Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,30,Mod(1,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 30, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.1");
S:= CuspForms(chi, 30);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 30 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.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: | \(111.883889004\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 110200839 x^{4} - 84515300136 x^{3} + \cdots - 12\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{8}\cdot 5^{2}\cdot 7^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-7908.19\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −30888.8 | −1.33311 | −0.666555 | − | 0.745456i | \(-0.732232\pi\) | ||||
−0.666555 | + | 0.745456i | \(0.732232\pi\) | |||||||
\(3\) | 4.78297e6 | 0.577350 | ||||||||
\(4\) | 4.17246e8 | 0.777181 | ||||||||
\(5\) | −8.65686e9 | −0.634301 | −0.317151 | − | 0.948375i | \(-0.602726\pi\) | ||||
−0.317151 | + | 0.948375i | \(0.602726\pi\) | |||||||
\(6\) | −1.47740e11 | −0.769671 | ||||||||
\(7\) | 6.78223e11 | 0.377964 | ||||||||
\(8\) | 3.69508e12 | 0.297043 | ||||||||
\(9\) | 2.28768e13 | 0.333333 | ||||||||
\(10\) | 2.67400e14 | 0.845593 | ||||||||
\(11\) | −2.24344e15 | −1.78123 | −0.890616 | − | 0.454756i | \(-0.849726\pi\) | ||||
−0.890616 | + | 0.454756i | \(0.849726\pi\) | |||||||
\(12\) | 1.99567e15 | 0.448705 | ||||||||
\(13\) | 1.22120e16 | 0.860216 | 0.430108 | − | 0.902778i | \(-0.358476\pi\) | ||||
0.430108 | + | 0.902778i | \(0.358476\pi\) | |||||||
\(14\) | −2.09495e16 | −0.503868 | ||||||||
\(15\) | −4.14055e16 | −0.366214 | ||||||||
\(16\) | −3.38144e17 | −1.17317 | ||||||||
\(17\) | 9.55820e17 | 1.37679 | 0.688394 | − | 0.725337i | \(-0.258316\pi\) | ||||
0.688394 | + | 0.725337i | \(0.258316\pi\) | |||||||
\(18\) | −7.06636e17 | −0.444370 | ||||||||
\(19\) | −1.62011e18 | −0.465175 | −0.232588 | − | 0.972575i | \(-0.574719\pi\) | ||||
−0.232588 | + | 0.972575i | \(0.574719\pi\) | |||||||
\(20\) | −3.61204e18 | −0.492966 | ||||||||
\(21\) | 3.24392e18 | 0.218218 | ||||||||
\(22\) | 6.92971e19 | 2.37458 | ||||||||
\(23\) | 3.65594e19 | 0.657576 | 0.328788 | − | 0.944404i | \(-0.393360\pi\) | ||||
0.328788 | + | 0.944404i | \(0.393360\pi\) | |||||||
\(24\) | 1.76734e19 | 0.171498 | ||||||||
\(25\) | −1.11323e20 | −0.597662 | ||||||||
\(26\) | −3.77213e20 | −1.14676 | ||||||||
\(27\) | 1.09419e20 | 0.192450 | ||||||||
\(28\) | 2.82986e20 | 0.293747 | ||||||||
\(29\) | 1.08298e21 | 0.675849 | 0.337925 | − | 0.941173i | \(-0.390275\pi\) | ||||
0.337925 | + | 0.941173i | \(0.390275\pi\) | |||||||
\(30\) | 1.27897e21 | 0.488203 | ||||||||
\(31\) | −6.95263e21 | −1.64970 | −0.824849 | − | 0.565353i | \(-0.808740\pi\) | ||||
−0.824849 | + | 0.565353i | \(0.808740\pi\) | |||||||
\(32\) | 8.46106e21 | 1.26692 | ||||||||
\(33\) | −1.07303e22 | −1.02839 | ||||||||
\(34\) | −2.95241e22 | −1.83541 | ||||||||
\(35\) | −5.87128e21 | −0.239743 | ||||||||
\(36\) | 9.54524e21 | 0.259060 | ||||||||
\(37\) | −9.83243e22 | −1.79364 | −0.896821 | − | 0.442394i | \(-0.854129\pi\) | ||||
−0.896821 | + | 0.442394i | \(0.854129\pi\) | |||||||
\(38\) | 5.00431e22 | 0.620130 | ||||||||
\(39\) | 5.84095e22 | 0.496646 | ||||||||
\(40\) | −3.19878e22 | −0.188415 | ||||||||
\(41\) | 3.16613e22 | 0.130366 | 0.0651828 | − | 0.997873i | \(-0.479237\pi\) | ||||
0.0651828 | + | 0.997873i | \(0.479237\pi\) | |||||||
\(42\) | −1.00201e23 | −0.290908 | ||||||||
\(43\) | 8.33832e23 | 1.72102 | 0.860510 | − | 0.509433i | \(-0.170145\pi\) | ||||
0.860510 | + | 0.509433i | \(0.170145\pi\) | |||||||
\(44\) | −9.36065e23 | −1.38434 | ||||||||
\(45\) | −1.98041e23 | −0.211434 | ||||||||
\(46\) | −1.12928e24 | −0.876620 | ||||||||
\(47\) | 1.90790e24 | 1.08427 | 0.542133 | − | 0.840293i | \(-0.317617\pi\) | ||||
0.542133 | + | 0.840293i | \(0.317617\pi\) | |||||||
\(48\) | −1.61733e24 | −0.677331 | ||||||||
\(49\) | 4.59987e23 | 0.142857 | ||||||||
\(50\) | 3.43864e24 | 0.796749 | ||||||||
\(51\) | 4.57166e24 | 0.794888 | ||||||||
\(52\) | 5.09539e24 | 0.668543 | ||||||||
\(53\) | −4.34860e24 | −0.432861 | −0.216431 | − | 0.976298i | \(-0.569442\pi\) | ||||
−0.216431 | + | 0.976298i | \(0.569442\pi\) | |||||||
\(54\) | −3.37982e24 | −0.256557 | ||||||||
\(55\) | 1.94211e25 | 1.12984 | ||||||||
\(56\) | 2.50609e24 | 0.112272 | ||||||||
\(57\) | −7.74893e24 | −0.268569 | ||||||||
\(58\) | −3.34520e25 | −0.900981 | ||||||||
\(59\) | 2.04999e24 | 0.0430922 | 0.0215461 | − | 0.999768i | \(-0.493141\pi\) | ||||
0.0215461 | + | 0.999768i | \(0.493141\pi\) | |||||||
\(60\) | −1.72763e25 | −0.284614 | ||||||||
\(61\) | 1.44716e26 | 1.87600 | 0.937999 | − | 0.346637i | \(-0.112676\pi\) | ||||
0.937999 | + | 0.346637i | \(0.112676\pi\) | |||||||
\(62\) | 2.14758e26 | 2.19923 | ||||||||
\(63\) | 1.55156e25 | 0.125988 | ||||||||
\(64\) | −7.98123e25 | −0.515775 | ||||||||
\(65\) | −1.05717e26 | −0.545636 | ||||||||
\(66\) | 3.31446e26 | 1.37096 | ||||||||
\(67\) | −1.63239e26 | −0.542923 | −0.271461 | − | 0.962449i | \(-0.587507\pi\) | ||||
−0.271461 | + | 0.962449i | \(0.587507\pi\) | |||||||
\(68\) | 3.98812e26 | 1.07001 | ||||||||
\(69\) | 1.74863e26 | 0.379651 | ||||||||
\(70\) | 1.81357e26 | 0.319604 | ||||||||
\(71\) | 5.57720e26 | 0.800148 | 0.400074 | − | 0.916483i | \(-0.368984\pi\) | ||||
0.400074 | + | 0.916483i | \(0.368984\pi\) | |||||||
\(72\) | 8.45316e25 | 0.0990142 | ||||||||
\(73\) | 1.06236e27 | 1.01880 | 0.509400 | − | 0.860530i | \(-0.329867\pi\) | ||||
0.509400 | + | 0.860530i | \(0.329867\pi\) | |||||||
\(74\) | 3.03712e27 | 2.39112 | ||||||||
\(75\) | −5.32456e26 | −0.345060 | ||||||||
\(76\) | −6.75983e26 | −0.361525 | ||||||||
\(77\) | −1.52155e27 | −0.673242 | ||||||||
\(78\) | −1.80420e27 | −0.662083 | ||||||||
\(79\) | −3.19168e26 | −0.0973702 | −0.0486851 | − | 0.998814i | \(-0.515503\pi\) | ||||
−0.0486851 | + | 0.998814i | \(0.515503\pi\) | |||||||
\(80\) | 2.92726e27 | 0.744144 | ||||||||
\(81\) | 5.23348e26 | 0.111111 | ||||||||
\(82\) | −9.77979e26 | −0.173792 | ||||||||
\(83\) | −1.02077e28 | −1.52158 | −0.760789 | − | 0.648999i | \(-0.775188\pi\) | ||||
−0.760789 | + | 0.648999i | \(0.775188\pi\) | |||||||
\(84\) | 1.35351e27 | 0.169595 | ||||||||
\(85\) | −8.27440e27 | −0.873298 | ||||||||
\(86\) | −2.57561e28 | −2.29431 | ||||||||
\(87\) | 5.17986e27 | 0.390202 | ||||||||
\(88\) | −8.28969e27 | −0.529102 | ||||||||
\(89\) | 3.36276e28 | 1.82197 | 0.910985 | − | 0.412439i | \(-0.135323\pi\) | ||||
0.910985 | + | 0.412439i | \(0.135323\pi\) | |||||||
\(90\) | 6.11725e27 | 0.281864 | ||||||||
\(91\) | 8.28244e27 | 0.325131 | ||||||||
\(92\) | 1.52543e28 | 0.511055 | ||||||||
\(93\) | −3.32542e28 | −0.952453 | ||||||||
\(94\) | −5.89326e28 | −1.44545 | ||||||||
\(95\) | 1.40251e28 | 0.295061 | ||||||||
\(96\) | 4.04690e28 | 0.731458 | ||||||||
\(97\) | −8.94109e28 | −1.39059 | −0.695297 | − | 0.718723i | \(-0.744727\pi\) | ||||
−0.695297 | + | 0.718723i | \(0.744727\pi\) | |||||||
\(98\) | −1.42084e28 | −0.190444 | ||||||||
\(99\) | −5.13227e28 | −0.593744 | ||||||||
\(100\) | −4.64491e28 | −0.464491 | ||||||||
\(101\) | 1.50865e28 | 0.130596 | 0.0652979 | − | 0.997866i | \(-0.479200\pi\) | ||||
0.0652979 | + | 0.997866i | \(0.479200\pi\) | |||||||
\(102\) | −1.41213e29 | −1.05967 | ||||||||
\(103\) | 5.98748e28 | 0.390036 | 0.195018 | − | 0.980800i | \(-0.437523\pi\) | ||||
0.195018 | + | 0.980800i | \(0.437523\pi\) | |||||||
\(104\) | 4.51242e28 | 0.255521 | ||||||||
\(105\) | −2.80822e28 | −0.138416 | ||||||||
\(106\) | 1.34323e29 | 0.577052 | ||||||||
\(107\) | −1.38251e29 | −0.518328 | −0.259164 | − | 0.965833i | \(-0.583447\pi\) | ||||
−0.259164 | + | 0.965833i | \(0.583447\pi\) | |||||||
\(108\) | 4.56546e28 | 0.149568 | ||||||||
\(109\) | −3.00269e29 | −0.860649 | −0.430324 | − | 0.902674i | \(-0.641601\pi\) | ||||
−0.430324 | + | 0.902674i | \(0.641601\pi\) | |||||||
\(110\) | −5.99896e29 | −1.50620 | ||||||||
\(111\) | −4.70282e29 | −1.03556 | ||||||||
\(112\) | −2.29337e29 | −0.443417 | ||||||||
\(113\) | 6.59917e29 | 1.12164 | 0.560818 | − | 0.827939i | \(-0.310487\pi\) | ||||
0.560818 | + | 0.827939i | \(0.310487\pi\) | |||||||
\(114\) | 2.39355e29 | 0.358032 | ||||||||
\(115\) | −3.16490e29 | −0.417101 | ||||||||
\(116\) | 4.51869e29 | 0.525257 | ||||||||
\(117\) | 2.79371e29 | 0.286739 | ||||||||
\(118\) | −6.33218e28 | −0.0574466 | ||||||||
\(119\) | 6.48259e29 | 0.520377 | ||||||||
\(120\) | −1.52997e29 | −0.108781 | ||||||||
\(121\) | 3.44671e30 | 2.17279 | ||||||||
\(122\) | −4.47009e30 | −2.50091 | ||||||||
\(123\) | 1.51435e29 | 0.0752666 | ||||||||
\(124\) | −2.90095e30 | −1.28211 | ||||||||
\(125\) | 2.57618e30 | 1.01340 | ||||||||
\(126\) | −4.79257e29 | −0.167956 | ||||||||
\(127\) | −5.55715e30 | −1.73659 | −0.868297 | − | 0.496044i | \(-0.834785\pi\) | ||||
−0.868297 | + | 0.496044i | \(0.834785\pi\) | |||||||
\(128\) | −2.07719e30 | −0.579338 | ||||||||
\(129\) | 3.98819e30 | 0.993632 | ||||||||
\(130\) | 3.26548e30 | 0.727392 | ||||||||
\(131\) | −1.14915e30 | −0.229056 | −0.114528 | − | 0.993420i | \(-0.536536\pi\) | ||||
−0.114528 | + | 0.993420i | \(0.536536\pi\) | |||||||
\(132\) | −4.47717e30 | −0.799248 | ||||||||
\(133\) | −1.09879e30 | −0.175820 | ||||||||
\(134\) | 5.04224e30 | 0.723776 | ||||||||
\(135\) | −9.47225e29 | −0.122071 | ||||||||
\(136\) | 3.53183e30 | 0.408965 | ||||||||
\(137\) | −1.26350e31 | −1.31561 | −0.657804 | − | 0.753189i | \(-0.728514\pi\) | ||||
−0.657804 | + | 0.753189i | \(0.728514\pi\) | |||||||
\(138\) | −5.40129e30 | −0.506117 | ||||||||
\(139\) | −1.81277e31 | −1.52977 | −0.764887 | − | 0.644164i | \(-0.777205\pi\) | ||||
−0.764887 | + | 0.644164i | \(0.777205\pi\) | |||||||
\(140\) | −2.44977e30 | −0.186324 | ||||||||
\(141\) | 9.12541e30 | 0.626002 | ||||||||
\(142\) | −1.72273e31 | −1.06668 | ||||||||
\(143\) | −2.73968e31 | −1.53224 | ||||||||
\(144\) | −7.73564e30 | −0.391057 | ||||||||
\(145\) | −9.37522e30 | −0.428692 | ||||||||
\(146\) | −3.28149e31 | −1.35817 | ||||||||
\(147\) | 2.20010e30 | 0.0824786 | ||||||||
\(148\) | −4.10254e31 | −1.39398 | ||||||||
\(149\) | −3.04363e31 | −0.937975 | −0.468988 | − | 0.883205i | \(-0.655381\pi\) | ||||
−0.468988 | + | 0.883205i | \(0.655381\pi\) | |||||||
\(150\) | 1.64469e31 | 0.460003 | ||||||||
\(151\) | −6.86856e31 | −1.74462 | −0.872308 | − | 0.488956i | \(-0.837378\pi\) | ||||
−0.872308 | + | 0.488956i | \(0.837378\pi\) | |||||||
\(152\) | −5.98643e30 | −0.138177 | ||||||||
\(153\) | 2.18661e31 | 0.458929 | ||||||||
\(154\) | 4.69989e31 | 0.897506 | ||||||||
\(155\) | 6.01879e31 | 1.04641 | ||||||||
\(156\) | 2.43711e31 | 0.385983 | ||||||||
\(157\) | −6.33549e31 | −0.914609 | −0.457304 | − | 0.889310i | \(-0.651185\pi\) | ||||
−0.457304 | + | 0.889310i | \(0.651185\pi\) | |||||||
\(158\) | 9.85869e30 | 0.129805 | ||||||||
\(159\) | −2.07992e31 | −0.249913 | ||||||||
\(160\) | −7.32462e31 | −0.803610 | ||||||||
\(161\) | 2.47954e31 | 0.248540 | ||||||||
\(162\) | −1.61656e31 | −0.148123 | ||||||||
\(163\) | 3.82410e30 | 0.0320486 | 0.0160243 | − | 0.999872i | \(-0.494899\pi\) | ||||
0.0160243 | + | 0.999872i | \(0.494899\pi\) | |||||||
\(164\) | 1.32105e31 | 0.101318 | ||||||||
\(165\) | 9.28908e31 | 0.652312 | ||||||||
\(166\) | 3.15302e32 | 2.02843 | ||||||||
\(167\) | 4.74464e31 | 0.279778 | 0.139889 | − | 0.990167i | \(-0.455325\pi\) | ||||
0.139889 | + | 0.990167i | \(0.455325\pi\) | |||||||
\(168\) | 1.19865e31 | 0.0648200 | ||||||||
\(169\) | −5.24058e31 | −0.260029 | ||||||||
\(170\) | 2.55586e32 | 1.16420 | ||||||||
\(171\) | −3.70629e31 | −0.155058 | ||||||||
\(172\) | 3.47913e32 | 1.33754 | ||||||||
\(173\) | 1.42061e32 | 0.502119 | 0.251060 | − | 0.967972i | \(-0.419221\pi\) | ||||
0.251060 | + | 0.967972i | \(0.419221\pi\) | |||||||
\(174\) | −1.60000e32 | −0.520182 | ||||||||
\(175\) | −7.55020e31 | −0.225895 | ||||||||
\(176\) | 7.58605e32 | 2.08969 | ||||||||
\(177\) | 9.80506e30 | 0.0248793 | ||||||||
\(178\) | −1.03872e33 | −2.42889 | ||||||||
\(179\) | −6.38161e32 | −1.37582 | −0.687909 | − | 0.725797i | \(-0.741471\pi\) | ||||
−0.687909 | + | 0.725797i | \(0.741471\pi\) | |||||||
\(180\) | −8.26318e31 | −0.164322 | ||||||||
\(181\) | 9.60436e32 | 1.76250 | 0.881250 | − | 0.472650i | \(-0.156703\pi\) | ||||
0.881250 | + | 0.472650i | \(0.156703\pi\) | |||||||
\(182\) | −2.55835e32 | −0.433435 | ||||||||
\(183\) | 6.92170e32 | 1.08311 | ||||||||
\(184\) | 1.35090e32 | 0.195328 | ||||||||
\(185\) | 8.51180e32 | 1.13771 | ||||||||
\(186\) | 1.02718e33 | 1.26972 | ||||||||
\(187\) | −2.14432e33 | −2.45238 | ||||||||
\(188\) | 7.96062e32 | 0.842671 | ||||||||
\(189\) | 7.42105e31 | 0.0727393 | ||||||||
\(190\) | −4.33217e32 | −0.393349 | ||||||||
\(191\) | 8.79105e32 | 0.739702 | 0.369851 | − | 0.929091i | \(-0.379409\pi\) | ||||
0.369851 | + | 0.929091i | \(0.379409\pi\) | |||||||
\(192\) | −3.81740e32 | −0.297783 | ||||||||
\(193\) | −8.01268e32 | −0.579691 | −0.289846 | − | 0.957073i | \(-0.593604\pi\) | ||||
−0.289846 | + | 0.957073i | \(0.593604\pi\) | |||||||
\(194\) | 2.76179e33 | 1.85381 | ||||||||
\(195\) | −5.05643e32 | −0.315023 | ||||||||
\(196\) | 1.91927e32 | 0.111026 | ||||||||
\(197\) | −7.50182e32 | −0.403094 | −0.201547 | − | 0.979479i | \(-0.564597\pi\) | ||||
−0.201547 | + | 0.979479i | \(0.564597\pi\) | |||||||
\(198\) | 1.58530e33 | 0.791526 | ||||||||
\(199\) | −1.54091e33 | −0.715168 | −0.357584 | − | 0.933881i | \(-0.616399\pi\) | ||||
−0.357584 | + | 0.933881i | \(0.616399\pi\) | |||||||
\(200\) | −4.11348e32 | −0.177531 | ||||||||
\(201\) | −7.80765e32 | −0.313457 | ||||||||
\(202\) | −4.66004e32 | −0.174098 | ||||||||
\(203\) | 7.34503e32 | 0.255447 | ||||||||
\(204\) | 1.90750e33 | 0.617772 | ||||||||
\(205\) | −2.74088e32 | −0.0826910 | ||||||||
\(206\) | −1.84946e33 | −0.519960 | ||||||||
\(207\) | 8.36362e32 | 0.219192 | ||||||||
\(208\) | −4.12940e33 | −1.00918 | ||||||||
\(209\) | 3.63461e33 | 0.828585 | ||||||||
\(210\) | 8.67424e32 | 0.184523 | ||||||||
\(211\) | −2.96174e33 | −0.588100 | −0.294050 | − | 0.955790i | \(-0.595003\pi\) | ||||
−0.294050 | + | 0.955790i | \(0.595003\pi\) | |||||||
\(212\) | −1.81443e33 | −0.336412 | ||||||||
\(213\) | 2.66756e33 | 0.461966 | ||||||||
\(214\) | 4.27042e33 | 0.690988 | ||||||||
\(215\) | −7.21837e33 | −1.09165 | ||||||||
\(216\) | 4.04312e32 | 0.0571659 | ||||||||
\(217\) | −4.71543e33 | −0.623527 | ||||||||
\(218\) | 9.27493e33 | 1.14734 | ||||||||
\(219\) | 5.08122e33 | 0.588205 | ||||||||
\(220\) | 8.10339e33 | 0.878088 | ||||||||
\(221\) | 1.16725e34 | 1.18433 | ||||||||
\(222\) | 1.45264e34 | 1.38051 | ||||||||
\(223\) | 1.43711e33 | 0.127958 | 0.0639791 | − | 0.997951i | \(-0.479621\pi\) | ||||
0.0639791 | + | 0.997951i | \(0.479621\pi\) | |||||||
\(224\) | 5.73849e33 | 0.478852 | ||||||||
\(225\) | −2.54672e33 | −0.199221 | ||||||||
\(226\) | −2.03840e34 | −1.49526 | ||||||||
\(227\) | −1.46215e34 | −1.00604 | −0.503021 | − | 0.864274i | \(-0.667778\pi\) | ||||
−0.503021 | + | 0.864274i | \(0.667778\pi\) | |||||||
\(228\) | −3.23321e33 | −0.208727 | ||||||||
\(229\) | −4.58587e33 | −0.277848 | −0.138924 | − | 0.990303i | \(-0.544364\pi\) | ||||
−0.138924 | + | 0.990303i | \(0.544364\pi\) | |||||||
\(230\) | 9.77598e33 | 0.556041 | ||||||||
\(231\) | −7.27754e33 | −0.388697 | ||||||||
\(232\) | 4.00170e33 | 0.200756 | ||||||||
\(233\) | 1.29997e33 | 0.0612735 | 0.0306368 | − | 0.999531i | \(-0.490246\pi\) | ||||
0.0306368 | + | 0.999531i | \(0.490246\pi\) | |||||||
\(234\) | −8.62942e33 | −0.382254 | ||||||||
\(235\) | −1.65164e34 | −0.687751 | ||||||||
\(236\) | 8.55351e32 | 0.0334904 | ||||||||
\(237\) | −1.52657e33 | −0.0562167 | ||||||||
\(238\) | −2.00239e34 | −0.693719 | ||||||||
\(239\) | −4.10278e33 | −0.133755 | −0.0668773 | − | 0.997761i | \(-0.521304\pi\) | ||||
−0.0668773 | + | 0.997761i | \(0.521304\pi\) | |||||||
\(240\) | 1.40010e34 | 0.429632 | ||||||||
\(241\) | −3.78274e34 | −1.09285 | −0.546424 | − | 0.837509i | \(-0.684011\pi\) | ||||
−0.546424 | + | 0.837509i | \(0.684011\pi\) | |||||||
\(242\) | −1.06465e35 | −2.89656 | ||||||||
\(243\) | 2.50316e33 | 0.0641500 | ||||||||
\(244\) | 6.03819e34 | 1.45799 | ||||||||
\(245\) | −3.98204e33 | −0.0906144 | ||||||||
\(246\) | −4.67764e33 | −0.100339 | ||||||||
\(247\) | −1.97847e34 | −0.400151 | ||||||||
\(248\) | −2.56905e34 | −0.490031 | ||||||||
\(249\) | −4.88230e34 | −0.878484 | ||||||||
\(250\) | −7.95749e34 | −1.35097 | ||||||||
\(251\) | 3.98771e34 | 0.638933 | 0.319466 | − | 0.947598i | \(-0.396496\pi\) | ||||
0.319466 | + | 0.947598i | \(0.396496\pi\) | |||||||
\(252\) | 6.47380e33 | 0.0979155 | ||||||||
\(253\) | −8.20188e34 | −1.17129 | ||||||||
\(254\) | 1.71654e35 | 2.31507 | ||||||||
\(255\) | −3.95762e34 | −0.504199 | ||||||||
\(256\) | 1.07011e35 | 1.28810 | ||||||||
\(257\) | −4.60277e34 | −0.523587 | −0.261794 | − | 0.965124i | \(-0.584314\pi\) | ||||
−0.261794 | + | 0.965124i | \(0.584314\pi\) | |||||||
\(258\) | −1.23190e35 | −1.32462 | ||||||||
\(259\) | −6.66858e34 | −0.677933 | ||||||||
\(260\) | −4.41101e34 | −0.424057 | ||||||||
\(261\) | 2.47751e34 | 0.225283 | ||||||||
\(262\) | 3.54957e34 | 0.305357 | ||||||||
\(263\) | −6.06941e34 | −0.494069 | −0.247035 | − | 0.969007i | \(-0.579456\pi\) | ||||
−0.247035 | + | 0.969007i | \(0.579456\pi\) | |||||||
\(264\) | −3.96493e34 | −0.305477 | ||||||||
\(265\) | 3.76452e34 | 0.274564 | ||||||||
\(266\) | 3.39404e34 | 0.234387 | ||||||||
\(267\) | 1.60840e35 | 1.05192 | ||||||||
\(268\) | −6.81106e34 | −0.421949 | ||||||||
\(269\) | 4.09618e34 | 0.240420 | 0.120210 | − | 0.992748i | \(-0.461643\pi\) | ||||
0.120210 | + | 0.992748i | \(0.461643\pi\) | |||||||
\(270\) | 2.92586e34 | 0.162734 | ||||||||
\(271\) | 1.78750e35 | 0.942302 | 0.471151 | − | 0.882052i | \(-0.343839\pi\) | ||||
0.471151 | + | 0.882052i | \(0.343839\pi\) | |||||||
\(272\) | −3.23204e35 | −1.61521 | ||||||||
\(273\) | 3.96147e34 | 0.187714 | ||||||||
\(274\) | 3.90279e35 | 1.75385 | ||||||||
\(275\) | 2.49747e35 | 1.06457 | ||||||||
\(276\) | 7.29606e34 | 0.295058 | ||||||||
\(277\) | −2.52704e35 | −0.969741 | −0.484870 | − | 0.874586i | \(-0.661133\pi\) | ||||
−0.484870 | + | 0.874586i | \(0.661133\pi\) | |||||||
\(278\) | 5.59942e35 | 2.03936 | ||||||||
\(279\) | −1.59054e35 | −0.549899 | ||||||||
\(280\) | −2.16949e34 | −0.0712140 | ||||||||
\(281\) | −5.43269e35 | −1.69345 | −0.846727 | − | 0.532028i | \(-0.821430\pi\) | ||||
−0.846727 | + | 0.532028i | \(0.821430\pi\) | |||||||
\(282\) | −2.81873e35 | −0.834529 | ||||||||
\(283\) | 2.46362e35 | 0.692899 | 0.346449 | − | 0.938069i | \(-0.387387\pi\) | ||||
0.346449 | + | 0.938069i | \(0.387387\pi\) | |||||||
\(284\) | 2.32706e35 | 0.621860 | ||||||||
\(285\) | 6.70814e34 | 0.170354 | ||||||||
\(286\) | 8.46255e35 | 2.04265 | ||||||||
\(287\) | 2.14734e34 | 0.0492735 | ||||||||
\(288\) | 1.93562e35 | 0.422307 | ||||||||
\(289\) | 4.31623e35 | 0.895543 | ||||||||
\(290\) | 2.89589e35 | 0.571493 | ||||||||
\(291\) | −4.27649e35 | −0.802859 | ||||||||
\(292\) | 4.43264e35 | 0.791792 | ||||||||
\(293\) | −1.66570e35 | −0.283149 | −0.141575 | − | 0.989928i | \(-0.545217\pi\) | ||||
−0.141575 | + | 0.989928i | \(0.545217\pi\) | |||||||
\(294\) | −6.79584e34 | −0.109953 | ||||||||
\(295\) | −1.77465e34 | −0.0273334 | ||||||||
\(296\) | −3.63316e35 | −0.532788 | ||||||||
\(297\) | −2.45475e35 | −0.342798 | ||||||||
\(298\) | 9.40141e35 | 1.25042 | ||||||||
\(299\) | 4.46463e35 | 0.565657 | ||||||||
\(300\) | −2.22165e35 | −0.268174 | ||||||||
\(301\) | 5.65524e35 | 0.650485 | ||||||||
\(302\) | 2.12161e36 | 2.32576 | ||||||||
\(303\) | 7.21583e34 | 0.0753995 | ||||||||
\(304\) | 5.47829e35 | 0.545730 | ||||||||
\(305\) | −1.25278e36 | −1.18995 | ||||||||
\(306\) | −6.75417e35 | −0.611803 | ||||||||
\(307\) | 5.24663e34 | 0.0453287 | 0.0226644 | − | 0.999743i | \(-0.492785\pi\) | ||||
0.0226644 | + | 0.999743i | \(0.492785\pi\) | |||||||
\(308\) | −6.34861e35 | −0.523231 | ||||||||
\(309\) | 2.86379e35 | 0.225187 | ||||||||
\(310\) | −1.85913e36 | −1.39497 | ||||||||
\(311\) | −9.88783e35 | −0.708068 | −0.354034 | − | 0.935232i | \(-0.615190\pi\) | ||||
−0.354034 | + | 0.935232i | \(0.615190\pi\) | |||||||
\(312\) | 2.15828e35 | 0.147525 | ||||||||
\(313\) | −3.78881e35 | −0.247235 | −0.123617 | − | 0.992330i | \(-0.539450\pi\) | ||||
−0.123617 | + | 0.992330i | \(0.539450\pi\) | |||||||
\(314\) | 1.95696e36 | 1.21927 | ||||||||
\(315\) | −1.34316e35 | −0.0799144 | ||||||||
\(316\) | −1.33171e35 | −0.0756742 | ||||||||
\(317\) | −2.72717e36 | −1.48031 | −0.740155 | − | 0.672437i | \(-0.765248\pi\) | ||||
−0.740155 | + | 0.672437i | \(0.765248\pi\) | |||||||
\(318\) | 6.42462e35 | 0.333161 | ||||||||
\(319\) | −2.42960e36 | −1.20384 | ||||||||
\(320\) | 6.90925e35 | 0.327157 | ||||||||
\(321\) | −6.61252e35 | −0.299257 | ||||||||
\(322\) | −7.65901e35 | −0.331331 | ||||||||
\(323\) | −1.54853e36 | −0.640447 | ||||||||
\(324\) | 2.18365e35 | 0.0863534 | ||||||||
\(325\) | −1.35948e36 | −0.514118 | ||||||||
\(326\) | −1.18122e35 | −0.0427243 | ||||||||
\(327\) | −1.43618e36 | −0.496896 | ||||||||
\(328\) | 1.16991e35 | 0.0387241 | ||||||||
\(329\) | 1.29398e36 | 0.409814 | ||||||||
\(330\) | −2.86928e36 | −0.869603 | ||||||||
\(331\) | −3.93676e35 | −0.114191 | −0.0570956 | − | 0.998369i | \(-0.518184\pi\) | ||||
−0.0570956 | + | 0.998369i | \(0.518184\pi\) | |||||||
\(332\) | −4.25911e36 | −1.18254 | ||||||||
\(333\) | −2.24934e36 | −0.597881 | ||||||||
\(334\) | −1.46556e36 | −0.372975 | ||||||||
\(335\) | 1.41313e36 | 0.344377 | ||||||||
\(336\) | −1.09691e36 | −0.256007 | ||||||||
\(337\) | −1.56266e36 | −0.349325 | −0.174662 | − | 0.984628i | \(-0.555883\pi\) | ||||
−0.174662 | + | 0.984628i | \(0.555883\pi\) | |||||||
\(338\) | 1.61875e36 | 0.346647 | ||||||||
\(339\) | 3.15636e36 | 0.647577 | ||||||||
\(340\) | −3.45246e36 | −0.678710 | ||||||||
\(341\) | 1.55978e37 | 2.93849 | ||||||||
\(342\) | 1.14483e36 | 0.206710 | ||||||||
\(343\) | 3.11973e35 | 0.0539949 | ||||||||
\(344\) | 3.08108e36 | 0.511217 | ||||||||
\(345\) | −1.51376e36 | −0.240813 | ||||||||
\(346\) | −4.38810e36 | −0.669380 | ||||||||
\(347\) | 1.22019e37 | 1.78504 | 0.892521 | − | 0.451005i | \(-0.148935\pi\) | ||||
0.892521 | + | 0.451005i | \(0.148935\pi\) | |||||||
\(348\) | 2.16128e36 | 0.303257 | ||||||||
\(349\) | −9.92389e36 | −1.33571 | −0.667857 | − | 0.744290i | \(-0.732788\pi\) | ||||
−0.667857 | + | 0.744290i | \(0.732788\pi\) | |||||||
\(350\) | 2.33216e36 | 0.301143 | ||||||||
\(351\) | 1.33622e36 | 0.165549 | ||||||||
\(352\) | −1.89819e37 | −2.25668 | ||||||||
\(353\) | 1.07725e37 | 1.22909 | 0.614543 | − | 0.788883i | \(-0.289340\pi\) | ||||
0.614543 | + | 0.788883i | \(0.289340\pi\) | |||||||
\(354\) | −3.02866e35 | −0.0331668 | ||||||||
\(355\) | −4.82811e36 | −0.507535 | ||||||||
\(356\) | 1.40310e37 | 1.41600 | ||||||||
\(357\) | 3.10060e36 | 0.300440 | ||||||||
\(358\) | 1.97120e37 | 1.83412 | ||||||||
\(359\) | −5.90053e36 | −0.527256 | −0.263628 | − | 0.964624i | \(-0.584919\pi\) | ||||
−0.263628 | + | 0.964624i | \(0.584919\pi\) | |||||||
\(360\) | −7.31778e35 | −0.0628048 | ||||||||
\(361\) | −9.50507e36 | −0.783612 | ||||||||
\(362\) | −2.96667e37 | −2.34961 | ||||||||
\(363\) | 1.64855e37 | 1.25446 | ||||||||
\(364\) | 3.45581e36 | 0.252685 | ||||||||
\(365\) | −9.19668e36 | −0.646226 | ||||||||
\(366\) | −2.13803e37 | −1.44390 | ||||||||
\(367\) | −8.73597e36 | −0.567091 | −0.283546 | − | 0.958959i | \(-0.591511\pi\) | ||||
−0.283546 | + | 0.958959i | \(0.591511\pi\) | |||||||
\(368\) | −1.23623e37 | −0.771449 | ||||||||
\(369\) | 7.24309e35 | 0.0434552 | ||||||||
\(370\) | −2.62919e37 | −1.51669 | ||||||||
\(371\) | −2.94932e36 | −0.163606 | ||||||||
\(372\) | −1.38752e37 | −0.740228 | ||||||||
\(373\) | 1.49457e37 | 0.766900 | 0.383450 | − | 0.923562i | \(-0.374736\pi\) | ||||
0.383450 | + | 0.923562i | \(0.374736\pi\) | |||||||
\(374\) | 6.62356e37 | 3.26929 | ||||||||
\(375\) | 1.23218e37 | 0.585086 | ||||||||
\(376\) | 7.04983e36 | 0.322073 | ||||||||
\(377\) | 1.32253e37 | 0.581376 | ||||||||
\(378\) | −2.29227e36 | −0.0969694 | ||||||||
\(379\) | −1.52013e37 | −0.618889 | −0.309445 | − | 0.950917i | \(-0.600143\pi\) | ||||
−0.309445 | + | 0.950917i | \(0.600143\pi\) | |||||||
\(380\) | 5.85189e36 | 0.229316 | ||||||||
\(381\) | −2.65797e37 | −1.00262 | ||||||||
\(382\) | −2.71545e37 | −0.986104 | ||||||||
\(383\) | 5.24927e36 | 0.183534 | 0.0917670 | − | 0.995781i | \(-0.470749\pi\) | ||||
0.0917670 | + | 0.995781i | \(0.470749\pi\) | |||||||
\(384\) | −9.93514e36 | −0.334481 | ||||||||
\(385\) | 1.31719e37 | 0.427038 | ||||||||
\(386\) | 2.47502e37 | 0.772792 | ||||||||
\(387\) | 1.90754e37 | 0.573673 | ||||||||
\(388\) | −3.73063e37 | −1.08074 | ||||||||
\(389\) | −4.27696e37 | −1.19362 | −0.596810 | − | 0.802382i | \(-0.703566\pi\) | ||||
−0.596810 | + | 0.802382i | \(0.703566\pi\) | |||||||
\(390\) | 1.56187e37 | 0.419960 | ||||||||
\(391\) | 3.49442e37 | 0.905341 | ||||||||
\(392\) | 1.69969e36 | 0.0424347 | ||||||||
\(393\) | −5.49633e36 | −0.132245 | ||||||||
\(394\) | 2.31722e37 | 0.537368 | ||||||||
\(395\) | 2.76299e36 | 0.0617620 | ||||||||
\(396\) | −2.14142e37 | −0.461446 | ||||||||
\(397\) | 1.50576e37 | 0.312819 | 0.156409 | − | 0.987692i | \(-0.450008\pi\) | ||||
0.156409 | + | 0.987692i | \(0.450008\pi\) | |||||||
\(398\) | 4.75969e37 | 0.953397 | ||||||||
\(399\) | −5.25550e36 | −0.101510 | ||||||||
\(400\) | 3.76432e37 | 0.701160 | ||||||||
\(401\) | 7.67293e37 | 1.37838 | 0.689188 | − | 0.724583i | \(-0.257967\pi\) | ||||
0.689188 | + | 0.724583i | \(0.257967\pi\) | |||||||
\(402\) | 2.41169e37 | 0.417872 | ||||||||
\(403\) | −8.49053e37 | −1.41910 | ||||||||
\(404\) | 6.29478e36 | 0.101496 | ||||||||
\(405\) | −4.53055e36 | −0.0704779 | ||||||||
\(406\) | −2.26879e37 | −0.340539 | ||||||||
\(407\) | 2.20585e38 | 3.19489 | ||||||||
\(408\) | 1.68926e37 | 0.236116 | ||||||||
\(409\) | 4.94517e37 | 0.667103 | 0.333552 | − | 0.942732i | \(-0.391753\pi\) | ||||
0.333552 | + | 0.942732i | \(0.391753\pi\) | |||||||
\(410\) | 8.46623e36 | 0.110236 | ||||||||
\(411\) | −6.04327e37 | −0.759567 | ||||||||
\(412\) | 2.49825e37 | 0.303128 | ||||||||
\(413\) | 1.39035e36 | 0.0162873 | ||||||||
\(414\) | −2.58342e37 | −0.292207 | ||||||||
\(415\) | 8.83664e37 | 0.965139 | ||||||||
\(416\) | 1.03326e38 | 1.08983 | ||||||||
\(417\) | −8.67041e37 | −0.883216 | ||||||||
\(418\) | −1.12269e38 | −1.10459 | ||||||||
\(419\) | 8.54276e36 | 0.0811886 | 0.0405943 | − | 0.999176i | \(-0.487075\pi\) | ||||
0.0405943 | + | 0.999176i | \(0.487075\pi\) | |||||||
\(420\) | −1.17172e37 | −0.107574 | ||||||||
\(421\) | −4.56419e37 | −0.404830 | −0.202415 | − | 0.979300i | \(-0.564879\pi\) | ||||
−0.202415 | + | 0.979300i | \(0.564879\pi\) | |||||||
\(422\) | 9.14845e37 | 0.784002 | ||||||||
\(423\) | 4.36466e37 | 0.361422 | ||||||||
\(424\) | −1.60684e37 | −0.128578 | ||||||||
\(425\) | −1.06405e38 | −0.822853 | ||||||||
\(426\) | −8.23976e37 | −0.615851 | ||||||||
\(427\) | 9.81494e37 | 0.709061 | ||||||||
\(428\) | −5.76848e37 | −0.402834 | ||||||||
\(429\) | −1.31038e38 | −0.884641 | ||||||||
\(430\) | 2.22967e38 | 1.45528 | ||||||||
\(431\) | −1.01193e38 | −0.638601 | −0.319301 | − | 0.947654i | \(-0.603448\pi\) | ||||
−0.319301 | + | 0.947654i | \(0.603448\pi\) | |||||||
\(432\) | −3.69993e37 | −0.225777 | ||||||||
\(433\) | 2.91333e38 | 1.71915 | 0.859577 | − | 0.511006i | \(-0.170727\pi\) | ||||
0.859577 | + | 0.511006i | \(0.170727\pi\) | |||||||
\(434\) | 1.45654e38 | 0.831230 | ||||||||
\(435\) | −4.48414e37 | −0.247505 | ||||||||
\(436\) | −1.25286e38 | −0.668879 | ||||||||
\(437\) | −5.92302e37 | −0.305888 | ||||||||
\(438\) | −1.56953e38 | −0.784141 | ||||||||
\(439\) | −3.78609e38 | −1.83002 | −0.915009 | − | 0.403434i | \(-0.867817\pi\) | ||||
−0.915009 | + | 0.403434i | \(0.867817\pi\) | |||||||
\(440\) | 7.17627e37 | 0.335610 | ||||||||
\(441\) | 1.05230e37 | 0.0476190 | ||||||||
\(442\) | −3.60548e38 | −1.57885 | ||||||||
\(443\) | −2.91221e38 | −1.23415 | −0.617076 | − | 0.786904i | \(-0.711683\pi\) | ||||
−0.617076 | + | 0.786904i | \(0.711683\pi\) | |||||||
\(444\) | −1.96223e38 | −0.804817 | ||||||||
\(445\) | −2.91110e38 | −1.15568 | ||||||||
\(446\) | −4.43905e37 | −0.170582 | ||||||||
\(447\) | −1.45576e38 | −0.541540 | ||||||||
\(448\) | −5.41306e37 | −0.194945 | ||||||||
\(449\) | −6.73368e37 | −0.234791 | −0.117395 | − | 0.993085i | \(-0.537454\pi\) | ||||
−0.117395 | + | 0.993085i | \(0.537454\pi\) | |||||||
\(450\) | 7.86650e37 | 0.265583 | ||||||||
\(451\) | −7.10302e37 | −0.232211 | ||||||||
\(452\) | 2.75348e38 | 0.871714 | ||||||||
\(453\) | −3.28521e38 | −1.00725 | ||||||||
\(454\) | 4.51639e38 | 1.34116 | ||||||||
\(455\) | −7.17000e37 | −0.206231 | ||||||||
\(456\) | −2.86329e37 | −0.0797765 | ||||||||
\(457\) | −4.64507e37 | −0.125374 | −0.0626870 | − | 0.998033i | \(-0.519967\pi\) | ||||
−0.0626870 | + | 0.998033i | \(0.519967\pi\) | |||||||
\(458\) | 1.41652e38 | 0.370402 | ||||||||
\(459\) | 1.04585e38 | 0.264963 | ||||||||
\(460\) | −1.32054e38 | −0.324163 | ||||||||
\(461\) | −9.77508e37 | −0.232518 | −0.116259 | − | 0.993219i | \(-0.537090\pi\) | ||||
−0.116259 | + | 0.993219i | \(0.537090\pi\) | |||||||
\(462\) | 2.24794e38 | 0.518175 | ||||||||
\(463\) | 2.31687e38 | 0.517581 | 0.258790 | − | 0.965934i | \(-0.416676\pi\) | ||||
0.258790 | + | 0.965934i | \(0.416676\pi\) | |||||||
\(464\) | −3.66203e38 | −0.792887 | ||||||||
\(465\) | 2.87877e38 | 0.604142 | ||||||||
\(466\) | −4.01545e37 | −0.0816843 | ||||||||
\(467\) | −1.90269e38 | −0.375209 | −0.187605 | − | 0.982245i | \(-0.560072\pi\) | ||||
−0.187605 | + | 0.982245i | \(0.560072\pi\) | |||||||
\(468\) | 1.16566e38 | 0.222848 | ||||||||
\(469\) | −1.10712e38 | −0.205206 | ||||||||
\(470\) | 5.10172e38 | 0.916848 | ||||||||
\(471\) | −3.03025e38 | −0.528050 | ||||||||
\(472\) | 7.57489e36 | 0.0128002 | ||||||||
\(473\) | −1.87065e39 | −3.06554 | ||||||||
\(474\) | 4.71538e37 | 0.0749430 | ||||||||
\(475\) | 1.80356e38 | 0.278018 | ||||||||
\(476\) | 2.70483e38 | 0.404427 | ||||||||
\(477\) | −9.94819e37 | −0.144287 | ||||||||
\(478\) | 1.26730e38 | 0.178309 | ||||||||
\(479\) | 5.73704e38 | 0.783110 | 0.391555 | − | 0.920155i | \(-0.371937\pi\) | ||||
0.391555 | + | 0.920155i | \(0.371937\pi\) | |||||||
\(480\) | −3.50334e38 | −0.463965 | ||||||||
\(481\) | −1.20073e39 | −1.54292 | ||||||||
\(482\) | 1.16844e39 | 1.45689 | ||||||||
\(483\) | 1.18596e38 | 0.143495 | ||||||||
\(484\) | 1.43813e39 | 1.68865 | ||||||||
\(485\) | 7.74018e38 | 0.882055 | ||||||||
\(486\) | −7.73194e37 | −0.0855190 | ||||||||
\(487\) | −5.36038e38 | −0.575473 | −0.287737 | − | 0.957710i | \(-0.592903\pi\) | ||||
−0.287737 | + | 0.957710i | \(0.592903\pi\) | |||||||
\(488\) | 5.34735e38 | 0.557252 | ||||||||
\(489\) | 1.82905e37 | 0.0185033 | ||||||||
\(490\) | 1.23000e38 | 0.120799 | ||||||||
\(491\) | 5.02527e38 | 0.479157 | 0.239579 | − | 0.970877i | \(-0.422991\pi\) | ||||
0.239579 | + | 0.970877i | \(0.422991\pi\) | |||||||
\(492\) | 6.31856e37 | 0.0584957 | ||||||||
\(493\) | 1.03513e39 | 0.930501 | ||||||||
\(494\) | 6.11126e38 | 0.533445 | ||||||||
\(495\) | 4.44294e38 | 0.376612 | ||||||||
\(496\) | 2.35099e39 | 1.93538 | ||||||||
\(497\) | 3.78259e38 | 0.302428 | ||||||||
\(498\) | 1.50808e39 | 1.17111 | ||||||||
\(499\) | −2.60379e39 | −1.96403 | −0.982015 | − | 0.188802i | \(-0.939540\pi\) | ||||
−0.982015 | + | 0.188802i | \(0.939540\pi\) | |||||||
\(500\) | 1.07490e39 | 0.787594 | ||||||||
\(501\) | 2.26934e38 | 0.161530 | ||||||||
\(502\) | −1.23176e39 | −0.851767 | ||||||||
\(503\) | −2.11973e38 | −0.142411 | −0.0712057 | − | 0.997462i | \(-0.522685\pi\) | ||||
−0.0712057 | + | 0.997462i | \(0.522685\pi\) | |||||||
\(504\) | 5.73312e37 | 0.0374239 | ||||||||
\(505\) | −1.30602e38 | −0.0828370 | ||||||||
\(506\) | 2.53346e39 | 1.56146 | ||||||||
\(507\) | −2.50655e38 | −0.150128 | ||||||||
\(508\) | −2.31870e39 | −1.34965 | ||||||||
\(509\) | 5.11976e38 | 0.289629 | 0.144814 | − | 0.989459i | \(-0.453741\pi\) | ||||
0.144814 | + | 0.989459i | \(0.453741\pi\) | |||||||
\(510\) | 1.22246e39 | 0.672152 | ||||||||
\(511\) | 7.20515e38 | 0.385071 | ||||||||
\(512\) | −2.19025e39 | −1.13783 | ||||||||
\(513\) | −1.77271e38 | −0.0895230 | ||||||||
\(514\) | 1.42174e39 | 0.697999 | ||||||||
\(515\) | −5.18328e38 | −0.247400 | ||||||||
\(516\) | 1.66406e39 | 0.772231 | ||||||||
\(517\) | −4.28025e39 | −1.93133 | ||||||||
\(518\) | 2.05984e39 | 0.903759 | ||||||||
\(519\) | 6.79474e38 | 0.289899 | ||||||||
\(520\) | −3.90634e38 | −0.162077 | ||||||||
\(521\) | 1.71985e39 | 0.693975 | 0.346988 | − | 0.937870i | \(-0.387205\pi\) | ||||
0.346988 | + | 0.937870i | \(0.387205\pi\) | |||||||
\(522\) | −7.65274e38 | −0.300327 | ||||||||
\(523\) | −8.39812e37 | −0.0320559 | −0.0160279 | − | 0.999872i | \(-0.505102\pi\) | ||||
−0.0160279 | + | 0.999872i | \(0.505102\pi\) | |||||||
\(524\) | −4.79476e38 | −0.178018 | ||||||||
\(525\) | −3.61124e38 | −0.130421 | ||||||||
\(526\) | 1.87477e39 | 0.658648 | ||||||||
\(527\) | −6.64546e39 | −2.27128 | ||||||||
\(528\) | 3.62838e39 | 1.20648 | ||||||||
\(529\) | −1.75447e39 | −0.567594 | ||||||||
\(530\) | −1.16281e39 | −0.366025 | ||||||||
\(531\) | 4.68973e37 | 0.0143641 | ||||||||
\(532\) | −4.58467e38 | −0.136644 | ||||||||
\(533\) | 3.86647e38 | 0.112142 | ||||||||
\(534\) | −4.96815e39 | −1.40232 | ||||||||
\(535\) | 1.19682e39 | 0.328776 | ||||||||
\(536\) | −6.03179e38 | −0.161271 | ||||||||
\(537\) | −3.05230e39 | −0.794329 | ||||||||
\(538\) | −1.26526e39 | −0.320507 | ||||||||
\(539\) | −1.03195e39 | −0.254462 | ||||||||
\(540\) | −3.95226e38 | −0.0948714 | ||||||||
\(541\) | 5.59912e39 | 1.30846 | 0.654229 | − | 0.756297i | \(-0.272993\pi\) | ||||
0.654229 | + | 0.756297i | \(0.272993\pi\) | |||||||
\(542\) | −5.52136e39 | −1.25619 | ||||||||
\(543\) | 4.59374e39 | 1.01758 | ||||||||
\(544\) | 8.08725e39 | 1.74428 | ||||||||
\(545\) | 2.59939e39 | 0.545910 | ||||||||
\(546\) | −1.22365e39 | −0.250244 | ||||||||
\(547\) | −2.35539e39 | −0.469080 | −0.234540 | − | 0.972107i | \(-0.575358\pi\) | ||||
−0.234540 | + | 0.972107i | \(0.575358\pi\) | |||||||
\(548\) | −5.27189e39 | −1.02246 | ||||||||
\(549\) | 3.31063e39 | 0.625333 | ||||||||
\(550\) | −7.71438e39 | −1.41919 | ||||||||
\(551\) | −1.75455e39 | −0.314388 | ||||||||
\(552\) | 6.46131e38 | 0.112773 | ||||||||
\(553\) | −2.16467e38 | −0.0368025 | ||||||||
\(554\) | 7.80572e39 | 1.29277 | ||||||||
\(555\) | 4.07117e39 | 0.656857 | ||||||||
\(556\) | −7.56369e39 | −1.18891 | ||||||||
\(557\) | −1.15628e40 | −1.77077 | −0.885387 | − | 0.464855i | \(-0.846106\pi\) | ||||
−0.885387 | + | 0.464855i | \(0.846106\pi\) | |||||||
\(558\) | 4.91298e39 | 0.733076 | ||||||||
\(559\) | 1.01827e40 | 1.48045 | ||||||||
\(560\) | 1.98534e39 | 0.281260 | ||||||||
\(561\) | −1.02562e40 | −1.41588 | ||||||||
\(562\) | 1.67809e40 | 2.25756 | ||||||||
\(563\) | 4.36317e39 | 0.572046 | 0.286023 | − | 0.958223i | \(-0.407667\pi\) | ||||
0.286023 | + | 0.958223i | \(0.407667\pi\) | |||||||
\(564\) | 3.80754e39 | 0.486516 | ||||||||
\(565\) | −5.71281e39 | −0.711455 | ||||||||
\(566\) | −7.60981e39 | −0.923710 | ||||||||
\(567\) | 3.54946e38 | 0.0419961 | ||||||||
\(568\) | 2.06082e39 | 0.237678 | ||||||||
\(569\) | −9.83480e39 | −1.10570 | −0.552850 | − | 0.833281i | \(-0.686460\pi\) | ||||
−0.552850 | + | 0.833281i | \(0.686460\pi\) | |||||||
\(570\) | −2.07206e39 | −0.227100 | ||||||||
\(571\) | −8.52295e39 | −0.910681 | −0.455341 | − | 0.890317i | \(-0.650483\pi\) | ||||
−0.455341 | + | 0.890317i | \(0.650483\pi\) | |||||||
\(572\) | −1.14312e40 | −1.19083 | ||||||||
\(573\) | 4.20473e39 | 0.427067 | ||||||||
\(574\) | −6.63288e38 | −0.0656870 | ||||||||
\(575\) | −4.06991e39 | −0.393008 | ||||||||
\(576\) | −1.82585e39 | −0.171925 | ||||||||
\(577\) | 4.58587e39 | 0.421087 | 0.210544 | − | 0.977584i | \(-0.432477\pi\) | ||||
0.210544 | + | 0.977584i | \(0.432477\pi\) | |||||||
\(578\) | −1.33323e40 | −1.19386 | ||||||||
\(579\) | −3.83244e39 | −0.334685 | ||||||||
\(580\) | −3.91177e39 | −0.333171 | ||||||||
\(581\) | −6.92308e39 | −0.575103 | ||||||||
\(582\) | 1.32096e40 | 1.07030 | ||||||||
\(583\) | 9.75581e39 | 0.771027 | ||||||||
\(584\) | 3.92550e39 | 0.302627 | ||||||||
\(585\) | −2.41847e39 | −0.181879 | ||||||||
\(586\) | 5.14514e39 | 0.377469 | ||||||||
\(587\) | −6.07209e39 | −0.434596 | −0.217298 | − | 0.976105i | \(-0.569724\pi\) | ||||
−0.217298 | + | 0.976105i | \(0.569724\pi\) | |||||||
\(588\) | 9.17983e38 | 0.0641008 | ||||||||
\(589\) | 1.12640e40 | 0.767399 | ||||||||
\(590\) | 5.48168e38 | 0.0364384 | ||||||||
\(591\) | −3.58809e39 | −0.232726 | ||||||||
\(592\) | 3.32477e40 | 2.10425 | ||||||||
\(593\) | 1.41593e40 | 0.874479 | 0.437240 | − | 0.899345i | \(-0.355956\pi\) | ||||
0.437240 | + | 0.899345i | \(0.355956\pi\) | |||||||
\(594\) | 7.58242e39 | 0.456988 | ||||||||
\(595\) | −5.61189e39 | −0.330075 | ||||||||
\(596\) | −1.26994e40 | −0.728976 | ||||||||
\(597\) | −7.37013e39 | −0.412903 | ||||||||
\(598\) | −1.37907e40 | −0.754082 | ||||||||
\(599\) | −1.06418e39 | −0.0567969 | −0.0283984 | − | 0.999597i | \(-0.509041\pi\) | ||||
−0.0283984 | + | 0.999597i | \(0.509041\pi\) | |||||||
\(600\) | −1.96747e39 | −0.102498 | ||||||||
\(601\) | 3.01640e40 | 1.53394 | 0.766970 | − | 0.641682i | \(-0.221763\pi\) | ||||
0.766970 | + | 0.641682i | \(0.221763\pi\) | |||||||
\(602\) | −1.74683e40 | −0.867167 | ||||||||
\(603\) | −3.73437e39 | −0.180974 | ||||||||
\(604\) | −2.86588e40 | −1.35588 | ||||||||
\(605\) | −2.98377e40 | −1.37820 | ||||||||
\(606\) | −2.22888e39 | −0.100516 | ||||||||
\(607\) | −4.98397e39 | −0.219452 | −0.109726 | − | 0.993962i | \(-0.534997\pi\) | ||||
−0.109726 | + | 0.993962i | \(0.534997\pi\) | |||||||
\(608\) | −1.37078e40 | −0.589341 | ||||||||
\(609\) | 3.51310e39 | 0.147482 | ||||||||
\(610\) | 3.86969e40 | 1.58633 | ||||||||
\(611\) | 2.32992e40 | 0.932703 | ||||||||
\(612\) | 9.12353e39 | 0.356671 | ||||||||
\(613\) | 9.73763e39 | 0.371772 | 0.185886 | − | 0.982571i | \(-0.440485\pi\) | ||||
0.185886 | + | 0.982571i | \(0.440485\pi\) | |||||||
\(614\) | −1.62062e39 | −0.0604282 | ||||||||
\(615\) | −1.31095e39 | −0.0477417 | ||||||||
\(616\) | −5.62226e39 | −0.199982 | ||||||||
\(617\) | −1.41936e40 | −0.493125 | −0.246562 | − | 0.969127i | \(-0.579301\pi\) | ||||
−0.246562 | + | 0.969127i | \(0.579301\pi\) | |||||||
\(618\) | −8.84591e39 | −0.300199 | ||||||||
\(619\) | −1.78871e40 | −0.592959 | −0.296480 | − | 0.955039i | \(-0.595813\pi\) | ||||
−0.296480 | + | 0.955039i | \(0.595813\pi\) | |||||||
\(620\) | 2.51132e40 | 0.813246 | ||||||||
\(621\) | 4.00029e39 | 0.126550 | ||||||||
\(622\) | 3.05423e40 | 0.943933 | ||||||||
\(623\) | 2.28070e40 | 0.688640 | ||||||||
\(624\) | −1.97508e40 | −0.582650 | ||||||||
\(625\) | −1.56603e39 | −0.0451379 | ||||||||
\(626\) | 1.17032e40 | 0.329591 | ||||||||
\(627\) | 1.73842e40 | 0.478384 | ||||||||
\(628\) | −2.64346e40 | −0.710816 | ||||||||
\(629\) | −9.39803e40 | −2.46946 | ||||||||
\(630\) | 4.14886e39 | 0.106535 | ||||||||
\(631\) | −6.50199e40 | −1.63163 | −0.815813 | − | 0.578316i | \(-0.803710\pi\) | ||||
−0.815813 | + | 0.578316i | \(0.803710\pi\) | |||||||
\(632\) | −1.17935e39 | −0.0289231 | ||||||||
\(633\) | −1.41659e40 | −0.339540 | ||||||||
\(634\) | 8.42389e40 | 1.97341 | ||||||||
\(635\) | 4.81075e40 | 1.10152 | ||||||||
\(636\) | −8.67837e39 | −0.194227 | ||||||||
\(637\) | 5.61734e39 | 0.122888 | ||||||||
\(638\) | 7.50474e40 | 1.60486 | ||||||||
\(639\) | 1.27589e40 | 0.266716 | ||||||||
\(640\) | 1.79820e40 | 0.367475 | ||||||||
\(641\) | 9.19232e40 | 1.83647 | 0.918235 | − | 0.396035i | \(-0.129614\pi\) | ||||
0.918235 | + | 0.396035i | \(0.129614\pi\) | |||||||
\(642\) | 2.04253e40 | 0.398942 | ||||||||
\(643\) | −5.16413e40 | −0.986139 | −0.493070 | − | 0.869990i | \(-0.664125\pi\) | ||||
−0.493070 | + | 0.869990i | \(0.664125\pi\) | |||||||
\(644\) | 1.03458e40 | 0.193161 | ||||||||
\(645\) | −3.45252e40 | −0.630262 | ||||||||
\(646\) | 4.78322e40 | 0.853786 | ||||||||
\(647\) | −6.55912e40 | −1.14481 | −0.572406 | − | 0.819971i | \(-0.693990\pi\) | ||||
−0.572406 | + | 0.819971i | \(0.693990\pi\) | |||||||
\(648\) | 1.93381e39 | 0.0330047 | ||||||||
\(649\) | −4.59904e39 | −0.0767572 | ||||||||
\(650\) | 4.19926e40 | 0.685376 | ||||||||
\(651\) | −2.25538e40 | −0.359994 | ||||||||
\(652\) | 1.59559e39 | 0.0249075 | ||||||||
\(653\) | 7.10534e40 | 1.08479 | 0.542393 | − | 0.840125i | \(-0.317519\pi\) | ||||
0.542393 | + | 0.840125i | \(0.317519\pi\) | |||||||
\(654\) | 4.43617e40 | 0.662416 | ||||||||
\(655\) | 9.94800e39 | 0.145290 | ||||||||
\(656\) | −1.07061e40 | −0.152941 | ||||||||
\(657\) | 2.43033e40 | 0.339600 | ||||||||
\(658\) | −3.99695e40 | −0.546327 | ||||||||
\(659\) | 8.95221e40 | 1.19699 | 0.598497 | − | 0.801125i | \(-0.295765\pi\) | ||||
0.598497 | + | 0.801125i | \(0.295765\pi\) | |||||||
\(660\) | 3.87583e40 | 0.506964 | ||||||||
\(661\) | 1.26579e41 | 1.61972 | 0.809862 | − | 0.586620i | \(-0.199542\pi\) | ||||
0.809862 | + | 0.586620i | \(0.199542\pi\) | |||||||
\(662\) | 1.21602e40 | 0.152229 | ||||||||
\(663\) | 5.58290e40 | 0.683775 | ||||||||
\(664\) | −3.77181e40 | −0.451974 | ||||||||
\(665\) | 9.51211e39 | 0.111523 | ||||||||
\(666\) | 6.94795e40 | 0.797040 | ||||||||
\(667\) | 3.95932e40 | 0.444422 | ||||||||
\(668\) | 1.97968e40 | 0.217438 | ||||||||
\(669\) | 6.87364e39 | 0.0738768 | ||||||||
\(670\) | −4.36500e40 | −0.459092 | ||||||||
\(671\) | −3.24661e41 | −3.34159 | ||||||||
\(672\) | 2.74470e40 | 0.276465 | ||||||||
\(673\) | −3.05450e40 | −0.301108 | −0.150554 | − | 0.988602i | \(-0.548106\pi\) | ||||
−0.150554 | + | 0.988602i | \(0.548106\pi\) | |||||||
\(674\) | 4.82685e40 | 0.465688 | ||||||||
\(675\) | −1.21809e40 | −0.115020 | ||||||||
\(676\) | −2.18661e40 | −0.202090 | ||||||||
\(677\) | −4.39630e40 | −0.397696 | −0.198848 | − | 0.980030i | \(-0.563720\pi\) | ||||
−0.198848 | + | 0.980030i | \(0.563720\pi\) | |||||||
\(678\) | −9.74962e40 | −0.863291 | ||||||||
\(679\) | −6.06405e40 | −0.525595 | ||||||||
\(680\) | −3.05746e40 | −0.259407 | ||||||||
\(681\) | −6.99340e40 | −0.580838 | ||||||||
\(682\) | −4.81797e41 | −3.91733 | ||||||||
\(683\) | 1.17734e41 | 0.937131 | 0.468565 | − | 0.883429i | \(-0.344771\pi\) | ||||
0.468565 | + | 0.883429i | \(0.344771\pi\) | |||||||
\(684\) | −1.54643e40 | −0.120508 | ||||||||
\(685\) | 1.09379e41 | 0.834491 | ||||||||
\(686\) | −9.63648e39 | −0.0719811 | ||||||||
\(687\) | −2.19341e40 | −0.160416 | ||||||||
\(688\) | −2.81955e41 | −2.01905 | ||||||||
\(689\) | −5.31049e40 | −0.372354 | ||||||||
\(690\) | 4.67582e40 | 0.321030 | ||||||||
\(691\) | −5.40635e40 | −0.363473 | −0.181737 | − | 0.983347i | \(-0.558172\pi\) | ||||
−0.181737 | + | 0.983347i | \(0.558172\pi\) | |||||||
\(692\) | 5.92744e40 | 0.390237 | ||||||||
\(693\) | −3.48082e40 | −0.224414 | ||||||||
\(694\) | −3.76900e41 | −2.37966 | ||||||||
\(695\) | 1.56929e41 | 0.970338 | ||||||||
\(696\) | 1.91400e40 | 0.115907 | ||||||||
\(697\) | 3.02625e40 | 0.179486 | ||||||||
\(698\) | 3.06537e41 | 1.78065 | ||||||||
\(699\) | 6.21772e39 | 0.0353763 | ||||||||
\(700\) | −3.15029e40 | −0.175561 | ||||||||
\(701\) | −3.18652e41 | −1.73942 | −0.869712 | − | 0.493559i | \(-0.835696\pi\) | ||||
−0.869712 | + | 0.493559i | \(0.835696\pi\) | |||||||
\(702\) | −4.12743e40 | −0.220694 | ||||||||
\(703\) | 1.59296e41 | 0.834358 | ||||||||
\(704\) | 1.79054e41 | 0.918715 | ||||||||
\(705\) | −7.89974e40 | −0.397073 | ||||||||
\(706\) | −3.32749e41 | −1.63851 | ||||||||
\(707\) | 1.02320e40 | 0.0493606 | ||||||||
\(708\) | 4.09112e39 | 0.0193357 | ||||||||
\(709\) | −2.38651e41 | −1.10508 | −0.552538 | − | 0.833488i | \(-0.686341\pi\) | ||||
−0.552538 | + | 0.833488i | \(0.686341\pi\) | |||||||
\(710\) | 1.49134e41 | 0.676599 | ||||||||
\(711\) | −7.30153e39 | −0.0324567 | ||||||||
\(712\) | 1.24257e41 | 0.541203 | ||||||||
\(713\) | −2.54184e41 | −1.08480 | ||||||||
\(714\) | −9.57739e40 | −0.400519 | ||||||||
\(715\) | 2.37171e41 | 0.971904 | ||||||||
\(716\) | −2.66270e41 | −1.06926 | ||||||||
\(717\) | −1.96235e40 | −0.0772232 | ||||||||
\(718\) | 1.82260e41 | 0.702890 | ||||||||
\(719\) | −1.96842e41 | −0.743959 | −0.371980 | − | 0.928241i | \(-0.621321\pi\) | ||||
−0.371980 | + | 0.928241i | \(0.621321\pi\) | |||||||
\(720\) | 6.69664e40 | 0.248048 | ||||||||
\(721\) | 4.06085e40 | 0.147420 | ||||||||
\(722\) | 2.93600e41 | 1.04464 | ||||||||
\(723\) | −1.80927e41 | −0.630956 | ||||||||
\(724\) | 4.00738e41 | 1.36978 | ||||||||
\(725\) | −1.20561e41 | −0.403930 | ||||||||
\(726\) | −5.09217e41 | −1.67233 | ||||||||
\(727\) | −6.04250e40 | −0.194522 | −0.0972608 | − | 0.995259i | \(-0.531008\pi\) | ||||
−0.0972608 | + | 0.995259i | \(0.531008\pi\) | |||||||
\(728\) | 3.06043e40 | 0.0965778 | ||||||||
\(729\) | 1.19725e40 | 0.0370370 | ||||||||
\(730\) | 2.84074e41 | 0.861491 | ||||||||
\(731\) | 7.96993e41 | 2.36948 | ||||||||
\(732\) | 2.88805e41 | 0.841771 | ||||||||
\(733\) | −3.82878e40 | −0.109409 | −0.0547045 | − | 0.998503i | \(-0.517422\pi\) | ||||
−0.0547045 | + | 0.998503i | \(0.517422\pi\) | |||||||
\(734\) | 2.69843e41 | 0.755995 | ||||||||
\(735\) | −1.90460e40 | −0.0523163 | ||||||||
\(736\) | 3.09331e41 | 0.833097 | ||||||||
\(737\) | 3.66216e41 | 0.967071 | ||||||||
\(738\) | −2.23730e40 | −0.0579305 | ||||||||
\(739\) | 7.59644e41 | 1.92870 | 0.964352 | − | 0.264623i | \(-0.0852476\pi\) | ||||
0.964352 | + | 0.264623i | \(0.0852476\pi\) | |||||||
\(740\) | 3.55151e41 | 0.884205 | ||||||||
\(741\) | −9.46297e40 | −0.231027 | ||||||||
\(742\) | 9.11008e40 | 0.218105 | ||||||||
\(743\) | 7.01191e41 | 1.64626 | 0.823130 | − | 0.567853i | \(-0.192226\pi\) | ||||
0.823130 | + | 0.567853i | \(0.192226\pi\) | |||||||
\(744\) | −1.22877e41 | −0.282919 | ||||||||
\(745\) | 2.63483e41 | 0.594959 | ||||||||
\(746\) | −4.61655e41 | −1.02236 | ||||||||
\(747\) | −2.33519e41 | −0.507193 | ||||||||
\(748\) | −8.94710e41 | −1.90594 | ||||||||
\(749\) | −9.37653e40 | −0.195910 | ||||||||
\(750\) | −3.80604e41 | −0.779984 | ||||||||
\(751\) | 1.74160e41 | 0.350082 | 0.175041 | − | 0.984561i | \(-0.443994\pi\) | ||||
0.175041 | + | 0.984561i | \(0.443994\pi\) | |||||||
\(752\) | −6.45143e41 | −1.27203 | ||||||||
\(753\) | 1.90731e41 | 0.368888 | ||||||||
\(754\) | −4.08515e41 | −0.775038 | ||||||||
\(755\) | 5.94602e41 | 1.10661 | ||||||||
\(756\) | 3.09640e40 | 0.0565316 | ||||||||
\(757\) | 1.20658e40 | 0.0216106 | 0.0108053 | − | 0.999942i | \(-0.496561\pi\) | ||||
0.0108053 | + | 0.999942i | \(0.496561\pi\) | |||||||
\(758\) | 4.69550e41 | 0.825047 | ||||||||
\(759\) | −3.92294e41 | −0.676247 | ||||||||
\(760\) | 5.18237e40 | 0.0876458 | ||||||||
\(761\) | 3.98373e41 | 0.661017 | 0.330508 | − | 0.943803i | \(-0.392780\pi\) | ||||
0.330508 | + | 0.943803i | \(0.392780\pi\) | |||||||
\(762\) | 8.21014e41 | 1.33661 | ||||||||
\(763\) | −2.03649e41 | −0.325295 | ||||||||
\(764\) | 3.66803e41 | 0.574882 | ||||||||
\(765\) | −1.89292e41 | −0.291099 | ||||||||
\(766\) | −1.62143e41 | −0.244671 | ||||||||
\(767\) | 2.50345e40 | 0.0370686 | ||||||||
\(768\) | 5.11829e41 | 0.743682 | ||||||||
\(769\) | 8.20510e41 | 1.16991 | 0.584954 | − | 0.811066i | \(-0.301113\pi\) | ||||
0.584954 | + | 0.811066i | \(0.301113\pi\) | |||||||
\(770\) | −4.06863e41 | −0.569289 | ||||||||
\(771\) | −2.20149e41 | −0.302293 | ||||||||
\(772\) | −3.34326e41 | −0.450525 | ||||||||
\(773\) | −8.53207e41 | −1.12837 | −0.564185 | − | 0.825648i | \(-0.690810\pi\) | ||||
−0.564185 | + | 0.825648i | \(0.690810\pi\) | |||||||
\(774\) | −5.89216e41 | −0.764769 | ||||||||
\(775\) | 7.73989e41 | 0.985962 | ||||||||
\(776\) | −3.30380e41 | −0.413066 | ||||||||
\(777\) | −3.18956e41 | −0.391405 | ||||||||
\(778\) | 1.32110e42 | 1.59123 | ||||||||
\(779\) | −5.12947e40 | −0.0606428 | ||||||||
\(780\) | −2.10977e41 | −0.244830 | ||||||||
\(781\) | −1.25121e42 | −1.42525 | ||||||||
\(782\) | −1.07938e42 | −1.20692 | ||||||||
\(783\) | 1.18499e41 | 0.130067 | ||||||||
\(784\) | −1.55541e41 | −0.167596 | ||||||||
\(785\) | 5.48455e41 | 0.580137 | ||||||||
\(786\) | 1.69775e41 | 0.176298 | ||||||||
\(787\) | 8.22773e41 | 0.838777 | 0.419389 | − | 0.907807i | \(-0.362244\pi\) | ||||
0.419389 | + | 0.907807i | \(0.362244\pi\) | |||||||
\(788\) | −3.13010e41 | −0.313277 | ||||||||
\(789\) | −2.90298e41 | −0.285251 | ||||||||
\(790\) | −8.53454e40 | −0.0823355 | ||||||||
\(791\) | 4.47571e41 | 0.423939 | ||||||||
\(792\) | −1.89641e41 | −0.176367 | ||||||||
\(793\) | 1.76726e42 | 1.61376 | ||||||||
\(794\) | −4.65110e41 | −0.417022 | ||||||||
\(795\) | 1.80056e41 | 0.158520 | ||||||||
\(796\) | −6.42939e41 | −0.555815 | ||||||||
\(797\) | −1.03982e42 | −0.882701 | −0.441350 | − | 0.897335i | \(-0.645500\pi\) | ||||
−0.441350 | + | 0.897335i | \(0.645500\pi\) | |||||||
\(798\) | 1.62336e41 | 0.135323 | ||||||||
\(799\) | 1.82361e42 | 1.49280 | ||||||||
\(800\) | −9.41913e41 | −0.757192 | ||||||||
\(801\) | 7.69293e41 | 0.607323 | ||||||||
\(802\) | −2.37007e42 | −1.83753 | ||||||||
\(803\) | −2.38334e42 | −1.81472 | ||||||||
\(804\) | −3.25771e41 | −0.243612 | ||||||||
\(805\) | −2.14651e41 | −0.157649 | ||||||||
\(806\) | 2.62262e42 | 1.89181 | ||||||||
\(807\) | 1.95919e41 | 0.138807 | ||||||||
\(808\) | 5.57459e40 | 0.0387925 | ||||||||
\(809\) | 1.08854e42 | 0.744031 | 0.372015 | − | 0.928227i | \(-0.378667\pi\) | ||||
0.372015 | + | 0.928227i | \(0.378667\pi\) | |||||||
\(810\) | 1.39943e41 | 0.0939547 | ||||||||
\(811\) | 1.94986e42 | 1.28588 | 0.642941 | − | 0.765916i | \(-0.277714\pi\) | ||||
0.642941 | + | 0.765916i | \(0.277714\pi\) | |||||||
\(812\) | 3.06468e41 | 0.198528 | ||||||||
\(813\) | 8.54954e41 | 0.544039 | ||||||||
\(814\) | −6.81359e42 | −4.25914 | ||||||||
\(815\) | −3.31047e40 | −0.0203285 | ||||||||
\(816\) | −1.54588e42 | −0.932540 | ||||||||
\(817\) | −1.35090e42 | −0.800576 | ||||||||
\(818\) | −1.52750e42 | −0.889321 | ||||||||
\(819\) | 1.89476e41 | 0.108377 | ||||||||
\(820\) | −1.14362e41 | −0.0642658 | ||||||||
\(821\) | −3.00016e41 | −0.165641 | −0.0828205 | − | 0.996564i | \(-0.526393\pi\) | ||||
−0.0828205 | + | 0.996564i | \(0.526393\pi\) | |||||||
\(822\) | 1.86669e42 | 1.01259 | ||||||||
\(823\) | 1.07893e42 | 0.575037 | 0.287519 | − | 0.957775i | \(-0.407170\pi\) | ||||
0.287519 | + | 0.957775i | \(0.407170\pi\) | |||||||
\(824\) | 2.21242e41 | 0.115857 | ||||||||
\(825\) | 1.19453e42 | 0.614633 | ||||||||
\(826\) | −4.29463e40 | −0.0217128 | ||||||||
\(827\) | 1.02449e42 | 0.508952 | 0.254476 | − | 0.967079i | \(-0.418097\pi\) | ||||
0.254476 | + | 0.967079i | \(0.418097\pi\) | |||||||
\(828\) | 3.48968e41 | 0.170352 | ||||||||
\(829\) | 1.75052e42 | 0.839703 | 0.419852 | − | 0.907593i | \(-0.362082\pi\) | ||||
0.419852 | + | 0.907593i | \(0.362082\pi\) | |||||||
\(830\) | −2.72953e42 | −1.28664 | ||||||||
\(831\) | −1.20868e42 | −0.559880 | ||||||||
\(832\) | −9.74666e41 | −0.443678 | ||||||||
\(833\) | 4.39664e41 | 0.196684 | ||||||||
\(834\) | 2.67818e42 | 1.17742 | ||||||||
\(835\) | −4.10737e41 | −0.177464 | ||||||||
\(836\) | 1.51653e42 | 0.643960 | ||||||||
\(837\) | −7.60749e41 | −0.317484 | ||||||||
\(838\) | −2.63875e41 | −0.108233 | ||||||||
\(839\) | −3.66014e41 | −0.147553 | −0.0737766 | − | 0.997275i | \(-0.523505\pi\) | ||||
−0.0737766 | + | 0.997275i | \(0.523505\pi\) | |||||||
\(840\) | −1.03766e41 | −0.0411154 | ||||||||
\(841\) | −1.39484e42 | −0.543228 | ||||||||
\(842\) | 1.40982e42 | 0.539683 | ||||||||
\(843\) | −2.59844e42 | −0.977716 | ||||||||
\(844\) | −1.23577e42 | −0.457060 | ||||||||
\(845\) | 4.53670e41 | 0.164937 | ||||||||
\(846\) | −1.34819e42 | −0.481815 | ||||||||
\(847\) | 2.33764e42 | 0.821236 | ||||||||
\(848\) | 1.47045e42 | 0.507820 | ||||||||
\(849\) | 1.17834e42 | 0.400045 | ||||||||
\(850\) | 3.28672e42 | 1.09695 | ||||||||
\(851\) | −3.59468e42 | −1.17945 | ||||||||
\(852\) | 1.11303e42 | 0.359031 | ||||||||
\(853\) | −6.63603e41 | −0.210449 | −0.105225 | − | 0.994448i | \(-0.533556\pi\) | ||||
−0.105225 | + | 0.994448i | \(0.533556\pi\) | |||||||
\(854\) | −3.03172e42 | −0.945256 | ||||||||
\(855\) | 3.20848e41 | 0.0983537 | ||||||||
\(856\) | −5.10850e41 | −0.153966 | ||||||||
\(857\) | 5.53619e42 | 1.64055 | 0.820274 | − | 0.571971i | \(-0.193821\pi\) | ||||
0.820274 | + | 0.571971i | \(0.193821\pi\) | |||||||
\(858\) | 4.04761e42 | 1.17932 | ||||||||
\(859\) | 1.48226e41 | 0.0424643 | 0.0212322 | − | 0.999775i | \(-0.493241\pi\) | ||||
0.0212322 | + | 0.999775i | \(0.493241\pi\) | |||||||
\(860\) | −3.01183e42 | −0.848405 | ||||||||
\(861\) | 1.02707e41 | 0.0284481 | ||||||||
\(862\) | 3.12572e42 | 0.851325 | ||||||||
\(863\) | −6.02545e42 | −1.61374 | −0.806869 | − | 0.590730i | \(-0.798840\pi\) | ||||
−0.806869 | + | 0.590730i | \(0.798840\pi\) | |||||||
\(864\) | 9.25801e41 | 0.243819 | ||||||||
\(865\) | −1.22980e42 | −0.318495 | ||||||||
\(866\) | −8.99891e42 | −2.29182 | ||||||||
\(867\) | 2.06444e42 | 0.517042 | ||||||||
\(868\) | −1.96749e42 | −0.484593 | ||||||||
\(869\) | 7.16033e41 | 0.173439 | ||||||||
\(870\) | 1.38510e42 | 0.329952 | ||||||||
\(871\) | −1.99347e42 | −0.467031 | ||||||||
\(872\) | −1.10952e42 | −0.255649 | ||||||||
\(873\) | −2.04543e42 | −0.463531 | ||||||||
\(874\) | 1.82955e42 | 0.407782 | ||||||||
\(875\) | 1.74722e42 | 0.383029 | ||||||||
\(876\) | 2.12012e42 | 0.457141 | ||||||||
\(877\) | −7.08427e42 | −1.50245 | −0.751227 | − | 0.660044i | \(-0.770538\pi\) | ||||
−0.751227 | + | 0.660044i | \(0.770538\pi\) | |||||||
\(878\) | 1.16948e43 | 2.43961 | ||||||||
\(879\) | −7.96698e41 | −0.163476 | ||||||||
\(880\) | −6.56714e42 | −1.32549 | ||||||||
\(881\) | −4.20382e42 | −0.834630 | −0.417315 | − | 0.908762i | \(-0.637029\pi\) | ||||
−0.417315 | + | 0.908762i | \(0.637029\pi\) | |||||||
\(882\) | −3.25043e41 | −0.0634814 | ||||||||
\(883\) | 7.79972e41 | 0.149847 | 0.0749236 | − | 0.997189i | \(-0.476129\pi\) | ||||
0.0749236 | + | 0.997189i | \(0.476129\pi\) | |||||||
\(884\) | 4.87028e42 | 0.920441 | ||||||||
\(885\) | −8.48810e40 | −0.0157810 | ||||||||
\(886\) | 8.99545e42 | 1.64526 | ||||||||
\(887\) | −2.79977e42 | −0.503768 | −0.251884 | − | 0.967757i | \(-0.581050\pi\) | ||||
−0.251884 | + | 0.967757i | \(0.581050\pi\) | |||||||
\(888\) | −1.73773e42 | −0.307605 | ||||||||
\(889\) | −3.76899e42 | −0.656371 | ||||||||
\(890\) | 8.99203e42 | 1.54064 | ||||||||
\(891\) | −1.17410e42 | −0.197915 | ||||||||
\(892\) | 5.99626e41 | 0.0994467 | ||||||||
\(893\) | −3.09100e42 | −0.504374 | ||||||||
\(894\) | 4.49666e42 | 0.721932 | ||||||||
\(895\) | 5.52447e42 | 0.872683 | ||||||||
\(896\) | −1.40880e42 | −0.218969 | ||||||||
\(897\) | 2.13542e42 | 0.326582 | ||||||||
\(898\) | 2.07995e42 | 0.313002 | ||||||||
\(899\) | −7.52956e42 | −1.11495 | ||||||||
\(900\) | −1.06261e42 | −0.154830 | ||||||||
\(901\) | −4.15647e42 | −0.595958 | ||||||||
\(902\) | 2.19404e42 | 0.309563 | ||||||||
\(903\) | 2.70488e42 | 0.375557 | ||||||||
\(904\) | 2.43845e42 | 0.333174 | ||||||||
\(905\) | −8.31436e42 | −1.11796 | ||||||||
\(906\) | 1.01476e43 | 1.34278 | ||||||||
\(907\) | −4.53883e42 | −0.591069 | −0.295534 | − | 0.955332i | \(-0.595498\pi\) | ||||
−0.295534 | + | 0.955332i | \(0.595498\pi\) | |||||||
\(908\) | −6.10074e42 | −0.781876 | ||||||||
\(909\) | 3.45131e41 | 0.0435319 | ||||||||
\(910\) | 2.21472e42 | 0.274928 | ||||||||
\(911\) | −1.15803e42 | −0.141483 | −0.0707414 | − | 0.997495i | \(-0.522536\pi\) | ||||
−0.0707414 | + | 0.997495i | \(0.522536\pi\) | |||||||
\(912\) | 2.62025e42 | 0.315077 | ||||||||
\(913\) | 2.29003e43 | 2.71028 | ||||||||
\(914\) | 1.43481e42 | 0.167137 | ||||||||
\(915\) | −5.99202e42 | −0.687017 | ||||||||
\(916\) | −1.91343e42 | −0.215938 | ||||||||
\(917\) | −7.79377e41 | −0.0865750 | ||||||||
\(918\) | −3.23050e42 | −0.353224 | ||||||||
\(919\) | 6.69251e42 | 0.720301 | 0.360150 | − | 0.932894i | \(-0.382725\pi\) | ||||
0.360150 | + | 0.932894i | \(0.382725\pi\) | |||||||
\(920\) | −1.16945e42 | −0.123897 | ||||||||
\(921\) | 2.50944e41 | 0.0261706 | ||||||||
\(922\) | 3.01940e42 | 0.309972 | ||||||||
\(923\) | 6.81087e42 | 0.688300 | ||||||||
\(924\) | −3.03652e42 | −0.302087 | ||||||||
\(925\) | 1.09458e43 | 1.07199 | ||||||||
\(926\) | −7.15654e42 | −0.689992 | ||||||||
\(927\) | 1.36974e42 | 0.130012 | ||||||||
\(928\) | 9.16317e42 | 0.856249 | ||||||||
\(929\) | 7.56474e42 | 0.695931 | 0.347965 | − | 0.937507i | \(-0.386873\pi\) | ||||
0.347965 | + | 0.937507i | \(0.386873\pi\) | |||||||
\(930\) | −8.89217e42 | −0.805388 | ||||||||
\(931\) | −7.45228e41 | −0.0664536 | ||||||||
\(932\) | 5.42407e41 | 0.0476206 | ||||||||
\(933\) | −4.72932e42 | −0.408804 | ||||||||
\(934\) | 5.87718e42 | 0.500195 | ||||||||
\(935\) | 1.85631e43 | 1.55555 | ||||||||
\(936\) | 1.03230e42 | 0.0851736 | ||||||||
\(937\) | −2.01813e43 | −1.63955 | −0.819774 | − | 0.572687i | \(-0.805901\pi\) | ||||
−0.819774 | + | 0.572687i | \(0.805901\pi\) | |||||||
\(938\) | 3.41976e42 | 0.273561 | ||||||||
\(939\) | −1.81218e42 | −0.142741 | ||||||||
\(940\) | −6.89140e42 | −0.534507 | ||||||||
\(941\) | −2.21689e43 | −1.69315 | −0.846575 | − | 0.532270i | \(-0.821339\pi\) | ||||
−0.846575 | + | 0.532270i | \(0.821339\pi\) | |||||||
\(942\) | 9.36006e42 | 0.703948 | ||||||||
\(943\) | 1.15752e42 | 0.0857252 | ||||||||
\(944\) | −6.93192e41 | −0.0505545 | ||||||||
\(945\) | −6.42430e41 | −0.0461386 | ||||||||
\(946\) | 5.77821e43 | 4.08669 | ||||||||
\(947\) | −2.42844e43 | −1.69142 | −0.845711 | − | 0.533641i | \(-0.820823\pi\) | ||||
−0.845711 | + | 0.533641i | \(0.820823\pi\) | |||||||
\(948\) | −6.36954e41 | −0.0436905 | ||||||||
\(949\) | 1.29735e43 | 0.876388 | ||||||||
\(950\) | −5.57097e42 | −0.370628 | ||||||||
\(951\) | −1.30440e43 | −0.854657 | ||||||||
\(952\) | 2.39537e42 | 0.154574 | ||||||||
\(953\) | −1.45517e43 | −0.924839 | −0.462420 | − | 0.886661i | \(-0.653019\pi\) | ||||
−0.462420 | + | 0.886661i | \(0.653019\pi\) | |||||||
\(954\) | 3.07287e42 | 0.192351 | ||||||||
\(955\) | −7.61029e42 | −0.469194 | ||||||||
\(956\) | −1.71187e42 | −0.103951 | ||||||||
\(957\) | −1.16207e43 | −0.695040 | ||||||||
\(958\) | −1.77210e43 | −1.04397 | ||||||||
\(959\) | −8.56934e42 | −0.497253 | ||||||||
\(960\) | 3.30467e42 | 0.188884 | ||||||||
\(961\) | 3.05771e43 | 1.72150 | ||||||||
\(962\) | 3.70892e43 | 2.05688 | ||||||||
\(963\) | −3.16275e42 | −0.172776 | ||||||||
\(964\) | −1.57833e43 | −0.849340 | ||||||||
\(965\) | 6.93647e42 | 0.367699 | ||||||||
\(966\) | −3.66328e42 | −0.191294 | ||||||||
\(967\) | 8.30591e42 | 0.427271 | 0.213635 | − | 0.976913i | \(-0.431470\pi\) | ||||
0.213635 | + | 0.976913i | \(0.431470\pi\) | |||||||
\(968\) | 1.27359e43 | 0.645411 | ||||||||
\(969\) | −7.40658e42 | −0.369762 | ||||||||
\(970\) | −2.39085e43 | −1.17588 | ||||||||
\(971\) | −1.55969e43 | −0.755718 | −0.377859 | − | 0.925863i | \(-0.623340\pi\) | ||||
−0.377859 | + | 0.925863i | \(0.623340\pi\) | |||||||
\(972\) | 1.04443e42 | 0.0498562 | ||||||||
\(973\) | −1.22946e43 | −0.578201 | ||||||||
\(974\) | 1.65575e43 | 0.767169 | ||||||||
\(975\) | −6.50234e42 | −0.296826 | ||||||||
\(976\) | −4.89346e43 | −2.20087 | ||||||||
\(977\) | 8.29683e42 | 0.367656 | 0.183828 | − | 0.982958i | \(-0.441151\pi\) | ||||
0.183828 | + | 0.982958i | \(0.441151\pi\) | |||||||
\(978\) | −5.64973e41 | −0.0246669 | ||||||||
\(979\) | −7.54416e43 | −3.24535 | ||||||||
\(980\) | −1.66149e42 | −0.0704238 | ||||||||
\(981\) | −6.86919e42 | −0.286883 | ||||||||
\(982\) | −1.55225e43 | −0.638769 | ||||||||
\(983\) | 4.23448e42 | 0.171701 | 0.0858507 | − | 0.996308i | \(-0.472639\pi\) | ||||
0.0858507 | + | 0.996308i | \(0.472639\pi\) | |||||||
\(984\) | 5.59564e41 | 0.0223574 | ||||||||
\(985\) | 6.49422e42 | 0.255683 | ||||||||
\(986\) | −3.19741e43 | −1.24046 | ||||||||
\(987\) | 6.18907e42 | 0.236606 | ||||||||
\(988\) | −8.25509e42 | −0.310990 | ||||||||
\(989\) | 3.04844e43 | 1.13170 | ||||||||
\(990\) | −1.37237e43 | −0.502066 | ||||||||
\(991\) | 1.25102e43 | 0.451019 | 0.225510 | − | 0.974241i | \(-0.427595\pi\) | ||||
0.225510 | + | 0.974241i | \(0.427595\pi\) | |||||||
\(992\) | −5.88266e43 | −2.09004 | ||||||||
\(993\) | −1.88294e42 | −0.0659283 | ||||||||
\(994\) | −1.16840e43 | −0.403169 | ||||||||
\(995\) | 1.33395e43 | 0.453632 | ||||||||
\(996\) | −2.03712e43 | −0.682740 | ||||||||
\(997\) | −1.78459e43 | −0.589467 | −0.294734 | − | 0.955579i | \(-0.595231\pi\) | ||||
−0.294734 | + | 0.955579i | \(0.595231\pi\) | |||||||
\(998\) | 8.04279e43 | 2.61827 | ||||||||
\(999\) | −1.07585e43 | −0.345186 |
(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 | 21.30.a.a.1.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.30.a.a.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial |