Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,11,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(112.458233723\) |
Analytic rank: | \(0\) |
Dimension: | \(100\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.89 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.11.c.a.58.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 51.4146i | 1.60671i | 0.595502 | + | 0.803353i | \(0.296953\pi\) | ||||
−0.595502 | + | 0.803353i | \(0.703047\pi\) | |||||||
\(3\) | −140.296 | −0.577350 | ||||||||
\(4\) | −1619.46 | −1.58151 | ||||||||
\(5\) | −2372.07 | −0.759061 | −0.379530 | − | 0.925179i | \(-0.623914\pi\) | ||||
−0.379530 | + | 0.925179i | \(0.623914\pi\) | |||||||
\(6\) | − | 7213.27i | − | 0.927633i | ||||||
\(7\) | 15485.2 | 0.921353 | 0.460676 | − | 0.887568i | \(-0.347607\pi\) | ||||
0.460676 | + | 0.887568i | \(0.347607\pi\) | |||||||
\(8\) | − | 30615.5i | − | 0.934312i | ||||||
\(9\) | 19683.0 | 0.333333 | ||||||||
\(10\) | − | 121959.i | − | 1.21959i | ||||||
\(11\) | 207798.i | 1.29026i | 0.764072 | + | 0.645131i | \(0.223197\pi\) | ||||
−0.764072 | + | 0.645131i | \(0.776803\pi\) | |||||||
\(12\) | 227204. | 0.913084 | ||||||||
\(13\) | − | 9463.66i | − | 0.0254884i | −0.999919 | − | 0.0127442i | \(-0.995943\pi\) | ||
0.999919 | − | 0.0127442i | \(-0.00405671\pi\) | |||||||
\(14\) | 796164.i | 1.48034i | ||||||||
\(15\) | 332792. | 0.438244 | ||||||||
\(16\) | −84244.9 | −0.0803422 | ||||||||
\(17\) | 393426. | 0.277089 | 0.138544 | − | 0.990356i | \(-0.455758\pi\) | ||||
0.138544 | + | 0.990356i | \(0.455758\pi\) | |||||||
\(18\) | 1.01199e6i | 0.535569i | ||||||||
\(19\) | −3.27325e6 | −1.32194 | −0.660969 | − | 0.750413i | \(-0.729855\pi\) | ||||
−0.660969 | + | 0.750413i | \(0.729855\pi\) | |||||||
\(20\) | 3.84147e6 | 1.20046 | ||||||||
\(21\) | −2.17251e6 | −0.531943 | ||||||||
\(22\) | −1.06839e7 | −2.07307 | ||||||||
\(23\) | 3.87647e6i | 0.602278i | 0.953580 | + | 0.301139i | \(0.0973669\pi\) | ||||
−0.953580 | + | 0.301139i | \(0.902633\pi\) | |||||||
\(24\) | 4.29524e6i | 0.539425i | ||||||||
\(25\) | −4.13893e6 | −0.423827 | ||||||||
\(26\) | 486571. | 0.0409524 | ||||||||
\(27\) | −2.76145e6 | −0.192450 | ||||||||
\(28\) | −2.50777e7 | −1.45713 | ||||||||
\(29\) | 1.36358e7 | 0.664800 | 0.332400 | − | 0.943139i | \(-0.392142\pi\) | ||||
0.332400 | + | 0.943139i | \(0.392142\pi\) | |||||||
\(30\) | 1.71104e7i | 0.704130i | ||||||||
\(31\) | − | 2.27647e7i | − | 0.795158i | −0.917568 | − | 0.397579i | \(-0.869850\pi\) | ||
0.917568 | − | 0.397579i | \(-0.130150\pi\) | |||||||
\(32\) | − | 3.56817e7i | − | 1.06340i | ||||||
\(33\) | − | 2.91533e7i | − | 0.744934i | ||||||
\(34\) | 2.02279e7i | 0.445200i | ||||||||
\(35\) | −3.67318e7 | −0.699363 | ||||||||
\(36\) | −3.18759e7 | −0.527169 | ||||||||
\(37\) | − | 8.26010e7i | − | 1.19118i | −0.803289 | − | 0.595589i | \(-0.796919\pi\) | ||
0.803289 | − | 0.595589i | \(-0.203081\pi\) | |||||||
\(38\) | − | 1.68293e8i | − | 2.12397i | ||||||
\(39\) | 1.32772e6i | 0.0147157i | ||||||||
\(40\) | 7.26220e7i | 0.709199i | ||||||||
\(41\) | −1.06754e8 | −0.921437 | −0.460718 | − | 0.887546i | \(-0.652408\pi\) | ||||
−0.460718 | + | 0.887546i | \(0.652408\pi\) | |||||||
\(42\) | − | 1.11699e8i | − | 0.854677i | ||||||
\(43\) | 7.40752e7i | 0.503884i | 0.967742 | + | 0.251942i | \(0.0810692\pi\) | ||||
−0.967742 | + | 0.251942i | \(0.918931\pi\) | |||||||
\(44\) | − | 3.36521e8i | − | 2.04056i | ||||||
\(45\) | −4.66894e7 | −0.253020 | ||||||||
\(46\) | −1.99307e8 | −0.967685 | ||||||||
\(47\) | − | 2.11955e7i | − | 0.0924176i | −0.998932 | − | 0.0462088i | \(-0.985286\pi\) | ||
0.998932 | − | 0.0462088i | \(-0.0147140\pi\) | |||||||
\(48\) | 1.18192e7 | 0.0463856 | ||||||||
\(49\) | −4.26846e7 | −0.151109 | ||||||||
\(50\) | − | 2.12802e8i | − | 0.680965i | ||||||
\(51\) | −5.51962e7 | −0.159977 | ||||||||
\(52\) | 1.53261e7i | 0.0403101i | ||||||||
\(53\) | 2.58725e7 | 0.0618671 | 0.0309335 | − | 0.999521i | \(-0.490152\pi\) | ||||
0.0309335 | + | 0.999521i | \(0.490152\pi\) | |||||||
\(54\) | − | 1.41979e8i | − | 0.309211i | ||||||
\(55\) | − | 4.92911e8i | − | 0.979388i | ||||||
\(56\) | − | 4.74087e8i | − | 0.860830i | ||||||
\(57\) | 4.59224e8 | 0.763221 | ||||||||
\(58\) | 7.01080e8i | 1.06814i | ||||||||
\(59\) | −5.38229e8 | + | 4.70560e8i | −0.752847 | + | 0.658195i | ||||
\(60\) | −5.38944e8 | −0.693086 | ||||||||
\(61\) | − | 1.35826e9i | − | 1.60818i | −0.594509 | − | 0.804089i | \(-0.702653\pi\) | ||
0.594509 | − | 0.804089i | \(-0.297347\pi\) | |||||||
\(62\) | 1.17044e9 | 1.27759 | ||||||||
\(63\) | 3.04795e8 | 0.307118 | ||||||||
\(64\) | 1.74830e9 | 1.62823 | ||||||||
\(65\) | 2.24484e7i | 0.0193472i | ||||||||
\(66\) | 1.49890e9 | 1.19689 | ||||||||
\(67\) | 1.48600e9i | 1.10064i | 0.834953 | + | 0.550321i | \(0.185495\pi\) | ||||
−0.834953 | + | 0.550321i | \(0.814505\pi\) | |||||||
\(68\) | −6.37140e8 | −0.438218 | ||||||||
\(69\) | − | 5.43854e8i | − | 0.347726i | ||||||
\(70\) | − | 1.88855e9i | − | 1.12367i | ||||||
\(71\) | −8.76816e8 | −0.485978 | −0.242989 | − | 0.970029i | \(-0.578128\pi\) | ||||
−0.242989 | + | 0.970029i | \(0.578128\pi\) | |||||||
\(72\) | − | 6.02605e8i | − | 0.311437i | ||||||
\(73\) | 8.52461e8i | 0.411207i | 0.978635 | + | 0.205603i | \(0.0659157\pi\) | ||||
−0.978635 | + | 0.205603i | \(0.934084\pi\) | |||||||
\(74\) | 4.24690e9 | 1.91387 | ||||||||
\(75\) | 5.80676e8 | 0.244696 | ||||||||
\(76\) | 5.30091e9 | 2.09065 | ||||||||
\(77\) | 3.21779e9i | 1.18879i | ||||||||
\(78\) | −6.82640e7 | −0.0236439 | ||||||||
\(79\) | −9.09746e7 | −0.0295655 | −0.0147827 | − | 0.999891i | \(-0.504706\pi\) | ||||
−0.0147827 | + | 0.999891i | \(0.504706\pi\) | |||||||
\(80\) | 1.99834e8 | 0.0609846 | ||||||||
\(81\) | 3.87420e8 | 0.111111 | ||||||||
\(82\) | − | 5.48872e9i | − | 1.48048i | ||||||
\(83\) | − | 1.22363e8i | − | 0.0310642i | −0.999879 | − | 0.0155321i | \(-0.995056\pi\) | ||
0.999879 | − | 0.0155321i | \(-0.00494423\pi\) | |||||||
\(84\) | 3.51830e9 | 0.841272 | ||||||||
\(85\) | −9.33233e8 | −0.210327 | ||||||||
\(86\) | −3.80855e9 | −0.809594 | ||||||||
\(87\) | −1.91305e9 | −0.383822 | ||||||||
\(88\) | 6.36185e9 | 1.20551 | ||||||||
\(89\) | 5.23788e8i | 0.0938005i | 0.998900 | + | 0.0469002i | \(0.0149343\pi\) | ||||
−0.998900 | + | 0.0469002i | \(0.985066\pi\) | |||||||
\(90\) | − | 2.40052e9i | − | 0.406529i | ||||||
\(91\) | − | 1.46546e8i | − | 0.0234838i | ||||||
\(92\) | − | 6.27780e9i | − | 0.952508i | ||||||
\(93\) | 3.19380e9i | 0.459085i | ||||||||
\(94\) | 1.08976e9 | 0.148488 | ||||||||
\(95\) | 7.76436e9 | 1.00343 | ||||||||
\(96\) | 5.00601e9i | 0.613953i | ||||||||
\(97\) | − | 6.29776e9i | − | 0.733377i | −0.930344 | − | 0.366689i | \(-0.880491\pi\) | ||
0.930344 | − | 0.366689i | \(-0.119509\pi\) | |||||||
\(98\) | − | 2.19462e9i | − | 0.242788i | ||||||
\(99\) | 4.09009e9i | 0.430088i | ||||||||
\(100\) | 6.70285e9 | 0.670285 | ||||||||
\(101\) | − | 9.07488e9i | − | 0.863444i | −0.902007 | − | 0.431722i | \(-0.857906\pi\) | ||
0.902007 | − | 0.431722i | \(-0.142094\pi\) | |||||||
\(102\) | − | 2.83789e9i | − | 0.257037i | ||||||
\(103\) | − | 5.43941e9i | − | 0.469209i | −0.972091 | − | 0.234604i | \(-0.924621\pi\) | ||
0.972091 | − | 0.234604i | \(-0.0753794\pi\) | |||||||
\(104\) | −2.89735e8 | −0.0238141 | ||||||||
\(105\) | 5.15333e9 | 0.403777 | ||||||||
\(106\) | 1.33023e9i | 0.0994023i | ||||||||
\(107\) | 6.07134e8 | 0.0432878 | 0.0216439 | − | 0.999766i | \(-0.493110\pi\) | ||||
0.0216439 | + | 0.999766i | \(0.493110\pi\) | |||||||
\(108\) | 4.47206e9 | 0.304361 | ||||||||
\(109\) | 8.52551e9i | 0.554100i | 0.960856 | + | 0.277050i | \(0.0893568\pi\) | ||||
−0.960856 | + | 0.277050i | \(0.910643\pi\) | |||||||
\(110\) | 2.53428e10 | 1.57359 | ||||||||
\(111\) | 1.15886e10i | 0.687727i | ||||||||
\(112\) | −1.30455e9 | −0.0740235 | ||||||||
\(113\) | − | 2.98035e10i | − | 1.61762i | −0.588072 | − | 0.808808i | \(-0.700113\pi\) | ||
0.588072 | − | 0.808808i | \(-0.299887\pi\) | |||||||
\(114\) | 2.36108e10i | 1.22627i | ||||||||
\(115\) | − | 9.19524e9i | − | 0.457166i | ||||||
\(116\) | −2.20827e10 | −1.05139 | ||||||||
\(117\) | − | 1.86273e8i | − | 0.00849613i | ||||||
\(118\) | −2.41937e10 | − | 2.76728e10i | −1.05753 | − | 1.20960i | ||||
\(119\) | 6.09228e9 | 0.255296 | ||||||||
\(120\) | − | 1.01886e10i | − | 0.409456i | ||||||
\(121\) | −1.72426e10 | −0.664779 | ||||||||
\(122\) | 6.98345e10 | 2.58387 | ||||||||
\(123\) | 1.49772e10 | 0.531992 | ||||||||
\(124\) | 3.68666e10i | 1.25755i | ||||||||
\(125\) | 3.29825e10 | 1.08077 | ||||||||
\(126\) | 1.56709e10i | 0.493448i | ||||||||
\(127\) | −8.16922e9 | −0.247265 | −0.123632 | − | 0.992328i | \(-0.539454\pi\) | ||||
−0.123632 | + | 0.992328i | \(0.539454\pi\) | |||||||
\(128\) | 5.33499e10i | 1.55269i | ||||||||
\(129\) | − | 1.03925e10i | − | 0.290918i | ||||||
\(130\) | −1.15418e9 | −0.0310854 | ||||||||
\(131\) | 2.12207e10i | 0.550051i | 0.961437 | + | 0.275025i | \(0.0886863\pi\) | ||||
−0.961437 | + | 0.275025i | \(0.911314\pi\) | |||||||
\(132\) | 4.72127e10i | 1.17812i | ||||||||
\(133\) | −5.06868e10 | −1.21797 | ||||||||
\(134\) | −7.64024e10 | −1.76841 | ||||||||
\(135\) | 6.55034e9 | 0.146081 | ||||||||
\(136\) | − | 1.20450e10i | − | 0.258887i | ||||||
\(137\) | 6.03369e10 | 1.25020 | 0.625101 | − | 0.780544i | \(-0.285058\pi\) | ||||
0.625101 | + | 0.780544i | \(0.285058\pi\) | |||||||
\(138\) | 2.79620e10 | 0.558693 | ||||||||
\(139\) | −2.81739e10 | −0.542966 | −0.271483 | − | 0.962443i | \(-0.587514\pi\) | ||||
−0.271483 | + | 0.962443i | \(0.587514\pi\) | |||||||
\(140\) | 5.94859e10 | 1.10605 | ||||||||
\(141\) | 2.97365e9i | 0.0533573i | ||||||||
\(142\) | − | 4.50812e10i | − | 0.780825i | ||||||
\(143\) | 1.96653e9 | 0.0328867 | ||||||||
\(144\) | −1.65819e9 | −0.0267807 | ||||||||
\(145\) | −3.23450e10 | −0.504623 | ||||||||
\(146\) | −4.38290e10 | −0.660689 | ||||||||
\(147\) | 5.98849e9 | 0.0872430 | ||||||||
\(148\) | 1.33769e11i | 1.88386i | ||||||||
\(149\) | 3.53969e10i | 0.481985i | 0.970527 | + | 0.240993i | \(0.0774730\pi\) | ||||
−0.970527 | + | 0.240993i | \(0.922527\pi\) | |||||||
\(150\) | 2.98552e10i | 0.393155i | ||||||||
\(151\) | 7.55219e10i | 0.962029i | 0.876713 | + | 0.481015i | \(0.159732\pi\) | ||||
−0.876713 | + | 0.481015i | \(0.840268\pi\) | |||||||
\(152\) | 1.00212e11i | 1.23510i | ||||||||
\(153\) | 7.74381e9 | 0.0923629 | ||||||||
\(154\) | −1.65441e11 | −1.91003 | ||||||||
\(155\) | 5.39994e10i | 0.603574i | ||||||||
\(156\) | − | 2.15019e9i | − | 0.0232730i | ||||||
\(157\) | 7.86464e10i | 0.824481i | 0.911075 | + | 0.412240i | \(0.135254\pi\) | ||||
−0.911075 | + | 0.412240i | \(0.864746\pi\) | |||||||
\(158\) | − | 4.67742e9i | − | 0.0475030i | ||||||
\(159\) | −3.62982e9 | −0.0357190 | ||||||||
\(160\) | 8.46394e10i | 0.807184i | ||||||||
\(161\) | 6.00278e10i | 0.554911i | ||||||||
\(162\) | 1.99191e10i | 0.178523i | ||||||||
\(163\) | 1.75024e11 | 1.52110 | 0.760552 | − | 0.649277i | \(-0.224928\pi\) | ||||
0.760552 | + | 0.649277i | \(0.224928\pi\) | |||||||
\(164\) | 1.72884e11 | 1.45726 | ||||||||
\(165\) | 6.91535e10i | 0.565450i | ||||||||
\(166\) | 6.29126e9 | 0.0499111 | ||||||||
\(167\) | −9.22995e9 | −0.0710586 | −0.0355293 | − | 0.999369i | \(-0.511312\pi\) | ||||
−0.0355293 | + | 0.999369i | \(0.511312\pi\) | |||||||
\(168\) | 6.65125e10i | 0.497001i | ||||||||
\(169\) | 1.37769e11 | 0.999350 | ||||||||
\(170\) | − | 4.79818e10i | − | 0.337934i | ||||||
\(171\) | −6.44274e10 | −0.440646 | ||||||||
\(172\) | − | 1.19962e11i | − | 0.796896i | ||||||
\(173\) | 5.92302e10i | 0.382219i | 0.981569 | + | 0.191110i | \(0.0612086\pi\) | ||||
−0.981569 | + | 0.191110i | \(0.938791\pi\) | |||||||
\(174\) | − | 9.83588e10i | − | 0.616690i | ||||||
\(175\) | −6.40921e10 | −0.390494 | ||||||||
\(176\) | − | 1.75059e10i | − | 0.103663i | ||||||
\(177\) | 7.55114e10 | − | 6.60177e10i | 0.434657 | − | 0.380009i | ||||
\(178\) | −2.69303e10 | −0.150710 | ||||||||
\(179\) | − | 2.00252e11i | − | 1.08971i | −0.838530 | − | 0.544855i | \(-0.816585\pi\) | ||
0.838530 | − | 0.544855i | \(-0.183415\pi\) | |||||||
\(180\) | 7.56117e10 | 0.400153 | ||||||||
\(181\) | −1.09128e11 | −0.561750 | −0.280875 | − | 0.959744i | \(-0.590625\pi\) | ||||
−0.280875 | + | 0.959744i | \(0.590625\pi\) | |||||||
\(182\) | 7.53463e9 | 0.0377316 | ||||||||
\(183\) | 1.90559e11i | 0.928482i | ||||||||
\(184\) | 1.18680e11 | 0.562716 | ||||||||
\(185\) | 1.95935e11i | 0.904177i | ||||||||
\(186\) | −1.64208e11 | −0.737615 | ||||||||
\(187\) | 8.17533e10i | 0.357517i | ||||||||
\(188\) | 3.43254e10i | 0.146159i | ||||||||
\(189\) | −4.27615e10 | −0.177314 | ||||||||
\(190\) | 3.99202e11i | 1.61222i | ||||||||
\(191\) | 2.66205e11i | 1.04725i | 0.851950 | + | 0.523623i | \(0.175420\pi\) | ||||
−0.851950 | + | 0.523623i | \(0.824580\pi\) | |||||||
\(192\) | −2.45279e11 | −0.940057 | ||||||||
\(193\) | 1.58248e11 | 0.590952 | 0.295476 | − | 0.955350i | \(-0.404522\pi\) | ||||
0.295476 | + | 0.955350i | \(0.404522\pi\) | |||||||
\(194\) | 3.23797e11 | 1.17832 | ||||||||
\(195\) | − | 3.14943e9i | − | 0.0111701i | ||||||
\(196\) | 6.91262e10 | 0.238981 | ||||||||
\(197\) | 3.48221e11 | 1.17361 | 0.586806 | − | 0.809728i | \(-0.300385\pi\) | ||||
0.586806 | + | 0.809728i | \(0.300385\pi\) | |||||||
\(198\) | −2.10290e11 | −0.691025 | ||||||||
\(199\) | −3.62970e11 | −1.16307 | −0.581534 | − | 0.813522i | \(-0.697547\pi\) | ||||
−0.581534 | + | 0.813522i | \(0.697547\pi\) | |||||||
\(200\) | 1.26716e11i | 0.395986i | ||||||||
\(201\) | − | 2.08481e11i | − | 0.635456i | ||||||
\(202\) | 4.66581e11 | 1.38730 | ||||||||
\(203\) | 2.11153e11 | 0.612515 | ||||||||
\(204\) | 8.93882e10 | 0.253005 | ||||||||
\(205\) | 2.53228e11 | 0.699426 | ||||||||
\(206\) | 2.79665e11 | 0.753881 | ||||||||
\(207\) | 7.63006e10i | 0.200759i | ||||||||
\(208\) | 7.97266e8i | 0.00204779i | ||||||||
\(209\) | − | 6.80175e11i | − | 1.70565i | ||||||
\(210\) | 2.64957e11i | 0.648752i | ||||||||
\(211\) | 3.43143e11i | 0.820471i | 0.911980 | + | 0.410236i | \(0.134554\pi\) | ||||
−0.911980 | + | 0.410236i | \(0.865446\pi\) | |||||||
\(212\) | −4.18996e10 | −0.0978433 | ||||||||
\(213\) | 1.23014e11 | 0.280580 | ||||||||
\(214\) | 3.12156e10i | 0.0695509i | ||||||||
\(215\) | − | 1.75711e11i | − | 0.382479i | ||||||
\(216\) | 8.45432e10i | 0.179808i | ||||||||
\(217\) | − | 3.52516e11i | − | 0.732621i | ||||||
\(218\) | −4.38336e11 | −0.890276 | ||||||||
\(219\) | − | 1.19597e11i | − | 0.237410i | ||||||
\(220\) | 7.98251e11i | 1.54891i | ||||||||
\(221\) | − | 3.72325e9i | − | 0.00706255i | ||||||
\(222\) | −5.95824e11 | −1.10498 | ||||||||
\(223\) | −1.45253e11 | −0.263391 | −0.131695 | − | 0.991290i | \(-0.542042\pi\) | ||||
−0.131695 | + | 0.991290i | \(0.542042\pi\) | |||||||
\(224\) | − | 5.52538e11i | − | 0.979765i | ||||||
\(225\) | −8.14666e10 | −0.141276 | ||||||||
\(226\) | 1.53234e12 | 2.59904 | ||||||||
\(227\) | − | 8.25512e11i | − | 1.36960i | −0.728731 | − | 0.684801i | \(-0.759889\pi\) | ||
0.728731 | − | 0.684801i | \(-0.240111\pi\) | |||||||
\(228\) | −7.43697e11 | −1.20704 | ||||||||
\(229\) | − | 2.38084e11i | − | 0.378052i | −0.981972 | − | 0.189026i | \(-0.939467\pi\) | ||
0.981972 | − | 0.189026i | \(-0.0605331\pi\) | |||||||
\(230\) | 4.72770e11 | 0.734532 | ||||||||
\(231\) | − | 4.51443e11i | − | 0.686347i | ||||||
\(232\) | − | 4.17467e11i | − | 0.621130i | ||||||
\(233\) | − | 1.15231e12i | − | 1.67799i | −0.544140 | − | 0.838994i | \(-0.683144\pi\) | ||
0.544140 | − | 0.838994i | \(-0.316856\pi\) | |||||||
\(234\) | 9.57717e9 | 0.0136508 | ||||||||
\(235\) | 5.02772e10i | 0.0701506i | ||||||||
\(236\) | 8.71642e11 | − | 7.62054e11i | 1.19063 | − | 1.04094i | ||||
\(237\) | 1.27634e10 | 0.0170696 | ||||||||
\(238\) | 3.13232e11i | 0.410187i | ||||||||
\(239\) | 5.78195e11 | 0.741455 | 0.370728 | − | 0.928742i | \(-0.379108\pi\) | ||||
0.370728 | + | 0.928742i | \(0.379108\pi\) | |||||||
\(240\) | −2.80360e10 | −0.0352095 | ||||||||
\(241\) | 4.61412e11 | 0.567550 | 0.283775 | − | 0.958891i | \(-0.408413\pi\) | ||||
0.283775 | + | 0.958891i | \(0.408413\pi\) | |||||||
\(242\) | − | 8.86524e11i | − | 1.06810i | ||||||
\(243\) | −5.43536e10 | −0.0641500 | ||||||||
\(244\) | 2.19965e12i | 2.54335i | ||||||||
\(245\) | 1.01251e11 | 0.114701 | ||||||||
\(246\) | 7.70047e11i | 0.854755i | ||||||||
\(247\) | 3.09769e10i | 0.0336941i | ||||||||
\(248\) | −6.96954e11 | −0.742926 | ||||||||
\(249\) | 1.71671e10i | 0.0179349i | ||||||||
\(250\) | 1.69578e12i | 1.73648i | ||||||||
\(251\) | −7.89068e10 | −0.0792038 | −0.0396019 | − | 0.999216i | \(-0.512609\pi\) | ||||
−0.0396019 | + | 0.999216i | \(0.512609\pi\) | |||||||
\(252\) | −4.93604e11 | −0.485709 | ||||||||
\(253\) | −8.05523e11 | −0.777098 | ||||||||
\(254\) | − | 4.20017e11i | − | 0.397282i | ||||||
\(255\) | 1.30929e11 | 0.121432 | ||||||||
\(256\) | −9.52708e11 | −0.866483 | ||||||||
\(257\) | 1.38822e12 | 1.23821 | 0.619104 | − | 0.785309i | \(-0.287496\pi\) | ||||
0.619104 | + | 0.785309i | \(0.287496\pi\) | |||||||
\(258\) | 5.34325e11 | 0.467419 | ||||||||
\(259\) | − | 1.27909e12i | − | 1.09750i | ||||||
\(260\) | − | 3.63544e10i | − | 0.0305978i | ||||||
\(261\) | 2.68394e11 | 0.221600 | ||||||||
\(262\) | −1.09105e12 | −0.883771 | ||||||||
\(263\) | 2.06493e12 | 1.64107 | 0.820535 | − | 0.571596i | \(-0.193676\pi\) | ||||
0.820535 | + | 0.571596i | \(0.193676\pi\) | |||||||
\(264\) | −8.92543e11 | −0.696000 | ||||||||
\(265\) | −6.13714e10 | −0.0469609 | ||||||||
\(266\) | − | 2.60604e12i | − | 1.95692i | ||||||
\(267\) | − | 7.34854e10i | − | 0.0541557i | ||||||
\(268\) | − | 2.40653e12i | − | 1.74067i | ||||||
\(269\) | − | 7.98504e10i | − | 0.0566912i | −0.999598 | − | 0.0283456i | \(-0.990976\pi\) | ||
0.999598 | − | 0.0283456i | \(-0.00902390\pi\) | |||||||
\(270\) | 3.36783e11i | 0.234710i | ||||||||
\(271\) | 8.27816e11 | 0.566353 | 0.283177 | − | 0.959068i | \(-0.408612\pi\) | ||||
0.283177 | + | 0.959068i | \(0.408612\pi\) | |||||||
\(272\) | −3.31442e10 | −0.0222619 | ||||||||
\(273\) | 2.05599e10i | 0.0135584i | ||||||||
\(274\) | 3.10220e12i | 2.00871i | ||||||||
\(275\) | − | 8.60062e11i | − | 0.546848i | ||||||
\(276\) | 8.80751e11i | 0.549931i | ||||||||
\(277\) | 2.75212e12 | 1.68760 | 0.843799 | − | 0.536659i | \(-0.180314\pi\) | ||||
0.843799 | + | 0.536659i | \(0.180314\pi\) | |||||||
\(278\) | − | 1.44855e12i | − | 0.872387i | ||||||
\(279\) | − | 4.48078e11i | − | 0.265053i | ||||||
\(280\) | 1.12456e12i | 0.653423i | ||||||||
\(281\) | −9.85832e10 | −0.0562693 | −0.0281346 | − | 0.999604i | \(-0.508957\pi\) | ||||
−0.0281346 | + | 0.999604i | \(0.508957\pi\) | |||||||
\(282\) | −1.52889e11 | −0.0857296 | ||||||||
\(283\) | − | 8.55168e11i | − | 0.471107i | −0.971861 | − | 0.235553i | \(-0.924310\pi\) | ||
0.971861 | − | 0.235553i | \(-0.0756902\pi\) | |||||||
\(284\) | 1.41997e12 | 0.768578 | ||||||||
\(285\) | −1.08931e12 | −0.579331 | ||||||||
\(286\) | 1.01108e11i | 0.0528393i | ||||||||
\(287\) | −1.65311e12 | −0.848968 | ||||||||
\(288\) | − | 7.02323e11i | − | 0.354466i | ||||||
\(289\) | −1.86121e12 | −0.923222 | ||||||||
\(290\) | − | 1.66301e12i | − | 0.810782i | ||||||
\(291\) | 8.83551e11i | 0.423416i | ||||||||
\(292\) | − | 1.38053e12i | − | 0.650326i | ||||||
\(293\) | 3.40558e12 | 1.57708 | 0.788538 | − | 0.614986i | \(-0.210838\pi\) | ||||
0.788538 | + | 0.614986i | \(0.210838\pi\) | |||||||
\(294\) | 3.07896e11i | 0.140174i | ||||||||
\(295\) | 1.27671e12 | − | 1.11620e12i | 0.571457 | − | 0.499610i | ||||
\(296\) | −2.52887e12 | −1.11293 | ||||||||
\(297\) | − | 5.73824e11i | − | 0.248311i | ||||||
\(298\) | −1.81992e12 | −0.774409 | ||||||||
\(299\) | 3.66856e10 | 0.0153511 | ||||||||
\(300\) | −9.40384e11 | −0.386989 | ||||||||
\(301\) | 1.14707e12i | 0.464255i | ||||||||
\(302\) | −3.88293e12 | −1.54570 | ||||||||
\(303\) | 1.27317e12i | 0.498509i | ||||||||
\(304\) | 2.75755e11 | 0.106207 | ||||||||
\(305\) | 3.22188e12i | 1.22071i | ||||||||
\(306\) | 3.98145e11i | 0.148400i | ||||||||
\(307\) | −3.76502e12 | −1.38062 | −0.690312 | − | 0.723512i | \(-0.742527\pi\) | ||||
−0.690312 | + | 0.723512i | \(0.742527\pi\) | |||||||
\(308\) | − | 5.21109e12i | − | 1.88008i | ||||||
\(309\) | 7.63128e11i | 0.270898i | ||||||||
\(310\) | −2.77636e12 | −0.969766 | ||||||||
\(311\) | −5.66700e12 | −1.94783 | −0.973915 | − | 0.226912i | \(-0.927137\pi\) | ||||
−0.973915 | + | 0.226912i | \(0.927137\pi\) | |||||||
\(312\) | 4.06487e10 | 0.0137491 | ||||||||
\(313\) | − | 1.16286e12i | − | 0.387084i | −0.981092 | − | 0.193542i | \(-0.938002\pi\) | ||
0.981092 | − | 0.193542i | \(-0.0619976\pi\) | |||||||
\(314\) | −4.04358e12 | −1.32470 | ||||||||
\(315\) | −7.22993e11 | −0.233121 | ||||||||
\(316\) | 1.47330e11 | 0.0467580 | ||||||||
\(317\) | −1.75108e12 | −0.547028 | −0.273514 | − | 0.961868i | \(-0.588186\pi\) | ||||
−0.273514 | + | 0.961868i | \(0.588186\pi\) | |||||||
\(318\) | − | 1.86626e11i | − | 0.0573899i | ||||||
\(319\) | 2.83350e12i | 0.857766i | ||||||||
\(320\) | −4.14707e12 | −1.23592 | ||||||||
\(321\) | −8.51786e10 | −0.0249922 | ||||||||
\(322\) | −3.08631e12 | −0.891579 | ||||||||
\(323\) | −1.28778e12 | −0.366294 | ||||||||
\(324\) | −6.27413e11 | −0.175723 | ||||||||
\(325\) | 3.91695e10i | 0.0108027i | ||||||||
\(326\) | 8.99878e12i | 2.44397i | ||||||||
\(327\) | − | 1.19610e12i | − | 0.319910i | ||||||
\(328\) | 3.26833e12i | 0.860909i | ||||||||
\(329\) | − | 3.28216e11i | − | 0.0851492i | ||||||
\(330\) | −3.55550e12 | −0.908512 | ||||||||
\(331\) | −6.66533e12 | −1.67758 | −0.838788 | − | 0.544459i | \(-0.816735\pi\) | ||||
−0.838788 | + | 0.544459i | \(0.816735\pi\) | |||||||
\(332\) | 1.98163e11i | 0.0491283i | ||||||||
\(333\) | − | 1.62584e12i | − | 0.397059i | ||||||
\(334\) | − | 4.74554e11i | − | 0.114170i | ||||||
\(335\) | − | 3.52490e12i | − | 0.835454i | ||||||
\(336\) | 1.83023e11 | 0.0427375 | ||||||||
\(337\) | − | 3.31280e12i | − | 0.762160i | −0.924542 | − | 0.381080i | \(-0.875552\pi\) | ||
0.924542 | − | 0.381080i | \(-0.124448\pi\) | |||||||
\(338\) | 7.08334e12i | 1.60566i | ||||||||
\(339\) | 4.18132e12i | 0.933931i | ||||||||
\(340\) | 1.51134e12 | 0.332634 | ||||||||
\(341\) | 4.73046e12 | 1.02596 | ||||||||
\(342\) | − | 3.31251e12i | − | 0.707989i | ||||||
\(343\) | −5.03516e12 | −1.06058 | ||||||||
\(344\) | 2.26785e12 | 0.470785 | ||||||||
\(345\) | 1.29006e12i | 0.263945i | ||||||||
\(346\) | −3.04530e12 | −0.614114 | ||||||||
\(347\) | − | 4.81033e12i | − | 0.956153i | −0.878318 | − | 0.478076i | \(-0.841334\pi\) | ||
0.878318 | − | 0.478076i | \(-0.158666\pi\) | |||||||
\(348\) | 3.09812e12 | 0.607018 | ||||||||
\(349\) | − | 1.57464e12i | − | 0.304126i | −0.988371 | − | 0.152063i | \(-0.951408\pi\) | ||
0.988371 | − | 0.152063i | \(-0.0485917\pi\) | |||||||
\(350\) | − | 3.29527e12i | − | 0.627409i | ||||||
\(351\) | 2.61334e10i | 0.00490524i | ||||||||
\(352\) | 7.41459e12 | 1.37206 | ||||||||
\(353\) | − | 2.26537e12i | − | 0.413300i | −0.978415 | − | 0.206650i | \(-0.933744\pi\) | ||
0.978415 | − | 0.206650i | \(-0.0662562\pi\) | |||||||
\(354\) | 3.39428e12 | + | 3.88239e12i | 0.610563 | + | 0.698366i | ||||
\(355\) | 2.07987e12 | 0.368887 | ||||||||
\(356\) | − | 8.48255e11i | − | 0.148346i | ||||||
\(357\) | −8.54723e11 | −0.147395 | ||||||||
\(358\) | 1.02959e13 | 1.75084 | ||||||||
\(359\) | 6.50960e12 | 1.09165 | 0.545824 | − | 0.837900i | \(-0.316217\pi\) | ||||
0.545824 | + | 0.837900i | \(0.316217\pi\) | |||||||
\(360\) | 1.42942e12i | 0.236400i | ||||||||
\(361\) | 4.58309e12 | 0.747520 | ||||||||
\(362\) | − | 5.61077e12i | − | 0.902567i | ||||||
\(363\) | 2.41908e12 | 0.383810 | ||||||||
\(364\) | 2.37327e11i | 0.0371398i | ||||||||
\(365\) | − | 2.02209e12i | − | 0.312131i | ||||||
\(366\) | −9.79751e12 | −1.49180 | ||||||||
\(367\) | − | 6.69893e12i | − | 1.00618i | −0.864234 | − | 0.503090i | \(-0.832197\pi\) | ||
0.864234 | − | 0.503090i | \(-0.167803\pi\) | |||||||
\(368\) | − | 3.26573e11i | − | 0.0483884i | ||||||
\(369\) | −2.10124e12 | −0.307146 | ||||||||
\(370\) | −1.00739e13 | −1.45275 | ||||||||
\(371\) | 4.00641e11 | 0.0570014 | ||||||||
\(372\) | − | 5.17224e12i | − | 0.726046i | ||||||
\(373\) | 2.32947e12 | 0.322635 | 0.161318 | − | 0.986903i | \(-0.448426\pi\) | ||||
0.161318 | + | 0.986903i | \(0.448426\pi\) | |||||||
\(374\) | −4.20331e12 | −0.574426 | ||||||||
\(375\) | −4.62732e12 | −0.623983 | ||||||||
\(376\) | −6.48912e11 | −0.0863469 | ||||||||
\(377\) | − | 1.29045e11i | − | 0.0169447i | ||||||
\(378\) | − | 2.19857e12i | − | 0.284892i | ||||||
\(379\) | 1.03290e13 | 1.32087 | 0.660436 | − | 0.750882i | \(-0.270371\pi\) | ||||
0.660436 | + | 0.750882i | \(0.270371\pi\) | |||||||
\(380\) | −1.25741e13 | −1.58693 | ||||||||
\(381\) | 1.14611e12 | 0.142758 | ||||||||
\(382\) | −1.36868e13 | −1.68262 | ||||||||
\(383\) | 1.21823e13 | 1.47820 | 0.739102 | − | 0.673594i | \(-0.235250\pi\) | ||||
0.739102 | + | 0.673594i | \(0.235250\pi\) | |||||||
\(384\) | − | 7.48478e12i | − | 0.896443i | ||||||
\(385\) | − | 7.63281e12i | − | 0.902362i | ||||||
\(386\) | 8.13627e12i | 0.949486i | ||||||||
\(387\) | 1.45802e12i | 0.167961i | ||||||||
\(388\) | 1.01990e13i | 1.15984i | ||||||||
\(389\) | 1.17149e13 | 1.31520 | 0.657599 | − | 0.753368i | \(-0.271572\pi\) | ||||
0.657599 | + | 0.753368i | \(0.271572\pi\) | |||||||
\(390\) | 1.61927e11 | 0.0179471 | ||||||||
\(391\) | 1.52511e12i | 0.166885i | ||||||||
\(392\) | 1.30681e12i | 0.141183i | ||||||||
\(393\) | − | 2.97718e12i | − | 0.317572i | ||||||
\(394\) | 1.79037e13i | 1.88565i | ||||||||
\(395\) | 2.15798e11 | 0.0224420 | ||||||||
\(396\) | − | 6.62375e12i | − | 0.680187i | ||||||
\(397\) | 8.14478e12i | 0.825899i | 0.910754 | + | 0.412950i | \(0.135501\pi\) | ||||
−0.910754 | + | 0.412950i | \(0.864499\pi\) | |||||||
\(398\) | − | 1.86620e13i | − | 1.86871i | ||||||
\(399\) | 7.11117e12 | 0.703196 | ||||||||
\(400\) | 3.48684e11 | 0.0340512 | ||||||||
\(401\) | 9.47598e12i | 0.913907i | 0.889491 | + | 0.456954i | \(0.151059\pi\) | ||||
−0.889491 | + | 0.456954i | \(0.848941\pi\) | |||||||
\(402\) | 1.07190e13 | 1.02099 | ||||||||
\(403\) | −2.15438e11 | −0.0202673 | ||||||||
\(404\) | 1.46964e13i | 1.36554i | ||||||||
\(405\) | −9.18987e11 | −0.0843401 | ||||||||
\(406\) | 1.08563e13i | 0.984132i | ||||||||
\(407\) | 1.71643e13 | 1.53693 | ||||||||
\(408\) | 1.68986e12i | 0.149469i | ||||||||
\(409\) | − | 1.12656e12i | − | 0.0984326i | −0.998788 | − | 0.0492163i | \(-0.984328\pi\) | ||
0.998788 | − | 0.0492163i | \(-0.0156724\pi\) | |||||||
\(410\) | 1.30196e13i | 1.12377i | ||||||||
\(411\) | −8.46503e12 | −0.721804 | ||||||||
\(412\) | 8.80893e12i | 0.742057i | ||||||||
\(413\) | −8.33457e12 | + | 7.28670e12i | −0.693638 | + | 0.606430i | ||||
\(414\) | −3.92297e12 | −0.322562 | ||||||||
\(415\) | 2.90254e11i | 0.0235796i | ||||||||
\(416\) | −3.37680e11 | −0.0271043 | ||||||||
\(417\) | 3.95268e12 | 0.313481 | ||||||||
\(418\) | 3.49709e13 | 2.74048 | ||||||||
\(419\) | − | 2.01771e13i | − | 1.56239i | −0.624289 | − | 0.781193i | \(-0.714611\pi\) | ||
0.624289 | − | 0.781193i | \(-0.285389\pi\) | |||||||
\(420\) | −8.34564e12 | −0.638577 | ||||||||
\(421\) | − | 1.04111e13i | − | 0.787199i | −0.919282 | − | 0.393600i | \(-0.871230\pi\) | ||
0.919282 | − | 0.393600i | \(-0.128770\pi\) | |||||||
\(422\) | −1.76426e13 | −1.31826 | ||||||||
\(423\) | − | 4.17191e11i | − | 0.0308059i | ||||||
\(424\) | − | 7.92101e11i | − | 0.0578031i | ||||||
\(425\) | −1.62836e12 | −0.117438 | ||||||||
\(426\) | 6.32471e12i | 0.450809i | ||||||||
\(427\) | − | 2.10329e13i | − | 1.48170i | ||||||
\(428\) | −9.83232e11 | −0.0684600 | ||||||||
\(429\) | −2.75897e11 | −0.0189872 | ||||||||
\(430\) | 9.03413e12 | 0.614531 | ||||||||
\(431\) | − | 1.69638e13i | − | 1.14061i | −0.821433 | − | 0.570305i | \(-0.806825\pi\) | ||
0.821433 | − | 0.570305i | \(-0.193175\pi\) | |||||||
\(432\) | 2.32638e11 | 0.0154619 | ||||||||
\(433\) | 1.53769e13 | 1.01025 | 0.505127 | − | 0.863045i | \(-0.331446\pi\) | ||||
0.505127 | + | 0.863045i | \(0.331446\pi\) | |||||||
\(434\) | 1.81245e13 | 1.17711 | ||||||||
\(435\) | 4.53788e12 | 0.291344 | ||||||||
\(436\) | − | 1.38068e13i | − | 0.876313i | ||||||
\(437\) | − | 1.26887e13i | − | 0.796175i | ||||||
\(438\) | 6.14903e12 | 0.381449 | ||||||||
\(439\) | −1.65688e13 | −1.01618 | −0.508088 | − | 0.861305i | \(-0.669648\pi\) | ||||
−0.508088 | + | 0.861305i | \(0.669648\pi\) | |||||||
\(440\) | −1.50907e13 | −0.915054 | ||||||||
\(441\) | −8.40162e11 | −0.0503698 | ||||||||
\(442\) | 1.91430e11 | 0.0113474 | ||||||||
\(443\) | 8.43036e12i | 0.494114i | 0.969001 | + | 0.247057i | \(0.0794636\pi\) | ||||
−0.969001 | + | 0.247057i | \(0.920536\pi\) | |||||||
\(444\) | − | 1.87673e13i | − | 1.08765i | ||||||
\(445\) | − | 1.24246e12i | − | 0.0712003i | ||||||
\(446\) | − | 7.46813e12i | − | 0.423192i | ||||||
\(447\) | − | 4.96605e12i | − | 0.278274i | ||||||
\(448\) | 2.70727e13 | 1.50017 | ||||||||
\(449\) | −2.91559e13 | −1.59770 | −0.798849 | − | 0.601531i | \(-0.794558\pi\) | ||||
−0.798849 | + | 0.601531i | \(0.794558\pi\) | |||||||
\(450\) | − | 4.18857e12i | − | 0.226988i | ||||||
\(451\) | − | 2.21833e13i | − | 1.18890i | ||||||
\(452\) | 4.82657e13i | 2.55827i | ||||||||
\(453\) | − | 1.05954e13i | − | 0.555428i | ||||||
\(454\) | 4.24434e13 | 2.20055 | ||||||||
\(455\) | 3.47618e11i | 0.0178256i | ||||||||
\(456\) | − | 1.40594e13i | − | 0.713086i | ||||||
\(457\) | − | 1.45565e13i | − | 0.730259i | −0.930957 | − | 0.365129i | \(-0.881025\pi\) | ||
0.930957 | − | 0.365129i | \(-0.118975\pi\) | |||||||
\(458\) | 1.22410e13 | 0.607420 | ||||||||
\(459\) | −1.08643e12 | −0.0533257 | ||||||||
\(460\) | 1.48914e13i | 0.723011i | ||||||||
\(461\) | 7.73613e12 | 0.371552 | 0.185776 | − | 0.982592i | \(-0.440520\pi\) | ||||
0.185776 | + | 0.982592i | \(0.440520\pi\) | |||||||
\(462\) | 2.32108e13 | 1.10276 | ||||||||
\(463\) | − | 1.09254e13i | − | 0.513490i | −0.966479 | − | 0.256745i | \(-0.917350\pi\) | ||
0.966479 | − | 0.256745i | \(-0.0826501\pi\) | |||||||
\(464\) | −1.14875e12 | −0.0534115 | ||||||||
\(465\) | − | 7.57590e12i | − | 0.348473i | ||||||
\(466\) | 5.92455e13 | 2.69604 | ||||||||
\(467\) | 1.60922e13i | 0.724488i | 0.932083 | + | 0.362244i | \(0.117989\pi\) | ||||
−0.932083 | + | 0.362244i | \(0.882011\pi\) | |||||||
\(468\) | 3.01663e11i | 0.0134367i | ||||||||
\(469\) | 2.30110e13i | 1.01408i | ||||||||
\(470\) | −2.58498e12 | −0.112711 | ||||||||
\(471\) | − | 1.10338e13i | − | 0.476014i | ||||||
\(472\) | 1.44064e13 | + | 1.64782e13i | 0.614959 | + | 0.703394i | ||||
\(473\) | −1.53927e13 | −0.650143 | ||||||||
\(474\) | 6.56224e11i | 0.0274259i | ||||||||
\(475\) | 1.35478e13 | 0.560272 | ||||||||
\(476\) | −9.86622e12 | −0.403753 | ||||||||
\(477\) | 5.09249e11 | 0.0206224 | ||||||||
\(478\) | 2.97277e13i | 1.19130i | ||||||||
\(479\) | −3.75735e13 | −1.49006 | −0.745031 | − | 0.667030i | \(-0.767565\pi\) | ||||
−0.745031 | + | 0.667030i | \(0.767565\pi\) | |||||||
\(480\) | − | 1.18746e13i | − | 0.466028i | ||||||
\(481\) | −7.81708e11 | −0.0303612 | ||||||||
\(482\) | 2.37233e13i | 0.911886i | ||||||||
\(483\) | − | 8.42167e12i | − | 0.320378i | ||||||
\(484\) | 2.79238e13 | 1.05135 | ||||||||
\(485\) | 1.49387e13i | 0.556678i | ||||||||
\(486\) | − | 2.79457e12i | − | 0.103070i | ||||||
\(487\) | −3.48485e13 | −1.27215 | −0.636076 | − | 0.771626i | \(-0.719444\pi\) | ||||
−0.636076 | + | 0.771626i | \(0.719444\pi\) | |||||||
\(488\) | −4.15839e13 | −1.50254 | ||||||||
\(489\) | −2.45552e13 | −0.878210 | ||||||||
\(490\) | 5.20577e12i | 0.184291i | ||||||||
\(491\) | −2.22606e13 | −0.780061 | −0.390031 | − | 0.920802i | \(-0.627536\pi\) | ||||
−0.390031 | + | 0.920802i | \(0.627536\pi\) | |||||||
\(492\) | −2.42550e13 | −0.841349 | ||||||||
\(493\) | 5.36469e12 | 0.184208 | ||||||||
\(494\) | −1.59267e12 | −0.0541365 | ||||||||
\(495\) | − | 9.70196e12i | − | 0.326463i | ||||||
\(496\) | 1.91781e12i | 0.0638848i | ||||||||
\(497\) | −1.35777e13 | −0.447757 | ||||||||
\(498\) | −8.82640e11 | −0.0288162 | ||||||||
\(499\) | 4.69879e13 | 1.51874 | 0.759370 | − | 0.650659i | \(-0.225507\pi\) | ||||
0.759370 | + | 0.650659i | \(0.225507\pi\) | |||||||
\(500\) | −5.34140e13 | −1.70925 | ||||||||
\(501\) | 1.29493e12 | 0.0410257 | ||||||||
\(502\) | − | 4.05697e12i | − | 0.127257i | ||||||
\(503\) | − | 1.27426e13i | − | 0.395748i | −0.980227 | − | 0.197874i | \(-0.936596\pi\) | ||
0.980227 | − | 0.197874i | \(-0.0634037\pi\) | |||||||
\(504\) | − | 9.33145e12i | − | 0.286943i | ||||||
\(505\) | 2.15262e13i | 0.655406i | ||||||||
\(506\) | − | 4.14157e13i | − | 1.24857i | ||||||
\(507\) | −1.93284e13 | −0.576975 | ||||||||
\(508\) | 1.32298e13 | 0.391051 | ||||||||
\(509\) | 5.19116e13i | 1.51941i | 0.650267 | + | 0.759706i | \(0.274657\pi\) | ||||
−0.650267 | + | 0.759706i | \(0.725343\pi\) | |||||||
\(510\) | 6.73166e12i | 0.195106i | ||||||||
\(511\) | 1.32005e13i | 0.378866i | ||||||||
\(512\) | 5.64711e12i | 0.160500i | ||||||||
\(513\) | 9.03891e12 | 0.254407 | ||||||||
\(514\) | 7.13750e13i | 1.98944i | ||||||||
\(515\) | 1.29026e13i | 0.356158i | ||||||||
\(516\) | 1.68302e13i | 0.460088i | ||||||||
\(517\) | 4.40439e12 | 0.119243 | ||||||||
\(518\) | 6.57640e13 | 1.76335 | ||||||||
\(519\) | − | 8.30976e12i | − | 0.220674i | ||||||
\(520\) | 6.87270e11 | 0.0180764 | ||||||||
\(521\) | −1.40221e13 | −0.365278 | −0.182639 | − | 0.983180i | \(-0.558464\pi\) | ||||
−0.182639 | + | 0.983180i | \(0.558464\pi\) | |||||||
\(522\) | 1.37994e13i | 0.356046i | ||||||||
\(523\) | −5.23571e13 | −1.33803 | −0.669017 | − | 0.743247i | \(-0.733285\pi\) | ||||
−0.669017 | + | 0.743247i | \(0.733285\pi\) | |||||||
\(524\) | − | 3.43661e13i | − | 0.869909i | ||||||
\(525\) | 8.99187e12 | 0.225452 | ||||||||
\(526\) | 1.06168e14i | 2.63672i | ||||||||
\(527\) | − | 8.95624e12i | − | 0.220329i | ||||||
\(528\) | 2.45602e12i | 0.0598496i | ||||||||
\(529\) | 2.63995e13 | 0.637261 | ||||||||
\(530\) | − | 3.15538e12i | − | 0.0754524i | ||||||
\(531\) | −1.05940e13 | + | 9.26203e12i | −0.250949 | + | 0.219398i | ||||
\(532\) | 8.20855e13 | 1.92623 | ||||||||
\(533\) | 1.01029e12i | 0.0234859i | ||||||||
\(534\) | 3.77822e12 | 0.0870124 | ||||||||
\(535\) | −1.44016e12 | −0.0328581 | ||||||||
\(536\) | 4.54948e13 | 1.02834 | ||||||||
\(537\) | 2.80945e13i | 0.629144i | ||||||||
\(538\) | 4.10548e12 | 0.0910862 | ||||||||
\(539\) | − | 8.86979e12i | − | 0.194971i | ||||||
\(540\) | −1.06080e13 | −0.231029 | ||||||||
\(541\) | 7.10673e13i | 1.53350i | 0.641947 | + | 0.766749i | \(0.278127\pi\) | ||||
−0.641947 | + | 0.766749i | \(0.721873\pi\) | |||||||
\(542\) | 4.25618e13i | 0.909963i | ||||||||
\(543\) | 1.53102e13 | 0.324326 | ||||||||
\(544\) | − | 1.40381e13i | − | 0.294656i | ||||||
\(545\) | − | 2.02231e13i | − | 0.420596i | ||||||
\(546\) | −1.05708e12 | −0.0217843 | ||||||||
\(547\) | −1.72935e13 | −0.353140 | −0.176570 | − | 0.984288i | \(-0.556500\pi\) | ||||
−0.176570 | + | 0.984288i | \(0.556500\pi\) | |||||||
\(548\) | −9.77134e13 | −1.97720 | ||||||||
\(549\) | − | 2.67347e13i | − | 0.536059i | ||||||
\(550\) | 4.42198e13 | 0.878624 | ||||||||
\(551\) | −4.46334e13 | −0.878824 | ||||||||
\(552\) | −1.66504e13 | −0.324884 | ||||||||
\(553\) | −1.40876e12 | −0.0272402 | ||||||||
\(554\) | 1.41499e14i | 2.71148i | ||||||||
\(555\) | − | 2.74889e13i | − | 0.522027i | ||||||
\(556\) | 4.56266e13 | 0.858704 | ||||||||
\(557\) | −3.54388e13 | −0.661003 | −0.330502 | − | 0.943805i | \(-0.607218\pi\) | ||||
−0.330502 | + | 0.943805i | \(0.607218\pi\) | |||||||
\(558\) | 2.30378e13 | 0.425862 | ||||||||
\(559\) | 7.01023e11 | 0.0128432 | ||||||||
\(560\) | 3.09447e12 | 0.0561884 | ||||||||
\(561\) | − | 1.14697e13i | − | 0.206413i | ||||||
\(562\) | − | 5.06862e12i | − | 0.0904082i | ||||||
\(563\) | 3.72684e13i | 0.658869i | 0.944178 | + | 0.329435i | \(0.106858\pi\) | ||||
−0.944178 | + | 0.329435i | \(0.893142\pi\) | |||||||
\(564\) | − | 4.81572e12i | − | 0.0843850i | ||||||
\(565\) | 7.06959e13i | 1.22787i | ||||||||
\(566\) | 4.39681e13 | 0.756930 | ||||||||
\(567\) | 5.99927e12 | 0.102373 | ||||||||
\(568\) | 2.68442e13i | 0.454055i | ||||||||
\(569\) | − | 3.76671e13i | − | 0.631541i | −0.948836 | − | 0.315770i | \(-0.897737\pi\) | ||
0.948836 | − | 0.315770i | \(-0.102263\pi\) | |||||||
\(570\) | − | 5.60064e13i | − | 0.930816i | ||||||
\(571\) | 3.06504e13i | 0.504959i | 0.967602 | + | 0.252479i | \(0.0812460\pi\) | ||||
−0.967602 | + | 0.252479i | \(0.918754\pi\) | |||||||
\(572\) | −3.18473e12 | −0.0520106 | ||||||||
\(573\) | − | 3.73475e13i | − | 0.604628i | ||||||
\(574\) | − | 8.49938e13i | − | 1.36404i | ||||||
\(575\) | − | 1.60444e13i | − | 0.255262i | ||||||
\(576\) | 3.44117e13 | 0.542742 | ||||||||
\(577\) | 2.72045e11 | 0.00425364 | 0.00212682 | − | 0.999998i | \(-0.499323\pi\) | ||||
0.00212682 | + | 0.999998i | \(0.499323\pi\) | |||||||
\(578\) | − | 9.56934e13i | − | 1.48335i | ||||||
\(579\) | −2.22016e13 | −0.341186 | ||||||||
\(580\) | 5.23816e13 | 0.798066 | ||||||||
\(581\) | − | 1.89482e12i | − | 0.0286211i | ||||||
\(582\) | −4.54275e13 | −0.680305 | ||||||||
\(583\) | 5.37627e12i | 0.0798248i | ||||||||
\(584\) | 2.60985e13 | 0.384195 | ||||||||
\(585\) | 4.41852e11i | 0.00644908i | ||||||||
\(586\) | 1.75097e14i | 2.53390i | ||||||||
\(587\) | − | 6.02247e13i | − | 0.864139i | −0.901840 | − | 0.432070i | \(-0.857783\pi\) | ||
0.901840 | − | 0.432070i | \(-0.142217\pi\) | |||||||
\(588\) | −9.69814e12 | −0.137975 | ||||||||
\(589\) | 7.45146e13i | 1.05115i | ||||||||
\(590\) | 5.73889e13 | + | 6.56418e13i | 0.802727 | + | 0.918164i | ||||
\(591\) | −4.88541e13 | −0.677585 | ||||||||
\(592\) | 6.95872e12i | 0.0957019i | ||||||||
\(593\) | −4.32391e13 | −0.589662 | −0.294831 | − | 0.955549i | \(-0.595263\pi\) | ||||
−0.294831 | + | 0.955549i | \(0.595263\pi\) | |||||||
\(594\) | 2.95029e13 | 0.398963 | ||||||||
\(595\) | −1.44513e13 | −0.193786 | ||||||||
\(596\) | − | 5.73240e13i | − | 0.762263i | ||||||
\(597\) | 5.09233e13 | 0.671498 | ||||||||
\(598\) | 1.88618e12i | 0.0246647i | ||||||||
\(599\) | −5.02386e13 | −0.651483 | −0.325742 | − | 0.945459i | \(-0.605614\pi\) | ||||
−0.325742 | + | 0.945459i | \(0.605614\pi\) | |||||||
\(600\) | − | 1.77777e13i | − | 0.228623i | ||||||
\(601\) | − | 4.09214e13i | − | 0.521889i | −0.965354 | − | 0.260945i | \(-0.915966\pi\) | ||
0.965354 | − | 0.260945i | \(-0.0840340\pi\) | |||||||
\(602\) | −5.89760e13 | −0.745922 | ||||||||
\(603\) | 2.92490e13i | 0.366881i | ||||||||
\(604\) | − | 1.22305e14i | − | 1.52146i | ||||||
\(605\) | 4.09007e13 | 0.504607 | ||||||||
\(606\) | −6.54596e13 | −0.800958 | ||||||||
\(607\) | −6.92676e13 | −0.840595 | −0.420298 | − | 0.907386i | \(-0.638074\pi\) | ||||
−0.420298 | + | 0.907386i | \(0.638074\pi\) | |||||||
\(608\) | 1.16795e14i | 1.40575i | ||||||||
\(609\) | −2.96239e13 | −0.353636 | ||||||||
\(610\) | −1.65652e14 | −1.96132 | ||||||||
\(611\) | −2.00587e11 | −0.00235558 | ||||||||
\(612\) | −1.25408e13 | −0.146073 | ||||||||
\(613\) | − | 8.23233e13i | − | 0.951087i | −0.879692 | − | 0.475543i | \(-0.842251\pi\) | ||
0.879692 | − | 0.475543i | \(-0.157749\pi\) | |||||||
\(614\) | − | 1.93577e14i | − | 2.21826i | ||||||
\(615\) | −3.55269e13 | −0.403814 | ||||||||
\(616\) | 9.85143e13 | 1.11070 | ||||||||
\(617\) | −7.21436e12 | −0.0806811 | −0.0403406 | − | 0.999186i | \(-0.512844\pi\) | ||||
−0.0403406 | + | 0.999186i | \(0.512844\pi\) | |||||||
\(618\) | −3.92360e13 | −0.435253 | ||||||||
\(619\) | −4.97946e13 | −0.547935 | −0.273968 | − | 0.961739i | \(-0.588336\pi\) | ||||
−0.273968 | + | 0.961739i | \(0.588336\pi\) | |||||||
\(620\) | − | 8.74500e13i | − | 0.954556i | ||||||
\(621\) | − | 1.07047e13i | − | 0.115909i | ||||||
\(622\) | − | 2.91367e14i | − | 3.12959i | ||||||
\(623\) | 8.11094e12i | 0.0864233i | ||||||||
\(624\) | − | 1.11853e11i | − | 0.00118229i | ||||||
\(625\) | −3.78174e13 | −0.396544 | ||||||||
\(626\) | 5.97880e13 | 0.621931 | ||||||||
\(627\) | 9.54259e13i | 0.984756i | ||||||||
\(628\) | − | 1.27365e14i | − | 1.30392i | ||||||
\(629\) | − | 3.24974e13i | − | 0.330062i | ||||||
\(630\) | − | 3.71724e13i | − | 0.374557i | ||||||
\(631\) | −8.82637e13 | −0.882339 | −0.441169 | − | 0.897424i | \(-0.645436\pi\) | ||||
−0.441169 | + | 0.897424i | \(0.645436\pi\) | |||||||
\(632\) | 2.78523e12i | 0.0276233i | ||||||||
\(633\) | − | 4.81417e13i | − | 0.473699i | ||||||
\(634\) | − | 9.00311e13i | − | 0.878914i | ||||||
\(635\) | 1.93779e13 | 0.187689 | ||||||||
\(636\) | 5.87836e12 | 0.0564898 | ||||||||
\(637\) | 4.03953e11i | 0.00385153i | ||||||||
\(638\) | −1.45683e14 | −1.37818 | ||||||||
\(639\) | −1.72584e13 | −0.161993 | ||||||||
\(640\) | − | 1.26549e14i | − | 1.17858i | ||||||
\(641\) | −6.88079e13 | −0.635840 | −0.317920 | − | 0.948117i | \(-0.602984\pi\) | ||||
−0.317920 | + | 0.948117i | \(0.602984\pi\) | |||||||
\(642\) | − | 4.37943e12i | − | 0.0401552i | ||||||
\(643\) | 1.12758e14 | 1.02587 | 0.512937 | − | 0.858426i | \(-0.328557\pi\) | ||||
0.512937 | + | 0.858426i | \(0.328557\pi\) | |||||||
\(644\) | − | 9.72129e13i | − | 0.877595i | ||||||
\(645\) | 2.46516e13i | 0.220824i | ||||||||
\(646\) | − | 6.62108e13i | − | 0.588527i | ||||||
\(647\) | −8.96543e13 | −0.790769 | −0.395385 | − | 0.918516i | \(-0.629389\pi\) | ||||
−0.395385 | + | 0.918516i | \(0.629389\pi\) | |||||||
\(648\) | − | 1.18611e13i | − | 0.103812i | ||||||
\(649\) | −9.77815e13 | − | 1.11843e14i | −0.849245 | − | 0.971371i | ||||
\(650\) | −2.01388e12 | −0.0173567 | ||||||||
\(651\) | 4.94566e13i | 0.422979i | ||||||||
\(652\) | −2.83445e14 | −2.40564 | ||||||||
\(653\) | 8.89596e13 | 0.749251 | 0.374625 | − | 0.927176i | \(-0.377771\pi\) | ||||
0.374625 | + | 0.927176i | \(0.377771\pi\) | |||||||
\(654\) | 6.14969e13 | 0.514001 | ||||||||
\(655\) | − | 5.03368e13i | − | 0.417522i | ||||||
\(656\) | 8.99349e12 | 0.0740303 | ||||||||
\(657\) | 1.67790e13i | 0.137069i | ||||||||
\(658\) | 1.68751e13 | 0.136810 | ||||||||
\(659\) | 3.64044e13i | 0.292905i | 0.989218 | + | 0.146453i | \(0.0467856\pi\) | ||||
−0.989218 | + | 0.146453i | \(0.953214\pi\) | |||||||
\(660\) | − | 1.11991e14i | − | 0.894263i | ||||||
\(661\) | −4.09725e13 | −0.324702 | −0.162351 | − | 0.986733i | \(-0.551908\pi\) | ||||
−0.162351 | + | 0.986733i | \(0.551908\pi\) | |||||||
\(662\) | − | 3.42696e14i | − | 2.69537i | ||||||
\(663\) | 5.22358e11i | 0.00407756i | ||||||||
\(664\) | −3.74622e12 | −0.0290237 | ||||||||
\(665\) | 1.20232e14 | 0.924514 | ||||||||
\(666\) | 8.35917e13 | 0.637958 | ||||||||
\(667\) | 5.28588e13i | 0.400395i | ||||||||
\(668\) | 1.49476e13 | 0.112380 | ||||||||
\(669\) | 2.03784e13 | 0.152069 | ||||||||
\(670\) | 1.81231e14 | 1.34233 | ||||||||
\(671\) | 2.82244e14 | 2.07497 | ||||||||
\(672\) | 7.75189e13i | 0.565667i | ||||||||
\(673\) | 4.87480e12i | 0.0353087i | 0.999844 | + | 0.0176544i | \(0.00561985\pi\) | ||||
−0.999844 | + | 0.0176544i | \(0.994380\pi\) | |||||||
\(674\) | 1.70326e14 | 1.22457 | ||||||||
\(675\) | 1.14294e13 | 0.0815655 | ||||||||
\(676\) | −2.23112e14 | −1.58048 | ||||||||
\(677\) | 9.64158e13 | 0.677961 | 0.338981 | − | 0.940793i | \(-0.389918\pi\) | ||||
0.338981 | + | 0.940793i | \(0.389918\pi\) | |||||||
\(678\) | −2.14981e14 | −1.50055 | ||||||||
\(679\) | − | 9.75219e13i | − | 0.675699i | ||||||
\(680\) | 2.85714e13i | 0.196511i | ||||||||
\(681\) | 1.15816e14i | 0.790740i | ||||||||
\(682\) | 2.43215e14i | 1.64842i | ||||||||
\(683\) | − | 7.87699e13i | − | 0.529977i | −0.964252 | − | 0.264988i | \(-0.914632\pi\) | ||
0.964252 | − | 0.264988i | \(-0.0853682\pi\) | |||||||
\(684\) | 1.04338e14 | 0.696885 | ||||||||
\(685\) | −1.43123e14 | −0.948979 | ||||||||
\(686\) | − | 2.58881e14i | − | 1.70404i | ||||||
\(687\) | 3.34022e13i | 0.218269i | ||||||||
\(688\) | − | 6.24046e12i | − | 0.0404832i | ||||||
\(689\) | − | 2.44849e11i | − | 0.00157689i | ||||||
\(690\) | −6.63278e13 | −0.424082 | ||||||||
\(691\) | 6.25229e13i | 0.396871i | 0.980114 | + | 0.198435i | \(0.0635860\pi\) | ||||
−0.980114 | + | 0.198435i | \(0.936414\pi\) | |||||||
\(692\) | − | 9.59211e13i | − | 0.604482i | ||||||
\(693\) | 6.33358e13i | 0.396262i | ||||||||
\(694\) | 2.47321e14 | 1.53626 | ||||||||
\(695\) | 6.68303e13 | 0.412144 | ||||||||
\(696\) | 5.85690e13i | 0.358610i | ||||||||
\(697\) | −4.19999e13 | −0.255320 | ||||||||
\(698\) | 8.09595e13 | 0.488642 | ||||||||
\(699\) | 1.61664e14i | 0.968787i | ||||||||
\(700\) | 1.03795e14 | 0.617569 | ||||||||
\(701\) | − | 2.41001e14i | − | 1.42373i | −0.702316 | − | 0.711865i | \(-0.747851\pi\) | ||
0.702316 | − | 0.711865i | \(-0.252149\pi\) | |||||||
\(702\) | −1.34364e12 | −0.00788129 | ||||||||
\(703\) | 2.70374e14i | 1.57466i | ||||||||
\(704\) | 3.63292e14i | 2.10084i | ||||||||
\(705\) | − | 7.05369e12i | − | 0.0405015i | ||||||
\(706\) | 1.16473e14 | 0.664052 | ||||||||
\(707\) | − | 1.40526e14i | − | 0.795536i | ||||||
\(708\) | −1.22288e14 | + | 1.06913e14i | −0.687412 | + | 0.600987i | ||||
\(709\) | −2.57817e14 | −1.43906 | −0.719532 | − | 0.694459i | \(-0.755644\pi\) | ||||
−0.719532 | + | 0.694459i | \(0.755644\pi\) | |||||||
\(710\) | 1.06935e14i | 0.592693i | ||||||||
\(711\) | −1.79065e12 | −0.00985515 | ||||||||
\(712\) | 1.60360e13 | 0.0876389 | ||||||||
\(713\) | 8.82467e13 | 0.478907 | ||||||||
\(714\) | − | 4.39452e13i | − | 0.236821i | ||||||
\(715\) | −4.66474e12 | −0.0249630 | ||||||||
\(716\) | 3.24300e14i | 1.72338i | ||||||||
\(717\) | −8.11185e13 | −0.428079 | ||||||||
\(718\) | 3.34689e14i | 1.75396i | ||||||||
\(719\) | − | 1.74694e14i | − | 0.909148i | −0.890709 | − | 0.454574i | \(-0.849791\pi\) | ||
0.890709 | − | 0.454574i | \(-0.150209\pi\) | |||||||
\(720\) | 3.93334e12 | 0.0203282 | ||||||||
\(721\) | − | 8.42302e13i | − | 0.432306i | ||||||
\(722\) | 2.35638e14i | 1.20105i | ||||||||
\(723\) | −6.47344e13 | −0.327675 | ||||||||
\(724\) | 1.76729e14 | 0.888411 | ||||||||
\(725\) | −5.64377e13 | −0.281760 | ||||||||
\(726\) | 1.24376e14i | 0.616670i | ||||||||
\(727\) | −1.26239e13 | −0.0621617 | −0.0310809 | − | 0.999517i | \(-0.509895\pi\) | ||||
−0.0310809 | + | 0.999517i | \(0.509895\pi\) | |||||||
\(728\) | −4.48660e12 | −0.0219412 | ||||||||
\(729\) | 7.62560e12 | 0.0370370 | ||||||||
\(730\) | 1.03965e14 | 0.501503 | ||||||||
\(731\) | 2.91431e13i | 0.139621i | ||||||||
\(732\) | − | 3.08603e14i | − | 1.46840i | ||||||
\(733\) | −2.14382e13 | −0.101314 | −0.0506569 | − | 0.998716i | \(-0.516131\pi\) | ||||
−0.0506569 | + | 0.998716i | \(0.516131\pi\) | |||||||
\(734\) | 3.44423e14 | 1.61664 | ||||||||
\(735\) | −1.42051e13 | −0.0662228 | ||||||||
\(736\) | 1.38319e14 | 0.640462 | ||||||||
\(737\) | −3.08789e14 | −1.42012 | ||||||||
\(738\) | − | 1.08035e14i | − | 0.493493i | ||||||
\(739\) | 1.33153e14i | 0.604127i | 0.953288 | + | 0.302063i | \(0.0976754\pi\) | ||||
−0.953288 | + | 0.302063i | \(0.902325\pi\) | |||||||
\(740\) | − | 3.17310e14i | − | 1.42996i | ||||||
\(741\) | − | 4.34594e12i | − | 0.0194533i | ||||||
\(742\) | 2.05988e13i | 0.0915846i | ||||||||
\(743\) | 1.42151e14 | 0.627777 | 0.313889 | − | 0.949460i | \(-0.398368\pi\) | ||||
0.313889 | + | 0.949460i | \(0.398368\pi\) | |||||||
\(744\) | 9.77799e13 | 0.428928 | ||||||||
\(745\) | − | 8.39638e13i | − | 0.365856i | ||||||
\(746\) | 1.19769e14i | 0.518381i | ||||||||
\(747\) | − | 2.40848e12i | − | 0.0103547i | ||||||
\(748\) | − | 1.32396e14i | − | 0.565416i | ||||||
\(749\) | 9.40158e12 | 0.0398834 | ||||||||
\(750\) | − | 2.37912e14i | − | 1.00256i | ||||||
\(751\) | 2.91415e14i | 1.21986i | 0.792453 | + | 0.609932i | \(0.208803\pi\) | ||||
−0.792453 | + | 0.609932i | \(0.791197\pi\) | |||||||
\(752\) | 1.78562e12i | 0.00742504i | ||||||||
\(753\) | 1.10703e13 | 0.0457283 | ||||||||
\(754\) | 6.63478e12 | 0.0272251 | ||||||||
\(755\) | − | 1.79143e14i | − | 0.730239i | ||||||
\(756\) | 6.92507e13 | 0.280424 | ||||||||
\(757\) | −1.57836e14 | −0.634933 | −0.317466 | − | 0.948269i | \(-0.602832\pi\) | ||||
−0.317466 | + | 0.948269i | \(0.602832\pi\) | |||||||
\(758\) | 5.31060e14i | 2.12226i | ||||||||
\(759\) | 1.13012e14 | 0.448657 | ||||||||
\(760\) | − | 2.37710e14i | − | 0.937518i | ||||||
\(761\) | −2.73383e14 | −1.07115 | −0.535573 | − | 0.844489i | \(-0.679904\pi\) | ||||
−0.535573 | + | 0.844489i | \(0.679904\pi\) | |||||||
\(762\) | 5.89268e13i | 0.229371i | ||||||||
\(763\) | 1.32019e14i | 0.510521i | ||||||||
\(764\) | − | 4.31109e14i | − | 1.65623i | ||||||
\(765\) | −1.83688e13 | −0.0701091 | ||||||||
\(766\) | 6.26346e14i | 2.37504i | ||||||||
\(767\) | 4.45322e12 | + | 5.09362e12i | 0.0167763 | + | 0.0191889i | ||||
\(768\) | 1.33661e14 | 0.500264 | ||||||||
\(769\) | − | 4.46828e14i | − | 1.66153i | −0.556622 | − | 0.830766i | \(-0.687903\pi\) | ||
0.556622 | − | 0.830766i | \(-0.312097\pi\) | |||||||
\(770\) | 3.92438e14 | 1.44983 | ||||||||
\(771\) | −1.94762e14 | −0.714880 | ||||||||
\(772\) | −2.56277e14 | −0.934594 | ||||||||
\(773\) | 2.97425e12i | 0.0107766i | 0.999985 | + | 0.00538828i | \(0.00171515\pi\) | ||||
−0.999985 | + | 0.00538828i | \(0.998285\pi\) | |||||||
\(774\) | −7.49637e13 | −0.269865 | ||||||||
\(775\) | 9.42216e13i | 0.337009i | ||||||||
\(776\) | −1.92809e14 | −0.685203 | ||||||||
\(777\) | 1.79451e14i | 0.633639i | ||||||||
\(778\) | 6.02318e14i | 2.11314i | ||||||||
\(779\) | 3.49433e14 | 1.21808 | ||||||||
\(780\) | 5.10038e12i | 0.0176657i | ||||||||
\(781\) | − | 1.82201e14i | − | 0.627040i | ||||||
\(782\) | −7.84127e13 | −0.268135 | ||||||||
\(783\) | −3.76546e13 | −0.127941 | ||||||||
\(784\) | 3.59597e12 | 0.0121405 | ||||||||
\(785\) | − | 1.86554e14i | − | 0.625831i | ||||||
\(786\) | 1.53071e14 | 0.510245 | ||||||||
\(787\) | −6.69184e13 | −0.221652 | −0.110826 | − | 0.993840i | \(-0.535350\pi\) | ||||
−0.110826 | + | 0.993840i | \(0.535350\pi\) | |||||||
\(788\) | −5.63932e14 | −1.85607 | ||||||||
\(789\) | −2.89702e14 | −0.947472 | ||||||||
\(790\) | 1.10952e13i | 0.0360577i | ||||||||
\(791\) | − | 4.61513e14i | − | 1.49040i | ||||||
\(792\) | 1.25220e14 | 0.401836 | ||||||||
\(793\) | −1.28541e13 | −0.0409899 | ||||||||
\(794\) | −4.18761e14 | −1.32698 | ||||||||
\(795\) | 8.61016e12 | 0.0271129 | ||||||||
\(796\) | 5.87816e14 | 1.83940 | ||||||||
\(797\) | 1.03608e14i | 0.322183i | 0.986939 | + | 0.161092i | \(0.0515014\pi\) | ||||
−0.986939 | + | 0.161092i | \(0.948499\pi\) | |||||||
\(798\) | 3.65618e14i | 1.12983i | ||||||||
\(799\) | − | 8.33888e12i | − | 0.0256079i | ||||||
\(800\) | 1.47684e14i | 0.450696i | ||||||||
\(801\) | 1.03097e13i | 0.0312668i | ||||||||
\(802\) | −4.87204e14 | −1.46838 | ||||||||
\(803\) | −1.77140e14 | −0.530565 | ||||||||
\(804\) | 3.37627e14i | 1.00498i | ||||||||
\(805\) | − | 1.42390e14i | − | 0.421211i | ||||||
\(806\) | − | 1.10766e13i | − | 0.0325636i | ||||||
\(807\) | 1.12027e13i | 0.0327307i | ||||||||
\(808\) | −2.77832e14 | −0.806725 | ||||||||
\(809\) | − | 4.92935e14i | − | 1.42248i | −0.702948 | − | 0.711241i | \(-0.748133\pi\) | ||
0.702948 | − | 0.711241i | \(-0.251867\pi\) | |||||||
\(810\) | − | 4.72494e13i | − | 0.135510i | ||||||
\(811\) | 1.16614e14i | 0.332388i | 0.986093 | + | 0.166194i | \(0.0531478\pi\) | ||||
−0.986093 | + | 0.166194i | \(0.946852\pi\) | |||||||
\(812\) | −3.41954e14 | −0.968697 | ||||||||
\(813\) | −1.16139e14 | −0.326984 | ||||||||
\(814\) | 8.82498e14i | 2.46940i | ||||||||
\(815\) | −4.15168e14 | −1.15461 | ||||||||
\(816\) | 4.65000e12 | 0.0128529 | ||||||||
\(817\) | − | 2.42467e14i | − | 0.666103i | ||||||
\(818\) | 5.79218e13 | 0.158152 | ||||||||
\(819\) | − | 2.88447e12i | − | 0.00782793i | ||||||
\(820\) | −4.10093e14 | −1.10615 | ||||||||
\(821\) | 4.94348e14i | 1.32531i | 0.748925 | + | 0.662655i | \(0.230570\pi\) | ||||
−0.748925 | + | 0.662655i | \(0.769430\pi\) | |||||||
\(822\) | − | 4.35226e14i | − | 1.15973i | ||||||
\(823\) | 6.89751e14i | 1.82681i | 0.407054 | + | 0.913404i | \(0.366556\pi\) | ||||
−0.407054 | + | 0.913404i | \(0.633444\pi\) | |||||||
\(824\) | −1.66530e14 | −0.438387 | ||||||||
\(825\) | 1.20663e14i | 0.315723i | ||||||||
\(826\) | −3.74643e14 | − | 4.28519e14i | −0.974355 | − | 1.11447i | ||||
\(827\) | −1.32847e14 | −0.343420 | −0.171710 | − | 0.985148i | \(-0.554929\pi\) | ||||
−0.171710 | + | 0.985148i | \(0.554929\pi\) | |||||||
\(828\) | − | 1.23566e14i | − | 0.317503i | ||||||
\(829\) | 2.90319e14 | 0.741486 | 0.370743 | − | 0.928736i | \(-0.379103\pi\) | ||||
0.370743 | + | 0.928736i | \(0.379103\pi\) | |||||||
\(830\) | −1.49233e13 | −0.0378856 | ||||||||
\(831\) | −3.86112e14 | −0.974335 | ||||||||
\(832\) | − | 1.65453e13i | − | 0.0415009i | ||||||
\(833\) | −1.67933e13 | −0.0418707 | ||||||||
\(834\) | 2.03226e14i | 0.503673i | ||||||||
\(835\) | 2.18940e13 | 0.0539378 | ||||||||
\(836\) | 1.10152e15i | 2.69749i | ||||||||
\(837\) | 6.28636e13i | 0.153028i | ||||||||
\(838\) | 1.03740e15 | 2.51030 | ||||||||
\(839\) | − | 1.26829e14i | − | 0.305077i | −0.988298 | − | 0.152539i | \(-0.951255\pi\) | ||
0.988298 | − | 0.152539i | \(-0.0487448\pi\) | |||||||
\(840\) | − | 1.57772e14i | − | 0.377254i | ||||||
\(841\) | −2.34772e14 | −0.558041 | ||||||||
\(842\) | 5.35281e14 | 1.26480 | ||||||||
\(843\) | 1.38308e13 | 0.0324871 | ||||||||
\(844\) | − | 5.55708e14i | − | 1.29758i | ||||||
\(845\) | −3.26797e14 | −0.758568 | ||||||||
\(846\) | 2.14497e13 | 0.0494960 | ||||||||
\(847\) | −2.67005e14 | −0.612495 | ||||||||
\(848\) | −2.17963e12 | −0.00497054 | ||||||||
\(849\) | 1.19977e14i | 0.271994i | ||||||||
\(850\) | − | 8.37218e13i | − | 0.188688i | ||||||
\(851\) | 3.20200e14 | 0.717421 | ||||||||
\(852\) | −1.99216e14 | −0.443739 | ||||||||
\(853\) | −2.40238e13 | −0.0531982 | −0.0265991 | − | 0.999646i | \(-0.508468\pi\) | ||||
−0.0265991 | + | 0.999646i | \(0.508468\pi\) | |||||||
\(854\) | 1.08140e15 | 2.38066 | ||||||||
\(855\) | 1.52826e14 | 0.334477 | ||||||||
\(856\) | − | 1.85877e13i | − | 0.0404443i | ||||||
\(857\) | − | 7.67519e14i | − | 1.66029i | −0.557544 | − | 0.830147i | \(-0.688256\pi\) | ||
0.557544 | − | 0.830147i | \(-0.311744\pi\) | |||||||
\(858\) | − | 1.41851e13i | − | 0.0305068i | ||||||
\(859\) | − | 3.24851e14i | − | 0.694574i | −0.937759 | − | 0.347287i | \(-0.887103\pi\) | ||
0.937759 | − | 0.347287i | \(-0.112897\pi\) | |||||||
\(860\) | 2.84558e14i | 0.604893i | ||||||||
\(861\) | 2.31924e14 | 0.490152 | ||||||||
\(862\) | 8.72188e14 | 1.83262 | ||||||||
\(863\) | − | 2.12598e14i | − | 0.444125i | −0.975032 | − | 0.222062i | \(-0.928721\pi\) | ||
0.975032 | − | 0.222062i | \(-0.0712789\pi\) | |||||||
\(864\) | 9.85332e13i | 0.204651i | ||||||||
\(865\) | − | 1.40498e14i | − | 0.290128i | ||||||
\(866\) | 7.90599e14i | 1.62318i | ||||||||
\(867\) | 2.61120e14 | 0.533022 | ||||||||
\(868\) | 5.70886e14i | 1.15865i | ||||||||
\(869\) | − | 1.89043e13i | − | 0.0381472i | ||||||
\(870\) | 2.33313e14i | 0.468105i | ||||||||
\(871\) | 1.40630e13 | 0.0280536 | ||||||||
\(872\) | 2.61013e14 | 0.517702 | ||||||||
\(873\) | − | 1.23959e14i | − | 0.244459i | ||||||
\(874\) | 6.52382e14 | 1.27922 | ||||||||
\(875\) | 5.10740e14 | 0.995771 | ||||||||
\(876\) | 1.93683e14i | 0.375466i | ||||||||
\(877\) | −3.96103e14 | −0.763502 | −0.381751 | − | 0.924265i | \(-0.624679\pi\) | ||||
−0.381751 | + | 0.924265i | \(0.624679\pi\) | |||||||
\(878\) | − | 8.51880e14i | − | 1.63270i | ||||||
\(879\) | −4.77789e14 | −0.910526 | ||||||||
\(880\) | 4.15252e13i | 0.0786862i | ||||||||
\(881\) | − | 3.93898e14i | − | 0.742172i | −0.928599 | − | 0.371086i | \(-0.878986\pi\) | ||
0.928599 | − | 0.371086i | \(-0.121014\pi\) | |||||||
\(882\) | − | 4.31966e13i | − | 0.0809295i | ||||||
\(883\) | 8.81331e14 | 1.64186 | 0.820928 | − | 0.571031i | \(-0.193456\pi\) | ||||
0.820928 | + | 0.571031i | \(0.193456\pi\) | |||||||
\(884\) | 6.02967e12i | 0.0111695i | ||||||||
\(885\) | −1.79118e14 | + | 1.56598e14i | −0.329931 | + | 0.288450i | ||||
\(886\) | −4.33444e14 | −0.793897 | ||||||||
\(887\) | 3.26500e14i | 0.594655i | 0.954775 | + | 0.297328i | \(0.0960954\pi\) | ||||
−0.954775 | + | 0.297328i | \(0.903905\pi\) | |||||||
\(888\) | 3.54791e14 | 0.642551 | ||||||||
\(889\) | −1.26502e14 | −0.227818 | ||||||||
\(890\) | 6.38805e13 | 0.114398 | ||||||||
\(891\) | 8.05053e13i | 0.143363i | ||||||||
\(892\) | 2.35232e14 | 0.416555 | ||||||||
\(893\) | 6.93782e13i | 0.122170i | ||||||||
\(894\) | 2.55327e14 | 0.447105 | ||||||||
\(895\) | 4.75010e14i | 0.827156i | ||||||||
\(896\) | 8.26132e14i | 1.43057i | ||||||||
\(897\) | −5.14685e12 | −0.00886297 | ||||||||
\(898\) | − | 1.49904e15i | − | 2.56703i | ||||||
\(899\) | − | 3.10415e14i | − | 0.528621i | ||||||
\(900\) | 1.31932e14 | 0.223428 | ||||||||
\(901\) | 1.01789e13 | 0.0171427 | ||||||||
\(902\) | 1.14055e15 | 1.91021 | ||||||||
\(903\) | − | 1.60929e14i | − | 0.268038i | ||||||
\(904\) | −9.12451e14 | −1.51136 | ||||||||
\(905\) | 2.58858e14 | 0.426402 | ||||||||
\(906\) | 5.44760e14 | 0.892410 | ||||||||
\(907\) | 4.17086e14 | 0.679500 | 0.339750 | − | 0.940516i | \(-0.389658\pi\) | ||||
0.339750 | + | 0.940516i | \(0.389658\pi\) | |||||||
\(908\) | 1.33689e15i | 2.16603i | ||||||||
\(909\) | − | 1.78621e14i | − | 0.287815i | ||||||
\(910\) | −1.78726e13 | −0.0286406 | ||||||||
\(911\) | 9.66237e14 | 1.53990 | 0.769949 | − | 0.638106i | \(-0.220282\pi\) | ||||
0.769949 | + | 0.638106i | \(0.220282\pi\) | |||||||
\(912\) | −3.86873e13 | −0.0613189 | ||||||||
\(913\) | 2.54269e13 | 0.0400810 | ||||||||
\(914\) | 7.48418e14 | 1.17331 | ||||||||
\(915\) | − | 4.52018e14i | − | 0.704774i | ||||||
\(916\) | 3.85568e14i | 0.597893i | ||||||||
\(917\) | 3.28606e14i | 0.506791i | ||||||||
\(918\) | − | 5.58582e13i | − | 0.0856789i | ||||||
\(919\) | − | 8.27876e14i | − | 1.26295i | −0.775395 | − | 0.631477i | \(-0.782449\pi\) | ||
0.775395 | − | 0.631477i | \(-0.217551\pi\) | |||||||
\(920\) | −2.81517e14 | −0.427135 | ||||||||
\(921\) | 5.28218e14 | 0.797103 | ||||||||
\(922\) | 3.97750e14i | 0.596975i | ||||||||
\(923\) | 8.29789e12i | 0.0123868i | ||||||||
\(924\) | 7.31096e14i | 1.08546i | ||||||||
\(925\) | 3.41880e14i | 0.504853i | ||||||||
\(926\) | 5.61725e14 | 0.825028 | ||||||||
\(927\) | − | 1.07064e14i | − | 0.156403i | ||||||
\(928\) | − | 4.86549e14i | − | 0.706947i | ||||||
\(929\) | 7.67381e13i | 0.110900i | 0.998461 | + | 0.0554501i | \(0.0176594\pi\) | ||||
−0.998461 | + | 0.0554501i | \(0.982341\pi\) | |||||||
\(930\) | 3.89512e14 | 0.559895 | ||||||||
\(931\) | 1.39717e14 | 0.199757 | ||||||||
\(932\) | 1.86612e15i | 2.65375i | ||||||||
\(933\) | 7.95058e14 | 1.12458 | ||||||||
\(934\) | −8.27375e14 | −1.16404 | ||||||||
\(935\) | − | 1.93924e14i | − | 0.271377i | ||||||
\(936\) | −5.70285e12 | −0.00793803 | ||||||||
\(937\) | − | 1.38081e15i | − | 1.91177i | −0.293744 | − | 0.955884i | \(-0.594901\pi\) | ||
0.293744 | − | 0.955884i | \(-0.405099\pi\) | |||||||
\(938\) | −1.18310e15 | −1.62933 | ||||||||
\(939\) | 1.63145e14i | 0.223483i | ||||||||
\(940\) | − | 8.14220e13i | − | 0.110944i | ||||||
\(941\) | 8.93832e14i | 1.21146i | 0.795671 | + | 0.605728i | \(0.207118\pi\) | ||||
−0.795671 | + | 0.605728i | \(0.792882\pi\) | |||||||
\(942\) | 5.67298e14 | 0.764815 | ||||||||
\(943\) | − | 4.13829e14i | − | 0.554961i | ||||||
\(944\) | 4.53430e13 | − | 3.96423e13i | 0.0604854 | − | 0.0528809i | ||||
\(945\) | 1.01433e14 | 0.134592 | ||||||||
\(946\) | − | 7.91409e14i | − | 1.04459i | ||||||
\(947\) | −1.13790e15 | −1.49401 | −0.747007 | − | 0.664816i | \(-0.768510\pi\) | ||||
−0.747007 | + | 0.664816i | \(0.768510\pi\) | |||||||
\(948\) | −2.06698e13 | −0.0269957 | ||||||||
\(949\) | 8.06740e12 | 0.0104810 | ||||||||
\(950\) | 6.96553e14i | 0.900194i | ||||||||
\(951\) | 2.45670e14 | 0.315827 | ||||||||
\(952\) | − | 1.86518e14i | − | 0.238526i | ||||||
\(953\) | 2.06111e14 | 0.262202 | 0.131101 | − | 0.991369i | \(-0.458149\pi\) | ||||
0.131101 | + | 0.991369i | \(0.458149\pi\) | |||||||
\(954\) | 2.61829e13i | 0.0331341i | ||||||||
\(955\) | − | 6.31455e14i | − | 0.794924i | ||||||
\(956\) | −9.36366e14 | −1.17262 | ||||||||
\(957\) | − | 3.97528e14i | − | 0.495232i | ||||||
\(958\) | − | 1.93183e15i | − | 2.39409i | ||||||
\(959\) | 9.34327e14 | 1.15188 | ||||||||
\(960\) | 5.81818e14 | 0.713561 | ||||||||
\(961\) | 3.01396e14 | 0.367723 | ||||||||
\(962\) | − | 4.01912e13i | − | 0.0487816i | ||||||
\(963\) | 1.19502e13 | 0.0144293 | ||||||||
\(964\) | −7.47241e14 | −0.897584 | ||||||||
\(965\) | −3.75375e14 | −0.448568 | ||||||||
\(966\) | 4.32997e14 | 0.514753 | ||||||||
\(967\) | − | 3.67211e14i | − | 0.434294i | −0.976139 | − | 0.217147i | \(-0.930325\pi\) | ||
0.976139 | − | 0.217147i | \(-0.0696750\pi\) | |||||||
\(968\) | 5.27893e14i | 0.621110i | ||||||||
\(969\) | 1.80671e14 | 0.211480 | ||||||||
\(970\) | −7.68067e14 | −0.894418 | ||||||||
\(971\) | 5.49274e14 | 0.636346 | 0.318173 | − | 0.948033i | \(-0.396931\pi\) | ||||
0.318173 | + | 0.948033i | \(0.396931\pi\) | |||||||
\(972\) | 8.80236e13 | 0.101454 | ||||||||
\(973\) | −4.36277e14 | −0.500263 | ||||||||
\(974\) | − | 1.79172e15i | − | 2.04398i | ||||||
\(975\) | − | 5.49532e12i | − | 0.00623692i | ||||||
\(976\) | 1.14427e14i | 0.129205i | ||||||||
\(977\) | − | 2.57632e14i | − | 0.289419i | −0.989474 | − | 0.144709i | \(-0.953775\pi\) | ||
0.989474 | − | 0.144709i | \(-0.0462247\pi\) | |||||||
\(978\) | − | 1.26249e15i | − | 1.41103i | ||||||
\(979\) | −1.08842e14 | −0.121027 | ||||||||
\(980\) | −1.63972e14 | −0.181401 | ||||||||
\(981\) | 1.67808e14i | 0.184700i | ||||||||
\(982\) | − | 1.14452e15i | − | 1.25333i | ||||||
\(983\) | 5.09212e14i | 0.554793i | 0.960755 | + | 0.277397i | \(0.0894716\pi\) | ||||
−0.960755 | + | 0.277397i | \(0.910528\pi\) | |||||||
\(984\) | − | 4.58535e14i | − | 0.497046i | ||||||
\(985\) | −8.26004e14 | −0.890842 | ||||||||
\(986\) | 2.75823e14i | 0.295969i | ||||||||
\(987\) | 4.60475e13i | 0.0491609i | ||||||||
\(988\) | − | 5.01660e13i | − | 0.0532874i | ||||||
\(989\) | −2.87150e14 | −0.303479 | ||||||||
\(990\) | 4.98823e14 | 0.524530 | ||||||||
\(991\) | − | 9.96787e14i | − | 1.04288i | −0.853288 | − | 0.521440i | \(-0.825395\pi\) | ||
0.853288 | − | 0.521440i | \(-0.174605\pi\) | |||||||
\(992\) | −8.12284e14 | −0.845570 | ||||||||
\(993\) | 9.35121e14 | 0.968549 | ||||||||
\(994\) | − | 6.98090e14i | − | 0.719415i | ||||||
\(995\) | 8.60988e14 | 0.882840 | ||||||||
\(996\) | − | 2.78015e13i | − | 0.0283642i | ||||||
\(997\) | −1.17690e15 | −1.19471 | −0.597355 | − | 0.801977i | \(-0.703782\pi\) | ||||
−0.597355 | + | 0.801977i | \(0.703782\pi\) | |||||||
\(998\) | 2.41587e15i | 2.44017i | ||||||||
\(999\) | 2.28098e14i | 0.229242i |
(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 | 177.11.c.a.58.89 | yes | 100 | |
59.58 | odd | 2 | inner | 177.11.c.a.58.12 | ✓ | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.11.c.a.58.12 | ✓ | 100 | 59.58 | odd | 2 | inner | |
177.11.c.a.58.89 | yes | 100 | 1.1 | even | 1 | trivial |