Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [18,26,Mod(1,18)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(18, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("18.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 18 = 2 \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 18.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: | \(71.2794203914\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{106705}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 26676 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{5}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 2) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(163.829\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 18.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4096.00 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | −8.78994e8 | −1.61013 | −0.805065 | − | 0.593187i | \(-0.797870\pi\) | ||||
−0.805065 | + | 0.593187i | \(0.797870\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00388e10 | 0.820270 | 0.410135 | − | 0.912025i | \(-0.365482\pi\) | ||||
0.410135 | + | 0.912025i | \(0.365482\pi\) | |||||||
\(8\) | −6.87195e10 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.60036e12 | 1.13853 | ||||||||
\(11\) | −5.73599e12 | −0.551061 | −0.275531 | − | 0.961292i | \(-0.588854\pi\) | ||||
−0.275531 | + | 0.961292i | \(0.588854\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.07343e13 | −0.127786 | −0.0638928 | − | 0.997957i | \(-0.520352\pi\) | ||||
−0.0638928 | + | 0.997957i | \(0.520352\pi\) | |||||||
\(14\) | −1.23039e14 | −0.580018 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | −2.97473e15 | −1.23833 | −0.619164 | − | 0.785262i | \(-0.712528\pi\) | ||||
−0.619164 | + | 0.785262i | \(0.712528\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.42738e15 | −0.562561 | −0.281281 | − | 0.959626i | \(-0.590759\pi\) | ||||
−0.281281 | + | 0.959626i | \(0.590759\pi\) | |||||||
\(20\) | −1.47471e16 | −0.805065 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.34946e16 | 0.389659 | ||||||||
\(23\) | 1.04540e17 | 0.994683 | 0.497341 | − | 0.867555i | \(-0.334310\pi\) | ||||
0.497341 | + | 0.867555i | \(0.334310\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.74607e17 | 1.59252 | ||||||||
\(26\) | 4.39677e16 | 0.0903581 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.03967e17 | 0.410135 | ||||||||
\(29\) | −3.09182e18 | −1.62270 | −0.811352 | − | 0.584558i | \(-0.801268\pi\) | ||||
−0.811352 | + | 0.584558i | \(0.801268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.26809e18 | −0.973222 | −0.486611 | − | 0.873619i | \(-0.661767\pi\) | ||||
−0.486611 | + | 0.873619i | \(0.661767\pi\) | |||||||
\(32\) | −1.15292e18 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.21845e19 | 0.875630 | ||||||||
\(35\) | −2.64039e19 | −1.32074 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.51028e19 | −1.12637 | −0.563186 | − | 0.826330i | \(-0.690424\pi\) | ||||
−0.563186 | + | 0.826330i | \(0.690424\pi\) | |||||||
\(38\) | 2.22305e19 | 0.397791 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.04040e19 | 0.569267 | ||||||||
\(41\) | 7.56724e19 | 0.523769 | 0.261884 | − | 0.965099i | \(-0.415656\pi\) | ||||
0.261884 | + | 0.965099i | \(0.415656\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.39036e20 | −0.530605 | −0.265302 | − | 0.964165i | \(-0.585472\pi\) | ||||
−0.265302 | + | 0.964165i | \(0.585472\pi\) | |||||||
\(44\) | −9.62339e19 | −0.275531 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.28196e20 | −0.703347 | ||||||||
\(47\) | −4.67328e20 | −0.586676 | −0.293338 | − | 0.956009i | \(-0.594766\pi\) | ||||
−0.293338 | + | 0.956009i | \(0.594766\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.38741e20 | −0.327158 | ||||||||
\(50\) | −1.94399e21 | −1.12608 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.80092e20 | −0.0638928 | ||||||||
\(53\) | 1.24315e21 | 0.347595 | 0.173797 | − | 0.984781i | \(-0.444396\pi\) | ||||
0.173797 | + | 0.984781i | \(0.444396\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.04190e21 | 0.887280 | ||||||||
\(56\) | −2.06425e21 | −0.290009 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.26641e22 | 1.14743 | ||||||||
\(59\) | 1.32468e22 | 0.969303 | 0.484652 | − | 0.874707i | \(-0.338946\pi\) | ||||
0.484652 | + | 0.874707i | \(0.338946\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.36984e20 | −0.0114313 | −0.00571565 | − | 0.999984i | \(-0.501819\pi\) | ||||
−0.00571565 | + | 0.999984i | \(0.501819\pi\) | |||||||
\(62\) | 1.74821e22 | 0.688172 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | 9.43539e21 | 0.205752 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.36922e22 | −0.801634 | −0.400817 | − | 0.916158i | \(-0.631274\pi\) | ||||
−0.400817 | + | 0.916158i | \(0.631274\pi\) | |||||||
\(68\) | −4.99076e22 | −0.619164 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.08150e23 | 0.933905 | ||||||||
\(71\) | 2.27032e23 | 1.64194 | 0.820971 | − | 0.570970i | \(-0.193433\pi\) | ||||
0.820971 | + | 0.570970i | \(0.193433\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.78528e23 | 1.42342 | 0.711710 | − | 0.702473i | \(-0.247921\pi\) | ||||
0.711710 | + | 0.702473i | \(0.247921\pi\) | |||||||
\(74\) | 1.84741e23 | 0.796465 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.10563e22 | −0.281281 | ||||||||
\(77\) | −1.72302e23 | −0.452019 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.36958e23 | 1.21275 | 0.606376 | − | 0.795178i | \(-0.292622\pi\) | ||||
0.606376 | + | 0.795178i | \(0.292622\pi\) | |||||||
\(80\) | −2.47415e23 | −0.402532 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.09954e23 | −0.370360 | ||||||||
\(83\) | −1.19662e24 | −1.22880 | −0.614398 | − | 0.788996i | \(-0.710601\pi\) | ||||
−0.614398 | + | 0.788996i | \(0.710601\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.61477e24 | 1.99387 | ||||||||
\(86\) | 5.69491e23 | 0.375194 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.94174e23 | 0.194830 | ||||||||
\(89\) | 3.22134e24 | 1.38249 | 0.691244 | − | 0.722621i | \(-0.257063\pi\) | ||||
0.691244 | + | 0.722621i | \(0.257063\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.22445e23 | −0.104819 | ||||||||
\(92\) | 1.75389e24 | 0.497341 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.91418e24 | 0.414843 | ||||||||
\(95\) | 4.77063e24 | 0.905797 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.58465e24 | 0.524566 | 0.262283 | − | 0.964991i | \(-0.415525\pi\) | ||||
0.262283 | + | 0.964991i | \(0.415525\pi\) | |||||||
\(98\) | 1.79708e24 | 0.231335 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.96259e24 | 0.796259 | ||||||||
\(101\) | 3.40630e24 | 0.300792 | 0.150396 | − | 0.988626i | \(-0.451945\pi\) | ||||
0.150396 | + | 0.988626i | \(0.451945\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.27075e24 | 0.571583 | 0.285792 | − | 0.958292i | \(-0.407743\pi\) | ||||
0.285792 | + | 0.958292i | \(0.407743\pi\) | |||||||
\(104\) | 7.37656e23 | 0.0451791 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.09192e24 | −0.245787 | ||||||||
\(107\) | −1.57986e25 | −0.678142 | −0.339071 | − | 0.940761i | \(-0.610113\pi\) | ||||
−0.339071 | + | 0.940761i | \(0.610113\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.00869e25 | 1.02458 | 0.512290 | − | 0.858813i | \(-0.328797\pi\) | ||||
0.512290 | + | 0.858813i | \(0.328797\pi\) | |||||||
\(110\) | −2.06516e25 | −0.627402 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.45516e24 | 0.205067 | ||||||||
\(113\) | 8.06745e25 | 1.75088 | 0.875439 | − | 0.483329i | \(-0.160572\pi\) | ||||
0.875439 | + | 0.483329i | \(0.160572\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.18901e25 | −1.60157 | ||||||||
\(116\) | −5.18722e25 | −0.811352 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.42587e25 | −0.685401 | ||||||||
\(119\) | −8.93571e25 | −1.01576 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.54455e25 | −0.696332 | ||||||||
\(122\) | 9.70685e23 | 0.00808315 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.16066e25 | −0.486611 | ||||||||
\(125\) | −1.55216e26 | −0.954030 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.32973e26 | −0.670221 | −0.335111 | − | 0.942179i | \(-0.608774\pi\) | ||||
−0.335111 | + | 0.942179i | \(0.608774\pi\) | |||||||
\(128\) | −1.93428e25 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.86474e25 | −0.145488 | ||||||||
\(131\) | −6.73908e25 | −0.230520 | −0.115260 | − | 0.993335i | \(-0.536770\pi\) | ||||
−0.115260 | + | 0.993335i | \(0.536770\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.63032e26 | −0.461452 | ||||||||
\(134\) | 2.19923e26 | 0.566841 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.04422e26 | 0.437815 | ||||||||
\(137\) | 3.22963e26 | 0.631170 | 0.315585 | − | 0.948897i | \(-0.397799\pi\) | ||||
0.315585 | + | 0.948897i | \(0.397799\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.21581e25 | −0.150262 | −0.0751309 | − | 0.997174i | \(-0.523937\pi\) | ||||
−0.0751309 | + | 0.997174i | \(0.523937\pi\) | |||||||
\(140\) | −4.42984e26 | −0.660370 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.29923e26 | −1.16103 | ||||||||
\(143\) | 6.15719e25 | 0.0704177 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.71769e27 | 2.61276 | ||||||||
\(146\) | −1.14085e27 | −1.00651 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.56699e26 | −0.563186 | ||||||||
\(149\) | 7.12667e26 | 0.487594 | 0.243797 | − | 0.969826i | \(-0.421607\pi\) | ||||
0.243797 | + | 0.969826i | \(0.421607\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.06161e27 | −1.77312 | −0.886559 | − | 0.462616i | \(-0.846911\pi\) | ||||
−0.886559 | + | 0.462616i | \(0.846911\pi\) | |||||||
\(152\) | 3.72966e26 | 0.198895 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.05749e26 | 0.319626 | ||||||||
\(155\) | 3.75162e27 | 1.56701 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.38960e27 | 0.850315 | 0.425157 | − | 0.905119i | \(-0.360219\pi\) | ||||
0.425157 | + | 0.905119i | \(0.360219\pi\) | |||||||
\(158\) | −2.60898e27 | −0.857546 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.01341e27 | 0.284633 | ||||||||
\(161\) | 3.14025e27 | 0.815908 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.63092e27 | 1.47648 | 0.738242 | − | 0.674536i | \(-0.235656\pi\) | ||||
0.738242 | + | 0.674536i | \(0.235656\pi\) | |||||||
\(164\) | 1.26957e27 | 0.261884 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.90135e27 | 0.868890 | ||||||||
\(167\) | −4.06997e27 | −0.669323 | −0.334662 | − | 0.942338i | \(-0.608622\pi\) | ||||
−0.334662 | + | 0.942338i | \(0.608622\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.94118e27 | −0.983671 | ||||||||
\(170\) | −1.07101e28 | −1.40988 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.33263e27 | −0.265302 | ||||||||
\(173\) | 8.68916e27 | 0.919182 | 0.459591 | − | 0.888131i | \(-0.347996\pi\) | ||||
0.459591 | + | 0.888131i | \(0.347996\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.42566e28 | 1.30629 | ||||||||
\(176\) | −1.61454e27 | −0.137765 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.31946e28 | −0.977567 | ||||||||
\(179\) | 4.31406e27 | 0.298005 | 0.149002 | − | 0.988837i | \(-0.452394\pi\) | ||||
0.149002 | + | 0.988837i | \(0.452394\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.22969e28 | 1.34049 | 0.670243 | − | 0.742142i | \(-0.266190\pi\) | ||||
0.670243 | + | 0.742142i | \(0.266190\pi\) | |||||||
\(182\) | 1.32074e27 | 0.0741180 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.18394e27 | −0.351674 | ||||||||
\(185\) | 3.96451e28 | 1.81360 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.70630e28 | 0.682394 | ||||||||
\(188\) | −7.84046e27 | −0.293338 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.95405e28 | −0.640495 | ||||||||
\(191\) | 1.91337e28 | 0.587329 | 0.293665 | − | 0.955908i | \(-0.405125\pi\) | ||||
0.293665 | + | 0.955908i | \(0.405125\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.96748e28 | −1.60814 | −0.804071 | − | 0.594533i | \(-0.797337\pi\) | ||||
−0.804071 | + | 0.594533i | \(0.797337\pi\) | |||||||
\(194\) | −1.46827e28 | −0.370924 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.36085e27 | −0.163579 | ||||||||
\(197\) | −6.24204e28 | −1.30166 | −0.650832 | − | 0.759222i | \(-0.725580\pi\) | ||||
−0.650832 | + | 0.759222i | \(0.725580\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.24229e28 | −0.595921 | −0.297960 | − | 0.954578i | \(-0.596306\pi\) | ||||
−0.297960 | + | 0.954578i | \(0.596306\pi\) | |||||||
\(200\) | −3.26148e28 | −0.563040 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.39522e28 | −0.212692 | ||||||||
\(203\) | −9.28745e28 | −1.33106 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.65156e28 | −0.843335 | ||||||||
\(206\) | −3.38770e28 | −0.404171 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.02144e27 | −0.0319464 | ||||||||
\(209\) | 3.11314e28 | 0.310006 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.82197e28 | 0.337875 | 0.168938 | − | 0.985627i | \(-0.445966\pi\) | ||||
0.168938 | + | 0.985627i | \(0.445966\pi\) | |||||||
\(212\) | 2.08565e28 | 0.173797 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.47109e28 | 0.479519 | ||||||||
\(215\) | 1.22212e29 | 0.854342 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.28208e29 | −0.798305 | ||||||||
\(218\) | −1.23236e29 | −0.724487 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.45891e28 | 0.443640 | ||||||||
\(221\) | 3.19316e28 | 0.158241 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.11100e29 | 1.37749 | 0.688746 | − | 0.725003i | \(-0.258161\pi\) | ||||
0.688746 | + | 0.725003i | \(0.258161\pi\) | |||||||
\(224\) | −3.46323e28 | −0.145005 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.30443e29 | −1.23806 | ||||||||
\(227\) | 1.05572e29 | 0.374304 | 0.187152 | − | 0.982331i | \(-0.440074\pi\) | ||||
0.187152 | + | 0.982331i | \(0.440074\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.70322e29 | −1.17662 | −0.588310 | − | 0.808635i | \(-0.700207\pi\) | ||||
−0.588310 | + | 0.808635i | \(0.700207\pi\) | |||||||
\(230\) | 3.76382e29 | 1.13248 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.12468e29 | 0.573713 | ||||||||
\(233\) | 6.84781e28 | 0.175228 | 0.0876138 | − | 0.996155i | \(-0.472076\pi\) | ||||
0.0876138 | + | 0.996155i | \(0.472076\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.10778e29 | 0.944625 | ||||||||
\(236\) | 2.22244e29 | 0.484652 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.66007e29 | 0.718253 | ||||||||
\(239\) | −3.87773e29 | −0.722111 | −0.361055 | − | 0.932544i | \(-0.617583\pi\) | ||||
−0.361055 | + | 0.932544i | \(0.617583\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.03723e30 | 1.74046 | 0.870230 | − | 0.492646i | \(-0.163970\pi\) | ||||
0.870230 | + | 0.492646i | \(0.163970\pi\) | |||||||
\(242\) | 3.09025e29 | 0.492381 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.97593e27 | −0.00571565 | ||||||||
\(245\) | 3.85651e29 | 0.526766 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.82591e28 | 0.0718873 | ||||||||
\(248\) | 2.93301e29 | 0.344086 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.35766e29 | 0.674601 | ||||||||
\(251\) | −1.47990e30 | −1.49386 | −0.746930 | − | 0.664903i | \(-0.768473\pi\) | ||||
−0.746930 | + | 0.664903i | \(0.768473\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.99641e29 | −0.548131 | ||||||||
\(254\) | 5.44659e29 | 0.473918 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | −6.75384e29 | −0.507442 | −0.253721 | − | 0.967277i | \(-0.581655\pi\) | ||||
−0.253721 | + | 0.967277i | \(0.581655\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.35483e30 | −0.923929 | ||||||||
\(260\) | 1.58300e29 | 0.102876 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.76033e29 | 0.163003 | ||||||||
\(263\) | −1.42102e30 | −0.800119 | −0.400059 | − | 0.916489i | \(-0.631011\pi\) | ||||
−0.400059 | + | 0.916489i | \(0.631011\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.09272e30 | −0.559673 | ||||||||
\(266\) | 6.67778e29 | 0.326296 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.00805e29 | −0.400817 | ||||||||
\(269\) | 1.90129e30 | 0.807504 | 0.403752 | − | 0.914868i | \(-0.367706\pi\) | ||||
0.403752 | + | 0.914868i | \(0.367706\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.45800e30 | −0.564471 | −0.282236 | − | 0.959345i | \(-0.591076\pi\) | ||||
−0.282236 | + | 0.959345i | \(0.591076\pi\) | |||||||
\(272\) | −8.37311e29 | −0.309582 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.32286e30 | −0.446304 | ||||||||
\(275\) | −2.72234e30 | −0.877575 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.31088e29 | −0.156376 | −0.0781879 | − | 0.996939i | \(-0.524913\pi\) | ||||
−0.0781879 | + | 0.996939i | \(0.524913\pi\) | |||||||
\(278\) | 3.77479e29 | 0.106251 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.81446e30 | 0.466952 | ||||||||
\(281\) | 3.64974e30 | 0.898323 | 0.449161 | − | 0.893451i | \(-0.351723\pi\) | ||||
0.449161 | + | 0.893451i | \(0.351723\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.43965e30 | −0.324285 | −0.162143 | − | 0.986767i | \(-0.551840\pi\) | ||||
−0.162143 | + | 0.986767i | \(0.551840\pi\) | |||||||
\(284\) | 3.80897e30 | 0.820971 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.52199e29 | −0.0497929 | ||||||||
\(287\) | 2.27311e30 | 0.429632 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.07837e30 | 0.533456 | ||||||||
\(290\) | −1.11317e31 | −1.84750 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.67292e30 | 0.711710 | ||||||||
\(293\) | −1.24504e31 | −1.81692 | −0.908462 | − | 0.417967i | \(-0.862743\pi\) | ||||
−0.908462 | + | 0.417967i | \(0.862743\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.16438e31 | −1.56070 | ||||||||
\(296\) | 3.09944e30 | 0.398233 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.91909e30 | −0.344781 | ||||||||
\(299\) | −1.12217e30 | −0.127106 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.17647e30 | −0.435239 | ||||||||
\(302\) | 1.25403e31 | 1.25378 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.52767e30 | −0.140640 | ||||||||
\(305\) | 2.08307e29 | 0.0184059 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.27193e31 | 1.84997 | 0.924986 | − | 0.380001i | \(-0.124076\pi\) | ||||
0.924986 | + | 0.380001i | \(0.124076\pi\) | |||||||
\(308\) | −2.89075e30 | −0.226009 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.53666e31 | −1.10805 | ||||||||
\(311\) | 1.84336e31 | 1.27675 | 0.638374 | − | 0.769726i | \(-0.279607\pi\) | ||||
0.638374 | + | 0.769726i | \(0.279607\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.98693e30 | 0.318808 | 0.159404 | − | 0.987213i | \(-0.449043\pi\) | ||||
0.159404 | + | 0.987213i | \(0.449043\pi\) | |||||||
\(314\) | −9.78780e30 | −0.601263 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.06864e31 | 0.606376 | ||||||||
\(317\) | 8.79478e30 | 0.479716 | 0.239858 | − | 0.970808i | \(-0.422899\pi\) | ||||
0.239858 | + | 0.970808i | \(0.422899\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.77347e31 | 0.894209 | ||||||||
\(320\) | −4.15093e30 | −0.201266 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.28625e31 | −0.576934 | ||||||||
\(323\) | 1.61450e31 | 0.696635 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.09458e30 | −0.203501 | ||||||||
\(326\) | −2.71602e31 | −1.04403 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.20017e30 | −0.185180 | ||||||||
\(329\) | −1.40380e31 | −0.481233 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.97122e31 | 1.89764 | 0.948818 | − | 0.315822i | \(-0.102280\pi\) | ||||
0.948818 | + | 0.315822i | \(0.102280\pi\) | |||||||
\(332\) | −2.00759e31 | −0.614398 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.66706e31 | 0.473283 | ||||||||
\(335\) | 4.71951e31 | 1.29073 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.08428e31 | 0.275275 | 0.137638 | − | 0.990483i | \(-0.456049\pi\) | ||||
0.137638 | + | 0.990483i | \(0.456049\pi\) | |||||||
\(338\) | 2.84311e31 | 0.695560 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.38685e31 | 0.996934 | ||||||||
\(341\) | 2.44817e31 | 0.536305 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.34633e31 | −1.08863 | ||||||||
\(344\) | 9.55447e30 | 0.187597 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.55908e31 | −0.649960 | ||||||||
\(347\) | −7.20193e30 | −0.126862 | −0.0634308 | − | 0.997986i | \(-0.520204\pi\) | ||||
−0.0634308 | + | 0.997986i | \(0.520204\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.27779e31 | 0.865235 | 0.432618 | − | 0.901577i | \(-0.357590\pi\) | ||||
0.432618 | + | 0.901577i | \(0.357590\pi\) | |||||||
\(350\) | −5.83951e31 | −0.923689 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.61315e30 | 0.0974148 | ||||||||
\(353\) | 5.67715e31 | 0.807135 | 0.403567 | − | 0.914950i | \(-0.367770\pi\) | ||||
0.403567 | + | 0.914950i | \(0.367770\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.99560e32 | −2.64374 | ||||||||
\(356\) | 5.40451e31 | 0.691244 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.76704e31 | −0.210721 | ||||||||
\(359\) | −2.18925e31 | −0.252125 | −0.126062 | − | 0.992022i | \(-0.540234\pi\) | ||||
−0.126062 | + | 0.992022i | \(0.540234\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.36201e31 | −0.683525 | ||||||||
\(362\) | −9.13280e31 | −0.947866 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.40974e30 | −0.0524094 | ||||||||
\(365\) | −2.44824e32 | −2.29189 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.00500e32 | 0.878699 | 0.439349 | − | 0.898316i | \(-0.355209\pi\) | ||||
0.439349 | + | 0.898316i | \(0.355209\pi\) | |||||||
\(368\) | 2.94254e31 | 0.248671 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.62386e32 | −1.28241 | ||||||||
\(371\) | 3.73425e31 | 0.285122 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.31052e31 | 0.450510 | 0.225255 | − | 0.974300i | \(-0.427678\pi\) | ||||
0.225255 | + | 0.974300i | \(0.427678\pi\) | |||||||
\(374\) | −6.98901e31 | −0.482526 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.21145e31 | 0.207421 | ||||||||
\(377\) | 3.31886e31 | 0.207358 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.85755e31 | −0.517993 | −0.258996 | − | 0.965878i | \(-0.583392\pi\) | ||||
−0.258996 | + | 0.965878i | \(0.583392\pi\) | |||||||
\(380\) | 8.00379e31 | 0.452898 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.83716e31 | −0.415305 | ||||||||
\(383\) | −9.08315e31 | −0.465856 | −0.232928 | − | 0.972494i | \(-0.574831\pi\) | ||||
−0.232928 | + | 0.972494i | \(0.574831\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.51453e32 | 0.727809 | ||||||||
\(386\) | 2.44428e32 | 1.13713 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.01405e31 | 0.262283 | ||||||||
\(389\) | −7.13043e31 | −0.301124 | −0.150562 | − | 0.988601i | \(-0.548108\pi\) | ||||
−0.150562 | + | 0.988601i | \(0.548108\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.10978e32 | −1.23174 | ||||||||
\(392\) | 3.01500e31 | 0.115668 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.55674e32 | 0.920416 | ||||||||
\(395\) | −5.59883e32 | −1.95269 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.99427e31 | 0.0980413 | 0.0490206 | − | 0.998798i | \(-0.484390\pi\) | ||||
0.0490206 | + | 0.998798i | \(0.484390\pi\) | |||||||
\(398\) | 1.32804e32 | 0.421380 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.33590e32 | 0.398129 | ||||||||
\(401\) | 5.00588e32 | 1.44603 | 0.723013 | − | 0.690835i | \(-0.242757\pi\) | ||||
0.723013 | + | 0.690835i | \(0.242757\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.58150e31 | 0.124364 | ||||||||
\(404\) | 5.71482e31 | 0.150396 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.80414e32 | 0.941198 | ||||||||
\(407\) | 2.58709e32 | 0.620700 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.78379e32 | −0.628195 | −0.314097 | − | 0.949391i | \(-0.601702\pi\) | ||||
−0.314097 | + | 0.949391i | \(0.601702\pi\) | |||||||
\(410\) | 2.72448e32 | 0.596328 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.38760e32 | 0.285792 | ||||||||
\(413\) | 3.97916e32 | 0.795090 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.05182e33 | 1.97852 | ||||||||
\(416\) | 1.23758e31 | 0.0225895 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.27514e32 | −0.219207 | ||||||||
\(419\) | 6.36828e32 | 1.06254 | 0.531272 | − | 0.847201i | \(-0.321714\pi\) | ||||
0.531272 | + | 0.847201i | \(0.321714\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.92275e32 | −0.616686 | −0.308343 | − | 0.951275i | \(-0.599775\pi\) | ||||
−0.308343 | + | 0.951275i | \(0.599775\pi\) | |||||||
\(422\) | −1.56548e32 | −0.238914 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.54283e31 | −0.122893 | ||||||||
\(425\) | −1.41183e33 | −1.97206 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.11870e30 | −0.00937675 | ||||||||
\(428\) | −2.65056e32 | −0.339071 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.00579e32 | −0.604111 | ||||||||
\(431\) | −2.44178e32 | −0.286247 | −0.143124 | − | 0.989705i | \(-0.545715\pi\) | ||||
−0.143124 | + | 0.989705i | \(0.545715\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.12872e32 | 1.00998 | 0.504988 | − | 0.863126i | \(-0.331497\pi\) | ||||
0.504988 | + | 0.863126i | \(0.331497\pi\) | |||||||
\(434\) | 5.25140e32 | 0.564487 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.04774e32 | 0.512290 | ||||||||
\(437\) | −5.67378e32 | −0.559570 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.07601e32 | 0.565995 | 0.282997 | − | 0.959121i | \(-0.408671\pi\) | ||||
0.282997 | + | 0.959121i | \(0.408671\pi\) | |||||||
\(440\) | −3.46477e32 | −0.313701 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.30792e32 | −0.111893 | ||||||||
\(443\) | −9.06289e32 | −0.753737 | −0.376869 | − | 0.926267i | \(-0.622999\pi\) | ||||
−0.376869 | + | 0.926267i | \(0.622999\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.83154e33 | −2.22598 | ||||||||
\(446\) | −1.27427e33 | −0.974034 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.41854e32 | 0.102534 | ||||||||
\(449\) | 1.21579e33 | 0.854630 | 0.427315 | − | 0.904103i | \(-0.359460\pi\) | ||||
0.427315 | + | 0.904103i | \(0.359460\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.34056e32 | −0.288629 | ||||||||
\(452\) | 1.35349e33 | 0.875439 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.32422e32 | −0.264673 | ||||||||
\(455\) | 2.83428e32 | 0.168772 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.59530e32 | −0.315407 | −0.157703 | − | 0.987487i | \(-0.550409\pi\) | ||||
−0.157703 | + | 0.987487i | \(0.550409\pi\) | |||||||
\(458\) | 1.51684e33 | 0.831997 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.54166e33 | −0.800784 | ||||||||
\(461\) | 3.78592e32 | 0.191386 | 0.0956930 | − | 0.995411i | \(-0.469493\pi\) | ||||
0.0956930 | + | 0.995411i | \(0.469493\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.77039e33 | 1.32672 | 0.663359 | − | 0.748301i | \(-0.269130\pi\) | ||||
0.663359 | + | 0.748301i | \(0.269130\pi\) | |||||||
\(464\) | −8.70270e32 | −0.405676 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.80486e32 | −0.123905 | ||||||||
\(467\) | 2.31922e33 | 0.997428 | 0.498714 | − | 0.866767i | \(-0.333806\pi\) | ||||
0.498714 | + | 0.866767i | \(0.333806\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.61285e33 | −0.657556 | ||||||||
\(470\) | −1.68255e33 | −0.667951 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.10311e32 | −0.342700 | ||||||||
\(473\) | 7.97508e32 | 0.292396 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.57587e33 | −0.895889 | ||||||||
\(476\) | −1.49916e33 | −0.507881 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.58832e33 | 0.510609 | ||||||||
\(479\) | −2.24376e33 | −0.702720 | −0.351360 | − | 0.936240i | \(-0.614281\pi\) | ||||
−0.351360 | + | 0.936240i | \(0.614281\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.84147e32 | 0.143934 | ||||||||
\(482\) | −4.24851e33 | −1.23069 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.26577e33 | −0.348166 | ||||||||
\(485\) | −3.15089e33 | −0.844620 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.71393e32 | 0.0945632 | 0.0472816 | − | 0.998882i | \(-0.484944\pi\) | ||||
0.0472816 | + | 0.998882i | \(0.484944\pi\) | |||||||
\(488\) | 1.62854e31 | 0.00404157 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.57963e33 | −0.372480 | ||||||||
\(491\) | 2.65508e33 | 0.610323 | 0.305161 | − | 0.952301i | \(-0.401290\pi\) | ||||
0.305161 | + | 0.952301i | \(0.401290\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.19732e33 | 2.00944 | ||||||||
\(494\) | −2.38629e32 | −0.0508320 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.20136e33 | −0.243306 | ||||||||
\(497\) | 6.81976e33 | 1.34684 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.39117e33 | −0.449111 | −0.224556 | − | 0.974461i | \(-0.572093\pi\) | ||||
−0.224556 | + | 0.974461i | \(0.572093\pi\) | |||||||
\(500\) | −2.60410e33 | −0.477015 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.06166e33 | 1.05632 | ||||||||
\(503\) | 6.34146e33 | 1.07793 | 0.538964 | − | 0.842329i | \(-0.318816\pi\) | ||||
0.538964 | + | 0.842329i | \(0.318816\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.99412e33 | −0.484314 | ||||||||
\(506\) | 2.45613e33 | 0.387587 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.23092e33 | −0.335111 | ||||||||
\(509\) | 3.62528e32 | 0.0531337 | 0.0265668 | − | 0.999647i | \(-0.491543\pi\) | ||||
0.0265668 | + | 0.999647i | \(0.491543\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.36664e33 | 1.16759 | ||||||||
\(512\) | −3.24519e32 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.76637e33 | 0.358816 | ||||||||
\(515\) | −7.26994e33 | −0.920323 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.68059e33 | 0.323295 | ||||||||
\(518\) | 5.54939e33 | 0.653316 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.48395e32 | −0.0727442 | ||||||||
\(521\) | −8.23573e33 | −0.902050 | −0.451025 | − | 0.892511i | \(-0.648942\pi\) | ||||
−0.451025 | + | 0.892511i | \(0.648942\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.20443e34 | −1.25750 | −0.628752 | − | 0.777606i | \(-0.716434\pi\) | ||||
−0.628752 | + | 0.777606i | \(0.716434\pi\) | |||||||
\(524\) | −1.13063e33 | −0.115260 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.82051e33 | 0.565770 | ||||||||
\(527\) | 1.26964e34 | 1.20517 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.17149e32 | −0.0106057 | ||||||||
\(530\) | 4.47577e33 | 0.395749 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.73522e33 | −0.230726 | ||||||||
\(533\) | −8.12291e32 | −0.0669301 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.38868e34 | 1.09190 | ||||||||
\(536\) | 3.68970e33 | 0.283420 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.78769e33 | −0.570992 | ||||||||
\(539\) | 2.51661e33 | 0.180284 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.30366e34 | 0.891657 | 0.445829 | − | 0.895118i | \(-0.352909\pi\) | ||||
0.445829 | + | 0.895118i | \(0.352909\pi\) | |||||||
\(542\) | 5.97197e33 | 0.399141 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.42963e33 | 0.218907 | ||||||||
\(545\) | −2.64462e34 | −1.64971 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.78334e34 | −1.06266 | −0.531328 | − | 0.847166i | \(-0.678307\pi\) | ||||
−0.531328 | + | 0.847166i | \(0.678307\pi\) | |||||||
\(548\) | 5.41843e33 | 0.315585 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.11507e34 | 0.620539 | ||||||||
\(551\) | 1.67805e34 | 0.912871 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.91334e34 | 0.994784 | ||||||||
\(554\) | 2.17534e33 | 0.110574 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.54616e33 | −0.0751309 | ||||||||
\(557\) | −8.73339e33 | −0.414947 | −0.207474 | − | 0.978241i | \(-0.566524\pi\) | ||||
−0.207474 | + | 0.978241i | \(0.566524\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.49245e33 | 0.0678037 | ||||||||
\(560\) | −7.43204e33 | −0.330185 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.49493e34 | −0.635210 | ||||||||
\(563\) | −3.82416e34 | −1.58921 | −0.794606 | − | 0.607126i | \(-0.792322\pi\) | ||||
−0.794606 | + | 0.607126i | \(0.792322\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.09124e34 | −2.81914 | ||||||||
\(566\) | 5.89682e33 | 0.229304 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.56015e34 | −0.580514 | ||||||||
\(569\) | −3.49591e34 | −1.27250 | −0.636248 | − | 0.771484i | \(-0.719515\pi\) | ||||
−0.636248 | + | 0.771484i | \(0.719515\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.60524e34 | −1.25598 | −0.627989 | − | 0.778222i | \(-0.716122\pi\) | ||||
−0.627989 | + | 0.778222i | \(0.716122\pi\) | |||||||
\(572\) | 1.03301e33 | 0.0352089 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.31065e33 | −0.303795 | ||||||||
\(575\) | 4.96155e34 | 1.58405 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.45926e34 | −1.36322 | −0.681609 | − | 0.731717i | \(-0.738719\pi\) | ||||
−0.681609 | + | 0.731717i | \(0.738719\pi\) | |||||||
\(578\) | −1.26090e34 | −0.377210 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.55953e34 | 1.30638 | ||||||||
\(581\) | −3.59450e34 | −1.00794 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.13067e33 | −0.191546 | ||||||||
\(584\) | −1.91403e34 | −0.503255 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.09967e34 | 1.28476 | ||||||||
\(587\) | 2.50958e34 | 0.618905 | 0.309452 | − | 0.950915i | \(-0.399854\pi\) | ||||
0.309452 | + | 0.950915i | \(0.399854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.31645e34 | 0.547497 | ||||||||
\(590\) | 4.76931e34 | 1.10358 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.26953e34 | −0.281593 | ||||||||
\(593\) | 4.88078e33 | 0.106000 | 0.0530000 | − | 0.998595i | \(-0.483122\pi\) | ||||
0.0530000 | + | 0.998595i | \(0.483122\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.85444e34 | 1.63551 | ||||||||
\(596\) | 1.19566e34 | 0.243797 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.59639e33 | 0.0898777 | ||||||||
\(599\) | −4.61838e34 | −0.884412 | −0.442206 | − | 0.896914i | \(-0.645804\pi\) | ||||
−0.442206 | + | 0.896914i | \(0.645804\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.07405e34 | −0.564651 | −0.282325 | − | 0.959319i | \(-0.591106\pi\) | ||||
−0.282325 | + | 0.959319i | \(0.591106\pi\) | |||||||
\(602\) | 1.71068e34 | 0.307760 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.13652e34 | −0.886559 | ||||||||
\(605\) | 6.63161e34 | 1.12118 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.03737e35 | 1.68297 | 0.841484 | − | 0.540282i | \(-0.181682\pi\) | ||||
0.841484 | + | 0.540282i | \(0.181682\pi\) | |||||||
\(608\) | 6.25734e33 | 0.0994477 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.53226e32 | −0.0130149 | ||||||||
\(611\) | 5.01644e33 | 0.0749688 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.85744e34 | 0.409941 | 0.204970 | − | 0.978768i | \(-0.434290\pi\) | ||||
0.204970 | + | 0.978768i | \(0.434290\pi\) | |||||||
\(614\) | −9.30582e34 | −1.30813 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.18405e34 | 0.159813 | ||||||||
\(617\) | −5.36336e34 | −0.709370 | −0.354685 | − | 0.934986i | \(-0.615412\pi\) | ||||
−0.354685 | + | 0.934986i | \(0.615412\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.60909e34 | 0.839477 | 0.419738 | − | 0.907645i | \(-0.362122\pi\) | ||||
0.419738 | + | 0.907645i | \(0.362122\pi\) | |||||||
\(620\) | 6.29418e34 | 0.783507 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.55041e34 | −0.902798 | ||||||||
\(623\) | 9.67651e34 | 1.13401 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.00979e33 | −0.0564053 | ||||||||
\(626\) | −2.04264e34 | −0.225431 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.00908e34 | 0.425157 | ||||||||
\(629\) | 1.34168e35 | 1.39482 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.62816e34 | 0.862087 | 0.431043 | − | 0.902331i | \(-0.358146\pi\) | ||||
0.431043 | + | 0.902331i | \(0.358146\pi\) | |||||||
\(632\) | −4.37714e34 | −0.428773 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.60234e34 | −0.339210 | ||||||||
\(635\) | 1.16883e35 | 1.07914 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.70958e33 | 0.0418061 | ||||||||
\(638\) | −7.26412e34 | −0.632302 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.70022e34 | 0.142317 | ||||||||
\(641\) | −1.77093e35 | −1.45370 | −0.726850 | − | 0.686796i | \(-0.759017\pi\) | ||||
−0.726850 | + | 0.686796i | \(0.759017\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.98617e34 | −0.630524 | −0.315262 | − | 0.949005i | \(-0.602092\pi\) | ||||
−0.315262 | + | 0.949005i | \(0.602092\pi\) | |||||||
\(644\) | 5.26847e34 | 0.407954 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.61298e34 | −0.492596 | ||||||||
\(647\) | 2.16671e35 | 1.58306 | 0.791530 | − | 0.611130i | \(-0.209285\pi\) | ||||
0.791530 | + | 0.611130i | \(0.209285\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.59833e34 | −0.534145 | ||||||||
\(650\) | 2.08674e34 | 0.143897 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.11248e35 | 0.738242 | ||||||||
\(653\) | −2.41184e35 | −1.57013 | −0.785063 | − | 0.619416i | \(-0.787369\pi\) | ||||
−0.785063 | + | 0.619416i | \(0.787369\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.92361e34 | 0.371168 | ||||||||
\(656\) | 2.12999e34 | 0.130942 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.74995e34 | 0.340283 | ||||||||
\(659\) | −2.18788e35 | −1.27045 | −0.635223 | − | 0.772329i | \(-0.719092\pi\) | ||||
−0.635223 | + | 0.772329i | \(0.719092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.90411e34 | −0.497820 | −0.248910 | − | 0.968527i | \(-0.580072\pi\) | ||||
−0.248910 | + | 0.968527i | \(0.580072\pi\) | |||||||
\(662\) | −2.44581e35 | −1.34183 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.22310e34 | 0.434445 | ||||||||
\(665\) | 1.43304e35 | 0.742998 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.23219e35 | −1.61408 | ||||||||
\(668\) | −6.82828e34 | −0.334662 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.93311e35 | −0.912687 | ||||||||
\(671\) | 1.35934e33 | 0.00629934 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.39665e35 | 1.07008 | 0.535040 | − | 0.844827i | \(-0.320297\pi\) | ||||
0.535040 | + | 0.844827i | \(0.320297\pi\) | |||||||
\(674\) | −4.44120e34 | −0.194649 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.16454e35 | −0.491835 | ||||||||
\(677\) | 3.79216e34 | 0.157227 | 0.0786137 | − | 0.996905i | \(-0.474951\pi\) | ||||
0.0786137 | + | 0.996905i | \(0.474951\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.07679e35 | 0.430286 | ||||||||
\(680\) | −1.79685e35 | −0.704939 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.00277e35 | −0.379225 | ||||||||
\(683\) | 3.21208e35 | 1.19269 | 0.596345 | − | 0.802729i | \(-0.296619\pi\) | ||||
0.596345 | + | 0.802729i | \(0.296619\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.83883e35 | −1.01627 | ||||||||
\(686\) | 2.18986e35 | 0.769776 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.91351e34 | −0.132651 | ||||||||
\(689\) | −1.33443e34 | −0.0444177 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.34540e34 | 0.267899 | 0.133950 | − | 0.990988i | \(-0.457234\pi\) | ||||
0.133950 | + | 0.990988i | \(0.457234\pi\) | |||||||
\(692\) | 1.45780e35 | 0.459591 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.94991e34 | 0.0897047 | ||||||||
\(695\) | 8.10064e34 | 0.241941 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.25105e35 | −0.648597 | ||||||||
\(698\) | −2.16178e35 | −0.611814 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.39186e35 | 0.653147 | ||||||||
\(701\) | −1.50008e35 | −0.402383 | −0.201191 | − | 0.979552i | \(-0.564481\pi\) | ||||
−0.201191 | + | 0.979552i | \(0.564481\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.44790e35 | 0.633653 | ||||||||
\(704\) | −2.70874e34 | −0.0688827 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.32536e35 | −0.570731 | ||||||||
\(707\) | 1.02321e35 | 0.246730 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.12042e35 | −0.493564 | −0.246782 | − | 0.969071i | \(-0.579373\pi\) | ||||
−0.246782 | + | 0.969071i | \(0.579373\pi\) | |||||||
\(710\) | 8.17397e35 | 1.86941 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.21369e35 | −0.488783 | ||||||||
\(713\) | −4.46186e35 | −0.968048 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.41213e34 | −0.113382 | ||||||||
\(716\) | 7.23778e34 | 0.149002 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.96718e34 | 0.178279 | ||||||||
\(719\) | −3.27911e35 | −0.640686 | −0.320343 | − | 0.947302i | \(-0.603798\pi\) | ||||
−0.320343 | + | 0.947302i | \(0.603798\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.48443e35 | 0.468853 | ||||||||
\(722\) | 2.60588e35 | 0.483325 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.74080e35 | 0.670243 | ||||||||
\(725\) | −1.46740e36 | −2.58419 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.40795e35 | 0.409701 | 0.204850 | − | 0.978793i | \(-0.434329\pi\) | ||||
0.204850 | + | 0.978793i | \(0.434329\pi\) | |||||||
\(728\) | 2.21583e34 | 0.0370590 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.00280e36 | 1.62061 | ||||||||
\(731\) | 4.13594e35 | 0.657063 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.39196e35 | −0.520776 | −0.260388 | − | 0.965504i | \(-0.583850\pi\) | ||||
−0.260388 | + | 0.965504i | \(0.583850\pi\) | |||||||
\(734\) | −4.11648e35 | −0.621334 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.20526e35 | −0.175837 | ||||||||
\(737\) | 3.07978e35 | 0.441749 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.23366e36 | 1.71057 | 0.855284 | − | 0.518159i | \(-0.173383\pi\) | ||||
0.855284 | + | 0.518159i | \(0.173383\pi\) | |||||||
\(740\) | 6.65134e35 | 0.906802 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.52955e35 | −0.201611 | ||||||||
\(743\) | 6.24478e35 | 0.809389 | 0.404694 | − | 0.914452i | \(-0.367378\pi\) | ||||
0.404694 | + | 0.914452i | \(0.367378\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.26430e35 | −0.785090 | ||||||||
\(746\) | −2.58479e35 | −0.318559 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.86270e35 | 0.341197 | ||||||||
\(749\) | −4.74570e35 | −0.556259 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.41291e35 | −0.500294 | −0.250147 | − | 0.968208i | \(-0.580479\pi\) | ||||
−0.250147 | + | 0.968208i | \(0.580479\pi\) | |||||||
\(752\) | −1.31541e35 | −0.146669 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.35940e35 | −0.146625 | ||||||||
\(755\) | 2.69113e36 | 2.85495 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.83266e35 | 0.188098 | 0.0940489 | − | 0.995568i | \(-0.470019\pi\) | ||||
0.0940489 | + | 0.995568i | \(0.470019\pi\) | |||||||
\(758\) | 3.62805e35 | 0.366276 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.27835e35 | −0.320247 | ||||||||
\(761\) | −1.88027e36 | −1.80681 | −0.903406 | − | 0.428787i | \(-0.858941\pi\) | ||||
−0.903406 | + | 0.428787i | \(0.858941\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.03772e35 | 0.840431 | ||||||||
\(764\) | 3.21010e35 | 0.293665 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.72046e35 | 0.329410 | ||||||||
\(767\) | −1.42195e35 | −0.123863 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.28453e36 | 1.08309 | 0.541546 | − | 0.840671i | \(-0.317839\pi\) | ||||
0.541546 | + | 0.840671i | \(0.317839\pi\) | |||||||
\(770\) | −6.20349e35 | −0.514639 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.00118e36 | −0.804071 | ||||||||
\(773\) | 1.04808e36 | 0.828226 | 0.414113 | − | 0.910225i | \(-0.364092\pi\) | ||||
0.414113 | + | 0.910225i | \(0.364092\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.02566e36 | −1.54987 | ||||||||
\(776\) | −2.46335e35 | −0.185462 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.92063e35 | 0.212927 | ||||||||
\(779\) | −4.10703e35 | −0.294652 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.30225e36 | −0.904811 | ||||||||
\(782\) | 1.27377e36 | 0.870974 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.23495e35 | −0.0817894 | ||||||||
\(785\) | −2.10044e36 | −1.36912 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.93146e35 | −0.563947 | −0.281974 | − | 0.959422i | \(-0.590989\pi\) | ||||
−0.281974 | + | 0.959422i | \(0.590989\pi\) | |||||||
\(788\) | −1.04724e36 | −0.650832 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.29328e36 | 1.38076 | ||||||||
\(791\) | 2.42336e36 | 1.43619 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.54386e33 | 0.00146076 | ||||||||
\(794\) | −1.22645e35 | −0.0693257 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.43966e35 | −0.297960 | ||||||||
\(797\) | 1.02840e36 | 0.554540 | 0.277270 | − | 0.960792i | \(-0.410570\pi\) | ||||
0.277270 | + | 0.960792i | \(0.410570\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.39017e36 | 0.726498 | ||||||||
\(800\) | −5.47185e35 | −0.281520 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.05041e36 | −1.02249 | ||||||||
\(803\) | −1.59763e36 | −0.784392 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.76026e36 | −1.31372 | ||||||||
\(806\) | −1.87658e35 | −0.0879385 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.34079e35 | −0.106346 | ||||||||
\(809\) | −1.33897e36 | −0.598981 | −0.299490 | − | 0.954099i | \(-0.596817\pi\) | ||||
−0.299490 | + | 0.954099i | \(0.596817\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.29485e36 | 0.561643 | 0.280821 | − | 0.959760i | \(-0.409393\pi\) | ||||
0.280821 | + | 0.959760i | \(0.409393\pi\) | |||||||
\(812\) | −1.55818e36 | −0.665528 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.05967e36 | −0.438901 | ||||||||
\(815\) | −5.82854e36 | −2.37733 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.54600e35 | 0.298498 | ||||||||
\(818\) | 1.14024e36 | 0.444201 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.11595e36 | −0.421668 | ||||||||
\(821\) | −3.91664e34 | −0.0145755 | −0.00728777 | − | 0.999973i | \(-0.502320\pi\) | ||||
−0.00728777 | + | 0.999973i | \(0.502320\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.40400e36 | −1.22883 | −0.614414 | − | 0.788984i | \(-0.710608\pi\) | ||||
−0.614414 | + | 0.788984i | \(0.710608\pi\) | |||||||
\(824\) | −5.68362e35 | −0.202085 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.62987e36 | −0.562213 | ||||||||
\(827\) | 5.02186e36 | 1.70626 | 0.853132 | − | 0.521696i | \(-0.174700\pi\) | ||||
0.853132 | + | 0.521696i | \(0.174700\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.20485e35 | 0.270482 | 0.135241 | − | 0.990813i | \(-0.456819\pi\) | ||||
0.135241 | + | 0.990813i | \(0.456819\pi\) | |||||||
\(830\) | −4.30826e36 | −1.39902 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.06913e34 | −0.0159732 | ||||||||
\(833\) | 1.30513e36 | 0.405128 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.57748e36 | 1.07770 | ||||||||
\(836\) | 5.22298e35 | 0.155003 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.60845e36 | −0.751332 | ||||||||
\(839\) | 5.38664e36 | 1.52860 | 0.764300 | − | 0.644861i | \(-0.223085\pi\) | ||||
0.764300 | + | 0.644861i | \(0.223085\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.92900e36 | 1.63317 | ||||||||
\(842\) | 1.60676e36 | 0.436063 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.41220e35 | 0.168938 | ||||||||
\(845\) | 6.10126e36 | 1.58384 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.26629e36 | −0.571180 | ||||||||
\(848\) | 3.49914e35 | 0.0868987 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.78284e36 | 1.39446 | ||||||||
\(851\) | −4.71505e36 | −1.12038 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.55369e35 | 0.220449 | 0.110225 | − | 0.993907i | \(-0.464843\pi\) | ||||
0.110225 | + | 0.993907i | \(0.464843\pi\) | |||||||
\(854\) | 2.91582e34 | 0.00663036 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.08567e36 | 0.239759 | ||||||||
\(857\) | 5.39118e36 | 1.17334 | 0.586669 | − | 0.809827i | \(-0.300439\pi\) | ||||
0.586669 | + | 0.809827i | \(0.300439\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.48992e36 | 1.16052 | 0.580258 | − | 0.814432i | \(-0.302952\pi\) | ||||
0.580258 | + | 0.814432i | \(0.302952\pi\) | |||||||
\(860\) | 2.05037e36 | 0.427171 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.00016e36 | 0.202407 | ||||||||
\(863\) | 2.89510e36 | 0.577469 | 0.288735 | − | 0.957409i | \(-0.406766\pi\) | ||||
0.288735 | + | 0.957409i | \(0.406766\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.63772e36 | −1.48000 | ||||||||
\(866\) | −3.73912e36 | −0.714161 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.15097e36 | −0.399152 | ||||||||
\(869\) | −3.65359e36 | −0.668301 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.76349e35 | 0.102437 | ||||||||
\(872\) | −2.06755e36 | −0.362244 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.32398e36 | 0.395676 | ||||||||
\(875\) | −4.66251e36 | −0.782562 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.04429e36 | 0.333463 | 0.166731 | − | 0.986002i | \(-0.446679\pi\) | ||||
0.166731 | + | 0.986002i | \(0.446679\pi\) | |||||||
\(878\) | −2.48874e36 | −0.400219 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.41917e36 | 0.221820 | ||||||||
\(881\) | 1.76163e36 | 0.271466 | 0.135733 | − | 0.990745i | \(-0.456661\pi\) | ||||
0.135733 | + | 0.990745i | \(0.456661\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.25672e37 | 1.88248 | 0.941240 | − | 0.337738i | \(-0.109662\pi\) | ||||
0.941240 | + | 0.337738i | \(0.109662\pi\) | |||||||
\(884\) | 5.35724e35 | 0.0791203 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.71216e36 | 0.532973 | ||||||||
\(887\) | −8.81003e36 | −1.24719 | −0.623595 | − | 0.781748i | \(-0.714328\pi\) | ||||
−0.623595 | + | 0.781748i | \(0.714328\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.99436e36 | −0.549762 | ||||||||
\(890\) | 1.15980e37 | 1.57401 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.21939e36 | 0.688746 | ||||||||
\(893\) | 2.53636e36 | 0.330041 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.79203e36 | −0.479826 | ||||||||
\(896\) | −5.81034e35 | −0.0725023 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.97986e36 | −0.604315 | ||||||||
\(899\) | 1.31962e37 | 1.57925 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.69802e36 | −0.430436 | ||||||||
\(902\) | 1.77789e36 | 0.204091 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.54391e36 | −0.619029 | ||||||||
\(905\) | −1.95988e37 | −2.15835 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.59523e37 | −1.70896 | −0.854482 | − | 0.519481i | \(-0.826125\pi\) | ||||
−0.854482 | + | 0.519481i | \(0.826125\pi\) | |||||||
\(908\) | 1.77120e36 | 0.187152 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.16092e36 | −0.119340 | ||||||||
\(911\) | 1.71775e36 | 0.174172 | 0.0870862 | − | 0.996201i | \(-0.472244\pi\) | ||||
0.0870862 | + | 0.996201i | \(0.472244\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.86379e36 | 0.677142 | ||||||||
\(914\) | 2.29183e36 | 0.223026 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.21298e36 | −0.588310 | ||||||||
\(917\) | −2.02434e36 | −0.189089 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.70373e35 | −0.0700256 | −0.0350128 | − | 0.999387i | \(-0.511147\pi\) | ||||
−0.0350128 | + | 0.999387i | \(0.511147\pi\) | |||||||
\(920\) | 6.31464e36 | 0.566240 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.55071e36 | −0.135330 | ||||||||
\(923\) | −2.43703e36 | −0.209817 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.14061e37 | −1.79377 | ||||||||
\(926\) | −1.13475e37 | −0.938132 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.56463e36 | 0.286856 | ||||||||
\(929\) | −1.66420e37 | −1.32132 | −0.660662 | − | 0.750684i | \(-0.729724\pi\) | ||||
−0.660662 | + | 0.750684i | \(0.729724\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.38121e36 | 0.184046 | ||||||||
\(932\) | 1.14887e36 | 0.0876138 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.49954e36 | −0.705288 | ||||||||
\(935\) | −1.49983e37 | −1.09874 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.66427e36 | 0.689325 | 0.344663 | − | 0.938727i | \(-0.387993\pi\) | ||||
0.344663 | + | 0.938727i | \(0.387993\pi\) | |||||||
\(938\) | 6.60622e36 | 0.464962 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.89172e36 | 0.472312 | ||||||||
\(941\) | 1.33808e37 | 0.904923 | 0.452461 | − | 0.891784i | \(-0.350546\pi\) | ||||
0.452461 | + | 0.891784i | \(0.350546\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.91080e36 | 0.520984 | ||||||||
\(944\) | 3.72863e36 | 0.242326 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.26659e36 | −0.206755 | ||||||||
\(947\) | −2.63078e37 | −1.64328 | −0.821638 | − | 0.570010i | \(-0.806939\pi\) | ||||
−0.821638 | + | 0.570010i | \(0.806939\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.98981e36 | −0.181893 | ||||||||
\(950\) | 1.05508e37 | 0.633489 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.14058e36 | 0.359126 | ||||||||
\(953\) | 9.10378e36 | 0.525485 | 0.262742 | − | 0.964866i | \(-0.415373\pi\) | ||||
0.262742 | + | 0.964866i | \(0.415373\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.68184e37 | −0.945677 | ||||||||
\(956\) | −6.50575e36 | −0.361055 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.19044e36 | 0.496898 | ||||||||
\(959\) | 9.70142e36 | 0.517729 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.01623e36 | −0.0528386 | ||||||||
\(962\) | −1.98307e36 | −0.101777 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.74019e37 | 0.870230 | ||||||||
\(965\) | 5.24538e37 | 2.58932 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.34794e36 | −0.0648394 | −0.0324197 | − | 0.999474i | \(-0.510321\pi\) | ||||
−0.0324197 | + | 0.999474i | \(0.510321\pi\) | |||||||
\(968\) | 5.18457e36 | 0.246190 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.29060e37 | 0.597236 | ||||||||
\(971\) | −3.82504e36 | −0.174741 | −0.0873707 | − | 0.996176i | \(-0.527846\pi\) | ||||
−0.0873707 | + | 0.996176i | \(0.527846\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.76831e36 | −0.123255 | ||||||||
\(974\) | −1.52123e36 | −0.0668663 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.67050e34 | −0.00285782 | ||||||||
\(977\) | −1.16914e37 | −0.494522 | −0.247261 | − | 0.968949i | \(-0.579530\pi\) | ||||
−0.247261 | + | 0.968949i | \(0.579530\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.84776e37 | −0.761835 | ||||||||
\(980\) | 6.47014e36 | 0.263383 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.08752e37 | −0.431563 | ||||||||
\(983\) | −1.38138e37 | −0.541244 | −0.270622 | − | 0.962686i | \(-0.587229\pi\) | ||||
−0.270622 | + | 0.962686i | \(0.587229\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.48672e37 | 2.09585 | ||||||||
\(986\) | −3.76722e37 | −1.42089 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.77426e35 | 0.0359436 | ||||||||
\(989\) | −1.45348e37 | −0.527784 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.79186e37 | −1.34255 | −0.671276 | − | 0.741207i | \(-0.734254\pi\) | ||||
−0.671276 | + | 0.741207i | \(0.734254\pi\) | |||||||
\(992\) | 4.92077e36 | 0.172043 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.79338e37 | −0.952356 | ||||||||
\(995\) | 2.84995e37 | 0.959510 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.34619e37 | 1.75531 | 0.877657 | − | 0.479289i | \(-0.159106\pi\) | ||||
0.877657 | + | 0.479289i | \(0.159106\pi\) | |||||||
\(998\) | 9.79424e36 | 0.317570 | ||||||||
\(999\) | 0 | 0 |
(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 | 18.26.a.e.1.1 | 2 | ||
3.2 | odd | 2 | 2.26.a.b.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 16.26.a.c.1.2 | 2 | |||
15.2 | even | 4 | 50.26.b.e.49.4 | 4 | |||
15.8 | even | 4 | 50.26.b.e.49.1 | 4 | |||
15.14 | odd | 2 | 50.26.a.c.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.26.a.b.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
16.26.a.c.1.2 | 2 | 12.11 | even | 2 | |||
18.26.a.e.1.1 | 2 | 1.1 | even | 1 | trivial | ||
50.26.a.c.1.2 | 2 | 15.14 | odd | 2 | |||
50.26.b.e.49.1 | 4 | 15.8 | even | 4 | |||
50.26.b.e.49.4 | 4 | 15.2 | even | 4 |