i | \(-0.495007\pi\) | ||||
0.0156838 | + | 0.999877i | \(0.495007\pi\) | |||||||
\(48\) | 2.92243e91 | 0.688807 | ||||||||
\(49\) | −5.77907e91 | −0.442764 | ||||||||
\(50\) | 5.69368e92 | 1.45053 | ||||||||
\(51\) | −1.99088e91 | −0.0172373 | ||||||||
\(52\) | −1.27690e94 | −3.83685 | ||||||||
\(53\) | 5.60887e93 | 0.596816 | 0.298408 | − | 0.954438i | \(-0.403544\pi\) | ||||
0.298408 | + | 0.954438i | \(0.403544\pi\) | |||||||
\(54\) | −2.78865e94 | −1.07136 | ||||||||
\(55\) | 6.93596e94 | 0.980257 | ||||||||
\(56\) | 3.54929e95 | 1.87886 | ||||||||
\(57\) | −1.92358e95 | −0.388089 | ||||||||
\(58\) | 5.40556e95 | 0.422683 | ||||||||
\(59\) | 2.61491e96 | 0.805419 | 0.402709 | − | 0.915328i | \(-0.368069\pi\) | ||||
0.402709 | + | 0.915328i | \(0.368069\pi\) | |||||||
\(60\) | −7.87876e96 | −0.970990 | ||||||||
\(61\) | 2.27336e96 | 0.113813 | 0.0569066 | − | 0.998380i | \(-0.481876\pi\) | ||||
0.0569066 | + | 0.998380i | \(0.481876\pi\) | |||||||
\(62\) | −1.02610e98 | −2.11758 | ||||||||
\(63\) | −7.84064e97 | −0.676537 | ||||||||
\(64\) | 1.95192e98 | 0.713925 | ||||||||
\(65\) | 1.37808e99 | 2.16519 | ||||||||
\(66\) | −6.02275e98 | −0.411766 | ||||||||
\(67\) | −1.52450e98 | −0.0459253 | −0.0229626 | − | 0.999736i | \(-0.507310\pi\) | ||||
−0.0229626 | + | 0.999736i | \(0.507310\pi\) | |||||||
\(68\) | −9.93680e98 | −0.133509 | ||||||||
\(69\) | 7.65389e99 | 0.464095 | ||||||||
\(70\) | −6.62473e100 | −1.83369 | ||||||||
\(71\) | −2.16290e100 | −0.276349 | −0.138174 | − | 0.990408i | \(-0.544123\pi\) | ||||
−0.138174 | + | 0.990408i | \(0.544123\pi\) | |||||||
\(72\) | −3.82620e101 | −2.28111 | ||||||||
\(73\) | −1.09055e101 | −0.306583 | −0.153291 | − | 0.988181i | \(-0.548987\pi\) | ||||
−0.153291 | + | 0.988181i | \(0.548987\pi\) | |||||||
\(74\) | 2.40171e102 | 3.21656 | ||||||||
\(75\) | 3.75288e101 | 0.241839 | ||||||||
\(76\) | −9.60092e102 | −3.00588 | ||||||||
\(77\) | −3.56181e102 | −0.546924 | ||||||||
\(78\) | −1.19664e103 | −0.909508 | ||||||||
\(79\) | −1.07406e103 | −0.407709 | −0.203855 | − | 0.979001i | \(-0.565347\pi\) | ||||
−0.203855 | + | 0.979001i | \(0.565347\pi\) | |||||||
\(80\) | −1.57421e104 | −3.01064 | ||||||||
\(81\) | 7.48812e103 | 0.727678 | ||||||||
\(82\) | −5.11965e104 | −2.54909 | ||||||||
\(83\) | 3.89026e104 | 1.00051 | 0.500256 | − | 0.865878i | \(-0.333239\pi\) | ||||
0.500256 | + | 0.865878i | \(0.333239\pi\) | |||||||
\(84\) | 4.04597e104 | 0.541754 | ||||||||
\(85\) | 1.07242e104 | 0.0753412 | ||||||||
\(86\) | −6.14537e105 | −2.28235 | ||||||||
\(87\) | 3.56298e104 | 0.0704715 | ||||||||
\(88\) | −1.73815e106 | −1.84409 | ||||||||
\(89\) | −1.88126e105 | −0.107818 | −0.0539092 | − | 0.998546i | \(-0.517168\pi\) | ||||
−0.0539092 | + | 0.998546i | \(0.517168\pi\) | |||||||
\(90\) | 7.14157e106 | 2.22626 | ||||||||
\(91\) | −7.07684e106 | −1.20805 | ||||||||
\(92\) | 3.82018e107 | 3.59457 | ||||||||
\(93\) | −6.76332e106 | −0.353052 | ||||||||
\(94\) | 1.97616e106 | 0.0575909 | ||||||||
\(95\) | 1.03617e108 | 1.69626 | ||||||||
\(96\) | 5.34172e107 | 0.494196 | ||||||||
\(97\) | −3.05793e108 | −1.60830 | −0.804152 | − | 0.594424i | \(-0.797380\pi\) | ||||
−0.804152 | + | 0.594424i | \(0.797380\pi\) | |||||||
\(98\) | −2.70312e108 | −0.812913 | ||||||||
\(99\) | 3.83970e108 | 0.664016 | ||||||||
\(100\) | 1.87312e109 | 1.87312 | ||||||||
\(101\) | −2.94022e108 | −0.170949 | −0.0854743 | − | 0.996340i | \(-0.527241\pi\) | ||||
−0.0854743 | + | 0.996340i | \(0.527241\pi\) | |||||||
\(102\) | −9.31220e107 | −0.0316477 | ||||||||
\(103\) | 1.50195e109 | 0.299935 | 0.149967 | − | 0.988691i | \(-0.452083\pi\) | ||||
0.149967 | + | 0.988691i | \(0.452083\pi\) | |||||||
\(104\) | −3.45347e110 | −4.07322 | ||||||||
\(105\) | −4.36657e109 | −0.305720 | ||||||||
\(106\) | 2.62351e110 | 1.09575 | ||||||||
\(107\) | −2.81838e110 | −0.705642 | −0.352821 | − | 0.935691i | \(-0.614777\pi\) | ||||
−0.352821 | + | 0.935691i | \(0.614777\pi\) | |||||||
\(108\) | −9.17419e110 | −1.38348 | ||||||||
\(109\) | −1.73813e110 | −0.158613 | −0.0793063 | − | 0.996850i | \(-0.525271\pi\) | ||||
−0.0793063 | + | 0.996850i | \(0.525271\pi\) | |||||||
\(110\) | 3.24424e111 | 1.79975 | ||||||||
\(111\) | 1.58304e111 | 0.536278 | ||||||||
\(112\) | 8.08404e111 | 1.67976 | ||||||||
\(113\) | 4.30162e111 | 0.550626 | 0.275313 | − | 0.961355i | \(-0.411218\pi\) | ||||
0.275313 | + | 0.961355i | \(0.411218\pi\) | |||||||
\(114\) | −8.99743e111 | −0.712531 | ||||||||
\(115\) | −4.12288e112 | −2.02847 | ||||||||
\(116\) | 1.77834e112 | 0.545826 | ||||||||
\(117\) | 7.62895e112 | 1.46668 | ||||||||
\(118\) | 1.22310e113 | 1.47875 | ||||||||
\(119\) | −5.50717e111 | −0.0420358 | ||||||||
\(120\) | −2.13087e113 | −1.03081 | ||||||||
\(121\) | −1.50511e113 | −0.463198 | ||||||||
\(122\) | 1.06335e113 | 0.208961 | ||||||||
\(123\) | −3.37452e113 | −0.424995 | ||||||||
\(124\) | −3.37568e114 | −2.73451 | ||||||||
\(125\) | 5.37207e113 | 0.280896 | ||||||||
\(126\) | −3.66740e114 | −1.24212 | ||||||||
\(127\) | 8.64009e114 | 1.90202 | 0.951011 | − | 0.309157i | \(-0.100047\pi\) | ||||
0.951011 | + | 0.309157i | \(0.100047\pi\) | |||||||
\(128\) | −2.11537e114 | −0.303699 | ||||||||
\(129\) | −4.05061e114 | −0.380523 | ||||||||
\(130\) | 6.44587e115 | 3.97529 | ||||||||
\(131\) | −1.38263e115 | −0.561591 | −0.280796 | − | 0.959768i | \(-0.590598\pi\) | ||||
−0.280796 | + | 0.959768i | \(0.590598\pi\) | |||||||
\(132\) | −1.98138e115 | −0.531728 | ||||||||
\(133\) | −5.32102e115 | −0.946413 | ||||||||
\(134\) | −7.13076e114 | −0.0843188 | ||||||||
\(135\) | 9.90114e115 | 0.780719 | ||||||||
\(136\) | −2.68748e115 | −0.141734 | ||||||||
\(137\) | 3.52196e115 | 0.124599 | 0.0622994 | − | 0.998058i | \(-0.480157\pi\) | ||||
0.0622994 | + | 0.998058i | \(0.480157\pi\) | |||||||
\(138\) | 3.58005e116 | 0.852078 | ||||||||
\(139\) | 1.75361e116 | 0.281596 | 0.140798 | − | 0.990038i | \(-0.455033\pi\) | ||||
0.140798 | + | 0.990038i | \(0.455033\pi\) | |||||||
\(140\) | −2.17942e117 | −2.36790 | ||||||||
\(141\) | 1.30255e115 | 0.00960179 | ||||||||
\(142\) | −1.01168e117 | −0.507376 | ||||||||
\(143\) | 3.46565e117 | 1.18569 | ||||||||
\(144\) | −8.71473e117 | −2.03938 | ||||||||
\(145\) | −1.91925e117 | −0.308018 | ||||||||
\(146\) | −5.10095e117 | −0.562886 | ||||||||
\(147\) | −1.78171e117 | −0.135532 | ||||||||
\(148\) | 7.90121e118 | 4.15365 | ||||||||
\(149\) | 1.23479e118 | 0.449720 | 0.224860 | − | 0.974391i | \(-0.427808\pi\) | ||||
0.224860 | + | 0.974391i | \(0.427808\pi\) | |||||||
\(150\) | 1.75538e118 | 0.444016 | ||||||||
\(151\) | 6.97436e118 | 1.22818 | 0.614088 | − | 0.789238i | \(-0.289524\pi\) | ||||
0.614088 | + | 0.789238i | \(0.289524\pi\) | |||||||
\(152\) | −2.59664e119 | −3.19106 | ||||||||
\(153\) | 5.93683e117 | 0.0510354 | ||||||||
\(154\) | −1.66601e119 | −1.00415 | ||||||||
\(155\) | 3.64316e119 | 1.54312 | ||||||||
\(156\) | −3.93674e119 | −1.17448 | ||||||||
\(157\) | 4.92390e119 | 1.03700 | 0.518499 | − | 0.855078i | \(-0.326491\pi\) | ||||
0.518499 | + | 0.855078i | \(0.326491\pi\) | |||||||
\(158\) | −5.02382e119 | −0.748554 | ||||||||
\(159\) | 1.72924e119 | 0.182688 | ||||||||
\(160\) | −2.87740e120 | −2.16004 | ||||||||
\(161\) | 2.11722e120 | 1.13176 | ||||||||
\(162\) | 3.50252e120 | 1.33602 | ||||||||
\(163\) | 8.28398e119 | 0.225951 | 0.112976 | − | 0.993598i | \(-0.463962\pi\) | ||||
0.112976 | + | 0.993598i | \(0.463962\pi\) | |||||||
\(164\) | −1.68428e121 | −3.29173 | ||||||||
\(165\) | 2.13838e120 | 0.300062 | ||||||||
\(166\) | 1.81964e121 | 1.83694 | ||||||||
\(167\) | 8.40831e120 | 0.611873 | 0.305936 | − | 0.952052i | \(-0.401031\pi\) | ||||
0.305936 | + | 0.952052i | \(0.401031\pi\) | |||||||
\(168\) | 1.09426e121 | 0.575129 | ||||||||
\(169\) | 4.25656e121 | 1.61895 | ||||||||
\(170\) | 5.01615e120 | 0.138326 | ||||||||
\(171\) | 5.73615e121 | 1.14903 | ||||||||
\(172\) | −2.02172e122 | −2.94728 | ||||||||
\(173\) | −1.26829e122 | −1.34805 | −0.674026 | − | 0.738708i | \(-0.735436\pi\) | ||||
−0.674026 | + | 0.738708i | \(0.735436\pi\) | |||||||
\(174\) | 1.66656e121 | 0.129386 | ||||||||
\(175\) | 1.03812e122 | 0.589760 | ||||||||
\(176\) | −3.95889e122 | −1.64867 | ||||||||
\(177\) | 8.06186e121 | 0.246543 | ||||||||
\(178\) | −8.79944e121 | −0.197954 | ||||||||
\(179\) | −3.37812e122 | −0.559996 | −0.279998 | − | 0.960001i | \(-0.590334\pi\) | ||||
−0.279998 | + | 0.960001i | \(0.590334\pi\) | |||||||
\(180\) | 2.34946e123 | 2.87485 | ||||||||
\(181\) | 4.26762e122 | 0.386103 | 0.193051 | − | 0.981189i | \(-0.438162\pi\) | ||||
0.193051 | + | 0.981189i | \(0.438162\pi\) | |||||||
\(182\) | −3.31014e123 | −2.21797 | ||||||||
\(183\) | 7.00887e121 | 0.0348388 | ||||||||
\(184\) | 1.03319e124 | 3.81602 | ||||||||
\(185\) | −8.52728e123 | −2.34397 | ||||||||
\(186\) | −3.16349e123 | −0.648204 | ||||||||
\(187\) | 2.69696e122 | 0.0412579 | ||||||||
\(188\) | 6.50123e122 | 0.0743691 | ||||||||
\(189\) | −5.08452e123 | −0.435594 | ||||||||
\(190\) | 4.84660e124 | 3.11434 | ||||||||
\(191\) | −8.64736e123 | −0.417412 | −0.208706 | − | 0.977978i | \(-0.566925\pi\) | ||||
−0.208706 | + | 0.977978i | \(0.566925\pi\) | |||||||
\(192\) | 6.01783e123 | 0.218536 | ||||||||
\(193\) | −5.71799e124 | −1.56448 | −0.782240 | − | 0.622977i | \(-0.785923\pi\) | ||||
−0.782240 | + | 0.622977i | \(0.785923\pi\) | |||||||
\(194\) | −1.43032e125 | −2.95284 | ||||||||
\(195\) | 4.24867e124 | 0.662777 | ||||||||
\(196\) | −8.89281e124 | −1.04974 | ||||||||
\(197\) | 1.17702e124 | 0.105287 | 0.0526435 | − | 0.998613i | \(-0.483235\pi\) | ||||
0.0526435 | + | 0.998613i | \(0.483235\pi\) | |||||||
\(198\) | 1.79599e125 | 1.21913 | ||||||||
\(199\) | 8.00207e123 | 0.0412772 | 0.0206386 | − | 0.999787i | \(-0.493430\pi\) | ||||
0.0206386 | + | 0.999787i | \(0.493430\pi\) | |||||||
\(200\) | 5.06600e125 | 1.98852 | ||||||||
\(201\) | −4.70011e123 | −0.0140580 | ||||||||
\(202\) | −1.37527e125 | −0.313861 | ||||||||
\(203\) | 9.85591e124 | 0.171855 | ||||||||
\(204\) | −3.06356e124 | −0.0408678 | ||||||||
\(205\) | 1.81774e126 | 1.85757 | ||||||||
\(206\) | 7.02526e125 | 0.550680 | ||||||||
\(207\) | −2.28240e126 | −1.37407 | ||||||||
\(208\) | −7.86578e126 | −3.64158 | ||||||||
\(209\) | 2.60580e126 | 0.928898 | ||||||||
\(210\) | −2.04243e126 | −0.561301 | ||||||||
\(211\) | 3.87399e126 | 0.821797 | 0.410899 | − | 0.911681i | \(-0.365215\pi\) | ||||
0.410899 | + | 0.911681i | \(0.365215\pi\) | |||||||
\(212\) | 8.63090e126 | 1.41498 | ||||||||
\(213\) | −6.66832e125 | −0.0845918 | ||||||||
\(214\) | −1.31828e127 | −1.29556 | ||||||||
\(215\) | 2.18192e127 | 1.66319 | ||||||||
\(216\) | −2.48123e127 | −1.46871 | ||||||||
\(217\) | −1.87087e127 | −0.860970 | ||||||||
\(218\) | −8.12997e126 | −0.291212 | ||||||||
\(219\) | −3.36220e126 | −0.0938466 | ||||||||
\(220\) | 1.06730e128 | 2.32408 | ||||||||
\(221\) | 5.35849e126 | 0.0911304 | ||||||||
\(222\) | 7.40455e127 | 0.984605 | ||||||||
\(223\) | −1.11748e128 | −1.16312 | −0.581562 | − | 0.813502i | \(-0.697558\pi\) | ||||
−0.581562 | + | 0.813502i | \(0.697558\pi\) | |||||||
\(224\) | 1.47763e128 | 1.20517 | ||||||||
\(225\) | −1.11911e128 | −0.716023 | ||||||||
\(226\) | 2.01205e128 | 1.01095 | ||||||||
\(227\) | −6.90551e127 | −0.272764 | −0.136382 | − | 0.990656i | \(-0.543547\pi\) | ||||
−0.136382 | + | 0.990656i | \(0.543547\pi\) | |||||||
\(228\) | −2.96000e128 | −0.920117 | ||||||||
\(229\) | 2.75512e128 | 0.674695 | 0.337347 | − | 0.941380i | \(-0.390470\pi\) | ||||
0.337347 | + | 0.941380i | \(0.390470\pi\) | |||||||
\(230\) | −1.92845e129 | −3.72427 | ||||||||
\(231\) | −1.09812e128 | −0.167416 | ||||||||
\(232\) | 4.80964e128 | 0.579452 | ||||||||
\(233\) | −1.59553e129 | −1.52057 | −0.760286 | − | 0.649588i | \(-0.774941\pi\) | ||||
−0.760286 | + | 0.649588i | \(0.774941\pi\) | |||||||
\(234\) | 3.56839e129 | 2.69282 | ||||||||
\(235\) | −7.01637e127 | −0.0419676 | ||||||||
\(236\) | 4.02381e129 | 1.90956 | ||||||||
\(237\) | −3.31136e128 | −0.124802 | ||||||||
\(238\) | −2.57594e128 | −0.0771777 | ||||||||
\(239\) | 5.26428e129 | 1.25503 | 0.627514 | − | 0.778605i | \(-0.284072\pi\) | ||||
0.627514 | + | 0.778605i | \(0.284072\pi\) | |||||||
\(240\) | −4.85336e129 | −0.921574 | ||||||||
\(241\) | −8.15453e129 | −1.23444 | −0.617220 | − | 0.786791i | \(-0.711741\pi\) | ||||
−0.617220 | + | 0.786791i | \(0.711741\pi\) | |||||||
\(242\) | −7.04006e129 | −0.850431 | ||||||||
\(243\) | 8.35651e129 | 0.806275 | ||||||||
\(244\) | 3.49824e129 | 0.269838 | ||||||||
\(245\) | 9.59746e129 | 0.592386 | ||||||||
\(246\) | −1.57841e130 | −0.780289 | ||||||||
\(247\) | 5.17736e130 | 2.05175 | ||||||||
\(248\) | −9.12977e130 | −2.90297 | ||||||||
\(249\) | 1.19938e130 | 0.306262 | ||||||||
\(250\) | 2.51275e130 | 0.515725 | ||||||||
\(251\) | −1.11197e130 | −0.183601 | −0.0918003 | − | 0.995777i | \(-0.529262\pi\) | ||||
−0.0918003 | + | 0.995777i | \(0.529262\pi\) | |||||||
\(252\) | −1.20651e131 | −1.60399 | ||||||||
\(253\) | −1.03684e131 | −1.11082 | ||||||||
\(254\) | 4.04134e131 | 3.49211 | ||||||||
\(255\) | 3.30631e129 | 0.0230623 | ||||||||
\(256\) | −2.25632e131 | −1.27152 | ||||||||
\(257\) | −2.28561e131 | −1.04147 | −0.520736 | − | 0.853718i | \(-0.674342\pi\) | ||||
−0.520736 | + | 0.853718i | \(0.674342\pi\) | |||||||
\(258\) | −1.89464e131 | −0.698640 | ||||||||
\(259\) | 4.37901e131 | 1.30779 | ||||||||
\(260\) | 2.12058e132 | 5.13343 | ||||||||
\(261\) | −1.06248e131 | −0.208648 | ||||||||
\(262\) | −6.46715e131 | −1.03108 | ||||||||
\(263\) | −1.00442e132 | −1.30115 | −0.650576 | − | 0.759441i | \(-0.725472\pi\) | ||||
−0.650576 | + | 0.759441i | \(0.725472\pi\) | |||||||
\(264\) | −5.35879e131 | −0.564485 | ||||||||
\(265\) | −9.31479e131 | −0.798496 | ||||||||
\(266\) | −2.48887e132 | −1.73761 | ||||||||
\(267\) | −5.79999e130 | −0.0330038 | ||||||||
\(268\) | −2.34590e131 | −0.108884 | ||||||||
\(269\) | −2.10455e132 | −0.797371 | −0.398685 | − | 0.917088i | \(-0.630533\pi\) | ||||
−0.398685 | + | 0.917088i | \(0.630533\pi\) | |||||||
\(270\) | 4.63118e132 | 1.43340 | ||||||||
\(271\) | 4.86507e132 | 1.23101 | 0.615507 | − | 0.788131i | \(-0.288951\pi\) | ||||
0.615507 | + | 0.788131i | \(0.288951\pi\) | |||||||
\(272\) | −6.12113e131 | −0.126714 | ||||||||
\(273\) | −2.18182e132 | −0.369789 | ||||||||
\(274\) | 1.64737e132 | 0.228763 | ||||||||
\(275\) | −5.08387e132 | −0.578845 | ||||||||
\(276\) | 1.17778e133 | 1.10032 | ||||||||
\(277\) | 6.63632e132 | 0.509073 | 0.254536 | − | 0.967063i | \(-0.418077\pi\) | ||||
0.254536 | + | 0.967063i | \(0.418077\pi\) | |||||||
\(278\) | 8.20240e132 | 0.517011 | ||||||||
\(279\) | 2.01683e133 | 1.04530 | ||||||||
\(280\) | −5.89441e133 | −2.51378 | ||||||||
\(281\) | −2.97492e133 | −1.04468 | −0.522338 | − | 0.852739i | \(-0.674940\pi\) | ||||
−0.522338 | + | 0.852739i | \(0.674940\pi\) | |||||||
\(282\) | 6.09257e131 | 0.0176289 | ||||||||
\(283\) | 6.85225e133 | 1.63483 | 0.817415 | − | 0.576050i | \(-0.195407\pi\) | ||||
0.817415 | + | 0.576050i | \(0.195407\pi\) | |||||||
\(284\) | −3.32827e133 | −0.655192 | ||||||||
\(285\) | 3.19455e133 | 0.519235 | ||||||||
\(286\) | 1.62103e134 | 2.17692 | ||||||||
\(287\) | −9.33460e133 | −1.03641 | ||||||||
\(288\) | −1.59291e134 | −1.46319 | ||||||||
\(289\) | −1.31085e134 | −0.996829 | ||||||||
\(290\) | −8.97716e133 | −0.565520 | ||||||||
\(291\) | −9.42772e133 | −0.492310 | ||||||||
\(292\) | −1.67813e134 | −0.726874 | ||||||||
\(293\) | 3.70158e134 | 1.33077 | 0.665383 | − | 0.746502i | \(-0.268268\pi\) | ||||
0.665383 | + | 0.746502i | \(0.268268\pi\) | |||||||
\(294\) | −8.33383e133 | −0.248837 | ||||||||
\(295\) | −4.34264e134 | −1.07759 | ||||||||
\(296\) | 2.13694e135 | 4.40954 | ||||||||
\(297\) | 2.48998e134 | 0.427532 | ||||||||
\(298\) | 5.77565e134 | 0.825685 | ||||||||
\(299\) | −2.06006e135 | −2.45358 | ||||||||
\(300\) | 5.77492e134 | 0.573373 | ||||||||
\(301\) | −1.12048e135 | −0.927961 | ||||||||
\(302\) | 3.26220e135 | 2.25493 | ||||||||
\(303\) | −9.06483e133 | −0.0523283 | ||||||||
\(304\) | −5.91422e135 | −2.85290 | ||||||||
\(305\) | −3.77543e134 | −0.152274 | ||||||||
\(306\) | 2.77691e134 | 0.0937009 | ||||||||
\(307\) | −2.38576e135 | −0.673885 | −0.336942 | − | 0.941525i | \(-0.609393\pi\) | ||||
−0.336942 | + | 0.941525i | \(0.609393\pi\) | |||||||
\(308\) | −5.48090e135 | −1.29670 | ||||||||
\(309\) | 4.63057e134 | 0.0918116 | ||||||||
\(310\) | 1.70406e136 | 2.83317 | ||||||||
\(311\) | −7.97308e135 | −1.11221 | −0.556103 | − | 0.831114i | \(-0.687704\pi\) | ||||
−0.556103 | + | 0.831114i | \(0.687704\pi\) | |||||||
\(312\) | −1.06472e136 | −1.24684 | ||||||||
\(313\) | 1.42971e136 | 1.40631 | 0.703157 | − | 0.711034i | \(-0.251773\pi\) | ||||
0.703157 | + | 0.711034i | \(0.251773\pi\) | |||||||
\(314\) | 2.30312e136 | 1.90393 | ||||||||
\(315\) | 1.30212e136 | 0.905158 | ||||||||
\(316\) | −1.65275e136 | −0.966634 | ||||||||
\(317\) | −3.23507e136 | −1.59277 | −0.796386 | − | 0.604788i | \(-0.793258\pi\) | ||||
−0.796386 | + | 0.604788i | \(0.793258\pi\) | |||||||
\(318\) | 8.08838e135 | 0.335416 | ||||||||
\(319\) | −4.82661e135 | −0.168675 | ||||||||
\(320\) | −3.24160e136 | −0.955180 | ||||||||
\(321\) | −8.68919e135 | −0.216001 | ||||||||
\(322\) | 9.90315e136 | 2.07792 | ||||||||
\(323\) | 4.02901e135 | 0.0713938 | ||||||||
\(324\) | 1.15227e137 | 1.72525 | ||||||||
\(325\) | −1.01009e137 | −1.27855 | ||||||||
\(326\) | 3.87477e136 | 0.414846 | ||||||||
\(327\) | −5.35872e135 | −0.0485521 | ||||||||
\(328\) | −4.55525e137 | −3.49452 | ||||||||
\(329\) | 3.60311e135 | 0.0234154 | ||||||||
\(330\) | 1.00021e137 | 0.550913 | ||||||||
\(331\) | −2.97402e137 | −1.38905 | −0.694525 | − | 0.719469i | \(-0.744385\pi\) | ||||
−0.694525 | + | 0.719469i | \(0.744385\pi\) | |||||||
\(332\) | 5.98631e137 | 2.37210 | ||||||||
\(333\) | −4.72064e137 | −1.58778 | ||||||||
\(334\) | 3.93293e137 | 1.12340 | ||||||||
\(335\) | 2.53178e136 | 0.0614447 | ||||||||
\(336\) | 2.49234e137 | 0.514182 | ||||||||
\(337\) | −9.92582e137 | −1.74155 | −0.870777 | − | 0.491679i | \(-0.836383\pi\) | ||||
−0.870777 | + | 0.491679i | \(0.836383\pi\) | |||||||
\(338\) | 1.99098e138 | 2.97239 | ||||||||
\(339\) | 1.32621e137 | 0.168550 | ||||||||
\(340\) | 1.65023e137 | 0.178626 | ||||||||
\(341\) | 9.16197e137 | 0.845036 | ||||||||
\(342\) | 2.68304e138 | 2.10962 | ||||||||
\(343\) | −1.60600e138 | −1.07700 | ||||||||
\(344\) | −5.46789e138 | −3.12885 | ||||||||
\(345\) | −1.27110e138 | −0.620926 | ||||||||
\(346\) | −5.93234e138 | −2.47502 | ||||||||
\(347\) | 2.45412e138 | 0.874863 | 0.437431 | − | 0.899252i | \(-0.355888\pi\) | ||||
0.437431 | + | 0.899252i | \(0.355888\pi\) | |||||||
\(348\) | 5.48269e137 | 0.167080 | ||||||||
\(349\) | 1.36925e138 | 0.356860 | 0.178430 | − | 0.983953i | \(-0.442898\pi\) | ||||
0.178430 | + | 0.983953i | \(0.442898\pi\) | |||||||
\(350\) | 4.85574e138 | 1.08280 | ||||||||
\(351\) | 4.94724e138 | 0.944334 | ||||||||
\(352\) | −7.23620e138 | −1.18287 | ||||||||
\(353\) | 2.45582e138 | 0.343934 | 0.171967 | − | 0.985103i | \(-0.444988\pi\) | ||||
0.171967 | + | 0.985103i | \(0.444988\pi\) | |||||||
\(354\) | 3.77088e138 | 0.452652 | ||||||||
\(355\) | 3.59199e138 | 0.369735 | ||||||||
\(356\) | −2.89487e138 | −0.255625 | ||||||||
\(357\) | −1.69788e137 | −0.0128674 | ||||||||
\(358\) | −1.58009e139 | −1.02815 | ||||||||
\(359\) | −2.52971e139 | −1.41392 | −0.706958 | − | 0.707256i | \(-0.749933\pi\) | ||||
−0.706958 | + | 0.707256i | \(0.749933\pi\) | |||||||
\(360\) | 6.35427e139 | 3.05196 | ||||||||
\(361\) | 1.47099e139 | 0.607391 | ||||||||
\(362\) | 1.99615e139 | 0.708884 | ||||||||
\(363\) | −4.64033e138 | −0.141787 | ||||||||
\(364\) | −1.08898e140 | −2.86414 | ||||||||
\(365\) | 1.81110e139 | 0.410186 | ||||||||
\(366\) | 3.27835e138 | 0.0639640 | ||||||||
\(367\) | −3.84161e139 | −0.645970 | −0.322985 | − | 0.946404i | \(-0.604686\pi\) | ||||
−0.322985 | + | 0.946404i | \(0.604686\pi\) | |||||||
\(368\) | 2.35325e140 | 3.41164 | ||||||||
\(369\) | 1.00629e140 | 1.25830 | ||||||||
\(370\) | −3.98857e140 | −4.30352 | ||||||||
\(371\) | 4.78342e139 | 0.445513 | ||||||||
\(372\) | −1.04074e140 | −0.837048 | ||||||||
\(373\) | −1.16147e140 | −0.807003 | −0.403502 | − | 0.914979i | \(-0.632207\pi\) | ||||
−0.403502 | + | 0.914979i | \(0.632207\pi\) | |||||||
\(374\) | 1.26148e139 | 0.0757494 | ||||||||
\(375\) | 1.65623e139 | 0.0859838 | ||||||||
\(376\) | 1.75830e139 | 0.0789507 | ||||||||
\(377\) | −9.58981e139 | −0.372569 | ||||||||
\(378\) | −2.37825e140 | −0.799750 | ||||||||
\(379\) | 4.20001e140 | 1.22296 | 0.611481 | − | 0.791259i | \(-0.290574\pi\) | ||||
0.611481 | + | 0.791259i | \(0.290574\pi\) | |||||||
\(380\) | 1.59445e141 | 4.02166 | ||||||||
\(381\) | 2.66377e140 | 0.582219 | ||||||||
\(382\) | −4.04474e140 | −0.766368 | ||||||||
\(383\) | 4.92224e138 | 0.00808778 | 0.00404389 | − | 0.999992i | \(-0.498713\pi\) | ||||
0.00404389 | + | 0.999992i | \(0.498713\pi\) | |||||||
\(384\) | −6.52178e139 | −0.0929640 | ||||||||
\(385\) | 5.91520e140 | 0.731745 | ||||||||
\(386\) | −2.67455e141 | −2.87238 | ||||||||
\(387\) | 1.20790e141 | 1.12663 | ||||||||
\(388\) | −4.70553e141 | −3.81311 | ||||||||
\(389\) | 1.77397e141 | 1.24937 | 0.624686 | − | 0.780876i | \(-0.285227\pi\) | ||||
0.624686 | + | 0.780876i | \(0.285227\pi\) | |||||||
\(390\) | 1.98729e141 | 1.21686 | ||||||||
\(391\) | −1.60313e140 | −0.0853760 | ||||||||
\(392\) | −2.40512e141 | −1.11441 | ||||||||
\(393\) | −4.26270e140 | −0.171906 | ||||||||
\(394\) | 5.50543e140 | 0.193307 | ||||||||
\(395\) | 1.78371e141 | 0.545486 | ||||||||
\(396\) | 5.90851e141 | 1.57431 | ||||||||
\(397\) | −4.99793e141 | −1.16067 | −0.580334 | − | 0.814379i | \(-0.697078\pi\) | ||||
−0.580334 | + | 0.814379i | \(0.697078\pi\) | |||||||
\(398\) | 3.74291e140 | 0.0757848 | ||||||||
\(399\) | −1.64049e141 | −0.289702 | ||||||||
\(400\) | 1.15386e142 | 1.77780 | ||||||||
\(401\) | −1.08238e142 | −1.45549 | −0.727745 | − | 0.685847i | \(-0.759432\pi\) | ||||
−0.727745 | + | 0.685847i | \(0.759432\pi\) | |||||||
\(402\) | −2.19844e140 | −0.0258104 | ||||||||
\(403\) | 1.82036e142 | 1.86652 | ||||||||
\(404\) | −4.52440e141 | −0.405300 | ||||||||
\(405\) | −1.24357e142 | −0.973581 | ||||||||
\(406\) | 4.61003e141 | 0.315526 | ||||||||
\(407\) | −2.14448e142 | −1.28359 | ||||||||
\(408\) | −8.28560e140 | −0.0433856 | ||||||||
\(409\) | −1.56829e142 | −0.718630 | −0.359315 | − | 0.933216i | \(-0.616990\pi\) | ||||
−0.359315 | + | 0.933216i | \(0.616990\pi\) | |||||||
\(410\) | 8.50233e142 | 3.41050 | ||||||||
\(411\) | 1.08583e141 | 0.0381403 | ||||||||
\(412\) | 2.31119e142 | 0.711112 | ||||||||
\(413\) | 2.23007e142 | 0.601231 | ||||||||
\(414\) | −1.06758e143 | −2.52278 | ||||||||
\(415\) | −6.46065e142 | −1.33861 | ||||||||
\(416\) | −1.43773e143 | −2.61271 | ||||||||
\(417\) | 5.40646e141 | 0.0861982 | ||||||||
\(418\) | 1.21884e143 | 1.70545 | ||||||||
\(419\) | −3.35220e142 | −0.411781 | −0.205890 | − | 0.978575i | \(-0.566009\pi\) | ||||
−0.205890 | + | 0.978575i | \(0.566009\pi\) | |||||||
\(420\) | −6.71925e142 | −0.724827 | ||||||||
\(421\) | 1.22649e143 | 1.16223 | 0.581113 | − | 0.813823i | \(-0.302617\pi\) | ||||
0.581113 | + | 0.813823i | \(0.302617\pi\) | |||||||
\(422\) | 1.81203e143 | 1.50882 | ||||||||
\(423\) | −3.88421e141 | −0.0284284 | ||||||||
\(424\) | 2.33429e143 | 1.50216 | ||||||||
\(425\) | −7.86053e141 | −0.0444892 | ||||||||
\(426\) | −3.11906e142 | −0.155310 | ||||||||
\(427\) | 1.93879e142 | 0.0849596 | ||||||||
\(428\) | −4.33691e143 | −1.67300 | ||||||||
\(429\) | 1.06847e143 | 0.362946 | ||||||||
\(430\) | 1.02058e144 | 3.05362 | ||||||||
\(431\) | −9.65530e142 | −0.254539 | −0.127270 | − | 0.991868i | \(-0.540621\pi\) | ||||
−0.127270 | + | 0.991868i | \(0.540621\pi\) | |||||||
\(432\) | −5.65136e143 | −1.31307 | ||||||||
\(433\) | −3.83027e143 | −0.784582 | −0.392291 | − | 0.919841i | \(-0.628317\pi\) | ||||
−0.392291 | + | 0.919841i | \(0.628317\pi\) | |||||||
\(434\) | −8.75086e143 | −1.58074 | ||||||||
\(435\) | −5.91713e142 | −0.0942858 | ||||||||
\(436\) | −2.67462e143 | −0.376053 | ||||||||
\(437\) | −1.54894e144 | −1.92219 | ||||||||
\(438\) | −1.57264e143 | −0.172302 | ||||||||
\(439\) | 6.91926e143 | 0.669489 | 0.334745 | − | 0.942309i | \(-0.391350\pi\) | ||||
0.334745 | + | 0.942309i | \(0.391350\pi\) | |||||||
\(440\) | 2.88659e144 | 2.46726 | ||||||||
\(441\) | 5.31308e143 | 0.401276 | ||||||||
\(442\) | 2.50639e143 | 0.167315 | ||||||||
\(443\) | 1.62442e143 | 0.0958727 | 0.0479364 | − | 0.998850i | \(-0.484736\pi\) | ||||
0.0479364 | + | 0.998850i | \(0.484736\pi\) | |||||||
\(444\) | 2.43597e144 | 1.27145 | ||||||||
\(445\) | 3.12425e143 | 0.144253 | ||||||||
\(446\) | −5.22695e144 | −2.13549 | ||||||||
\(447\) | 3.80691e143 | 0.137662 | ||||||||
\(448\) | 1.66465e144 | 0.532932 | ||||||||
\(449\) | −2.91783e144 | −0.827245 | −0.413623 | − | 0.910448i | \(-0.635737\pi\) | ||||
−0.413623 | + | 0.910448i | \(0.635737\pi\) | |||||||
\(450\) | −5.23457e144 | −1.31462 | ||||||||
\(451\) | 4.57132e144 | 1.01723 | ||||||||
\(452\) | 6.61932e144 | 1.30547 | ||||||||
\(453\) | 2.15022e144 | 0.375951 | ||||||||
\(454\) | −3.23000e144 | −0.500793 | ||||||||
\(455\) | 1.17527e145 | 1.61628 | ||||||||
\(456\) | −8.00553e144 | −0.976802 | ||||||||
\(457\) | −2.54726e144 | −0.275829 | −0.137915 | − | 0.990444i | \(-0.544040\pi\) | ||||
−0.137915 | + | 0.990444i | \(0.544040\pi\) | |||||||
\(458\) | 1.28869e145 | 1.23874 | ||||||||
\(459\) | 3.84993e143 | 0.0328595 | ||||||||
\(460\) | −6.34427e145 | −4.80928 | ||||||||
\(461\) | 1.99590e145 | 1.34412 | 0.672060 | − | 0.740496i | \(-0.265409\pi\) | ||||
0.672060 | + | 0.740496i | \(0.265409\pi\) | |||||||
\(462\) | −5.13638e144 | −0.307376 | ||||||||
\(463\) | 1.76946e145 | 0.941186 | 0.470593 | − | 0.882350i | \(-0.344040\pi\) | ||||
0.470593 | + | 0.882350i | \(0.344040\pi\) | |||||||
\(464\) | 1.09547e145 | 0.518047 | ||||||||
\(465\) | 1.12320e145 | 0.472359 | ||||||||
\(466\) | −7.46297e145 | −2.79177 | ||||||||
\(467\) | −4.46078e145 | −1.48471 | −0.742354 | − | 0.670007i | \(-0.766291\pi\) | ||||
−0.742354 | + | 0.670007i | \(0.766291\pi\) | |||||||
\(468\) | 1.17394e146 | 3.47734 | ||||||||
\(469\) | −1.30014e144 | −0.0342824 | ||||||||
\(470\) | −3.28186e144 | −0.0770524 | ||||||||
\(471\) | 1.51806e145 | 0.317430 | ||||||||
\(472\) | 1.08827e146 | 2.02720 | ||||||||
\(473\) | 5.48718e145 | 0.910788 | ||||||||
\(474\) | −1.54886e145 | −0.229136 | ||||||||
\(475\) | −7.59482e145 | −1.00165 | ||||||||
\(476\) | −8.47441e144 | −0.0996623 | ||||||||
\(477\) | −5.15660e145 | −0.540894 | ||||||||
\(478\) | 2.46233e146 | 2.30423 | ||||||||
\(479\) | −6.72192e145 | −0.561317 | −0.280658 | − | 0.959808i | \(-0.590553\pi\) | ||||
−0.280658 | + | 0.959808i | \(0.590553\pi\) | |||||||
\(480\) | −8.87114e145 | −0.661198 | ||||||||
\(481\) | −4.26078e146 | −2.83519 | ||||||||
\(482\) | −3.81422e146 | −2.26643 | ||||||||
\(483\) | 6.52748e145 | 0.346439 | ||||||||
\(484\) | −2.31606e146 | −1.09819 | ||||||||
\(485\) | 5.07838e146 | 2.15179 | ||||||||
\(486\) | 3.90870e146 | 1.48032 | ||||||||
\(487\) | 9.21076e145 | 0.311865 | 0.155933 | − | 0.987768i | \(-0.450162\pi\) | ||||
0.155933 | + | 0.987768i | \(0.450162\pi\) | |||||||
\(488\) | 9.46123e145 | 0.286462 | ||||||||
\(489\) | 2.55398e145 | 0.0691648 | ||||||||
\(490\) | 4.48914e146 | 1.08762 | ||||||||
\(491\) | −6.72259e146 | −1.45745 | −0.728727 | − | 0.684804i | \(-0.759888\pi\) | ||||
−0.728727 | + | 0.684804i | \(0.759888\pi\) | |||||||
\(492\) | −5.19270e146 | −1.00762 | ||||||||
\(493\) | −7.46276e144 | −0.0129641 | ||||||||
\(494\) | 2.42167e147 | 3.76701 | ||||||||
\(495\) | −6.37668e146 | −0.888406 | ||||||||
\(496\) | −2.07944e147 | −2.59534 | ||||||||
\(497\) | −1.84459e146 | −0.206289 | ||||||||
\(498\) | 5.61002e146 | 0.562297 | ||||||||
\(499\) | 1.28052e147 | 1.15055 | 0.575276 | − | 0.817960i | \(-0.304895\pi\) | ||||
0.575276 | + | 0.817960i | \(0.304895\pi\) | |||||||
\(500\) | 8.26652e146 | 0.665974 | ||||||||
\(501\) | 2.59232e146 | 0.187297 | ||||||||
\(502\) | −5.20114e146 | −0.337090 | ||||||||
\(503\) | 1.51237e146 | 0.0879434 | 0.0439717 | − | 0.999033i | \(-0.485999\pi\) | ||||
0.0439717 | + | 0.999033i | \(0.485999\pi\) | |||||||
\(504\) | −3.26310e147 | −1.70281 | ||||||||
\(505\) | 4.88291e146 | 0.228717 | ||||||||
\(506\) | −4.84974e147 | −2.03946 | ||||||||
\(507\) | 1.31231e147 | 0.495569 | ||||||||
\(508\) | 1.32953e148 | 4.50948 | ||||||||
\(509\) | −5.68917e147 | −1.73352 | −0.866762 | − | 0.498722i | \(-0.833803\pi\) | ||||
−0.866762 | + | 0.498722i | \(0.833803\pi\) | |||||||
\(510\) | 1.54650e146 | 0.0423424 | ||||||||
\(511\) | −9.30051e146 | −0.228859 | ||||||||
\(512\) | −9.18080e147 | −2.03080 | ||||||||
\(513\) | 3.71980e147 | 0.739814 | ||||||||
\(514\) | −1.06908e148 | −1.91214 | ||||||||
\(515\) | −2.49433e147 | −0.401291 | ||||||||
\(516\) | −6.23306e147 | −0.902178 | ||||||||
\(517\) | −1.76450e146 | −0.0229820 | ||||||||
\(518\) | 2.04825e148 | 2.40110 | ||||||||
\(519\) | −3.91019e147 | −0.412646 | ||||||||
\(520\) | 5.73526e148 | 5.44968 | ||||||||
\(521\) | −7.37505e147 | −0.631116 | −0.315558 | − | 0.948906i | \(-0.602192\pi\) | ||||
−0.315558 | + | 0.948906i | \(0.602192\pi\) | |||||||
\(522\) | −4.96969e147 | −0.383078 | ||||||||
\(523\) | 1.34235e148 | 0.932228 | 0.466114 | − | 0.884725i | \(-0.345654\pi\) | ||||
0.466114 | + | 0.884725i | \(0.345654\pi\) | |||||||
\(524\) | −2.12758e148 | −1.33147 | ||||||||
\(525\) | 3.20057e147 | 0.180529 | ||||||||
\(526\) | −4.69811e148 | −2.38891 | ||||||||
\(527\) | 1.41660e147 | 0.0649483 | ||||||||
\(528\) | −1.22054e148 | −0.504666 | ||||||||
\(529\) | 3.48197e148 | 1.29865 | ||||||||
\(530\) | −4.35693e148 | −1.46604 | ||||||||
\(531\) | −2.40406e148 | −0.729951 | ||||||||
\(532\) | −8.18796e148 | −2.24384 | ||||||||
\(533\) | 9.08258e148 | 2.24686 | ||||||||
\(534\) | −2.71290e147 | −0.0605949 | ||||||||
\(535\) | 4.68056e148 | 0.944098 | ||||||||
\(536\) | −6.34465e147 | −0.115592 | ||||||||
\(537\) | −1.04149e148 | −0.171418 | ||||||||
\(538\) | −9.84388e148 | −1.46397 | ||||||||
\(539\) | 2.41361e148 | 0.324398 | ||||||||
\(540\) | 1.52358e149 | 1.85100 | ||||||||
\(541\) | −7.73821e148 | −0.849942 | −0.424971 | − | 0.905207i | \(-0.639716\pi\) | ||||
−0.424971 | + | 0.905207i | \(0.639716\pi\) | |||||||
\(542\) | 2.27560e149 | 2.26014 | ||||||||
\(543\) | 1.31572e148 | 0.118188 | ||||||||
\(544\) | −1.11884e148 | −0.0909134 | ||||||||
\(545\) | 2.88655e148 | 0.212212 | ||||||||
\(546\) | −1.02053e149 | −0.678932 | ||||||||
\(547\) | −1.47788e149 | −0.889877 | −0.444939 | − | 0.895561i | \(-0.646775\pi\) | ||||
−0.444939 | + | 0.895561i | \(0.646775\pi\) | |||||||
\(548\) | 5.41958e148 | 0.295410 | ||||||||
\(549\) | −2.09005e148 | −0.103149 | ||||||||
\(550\) | −2.37794e149 | −1.06276 | ||||||||
\(551\) | −7.21051e148 | −0.291880 | ||||||||
\(552\) | 3.18538e149 | 1.16810 | ||||||||
\(553\) | −9.15989e148 | −0.304348 | ||||||||
\(554\) | 3.10409e149 | 0.934657 | ||||||||
\(555\) | −2.62900e149 | −0.717501 | ||||||||
\(556\) | 2.69845e149 | 0.667634 | ||||||||
\(557\) | −8.71713e149 | −1.95553 | −0.977767 | − | 0.209696i | \(-0.932753\pi\) | ||||
−0.977767 | + | 0.209696i | \(0.932753\pi\) | |||||||
\(558\) | 9.43357e149 | 1.91917 | ||||||||
\(559\) | 1.09023e150 | 2.01175 | ||||||||
\(560\) | −1.34254e150 | −2.24739 | ||||||||
\(561\) | 8.31483e147 | 0.0126292 | ||||||||
\(562\) | −1.39150e150 | −1.91802 | ||||||||
\(563\) | −1.15897e150 | −1.44999 | −0.724997 | − | 0.688752i | \(-0.758159\pi\) | ||||
−0.724997 | + | 0.688752i | \(0.758159\pi\) | |||||||
\(564\) | 2.00435e148 | 0.0227648 | ||||||||
\(565\) | −7.14381e149 | −0.736698 | ||||||||
\(566\) | 3.20509e150 | 3.00154 | ||||||||
\(567\) | 6.38610e149 | 0.543199 | ||||||||
\(568\) | −9.00153e149 | −0.695556 | ||||||||
\(569\) | −5.05714e149 | −0.355048 | −0.177524 | − | 0.984116i | \(-0.556809\pi\) | ||||
−0.177524 | + | 0.984116i | \(0.556809\pi\) | |||||||
\(570\) | 1.49423e150 | 0.953315 | ||||||||
\(571\) | 4.44981e149 | 0.258032 | 0.129016 | − | 0.991643i | \(-0.458818\pi\) | ||||
0.129016 | + | 0.991643i | \(0.458818\pi\) | |||||||
\(572\) | 5.33293e150 | 2.81114 | ||||||||
\(573\) | −2.66602e149 | −0.127772 | ||||||||
\(574\) | −4.36619e150 | −1.90285 | ||||||||
\(575\) | 3.02196e150 | 1.19782 | ||||||||
\(576\) | −1.79452e150 | −0.647030 | ||||||||
\(577\) | 4.06700e150 | 1.33411 | 0.667057 | − | 0.745007i | \(-0.267554\pi\) | ||||
0.667057 | + | 0.745007i | \(0.267554\pi\) | |||||||
\(578\) | −6.13141e150 | −1.83018 | ||||||||
\(579\) | −1.76288e150 | −0.478895 | ||||||||
\(580\) | −2.95333e150 | −0.730276 | ||||||||
\(581\) | 3.31773e150 | 0.746865 | ||||||||
\(582\) | −4.40975e150 | −0.903881 | ||||||||
\(583\) | −2.34252e150 | −0.437268 | ||||||||
\(584\) | −4.53861e150 | −0.771654 | ||||||||
\(585\) | −1.26696e151 | −1.96231 | ||||||||
\(586\) | 1.73139e151 | 2.44328 | ||||||||
\(587\) | −5.98154e150 | −0.769195 | −0.384598 | − | 0.923084i | \(-0.625660\pi\) | ||||
−0.384598 | + | 0.923084i | \(0.625660\pi\) | |||||||
\(588\) | −2.74169e150 | −0.321332 | ||||||||
\(589\) | 1.36871e151 | 1.46228 | ||||||||
\(590\) | −2.03124e151 | −1.97846 | ||||||||
\(591\) | 3.62880e149 | 0.0322289 | ||||||||
\(592\) | 4.86719e151 | 3.94226 | ||||||||
\(593\) | 7.93269e150 | 0.586057 | 0.293028 | − | 0.956104i | \(-0.405337\pi\) | ||||
0.293028 | + | 0.956104i | \(0.405337\pi\) | |||||||
\(594\) | 1.16467e151 | 0.784949 | ||||||||
\(595\) | 9.14591e149 | 0.0562409 | ||||||||
\(596\) | 1.90009e151 | 1.06624 | ||||||||
\(597\) | 2.46707e149 | 0.0126352 | ||||||||
\(598\) | −9.63577e151 | −4.50476 | ||||||||
\(599\) | −1.69552e151 | −0.723671 | −0.361836 | − | 0.932242i | \(-0.617850\pi\) | ||||
−0.361836 | + | 0.932242i | \(0.617850\pi\) | |||||||
\(600\) | 1.56187e151 | 0.608697 | ||||||||
\(601\) | 1.36331e151 | 0.485216 | 0.242608 | − | 0.970124i | \(-0.421997\pi\) | ||||
0.242608 | + | 0.970124i | \(0.421997\pi\) | |||||||
\(602\) | −5.24096e151 | −1.70374 | ||||||||
\(603\) | 1.40158e150 | 0.0416221 | ||||||||
\(604\) | 1.07321e152 | 2.91187 | ||||||||
\(605\) | 2.49958e151 | 0.619726 | ||||||||
\(606\) | −4.24001e150 | −0.0960746 | ||||||||
\(607\) | 3.55026e151 | 0.735321 | 0.367660 | − | 0.929960i | \(-0.380159\pi\) | ||||
0.367660 | + | 0.929960i | \(0.380159\pi\) | |||||||
\(608\) | −1.08102e152 | −2.04686 | ||||||||
\(609\) | 3.03862e150 | 0.0526058 | ||||||||
\(610\) | −1.76593e151 | −0.279575 | ||||||||
\(611\) | −3.50583e150 | −0.0507627 | ||||||||
\(612\) | 9.13556e150 | 0.120999 | ||||||||
\(613\) | −2.55291e151 | −0.309342 | −0.154671 | − | 0.987966i | \(-0.549432\pi\) | ||||
−0.154671 | + | 0.987966i | \(0.549432\pi\) | |||||||
\(614\) | −1.11592e152 | −1.23725 | ||||||||
\(615\) | 5.60415e151 | 0.568612 | ||||||||
\(616\) | −1.48235e152 | −1.37658 | ||||||||
\(617\) | 1.61774e151 | 0.137520 | 0.0687601 | − | 0.997633i | \(-0.478096\pi\) | ||||
0.0687601 | + | 0.997633i | \(0.478096\pi\) | |||||||
\(618\) | 2.16592e151 | 0.168566 | ||||||||
\(619\) | 1.90686e152 | 1.35887 | 0.679434 | − | 0.733736i | \(-0.262225\pi\) | ||||
0.679434 | + | 0.733736i | \(0.262225\pi\) | |||||||
\(620\) | 5.60608e152 | 3.65858 | ||||||||
\(621\) | −1.48010e152 | −0.884704 | ||||||||
\(622\) | −3.72935e152 | −2.04201 | ||||||||
\(623\) | −1.60439e151 | −0.0804845 | ||||||||
\(624\) | −2.42505e152 | −1.11471 | ||||||||
\(625\) | −2.76765e152 | −1.16587 | ||||||||
\(626\) | 6.68738e152 | 2.58199 | ||||||||
\(627\) | 8.03377e151 | 0.284340 | ||||||||
\(628\) | 7.57687e152 | 2.45861 | ||||||||
\(629\) | −3.31573e151 | −0.0986548 | ||||||||
\(630\) | 6.09055e152 | 1.66187 | ||||||||
\(631\) | −5.64845e152 | −1.41361 | −0.706804 | − | 0.707410i | \(-0.749864\pi\) | ||||
−0.706804 | + | 0.707410i | \(0.749864\pi\) | |||||||
\(632\) | −4.46999e152 | −1.02618 | ||||||||
\(633\) | 1.19437e152 | 0.251556 | ||||||||
\(634\) | −1.51318e153 | −2.92433 | ||||||||
\(635\) | −1.43488e153 | −2.54477 | ||||||||
\(636\) | 2.66094e152 | 0.433134 | ||||||||
\(637\) | 4.79551e152 | 0.716532 | ||||||||
\(638\) | −2.25761e152 | −0.309686 | ||||||||
\(639\) | 1.98850e152 | 0.250455 | ||||||||
\(640\) | 3.51306e152 | 0.406328 | ||||||||
\(641\) | −4.43476e152 | −0.471094 | −0.235547 | − | 0.971863i | \(-0.575688\pi\) | ||||
−0.235547 | + | 0.971863i | \(0.575688\pi\) | |||||||
\(642\) | −4.06430e152 | −0.396577 | ||||||||
\(643\) | 2.48936e152 | 0.223146 | 0.111573 | − | 0.993756i | \(-0.464411\pi\) | ||||
0.111573 | + | 0.993756i | \(0.464411\pi\) | |||||||
\(644\) | 3.25797e153 | 2.68329 | ||||||||
\(645\) | 6.72695e152 | 0.509112 | ||||||||
\(646\) | 1.88454e152 | 0.131079 | ||||||||
\(647\) | 5.34940e152 | 0.341997 | 0.170998 | − | 0.985271i | \(-0.445301\pi\) | ||||
0.170998 | + | 0.985271i | \(0.445301\pi\) | |||||||
\(648\) | 3.11639e153 | 1.83153 | ||||||||
\(649\) | −1.09211e153 | −0.590104 | ||||||||
\(650\) | −4.72464e153 | −2.34742 | ||||||||
\(651\) | −5.76797e152 | −0.263548 | ||||||||
\(652\) | 1.27474e153 | 0.535705 | ||||||||
\(653\) | 1.89403e153 | 0.732181 | 0.366090 | − | 0.930579i | \(-0.380696\pi\) | ||||
0.366090 | + | 0.930579i | \(0.380696\pi\) | |||||||
\(654\) | −2.50650e152 | −0.0891417 | ||||||||
\(655\) | 2.29617e153 | 0.751369 | ||||||||
\(656\) | −1.03752e154 | −3.12420 | ||||||||
\(657\) | 1.00261e153 | 0.277856 | ||||||||
\(658\) | 1.68533e152 | 0.0429906 | ||||||||
\(659\) | 6.39578e153 | 1.50189 | 0.750945 | − | 0.660364i | \(-0.229598\pi\) | ||||
0.750945 | + | 0.660364i | \(0.229598\pi\) | |||||||
\(660\) | 3.29053e153 | 0.711413 | ||||||||
\(661\) | −5.33971e153 | −1.06301 | −0.531506 | − | 0.847055i | \(-0.678374\pi\) | ||||
−0.531506 | + | 0.847055i | \(0.678374\pi\) | |||||||
\(662\) | −1.39107e154 | −2.55029 | ||||||||
\(663\) | 1.65204e152 | 0.0278955 | ||||||||
\(664\) | 1.61904e154 | 2.51824 | ||||||||
\(665\) | 8.83676e153 | 1.26623 | ||||||||
\(666\) | −2.20805e154 | −2.91516 | ||||||||
\(667\) | 2.86904e153 | 0.349043 | ||||||||
\(668\) | 1.29387e154 | 1.45068 | ||||||||
\(669\) | −3.44525e153 | −0.356039 | ||||||||
\(670\) | 1.18422e153 | 0.112812 | ||||||||
\(671\) | −9.49461e152 | −0.0833872 | ||||||||
\(672\) | 4.55559e153 | 0.368909 | ||||||||
\(673\) | −3.31144e153 | −0.247284 | −0.123642 | − | 0.992327i | \(-0.539457\pi\) | ||||
−0.123642 | + | 0.992327i | \(0.539457\pi\) | |||||||
\(674\) | −4.64273e154 | −3.19749 | ||||||||
\(675\) | −7.25726e153 | −0.461017 | ||||||||
\(676\) | 6.54998e154 | 3.83835 | ||||||||
\(677\) | −1.62873e151 | −0.000880578 0 | −0.000440289 | − | 1.00000i | \(-0.500140\pi\) | ||||
−0.000440289 | 1.00000i | \(0.500140\pi\) | ||||||||
\(678\) | 6.20324e153 | 0.309457 | ||||||||
\(679\) | −2.60790e154 | −1.20057 | ||||||||
\(680\) | 4.46316e153 | 0.189630 | ||||||||
\(681\) | −2.12900e153 | −0.0834944 | ||||||||
\(682\) | 4.28545e154 | 1.55149 | ||||||||
\(683\) | 2.33523e154 | 0.780549 | 0.390275 | − | 0.920698i | \(-0.372380\pi\) | ||||
0.390275 | + | 0.920698i | \(0.372380\pi\) | |||||||
\(684\) | 8.82676e154 | 2.72423 | ||||||||
\(685\) | −5.84901e153 | −0.166704 | ||||||||
\(686\) | −7.51193e154 | −1.97737 | ||||||||
\(687\) | 8.49416e153 | 0.206528 | ||||||||
\(688\) | −1.24539e155 | −2.79728 | ||||||||
\(689\) | −4.65427e154 | −0.965837 | ||||||||
\(690\) | −5.94549e154 | −1.14002 | ||||||||
\(691\) | 9.64926e154 | 1.70978 | 0.854890 | − | 0.518809i | \(-0.173624\pi\) | ||||
0.854890 | + | 0.518809i | \(0.173624\pi\) | |||||||
\(692\) | −1.95164e155 | −3.19608 | ||||||||
\(693\) | 3.27461e154 | 0.495677 | ||||||||
\(694\) | 1.14790e155 | 1.60625 | ||||||||
\(695\) | −2.91227e154 | −0.376756 | ||||||||
\(696\) | 1.48283e154 | 0.177373 | ||||||||
\(697\) | 7.06803e153 | 0.0781830 | ||||||||
\(698\) | 6.40458e154 | 0.655195 | ||||||||
\(699\) | −4.91908e154 | −0.465455 | ||||||||
\(700\) | 1.59746e155 | 1.39825 | ||||||||
\(701\) | 1.63235e155 | 1.32184 | 0.660922 | − | 0.750455i | \(-0.270165\pi\) | ||||
0.660922 | + | 0.750455i | \(0.270165\pi\) | |||||||
\(702\) | 2.31404e155 | 1.73380 | ||||||||
\(703\) | −3.20365e155 | −2.22116 | ||||||||
\(704\) | −8.15210e154 | −0.523069 | ||||||||
\(705\) | −2.16318e153 | −0.0128465 | ||||||||
\(706\) | 1.14869e155 | 0.631461 | ||||||||
\(707\) | −2.50751e154 | −0.127610 | ||||||||
\(708\) | 1.24056e155 | 0.584526 | ||||||||
\(709\) | 6.64908e154 | 0.290096 | 0.145048 | − | 0.989425i | \(-0.453666\pi\) | ||||
0.145048 | + | 0.989425i | \(0.453666\pi\) | |||||||
\(710\) | 1.68013e155 | 0.678832 | ||||||||
\(711\) | 9.87451e154 | 0.369507 | ||||||||
\(712\) | −7.82938e154 | −0.271374 | ||||||||
\(713\) | −5.44608e155 | −1.74866 | ||||||||
\(714\) | −7.94173e153 | −0.0236245 | ||||||||
\(715\) | −5.75549e155 | −1.58637 | ||||||||
\(716\) | −5.19824e155 | −1.32769 | ||||||||
\(717\) | 1.62300e155 | 0.384171 | ||||||||
\(718\) | −1.18325e156 | −2.59595 | ||||||||
\(719\) | 6.77304e155 | 1.37740 | 0.688699 | − | 0.725048i | \(-0.258182\pi\) | ||||
0.688699 | + | 0.725048i | \(0.258182\pi\) | |||||||
\(720\) | 1.44728e156 | 2.72854 | ||||||||
\(721\) | 1.28091e155 | 0.223896 | ||||||||
\(722\) | 6.88047e155 | 1.11517 | ||||||||
\(723\) | −2.51407e155 | −0.377868 | ||||||||
\(724\) | 6.56699e155 | 0.915408 | ||||||||
\(725\) | 1.40676e155 | 0.181886 | ||||||||
\(726\) | −2.17048e155 | −0.260321 | ||||||||
\(727\) | 1.43056e155 | 0.159177 | 0.0795885 | − | 0.996828i | \(-0.474639\pi\) | ||||
0.0795885 | + | 0.996828i | \(0.474639\pi\) | |||||||
\(728\) | −2.94522e156 | −3.04059 | ||||||||
\(729\) | −5.01974e155 | −0.480874 | ||||||||
\(730\) | 8.47127e155 | 0.753100 | ||||||||
\(731\) | 8.48412e154 | 0.0700019 | ||||||||
\(732\) | 1.07852e155 | 0.0825990 | ||||||||
\(733\) | 9.45126e155 | 0.671929 | 0.335964 | − | 0.941875i | \(-0.390938\pi\) | ||||
0.335964 | + | 0.941875i | \(0.390938\pi\) | |||||||
\(734\) | −1.79688e156 | −1.18600 | ||||||||
\(735\) | 2.95893e155 | 0.181332 | ||||||||
\(736\) | 4.30135e156 | 2.44773 | ||||||||
\(737\) | 6.36703e154 | 0.0336480 | ||||||||
\(738\) | 4.70683e156 | 2.31024 | ||||||||
\(739\) | 3.62912e156 | 1.65455 | 0.827275 | − | 0.561798i | \(-0.189890\pi\) | ||||
0.827275 | + | 0.561798i | \(0.189890\pi\) | |||||||
\(740\) | −1.31217e157 | −5.55729 | ||||||||
\(741\) | 1.59620e156 | 0.628051 | ||||||||
\(742\) | 2.23741e156 | 0.817960 | ||||||||
\(743\) | 5.08282e156 | 1.72669 | 0.863345 | − | 0.504613i | \(-0.168365\pi\) | ||||
0.863345 | + | 0.504613i | \(0.168365\pi\) | |||||||
\(744\) | −2.81474e156 | −0.888616 | ||||||||
\(745\) | −2.05065e156 | −0.601693 | ||||||||
\(746\) | −5.43267e156 | −1.48166 | ||||||||
\(747\) | −3.57657e156 | −0.906764 | ||||||||
\(748\) | 4.15007e155 | 0.0978178 | ||||||||
\(749\) | −2.40360e156 | −0.526749 | ||||||||
\(750\) | 7.74690e155 | 0.157866 | ||||||||
\(751\) | 5.04119e156 | 0.955337 | 0.477668 | − | 0.878540i | \(-0.341482\pi\) | ||||
0.477668 | + | 0.878540i | \(0.341482\pi\) | |||||||
\(752\) | 4.00479e155 | 0.0705842 | ||||||||
\(753\) | −3.42824e155 | −0.0562011 | ||||||||
\(754\) | −4.48556e156 | −0.684036 | ||||||||
\(755\) | −1.15825e157 | −1.64321 | ||||||||
\(756\) | −7.82404e156 | −1.03274 | ||||||||
\(757\) | 1.21571e156 | 0.149316 | 0.0746579 | − | 0.997209i | \(-0.476214\pi\) | ||||
0.0746579 | + | 0.997209i | \(0.476214\pi\) | |||||||
\(758\) | 1.96452e157 | 2.24536 | ||||||||
\(759\) | −3.19662e156 | −0.340027 | ||||||||
\(760\) | 4.31230e157 | 4.26941 | ||||||||
\(761\) | −1.51125e155 | −0.0139275 | −0.00696373 | − | 0.999976i | \(-0.502217\pi\) | ||||
−0.00696373 | + | 0.999976i | \(0.502217\pi\) | |||||||
\(762\) | 1.24596e157 | 1.06895 | ||||||||
\(763\) | −1.48233e156 | −0.118402 | ||||||||
\(764\) | −1.33065e157 | −0.989638 | ||||||||
\(765\) | −9.85944e155 | −0.0682817 | ||||||||
\(766\) | 2.30234e155 | 0.0148492 | ||||||||
\(767\) | −2.16986e157 | −1.30342 | ||||||||
\(768\) | −6.95631e156 | −0.389218 | ||||||||
\(769\) | −2.41564e156 | −0.125906 | −0.0629529 | − | 0.998016i | \(-0.520052\pi\) | ||||
−0.0629529 | + | 0.998016i | \(0.520052\pi\) | |||||||
\(770\) | 2.76679e157 | 1.34348 | ||||||||
\(771\) | −7.04664e156 | −0.318800 | ||||||||
\(772\) | −8.79881e157 | −3.70921 | ||||||||
\(773\) | 1.09751e157 | 0.431148 | 0.215574 | − | 0.976487i | \(-0.430838\pi\) | ||||
0.215574 | + | 0.976487i | \(0.430838\pi\) | |||||||
\(774\) | 5.64985e157 | 2.06849 | ||||||||
\(775\) | −2.67034e157 | −0.911221 | ||||||||
\(776\) | −1.27264e158 | −4.04802 | ||||||||
\(777\) | 1.35007e157 | 0.400322 | ||||||||
\(778\) | 8.29760e157 | 2.29385 | ||||||||
\(779\) | 6.82912e157 | 1.76025 | ||||||||
\(780\) | 6.53784e157 | 1.57137 | ||||||||
\(781\) | 9.03328e156 | 0.202472 | ||||||||
\(782\) | −7.49853e156 | −0.156750 | ||||||||
\(783\) | −6.89003e156 | −0.134340 | ||||||||
\(784\) | −5.47802e157 | −0.996319 | ||||||||
\(785\) | −8.17724e157 | −1.38743 | ||||||||
\(786\) | −1.99385e157 | −0.315619 | ||||||||
\(787\) | 3.36137e157 | 0.496470 | 0.248235 | − | 0.968700i | \(-0.420150\pi\) | ||||
0.248235 | + | 0.968700i | \(0.420150\pi\) | |||||||
\(788\) | 1.81119e157 | 0.249624 | ||||||||
\(789\) | −3.09667e157 | −0.398290 | ||||||||
\(790\) | 8.34319e157 | 1.00151 | ||||||||
\(791\) | 3.66856e157 | 0.411033 | ||||||||
\(792\) | 1.59800e158 | 1.67130 | ||||||||
\(793\) | −1.88645e157 | −0.184186 | ||||||||
\(794\) | −2.33775e158 | −2.13098 | ||||||||
\(795\) | −2.87179e157 | −0.244424 | ||||||||
\(796\) | 1.23135e157 | 0.0978636 | ||||||||
\(797\) | 2.38250e158 | 1.76829 | 0.884145 | − | 0.467212i | \(-0.154742\pi\) | ||||
0.884145 | + | 0.467212i | \(0.154742\pi\) | |||||||
\(798\) | −7.67328e157 | −0.531892 | ||||||||
\(799\) | −2.72823e155 | −0.00176637 | ||||||||
\(800\) | 2.10905e158 | 1.27551 | ||||||||
\(801\) | 1.72956e157 | 0.0977157 | ||||||||
\(802\) | −5.06273e158 | −2.67228 | ||||||||
\(803\) | 4.55462e157 | 0.224623 | ||||||||
\(804\) | −7.23250e156 | −0.0333299 | ||||||||
\(805\) | −3.51612e158 | −1.51422 | ||||||||
\(806\) | 8.51460e158 | 3.42692 | ||||||||
\(807\) | −6.48842e157 | −0.244079 | ||||||||
\(808\) | −1.22366e158 | −0.430269 | ||||||||
\(809\) | −7.61845e157 | −0.250422 | −0.125211 | − | 0.992130i | \(-0.539961\pi\) | ||||
−0.125211 | + | 0.992130i | \(0.539961\pi\) | |||||||
\(810\) | −5.81672e158 | −1.78749 | ||||||||
\(811\) | −1.53803e158 | −0.441903 | −0.220952 | − | 0.975285i | \(-0.570916\pi\) | ||||
−0.220952 | + | 0.975285i | \(0.570916\pi\) | |||||||
\(812\) | 1.51662e158 | 0.407450 | ||||||||
\(813\) | 1.49992e158 | 0.376820 | ||||||||
\(814\) | −1.00306e159 | −2.35667 | ||||||||
\(815\) | −1.37574e158 | −0.302306 | ||||||||
\(816\) | −1.88717e157 | −0.0387880 | ||||||||
\(817\) | 8.19734e158 | 1.57605 | ||||||||
\(818\) | −7.33555e158 | −1.31940 | ||||||||
\(819\) | 6.50621e158 | 1.09485 | ||||||||
\(820\) | 2.79712e159 | 4.40410 | ||||||||
\(821\) | −1.76748e157 | −0.0260407 | −0.0130203 | − | 0.999915i | \(-0.504145\pi\) | ||||
−0.0130203 | + | 0.999915i | \(0.504145\pi\) | |||||||
\(822\) | 5.07891e157 | 0.0700256 | ||||||||
\(823\) | 4.09162e158 | 0.527964 | 0.263982 | − | 0.964528i | \(-0.414964\pi\) | ||||
0.263982 | + | 0.964528i | \(0.414964\pi\) | |||||||
\(824\) | 6.25079e158 | 0.754921 | ||||||||
\(825\) | −1.56738e158 | −0.177187 | ||||||||
\(826\) | 1.04310e159 | 1.10386 | ||||||||
\(827\) | −7.97799e158 | −0.790393 | −0.395197 | − | 0.918597i | \(-0.629324\pi\) | ||||
−0.395197 | + | 0.918597i | \(0.629324\pi\) | |||||||
\(828\) | −3.51215e159 | −3.25776 | ||||||||
\(829\) | 1.11401e159 | 0.967538 | 0.483769 | − | 0.875196i | \(-0.339268\pi\) | ||||
0.483769 | + | 0.875196i | \(0.339268\pi\) | |||||||
\(830\) | −3.02192e159 | −2.45769 | ||||||||
\(831\) | 2.04600e158 | 0.155830 | ||||||||
\(832\) | −1.61971e159 | −1.15536 | ||||||||
\(833\) | 3.73185e157 | 0.0249328 | ||||||||
\(834\) | 2.52883e158 | 0.158260 | ||||||||
\(835\) | −1.39639e159 | −0.818642 | ||||||||
\(836\) | 4.00979e159 | 2.20231 | ||||||||
\(837\) | 1.30788e159 | 0.673024 | ||||||||
\(838\) | −1.56797e159 | −0.756029 | ||||||||
\(839\) | −4.56509e158 | −0.206264 | −0.103132 | − | 0.994668i | \(-0.532886\pi\) | ||||
−0.103132 | + | 0.994668i | \(0.532886\pi\) | |||||||
\(840\) | −1.81727e159 | −0.769481 | ||||||||
\(841\) | −2.38633e159 | −0.946999 | ||||||||
\(842\) | 5.73683e159 | 2.13385 | ||||||||
\(843\) | −9.17181e158 | −0.319781 | ||||||||
\(844\) | 5.96128e159 | 1.94839 | ||||||||
\(845\) | −7.06898e159 | −2.16604 | ||||||||
\(846\) | −1.81681e158 | −0.0521946 | ||||||||
\(847\) | −1.28361e159 | −0.345769 | ||||||||
\(848\) | 5.31668e159 | 1.34297 | ||||||||
\(849\) | 2.11258e159 | 0.500430 | ||||||||
\(850\) | −3.67670e158 | −0.0816822 | ||||||||
\(851\) | 1.27472e160 | 2.65616 | ||||||||
\(852\) | −1.02612e159 | −0.200558 | ||||||||
\(853\) | −5.02688e159 | −0.921672 | −0.460836 | − | 0.887485i | \(-0.652450\pi\) | ||||
−0.460836 | + | 0.887485i | \(0.652450\pi\) | |||||||
\(854\) | 9.06856e158 | 0.155986 | ||||||||
\(855\) | −9.52617e159 | −1.53732 | ||||||||
\(856\) | −1.17295e160 | −1.77607 | ||||||||
\(857\) | −1.02689e160 | −1.45904 | −0.729521 | − | 0.683958i | \(-0.760257\pi\) | ||||
−0.729521 | + | 0.683958i | \(0.760257\pi\) | |||||||
\(858\) | 4.99771e159 | 0.666367 | ||||||||
\(859\) | −8.31230e159 | −1.04015 | −0.520073 | − | 0.854122i | \(-0.674095\pi\) | ||||
−0.520073 | + | 0.854122i | \(0.674095\pi\) | |||||||
\(860\) | 3.35753e160 | 3.94325 | ||||||||
\(861\) | −2.87790e159 | −0.317251 | ||||||||
\(862\) | −4.51620e159 | −0.467334 | ||||||||
\(863\) | 1.87873e160 | 1.82506 | 0.912528 | − | 0.409013i | \(-0.134127\pi\) | ||||
0.912528 | + | 0.409013i | \(0.134127\pi\) | |||||||
\(864\) | −1.03297e160 | −0.942085 | ||||||||
\(865\) | 2.10629e160 | 1.80360 | ||||||||
\(866\) | −1.79158e160 | −1.44049 | ||||||||
\(867\) | −4.04140e159 | −0.305135 | ||||||||
\(868\) | −2.87889e160 | −2.04127 | ||||||||
\(869\) | 4.48575e159 | 0.298715 | ||||||||
\(870\) | −2.76769e159 | −0.173109 | ||||||||
\(871\) | 1.26504e159 | 0.0743217 | ||||||||
\(872\) | −7.23371e159 | −0.399220 | ||||||||
\(873\) | 2.81136e160 | 1.45760 | ||||||||
\(874\) | −7.24506e160 | −3.52914 | ||||||||
\(875\) | 4.58147e159 | 0.209684 | ||||||||
\(876\) | −5.17373e159 | −0.222500 | ||||||||
\(877\) | 4.79045e159 | 0.193597 | 0.0967986 | − | 0.995304i | \(-0.469140\pi\) | ||||
0.0967986 | + | 0.995304i | \(0.469140\pi\) | |||||||
\(878\) | 3.23643e160 | 1.22918 | ||||||||
\(879\) | 1.14121e160 | 0.407354 | ||||||||
\(880\) | 6.57464e160 | 2.20580 | ||||||||
\(881\) | −6.08119e159 | −0.191779 | −0.0958895 | − | 0.995392i | \(-0.530570\pi\) | ||||
−0.0958895 | + | 0.995392i | \(0.530570\pi\) | |||||||
\(882\) | 2.48516e160 | 0.736743 | ||||||||
\(883\) | 1.48178e160 | 0.412976 | 0.206488 | − | 0.978449i | \(-0.433797\pi\) | ||||
0.206488 | + | 0.978449i | \(0.433797\pi\) | |||||||
\(884\) | 8.24561e159 | 0.216060 | ||||||||
\(885\) | −1.33885e160 | −0.329857 | ||||||||
\(886\) | 7.59810e159 | 0.176022 | ||||||||
\(887\) | −8.37924e160 | −1.82544 | −0.912720 | − | 0.408586i | \(-0.866022\pi\) | ||||
−0.912720 | + | 0.408586i | \(0.866022\pi\) | |||||||
\(888\) | 6.58826e160 | 1.34978 | ||||||||
\(889\) | 7.36854e160 | 1.41983 | ||||||||
\(890\) | 1.46135e160 | 0.264849 | ||||||||
\(891\) | −3.12739e160 | −0.533146 | ||||||||
\(892\) | −1.71958e161 | −2.75764 | ||||||||
\(893\) | −2.63601e159 | −0.0397688 | ||||||||
\(894\) | 1.78065e160 | 0.252746 | ||||||||
\(895\) | 5.61013e160 | 0.749234 | ||||||||
\(896\) | −1.80406e160 | −0.226706 | ||||||||
\(897\) | −6.35124e160 | −0.751053 | ||||||||
\(898\) | −1.36479e161 | −1.51882 | ||||||||
\(899\) | −2.53521e160 | −0.265529 | ||||||||
\(900\) | −1.72209e161 | −1.69761 | ||||||||
\(901\) | −3.62194e159 | −0.0336078 | ||||||||
\(902\) | 2.13820e161 | 1.86763 | ||||||||
\(903\) | −3.45448e160 | −0.284054 | ||||||||
\(904\) | 1.79024e161 | 1.38590 | ||||||||
\(905\) | −7.08734e160 | −0.516578 | ||||||||
\(906\) | 1.00575e161 | 0.690245 | ||||||||
\(907\) | −1.36362e160 | −0.0881247 | −0.0440624 | − | 0.999029i | \(-0.514030\pi\) | ||||
−0.0440624 | + | 0.999029i | \(0.514030\pi\) | |||||||
\(908\) | −1.06262e161 | −0.646692 | ||||||||
\(909\) | 2.70314e160 | 0.154931 | ||||||||
\(910\) | 5.49723e161 | 2.96748 | ||||||||
\(911\) | 3.18163e161 | 1.61770 | 0.808851 | − | 0.588014i | \(-0.200090\pi\) | ||||
0.808851 | + | 0.588014i | \(0.200090\pi\) | |||||||
\(912\) | −1.82338e161 | −0.873289 | ||||||||
\(913\) | −1.62475e161 | −0.733043 | ||||||||
\(914\) | −1.19146e161 | −0.506422 | ||||||||
\(915\) | −1.16398e160 | −0.0466118 | ||||||||
\(916\) | 4.23957e161 | 1.59963 | ||||||||
\(917\) | −1.17915e161 | −0.419218 | ||||||||
\(918\) | 1.80078e160 | 0.0603301 | ||||||||
\(919\) | −4.14517e161 | −1.30872 | −0.654360 | − | 0.756183i | \(-0.727062\pi\) | ||||
−0.654360 | + | 0.756183i | \(0.727062\pi\) | |||||||
\(920\) | −1.71585e162 | −5.10556 | ||||||||
\(921\) | −7.35540e160 | −0.206280 | ||||||||
\(922\) | 9.33568e161 | 2.46780 | ||||||||
\(923\) | 1.79479e161 | 0.447220 | ||||||||
\(924\) | −1.68978e161 | −0.396925 | ||||||||
\(925\) | 6.25027e161 | 1.38412 | ||||||||
\(926\) | 8.27650e161 | 1.72802 | ||||||||
\(927\) | −1.38084e161 | −0.271831 | ||||||||
\(928\) | 2.00233e161 | 0.371682 | ||||||||
\(929\) | −3.95959e160 | −0.0693096 | −0.0346548 | − | 0.999399i | \(-0.511033\pi\) | ||||
−0.0346548 | + | 0.999399i | \(0.511033\pi\) | |||||||
\(930\) | 5.25369e161 | 0.867250 | ||||||||
\(931\) | 3.60571e161 | 0.561349 | ||||||||
\(932\) | −2.45519e162 | −3.60511 | ||||||||
\(933\) | −2.45813e161 | −0.340452 | ||||||||
\(934\) | −2.08650e162 | −2.72592 | ||||||||
\(935\) | −4.47891e160 | −0.0552000 | ||||||||
\(936\) | 3.17500e162 | 3.69156 | ||||||||
\(937\) | −6.80252e161 | −0.746212 | −0.373106 | − | 0.927789i | \(-0.621707\pi\) | ||||
−0.373106 | + | 0.927789i | \(0.621707\pi\) | |||||||
\(938\) | −6.08133e160 | −0.0629425 | ||||||||
\(939\) | 4.40786e161 | 0.430480 | ||||||||
\(940\) | −1.07968e161 | −0.0995005 | ||||||||
\(941\) | −1.04634e162 | −0.909994 | −0.454997 | − | 0.890493i | \(-0.650360\pi\) | ||||
−0.454997 | + | 0.890493i | \(0.650360\pi\) | |||||||
\(942\) | 7.10060e161 | 0.582802 | ||||||||
\(943\) | −2.71729e162 | −2.10498 | ||||||||
\(944\) | 2.47869e162 | 1.81238 | ||||||||
\(945\) | 8.44400e161 | 0.582793 | ||||||||
\(946\) | 2.56659e162 | 1.67220 | ||||||||
\(947\) | 2.71740e162 | 1.67139 | 0.835697 | − | 0.549191i | \(-0.185064\pi\) | ||||
0.835697 | + | 0.549191i | \(0.185064\pi\) | |||||||
\(948\) | −5.09550e161 | −0.295892 | ||||||||
\(949\) | 9.04941e161 | 0.496148 | ||||||||
\(950\) | −3.55242e162 | −1.83903 | ||||||||
\(951\) | −9.97385e161 | −0.487556 | ||||||||
\(952\) | −2.29196e161 | −0.105802 | ||||||||
\(953\) | 1.88375e160 | 0.00821220 | 0.00410610 | − | 0.999992i | \(-0.498693\pi\) | ||||
0.00410610 | + | 0.999992i | \(0.498693\pi\) | |||||||
\(954\) | −2.41196e162 | −0.993080 | ||||||||
\(955\) | 1.43609e162 | 0.558467 | ||||||||
\(956\) | 8.10065e162 | 2.97553 | ||||||||
\(957\) | −1.48806e161 | −0.0516322 | ||||||||
\(958\) | −3.14413e162 | −1.03058 | ||||||||
\(959\) | 3.00364e161 | 0.0930108 | ||||||||
\(960\) | −9.99397e161 | −0.292386 | ||||||||
\(961\) | 1.19476e162 | 0.330261 | ||||||||
\(962\) | −1.99295e163 | −5.20541 | ||||||||
\(963\) | 2.59113e162 | 0.639523 | ||||||||
\(964\) | −1.25481e163 | −2.92672 | ||||||||
\(965\) | 9.49601e162 | 2.09316 | ||||||||
\(966\) | 3.05318e162 | 0.636061 | ||||||||
\(967\) | −3.29644e162 | −0.649087 | −0.324543 | − | 0.945871i | \(-0.605211\pi\) | ||||
−0.324543 | + | 0.945871i | \(0.605211\pi\) | |||||||
\(968\) | −6.26395e162 | −1.16585 | ||||||||
\(969\) | 1.24216e161 | 0.0218540 | ||||||||
\(970\) | 2.37538e163 | 3.95069 | ||||||||
\(971\) | 1.24152e162 | 0.195211 | 0.0976054 | − | 0.995225i | \(-0.468882\pi\) | ||||
0.0976054 | + | 0.995225i | \(0.468882\pi\) | |||||||
\(972\) | 1.28590e163 | 1.91159 | ||||||||
\(973\) | 1.49554e162 | 0.210207 | ||||||||
\(974\) | 4.30827e162 | 0.572584 | ||||||||
\(975\) | −3.11416e162 | −0.391372 | ||||||||
\(976\) | 2.15493e162 | 0.256106 | ||||||||
\(977\) | −9.88178e162 | −1.11066 | −0.555330 | − | 0.831630i | \(-0.687408\pi\) | ||||
−0.555330 | + | 0.831630i | \(0.687408\pi\) | |||||||
\(978\) | 1.19461e162 | 0.126987 | ||||||||
\(979\) | 7.85699e161 | 0.0789950 | ||||||||
\(980\) | 1.47685e163 | 1.40448 | ||||||||
\(981\) | 1.59798e162 | 0.143751 | ||||||||
\(982\) | −3.14444e163 | −2.67588 | ||||||||
\(983\) | −4.55541e162 | −0.366742 | −0.183371 | − | 0.983044i | \(-0.558701\pi\) | ||||
−0.183371 | + | 0.983044i | \(0.558701\pi\) | |||||||
\(984\) | −1.40440e163 | −1.06969 | ||||||||
\(985\) | −1.95471e162 | −0.140866 | ||||||||
\(986\) | −3.49065e161 | −0.0238021 | ||||||||
\(987\) | 1.11085e161 | 0.00716757 | ||||||||
\(988\) | 7.96690e163 | 4.86447 | ||||||||
\(989\) | −3.26170e163 | −1.88472 | ||||||||
\(990\) | −2.98265e163 | −1.63111 | ||||||||
\(991\) | 1.87254e163 | 0.969207 | 0.484603 | − | 0.874734i | \(-0.338964\pi\) | ||||
0.484603 | + | 0.874734i | \(0.338964\pi\) | |||||||
\(992\) | −3.80087e163 | −1.86207 | ||||||||
\(993\) | −9.16901e162 | −0.425195 | ||||||||
\(994\) | −8.62794e162 | −0.378747 | ||||||||
\(995\) | −1.32892e162 | −0.0552259 | ||||||||
\(996\) | 1.84560e163 | 0.726114 | ||||||||
\(997\) | −3.16611e163 | −1.17934 | −0.589672 | − | 0.807643i | \(-0.700743\pi\) | ||||
−0.589672 | + | 0.807643i | \(0.700743\pi\) | |||||||
\(998\) | 5.98953e163 | 2.11241 | ||||||||
\(999\) | −3.06126e163 | −1.02231 |
(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.1.8 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.110.a.a.1.8 | ✓ | 8 | 1.1 | even | 1 | trivial |