Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,74,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 74, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 74);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 74 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(67.4967947474\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 413501459186944860372404680x - 2966140105783309949999568694815716833028 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{23}\cdot 3^{7}\cdot 5^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.32599e13\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.87195e10 | −0.707107 | ||||||||
\(3\) | 3.00585e17 | 1.15622 | 0.578111 | − | 0.815958i | \(-0.303790\pi\) | ||||
0.578111 | + | 0.815958i | \(0.303790\pi\) | |||||||
\(4\) | 4.72237e21 | 0.500000 | ||||||||
\(5\) | −1.10375e25 | −0.339206 | −0.169603 | − | 0.985512i | \(-0.554249\pi\) | ||||
−0.169603 | + | 0.985512i | \(0.554249\pi\) | |||||||
\(6\) | −2.06560e28 | −0.817572 | ||||||||
\(7\) | 7.83423e29 | 0.111665 | 0.0558326 | − | 0.998440i | \(-0.482219\pi\) | ||||
0.0558326 | + | 0.998440i | \(0.482219\pi\) | |||||||
\(8\) | −3.24519e32 | −0.353553 | ||||||||
\(9\) | 2.27660e34 | 0.336848 | ||||||||
\(10\) | 7.58489e35 | 0.239855 | ||||||||
\(11\) | 3.40887e36 | 0.0332489 | 0.0166245 | − | 0.999862i | \(-0.494708\pi\) | ||||
0.0166245 | + | 0.999862i | \(0.494708\pi\) | |||||||
\(12\) | 1.41947e39 | 0.578111 | ||||||||
\(13\) | 3.80927e40 | 0.835429 | 0.417714 | − | 0.908578i | \(-0.362831\pi\) | ||||
0.417714 | + | 0.908578i | \(0.362831\pi\) | |||||||
\(14\) | −5.38364e40 | −0.0789592 | ||||||||
\(15\) | −3.31769e42 | −0.392198 | ||||||||
\(16\) | 2.23007e43 | 0.250000 | ||||||||
\(17\) | −2.38211e44 | −0.292130 | −0.146065 | − | 0.989275i | \(-0.546661\pi\) | ||||
−0.146065 | + | 0.989275i | \(0.546661\pi\) | |||||||
\(18\) | −1.56447e45 | −0.238188 | ||||||||
\(19\) | −4.58511e46 | −0.970160 | −0.485080 | − | 0.874470i | \(-0.661210\pi\) | ||||
−0.485080 | + | 0.874470i | \(0.661210\pi\) | |||||||
\(20\) | −5.21229e46 | −0.169603 | ||||||||
\(21\) | 2.35485e47 | 0.129110 | ||||||||
\(22\) | −2.34256e47 | −0.0235105 | ||||||||
\(23\) | −5.99384e49 | −1.18752 | −0.593758 | − | 0.804644i | \(-0.702356\pi\) | ||||
−0.593758 | + | 0.804644i | \(0.702356\pi\) | |||||||
\(24\) | −9.75453e49 | −0.408786 | ||||||||
\(25\) | −9.36966e50 | −0.884939 | ||||||||
\(26\) | −2.61771e51 | −0.590737 | ||||||||
\(27\) | −1.34720e52 | −0.766750 | ||||||||
\(28\) | 3.69961e51 | 0.0558326 | ||||||||
\(29\) | 3.66647e53 | 1.53717 | 0.768583 | − | 0.639750i | \(-0.220962\pi\) | ||||
0.768583 | + | 0.639750i | \(0.220962\pi\) | |||||||
\(30\) | 2.27990e53 | 0.277326 | ||||||||
\(31\) | 1.75180e54 | 0.643847 | 0.321924 | − | 0.946766i | \(-0.395671\pi\) | ||||
0.321924 | + | 0.946766i | \(0.395671\pi\) | |||||||
\(32\) | −1.53250e54 | −0.176777 | ||||||||
\(33\) | 1.02465e54 | 0.0384431 | ||||||||
\(34\) | 1.63697e55 | 0.206567 | ||||||||
\(35\) | −8.64700e54 | −0.0378776 | ||||||||
\(36\) | 1.07509e56 | 0.168424 | ||||||||
\(37\) | 1.64193e57 | 0.946217 | 0.473109 | − | 0.881004i | \(-0.343132\pi\) | ||||
0.473109 | + | 0.881004i | \(0.343132\pi\) | |||||||
\(38\) | 3.15086e57 | 0.686007 | ||||||||
\(39\) | 1.14501e58 | 0.965941 | ||||||||
\(40\) | 3.58186e57 | 0.119928 | ||||||||
\(41\) | 1.95654e58 | 0.265998 | 0.132999 | − | 0.991116i | \(-0.457539\pi\) | ||||
0.132999 | + | 0.991116i | \(0.457539\pi\) | |||||||
\(42\) | −1.61824e58 | −0.0912944 | ||||||||
\(43\) | −7.77238e59 | −1.85761 | −0.928806 | − | 0.370565i | \(-0.879164\pi\) | ||||
−0.928806 | + | 0.370565i | \(0.879164\pi\) | |||||||
\(44\) | 1.60979e58 | 0.0166245 | ||||||||
\(45\) | −2.51279e59 | −0.114261 | ||||||||
\(46\) | 4.11894e60 | 0.839700 | ||||||||
\(47\) | −5.34256e60 | −0.496795 | −0.248398 | − | 0.968658i | \(-0.579904\pi\) | ||||
−0.248398 | + | 0.968658i | \(0.579904\pi\) | |||||||
\(48\) | 6.70326e60 | 0.289055 | ||||||||
\(49\) | −4.86080e61 | −0.987531 | ||||||||
\(50\) | 6.43878e61 | 0.625746 | ||||||||
\(51\) | −7.16026e61 | −0.337767 | ||||||||
\(52\) | 1.79888e62 | 0.417714 | ||||||||
\(53\) | 5.17851e62 | 0.599979 | 0.299989 | − | 0.953943i | \(-0.403017\pi\) | ||||
0.299989 | + | 0.953943i | \(0.403017\pi\) | |||||||
\(54\) | 9.25787e62 | 0.542174 | ||||||||
\(55\) | −3.76253e61 | −0.0112782 | ||||||||
\(56\) | −2.54235e62 | −0.0394796 | ||||||||
\(57\) | −1.37821e64 | −1.12172 | ||||||||
\(58\) | −2.51958e64 | −1.08694 | ||||||||
\(59\) | −1.88861e63 | −0.0436560 | −0.0218280 | − | 0.999762i | \(-0.506949\pi\) | ||||
−0.0218280 | + | 0.999762i | \(0.506949\pi\) | |||||||
\(60\) | −1.56674e64 | −0.196099 | ||||||||
\(61\) | 1.49443e65 | 1.02315 | 0.511573 | − | 0.859240i | \(-0.329063\pi\) | ||||
0.511573 | + | 0.859240i | \(0.329063\pi\) | |||||||
\(62\) | −1.20383e65 | −0.455269 | ||||||||
\(63\) | 1.78354e64 | 0.0376143 | ||||||||
\(64\) | 1.05312e65 | 0.125000 | ||||||||
\(65\) | −4.20447e65 | −0.283383 | ||||||||
\(66\) | −7.04137e64 | −0.0271834 | ||||||||
\(67\) | −8.11124e66 | −1.80866 | −0.904330 | − | 0.426834i | \(-0.859629\pi\) | ||||
−0.904330 | + | 0.426834i | \(0.859629\pi\) | |||||||
\(68\) | −1.12492e66 | −0.146065 | ||||||||
\(69\) | −1.80166e67 | −1.37303 | ||||||||
\(70\) | 5.94218e65 | 0.0267835 | ||||||||
\(71\) | −2.29663e67 | −0.616823 | −0.308412 | − | 0.951253i | \(-0.599797\pi\) | ||||
−0.308412 | + | 0.951253i | \(0.599797\pi\) | |||||||
\(72\) | −7.38798e66 | −0.119094 | ||||||||
\(73\) | −1.30543e68 | −1.27195 | −0.635974 | − | 0.771711i | \(-0.719401\pi\) | ||||
−0.635974 | + | 0.771711i | \(0.719401\pi\) | |||||||
\(74\) | −1.12832e68 | −0.669077 | ||||||||
\(75\) | −2.81638e68 | −1.02319 | ||||||||
\(76\) | −2.16526e68 | −0.485080 | ||||||||
\(77\) | 2.67059e66 | 0.00371275 | ||||||||
\(78\) | −7.86844e68 | −0.683023 | ||||||||
\(79\) | −7.20690e67 | −0.0392970 | −0.0196485 | − | 0.999807i | \(-0.506255\pi\) | ||||
−0.0196485 | + | 0.999807i | \(0.506255\pi\) | |||||||
\(80\) | −2.46144e68 | −0.0848016 | ||||||||
\(81\) | −5.58811e69 | −1.22338 | ||||||||
\(82\) | −1.34452e69 | −0.188089 | ||||||||
\(83\) | −1.10136e70 | −0.989876 | −0.494938 | − | 0.868928i | \(-0.664809\pi\) | ||||
−0.494938 | + | 0.868928i | \(0.664809\pi\) | |||||||
\(84\) | 1.11205e69 | 0.0645549 | ||||||||
\(85\) | 2.62925e69 | 0.0990924 | ||||||||
\(86\) | 5.34114e70 | 1.31353 | ||||||||
\(87\) | 1.10208e71 | 1.77731 | ||||||||
\(88\) | −1.10624e69 | −0.0117553 | ||||||||
\(89\) | 1.46084e71 | 1.02770 | 0.513851 | − | 0.857879i | \(-0.328218\pi\) | ||||
0.513851 | + | 0.857879i | \(0.328218\pi\) | |||||||
\(90\) | 1.72677e70 | 0.0807949 | ||||||||
\(91\) | 2.98427e70 | 0.0932883 | ||||||||
\(92\) | −2.83051e71 | −0.593758 | ||||||||
\(93\) | 5.26565e71 | 0.744430 | ||||||||
\(94\) | 3.67138e71 | 0.351287 | ||||||||
\(95\) | 5.06080e71 | 0.329085 | ||||||||
\(96\) | −4.60645e71 | −0.204393 | ||||||||
\(97\) | 7.46916e71 | 0.227040 | 0.113520 | − | 0.993536i | \(-0.463787\pi\) | ||||
0.113520 | + | 0.993536i | \(0.463787\pi\) | |||||||
\(98\) | 3.34032e72 | 0.698290 | ||||||||
\(99\) | 7.76062e70 | 0.0111998 | ||||||||
\(100\) | −4.42469e72 | −0.442469 | ||||||||
\(101\) | −2.51591e73 | −1.74971 | −0.874854 | − | 0.484387i | \(-0.839043\pi\) | ||||
−0.874854 | + | 0.484387i | \(0.839043\pi\) | |||||||
\(102\) | 4.92049e72 | 0.238837 | ||||||||
\(103\) | −2.90445e73 | −0.987428 | −0.493714 | − | 0.869624i | \(-0.664361\pi\) | ||||
−0.493714 | + | 0.869624i | \(0.664361\pi\) | |||||||
\(104\) | −1.23618e73 | −0.295369 | ||||||||
\(105\) | −2.59916e72 | −0.0437949 | ||||||||
\(106\) | −3.55865e73 | −0.424249 | ||||||||
\(107\) | −5.02253e73 | −0.425025 | −0.212513 | − | 0.977158i | \(-0.568165\pi\) | ||||
−0.212513 | + | 0.977158i | \(0.568165\pi\) | |||||||
\(108\) | −6.36196e73 | −0.383375 | ||||||||
\(109\) | 1.37500e73 | 0.0591885 | 0.0295942 | − | 0.999562i | \(-0.490578\pi\) | ||||
0.0295942 | + | 0.999562i | \(0.490578\pi\) | |||||||
\(110\) | 2.58559e72 | 0.00797492 | ||||||||
\(111\) | 4.93538e74 | 1.09404 | ||||||||
\(112\) | 1.74709e73 | 0.0279163 | ||||||||
\(113\) | 2.27517e74 | 0.262816 | 0.131408 | − | 0.991328i | \(-0.458050\pi\) | ||||
0.131408 | + | 0.991328i | \(0.458050\pi\) | |||||||
\(114\) | 9.47102e74 | 0.793176 | ||||||||
\(115\) | 6.61568e74 | 0.402813 | ||||||||
\(116\) | 1.73144e75 | 0.768583 | ||||||||
\(117\) | 8.67217e74 | 0.281413 | ||||||||
\(118\) | 1.29784e74 | 0.0308694 | ||||||||
\(119\) | −1.86620e74 | −0.0326208 | ||||||||
\(120\) | 1.07665e75 | 0.138663 | ||||||||
\(121\) | −1.04999e76 | −0.998895 | ||||||||
\(122\) | −1.02697e76 | −0.723473 | ||||||||
\(123\) | 5.88106e75 | 0.307552 | ||||||||
\(124\) | 8.27265e75 | 0.321924 | ||||||||
\(125\) | 2.20281e76 | 0.639383 | ||||||||
\(126\) | −1.22564e75 | −0.0265973 | ||||||||
\(127\) | −3.15624e76 | −0.513256 | −0.256628 | − | 0.966510i | \(-0.582611\pi\) | ||||
−0.256628 | + | 0.966510i | \(0.582611\pi\) | |||||||
\(128\) | −7.23701e75 | −0.0883883 | ||||||||
\(129\) | −2.33626e77 | −2.14781 | ||||||||
\(130\) | 2.88929e76 | 0.200382 | ||||||||
\(131\) | −2.21932e77 | −1.16364 | −0.581820 | − | 0.813318i | \(-0.697659\pi\) | ||||
−0.581820 | + | 0.813318i | \(0.697659\pi\) | |||||||
\(132\) | 4.83879e75 | 0.0192216 | ||||||||
\(133\) | −3.59208e76 | −0.108333 | ||||||||
\(134\) | 5.57400e77 | 1.27892 | ||||||||
\(135\) | 1.48696e77 | 0.260087 | ||||||||
\(136\) | 7.73039e76 | 0.103284 | ||||||||
\(137\) | 1.27232e78 | 1.30105 | 0.650526 | − | 0.759484i | \(-0.274549\pi\) | ||||
0.650526 | + | 0.759484i | \(0.274549\pi\) | |||||||
\(138\) | 1.23809e78 | 0.970880 | ||||||||
\(139\) | −5.43939e75 | −0.00327726 | −0.00163863 | − | 0.999999i | \(-0.500522\pi\) | ||||
−0.00163863 | + | 0.999999i | \(0.500522\pi\) | |||||||
\(140\) | −4.08343e76 | −0.0189388 | ||||||||
\(141\) | −1.60589e78 | −0.574405 | ||||||||
\(142\) | 1.57823e78 | 0.436160 | ||||||||
\(143\) | 1.29853e77 | 0.0277771 | ||||||||
\(144\) | 5.07698e77 | 0.0842121 | ||||||||
\(145\) | −4.04685e78 | −0.521417 | ||||||||
\(146\) | 8.97085e78 | 0.899403 | ||||||||
\(147\) | −1.46108e79 | −1.14180 | ||||||||
\(148\) | 7.75378e78 | 0.473109 | ||||||||
\(149\) | −3.22048e79 | −1.53682 | −0.768408 | − | 0.639960i | \(-0.778951\pi\) | ||||
−0.768408 | + | 0.639960i | \(0.778951\pi\) | |||||||
\(150\) | 1.93540e79 | 0.723501 | ||||||||
\(151\) | −5.09160e79 | −1.49347 | −0.746734 | − | 0.665123i | \(-0.768379\pi\) | ||||
−0.746734 | + | 0.665123i | \(0.768379\pi\) | |||||||
\(152\) | 1.48795e79 | 0.343003 | ||||||||
\(153\) | −5.42311e78 | −0.0984036 | ||||||||
\(154\) | −1.83521e77 | −0.00262531 | ||||||||
\(155\) | −1.93354e79 | −0.218397 | ||||||||
\(156\) | 5.40715e79 | 0.482970 | ||||||||
\(157\) | −4.68516e79 | −0.331427 | −0.165713 | − | 0.986174i | \(-0.552993\pi\) | ||||
−0.165713 | + | 0.986174i | \(0.552993\pi\) | |||||||
\(158\) | 4.95254e78 | 0.0277872 | ||||||||
\(159\) | 1.55658e80 | 0.693709 | ||||||||
\(160\) | 1.69149e79 | 0.0599638 | ||||||||
\(161\) | −4.69572e79 | −0.132604 | ||||||||
\(162\) | 3.84012e80 | 0.865061 | ||||||||
\(163\) | −5.74321e79 | −0.103349 | −0.0516746 | − | 0.998664i | \(-0.516456\pi\) | ||||
−0.0516746 | + | 0.998664i | \(0.516456\pi\) | |||||||
\(164\) | 9.23950e79 | 0.132999 | ||||||||
\(165\) | −1.13096e79 | −0.0130401 | ||||||||
\(166\) | 7.56852e80 | 0.699948 | ||||||||
\(167\) | 1.49912e81 | 1.11349 | 0.556743 | − | 0.830685i | \(-0.312051\pi\) | ||||
0.556743 | + | 0.830685i | \(0.312051\pi\) | |||||||
\(168\) | −7.64193e79 | −0.0456472 | ||||||||
\(169\) | −6.27995e80 | −0.302059 | ||||||||
\(170\) | −1.80680e80 | −0.0700689 | ||||||||
\(171\) | −1.04385e81 | −0.326797 | ||||||||
\(172\) | −3.67040e81 | −0.928806 | ||||||||
\(173\) | −3.84638e81 | −0.787716 | −0.393858 | − | 0.919171i | \(-0.628860\pi\) | ||||
−0.393858 | + | 0.919171i | \(0.628860\pi\) | |||||||
\(174\) | −7.57346e81 | −1.25674 | ||||||||
\(175\) | −7.34041e80 | −0.0988169 | ||||||||
\(176\) | 7.60203e79 | 0.00831223 | ||||||||
\(177\) | −5.67687e80 | −0.0504760 | ||||||||
\(178\) | −1.00388e82 | −0.726695 | ||||||||
\(179\) | 2.01708e82 | 1.19011 | 0.595057 | − | 0.803684i | \(-0.297129\pi\) | ||||
0.595057 | + | 0.803684i | \(0.297129\pi\) | |||||||
\(180\) | −1.18663e81 | −0.0571306 | ||||||||
\(181\) | 2.00764e82 | 0.789621 | 0.394810 | − | 0.918763i | \(-0.370810\pi\) | ||||
0.394810 | + | 0.918763i | \(0.370810\pi\) | |||||||
\(182\) | −2.05077e81 | −0.0659648 | ||||||||
\(183\) | 4.49204e82 | 1.18298 | ||||||||
\(184\) | 1.94511e82 | 0.419850 | ||||||||
\(185\) | −1.81227e82 | −0.320963 | ||||||||
\(186\) | −3.61852e82 | −0.526392 | ||||||||
\(187\) | −8.12031e80 | −0.00971301 | ||||||||
\(188\) | −2.52295e82 | −0.248398 | ||||||||
\(189\) | −1.05543e82 | −0.0856193 | ||||||||
\(190\) | −3.47775e82 | −0.232698 | ||||||||
\(191\) | 3.45352e83 | 1.90785 | 0.953924 | − | 0.300049i | \(-0.0970031\pi\) | ||||
0.953924 | + | 0.300049i | \(0.0970031\pi\) | |||||||
\(192\) | 3.16553e82 | 0.144528 | ||||||||
\(193\) | 6.03025e82 | 0.227768 | 0.113884 | − | 0.993494i | \(-0.463671\pi\) | ||||
0.113884 | + | 0.993494i | \(0.463671\pi\) | |||||||
\(194\) | −5.13276e82 | −0.160542 | ||||||||
\(195\) | −1.26380e83 | −0.327653 | ||||||||
\(196\) | −2.29545e83 | −0.493765 | ||||||||
\(197\) | −9.47960e83 | −1.69345 | −0.846726 | − | 0.532030i | \(-0.821430\pi\) | ||||
−0.846726 | + | 0.532030i | \(0.821430\pi\) | |||||||
\(198\) | −5.33306e81 | −0.00791949 | ||||||||
\(199\) | 1.05949e83 | 0.130906 | 0.0654530 | − | 0.997856i | \(-0.479151\pi\) | ||||
0.0654530 | + | 0.997856i | \(0.479151\pi\) | |||||||
\(200\) | 3.04063e83 | 0.312873 | ||||||||
\(201\) | −2.43811e84 | −2.09121 | ||||||||
\(202\) | 1.72892e84 | 1.23723 | ||||||||
\(203\) | 2.87240e83 | 0.171648 | ||||||||
\(204\) | −3.38134e83 | −0.168884 | ||||||||
\(205\) | −2.15952e83 | −0.0902282 | ||||||||
\(206\) | 1.99592e84 | 0.698217 | ||||||||
\(207\) | −1.36456e84 | −0.400013 | ||||||||
\(208\) | 8.49496e83 | 0.208857 | ||||||||
\(209\) | −1.56300e83 | −0.0322568 | ||||||||
\(210\) | 1.78613e83 | 0.0309676 | ||||||||
\(211\) | 1.32481e85 | 1.93127 | 0.965636 | − | 0.259898i | \(-0.0836889\pi\) | ||||
0.965636 | + | 0.259898i | \(0.0836889\pi\) | |||||||
\(212\) | 2.44548e84 | 0.299989 | ||||||||
\(213\) | −6.90331e84 | −0.713184 | ||||||||
\(214\) | 3.45146e84 | 0.300538 | ||||||||
\(215\) | 8.57873e84 | 0.630114 | ||||||||
\(216\) | 4.37191e84 | 0.271087 | ||||||||
\(217\) | 1.37240e84 | 0.0718954 | ||||||||
\(218\) | −9.44896e83 | −0.0418526 | ||||||||
\(219\) | −3.92392e85 | −1.47065 | ||||||||
\(220\) | −1.77680e83 | −0.00563912 | ||||||||
\(221\) | −9.07410e84 | −0.244054 | ||||||||
\(222\) | −3.39157e85 | −0.773601 | ||||||||
\(223\) | −5.18131e85 | −1.00303 | −0.501513 | − | 0.865150i | \(-0.667223\pi\) | ||||
−0.501513 | + | 0.865150i | \(0.667223\pi\) | |||||||
\(224\) | −1.20059e84 | −0.0197398 | ||||||||
\(225\) | −2.13309e85 | −0.298090 | ||||||||
\(226\) | −1.56349e85 | −0.185839 | ||||||||
\(227\) | 1.31843e86 | 1.33387 | 0.666934 | − | 0.745117i | \(-0.267606\pi\) | ||||
0.666934 | + | 0.745117i | \(0.267606\pi\) | |||||||
\(228\) | −6.50843e85 | −0.560860 | ||||||||
\(229\) | 1.61169e86 | 1.18382 | 0.591911 | − | 0.806003i | \(-0.298374\pi\) | ||||
0.591911 | + | 0.806003i | \(0.298374\pi\) | |||||||
\(230\) | −4.54626e85 | −0.284832 | ||||||||
\(231\) | 8.02738e83 | 0.00429276 | ||||||||
\(232\) | −1.18984e86 | −0.543470 | ||||||||
\(233\) | 2.90032e86 | 1.13228 | 0.566142 | − | 0.824308i | \(-0.308435\pi\) | ||||
0.566142 | + | 0.824308i | \(0.308435\pi\) | |||||||
\(234\) | −5.95947e85 | −0.198989 | ||||||||
\(235\) | 5.89683e85 | 0.168516 | ||||||||
\(236\) | −8.91870e84 | −0.0218280 | ||||||||
\(237\) | −2.16628e85 | −0.0454361 | ||||||||
\(238\) | 1.28244e85 | 0.0230664 | ||||||||
\(239\) | −9.99267e85 | −0.154226 | −0.0771131 | − | 0.997022i | \(-0.524570\pi\) | ||||
−0.0771131 | + | 0.997022i | \(0.524570\pi\) | |||||||
\(240\) | −7.39870e85 | −0.0980495 | ||||||||
\(241\) | 9.58884e86 | 1.09180 | 0.545901 | − | 0.837850i | \(-0.316187\pi\) | ||||
0.545901 | + | 0.837850i | \(0.316187\pi\) | |||||||
\(242\) | 7.21548e86 | 0.706325 | ||||||||
\(243\) | −7.69195e86 | −0.647750 | ||||||||
\(244\) | 7.05726e86 | 0.511573 | ||||||||
\(245\) | 5.36509e86 | 0.334977 | ||||||||
\(246\) | −4.04143e86 | −0.217472 | ||||||||
\(247\) | −1.74659e87 | −0.810500 | ||||||||
\(248\) | −5.68492e86 | −0.227634 | ||||||||
\(249\) | −3.31053e87 | −1.14452 | ||||||||
\(250\) | −1.51376e87 | −0.452112 | ||||||||
\(251\) | −4.43152e87 | −1.14410 | −0.572048 | − | 0.820220i | \(-0.693851\pi\) | ||||
−0.572048 | + | 0.820220i | \(0.693851\pi\) | |||||||
\(252\) | 8.42253e85 | 0.0188071 | ||||||||
\(253\) | −2.04322e86 | −0.0394836 | ||||||||
\(254\) | 2.16895e87 | 0.362927 | ||||||||
\(255\) | 7.90311e86 | 0.114573 | ||||||||
\(256\) | 4.97323e86 | 0.0625000 | ||||||||
\(257\) | 8.23323e85 | 0.00897452 | 0.00448726 | − | 0.999990i | \(-0.498572\pi\) | ||||
0.00448726 | + | 0.999990i | \(0.498572\pi\) | |||||||
\(258\) | 1.60546e88 | 1.51873 | ||||||||
\(259\) | 1.28632e87 | 0.105660 | ||||||||
\(260\) | −1.98550e87 | −0.141691 | ||||||||
\(261\) | 8.34707e87 | 0.517792 | ||||||||
\(262\) | 1.52511e88 | 0.822818 | ||||||||
\(263\) | −7.47321e87 | −0.350851 | −0.175425 | − | 0.984493i | \(-0.556130\pi\) | ||||
−0.175425 | + | 0.984493i | \(0.556130\pi\) | |||||||
\(264\) | −3.32519e86 | −0.0135917 | ||||||||
\(265\) | −5.71577e87 | −0.203517 | ||||||||
\(266\) | 2.46846e87 | 0.0766031 | ||||||||
\(267\) | 4.39106e88 | 1.18825 | ||||||||
\(268\) | −3.83042e88 | −0.904330 | ||||||||
\(269\) | −1.88616e88 | −0.388704 | −0.194352 | − | 0.980932i | \(-0.562260\pi\) | ||||
−0.194352 | + | 0.980932i | \(0.562260\pi\) | |||||||
\(270\) | −1.02183e88 | −0.183909 | ||||||||
\(271\) | 3.28777e88 | 0.517038 | 0.258519 | − | 0.966006i | \(-0.416766\pi\) | ||||
0.258519 | + | 0.966006i | \(0.416766\pi\) | |||||||
\(272\) | −5.31229e87 | −0.0730325 | ||||||||
\(273\) | 8.97026e87 | 0.107862 | ||||||||
\(274\) | −8.74329e88 | −0.919982 | ||||||||
\(275\) | −3.19399e87 | −0.0294233 | ||||||||
\(276\) | −8.50809e88 | −0.686516 | ||||||||
\(277\) | −2.09853e89 | −1.48390 | −0.741948 | − | 0.670458i | \(-0.766098\pi\) | ||||
−0.741948 | + | 0.670458i | \(0.766098\pi\) | |||||||
\(278\) | 3.73792e86 | 0.00231737 | ||||||||
\(279\) | 3.98814e88 | 0.216879 | ||||||||
\(280\) | 2.80611e87 | 0.0133917 | ||||||||
\(281\) | 9.69508e88 | 0.406229 | 0.203114 | − | 0.979155i | \(-0.434894\pi\) | ||||
0.203114 | + | 0.979155i | \(0.434894\pi\) | |||||||
\(282\) | 1.10356e89 | 0.406166 | ||||||||
\(283\) | 3.94495e89 | 1.27596 | 0.637980 | − | 0.770053i | \(-0.279770\pi\) | ||||
0.637980 | + | 0.770053i | \(0.279770\pi\) | |||||||
\(284\) | −1.08455e89 | −0.308412 | ||||||||
\(285\) | 1.52120e89 | 0.380495 | ||||||||
\(286\) | −8.92343e87 | −0.0196414 | ||||||||
\(287\) | 1.53280e88 | 0.0297027 | ||||||||
\(288\) | −3.48888e88 | −0.0595470 | ||||||||
\(289\) | −6.08178e89 | −0.914660 | ||||||||
\(290\) | 2.78097e89 | 0.368697 | ||||||||
\(291\) | 2.24511e89 | 0.262509 | ||||||||
\(292\) | −6.16472e89 | −0.635974 | ||||||||
\(293\) | 1.44439e90 | 1.31527 | 0.657637 | − | 0.753335i | \(-0.271556\pi\) | ||||
0.657637 | + | 0.753335i | \(0.271556\pi\) | |||||||
\(294\) | 1.00405e90 | 0.807378 | ||||||||
\(295\) | 2.08454e88 | 0.0148084 | ||||||||
\(296\) | −5.32836e89 | −0.334538 | ||||||||
\(297\) | −4.59242e88 | −0.0254936 | ||||||||
\(298\) | 2.21310e90 | 1.08669 | ||||||||
\(299\) | −2.28322e90 | −0.992085 | ||||||||
\(300\) | −1.33000e90 | −0.511593 | ||||||||
\(301\) | −6.08906e89 | −0.207431 | ||||||||
\(302\) | 3.49892e90 | 1.05604 | ||||||||
\(303\) | −7.56245e90 | −2.02305 | ||||||||
\(304\) | −1.02251e90 | −0.242540 | ||||||||
\(305\) | −1.64948e90 | −0.347058 | ||||||||
\(306\) | 3.72673e89 | 0.0695819 | ||||||||
\(307\) | −5.93114e90 | −0.983077 | −0.491538 | − | 0.870856i | \(-0.663565\pi\) | ||||
−0.491538 | + | 0.870856i | \(0.663565\pi\) | |||||||
\(308\) | 1.26115e88 | 0.00185637 | ||||||||
\(309\) | −8.73034e90 | −1.14169 | ||||||||
\(310\) | 1.32872e90 | 0.154430 | ||||||||
\(311\) | 1.55230e91 | 1.60406 | 0.802031 | − | 0.597282i | \(-0.203753\pi\) | ||||
0.802031 | + | 0.597282i | \(0.203753\pi\) | |||||||
\(312\) | −3.71576e90 | −0.341512 | ||||||||
\(313\) | 2.15089e91 | 1.75893 | 0.879467 | − | 0.475960i | \(-0.157899\pi\) | ||||
0.879467 | + | 0.475960i | \(0.157899\pi\) | |||||||
\(314\) | 3.21962e90 | 0.234354 | ||||||||
\(315\) | −1.96857e89 | −0.0127590 | ||||||||
\(316\) | −3.40336e89 | −0.0196485 | ||||||||
\(317\) | 3.35164e91 | 1.72423 | 0.862114 | − | 0.506714i | \(-0.169140\pi\) | ||||
0.862114 | + | 0.506714i | \(0.169140\pi\) | |||||||
\(318\) | −1.06968e91 | −0.490526 | ||||||||
\(319\) | 1.24985e90 | 0.0511091 | ||||||||
\(320\) | −1.16238e90 | −0.0424008 | ||||||||
\(321\) | −1.50970e91 | −0.491423 | ||||||||
\(322\) | 3.22687e90 | 0.0937653 | ||||||||
\(323\) | 1.09222e91 | 0.283413 | ||||||||
\(324\) | −2.63891e91 | −0.611691 | ||||||||
\(325\) | −3.56915e91 | −0.739303 | ||||||||
\(326\) | 3.94671e90 | 0.0730790 | ||||||||
\(327\) | 4.13305e90 | 0.0684350 | ||||||||
\(328\) | −6.34934e90 | −0.0940444 | ||||||||
\(329\) | −4.18548e90 | −0.0554747 | ||||||||
\(330\) | 7.77189e89 | 0.00922078 | ||||||||
\(331\) | −1.07776e91 | −0.114499 | −0.0572493 | − | 0.998360i | \(-0.518233\pi\) | ||||
−0.0572493 | + | 0.998360i | \(0.518233\pi\) | |||||||
\(332\) | −5.20105e91 | −0.494938 | ||||||||
\(333\) | 3.73801e91 | 0.318732 | ||||||||
\(334\) | −1.03019e92 | −0.787354 | ||||||||
\(335\) | 8.95275e91 | 0.613509 | ||||||||
\(336\) | 5.25149e90 | 0.0322774 | ||||||||
\(337\) | −2.38012e92 | −1.31252 | −0.656262 | − | 0.754533i | \(-0.727863\pi\) | ||||
−0.656262 | + | 0.754533i | \(0.727863\pi\) | |||||||
\(338\) | 4.31555e91 | 0.213588 | ||||||||
\(339\) | 6.83882e91 | 0.303873 | ||||||||
\(340\) | 1.24163e91 | 0.0495462 | ||||||||
\(341\) | 5.97166e90 | 0.0214072 | ||||||||
\(342\) | 7.17325e91 | 0.231080 | ||||||||
\(343\) | −7.66421e91 | −0.221938 | ||||||||
\(344\) | 2.52228e92 | 0.656765 | ||||||||
\(345\) | 1.98857e92 | 0.465741 | ||||||||
\(346\) | 2.64321e92 | 0.556999 | ||||||||
\(347\) | 3.41200e92 | 0.647117 | 0.323559 | − | 0.946208i | \(-0.395121\pi\) | ||||
0.323559 | + | 0.946208i | \(0.395121\pi\) | |||||||
\(348\) | 5.20444e92 | 0.888653 | ||||||||
\(349\) | −5.66523e92 | −0.871143 | −0.435572 | − | 0.900154i | \(-0.643454\pi\) | ||||
−0.435572 | + | 0.900154i | \(0.643454\pi\) | |||||||
\(350\) | 5.04429e91 | 0.0698741 | ||||||||
\(351\) | −5.13184e92 | −0.640565 | ||||||||
\(352\) | −5.22408e90 | −0.00587763 | ||||||||
\(353\) | −2.42064e92 | −0.245557 | −0.122779 | − | 0.992434i | \(-0.539181\pi\) | ||||
−0.122779 | + | 0.992434i | \(0.539181\pi\) | |||||||
\(354\) | 3.90111e91 | 0.0356919 | ||||||||
\(355\) | 2.53489e92 | 0.209230 | ||||||||
\(356\) | 6.89862e92 | 0.513851 | ||||||||
\(357\) | −5.60952e91 | −0.0377169 | ||||||||
\(358\) | −1.38613e93 | −0.841538 | ||||||||
\(359\) | 4.04247e92 | 0.221666 | 0.110833 | − | 0.993839i | \(-0.464648\pi\) | ||||
0.110833 | + | 0.993839i | \(0.464648\pi\) | |||||||
\(360\) | 8.15446e91 | 0.0403974 | ||||||||
\(361\) | −1.31314e92 | −0.0587894 | ||||||||
\(362\) | −1.37964e93 | −0.558346 | ||||||||
\(363\) | −3.15611e93 | −1.15494 | ||||||||
\(364\) | 1.40928e92 | 0.0466442 | ||||||||
\(365\) | 1.44086e93 | 0.431453 | ||||||||
\(366\) | −3.08691e93 | −0.836496 | ||||||||
\(367\) | −1.78274e93 | −0.437297 | −0.218649 | − | 0.975804i | \(-0.570165\pi\) | ||||
−0.218649 | + | 0.975804i | \(0.570165\pi\) | |||||||
\(368\) | −1.33667e93 | −0.296879 | ||||||||
\(369\) | 4.45425e92 | 0.0896010 | ||||||||
\(370\) | 1.24538e93 | 0.226955 | ||||||||
\(371\) | 4.05697e92 | 0.0669968 | ||||||||
\(372\) | 2.48663e93 | 0.372215 | ||||||||
\(373\) | 1.06369e94 | 1.44358 | 0.721791 | − | 0.692111i | \(-0.243319\pi\) | ||||
0.721791 | + | 0.692111i | \(0.243319\pi\) | |||||||
\(374\) | 5.58023e91 | 0.00686813 | ||||||||
\(375\) | 6.62131e93 | 0.739269 | ||||||||
\(376\) | 1.73376e93 | 0.175644 | ||||||||
\(377\) | 1.39666e94 | 1.28419 | ||||||||
\(378\) | 7.25283e92 | 0.0605420 | ||||||||
\(379\) | 9.65049e93 | 0.731506 | 0.365753 | − | 0.930712i | \(-0.380811\pi\) | ||||
0.365753 | + | 0.930712i | \(0.380811\pi\) | |||||||
\(380\) | 2.38989e93 | 0.164542 | ||||||||
\(381\) | −9.48717e93 | −0.593437 | ||||||||
\(382\) | −2.37324e94 | −1.34905 | ||||||||
\(383\) | −1.87302e94 | −0.967805 | −0.483902 | − | 0.875122i | \(-0.660781\pi\) | ||||
−0.483902 | + | 0.875122i | \(0.660781\pi\) | |||||||
\(384\) | −2.17533e93 | −0.102197 | ||||||||
\(385\) | −2.94765e91 | −0.00125939 | ||||||||
\(386\) | −4.14396e93 | −0.161057 | ||||||||
\(387\) | −1.76946e94 | −0.625734 | ||||||||
\(388\) | 3.52721e93 | 0.113520 | ||||||||
\(389\) | −6.73964e93 | −0.197459 | −0.0987294 | − | 0.995114i | \(-0.531478\pi\) | ||||
−0.0987294 | + | 0.995114i | \(0.531478\pi\) | |||||||
\(390\) | 8.68476e93 | 0.231686 | ||||||||
\(391\) | 1.42780e94 | 0.346909 | ||||||||
\(392\) | 1.57742e94 | 0.349145 | ||||||||
\(393\) | −6.67095e94 | −1.34543 | ||||||||
\(394\) | 6.51433e94 | 1.19745 | ||||||||
\(395\) | 7.95459e92 | 0.0133298 | ||||||||
\(396\) | 3.66485e92 | 0.00559992 | ||||||||
\(397\) | −7.26937e94 | −1.01308 | −0.506539 | − | 0.862217i | \(-0.669075\pi\) | ||||
−0.506539 | + | 0.862217i | \(0.669075\pi\) | |||||||
\(398\) | −7.28076e93 | −0.0925645 | ||||||||
\(399\) | −1.07973e94 | −0.125257 | ||||||||
\(400\) | −2.08950e94 | −0.221235 | ||||||||
\(401\) | −2.50487e94 | −0.242111 | −0.121056 | − | 0.992646i | \(-0.538628\pi\) | ||||
−0.121056 | + | 0.992646i | \(0.538628\pi\) | |||||||
\(402\) | 1.67546e95 | 1.47871 | ||||||||
\(403\) | 6.67308e94 | 0.537888 | ||||||||
\(404\) | −1.18811e95 | −0.874854 | ||||||||
\(405\) | 6.16786e94 | 0.414979 | ||||||||
\(406\) | −1.97390e94 | −0.121373 | ||||||||
\(407\) | 5.59711e93 | 0.0314607 | ||||||||
\(408\) | 2.32364e94 | 0.119419 | ||||||||
\(409\) | 8.94100e94 | 0.420229 | 0.210114 | − | 0.977677i | \(-0.432616\pi\) | ||||
0.210114 | + | 0.977677i | \(0.432616\pi\) | |||||||
\(410\) | 1.48401e94 | 0.0638009 | ||||||||
\(411\) | 3.82439e95 | 1.50430 | ||||||||
\(412\) | −1.37159e95 | −0.493714 | ||||||||
\(413\) | −1.47958e93 | −0.00487485 | ||||||||
\(414\) | 9.37716e94 | 0.282852 | ||||||||
\(415\) | 1.21563e95 | 0.335772 | ||||||||
\(416\) | −5.83769e94 | −0.147684 | ||||||||
\(417\) | −1.63500e93 | −0.00378923 | ||||||||
\(418\) | 1.07409e94 | 0.0228090 | ||||||||
\(419\) | −9.04238e95 | −1.75983 | −0.879916 | − | 0.475130i | \(-0.842401\pi\) | ||||
−0.879916 | + | 0.475130i | \(0.842401\pi\) | |||||||
\(420\) | −1.22742e94 | −0.0218974 | ||||||||
\(421\) | −2.03426e94 | −0.0332744 | −0.0166372 | − | 0.999862i | \(-0.505296\pi\) | ||||
−0.0166372 | + | 0.999862i | \(0.505296\pi\) | |||||||
\(422\) | −9.10402e95 | −1.36562 | ||||||||
\(423\) | −1.21628e95 | −0.167345 | ||||||||
\(424\) | −1.68052e95 | −0.212125 | ||||||||
\(425\) | 2.23196e95 | 0.258517 | ||||||||
\(426\) | 4.74392e95 | 0.504297 | ||||||||
\(427\) | 1.17077e95 | 0.114250 | ||||||||
\(428\) | −2.37182e95 | −0.212513 | ||||||||
\(429\) | 3.90318e94 | 0.0321165 | ||||||||
\(430\) | −5.89526e95 | −0.445558 | ||||||||
\(431\) | 2.07560e95 | 0.144120 | 0.0720600 | − | 0.997400i | \(-0.477043\pi\) | ||||
0.0720600 | + | 0.997400i | \(0.477043\pi\) | |||||||
\(432\) | −3.00435e95 | −0.191688 | ||||||||
\(433\) | 1.66164e96 | 0.974382 | 0.487191 | − | 0.873295i | \(-0.338022\pi\) | ||||
0.487191 | + | 0.873295i | \(0.338022\pi\) | |||||||
\(434\) | −9.43107e94 | −0.0508377 | ||||||||
\(435\) | −1.21642e96 | −0.602873 | ||||||||
\(436\) | 6.49328e94 | 0.0295942 | ||||||||
\(437\) | 2.74824e96 | 1.15208 | ||||||||
\(438\) | 2.69650e96 | 1.03991 | ||||||||
\(439\) | −1.34901e95 | −0.0478698 | −0.0239349 | − | 0.999714i | \(-0.507619\pi\) | ||||
−0.0239349 | + | 0.999714i | \(0.507619\pi\) | |||||||
\(440\) | 1.22101e94 | 0.00398746 | ||||||||
\(441\) | −1.10661e96 | −0.332648 | ||||||||
\(442\) | 6.23568e95 | 0.172572 | ||||||||
\(443\) | 3.93171e96 | 1.00195 | 0.500974 | − | 0.865462i | \(-0.332975\pi\) | ||||
0.500974 | + | 0.865462i | \(0.332975\pi\) | |||||||
\(444\) | 2.33067e96 | 0.547018 | ||||||||
\(445\) | −1.61240e96 | −0.348603 | ||||||||
\(446\) | 3.56057e96 | 0.709246 | ||||||||
\(447\) | −9.68027e96 | −1.77690 | ||||||||
\(448\) | 8.25041e94 | 0.0139582 | ||||||||
\(449\) | −3.39101e96 | −0.528856 | −0.264428 | − | 0.964405i | \(-0.585183\pi\) | ||||
−0.264428 | + | 0.964405i | \(0.585183\pi\) | |||||||
\(450\) | 1.46585e96 | 0.210782 | ||||||||
\(451\) | 6.66959e94 | 0.00884414 | ||||||||
\(452\) | 1.07442e96 | 0.131408 | ||||||||
\(453\) | −1.53046e97 | −1.72678 | ||||||||
\(454\) | −9.06017e96 | −0.943187 | ||||||||
\(455\) | −3.29388e95 | −0.0316440 | ||||||||
\(456\) | 4.47256e96 | 0.396588 | ||||||||
\(457\) | 5.34948e95 | 0.0437896 | 0.0218948 | − | 0.999760i | \(-0.493030\pi\) | ||||
0.0218948 | + | 0.999760i | \(0.493030\pi\) | |||||||
\(458\) | −1.10755e97 | −0.837089 | ||||||||
\(459\) | 3.20917e96 | 0.223991 | ||||||||
\(460\) | 3.12417e96 | 0.201407 | ||||||||
\(461\) | 2.66238e97 | 1.58557 | 0.792787 | − | 0.609498i | \(-0.208629\pi\) | ||||
0.792787 | + | 0.609498i | \(0.208629\pi\) | |||||||
\(462\) | −5.51637e94 | −0.00303544 | ||||||||
\(463\) | 1.21242e97 | 0.616518 | 0.308259 | − | 0.951302i | \(-0.400254\pi\) | ||||
0.308259 | + | 0.951302i | \(0.400254\pi\) | |||||||
\(464\) | 8.17650e96 | 0.384292 | ||||||||
\(465\) | −5.81194e96 | −0.252516 | ||||||||
\(466\) | −1.99309e97 | −0.800646 | ||||||||
\(467\) | 1.17202e97 | 0.435381 | 0.217690 | − | 0.976018i | \(-0.430148\pi\) | ||||
0.217690 | + | 0.976018i | \(0.430148\pi\) | |||||||
\(468\) | 4.09532e96 | 0.140706 | ||||||||
\(469\) | −6.35453e96 | −0.201964 | ||||||||
\(470\) | −4.05227e96 | −0.119159 | ||||||||
\(471\) | −1.40829e97 | −0.383203 | ||||||||
\(472\) | 6.12889e95 | 0.0154347 | ||||||||
\(473\) | −2.64950e96 | −0.0617636 | ||||||||
\(474\) | 1.48866e96 | 0.0321281 | ||||||||
\(475\) | 4.29609e97 | 0.858532 | ||||||||
\(476\) | −8.81289e95 | −0.0163104 | ||||||||
\(477\) | 1.17894e97 | 0.202102 | ||||||||
\(478\) | 6.86691e96 | 0.109054 | ||||||||
\(479\) | 7.40786e97 | 1.09005 | 0.545025 | − | 0.838420i | \(-0.316520\pi\) | ||||
0.545025 | + | 0.838420i | \(0.316520\pi\) | |||||||
\(480\) | 5.08435e96 | 0.0693314 | ||||||||
\(481\) | 6.25454e97 | 0.790497 | ||||||||
\(482\) | −6.58940e97 | −0.772021 | ||||||||
\(483\) | −1.41146e97 | −0.153320 | ||||||||
\(484\) | −4.95844e97 | −0.499447 | ||||||||
\(485\) | −8.24405e96 | −0.0770136 | ||||||||
\(486\) | 5.28587e97 | 0.458029 | ||||||||
\(487\) | −2.37959e98 | −1.91291 | −0.956456 | − | 0.291877i | \(-0.905720\pi\) | ||||
−0.956456 | + | 0.291877i | \(0.905720\pi\) | |||||||
\(488\) | −4.84971e97 | −0.361737 | ||||||||
\(489\) | −1.72632e97 | −0.119495 | ||||||||
\(490\) | −3.68686e97 | −0.236864 | ||||||||
\(491\) | −1.97492e98 | −1.17781 | −0.588906 | − | 0.808202i | \(-0.700441\pi\) | ||||
−0.588906 | + | 0.808202i | \(0.700441\pi\) | |||||||
\(492\) | 2.77725e97 | 0.153776 | ||||||||
\(493\) | −8.73393e97 | −0.449053 | ||||||||
\(494\) | 1.20025e98 | 0.573110 | ||||||||
\(495\) | −8.56576e95 | −0.00379906 | ||||||||
\(496\) | 3.90665e97 | 0.160962 | ||||||||
\(497\) | −1.79923e97 | −0.0688777 | ||||||||
\(498\) | 2.27498e98 | 0.809295 | ||||||||
\(499\) | −1.14951e98 | −0.380052 | −0.190026 | − | 0.981779i | \(-0.560857\pi\) | ||||
−0.190026 | + | 0.981779i | \(0.560857\pi\) | |||||||
\(500\) | 1.04025e98 | 0.319692 | ||||||||
\(501\) | 4.50612e98 | 1.28744 | ||||||||
\(502\) | 3.04532e98 | 0.808998 | ||||||||
\(503\) | −5.91076e97 | −0.146020 | −0.0730100 | − | 0.997331i | \(-0.523260\pi\) | ||||
−0.0730100 | + | 0.997331i | \(0.523260\pi\) | |||||||
\(504\) | −5.78792e96 | −0.0132987 | ||||||||
\(505\) | 2.77693e98 | 0.593512 | ||||||||
\(506\) | 1.40409e97 | 0.0279191 | ||||||||
\(507\) | −1.88766e98 | −0.349247 | ||||||||
\(508\) | −1.49049e98 | −0.256628 | ||||||||
\(509\) | 1.52382e98 | 0.244194 | 0.122097 | − | 0.992518i | \(-0.461038\pi\) | ||||
0.122097 | + | 0.992518i | \(0.461038\pi\) | |||||||
\(510\) | −5.43098e97 | −0.0810152 | ||||||||
\(511\) | −1.02270e98 | −0.142032 | ||||||||
\(512\) | −3.41758e97 | −0.0441942 | ||||||||
\(513\) | 6.17705e98 | 0.743870 | ||||||||
\(514\) | −5.65783e96 | −0.00634595 | ||||||||
\(515\) | 3.20578e98 | 0.334942 | ||||||||
\(516\) | −1.10327e99 | −1.07391 | ||||||||
\(517\) | −1.82121e97 | −0.0165179 | ||||||||
\(518\) | −8.83955e97 | −0.0747126 | ||||||||
\(519\) | −1.15616e99 | −0.910774 | ||||||||
\(520\) | 1.36443e98 | 0.100191 | ||||||||
\(521\) | −1.55565e99 | −1.06497 | −0.532483 | − | 0.846441i | \(-0.678741\pi\) | ||||
−0.532483 | + | 0.846441i | \(0.678741\pi\) | |||||||
\(522\) | −5.73606e98 | −0.366134 | ||||||||
\(523\) | 1.35187e99 | 0.804677 | 0.402339 | − | 0.915491i | \(-0.368197\pi\) | ||||
0.402339 | + | 0.915491i | \(0.368197\pi\) | |||||||
\(524\) | −1.04805e99 | −0.581820 | ||||||||
\(525\) | −2.20641e98 | −0.114254 | ||||||||
\(526\) | 5.13555e98 | 0.248089 | ||||||||
\(527\) | −4.17298e98 | −0.188087 | ||||||||
\(528\) | 2.28505e97 | 0.00961078 | ||||||||
\(529\) | 1.04501e99 | 0.410194 | ||||||||
\(530\) | 3.92784e98 | 0.143908 | ||||||||
\(531\) | −4.29960e97 | −0.0147054 | ||||||||
\(532\) | −1.69631e98 | −0.0541666 | ||||||||
\(533\) | 7.45299e98 | 0.222222 | ||||||||
\(534\) | −3.01751e99 | −0.840221 | ||||||||
\(535\) | 5.54360e98 | 0.144171 | ||||||||
\(536\) | 2.63225e99 | 0.639458 | ||||||||
\(537\) | 6.06305e99 | 1.37604 | ||||||||
\(538\) | 1.29616e99 | 0.274855 | ||||||||
\(539\) | −1.65698e98 | −0.0328343 | ||||||||
\(540\) | 7.02199e98 | 0.130043 | ||||||||
\(541\) | −5.01024e98 | −0.0867279 | −0.0433639 | − | 0.999059i | \(-0.513807\pi\) | ||||
−0.0433639 | + | 0.999059i | \(0.513807\pi\) | |||||||
\(542\) | −2.25934e99 | −0.365601 | ||||||||
\(543\) | 6.03467e99 | 0.912977 | ||||||||
\(544\) | 3.65057e98 | 0.0516418 | ||||||||
\(545\) | −1.51766e98 | −0.0200771 | ||||||||
\(546\) | −6.16432e98 | −0.0762699 | ||||||||
\(547\) | −1.48570e100 | −1.71946 | −0.859731 | − | 0.510746i | \(-0.829369\pi\) | ||||
−0.859731 | + | 0.510746i | \(0.829369\pi\) | |||||||
\(548\) | 6.00834e99 | 0.650526 | ||||||||
\(549\) | 3.40222e99 | 0.344645 | ||||||||
\(550\) | 2.19490e98 | 0.0208054 | ||||||||
\(551\) | −1.68112e100 | −1.49130 | ||||||||
\(552\) | 5.84671e99 | 0.485440 | ||||||||
\(553\) | −5.64605e97 | −0.00438811 | ||||||||
\(554\) | 1.44210e100 | 1.04927 | ||||||||
\(555\) | −5.44741e99 | −0.371104 | ||||||||
\(556\) | −2.56868e97 | −0.00163863 | ||||||||
\(557\) | 1.80353e100 | 1.07748 | 0.538740 | − | 0.842472i | \(-0.318900\pi\) | ||||
0.538740 | + | 0.842472i | \(0.318900\pi\) | |||||||
\(558\) | −2.74063e99 | −0.153357 | ||||||||
\(559\) | −2.96071e100 | −1.55190 | ||||||||
\(560\) | −1.92835e98 | −0.00946939 | ||||||||
\(561\) | −2.44084e98 | −0.0112304 | ||||||||
\(562\) | −6.66241e99 | −0.287247 | ||||||||
\(563\) | −2.47834e100 | −1.00139 | −0.500697 | − | 0.865623i | \(-0.666923\pi\) | ||||
−0.500697 | + | 0.865623i | \(0.666923\pi\) | |||||||
\(564\) | −7.58360e99 | −0.287203 | ||||||||
\(565\) | −2.51121e99 | −0.0891488 | ||||||||
\(566\) | −2.71095e100 | −0.902240 | ||||||||
\(567\) | −4.37786e99 | −0.136609 | ||||||||
\(568\) | 7.45298e99 | 0.218080 | ||||||||
\(569\) | 6.22010e100 | 1.70687 | 0.853433 | − | 0.521202i | \(-0.174516\pi\) | ||||
0.853433 | + | 0.521202i | \(0.174516\pi\) | |||||||
\(570\) | −1.04536e100 | −0.269050 | ||||||||
\(571\) | −3.07431e100 | −0.742216 | −0.371108 | − | 0.928590i | \(-0.621022\pi\) | ||||
−0.371108 | + | 0.928590i | \(0.621022\pi\) | |||||||
\(572\) | 6.13214e98 | 0.0138885 | ||||||||
\(573\) | 1.03807e101 | 2.20589 | ||||||||
\(574\) | −1.05333e99 | −0.0210030 | ||||||||
\(575\) | 5.61603e100 | 1.05088 | ||||||||
\(576\) | 2.39754e99 | 0.0421061 | ||||||||
\(577\) | 2.06343e100 | 0.340152 | 0.170076 | − | 0.985431i | \(-0.445599\pi\) | ||||
0.170076 | + | 0.985431i | \(0.445599\pi\) | |||||||
\(578\) | 4.17937e100 | 0.646762 | ||||||||
\(579\) | 1.81260e100 | 0.263351 | ||||||||
\(580\) | −1.91107e100 | −0.260708 | ||||||||
\(581\) | −8.62835e99 | −0.110535 | ||||||||
\(582\) | −1.54283e100 | −0.185622 | ||||||||
\(583\) | 1.76529e99 | 0.0199486 | ||||||||
\(584\) | 4.23636e100 | 0.449701 | ||||||||
\(585\) | −9.57188e99 | −0.0954571 | ||||||||
\(586\) | −9.92577e100 | −0.930040 | ||||||||
\(587\) | −1.15251e101 | −1.01474 | −0.507368 | − | 0.861729i | \(-0.669382\pi\) | ||||
−0.507368 | + | 0.861729i | \(0.669382\pi\) | |||||||
\(588\) | −6.89976e100 | −0.570902 | ||||||||
\(589\) | −8.03220e100 | −0.624635 | ||||||||
\(590\) | −1.43249e99 | −0.0104711 | ||||||||
\(591\) | −2.84942e101 | −1.95801 | ||||||||
\(592\) | 3.66162e100 | 0.236554 | ||||||||
\(593\) | 2.83611e101 | 1.72277 | 0.861385 | − | 0.507953i | \(-0.169598\pi\) | ||||
0.861385 | + | 0.507953i | \(0.169598\pi\) | |||||||
\(594\) | 3.15589e99 | 0.0180267 | ||||||||
\(595\) | 2.05981e99 | 0.0110652 | ||||||||
\(596\) | −1.52083e101 | −0.768408 | ||||||||
\(597\) | 3.18466e100 | 0.151356 | ||||||||
\(598\) | 1.56901e101 | 0.701510 | ||||||||
\(599\) | 1.40873e101 | 0.592584 | 0.296292 | − | 0.955097i | \(-0.404250\pi\) | ||||
0.296292 | + | 0.955097i | \(0.404250\pi\) | |||||||
\(600\) | 9.13966e100 | 0.361751 | ||||||||
\(601\) | −1.94434e101 | −0.724191 | −0.362096 | − | 0.932141i | \(-0.617939\pi\) | ||||
−0.362096 | + | 0.932141i | \(0.617939\pi\) | |||||||
\(602\) | 4.18437e100 | 0.146676 | ||||||||
\(603\) | −1.84660e101 | −0.609244 | ||||||||
\(604\) | −2.40444e101 | −0.746734 | ||||||||
\(605\) | 1.15892e101 | 0.338831 | ||||||||
\(606\) | 5.19688e101 | 1.43051 | ||||||||
\(607\) | −3.29029e101 | −0.852800 | −0.426400 | − | 0.904535i | \(-0.640218\pi\) | ||||
−0.426400 | + | 0.904535i | \(0.640218\pi\) | |||||||
\(608\) | 7.02666e100 | 0.171502 | ||||||||
\(609\) | 8.63398e100 | 0.198463 | ||||||||
\(610\) | 1.13351e101 | 0.245407 | ||||||||
\(611\) | −2.03512e101 | −0.415037 | ||||||||
\(612\) | −2.56099e100 | −0.0492018 | ||||||||
\(613\) | 7.67313e101 | 1.38888 | 0.694440 | − | 0.719550i | \(-0.255652\pi\) | ||||
0.694440 | + | 0.719550i | \(0.255652\pi\) | |||||||
\(614\) | 4.07585e101 | 0.695140 | ||||||||
\(615\) | −6.49120e100 | −0.104324 | ||||||||
\(616\) | −8.66655e98 | −0.00131265 | ||||||||
\(617\) | 1.49318e101 | 0.213159 | 0.106580 | − | 0.994304i | \(-0.466010\pi\) | ||||
0.106580 | + | 0.994304i | \(0.466010\pi\) | |||||||
\(618\) | 5.99944e101 | 0.807294 | ||||||||
\(619\) | −1.23916e102 | −1.57187 | −0.785936 | − | 0.618308i | \(-0.787818\pi\) | ||||
−0.785936 | + | 0.618308i | \(0.787818\pi\) | |||||||
\(620\) | −9.13090e100 | −0.109199 | ||||||||
\(621\) | 8.07489e101 | 0.910528 | ||||||||
\(622\) | −1.06673e102 | −1.13424 | ||||||||
\(623\) | 1.14446e101 | 0.114759 | ||||||||
\(624\) | 2.55345e101 | 0.241485 | ||||||||
\(625\) | 7.48917e101 | 0.668056 | ||||||||
\(626\) | −1.47808e102 | −1.24375 | ||||||||
\(627\) | −4.69815e100 | −0.0372960 | ||||||||
\(628\) | −2.21251e101 | −0.165713 | ||||||||
\(629\) | −3.91125e101 | −0.276419 | ||||||||
\(630\) | 1.35279e100 | 0.00902198 | ||||||||
\(631\) | −2.75337e102 | −1.73298 | −0.866490 | − | 0.499195i | \(-0.833629\pi\) | ||||
−0.866490 | + | 0.499195i | \(0.833629\pi\) | |||||||
\(632\) | 2.33877e100 | 0.0138936 | ||||||||
\(633\) | 3.98217e102 | 2.23298 | ||||||||
\(634\) | −2.30323e102 | −1.21921 | ||||||||
\(635\) | 3.48369e101 | 0.174100 | ||||||||
\(636\) | 7.35075e101 | 0.346854 | ||||||||
\(637\) | −1.85161e102 | −0.825012 | ||||||||
\(638\) | −8.58891e100 | −0.0361396 | ||||||||
\(639\) | −5.22849e101 | −0.207776 | ||||||||
\(640\) | 7.98782e100 | 0.0299819 | ||||||||
\(641\) | 5.79044e101 | 0.205302 | 0.102651 | − | 0.994717i | \(-0.467267\pi\) | ||||
0.102651 | + | 0.994717i | \(0.467267\pi\) | |||||||
\(642\) | 1.03745e102 | 0.347489 | ||||||||
\(643\) | −3.89322e101 | −0.123199 | −0.0615996 | − | 0.998101i | \(-0.519620\pi\) | ||||
−0.0615996 | + | 0.998101i | \(0.519620\pi\) | |||||||
\(644\) | −2.21749e101 | −0.0663021 | ||||||||
\(645\) | 2.57864e102 | 0.728552 | ||||||||
\(646\) | −7.50571e101 | −0.200403 | ||||||||
\(647\) | −1.64739e102 | −0.415708 | −0.207854 | − | 0.978160i | \(-0.566648\pi\) | ||||
−0.207854 | + | 0.978160i | \(0.566648\pi\) | |||||||
\(648\) | 1.81345e102 | 0.432531 | ||||||||
\(649\) | −6.43802e99 | −0.00145151 | ||||||||
\(650\) | 2.45270e102 | 0.522766 | ||||||||
\(651\) | 4.12523e101 | 0.0831270 | ||||||||
\(652\) | −2.71216e101 | −0.0516746 | ||||||||
\(653\) | 9.50113e102 | 1.71177 | 0.855883 | − | 0.517170i | \(-0.173015\pi\) | ||||
0.855883 | + | 0.517170i | \(0.173015\pi\) | |||||||
\(654\) | −2.84021e101 | −0.0483908 | ||||||||
\(655\) | 2.44957e102 | 0.394714 | ||||||||
\(656\) | 4.36323e101 | 0.0664994 | ||||||||
\(657\) | −2.97194e102 | −0.428454 | ||||||||
\(658\) | 2.87624e101 | 0.0392266 | ||||||||
\(659\) | 7.31327e102 | 0.943614 | 0.471807 | − | 0.881702i | \(-0.343602\pi\) | ||||
0.471807 | + | 0.881702i | \(0.343602\pi\) | |||||||
\(660\) | −5.34080e100 | −0.00652007 | ||||||||
\(661\) | −1.56804e103 | −1.81136 | −0.905680 | − | 0.423963i | \(-0.860639\pi\) | ||||
−0.905680 | + | 0.423963i | \(0.860639\pi\) | |||||||
\(662\) | 7.40631e101 | 0.0809627 | ||||||||
\(663\) | −2.72754e102 | −0.282180 | ||||||||
\(664\) | 3.57413e102 | 0.349974 | ||||||||
\(665\) | 3.96475e101 | 0.0367473 | ||||||||
\(666\) | −2.56874e102 | −0.225377 | ||||||||
\(667\) | −2.19762e103 | −1.82541 | ||||||||
\(668\) | 7.07939e102 | 0.556743 | ||||||||
\(669\) | −1.55742e103 | −1.15972 | ||||||||
\(670\) | −6.15228e102 | −0.433816 | ||||||||
\(671\) | 5.09433e101 | 0.0340185 | ||||||||
\(672\) | −3.60880e101 | −0.0228236 | ||||||||
\(673\) | −2.13281e103 | −1.27762 | −0.638812 | − | 0.769363i | \(-0.720574\pi\) | ||||
−0.638812 | + | 0.769363i | \(0.720574\pi\) | |||||||
\(674\) | 1.63560e103 | 0.928094 | ||||||||
\(675\) | 1.26228e103 | 0.678527 | ||||||||
\(676\) | −2.96562e102 | −0.151030 | ||||||||
\(677\) | 4.75816e102 | 0.229590 | 0.114795 | − | 0.993389i | \(-0.463379\pi\) | ||||
0.114795 | + | 0.993389i | \(0.463379\pi\) | |||||||
\(678\) | −4.69960e102 | −0.214871 | ||||||||
\(679\) | 5.85151e101 | 0.0253525 | ||||||||
\(680\) | −8.53239e101 | −0.0350345 | ||||||||
\(681\) | 3.96300e103 | 1.54225 | ||||||||
\(682\) | −4.10369e101 | −0.0151372 | ||||||||
\(683\) | 4.75457e103 | 1.66248 | 0.831238 | − | 0.555916i | \(-0.187632\pi\) | ||||
0.831238 | + | 0.555916i | \(0.187632\pi\) | |||||||
\(684\) | −4.92942e102 | −0.163398 | ||||||||
\(685\) | −1.40431e103 | −0.441325 | ||||||||
\(686\) | 5.26680e102 | 0.156934 | ||||||||
\(687\) | 4.84450e103 | 1.36876 | ||||||||
\(688\) | −1.73330e103 | −0.464403 | ||||||||
\(689\) | 1.97264e103 | 0.501240 | ||||||||
\(690\) | −1.36654e103 | −0.329329 | ||||||||
\(691\) | −6.23923e103 | −1.42621 | −0.713103 | − | 0.701059i | \(-0.752711\pi\) | ||||
−0.713103 | + | 0.701059i | \(0.752711\pi\) | |||||||
\(692\) | −1.81640e103 | −0.393858 | ||||||||
\(693\) | 6.07985e100 | 0.00125063 | ||||||||
\(694\) | −2.34471e103 | −0.457581 | ||||||||
\(695\) | 6.00371e100 | 0.00111167 | ||||||||
\(696\) | −3.57647e103 | −0.628372 | ||||||||
\(697\) | −4.66070e102 | −0.0777060 | ||||||||
\(698\) | 3.89312e103 | 0.615991 | ||||||||
\(699\) | 8.71793e103 | 1.30917 | ||||||||
\(700\) | −3.46641e102 | −0.0494085 | ||||||||
\(701\) | 2.75532e103 | 0.372790 | 0.186395 | − | 0.982475i | \(-0.440320\pi\) | ||||
0.186395 | + | 0.982475i | \(0.440320\pi\) | |||||||
\(702\) | 3.52657e103 | 0.452948 | ||||||||
\(703\) | −7.52842e103 | −0.917982 | ||||||||
\(704\) | 3.58996e101 | 0.00415611 | ||||||||
\(705\) | 1.77250e103 | 0.194842 | ||||||||
\(706\) | 1.66345e103 | 0.173635 | ||||||||
\(707\) | −1.97103e103 | −0.195382 | ||||||||
\(708\) | −2.68083e102 | −0.0252380 | ||||||||
\(709\) | −1.90532e104 | −1.70365 | −0.851823 | − | 0.523830i | \(-0.824503\pi\) | ||||
−0.851823 | + | 0.523830i | \(0.824503\pi\) | |||||||
\(710\) | −1.74197e103 | −0.147948 | ||||||||
\(711\) | −1.64072e102 | −0.0132371 | ||||||||
\(712\) | −4.74070e103 | −0.363348 | ||||||||
\(713\) | −1.05000e104 | −0.764579 | ||||||||
\(714\) | 3.85483e102 | 0.0266698 | ||||||||
\(715\) | −1.43325e102 | −0.00942217 | ||||||||
\(716\) | 9.52541e103 | 0.595057 | ||||||||
\(717\) | −3.00364e103 | −0.178320 | ||||||||
\(718\) | −2.77796e103 | −0.156741 | ||||||||
\(719\) | 5.28737e103 | 0.283553 | 0.141777 | − | 0.989899i | \(-0.454719\pi\) | ||||
0.141777 | + | 0.989899i | \(0.454719\pi\) | |||||||
\(720\) | −5.60370e102 | −0.0285653 | ||||||||
\(721\) | −2.27542e103 | −0.110261 | ||||||||
\(722\) | 9.02385e102 | 0.0415704 | ||||||||
\(723\) | 2.88226e104 | 1.26237 | ||||||||
\(724\) | 9.48083e103 | 0.394810 | ||||||||
\(725\) | −3.43535e104 | −1.36030 | ||||||||
\(726\) | 2.16886e104 | 0.816668 | ||||||||
\(727\) | 4.43475e104 | 1.58805 | 0.794023 | − | 0.607888i | \(-0.207983\pi\) | ||||
0.794023 | + | 0.607888i | \(0.207983\pi\) | |||||||
\(728\) | −9.68451e102 | −0.0329824 | ||||||||
\(729\) | 1.46465e104 | 0.474439 | ||||||||
\(730\) | −9.90154e103 | −0.305083 | ||||||||
\(731\) | 1.85147e104 | 0.542665 | ||||||||
\(732\) | 2.12131e104 | 0.591492 | ||||||||
\(733\) | −6.26266e104 | −1.66136 | −0.830681 | − | 0.556749i | \(-0.812048\pi\) | ||||
−0.830681 | + | 0.556749i | \(0.812048\pi\) | |||||||
\(734\) | 1.22509e104 | 0.309216 | ||||||||
\(735\) | 1.61266e104 | 0.387307 | ||||||||
\(736\) | 9.18554e103 | 0.209925 | ||||||||
\(737\) | −2.76502e103 | −0.0601360 | ||||||||
\(738\) | −3.06094e103 | −0.0633574 | ||||||||
\(739\) | −1.72996e104 | −0.340811 | −0.170406 | − | 0.985374i | \(-0.554508\pi\) | ||||
−0.170406 | + | 0.985374i | \(0.554508\pi\) | |||||||
\(740\) | −8.55821e103 | −0.160481 | ||||||||
\(741\) | −5.24999e104 | −0.937117 | ||||||||
\(742\) | −2.78793e103 | −0.0473739 | ||||||||
\(743\) | 3.33964e104 | 0.540267 | 0.270134 | − | 0.962823i | \(-0.412932\pi\) | ||||
0.270134 | + | 0.962823i | \(0.412932\pi\) | |||||||
\(744\) | −1.70880e104 | −0.263196 | ||||||||
\(745\) | 3.55459e104 | 0.521298 | ||||||||
\(746\) | −7.30960e104 | −1.02077 | ||||||||
\(747\) | −2.50736e104 | −0.333438 | ||||||||
\(748\) | −3.83471e102 | −0.00485650 | ||||||||
\(749\) | −3.93477e103 | −0.0474605 | ||||||||
\(750\) | −4.55013e104 | −0.522742 | ||||||||
\(751\) | 9.73411e104 | 1.06522 | 0.532609 | − | 0.846362i | \(-0.321212\pi\) | ||||
0.532609 | + | 0.846362i | \(0.321212\pi\) | |||||||
\(752\) | −1.19143e104 | −0.124199 | ||||||||
\(753\) | −1.33205e105 | −1.32283 | ||||||||
\(754\) | −9.59775e104 | −0.908061 | ||||||||
\(755\) | 5.61984e104 | 0.506594 | ||||||||
\(756\) | −4.98411e103 | −0.0428097 | ||||||||
\(757\) | −4.34695e104 | −0.355783 | −0.177891 | − | 0.984050i | \(-0.556928\pi\) | ||||
−0.177891 | + | 0.984050i | \(0.556928\pi\) | |||||||
\(758\) | −6.63177e104 | −0.517253 | ||||||||
\(759\) | −6.14162e103 | −0.0456518 | ||||||||
\(760\) | −1.64232e104 | −0.116349 | ||||||||
\(761\) | 2.66509e105 | 1.79958 | 0.899792 | − | 0.436319i | \(-0.143718\pi\) | ||||
0.899792 | + | 0.436319i | \(0.143718\pi\) | |||||||
\(762\) | 6.51953e104 | 0.419624 | ||||||||
\(763\) | 1.07721e103 | 0.00660929 | ||||||||
\(764\) | 1.63088e105 | 0.953924 | ||||||||
\(765\) | 5.98574e103 | 0.0333791 | ||||||||
\(766\) | 1.28713e105 | 0.684341 | ||||||||
\(767\) | −7.19422e103 | −0.0364714 | ||||||||
\(768\) | 1.49488e104 | 0.0722639 | ||||||||
\(769\) | 3.43153e105 | 1.58189 | 0.790944 | − | 0.611888i | \(-0.209590\pi\) | ||||
0.790944 | + | 0.611888i | \(0.209590\pi\) | |||||||
\(770\) | 2.02561e102 | 0.000890522 0 | ||||||||
\(771\) | 2.47478e103 | 0.0103765 | ||||||||
\(772\) | 2.84771e104 | 0.113884 | ||||||||
\(773\) | −4.29363e105 | −1.63785 | −0.818924 | − | 0.573902i | \(-0.805429\pi\) | ||||
−0.818924 | + | 0.573902i | \(0.805429\pi\) | |||||||
\(774\) | 1.21596e105 | 0.442461 | ||||||||
\(775\) | −1.64138e105 | −0.569766 | ||||||||
\(776\) | −2.42388e104 | −0.0802709 | ||||||||
\(777\) | 3.86649e104 | 0.122166 | ||||||||
\(778\) | 4.63145e104 | 0.139624 | ||||||||
\(779\) | −8.97095e104 | −0.258060 | ||||||||
\(780\) | −5.96812e104 | −0.163827 | ||||||||
\(781\) | −7.82890e103 | −0.0205087 | ||||||||
\(782\) | −9.81177e104 | −0.245302 | ||||||||
\(783\) | −4.93946e105 | −1.17862 | ||||||||
\(784\) | −1.08399e105 | −0.246883 | ||||||||
\(785\) | 5.17123e104 | 0.112422 | ||||||||
\(786\) | 4.58424e105 | 0.951359 | ||||||||
\(787\) | −5.62421e104 | −0.111425 | −0.0557127 | − | 0.998447i | \(-0.517743\pi\) | ||||
−0.0557127 | + | 0.998447i | \(0.517743\pi\) | |||||||
\(788\) | −4.47661e105 | −0.846726 | ||||||||
\(789\) | −2.24633e105 | −0.405661 | ||||||||
\(790\) | −5.46635e103 | −0.00942559 | ||||||||
\(791\) | 1.78242e104 | 0.0293474 | ||||||||
\(792\) | −2.51847e103 | −0.00395974 | ||||||||
\(793\) | 5.69270e105 | 0.854765 | ||||||||
\(794\) | 4.99547e105 | 0.716355 | ||||||||
\(795\) | −1.71807e105 | −0.235310 | ||||||||
\(796\) | 5.00330e104 | 0.0654530 | ||||||||
\(797\) | −8.98427e105 | −1.12267 | −0.561337 | − | 0.827587i | \(-0.689713\pi\) | ||||
−0.561337 | + | 0.827587i | \(0.689713\pi\) | |||||||
\(798\) | 7.41981e104 | 0.0885702 | ||||||||
\(799\) | 1.27266e105 | 0.145129 | ||||||||
\(800\) | 1.43590e105 | 0.156437 | ||||||||
\(801\) | 3.32574e105 | 0.346180 | ||||||||
\(802\) | 1.72133e105 | 0.171198 | ||||||||
\(803\) | −4.45004e104 | −0.0422909 | ||||||||
\(804\) | −1.15137e106 | −1.04561 | ||||||||
\(805\) | 5.18288e104 | 0.0449802 | ||||||||
\(806\) | −4.58571e105 | −0.380345 | ||||||||
\(807\) | −5.66950e105 | −0.449428 | ||||||||
\(808\) | 8.16461e105 | 0.618615 | ||||||||
\(809\) | 1.36941e106 | 0.991770 | 0.495885 | − | 0.868388i | \(-0.334844\pi\) | ||||
0.495885 | + | 0.868388i | \(0.334844\pi\) | |||||||
\(810\) | −4.23852e105 | −0.293434 | ||||||||
\(811\) | 1.27012e106 | 0.840590 | 0.420295 | − | 0.907387i | \(-0.361927\pi\) | ||||
0.420295 | + | 0.907387i | \(0.361927\pi\) | |||||||
\(812\) | 1.35645e105 | 0.0858240 | ||||||||
\(813\) | 9.88254e105 | 0.597811 | ||||||||
\(814\) | −3.84631e104 | −0.0222461 | ||||||||
\(815\) | 6.33905e104 | 0.0350567 | ||||||||
\(816\) | −1.59679e105 | −0.0844418 | ||||||||
\(817\) | 3.56372e106 | 1.80218 | ||||||||
\(818\) | −6.14421e105 | −0.297146 | ||||||||
\(819\) | 6.79398e104 | 0.0314240 | ||||||||
\(820\) | −1.01981e105 | −0.0451141 | ||||||||
\(821\) | −7.14465e105 | −0.302312 | −0.151156 | − | 0.988510i | \(-0.548300\pi\) | ||||
−0.151156 | + | 0.988510i | \(0.548300\pi\) | |||||||
\(822\) | −2.62810e106 | −1.06370 | ||||||||
\(823\) | 2.85583e106 | 1.10570 | 0.552851 | − | 0.833280i | \(-0.313540\pi\) | ||||
0.552851 | + | 0.833280i | \(0.313540\pi\) | |||||||
\(824\) | 9.42549e105 | 0.349109 | ||||||||
\(825\) | −9.60066e104 | −0.0340198 | ||||||||
\(826\) | 1.01676e104 | 0.00344704 | ||||||||
\(827\) | −5.39859e106 | −1.75118 | −0.875588 | − | 0.483059i | \(-0.839526\pi\) | ||||
−0.875588 | + | 0.483059i | \(0.839526\pi\) | |||||||
\(828\) | −6.44394e105 | −0.200006 | ||||||||
\(829\) | −2.39224e106 | −0.710499 | −0.355250 | − | 0.934771i | \(-0.615604\pi\) | ||||
−0.355250 | + | 0.934771i | \(0.615604\pi\) | |||||||
\(830\) | −8.35373e105 | −0.237427 | ||||||||
\(831\) | −6.30786e106 | −1.71571 | ||||||||
\(832\) | 4.01163e105 | 0.104429 | ||||||||
\(833\) | 1.15790e106 | 0.288488 | ||||||||
\(834\) | 1.12356e104 | 0.00267939 | ||||||||
\(835\) | −1.65465e106 | −0.377702 | ||||||||
\(836\) | −7.38108e104 | −0.0161284 | ||||||||
\(837\) | −2.36002e106 | −0.493670 | ||||||||
\(838\) | 6.21388e106 | 1.24439 | ||||||||
\(839\) | −6.91196e106 | −1.32522 | −0.662612 | − | 0.748963i | \(-0.730552\pi\) | ||||
−0.662612 | + | 0.748963i | \(0.730552\pi\) | |||||||
\(840\) | 8.43475e104 | 0.0154838 | ||||||||
\(841\) | 7.75375e106 | 1.36288 | ||||||||
\(842\) | 1.39793e105 | 0.0235285 | ||||||||
\(843\) | 2.91419e106 | 0.469690 | ||||||||
\(844\) | 6.25623e106 | 0.965636 | ||||||||
\(845\) | 6.93148e105 | 0.102460 | ||||||||
\(846\) | 8.35825e105 | 0.118331 | ||||||||
\(847\) | −8.22587e105 | −0.111542 | ||||||||
\(848\) | 1.15485e106 | 0.149995 | ||||||||
\(849\) | 1.18579e107 | 1.47529 | ||||||||
\(850\) | −1.53379e106 | −0.182799 | ||||||||
\(851\) | −9.84145e106 | −1.12365 | ||||||||
\(852\) | −3.26000e106 | −0.356592 | ||||||||
\(853\) | 4.32735e106 | 0.453505 | 0.226753 | − | 0.973952i | \(-0.427189\pi\) | ||||
0.226753 | + | 0.973952i | \(0.427189\pi\) | |||||||
\(854\) | −8.04550e105 | −0.0807868 | ||||||||
\(855\) | 1.15214e106 | 0.110852 | ||||||||
\(856\) | 1.62990e106 | 0.150269 | ||||||||
\(857\) | −2.66836e106 | −0.235746 | −0.117873 | − | 0.993029i | \(-0.537608\pi\) | ||||
−0.117873 | + | 0.993029i | \(0.537608\pi\) | |||||||
\(858\) | −2.68225e105 | −0.0227098 | ||||||||
\(859\) | 8.23486e106 | 0.668199 | 0.334100 | − | 0.942538i | \(-0.391568\pi\) | ||||
0.334100 | + | 0.942538i | \(0.391568\pi\) | |||||||
\(860\) | 4.05119e106 | 0.315057 | ||||||||
\(861\) | 4.60736e105 | 0.0343429 | ||||||||
\(862\) | −1.42634e106 | −0.101908 | ||||||||
\(863\) | 8.24432e106 | 0.564626 | 0.282313 | − | 0.959322i | \(-0.408898\pi\) | ||||
0.282313 | + | 0.959322i | \(0.408898\pi\) | |||||||
\(864\) | 2.06457e106 | 0.135544 | ||||||||
\(865\) | 4.24543e106 | 0.267198 | ||||||||
\(866\) | −1.14187e107 | −0.688992 | ||||||||
\(867\) | −1.82809e107 | −1.05755 | ||||||||
\(868\) | 6.48098e105 | 0.0359477 | ||||||||
\(869\) | −2.45674e104 | −0.00130658 | ||||||||
\(870\) | 8.35918e106 | 0.426296 | ||||||||
\(871\) | −3.08979e107 | −1.51101 | ||||||||
\(872\) | −4.46215e105 | −0.0209263 | ||||||||
\(873\) | 1.70043e106 | 0.0764782 | ||||||||
\(874\) | −1.88858e107 | −0.814644 | ||||||||
\(875\) | 1.72573e106 | 0.0713969 | ||||||||
\(876\) | −1.85302e107 | −0.735327 | ||||||||
\(877\) | −3.47099e107 | −1.32120 | −0.660600 | − | 0.750738i | \(-0.729698\pi\) | ||||
−0.660600 | + | 0.750738i | \(0.729698\pi\) | |||||||
\(878\) | 9.27035e105 | 0.0338491 | ||||||||
\(879\) | 4.34162e107 | 1.52075 | ||||||||
\(880\) | −8.39072e104 | −0.00281956 | ||||||||
\(881\) | −5.58005e106 | −0.179894 | −0.0899472 | − | 0.995947i | \(-0.528670\pi\) | ||||
−0.0899472 | + | 0.995947i | \(0.528670\pi\) | |||||||
\(882\) | 7.60455e106 | 0.235218 | ||||||||
\(883\) | 4.50047e107 | 1.33565 | 0.667824 | − | 0.744320i | \(-0.267226\pi\) | ||||
0.667824 | + | 0.744320i | \(0.267226\pi\) | |||||||
\(884\) | −4.28512e106 | −0.122027 | ||||||||
\(885\) | 6.26582e105 | 0.0171218 | ||||||||
\(886\) | −2.70185e107 | −0.708484 | ||||||||
\(887\) | 5.29484e107 | 1.33242 | 0.666209 | − | 0.745765i | \(-0.267916\pi\) | ||||
0.666209 | + | 0.745765i | \(0.267916\pi\) | |||||||
\(888\) | −1.60162e107 | −0.386800 | ||||||||
\(889\) | −2.47267e106 | −0.0573128 | ||||||||
\(890\) | 1.10803e107 | 0.246500 | ||||||||
\(891\) | −1.90491e106 | −0.0406761 | ||||||||
\(892\) | −2.44680e107 | −0.501513 | ||||||||
\(893\) | 2.44962e107 | 0.481971 | ||||||||
\(894\) | 6.65223e107 | 1.25646 | ||||||||
\(895\) | −2.22635e107 | −0.403694 | ||||||||
\(896\) | −5.66964e105 | −0.00986991 | ||||||||
\(897\) | −6.86300e107 | −1.14707 | ||||||||
\(898\) | 2.33028e107 | 0.373958 | ||||||||
\(899\) | 6.42292e107 | 0.989701 | ||||||||
\(900\) | −1.00732e107 | −0.149045 | ||||||||
\(901\) | −1.23358e107 | −0.175272 | ||||||||
\(902\) | −4.58331e105 | −0.00625375 | ||||||||
\(903\) | −1.83028e107 | −0.239836 | ||||||||
\(904\) | −7.38336e106 | −0.0929194 | ||||||||
\(905\) | −2.21593e107 | −0.267844 | ||||||||
\(906\) | 1.05172e108 | 1.22102 | ||||||||
\(907\) | −7.96720e107 | −0.888464 | −0.444232 | − | 0.895912i | \(-0.646523\pi\) | ||||
−0.444232 | + | 0.895912i | \(0.646523\pi\) | |||||||
\(908\) | 6.22610e107 | 0.666934 | ||||||||
\(909\) | −5.72772e107 | −0.589387 | ||||||||
\(910\) | 2.26354e106 | 0.0223757 | ||||||||
\(911\) | 9.49752e107 | 0.901965 | 0.450982 | − | 0.892533i | \(-0.351074\pi\) | ||||
0.450982 | + | 0.892533i | \(0.351074\pi\) | |||||||
\(912\) | −3.07352e107 | −0.280430 | ||||||||
\(913\) | −3.75441e106 | −0.0329123 | ||||||||
\(914\) | −3.67614e106 | −0.0309639 | ||||||||
\(915\) | −4.95807e107 | −0.401276 | ||||||||
\(916\) | 7.61099e107 | 0.591911 | ||||||||
\(917\) | −1.73867e107 | −0.129938 | ||||||||
\(918\) | −2.20533e107 | −0.158385 | ||||||||
\(919\) | 4.69059e106 | 0.0323751 | 0.0161876 | − | 0.999869i | \(-0.494847\pi\) | ||||
0.0161876 | + | 0.999869i | \(0.494847\pi\) | |||||||
\(920\) | −2.14691e107 | −0.142416 | ||||||||
\(921\) | −1.78281e108 | −1.13665 | ||||||||
\(922\) | −1.82958e108 | −1.12117 | ||||||||
\(923\) | −8.74847e107 | −0.515312 | ||||||||
\(924\) | 3.79082e105 | 0.00214638 | ||||||||
\(925\) | −1.53843e108 | −0.837345 | ||||||||
\(926\) | −8.33167e107 | −0.435944 | ||||||||
\(927\) | −6.61227e107 | −0.332614 | ||||||||
\(928\) | −5.61884e107 | −0.271735 | ||||||||
\(929\) | 9.33420e107 | 0.434014 | 0.217007 | − | 0.976170i | \(-0.430371\pi\) | ||||
0.217007 | + | 0.976170i | \(0.430371\pi\) | |||||||
\(930\) | 3.99393e107 | 0.178555 | ||||||||
\(931\) | 2.22873e108 | 0.958063 | ||||||||
\(932\) | 1.36964e108 | 0.566142 | ||||||||
\(933\) | 4.66597e108 | 1.85465 | ||||||||
\(934\) | −8.05407e107 | −0.307861 | ||||||||
\(935\) | 8.96276e105 | 0.00329472 | ||||||||
\(936\) | −2.81428e107 | −0.0994945 | ||||||||
\(937\) | −3.60458e108 | −1.22563 | −0.612815 | − | 0.790227i | \(-0.709963\pi\) | ||||
−0.612815 | + | 0.790227i | \(0.709963\pi\) | |||||||
\(938\) | 4.36680e107 | 0.142810 | ||||||||
\(939\) | 6.46524e108 | 2.03372 | ||||||||
\(940\) | 2.78470e107 | 0.0842580 | ||||||||
\(941\) | 4.97283e108 | 1.44738 | 0.723690 | − | 0.690125i | \(-0.242445\pi\) | ||||
0.723690 | + | 0.690125i | \(0.242445\pi\) | |||||||
\(942\) | 9.67768e107 | 0.270965 | ||||||||
\(943\) | −1.17272e108 | −0.315877 | ||||||||
\(944\) | −4.21174e106 | −0.0109140 | ||||||||
\(945\) | 1.16492e107 | 0.0290426 | ||||||||
\(946\) | 1.82072e107 | 0.0436735 | ||||||||
\(947\) | −2.44879e107 | −0.0565169 | −0.0282584 | − | 0.999601i | \(-0.508996\pi\) | ||||
−0.0282584 | + | 0.999601i | \(0.508996\pi\) | |||||||
\(948\) | −1.02300e107 | −0.0227180 | ||||||||
\(949\) | −4.97273e108 | −1.06262 | ||||||||
\(950\) | −2.95225e108 | −0.607074 | ||||||||
\(951\) | 1.00745e109 | 1.99359 | ||||||||
\(952\) | 6.05617e106 | 0.0115332 | ||||||||
\(953\) | −9.43485e108 | −1.72920 | −0.864598 | − | 0.502464i | \(-0.832427\pi\) | ||||
−0.864598 | + | 0.502464i | \(0.832427\pi\) | |||||||
\(954\) | −8.10161e107 | −0.142908 | ||||||||
\(955\) | −3.81181e108 | −0.647154 | ||||||||
\(956\) | −4.71891e107 | −0.0771131 | ||||||||
\(957\) | 3.75686e107 | 0.0590935 | ||||||||
\(958\) | −5.09064e108 | −0.770782 | ||||||||
\(959\) | 9.96762e107 | 0.145282 | ||||||||
\(960\) | −3.49394e107 | −0.0490247 | ||||||||
\(961\) | −4.33412e108 | −0.585461 | ||||||||
\(962\) | −4.29809e108 | −0.558966 | ||||||||
\(963\) | −1.14343e108 | −0.143169 | ||||||||
\(964\) | 4.52820e108 | 0.545901 | ||||||||
\(965\) | −6.65587e107 | −0.0772605 | ||||||||
\(966\) | 9.69948e107 | 0.108414 | ||||||||
\(967\) | −1.61324e108 | −0.173633 | −0.0868164 | − | 0.996224i | \(-0.527669\pi\) | ||||
−0.0868164 | + | 0.996224i | \(0.527669\pi\) | |||||||
\(968\) | 3.40742e108 | 0.353163 | ||||||||
\(969\) | 3.28306e108 | 0.327688 | ||||||||
\(970\) | 5.66527e107 | 0.0544568 | ||||||||
\(971\) | 3.21844e108 | 0.297950 | 0.148975 | − | 0.988841i | \(-0.452403\pi\) | ||||
0.148975 | + | 0.988841i | \(0.452403\pi\) | |||||||
\(972\) | −3.63242e108 | −0.323875 | ||||||||
\(973\) | −4.26135e105 | −0.000365955 0 | ||||||||
\(974\) | 1.63524e109 | 1.35263 | ||||||||
\(975\) | −1.07283e109 | −0.854799 | ||||||||
\(976\) | 3.33270e108 | 0.255787 | ||||||||
\(977\) | −1.43332e109 | −1.05972 | −0.529862 | − | 0.848084i | \(-0.677756\pi\) | ||||
−0.529862 | + | 0.848084i | \(0.677756\pi\) | |||||||
\(978\) | 1.18632e108 | 0.0844955 | ||||||||
\(979\) | 4.97981e107 | 0.0341700 | ||||||||
\(980\) | 2.53359e108 | 0.167488 | ||||||||
\(981\) | 3.13033e107 | 0.0199375 | ||||||||
\(982\) | 1.35716e109 | 0.832838 | ||||||||
\(983\) | −1.45244e109 | −0.858805 | −0.429403 | − | 0.903113i | \(-0.641276\pi\) | ||||
−0.429403 | + | 0.903113i | \(0.641276\pi\) | |||||||
\(984\) | −1.90851e108 | −0.108736 | ||||||||
\(985\) | 1.04631e109 | 0.574430 | ||||||||
\(986\) | 6.00191e108 | 0.317528 | ||||||||
\(987\) | −1.25809e108 | −0.0641411 | ||||||||
\(988\) | −8.24805e108 | −0.405250 | ||||||||
\(989\) | 4.65864e109 | 2.20594 | ||||||||
\(990\) | 5.88634e106 | 0.00268634 | ||||||||
\(991\) | 8.66392e108 | 0.381089 | 0.190544 | − | 0.981679i | \(-0.438975\pi\) | ||||
0.190544 | + | 0.981679i | \(0.438975\pi\) | |||||||
\(992\) | −2.68463e108 | −0.113817 | ||||||||
\(993\) | −3.23958e108 | −0.132386 | ||||||||
\(994\) | 1.23642e108 | 0.0487039 | ||||||||
\(995\) | −1.16941e108 | −0.0444042 | ||||||||
\(996\) | −1.56336e109 | −0.572258 | ||||||||
\(997\) | 1.09926e109 | 0.387905 | 0.193953 | − | 0.981011i | \(-0.437869\pi\) | ||||
0.193953 | + | 0.981011i | \(0.437869\pi\) | |||||||
\(998\) | 7.89938e108 | 0.268738 | ||||||||
\(999\) | −2.21200e109 | −0.725512 |
(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 | 2.74.a.a.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.74.a.a.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial |