Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,13,Mod(97,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.97");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.b (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: | \(89.5713940931\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 6613776 x^{14} + 17532494948988 x^{12} + \cdots + 16\!\cdots\!41 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{56}\cdot 3^{8}\cdot 7^{24} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.5 | ||
Root | \(39.0012i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.97 |
Dual form | 98.13.b.c.97.4 |
$q$-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 \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −45.2548 | −0.707107 | ||||||||
\(3\) | 39.0012i | 0.0534997i | 0.999642 | + | 0.0267498i | \(0.00851575\pi\) | ||||
−0.999642 | + | 0.0267498i | \(0.991484\pi\) | |||||||
\(4\) | 2048.00 | 0.500000 | ||||||||
\(5\) | 2865.82i | 0.183413i | 0.995786 | + | 0.0917063i | \(0.0292321\pi\) | ||||
−0.995786 | + | 0.0917063i | \(0.970768\pi\) | |||||||
\(6\) | − 1764.99i | − 0.0378300i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −92681.9 | −0.353553 | ||||||||
\(9\) | 529920. | 0.997138 | ||||||||
\(10\) | − 129692.i | − 0.129692i | ||||||||
\(11\) | 3.41289e6 | 1.92649 | 0.963243 | − | 0.268631i | \(-0.0865712\pi\) | ||||
0.963243 | + | 0.268631i | \(0.0865712\pi\) | |||||||
\(12\) | 79874.6i | 0.0267498i | ||||||||
\(13\) | − 6.97895e6i | − 1.44587i | −0.690915 | − | 0.722936i | \(-0.742792\pi\) | ||||
0.690915 | − | 0.722936i | \(-0.257208\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −111771. | −0.00981251 | ||||||||
\(16\) | 4.19430e6 | 0.250000 | ||||||||
\(17\) | 2.85574e7i | 1.18311i | 0.806265 | + | 0.591555i | \(0.201486\pi\) | ||||
−0.806265 | + | 0.591555i | \(0.798514\pi\) | |||||||
\(18\) | −2.39814e7 | −0.705083 | ||||||||
\(19\) | − 5.25546e7i | − 1.11709i | −0.829473 | − | 0.558546i | \(-0.811359\pi\) | ||||
0.829473 | − | 0.558546i | \(-0.188641\pi\) | |||||||
\(20\) | 5.86920e6i | 0.0917063i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.54450e8 | −1.36223 | ||||||||
\(23\) | 3.11954e7 | 0.210729 | 0.105364 | − | 0.994434i | \(-0.466399\pi\) | ||||
0.105364 | + | 0.994434i | \(0.466399\pi\) | |||||||
\(24\) | − 3.61471e6i | − 0.0189150i | ||||||||
\(25\) | 2.35928e8 | 0.966360 | ||||||||
\(26\) | 3.15831e8i | 1.02239i | ||||||||
\(27\) | 4.13944e7i | 0.106846i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.56209e8 | 0.766966 | 0.383483 | − | 0.923548i | \(-0.374724\pi\) | ||||
0.383483 | + | 0.923548i | \(0.374724\pi\) | |||||||
\(30\) | 5.05816e6 | 0.00693849 | ||||||||
\(31\) | − 1.75305e9i | − 1.97526i | −0.156817 | − | 0.987628i | \(-0.550123\pi\) | ||||
0.156817 | − | 0.987628i | \(-0.449877\pi\) | |||||||
\(32\) | −1.89813e8 | −0.176777 | ||||||||
\(33\) | 1.33107e8i | 0.103066i | ||||||||
\(34\) | − 1.29236e9i | − 0.836585i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.08528e9 | 0.498569 | ||||||||
\(37\) | −1.81676e9 | −0.708087 | −0.354043 | − | 0.935229i | \(-0.615194\pi\) | ||||
−0.354043 | + | 0.935229i | \(0.615194\pi\) | |||||||
\(38\) | 2.37835e9i | 0.789904i | ||||||||
\(39\) | 2.72188e8 | 0.0773536 | ||||||||
\(40\) | − 2.65610e8i | − 0.0648462i | ||||||||
\(41\) | 5.14132e9i | 1.08236i | 0.840907 | + | 0.541180i | \(0.182022\pi\) | ||||
−0.840907 | + | 0.541180i | \(0.817978\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.27073e9 | −1.15018 | −0.575092 | − | 0.818089i | \(-0.695034\pi\) | ||||
−0.575092 | + | 0.818089i | \(0.695034\pi\) | |||||||
\(44\) | 6.98959e9 | 0.963243 | ||||||||
\(45\) | 1.51866e9i | 0.182888i | ||||||||
\(46\) | −1.41174e9 | −0.149008 | ||||||||
\(47\) | 4.28207e9i | 0.397252i | 0.980075 | + | 0.198626i | \(0.0636479\pi\) | ||||
−0.980075 | + | 0.198626i | \(0.936352\pi\) | |||||||
\(48\) | 1.63583e8i | 0.0133749i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.06769e10 | −0.683320 | ||||||||
\(51\) | −1.11377e9 | −0.0632959 | ||||||||
\(52\) | − 1.42929e10i | − 0.722936i | ||||||||
\(53\) | −7.22753e9 | −0.326088 | −0.163044 | − | 0.986619i | \(-0.552131\pi\) | ||||
−0.163044 | + | 0.986619i | \(0.552131\pi\) | |||||||
\(54\) | − 1.87330e9i | − 0.0755517i | ||||||||
\(55\) | 9.78073e9i | 0.353342i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.04970e9 | 0.0597641 | ||||||||
\(58\) | −2.06457e10 | −0.542327 | ||||||||
\(59\) | 5.15674e9i | 0.122254i | 0.998130 | + | 0.0611270i | \(0.0194695\pi\) | ||||
−0.998130 | + | 0.0611270i | \(0.980531\pi\) | |||||||
\(60\) | −2.28906e8 | −0.00490626 | ||||||||
\(61\) | 5.11141e9i | 0.0992114i | 0.998769 | + | 0.0496057i | \(0.0157965\pi\) | ||||
−0.998769 | + | 0.0496057i | \(0.984204\pi\) | |||||||
\(62\) | 7.93338e10i | 1.39672i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.58993e9 | 0.125000 | ||||||||
\(65\) | 2.00004e10 | 0.265191 | ||||||||
\(66\) | − 6.02373e9i | − 0.0728789i | ||||||||
\(67\) | −7.59045e10 | −0.839109 | −0.419555 | − | 0.907730i | \(-0.637814\pi\) | ||||
−0.419555 | + | 0.907730i | \(0.637814\pi\) | |||||||
\(68\) | 5.84855e10i | 0.591555i | ||||||||
\(69\) | 1.21666e9i | 0.0112739i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.13092e11 | −0.882838 | −0.441419 | − | 0.897301i | \(-0.645525\pi\) | ||||
−0.441419 | + | 0.897301i | \(0.645525\pi\) | |||||||
\(72\) | −4.91140e10 | −0.352541 | ||||||||
\(73\) | − 1.74577e11i | − 1.15359i | −0.816890 | − | 0.576794i | \(-0.804304\pi\) | ||||
0.816890 | − | 0.576794i | \(-0.195696\pi\) | |||||||
\(74\) | 8.22171e10 | 0.500693 | ||||||||
\(75\) | 9.20147e9i | 0.0516999i | ||||||||
\(76\) | − 1.07632e11i | − 0.558546i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.23178e10 | −0.0546973 | ||||||||
\(79\) | 2.26089e11 | 0.930071 | 0.465036 | − | 0.885292i | \(-0.346042\pi\) | ||||
0.465036 | + | 0.885292i | \(0.346042\pi\) | |||||||
\(80\) | 1.20201e10i | 0.0458532i | ||||||||
\(81\) | 2.80007e11 | 0.991422 | ||||||||
\(82\) | − 2.32670e11i | − 0.765344i | ||||||||
\(83\) | 4.13229e11i | 1.26393i | 0.774998 | + | 0.631964i | \(0.217751\pi\) | ||||
−0.774998 | + | 0.631964i | \(0.782249\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.18404e10 | −0.216997 | ||||||||
\(86\) | 3.29036e11 | 0.813303 | ||||||||
\(87\) | 1.77927e10i | 0.0410324i | ||||||||
\(88\) | −3.16313e11 | −0.681116 | ||||||||
\(89\) | − 2.60295e11i | − 0.523753i | −0.965101 | − | 0.261876i | \(-0.915659\pi\) | ||||
0.965101 | − | 0.261876i | \(-0.0843413\pi\) | |||||||
\(90\) | − 6.87265e10i | − 0.129321i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.38882e10 | 0.105364 | ||||||||
\(93\) | 6.83710e10 | 0.105675 | ||||||||
\(94\) | − 1.93784e11i | − 0.280900i | ||||||||
\(95\) | 1.50612e11 | 0.204889 | ||||||||
\(96\) | − 7.40293e9i | − 0.00945749i | ||||||||
\(97\) | − 4.10959e11i | − 0.493364i | −0.969096 | − | 0.246682i | \(-0.920660\pi\) | ||||
0.969096 | − | 0.246682i | \(-0.0793404\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.80856e12 | 1.92097 | ||||||||
\(100\) | 4.83180e11 | 0.483180 | ||||||||
\(101\) | − 1.39405e12i | − 1.31326i | −0.754214 | − | 0.656628i | \(-0.771982\pi\) | ||||
0.754214 | − | 0.656628i | \(-0.228018\pi\) | |||||||
\(102\) | 5.04036e10 | 0.0447570 | ||||||||
\(103\) | − 1.44553e12i | − 1.21061i | −0.795993 | − | 0.605306i | \(-0.793051\pi\) | ||||
0.795993 | − | 0.605306i | \(-0.206949\pi\) | |||||||
\(104\) | 6.46822e11i | 0.511193i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.27081e11 | 0.230579 | ||||||||
\(107\) | 5.70567e11 | 0.380193 | 0.190097 | − | 0.981765i | \(-0.439120\pi\) | ||||
0.190097 | + | 0.981765i | \(0.439120\pi\) | |||||||
\(108\) | 8.47757e10i | 0.0534231i | ||||||||
\(109\) | 2.82818e11 | 0.168635 | 0.0843176 | − | 0.996439i | \(-0.473129\pi\) | ||||
0.0843176 | + | 0.996439i | \(0.473129\pi\) | |||||||
\(110\) | − 4.42625e11i | − 0.249850i | ||||||||
\(111\) | − 7.08558e10i | − 0.0378824i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.58024e12 | −0.759017 | −0.379509 | − | 0.925188i | \(-0.623907\pi\) | ||||
−0.379509 | + | 0.925188i | \(0.623907\pi\) | |||||||
\(114\) | −9.27586e10 | −0.0422596 | ||||||||
\(115\) | 8.94005e10i | 0.0386503i | ||||||||
\(116\) | 9.34317e11 | 0.383483 | ||||||||
\(117\) | − 3.69828e12i | − 1.44173i | ||||||||
\(118\) | − 2.33367e11i | − 0.0864466i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.03591e10 | 0.00346925 | ||||||||
\(121\) | 8.50938e12 | 2.71135 | ||||||||
\(122\) | − 2.31316e11i | − 0.0701530i | ||||||||
\(123\) | −2.00518e11 | −0.0579059 | ||||||||
\(124\) | − 3.59024e12i | − 0.987628i | ||||||||
\(125\) | 1.37579e12i | 0.360655i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.21870e12 | 1.24377 | 0.621885 | − | 0.783109i | \(-0.286367\pi\) | ||||
0.621885 | + | 0.783109i | \(0.286367\pi\) | |||||||
\(128\) | −3.88736e11 | −0.0883883 | ||||||||
\(129\) | − 2.83568e11i | − 0.0615345i | ||||||||
\(130\) | −9.05116e11 | −0.187518 | ||||||||
\(131\) | − 4.57350e12i | − 0.904942i | −0.891779 | − | 0.452471i | \(-0.850543\pi\) | ||||
0.891779 | − | 0.452471i | \(-0.149457\pi\) | |||||||
\(132\) | 2.72603e11i | 0.0515332i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.43504e12 | 0.593340 | ||||||||
\(135\) | −1.18629e11 | −0.0195969 | ||||||||
\(136\) | − 2.64675e12i | − 0.418292i | ||||||||
\(137\) | 5.69134e12 | 0.860778 | 0.430389 | − | 0.902644i | \(-0.358376\pi\) | ||||
0.430389 | + | 0.902644i | \(0.358376\pi\) | |||||||
\(138\) | − 5.50597e10i | − 0.00797186i | ||||||||
\(139\) | − 3.77435e12i | − 0.523304i | −0.965162 | − | 0.261652i | \(-0.915733\pi\) | ||||
0.965162 | − | 0.261652i | \(-0.0842672\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.67006e11 | −0.0212529 | ||||||||
\(142\) | 5.11795e12 | 0.624261 | ||||||||
\(143\) | − 2.38184e13i | − 2.78545i | ||||||||
\(144\) | 2.22265e12 | 0.249284 | ||||||||
\(145\) | 1.30741e12i | 0.140671i | ||||||||
\(146\) | 7.90047e12i | 0.815710i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.72072e12 | −0.354043 | ||||||||
\(149\) | 6.68941e12 | 0.611323 | 0.305661 | − | 0.952140i | \(-0.401122\pi\) | ||||
0.305661 | + | 0.952140i | \(0.401122\pi\) | |||||||
\(150\) | − 4.16411e11i | − 0.0365574i | ||||||||
\(151\) | 5.23680e11 | 0.0441778 | 0.0220889 | − | 0.999756i | \(-0.492968\pi\) | ||||
0.0220889 | + | 0.999756i | \(0.492968\pi\) | |||||||
\(152\) | 4.87086e12i | 0.394952i | ||||||||
\(153\) | 1.51331e13i | 1.17972i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.02392e12 | 0.362287 | ||||||||
\(156\) | 5.57440e11 | 0.0386768 | ||||||||
\(157\) | 1.56303e13i | 1.04369i | 0.853041 | + | 0.521844i | \(0.174756\pi\) | ||||
−0.853041 | + | 0.521844i | \(0.825244\pi\) | |||||||
\(158\) | −1.02316e13 | −0.657660 | ||||||||
\(159\) | − 2.81883e11i | − 0.0174456i | ||||||||
\(160\) | − 5.43969e11i | − 0.0324231i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.26717e13 | −0.701041 | ||||||||
\(163\) | 2.43293e12 | 0.129719 | 0.0648597 | − | 0.997894i | \(-0.479340\pi\) | ||||
0.0648597 | + | 0.997894i | \(0.479340\pi\) | |||||||
\(164\) | 1.05294e13i | 0.541180i | ||||||||
\(165\) | −3.81461e11 | −0.0189037 | ||||||||
\(166\) | − 1.87006e13i | − 0.893732i | ||||||||
\(167\) | 5.39380e12i | 0.248654i | 0.992241 | + | 0.124327i | \(0.0396772\pi\) | ||||
−0.992241 | + | 0.124327i | \(0.960323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.54076e13 | −1.09055 | ||||||||
\(170\) | 3.70367e12 | 0.153440 | ||||||||
\(171\) | − 2.78497e13i | − 1.11390i | ||||||||
\(172\) | −1.48905e13 | −0.575092 | ||||||||
\(173\) | − 2.54933e13i | − 0.950934i | −0.879734 | − | 0.475467i | \(-0.842279\pi\) | ||||
0.879734 | − | 0.475467i | \(-0.157721\pi\) | |||||||
\(174\) | − 8.05207e11i | − 0.0290143i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.43147e13 | 0.481622 | ||||||||
\(177\) | −2.01119e11 | −0.00654055 | ||||||||
\(178\) | 1.17796e13i | 0.370349i | ||||||||
\(179\) | 3.59883e13 | 1.09407 | 0.547033 | − | 0.837111i | \(-0.315757\pi\) | ||||
0.547033 | + | 0.837111i | \(0.315757\pi\) | |||||||
\(180\) | 3.11021e12i | 0.0914438i | ||||||||
\(181\) | − 1.12708e13i | − 0.320542i | −0.987073 | − | 0.160271i | \(-0.948763\pi\) | ||||
0.987073 | − | 0.160271i | \(-0.0512368\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.99351e11 | −0.00530777 | ||||||||
\(184\) | −2.89125e12 | −0.0745038 | ||||||||
\(185\) | − 5.20650e12i | − 0.129872i | ||||||||
\(186\) | −3.09412e12 | −0.0747238 | ||||||||
\(187\) | 9.74632e13i | 2.27924i | ||||||||
\(188\) | 8.76967e12i | 0.198626i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.81593e12 | −0.144878 | ||||||||
\(191\) | −9.89329e12 | −0.203770 | −0.101885 | − | 0.994796i | \(-0.532487\pi\) | ||||
−0.101885 | + | 0.994796i | \(0.532487\pi\) | |||||||
\(192\) | 3.35018e11i | 0.00668746i | ||||||||
\(193\) | −4.39071e13 | −0.849555 | −0.424777 | − | 0.905298i | \(-0.639648\pi\) | ||||
−0.424777 | + | 0.905298i | \(0.639648\pi\) | |||||||
\(194\) | 1.85979e13i | 0.348861i | ||||||||
\(195\) | 7.80041e11i | 0.0141876i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.88271e13 | 0.664259 | 0.332129 | − | 0.943234i | \(-0.392233\pi\) | ||||
0.332129 | + | 0.943234i | \(0.392233\pi\) | |||||||
\(198\) | −8.18460e13 | −1.35833 | ||||||||
\(199\) | 1.89326e13i | 0.304854i | 0.988315 | + | 0.152427i | \(0.0487089\pi\) | ||||
−0.988315 | + | 0.152427i | \(0.951291\pi\) | |||||||
\(200\) | −2.18662e13 | −0.341660 | ||||||||
\(201\) | − 2.96037e12i | − 0.0448921i | ||||||||
\(202\) | 6.30874e13i | 0.928613i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.28101e12 | −0.0316480 | ||||||||
\(205\) | −1.47341e13 | −0.198518 | ||||||||
\(206\) | 6.54174e13i | 0.856031i | ||||||||
\(207\) | 1.65311e13 | 0.210125 | ||||||||
\(208\) | − 2.92718e13i | − 0.361468i | ||||||||
\(209\) | − 1.79363e14i | − 2.15206i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.19733e13 | −0.362320 | −0.181160 | − | 0.983454i | \(-0.557985\pi\) | ||||
−0.181160 | + | 0.983454i | \(0.557985\pi\) | |||||||
\(212\) | −1.48020e13 | −0.163044 | ||||||||
\(213\) | − 4.41072e12i | − 0.0472315i | ||||||||
\(214\) | −2.58209e13 | −0.268837 | ||||||||
\(215\) | − 2.08366e13i | − 0.210958i | ||||||||
\(216\) | − 3.83651e12i | − 0.0377758i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.27989e13 | −0.119243 | ||||||||
\(219\) | 6.80873e12 | 0.0617166 | ||||||||
\(220\) | 2.00309e13i | 0.176671i | ||||||||
\(221\) | 1.99301e14 | 1.71063 | ||||||||
\(222\) | 3.20657e12i | 0.0267869i | ||||||||
\(223\) | − 1.78662e14i | − 1.45279i | −0.687279 | − | 0.726394i | \(-0.741195\pi\) | ||||
0.687279 | − | 0.726394i | \(-0.258805\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.25023e14 | 0.963594 | ||||||||
\(226\) | 7.15134e13 | 0.536706 | ||||||||
\(227\) | 1.63219e14i | 1.19293i | 0.802639 | + | 0.596465i | \(0.203429\pi\) | ||||
−0.802639 | + | 0.596465i | \(0.796571\pi\) | |||||||
\(228\) | 4.19778e12 | 0.0298820 | ||||||||
\(229\) | 1.97880e14i | 1.37211i | 0.727549 | + | 0.686056i | \(0.240659\pi\) | ||||
−0.727549 | + | 0.686056i | \(0.759341\pi\) | |||||||
\(230\) | − 4.04580e12i | − 0.0273299i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.22823e13 | −0.271163 | ||||||||
\(233\) | −1.90911e14 | −1.19315 | −0.596576 | − | 0.802557i | \(-0.703473\pi\) | ||||
−0.596576 | + | 0.802557i | \(0.703473\pi\) | |||||||
\(234\) | 1.67365e14i | 1.01946i | ||||||||
\(235\) | −1.22716e13 | −0.0728611 | ||||||||
\(236\) | 1.05610e13i | 0.0611270i | ||||||||
\(237\) | 8.81774e12i | 0.0497585i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.79102e14 | −0.960979 | −0.480490 | − | 0.877000i | \(-0.659541\pi\) | ||||
−0.480490 | + | 0.877000i | \(0.659541\pi\) | |||||||
\(240\) | −4.68800e11 | −0.00245313 | ||||||||
\(241\) | − 1.98275e14i | − 1.01197i | −0.862543 | − | 0.505984i | \(-0.831130\pi\) | ||||
0.862543 | − | 0.505984i | \(-0.168870\pi\) | |||||||
\(242\) | −3.85090e14 | −1.91721 | ||||||||
\(243\) | 3.29193e13i | 0.159887i | ||||||||
\(244\) | 1.04682e13i | 0.0496057i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.07440e12 | 0.0409456 | ||||||||
\(247\) | −3.66776e14 | −1.61517 | ||||||||
\(248\) | 1.62476e14i | 0.698358i | ||||||||
\(249\) | −1.61165e13 | −0.0676197 | ||||||||
\(250\) | − 6.22612e13i | − 0.255022i | ||||||||
\(251\) | 2.18276e14i | 0.872897i | 0.899729 | + | 0.436448i | \(0.143764\pi\) | ||||
−0.899729 | + | 0.436448i | \(0.856236\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.06466e14 | 0.405966 | ||||||||
\(254\) | −2.36171e14 | −0.879478 | ||||||||
\(255\) | − 3.19188e12i | − 0.0116093i | ||||||||
\(256\) | 1.75922e13 | 0.0625000 | ||||||||
\(257\) | 4.14883e14i | 1.43988i | 0.694036 | + | 0.719941i | \(0.255831\pi\) | ||||
−0.694036 | + | 0.719941i | \(0.744169\pi\) | |||||||
\(258\) | 1.28328e13i | 0.0435114i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.09609e13 | 0.132596 | ||||||||
\(261\) | 2.41754e14 | 0.764771 | ||||||||
\(262\) | 2.06973e14i | 0.639891i | ||||||||
\(263\) | 1.17695e14 | 0.355651 | 0.177825 | − | 0.984062i | \(-0.443094\pi\) | ||||
0.177825 | + | 0.984062i | \(0.443094\pi\) | |||||||
\(264\) | − 1.23366e13i | − 0.0364395i | ||||||||
\(265\) | − 2.07128e13i | − 0.0598087i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.01518e13 | 0.0280206 | ||||||||
\(268\) | −1.55452e14 | −0.419555 | ||||||||
\(269\) | − 3.96686e14i | − 1.04697i | −0.852036 | − | 0.523483i | \(-0.824632\pi\) | ||||
0.852036 | − | 0.523483i | \(-0.175368\pi\) | |||||||
\(270\) | 5.36853e12 | 0.0138571 | ||||||||
\(271\) | − 2.07647e14i | − 0.524215i | −0.965039 | − | 0.262107i | \(-0.915583\pi\) | ||||
0.965039 | − | 0.262107i | \(-0.0844174\pi\) | |||||||
\(272\) | 1.19778e14i | 0.295777i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.57561e14 | −0.608662 | ||||||||
\(275\) | 8.05195e14 | 1.86168 | ||||||||
\(276\) | 2.49172e12i | 0.00563695i | ||||||||
\(277\) | 3.15993e14 | 0.699518 | 0.349759 | − | 0.936840i | \(-0.386263\pi\) | ||||
0.349759 | + | 0.936840i | \(0.386263\pi\) | |||||||
\(278\) | 1.70808e14i | 0.370032i | ||||||||
\(279\) | − 9.28974e14i | − 1.96960i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.27034e14 | −0.664286 | −0.332143 | − | 0.943229i | \(-0.607772\pi\) | ||||
−0.332143 | + | 0.943229i | \(0.607772\pi\) | |||||||
\(282\) | 7.55783e12 | 0.0150280 | ||||||||
\(283\) | − 8.02664e13i | − 0.156248i | −0.996944 | − | 0.0781242i | \(-0.975107\pi\) | ||||
0.996944 | − | 0.0781242i | \(-0.0248931\pi\) | |||||||
\(284\) | −2.31612e14 | −0.441419 | ||||||||
\(285\) | 5.87406e12i | 0.0109615i | ||||||||
\(286\) | 1.07790e15i | 1.96961i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00585e14 | −0.176271 | ||||||||
\(289\) | −2.32902e14 | −0.399748 | ||||||||
\(290\) | − 5.91668e13i | − 0.0994696i | ||||||||
\(291\) | 1.60279e13 | 0.0263948 | ||||||||
\(292\) | − 3.57534e14i | − 0.576794i | ||||||||
\(293\) | 3.68606e14i | 0.582581i | 0.956635 | + | 0.291290i | \(0.0940846\pi\) | ||||
−0.956635 | + | 0.291290i | \(0.905915\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.47783e13 | −0.0224229 | ||||||||
\(296\) | 1.68381e14 | 0.250347 | ||||||||
\(297\) | 1.41274e14i | 0.205838i | ||||||||
\(298\) | −3.02728e14 | −0.432270 | ||||||||
\(299\) | − 2.17711e14i | − 0.304687i | ||||||||
\(300\) | 1.88446e13i | 0.0258500i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.36990e13 | −0.0312384 | ||||||||
\(303\) | 5.43696e13 | 0.0702588 | ||||||||
\(304\) | − 2.20430e14i | − 0.279273i | ||||||||
\(305\) | −1.46484e13 | −0.0181966 | ||||||||
\(306\) | − 6.84847e14i | − 0.834190i | ||||||||
\(307\) | 6.36629e14i | 0.760425i | 0.924899 | + | 0.380212i | \(0.124149\pi\) | ||||
−0.924899 | + | 0.380212i | \(0.875851\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.63776e13 | 0.0647673 | ||||||||
\(310\) | −2.27357e14 | −0.256175 | ||||||||
\(311\) | − 1.31752e15i | − 1.45612i | −0.685515 | − | 0.728059i | \(-0.740423\pi\) | ||||
0.685515 | − | 0.728059i | \(-0.259577\pi\) | |||||||
\(312\) | −2.52269e13 | −0.0273486 | ||||||||
\(313\) | 7.06353e14i | 0.751200i | 0.926782 | + | 0.375600i | \(0.122563\pi\) | ||||
−0.926782 | + | 0.375600i | \(0.877437\pi\) | |||||||
\(314\) | − 7.07348e14i | − 0.737999i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.63030e14 | 0.465036 | ||||||||
\(317\) | 7.46432e14 | 0.735588 | 0.367794 | − | 0.929907i | \(-0.380113\pi\) | ||||
0.367794 | + | 0.929907i | \(0.380113\pi\) | |||||||
\(318\) | 1.27566e13i | 0.0123359i | ||||||||
\(319\) | 1.55699e15 | 1.47755 | ||||||||
\(320\) | 2.46172e13i | 0.0229266i | ||||||||
\(321\) | 2.22528e13i | 0.0203402i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.50082e15 | 1.32164 | ||||||||
\(324\) | 5.73454e14 | 0.495711 | ||||||||
\(325\) | − 1.64653e15i | − 1.39723i | ||||||||
\(326\) | −1.10102e14 | −0.0917255 | ||||||||
\(327\) | 1.10303e13i | 0.00902193i | ||||||||
\(328\) | − 4.76507e14i | − 0.382672i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.72629e13 | 0.0133669 | ||||||||
\(331\) | 1.13325e15 | 0.861701 | 0.430850 | − | 0.902423i | \(-0.358214\pi\) | ||||
0.430850 | + | 0.902423i | \(0.358214\pi\) | |||||||
\(332\) | 8.46293e14i | 0.631964i | ||||||||
\(333\) | −9.62736e14 | −0.706060 | ||||||||
\(334\) | − 2.44095e14i | − 0.175825i | ||||||||
\(335\) | − 2.17529e14i | − 0.153903i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.02783e13 | −0.0343242 | −0.0171621 | − | 0.999853i | \(-0.505463\pi\) | ||||
−0.0171621 | + | 0.999853i | \(0.505463\pi\) | |||||||
\(338\) | 1.14982e15 | 0.771132 | ||||||||
\(339\) | − 6.16312e13i | − 0.0406072i | ||||||||
\(340\) | −1.67609e14 | −0.108499 | ||||||||
\(341\) | − 5.98295e15i | − 3.80530i | ||||||||
\(342\) | 1.26034e15i | 0.787643i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.73865e14 | 0.406652 | ||||||||
\(345\) | −3.48673e12 | −0.00206778 | ||||||||
\(346\) | 1.15370e15i | 0.672412i | ||||||||
\(347\) | 8.40065e14 | 0.481212 | 0.240606 | − | 0.970623i | \(-0.422654\pi\) | ||||
0.240606 | + | 0.970623i | \(0.422654\pi\) | |||||||
\(348\) | 3.64395e13i | 0.0205162i | ||||||||
\(349\) | 4.32312e14i | 0.239246i | 0.992819 | + | 0.119623i | \(0.0381686\pi\) | ||||
−0.992819 | + | 0.119623i | \(0.961831\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.88889e14 | 0.154486 | ||||||||
\(352\) | −6.47809e14 | −0.340558 | ||||||||
\(353\) | 2.41123e15i | 1.24621i | 0.782140 | + | 0.623103i | \(0.214128\pi\) | ||||
−0.782140 | + | 0.623103i | \(0.785872\pi\) | |||||||
\(354\) | 9.10162e12 | 0.00462487 | ||||||||
\(355\) | − 3.24101e14i | − 0.161924i | ||||||||
\(356\) | − 5.33085e14i | − 0.261876i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.62865e15 | −0.773622 | ||||||||
\(359\) | 6.44763e14 | 0.301185 | 0.150593 | − | 0.988596i | \(-0.451882\pi\) | ||||
0.150593 | + | 0.988596i | \(0.451882\pi\) | |||||||
\(360\) | − 1.40752e14i | − 0.0646605i | ||||||||
\(361\) | −5.48673e14 | −0.247896 | ||||||||
\(362\) | 5.10060e14i | 0.226658i | ||||||||
\(363\) | 3.31876e14i | 0.145056i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.00308e14 | 0.211583 | ||||||||
\(366\) | 9.02161e12 | 0.00375316 | ||||||||
\(367\) | − 1.41994e15i | − 0.581130i | −0.956855 | − | 0.290565i | \(-0.906157\pi\) | ||||
0.956855 | − | 0.290565i | \(-0.0938432\pi\) | |||||||
\(368\) | 1.30843e14 | 0.0526822 | ||||||||
\(369\) | 2.72449e15i | 1.07926i | ||||||||
\(370\) | 2.35619e14i | 0.0918334i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.40024e14 | 0.0528377 | ||||||||
\(373\) | 2.91410e15 | 1.08206 | 0.541030 | − | 0.841003i | \(-0.318034\pi\) | ||||
0.541030 | + | 0.841003i | \(0.318034\pi\) | |||||||
\(374\) | − 4.41068e15i | − 1.61167i | ||||||||
\(375\) | −5.36575e13 | −0.0192949 | ||||||||
\(376\) | − 3.96870e14i | − 0.140450i | ||||||||
\(377\) | − 3.18386e15i | − 1.10893i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.27572e15 | 0.430446 | 0.215223 | − | 0.976565i | \(-0.430952\pi\) | ||||
0.215223 | + | 0.976565i | \(0.430952\pi\) | |||||||
\(380\) | 3.08454e14 | 0.102444 | ||||||||
\(381\) | 2.03536e14i | 0.0665413i | ||||||||
\(382\) | 4.47719e14 | 0.144087 | ||||||||
\(383\) | 2.58299e15i | 0.818332i | 0.912460 | + | 0.409166i | \(0.134180\pi\) | ||||
−0.912460 | + | 0.409166i | \(0.865820\pi\) | |||||||
\(384\) | − 1.51612e13i | − 0.00472875i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.98701e15 | 0.600726 | ||||||||
\(387\) | −3.85291e15 | −1.14689 | ||||||||
\(388\) | − 8.41643e14i | − 0.246682i | ||||||||
\(389\) | 3.87640e15 | 1.11875 | 0.559373 | − | 0.828916i | \(-0.311042\pi\) | ||||
0.559373 | + | 0.828916i | \(0.311042\pi\) | |||||||
\(390\) | − 3.53006e13i | − 0.0100322i | ||||||||
\(391\) | 8.90859e14i | 0.249315i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.78372e14 | 0.0484141 | ||||||||
\(394\) | −1.75711e15 | −0.469702 | ||||||||
\(395\) | 6.47930e14i | 0.170587i | ||||||||
\(396\) | 3.70393e15 | 0.960486 | ||||||||
\(397\) | 7.38279e13i | 0.0188572i | 0.999956 | + | 0.00942861i | \(0.00300126\pi\) | ||||
−0.999956 | + | 0.00942861i | \(0.996999\pi\) | |||||||
\(398\) | − 8.56791e14i | − 0.215564i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.89552e14 | 0.241590 | ||||||||
\(401\) | −4.02524e15 | −0.968111 | −0.484055 | − | 0.875037i | \(-0.660837\pi\) | ||||
−0.484055 | + | 0.875037i | \(0.660837\pi\) | |||||||
\(402\) | 1.33971e14i | 0.0317435i | ||||||||
\(403\) | −1.22344e16 | −2.85597 | ||||||||
\(404\) | − 2.85501e15i | − 0.656628i | ||||||||
\(405\) | 8.02449e14i | 0.181839i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.20039e15 | −1.36412 | ||||||||
\(408\) | 1.03227e14 | 0.0223785 | ||||||||
\(409\) | 5.75990e15i | 1.23048i | 0.788340 | + | 0.615240i | \(0.210941\pi\) | ||||
−0.788340 | + | 0.615240i | \(0.789059\pi\) | |||||||
\(410\) | 6.66790e14 | 0.140374 | ||||||||
\(411\) | 2.21969e14i | 0.0460513i | ||||||||
\(412\) | − 2.96045e15i | − 0.605306i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −7.48110e14 | −0.148581 | ||||||||
\(415\) | −1.18424e15 | −0.231820 | ||||||||
\(416\) | 1.32469e15i | 0.255596i | ||||||||
\(417\) | 1.47205e14 | 0.0279966 | ||||||||
\(418\) | 8.11704e15i | 1.52174i | ||||||||
\(419\) | 9.49384e15i | 1.75452i | 0.480018 | + | 0.877259i | \(0.340630\pi\) | ||||
−0.480018 | + | 0.877259i | \(0.659370\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.68328e15 | −1.55952 | −0.779761 | − | 0.626078i | \(-0.784659\pi\) | ||||
−0.779761 | + | 0.626078i | \(0.784659\pi\) | |||||||
\(422\) | 1.44695e15 | 0.256199 | ||||||||
\(423\) | 2.26915e15i | 0.396115i | ||||||||
\(424\) | 6.69861e14 | 0.115290 | ||||||||
\(425\) | 6.73748e15i | 1.14331i | ||||||||
\(426\) | 1.99606e14i | 0.0333977i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.16852e15 | 0.190097 | ||||||||
\(429\) | 9.28946e14 | 0.149021 | ||||||||
\(430\) | 9.42958e14i | 0.149170i | ||||||||
\(431\) | 2.69513e14 | 0.0420451 | 0.0210226 | − | 0.999779i | \(-0.493308\pi\) | ||||
0.0210226 | + | 0.999779i | \(0.493308\pi\) | |||||||
\(432\) | 1.73621e14i | 0.0267115i | ||||||||
\(433\) | − 5.06968e15i | − 0.769224i | −0.923078 | − | 0.384612i | \(-0.874335\pi\) | ||||
0.923078 | − | 0.384612i | \(-0.125665\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.09908e13 | −0.00752586 | ||||||||
\(436\) | 5.79212e14 | 0.0843176 | ||||||||
\(437\) | − 1.63946e15i | − 0.235403i | ||||||||
\(438\) | −3.08128e14 | −0.0436402 | ||||||||
\(439\) | 1.63813e14i | 0.0228855i | 0.999935 | + | 0.0114427i | \(0.00364242\pi\) | ||||
−0.999935 | + | 0.0114427i | \(0.996358\pi\) | |||||||
\(440\) | − 9.06497e14i | − 0.124925i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.01931e15 | −1.20959 | ||||||||
\(443\) | −8.71487e15 | −1.15302 | −0.576512 | − | 0.817089i | \(-0.695587\pi\) | ||||
−0.576512 | + | 0.817089i | \(0.695587\pi\) | |||||||
\(444\) | − 1.45113e14i | − 0.0189412i | ||||||||
\(445\) | 7.45960e14 | 0.0960629 | ||||||||
\(446\) | 8.08530e15i | 1.02728i | ||||||||
\(447\) | 2.60895e14i | 0.0327055i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.38504e15 | 0.657220 | 0.328610 | − | 0.944466i | \(-0.393420\pi\) | ||||
0.328610 | + | 0.944466i | \(0.393420\pi\) | |||||||
\(450\) | −5.65789e15 | −0.681364 | ||||||||
\(451\) | 1.75468e16i | 2.08515i | ||||||||
\(452\) | −3.23633e15 | −0.379509 | ||||||||
\(453\) | 2.04242e13i | 0.00236350i | ||||||||
\(454\) | − 7.38644e15i | − 0.843529i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.89970e14 | −0.0211298 | ||||||||
\(457\) | −1.32562e16 | −1.45519 | −0.727596 | − | 0.686005i | \(-0.759363\pi\) | ||||
−0.727596 | + | 0.686005i | \(0.759363\pi\) | |||||||
\(458\) | − 8.95504e15i | − 0.970230i | ||||||||
\(459\) | −1.18212e15 | −0.126411 | ||||||||
\(460\) | 1.83092e14i | 0.0193251i | ||||||||
\(461\) | 1.36310e16i | 1.42011i | 0.704144 | + | 0.710057i | \(0.251331\pi\) | ||||
−0.704144 | + | 0.710057i | \(0.748669\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.32894e16 | 1.34902 | 0.674511 | − | 0.738265i | \(-0.264354\pi\) | ||||
0.674511 | + | 0.738265i | \(0.264354\pi\) | |||||||
\(464\) | 1.91348e15 | 0.191742 | ||||||||
\(465\) | 1.95939e14i | 0.0193822i | ||||||||
\(466\) | 8.63965e15 | 0.843686 | ||||||||
\(467\) | − 6.87464e15i | − 0.662748i | −0.943499 | − | 0.331374i | \(-0.892488\pi\) | ||||
0.943499 | − | 0.331374i | \(-0.107512\pi\) | |||||||
\(468\) | − 7.57408e15i | − 0.720867i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.55351e14 | 0.0515206 | ||||||||
\(471\) | −6.09603e14 | −0.0558369 | ||||||||
\(472\) | − 4.77936e14i | − 0.0432233i | ||||||||
\(473\) | −2.48142e16 | −2.21581 | ||||||||
\(474\) | − 3.99045e14i | − 0.0351846i | ||||||||
\(475\) | − 1.23991e16i | − 1.07951i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.83001e15 | −0.325155 | ||||||||
\(478\) | 8.10525e15 | 0.679515 | ||||||||
\(479\) | − 3.42398e15i | − 0.283478i | −0.989904 | − | 0.141739i | \(-0.954731\pi\) | ||||
0.989904 | − | 0.141739i | \(-0.0452693\pi\) | |||||||
\(480\) | 2.12155e13 | 0.00173462 | ||||||||
\(481\) | 1.26791e16i | 1.02380i | ||||||||
\(482\) | 8.97292e15i | 0.715569i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.74272e16 | 1.35567 | ||||||||
\(485\) | 1.17773e15 | 0.0904892 | ||||||||
\(486\) | − 1.48976e15i | − 0.113057i | ||||||||
\(487\) | 1.58272e16 | 1.18640 | 0.593200 | − | 0.805055i | \(-0.297864\pi\) | ||||
0.593200 | + | 0.805055i | \(0.297864\pi\) | |||||||
\(488\) | − 4.73735e14i | − 0.0350765i | ||||||||
\(489\) | 9.48875e13i | 0.00693994i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.26555e16 | −1.61690 | −0.808452 | − | 0.588563i | \(-0.799694\pi\) | ||||
−0.808452 | + | 0.588563i | \(0.799694\pi\) | |||||||
\(492\) | −4.10661e14 | −0.0289529 | ||||||||
\(493\) | 1.30281e16i | 0.907405i | ||||||||
\(494\) | 1.65984e16 | 1.14210 | ||||||||
\(495\) | 5.18300e15i | 0.352331i | ||||||||
\(496\) | − 7.35281e15i | − 0.493814i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.29347e14 | 0.0478144 | ||||||||
\(499\) | 9.07153e15 | 0.587594 | 0.293797 | − | 0.955868i | \(-0.405081\pi\) | ||||
0.293797 | + | 0.955868i | \(0.405081\pi\) | |||||||
\(500\) | 2.81762e15i | 0.180328i | ||||||||
\(501\) | −2.10365e14 | −0.0133029 | ||||||||
\(502\) | − 9.87803e15i | − 0.617231i | ||||||||
\(503\) | − 2.00202e16i | − 1.23612i | −0.786131 | − | 0.618060i | \(-0.787919\pi\) | ||||
0.786131 | − | 0.618060i | \(-0.212081\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.99509e15 | 0.240868 | ||||||||
\(506\) | −4.81812e15 | −0.287061 | ||||||||
\(507\) | − 9.90929e14i | − 0.0583438i | ||||||||
\(508\) | 1.06879e16 | 0.621885 | ||||||||
\(509\) | − 2.26064e16i | − 1.29995i | −0.759957 | − | 0.649973i | \(-0.774780\pi\) | ||||
0.759957 | − | 0.649973i | \(-0.225220\pi\) | |||||||
\(510\) | 1.44448e14i | 0.00820900i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −7.96131e14 | −0.0441942 | ||||||||
\(513\) | 2.17547e15 | 0.119357 | ||||||||
\(514\) | − 1.87755e16i | − 1.01815i | ||||||||
\(515\) | 4.14264e15 | 0.222041 | ||||||||
\(516\) | − 5.80747e14i | − 0.0307672i | ||||||||
\(517\) | 1.46142e16i | 0.765301i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.94272e14 | 0.0508746 | ||||||||
\(520\) | −1.85368e15 | −0.0937592 | ||||||||
\(521\) | − 4.83379e15i | − 0.241692i | −0.992671 | − | 0.120846i | \(-0.961439\pi\) | ||||
0.992671 | − | 0.120846i | \(-0.0385606\pi\) | |||||||
\(522\) | −1.09406e16 | −0.540775 | ||||||||
\(523\) | − 2.06681e16i | − 1.00993i | −0.863141 | − | 0.504964i | \(-0.831506\pi\) | ||||
0.863141 | − | 0.504964i | \(-0.168494\pi\) | |||||||
\(524\) | − 9.36653e15i | − 0.452471i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.32627e15 | −0.251483 | ||||||||
\(527\) | 5.00624e16 | 2.33694 | ||||||||
\(528\) | 5.58291e14i | 0.0257666i | ||||||||
\(529\) | −2.09415e16 | −0.955593 | ||||||||
\(530\) | 9.37355e14i | 0.0422911i | ||||||||
\(531\) | 2.73266e15i | 0.121904i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.58810e16 | 1.56495 | ||||||||
\(534\) | −4.59420e14 | −0.0198135 | ||||||||
\(535\) | 1.63514e15i | 0.0697322i | ||||||||
\(536\) | 7.03497e15 | 0.296670 | ||||||||
\(537\) | 1.40359e15i | 0.0585322i | ||||||||
\(538\) | 1.79519e16i | 0.740317i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.42952e14 | −0.00979847 | ||||||||
\(541\) | −4.12580e16 | −1.64560 | −0.822801 | − | 0.568329i | \(-0.807590\pi\) | ||||
−0.822801 | + | 0.568329i | \(0.807590\pi\) | |||||||
\(542\) | 9.39701e15i | 0.370676i | ||||||||
\(543\) | 4.39577e14 | 0.0171489 | ||||||||
\(544\) | − 5.42055e15i | − 0.209146i | ||||||||
\(545\) | 8.10507e14i | 0.0309298i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.32093e16 | 0.493124 | 0.246562 | − | 0.969127i | \(-0.420699\pi\) | ||||
0.246562 | + | 0.969127i | \(0.420699\pi\) | |||||||
\(548\) | 1.16559e16 | 0.430389 | ||||||||
\(549\) | 2.70864e15i | 0.0989274i | ||||||||
\(550\) | −3.64390e16 | −1.31641 | ||||||||
\(551\) | − 2.39759e16i | − 0.856772i | ||||||||
\(552\) | − 1.12762e14i | − 0.00398593i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.43002e16 | −0.494634 | ||||||||
\(555\) | 2.03060e14 | 0.00694811 | ||||||||
\(556\) | − 7.72988e15i | − 0.261652i | ||||||||
\(557\) | 3.67951e16 | 1.23214 | 0.616069 | − | 0.787692i | \(-0.288724\pi\) | ||||
0.616069 | + | 0.787692i | \(0.288724\pi\) | |||||||
\(558\) | 4.20406e16i | 1.39272i | ||||||||
\(559\) | 5.07421e16i | 1.66302i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.80118e15 | −0.121939 | ||||||||
\(562\) | 1.47999e16 | 0.469721 | ||||||||
\(563\) | − 5.22593e16i | − 1.64102i | −0.571635 | − | 0.820508i | \(-0.693690\pi\) | ||||
0.571635 | − | 0.820508i | \(-0.306310\pi\) | |||||||
\(564\) | −3.42028e14 | −0.0106264 | ||||||||
\(565\) | − 4.52868e15i | − 0.139213i | ||||||||
\(566\) | 3.63244e15i | 0.110484i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.04816e16 | 0.312130 | ||||||||
\(569\) | 6.20823e16 | 1.82934 | 0.914669 | − | 0.404204i | \(-0.132451\pi\) | ||||
0.914669 | + | 0.404204i | \(0.132451\pi\) | |||||||
\(570\) | − 2.65830e14i | − 0.00775094i | ||||||||
\(571\) | 9.20520e15 | 0.265593 | 0.132796 | − | 0.991143i | \(-0.457604\pi\) | ||||
0.132796 | + | 0.991143i | \(0.457604\pi\) | |||||||
\(572\) | − 4.87800e16i | − 1.39273i | ||||||||
\(573\) | − 3.85851e14i | − 0.0109016i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.35986e15 | 0.203640 | ||||||||
\(576\) | 4.55198e15 | 0.124642 | ||||||||
\(577\) | − 5.92325e16i | − 1.60511i | −0.596577 | − | 0.802556i | \(-0.703473\pi\) | ||||
0.596577 | − | 0.802556i | \(-0.296527\pi\) | |||||||
\(578\) | 1.05400e16 | 0.282665 | ||||||||
\(579\) | − 1.71243e15i | − 0.0454509i | ||||||||
\(580\) | 2.67759e15i | 0.0703356i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −7.25340e14 | −0.0186640 | ||||||||
\(583\) | −2.46668e16 | −0.628204 | ||||||||
\(584\) | 1.61802e16i | 0.407855i | ||||||||
\(585\) | 1.05986e16 | 0.264432 | ||||||||
\(586\) | − 1.66812e16i | − 0.411947i | ||||||||
\(587\) | 1.82380e16i | 0.445808i | 0.974840 | + | 0.222904i | \(0.0715536\pi\) | ||||
−0.974840 | + | 0.222904i | \(0.928446\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.21307e16 | −2.20654 | ||||||||
\(590\) | 6.68789e14 | 0.0158554 | ||||||||
\(591\) | 1.51430e15i | 0.0355376i | ||||||||
\(592\) | −7.62003e15 | −0.177022 | ||||||||
\(593\) | 2.59009e16i | 0.595644i | 0.954621 | + | 0.297822i | \(0.0962601\pi\) | ||||
−0.954621 | + | 0.297822i | \(0.903740\pi\) | |||||||
\(594\) | − 6.39335e15i | − 0.145549i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.36999e16 | 0.305661 | ||||||||
\(597\) | −7.38394e14 | −0.0163096 | ||||||||
\(598\) | 9.85248e15i | 0.215446i | ||||||||
\(599\) | −4.89381e16 | −1.05946 | −0.529732 | − | 0.848165i | \(-0.677707\pi\) | ||||
−0.529732 | + | 0.848165i | \(0.677707\pi\) | |||||||
\(600\) | − 8.52810e14i | − 0.0182787i | ||||||||
\(601\) | − 2.83221e16i | − 0.601005i | −0.953781 | − | 0.300503i | \(-0.902846\pi\) | ||||
0.953781 | − | 0.300503i | \(-0.0971544\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.02233e16 | −0.836708 | ||||||||
\(604\) | 1.07250e15 | 0.0220889 | ||||||||
\(605\) | 2.43864e16i | 0.497296i | ||||||||
\(606\) | −2.46049e15 | −0.0496804 | ||||||||
\(607\) | 6.25489e15i | 0.125051i | 0.998043 | + | 0.0625256i | \(0.0199155\pi\) | ||||
−0.998043 | + | 0.0625256i | \(0.980084\pi\) | |||||||
\(608\) | 9.97552e15i | 0.197476i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.62910e14 | 0.0128670 | ||||||||
\(611\) | 2.98843e16 | 0.574376 | ||||||||
\(612\) | 3.09926e16i | 0.589862i | ||||||||
\(613\) | 5.55586e16 | 1.04710 | 0.523551 | − | 0.851995i | \(-0.324607\pi\) | ||||
0.523551 | + | 0.851995i | \(0.324607\pi\) | |||||||
\(614\) | − 2.88105e16i | − 0.537701i | ||||||||
\(615\) | − 5.74649e14i | − 0.0106207i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.06869e16 | 1.46249 | 0.731243 | − | 0.682117i | \(-0.238940\pi\) | ||||
0.731243 | + | 0.682117i | \(0.238940\pi\) | |||||||
\(618\) | −2.55136e15 | −0.0457974 | ||||||||
\(619\) | 3.93731e15i | 0.0699931i | 0.999387 | + | 0.0349966i | \(0.0111420\pi\) | ||||
−0.999387 | + | 0.0349966i | \(0.988858\pi\) | |||||||
\(620\) | 1.02890e16 | 0.181143 | ||||||||
\(621\) | 1.29131e15i | 0.0225155i | ||||||||
\(622\) | 5.96244e16i | 1.02963i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.14164e15 | 0.0193384 | ||||||||
\(625\) | 5.36568e16 | 0.900211 | ||||||||
\(626\) | − 3.19659e16i | − 0.531179i | ||||||||
\(627\) | 6.99538e15 | 0.115135 | ||||||||
\(628\) | 3.20109e16i | 0.521844i | ||||||||
\(629\) | − 5.18818e16i | − 0.837744i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.92232e16 | 1.09667 | 0.548334 | − | 0.836259i | \(-0.315262\pi\) | ||||
0.548334 | + | 0.836259i | \(0.315262\pi\) | |||||||
\(632\) | −2.09543e16 | −0.328830 | ||||||||
\(633\) | − 1.24700e15i | − 0.0193840i | ||||||||
\(634\) | −3.37797e16 | −0.520139 | ||||||||
\(635\) | 1.49559e16i | 0.228123i | ||||||||
\(636\) | − 5.77296e14i | − 0.00872280i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.04614e16 | −1.04479 | ||||||||
\(639\) | −5.99296e16 | −0.880311 | ||||||||
\(640\) | − 1.11405e15i | − 0.0162115i | ||||||||
\(641\) | 3.16865e16 | 0.456800 | 0.228400 | − | 0.973567i | \(-0.426651\pi\) | ||||
0.228400 | + | 0.973567i | \(0.426651\pi\) | |||||||
\(642\) | − 1.00705e15i | − 0.0143827i | ||||||||
\(643\) | − 5.19233e16i | − 0.734678i | −0.930087 | − | 0.367339i | \(-0.880269\pi\) | ||||
0.930087 | − | 0.367339i | \(-0.119731\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.12655e14 | 0.0112862 | ||||||||
\(646\) | −6.79195e16 | −0.934543 | ||||||||
\(647\) | − 1.20952e17i | − 1.64888i | −0.565951 | − | 0.824439i | \(-0.691491\pi\) | ||||
0.565951 | − | 0.824439i | \(-0.308509\pi\) | |||||||
\(648\) | −2.59516e16 | −0.350520 | ||||||||
\(649\) | 1.75994e16i | 0.235521i | ||||||||
\(650\) | 7.45133e16i | 0.987993i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.98265e15 | 0.0648597 | ||||||||
\(653\) | −4.65159e16 | −0.599960 | −0.299980 | − | 0.953945i | \(-0.596980\pi\) | ||||
−0.299980 | + | 0.953945i | \(0.596980\pi\) | |||||||
\(654\) | − 4.99173e14i | − 0.00637947i | ||||||||
\(655\) | 1.31068e16 | 0.165978 | ||||||||
\(656\) | 2.15643e16i | 0.270590i | ||||||||
\(657\) | − 9.25120e16i | − 1.15029i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.88240e16 | 0.474011 | 0.237005 | − | 0.971508i | \(-0.423834\pi\) | ||||
0.237005 | + | 0.971508i | \(0.423834\pi\) | |||||||
\(660\) | −7.81231e14 | −0.00945183 | ||||||||
\(661\) | 1.08911e17i | 1.30576i | 0.757463 | + | 0.652878i | \(0.226439\pi\) | ||||
−0.757463 | + | 0.652878i | \(0.773561\pi\) | |||||||
\(662\) | −5.12849e16 | −0.609314 | ||||||||
\(663\) | 7.77297e15i | 0.0915178i | ||||||||
\(664\) | − 3.82989e16i | − 0.446866i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.35685e16 | 0.499260 | ||||||||
\(667\) | 1.42316e16 | 0.161622 | ||||||||
\(668\) | 1.10465e16i | 0.124327i | ||||||||
\(669\) | 6.96803e15 | 0.0777236 | ||||||||
\(670\) | 9.84423e15i | 0.108826i | ||||||||
\(671\) | 1.74447e16i | 0.191129i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.67477e16 | −0.503118 | −0.251559 | − | 0.967842i | \(-0.580943\pi\) | ||||
−0.251559 | + | 0.967842i | \(0.580943\pi\) | |||||||
\(674\) | 2.27534e15 | 0.0242709 | ||||||||
\(675\) | 9.76608e15i | 0.103252i | ||||||||
\(676\) | −5.20348e16 | −0.545273 | ||||||||
\(677\) | 6.23836e16i | 0.647945i | 0.946066 | + | 0.323973i | \(0.105019\pi\) | ||||
−0.946066 | + | 0.323973i | \(0.894981\pi\) | |||||||
\(678\) | 2.78911e15i | 0.0287136i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.58512e15 | 0.0767201 | ||||||||
\(681\) | −6.36574e15 | −0.0638214 | ||||||||
\(682\) | 2.70757e17i | 2.69075i | ||||||||
\(683\) | 6.73352e16 | 0.663312 | 0.331656 | − | 0.943400i | \(-0.392393\pi\) | ||||
0.331656 | + | 0.943400i | \(0.392393\pi\) | |||||||
\(684\) | − 5.70363e16i | − 0.556948i | ||||||||
\(685\) | 1.63104e16i | 0.157877i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.71758e15 | −0.0734075 | ||||||||
\(688\) | −3.04957e16 | −0.287546 | ||||||||
\(689\) | 5.04406e16i | 0.471482i | ||||||||
\(690\) | 1.57791e14 | 0.00146214 | ||||||||
\(691\) | 2.39079e16i | 0.219621i | 0.993953 | + | 0.109810i | \(0.0350244\pi\) | ||||
−0.993953 | + | 0.109810i | \(0.964976\pi\) | |||||||
\(692\) | − 5.22104e16i | − 0.475467i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.80170e16 | −0.340268 | ||||||||
\(695\) | 1.08166e16 | 0.0959805 | ||||||||
\(696\) | − 1.64906e15i | − 0.0145072i | ||||||||
\(697\) | −1.46823e17 | −1.28055 | ||||||||
\(698\) | − 1.95642e16i | − 0.169172i | ||||||||
\(699\) | − 7.44577e15i | − 0.0638332i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.42561e17 | −1.20141 | −0.600707 | − | 0.799469i | \(-0.705114\pi\) | ||||
−0.600707 | + | 0.799469i | \(0.705114\pi\) | |||||||
\(702\) | −1.30736e16 | −0.109238 | ||||||||
\(703\) | 9.54790e16i | 0.790999i | ||||||||
\(704\) | 2.93165e16 | 0.240811 | ||||||||
\(705\) | − 4.78609e14i | − 0.00389804i | ||||||||
\(706\) | − 1.09120e17i | − 0.881201i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.11892e14 | −0.00327027 | ||||||||
\(709\) | −2.16853e17 | −1.70721 | −0.853607 | − | 0.520917i | \(-0.825590\pi\) | ||||
−0.853607 | + | 0.520917i | \(0.825590\pi\) | |||||||
\(710\) | 1.46671e16i | 0.114497i | ||||||||
\(711\) | 1.19809e17 | 0.927409 | ||||||||
\(712\) | 2.41247e16i | 0.185175i | ||||||||
\(713\) | − 5.46870e16i | − 0.416243i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.82592e16 | 0.510887 | ||||||||
\(716\) | 7.37041e16 | 0.547033 | ||||||||
\(717\) | − 6.98522e15i | − 0.0514121i | ||||||||
\(718\) | −2.91786e16 | −0.212970 | ||||||||
\(719\) | 1.72963e16i | 0.125193i | 0.998039 | + | 0.0625966i | \(0.0199381\pi\) | ||||
−0.998039 | + | 0.0625966i | \(0.980062\pi\) | |||||||
\(720\) | 6.36971e15i | 0.0457219i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.48301e16 | 0.175289 | ||||||||
\(723\) | 7.73299e15 | 0.0541399 | ||||||||
\(724\) | − 2.30827e16i | − 0.160271i | ||||||||
\(725\) | 1.07632e17 | 0.741165 | ||||||||
\(726\) | − 1.50190e16i | − 0.102570i | ||||||||
\(727\) | − 1.17362e17i | − 0.794915i | −0.917621 | − | 0.397458i | \(-0.869893\pi\) | ||||
0.917621 | − | 0.397458i | \(-0.130107\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.47523e17 | 0.982868 | ||||||||
\(730\) | −2.26413e16 | −0.149611 | ||||||||
\(731\) | − 2.07633e17i | − 1.36079i | ||||||||
\(732\) | −4.08271e14 | −0.00265389 | ||||||||
\(733\) | 1.72659e17i | 1.11318i | 0.830787 | + | 0.556591i | \(0.187891\pi\) | ||||
−0.830787 | + | 0.556591i | \(0.812109\pi\) | |||||||
\(734\) | 6.42591e16i | 0.410921i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.92128e15 | −0.0372519 | ||||||||
\(737\) | −2.59053e17 | −1.61653 | ||||||||
\(738\) | − 1.23296e17i | − 0.763153i | ||||||||
\(739\) | −1.90886e16 | −0.117195 | −0.0585974 | − | 0.998282i | \(-0.518663\pi\) | ||||
−0.0585974 | + | 0.998282i | \(0.518663\pi\) | |||||||
\(740\) | − 1.06629e16i | − 0.0649360i | ||||||||
\(741\) | − 1.43047e16i | − 0.0864112i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.56299e16 | −0.330655 | −0.165328 | − | 0.986239i | \(-0.552868\pi\) | ||||
−0.165328 | + | 0.986239i | \(0.552868\pi\) | |||||||
\(744\) | −6.33675e15 | −0.0373619 | ||||||||
\(745\) | 1.91707e16i | 0.112124i | ||||||||
\(746\) | −1.31877e17 | −0.765132 | ||||||||
\(747\) | 2.18978e17i | 1.26031i | ||||||||
\(748\) | 1.99605e17i | 1.13962i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.42826e15 | 0.0136436 | ||||||||
\(751\) | 2.73102e17 | 1.52225 | 0.761125 | − | 0.648605i | \(-0.224647\pi\) | ||||
0.761125 | + | 0.648605i | \(0.224647\pi\) | |||||||
\(752\) | 1.79603e16i | 0.0993131i | ||||||||
\(753\) | −8.51302e15 | −0.0466997 | ||||||||
\(754\) | 1.44085e17i | 0.784135i | ||||||||
\(755\) | 1.50077e15i | 0.00810276i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.53508e16 | −0.506698 | −0.253349 | − | 0.967375i | \(-0.581532\pi\) | ||||
−0.253349 | + | 0.967375i | \(0.581532\pi\) | |||||||
\(758\) | −5.77323e16 | −0.304371 | ||||||||
\(759\) | 4.15232e15i | 0.0217190i | ||||||||
\(760\) | −1.39590e16 | −0.0724392 | ||||||||
\(761\) | 8.72482e16i | 0.449209i | 0.974450 | + | 0.224605i | \(0.0721090\pi\) | ||||
−0.974450 | + | 0.224605i | \(0.927891\pi\) | |||||||
\(762\) | − 9.21098e15i | − 0.0470518i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.02615e16 | −0.101885 | ||||||||
\(765\) | −4.33689e16 | −0.216376 | ||||||||
\(766\) | − 1.16893e17i | − 0.578648i | ||||||||
\(767\) | 3.59886e16 | 0.176764 | ||||||||
\(768\) | 6.86117e14i | 0.00334373i | ||||||||
\(769\) | 2.35317e17i | 1.13787i | 0.822381 | + | 0.568937i | \(0.192645\pi\) | ||||
−0.822381 | + | 0.568937i | \(0.807355\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.61809e16 | −0.0770331 | ||||||||
\(772\) | −8.99218e16 | −0.424777 | ||||||||
\(773\) | 2.20992e17i | 1.03586i | 0.855423 | + | 0.517929i | \(0.173297\pi\) | ||||
−0.855423 | + | 0.517929i | \(0.826703\pi\) | |||||||
\(774\) | 1.74363e17 | 0.810975 | ||||||||
\(775\) | − 4.13592e17i | − 1.90881i | ||||||||
\(776\) | 3.80884e16i | 0.174431i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.75426e17 | −0.791072 | ||||||||
\(779\) | 2.70200e17 | 1.20910 | ||||||||
\(780\) | 1.59752e15i | 0.00709382i | ||||||||
\(781\) | −3.85970e17 | −1.70077 | ||||||||
\(782\) | − 4.03157e16i | − 0.176292i | ||||||||
\(783\) | 1.88845e16i | 0.0819474i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.47938e16 | −0.191425 | ||||||||
\(786\) | −8.07220e15 | −0.0342339 | ||||||||
\(787\) | 1.83402e16i | 0.0771892i | 0.999255 | + | 0.0385946i | \(0.0122881\pi\) | ||||
−0.999255 | + | 0.0385946i | \(0.987712\pi\) | |||||||
\(788\) | 7.95179e16 | 0.332129 | ||||||||
\(789\) | 4.59025e15i | 0.0190272i | ||||||||
\(790\) | − 2.93220e16i | − 0.120623i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.67621e17 | −0.679166 | ||||||||
\(793\) | 3.56722e16 | 0.143447 | ||||||||
\(794\) | − 3.34107e15i | − 0.0133341i | ||||||||
\(795\) | 8.07826e14 | 0.00319974 | ||||||||
\(796\) | 3.87739e16i | 0.152427i | ||||||||
\(797\) | − 9.39084e16i | − 0.366399i | −0.983076 | − | 0.183200i | \(-0.941355\pi\) | ||||
0.983076 | − | 0.183200i | \(-0.0586454\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.22285e17 | −0.469993 | ||||||||
\(800\) | −4.47820e16 | −0.170830 | ||||||||
\(801\) | − 1.37936e17i | − 0.522254i | ||||||||
\(802\) | 1.82161e17 | 0.684558 | ||||||||
\(803\) | − 5.95813e17i | − 2.22237i | ||||||||
\(804\) | − 6.06284e15i | − 0.0224460i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.53667e17 | 2.01947 | ||||||||
\(807\) | 1.54712e16 | 0.0560123 | ||||||||
\(808\) | 1.29203e17i | 0.464306i | ||||||||
\(809\) | 1.00865e17 | 0.359789 | 0.179895 | − | 0.983686i | \(-0.442424\pi\) | ||||
0.179895 | + | 0.983686i | \(0.442424\pi\) | |||||||
\(810\) | − 3.63147e16i | − 0.128580i | ||||||||
\(811\) | 2.30062e17i | 0.808572i | 0.914633 | + | 0.404286i | \(0.132480\pi\) | ||||
−0.914633 | + | 0.404286i | \(0.867520\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.09848e15 | 0.0280453 | ||||||||
\(814\) | 2.80598e17 | 0.964578 | ||||||||
\(815\) | 6.97236e15i | 0.0237922i | ||||||||
\(816\) | −4.67151e15 | −0.0158240 | ||||||||
\(817\) | 3.82111e17i | 1.28486i | ||||||||
\(818\) | − 2.60663e17i | − 0.870081i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.01755e16 | −0.0992592 | ||||||||
\(821\) | 1.51990e17 | 0.496315 | 0.248157 | − | 0.968720i | \(-0.420175\pi\) | ||||
0.248157 | + | 0.968720i | \(0.420175\pi\) | |||||||
\(822\) | − 1.00452e16i | − 0.0325632i | ||||||||
\(823\) | −1.64859e17 | −0.530535 | −0.265268 | − | 0.964175i | \(-0.585460\pi\) | ||||
−0.265268 | + | 0.964175i | \(0.585460\pi\) | |||||||
\(824\) | 1.33975e17i | 0.428016i | ||||||||
\(825\) | 3.14036e16i | 0.0995992i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.48794e16 | 0.202803 | 0.101401 | − | 0.994846i | \(-0.467667\pi\) | ||||
0.101401 | + | 0.994846i | \(0.467667\pi\) | |||||||
\(828\) | 3.38556e16 | 0.105063 | ||||||||
\(829\) | − 4.54965e17i | − 1.40169i | −0.713315 | − | 0.700844i | \(-0.752807\pi\) | ||||
0.713315 | − | 0.700844i | \(-0.247193\pi\) | |||||||
\(830\) | 5.35927e16 | 0.163922 | ||||||||
\(831\) | 1.23241e16i | 0.0374240i | ||||||||
\(832\) | − 5.99487e16i | − 0.180734i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6.66172e15 | −0.0197966 | ||||||||
\(835\) | −1.54577e16 | −0.0456063 | ||||||||
\(836\) | − 3.67335e17i | − 1.07603i | ||||||||
\(837\) | 7.25663e16 | 0.211048 | ||||||||
\(838\) | − 4.29642e17i | − 1.24063i | ||||||||
\(839\) | 4.60417e17i | 1.32002i | 0.751259 | + | 0.660008i | \(0.229447\pi\) | ||||
−0.751259 | + | 0.660008i | \(0.770553\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.45688e17 | −0.411763 | ||||||||
\(842\) | 3.92961e17 | 1.10275 | ||||||||
\(843\) | − 1.27547e16i | − 0.0355391i | ||||||||
\(844\) | −6.54813e16 | −0.181160 | ||||||||
\(845\) | − 7.28138e16i | − 0.200020i | ||||||||
\(846\) | − 1.02690e17i | − 0.280096i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.03145e16 | −0.0815220 | ||||||||
\(849\) | 3.13049e15 | 0.00835923 | ||||||||
\(850\) | − 3.04903e17i | − 0.808442i | ||||||||
\(851\) | −5.66745e16 | −0.149214 | ||||||||
\(852\) | − 9.03315e15i | − 0.0236158i | ||||||||
\(853\) | 4.56236e17i | 1.18439i | 0.805794 | + | 0.592196i | \(0.201739\pi\) | ||||
−0.805794 | + | 0.592196i | \(0.798261\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.98124e16 | 0.204302 | ||||||||
\(856\) | −5.28813e16 | −0.134419 | ||||||||
\(857\) | 1.79216e17i | 0.452369i | 0.974084 | + | 0.226184i | \(0.0726252\pi\) | ||||
−0.974084 | + | 0.226184i | \(0.927375\pi\) | |||||||
\(858\) | −4.20393e16 | −0.105374 | ||||||||
\(859\) | − 6.75475e17i | − 1.68132i | −0.541563 | − | 0.840660i | \(-0.682167\pi\) | ||||
0.541563 | − | 0.840660i | \(-0.317833\pi\) | |||||||
\(860\) | − 4.26734e16i | − 0.105479i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.21968e16 | −0.0297304 | ||||||||
\(863\) | −2.08990e17 | −0.505896 | −0.252948 | − | 0.967480i | \(-0.581400\pi\) | ||||
−0.252948 | + | 0.967480i | \(0.581400\pi\) | |||||||
\(864\) | − 7.85718e15i | − 0.0188879i | ||||||||
\(865\) | 7.30594e16 | 0.174413 | ||||||||
\(866\) | 2.29427e17i | 0.543923i | ||||||||
\(867\) | − 9.08348e15i | − 0.0213864i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.71615e17 | 1.79177 | ||||||||
\(870\) | 2.30758e15 | 0.00532159 | ||||||||
\(871\) | 5.29733e17i | 1.21324i | ||||||||
\(872\) | −2.62121e16 | −0.0596216 | ||||||||
\(873\) | − 2.17775e17i | − 0.491952i | ||||||||
\(874\) | 7.41936e16i | 0.166455i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.39443e16 | 0.0308583 | ||||||||
\(877\) | −2.23561e17 | −0.491358 | −0.245679 | − | 0.969351i | \(-0.579011\pi\) | ||||
−0.245679 | + | 0.969351i | \(0.579011\pi\) | |||||||
\(878\) | − 7.41331e15i | − 0.0161825i | ||||||||
\(879\) | −1.43761e16 | −0.0311679 | ||||||||
\(880\) | 4.10234e16i | 0.0883355i | ||||||||
\(881\) | − 9.10277e17i | − 1.94678i | −0.229144 | − | 0.973392i | \(-0.573593\pi\) | ||||
0.229144 | − | 0.973392i | \(-0.426407\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.97000e17 | 1.04856 | 0.524279 | − | 0.851547i | \(-0.324335\pi\) | ||||
0.524279 | + | 0.851547i | \(0.324335\pi\) | |||||||
\(884\) | 4.08167e17 | 0.855313 | ||||||||
\(885\) | − 5.76372e14i | − 0.00119962i | ||||||||
\(886\) | 3.94390e17 | 0.815311 | ||||||||
\(887\) | − 2.86381e17i | − 0.588033i | −0.955800 | − | 0.294017i | \(-0.905008\pi\) | ||||
0.955800 | − | 0.294017i | \(-0.0949921\pi\) | |||||||
\(888\) | 6.56705e15i | 0.0133935i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.37583e16 | −0.0679267 | ||||||||
\(891\) | 9.55632e17 | 1.90996 | ||||||||
\(892\) | − 3.65899e17i | − 0.726394i | ||||||||
\(893\) | 2.25042e17 | 0.443768 | ||||||||
\(894\) | − 1.18068e16i | − 0.0231263i | ||||||||
\(895\) | 1.03136e17i | 0.200666i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.49100e15 | 0.0163006 | ||||||||
\(898\) | −2.43699e17 | −0.464725 | ||||||||
\(899\) | − 7.99756e17i | − 1.51495i | ||||||||
\(900\) | 2.56047e17 | 0.481797 | ||||||||
\(901\) | − 2.06399e17i | − 0.385798i | ||||||||
\(902\) | − 7.94075e17i | − 1.47442i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.46459e17 | 0.268353 | ||||||||
\(905\) | 3.23002e16 | 0.0587915 | ||||||||
\(906\) | − 9.24292e14i | − 0.00167124i | ||||||||
\(907\) | −3.30810e17 | −0.594203 | −0.297102 | − | 0.954846i | \(-0.596020\pi\) | ||||
−0.297102 | + | 0.954846i | \(0.596020\pi\) | |||||||
\(908\) | 3.34272e17i | 0.596465i | ||||||||
\(909\) | − 7.38734e17i | − 1.30950i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.13090e17 | −1.24748 | −0.623741 | − | 0.781631i | \(-0.714388\pi\) | ||||
−0.623741 | + | 0.781631i | \(0.714388\pi\) | |||||||
\(912\) | 8.59705e15 | 0.0149410 | ||||||||
\(913\) | 1.41031e18i | 2.43494i | ||||||||
\(914\) | 5.99905e17 | 1.02898 | ||||||||
\(915\) | − 5.71305e14i | 0 0.000973513i | ||||||||
\(916\) | 4.05259e17i | 0.686056i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.34965e16 | 0.0893859 | ||||||||
\(919\) | 3.82752e17 | 0.635367 | 0.317684 | − | 0.948197i | \(-0.397095\pi\) | ||||
0.317684 | + | 0.948197i | \(0.397095\pi\) | |||||||
\(920\) | − 8.28580e15i | − 0.0136649i | ||||||||
\(921\) | −2.48293e16 | −0.0406825 | ||||||||
\(922\) | − 6.16870e17i | − 1.00417i | ||||||||
\(923\) | 7.89262e17i | 1.27647i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.28623e17 | −0.684267 | ||||||||
\(926\) | −6.01409e17 | −0.953903 | ||||||||
\(927\) | − 7.66017e17i | − 1.20715i | ||||||||
\(928\) | −8.65942e16 | −0.135582 | ||||||||
\(929\) | 5.12377e17i | 0.797068i | 0.917154 | + | 0.398534i | \(0.130481\pi\) | ||||
−0.917154 | + | 0.398534i | \(0.869519\pi\) | |||||||
\(930\) | − 8.86719e15i | − 0.0137053i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.90986e17 | −0.596576 | ||||||||
\(933\) | 5.13851e16 | 0.0779018 | ||||||||
\(934\) | 3.11111e17i | 0.468634i | ||||||||
\(935\) | −2.79312e17 | −0.418042 | ||||||||
\(936\) | 3.42764e17i | 0.509730i | ||||||||
\(937\) | 1.03036e18i | 1.52248i | 0.648471 | + | 0.761239i | \(0.275409\pi\) | ||||
−0.648471 | + | 0.761239i | \(0.724591\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.75486e16 | −0.0401889 | ||||||||
\(940\) | −2.51323e16 | −0.0364305 | ||||||||
\(941\) | 9.64166e17i | 1.38872i | 0.719629 | + | 0.694359i | \(0.244312\pi\) | ||||
−0.719629 | + | 0.694359i | \(0.755688\pi\) | |||||||
\(942\) | 2.75875e16 | 0.0394827 | ||||||||
\(943\) | 1.60386e17i | 0.228084i | ||||||||
\(944\) | 2.16289e16i | 0.0305635i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.12296e18 | 1.56682 | ||||||||
\(947\) | −2.47776e17 | −0.343526 | −0.171763 | − | 0.985138i | \(-0.554946\pi\) | ||||
−0.171763 | + | 0.985138i | \(0.554946\pi\) | |||||||
\(948\) | 1.80587e16i | 0.0248792i | ||||||||
\(949\) | −1.21837e18 | −1.66794 | ||||||||
\(950\) | 5.61119e17i | 0.763331i | ||||||||
\(951\) | 2.91118e16i | 0.0393537i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.21407e18 | −1.62064 | −0.810320 | − | 0.585988i | \(-0.800707\pi\) | ||||
−0.810320 | + | 0.585988i | \(0.800707\pi\) | |||||||
\(954\) | 1.73327e17 | 0.229919 | ||||||||
\(955\) | − 2.83524e16i | − 0.0373740i | ||||||||
\(956\) | −3.66802e17 | −0.480490 | ||||||||
\(957\) | 6.07246e16i | 0.0790484i | ||||||||
\(958\) | 1.54952e17i | 0.200449i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −9.60102e14 | −0.00122656 | ||||||||
\(961\) | −2.28551e18 | −2.90163 | ||||||||
\(962\) | − 5.73789e17i | − 0.723938i | ||||||||
\(963\) | 3.02355e17 | 0.379105 | ||||||||
\(964\) | − 4.06068e17i | − 0.505984i | ||||||||
\(965\) | − 1.25830e17i | − 0.155819i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.21549e18 | 1.48660 | 0.743298 | − | 0.668960i | \(-0.233260\pi\) | ||||
0.743298 | + | 0.668960i | \(0.233260\pi\) | |||||||
\(968\) | −7.88665e17 | −0.958607 | ||||||||
\(969\) | 5.85339e16i | 0.0707074i | ||||||||
\(970\) | −5.32982e16 | −0.0639856 | ||||||||
\(971\) | 1.32675e18i | 1.58297i | 0.611187 | + | 0.791486i | \(0.290692\pi\) | ||||
−0.611187 | + | 0.791486i | \(0.709308\pi\) | |||||||
\(972\) | 6.74187e16i | 0.0799434i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −7.16259e17 | −0.838911 | ||||||||
\(975\) | 6.42166e16 | 0.0747515 | ||||||||
\(976\) | 2.14388e16i | 0.0248028i | ||||||||
\(977\) | −4.26902e17 | −0.490863 | −0.245432 | − | 0.969414i | \(-0.578930\pi\) | ||||
−0.245432 | + | 0.969414i | \(0.578930\pi\) | |||||||
\(978\) | − 4.29412e15i | − 0.00490728i | ||||||||
\(979\) | − 8.88359e17i | − 1.00900i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.49871e17 | 0.168153 | ||||||||
\(982\) | 1.02527e18 | 1.14332 | ||||||||
\(983\) | − 6.02837e17i | − 0.668157i | −0.942545 | − | 0.334079i | \(-0.891575\pi\) | ||||
0.942545 | − | 0.334079i | \(-0.108425\pi\) | |||||||
\(984\) | 1.85844e16 | 0.0204728 | ||||||||
\(985\) | 1.11272e17i | 0.121833i | ||||||||
\(986\) | − 5.89587e17i | − 0.641632i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.51157e17 | −0.807587 | ||||||||
\(989\) | −2.26813e17 | −0.242377 | ||||||||
\(990\) | − 2.34556e17i | − 0.249135i | ||||||||
\(991\) | 6.49021e17 | 0.685200 | 0.342600 | − | 0.939481i | \(-0.388693\pi\) | ||||
0.342600 | + | 0.939481i | \(0.388693\pi\) | |||||||
\(992\) | 3.32750e17i | 0.349179i | ||||||||
\(993\) | 4.41980e16i | 0.0461007i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.42574e16 | −0.0559140 | ||||||||
\(996\) | −3.30065e16 | −0.0338099 | ||||||||
\(997\) | 1.12875e18i | 1.14928i | 0.818407 | + | 0.574639i | \(0.194858\pi\) | ||||
−0.818407 | + | 0.574639i | \(0.805142\pi\) | |||||||
\(998\) | −4.10530e17 | −0.415491 | ||||||||
\(999\) | − 7.52036e16i | − 0.0756564i |
(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 | 98.13.b.c.97.5 | 16 | ||
7.2 | even | 3 | 14.13.d.a.3.7 | ✓ | 16 | ||
7.3 | odd | 6 | 14.13.d.a.5.7 | yes | 16 | ||
7.4 | even | 3 | 98.13.d.a.19.6 | 16 | |||
7.5 | odd | 6 | 98.13.d.a.31.6 | 16 | |||
7.6 | odd | 2 | inner | 98.13.b.c.97.4 | 16 | ||
21.2 | odd | 6 | 126.13.n.a.73.2 | 16 | |||
21.17 | even | 6 | 126.13.n.a.19.2 | 16 | |||
28.3 | even | 6 | 112.13.s.c.33.4 | 16 | |||
28.23 | odd | 6 | 112.13.s.c.17.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.13.d.a.3.7 | ✓ | 16 | 7.2 | even | 3 | ||
14.13.d.a.5.7 | yes | 16 | 7.3 | odd | 6 | ||
98.13.b.c.97.4 | 16 | 7.6 | odd | 2 | inner | ||
98.13.b.c.97.5 | 16 | 1.1 | even | 1 | trivial | ||
98.13.d.a.19.6 | 16 | 7.4 | even | 3 | |||
98.13.d.a.31.6 | 16 | 7.5 | odd | 6 | |||
112.13.s.c.17.4 | 16 | 28.23 | odd | 6 | |||
112.13.s.c.33.4 | 16 | 28.3 | even | 6 | |||
126.13.n.a.19.2 | 16 | 21.17 | even | 6 | |||
126.13.n.a.73.2 | 16 | 21.2 | odd | 6 |