Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,26,Mod(1,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, 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("50.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.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: | \(197.998389976\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7}\cdot 3\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 2) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-162.829\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.1 |
$q$-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 | ||||||||
\(3\) | 1.37803e6 | 1.49707 | 0.748537 | − | 0.663093i | \(-0.230757\pi\) | ||||
0.748537 | + | 0.663093i | \(0.230757\pi\) | |||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.64442e9 | −1.05859 | ||||||||
\(7\) | −3.00388e10 | −0.820270 | −0.410135 | − | 0.912025i | \(-0.634518\pi\) | ||||
−0.410135 | + | 0.912025i | \(0.634518\pi\) | |||||||
\(8\) | −6.87195e10 | −0.353553 | ||||||||
\(9\) | 1.05168e12 | 1.24123 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.73599e12 | 0.551061 | 0.275531 | − | 0.961292i | \(-0.411146\pi\) | ||||
0.275531 | + | 0.961292i | \(0.411146\pi\) | |||||||
\(12\) | 2.31195e13 | 0.748537 | ||||||||
\(13\) | 1.07343e13 | 0.127786 | 0.0638928 | − | 0.997957i | \(-0.479648\pi\) | ||||
0.0638928 | + | 0.997957i | \(0.479648\pi\) | |||||||
\(14\) | 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 | \(0.712528\pi\) | |||||||
\(18\) | −4.30769e15 | −0.877683 | ||||||||
\(19\) | −5.42738e15 | −0.562561 | −0.281281 | − | 0.959626i | \(-0.590759\pi\) | ||||
−0.281281 | + | 0.959626i | \(0.590759\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.13944e16 | −1.22800 | ||||||||
\(22\) | −2.34946e16 | −0.389659 | ||||||||
\(23\) | 1.04540e17 | 0.994683 | 0.497341 | − | 0.867555i | \(-0.334310\pi\) | ||||
0.497341 | + | 0.867555i | \(0.334310\pi\) | |||||||
\(24\) | −9.46976e16 | −0.529296 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.39677e16 | −0.0903581 | ||||||||
\(27\) | 2.81659e17 | 0.361141 | ||||||||
\(28\) | −5.03967e17 | −0.410135 | ||||||||
\(29\) | 3.09182e18 | 1.62270 | 0.811352 | − | 0.584558i | \(-0.198732\pi\) | ||||
0.811352 | + | 0.584558i | \(0.198732\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 7.90437e18 | 0.824980 | ||||||||
\(34\) | 1.21845e19 | 0.875630 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.76443e19 | 0.620616 | ||||||||
\(37\) | 4.51028e19 | 1.12637 | 0.563186 | − | 0.826330i | \(-0.309576\pi\) | ||||
0.563186 | + | 0.826330i | \(0.309576\pi\) | |||||||
\(38\) | 2.22305e19 | 0.397791 | ||||||||
\(39\) | 1.47922e19 | 0.191305 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.56724e19 | −0.523769 | −0.261884 | − | 0.965099i | \(-0.584344\pi\) | ||||
−0.261884 | + | 0.965099i | \(0.584344\pi\) | |||||||
\(42\) | 1.69551e20 | 0.868330 | ||||||||
\(43\) | 1.39036e20 | 0.530605 | 0.265302 | − | 0.964165i | \(-0.414528\pi\) | ||||
0.265302 | + | 0.964165i | \(0.414528\pi\) | |||||||
\(44\) | 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 | \(0.594766\pi\) | |||||||
\(48\) | 3.87881e20 | 0.374269 | ||||||||
\(49\) | −4.38741e20 | −0.327158 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.09927e21 | −1.85387 | ||||||||
\(52\) | 1.80092e20 | 0.0638928 | ||||||||
\(53\) | 1.24315e21 | 0.347595 | 0.173797 | − | 0.984781i | \(-0.444396\pi\) | ||||
0.173797 | + | 0.984781i | \(0.444396\pi\) | |||||||
\(54\) | −1.15368e21 | −0.255365 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.06425e21 | 0.290009 | ||||||||
\(57\) | −7.47909e21 | −0.842196 | ||||||||
\(58\) | −1.26641e22 | −1.14743 | ||||||||
\(59\) | −1.32468e22 | −0.969303 | −0.484652 | − | 0.874707i | \(-0.661054\pi\) | ||||
−0.484652 | + | 0.874707i | \(0.661054\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | −3.15912e22 | −1.01814 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.23763e22 | −0.583349 | ||||||||
\(67\) | 5.36922e22 | 0.801634 | 0.400817 | − | 0.916158i | \(-0.368726\pi\) | ||||
0.400817 | + | 0.916158i | \(0.368726\pi\) | |||||||
\(68\) | −4.99076e22 | −0.619164 | ||||||||
\(69\) | 1.44059e23 | 1.48911 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.27032e23 | −1.64194 | −0.820971 | − | 0.570970i | \(-0.806567\pi\) | ||||
−0.820971 | + | 0.570970i | \(0.806567\pi\) | |||||||
\(72\) | −7.22710e22 | −0.438842 | ||||||||
\(73\) | −2.78528e23 | −1.42342 | −0.711710 | − | 0.702473i | \(-0.752079\pi\) | ||||
−0.711710 | + | 0.702473i | \(0.752079\pi\) | |||||||
\(74\) | −1.84741e23 | −0.796465 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.10563e22 | −0.281281 | ||||||||
\(77\) | −1.72302e23 | −0.452019 | ||||||||
\(78\) | −6.05889e22 | −0.135273 | ||||||||
\(79\) | 6.36958e23 | 1.21275 | 0.606376 | − | 0.795178i | \(-0.292622\pi\) | ||||
0.606376 | + | 0.795178i | \(0.292622\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.02942e23 | −0.700576 | ||||||||
\(82\) | 3.09954e23 | 0.370360 | ||||||||
\(83\) | −1.19662e24 | −1.22880 | −0.614398 | − | 0.788996i | \(-0.710601\pi\) | ||||
−0.614398 | + | 0.788996i | \(0.710601\pi\) | |||||||
\(84\) | −6.94482e23 | −0.614002 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.69491e23 | −0.375194 | ||||||||
\(87\) | 4.26063e24 | 2.42931 | ||||||||
\(88\) | −3.94174e23 | −0.194830 | ||||||||
\(89\) | −3.22134e24 | −1.38249 | −0.691244 | − | 0.722621i | \(-0.742937\pi\) | ||||
−0.691244 | + | 0.722621i | \(0.742937\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.22445e23 | −0.104819 | ||||||||
\(92\) | 1.75389e24 | 0.497341 | ||||||||
\(93\) | −5.88156e24 | −1.45699 | ||||||||
\(94\) | 1.91418e24 | 0.414843 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.58876e24 | −0.264648 | ||||||||
\(97\) | −3.58465e24 | −0.524566 | −0.262283 | − | 0.964991i | \(-0.584475\pi\) | ||||
−0.262283 | + | 0.964991i | \(0.584475\pi\) | |||||||
\(98\) | 1.79708e24 | 0.231335 | ||||||||
\(99\) | 6.03243e24 | 0.683994 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.40630e24 | −0.300792 | −0.150396 | − | 0.988626i | \(-0.548055\pi\) | ||||
−0.150396 | + | 0.988626i | \(0.548055\pi\) | |||||||
\(102\) | 1.67906e25 | 1.31088 | ||||||||
\(103\) | −8.27075e24 | −0.571583 | −0.285792 | − | 0.958292i | \(-0.592257\pi\) | ||||
−0.285792 | + | 0.958292i | \(0.592257\pi\) | |||||||
\(104\) | −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 | \(0.610113\pi\) | |||||||
\(108\) | 4.72546e24 | 0.180571 | ||||||||
\(109\) | 3.00869e25 | 1.02458 | 0.512290 | − | 0.858813i | \(-0.328797\pi\) | ||||
0.512290 | + | 0.858813i | \(0.328797\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.21530e25 | 1.68626 | ||||||||
\(112\) | −8.45516e24 | −0.205067 | ||||||||
\(113\) | 8.06745e25 | 1.75088 | 0.875439 | − | 0.483329i | \(-0.160572\pi\) | ||||
0.875439 | + | 0.483329i | \(0.160572\pi\) | |||||||
\(114\) | 3.06344e25 | 0.595523 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.18722e25 | 0.811352 | ||||||||
\(117\) | 1.12891e25 | 0.158612 | ||||||||
\(118\) | 5.42587e25 | 0.685401 | ||||||||
\(119\) | 8.93571e25 | 1.01576 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.54455e25 | −0.696332 | ||||||||
\(122\) | 9.70685e23 | 0.00808315 | ||||||||
\(123\) | −1.04279e26 | −0.784121 | ||||||||
\(124\) | −7.16066e25 | −0.486611 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.29398e26 | 0.719937 | ||||||||
\(127\) | 1.32973e26 | 0.670221 | 0.335111 | − | 0.942179i | \(-0.391226\pi\) | ||||
0.335111 | + | 0.942179i | \(0.391226\pi\) | |||||||
\(128\) | −1.93428e25 | −0.0883883 | ||||||||
\(129\) | 1.91596e26 | 0.794355 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.73908e25 | 0.230520 | 0.115260 | − | 0.993335i | \(-0.463230\pi\) | ||||
0.115260 | + | 0.993335i | \(0.463230\pi\) | |||||||
\(132\) | 1.32613e26 | 0.412490 | ||||||||
\(133\) | 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 | \(0.397799\pi\) | |||||||
\(138\) | −5.90067e26 | −1.05296 | ||||||||
\(139\) | −9.21581e25 | −0.150262 | −0.0751309 | − | 0.997174i | \(-0.523937\pi\) | ||||
−0.0751309 | + | 0.997174i | \(0.523937\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.43992e26 | −0.878298 | ||||||||
\(142\) | 9.29923e26 | 1.16103 | ||||||||
\(143\) | 6.15719e25 | 0.0704177 | ||||||||
\(144\) | 2.96022e26 | 0.310308 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.14085e27 | 1.00651 | ||||||||
\(147\) | −6.04599e26 | −0.489779 | ||||||||
\(148\) | 7.56699e26 | 0.563186 | ||||||||
\(149\) | −7.12667e26 | −0.487594 | −0.243797 | − | 0.969826i | \(-0.578393\pi\) | ||||
−0.243797 | + | 0.969826i | \(0.578393\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | −3.12846e27 | −1.53705 | ||||||||
\(154\) | 7.05749e26 | 0.319626 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.48172e26 | 0.0956523 | ||||||||
\(157\) | −2.38960e27 | −0.850315 | −0.425157 | − | 0.905119i | \(-0.639781\pi\) | ||||
−0.425157 | + | 0.905119i | \(0.639781\pi\) | |||||||
\(158\) | −2.60898e27 | −0.857546 | ||||||||
\(159\) | 1.71309e27 | 0.520375 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.14025e27 | −0.815908 | ||||||||
\(162\) | 2.06005e27 | 0.495382 | ||||||||
\(163\) | −6.63092e27 | −1.47648 | −0.738242 | − | 0.674536i | \(-0.764344\pi\) | ||||
−0.738242 | + | 0.674536i | \(0.764344\pi\) | |||||||
\(164\) | −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 | \(0.608622\pi\) | |||||||
\(168\) | 2.84460e27 | 0.434165 | ||||||||
\(169\) | −6.94118e27 | −0.983671 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.70787e27 | −0.698269 | ||||||||
\(172\) | 2.33263e27 | 0.265302 | ||||||||
\(173\) | 8.68916e27 | 0.919182 | 0.459591 | − | 0.888131i | \(-0.347996\pi\) | ||||
0.459591 | + | 0.888131i | \(0.347996\pi\) | |||||||
\(174\) | −1.74515e28 | −1.71778 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.61454e27 | 0.137765 | ||||||||
\(177\) | −1.82545e28 | −1.45112 | ||||||||
\(178\) | 1.31946e28 | 0.977567 | ||||||||
\(179\) | −4.31406e27 | −0.298005 | −0.149002 | − | 0.988837i | \(-0.547606\pi\) | ||||
−0.149002 | + | 0.988837i | \(0.547606\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | −3.26571e26 | −0.0171135 | ||||||||
\(184\) | −7.18394e27 | −0.351674 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.40909e28 | 1.03024 | ||||||||
\(187\) | −1.70630e28 | −0.682394 | ||||||||
\(188\) | −7.84046e27 | −0.293338 | ||||||||
\(189\) | −8.46070e27 | −0.296233 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.91337e28 | −0.587329 | −0.293665 | − | 0.955908i | \(-0.594875\pi\) | ||||
−0.293665 | + | 0.955908i | \(0.594875\pi\) | |||||||
\(192\) | 6.50757e27 | 0.187134 | ||||||||
\(193\) | 5.96748e28 | 1.60814 | 0.804071 | − | 0.594533i | \(-0.202663\pi\) | ||||
0.804071 | + | 0.594533i | \(0.202663\pi\) | |||||||
\(194\) | 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 | \(0.725580\pi\) | |||||||
\(198\) | −2.47088e28 | −0.483657 | ||||||||
\(199\) | −3.24229e28 | −0.595921 | −0.297960 | − | 0.954578i | \(-0.596306\pi\) | ||||
−0.297960 | + | 0.954578i | \(0.596306\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.39895e28 | 1.20011 | ||||||||
\(202\) | 1.39522e28 | 0.212692 | ||||||||
\(203\) | −9.28745e28 | −1.33106 | ||||||||
\(204\) | −6.87743e28 | −0.926934 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.38770e28 | 0.404171 | ||||||||
\(207\) | 1.09943e29 | 1.23463 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | −3.12857e29 | −2.45811 | ||||||||
\(214\) | 6.47109e28 | 0.479519 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.93555e28 | −0.127683 | ||||||||
\(217\) | 1.28208e29 | 0.798305 | ||||||||
\(218\) | −1.23236e29 | −0.724487 | ||||||||
\(219\) | −3.83820e29 | −2.13097 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.19316e28 | −0.158241 | ||||||||
\(222\) | −2.54579e29 | −1.19237 | ||||||||
\(223\) | −3.11100e29 | −1.37749 | −0.688746 | − | 0.725003i | \(-0.741839\pi\) | ||||
−0.688746 | + | 0.725003i | \(0.741839\pi\) | |||||||
\(224\) | 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 | \(0.440074\pi\) | |||||||
\(228\) | −1.25478e29 | −0.421098 | ||||||||
\(229\) | −3.70322e29 | −1.17662 | −0.588310 | − | 0.808635i | \(-0.700207\pi\) | ||||
−0.588310 | + | 0.808635i | \(0.700207\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.37438e29 | −0.676706 | ||||||||
\(232\) | −2.12468e29 | −0.573713 | ||||||||
\(233\) | 6.84781e28 | 0.175228 | 0.0876138 | − | 0.996155i | \(-0.472076\pi\) | ||||
0.0876138 | + | 0.996155i | \(0.472076\pi\) | |||||||
\(234\) | −4.62400e28 | −0.112155 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.22244e29 | −0.484652 | ||||||||
\(237\) | 8.77748e29 | 1.81558 | ||||||||
\(238\) | −3.66007e29 | −0.718253 | ||||||||
\(239\) | 3.87773e29 | 0.722111 | 0.361055 | − | 0.932544i | \(-0.382417\pi\) | ||||
0.361055 | + | 0.932544i | \(0.382417\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | −9.31717e29 | −1.40996 | ||||||||
\(244\) | −3.97593e27 | −0.00571565 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.27127e29 | 0.554457 | ||||||||
\(247\) | −5.82591e28 | −0.0718873 | ||||||||
\(248\) | 2.93301e29 | 0.344086 | ||||||||
\(249\) | −1.64898e30 | −1.83960 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.47990e30 | 1.49386 | 0.746930 | − | 0.664903i | \(-0.231527\pi\) | ||||
0.746930 | + | 0.664903i | \(0.231527\pi\) | |||||||
\(252\) | −5.30013e29 | −0.509072 | ||||||||
\(253\) | 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 | \(0.581655\pi\) | |||||||
\(258\) | −7.84776e29 | −0.561694 | ||||||||
\(259\) | −1.35483e30 | −0.923929 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.25161e30 | 2.01415 | ||||||||
\(262\) | −2.76033e29 | −0.163003 | ||||||||
\(263\) | −1.42102e30 | −0.800119 | −0.400059 | − | 0.916489i | \(-0.631011\pi\) | ||||
−0.400059 | + | 0.916489i | \(0.631011\pi\) | |||||||
\(264\) | −5.43184e29 | −0.291674 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.67778e29 | −0.326296 | ||||||||
\(267\) | −4.43911e30 | −2.06969 | ||||||||
\(268\) | 9.00805e29 | 0.400817 | ||||||||
\(269\) | −1.90129e30 | −0.807504 | −0.403752 | − | 0.914868i | \(-0.632294\pi\) | ||||
−0.403752 | + | 0.914868i | \(0.632294\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | −4.44340e29 | −0.156921 | ||||||||
\(274\) | −1.32286e30 | −0.446304 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.41692e30 | 0.744557 | ||||||||
\(277\) | 5.31088e29 | 0.156376 | 0.0781879 | − | 0.996939i | \(-0.475087\pi\) | ||||
0.0781879 | + | 0.996939i | \(0.475087\pi\) | |||||||
\(278\) | 3.77479e29 | 0.106251 | ||||||||
\(279\) | −4.48867e30 | −1.20799 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.64974e30 | −0.898323 | −0.449161 | − | 0.893451i | \(-0.648277\pi\) | ||||
−0.449161 | + | 0.893451i | \(0.648277\pi\) | |||||||
\(282\) | 2.63779e30 | 0.621050 | ||||||||
\(283\) | 1.43965e30 | 0.324285 | 0.162143 | − | 0.986767i | \(-0.448160\pi\) | ||||
0.162143 | + | 0.986767i | \(0.448160\pi\) | |||||||
\(284\) | −3.80897e30 | −0.820971 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.52199e29 | −0.0497929 | ||||||||
\(287\) | 2.27311e30 | 0.429632 | ||||||||
\(288\) | −1.21251e30 | −0.219421 | ||||||||
\(289\) | 3.07837e30 | 0.533456 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.93976e30 | −0.785315 | ||||||||
\(292\) | −4.67292e30 | −0.711710 | ||||||||
\(293\) | −1.24504e31 | −1.81692 | −0.908462 | − | 0.417967i | \(-0.862743\pi\) | ||||
−0.908462 | + | 0.417967i | \(0.862743\pi\) | |||||||
\(294\) | 2.47644e30 | 0.346326 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.09944e30 | −0.398233 | ||||||||
\(297\) | 1.61559e30 | 0.199011 | ||||||||
\(298\) | 2.91909e30 | 0.344781 | ||||||||
\(299\) | 1.12217e30 | 0.127106 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.17647e30 | −0.435239 | ||||||||
\(302\) | 1.25403e31 | 1.25378 | ||||||||
\(303\) | −4.69399e30 | −0.450307 | ||||||||
\(304\) | −1.52767e30 | −0.140640 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.28142e31 | 1.08686 | ||||||||
\(307\) | −2.27193e31 | −1.84997 | −0.924986 | − | 0.380001i | \(-0.875924\pi\) | ||||
−0.924986 | + | 0.380001i | \(0.875924\pi\) | |||||||
\(308\) | −2.89075e30 | −0.226009 | ||||||||
\(309\) | −1.13974e31 | −0.855703 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.84336e31 | −1.27675 | −0.638374 | − | 0.769726i | \(-0.720393\pi\) | ||||
−0.638374 | + | 0.769726i | \(0.720393\pi\) | |||||||
\(312\) | −1.01651e30 | −0.0676364 | ||||||||
\(313\) | −4.98693e30 | −0.318808 | −0.159404 | − | 0.987213i | \(-0.550957\pi\) | ||||
−0.159404 | + | 0.987213i | \(0.550957\pi\) | |||||||
\(314\) | 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 | \(0.422899\pi\) | |||||||
\(318\) | −7.01683e30 | −0.367961 | ||||||||
\(319\) | 1.77347e31 | 0.894209 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.17709e31 | −1.01523 | ||||||||
\(322\) | 1.28625e31 | 0.576934 | ||||||||
\(323\) | 1.61450e31 | 0.696635 | ||||||||
\(324\) | −8.43797e30 | −0.350288 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.71602e31 | 1.04403 | ||||||||
\(327\) | 4.14606e31 | 1.53387 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 4.74337e31 | 1.39809 | ||||||||
\(334\) | 1.66706e31 | 0.473283 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.16515e31 | −0.307001 | ||||||||
\(337\) | −1.08428e31 | −0.275275 | −0.137638 | − | 0.990483i | \(-0.543951\pi\) | ||||
−0.137638 | + | 0.990483i | \(0.543951\pi\) | |||||||
\(338\) | 2.84311e31 | 0.695560 | ||||||||
\(339\) | 1.11172e32 | 2.62119 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.44817e31 | −0.536305 | ||||||||
\(342\) | 2.33794e31 | 0.493751 | ||||||||
\(343\) | 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 | \(0.520204\pi\) | |||||||
\(348\) | 7.14814e31 | 1.21465 | ||||||||
\(349\) | 5.27779e31 | 0.865235 | 0.432618 | − | 0.901577i | \(-0.357590\pi\) | ||||
0.432618 | + | 0.901577i | \(0.357590\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.02342e30 | 0.0461487 | ||||||||
\(352\) | −6.61315e30 | −0.0974148 | ||||||||
\(353\) | 5.67715e31 | 0.807135 | 0.403567 | − | 0.914950i | \(-0.367770\pi\) | ||||
0.403567 | + | 0.914950i | \(0.367770\pi\) | |||||||
\(354\) | 7.47702e31 | 1.02610 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.40451e31 | −0.691244 | ||||||||
\(357\) | 1.23137e32 | 1.52067 | ||||||||
\(358\) | 1.76704e31 | 0.210721 | ||||||||
\(359\) | 2.18925e31 | 0.252125 | 0.126062 | − | 0.992022i | \(-0.459766\pi\) | ||||
0.126062 | + | 0.992022i | \(0.459766\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.36201e31 | −0.683525 | ||||||||
\(362\) | −9.13280e31 | −0.947866 | ||||||||
\(363\) | −1.03966e32 | −1.04246 | ||||||||
\(364\) | −5.40974e30 | −0.0524094 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.33763e30 | 0.0121011 | ||||||||
\(367\) | −1.00500e32 | −0.878699 | −0.439349 | − | 0.898316i | \(-0.644791\pi\) | ||||
−0.439349 | + | 0.898316i | \(0.644791\pi\) | |||||||
\(368\) | 2.94254e31 | 0.248671 | ||||||||
\(369\) | −7.95833e31 | −0.650118 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.73425e31 | −0.285122 | ||||||||
\(372\) | −9.86761e31 | −0.728493 | ||||||||
\(373\) | −6.31052e31 | −0.450510 | −0.225255 | − | 0.974300i | \(-0.572322\pi\) | ||||
−0.225255 | + | 0.974300i | \(0.572322\pi\) | |||||||
\(374\) | 6.98901e31 | 0.482526 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.21145e31 | 0.207421 | ||||||||
\(377\) | 3.31886e31 | 0.207358 | ||||||||
\(378\) | 3.46550e31 | 0.209468 | ||||||||
\(379\) | −8.85755e31 | −0.517993 | −0.258996 | − | 0.965878i | \(-0.583392\pi\) | ||||
−0.258996 | + | 0.965878i | \(0.583392\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.83241e32 | 1.00337 | ||||||||
\(382\) | 7.83716e31 | 0.415305 | ||||||||
\(383\) | −9.08315e31 | −0.465856 | −0.232928 | − | 0.972494i | \(-0.574831\pi\) | ||||
−0.232928 | + | 0.972494i | \(0.574831\pi\) | |||||||
\(384\) | −2.66550e31 | −0.132324 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.44428e32 | −1.13713 | ||||||||
\(387\) | 1.46221e32 | 0.658603 | ||||||||
\(388\) | −6.01405e31 | −0.262283 | ||||||||
\(389\) | 7.13043e31 | 0.301124 | 0.150562 | − | 0.988601i | \(-0.451892\pi\) | ||||
0.150562 | + | 0.988601i | \(0.451892\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.10978e32 | −1.23174 | ||||||||
\(392\) | 3.01500e31 | 0.115668 | ||||||||
\(393\) | 9.28666e31 | 0.345106 | ||||||||
\(394\) | 2.55674e32 | 0.920416 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.01207e32 | 0.341997 | ||||||||
\(397\) | −2.99427e31 | −0.0980413 | −0.0490206 | − | 0.998798i | \(-0.515610\pi\) | ||||
−0.0490206 | + | 0.998798i | \(0.515610\pi\) | |||||||
\(398\) | 1.32804e32 | 0.421380 | ||||||||
\(399\) | 2.24663e32 | 0.690828 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.00588e32 | −1.44603 | −0.723013 | − | 0.690835i | \(-0.757243\pi\) | ||||
−0.723013 | + | 0.690835i | \(0.757243\pi\) | |||||||
\(402\) | −3.03061e32 | −0.848603 | ||||||||
\(403\) | −4.58150e31 | −0.124364 | ||||||||
\(404\) | −5.71482e31 | −0.150396 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.80414e32 | 0.941198 | ||||||||
\(407\) | 2.58709e32 | 0.620700 | ||||||||
\(408\) | 2.81699e32 | 0.655441 | ||||||||
\(409\) | −2.78379e32 | −0.628195 | −0.314097 | − | 0.949391i | \(-0.601702\pi\) | ||||
−0.314097 | + | 0.949391i | \(0.601702\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.45054e32 | 0.944908 | ||||||||
\(412\) | −1.38760e32 | −0.285792 | ||||||||
\(413\) | 3.97916e32 | 0.795090 | ||||||||
\(414\) | −4.50326e32 | −0.873016 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.23758e31 | −0.0225895 | ||||||||
\(417\) | −1.26997e32 | −0.224953 | ||||||||
\(418\) | 1.27514e32 | 0.219207 | ||||||||
\(419\) | −6.36828e32 | −1.06254 | −0.531272 | − | 0.847201i | \(-0.678286\pi\) | ||||
−0.531272 | + | 0.847201i | \(0.678286\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | −4.91480e32 | −0.728201 | ||||||||
\(424\) | −8.54283e31 | −0.122893 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.28146e33 | 1.73815 | ||||||||
\(427\) | 7.11870e30 | 0.00937675 | ||||||||
\(428\) | −2.65056e32 | −0.339071 | ||||||||
\(429\) | 8.48480e31 | 0.105421 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.44178e32 | 0.286247 | 0.143124 | − | 0.989705i | \(-0.454285\pi\) | ||||
0.143124 | + | 0.989705i | \(0.454285\pi\) | |||||||
\(432\) | 7.92800e31 | 0.0902853 | ||||||||
\(433\) | −9.12872e32 | −1.00998 | −0.504988 | − | 0.863126i | \(-0.668503\pi\) | ||||
−0.504988 | + | 0.863126i | \(0.668503\pi\) | |||||||
\(434\) | −5.25140e32 | −0.564487 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.04774e32 | 0.512290 | ||||||||
\(437\) | −5.67378e32 | −0.559570 | ||||||||
\(438\) | 1.57213e33 | 1.50682 | ||||||||
\(439\) | 6.07601e32 | 0.565995 | 0.282997 | − | 0.959121i | \(-0.408671\pi\) | ||||
0.282997 | + | 0.959121i | \(0.408671\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.61416e32 | −0.406078 | ||||||||
\(442\) | 1.30792e32 | 0.111893 | ||||||||
\(443\) | −9.06289e32 | −0.753737 | −0.376869 | − | 0.926267i | \(-0.622999\pi\) | ||||
−0.376869 | + | 0.926267i | \(0.622999\pi\) | |||||||
\(444\) | 1.04275e33 | 0.843131 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.27427e33 | 0.974034 | ||||||||
\(447\) | −9.82078e32 | −0.729965 | ||||||||
\(448\) | −1.41854e32 | −0.102534 | ||||||||
\(449\) | −1.21579e33 | −0.854630 | −0.427315 | − | 0.904103i | \(-0.640540\pi\) | ||||
−0.427315 | + | 0.904103i | \(0.640540\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.34056e32 | −0.288629 | ||||||||
\(452\) | 1.35349e33 | 0.875439 | ||||||||
\(453\) | −4.21899e33 | −2.65449 | ||||||||
\(454\) | −4.32422e32 | −0.264673 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.13959e32 | 0.297761 | ||||||||
\(457\) | 5.59530e32 | 0.315407 | 0.157703 | − | 0.987487i | \(-0.449591\pi\) | ||||
0.157703 | + | 0.987487i | \(0.449591\pi\) | |||||||
\(458\) | 1.51684e33 | 0.831997 | ||||||||
\(459\) | −8.37859e32 | −0.447211 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.78592e32 | −0.191386 | −0.0956930 | − | 0.995411i | \(-0.530507\pi\) | ||||
−0.0956930 | + | 0.995411i | \(0.530507\pi\) | |||||||
\(462\) | 9.72545e32 | 0.478503 | ||||||||
\(463\) | −2.77039e33 | −1.32672 | −0.663359 | − | 0.748301i | \(-0.730870\pi\) | ||||
−0.663359 | + | 0.748301i | \(0.730870\pi\) | |||||||
\(464\) | 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 | \(0.333806\pi\) | |||||||
\(468\) | 1.89399e32 | 0.0793058 | ||||||||
\(469\) | −1.61285e33 | −0.657556 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.29294e33 | −1.27298 | ||||||||
\(472\) | 9.10311e32 | 0.342700 | ||||||||
\(473\) | 7.97508e32 | 0.292396 | ||||||||
\(474\) | −3.59526e33 | −1.28381 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.49916e33 | 0.507881 | ||||||||
\(477\) | 1.30739e33 | 0.431446 | ||||||||
\(478\) | −1.58832e33 | −0.510609 | ||||||||
\(479\) | 2.24376e33 | 0.702720 | 0.351360 | − | 0.936240i | \(-0.385719\pi\) | ||||
0.351360 | + | 0.936240i | \(0.385719\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.84147e32 | 0.143934 | ||||||||
\(482\) | −4.24851e33 | −1.23069 | ||||||||
\(483\) | −4.32737e33 | −1.22148 | ||||||||
\(484\) | −1.26577e33 | −0.348166 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.81631e33 | 0.996989 | ||||||||
\(487\) | −3.71393e32 | −0.0945632 | −0.0472816 | − | 0.998882i | \(-0.515056\pi\) | ||||
−0.0472816 | + | 0.998882i | \(0.515056\pi\) | |||||||
\(488\) | 1.62854e31 | 0.00404157 | ||||||||
\(489\) | −9.13761e33 | −2.21041 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.65508e33 | −0.610323 | −0.305161 | − | 0.952301i | \(-0.598710\pi\) | ||||
−0.305161 | + | 0.952301i | \(0.598710\pi\) | |||||||
\(492\) | −1.74951e33 | −0.392060 | ||||||||
\(493\) | −9.19732e33 | −2.00944 | ||||||||
\(494\) | 2.38629e32 | 0.0508320 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.20136e33 | −0.243306 | ||||||||
\(497\) | 6.81976e33 | 1.34684 | ||||||||
\(498\) | 6.75421e33 | 1.30079 | ||||||||
\(499\) | −2.39117e33 | −0.449111 | −0.224556 | − | 0.974461i | \(-0.572093\pi\) | ||||
−0.224556 | + | 0.974461i | \(0.572093\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.60855e33 | −1.00203 | ||||||||
\(502\) | −6.06166e33 | −1.05632 | ||||||||
\(503\) | 6.34146e33 | 1.07793 | 0.538964 | − | 0.842329i | \(-0.318816\pi\) | ||||
0.538964 | + | 0.842329i | \(0.318816\pi\) | |||||||
\(504\) | 2.17093e33 | 0.359968 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.45613e33 | −0.387587 | ||||||||
\(507\) | −9.56517e33 | −1.47263 | ||||||||
\(508\) | 2.23092e33 | 0.335111 | ||||||||
\(509\) | −3.62528e32 | −0.0531337 | −0.0265668 | − | 0.999647i | \(-0.508457\pi\) | ||||
−0.0265668 | + | 0.999647i | \(0.508457\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.36664e33 | 1.16759 | ||||||||
\(512\) | −3.24519e32 | −0.0441942 | ||||||||
\(513\) | −1.52867e33 | −0.203164 | ||||||||
\(514\) | 2.76637e33 | 0.358816 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.21444e33 | 0.397177 | ||||||||
\(517\) | −2.68059e33 | −0.323295 | ||||||||
\(518\) | 5.54939e33 | 0.653316 | ||||||||
\(519\) | 1.19739e34 | 1.37608 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.23573e33 | 0.902050 | 0.451025 | − | 0.892511i | \(-0.351058\pi\) | ||||
0.451025 | + | 0.892511i | \(0.351058\pi\) | |||||||
\(522\) | −1.33186e34 | −1.42422 | ||||||||
\(523\) | 1.20443e34 | 1.25750 | 0.628752 | − | 0.777606i | \(-0.283566\pi\) | ||||
0.628752 | + | 0.777606i | \(0.283566\pi\) | |||||||
\(524\) | 1.13063e33 | 0.115260 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.82051e33 | 0.565770 | ||||||||
\(527\) | 1.26964e34 | 1.20517 | ||||||||
\(528\) | 2.22488e33 | 0.206245 | ||||||||
\(529\) | −1.17149e32 | −0.0106057 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.39314e34 | −1.20313 | ||||||||
\(532\) | 2.73522e33 | 0.230726 | ||||||||
\(533\) | −8.12291e32 | −0.0669301 | ||||||||
\(534\) | 1.81826e34 | 1.46349 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.68970e33 | −0.283420 | ||||||||
\(537\) | −5.94490e33 | −0.446135 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 3.07258e34 | 2.00681 | ||||||||
\(544\) | 3.42963e33 | 0.218907 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.82002e33 | 0.110960 | ||||||||
\(547\) | 1.78334e34 | 1.06266 | 0.531328 | − | 0.847166i | \(-0.321693\pi\) | ||||
0.531328 | + | 0.847166i | \(0.321693\pi\) | |||||||
\(548\) | 5.41843e33 | 0.315585 | ||||||||
\(549\) | −2.49231e32 | −0.0141889 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.67805e34 | −0.912871 | ||||||||
\(552\) | −9.89969e33 | −0.526481 | ||||||||
\(553\) | −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 | \(0.566524\pi\) | |||||||
\(558\) | 1.83856e34 | 0.854181 | ||||||||
\(559\) | 1.49245e33 | 0.0678037 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.35134e34 | −1.02160 | ||||||||
\(562\) | 1.49493e34 | 0.635210 | ||||||||
\(563\) | −3.82416e34 | −1.58921 | −0.794606 | − | 0.607126i | \(-0.792322\pi\) | ||||
−0.794606 | + | 0.607126i | \(0.792322\pi\) | |||||||
\(564\) | −1.08044e34 | −0.439149 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.89682e33 | −0.229304 | ||||||||
\(567\) | 1.51078e34 | 0.574661 | ||||||||
\(568\) | 1.56015e34 | 0.580514 | ||||||||
\(569\) | 3.49591e34 | 1.27250 | 0.636248 | − | 0.771484i | \(-0.280485\pi\) | ||||
0.636248 | + | 0.771484i | \(0.280485\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | −2.63668e34 | −0.879276 | ||||||||
\(574\) | −9.31065e33 | −0.303795 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.96642e33 | 0.155154 | ||||||||
\(577\) | 4.45926e34 | 1.36322 | 0.681609 | − | 0.731717i | \(-0.261281\pi\) | ||||
0.681609 | + | 0.731717i | \(0.261281\pi\) | |||||||
\(578\) | −1.26090e34 | −0.377210 | ||||||||
\(579\) | 8.22337e34 | 2.40751 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.59450e34 | 1.00794 | ||||||||
\(582\) | 2.02333e34 | 0.555301 | ||||||||
\(583\) | 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 | \(0.399854\pi\) | |||||||
\(588\) | −1.01435e34 | −0.244890 | ||||||||
\(589\) | 2.31645e34 | 0.547497 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.60173e34 | −1.94869 | ||||||||
\(592\) | 1.26953e34 | 0.281593 | ||||||||
\(593\) | 4.88078e33 | 0.106000 | 0.0530000 | − | 0.998595i | \(-0.483122\pi\) | ||||
0.0530000 | + | 0.998595i | \(0.483122\pi\) | |||||||
\(594\) | −6.61748e33 | −0.140722 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.19566e34 | −0.243797 | ||||||||
\(597\) | −4.46798e34 | −0.892138 | ||||||||
\(598\) | −4.59639e33 | −0.0898777 | ||||||||
\(599\) | 4.61838e34 | 0.884412 | 0.442206 | − | 0.896914i | \(-0.354196\pi\) | ||||
0.442206 | + | 0.896914i | \(0.354196\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | 5.64671e34 | 0.995013 | ||||||||
\(604\) | −5.13652e34 | −0.886559 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.92266e34 | 0.318415 | ||||||||
\(607\) | −1.03737e35 | −1.68297 | −0.841484 | − | 0.540282i | \(-0.818318\pi\) | ||||
−0.841484 | + | 0.540282i | \(0.818318\pi\) | |||||||
\(608\) | 6.25734e33 | 0.0994477 | ||||||||
\(609\) | −1.27984e35 | −1.99269 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.01644e33 | −0.0749688 | ||||||||
\(612\) | −5.24869e34 | −0.768526 | ||||||||
\(613\) | −2.85744e34 | −0.409941 | −0.204970 | − | 0.978768i | \(-0.565710\pi\) | ||||
−0.204970 | + | 0.978768i | \(0.565710\pi\) | |||||||
\(614\) | 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 | \(0.615412\pi\) | |||||||
\(618\) | 4.66836e34 | 0.605073 | ||||||||
\(619\) | 6.60909e34 | 0.839477 | 0.419738 | − | 0.907645i | \(-0.362122\pi\) | ||||
0.419738 | + | 0.907645i | \(0.362122\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.94447e34 | 0.359221 | ||||||||
\(622\) | 7.55041e34 | 0.902798 | ||||||||
\(623\) | 9.67651e34 | 1.13401 | ||||||||
\(624\) | 4.16364e33 | 0.0478262 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.04264e34 | 0.225431 | ||||||||
\(627\) | −4.29000e34 | −0.464102 | ||||||||
\(628\) | −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 | ||||||||
\(633\) | 5.26679e34 | 0.505824 | ||||||||
\(634\) | −3.60234e34 | −0.339210 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.87409e34 | 0.260188 | ||||||||
\(637\) | −4.70958e33 | −0.0418061 | ||||||||
\(638\) | −7.26412e34 | −0.632302 | ||||||||
\(639\) | −2.38765e35 | −2.03803 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.77093e35 | 1.45370 | 0.726850 | − | 0.686796i | \(-0.240983\pi\) | ||||
0.726850 | + | 0.686796i | \(0.240983\pi\) | |||||||
\(642\) | 8.91737e34 | 0.717875 | ||||||||
\(643\) | 7.98617e34 | 0.630524 | 0.315262 | − | 0.949005i | \(-0.397908\pi\) | ||||
0.315262 | + | 0.949005i | \(0.397908\pi\) | |||||||
\(644\) | −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 | \(0.209285\pi\) | |||||||
\(648\) | 3.45619e34 | 0.247691 | ||||||||
\(649\) | −7.59833e34 | −0.534145 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.76675e35 | 1.19512 | ||||||||
\(652\) | −1.11248e35 | −0.738242 | ||||||||
\(653\) | −2.41184e35 | −1.57013 | −0.785063 | − | 0.619416i | \(-0.787369\pi\) | ||||
−0.785063 | + | 0.619416i | \(0.787369\pi\) | |||||||
\(654\) | −1.69823e35 | −1.08461 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.12999e34 | −0.130942 | ||||||||
\(657\) | −2.92923e35 | −1.76679 | ||||||||
\(658\) | −5.74995e34 | −0.340283 | ||||||||
\(659\) | 2.18788e35 | 1.27045 | 0.635223 | − | 0.772329i | \(-0.280908\pi\) | ||||
0.635223 | + | 0.772329i | \(0.280908\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | −4.40028e34 | −0.236898 | ||||||||
\(664\) | 8.22310e34 | 0.434445 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.94289e35 | −0.988597 | ||||||||
\(667\) | 3.23219e35 | 1.61408 | ||||||||
\(668\) | −6.82828e34 | −0.334662 | ||||||||
\(669\) | −4.28705e35 | −2.06221 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.35934e33 | −0.00629934 | ||||||||
\(672\) | 4.77244e34 | 0.217083 | ||||||||
\(673\) | −2.39665e35 | −1.07008 | −0.535040 | − | 0.844827i | \(-0.679703\pi\) | ||||
−0.535040 | + | 0.844827i | \(0.679703\pi\) | |||||||
\(674\) | 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 | \(0.474951\pi\) | |||||||
\(678\) | −4.55360e35 | −1.85346 | ||||||||
\(679\) | 1.07679e35 | 0.430286 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.45481e35 | 0.560361 | ||||||||
\(682\) | 1.00277e35 | 0.379225 | ||||||||
\(683\) | 3.21208e35 | 1.19269 | 0.596345 | − | 0.802729i | \(-0.296619\pi\) | ||||
0.596345 | + | 0.802729i | \(0.296619\pi\) | |||||||
\(684\) | −9.57621e34 | −0.349134 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.18986e35 | −0.769776 | ||||||||
\(687\) | −5.10316e35 | −1.76149 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | −1.81207e35 | −0.561060 | ||||||||
\(694\) | 2.94991e34 | 0.0897047 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.92788e35 | −0.858890 | ||||||||
\(697\) | 2.25105e35 | 0.648597 | ||||||||
\(698\) | −2.16178e35 | −0.611814 | ||||||||
\(699\) | 9.43649e34 | 0.262329 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.50008e35 | 0.402383 | 0.201191 | − | 0.979552i | \(-0.435519\pi\) | ||||
0.201191 | + | 0.979552i | \(0.435519\pi\) | |||||||
\(702\) | −1.23839e34 | −0.0326320 | ||||||||
\(703\) | −2.44790e35 | −0.633653 | ||||||||
\(704\) | 2.70874e34 | 0.0688827 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.32536e35 | −0.570731 | ||||||||
\(707\) | 1.02321e35 | 0.246730 | ||||||||
\(708\) | −3.06259e35 | −0.725559 | ||||||||
\(709\) | −2.12042e35 | −0.493564 | −0.246782 | − | 0.969071i | \(-0.579373\pi\) | ||||
−0.246782 | + | 0.969071i | \(0.579373\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.69877e35 | 1.50531 | ||||||||
\(712\) | 2.21369e35 | 0.488783 | ||||||||
\(713\) | −4.46186e35 | −0.968048 | ||||||||
\(714\) | −5.04369e35 | −1.07528 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.23778e34 | −0.149002 | ||||||||
\(717\) | 5.34363e35 | 1.08105 | ||||||||
\(718\) | −8.96718e34 | −0.178279 | ||||||||
\(719\) | 3.27911e35 | 0.640686 | 0.320343 | − | 0.947302i | \(-0.396202\pi\) | ||||
0.320343 | + | 0.947302i | \(0.396202\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.48443e35 | 0.468853 | ||||||||
\(722\) | 2.60588e35 | 0.483325 | ||||||||
\(723\) | 1.42934e36 | 2.60560 | ||||||||
\(724\) | 3.74080e35 | 0.670243 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.25846e35 | 0.737131 | ||||||||
\(727\) | −2.40795e35 | −0.409701 | −0.204850 | − | 0.978793i | \(-0.565671\pi\) | ||||
−0.204850 | + | 0.978793i | \(0.565671\pi\) | |||||||
\(728\) | 2.21583e34 | 0.0370590 | ||||||||
\(729\) | −8.57797e35 | −1.41023 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.13594e35 | −0.657063 | ||||||||
\(732\) | −5.47895e33 | −0.00855675 | ||||||||
\(733\) | 3.39196e35 | 0.520776 | 0.260388 | − | 0.965504i | \(-0.416150\pi\) | ||||
0.260388 | + | 0.965504i | \(0.416150\pi\) | |||||||
\(734\) | 4.11648e35 | 0.621334 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.20526e35 | −0.175837 | ||||||||
\(737\) | 3.07978e35 | 0.441749 | ||||||||
\(738\) | 3.25973e35 | 0.459703 | ||||||||
\(739\) | 1.23366e36 | 1.71057 | 0.855284 | − | 0.518159i | \(-0.173383\pi\) | ||||
0.855284 | + | 0.518159i | \(0.173383\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.02829e34 | −0.107621 | ||||||||
\(742\) | 1.52955e35 | 0.201611 | ||||||||
\(743\) | 6.24478e35 | 0.809389 | 0.404694 | − | 0.914452i | \(-0.367378\pi\) | ||||
0.404694 | + | 0.914452i | \(0.367378\pi\) | |||||||
\(744\) | 4.04177e35 | 0.515122 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.58479e35 | 0.318559 | ||||||||
\(747\) | −1.25846e36 | −1.52522 | ||||||||
\(748\) | −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 | ||||||||
\(753\) | 2.03934e36 | 2.23642 | ||||||||
\(754\) | −1.35940e35 | −0.146625 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.41947e35 | −0.148117 | ||||||||
\(757\) | −1.83266e35 | −0.188098 | −0.0940489 | − | 0.995568i | \(-0.529981\pi\) | ||||
−0.0940489 | + | 0.995568i | \(0.529981\pi\) | |||||||
\(758\) | 3.62805e35 | 0.366276 | ||||||||
\(759\) | 8.26323e35 | 0.820593 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.88027e36 | 1.80681 | 0.903406 | − | 0.428787i | \(-0.141059\pi\) | ||||
0.903406 | + | 0.428787i | \(0.141059\pi\) | |||||||
\(762\) | −7.50557e35 | −0.709490 | ||||||||
\(763\) | −9.03772e35 | −0.840431 | ||||||||
\(764\) | −3.21010e35 | −0.293665 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.72046e35 | 0.329410 | ||||||||
\(767\) | −1.42195e35 | −0.123863 | ||||||||
\(768\) | 1.09179e35 | 0.0935671 | ||||||||
\(769\) | 1.28453e36 | 1.08309 | 0.541546 | − | 0.840671i | \(-0.317839\pi\) | ||||
0.541546 | + | 0.840671i | \(0.317839\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.30700e35 | −0.759679 | ||||||||
\(772\) | 1.00118e36 | 0.804071 | ||||||||
\(773\) | 1.04808e36 | 0.828226 | 0.414113 | − | 0.910225i | \(-0.364092\pi\) | ||||
0.414113 | + | 0.910225i | \(0.364092\pi\) | |||||||
\(774\) | −5.98923e35 | −0.465703 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.46335e35 | 0.185462 | ||||||||
\(777\) | −1.86700e36 | −1.38319 | ||||||||
\(778\) | −2.92063e35 | −0.212927 | ||||||||
\(779\) | 4.10703e35 | 0.294652 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.30225e36 | −0.904811 | ||||||||
\(782\) | 1.27377e36 | 0.870974 | ||||||||
\(783\) | 8.70840e35 | 0.586025 | ||||||||
\(784\) | −1.23495e35 | −0.0817894 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.80382e35 | −0.244027 | ||||||||
\(787\) | 8.93146e35 | 0.563947 | 0.281974 | − | 0.959422i | \(-0.409011\pi\) | ||||
0.281974 | + | 0.959422i | \(0.409011\pi\) | |||||||
\(788\) | −1.04724e36 | −0.650832 | ||||||||
\(789\) | −1.95822e36 | −1.19784 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.42336e36 | −1.43619 | ||||||||
\(792\) | −4.14546e35 | −0.241829 | ||||||||
\(793\) | −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 | \(0.410570\pi\) | |||||||
\(798\) | −9.20219e35 | −0.488489 | ||||||||
\(799\) | 1.39017e36 | 0.726498 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.38782e36 | −1.71599 | ||||||||
\(802\) | 2.05041e36 | 1.02249 | ||||||||
\(803\) | −1.59763e36 | −0.784392 | ||||||||
\(804\) | 1.24134e36 | 0.600053 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.87658e35 | 0.0879385 | ||||||||
\(807\) | −2.62004e36 | −1.20889 | ||||||||
\(808\) | 2.34079e35 | 0.106346 | ||||||||
\(809\) | 1.33897e36 | 0.598981 | 0.299490 | − | 0.954099i | \(-0.403183\pi\) | ||||
0.299490 | + | 0.954099i | \(0.403183\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | −2.00917e36 | −0.845055 | ||||||||
\(814\) | −1.05967e36 | −0.438901 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.15384e36 | −0.463467 | ||||||||
\(817\) | −7.54600e35 | −0.298498 | ||||||||
\(818\) | 1.14024e36 | 0.444201 | ||||||||
\(819\) | −3.39110e35 | −0.130104 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.91664e34 | 0.0145755 | 0.00728777 | − | 0.999973i | \(-0.497680\pi\) | ||||
0.00728777 | + | 0.999973i | \(0.497680\pi\) | |||||||
\(822\) | −1.82294e36 | −0.668151 | ||||||||
\(823\) | 3.40400e36 | 1.22883 | 0.614414 | − | 0.788984i | \(-0.289392\pi\) | ||||
0.614414 | + | 0.788984i | \(0.289392\pi\) | |||||||
\(824\) | 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 | \(0.174700\pi\) | |||||||
\(828\) | 1.84453e36 | 0.617316 | ||||||||
\(829\) | 8.20485e35 | 0.270482 | 0.135241 | − | 0.990813i | \(-0.456819\pi\) | ||||
0.135241 | + | 0.990813i | \(0.456819\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.31856e35 | 0.234106 | ||||||||
\(832\) | 5.06913e34 | 0.0159732 | ||||||||
\(833\) | 1.30513e36 | 0.405128 | ||||||||
\(834\) | 5.20178e35 | 0.159066 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.22298e35 | −0.155003 | ||||||||
\(837\) | −1.20215e36 | −0.351471 | ||||||||
\(838\) | 2.60845e36 | 0.751332 | ||||||||
\(839\) | −5.38664e36 | −1.52860 | −0.764300 | − | 0.644861i | \(-0.776915\pi\) | ||||
−0.764300 | + | 0.644861i | \(0.776915\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.92900e36 | 1.63317 | ||||||||
\(842\) | 1.60676e36 | 0.436063 | ||||||||
\(843\) | −5.02945e36 | −1.34486 | ||||||||
\(844\) | 6.41220e35 | 0.168938 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.01310e36 | 0.514916 | ||||||||
\(847\) | 2.26629e36 | 0.571180 | ||||||||
\(848\) | 3.49914e35 | 0.0868987 | ||||||||
\(849\) | 1.98389e36 | 0.485479 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.71505e36 | 1.12038 | ||||||||
\(852\) | −5.24887e36 | −1.22905 | ||||||||
\(853\) | −9.55369e35 | −0.220449 | −0.110225 | − | 0.993907i | \(-0.535157\pi\) | ||||
−0.110225 | + | 0.993907i | \(0.535157\pi\) | |||||||
\(854\) | −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 | \(0.300439\pi\) | |||||||
\(858\) | −3.47537e35 | −0.0745436 | ||||||||
\(859\) | 5.48992e36 | 1.16052 | 0.580258 | − | 0.814432i | \(-0.302952\pi\) | ||||
0.580258 | + | 0.814432i | \(0.302952\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.13241e36 | 0.643190 | ||||||||
\(862\) | −1.00016e36 | −0.202407 | ||||||||
\(863\) | 2.89510e36 | 0.577469 | 0.288735 | − | 0.957409i | \(-0.406766\pi\) | ||||
0.288735 | + | 0.957409i | \(0.406766\pi\) | |||||||
\(864\) | −3.24731e35 | −0.0638413 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.73912e36 | 0.714161 | ||||||||
\(867\) | 4.24209e36 | 0.798623 | ||||||||
\(868\) | 2.15097e36 | 0.399152 | ||||||||
\(869\) | 3.65359e36 | 0.668301 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.76349e35 | 0.102437 | ||||||||
\(872\) | −2.06755e36 | −0.362244 | ||||||||
\(873\) | −3.76991e36 | −0.651108 | ||||||||
\(874\) | 2.32398e36 | 0.395676 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.43943e36 | −1.06548 | ||||||||
\(877\) | −2.04429e36 | −0.333463 | −0.166731 | − | 0.986002i | \(-0.553321\pi\) | ||||
−0.166731 | + | 0.986002i | \(0.553321\pi\) | |||||||
\(878\) | −2.48874e36 | −0.400219 | ||||||||
\(879\) | −1.71570e37 | −2.72007 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.76163e36 | −0.271466 | −0.135733 | − | 0.990745i | \(-0.543339\pi\) | ||||
−0.135733 | + | 0.990745i | \(0.543339\pi\) | |||||||
\(882\) | 1.88996e36 | 0.287141 | ||||||||
\(883\) | −1.25672e37 | −1.88248 | −0.941240 | − | 0.337738i | \(-0.890338\pi\) | ||||
−0.941240 | + | 0.337738i | \(0.890338\pi\) | |||||||
\(884\) | −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 | \(0.714328\pi\) | |||||||
\(888\) | −4.27112e36 | −0.596184 | ||||||||
\(889\) | −3.99436e36 | −0.549762 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.88487e36 | −0.386060 | ||||||||
\(892\) | −5.21939e36 | −0.688746 | ||||||||
\(893\) | 2.53636e36 | 0.330041 | ||||||||
\(894\) | 4.02259e36 | 0.516163 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5.81034e35 | 0.0725023 | ||||||||
\(897\) | 1.54638e36 | 0.190288 | ||||||||
\(898\) | 4.97986e36 | 0.604315 | ||||||||
\(899\) | −1.31962e37 | −1.57925 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.69802e36 | −0.430436 | ||||||||
\(902\) | 1.77789e36 | 0.204091 | ||||||||
\(903\) | −5.75530e36 | −0.651585 | ||||||||
\(904\) | −5.54391e36 | −0.619029 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.72810e37 | 1.87701 | ||||||||
\(907\) | 1.59523e37 | 1.70896 | 0.854482 | − | 0.519481i | \(-0.173875\pi\) | ||||
0.854482 | + | 0.519481i | \(0.173875\pi\) | |||||||
\(908\) | 1.77120e36 | 0.187152 | ||||||||
\(909\) | −3.58234e36 | −0.373352 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.71775e36 | −0.174172 | −0.0870862 | − | 0.996201i | \(-0.527756\pi\) | ||||
−0.0870862 | + | 0.996201i | \(0.527756\pi\) | |||||||
\(912\) | −2.10518e36 | −0.210549 | ||||||||
\(913\) | −6.86379e36 | −0.677142 | ||||||||
\(914\) | −2.29183e36 | −0.223026 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.21298e36 | −0.588310 | ||||||||
\(917\) | −2.02434e36 | −0.189089 | ||||||||
\(918\) | 3.43187e36 | 0.316226 | ||||||||
\(919\) | −7.70373e35 | −0.0700256 | −0.0350128 | − | 0.999387i | \(-0.511147\pi\) | ||||
−0.0350128 | + | 0.999387i | \(0.511147\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.13079e37 | −2.76955 | ||||||||
\(922\) | 1.55071e36 | 0.135330 | ||||||||
\(923\) | −2.43703e36 | −0.209817 | ||||||||
\(924\) | −3.98354e36 | −0.338353 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.13475e37 | 0.938132 | ||||||||
\(927\) | −8.69819e36 | −0.709467 | ||||||||
\(928\) | −3.56463e36 | −0.286856 | ||||||||
\(929\) | 1.66420e37 | 1.32132 | 0.660662 | − | 0.750684i | \(-0.270276\pi\) | ||||
0.660662 | + | 0.750684i | \(0.270276\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.38121e36 | 0.184046 | ||||||||
\(932\) | 1.14887e36 | 0.0876138 | ||||||||
\(933\) | −2.54021e37 | −1.91139 | ||||||||
\(934\) | −9.49954e36 | −0.705288 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.75779e35 | −0.0560777 | ||||||||
\(937\) | −9.66427e36 | −0.689325 | −0.344663 | − | 0.938727i | \(-0.612007\pi\) | ||||
−0.344663 | + | 0.938727i | \(0.612007\pi\) | |||||||
\(938\) | 6.60622e36 | 0.464962 | ||||||||
\(939\) | −6.87214e36 | −0.477279 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.33808e37 | −0.904923 | −0.452461 | − | 0.891784i | \(-0.649454\pi\) | ||||
−0.452461 | + | 0.891784i | \(0.649454\pi\) | |||||||
\(942\) | 1.34879e37 | 0.900136 | ||||||||
\(943\) | −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 | \(0.806939\pi\) | |||||||
\(948\) | 1.47262e37 | 0.907791 | ||||||||
\(949\) | −2.98981e36 | −0.181893 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.21195e37 | 0.718170 | ||||||||
\(952\) | −6.14058e36 | −0.359126 | ||||||||
\(953\) | 9.10378e36 | 0.525485 | 0.262742 | − | 0.964866i | \(-0.415373\pi\) | ||||
0.262742 | + | 0.964866i | \(0.415373\pi\) | |||||||
\(954\) | −5.35508e36 | −0.305078 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.50575e36 | 0.361055 | ||||||||
\(957\) | 2.44389e37 | 1.33870 | ||||||||
\(958\) | −9.19044e36 | −0.496898 | ||||||||
\(959\) | −9.70142e36 | −0.517729 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.01623e36 | −0.0528386 | ||||||||
\(962\) | −1.98307e36 | −0.101777 | ||||||||
\(963\) | −1.66151e37 | −0.841731 | ||||||||
\(964\) | 1.74019e37 | 0.870230 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.77249e37 | 0.863713 | ||||||||
\(967\) | 1.34794e36 | 0.0648394 | 0.0324197 | − | 0.999474i | \(-0.489679\pi\) | ||||
0.0324197 | + | 0.999474i | \(0.489679\pi\) | |||||||
\(968\) | 5.18457e36 | 0.246190 | ||||||||
\(969\) | 2.22483e37 | 1.04291 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.82504e36 | 0.174741 | 0.0873707 | − | 0.996176i | \(-0.472154\pi\) | ||||
0.0873707 | + | 0.996176i | \(0.472154\pi\) | |||||||
\(972\) | −1.56316e37 | −0.704978 | ||||||||
\(973\) | 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 | \(0.579530\pi\) | |||||||
\(978\) | 3.74277e37 | 1.56299 | ||||||||
\(979\) | −1.84776e37 | −0.761835 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.16418e37 | 1.27174 | ||||||||
\(982\) | 1.08752e37 | 0.431563 | ||||||||
\(983\) | −1.38138e37 | −0.541244 | −0.270622 | − | 0.962686i | \(-0.587229\pi\) | ||||
−0.270622 | + | 0.962686i | \(0.587229\pi\) | |||||||
\(984\) | 7.16600e36 | 0.277228 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.76722e37 | 1.42089 | ||||||||
\(987\) | 1.93447e37 | 0.720441 | ||||||||
\(988\) | −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 | ||||||||
\(993\) | 8.22853e37 | 2.84090 | ||||||||
\(994\) | −2.79338e37 | −0.952356 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.76653e37 | −0.919799 | ||||||||
\(997\) | −5.34619e37 | −1.75531 | −0.877657 | − | 0.479289i | \(-0.840894\pi\) | ||||
−0.877657 | + | 0.479289i | \(0.840894\pi\) | |||||||
\(998\) | 9.79424e36 | 0.317570 | ||||||||
\(999\) | 1.27036e37 | 0.406779 |
(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 | 50.26.a.c.1.2 | 2 | ||
5.2 | odd | 4 | 50.26.b.e.49.1 | 4 | |||
5.3 | odd | 4 | 50.26.b.e.49.4 | 4 | |||
5.4 | even | 2 | 2.26.a.b.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 18.26.a.e.1.1 | 2 | |||
20.19 | odd | 2 | 16.26.a.c.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.26.a.b.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
16.26.a.c.1.2 | 2 | 20.19 | odd | 2 | |||
18.26.a.e.1.1 | 2 | 15.14 | odd | 2 | |||
50.26.a.c.1.2 | 2 | 1.1 | even | 1 | trivial | ||
50.26.b.e.49.1 | 4 | 5.2 | odd | 4 | |||
50.26.b.e.49.4 | 4 | 5.3 | odd | 4 |