Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,22,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(27.9477344287\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{157921}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 39480 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4}\cdot 5\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-198.196\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1024.00 | −0.707107 | ||||||||
\(3\) | 47924.0 | 0.468576 | 0.234288 | − | 0.972167i | \(-0.424724\pi\) | ||||
0.234288 | + | 0.972167i | \(0.424724\pi\) | |||||||
\(4\) | 1.04858e6 | 0.500000 | ||||||||
\(5\) | −9.76562e6 | −0.447214 | ||||||||
\(6\) | −4.90741e7 | −0.331333 | ||||||||
\(7\) | 6.67863e8 | 0.893631 | 0.446815 | − | 0.894626i | \(-0.352558\pi\) | ||||
0.446815 | + | 0.894626i | \(0.352558\pi\) | |||||||
\(8\) | −1.07374e9 | −0.353553 | ||||||||
\(9\) | −8.16365e9 | −0.780437 | ||||||||
\(10\) | 1.00000e10 | 0.316228 | ||||||||
\(11\) | −1.26793e11 | −1.47391 | −0.736957 | − | 0.675940i | \(-0.763738\pi\) | ||||
−0.736957 | + | 0.675940i | \(0.763738\pi\) | |||||||
\(12\) | 5.02519e10 | 0.234288 | ||||||||
\(13\) | 9.12750e11 | 1.83631 | 0.918156 | − | 0.396219i | \(-0.129678\pi\) | ||||
0.918156 | + | 0.396219i | \(0.129678\pi\) | |||||||
\(14\) | −6.83892e11 | −0.631892 | ||||||||
\(15\) | −4.68008e11 | −0.209553 | ||||||||
\(16\) | 1.09951e12 | 0.250000 | ||||||||
\(17\) | 8.60406e12 | 1.03512 | 0.517559 | − | 0.855648i | \(-0.326841\pi\) | ||||
0.517559 | + | 0.855648i | \(0.326841\pi\) | |||||||
\(18\) | 8.35957e12 | 0.551852 | ||||||||
\(19\) | −6.93702e12 | −0.259573 | −0.129787 | − | 0.991542i | \(-0.541429\pi\) | ||||
−0.129787 | + | 0.991542i | \(0.541429\pi\) | |||||||
\(20\) | −1.02400e13 | −0.223607 | ||||||||
\(21\) | 3.20066e13 | 0.418733 | ||||||||
\(22\) | 1.29836e14 | 1.04221 | ||||||||
\(23\) | −3.30974e14 | −1.66591 | −0.832955 | − | 0.553341i | \(-0.813352\pi\) | ||||
−0.832955 | + | 0.553341i | \(0.813352\pi\) | |||||||
\(24\) | −5.14580e13 | −0.165666 | ||||||||
\(25\) | 9.53674e13 | 0.200000 | ||||||||
\(26\) | −9.34656e14 | −1.29847 | ||||||||
\(27\) | −8.92536e14 | −0.834269 | ||||||||
\(28\) | 7.00305e14 | 0.446815 | ||||||||
\(29\) | −3.90534e15 | −1.72377 | −0.861886 | − | 0.507103i | \(-0.830716\pi\) | ||||
−0.861886 | + | 0.507103i | \(0.830716\pi\) | |||||||
\(30\) | 4.79240e14 | 0.148177 | ||||||||
\(31\) | 3.32185e15 | 0.727918 | 0.363959 | − | 0.931415i | \(-0.381425\pi\) | ||||
0.363959 | + | 0.931415i | \(0.381425\pi\) | |||||||
\(32\) | −1.12590e15 | −0.176777 | ||||||||
\(33\) | −6.07642e15 | −0.690640 | ||||||||
\(34\) | −8.81056e15 | −0.731939 | ||||||||
\(35\) | −6.52210e15 | −0.399644 | ||||||||
\(36\) | −8.56020e15 | −0.390218 | ||||||||
\(37\) | −4.33804e16 | −1.48312 | −0.741558 | − | 0.670889i | \(-0.765913\pi\) | ||||
−0.741558 | + | 0.670889i | \(0.765913\pi\) | |||||||
\(38\) | 7.10351e15 | 0.183546 | ||||||||
\(39\) | 4.37426e16 | 0.860451 | ||||||||
\(40\) | 1.04858e16 | 0.158114 | ||||||||
\(41\) | −9.56620e16 | −1.11304 | −0.556518 | − | 0.830836i | \(-0.687863\pi\) | ||||
−0.556518 | + | 0.830836i | \(0.687863\pi\) | |||||||
\(42\) | −3.27748e16 | −0.296089 | ||||||||
\(43\) | −7.81706e16 | −0.551601 | −0.275800 | − | 0.961215i | \(-0.588943\pi\) | ||||
−0.275800 | + | 0.961215i | \(0.588943\pi\) | |||||||
\(44\) | −1.32952e17 | −0.736957 | ||||||||
\(45\) | 7.97231e16 | 0.349022 | ||||||||
\(46\) | 3.38917e17 | 1.17798 | ||||||||
\(47\) | −2.03634e17 | −0.564707 | −0.282354 | − | 0.959310i | \(-0.591115\pi\) | ||||
−0.282354 | + | 0.959310i | \(0.591115\pi\) | |||||||
\(48\) | 5.26930e16 | 0.117144 | ||||||||
\(49\) | −1.12505e17 | −0.201425 | ||||||||
\(50\) | −9.76562e16 | −0.141421 | ||||||||
\(51\) | 4.12341e17 | 0.485031 | ||||||||
\(52\) | 9.57088e17 | 0.918156 | ||||||||
\(53\) | 1.42121e18 | 1.11625 | 0.558127 | − | 0.829756i | \(-0.311520\pi\) | ||||
0.558127 | + | 0.829756i | \(0.311520\pi\) | |||||||
\(54\) | 9.13957e17 | 0.589917 | ||||||||
\(55\) | 1.23821e18 | 0.659154 | ||||||||
\(56\) | −7.17112e17 | −0.315946 | ||||||||
\(57\) | −3.32449e17 | −0.121630 | ||||||||
\(58\) | 3.99907e18 | 1.21889 | ||||||||
\(59\) | 2.28919e18 | 0.583089 | 0.291545 | − | 0.956557i | \(-0.405831\pi\) | ||||
0.291545 | + | 0.956557i | \(0.405831\pi\) | |||||||
\(60\) | −4.90741e17 | −0.104777 | ||||||||
\(61\) | −5.32798e18 | −0.956311 | −0.478155 | − | 0.878275i | \(-0.658694\pi\) | ||||
−0.478155 | + | 0.878275i | \(0.658694\pi\) | |||||||
\(62\) | −3.40158e18 | −0.514716 | ||||||||
\(63\) | −5.45220e18 | −0.697422 | ||||||||
\(64\) | 1.15292e18 | 0.125000 | ||||||||
\(65\) | −8.91357e18 | −0.821224 | ||||||||
\(66\) | 6.22226e18 | 0.488356 | ||||||||
\(67\) | −1.31401e19 | −0.880668 | −0.440334 | − | 0.897834i | \(-0.645140\pi\) | ||||
−0.440334 | + | 0.897834i | \(0.645140\pi\) | |||||||
\(68\) | 9.02201e18 | 0.517559 | ||||||||
\(69\) | −1.58616e19 | −0.780604 | ||||||||
\(70\) | 6.67863e18 | 0.282591 | ||||||||
\(71\) | −2.98159e19 | −1.08702 | −0.543508 | − | 0.839404i | \(-0.682904\pi\) | ||||
−0.543508 | + | 0.839404i | \(0.682904\pi\) | |||||||
\(72\) | 8.76565e18 | 0.275926 | ||||||||
\(73\) | 1.37094e18 | 0.0373361 | 0.0186681 | − | 0.999826i | \(-0.494057\pi\) | ||||
0.0186681 | + | 0.999826i | \(0.494057\pi\) | |||||||
\(74\) | 4.44215e19 | 1.04872 | ||||||||
\(75\) | 4.57039e18 | 0.0937151 | ||||||||
\(76\) | −7.27399e18 | −0.129787 | ||||||||
\(77\) | −8.46803e19 | −1.31713 | ||||||||
\(78\) | −4.47924e19 | −0.608431 | ||||||||
\(79\) | 1.74281e19 | 0.207093 | 0.103546 | − | 0.994625i | \(-0.466981\pi\) | ||||
0.103546 | + | 0.994625i | \(0.466981\pi\) | |||||||
\(80\) | −1.07374e19 | −0.111803 | ||||||||
\(81\) | 4.26208e19 | 0.389519 | ||||||||
\(82\) | 9.79579e19 | 0.787035 | ||||||||
\(83\) | 3.75717e19 | 0.265792 | 0.132896 | − | 0.991130i | \(-0.457572\pi\) | ||||
0.132896 | + | 0.991130i | \(0.457572\pi\) | |||||||
\(84\) | 3.35614e19 | 0.209367 | ||||||||
\(85\) | −8.40240e19 | −0.462919 | ||||||||
\(86\) | 8.00467e19 | 0.390040 | ||||||||
\(87\) | −1.87159e20 | −0.807717 | ||||||||
\(88\) | 1.36143e20 | 0.521107 | ||||||||
\(89\) | 2.43231e20 | 0.826845 | 0.413423 | − | 0.910539i | \(-0.364333\pi\) | ||||
0.413423 | + | 0.910539i | \(0.364333\pi\) | |||||||
\(90\) | −8.16365e19 | −0.246796 | ||||||||
\(91\) | 6.09592e20 | 1.64098 | ||||||||
\(92\) | −3.47051e20 | −0.832955 | ||||||||
\(93\) | 1.59196e20 | 0.341084 | ||||||||
\(94\) | 2.08521e20 | 0.399308 | ||||||||
\(95\) | 6.77443e19 | 0.116085 | ||||||||
\(96\) | −5.39576e19 | −0.0828332 | ||||||||
\(97\) | −1.80740e20 | −0.248858 | −0.124429 | − | 0.992229i | \(-0.539710\pi\) | ||||
−0.124429 | + | 0.992229i | \(0.539710\pi\) | |||||||
\(98\) | 1.15205e20 | 0.142429 | ||||||||
\(99\) | 1.03509e21 | 1.15030 | ||||||||
\(100\) | 1.00000e20 | 0.100000 | ||||||||
\(101\) | −4.40260e20 | −0.396583 | −0.198292 | − | 0.980143i | \(-0.563539\pi\) | ||||
−0.198292 | + | 0.980143i | \(0.563539\pi\) | |||||||
\(102\) | −4.22237e20 | −0.342969 | ||||||||
\(103\) | −1.91819e21 | −1.40637 | −0.703186 | − | 0.711005i | \(-0.748240\pi\) | ||||
−0.703186 | + | 0.711005i | \(0.748240\pi\) | |||||||
\(104\) | −9.80058e20 | −0.649234 | ||||||||
\(105\) | −3.12565e20 | −0.187263 | ||||||||
\(106\) | −1.45532e21 | −0.789310 | ||||||||
\(107\) | 7.55037e20 | 0.371055 | 0.185528 | − | 0.982639i | \(-0.440601\pi\) | ||||
0.185528 | + | 0.982639i | \(0.440601\pi\) | |||||||
\(108\) | −9.35892e20 | −0.417135 | ||||||||
\(109\) | −9.55072e20 | −0.386418 | −0.193209 | − | 0.981158i | \(-0.561890\pi\) | ||||
−0.193209 | + | 0.981158i | \(0.561890\pi\) | |||||||
\(110\) | −1.26793e21 | −0.466092 | ||||||||
\(111\) | −2.07896e21 | −0.694952 | ||||||||
\(112\) | 7.34323e20 | 0.223408 | ||||||||
\(113\) | 5.50602e21 | 1.52586 | 0.762929 | − | 0.646482i | \(-0.223760\pi\) | ||||
0.762929 | + | 0.646482i | \(0.223760\pi\) | |||||||
\(114\) | 3.40428e20 | 0.0860052 | ||||||||
\(115\) | 3.23217e21 | 0.745017 | ||||||||
\(116\) | −4.09504e21 | −0.861886 | ||||||||
\(117\) | −7.45137e21 | −1.43313 | ||||||||
\(118\) | −2.34413e21 | −0.412306 | ||||||||
\(119\) | 5.74634e21 | 0.925013 | ||||||||
\(120\) | 5.02519e20 | 0.0740883 | ||||||||
\(121\) | 8.67620e21 | 1.17242 | ||||||||
\(122\) | 5.45585e21 | 0.676214 | ||||||||
\(123\) | −4.58450e21 | −0.521541 | ||||||||
\(124\) | 3.48321e21 | 0.363959 | ||||||||
\(125\) | −9.31323e20 | −0.0894427 | ||||||||
\(126\) | 5.58305e21 | 0.493152 | ||||||||
\(127\) | 2.04590e22 | 1.66320 | 0.831602 | − | 0.555371i | \(-0.187424\pi\) | ||||
0.831602 | + | 0.555371i | \(0.187424\pi\) | |||||||
\(128\) | −1.18059e21 | −0.0883883 | ||||||||
\(129\) | −3.74625e21 | −0.258467 | ||||||||
\(130\) | 9.12750e21 | 0.580693 | ||||||||
\(131\) | −1.03791e22 | −0.609271 | −0.304635 | − | 0.952469i | \(-0.598535\pi\) | ||||
−0.304635 | + | 0.952469i | \(0.598535\pi\) | |||||||
\(132\) | −6.37159e21 | −0.345320 | ||||||||
\(133\) | −4.63298e21 | −0.231963 | ||||||||
\(134\) | 1.34554e22 | 0.622727 | ||||||||
\(135\) | 8.71617e21 | 0.373097 | ||||||||
\(136\) | −9.23854e21 | −0.365969 | ||||||||
\(137\) | −9.13014e21 | −0.334897 | −0.167449 | − | 0.985881i | \(-0.553553\pi\) | ||||
−0.167449 | + | 0.985881i | \(0.553553\pi\) | |||||||
\(138\) | 1.62423e22 | 0.551971 | ||||||||
\(139\) | −3.18076e22 | −1.00202 | −0.501009 | − | 0.865442i | \(-0.667038\pi\) | ||||
−0.501009 | + | 0.865442i | \(0.667038\pi\) | |||||||
\(140\) | −6.83892e21 | −0.199822 | ||||||||
\(141\) | −9.75896e21 | −0.264608 | ||||||||
\(142\) | 3.05315e22 | 0.768636 | ||||||||
\(143\) | −1.15730e23 | −2.70656 | ||||||||
\(144\) | −8.97602e21 | −0.195109 | ||||||||
\(145\) | 3.81381e22 | 0.770894 | ||||||||
\(146\) | −1.40384e21 | −0.0264006 | ||||||||
\(147\) | −5.39168e21 | −0.0943826 | ||||||||
\(148\) | −4.54876e22 | −0.741558 | ||||||||
\(149\) | 1.17039e23 | 1.77777 | 0.888884 | − | 0.458133i | \(-0.151482\pi\) | ||||
0.888884 | + | 0.458133i | \(0.151482\pi\) | |||||||
\(150\) | −4.68008e21 | −0.0662666 | ||||||||
\(151\) | −1.57736e22 | −0.208293 | −0.104146 | − | 0.994562i | \(-0.533211\pi\) | ||||
−0.104146 | + | 0.994562i | \(0.533211\pi\) | |||||||
\(152\) | 7.44857e21 | 0.0917730 | ||||||||
\(153\) | −7.02405e22 | −0.807844 | ||||||||
\(154\) | 8.67126e22 | 0.931354 | ||||||||
\(155\) | −3.24399e22 | −0.325535 | ||||||||
\(156\) | 4.58674e22 | 0.430226 | ||||||||
\(157\) | −9.37324e22 | −0.822135 | −0.411068 | − | 0.911605i | \(-0.634844\pi\) | ||||
−0.411068 | + | 0.911605i | \(0.634844\pi\) | |||||||
\(158\) | −1.78464e22 | −0.146437 | ||||||||
\(159\) | 6.81102e22 | 0.523049 | ||||||||
\(160\) | 1.09951e22 | 0.0790569 | ||||||||
\(161\) | −2.21045e23 | −1.48871 | ||||||||
\(162\) | −4.36437e22 | −0.275431 | ||||||||
\(163\) | 1.15735e23 | 0.684691 | 0.342345 | − | 0.939574i | \(-0.388779\pi\) | ||||
0.342345 | + | 0.939574i | \(0.388779\pi\) | |||||||
\(164\) | −1.00309e23 | −0.556518 | ||||||||
\(165\) | 5.93400e22 | 0.308863 | ||||||||
\(166\) | −3.84734e22 | −0.187943 | ||||||||
\(167\) | 1.46022e23 | 0.669723 | 0.334862 | − | 0.942267i | \(-0.391310\pi\) | ||||
0.334862 | + | 0.942267i | \(0.391310\pi\) | |||||||
\(168\) | −3.43669e22 | −0.148045 | ||||||||
\(169\) | 5.86048e23 | 2.37204 | ||||||||
\(170\) | 8.60406e22 | 0.327333 | ||||||||
\(171\) | 5.66314e22 | 0.202581 | ||||||||
\(172\) | −8.19678e22 | −0.275800 | ||||||||
\(173\) | −2.62784e23 | −0.831984 | −0.415992 | − | 0.909368i | \(-0.636566\pi\) | ||||
−0.415992 | + | 0.909368i | \(0.636566\pi\) | |||||||
\(174\) | 1.91651e23 | 0.571142 | ||||||||
\(175\) | 6.36924e22 | 0.178726 | ||||||||
\(176\) | −1.39410e23 | −0.368478 | ||||||||
\(177\) | 1.09707e23 | 0.273221 | ||||||||
\(178\) | −2.49069e23 | −0.584668 | ||||||||
\(179\) | 8.92249e23 | 1.97483 | 0.987413 | − | 0.158160i | \(-0.0505562\pi\) | ||||
0.987413 | + | 0.158160i | \(0.0505562\pi\) | |||||||
\(180\) | 8.35957e22 | 0.174511 | ||||||||
\(181\) | 2.71393e23 | 0.534531 | 0.267266 | − | 0.963623i | \(-0.413880\pi\) | ||||
0.267266 | + | 0.963623i | \(0.413880\pi\) | |||||||
\(182\) | −6.24222e23 | −1.16035 | ||||||||
\(183\) | −2.55338e23 | −0.448104 | ||||||||
\(184\) | 3.55380e23 | 0.588988 | ||||||||
\(185\) | 4.23636e23 | 0.663269 | ||||||||
\(186\) | −1.63017e23 | −0.241183 | ||||||||
\(187\) | −1.09093e24 | −1.52567 | ||||||||
\(188\) | −2.13526e23 | −0.282354 | ||||||||
\(189\) | −5.96092e23 | −0.745528 | ||||||||
\(190\) | −6.93702e22 | −0.0820843 | ||||||||
\(191\) | −1.16742e24 | −1.30731 | −0.653654 | − | 0.756794i | \(-0.726765\pi\) | ||||
−0.653654 | + | 0.756794i | \(0.726765\pi\) | |||||||
\(192\) | 5.52526e22 | 0.0585719 | ||||||||
\(193\) | 8.18854e22 | 0.0821968 | 0.0410984 | − | 0.999155i | \(-0.486914\pi\) | ||||
0.0410984 | + | 0.999155i | \(0.486914\pi\) | |||||||
\(194\) | 1.85078e23 | 0.175969 | ||||||||
\(195\) | −4.27174e23 | −0.384805 | ||||||||
\(196\) | −1.17970e23 | −0.100712 | ||||||||
\(197\) | −6.59417e23 | −0.533660 | −0.266830 | − | 0.963744i | \(-0.585976\pi\) | ||||
−0.266830 | + | 0.963744i | \(0.585976\pi\) | |||||||
\(198\) | −1.05993e24 | −0.813382 | ||||||||
\(199\) | 1.82645e24 | 1.32938 | 0.664692 | − | 0.747117i | \(-0.268563\pi\) | ||||
0.664692 | + | 0.747117i | \(0.268563\pi\) | |||||||
\(200\) | −1.02400e23 | −0.0707107 | ||||||||
\(201\) | −6.29725e23 | −0.412660 | ||||||||
\(202\) | 4.50826e23 | 0.280427 | ||||||||
\(203\) | −2.60823e24 | −1.54041 | ||||||||
\(204\) | 4.32371e23 | 0.242515 | ||||||||
\(205\) | 9.34199e23 | 0.497764 | ||||||||
\(206\) | 1.96423e24 | 0.994456 | ||||||||
\(207\) | 2.70195e24 | 1.30014 | ||||||||
\(208\) | 1.00358e24 | 0.459078 | ||||||||
\(209\) | 8.79565e23 | 0.382588 | ||||||||
\(210\) | 3.20066e23 | 0.132415 | ||||||||
\(211\) | −3.36470e24 | −1.32428 | −0.662140 | − | 0.749380i | \(-0.730352\pi\) | ||||
−0.662140 | + | 0.749380i | \(0.730352\pi\) | |||||||
\(212\) | 1.49025e24 | 0.558127 | ||||||||
\(213\) | −1.42890e24 | −0.509349 | ||||||||
\(214\) | −7.73158e23 | −0.262376 | ||||||||
\(215\) | 7.63385e23 | 0.246683 | ||||||||
\(216\) | 9.58353e23 | 0.294959 | ||||||||
\(217\) | 2.21854e24 | 0.650490 | ||||||||
\(218\) | 9.77993e23 | 0.273239 | ||||||||
\(219\) | 6.57010e22 | 0.0174948 | ||||||||
\(220\) | 1.29836e24 | 0.329577 | ||||||||
\(221\) | 7.85336e24 | 1.90080 | ||||||||
\(222\) | 2.12885e24 | 0.491405 | ||||||||
\(223\) | 1.44704e23 | 0.0318626 | 0.0159313 | − | 0.999873i | \(-0.494929\pi\) | ||||
0.0159313 | + | 0.999873i | \(0.494929\pi\) | |||||||
\(224\) | −7.51947e23 | −0.157973 | ||||||||
\(225\) | −7.78546e23 | −0.156087 | ||||||||
\(226\) | −5.63817e24 | −1.07894 | ||||||||
\(227\) | −4.83544e24 | −0.883415 | −0.441707 | − | 0.897159i | \(-0.645627\pi\) | ||||
−0.441707 | + | 0.897159i | \(0.645627\pi\) | |||||||
\(228\) | −3.48598e23 | −0.0608148 | ||||||||
\(229\) | −4.35342e24 | −0.725367 | −0.362684 | − | 0.931912i | \(-0.618139\pi\) | ||||
−0.362684 | + | 0.931912i | \(0.618139\pi\) | |||||||
\(230\) | −3.30974e24 | −0.526807 | ||||||||
\(231\) | −4.05822e24 | −0.617177 | ||||||||
\(232\) | 4.19332e24 | 0.609445 | ||||||||
\(233\) | 1.03556e23 | 0.0143860 | 0.00719300 | − | 0.999974i | \(-0.497710\pi\) | ||||
0.00719300 | + | 0.999974i | \(0.497710\pi\) | |||||||
\(234\) | 7.63020e24 | 1.01337 | ||||||||
\(235\) | 1.98862e24 | 0.252545 | ||||||||
\(236\) | 2.40039e24 | 0.291545 | ||||||||
\(237\) | 8.35223e23 | 0.0970387 | ||||||||
\(238\) | −5.88425e24 | −0.654083 | ||||||||
\(239\) | −1.45089e25 | −1.54332 | −0.771660 | − | 0.636035i | \(-0.780573\pi\) | ||||
−0.771660 | + | 0.636035i | \(0.780573\pi\) | |||||||
\(240\) | −5.14580e23 | −0.0523883 | ||||||||
\(241\) | −2.10504e23 | −0.0205155 | −0.0102578 | − | 0.999947i | \(-0.503265\pi\) | ||||
−0.0102578 | + | 0.999947i | \(0.503265\pi\) | |||||||
\(242\) | −8.88443e24 | −0.829026 | ||||||||
\(243\) | 1.13788e25 | 1.01679 | ||||||||
\(244\) | −5.58679e24 | −0.478155 | ||||||||
\(245\) | 1.09868e24 | 0.0900798 | ||||||||
\(246\) | 4.69453e24 | 0.368785 | ||||||||
\(247\) | −6.33176e24 | −0.476658 | ||||||||
\(248\) | −3.56681e24 | −0.257358 | ||||||||
\(249\) | 1.80059e24 | 0.124543 | ||||||||
\(250\) | 9.53674e23 | 0.0632456 | ||||||||
\(251\) | −8.79823e24 | −0.559527 | −0.279764 | − | 0.960069i | \(-0.590256\pi\) | ||||
−0.279764 | + | 0.960069i | \(0.590256\pi\) | |||||||
\(252\) | −5.71704e24 | −0.348711 | ||||||||
\(253\) | 4.19651e25 | 2.45541 | ||||||||
\(254\) | −2.09500e25 | −1.17606 | ||||||||
\(255\) | −4.02677e24 | −0.216912 | ||||||||
\(256\) | 1.20893e24 | 0.0625000 | ||||||||
\(257\) | 2.93954e24 | 0.145875 | 0.0729376 | − | 0.997337i | \(-0.476763\pi\) | ||||
0.0729376 | + | 0.997337i | \(0.476763\pi\) | |||||||
\(258\) | 3.83616e24 | 0.182763 | ||||||||
\(259\) | −2.89721e25 | −1.32536 | ||||||||
\(260\) | −9.34656e24 | −0.410612 | ||||||||
\(261\) | 3.18818e25 | 1.34529 | ||||||||
\(262\) | 1.06282e25 | 0.430820 | ||||||||
\(263\) | −7.06799e23 | −0.0275271 | −0.0137636 | − | 0.999905i | \(-0.504381\pi\) | ||||
−0.0137636 | + | 0.999905i | \(0.504381\pi\) | |||||||
\(264\) | 6.52451e24 | 0.244178 | ||||||||
\(265\) | −1.38790e25 | −0.499204 | ||||||||
\(266\) | 4.74417e24 | 0.164022 | ||||||||
\(267\) | 1.16566e25 | 0.387439 | ||||||||
\(268\) | −1.37784e25 | −0.440334 | ||||||||
\(269\) | 4.29393e25 | 1.31964 | 0.659821 | − | 0.751423i | \(-0.270632\pi\) | ||||
0.659821 | + | 0.751423i | \(0.270632\pi\) | |||||||
\(270\) | −8.92536e24 | −0.263819 | ||||||||
\(271\) | 1.66203e25 | 0.472564 | 0.236282 | − | 0.971685i | \(-0.424071\pi\) | ||||
0.236282 | + | 0.971685i | \(0.424071\pi\) | |||||||
\(272\) | 9.46027e24 | 0.258780 | ||||||||
\(273\) | 2.92141e25 | 0.768925 | ||||||||
\(274\) | 9.34927e24 | 0.236808 | ||||||||
\(275\) | −1.20919e25 | −0.294783 | ||||||||
\(276\) | −1.66321e25 | −0.390302 | ||||||||
\(277\) | −2.85979e25 | −0.646095 | −0.323048 | − | 0.946383i | \(-0.604707\pi\) | ||||
−0.323048 | + | 0.946383i | \(0.604707\pi\) | |||||||
\(278\) | 3.25710e25 | 0.708534 | ||||||||
\(279\) | −2.71184e25 | −0.568094 | ||||||||
\(280\) | 7.00305e24 | 0.141295 | ||||||||
\(281\) | −5.58235e25 | −1.08493 | −0.542464 | − | 0.840079i | \(-0.682509\pi\) | ||||
−0.542464 | + | 0.840079i | \(0.682509\pi\) | |||||||
\(282\) | 9.99318e24 | 0.187106 | ||||||||
\(283\) | 6.54228e25 | 1.18024 | 0.590121 | − | 0.807315i | \(-0.299080\pi\) | ||||
0.590121 | + | 0.807315i | \(0.299080\pi\) | |||||||
\(284\) | −3.12643e25 | −0.543508 | ||||||||
\(285\) | 3.24658e24 | 0.0543944 | ||||||||
\(286\) | 1.18508e26 | 1.91383 | ||||||||
\(287\) | −6.38891e25 | −0.994642 | ||||||||
\(288\) | 9.19145e24 | 0.137963 | ||||||||
\(289\) | 4.93795e24 | 0.0714693 | ||||||||
\(290\) | −3.90534e25 | −0.545104 | ||||||||
\(291\) | −8.66179e24 | −0.116609 | ||||||||
\(292\) | 1.43754e24 | 0.0186681 | ||||||||
\(293\) | −1.10836e25 | −0.138858 | −0.0694289 | − | 0.997587i | \(-0.522118\pi\) | ||||
−0.0694289 | + | 0.997587i | \(0.522118\pi\) | |||||||
\(294\) | 5.52108e24 | 0.0667386 | ||||||||
\(295\) | −2.23553e25 | −0.260765 | ||||||||
\(296\) | 4.65793e25 | 0.524361 | ||||||||
\(297\) | 1.13167e26 | 1.22964 | ||||||||
\(298\) | −1.19848e26 | −1.25707 | ||||||||
\(299\) | −3.02096e26 | −3.05913 | ||||||||
\(300\) | 4.79240e24 | 0.0468576 | ||||||||
\(301\) | −5.22073e25 | −0.492927 | ||||||||
\(302\) | 1.61522e25 | 0.147285 | ||||||||
\(303\) | −2.10990e25 | −0.185829 | ||||||||
\(304\) | −7.62733e24 | −0.0648933 | ||||||||
\(305\) | 5.20310e25 | 0.427675 | ||||||||
\(306\) | 7.19263e25 | 0.571232 | ||||||||
\(307\) | −1.02459e26 | −0.786315 | −0.393157 | − | 0.919471i | \(-0.628617\pi\) | ||||
−0.393157 | + | 0.919471i | \(0.628617\pi\) | |||||||
\(308\) | −8.87937e25 | −0.658567 | ||||||||
\(309\) | −9.19272e25 | −0.658992 | ||||||||
\(310\) | 3.32185e25 | 0.230188 | ||||||||
\(311\) | −2.17194e26 | −1.45500 | −0.727502 | − | 0.686105i | \(-0.759319\pi\) | ||||
−0.727502 | + | 0.686105i | \(0.759319\pi\) | |||||||
\(312\) | −4.69683e25 | −0.304215 | ||||||||
\(313\) | 2.19829e26 | 1.37679 | 0.688397 | − | 0.725334i | \(-0.258315\pi\) | ||||
0.688397 | + | 0.725334i | \(0.258315\pi\) | |||||||
\(314\) | 9.59820e25 | 0.581337 | ||||||||
\(315\) | 5.32441e25 | 0.311897 | ||||||||
\(316\) | 1.82747e25 | 0.103546 | ||||||||
\(317\) | 1.26596e26 | 0.693901 | 0.346950 | − | 0.937883i | \(-0.387217\pi\) | ||||
0.346950 | + | 0.937883i | \(0.387217\pi\) | |||||||
\(318\) | −6.97449e25 | −0.369852 | ||||||||
\(319\) | 4.95169e26 | 2.54069 | ||||||||
\(320\) | −1.12590e25 | −0.0559017 | ||||||||
\(321\) | 3.61844e25 | 0.173867 | ||||||||
\(322\) | 2.26350e26 | 1.05267 | ||||||||
\(323\) | −5.96865e25 | −0.268689 | ||||||||
\(324\) | 4.46911e25 | 0.194759 | ||||||||
\(325\) | 8.70466e25 | 0.367262 | ||||||||
\(326\) | −1.18513e26 | −0.484150 | ||||||||
\(327\) | −4.57708e25 | −0.181066 | ||||||||
\(328\) | 1.02716e26 | 0.393517 | ||||||||
\(329\) | −1.36000e26 | −0.504640 | ||||||||
\(330\) | −6.07642e25 | −0.218399 | ||||||||
\(331\) | 1.93702e26 | 0.674433 | 0.337217 | − | 0.941427i | \(-0.390514\pi\) | ||||
0.337217 | + | 0.941427i | \(0.390514\pi\) | |||||||
\(332\) | 3.93968e25 | 0.132896 | ||||||||
\(333\) | 3.54142e26 | 1.15748 | ||||||||
\(334\) | −1.49527e26 | −0.473566 | ||||||||
\(335\) | 1.28321e26 | 0.393847 | ||||||||
\(336\) | 3.51917e25 | 0.104683 | ||||||||
\(337\) | 1.34839e26 | 0.388779 | 0.194389 | − | 0.980924i | \(-0.437727\pi\) | ||||
0.194389 | + | 0.980924i | \(0.437727\pi\) | |||||||
\(338\) | −6.00113e26 | −1.67729 | ||||||||
\(339\) | 2.63870e26 | 0.714980 | ||||||||
\(340\) | −8.81056e25 | −0.231459 | ||||||||
\(341\) | −4.21187e26 | −1.07289 | ||||||||
\(342\) | −5.79905e25 | −0.143246 | ||||||||
\(343\) | −4.48170e26 | −1.07363 | ||||||||
\(344\) | 8.39350e25 | 0.195020 | ||||||||
\(345\) | 1.54898e26 | 0.349097 | ||||||||
\(346\) | 2.69091e26 | 0.588302 | ||||||||
\(347\) | −6.73325e26 | −1.42812 | −0.714061 | − | 0.700084i | \(-0.753146\pi\) | ||||
−0.714061 | + | 0.700084i | \(0.753146\pi\) | |||||||
\(348\) | −1.96251e26 | −0.403859 | ||||||||
\(349\) | 9.07724e26 | 1.81254 | 0.906268 | − | 0.422703i | \(-0.138919\pi\) | ||||
0.906268 | + | 0.422703i | \(0.138919\pi\) | |||||||
\(350\) | −6.52210e25 | −0.126378 | ||||||||
\(351\) | −8.14662e26 | −1.53198 | ||||||||
\(352\) | 1.42756e26 | 0.260553 | ||||||||
\(353\) | 4.40145e25 | 0.0779761 | 0.0389880 | − | 0.999240i | \(-0.487587\pi\) | ||||
0.0389880 | + | 0.999240i | \(0.487587\pi\) | |||||||
\(354\) | −1.12340e26 | −0.193197 | ||||||||
\(355\) | 2.91171e26 | 0.486128 | ||||||||
\(356\) | 2.55046e26 | 0.413423 | ||||||||
\(357\) | 2.75387e26 | 0.433438 | ||||||||
\(358\) | −9.13663e26 | −1.39641 | ||||||||
\(359\) | −3.93523e26 | −0.584088 | −0.292044 | − | 0.956405i | \(-0.594335\pi\) | ||||
−0.292044 | + | 0.956405i | \(0.594335\pi\) | |||||||
\(360\) | −8.56020e25 | −0.123398 | ||||||||
\(361\) | −6.66087e26 | −0.932622 | ||||||||
\(362\) | −2.77906e26 | −0.377971 | ||||||||
\(363\) | 4.15798e26 | 0.549367 | ||||||||
\(364\) | 6.39203e26 | 0.820492 | ||||||||
\(365\) | −1.33881e25 | −0.0166972 | ||||||||
\(366\) | 2.61466e26 | 0.316857 | ||||||||
\(367\) | 1.48020e25 | 0.0174312 | 0.00871559 | − | 0.999962i | \(-0.497226\pi\) | ||||
0.00871559 | + | 0.999962i | \(0.497226\pi\) | |||||||
\(368\) | −3.63910e26 | −0.416477 | ||||||||
\(369\) | 7.80951e26 | 0.868654 | ||||||||
\(370\) | −4.33804e26 | −0.469002 | ||||||||
\(371\) | 9.49176e26 | 0.997518 | ||||||||
\(372\) | 1.66929e26 | 0.170542 | ||||||||
\(373\) | −1.57080e27 | −1.56019 | −0.780094 | − | 0.625662i | \(-0.784829\pi\) | ||||
−0.780094 | + | 0.625662i | \(0.784829\pi\) | |||||||
\(374\) | 1.11712e27 | 1.07881 | ||||||||
\(375\) | −4.46327e25 | −0.0419107 | ||||||||
\(376\) | 2.18651e26 | 0.199654 | ||||||||
\(377\) | −3.56460e27 | −3.16538 | ||||||||
\(378\) | 6.10398e26 | 0.527168 | ||||||||
\(379\) | −2.27703e26 | −0.191275 | −0.0956373 | − | 0.995416i | \(-0.530489\pi\) | ||||
−0.0956373 | + | 0.995416i | \(0.530489\pi\) | |||||||
\(380\) | 7.10351e25 | 0.0580423 | ||||||||
\(381\) | 9.80478e26 | 0.779337 | ||||||||
\(382\) | 1.19544e27 | 0.924406 | ||||||||
\(383\) | 2.29376e27 | 1.72569 | 0.862843 | − | 0.505472i | \(-0.168682\pi\) | ||||
0.862843 | + | 0.505472i | \(0.168682\pi\) | |||||||
\(384\) | −5.65786e25 | −0.0414166 | ||||||||
\(385\) | 8.26956e26 | 0.589040 | ||||||||
\(386\) | −8.38506e25 | −0.0581219 | ||||||||
\(387\) | 6.38157e26 | 0.430489 | ||||||||
\(388\) | −1.89520e26 | −0.124429 | ||||||||
\(389\) | 1.10508e27 | 0.706190 | 0.353095 | − | 0.935587i | \(-0.385129\pi\) | ||||
0.353095 | + | 0.935587i | \(0.385129\pi\) | |||||||
\(390\) | 4.37426e26 | 0.272099 | ||||||||
\(391\) | −2.84772e27 | −1.72441 | ||||||||
\(392\) | 1.20801e26 | 0.0712143 | ||||||||
\(393\) | −4.97407e26 | −0.285489 | ||||||||
\(394\) | 6.75243e26 | 0.377355 | ||||||||
\(395\) | −1.70196e26 | −0.0926148 | ||||||||
\(396\) | 1.08537e27 | 0.575148 | ||||||||
\(397\) | 1.88707e26 | 0.0973839 | 0.0486919 | − | 0.998814i | \(-0.484495\pi\) | ||||
0.0486919 | + | 0.998814i | \(0.484495\pi\) | |||||||
\(398\) | −1.87029e27 | −0.940017 | ||||||||
\(399\) | −2.22031e26 | −0.108692 | ||||||||
\(400\) | 1.04858e26 | 0.0500000 | ||||||||
\(401\) | −1.74678e27 | −0.811376 | −0.405688 | − | 0.914012i | \(-0.632968\pi\) | ||||
−0.405688 | + | 0.914012i | \(0.632968\pi\) | |||||||
\(402\) | 6.44838e26 | 0.291794 | ||||||||
\(403\) | 3.03202e27 | 1.33668 | ||||||||
\(404\) | −4.61646e26 | −0.198292 | ||||||||
\(405\) | −4.16218e26 | −0.174198 | ||||||||
\(406\) | 2.67083e27 | 1.08924 | ||||||||
\(407\) | 5.50032e27 | 2.18598 | ||||||||
\(408\) | −4.42748e26 | −0.171484 | ||||||||
\(409\) | −2.92958e27 | −1.10588 | −0.552942 | − | 0.833219i | \(-0.686495\pi\) | ||||
−0.552942 | + | 0.833219i | \(0.686495\pi\) | |||||||
\(410\) | −9.56620e26 | −0.351973 | ||||||||
\(411\) | −4.37553e26 | −0.156925 | ||||||||
\(412\) | −2.01137e27 | −0.703186 | ||||||||
\(413\) | 1.52886e27 | 0.521066 | ||||||||
\(414\) | −2.76680e27 | −0.919336 | ||||||||
\(415\) | −3.66911e26 | −0.118866 | ||||||||
\(416\) | −1.02766e27 | −0.324617 | ||||||||
\(417\) | −1.52435e27 | −0.469521 | ||||||||
\(418\) | −9.00674e26 | −0.270531 | ||||||||
\(419\) | −2.59534e27 | −0.760234 | −0.380117 | − | 0.924938i | \(-0.624116\pi\) | ||||
−0.380117 | + | 0.924938i | \(0.624116\pi\) | |||||||
\(420\) | −3.27748e26 | −0.0936316 | ||||||||
\(421\) | −2.08416e27 | −0.580723 | −0.290362 | − | 0.956917i | \(-0.593776\pi\) | ||||
−0.290362 | + | 0.956917i | \(0.593776\pi\) | |||||||
\(422\) | 3.44545e27 | 0.936408 | ||||||||
\(423\) | 1.66240e27 | 0.440718 | ||||||||
\(424\) | −1.52602e27 | −0.394655 | ||||||||
\(425\) | 8.20547e26 | 0.207024 | ||||||||
\(426\) | 1.46319e27 | 0.360164 | ||||||||
\(427\) | −3.55836e27 | −0.854588 | ||||||||
\(428\) | 7.91713e26 | 0.185528 | ||||||||
\(429\) | −5.54625e27 | −1.26823 | ||||||||
\(430\) | −7.81706e26 | −0.174431 | ||||||||
\(431\) | 1.85265e27 | 0.403444 | 0.201722 | − | 0.979443i | \(-0.435346\pi\) | ||||
0.201722 | + | 0.979443i | \(0.435346\pi\) | |||||||
\(432\) | −9.81354e26 | −0.208567 | ||||||||
\(433\) | 6.31486e26 | 0.130991 | 0.0654954 | − | 0.997853i | \(-0.479137\pi\) | ||||
0.0654954 | + | 0.997853i | \(0.479137\pi\) | |||||||
\(434\) | −2.27179e27 | −0.459966 | ||||||||
\(435\) | 1.82773e27 | 0.361222 | ||||||||
\(436\) | −1.00147e27 | −0.193209 | ||||||||
\(437\) | 2.29597e27 | 0.432425 | ||||||||
\(438\) | −6.72778e25 | −0.0123707 | ||||||||
\(439\) | 3.19822e27 | 0.574158 | 0.287079 | − | 0.957907i | \(-0.407316\pi\) | ||||
0.287079 | + | 0.957907i | \(0.407316\pi\) | |||||||
\(440\) | −1.32952e27 | −0.233046 | ||||||||
\(441\) | 9.18450e26 | 0.157199 | ||||||||
\(442\) | −8.04184e27 | −1.34407 | ||||||||
\(443\) | 7.29283e26 | 0.119030 | 0.0595151 | − | 0.998227i | \(-0.481045\pi\) | ||||
0.0595151 | + | 0.998227i | \(0.481045\pi\) | |||||||
\(444\) | −2.17995e27 | −0.347476 | ||||||||
\(445\) | −2.37530e27 | −0.369776 | ||||||||
\(446\) | −1.48177e26 | −0.0225302 | ||||||||
\(447\) | 5.60898e27 | 0.833018 | ||||||||
\(448\) | 7.69994e26 | 0.111704 | ||||||||
\(449\) | −1.59099e27 | −0.225466 | −0.112733 | − | 0.993625i | \(-0.535961\pi\) | ||||
−0.112733 | + | 0.993625i | \(0.535961\pi\) | |||||||
\(450\) | 7.97231e26 | 0.110370 | ||||||||
\(451\) | 1.21293e28 | 1.64052 | ||||||||
\(452\) | 5.77348e27 | 0.762929 | ||||||||
\(453\) | −7.55936e26 | −0.0976009 | ||||||||
\(454\) | 4.95149e27 | 0.624669 | ||||||||
\(455\) | −5.95305e27 | −0.733871 | ||||||||
\(456\) | 3.56965e26 | 0.0430026 | ||||||||
\(457\) | 8.94924e27 | 1.05358 | 0.526788 | − | 0.849997i | \(-0.323396\pi\) | ||||
0.526788 | + | 0.849997i | \(0.323396\pi\) | |||||||
\(458\) | 4.45790e27 | 0.512912 | ||||||||
\(459\) | −7.67944e27 | −0.863567 | ||||||||
\(460\) | 3.38917e27 | 0.372509 | ||||||||
\(461\) | 1.32946e28 | 1.42829 | 0.714144 | − | 0.699999i | \(-0.246816\pi\) | ||||
0.714144 | + | 0.699999i | \(0.246816\pi\) | |||||||
\(462\) | 4.15561e27 | 0.436410 | ||||||||
\(463\) | 1.29662e28 | 1.33110 | 0.665551 | − | 0.746352i | \(-0.268197\pi\) | ||||
0.665551 | + | 0.746352i | \(0.268197\pi\) | |||||||
\(464\) | −4.29396e27 | −0.430943 | ||||||||
\(465\) | −1.55465e27 | −0.152538 | ||||||||
\(466\) | −1.06042e26 | −0.0101724 | ||||||||
\(467\) | −5.02371e27 | −0.471191 | −0.235595 | − | 0.971851i | \(-0.575704\pi\) | ||||
−0.235595 | + | 0.971851i | \(0.575704\pi\) | |||||||
\(468\) | −7.81332e27 | −0.716563 | ||||||||
\(469\) | −8.77577e27 | −0.786992 | ||||||||
\(470\) | −2.03634e27 | −0.178576 | ||||||||
\(471\) | −4.49203e27 | −0.385232 | ||||||||
\(472\) | −2.45800e27 | −0.206153 | ||||||||
\(473\) | 9.91148e27 | 0.813011 | ||||||||
\(474\) | −8.55269e26 | −0.0686167 | ||||||||
\(475\) | −6.61565e26 | −0.0519147 | ||||||||
\(476\) | 6.02547e27 | 0.462507 | ||||||||
\(477\) | −1.16023e28 | −0.871165 | ||||||||
\(478\) | 1.48571e28 | 1.09129 | ||||||||
\(479\) | 1.23595e28 | 0.888132 | 0.444066 | − | 0.895994i | \(-0.353536\pi\) | ||||
0.444066 | + | 0.895994i | \(0.353536\pi\) | |||||||
\(480\) | 5.26930e26 | 0.0370441 | ||||||||
\(481\) | −3.95954e28 | −2.72346 | ||||||||
\(482\) | 2.15556e26 | 0.0145067 | ||||||||
\(483\) | −1.05934e28 | −0.697572 | ||||||||
\(484\) | 9.09765e27 | 0.586210 | ||||||||
\(485\) | 1.76504e27 | 0.111293 | ||||||||
\(486\) | −1.16519e28 | −0.718978 | ||||||||
\(487\) | −2.33221e28 | −1.40836 | −0.704179 | − | 0.710023i | \(-0.748685\pi\) | ||||
−0.704179 | + | 0.710023i | \(0.748685\pi\) | |||||||
\(488\) | 5.72087e27 | 0.338107 | ||||||||
\(489\) | 5.54648e27 | 0.320829 | ||||||||
\(490\) | −1.12505e27 | −0.0636960 | ||||||||
\(491\) | 2.65852e28 | 1.47328 | 0.736640 | − | 0.676286i | \(-0.236411\pi\) | ||||
0.736640 | + | 0.676286i | \(0.236411\pi\) | |||||||
\(492\) | −4.80720e27 | −0.260771 | ||||||||
\(493\) | −3.36018e28 | −1.78431 | ||||||||
\(494\) | 6.48372e27 | 0.337048 | ||||||||
\(495\) | −1.01083e28 | −0.514428 | ||||||||
\(496\) | 3.65241e27 | 0.181979 | ||||||||
\(497\) | −1.99130e28 | −0.971390 | ||||||||
\(498\) | −1.84380e27 | −0.0880655 | ||||||||
\(499\) | −1.38803e28 | −0.649148 | −0.324574 | − | 0.945860i | \(-0.605221\pi\) | ||||
−0.324574 | + | 0.945860i | \(0.605221\pi\) | |||||||
\(500\) | −9.76563e26 | −0.0447214 | ||||||||
\(501\) | 6.99795e27 | 0.313816 | ||||||||
\(502\) | 9.00939e27 | 0.395646 | ||||||||
\(503\) | −8.55444e27 | −0.367898 | −0.183949 | − | 0.982936i | \(-0.558888\pi\) | ||||
−0.183949 | + | 0.982936i | \(0.558888\pi\) | |||||||
\(504\) | 5.85425e27 | 0.246576 | ||||||||
\(505\) | 4.29941e27 | 0.177357 | ||||||||
\(506\) | −4.29723e28 | −1.73623 | ||||||||
\(507\) | 2.80857e28 | 1.11148 | ||||||||
\(508\) | 2.14528e28 | 0.831602 | ||||||||
\(509\) | 3.82946e28 | 1.45412 | 0.727060 | − | 0.686574i | \(-0.240886\pi\) | ||||
0.727060 | + | 0.686574i | \(0.240886\pi\) | |||||||
\(510\) | 4.12341e27 | 0.153380 | ||||||||
\(511\) | 9.15601e26 | 0.0333647 | ||||||||
\(512\) | −1.23794e27 | −0.0441942 | ||||||||
\(513\) | 6.19154e27 | 0.216554 | ||||||||
\(514\) | −3.01009e27 | −0.103149 | ||||||||
\(515\) | 1.87323e28 | 0.628949 | ||||||||
\(516\) | −3.92822e27 | −0.129233 | ||||||||
\(517\) | 2.58194e28 | 0.832329 | ||||||||
\(518\) | 2.96675e28 | 0.937169 | ||||||||
\(519\) | −1.25937e28 | −0.389847 | ||||||||
\(520\) | 9.57088e27 | 0.290346 | ||||||||
\(521\) | 2.56460e28 | 0.762471 | 0.381236 | − | 0.924478i | \(-0.375499\pi\) | ||||
0.381236 | + | 0.924478i | \(0.375499\pi\) | |||||||
\(522\) | −3.26470e28 | −0.951267 | ||||||||
\(523\) | −4.56980e28 | −1.30506 | −0.652529 | − | 0.757764i | \(-0.726292\pi\) | ||||
−0.652529 | + | 0.757764i | \(0.726292\pi\) | |||||||
\(524\) | −1.08833e28 | −0.304635 | ||||||||
\(525\) | 3.05239e27 | 0.0837467 | ||||||||
\(526\) | 7.23762e26 | 0.0194646 | ||||||||
\(527\) | 2.85814e28 | 0.753481 | ||||||||
\(528\) | −6.68110e27 | −0.172660 | ||||||||
\(529\) | 7.00720e28 | 1.77525 | ||||||||
\(530\) | 1.42121e28 | 0.352990 | ||||||||
\(531\) | −1.86881e28 | −0.455064 | ||||||||
\(532\) | −4.85803e27 | −0.115981 | ||||||||
\(533\) | −8.73155e28 | −2.04388 | ||||||||
\(534\) | −1.19364e28 | −0.273961 | ||||||||
\(535\) | −7.37341e27 | −0.165941 | ||||||||
\(536\) | 1.41090e28 | 0.311363 | ||||||||
\(537\) | 4.27601e28 | 0.925356 | ||||||||
\(538\) | −4.39699e28 | −0.933128 | ||||||||
\(539\) | 1.42648e28 | 0.296882 | ||||||||
\(540\) | 9.13957e27 | 0.186548 | ||||||||
\(541\) | 5.19261e28 | 1.03948 | 0.519738 | − | 0.854326i | \(-0.326029\pi\) | ||||
0.519738 | + | 0.854326i | \(0.326029\pi\) | |||||||
\(542\) | −1.70192e28 | −0.334153 | ||||||||
\(543\) | 1.30062e28 | 0.250468 | ||||||||
\(544\) | −9.68731e27 | −0.182985 | ||||||||
\(545\) | 9.32687e27 | 0.172812 | ||||||||
\(546\) | −2.99152e28 | −0.543712 | ||||||||
\(547\) | −4.55529e28 | −0.812173 | −0.406087 | − | 0.913835i | \(-0.633107\pi\) | ||||
−0.406087 | + | 0.913835i | \(0.633107\pi\) | |||||||
\(548\) | −9.57365e27 | −0.167449 | ||||||||
\(549\) | 4.34957e28 | 0.746340 | ||||||||
\(550\) | 1.23821e28 | 0.208443 | ||||||||
\(551\) | 2.70914e28 | 0.447445 | ||||||||
\(552\) | 1.70312e28 | 0.275985 | ||||||||
\(553\) | 1.16396e28 | 0.185065 | ||||||||
\(554\) | 2.92842e28 | 0.456858 | ||||||||
\(555\) | 2.03023e28 | 0.310792 | ||||||||
\(556\) | −3.33527e28 | −0.501009 | ||||||||
\(557\) | 2.98975e28 | 0.440713 | 0.220356 | − | 0.975419i | \(-0.429278\pi\) | ||||
0.220356 | + | 0.975419i | \(0.429278\pi\) | |||||||
\(558\) | 2.77693e28 | 0.401703 | ||||||||
\(559\) | −7.13502e28 | −1.01291 | ||||||||
\(560\) | −7.17112e27 | −0.0999109 | ||||||||
\(561\) | −5.22819e28 | −0.714894 | ||||||||
\(562\) | 5.71633e28 | 0.767160 | ||||||||
\(563\) | −4.42316e28 | −0.582632 | −0.291316 | − | 0.956627i | \(-0.594093\pi\) | ||||
−0.291316 | + | 0.956627i | \(0.594093\pi\) | |||||||
\(564\) | −1.02330e28 | −0.132304 | ||||||||
\(565\) | −5.37697e28 | −0.682385 | ||||||||
\(566\) | −6.69929e28 | −0.834558 | ||||||||
\(567\) | 2.84648e28 | 0.348086 | ||||||||
\(568\) | 3.20146e28 | 0.384318 | ||||||||
\(569\) | 2.66278e28 | 0.313803 | 0.156901 | − | 0.987614i | \(-0.449849\pi\) | ||||
0.156901 | + | 0.987614i | \(0.449849\pi\) | |||||||
\(570\) | −3.32449e27 | −0.0384627 | ||||||||
\(571\) | −5.39217e28 | −0.612469 | −0.306235 | − | 0.951956i | \(-0.599069\pi\) | ||||
−0.306235 | + | 0.951956i | \(0.599069\pi\) | |||||||
\(572\) | −1.21352e29 | −1.35328 | ||||||||
\(573\) | −5.59475e28 | −0.612572 | ||||||||
\(574\) | 6.54224e28 | 0.703318 | ||||||||
\(575\) | −3.15641e28 | −0.333182 | ||||||||
\(576\) | −9.41204e27 | −0.0975546 | ||||||||
\(577\) | −4.00855e28 | −0.407983 | −0.203991 | − | 0.978973i | \(-0.565391\pi\) | ||||
−0.203991 | + | 0.978973i | \(0.565391\pi\) | |||||||
\(578\) | −5.05646e27 | −0.0505364 | ||||||||
\(579\) | 3.92427e27 | 0.0385154 | ||||||||
\(580\) | 3.99907e28 | 0.385447 | ||||||||
\(581\) | 2.50928e28 | 0.237519 | ||||||||
\(582\) | 8.86967e27 | 0.0824548 | ||||||||
\(583\) | −1.80200e29 | −1.64526 | ||||||||
\(584\) | −1.47204e27 | −0.0132003 | ||||||||
\(585\) | 7.27673e28 | 0.640913 | ||||||||
\(586\) | 1.13496e28 | 0.0981873 | ||||||||
\(587\) | 6.52023e28 | 0.554068 | 0.277034 | − | 0.960860i | \(-0.410649\pi\) | ||||
0.277034 | + | 0.960860i | \(0.410649\pi\) | |||||||
\(588\) | −5.65358e27 | −0.0471913 | ||||||||
\(589\) | −2.30437e28 | −0.188948 | ||||||||
\(590\) | 2.28919e28 | 0.184389 | ||||||||
\(591\) | −3.16019e28 | −0.250060 | ||||||||
\(592\) | −4.76972e28 | −0.370779 | ||||||||
\(593\) | 7.72360e28 | 0.589855 | 0.294928 | − | 0.955520i | \(-0.404704\pi\) | ||||
0.294928 | + | 0.955520i | \(0.404704\pi\) | |||||||
\(594\) | −1.15883e29 | −0.869487 | ||||||||
\(595\) | −5.61166e28 | −0.413678 | ||||||||
\(596\) | 1.22724e29 | 0.888884 | ||||||||
\(597\) | 8.75308e28 | 0.622917 | ||||||||
\(598\) | 3.09347e29 | 2.16313 | ||||||||
\(599\) | 8.22197e28 | 0.564930 | 0.282465 | − | 0.959278i | \(-0.408848\pi\) | ||||
0.282465 | + | 0.959278i | \(0.408848\pi\) | |||||||
\(600\) | −4.90741e27 | −0.0331333 | ||||||||
\(601\) | 1.57712e29 | 1.04636 | 0.523181 | − | 0.852221i | \(-0.324745\pi\) | ||||
0.523181 | + | 0.852221i | \(0.324745\pi\) | |||||||
\(602\) | 5.34602e28 | 0.348552 | ||||||||
\(603\) | 1.07271e29 | 0.687306 | ||||||||
\(604\) | −1.65399e28 | −0.104146 | ||||||||
\(605\) | −8.47285e28 | −0.524322 | ||||||||
\(606\) | 2.16054e28 | 0.131401 | ||||||||
\(607\) | −3.31059e29 | −1.97890 | −0.989450 | − | 0.144877i | \(-0.953721\pi\) | ||||
−0.989450 | + | 0.144877i | \(0.953721\pi\) | |||||||
\(608\) | 7.81039e27 | 0.0458865 | ||||||||
\(609\) | −1.24997e29 | −0.721801 | ||||||||
\(610\) | −5.32798e28 | −0.302412 | ||||||||
\(611\) | −1.85867e29 | −1.03698 | ||||||||
\(612\) | −7.36525e28 | −0.403922 | ||||||||
\(613\) | 3.50723e29 | 1.89073 | 0.945363 | − | 0.326018i | \(-0.105707\pi\) | ||||
0.945363 | + | 0.326018i | \(0.105707\pi\) | |||||||
\(614\) | 1.04918e29 | 0.556008 | ||||||||
\(615\) | 4.47705e28 | 0.233240 | ||||||||
\(616\) | 9.09248e28 | 0.465677 | ||||||||
\(617\) | −2.45228e28 | −0.123474 | −0.0617371 | − | 0.998092i | \(-0.519664\pi\) | ||||
−0.0617371 | + | 0.998092i | \(0.519664\pi\) | |||||||
\(618\) | 9.41335e28 | 0.465978 | ||||||||
\(619\) | 1.47013e28 | 0.0715492 | 0.0357746 | − | 0.999360i | \(-0.488610\pi\) | ||||
0.0357746 | + | 0.999360i | \(0.488610\pi\) | |||||||
\(620\) | −3.40158e28 | −0.162767 | ||||||||
\(621\) | 2.95406e29 | 1.38982 | ||||||||
\(622\) | 2.22407e29 | 1.02884 | ||||||||
\(623\) | 1.62445e29 | 0.738894 | ||||||||
\(624\) | 4.80955e28 | 0.215113 | ||||||||
\(625\) | 9.09495e27 | 0.0400000 | ||||||||
\(626\) | −2.25105e29 | −0.973541 | ||||||||
\(627\) | 4.21522e28 | 0.179272 | ||||||||
\(628\) | −9.82855e28 | −0.411068 | ||||||||
\(629\) | −3.73247e29 | −1.53520 | ||||||||
\(630\) | −5.45220e28 | −0.220544 | ||||||||
\(631\) | 1.42534e29 | 0.567034 | 0.283517 | − | 0.958967i | \(-0.408499\pi\) | ||||
0.283517 | + | 0.958967i | \(0.408499\pi\) | |||||||
\(632\) | −1.87133e28 | −0.0732184 | ||||||||
\(633\) | −1.61250e29 | −0.620526 | ||||||||
\(634\) | −1.29634e29 | −0.490662 | ||||||||
\(635\) | −1.99795e29 | −0.743808 | ||||||||
\(636\) | 7.14187e28 | 0.261525 | ||||||||
\(637\) | −1.02689e29 | −0.369878 | ||||||||
\(638\) | −5.07053e29 | −1.79654 | ||||||||
\(639\) | 2.43407e29 | 0.848347 | ||||||||
\(640\) | 1.15292e28 | 0.0395285 | ||||||||
\(641\) | 2.82277e28 | 0.0952064 | 0.0476032 | − | 0.998866i | \(-0.484842\pi\) | ||||
0.0476032 | + | 0.998866i | \(0.484842\pi\) | |||||||
\(642\) | −3.70528e28 | −0.122943 | ||||||||
\(643\) | 1.52966e29 | 0.499321 | 0.249661 | − | 0.968333i | \(-0.419681\pi\) | ||||
0.249661 | + | 0.968333i | \(0.419681\pi\) | |||||||
\(644\) | −2.31783e29 | −0.744354 | ||||||||
\(645\) | 3.65844e28 | 0.115590 | ||||||||
\(646\) | 6.11190e28 | 0.189992 | ||||||||
\(647\) | −9.19042e28 | −0.281087 | −0.140543 | − | 0.990075i | \(-0.544885\pi\) | ||||
−0.140543 | + | 0.990075i | \(0.544885\pi\) | |||||||
\(648\) | −4.57637e28 | −0.137716 | ||||||||
\(649\) | −2.90253e29 | −0.859423 | ||||||||
\(650\) | −8.91357e28 | −0.259694 | ||||||||
\(651\) | 1.06321e29 | 0.304803 | ||||||||
\(652\) | 1.21357e29 | 0.342345 | ||||||||
\(653\) | −8.26379e28 | −0.229399 | −0.114699 | − | 0.993400i | \(-0.536590\pi\) | ||||
−0.114699 | + | 0.993400i | \(0.536590\pi\) | |||||||
\(654\) | 4.68693e28 | 0.128033 | ||||||||
\(655\) | 1.01358e29 | 0.272474 | ||||||||
\(656\) | −1.05181e29 | −0.278259 | ||||||||
\(657\) | −1.11919e28 | −0.0291385 | ||||||||
\(658\) | 1.39264e29 | 0.356834 | ||||||||
\(659\) | −7.76286e29 | −1.95760 | −0.978802 | − | 0.204807i | \(-0.934343\pi\) | ||||
−0.978802 | + | 0.204807i | \(0.934343\pi\) | |||||||
\(660\) | 6.22226e28 | 0.154432 | ||||||||
\(661\) | −6.63151e29 | −1.61993 | −0.809967 | − | 0.586476i | \(-0.800515\pi\) | ||||
−0.809967 | + | 0.586476i | \(0.800515\pi\) | |||||||
\(662\) | −1.98350e29 | −0.476896 | ||||||||
\(663\) | 3.76364e29 | 0.890668 | ||||||||
\(664\) | −4.03423e28 | −0.0939715 | ||||||||
\(665\) | 4.52439e28 | 0.103737 | ||||||||
\(666\) | −3.62641e29 | −0.818461 | ||||||||
\(667\) | 1.29256e30 | 2.87165 | ||||||||
\(668\) | 1.53115e29 | 0.334862 | ||||||||
\(669\) | 6.93481e27 | 0.0149300 | ||||||||
\(670\) | −1.31401e29 | −0.278492 | ||||||||
\(671\) | 6.75550e29 | 1.40952 | ||||||||
\(672\) | −3.60363e28 | −0.0740223 | ||||||||
\(673\) | 3.60156e29 | 0.728337 | 0.364169 | − | 0.931333i | \(-0.381353\pi\) | ||||
0.364169 | + | 0.931333i | \(0.381353\pi\) | |||||||
\(674\) | −1.38075e29 | −0.274908 | ||||||||
\(675\) | −8.51189e28 | −0.166854 | ||||||||
\(676\) | 6.14516e29 | 1.18602 | ||||||||
\(677\) | −1.28335e28 | −0.0243874 | −0.0121937 | − | 0.999926i | \(-0.503881\pi\) | ||||
−0.0121937 | + | 0.999926i | \(0.503881\pi\) | |||||||
\(678\) | −2.70203e29 | −0.505567 | ||||||||
\(679\) | −1.20710e29 | −0.222387 | ||||||||
\(680\) | 9.02201e28 | 0.163667 | ||||||||
\(681\) | −2.31734e29 | −0.413947 | ||||||||
\(682\) | 4.31296e29 | 0.758646 | ||||||||
\(683\) | −2.83065e29 | −0.490308 | −0.245154 | − | 0.969484i | \(-0.578838\pi\) | ||||
−0.245154 | + | 0.969484i | \(0.578838\pi\) | |||||||
\(684\) | 5.93823e28 | 0.101290 | ||||||||
\(685\) | 8.91616e28 | 0.149771 | ||||||||
\(686\) | 4.58926e29 | 0.759171 | ||||||||
\(687\) | −2.08633e29 | −0.339889 | ||||||||
\(688\) | −8.59495e28 | −0.137900 | ||||||||
\(689\) | 1.29721e30 | 2.04979 | ||||||||
\(690\) | −1.58616e29 | −0.246849 | ||||||||
\(691\) | −6.08933e29 | −0.933361 | −0.466681 | − | 0.884426i | \(-0.654550\pi\) | ||||
−0.466681 | + | 0.884426i | \(0.654550\pi\) | |||||||
\(692\) | −2.75549e29 | −0.415992 | ||||||||
\(693\) | 6.91300e29 | 1.02794 | ||||||||
\(694\) | 6.89485e29 | 1.00983 | ||||||||
\(695\) | 3.10621e29 | 0.448116 | ||||||||
\(696\) | 2.00961e29 | 0.285571 | ||||||||
\(697\) | −8.23082e29 | −1.15212 | ||||||||
\(698\) | −9.29509e29 | −1.28166 | ||||||||
\(699\) | 4.96284e27 | 0.00674093 | ||||||||
\(700\) | 6.67863e28 | 0.0893631 | ||||||||
\(701\) | −4.09891e29 | −0.540292 | −0.270146 | − | 0.962819i | \(-0.587072\pi\) | ||||
−0.270146 | + | 0.962819i | \(0.587072\pi\) | |||||||
\(702\) | 8.34214e29 | 1.08327 | ||||||||
\(703\) | 3.00930e29 | 0.384977 | ||||||||
\(704\) | −1.46182e29 | −0.184239 | ||||||||
\(705\) | 9.53024e28 | 0.118336 | ||||||||
\(706\) | −4.50709e28 | −0.0551374 | ||||||||
\(707\) | −2.94033e29 | −0.354399 | ||||||||
\(708\) | 1.15036e29 | 0.136611 | ||||||||
\(709\) | −1.14539e30 | −1.34020 | −0.670098 | − | 0.742273i | \(-0.733748\pi\) | ||||
−0.670098 | + | 0.742273i | \(0.733748\pi\) | |||||||
\(710\) | −2.98159e29 | −0.343745 | ||||||||
\(711\) | −1.42277e29 | −0.161623 | ||||||||
\(712\) | −2.61168e29 | −0.292334 | ||||||||
\(713\) | −1.09945e30 | −1.21264 | ||||||||
\(714\) | −2.81996e29 | −0.306487 | ||||||||
\(715\) | 1.13018e30 | 1.21041 | ||||||||
\(716\) | 9.35590e29 | 0.987413 | ||||||||
\(717\) | −6.95323e29 | −0.723162 | ||||||||
\(718\) | 4.02968e29 | 0.413013 | ||||||||
\(719\) | 1.29783e30 | 1.31088 | 0.655440 | − | 0.755247i | \(-0.272483\pi\) | ||||
0.655440 | + | 0.755247i | \(0.272483\pi\) | |||||||
\(720\) | 8.76565e28 | 0.0872555 | ||||||||
\(721\) | −1.28109e30 | −1.25678 | ||||||||
\(722\) | 6.82073e29 | 0.659463 | ||||||||
\(723\) | −1.00882e28 | −0.00961306 | ||||||||
\(724\) | 2.84576e29 | 0.267266 | ||||||||
\(725\) | −3.72442e29 | −0.344754 | ||||||||
\(726\) | −4.25777e29 | −0.388461 | ||||||||
\(727\) | −1.67396e30 | −1.50534 | −0.752669 | − | 0.658399i | \(-0.771234\pi\) | ||||
−0.752669 | + | 0.658399i | \(0.771234\pi\) | |||||||
\(728\) | −6.54544e29 | −0.580176 | ||||||||
\(729\) | 9.94890e28 | 0.0869233 | ||||||||
\(730\) | 1.37094e28 | 0.0118067 | ||||||||
\(731\) | −6.72585e29 | −0.570972 | ||||||||
\(732\) | −2.67741e29 | −0.224052 | ||||||||
\(733\) | 4.12599e29 | 0.340359 | 0.170179 | − | 0.985413i | \(-0.445565\pi\) | ||||
0.170179 | + | 0.985413i | \(0.445565\pi\) | |||||||
\(734\) | −1.51573e28 | −0.0123257 | ||||||||
\(735\) | 5.26531e28 | 0.0422092 | ||||||||
\(736\) | 3.72643e29 | 0.294494 | ||||||||
\(737\) | 1.66607e30 | 1.29803 | ||||||||
\(738\) | −7.99693e29 | −0.614231 | ||||||||
\(739\) | 1.73492e30 | 1.31375 | 0.656877 | − | 0.753998i | \(-0.271877\pi\) | ||||
0.656877 | + | 0.753998i | \(0.271877\pi\) | |||||||
\(740\) | 4.44215e29 | 0.331635 | ||||||||
\(741\) | −3.03443e29 | −0.223350 | ||||||||
\(742\) | −9.71956e29 | −0.705352 | ||||||||
\(743\) | −1.36497e30 | −0.976656 | −0.488328 | − | 0.872660i | \(-0.662393\pi\) | ||||
−0.488328 | + | 0.872660i | \(0.662393\pi\) | |||||||
\(744\) | −1.70936e29 | −0.120592 | ||||||||
\(745\) | −1.14296e30 | −0.795042 | ||||||||
\(746\) | 1.60849e30 | 1.10322 | ||||||||
\(747\) | −3.06722e29 | −0.207434 | ||||||||
\(748\) | −1.14393e30 | −0.762837 | ||||||||
\(749\) | 5.04261e29 | 0.331586 | ||||||||
\(750\) | 4.57039e28 | 0.0296353 | ||||||||
\(751\) | −1.35372e30 | −0.865587 | −0.432793 | − | 0.901493i | \(-0.642472\pi\) | ||||
−0.432793 | + | 0.901493i | \(0.642472\pi\) | |||||||
\(752\) | −2.23898e29 | −0.141177 | ||||||||
\(753\) | −4.21646e29 | −0.262181 | ||||||||
\(754\) | 3.65015e30 | 2.23826 | ||||||||
\(755\) | 1.54040e29 | 0.0931514 | ||||||||
\(756\) | −6.25048e29 | −0.372764 | ||||||||
\(757\) | −8.02724e29 | −0.472128 | −0.236064 | − | 0.971738i | \(-0.575857\pi\) | ||||
−0.236064 | + | 0.971738i | \(0.575857\pi\) | |||||||
\(758\) | 2.33168e29 | 0.135252 | ||||||||
\(759\) | 2.01114e30 | 1.15054 | ||||||||
\(760\) | −7.27399e28 | −0.0410421 | ||||||||
\(761\) | 2.59098e29 | 0.144186 | 0.0720932 | − | 0.997398i | \(-0.477032\pi\) | ||||
0.0720932 | + | 0.997398i | \(0.477032\pi\) | |||||||
\(762\) | −1.00401e30 | −0.551075 | ||||||||
\(763\) | −6.37857e29 | −0.345315 | ||||||||
\(764\) | −1.22413e30 | −0.653654 | ||||||||
\(765\) | 6.85943e29 | 0.361279 | ||||||||
\(766\) | −2.34882e30 | −1.22024 | ||||||||
\(767\) | 2.08945e30 | 1.07073 | ||||||||
\(768\) | 5.79365e28 | 0.0292860 | ||||||||
\(769\) | −9.50454e29 | −0.473919 | −0.236960 | − | 0.971519i | \(-0.576151\pi\) | ||||
−0.236960 | + | 0.971519i | \(0.576151\pi\) | |||||||
\(770\) | −8.46803e29 | −0.416514 | ||||||||
\(771\) | 1.40874e29 | 0.0683535 | ||||||||
\(772\) | 8.58631e28 | 0.0410984 | ||||||||
\(773\) | 3.15209e30 | 1.48838 | 0.744191 | − | 0.667967i | \(-0.232835\pi\) | ||||
0.744191 | + | 0.667967i | \(0.232835\pi\) | |||||||
\(774\) | −6.53473e29 | −0.304402 | ||||||||
\(775\) | 3.16796e29 | 0.145584 | ||||||||
\(776\) | 1.94068e29 | 0.0879846 | ||||||||
\(777\) | −1.38846e30 | −0.621030 | ||||||||
\(778\) | −1.13160e30 | −0.499352 | ||||||||
\(779\) | 6.63609e29 | 0.288914 | ||||||||
\(780\) | −4.47924e29 | −0.192403 | ||||||||
\(781\) | 3.78045e30 | 1.60217 | ||||||||
\(782\) | 2.91606e30 | 1.21934 | ||||||||
\(783\) | 3.48565e30 | 1.43809 | ||||||||
\(784\) | −1.23700e29 | −0.0503561 | ||||||||
\(785\) | 9.15355e29 | 0.367670 | ||||||||
\(786\) | 5.09345e29 | 0.201872 | ||||||||
\(787\) | −1.06937e30 | −0.418211 | −0.209105 | − | 0.977893i | \(-0.567055\pi\) | ||||
−0.209105 | + | 0.977893i | \(0.567055\pi\) | |||||||
\(788\) | −6.91449e29 | −0.266830 | ||||||||
\(789\) | −3.38726e28 | −0.0128985 | ||||||||
\(790\) | 1.74281e29 | 0.0654885 | ||||||||
\(791\) | 3.67727e30 | 1.36355 | ||||||||
\(792\) | −1.11142e30 | −0.406691 | ||||||||
\(793\) | −4.86311e30 | −1.75609 | ||||||||
\(794\) | −1.93236e29 | −0.0688608 | ||||||||
\(795\) | −6.65139e29 | −0.233915 | ||||||||
\(796\) | 1.91517e30 | 0.664692 | ||||||||
\(797\) | 2.66578e30 | 0.913086 | 0.456543 | − | 0.889701i | \(-0.349087\pi\) | ||||
0.456543 | + | 0.889701i | \(0.349087\pi\) | |||||||
\(798\) | 2.27359e29 | 0.0768568 | ||||||||
\(799\) | −1.75208e30 | −0.584539 | ||||||||
\(800\) | −1.07374e29 | −0.0353553 | ||||||||
\(801\) | −1.98565e30 | −0.645301 | ||||||||
\(802\) | 1.78870e30 | 0.573730 | ||||||||
\(803\) | −1.73826e29 | −0.0550302 | ||||||||
\(804\) | −6.60314e29 | −0.206330 | ||||||||
\(805\) | 2.15864e30 | 0.665770 | ||||||||
\(806\) | −3.10479e30 | −0.945179 | ||||||||
\(807\) | 2.05782e30 | 0.618352 | ||||||||
\(808\) | 4.72725e29 | 0.140213 | ||||||||
\(809\) | 1.67414e30 | 0.490153 | 0.245077 | − | 0.969504i | \(-0.421187\pi\) | ||||
0.245077 | + | 0.969504i | \(0.421187\pi\) | |||||||
\(810\) | 4.26208e29 | 0.123177 | ||||||||
\(811\) | −4.62583e30 | −1.31969 | −0.659843 | − | 0.751404i | \(-0.729377\pi\) | ||||
−0.659843 | + | 0.751404i | \(0.729377\pi\) | |||||||
\(812\) | −2.73493e30 | −0.770207 | ||||||||
\(813\) | 7.96509e29 | 0.221432 | ||||||||
\(814\) | −5.63233e30 | −1.54572 | ||||||||
\(815\) | −1.13022e30 | −0.306203 | ||||||||
\(816\) | 4.53374e29 | 0.121258 | ||||||||
\(817\) | 5.42271e29 | 0.143181 | ||||||||
\(818\) | 2.99988e30 | 0.781979 | ||||||||
\(819\) | −4.97649e30 | −1.28069 | ||||||||
\(820\) | 9.79579e29 | 0.248882 | ||||||||
\(821\) | −2.81912e30 | −0.707147 | −0.353573 | − | 0.935407i | \(-0.615034\pi\) | ||||
−0.353573 | + | 0.935407i | \(0.615034\pi\) | |||||||
\(822\) | 4.48054e29 | 0.110963 | ||||||||
\(823\) | −8.15621e29 | −0.199430 | −0.0997149 | − | 0.995016i | \(-0.531793\pi\) | ||||
−0.0997149 | + | 0.995016i | \(0.531793\pi\) | |||||||
\(824\) | 2.05964e30 | 0.497228 | ||||||||
\(825\) | −5.79493e29 | −0.138128 | ||||||||
\(826\) | −1.56556e30 | −0.368450 | ||||||||
\(827\) | −5.27710e30 | −1.22627 | −0.613137 | − | 0.789977i | \(-0.710093\pi\) | ||||
−0.613137 | + | 0.789977i | \(0.710093\pi\) | |||||||
\(828\) | 2.83320e30 | 0.650068 | ||||||||
\(829\) | −5.17029e30 | −1.17137 | −0.585683 | − | 0.810540i | \(-0.699174\pi\) | ||||
−0.585683 | + | 0.810540i | \(0.699174\pi\) | |||||||
\(830\) | 3.75717e29 | 0.0840507 | ||||||||
\(831\) | −1.37052e30 | −0.302744 | ||||||||
\(832\) | 1.05233e30 | 0.229539 | ||||||||
\(833\) | −9.67999e29 | −0.208498 | ||||||||
\(834\) | 1.56093e30 | 0.332002 | ||||||||
\(835\) | −1.42600e30 | −0.299509 | ||||||||
\(836\) | 9.22291e29 | 0.191294 | ||||||||
\(837\) | −2.96487e30 | −0.607279 | ||||||||
\(838\) | 2.65763e30 | 0.537567 | ||||||||
\(839\) | −9.14574e30 | −1.82692 | −0.913458 | − | 0.406934i | \(-0.866598\pi\) | ||||
−0.913458 | + | 0.406934i | \(0.866598\pi\) | |||||||
\(840\) | 3.35614e29 | 0.0662076 | ||||||||
\(841\) | 1.01188e31 | 1.97139 | ||||||||
\(842\) | 2.13418e30 | 0.410633 | ||||||||
\(843\) | −2.67529e30 | −0.508371 | ||||||||
\(844\) | −3.52814e30 | −0.662140 | ||||||||
\(845\) | −5.72312e30 | −1.06081 | ||||||||
\(846\) | −1.70230e30 | −0.311635 | ||||||||
\(847\) | 5.79451e30 | 1.04771 | ||||||||
\(848\) | 1.56264e30 | 0.279063 | ||||||||
\(849\) | 3.13532e30 | 0.553033 | ||||||||
\(850\) | −8.40240e29 | −0.146388 | ||||||||
\(851\) | 1.43578e31 | 2.47074 | ||||||||
\(852\) | −1.49831e30 | −0.254674 | ||||||||
\(853\) | 9.89405e30 | 1.66115 | 0.830576 | − | 0.556906i | \(-0.188011\pi\) | ||||
0.830576 | + | 0.556906i | \(0.188011\pi\) | |||||||
\(854\) | 3.64376e30 | 0.604285 | ||||||||
\(855\) | −5.53041e29 | −0.0905968 | ||||||||
\(856\) | −8.10714e29 | −0.131188 | ||||||||
\(857\) | 5.52749e30 | 0.883546 | 0.441773 | − | 0.897127i | \(-0.354350\pi\) | ||||
0.441773 | + | 0.897127i | \(0.354350\pi\) | |||||||
\(858\) | 5.67936e30 | 0.896774 | ||||||||
\(859\) | −3.34705e29 | −0.0522076 | −0.0261038 | − | 0.999659i | \(-0.508310\pi\) | ||||
−0.0261038 | + | 0.999659i | \(0.508310\pi\) | |||||||
\(860\) | 8.00467e29 | 0.123342 | ||||||||
\(861\) | −3.06182e30 | −0.466065 | ||||||||
\(862\) | −1.89712e30 | −0.285278 | ||||||||
\(863\) | −4.68654e30 | −0.696208 | −0.348104 | − | 0.937456i | \(-0.613174\pi\) | ||||
−0.348104 | + | 0.937456i | \(0.613174\pi\) | |||||||
\(864\) | 1.00491e30 | 0.147479 | ||||||||
\(865\) | 2.56625e30 | 0.372075 | ||||||||
\(866\) | −6.46641e29 | −0.0926244 | ||||||||
\(867\) | 2.36646e29 | 0.0334888 | ||||||||
\(868\) | 2.32631e30 | 0.325245 | ||||||||
\(869\) | −2.20976e30 | −0.305237 | ||||||||
\(870\) | −1.87159e30 | −0.255423 | ||||||||
\(871\) | −1.19936e31 | −1.61718 | ||||||||
\(872\) | 1.02550e30 | 0.136620 | ||||||||
\(873\) | 1.47550e30 | 0.194218 | ||||||||
\(874\) | −2.35107e30 | −0.305771 | ||||||||
\(875\) | −6.21996e29 | −0.0799287 | ||||||||
\(876\) | 6.88925e28 | 0.00874739 | ||||||||
\(877\) | 2.46570e30 | 0.309346 | 0.154673 | − | 0.987966i | \(-0.450568\pi\) | ||||
0.154673 | + | 0.987966i | \(0.450568\pi\) | |||||||
\(878\) | −3.27498e30 | −0.405991 | ||||||||
\(879\) | −5.31170e29 | −0.0650654 | ||||||||
\(880\) | 1.36143e30 | 0.164788 | ||||||||
\(881\) | 9.27878e30 | 1.10980 | 0.554899 | − | 0.831918i | \(-0.312757\pi\) | ||||
0.554899 | + | 0.831918i | \(0.312757\pi\) | |||||||
\(882\) | −9.40492e29 | −0.111157 | ||||||||
\(883\) | 1.09864e29 | 0.0128313 | 0.00641564 | − | 0.999979i | \(-0.497958\pi\) | ||||
0.00641564 | + | 0.999979i | \(0.497958\pi\) | |||||||
\(884\) | 8.23484e30 | 0.950400 | ||||||||
\(885\) | −1.07136e30 | −0.122188 | ||||||||
\(886\) | −7.46786e29 | −0.0841670 | ||||||||
\(887\) | 9.09262e30 | 1.01272 | 0.506362 | − | 0.862321i | \(-0.330990\pi\) | ||||
0.506362 | + | 0.862321i | \(0.330990\pi\) | |||||||
\(888\) | 2.23227e30 | 0.245703 | ||||||||
\(889\) | 1.36638e31 | 1.48629 | ||||||||
\(890\) | 2.43231e30 | 0.261471 | ||||||||
\(891\) | −5.40401e30 | −0.574117 | ||||||||
\(892\) | 1.51734e29 | 0.0159313 | ||||||||
\(893\) | 1.41261e30 | 0.146583 | ||||||||
\(894\) | −5.74359e30 | −0.589033 | ||||||||
\(895\) | −8.71337e30 | −0.883169 | ||||||||
\(896\) | −7.88474e29 | −0.0789865 | ||||||||
\(897\) | −1.44777e31 | −1.43343 | ||||||||
\(898\) | 1.62918e30 | 0.159429 | ||||||||
\(899\) | −1.29729e31 | −1.25476 | ||||||||
\(900\) | −8.16365e29 | −0.0780437 | ||||||||
\(901\) | 1.22282e31 | 1.15545 | ||||||||
\(902\) | −1.24204e31 | −1.16002 | ||||||||
\(903\) | −2.50198e30 | −0.230974 | ||||||||
\(904\) | −5.91205e30 | −0.539472 | ||||||||
\(905\) | −2.65032e30 | −0.239050 | ||||||||
\(906\) | 7.74078e29 | 0.0690143 | ||||||||
\(907\) | −4.70059e30 | −0.414263 | −0.207132 | − | 0.978313i | \(-0.566413\pi\) | ||||
−0.207132 | + | 0.978313i | \(0.566413\pi\) | |||||||
\(908\) | −5.07033e30 | −0.441707 | ||||||||
\(909\) | 3.59412e30 | 0.309508 | ||||||||
\(910\) | 6.09592e30 | 0.518925 | ||||||||
\(911\) | 1.05639e31 | 0.888960 | 0.444480 | − | 0.895789i | \(-0.353388\pi\) | ||||
0.444480 | + | 0.895789i | \(0.353388\pi\) | |||||||
\(912\) | −3.65532e29 | −0.0304074 | ||||||||
\(913\) | −4.76383e30 | −0.391754 | ||||||||
\(914\) | −9.16402e30 | −0.744991 | ||||||||
\(915\) | 2.49353e30 | 0.200398 | ||||||||
\(916\) | −4.56489e30 | −0.362684 | ||||||||
\(917\) | −6.93181e30 | −0.544463 | ||||||||
\(918\) | 7.86374e30 | 0.610634 | ||||||||
\(919\) | 2.15821e31 | 1.65684 | 0.828421 | − | 0.560105i | \(-0.189239\pi\) | ||||
0.828421 | + | 0.560105i | \(0.189239\pi\) | |||||||
\(920\) | −3.47051e30 | −0.263403 | ||||||||
\(921\) | −4.91023e30 | −0.368448 | ||||||||
\(922\) | −1.36137e31 | −1.00995 | ||||||||
\(923\) | −2.72145e31 | −1.99610 | ||||||||
\(924\) | −4.25535e30 | −0.308588 | ||||||||
\(925\) | −4.13707e30 | −0.296623 | ||||||||
\(926\) | −1.32774e31 | −0.941231 | ||||||||
\(927\) | 1.56594e31 | 1.09759 | ||||||||
\(928\) | 4.39702e30 | 0.304723 | ||||||||
\(929\) | 8.91027e30 | 0.610557 | 0.305278 | − | 0.952263i | \(-0.401250\pi\) | ||||
0.305278 | + | 0.952263i | \(0.401250\pi\) | |||||||
\(930\) | 1.59196e30 | 0.107860 | ||||||||
\(931\) | 7.80448e29 | 0.0522844 | ||||||||
\(932\) | 1.08587e29 | 0.00719300 | ||||||||
\(933\) | −1.04088e31 | −0.681780 | ||||||||
\(934\) | 5.14427e30 | 0.333182 | ||||||||
\(935\) | 1.06537e31 | 0.682302 | ||||||||
\(936\) | 8.00084e30 | 0.506687 | ||||||||
\(937\) | 8.67478e29 | 0.0543241 | 0.0271621 | − | 0.999631i | \(-0.491353\pi\) | ||||
0.0271621 | + | 0.999631i | \(0.491353\pi\) | |||||||
\(938\) | 8.98639e30 | 0.556487 | ||||||||
\(939\) | 1.05351e31 | 0.645132 | ||||||||
\(940\) | 2.08521e30 | 0.126272 | ||||||||
\(941\) | −1.58550e31 | −0.949459 | −0.474730 | − | 0.880132i | \(-0.657454\pi\) | ||||
−0.474730 | + | 0.880132i | \(0.657454\pi\) | |||||||
\(942\) | 4.59984e30 | 0.272401 | ||||||||
\(943\) | 3.16616e31 | 1.85422 | ||||||||
\(944\) | 2.51699e30 | 0.145772 | ||||||||
\(945\) | 5.82121e30 | 0.333410 | ||||||||
\(946\) | −1.01494e31 | −0.574886 | ||||||||
\(947\) | −2.27081e31 | −1.27206 | −0.636028 | − | 0.771666i | \(-0.719424\pi\) | ||||
−0.636028 | + | 0.771666i | \(0.719424\pi\) | |||||||
\(948\) | 8.75795e29 | 0.0485193 | ||||||||
\(949\) | 1.25133e30 | 0.0685607 | ||||||||
\(950\) | 6.77443e29 | 0.0367092 | ||||||||
\(951\) | 6.06698e30 | 0.325145 | ||||||||
\(952\) | −6.17008e30 | −0.327041 | ||||||||
\(953\) | −1.88217e31 | −0.986696 | −0.493348 | − | 0.869832i | \(-0.664227\pi\) | ||||
−0.493348 | + | 0.869832i | \(0.664227\pi\) | |||||||
\(954\) | 1.18807e31 | 0.616007 | ||||||||
\(955\) | 1.14006e31 | 0.584646 | ||||||||
\(956\) | −1.52137e31 | −0.771660 | ||||||||
\(957\) | 2.37305e31 | 1.19050 | ||||||||
\(958\) | −1.26561e31 | −0.628004 | ||||||||
\(959\) | −6.09769e30 | −0.299274 | ||||||||
\(960\) | −5.39576e29 | −0.0261942 | ||||||||
\(961\) | −9.79081e30 | −0.470136 | ||||||||
\(962\) | 4.05457e31 | 1.92578 | ||||||||
\(963\) | −6.16385e30 | −0.289585 | ||||||||
\(964\) | −2.20730e29 | −0.0102578 | ||||||||
\(965\) | −7.99662e29 | −0.0367595 | ||||||||
\(966\) | 1.08476e31 | 0.493258 | ||||||||
\(967\) | 1.59166e31 | 0.715934 | 0.357967 | − | 0.933734i | \(-0.383470\pi\) | ||||
0.357967 | + | 0.933734i | \(0.383470\pi\) | |||||||
\(968\) | −9.31600e30 | −0.414513 | ||||||||
\(969\) | −2.86042e30 | −0.125901 | ||||||||
\(970\) | −1.80740e30 | −0.0786958 | ||||||||
\(971\) | −1.49572e31 | −0.644239 | −0.322119 | − | 0.946699i | \(-0.604395\pi\) | ||||
−0.322119 | + | 0.946699i | \(0.604395\pi\) | |||||||
\(972\) | 1.19315e31 | 0.508394 | ||||||||
\(973\) | −2.12431e31 | −0.895434 | ||||||||
\(974\) | 2.38818e31 | 0.995859 | ||||||||
\(975\) | 4.17162e30 | 0.172090 | ||||||||
\(976\) | −5.85817e30 | −0.239078 | ||||||||
\(977\) | 2.26547e31 | 0.914672 | 0.457336 | − | 0.889294i | \(-0.348804\pi\) | ||||
0.457336 | + | 0.889294i | \(0.348804\pi\) | |||||||
\(978\) | −5.67959e30 | −0.226861 | ||||||||
\(979\) | −3.08400e31 | −1.21870 | ||||||||
\(980\) | 1.15205e30 | 0.0450399 | ||||||||
\(981\) | 7.79687e30 | 0.301575 | ||||||||
\(982\) | −2.72233e31 | −1.04177 | ||||||||
\(983\) | −7.38759e30 | −0.279699 | −0.139849 | − | 0.990173i | \(-0.544662\pi\) | ||||
−0.139849 | + | 0.990173i | \(0.544662\pi\) | |||||||
\(984\) | 4.92257e30 | 0.184393 | ||||||||
\(985\) | 6.43962e30 | 0.238660 | ||||||||
\(986\) | 3.44082e31 | 1.26170 | ||||||||
\(987\) | −6.51765e30 | −0.236462 | ||||||||
\(988\) | −6.63933e30 | −0.238329 | ||||||||
\(989\) | 2.58724e31 | 0.918916 | ||||||||
\(990\) | 1.03509e31 | 0.363756 | ||||||||
\(991\) | 1.82576e31 | 0.634849 | 0.317425 | − | 0.948284i | \(-0.397182\pi\) | ||||
0.317425 | + | 0.948284i | \(0.397182\pi\) | |||||||
\(992\) | −3.74007e30 | −0.128679 | ||||||||
\(993\) | 9.28295e30 | 0.316023 | ||||||||
\(994\) | 2.03909e31 | 0.686877 | ||||||||
\(995\) | −1.78364e31 | −0.594519 | ||||||||
\(996\) | 1.88805e30 | 0.0622717 | ||||||||
\(997\) | −3.18289e31 | −1.03878 | −0.519389 | − | 0.854538i | \(-0.673840\pi\) | ||||
−0.519389 | + | 0.854538i | \(0.673840\pi\) | |||||||
\(998\) | 1.42134e31 | 0.459017 | ||||||||
\(999\) | 3.87185e31 | 1.23732 |
(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 | 10.22.a.b.1.2 | ✓ | 2 | |
4.3 | odd | 2 | 80.22.a.d.1.1 | 2 | |||
5.2 | odd | 4 | 50.22.b.f.49.1 | 4 | |||
5.3 | odd | 4 | 50.22.b.f.49.4 | 4 | |||
5.4 | even | 2 | 50.22.a.f.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.22.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.22.a.f.1.1 | 2 | 5.4 | even | 2 | |||
50.22.b.f.49.1 | 4 | 5.2 | odd | 4 | |||
50.22.b.f.49.4 | 4 | 5.3 | odd | 4 | |||
80.22.a.d.1.1 | 2 | 4.3 | odd | 2 |