Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,18,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(18.3222087345\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{2941}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 735 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{5}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(27.6155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 256.000 | 0.707107 | ||||||||
\(3\) | −4201.44 | −0.369715 | −0.184858 | − | 0.982765i | \(-0.559182\pi\) | ||||
−0.184858 | + | 0.982765i | \(0.559182\pi\) | |||||||
\(4\) | 65536.0 | 0.500000 | ||||||||
\(5\) | −390625. | −0.447214 | ||||||||
\(6\) | −1.07557e6 | −0.261428 | ||||||||
\(7\) | 1.23193e7 | 0.807704 | 0.403852 | − | 0.914824i | \(-0.367671\pi\) | ||||
0.403852 | + | 0.914824i | \(0.367671\pi\) | |||||||
\(8\) | 1.67772e7 | 0.353553 | ||||||||
\(9\) | −1.11488e8 | −0.863311 | ||||||||
\(10\) | −1.00000e8 | −0.316228 | ||||||||
\(11\) | 1.21513e9 | 1.70916 | 0.854582 | − | 0.519317i | \(-0.173813\pi\) | ||||
0.854582 | + | 0.519317i | \(0.173813\pi\) | |||||||
\(12\) | −2.75345e8 | −0.184858 | ||||||||
\(13\) | 2.42392e9 | 0.824138 | 0.412069 | − | 0.911153i | \(-0.364806\pi\) | ||||
0.412069 | + | 0.911153i | \(0.364806\pi\) | |||||||
\(14\) | 3.15374e9 | 0.571133 | ||||||||
\(15\) | 1.64119e9 | 0.165342 | ||||||||
\(16\) | 4.29497e9 | 0.250000 | ||||||||
\(17\) | −1.73631e10 | −0.603688 | −0.301844 | − | 0.953357i | \(-0.597602\pi\) | ||||
−0.301844 | + | 0.953357i | \(0.597602\pi\) | |||||||
\(18\) | −2.85410e10 | −0.610453 | ||||||||
\(19\) | 1.15322e11 | 1.55779 | 0.778893 | − | 0.627157i | \(-0.215782\pi\) | ||||
0.778893 | + | 0.627157i | \(0.215782\pi\) | |||||||
\(20\) | −2.56000e10 | −0.223607 | ||||||||
\(21\) | −5.17587e10 | −0.298620 | ||||||||
\(22\) | 3.11072e11 | 1.20856 | ||||||||
\(23\) | 5.47905e11 | 1.45888 | 0.729439 | − | 0.684046i | \(-0.239781\pi\) | ||||
0.729439 | + | 0.684046i | \(0.239781\pi\) | |||||||
\(24\) | −7.04884e10 | −0.130714 | ||||||||
\(25\) | 1.52588e11 | 0.200000 | ||||||||
\(26\) | 6.20524e11 | 0.582754 | ||||||||
\(27\) | 1.01098e12 | 0.688894 | ||||||||
\(28\) | 8.07357e11 | 0.403852 | ||||||||
\(29\) | 2.02736e12 | 0.752573 | 0.376286 | − | 0.926503i | \(-0.377201\pi\) | ||||
0.376286 | + | 0.926503i | \(0.377201\pi\) | |||||||
\(30\) | 4.20144e11 | 0.116914 | ||||||||
\(31\) | −3.37643e12 | −0.711022 | −0.355511 | − | 0.934672i | \(-0.615693\pi\) | ||||
−0.355511 | + | 0.934672i | \(0.615693\pi\) | |||||||
\(32\) | 1.09951e12 | 0.176777 | ||||||||
\(33\) | −5.10528e12 | −0.631904 | ||||||||
\(34\) | −4.44497e12 | −0.426872 | ||||||||
\(35\) | −4.81222e12 | −0.361216 | ||||||||
\(36\) | −7.30648e12 | −0.431655 | ||||||||
\(37\) | −2.48073e13 | −1.16109 | −0.580545 | − | 0.814228i | \(-0.697160\pi\) | ||||
−0.580545 | + | 0.814228i | \(0.697160\pi\) | |||||||
\(38\) | 2.95225e13 | 1.10152 | ||||||||
\(39\) | −1.01840e13 | −0.304696 | ||||||||
\(40\) | −6.55360e12 | −0.158114 | ||||||||
\(41\) | −5.37038e13 | −1.05037 | −0.525185 | − | 0.850988i | \(-0.676004\pi\) | ||||
−0.525185 | + | 0.850988i | \(0.676004\pi\) | |||||||
\(42\) | −1.32502e13 | −0.211157 | ||||||||
\(43\) | −2.49397e13 | −0.325394 | −0.162697 | − | 0.986676i | \(-0.552019\pi\) | ||||
−0.162697 | + | 0.986676i | \(0.552019\pi\) | |||||||
\(44\) | 7.96345e13 | 0.854582 | ||||||||
\(45\) | 4.35500e13 | 0.386084 | ||||||||
\(46\) | 1.40264e14 | 1.03158 | ||||||||
\(47\) | −1.57049e14 | −0.962062 | −0.481031 | − | 0.876704i | \(-0.659738\pi\) | ||||
−0.481031 | + | 0.876704i | \(0.659738\pi\) | |||||||
\(48\) | −1.80450e13 | −0.0924288 | ||||||||
\(49\) | −8.08656e13 | −0.347614 | ||||||||
\(50\) | 3.90625e13 | 0.141421 | ||||||||
\(51\) | 7.29502e13 | 0.223193 | ||||||||
\(52\) | 1.58854e14 | 0.412069 | ||||||||
\(53\) | 5.06856e14 | 1.11825 | 0.559126 | − | 0.829083i | \(-0.311137\pi\) | ||||
0.559126 | + | 0.829083i | \(0.311137\pi\) | |||||||
\(54\) | 2.58812e14 | 0.487122 | ||||||||
\(55\) | −4.74659e14 | −0.764361 | ||||||||
\(56\) | 2.06683e14 | 0.285567 | ||||||||
\(57\) | −4.84519e14 | −0.575937 | ||||||||
\(58\) | 5.19005e14 | 0.532149 | ||||||||
\(59\) | 1.29796e15 | 1.15085 | 0.575424 | − | 0.817856i | \(-0.304837\pi\) | ||||
0.575424 | + | 0.817856i | \(0.304837\pi\) | |||||||
\(60\) | 1.07557e14 | 0.0826708 | ||||||||
\(61\) | 4.35989e14 | 0.291187 | 0.145593 | − | 0.989344i | \(-0.453491\pi\) | ||||
0.145593 | + | 0.989344i | \(0.453491\pi\) | |||||||
\(62\) | −8.64366e14 | −0.502769 | ||||||||
\(63\) | −1.37345e15 | −0.697300 | ||||||||
\(64\) | 2.81475e14 | 0.125000 | ||||||||
\(65\) | −9.46844e14 | −0.368566 | ||||||||
\(66\) | −1.30695e15 | −0.446823 | ||||||||
\(67\) | −2.50888e15 | −0.754820 | −0.377410 | − | 0.926046i | \(-0.623185\pi\) | ||||
−0.377410 | + | 0.926046i | \(0.623185\pi\) | |||||||
\(68\) | −1.13791e15 | −0.301844 | ||||||||
\(69\) | −2.30199e15 | −0.539369 | ||||||||
\(70\) | −1.23193e15 | −0.255419 | ||||||||
\(71\) | −3.06603e15 | −0.563483 | −0.281742 | − | 0.959490i | \(-0.590912\pi\) | ||||
−0.281742 | + | 0.959490i | \(0.590912\pi\) | |||||||
\(72\) | −1.87046e15 | −0.305226 | ||||||||
\(73\) | 4.56009e15 | 0.661804 | 0.330902 | − | 0.943665i | \(-0.392647\pi\) | ||||
0.330902 | + | 0.943665i | \(0.392647\pi\) | |||||||
\(74\) | −6.35068e15 | −0.821014 | ||||||||
\(75\) | −6.41088e14 | −0.0739430 | ||||||||
\(76\) | 7.55776e15 | 0.778893 | ||||||||
\(77\) | 1.49695e16 | 1.38050 | ||||||||
\(78\) | −2.60709e15 | −0.215453 | ||||||||
\(79\) | 1.40515e16 | 1.04206 | 0.521031 | − | 0.853538i | \(-0.325548\pi\) | ||||
0.521031 | + | 0.853538i | \(0.325548\pi\) | |||||||
\(80\) | −1.67772e15 | −0.111803 | ||||||||
\(81\) | 1.01500e16 | 0.608616 | ||||||||
\(82\) | −1.37482e16 | −0.742724 | ||||||||
\(83\) | 2.52434e16 | 1.23023 | 0.615113 | − | 0.788439i | \(-0.289111\pi\) | ||||
0.615113 | + | 0.788439i | \(0.289111\pi\) | |||||||
\(84\) | −3.39206e15 | −0.149310 | ||||||||
\(85\) | 6.78248e15 | 0.269978 | ||||||||
\(86\) | −6.38456e15 | −0.230088 | ||||||||
\(87\) | −8.51784e15 | −0.278237 | ||||||||
\(88\) | 2.03864e16 | 0.604281 | ||||||||
\(89\) | −6.68155e16 | −1.79913 | −0.899564 | − | 0.436790i | \(-0.856115\pi\) | ||||
−0.899564 | + | 0.436790i | \(0.856115\pi\) | |||||||
\(90\) | 1.11488e16 | 0.273003 | ||||||||
\(91\) | 2.98610e16 | 0.665660 | ||||||||
\(92\) | 3.59075e16 | 0.729439 | ||||||||
\(93\) | 1.41859e16 | 0.262876 | ||||||||
\(94\) | −4.02045e16 | −0.680281 | ||||||||
\(95\) | −4.50478e16 | −0.696663 | ||||||||
\(96\) | −4.61953e15 | −0.0653570 | ||||||||
\(97\) | 6.24209e16 | 0.808667 | 0.404334 | − | 0.914612i | \(-0.367503\pi\) | ||||
0.404334 | + | 0.914612i | \(0.367503\pi\) | |||||||
\(98\) | −2.07016e16 | −0.245800 | ||||||||
\(99\) | −1.35472e17 | −1.47554 | ||||||||
\(100\) | 1.00000e16 | 0.100000 | ||||||||
\(101\) | −1.29437e17 | −1.18940 | −0.594701 | − | 0.803947i | \(-0.702729\pi\) | ||||
−0.594701 | + | 0.803947i | \(0.702729\pi\) | |||||||
\(102\) | 1.86752e16 | 0.157821 | ||||||||
\(103\) | −1.62161e16 | −0.126134 | −0.0630668 | − | 0.998009i | \(-0.520088\pi\) | ||||
−0.0630668 | + | 0.998009i | \(0.520088\pi\) | |||||||
\(104\) | 4.06666e16 | 0.291377 | ||||||||
\(105\) | 2.02183e16 | 0.133547 | ||||||||
\(106\) | 1.29755e17 | 0.790724 | ||||||||
\(107\) | 7.54294e16 | 0.424403 | 0.212201 | − | 0.977226i | \(-0.431937\pi\) | ||||
0.212201 | + | 0.977226i | \(0.431937\pi\) | |||||||
\(108\) | 6.62559e16 | 0.344447 | ||||||||
\(109\) | −3.29149e17 | −1.58222 | −0.791112 | − | 0.611672i | \(-0.790497\pi\) | ||||
−0.791112 | + | 0.611672i | \(0.790497\pi\) | |||||||
\(110\) | −1.21513e17 | −0.540485 | ||||||||
\(111\) | 1.04227e17 | 0.429272 | ||||||||
\(112\) | 5.29110e16 | 0.201926 | ||||||||
\(113\) | 4.37906e17 | 1.54958 | 0.774791 | − | 0.632217i | \(-0.217855\pi\) | ||||
0.774791 | + | 0.632217i | \(0.217855\pi\) | |||||||
\(114\) | −1.24037e17 | −0.407249 | ||||||||
\(115\) | −2.14025e17 | −0.652430 | ||||||||
\(116\) | 1.32865e17 | 0.376286 | ||||||||
\(117\) | −2.70238e17 | −0.711487 | ||||||||
\(118\) | 3.32277e17 | 0.813772 | ||||||||
\(119\) | −2.13902e17 | −0.487602 | ||||||||
\(120\) | 2.75345e16 | 0.0584571 | ||||||||
\(121\) | 9.71086e17 | 1.92124 | ||||||||
\(122\) | 1.11613e17 | 0.205900 | ||||||||
\(123\) | 2.25633e17 | 0.388338 | ||||||||
\(124\) | −2.21278e17 | −0.355511 | ||||||||
\(125\) | −5.96046e16 | −0.0894427 | ||||||||
\(126\) | −3.51604e17 | −0.493065 | ||||||||
\(127\) | 4.26464e17 | 0.559179 | 0.279590 | − | 0.960120i | \(-0.409802\pi\) | ||||
0.279590 | + | 0.960120i | \(0.409802\pi\) | |||||||
\(128\) | 7.20576e16 | 0.0883883 | ||||||||
\(129\) | 1.04783e17 | 0.120303 | ||||||||
\(130\) | −2.42392e17 | −0.260615 | ||||||||
\(131\) | −1.99048e17 | −0.200517 | −0.100259 | − | 0.994961i | \(-0.531967\pi\) | ||||
−0.100259 | + | 0.994961i | \(0.531967\pi\) | |||||||
\(132\) | −3.34579e17 | −0.315952 | ||||||||
\(133\) | 1.42069e18 | 1.25823 | ||||||||
\(134\) | −6.42272e17 | −0.533738 | ||||||||
\(135\) | −3.94916e17 | −0.308083 | ||||||||
\(136\) | −2.91305e17 | −0.213436 | ||||||||
\(137\) | −2.15800e18 | −1.48569 | −0.742844 | − | 0.669465i | \(-0.766524\pi\) | ||||
−0.742844 | + | 0.669465i | \(0.766524\pi\) | |||||||
\(138\) | −5.89309e17 | −0.381391 | ||||||||
\(139\) | −2.69991e18 | −1.64332 | −0.821662 | − | 0.569975i | \(-0.806953\pi\) | ||||
−0.821662 | + | 0.569975i | \(0.806953\pi\) | |||||||
\(140\) | −3.15374e17 | −0.180608 | ||||||||
\(141\) | 6.59831e17 | 0.355689 | ||||||||
\(142\) | −7.84905e17 | −0.398443 | ||||||||
\(143\) | 2.94537e18 | 1.40859 | ||||||||
\(144\) | −4.78838e17 | −0.215828 | ||||||||
\(145\) | −7.91938e17 | −0.336561 | ||||||||
\(146\) | 1.16738e18 | 0.467966 | ||||||||
\(147\) | 3.39752e17 | 0.128518 | ||||||||
\(148\) | −1.62577e18 | −0.580545 | ||||||||
\(149\) | 1.38331e18 | 0.466484 | 0.233242 | − | 0.972419i | \(-0.425066\pi\) | ||||
0.233242 | + | 0.972419i | \(0.425066\pi\) | |||||||
\(150\) | −1.64119e17 | −0.0522856 | ||||||||
\(151\) | −3.60449e18 | −1.08528 | −0.542638 | − | 0.839967i | \(-0.682574\pi\) | ||||
−0.542638 | + | 0.839967i | \(0.682574\pi\) | |||||||
\(152\) | 1.93479e18 | 0.550760 | ||||||||
\(153\) | 1.93578e18 | 0.521170 | ||||||||
\(154\) | 3.83219e18 | 0.976160 | ||||||||
\(155\) | 1.31892e18 | 0.317979 | ||||||||
\(156\) | −6.67415e17 | −0.152348 | ||||||||
\(157\) | 6.76512e18 | 1.46261 | 0.731305 | − | 0.682051i | \(-0.238912\pi\) | ||||
0.731305 | + | 0.682051i | \(0.238912\pi\) | |||||||
\(158\) | 3.59719e18 | 0.736849 | ||||||||
\(159\) | −2.12952e18 | −0.413435 | ||||||||
\(160\) | −4.29497e17 | −0.0790569 | ||||||||
\(161\) | 6.74980e18 | 1.17834 | ||||||||
\(162\) | 2.59840e18 | 0.430357 | ||||||||
\(163\) | −1.06804e19 | −1.67877 | −0.839386 | − | 0.543536i | \(-0.817085\pi\) | ||||
−0.839386 | + | 0.543536i | \(0.817085\pi\) | |||||||
\(164\) | −3.51953e18 | −0.525185 | ||||||||
\(165\) | 1.99425e18 | 0.282596 | ||||||||
\(166\) | 6.46232e18 | 0.869900 | ||||||||
\(167\) | −2.93736e18 | −0.375722 | −0.187861 | − | 0.982196i | \(-0.560155\pi\) | ||||
−0.187861 | + | 0.982196i | \(0.560155\pi\) | |||||||
\(168\) | −8.68367e17 | −0.105578 | ||||||||
\(169\) | −2.77502e18 | −0.320797 | ||||||||
\(170\) | 1.73631e18 | 0.190903 | ||||||||
\(171\) | −1.28571e19 | −1.34485 | ||||||||
\(172\) | −1.63445e18 | −0.162697 | ||||||||
\(173\) | −3.04250e18 | −0.288296 | −0.144148 | − | 0.989556i | \(-0.546044\pi\) | ||||
−0.144148 | + | 0.989556i | \(0.546044\pi\) | |||||||
\(174\) | −2.18057e18 | −0.196744 | ||||||||
\(175\) | 1.87977e18 | 0.161541 | ||||||||
\(176\) | 5.21893e18 | 0.427291 | ||||||||
\(177\) | −5.45328e18 | −0.425486 | ||||||||
\(178\) | −1.71048e19 | −1.27218 | ||||||||
\(179\) | 1.82741e19 | 1.29594 | 0.647970 | − | 0.761666i | \(-0.275618\pi\) | ||||
0.647970 | + | 0.761666i | \(0.275618\pi\) | |||||||
\(180\) | 2.85410e18 | 0.193042 | ||||||||
\(181\) | −1.73562e19 | −1.11992 | −0.559959 | − | 0.828520i | \(-0.689183\pi\) | ||||
−0.559959 | + | 0.828520i | \(0.689183\pi\) | |||||||
\(182\) | 7.64441e18 | 0.470693 | ||||||||
\(183\) | −1.83178e18 | −0.107656 | ||||||||
\(184\) | 9.19232e18 | 0.515791 | ||||||||
\(185\) | 9.69037e18 | 0.519255 | ||||||||
\(186\) | 3.63158e18 | 0.185881 | ||||||||
\(187\) | −2.10984e19 | −1.03180 | ||||||||
\(188\) | −1.02924e19 | −0.481031 | ||||||||
\(189\) | 1.24546e19 | 0.556423 | ||||||||
\(190\) | −1.15322e19 | −0.492615 | ||||||||
\(191\) | −1.78696e19 | −0.730015 | −0.365007 | − | 0.931005i | \(-0.618934\pi\) | ||||
−0.365007 | + | 0.931005i | \(0.618934\pi\) | |||||||
\(192\) | −1.18260e18 | −0.0462144 | ||||||||
\(193\) | 9.94962e18 | 0.372023 | 0.186011 | − | 0.982548i | \(-0.440444\pi\) | ||||
0.186011 | + | 0.982548i | \(0.440444\pi\) | |||||||
\(194\) | 1.59797e19 | 0.571814 | ||||||||
\(195\) | 3.97811e18 | 0.136264 | ||||||||
\(196\) | −5.29961e18 | −0.173807 | ||||||||
\(197\) | 5.27173e19 | 1.65573 | 0.827866 | − | 0.560925i | \(-0.189554\pi\) | ||||
0.827866 | + | 0.560925i | \(0.189554\pi\) | |||||||
\(198\) | −3.46809e19 | −1.04336 | ||||||||
\(199\) | 2.02822e18 | 0.0584606 | 0.0292303 | − | 0.999573i | \(-0.490694\pi\) | ||||
0.0292303 | + | 0.999573i | \(0.490694\pi\) | |||||||
\(200\) | 2.56000e18 | 0.0707107 | ||||||||
\(201\) | 1.05409e19 | 0.279068 | ||||||||
\(202\) | −3.31360e19 | −0.841034 | ||||||||
\(203\) | 2.49757e19 | 0.607856 | ||||||||
\(204\) | 4.78086e18 | 0.111596 | ||||||||
\(205\) | 2.09781e19 | 0.469740 | ||||||||
\(206\) | −4.15133e18 | −0.0891899 | ||||||||
\(207\) | −6.10849e19 | −1.25946 | ||||||||
\(208\) | 1.04107e19 | 0.206034 | ||||||||
\(209\) | 1.40131e20 | 2.66251 | ||||||||
\(210\) | 5.17587e18 | 0.0944321 | ||||||||
\(211\) | −2.55219e19 | −0.447211 | −0.223606 | − | 0.974680i | \(-0.571783\pi\) | ||||
−0.223606 | + | 0.974680i | \(0.571783\pi\) | |||||||
\(212\) | 3.32173e19 | 0.559126 | ||||||||
\(213\) | 1.28817e19 | 0.208328 | ||||||||
\(214\) | 1.93099e19 | 0.300098 | ||||||||
\(215\) | 9.74207e18 | 0.145521 | ||||||||
\(216\) | 1.69615e19 | 0.243561 | ||||||||
\(217\) | −4.15952e19 | −0.574296 | ||||||||
\(218\) | −8.42622e19 | −1.11880 | ||||||||
\(219\) | −1.91589e19 | −0.244679 | ||||||||
\(220\) | −3.11072e19 | −0.382181 | ||||||||
\(221\) | −4.20869e19 | −0.497522 | ||||||||
\(222\) | 2.66820e19 | 0.303541 | ||||||||
\(223\) | −3.50141e19 | −0.383399 | −0.191700 | − | 0.981454i | \(-0.561400\pi\) | ||||
−0.191700 | + | 0.981454i | \(0.561400\pi\) | |||||||
\(224\) | 1.35452e19 | 0.142783 | ||||||||
\(225\) | −1.70117e19 | −0.172662 | ||||||||
\(226\) | 1.12104e20 | 1.09572 | ||||||||
\(227\) | −1.19657e20 | −1.12647 | −0.563233 | − | 0.826298i | \(-0.690443\pi\) | ||||
−0.563233 | + | 0.826298i | \(0.690443\pi\) | |||||||
\(228\) | −3.17535e19 | −0.287968 | ||||||||
\(229\) | −1.50518e20 | −1.31518 | −0.657591 | − | 0.753375i | \(-0.728424\pi\) | ||||
−0.657591 | + | 0.753375i | \(0.728424\pi\) | |||||||
\(230\) | −5.47905e19 | −0.461338 | ||||||||
\(231\) | −6.28934e19 | −0.510391 | ||||||||
\(232\) | 3.40135e19 | 0.266075 | ||||||||
\(233\) | 1.80295e20 | 1.35975 | 0.679875 | − | 0.733328i | \(-0.262034\pi\) | ||||
0.679875 | + | 0.733328i | \(0.262034\pi\) | |||||||
\(234\) | −6.91810e19 | −0.503097 | ||||||||
\(235\) | 6.13472e19 | 0.430247 | ||||||||
\(236\) | 8.50628e19 | 0.575424 | ||||||||
\(237\) | −5.90367e19 | −0.385266 | ||||||||
\(238\) | −5.47588e19 | −0.344786 | ||||||||
\(239\) | −1.50864e20 | −0.916650 | −0.458325 | − | 0.888785i | \(-0.651550\pi\) | ||||
−0.458325 | + | 0.888785i | \(0.651550\pi\) | |||||||
\(240\) | 7.04884e18 | 0.0413354 | ||||||||
\(241\) | −1.11959e20 | −0.633747 | −0.316874 | − | 0.948468i | \(-0.602633\pi\) | ||||
−0.316874 | + | 0.948468i | \(0.602633\pi\) | |||||||
\(242\) | 2.48598e20 | 1.35852 | ||||||||
\(243\) | −1.73203e20 | −0.913909 | ||||||||
\(244\) | 2.85730e19 | 0.145593 | ||||||||
\(245\) | 3.15881e19 | 0.155458 | ||||||||
\(246\) | 5.77621e19 | 0.274596 | ||||||||
\(247\) | 2.79532e20 | 1.28383 | ||||||||
\(248\) | −5.66471e19 | −0.251384 | ||||||||
\(249\) | −1.06059e20 | −0.454833 | ||||||||
\(250\) | −1.52588e19 | −0.0632456 | ||||||||
\(251\) | 2.00695e20 | 0.804098 | 0.402049 | − | 0.915618i | \(-0.368298\pi\) | ||||
0.402049 | + | 0.915618i | \(0.368298\pi\) | |||||||
\(252\) | −9.00107e19 | −0.348650 | ||||||||
\(253\) | 6.65774e20 | 2.49346 | ||||||||
\(254\) | 1.09175e20 | 0.395400 | ||||||||
\(255\) | −2.84962e19 | −0.0998148 | ||||||||
\(256\) | 1.84467e19 | 0.0625000 | ||||||||
\(257\) | 1.70143e20 | 0.557678 | 0.278839 | − | 0.960338i | \(-0.410050\pi\) | ||||
0.278839 | + | 0.960338i | \(0.410050\pi\) | |||||||
\(258\) | 2.68243e19 | 0.0850671 | ||||||||
\(259\) | −3.05609e20 | −0.937817 | ||||||||
\(260\) | −6.20524e19 | −0.184283 | ||||||||
\(261\) | −2.26027e20 | −0.649704 | ||||||||
\(262\) | −5.09563e19 | −0.141787 | ||||||||
\(263\) | 5.78686e20 | 1.55890 | 0.779452 | − | 0.626462i | \(-0.215498\pi\) | ||||
0.779452 | + | 0.626462i | \(0.215498\pi\) | |||||||
\(264\) | −8.56523e19 | −0.223412 | ||||||||
\(265\) | −1.97991e20 | −0.500098 | ||||||||
\(266\) | 3.63696e20 | 0.889703 | ||||||||
\(267\) | 2.80721e20 | 0.665165 | ||||||||
\(268\) | −1.64422e20 | −0.377410 | ||||||||
\(269\) | −5.13106e20 | −1.14107 | −0.570536 | − | 0.821273i | \(-0.693264\pi\) | ||||
−0.570536 | + | 0.821273i | \(0.693264\pi\) | |||||||
\(270\) | −1.01098e20 | −0.217847 | ||||||||
\(271\) | −4.64533e20 | −0.970013 | −0.485006 | − | 0.874511i | \(-0.661183\pi\) | ||||
−0.485006 | + | 0.874511i | \(0.661183\pi\) | |||||||
\(272\) | −7.45742e19 | −0.150922 | ||||||||
\(273\) | −1.25459e20 | −0.246104 | ||||||||
\(274\) | −5.52449e20 | −1.05054 | ||||||||
\(275\) | 1.85414e20 | 0.341833 | ||||||||
\(276\) | −1.50863e20 | −0.269684 | ||||||||
\(277\) | −9.72733e20 | −1.68623 | −0.843113 | − | 0.537737i | \(-0.819279\pi\) | ||||
−0.843113 | + | 0.537737i | \(0.819279\pi\) | |||||||
\(278\) | −6.91177e20 | −1.16201 | ||||||||
\(279\) | 3.76432e20 | 0.613833 | ||||||||
\(280\) | −8.07357e19 | −0.127709 | ||||||||
\(281\) | 6.76588e20 | 1.03830 | 0.519148 | − | 0.854685i | \(-0.326249\pi\) | ||||
0.519148 | + | 0.854685i | \(0.326249\pi\) | |||||||
\(282\) | 1.68917e20 | 0.251510 | ||||||||
\(283\) | 1.12202e21 | 1.62112 | 0.810560 | − | 0.585656i | \(-0.199163\pi\) | ||||
0.810560 | + | 0.585656i | \(0.199163\pi\) | |||||||
\(284\) | −2.00936e20 | −0.281742 | ||||||||
\(285\) | 1.89265e20 | 0.257567 | ||||||||
\(286\) | 7.54015e20 | 0.996021 | ||||||||
\(287\) | −6.61593e20 | −0.848389 | ||||||||
\(288\) | −1.22582e20 | −0.152613 | ||||||||
\(289\) | −5.25761e20 | −0.635561 | ||||||||
\(290\) | −2.02736e20 | −0.237984 | ||||||||
\(291\) | −2.62257e20 | −0.298977 | ||||||||
\(292\) | 2.98850e20 | 0.330902 | ||||||||
\(293\) | −3.05309e20 | −0.328371 | −0.164185 | − | 0.986429i | \(-0.552500\pi\) | ||||
−0.164185 | + | 0.986429i | \(0.552500\pi\) | |||||||
\(294\) | 8.69764e19 | 0.0908760 | ||||||||
\(295\) | −5.07014e20 | −0.514674 | ||||||||
\(296\) | −4.16198e20 | −0.410507 | ||||||||
\(297\) | 1.22847e21 | 1.17743 | ||||||||
\(298\) | 3.54128e20 | 0.329854 | ||||||||
\(299\) | 1.32808e21 | 1.20232 | ||||||||
\(300\) | −4.20144e19 | −0.0369715 | ||||||||
\(301\) | −3.07239e20 | −0.262822 | ||||||||
\(302\) | −9.22750e20 | −0.767406 | ||||||||
\(303\) | 5.43823e20 | 0.439740 | ||||||||
\(304\) | 4.95305e20 | 0.389446 | ||||||||
\(305\) | −1.70308e20 | −0.130223 | ||||||||
\(306\) | 4.95561e20 | 0.368523 | ||||||||
\(307\) | −3.66561e20 | −0.265137 | −0.132569 | − | 0.991174i | \(-0.542322\pi\) | ||||
−0.132569 | + | 0.991174i | \(0.542322\pi\) | |||||||
\(308\) | 9.81041e20 | 0.690250 | ||||||||
\(309\) | 6.81310e19 | 0.0466335 | ||||||||
\(310\) | 3.37643e20 | 0.224845 | ||||||||
\(311\) | −3.12925e19 | −0.0202758 | −0.0101379 | − | 0.999949i | \(-0.503227\pi\) | ||||
−0.0101379 | + | 0.999949i | \(0.503227\pi\) | |||||||
\(312\) | −1.70858e20 | −0.107726 | ||||||||
\(313\) | −2.54969e21 | −1.56444 | −0.782222 | − | 0.623000i | \(-0.785914\pi\) | ||||
−0.782222 | + | 0.623000i | \(0.785914\pi\) | |||||||
\(314\) | 1.73187e21 | 1.03422 | ||||||||
\(315\) | 5.36506e20 | 0.311842 | ||||||||
\(316\) | 9.20882e20 | 0.521031 | ||||||||
\(317\) | −1.42704e21 | −0.786018 | −0.393009 | − | 0.919535i | \(-0.628566\pi\) | ||||
−0.393009 | + | 0.919535i | \(0.628566\pi\) | |||||||
\(318\) | −5.45158e20 | −0.292343 | ||||||||
\(319\) | 2.46350e21 | 1.28627 | ||||||||
\(320\) | −1.09951e20 | −0.0559017 | ||||||||
\(321\) | −3.16912e20 | −0.156908 | ||||||||
\(322\) | 1.72795e21 | 0.833213 | ||||||||
\(323\) | −2.00236e21 | −0.940416 | ||||||||
\(324\) | 6.65191e20 | 0.304308 | ||||||||
\(325\) | 3.69861e20 | 0.164828 | ||||||||
\(326\) | −2.73417e21 | −1.18707 | ||||||||
\(327\) | 1.38290e21 | 0.584972 | ||||||||
\(328\) | −9.01001e20 | −0.371362 | ||||||||
\(329\) | −1.93473e21 | −0.777062 | ||||||||
\(330\) | 5.10528e20 | 0.199825 | ||||||||
\(331\) | −1.65282e20 | −0.0630503 | −0.0315251 | − | 0.999503i | \(-0.510036\pi\) | ||||
−0.0315251 | + | 0.999503i | \(0.510036\pi\) | |||||||
\(332\) | 1.65435e21 | 0.615113 | ||||||||
\(333\) | 2.76572e21 | 1.00238 | ||||||||
\(334\) | −7.51963e20 | −0.265676 | ||||||||
\(335\) | 9.80029e20 | 0.337566 | ||||||||
\(336\) | −2.22302e20 | −0.0746551 | ||||||||
\(337\) | −1.56766e21 | −0.513332 | −0.256666 | − | 0.966500i | \(-0.582624\pi\) | ||||
−0.256666 | + | 0.966500i | \(0.582624\pi\) | |||||||
\(338\) | −7.10406e20 | −0.226837 | ||||||||
\(339\) | −1.83984e21 | −0.572904 | ||||||||
\(340\) | 4.44497e20 | 0.134989 | ||||||||
\(341\) | −4.10279e21 | −1.21525 | ||||||||
\(342\) | −3.29141e21 | −0.950954 | ||||||||
\(343\) | −3.86205e21 | −1.08847 | ||||||||
\(344\) | −4.18419e20 | −0.115044 | ||||||||
\(345\) | 8.99214e20 | 0.241213 | ||||||||
\(346\) | −7.78881e20 | −0.203856 | ||||||||
\(347\) | 1.62532e21 | 0.415086 | 0.207543 | − | 0.978226i | \(-0.433453\pi\) | ||||
0.207543 | + | 0.978226i | \(0.433453\pi\) | |||||||
\(348\) | −5.58225e20 | −0.139119 | ||||||||
\(349\) | 3.60380e21 | 0.876486 | 0.438243 | − | 0.898857i | \(-0.355601\pi\) | ||||
0.438243 | + | 0.898857i | \(0.355601\pi\) | |||||||
\(350\) | 4.81222e20 | 0.114227 | ||||||||
\(351\) | 2.45055e21 | 0.567744 | ||||||||
\(352\) | 1.33605e21 | 0.302140 | ||||||||
\(353\) | −7.99561e21 | −1.76509 | −0.882544 | − | 0.470230i | \(-0.844171\pi\) | ||||
−0.882544 | + | 0.470230i | \(0.844171\pi\) | |||||||
\(354\) | −1.39604e21 | −0.300864 | ||||||||
\(355\) | 1.19767e21 | 0.251997 | ||||||||
\(356\) | −4.37882e21 | −0.899564 | ||||||||
\(357\) | 8.98694e20 | 0.180274 | ||||||||
\(358\) | 4.67817e21 | 0.916368 | ||||||||
\(359\) | 7.69221e21 | 1.47146 | 0.735730 | − | 0.677275i | \(-0.236839\pi\) | ||||
0.735730 | + | 0.677275i | \(0.236839\pi\) | |||||||
\(360\) | 7.30648e20 | 0.136501 | ||||||||
\(361\) | 7.81884e21 | 1.42669 | ||||||||
\(362\) | −4.44318e21 | −0.791902 | ||||||||
\(363\) | −4.07995e21 | −0.710312 | ||||||||
\(364\) | 1.95697e21 | 0.332830 | ||||||||
\(365\) | −1.78128e21 | −0.295968 | ||||||||
\(366\) | −4.68936e20 | −0.0761244 | ||||||||
\(367\) | 4.40761e21 | 0.699104 | 0.349552 | − | 0.936917i | \(-0.386334\pi\) | ||||
0.349552 | + | 0.936917i | \(0.386334\pi\) | |||||||
\(368\) | 2.35323e21 | 0.364719 | ||||||||
\(369\) | 5.98734e21 | 0.906796 | ||||||||
\(370\) | 2.48073e21 | 0.367169 | ||||||||
\(371\) | 6.24411e21 | 0.903217 | ||||||||
\(372\) | 9.29684e20 | 0.131438 | ||||||||
\(373\) | 7.73260e21 | 1.06856 | 0.534282 | − | 0.845306i | \(-0.320582\pi\) | ||||
0.534282 | + | 0.845306i | \(0.320582\pi\) | |||||||
\(374\) | −5.40120e21 | −0.729594 | ||||||||
\(375\) | 2.50425e20 | 0.0330683 | ||||||||
\(376\) | −2.63484e21 | −0.340140 | ||||||||
\(377\) | 4.91417e21 | 0.620224 | ||||||||
\(378\) | 3.18838e21 | 0.393450 | ||||||||
\(379\) | −6.86035e21 | −0.827776 | −0.413888 | − | 0.910328i | \(-0.635829\pi\) | ||||
−0.413888 | + | 0.910328i | \(0.635829\pi\) | |||||||
\(380\) | −2.95225e21 | −0.348331 | ||||||||
\(381\) | −1.79176e21 | −0.206737 | ||||||||
\(382\) | −4.57462e21 | −0.516198 | ||||||||
\(383\) | −4.86654e21 | −0.537070 | −0.268535 | − | 0.963270i | \(-0.586539\pi\) | ||||
−0.268535 | + | 0.963270i | \(0.586539\pi\) | |||||||
\(384\) | −3.02745e20 | −0.0326785 | ||||||||
\(385\) | −5.84746e21 | −0.617378 | ||||||||
\(386\) | 2.54710e21 | 0.263060 | ||||||||
\(387\) | 2.78048e21 | 0.280916 | ||||||||
\(388\) | 4.09081e21 | 0.404334 | ||||||||
\(389\) | −9.98351e21 | −0.965410 | −0.482705 | − | 0.875783i | \(-0.660346\pi\) | ||||
−0.482705 | + | 0.875783i | \(0.660346\pi\) | |||||||
\(390\) | 1.01840e21 | 0.0963534 | ||||||||
\(391\) | −9.51336e21 | −0.880707 | ||||||||
\(392\) | −1.35670e21 | −0.122900 | ||||||||
\(393\) | 8.36288e20 | 0.0741343 | ||||||||
\(394\) | 1.34956e22 | 1.17078 | ||||||||
\(395\) | −5.48888e21 | −0.466024 | ||||||||
\(396\) | −8.87830e21 | −0.737770 | ||||||||
\(397\) | −5.08435e21 | −0.413539 | −0.206769 | − | 0.978390i | \(-0.566295\pi\) | ||||
−0.206769 | + | 0.978390i | \(0.566295\pi\) | |||||||
\(398\) | 5.19224e20 | 0.0413379 | ||||||||
\(399\) | −5.96893e21 | −0.465187 | ||||||||
\(400\) | 6.55360e20 | 0.0500000 | ||||||||
\(401\) | 1.05661e22 | 0.789198 | 0.394599 | − | 0.918853i | \(-0.370883\pi\) | ||||
0.394599 | + | 0.918853i | \(0.370883\pi\) | |||||||
\(402\) | 2.69847e21 | 0.197331 | ||||||||
\(403\) | −8.18420e21 | −0.585980 | ||||||||
\(404\) | −8.48281e21 | −0.594701 | ||||||||
\(405\) | −3.96484e21 | −0.272181 | ||||||||
\(406\) | 6.39377e21 | 0.429819 | ||||||||
\(407\) | −3.01441e22 | −1.98449 | ||||||||
\(408\) | 1.22390e21 | 0.0789105 | ||||||||
\(409\) | 1.73559e21 | 0.109597 | 0.0547985 | − | 0.998497i | \(-0.482548\pi\) | ||||
0.0547985 | + | 0.998497i | \(0.482548\pi\) | |||||||
\(410\) | 5.37038e21 | 0.332156 | ||||||||
\(411\) | 9.06672e21 | 0.549281 | ||||||||
\(412\) | −1.06274e21 | −0.0630668 | ||||||||
\(413\) | 1.59899e22 | 0.929544 | ||||||||
\(414\) | −1.56377e22 | −0.890576 | ||||||||
\(415\) | −9.86071e21 | −0.550173 | ||||||||
\(416\) | 2.66513e21 | 0.145688 | ||||||||
\(417\) | 1.13435e22 | 0.607562 | ||||||||
\(418\) | 3.58736e22 | 1.88268 | ||||||||
\(419\) | −1.13030e22 | −0.581264 | −0.290632 | − | 0.956835i | \(-0.593866\pi\) | ||||
−0.290632 | + | 0.956835i | \(0.593866\pi\) | |||||||
\(420\) | 1.32502e21 | 0.0667736 | ||||||||
\(421\) | −1.06234e21 | −0.0524643 | −0.0262321 | − | 0.999656i | \(-0.508351\pi\) | ||||
−0.0262321 | + | 0.999656i | \(0.508351\pi\) | |||||||
\(422\) | −6.53361e21 | −0.316226 | ||||||||
\(423\) | 1.75091e22 | 0.830559 | ||||||||
\(424\) | 8.50363e21 | 0.395362 | ||||||||
\(425\) | −2.64941e21 | −0.120738 | ||||||||
\(426\) | 3.29773e21 | 0.147310 | ||||||||
\(427\) | 5.37108e21 | 0.235193 | ||||||||
\(428\) | 4.94334e21 | 0.212201 | ||||||||
\(429\) | −1.23748e22 | −0.520776 | ||||||||
\(430\) | 2.49397e21 | 0.102899 | ||||||||
\(431\) | 3.61567e22 | 1.46262 | 0.731310 | − | 0.682045i | \(-0.238909\pi\) | ||||
0.731310 | + | 0.682045i | \(0.238909\pi\) | |||||||
\(432\) | 4.34215e21 | 0.172224 | ||||||||
\(433\) | −2.15292e22 | −0.837298 | −0.418649 | − | 0.908148i | \(-0.637496\pi\) | ||||
−0.418649 | + | 0.908148i | \(0.637496\pi\) | |||||||
\(434\) | −1.06484e22 | −0.406088 | ||||||||
\(435\) | 3.32728e21 | 0.124432 | ||||||||
\(436\) | −2.15711e22 | −0.791112 | ||||||||
\(437\) | 6.31857e22 | 2.27262 | ||||||||
\(438\) | −4.90469e21 | −0.173014 | ||||||||
\(439\) | −2.88882e22 | −0.999476 | −0.499738 | − | 0.866177i | \(-0.666570\pi\) | ||||
−0.499738 | + | 0.866177i | \(0.666570\pi\) | |||||||
\(440\) | −7.96345e21 | −0.270243 | ||||||||
\(441\) | 9.01555e21 | 0.300099 | ||||||||
\(442\) | −1.07742e22 | −0.351801 | ||||||||
\(443\) | 3.43476e21 | 0.110018 | 0.0550091 | − | 0.998486i | \(-0.482481\pi\) | ||||
0.0550091 | + | 0.998486i | \(0.482481\pi\) | |||||||
\(444\) | 6.83059e21 | 0.214636 | ||||||||
\(445\) | 2.60998e22 | 0.804594 | ||||||||
\(446\) | −8.96360e21 | −0.271104 | ||||||||
\(447\) | −5.81190e21 | −0.172466 | ||||||||
\(448\) | 3.46757e21 | 0.100963 | ||||||||
\(449\) | 3.08875e22 | 0.882447 | 0.441223 | − | 0.897397i | \(-0.354545\pi\) | ||||
0.441223 | + | 0.897397i | \(0.354545\pi\) | |||||||
\(450\) | −4.35500e21 | −0.122091 | ||||||||
\(451\) | −6.52570e22 | −1.79526 | ||||||||
\(452\) | 2.86986e22 | 0.774791 | ||||||||
\(453\) | 1.51440e22 | 0.401243 | ||||||||
\(454\) | −3.06322e22 | −0.796532 | ||||||||
\(455\) | −1.16644e22 | −0.297692 | ||||||||
\(456\) | −8.12888e21 | −0.203624 | ||||||||
\(457\) | −3.83285e22 | −0.942398 | −0.471199 | − | 0.882027i | \(-0.656179\pi\) | ||||
−0.471199 | + | 0.882027i | \(0.656179\pi\) | |||||||
\(458\) | −3.85325e22 | −0.929974 | ||||||||
\(459\) | −1.75539e22 | −0.415877 | ||||||||
\(460\) | −1.40264e22 | −0.326215 | ||||||||
\(461\) | 6.80144e22 | 1.55290 | 0.776449 | − | 0.630180i | \(-0.217019\pi\) | ||||
0.776449 | + | 0.630180i | \(0.217019\pi\) | |||||||
\(462\) | −1.61007e22 | −0.360901 | ||||||||
\(463\) | 4.57341e21 | 0.100647 | 0.0503236 | − | 0.998733i | \(-0.483975\pi\) | ||||
0.0503236 | + | 0.998733i | \(0.483975\pi\) | |||||||
\(464\) | 8.70746e21 | 0.188143 | ||||||||
\(465\) | −5.54135e21 | −0.117562 | ||||||||
\(466\) | 4.61556e22 | 0.961489 | ||||||||
\(467\) | 4.97766e22 | 1.01820 | 0.509099 | − | 0.860708i | \(-0.329979\pi\) | ||||
0.509099 | + | 0.860708i | \(0.329979\pi\) | |||||||
\(468\) | −1.77103e22 | −0.355744 | ||||||||
\(469\) | −3.09076e22 | −0.609671 | ||||||||
\(470\) | 1.57049e22 | 0.304231 | ||||||||
\(471\) | −2.84232e22 | −0.540749 | ||||||||
\(472\) | 2.17761e22 | 0.406886 | ||||||||
\(473\) | −3.03049e22 | −0.556151 | ||||||||
\(474\) | −1.51134e22 | −0.272424 | ||||||||
\(475\) | 1.75968e22 | 0.311557 | ||||||||
\(476\) | −1.40183e22 | −0.243801 | ||||||||
\(477\) | −5.65084e22 | −0.965399 | ||||||||
\(478\) | −3.86212e22 | −0.648169 | ||||||||
\(479\) | 9.35494e22 | 1.54237 | 0.771186 | − | 0.636610i | \(-0.219664\pi\) | ||||
0.771186 | + | 0.636610i | \(0.219664\pi\) | |||||||
\(480\) | 1.80450e21 | 0.0292285 | ||||||||
\(481\) | −6.01310e22 | −0.956898 | ||||||||
\(482\) | −2.86616e22 | −0.448127 | ||||||||
\(483\) | −2.83589e22 | −0.435651 | ||||||||
\(484\) | 6.36411e22 | 0.960621 | ||||||||
\(485\) | −2.43831e22 | −0.361647 | ||||||||
\(486\) | −4.43400e22 | −0.646231 | ||||||||
\(487\) | −1.63934e22 | −0.234786 | −0.117393 | − | 0.993086i | \(-0.537454\pi\) | ||||
−0.117393 | + | 0.993086i | \(0.537454\pi\) | |||||||
\(488\) | 7.31468e21 | 0.102950 | ||||||||
\(489\) | 4.48729e22 | 0.620667 | ||||||||
\(490\) | 8.08656e21 | 0.109925 | ||||||||
\(491\) | −2.62500e22 | −0.350700 | −0.175350 | − | 0.984506i | \(-0.556106\pi\) | ||||
−0.175350 | + | 0.984506i | \(0.556106\pi\) | |||||||
\(492\) | 1.47871e22 | 0.194169 | ||||||||
\(493\) | −3.52014e22 | −0.454319 | ||||||||
\(494\) | 7.15602e22 | 0.907805 | ||||||||
\(495\) | 5.29188e22 | 0.659881 | ||||||||
\(496\) | −1.45017e22 | −0.177756 | ||||||||
\(497\) | −3.77714e22 | −0.455128 | ||||||||
\(498\) | −2.71510e22 | −0.321615 | ||||||||
\(499\) | 1.91458e22 | 0.222956 | 0.111478 | − | 0.993767i | \(-0.464442\pi\) | ||||
0.111478 | + | 0.993767i | \(0.464442\pi\) | |||||||
\(500\) | −3.90625e21 | −0.0447214 | ||||||||
\(501\) | 1.23411e22 | 0.138910 | ||||||||
\(502\) | 5.13778e22 | 0.568583 | ||||||||
\(503\) | 3.67210e22 | 0.399564 | 0.199782 | − | 0.979840i | \(-0.435977\pi\) | ||||
0.199782 | + | 0.979840i | \(0.435977\pi\) | |||||||
\(504\) | −2.30427e22 | −0.246533 | ||||||||
\(505\) | 5.05615e22 | 0.531916 | ||||||||
\(506\) | 1.70438e23 | 1.76314 | ||||||||
\(507\) | 1.16591e22 | 0.118603 | ||||||||
\(508\) | 2.79488e22 | 0.279590 | ||||||||
\(509\) | 6.75737e22 | 0.664778 | 0.332389 | − | 0.943142i | \(-0.392145\pi\) | ||||
0.332389 | + | 0.943142i | \(0.392145\pi\) | |||||||
\(510\) | −7.29502e21 | −0.0705797 | ||||||||
\(511\) | 5.61771e22 | 0.534542 | ||||||||
\(512\) | 4.72237e21 | 0.0441942 | ||||||||
\(513\) | 1.16589e23 | 1.07315 | ||||||||
\(514\) | 4.35567e22 | 0.394338 | ||||||||
\(515\) | 6.33442e21 | 0.0564086 | ||||||||
\(516\) | 6.86703e21 | 0.0601515 | ||||||||
\(517\) | −1.90834e23 | −1.64432 | ||||||||
\(518\) | −7.82359e22 | −0.663137 | ||||||||
\(519\) | 1.27829e22 | 0.106588 | ||||||||
\(520\) | −1.58854e22 | −0.130308 | ||||||||
\(521\) | −2.39219e23 | −1.93052 | −0.965262 | − | 0.261284i | \(-0.915854\pi\) | ||||
−0.965262 | + | 0.261284i | \(0.915854\pi\) | |||||||
\(522\) | −5.78629e22 | −0.459410 | ||||||||
\(523\) | −1.23467e22 | −0.0964465 | −0.0482233 | − | 0.998837i | \(-0.515356\pi\) | ||||
−0.0482233 | + | 0.998837i | \(0.515356\pi\) | |||||||
\(524\) | −1.30448e22 | −0.100259 | ||||||||
\(525\) | −7.89776e21 | −0.0597241 | ||||||||
\(526\) | 1.48144e23 | 1.10231 | ||||||||
\(527\) | 5.86254e22 | 0.429236 | ||||||||
\(528\) | −2.19270e22 | −0.157976 | ||||||||
\(529\) | 1.59150e23 | 1.12832 | ||||||||
\(530\) | −5.06856e22 | −0.353622 | ||||||||
\(531\) | −1.44707e23 | −0.993539 | ||||||||
\(532\) | 9.31063e22 | 0.629115 | ||||||||
\(533\) | −1.30174e23 | −0.865650 | ||||||||
\(534\) | 7.18646e22 | 0.470342 | ||||||||
\(535\) | −2.94646e22 | −0.189799 | ||||||||
\(536\) | −4.20919e22 | −0.266869 | ||||||||
\(537\) | −7.67774e22 | −0.479128 | ||||||||
\(538\) | −1.31355e23 | −0.806859 | ||||||||
\(539\) | −9.82619e22 | −0.594129 | ||||||||
\(540\) | −2.58812e22 | −0.154041 | ||||||||
\(541\) | −2.47773e23 | −1.45170 | −0.725851 | − | 0.687851i | \(-0.758554\pi\) | ||||
−0.725851 | + | 0.687851i | \(0.758554\pi\) | |||||||
\(542\) | −1.18920e23 | −0.685903 | ||||||||
\(543\) | 7.29209e22 | 0.414051 | ||||||||
\(544\) | −1.90910e22 | −0.106718 | ||||||||
\(545\) | 1.28574e23 | 0.707592 | ||||||||
\(546\) | −3.21175e22 | −0.174022 | ||||||||
\(547\) | 5.48101e22 | 0.292394 | 0.146197 | − | 0.989256i | \(-0.453297\pi\) | ||||
0.146197 | + | 0.989256i | \(0.453297\pi\) | |||||||
\(548\) | −1.41427e23 | −0.742844 | ||||||||
\(549\) | −4.86076e22 | −0.251385 | ||||||||
\(550\) | 4.74659e22 | 0.241712 | ||||||||
\(551\) | 2.33800e23 | 1.17235 | ||||||||
\(552\) | −3.86210e22 | −0.190696 | ||||||||
\(553\) | 1.73105e23 | 0.841678 | ||||||||
\(554\) | −2.49020e23 | −1.19234 | ||||||||
\(555\) | −4.07135e22 | −0.191976 | ||||||||
\(556\) | −1.76941e23 | −0.821662 | ||||||||
\(557\) | 2.57560e23 | 1.17790 | 0.588952 | − | 0.808168i | \(-0.299541\pi\) | ||||
0.588952 | + | 0.808168i | \(0.299541\pi\) | |||||||
\(558\) | 9.63665e22 | 0.434046 | ||||||||
\(559\) | −6.04519e22 | −0.268169 | ||||||||
\(560\) | −2.06683e22 | −0.0903041 | ||||||||
\(561\) | 8.86437e22 | 0.381473 | ||||||||
\(562\) | 1.73207e23 | 0.734186 | ||||||||
\(563\) | 6.37462e22 | 0.266154 | 0.133077 | − | 0.991106i | \(-0.457514\pi\) | ||||
0.133077 | + | 0.991106i | \(0.457514\pi\) | |||||||
\(564\) | 4.32427e22 | 0.177844 | ||||||||
\(565\) | −1.71057e23 | −0.692994 | ||||||||
\(566\) | 2.87237e23 | 1.14630 | ||||||||
\(567\) | 1.25041e23 | 0.491582 | ||||||||
\(568\) | −5.14395e22 | −0.199221 | ||||||||
\(569\) | −2.97128e23 | −1.13368 | −0.566839 | − | 0.823829i | \(-0.691834\pi\) | ||||
−0.566839 | + | 0.823829i | \(0.691834\pi\) | |||||||
\(570\) | 4.84519e22 | 0.182127 | ||||||||
\(571\) | 3.65472e23 | 1.35347 | 0.676733 | − | 0.736228i | \(-0.263395\pi\) | ||||
0.676733 | + | 0.736228i | \(0.263395\pi\) | |||||||
\(572\) | 1.93028e23 | 0.704293 | ||||||||
\(573\) | 7.50781e22 | 0.269898 | ||||||||
\(574\) | −1.69368e23 | −0.599901 | ||||||||
\(575\) | 8.36037e22 | 0.291775 | ||||||||
\(576\) | −3.13811e22 | −0.107914 | ||||||||
\(577\) | 1.73713e23 | 0.588623 | 0.294312 | − | 0.955710i | \(-0.404910\pi\) | ||||
0.294312 | + | 0.955710i | \(0.404910\pi\) | |||||||
\(578\) | −1.34595e23 | −0.449409 | ||||||||
\(579\) | −4.18027e22 | −0.137542 | ||||||||
\(580\) | −5.19005e22 | −0.168280 | ||||||||
\(581\) | 3.10981e23 | 0.993658 | ||||||||
\(582\) | −6.71379e22 | −0.211408 | ||||||||
\(583\) | 6.15894e23 | 1.91128 | ||||||||
\(584\) | 7.65056e22 | 0.233983 | ||||||||
\(585\) | 1.05562e23 | 0.318187 | ||||||||
\(586\) | −7.81590e22 | −0.232193 | ||||||||
\(587\) | −4.20741e23 | −1.23194 | −0.615972 | − | 0.787768i | \(-0.711237\pi\) | ||||
−0.615972 | + | 0.787768i | \(0.711237\pi\) | |||||||
\(588\) | 2.22660e22 | 0.0642590 | ||||||||
\(589\) | −3.89377e23 | −1.10762 | ||||||||
\(590\) | −1.29796e23 | −0.363930 | ||||||||
\(591\) | −2.21488e23 | −0.612149 | ||||||||
\(592\) | −1.06547e23 | −0.290272 | ||||||||
\(593\) | −4.26727e23 | −1.14600 | −0.573000 | − | 0.819555i | \(-0.694221\pi\) | ||||
−0.573000 | + | 0.819555i | \(0.694221\pi\) | |||||||
\(594\) | 3.14489e23 | 0.832571 | ||||||||
\(595\) | 8.35553e22 | 0.218062 | ||||||||
\(596\) | 9.06568e22 | 0.233242 | ||||||||
\(597\) | −8.52143e21 | −0.0216138 | ||||||||
\(598\) | 3.39988e23 | 0.850166 | ||||||||
\(599\) | −1.66085e23 | −0.409451 | −0.204726 | − | 0.978819i | \(-0.565630\pi\) | ||||
−0.204726 | + | 0.978819i | \(0.565630\pi\) | |||||||
\(600\) | −1.07557e22 | −0.0261428 | ||||||||
\(601\) | −3.30613e23 | −0.792294 | −0.396147 | − | 0.918187i | \(-0.629653\pi\) | ||||
−0.396147 | + | 0.918187i | \(0.629653\pi\) | |||||||
\(602\) | −7.86533e22 | −0.185843 | ||||||||
\(603\) | 2.79710e23 | 0.651644 | ||||||||
\(604\) | −2.36224e23 | −0.542638 | ||||||||
\(605\) | −3.79330e23 | −0.859205 | ||||||||
\(606\) | 1.39219e23 | 0.310943 | ||||||||
\(607\) | 3.28253e23 | 0.722944 | 0.361472 | − | 0.932383i | \(-0.382274\pi\) | ||||
0.361472 | + | 0.932383i | \(0.382274\pi\) | |||||||
\(608\) | 1.26798e23 | 0.275380 | ||||||||
\(609\) | −1.04934e23 | −0.224734 | ||||||||
\(610\) | −4.35989e22 | −0.0920814 | ||||||||
\(611\) | −3.80674e23 | −0.792872 | ||||||||
\(612\) | 1.26864e23 | 0.260585 | ||||||||
\(613\) | 4.83476e23 | 0.979401 | 0.489701 | − | 0.871891i | \(-0.337106\pi\) | ||||
0.489701 | + | 0.871891i | \(0.337106\pi\) | |||||||
\(614\) | −9.38397e22 | −0.187480 | ||||||||
\(615\) | −8.81380e22 | −0.173670 | ||||||||
\(616\) | 2.51147e23 | 0.488080 | ||||||||
\(617\) | −4.09399e23 | −0.784736 | −0.392368 | − | 0.919808i | \(-0.628344\pi\) | ||||
−0.392368 | + | 0.919808i | \(0.628344\pi\) | |||||||
\(618\) | 1.74415e22 | 0.0329748 | ||||||||
\(619\) | −5.33004e23 | −0.993940 | −0.496970 | − | 0.867768i | \(-0.665554\pi\) | ||||
−0.496970 | + | 0.867768i | \(0.665554\pi\) | |||||||
\(620\) | 8.64366e22 | 0.158989 | ||||||||
\(621\) | 5.53924e23 | 1.00501 | ||||||||
\(622\) | −8.01089e21 | −0.0143371 | ||||||||
\(623\) | −8.23119e23 | −1.45316 | ||||||||
\(624\) | −4.37397e22 | −0.0761741 | ||||||||
\(625\) | 2.32831e22 | 0.0400000 | ||||||||
\(626\) | −6.52720e23 | −1.10623 | ||||||||
\(627\) | −5.88752e23 | −0.984370 | ||||||||
\(628\) | 4.43359e23 | 0.731305 | ||||||||
\(629\) | 4.30734e23 | 0.700936 | ||||||||
\(630\) | 1.37345e23 | 0.220506 | ||||||||
\(631\) | −2.81823e22 | −0.0446402 | −0.0223201 | − | 0.999751i | \(-0.507105\pi\) | ||||
−0.0223201 | + | 0.999751i | \(0.507105\pi\) | |||||||
\(632\) | 2.35746e23 | 0.368425 | ||||||||
\(633\) | 1.07229e23 | 0.165341 | ||||||||
\(634\) | −3.65322e23 | −0.555799 | ||||||||
\(635\) | −1.66588e23 | −0.250073 | ||||||||
\(636\) | −1.39560e23 | −0.206717 | ||||||||
\(637\) | −1.96012e23 | −0.286482 | ||||||||
\(638\) | 6.30657e23 | 0.909530 | ||||||||
\(639\) | 3.41826e23 | 0.486461 | ||||||||
\(640\) | −2.81475e22 | −0.0395285 | ||||||||
\(641\) | 5.47552e23 | 0.758809 | 0.379404 | − | 0.925231i | \(-0.376129\pi\) | ||||
0.379404 | + | 0.925231i | \(0.376129\pi\) | |||||||
\(642\) | −8.11294e22 | −0.110951 | ||||||||
\(643\) | −1.13082e24 | −1.52616 | −0.763079 | − | 0.646305i | \(-0.776313\pi\) | ||||
−0.763079 | + | 0.646305i | \(0.776313\pi\) | |||||||
\(644\) | 4.42355e23 | 0.589171 | ||||||||
\(645\) | −4.09307e22 | −0.0538011 | ||||||||
\(646\) | −5.12604e23 | −0.664975 | ||||||||
\(647\) | 9.71467e23 | 1.24377 | 0.621887 | − | 0.783107i | \(-0.286366\pi\) | ||||
0.621887 | + | 0.783107i | \(0.286366\pi\) | |||||||
\(648\) | 1.70289e23 | 0.215178 | ||||||||
\(649\) | 1.57718e24 | 1.96699 | ||||||||
\(650\) | 9.46844e22 | 0.116551 | ||||||||
\(651\) | 1.74760e23 | 0.212326 | ||||||||
\(652\) | −6.99949e23 | −0.839386 | ||||||||
\(653\) | 8.71125e22 | 0.103114 | 0.0515571 | − | 0.998670i | \(-0.483582\pi\) | ||||
0.0515571 | + | 0.998670i | \(0.483582\pi\) | |||||||
\(654\) | 3.54023e23 | 0.413638 | ||||||||
\(655\) | 7.77532e22 | 0.0896741 | ||||||||
\(656\) | −2.30656e23 | −0.262593 | ||||||||
\(657\) | −5.08396e23 | −0.571342 | ||||||||
\(658\) | −4.95291e23 | −0.549466 | ||||||||
\(659\) | −5.51481e23 | −0.603955 | −0.301978 | − | 0.953315i | \(-0.597647\pi\) | ||||
−0.301978 | + | 0.953315i | \(0.597647\pi\) | |||||||
\(660\) | 1.30695e23 | 0.141298 | ||||||||
\(661\) | 1.72983e23 | 0.184626 | 0.0923128 | − | 0.995730i | \(-0.470574\pi\) | ||||
0.0923128 | + | 0.995730i | \(0.470574\pi\) | |||||||
\(662\) | −4.23121e22 | −0.0445833 | ||||||||
\(663\) | 1.76825e23 | 0.183942 | ||||||||
\(664\) | 4.23514e23 | 0.434950 | ||||||||
\(665\) | −5.54957e23 | −0.562697 | ||||||||
\(666\) | 7.08025e23 | 0.708790 | ||||||||
\(667\) | 1.11080e24 | 1.09791 | ||||||||
\(668\) | −1.92503e23 | −0.187861 | ||||||||
\(669\) | 1.47109e23 | 0.141748 | ||||||||
\(670\) | 2.50888e23 | 0.238695 | ||||||||
\(671\) | 5.29782e23 | 0.497686 | ||||||||
\(672\) | −5.69093e22 | −0.0527891 | ||||||||
\(673\) | 9.31240e23 | 0.852970 | 0.426485 | − | 0.904495i | \(-0.359752\pi\) | ||||
0.426485 | + | 0.904495i | \(0.359752\pi\) | |||||||
\(674\) | −4.01321e23 | −0.362981 | ||||||||
\(675\) | 1.54264e23 | 0.137779 | ||||||||
\(676\) | −1.81864e23 | −0.160398 | ||||||||
\(677\) | −8.38487e21 | −0.00730286 | −0.00365143 | − | 0.999993i | \(-0.501162\pi\) | ||||
−0.00365143 | + | 0.999993i | \(0.501162\pi\) | |||||||
\(678\) | −4.70998e23 | −0.405104 | ||||||||
\(679\) | 7.68981e23 | 0.653164 | ||||||||
\(680\) | 1.13791e23 | 0.0954515 | ||||||||
\(681\) | 5.02732e23 | 0.416472 | ||||||||
\(682\) | −1.05031e24 | −0.859314 | ||||||||
\(683\) | −2.03510e24 | −1.64440 | −0.822202 | − | 0.569195i | \(-0.807255\pi\) | ||||
−0.822202 | + | 0.569195i | \(0.807255\pi\) | |||||||
\(684\) | −8.42600e23 | −0.672426 | ||||||||
\(685\) | 8.42971e23 | 0.664420 | ||||||||
\(686\) | −9.88685e23 | −0.769667 | ||||||||
\(687\) | 6.32390e23 | 0.486243 | ||||||||
\(688\) | −1.07115e23 | −0.0813485 | ||||||||
\(689\) | 1.22858e24 | 0.921594 | ||||||||
\(690\) | 2.30199e23 | 0.170563 | ||||||||
\(691\) | −1.51213e24 | −1.10669 | −0.553343 | − | 0.832953i | \(-0.686648\pi\) | ||||
−0.553343 | + | 0.832953i | \(0.686648\pi\) | |||||||
\(692\) | −1.99393e23 | −0.144148 | ||||||||
\(693\) | −1.66892e24 | −1.19180 | ||||||||
\(694\) | 4.16082e23 | 0.293510 | ||||||||
\(695\) | 1.05465e24 | 0.734917 | ||||||||
\(696\) | −1.42906e23 | −0.0983718 | ||||||||
\(697\) | 9.32468e23 | 0.634096 | ||||||||
\(698\) | 9.22574e23 | 0.619769 | ||||||||
\(699\) | −7.57500e23 | −0.502720 | ||||||||
\(700\) | 1.23193e23 | 0.0807704 | ||||||||
\(701\) | 8.28511e23 | 0.536655 | 0.268328 | − | 0.963328i | \(-0.413529\pi\) | ||||
0.268328 | + | 0.963328i | \(0.413529\pi\) | |||||||
\(702\) | 6.27340e23 | 0.401456 | ||||||||
\(703\) | −2.86084e24 | −1.80873 | ||||||||
\(704\) | 3.42028e23 | 0.213645 | ||||||||
\(705\) | −2.57747e23 | −0.159069 | ||||||||
\(706\) | −2.04688e24 | −1.24811 | ||||||||
\(707\) | −1.59458e24 | −0.960684 | ||||||||
\(708\) | −3.57386e23 | −0.212743 | ||||||||
\(709\) | −3.32788e22 | −0.0195738 | −0.00978689 | − | 0.999952i | \(-0.503115\pi\) | ||||
−0.00978689 | + | 0.999952i | \(0.503115\pi\) | |||||||
\(710\) | 3.06603e23 | 0.178189 | ||||||||
\(711\) | −1.56658e24 | −0.899623 | ||||||||
\(712\) | −1.12098e24 | −0.636088 | ||||||||
\(713\) | −1.84996e24 | −1.03729 | ||||||||
\(714\) | 2.30066e23 | 0.127473 | ||||||||
\(715\) | −1.15054e24 | −0.629939 | ||||||||
\(716\) | 1.19761e24 | 0.647970 | ||||||||
\(717\) | 6.33846e23 | 0.338899 | ||||||||
\(718\) | 1.96921e24 | 1.04048 | ||||||||
\(719\) | 2.74357e23 | 0.143258 | 0.0716292 | − | 0.997431i | \(-0.477180\pi\) | ||||
0.0716292 | + | 0.997431i | \(0.477180\pi\) | |||||||
\(720\) | 1.87046e23 | 0.0965211 | ||||||||
\(721\) | −1.99771e23 | −0.101879 | ||||||||
\(722\) | 2.00162e24 | 1.00883 | ||||||||
\(723\) | 4.70391e23 | 0.234306 | ||||||||
\(724\) | −1.13745e24 | −0.559959 | ||||||||
\(725\) | 3.09351e23 | 0.150515 | ||||||||
\(726\) | −1.04447e24 | −0.502266 | ||||||||
\(727\) | 3.38639e24 | 1.60951 | 0.804756 | − | 0.593606i | \(-0.202296\pi\) | ||||
0.804756 | + | 0.593606i | \(0.202296\pi\) | |||||||
\(728\) | 5.00984e23 | 0.235346 | ||||||||
\(729\) | −5.83070e23 | −0.270730 | ||||||||
\(730\) | −4.56009e23 | −0.209281 | ||||||||
\(731\) | 4.33032e23 | 0.196436 | ||||||||
\(732\) | −1.20048e23 | −0.0538281 | ||||||||
\(733\) | 2.34817e24 | 1.04075 | 0.520375 | − | 0.853938i | \(-0.325792\pi\) | ||||
0.520375 | + | 0.853938i | \(0.325792\pi\) | |||||||
\(734\) | 1.12835e24 | 0.494341 | ||||||||
\(735\) | −1.32715e23 | −0.0574750 | ||||||||
\(736\) | 6.02428e23 | 0.257896 | ||||||||
\(737\) | −3.04860e24 | −1.29011 | ||||||||
\(738\) | 1.53276e24 | 0.641202 | ||||||||
\(739\) | 2.65236e24 | 1.09687 | 0.548434 | − | 0.836194i | \(-0.315224\pi\) | ||||
0.548434 | + | 0.836194i | \(0.315224\pi\) | |||||||
\(740\) | 6.35068e23 | 0.259627 | ||||||||
\(741\) | −1.17444e24 | −0.474651 | ||||||||
\(742\) | 1.59849e24 | 0.638671 | ||||||||
\(743\) | 4.48213e24 | 1.77043 | 0.885217 | − | 0.465178i | \(-0.154010\pi\) | ||||
0.885217 | + | 0.465178i | \(0.154010\pi\) | |||||||
\(744\) | 2.37999e23 | 0.0929406 | ||||||||
\(745\) | −5.40357e23 | −0.208618 | ||||||||
\(746\) | 1.97955e24 | 0.755589 | ||||||||
\(747\) | −2.81434e24 | −1.06207 | ||||||||
\(748\) | −1.38271e24 | −0.515901 | ||||||||
\(749\) | 9.29236e23 | 0.342792 | ||||||||
\(750\) | 6.41088e22 | 0.0233828 | ||||||||
\(751\) | 3.89653e24 | 1.40520 | 0.702600 | − | 0.711585i | \(-0.252022\pi\) | ||||
0.702600 | + | 0.711585i | \(0.252022\pi\) | |||||||
\(752\) | −6.74520e23 | −0.240516 | ||||||||
\(753\) | −8.43206e23 | −0.297287 | ||||||||
\(754\) | 1.25803e24 | 0.438564 | ||||||||
\(755\) | 1.40800e24 | 0.485350 | ||||||||
\(756\) | 8.16225e23 | 0.278211 | ||||||||
\(757\) | −2.72183e24 | −0.917373 | −0.458687 | − | 0.888598i | \(-0.651680\pi\) | ||||
−0.458687 | + | 0.888598i | \(0.651680\pi\) | |||||||
\(758\) | −1.75625e24 | −0.585326 | ||||||||
\(759\) | −2.79721e24 | −0.921870 | ||||||||
\(760\) | −7.55776e23 | −0.246307 | ||||||||
\(761\) | 3.88834e23 | 0.125312 | 0.0626562 | − | 0.998035i | \(-0.480043\pi\) | ||||
0.0626562 | + | 0.998035i | \(0.480043\pi\) | |||||||
\(762\) | −4.58691e23 | −0.146185 | ||||||||
\(763\) | −4.05489e24 | −1.27797 | ||||||||
\(764\) | −1.17110e24 | −0.365007 | ||||||||
\(765\) | −7.56166e23 | −0.233075 | ||||||||
\(766\) | −1.24583e24 | −0.379766 | ||||||||
\(767\) | 3.14614e24 | 0.948457 | ||||||||
\(768\) | −7.75028e22 | −0.0231072 | ||||||||
\(769\) | −2.20996e24 | −0.651645 | −0.325823 | − | 0.945431i | \(-0.605641\pi\) | ||||
−0.325823 | + | 0.945431i | \(0.605641\pi\) | |||||||
\(770\) | −1.49695e24 | −0.436552 | ||||||||
\(771\) | −7.14847e23 | −0.206182 | ||||||||
\(772\) | 6.52058e23 | 0.186011 | ||||||||
\(773\) | 5.39261e24 | 1.52151 | 0.760753 | − | 0.649042i | \(-0.224830\pi\) | ||||
0.760753 | + | 0.649042i | \(0.224830\pi\) | |||||||
\(774\) | 7.11803e23 | 0.198638 | ||||||||
\(775\) | −5.15202e23 | −0.142204 | ||||||||
\(776\) | 1.04725e24 | 0.285907 | ||||||||
\(777\) | 1.28400e24 | 0.346725 | ||||||||
\(778\) | −2.55578e24 | −0.682648 | ||||||||
\(779\) | −6.19325e24 | −1.63625 | ||||||||
\(780\) | 2.60709e23 | 0.0681322 | ||||||||
\(781\) | −3.72562e24 | −0.963085 | ||||||||
\(782\) | −2.43542e24 | −0.622754 | ||||||||
\(783\) | 2.04963e24 | 0.518443 | ||||||||
\(784\) | −3.47315e23 | −0.0869034 | ||||||||
\(785\) | −2.64262e24 | −0.654099 | ||||||||
\(786\) | 2.14090e23 | 0.0524209 | ||||||||
\(787\) | −1.11664e24 | −0.270475 | −0.135238 | − | 0.990813i | \(-0.543180\pi\) | ||||
−0.135238 | + | 0.990813i | \(0.543180\pi\) | |||||||
\(788\) | 3.45488e24 | 0.827866 | ||||||||
\(789\) | −2.43131e24 | −0.576350 | ||||||||
\(790\) | −1.40515e24 | −0.329529 | ||||||||
\(791\) | 5.39470e24 | 1.25160 | ||||||||
\(792\) | −2.27285e24 | −0.521682 | ||||||||
\(793\) | 1.05680e24 | 0.239978 | ||||||||
\(794\) | −1.30159e24 | −0.292416 | ||||||||
\(795\) | 8.31845e23 | 0.184894 | ||||||||
\(796\) | 1.32921e23 | 0.0292303 | ||||||||
\(797\) | −4.11242e24 | −0.894751 | −0.447375 | − | 0.894346i | \(-0.647641\pi\) | ||||
−0.447375 | + | 0.894346i | \(0.647641\pi\) | |||||||
\(798\) | −1.52805e24 | −0.328937 | ||||||||
\(799\) | 2.72686e24 | 0.580786 | ||||||||
\(800\) | 1.67772e23 | 0.0353553 | ||||||||
\(801\) | 7.44913e24 | 1.55321 | ||||||||
\(802\) | 2.70491e24 | 0.558047 | ||||||||
\(803\) | 5.54109e24 | 1.13113 | ||||||||
\(804\) | 6.90807e23 | 0.139534 | ||||||||
\(805\) | −2.63664e24 | −0.526970 | ||||||||
\(806\) | −2.09515e24 | −0.414351 | ||||||||
\(807\) | 2.15578e24 | 0.421871 | ||||||||
\(808\) | −2.17160e24 | −0.420517 | ||||||||
\(809\) | 1.99425e24 | 0.382135 | 0.191068 | − | 0.981577i | \(-0.438805\pi\) | ||||
0.191068 | + | 0.981577i | \(0.438805\pi\) | |||||||
\(810\) | −1.01500e24 | −0.192461 | ||||||||
\(811\) | −6.54121e24 | −1.22739 | −0.613693 | − | 0.789545i | \(-0.710317\pi\) | ||||
−0.613693 | + | 0.789545i | \(0.710317\pi\) | |||||||
\(812\) | 1.63681e24 | 0.303928 | ||||||||
\(813\) | 1.95171e24 | 0.358628 | ||||||||
\(814\) | −7.71688e24 | −1.40325 | ||||||||
\(815\) | 4.17202e24 | 0.750769 | ||||||||
\(816\) | 3.13319e23 | 0.0557982 | ||||||||
\(817\) | −2.87610e24 | −0.506894 | ||||||||
\(818\) | 4.44311e23 | 0.0774968 | ||||||||
\(819\) | −3.32914e24 | −0.574671 | ||||||||
\(820\) | 1.37482e24 | 0.234870 | ||||||||
\(821\) | −8.88770e24 | −1.50270 | −0.751351 | − | 0.659903i | \(-0.770597\pi\) | ||||
−0.751351 | + | 0.659903i | \(0.770597\pi\) | |||||||
\(822\) | 2.32108e24 | 0.388400 | ||||||||
\(823\) | 6.84928e24 | 1.13435 | 0.567174 | − | 0.823598i | \(-0.308037\pi\) | ||||
0.567174 | + | 0.823598i | \(0.308037\pi\) | |||||||
\(824\) | −2.72061e23 | −0.0445949 | ||||||||
\(825\) | −7.79004e23 | −0.126381 | ||||||||
\(826\) | 4.09341e24 | 0.657287 | ||||||||
\(827\) | 9.77573e24 | 1.55365 | 0.776824 | − | 0.629718i | \(-0.216830\pi\) | ||||
0.776824 | + | 0.629718i | \(0.216830\pi\) | |||||||
\(828\) | −4.00326e24 | −0.629732 | ||||||||
\(829\) | 7.90775e24 | 1.23123 | 0.615615 | − | 0.788047i | \(-0.288908\pi\) | ||||
0.615615 | + | 0.788047i | \(0.288908\pi\) | |||||||
\(830\) | −2.52434e24 | −0.389031 | ||||||||
\(831\) | 4.08688e24 | 0.623423 | ||||||||
\(832\) | 6.82273e23 | 0.103017 | ||||||||
\(833\) | 1.40408e24 | 0.209850 | ||||||||
\(834\) | 2.90394e24 | 0.429611 | ||||||||
\(835\) | 1.14740e24 | 0.168028 | ||||||||
\(836\) | 9.18364e24 | 1.33126 | ||||||||
\(837\) | −3.41352e24 | −0.489819 | ||||||||
\(838\) | −2.89356e24 | −0.411016 | ||||||||
\(839\) | −7.46885e24 | −1.05021 | −0.525106 | − | 0.851037i | \(-0.675974\pi\) | ||||
−0.525106 | + | 0.851037i | \(0.675974\pi\) | |||||||
\(840\) | 3.39206e23 | 0.0472160 | ||||||||
\(841\) | −3.14695e24 | −0.433634 | ||||||||
\(842\) | −2.71958e23 | −0.0370978 | ||||||||
\(843\) | −2.84264e24 | −0.383873 | ||||||||
\(844\) | −1.67260e24 | −0.223606 | ||||||||
\(845\) | 1.08399e24 | 0.143465 | ||||||||
\(846\) | 4.48233e24 | 0.587294 | ||||||||
\(847\) | 1.19631e25 | 1.55179 | ||||||||
\(848\) | 2.17693e24 | 0.279563 | ||||||||
\(849\) | −4.71409e24 | −0.599352 | ||||||||
\(850\) | −6.78248e23 | −0.0853744 | ||||||||
\(851\) | −1.35921e25 | −1.69389 | ||||||||
\(852\) | 8.44218e23 | 0.104164 | ||||||||
\(853\) | 4.59203e24 | 0.560967 | 0.280484 | − | 0.959859i | \(-0.409505\pi\) | ||||
0.280484 | + | 0.959859i | \(0.409505\pi\) | |||||||
\(854\) | 1.37500e24 | 0.166307 | ||||||||
\(855\) | 5.02229e24 | 0.601436 | ||||||||
\(856\) | 1.26549e24 | 0.150049 | ||||||||
\(857\) | −8.74464e24 | −1.02661 | −0.513304 | − | 0.858207i | \(-0.671579\pi\) | ||||
−0.513304 | + | 0.858207i | \(0.671579\pi\) | |||||||
\(858\) | −3.16795e24 | −0.368244 | ||||||||
\(859\) | −1.25157e25 | −1.44050 | −0.720251 | − | 0.693714i | \(-0.755973\pi\) | ||||
−0.720251 | + | 0.693714i | \(0.755973\pi\) | |||||||
\(860\) | 6.38456e23 | 0.0727603 | ||||||||
\(861\) | 2.77964e24 | 0.313662 | ||||||||
\(862\) | 9.25611e24 | 1.03423 | ||||||||
\(863\) | 4.23769e22 | 0.00468854 | 0.00234427 | − | 0.999997i | \(-0.499254\pi\) | ||||
0.00234427 | + | 0.999997i | \(0.499254\pi\) | |||||||
\(864\) | 1.11159e24 | 0.121780 | ||||||||
\(865\) | 1.18848e24 | 0.128930 | ||||||||
\(866\) | −5.51147e24 | −0.592059 | ||||||||
\(867\) | 2.20895e24 | 0.234976 | ||||||||
\(868\) | −2.72598e24 | −0.287148 | ||||||||
\(869\) | 1.70744e25 | 1.78105 | ||||||||
\(870\) | 8.51784e23 | 0.0879864 | ||||||||
\(871\) | −6.08132e24 | −0.622076 | ||||||||
\(872\) | −5.52221e24 | −0.559401 | ||||||||
\(873\) | −6.95918e24 | −0.698131 | ||||||||
\(874\) | 1.61755e25 | 1.60698 | ||||||||
\(875\) | −7.34287e23 | −0.0722433 | ||||||||
\(876\) | −1.25560e24 | −0.122339 | ||||||||
\(877\) | −1.33197e25 | −1.28528 | −0.642638 | − | 0.766170i | \(-0.722160\pi\) | ||||
−0.642638 | + | 0.766170i | \(0.722160\pi\) | |||||||
\(878\) | −7.39538e24 | −0.706736 | ||||||||
\(879\) | 1.28274e24 | 0.121404 | ||||||||
\(880\) | −2.03864e24 | −0.191090 | ||||||||
\(881\) | 3.37699e23 | 0.0313498 | 0.0156749 | − | 0.999877i | \(-0.495010\pi\) | ||||
0.0156749 | + | 0.999877i | \(0.495010\pi\) | |||||||
\(882\) | 2.30798e24 | 0.212202 | ||||||||
\(883\) | −1.43309e25 | −1.30499 | −0.652495 | − | 0.757793i | \(-0.726278\pi\) | ||||
−0.652495 | + | 0.757793i | \(0.726278\pi\) | |||||||
\(884\) | −2.75821e24 | −0.248761 | ||||||||
\(885\) | 2.13019e24 | 0.190283 | ||||||||
\(886\) | 8.79298e23 | 0.0777946 | ||||||||
\(887\) | −1.41818e25 | −1.24274 | −0.621369 | − | 0.783518i | \(-0.713423\pi\) | ||||
−0.621369 | + | 0.783518i | \(0.713423\pi\) | |||||||
\(888\) | 1.74863e24 | 0.151771 | ||||||||
\(889\) | 5.25374e24 | 0.451652 | ||||||||
\(890\) | 6.68155e24 | 0.568934 | ||||||||
\(891\) | 1.23335e25 | 1.04022 | ||||||||
\(892\) | −2.29468e24 | −0.191700 | ||||||||
\(893\) | −1.81112e25 | −1.49869 | ||||||||
\(894\) | −1.48785e24 | −0.121952 | ||||||||
\(895\) | −7.13831e24 | −0.579562 | ||||||||
\(896\) | 8.87699e23 | 0.0713917 | ||||||||
\(897\) | −5.57984e24 | −0.444514 | ||||||||
\(898\) | 7.90719e24 | 0.623984 | ||||||||
\(899\) | −6.84525e24 | −0.535096 | ||||||||
\(900\) | −1.11488e24 | −0.0863311 | ||||||||
\(901\) | −8.80062e24 | −0.675076 | ||||||||
\(902\) | −1.67058e25 | −1.26944 | ||||||||
\(903\) | 1.29085e24 | 0.0971693 | ||||||||
\(904\) | 7.34685e24 | 0.547860 | ||||||||
\(905\) | 6.77976e24 | 0.500843 | ||||||||
\(906\) | 3.87688e24 | 0.283721 | ||||||||
\(907\) | 2.50957e25 | 1.81944 | 0.909720 | − | 0.415222i | \(-0.136296\pi\) | ||||
0.909720 | + | 0.415222i | \(0.136296\pi\) | |||||||
\(908\) | −7.84184e24 | −0.563233 | ||||||||
\(909\) | 1.44307e25 | 1.02682 | ||||||||
\(910\) | −2.98610e24 | −0.210500 | ||||||||
\(911\) | −2.35966e24 | −0.164794 | −0.0823972 | − | 0.996600i | \(-0.526258\pi\) | ||||
−0.0823972 | + | 0.996600i | \(0.526258\pi\) | |||||||
\(912\) | −2.08099e24 | −0.143984 | ||||||||
\(913\) | 3.06740e25 | 2.10266 | ||||||||
\(914\) | −9.81210e24 | −0.666376 | ||||||||
\(915\) | 7.15539e23 | 0.0481453 | ||||||||
\(916\) | −9.86433e24 | −0.657591 | ||||||||
\(917\) | −2.45213e24 | −0.161959 | ||||||||
\(918\) | −4.49379e24 | −0.294070 | ||||||||
\(919\) | 2.94936e25 | 1.91226 | 0.956129 | − | 0.292946i | \(-0.0946357\pi\) | ||||
0.956129 | + | 0.292946i | \(0.0946357\pi\) | |||||||
\(920\) | −3.59075e24 | −0.230669 | ||||||||
\(921\) | 1.54008e24 | 0.0980252 | ||||||||
\(922\) | 1.74117e25 | 1.09807 | ||||||||
\(923\) | −7.43182e24 | −0.464388 | ||||||||
\(924\) | −4.12178e24 | −0.255196 | ||||||||
\(925\) | −3.78530e24 | −0.232218 | ||||||||
\(926\) | 1.17079e24 | 0.0711684 | ||||||||
\(927\) | 1.80790e24 | 0.108892 | ||||||||
\(928\) | 2.22911e24 | 0.133037 | ||||||||
\(929\) | 1.27862e25 | 0.756150 | 0.378075 | − | 0.925775i | \(-0.376586\pi\) | ||||
0.378075 | + | 0.925775i | \(0.376586\pi\) | |||||||
\(930\) | −1.41859e24 | −0.0831286 | ||||||||
\(931\) | −9.32560e24 | −0.541508 | ||||||||
\(932\) | 1.18158e25 | 0.679875 | ||||||||
\(933\) | 1.31474e23 | 0.00749626 | ||||||||
\(934\) | 1.27428e25 | 0.719975 | ||||||||
\(935\) | 8.24157e24 | 0.461436 | ||||||||
\(936\) | −4.53385e24 | −0.251549 | ||||||||
\(937\) | 5.20286e24 | 0.286059 | 0.143029 | − | 0.989718i | \(-0.454316\pi\) | ||||
0.143029 | + | 0.989718i | \(0.454316\pi\) | |||||||
\(938\) | −7.91234e24 | −0.431103 | ||||||||
\(939\) | 1.07123e25 | 0.578398 | ||||||||
\(940\) | 4.02045e24 | 0.215124 | ||||||||
\(941\) | 2.51815e25 | 1.33527 | 0.667635 | − | 0.744488i | \(-0.267306\pi\) | ||||
0.667635 | + | 0.744488i | \(0.267306\pi\) | |||||||
\(942\) | −7.27635e24 | −0.382367 | ||||||||
\(943\) | −2.94246e25 | −1.53236 | ||||||||
\(944\) | 5.57467e24 | 0.287712 | ||||||||
\(945\) | −4.86508e24 | −0.248840 | ||||||||
\(946\) | −7.75805e24 | −0.393258 | ||||||||
\(947\) | −2.26103e25 | −1.13588 | −0.567939 | − | 0.823071i | \(-0.692259\pi\) | ||||
−0.567939 | + | 0.823071i | \(0.692259\pi\) | |||||||
\(948\) | −3.86903e24 | −0.192633 | ||||||||
\(949\) | 1.10533e25 | 0.545417 | ||||||||
\(950\) | 4.50478e24 | 0.220304 | ||||||||
\(951\) | 5.99562e24 | 0.290603 | ||||||||
\(952\) | −3.58867e24 | −0.172393 | ||||||||
\(953\) | 2.71240e25 | 1.29141 | 0.645706 | − | 0.763586i | \(-0.276563\pi\) | ||||
0.645706 | + | 0.763586i | \(0.276563\pi\) | |||||||
\(954\) | −1.44662e25 | −0.682640 | ||||||||
\(955\) | 6.98032e24 | 0.326473 | ||||||||
\(956\) | −9.88702e24 | −0.458325 | ||||||||
\(957\) | −1.03502e25 | −0.475553 | ||||||||
\(958\) | 2.39486e25 | 1.09062 | ||||||||
\(959\) | −2.65851e25 | −1.20000 | ||||||||
\(960\) | 4.61953e23 | 0.0206677 | ||||||||
\(961\) | −1.11498e25 | −0.494447 | ||||||||
\(962\) | −1.53935e25 | −0.676629 | ||||||||
\(963\) | −8.40947e24 | −0.366392 | ||||||||
\(964\) | −7.33738e24 | −0.316874 | ||||||||
\(965\) | −3.88657e24 | −0.166374 | ||||||||
\(966\) | −7.25987e24 | −0.308052 | ||||||||
\(967\) | 2.72568e25 | 1.14644 | 0.573218 | − | 0.819403i | \(-0.305695\pi\) | ||||
0.573218 | + | 0.819403i | \(0.305695\pi\) | |||||||
\(968\) | 1.62921e25 | 0.679261 | ||||||||
\(969\) | 8.41278e24 | 0.347686 | ||||||||
\(970\) | −6.24209e24 | −0.255723 | ||||||||
\(971\) | −5.68052e24 | −0.230688 | −0.115344 | − | 0.993326i | \(-0.536797\pi\) | ||||
−0.115344 | + | 0.993326i | \(0.536797\pi\) | |||||||
\(972\) | −1.13511e25 | −0.456954 | ||||||||
\(973\) | −3.32610e25 | −1.32732 | ||||||||
\(974\) | −4.19670e24 | −0.166019 | ||||||||
\(975\) | −1.55395e24 | −0.0609393 | ||||||||
\(976\) | 1.87256e24 | 0.0727967 | ||||||||
\(977\) | −2.19879e25 | −0.847383 | −0.423691 | − | 0.905807i | \(-0.639266\pi\) | ||||
−0.423691 | + | 0.905807i | \(0.639266\pi\) | |||||||
\(978\) | 1.14875e25 | 0.438878 | ||||||||
\(979\) | −8.11892e25 | −3.07500 | ||||||||
\(980\) | 2.07016e24 | 0.0777288 | ||||||||
\(981\) | 3.66962e25 | 1.36595 | ||||||||
\(982\) | −6.71999e24 | −0.247983 | ||||||||
\(983\) | 1.62023e25 | 0.592748 | 0.296374 | − | 0.955072i | \(-0.404222\pi\) | ||||
0.296374 | + | 0.955072i | \(0.404222\pi\) | |||||||
\(984\) | 3.78550e24 | 0.137298 | ||||||||
\(985\) | −2.05927e25 | −0.740466 | ||||||||
\(986\) | −9.01156e24 | −0.321252 | ||||||||
\(987\) | 8.12865e24 | 0.287291 | ||||||||
\(988\) | 1.83194e25 | 0.641915 | ||||||||
\(989\) | −1.36646e25 | −0.474710 | ||||||||
\(990\) | 1.35472e25 | 0.466607 | ||||||||
\(991\) | −1.63414e25 | −0.558036 | −0.279018 | − | 0.960286i | \(-0.590009\pi\) | ||||
−0.279018 | + | 0.960286i | \(0.590009\pi\) | |||||||
\(992\) | −3.71242e24 | −0.125692 | ||||||||
\(993\) | 6.94421e23 | 0.0233106 | ||||||||
\(994\) | −9.66947e24 | −0.321824 | ||||||||
\(995\) | −7.92273e23 | −0.0261444 | ||||||||
\(996\) | −6.95066e24 | −0.227416 | ||||||||
\(997\) | 3.96008e25 | 1.28468 | 0.642340 | − | 0.766420i | \(-0.277964\pi\) | ||||
0.642340 | + | 0.766420i | \(0.277964\pi\) | |||||||
\(998\) | 4.90132e24 | 0.157653 | ||||||||
\(999\) | −2.50798e25 | −0.799868 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 10.18.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 90.18.a.j.1.1 | 2 | |||
4.3 | odd | 2 | 80.18.a.b.1.2 | 2 | |||
5.2 | odd | 4 | 50.18.b.f.49.4 | 4 | |||
5.3 | odd | 4 | 50.18.b.f.49.1 | 4 | |||
5.4 | even | 2 | 50.18.a.c.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.18.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.18.a.c.1.2 | 2 | 5.4 | even | 2 | |||
50.18.b.f.49.1 | 4 | 5.3 | odd | 4 | |||
50.18.b.f.49.4 | 4 | 5.2 | odd | 4 | |||
80.18.a.b.1.2 | 2 | 4.3 | odd | 2 | |||
90.18.a.j.1.1 | 2 | 3.2 | odd | 2 |