Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,116,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, 116, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 116);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 116 \) |
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: | \(83.7504016273\) |
Analytic rank: | \(0\) |
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: | \( x^{9} - 2 x^{8} + \cdots + 17\!\cdots\!50 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{142}\cdot 3^{52}\cdot 5^{17}\cdot 7^{8}\cdot 11^{3}\cdot 13^{3}\cdot 17\cdot 19^{3}\cdot 23^{3}\cdot 29^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-4.70183e14\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.62458e15 | −0.00797104 | −0.00398552 | − | 0.999992i | \(-0.501269\pi\) | ||||
−0.00398552 | + | 0.999992i | \(0.501269\pi\) | |||||||
\(3\) | −2.61982e27 | −0.963383 | −0.481691 | − | 0.876341i | \(-0.659977\pi\) | ||||
−0.481691 | + | 0.876341i | \(0.659977\pi\) | |||||||
\(4\) | −4.15357e34 | −0.999936 | ||||||||
\(5\) | 1.47212e40 | 0.948783 | 0.474391 | − | 0.880314i | \(-0.342668\pi\) | ||||
0.474391 | + | 0.880314i | \(0.342668\pi\) | |||||||
\(6\) | 4.25609e42 | 0.00767916 | ||||||||
\(7\) | 6.19961e48 | 1.58207 | 0.791037 | − | 0.611768i | \(-0.209542\pi\) | ||||
0.791037 | + | 0.611768i | \(0.209542\pi\) | |||||||
\(8\) | 1.34960e50 | 0.0159416 | ||||||||
\(9\) | −5.31663e53 | −0.0718939 | ||||||||
\(10\) | −2.39156e55 | −0.00756279 | ||||||||
\(11\) | 2.18993e59 | 0.288636 | 0.144318 | − | 0.989531i | \(-0.453901\pi\) | ||||
0.144318 | + | 0.989531i | \(0.453901\pi\) | |||||||
\(12\) | 1.08816e62 | 0.963321 | ||||||||
\(13\) | 1.46197e64 | 1.29776 | 0.648880 | − | 0.760890i | \(-0.275238\pi\) | ||||
0.648880 | + | 0.760890i | \(0.275238\pi\) | |||||||
\(14\) | −1.00717e64 | −0.0126108 | ||||||||
\(15\) | −3.85667e67 | −0.914041 | ||||||||
\(16\) | 1.72511e69 | 0.999809 | ||||||||
\(17\) | 4.52776e70 | 0.803657 | 0.401829 | − | 0.915715i | \(-0.368375\pi\) | ||||
0.401829 | + | 0.915715i | \(0.368375\pi\) | |||||||
\(18\) | 8.63727e68 | 0.000573069 0 | ||||||||
\(19\) | 3.61811e73 | 1.07189 | 0.535945 | − | 0.844253i | \(-0.319956\pi\) | ||||
0.535945 | + | 0.844253i | \(0.319956\pi\) | |||||||
\(20\) | −6.11454e74 | −0.948723 | ||||||||
\(21\) | −1.62418e76 | −1.52414 | ||||||||
\(22\) | −3.55771e74 | −0.00230073 | ||||||||
\(23\) | −1.94208e78 | −0.974802 | −0.487401 | − | 0.873178i | \(-0.662055\pi\) | ||||
−0.487401 | + | 0.873178i | \(0.662055\pi\) | |||||||
\(24\) | −3.53571e77 | −0.0153578 | ||||||||
\(25\) | −2.40286e79 | −0.0998111 | ||||||||
\(26\) | −2.37507e79 | −0.0103445 | ||||||||
\(27\) | 2.07667e82 | 1.03264 | ||||||||
\(28\) | −2.57505e83 | −1.58197 | ||||||||
\(29\) | −2.21850e84 | −1.81207 | −0.906034 | − | 0.423205i | \(-0.860905\pi\) | ||||
−0.906034 | + | 0.423205i | \(0.860905\pi\) | |||||||
\(30\) | 6.26546e82 | 0.00728586 | ||||||||
\(31\) | −2.45370e85 | −0.433035 | −0.216518 | − | 0.976279i | \(-0.569470\pi\) | ||||
−0.216518 | + | 0.976279i | \(0.569470\pi\) | |||||||
\(32\) | −8.40859e84 | −0.0239111 | ||||||||
\(33\) | −5.73722e86 | −0.278067 | ||||||||
\(34\) | −7.35569e85 | −0.00640599 | ||||||||
\(35\) | 9.12654e88 | 1.50104 | ||||||||
\(36\) | 2.20830e88 | 0.0718894 | ||||||||
\(37\) | −7.78368e89 | −0.524307 | −0.262154 | − | 0.965026i | \(-0.584433\pi\) | ||||
−0.262154 | + | 0.965026i | \(0.584433\pi\) | |||||||
\(38\) | −5.87790e88 | −0.00854408 | ||||||||
\(39\) | −3.83008e91 | −1.25024 | ||||||||
\(40\) | 1.98677e90 | 0.0151251 | ||||||||
\(41\) | 8.43624e92 | 1.55266 | 0.776332 | − | 0.630324i | \(-0.217078\pi\) | ||||
0.776332 | + | 0.630324i | \(0.217078\pi\) | |||||||
\(42\) | 2.63861e91 | 0.0121490 | ||||||||
\(43\) | −4.15081e93 | −0.493966 | −0.246983 | − | 0.969020i | \(-0.579439\pi\) | ||||
−0.246983 | + | 0.969020i | \(0.579439\pi\) | |||||||
\(44\) | −9.09604e93 | −0.288618 | ||||||||
\(45\) | −7.82670e93 | −0.0682117 | ||||||||
\(46\) | 3.15505e93 | 0.00777018 | ||||||||
\(47\) | 5.23101e95 | 0.374075 | 0.187038 | − | 0.982353i | \(-0.440111\pi\) | ||||
0.187038 | + | 0.982353i | \(0.440111\pi\) | |||||||
\(48\) | −4.51947e96 | −0.963199 | ||||||||
\(49\) | 2.30792e97 | 1.50296 | ||||||||
\(50\) | 3.90363e94 | 0.000795598 0 | ||||||||
\(51\) | −1.18619e98 | −0.774229 | ||||||||
\(52\) | −6.07239e98 | −1.29768 | ||||||||
\(53\) | 2.18808e99 | 1.56387 | 0.781936 | − | 0.623358i | \(-0.214232\pi\) | ||||
0.781936 | + | 0.623358i | \(0.214232\pi\) | |||||||
\(54\) | −3.37370e97 | −0.00823125 | ||||||||
\(55\) | 3.22383e99 | 0.273853 | ||||||||
\(56\) | 8.36700e98 | 0.0252208 | ||||||||
\(57\) | −9.47879e100 | −1.03264 | ||||||||
\(58\) | 3.60412e99 | 0.0144441 | ||||||||
\(59\) | 1.47847e101 | 0.221728 | 0.110864 | − | 0.993836i | \(-0.464638\pi\) | ||||
0.110864 | + | 0.993836i | \(0.464638\pi\) | |||||||
\(60\) | 1.60190e102 | 0.913983 | ||||||||
\(61\) | −2.05936e102 | −0.454220 | −0.227110 | − | 0.973869i | \(-0.572928\pi\) | ||||
−0.227110 | + | 0.973869i | \(0.572928\pi\) | |||||||
\(62\) | 3.98621e100 | 0.00345174 | ||||||||
\(63\) | −3.29610e102 | −0.113741 | ||||||||
\(64\) | −7.16445e103 | −0.999619 | ||||||||
\(65\) | 2.15218e104 | 1.23129 | ||||||||
\(66\) | 9.32055e101 | 0.00221649 | ||||||||
\(67\) | 9.97754e102 | 0.00999361 | 0.00499680 | − | 0.999988i | \(-0.498409\pi\) | ||||
0.00499680 | + | 0.999988i | \(0.498409\pi\) | |||||||
\(68\) | −1.88064e105 | −0.803606 | ||||||||
\(69\) | 5.08789e105 | 0.939107 | ||||||||
\(70\) | −1.48267e104 | −0.0119649 | ||||||||
\(71\) | −2.71729e106 | −0.970021 | −0.485010 | − | 0.874508i | \(-0.661184\pi\) | ||||
−0.485010 | + | 0.874508i | \(0.661184\pi\) | |||||||
\(72\) | −7.17533e103 | −0.00114610 | ||||||||
\(73\) | 1.83490e107 | 1.32601 | 0.663005 | − | 0.748615i | \(-0.269281\pi\) | ||||
0.663005 | + | 0.748615i | \(0.269281\pi\) | |||||||
\(74\) | 1.26452e105 | 0.00417927 | ||||||||
\(75\) | 6.29506e106 | 0.0961562 | ||||||||
\(76\) | −1.50281e108 | −1.07182 | ||||||||
\(77\) | 1.35767e108 | 0.456644 | ||||||||
\(78\) | 6.22226e106 | 0.00996572 | ||||||||
\(79\) | 1.76884e109 | 1.36186 | 0.680929 | − | 0.732350i | \(-0.261576\pi\) | ||||
0.680929 | + | 0.732350i | \(0.261576\pi\) | |||||||
\(80\) | 2.53956e109 | 0.948602 | ||||||||
\(81\) | −5.04732e109 | −0.922937 | ||||||||
\(82\) | −1.37053e108 | −0.0123763 | ||||||||
\(83\) | 1.20242e110 | 0.540836 | 0.270418 | − | 0.962743i | \(-0.412838\pi\) | ||||
0.270418 | + | 0.962743i | \(0.412838\pi\) | |||||||
\(84\) | 6.74616e110 | 1.52405 | ||||||||
\(85\) | 6.66540e110 | 0.762496 | ||||||||
\(86\) | 6.74330e108 | 0.00393742 | ||||||||
\(87\) | 5.81206e111 | 1.74572 | ||||||||
\(88\) | 2.95554e109 | 0.00460132 | ||||||||
\(89\) | 1.26336e112 | 1.02708 | 0.513539 | − | 0.858066i | \(-0.328334\pi\) | ||||
0.513539 | + | 0.858066i | \(0.328334\pi\) | |||||||
\(90\) | 1.27151e109 | 0.000543718 0 | ||||||||
\(91\) | 9.06361e112 | 2.05315 | ||||||||
\(92\) | 8.06657e112 | 0.974740 | ||||||||
\(93\) | 6.42824e112 | 0.417179 | ||||||||
\(94\) | −8.49817e110 | −0.00298177 | ||||||||
\(95\) | 5.32628e113 | 1.01699 | ||||||||
\(96\) | 2.20290e112 | 0.0230355 | ||||||||
\(97\) | 6.14831e112 | 0.0354308 | 0.0177154 | − | 0.999843i | \(-0.494361\pi\) | ||||
0.0177154 | + | 0.999843i | \(0.494361\pi\) | |||||||
\(98\) | −3.74939e112 | −0.0119801 | ||||||||
\(99\) | −1.16431e113 | −0.0207512 | ||||||||
\(100\) | 9.98047e113 | 0.0998047 | ||||||||
\(101\) | −2.04862e115 | −1.15606 | −0.578032 | − | 0.816014i | \(-0.696179\pi\) | ||||
−0.578032 | + | 0.816014i | \(0.696179\pi\) | |||||||
\(102\) | 1.92706e113 | 0.00617142 | ||||||||
\(103\) | −9.39193e115 | −1.71638 | −0.858192 | − | 0.513329i | \(-0.828412\pi\) | ||||
−0.858192 | + | 0.513329i | \(0.828412\pi\) | |||||||
\(104\) | 1.97307e114 | 0.0206884 | ||||||||
\(105\) | −2.39099e116 | −1.44608 | ||||||||
\(106\) | −3.55471e114 | −0.0124657 | ||||||||
\(107\) | 6.02443e116 | 1.23126 | 0.615628 | − | 0.788037i | \(-0.288902\pi\) | ||||
0.615628 | + | 0.788037i | \(0.288902\pi\) | |||||||
\(108\) | −8.62559e116 | −1.03258 | ||||||||
\(109\) | −2.07798e117 | −1.46426 | −0.732130 | − | 0.681165i | \(-0.761474\pi\) | ||||
−0.732130 | + | 0.681165i | \(0.761474\pi\) | |||||||
\(110\) | −5.23736e114 | −0.00218290 | ||||||||
\(111\) | 2.03918e117 | 0.505108 | ||||||||
\(112\) | 1.06950e118 | 1.58177 | ||||||||
\(113\) | 1.21712e118 | 1.07974 | 0.539872 | − | 0.841747i | \(-0.318472\pi\) | ||||
0.539872 | + | 0.841747i | \(0.318472\pi\) | |||||||
\(114\) | 1.53990e116 | 0.00823121 | ||||||||
\(115\) | −2.85897e118 | −0.924875 | ||||||||
\(116\) | 9.21470e118 | 1.81195 | ||||||||
\(117\) | −7.77274e117 | −0.0933011 | ||||||||
\(118\) | −2.40188e116 | −0.00176740 | ||||||||
\(119\) | 2.80704e119 | 1.27145 | ||||||||
\(120\) | −5.20497e117 | −0.0145713 | ||||||||
\(121\) | −5.27692e119 | −0.916689 | ||||||||
\(122\) | 3.34558e117 | 0.00362061 | ||||||||
\(123\) | −2.21014e120 | −1.49581 | ||||||||
\(124\) | 1.01916e120 | 0.433008 | ||||||||
\(125\) | −3.89772e120 | −1.04348 | ||||||||
\(126\) | 5.35476e117 | 0.000906638 0 | ||||||||
\(127\) | −8.61025e120 | −0.925341 | −0.462670 | − | 0.886530i | \(-0.653109\pi\) | ||||
−0.462670 | + | 0.886530i | \(0.653109\pi\) | |||||||
\(128\) | 4.65671e119 | 0.0318791 | ||||||||
\(129\) | 1.08744e121 | 0.475878 | ||||||||
\(130\) | −3.49639e119 | −0.00981469 | ||||||||
\(131\) | −4.62276e121 | −0.835221 | −0.417611 | − | 0.908626i | \(-0.637132\pi\) | ||||
−0.417611 | + | 0.908626i | \(0.637132\pi\) | |||||||
\(132\) | 2.38300e121 | 0.278050 | ||||||||
\(133\) | 2.24309e122 | 1.69581 | ||||||||
\(134\) | −1.62093e118 | −7.96595e−5 0 | ||||||||
\(135\) | 3.05710e122 | 0.979755 | ||||||||
\(136\) | 6.11068e120 | 0.0128116 | ||||||||
\(137\) | 2.86128e122 | 0.393665 | 0.196833 | − | 0.980437i | \(-0.436934\pi\) | ||||
0.196833 | + | 0.980437i | \(0.436934\pi\) | |||||||
\(138\) | −8.26566e120 | −0.00748566 | ||||||||
\(139\) | 1.27509e123 | 0.762410 | 0.381205 | − | 0.924491i | \(-0.375509\pi\) | ||||
0.381205 | + | 0.924491i | \(0.375509\pi\) | |||||||
\(140\) | −3.79078e123 | −1.50095 | ||||||||
\(141\) | −1.37043e123 | −0.360377 | ||||||||
\(142\) | 4.41444e121 | 0.00773208 | ||||||||
\(143\) | 3.20161e123 | 0.374581 | ||||||||
\(144\) | −9.17176e122 | −0.0718802 | ||||||||
\(145\) | −3.26589e124 | −1.71926 | ||||||||
\(146\) | −2.98093e122 | −0.0105697 | ||||||||
\(147\) | −6.04634e124 | −1.44792 | ||||||||
\(148\) | 3.23301e124 | 0.524274 | ||||||||
\(149\) | 9.52826e124 | 1.04907 | 0.524534 | − | 0.851390i | \(-0.324240\pi\) | ||||
0.524534 | + | 0.851390i | \(0.324240\pi\) | |||||||
\(150\) | −1.02268e122 | −0.000766465 0 | ||||||||
\(151\) | 2.48757e125 | 1.27234 | 0.636168 | − | 0.771551i | \(-0.280519\pi\) | ||||
0.636168 | + | 0.771551i | \(0.280519\pi\) | |||||||
\(152\) | 4.88301e123 | 0.0170876 | ||||||||
\(153\) | −2.40725e124 | −0.0577781 | ||||||||
\(154\) | −2.20564e123 | −0.00363993 | ||||||||
\(155\) | −3.61213e125 | −0.410857 | ||||||||
\(156\) | 1.59085e126 | 1.25016 | ||||||||
\(157\) | 2.34288e126 | 1.27503 | 0.637514 | − | 0.770438i | \(-0.279963\pi\) | ||||
0.637514 | + | 0.770438i | \(0.279963\pi\) | |||||||
\(158\) | −2.87362e124 | −0.0108554 | ||||||||
\(159\) | −5.73238e126 | −1.50661 | ||||||||
\(160\) | −1.23784e125 | −0.0226864 | ||||||||
\(161\) | −1.20401e127 | −1.54221 | ||||||||
\(162\) | 8.19975e124 | 0.00735677 | ||||||||
\(163\) | 1.61392e127 | 1.01647 | 0.508234 | − | 0.861219i | \(-0.330298\pi\) | ||||
0.508234 | + | 0.861219i | \(0.330298\pi\) | |||||||
\(164\) | −3.50406e127 | −1.55257 | ||||||||
\(165\) | −8.44586e126 | −0.263826 | ||||||||
\(166\) | −1.95342e125 | −0.00431103 | ||||||||
\(167\) | 3.44692e127 | 0.538560 | 0.269280 | − | 0.963062i | \(-0.413214\pi\) | ||||
0.269280 | + | 0.963062i | \(0.413214\pi\) | |||||||
\(168\) | −2.19200e126 | −0.0242972 | ||||||||
\(169\) | 8.68276e127 | 0.684183 | ||||||||
\(170\) | −1.08284e126 | −0.00607789 | ||||||||
\(171\) | −1.92362e127 | −0.0770623 | ||||||||
\(172\) | 1.72407e128 | 0.493934 | ||||||||
\(173\) | 6.31383e128 | 1.29611 | 0.648055 | − | 0.761594i | \(-0.275583\pi\) | ||||
0.648055 | + | 0.761594i | \(0.275583\pi\) | |||||||
\(174\) | −9.44214e126 | −0.0139152 | ||||||||
\(175\) | −1.48968e128 | −0.157908 | ||||||||
\(176\) | 3.77787e128 | 0.288581 | ||||||||
\(177\) | −3.87331e128 | −0.213609 | ||||||||
\(178\) | −2.05243e127 | −0.00818688 | ||||||||
\(179\) | −5.59755e129 | −1.61789 | −0.808944 | − | 0.587885i | \(-0.799961\pi\) | ||||
−0.808944 | + | 0.587885i | \(0.799961\pi\) | |||||||
\(180\) | 3.25088e128 | 0.0682074 | ||||||||
\(181\) | −5.19054e129 | −0.791943 | −0.395972 | − | 0.918263i | \(-0.629592\pi\) | ||||
−0.395972 | + | 0.918263i | \(0.629592\pi\) | |||||||
\(182\) | −1.47245e128 | −0.0163658 | ||||||||
\(183\) | 5.39514e129 | 0.437588 | ||||||||
\(184\) | −2.62103e128 | −0.0155399 | ||||||||
\(185\) | −1.14585e130 | −0.497454 | ||||||||
\(186\) | −1.04432e128 | −0.00332535 | ||||||||
\(187\) | 9.91550e129 | 0.231965 | ||||||||
\(188\) | −2.17274e130 | −0.374051 | ||||||||
\(189\) | 1.28745e131 | 1.63372 | ||||||||
\(190\) | −8.65295e128 | −0.00810647 | ||||||||
\(191\) | −1.41019e130 | −0.0976920 | −0.0488460 | − | 0.998806i | \(-0.515554\pi\) | ||||
−0.0488460 | + | 0.998806i | \(0.515554\pi\) | |||||||
\(192\) | 1.87696e131 | 0.963015 | ||||||||
\(193\) | 2.91112e131 | 1.10794 | 0.553968 | − | 0.832538i | \(-0.313113\pi\) | ||||
0.553968 | + | 0.832538i | \(0.313113\pi\) | |||||||
\(194\) | −9.98839e127 | −0.000282421 0 | ||||||||
\(195\) | −5.63833e131 | −1.18621 | ||||||||
\(196\) | −9.58613e131 | −1.50286 | ||||||||
\(197\) | 2.52276e130 | 0.0295167 | 0.0147583 | − | 0.999891i | \(-0.495302\pi\) | ||||
0.0147583 | + | 0.999891i | \(0.495302\pi\) | |||||||
\(198\) | 1.89150e128 | 0.000165409 0 | ||||||||
\(199\) | 4.98876e131 | 0.326543 | 0.163272 | − | 0.986581i | \(-0.447795\pi\) | ||||
0.163272 | + | 0.986581i | \(0.447795\pi\) | |||||||
\(200\) | −3.24291e129 | −0.00159115 | ||||||||
\(201\) | −2.61393e130 | −0.00962767 | ||||||||
\(202\) | 3.32813e130 | 0.00921503 | ||||||||
\(203\) | −1.37538e133 | −2.86683 | ||||||||
\(204\) | 4.92693e132 | 0.774180 | ||||||||
\(205\) | 1.24191e133 | 1.47314 | ||||||||
\(206\) | 1.52579e131 | 0.0136814 | ||||||||
\(207\) | 1.03253e132 | 0.0700823 | ||||||||
\(208\) | 2.52205e133 | 1.29751 | ||||||||
\(209\) | 7.92342e132 | 0.309386 | ||||||||
\(210\) | 3.88434e131 | 0.0115268 | ||||||||
\(211\) | 2.97918e133 | 0.672753 | 0.336377 | − | 0.941728i | \(-0.390798\pi\) | ||||
0.336377 | + | 0.941728i | \(0.390798\pi\) | |||||||
\(212\) | −9.08836e133 | −1.56377 | ||||||||
\(213\) | 7.11880e133 | 0.934501 | ||||||||
\(214\) | −9.78714e131 | −0.00981440 | ||||||||
\(215\) | −6.11047e133 | −0.468666 | ||||||||
\(216\) | 2.80267e132 | 0.0164620 | ||||||||
\(217\) | −1.52119e134 | −0.685094 | ||||||||
\(218\) | 3.37584e132 | 0.0116717 | ||||||||
\(219\) | −4.80709e134 | −1.27746 | ||||||||
\(220\) | −1.33904e134 | −0.273836 | ||||||||
\(221\) | 6.61944e134 | 1.04295 | ||||||||
\(222\) | −3.31280e132 | −0.00402624 | ||||||||
\(223\) | −6.35559e134 | −0.596522 | −0.298261 | − | 0.954484i | \(-0.596407\pi\) | ||||
−0.298261 | + | 0.954484i | \(0.596407\pi\) | |||||||
\(224\) | −5.21300e133 | −0.0378291 | ||||||||
\(225\) | 1.27751e133 | 0.00717581 | ||||||||
\(226\) | −1.97730e133 | −0.00860669 | ||||||||
\(227\) | 5.60799e135 | 1.89374 | 0.946869 | − | 0.321618i | \(-0.104227\pi\) | ||||
0.946869 | + | 0.321618i | \(0.104227\pi\) | |||||||
\(228\) | 3.93709e135 | 1.03257 | ||||||||
\(229\) | −1.66776e135 | −0.340089 | −0.170045 | − | 0.985436i | \(-0.554391\pi\) | ||||
−0.170045 | + | 0.985436i | \(0.554391\pi\) | |||||||
\(230\) | 4.64460e133 | 0.00737222 | ||||||||
\(231\) | −3.55685e135 | −0.439923 | ||||||||
\(232\) | −2.99409e134 | −0.0288872 | ||||||||
\(233\) | −8.65932e135 | −0.652407 | −0.326203 | − | 0.945300i | \(-0.605769\pi\) | ||||
−0.326203 | + | 0.945300i | \(0.605769\pi\) | |||||||
\(234\) | 1.26274e133 | 0.000743707 0 | ||||||||
\(235\) | 7.70066e135 | 0.354916 | ||||||||
\(236\) | −6.14092e135 | −0.221714 | ||||||||
\(237\) | −4.63405e136 | −1.31199 | ||||||||
\(238\) | −4.56024e134 | −0.0101347 | ||||||||
\(239\) | 5.88042e136 | 1.02690 | 0.513451 | − | 0.858119i | \(-0.328367\pi\) | ||||
0.513451 | + | 0.858119i | \(0.328367\pi\) | |||||||
\(240\) | −6.65318e136 | −0.913867 | ||||||||
\(241\) | −6.96996e136 | −0.753789 | −0.376895 | − | 0.926256i | \(-0.623008\pi\) | ||||
−0.376895 | + | 0.926256i | \(0.623008\pi\) | |||||||
\(242\) | 8.57276e134 | 0.00730697 | ||||||||
\(243\) | −2.13412e136 | −0.143502 | ||||||||
\(244\) | 8.55370e136 | 0.454192 | ||||||||
\(245\) | 3.39753e137 | 1.42598 | ||||||||
\(246\) | 3.59054e135 | 0.0119232 | ||||||||
\(247\) | 5.28956e137 | 1.39106 | ||||||||
\(248\) | −3.31151e135 | −0.00690327 | ||||||||
\(249\) | −3.15012e137 | −0.521032 | ||||||||
\(250\) | 6.33214e135 | 0.00831764 | ||||||||
\(251\) | −5.22050e137 | −0.545096 | −0.272548 | − | 0.962142i | \(-0.587866\pi\) | ||||
−0.272548 | + | 0.962142i | \(0.587866\pi\) | |||||||
\(252\) | 1.36906e137 | 0.113734 | ||||||||
\(253\) | −4.25302e137 | −0.281363 | ||||||||
\(254\) | 1.39880e136 | 0.00737593 | ||||||||
\(255\) | −1.74621e138 | −0.734576 | ||||||||
\(256\) | 2.97524e138 | 0.999365 | ||||||||
\(257\) | −2.81349e138 | −0.755249 | −0.377624 | − | 0.925959i | \(-0.623259\pi\) | ||||
−0.377624 | + | 0.925959i | \(0.623259\pi\) | |||||||
\(258\) | −1.76662e136 | −0.00379324 | ||||||||
\(259\) | −4.82557e138 | −0.829492 | ||||||||
\(260\) | −8.93926e138 | −1.23121 | ||||||||
\(261\) | 1.17949e138 | 0.130277 | ||||||||
\(262\) | 7.51002e136 | 0.00665758 | ||||||||
\(263\) | 2.55665e139 | 1.82061 | 0.910303 | − | 0.413942i | \(-0.135848\pi\) | ||||
0.910303 | + | 0.413942i | \(0.135848\pi\) | |||||||
\(264\) | −7.74296e136 | −0.00443283 | ||||||||
\(265\) | 3.22111e139 | 1.48378 | ||||||||
\(266\) | −3.64406e137 | −0.0135174 | ||||||||
\(267\) | −3.30978e139 | −0.989468 | ||||||||
\(268\) | −4.14424e137 | −0.00999297 | ||||||||
\(269\) | 3.45524e139 | 0.672545 | 0.336273 | − | 0.941765i | \(-0.390834\pi\) | ||||
0.336273 | + | 0.941765i | \(0.390834\pi\) | |||||||
\(270\) | −4.96648e137 | −0.00780967 | ||||||||
\(271\) | 2.56173e139 | 0.325686 | 0.162843 | − | 0.986652i | \(-0.447934\pi\) | ||||
0.162843 | + | 0.986652i | \(0.447934\pi\) | |||||||
\(272\) | 7.81088e139 | 0.803504 | ||||||||
\(273\) | −2.37450e140 | −1.97797 | ||||||||
\(274\) | −4.64836e137 | −0.00313792 | ||||||||
\(275\) | −5.26211e138 | −0.0288091 | ||||||||
\(276\) | −2.11329e140 | −0.939047 | ||||||||
\(277\) | 7.50119e139 | 0.270734 | 0.135367 | − | 0.990796i | \(-0.456779\pi\) | ||||
0.135367 | + | 0.990796i | \(0.456779\pi\) | |||||||
\(278\) | −2.07147e138 | −0.00607720 | ||||||||
\(279\) | 1.30454e139 | 0.0311326 | ||||||||
\(280\) | 1.23172e139 | 0.0239290 | ||||||||
\(281\) | −7.56779e140 | −1.19772 | −0.598861 | − | 0.800853i | \(-0.704380\pi\) | ||||
−0.598861 | + | 0.800853i | \(0.704380\pi\) | |||||||
\(282\) | 2.22637e138 | 0.00287258 | ||||||||
\(283\) | 1.09452e141 | 1.15213 | 0.576066 | − | 0.817403i | \(-0.304587\pi\) | ||||
0.576066 | + | 0.817403i | \(0.304587\pi\) | |||||||
\(284\) | 1.12865e141 | 0.969959 | ||||||||
\(285\) | −1.39539e141 | −0.979751 | ||||||||
\(286\) | −5.20125e138 | −0.00298580 | ||||||||
\(287\) | 5.23014e141 | 2.45643 | ||||||||
\(288\) | 4.47054e138 | 0.00171906 | ||||||||
\(289\) | −1.12407e141 | −0.354135 | ||||||||
\(290\) | 5.30568e139 | 0.0137043 | ||||||||
\(291\) | −1.61075e140 | −0.0341334 | ||||||||
\(292\) | −7.62137e141 | −1.32593 | ||||||||
\(293\) | −3.01490e141 | −0.430909 | −0.215454 | − | 0.976514i | \(-0.569123\pi\) | ||||
−0.215454 | + | 0.976514i | \(0.569123\pi\) | |||||||
\(294\) | 9.82273e139 | 0.0115415 | ||||||||
\(295\) | 2.17647e141 | 0.210372 | ||||||||
\(296\) | −1.05049e140 | −0.00835828 | ||||||||
\(297\) | 4.54776e141 | 0.298059 | ||||||||
\(298\) | −1.54794e140 | −0.00836216 | ||||||||
\(299\) | −2.83925e142 | −1.26506 | ||||||||
\(300\) | −2.61470e141 | −0.0961501 | ||||||||
\(301\) | −2.57334e142 | −0.781490 | ||||||||
\(302\) | −4.04125e140 | −0.0101418 | ||||||||
\(303\) | 5.36700e142 | 1.11373 | ||||||||
\(304\) | 6.24163e142 | 1.07169 | ||||||||
\(305\) | −3.03162e142 | −0.430957 | ||||||||
\(306\) | 3.91075e139 | 0.000460551 0 | ||||||||
\(307\) | 1.31713e143 | 1.28580 | 0.642898 | − | 0.765952i | \(-0.277732\pi\) | ||||
0.642898 | + | 0.765952i | \(0.277732\pi\) | |||||||
\(308\) | −5.63919e142 | −0.456615 | ||||||||
\(309\) | 2.46051e143 | 1.65353 | ||||||||
\(310\) | 5.86817e140 | 0.00327496 | ||||||||
\(311\) | −3.57939e143 | −1.65992 | −0.829959 | − | 0.557824i | \(-0.811636\pi\) | ||||
−0.829959 | + | 0.557824i | \(0.811636\pi\) | |||||||
\(312\) | −5.16909e141 | −0.0199308 | ||||||||
\(313\) | −1.61081e143 | −0.516706 | −0.258353 | − | 0.966051i | \(-0.583180\pi\) | ||||
−0.258353 | + | 0.966051i | \(0.583180\pi\) | |||||||
\(314\) | −3.80619e141 | −0.0101633 | ||||||||
\(315\) | −4.85224e142 | −0.107916 | ||||||||
\(316\) | −7.34702e143 | −1.36177 | ||||||||
\(317\) | 1.23920e144 | 1.91529 | 0.957645 | − | 0.287950i | \(-0.0929738\pi\) | ||||
0.957645 | + | 0.287950i | \(0.0929738\pi\) | |||||||
\(318\) | 9.31268e141 | 0.0120092 | ||||||||
\(319\) | −4.85836e143 | −0.523029 | ||||||||
\(320\) | −1.05469e144 | −0.948421 | ||||||||
\(321\) | −1.57829e144 | −1.18617 | ||||||||
\(322\) | 1.95601e142 | 0.0122930 | ||||||||
\(323\) | 1.63820e144 | 0.861432 | ||||||||
\(324\) | 2.09644e144 | 0.922879 | ||||||||
\(325\) | −3.51291e143 | −0.129531 | ||||||||
\(326\) | −2.62193e142 | −0.00810232 | ||||||||
\(327\) | 5.44393e144 | 1.41064 | ||||||||
\(328\) | 1.13856e143 | 0.0247519 | ||||||||
\(329\) | 3.24302e144 | 0.591814 | ||||||||
\(330\) | 1.37209e142 | 0.00210296 | ||||||||
\(331\) | −3.05925e144 | −0.394009 | −0.197004 | − | 0.980403i | \(-0.563121\pi\) | ||||
−0.197004 | + | 0.980403i | \(0.563121\pi\) | |||||||
\(332\) | −4.99434e144 | −0.540802 | ||||||||
\(333\) | 4.13829e143 | 0.0376945 | ||||||||
\(334\) | −5.59979e142 | −0.00429289 | ||||||||
\(335\) | 1.46881e143 | 0.00948176 | ||||||||
\(336\) | −2.80189e145 | −1.52385 | ||||||||
\(337\) | 2.65995e145 | 1.21942 | 0.609712 | − | 0.792623i | \(-0.291285\pi\) | ||||
0.609712 | + | 0.792623i | \(0.291285\pi\) | |||||||
\(338\) | −1.41058e143 | −0.00545365 | ||||||||
\(339\) | −3.18862e145 | −1.04021 | ||||||||
\(340\) | −2.76852e145 | −0.762448 | ||||||||
\(341\) | −5.37343e144 | −0.124990 | ||||||||
\(342\) | 3.12506e142 | 0.000614267 0 | ||||||||
\(343\) | 4.78817e145 | 0.795716 | ||||||||
\(344\) | −5.60194e143 | −0.00787459 | ||||||||
\(345\) | 7.48997e145 | 0.891009 | ||||||||
\(346\) | −1.02573e144 | −0.0103313 | ||||||||
\(347\) | 1.27354e145 | 0.108660 | 0.0543299 | − | 0.998523i | \(-0.482698\pi\) | ||||
0.0543299 | + | 0.998523i | \(0.482698\pi\) | |||||||
\(348\) | −2.41408e146 | −1.74560 | ||||||||
\(349\) | 2.91182e146 | 1.78526 | 0.892631 | − | 0.450789i | \(-0.148857\pi\) | ||||
0.892631 | + | 0.450789i | \(0.148857\pi\) | |||||||
\(350\) | 2.42010e143 | 0.00125870 | ||||||||
\(351\) | 3.03602e146 | 1.34012 | ||||||||
\(352\) | −1.84142e144 | −0.00690162 | ||||||||
\(353\) | 1.89065e146 | 0.601956 | 0.300978 | − | 0.953631i | \(-0.402687\pi\) | ||||
0.300978 | + | 0.953631i | \(0.402687\pi\) | |||||||
\(354\) | 6.29249e143 | 0.00170269 | ||||||||
\(355\) | −4.00017e146 | −0.920339 | ||||||||
\(356\) | −5.24748e146 | −1.02701 | ||||||||
\(357\) | −7.35392e146 | −1.22489 | ||||||||
\(358\) | 9.09364e144 | 0.0128963 | ||||||||
\(359\) | 1.20462e146 | 0.145519 | 0.0727596 | − | 0.997350i | \(-0.476819\pi\) | ||||
0.0727596 | + | 0.997350i | \(0.476819\pi\) | |||||||
\(360\) | −1.05629e144 | −0.00108740 | ||||||||
\(361\) | 1.69705e146 | 0.148947 | ||||||||
\(362\) | 8.43242e144 | 0.00631261 | ||||||||
\(363\) | 1.38246e147 | 0.883122 | ||||||||
\(364\) | −3.76464e147 | −2.05302 | ||||||||
\(365\) | 2.70118e147 | 1.25810 | ||||||||
\(366\) | −8.76482e144 | −0.00348803 | ||||||||
\(367\) | 1.97259e147 | 0.671022 | 0.335511 | − | 0.942036i | \(-0.391091\pi\) | ||||
0.335511 | + | 0.942036i | \(0.391091\pi\) | |||||||
\(368\) | −3.35030e147 | −0.974616 | ||||||||
\(369\) | −4.48524e146 | −0.111627 | ||||||||
\(370\) | 1.86152e145 | 0.00396522 | ||||||||
\(371\) | 1.35653e148 | 2.47416 | ||||||||
\(372\) | −2.67001e147 | −0.417152 | ||||||||
\(373\) | 2.30431e147 | 0.308519 | 0.154260 | − | 0.988030i | \(-0.450701\pi\) | ||||
0.154260 | + | 0.988030i | \(0.450701\pi\) | |||||||
\(374\) | −1.61085e145 | −0.00184900 | ||||||||
\(375\) | 1.02113e148 | 1.00527 | ||||||||
\(376\) | 7.05978e145 | 0.00596335 | ||||||||
\(377\) | −3.24337e148 | −2.35163 | ||||||||
\(378\) | −2.09156e146 | −0.0130224 | ||||||||
\(379\) | −4.02043e147 | −0.215039 | −0.107520 | − | 0.994203i | \(-0.534291\pi\) | ||||
−0.107520 | + | 0.994203i | \(0.534291\pi\) | |||||||
\(380\) | −2.21231e148 | −1.01693 | ||||||||
\(381\) | 2.25573e148 | 0.891457 | ||||||||
\(382\) | 2.29096e145 | 0.000778707 0 | ||||||||
\(383\) | −2.98479e148 | −0.872941 | −0.436471 | − | 0.899719i | \(-0.643772\pi\) | ||||
−0.436471 | + | 0.899719i | \(0.643772\pi\) | |||||||
\(384\) | −1.21997e147 | −0.0307118 | ||||||||
\(385\) | 1.99865e148 | 0.433256 | ||||||||
\(386\) | −4.72933e146 | −0.00883140 | ||||||||
\(387\) | 2.20683e147 | 0.0355131 | ||||||||
\(388\) | −2.55375e147 | −0.0354286 | ||||||||
\(389\) | 7.83898e148 | 0.937903 | 0.468951 | − | 0.883224i | \(-0.344632\pi\) | ||||
0.468951 | + | 0.883224i | \(0.344632\pi\) | |||||||
\(390\) | 9.15989e146 | 0.00945530 | ||||||||
\(391\) | −8.79328e148 | −0.783406 | ||||||||
\(392\) | 3.11478e147 | 0.0239595 | ||||||||
\(393\) | 1.21108e149 | 0.804638 | ||||||||
\(394\) | −4.09841e145 | −0.000235279 0 | ||||||||
\(395\) | 2.60394e149 | 1.29211 | ||||||||
\(396\) | 4.83603e147 | 0.0207499 | ||||||||
\(397\) | 2.24295e149 | 0.832464 | 0.416232 | − | 0.909258i | \(-0.363350\pi\) | ||||
0.416232 | + | 0.909258i | \(0.363350\pi\) | |||||||
\(398\) | −8.10462e146 | −0.00260289 | ||||||||
\(399\) | −5.87648e149 | −1.63371 | ||||||||
\(400\) | −4.14520e148 | −0.0997920 | ||||||||
\(401\) | −5.56701e149 | −1.16097 | −0.580485 | − | 0.814271i | \(-0.697137\pi\) | ||||
−0.580485 | + | 0.814271i | \(0.697137\pi\) | |||||||
\(402\) | 4.24653e145 | 7.67425e−5 0 | ||||||||
\(403\) | −3.58722e149 | −0.561976 | ||||||||
\(404\) | 8.50908e149 | 1.15599 | ||||||||
\(405\) | −7.43024e149 | −0.875667 | ||||||||
\(406\) | 2.23441e148 | 0.0228516 | ||||||||
\(407\) | −1.70457e149 | −0.151334 | ||||||||
\(408\) | −1.60089e148 | −0.0123424 | ||||||||
\(409\) | −3.09893e149 | −0.207549 | −0.103775 | − | 0.994601i | \(-0.533092\pi\) | ||||
−0.103775 | + | 0.994601i | \(0.533092\pi\) | |||||||
\(410\) | −2.01758e148 | −0.0117425 | ||||||||
\(411\) | −7.49602e149 | −0.379250 | ||||||||
\(412\) | 3.90101e150 | 1.71627 | ||||||||
\(413\) | 9.16591e149 | 0.350790 | ||||||||
\(414\) | −1.67743e147 | −0.000558629 0 | ||||||||
\(415\) | 1.77010e150 | 0.513136 | ||||||||
\(416\) | −1.22931e149 | −0.0310309 | ||||||||
\(417\) | −3.34049e150 | −0.734492 | ||||||||
\(418\) | −1.28722e148 | −0.00246613 | ||||||||
\(419\) | 3.68395e150 | 0.615187 | 0.307593 | − | 0.951518i | \(-0.400476\pi\) | ||||
0.307593 | + | 0.951518i | \(0.400476\pi\) | |||||||
\(420\) | 9.93114e150 | 1.44599 | ||||||||
\(421\) | −1.33076e151 | −1.68997 | −0.844987 | − | 0.534786i | \(-0.820392\pi\) | ||||
−0.844987 | + | 0.534786i | \(0.820392\pi\) | |||||||
\(422\) | −4.83991e148 | −0.00536254 | ||||||||
\(423\) | −2.78114e149 | −0.0268937 | ||||||||
\(424\) | 2.95304e149 | 0.0249306 | ||||||||
\(425\) | −1.08796e150 | −0.0802139 | ||||||||
\(426\) | −1.15650e149 | −0.00744895 | ||||||||
\(427\) | −1.27672e151 | −0.718610 | ||||||||
\(428\) | −2.50229e151 | −1.23118 | ||||||||
\(429\) | −8.38762e150 | −0.360865 | ||||||||
\(430\) | 9.92693e148 | 0.00373576 | ||||||||
\(431\) | −1.47034e151 | −0.484145 | −0.242073 | − | 0.970258i | \(-0.577827\pi\) | ||||
−0.242073 | + | 0.970258i | \(0.577827\pi\) | |||||||
\(432\) | 3.58248e151 | 1.03245 | ||||||||
\(433\) | 8.18435e150 | 0.206505 | 0.103252 | − | 0.994655i | \(-0.467075\pi\) | ||||
0.103252 | + | 0.994655i | \(0.467075\pi\) | |||||||
\(434\) | 2.47130e149 | 0.00546091 | ||||||||
\(435\) | 8.55603e151 | 1.65630 | ||||||||
\(436\) | 8.63105e151 | 1.46417 | ||||||||
\(437\) | −7.02666e151 | −1.04488 | ||||||||
\(438\) | 7.80948e149 | 0.0101827 | ||||||||
\(439\) | −9.86539e151 | −1.12825 | −0.564124 | − | 0.825690i | \(-0.690786\pi\) | ||||
−0.564124 | + | 0.825690i | \(0.690786\pi\) | |||||||
\(440\) | 4.35089e149 | 0.00436565 | ||||||||
\(441\) | −1.22704e151 | −0.108054 | ||||||||
\(442\) | −1.07538e150 | −0.00831344 | ||||||||
\(443\) | 2.53820e152 | 1.72311 | 0.861553 | − | 0.507667i | \(-0.169492\pi\) | ||||
0.861553 | + | 0.507667i | \(0.169492\pi\) | |||||||
\(444\) | −8.46989e151 | −0.505076 | ||||||||
\(445\) | 1.85982e152 | 0.974473 | ||||||||
\(446\) | 1.03251e150 | 0.00475490 | ||||||||
\(447\) | −2.49623e152 | −1.01065 | ||||||||
\(448\) | −4.44168e152 | −1.58147 | ||||||||
\(449\) | 4.51737e150 | 0.0141488 | 0.00707442 | − | 0.999975i | \(-0.497748\pi\) | ||||
0.00707442 | + | 0.999975i | \(0.497748\pi\) | |||||||
\(450\) | −2.07542e148 | −5.71987e−5 0 | ||||||||
\(451\) | 1.84748e152 | 0.448155 | ||||||||
\(452\) | −5.05538e152 | −1.07968 | ||||||||
\(453\) | −6.51699e152 | −1.22575 | ||||||||
\(454\) | −9.11059e150 | −0.0150951 | ||||||||
\(455\) | 1.33427e153 | 1.94800 | ||||||||
\(456\) | −1.27926e151 | −0.0164619 | ||||||||
\(457\) | −4.05863e152 | −0.460467 | −0.230233 | − | 0.973135i | \(-0.573949\pi\) | ||||
−0.230233 | + | 0.973135i | \(0.573949\pi\) | |||||||
\(458\) | 2.70940e150 | 0.00271087 | ||||||||
\(459\) | 9.40266e152 | 0.829892 | ||||||||
\(460\) | 1.18749e153 | 0.924816 | ||||||||
\(461\) | 7.16459e152 | 0.492479 | 0.246240 | − | 0.969209i | \(-0.420805\pi\) | ||||
0.246240 | + | 0.969209i | \(0.420805\pi\) | |||||||
\(462\) | 5.77837e150 | 0.00350665 | ||||||||
\(463\) | 7.38254e152 | 0.395639 | 0.197819 | − | 0.980238i | \(-0.436614\pi\) | ||||
0.197819 | + | 0.980238i | \(0.436614\pi\) | |||||||
\(464\) | −3.82715e153 | −1.81172 | ||||||||
\(465\) | 9.46311e152 | 0.395812 | ||||||||
\(466\) | 1.40677e151 | 0.00520036 | ||||||||
\(467\) | 2.49693e153 | 0.815992 | 0.407996 | − | 0.912984i | \(-0.366228\pi\) | ||||
0.407996 | + | 0.912984i | \(0.366228\pi\) | |||||||
\(468\) | 3.22846e152 | 0.0932952 | ||||||||
\(469\) | 6.18568e151 | 0.0158106 | ||||||||
\(470\) | −1.25103e151 | −0.00282905 | ||||||||
\(471\) | −6.13792e153 | −1.22834 | ||||||||
\(472\) | 1.99534e151 | 0.00353470 | ||||||||
\(473\) | −9.08999e152 | −0.142576 | ||||||||
\(474\) | 7.52836e151 | 0.0104579 | ||||||||
\(475\) | −8.69383e152 | −0.106986 | ||||||||
\(476\) | −1.16592e154 | −1.27136 | ||||||||
\(477\) | −1.16332e153 | −0.112433 | ||||||||
\(478\) | −9.55319e151 | −0.00818548 | ||||||||
\(479\) | 1.11081e154 | 0.844011 | 0.422006 | − | 0.906593i | \(-0.361326\pi\) | ||||
0.422006 | + | 0.906593i | \(0.361326\pi\) | |||||||
\(480\) | 3.24292e152 | 0.0218557 | ||||||||
\(481\) | −1.13795e154 | −0.680425 | ||||||||
\(482\) | 1.13232e152 | 0.00600849 | ||||||||
\(483\) | 3.15429e154 | 1.48574 | ||||||||
\(484\) | 2.19181e154 | 0.916631 | ||||||||
\(485\) | 9.05103e152 | 0.0336161 | ||||||||
\(486\) | 3.46704e151 | 0.00114386 | ||||||||
\(487\) | 1.39646e154 | 0.409366 | 0.204683 | − | 0.978828i | \(-0.434384\pi\) | ||||
0.204683 | + | 0.978828i | \(0.434384\pi\) | |||||||
\(488\) | −2.77931e152 | −0.00724099 | ||||||||
\(489\) | −4.22817e154 | −0.979248 | ||||||||
\(490\) | −5.51954e152 | −0.0113665 | ||||||||
\(491\) | 1.61060e154 | 0.294986 | 0.147493 | − | 0.989063i | \(-0.452880\pi\) | ||||
0.147493 | + | 0.989063i | \(0.452880\pi\) | |||||||
\(492\) | 9.17999e154 | 1.49571 | ||||||||
\(493\) | −1.00448e155 | −1.45628 | ||||||||
\(494\) | −8.59329e152 | −0.0110882 | ||||||||
\(495\) | −1.71399e153 | −0.0196884 | ||||||||
\(496\) | −4.23289e154 | −0.432953 | ||||||||
\(497\) | −1.68461e155 | −1.53464 | ||||||||
\(498\) | 5.11761e152 | 0.00415317 | ||||||||
\(499\) | −1.15267e154 | −0.0833532 | −0.0416766 | − | 0.999131i | \(-0.513270\pi\) | ||||
−0.0416766 | + | 0.999131i | \(0.513270\pi\) | |||||||
\(500\) | 1.61895e155 | 1.04342 | ||||||||
\(501\) | −9.03031e154 | −0.518840 | ||||||||
\(502\) | 8.48110e152 | 0.00434498 | ||||||||
\(503\) | 1.73196e155 | 0.791370 | 0.395685 | − | 0.918386i | \(-0.370507\pi\) | ||||
0.395685 | + | 0.918386i | \(0.370507\pi\) | |||||||
\(504\) | −4.44842e152 | −0.00181322 | ||||||||
\(505\) | −3.01580e155 | −1.09685 | ||||||||
\(506\) | 6.90935e152 | 0.00224276 | ||||||||
\(507\) | −2.27472e155 | −0.659130 | ||||||||
\(508\) | 3.57633e155 | 0.925282 | ||||||||
\(509\) | 2.00777e155 | 0.463917 | 0.231959 | − | 0.972726i | \(-0.425487\pi\) | ||||
0.231959 | + | 0.972726i | \(0.425487\pi\) | |||||||
\(510\) | 2.83685e153 | 0.00585533 | ||||||||
\(511\) | 1.13756e156 | 2.09785 | ||||||||
\(512\) | −2.41767e154 | −0.0398451 | ||||||||
\(513\) | 7.51362e155 | 1.10688 | ||||||||
\(514\) | 4.57072e153 | 0.00602012 | ||||||||
\(515\) | −1.38260e156 | −1.62847 | ||||||||
\(516\) | −4.51675e155 | −0.475848 | ||||||||
\(517\) | 1.14556e155 | 0.107972 | ||||||||
\(518\) | 7.83951e153 | 0.00661192 | ||||||||
\(519\) | −1.65411e156 | −1.24865 | ||||||||
\(520\) | 2.90459e154 | 0.0196288 | ||||||||
\(521\) | −7.35144e155 | −0.444839 | −0.222420 | − | 0.974951i | \(-0.571395\pi\) | ||||
−0.222420 | + | 0.974951i | \(0.571395\pi\) | |||||||
\(522\) | −1.91618e153 | −0.00103844 | ||||||||
\(523\) | −4.27171e155 | −0.207374 | −0.103687 | − | 0.994610i | \(-0.533064\pi\) | ||||
−0.103687 | + | 0.994610i | \(0.533064\pi\) | |||||||
\(524\) | 1.92010e156 | 0.835168 | ||||||||
\(525\) | 3.90269e155 | 0.152126 | ||||||||
\(526\) | −4.15347e154 | −0.0145121 | ||||||||
\(527\) | −1.11098e156 | −0.348012 | ||||||||
\(528\) | −9.89732e155 | −0.278014 | ||||||||
\(529\) | −1.97513e155 | −0.0497617 | ||||||||
\(530\) | −5.23294e154 | −0.0118272 | ||||||||
\(531\) | −7.86046e154 | −0.0159409 | ||||||||
\(532\) | −9.31683e156 | −1.69570 | ||||||||
\(533\) | 1.23335e157 | 2.01499 | ||||||||
\(534\) | 5.37699e154 | 0.00788709 | ||||||||
\(535\) | 8.86866e156 | 1.16820 | ||||||||
\(536\) | 1.34657e153 | 0.000159314 0 | ||||||||
\(537\) | 1.46646e157 | 1.55865 | ||||||||
\(538\) | −5.61329e154 | −0.00536089 | ||||||||
\(539\) | 5.05419e156 | 0.433808 | ||||||||
\(540\) | −1.26979e157 | −0.979693 | ||||||||
\(541\) | −2.22349e157 | −1.54238 | −0.771191 | − | 0.636604i | \(-0.780339\pi\) | ||||
−0.771191 | + | 0.636604i | \(0.780339\pi\) | |||||||
\(542\) | −4.16172e154 | −0.00259605 | ||||||||
\(543\) | 1.35983e157 | 0.762944 | ||||||||
\(544\) | −3.80721e155 | −0.0192163 | ||||||||
\(545\) | −3.05903e157 | −1.38926 | ||||||||
\(546\) | 3.85756e155 | 0.0157665 | ||||||||
\(547\) | 1.07884e157 | 0.396905 | 0.198453 | − | 0.980110i | \(-0.436408\pi\) | ||||
0.198453 | + | 0.980110i | \(0.436408\pi\) | |||||||
\(548\) | −1.18845e157 | −0.393640 | ||||||||
\(549\) | 1.09489e156 | 0.0326557 | ||||||||
\(550\) | 8.54869e153 | 0.000229639 0 | ||||||||
\(551\) | −8.02678e157 | −1.94234 | ||||||||
\(552\) | 6.86663e155 | 0.0149708 | ||||||||
\(553\) | 1.09661e158 | 2.15456 | ||||||||
\(554\) | −1.21862e155 | −0.00215803 | ||||||||
\(555\) | 3.00191e157 | 0.479238 | ||||||||
\(556\) | −5.29616e157 | −0.762361 | ||||||||
\(557\) | 1.33887e157 | 0.173806 | 0.0869028 | − | 0.996217i | \(-0.472303\pi\) | ||||
0.0869028 | + | 0.996217i | \(0.472303\pi\) | |||||||
\(558\) | −2.11932e154 | −0.000248159 0 | ||||||||
\(559\) | −6.06834e157 | −0.641049 | ||||||||
\(560\) | 1.57443e158 | 1.50076 | ||||||||
\(561\) | −2.59768e157 | −0.223471 | ||||||||
\(562\) | 1.22945e156 | 0.00954709 | ||||||||
\(563\) | 8.65513e157 | 0.606793 | 0.303397 | − | 0.952864i | \(-0.401879\pi\) | ||||
0.303397 | + | 0.952864i | \(0.401879\pi\) | |||||||
\(564\) | 5.69218e157 | 0.360355 | ||||||||
\(565\) | 1.79173e158 | 1.02444 | ||||||||
\(566\) | −1.77813e156 | −0.00918370 | ||||||||
\(567\) | −3.12914e158 | −1.46015 | ||||||||
\(568\) | −3.66726e156 | −0.0154637 | ||||||||
\(569\) | 1.11867e157 | 0.0426330 | 0.0213165 | − | 0.999773i | \(-0.493214\pi\) | ||||
0.0213165 | + | 0.999773i | \(0.493214\pi\) | |||||||
\(570\) | 2.26691e156 | 0.00780963 | ||||||||
\(571\) | −3.78486e158 | −1.17889 | −0.589446 | − | 0.807808i | \(-0.700654\pi\) | ||||
−0.589446 | + | 0.807808i | \(0.700654\pi\) | |||||||
\(572\) | −1.32981e158 | −0.374557 | ||||||||
\(573\) | 3.69444e157 | 0.0941147 | ||||||||
\(574\) | −8.49675e156 | −0.0195803 | ||||||||
\(575\) | 4.66655e157 | 0.0972960 | ||||||||
\(576\) | 3.80907e157 | 0.0718665 | ||||||||
\(577\) | −6.89298e158 | −1.17706 | −0.588529 | − | 0.808476i | \(-0.700293\pi\) | ||||
−0.588529 | + | 0.808476i | \(0.700293\pi\) | |||||||
\(578\) | 1.82614e156 | 0.00282283 | ||||||||
\(579\) | −7.62660e158 | −1.06737 | ||||||||
\(580\) | 1.35651e159 | 1.71915 | ||||||||
\(581\) | 7.45453e158 | 0.855643 | ||||||||
\(582\) | 2.61678e155 | 0.000272079 0 | ||||||||
\(583\) | 4.79175e158 | 0.451391 | ||||||||
\(584\) | 2.47638e157 | 0.0211387 | ||||||||
\(585\) | −1.14424e158 | −0.0885225 | ||||||||
\(586\) | 4.89794e156 | 0.00343479 | ||||||||
\(587\) | −2.75880e158 | −0.175400 | −0.0877000 | − | 0.996147i | \(-0.527952\pi\) | ||||
−0.0877000 | + | 0.996147i | \(0.527952\pi\) | |||||||
\(588\) | 2.51139e159 | 1.44783 | ||||||||
\(589\) | −8.87775e158 | −0.464166 | ||||||||
\(590\) | −3.53585e156 | −0.00167688 | ||||||||
\(591\) | −6.60916e157 | −0.0284358 | ||||||||
\(592\) | −1.34277e159 | −0.524207 | ||||||||
\(593\) | −1.62267e158 | −0.0574891 | −0.0287445 | − | 0.999587i | \(-0.509151\pi\) | ||||
−0.0287445 | + | 0.999587i | \(0.509151\pi\) | |||||||
\(594\) | −7.38818e156 | −0.00237584 | ||||||||
\(595\) | 4.13228e159 | 1.20633 | ||||||||
\(596\) | −3.95763e159 | −1.04900 | ||||||||
\(597\) | −1.30696e159 | −0.314586 | ||||||||
\(598\) | 4.61258e157 | 0.0100838 | ||||||||
\(599\) | 3.63775e156 | 0.000722421 0 | 0.000361210 | − | 1.00000i | \(-0.499885\pi\) | ||||
0.000361210 | 1.00000i | \(0.499885\pi\) | ||||||||
\(600\) | 8.49583e156 | 0.00153288 | ||||||||
\(601\) | −7.08617e159 | −1.16179 | −0.580897 | − | 0.813977i | \(-0.697298\pi\) | ||||
−0.580897 | + | 0.813977i | \(0.697298\pi\) | |||||||
\(602\) | 4.18058e157 | 0.00622929 | ||||||||
\(603\) | −5.30469e156 | −0.000718480 0 | ||||||||
\(604\) | −1.03323e160 | −1.27225 | ||||||||
\(605\) | −7.76824e159 | −0.869739 | ||||||||
\(606\) | −8.71910e157 | −0.00887760 | ||||||||
\(607\) | 1.57783e160 | 1.46120 | 0.730601 | − | 0.682805i | \(-0.239240\pi\) | ||||
0.730601 | + | 0.682805i | \(0.239240\pi\) | |||||||
\(608\) | −3.04232e158 | −0.0256301 | ||||||||
\(609\) | 3.60325e160 | 2.76185 | ||||||||
\(610\) | 4.92509e157 | 0.00343517 | ||||||||
\(611\) | 7.64756e159 | 0.485460 | ||||||||
\(612\) | 9.99867e158 | 0.0577744 | ||||||||
\(613\) | −8.70148e159 | −0.457737 | −0.228868 | − | 0.973457i | \(-0.573503\pi\) | ||||
−0.228868 | + | 0.973457i | \(0.573503\pi\) | |||||||
\(614\) | −2.13978e158 | −0.0102491 | ||||||||
\(615\) | −3.25359e160 | −1.41920 | ||||||||
\(616\) | 1.83232e158 | 0.00727963 | ||||||||
\(617\) | 4.79825e159 | 0.173655 | 0.0868273 | − | 0.996223i | \(-0.472327\pi\) | ||||
0.0868273 | + | 0.996223i | \(0.472327\pi\) | |||||||
\(618\) | −3.99729e158 | −0.0131804 | ||||||||
\(619\) | 3.52731e160 | 1.05982 | 0.529909 | − | 0.848054i | \(-0.322226\pi\) | ||||
0.529909 | + | 0.848054i | \(0.322226\pi\) | |||||||
\(620\) | 1.50032e160 | 0.410830 | ||||||||
\(621\) | −4.03305e160 | −1.00662 | ||||||||
\(622\) | 5.81499e158 | 0.0132313 | ||||||||
\(623\) | 7.83236e160 | 1.62491 | ||||||||
\(624\) | −6.60731e160 | −1.25000 | ||||||||
\(625\) | −5.15943e160 | −0.890227 | ||||||||
\(626\) | 2.61687e158 | 0.00411869 | ||||||||
\(627\) | −2.07579e160 | −0.298057 | ||||||||
\(628\) | −9.73132e160 | −1.27495 | ||||||||
\(629\) | −3.52427e160 | −0.421363 | ||||||||
\(630\) | 7.88283e157 | 0.000860203 0 | ||||||||
\(631\) | 1.23110e161 | 1.22632 | 0.613161 | − | 0.789958i | \(-0.289898\pi\) | ||||
0.613161 | + | 0.789958i | \(0.289898\pi\) | |||||||
\(632\) | 2.38723e159 | 0.0217102 | ||||||||
\(633\) | −7.80491e160 | −0.648119 | ||||||||
\(634\) | −2.01318e159 | −0.0152669 | ||||||||
\(635\) | −1.26753e161 | −0.877947 | ||||||||
\(636\) | 2.38099e161 | 1.50651 | ||||||||
\(637\) | 3.37411e161 | 1.95048 | ||||||||
\(638\) | 7.89278e158 | 0.00416909 | ||||||||
\(639\) | 1.44468e160 | 0.0697386 | ||||||||
\(640\) | 6.85522e159 | 0.0302463 | ||||||||
\(641\) | −1.05174e161 | −0.424201 | −0.212101 | − | 0.977248i | \(-0.568030\pi\) | ||||
−0.212101 | + | 0.977248i | \(0.568030\pi\) | |||||||
\(642\) | 2.56405e159 | 0.00945502 | ||||||||
\(643\) | −3.21803e161 | −1.08507 | −0.542537 | − | 0.840032i | \(-0.682536\pi\) | ||||
−0.542537 | + | 0.840032i | \(0.682536\pi\) | |||||||
\(644\) | 5.00095e161 | 1.54211 | ||||||||
\(645\) | 1.60083e161 | 0.451505 | ||||||||
\(646\) | −2.66137e159 | −0.00686651 | ||||||||
\(647\) | −5.92463e161 | −1.39851 | −0.699255 | − | 0.714873i | \(-0.746485\pi\) | ||||
−0.699255 | + | 0.714873i | \(0.746485\pi\) | |||||||
\(648\) | −6.81187e159 | −0.0147131 | ||||||||
\(649\) | 3.23774e160 | 0.0639988 | ||||||||
\(650\) | 5.70698e158 | 0.00103250 | ||||||||
\(651\) | 3.98525e161 | 0.660008 | ||||||||
\(652\) | −6.70353e161 | −1.01640 | ||||||||
\(653\) | −8.21189e161 | −1.14008 | −0.570040 | − | 0.821617i | \(-0.693072\pi\) | ||||
−0.570040 | + | 0.821617i | \(0.693072\pi\) | |||||||
\(654\) | −8.84408e159 | −0.0112443 | ||||||||
\(655\) | −6.80523e161 | −0.792443 | ||||||||
\(656\) | 1.45534e162 | 1.55237 | ||||||||
\(657\) | −9.75546e160 | −0.0953321 | ||||||||
\(658\) | −5.26853e159 | −0.00471738 | ||||||||
\(659\) | −7.69425e161 | −0.631328 | −0.315664 | − | 0.948871i | \(-0.602227\pi\) | ||||
−0.315664 | + | 0.948871i | \(0.602227\pi\) | |||||||
\(660\) | 3.50805e161 | 0.263809 | ||||||||
\(661\) | 4.39883e160 | 0.0303217 | 0.0151608 | − | 0.999885i | \(-0.495174\pi\) | ||||
0.0151608 | + | 0.999885i | \(0.495174\pi\) | |||||||
\(662\) | 4.96999e159 | 0.00314066 | ||||||||
\(663\) | −1.73417e162 | −1.00476 | ||||||||
\(664\) | 1.62279e160 | 0.00862179 | ||||||||
\(665\) | 3.30208e162 | 1.60895 | ||||||||
\(666\) | −6.72297e158 | −0.000300464 0 | ||||||||
\(667\) | 4.30850e162 | 1.76641 | ||||||||
\(668\) | −1.43170e162 | −0.538526 | ||||||||
\(669\) | 1.66505e162 | 0.574678 | ||||||||
\(670\) | −2.38619e158 | −7.55795e−5 0 | ||||||||
\(671\) | −4.50986e161 | −0.131105 | ||||||||
\(672\) | 1.36571e161 | 0.0364439 | ||||||||
\(673\) | −1.88994e162 | −0.463002 | −0.231501 | − | 0.972835i | \(-0.574364\pi\) | ||||
−0.231501 | + | 0.972835i | \(0.574364\pi\) | |||||||
\(674\) | −4.32129e160 | −0.00972007 | ||||||||
\(675\) | −4.98995e161 | −0.103069 | ||||||||
\(676\) | −3.60645e162 | −0.684140 | ||||||||
\(677\) | 1.09963e161 | 0.0191601 | 0.00958006 | − | 0.999954i | \(-0.496951\pi\) | ||||
0.00958006 | + | 0.999954i | \(0.496951\pi\) | |||||||
\(678\) | 5.18015e160 | 0.00829154 | ||||||||
\(679\) | 3.81171e161 | 0.0560542 | ||||||||
\(680\) | 8.99563e160 | 0.0121554 | ||||||||
\(681\) | −1.46919e163 | −1.82440 | ||||||||
\(682\) | 8.72954e159 | 0.000996299 0 | ||||||||
\(683\) | −1.01812e162 | −0.106809 | −0.0534045 | − | 0.998573i | \(-0.517007\pi\) | ||||
−0.0534045 | + | 0.998573i | \(0.517007\pi\) | |||||||
\(684\) | 7.98988e161 | 0.0770574 | ||||||||
\(685\) | 4.21213e162 | 0.373503 | ||||||||
\(686\) | −7.77875e160 | −0.00634268 | ||||||||
\(687\) | 4.36922e162 | 0.327636 | ||||||||
\(688\) | −7.16059e162 | −0.493871 | ||||||||
\(689\) | 3.19890e163 | 2.02953 | ||||||||
\(690\) | −1.21680e161 | −0.00710227 | ||||||||
\(691\) | −7.27763e162 | −0.390843 | −0.195421 | − | 0.980719i | \(-0.562607\pi\) | ||||
−0.195421 | + | 0.980719i | \(0.562607\pi\) | |||||||
\(692\) | −2.62249e163 | −1.29603 | ||||||||
\(693\) | −7.21824e161 | −0.0328299 | ||||||||
\(694\) | −2.06897e160 | −0.000866132 0 | ||||||||
\(695\) | 1.87707e163 | 0.723361 | ||||||||
\(696\) | 7.84397e161 | 0.0278295 | ||||||||
\(697\) | 3.81973e163 | 1.24781 | ||||||||
\(698\) | −4.73046e161 | −0.0142304 | ||||||||
\(699\) | 2.26858e163 | 0.628517 | ||||||||
\(700\) | 6.18750e162 | 0.157898 | ||||||||
\(701\) | 1.33169e163 | 0.313053 | 0.156527 | − | 0.987674i | \(-0.449970\pi\) | ||||
0.156527 | + | 0.987674i | \(0.449970\pi\) | |||||||
\(702\) | −4.93224e161 | −0.0106822 | ||||||||
\(703\) | −2.81622e163 | −0.561999 | ||||||||
\(704\) | −1.56897e163 | −0.288526 | ||||||||
\(705\) | −2.01743e163 | −0.341920 | ||||||||
\(706\) | −3.07150e161 | −0.00479822 | ||||||||
\(707\) | −1.27006e164 | −1.82898 | ||||||||
\(708\) | 1.60881e163 | 0.213595 | ||||||||
\(709\) | −7.79346e163 | −0.954052 | −0.477026 | − | 0.878889i | \(-0.658285\pi\) | ||||
−0.477026 | + | 0.878889i | \(0.658285\pi\) | |||||||
\(710\) | 6.49857e161 | 0.00733606 | ||||||||
\(711\) | −9.40429e162 | −0.0979093 | ||||||||
\(712\) | 1.70504e162 | 0.0163732 | ||||||||
\(713\) | 4.76527e163 | 0.422124 | ||||||||
\(714\) | 1.19470e162 | 0.00976363 | ||||||||
\(715\) | 4.71314e163 | 0.355396 | ||||||||
\(716\) | 2.32498e164 | 1.61779 | ||||||||
\(717\) | −1.54056e164 | −0.989300 | ||||||||
\(718\) | −1.95700e161 | −0.00115994 | ||||||||
\(719\) | 2.98307e164 | 1.63212 | 0.816060 | − | 0.577967i | \(-0.196154\pi\) | ||||
0.816060 | + | 0.577967i | \(0.196154\pi\) | |||||||
\(720\) | −1.35019e163 | −0.0681987 | ||||||||
\(721\) | −5.82262e164 | −2.71544 | ||||||||
\(722\) | −2.75699e161 | −0.00118726 | ||||||||
\(723\) | 1.82600e164 | 0.726188 | ||||||||
\(724\) | 2.15593e164 | 0.791893 | ||||||||
\(725\) | 5.33075e163 | 0.180864 | ||||||||
\(726\) | −2.24591e162 | −0.00703940 | ||||||||
\(727\) | 4.23599e164 | 1.22667 | 0.613333 | − | 0.789824i | \(-0.289828\pi\) | ||||
0.613333 | + | 0.789824i | \(0.289828\pi\) | |||||||
\(728\) | 1.22323e163 | 0.0327305 | ||||||||
\(729\) | 4.29165e164 | 1.06118 | ||||||||
\(730\) | −4.38827e162 | −0.0100283 | ||||||||
\(731\) | −1.87939e164 | −0.396979 | ||||||||
\(732\) | −2.24091e164 | −0.437560 | ||||||||
\(733\) | −7.22331e164 | −1.30394 | −0.651970 | − | 0.758245i | \(-0.726057\pi\) | ||||
−0.651970 | + | 0.758245i | \(0.726057\pi\) | |||||||
\(734\) | −3.20461e162 | −0.00534875 | ||||||||
\(735\) | −8.90091e164 | −1.37376 | ||||||||
\(736\) | 1.63301e163 | 0.0233086 | ||||||||
\(737\) | 2.18501e162 | 0.00288452 | ||||||||
\(738\) | 7.28661e161 | 0.000889784 0 | ||||||||
\(739\) | 5.23614e164 | 0.591501 | 0.295751 | − | 0.955265i | \(-0.404430\pi\) | ||||
0.295751 | + | 0.955265i | \(0.404430\pi\) | |||||||
\(740\) | 4.75936e164 | 0.497422 | ||||||||
\(741\) | −1.38577e165 | −1.34012 | ||||||||
\(742\) | −2.20378e163 | −0.0197216 | ||||||||
\(743\) | −7.62830e164 | −0.631788 | −0.315894 | − | 0.948795i | \(-0.602304\pi\) | ||||
−0.315894 | + | 0.948795i | \(0.602304\pi\) | |||||||
\(744\) | 8.67556e162 | 0.00665049 | ||||||||
\(745\) | 1.40267e165 | 0.995337 | ||||||||
\(746\) | −3.74352e162 | −0.00245922 | ||||||||
\(747\) | −6.39282e163 | −0.0388829 | ||||||||
\(748\) | −4.11847e164 | −0.231950 | ||||||||
\(749\) | 3.73491e165 | 1.94794 | ||||||||
\(750\) | −1.65890e163 | −0.00801307 | ||||||||
\(751\) | −1.43926e165 | −0.643934 | −0.321967 | − | 0.946751i | \(-0.604344\pi\) | ||||
−0.321967 | + | 0.946751i | \(0.604344\pi\) | |||||||
\(752\) | 9.02406e164 | 0.374004 | ||||||||
\(753\) | 1.36768e165 | 0.525136 | ||||||||
\(754\) | 5.26910e163 | 0.0187450 | ||||||||
\(755\) | 3.66200e165 | 1.20717 | ||||||||
\(756\) | −5.34753e165 | −1.63362 | ||||||||
\(757\) | −1.10275e165 | −0.312224 | −0.156112 | − | 0.987739i | \(-0.549896\pi\) | ||||
−0.156112 | + | 0.987739i | \(0.549896\pi\) | |||||||
\(758\) | 6.53149e162 | 0.00171409 | ||||||||
\(759\) | 1.11421e165 | 0.271061 | ||||||||
\(760\) | 7.18836e163 | 0.0162124 | ||||||||
\(761\) | 6.71001e165 | 1.40315 | 0.701577 | − | 0.712594i | \(-0.252480\pi\) | ||||
0.701577 | + | 0.712594i | \(0.252480\pi\) | |||||||
\(762\) | −3.66460e163 | −0.00710584 | ||||||||
\(763\) | −1.28827e166 | −2.31657 | ||||||||
\(764\) | 5.85732e164 | 0.0976857 | ||||||||
\(765\) | −3.54374e164 | −0.0548188 | ||||||||
\(766\) | 4.84902e163 | 0.00695825 | ||||||||
\(767\) | 2.16147e165 | 0.287750 | ||||||||
\(768\) | −7.79458e165 | −0.962771 | ||||||||
\(769\) | 1.13066e165 | 0.129588 | 0.0647942 | − | 0.997899i | \(-0.479361\pi\) | ||||
0.0647942 | + | 0.997899i | \(0.479361\pi\) | |||||||
\(770\) | −3.24696e163 | −0.00345350 | ||||||||
\(771\) | 7.37082e165 | 0.727594 | ||||||||
\(772\) | −1.20915e166 | −1.10787 | ||||||||
\(773\) | −8.71638e165 | −0.741336 | −0.370668 | − | 0.928765i | \(-0.620871\pi\) | ||||
−0.370668 | + | 0.928765i | \(0.620871\pi\) | |||||||
\(774\) | −3.58517e162 | −0.000283077 0 | ||||||||
\(775\) | 5.89590e164 | 0.0432217 | ||||||||
\(776\) | 8.29777e162 | 0.000564823 0 | ||||||||
\(777\) | 1.26421e166 | 0.799119 | ||||||||
\(778\) | −1.27350e164 | −0.00747606 | ||||||||
\(779\) | 3.05233e166 | 1.66428 | ||||||||
\(780\) | 2.34192e166 | 1.18613 | ||||||||
\(781\) | −5.95068e165 | −0.279983 | ||||||||
\(782\) | 1.42853e164 | 0.00624457 | ||||||||
\(783\) | −4.60709e166 | −1.87122 | ||||||||
\(784\) | 3.98142e166 | 1.50267 | ||||||||
\(785\) | 3.44899e166 | 1.20973 | ||||||||
\(786\) | −1.96749e164 | −0.00641380 | ||||||||
\(787\) | −3.70181e166 | −1.12167 | −0.560837 | − | 0.827926i | \(-0.689521\pi\) | ||||
−0.560837 | + | 0.827926i | \(0.689521\pi\) | |||||||
\(788\) | −1.04785e165 | −0.0295148 | ||||||||
\(789\) | −6.69796e166 | −1.75394 | ||||||||
\(790\) | −4.23030e164 | −0.0102994 | ||||||||
\(791\) | 7.54563e166 | 1.70824 | ||||||||
\(792\) | −1.57135e163 | −0.000330807 0 | ||||||||
\(793\) | −3.01071e166 | −0.589469 | ||||||||
\(794\) | −3.64384e164 | −0.00663561 | ||||||||
\(795\) | −8.43873e166 | −1.42944 | ||||||||
\(796\) | −2.07212e166 | −0.326523 | ||||||||
\(797\) | 2.81578e166 | 0.412806 | 0.206403 | − | 0.978467i | \(-0.433824\pi\) | ||||
0.206403 | + | 0.978467i | \(0.433824\pi\) | |||||||
\(798\) | 9.54678e164 | 0.0130224 | ||||||||
\(799\) | 2.36848e166 | 0.300628 | ||||||||
\(800\) | 2.02047e164 | 0.00238659 | ||||||||
\(801\) | −6.71684e165 | −0.0738406 | ||||||||
\(802\) | 9.04403e164 | 0.00925414 | ||||||||
\(803\) | 4.01830e166 | 0.382735 | ||||||||
\(804\) | 1.08572e165 | 0.00962706 | ||||||||
\(805\) | −1.77245e167 | −1.46322 | ||||||||
\(806\) | 5.82771e164 | 0.00447954 | ||||||||
\(807\) | −9.05209e166 | −0.647919 | ||||||||
\(808\) | −2.76482e165 | −0.0184295 | ||||||||
\(809\) | 3.11134e167 | 1.93156 | 0.965779 | − | 0.259367i | \(-0.0835140\pi\) | ||||
0.965779 | + | 0.259367i | \(0.0835140\pi\) | |||||||
\(810\) | 1.20710e165 | 0.00697998 | ||||||||
\(811\) | −2.71844e166 | −0.146427 | −0.0732133 | − | 0.997316i | \(-0.523325\pi\) | ||||
−0.0732133 | + | 0.997316i | \(0.523325\pi\) | |||||||
\(812\) | 5.71275e167 | 2.86664 | ||||||||
\(813\) | −6.71126e166 | −0.313760 | ||||||||
\(814\) | 2.76921e164 | 0.00120629 | ||||||||
\(815\) | 2.37587e167 | 0.964408 | ||||||||
\(816\) | −2.04631e167 | −0.774082 | ||||||||
\(817\) | −1.50181e167 | −0.529476 | ||||||||
\(818\) | 5.03445e164 | 0.00165439 | ||||||||
\(819\) | −4.81879e166 | −0.147609 | ||||||||
\(820\) | −5.15838e167 | −1.47305 | ||||||||
\(821\) | −4.32991e167 | −1.15278 | −0.576391 | − | 0.817174i | \(-0.695539\pi\) | ||||
−0.576391 | + | 0.817174i | \(0.695539\pi\) | |||||||
\(822\) | 1.21778e165 | 0.00302302 | ||||||||
\(823\) | 2.56133e167 | 0.592891 | 0.296446 | − | 0.955050i | \(-0.404199\pi\) | ||||
0.296446 | + | 0.955050i | \(0.404199\pi\) | |||||||
\(824\) | −1.26754e166 | −0.0273619 | ||||||||
\(825\) | 1.37858e166 | 0.0277542 | ||||||||
\(826\) | −1.48907e165 | −0.00279616 | ||||||||
\(827\) | 4.60673e167 | 0.806912 | 0.403456 | − | 0.914999i | \(-0.367809\pi\) | ||||
0.403456 | + | 0.914999i | \(0.367809\pi\) | |||||||
\(828\) | −4.28870e166 | −0.0700779 | ||||||||
\(829\) | −5.24129e167 | −0.799010 | −0.399505 | − | 0.916731i | \(-0.630818\pi\) | ||||
−0.399505 | + | 0.916731i | \(0.630818\pi\) | |||||||
\(830\) | −2.87566e165 | −0.00409023 | ||||||||
\(831\) | −1.96517e167 | −0.260821 | ||||||||
\(832\) | −1.04742e168 | −1.29727 | ||||||||
\(833\) | 1.04497e168 | 1.20786 | ||||||||
\(834\) | 5.42688e165 | 0.00585467 | ||||||||
\(835\) | 5.07427e167 | 0.510977 | ||||||||
\(836\) | −3.29105e167 | −0.309367 | ||||||||
\(837\) | −5.09551e167 | −0.447171 | ||||||||
\(838\) | −5.98485e165 | −0.00490368 | ||||||||
\(839\) | −3.73650e167 | −0.285859 | −0.142930 | − | 0.989733i | \(-0.545652\pi\) | ||||
−0.142930 | + | 0.989733i | \(0.545652\pi\) | |||||||
\(840\) | −3.22688e166 | −0.0230528 | ||||||||
\(841\) | 3.42285e168 | 2.28359 | ||||||||
\(842\) | 2.16192e166 | 0.0134709 | ||||||||
\(843\) | 1.98262e168 | 1.15386 | ||||||||
\(844\) | −1.23743e168 | −0.672711 | ||||||||
\(845\) | 1.27820e168 | 0.649141 | ||||||||
\(846\) | 4.51816e164 | 0.000214371 0 | ||||||||
\(847\) | −3.27148e168 | −1.45027 | ||||||||
\(848\) | 3.77468e168 | 1.56357 | ||||||||
\(849\) | −2.86744e168 | −1.10994 | ||||||||
\(850\) | 1.76747e165 | 0.000639388 0 | ||||||||
\(851\) | 1.51165e168 | 0.511095 | ||||||||
\(852\) | −2.95685e168 | −0.934442 | ||||||||
\(853\) | −3.79346e168 | −1.12064 | −0.560321 | − | 0.828276i | \(-0.689322\pi\) | ||||
−0.560321 | + | 0.828276i | \(0.689322\pi\) | |||||||
\(854\) | 2.07413e166 | 0.00572807 | ||||||||
\(855\) | −2.83179e167 | −0.0731154 | ||||||||
\(856\) | 8.13058e166 | 0.0196282 | ||||||||
\(857\) | 6.21573e168 | 1.40312 | 0.701560 | − | 0.712610i | \(-0.252487\pi\) | ||||
0.701560 | + | 0.712610i | \(0.252487\pi\) | |||||||
\(858\) | 1.36263e166 | 0.00287647 | ||||||||
\(859\) | −8.56154e168 | −1.69023 | −0.845113 | − | 0.534587i | \(-0.820467\pi\) | ||||
−0.845113 | + | 0.534587i | \(0.820467\pi\) | |||||||
\(860\) | 2.53803e168 | 0.468636 | ||||||||
\(861\) | −1.37020e169 | −2.36648 | ||||||||
\(862\) | 2.38868e166 | 0.00385914 | ||||||||
\(863\) | 5.82180e168 | 0.879907 | 0.439953 | − | 0.898021i | \(-0.354995\pi\) | ||||
0.439953 | + | 0.898021i | \(0.354995\pi\) | |||||||
\(864\) | −1.74619e167 | −0.0246917 | ||||||||
\(865\) | 9.29469e168 | 1.22973 | ||||||||
\(866\) | −1.32961e166 | −0.00164606 | ||||||||
\(867\) | 2.94487e168 | 0.341168 | ||||||||
\(868\) | 6.31839e168 | 0.685050 | ||||||||
\(869\) | 3.87365e168 | 0.393082 | ||||||||
\(870\) | −1.38999e167 | −0.0132025 | ||||||||
\(871\) | 1.45868e167 | 0.0129693 | ||||||||
\(872\) | −2.80445e167 | −0.0233426 | ||||||||
\(873\) | −3.26883e166 | −0.00254726 | ||||||||
\(874\) | 1.14153e167 | 0.00832878 | ||||||||
\(875\) | −2.41643e169 | −1.65087 | ||||||||
\(876\) | 1.99666e169 | 1.27737 | ||||||||
\(877\) | 7.89824e168 | 0.473210 | 0.236605 | − | 0.971606i | \(-0.423965\pi\) | ||||
0.236605 | + | 0.971606i | \(0.423965\pi\) | |||||||
\(878\) | 1.60271e167 | 0.00899331 | ||||||||
\(879\) | 7.89850e168 | 0.415130 | ||||||||
\(880\) | 5.56146e168 | 0.273801 | ||||||||
\(881\) | 4.01189e168 | 0.185027 | 0.0925133 | − | 0.995711i | \(-0.470510\pi\) | ||||
0.0925133 | + | 0.995711i | \(0.470510\pi\) | |||||||
\(882\) | 1.99341e166 | 0.000861299 0 | ||||||||
\(883\) | −7.29233e167 | −0.0295206 | −0.0147603 | − | 0.999891i | \(-0.504699\pi\) | ||||
−0.0147603 | + | 0.999891i | \(0.504699\pi\) | |||||||
\(884\) | −2.74943e169 | −1.04289 | ||||||||
\(885\) | −5.70196e168 | −0.202669 | ||||||||
\(886\) | −4.12350e167 | −0.0137350 | ||||||||
\(887\) | −1.65482e169 | −0.516585 | −0.258292 | − | 0.966067i | \(-0.583160\pi\) | ||||
−0.258292 | + | 0.966067i | \(0.583160\pi\) | |||||||
\(888\) | 2.75208e167 | 0.00805222 | ||||||||
\(889\) | −5.33801e169 | −1.46396 | ||||||||
\(890\) | −3.02142e167 | −0.00776757 | ||||||||
\(891\) | −1.10533e169 | −0.266393 | ||||||||
\(892\) | 2.63984e169 | 0.596484 | ||||||||
\(893\) | 1.89264e169 | 0.400967 | ||||||||
\(894\) | 4.05531e167 | 0.00805596 | ||||||||
\(895\) | −8.24024e169 | −1.53502 | ||||||||
\(896\) | 2.88698e168 | 0.0504351 | ||||||||
\(897\) | 7.43833e169 | 1.21874 | ||||||||
\(898\) | −7.33880e165 | −0.000112781 0 | ||||||||
\(899\) | 5.44353e169 | 0.784690 | ||||||||
\(900\) | −5.30625e167 | −0.00717535 | ||||||||
\(901\) | 9.90713e169 | 1.25682 | ||||||||
\(902\) | −3.00137e167 | −0.00357227 | ||||||||
\(903\) | 6.74168e169 | 0.752874 | ||||||||
\(904\) | 1.64262e168 | 0.0172128 | ||||||||
\(905\) | −7.64107e169 | −0.751382 | ||||||||
\(906\) | 1.05873e168 | 0.00977047 | ||||||||
\(907\) | 9.78926e169 | 0.847873 | 0.423937 | − | 0.905692i | \(-0.360648\pi\) | ||||
0.423937 | + | 0.905692i | \(0.360648\pi\) | |||||||
\(908\) | −2.32932e170 | −1.89362 | ||||||||
\(909\) | 1.08917e169 | 0.0831139 | ||||||||
\(910\) | −2.16762e168 | −0.0155276 | ||||||||
\(911\) | 2.27135e170 | 1.52749 | 0.763744 | − | 0.645519i | \(-0.223359\pi\) | ||||
0.763744 | + | 0.645519i | \(0.223359\pi\) | |||||||
\(912\) | −1.63519e170 | −1.03244 | ||||||||
\(913\) | 2.63322e169 | 0.156105 | ||||||||
\(914\) | 6.59356e167 | 0.00367040 | ||||||||
\(915\) | 7.94228e169 | 0.415176 | ||||||||
\(916\) | 6.92716e169 | 0.340068 | ||||||||
\(917\) | −2.86593e170 | −1.32138 | ||||||||
\(918\) | −1.52753e168 | −0.00661510 | ||||||||
\(919\) | 1.31904e170 | 0.536558 | 0.268279 | − | 0.963341i | \(-0.413545\pi\) | ||||
0.268279 | + | 0.963341i | \(0.413545\pi\) | |||||||
\(920\) | −3.85846e168 | −0.0147440 | ||||||||
\(921\) | −3.45064e170 | −1.23871 | ||||||||
\(922\) | −1.16394e168 | −0.00392557 | ||||||||
\(923\) | −3.97259e170 | −1.25885 | ||||||||
\(924\) | 1.47736e170 | 0.439895 | ||||||||
\(925\) | 1.87031e169 | 0.0523316 | ||||||||
\(926\) | −1.19935e168 | −0.00315365 | ||||||||
\(927\) | 4.99334e169 | 0.123398 | ||||||||
\(928\) | 1.86545e169 | 0.0433285 | ||||||||
\(929\) | −6.52268e170 | −1.42404 | −0.712021 | − | 0.702158i | \(-0.752220\pi\) | ||||
−0.712021 | + | 0.702158i | \(0.752220\pi\) | |||||||
\(930\) | −1.53735e168 | −0.00315503 | ||||||||
\(931\) | 8.35032e170 | 1.61100 | ||||||||
\(932\) | 3.59671e170 | 0.652365 | ||||||||
\(933\) | 9.37735e170 | 1.59914 | ||||||||
\(934\) | −4.05645e168 | −0.00650431 | ||||||||
\(935\) | 1.45968e170 | 0.220084 | ||||||||
\(936\) | −1.04901e168 | −0.00148737 | ||||||||
\(937\) | 4.54488e170 | 0.606033 | 0.303016 | − | 0.952985i | \(-0.402006\pi\) | ||||
0.303016 | + | 0.952985i | \(0.402006\pi\) | |||||||
\(938\) | −1.00491e167 | −0.000126027 0 | ||||||||
\(939\) | 4.22002e170 | 0.497786 | ||||||||
\(940\) | −3.19852e170 | −0.354893 | ||||||||
\(941\) | −1.60984e171 | −1.68028 | −0.840138 | − | 0.542373i | \(-0.817526\pi\) | ||||
−0.840138 | + | 0.542373i | \(0.817526\pi\) | |||||||
\(942\) | 9.97151e168 | 0.00979116 | ||||||||
\(943\) | −1.63839e171 | −1.51354 | ||||||||
\(944\) | 2.55051e170 | 0.221686 | ||||||||
\(945\) | 1.89528e171 | 1.55004 | ||||||||
\(946\) | 1.47674e168 | 0.00113648 | ||||||||
\(947\) | −2.25031e171 | −1.62974 | −0.814870 | − | 0.579644i | \(-0.803191\pi\) | ||||
−0.814870 | + | 0.579644i | \(0.803191\pi\) | |||||||
\(948\) | 1.92479e171 | 1.31191 | ||||||||
\(949\) | 2.68256e171 | 1.72084 | ||||||||
\(950\) | 1.41238e168 | 0.000852793 0 | ||||||||
\(951\) | −3.24648e171 | −1.84516 | ||||||||
\(952\) | 3.78838e169 | 0.0202688 | ||||||||
\(953\) | −3.01429e171 | −1.51825 | −0.759126 | − | 0.650944i | \(-0.774373\pi\) | ||||
−0.759126 | + | 0.650944i | \(0.774373\pi\) | |||||||
\(954\) | 1.88991e168 | 0.000896207 0 | ||||||||
\(955\) | −2.07596e170 | −0.0926884 | ||||||||
\(956\) | −2.44248e171 | −1.02684 | ||||||||
\(957\) | 1.27280e171 | 0.503877 | ||||||||
\(958\) | −1.80460e169 | −0.00672765 | ||||||||
\(959\) | 1.77388e171 | 0.622808 | ||||||||
\(960\) | 2.76310e171 | 0.913692 | ||||||||
\(961\) | −2.60860e171 | −0.812480 | ||||||||
\(962\) | 1.84868e169 | 0.00542370 | ||||||||
\(963\) | −3.20297e170 | −0.0885199 | ||||||||
\(964\) | 2.89502e171 | 0.753742 | ||||||||
\(965\) | 4.28551e171 | 1.05119 | ||||||||
\(966\) | −5.12438e169 | −0.0118429 | ||||||||
\(967\) | 1.35320e171 | 0.294673 | 0.147337 | − | 0.989086i | \(-0.452930\pi\) | ||||
0.147337 | + | 0.989086i | \(0.452930\pi\) | |||||||
\(968\) | −7.12174e169 | −0.0146135 | ||||||||
\(969\) | −4.29177e171 | −0.829888 | ||||||||
\(970\) | −1.47041e168 | −0.000267956 0 | ||||||||
\(971\) | 4.11549e171 | 0.706832 | 0.353416 | − | 0.935466i | \(-0.385020\pi\) | ||||
0.353416 | + | 0.935466i | \(0.385020\pi\) | |||||||
\(972\) | 8.86423e170 | 0.143493 | ||||||||
\(973\) | 7.90503e171 | 1.20619 | ||||||||
\(974\) | −2.26865e169 | −0.00326307 | ||||||||
\(975\) | 9.20317e170 | 0.124788 | ||||||||
\(976\) | −3.55262e171 | −0.454134 | ||||||||
\(977\) | −7.47661e171 | −0.901088 | −0.450544 | − | 0.892754i | \(-0.648770\pi\) | ||||
−0.450544 | + | 0.892754i | \(0.648770\pi\) | |||||||
\(978\) | 6.86898e169 | 0.00780563 | ||||||||
\(979\) | 2.76668e171 | 0.296452 | ||||||||
\(980\) | −1.41119e172 | −1.42589 | ||||||||
\(981\) | 1.10479e171 | 0.105271 | ||||||||
\(982\) | −2.61654e169 | −0.00235134 | ||||||||
\(983\) | −5.23743e171 | −0.443906 | −0.221953 | − | 0.975057i | \(-0.571243\pi\) | ||||
−0.221953 | + | 0.975057i | \(0.571243\pi\) | |||||||
\(984\) | −2.98281e170 | −0.0238456 | ||||||||
\(985\) | 3.71379e170 | 0.0280049 | ||||||||
\(986\) | 1.63186e170 | 0.0116081 | ||||||||
\(987\) | −8.49612e171 | −0.570144 | ||||||||
\(988\) | −2.19706e172 | −1.39097 | ||||||||
\(989\) | 8.06120e171 | 0.481518 | ||||||||
\(990\) | 2.78451e168 | 0.000156937 0 | ||||||||
\(991\) | 2.83687e172 | 1.50870 | 0.754351 | − | 0.656471i | \(-0.227952\pi\) | ||||
0.754351 | + | 0.656471i | \(0.227952\pi\) | |||||||
\(992\) | 2.06321e170 | 0.0103544 | ||||||||
\(993\) | 8.01468e171 | 0.379581 | ||||||||
\(994\) | 2.73678e170 | 0.0122327 | ||||||||
\(995\) | 7.34404e171 | 0.309819 | ||||||||
\(996\) | 1.30843e172 | 0.520999 | ||||||||
\(997\) | −2.05510e172 | −0.772436 | −0.386218 | − | 0.922408i | \(-0.626219\pi\) | ||||
−0.386218 | + | 0.922408i | \(0.626219\pi\) | |||||||
\(998\) | 1.87259e169 | 0.000664412 0 | ||||||||
\(999\) | −1.61641e172 | −0.541423 |
(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 | 1.116.a.a.1.5 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.116.a.a.1.5 | ✓ | 9 | 1.1 | even | 1 | trivial |