Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,25,Mod(5,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 25, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.5");
S:= CuspForms(chi, 25);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 25 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.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: | \(21.8980291355\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 9921984x^{6} + 31297402621425x^{4} + 35629505313218665424x^{2} + 11190322069687119538557504 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{53}\cdot 3^{32}\cdot 17^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.3 | ||
Root | \(-708.500i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6.5 |
Dual form | 6.25.b.a.5.7 |
$q$-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 \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2896.31i | − | 0.707107i | ||||||
\(3\) | 269557. | − | 458005.i | 0.507220 | − | 0.861817i | ||||
\(4\) | −8.38861e6 | −0.500000 | ||||||||
\(5\) | − | 4.56581e8i | − | 1.87016i | −0.354441 | − | 0.935078i | \(-0.615329\pi\) | ||
0.354441 | − | 0.935078i | \(-0.384671\pi\) | |||||||
\(6\) | −1.32652e9 | − | 7.80721e8i | −0.609396 | − | 0.358658i | ||||
\(7\) | 1.81935e9 | 0.131444 | 0.0657220 | − | 0.997838i | \(-0.479065\pi\) | ||||
0.0657220 | + | 0.997838i | \(0.479065\pi\) | |||||||
\(8\) | 2.42960e10i | 0.353553i | ||||||||
\(9\) | −1.37107e11 | − | 2.46917e11i | −0.485456 | − | 0.874261i | ||||
\(10\) | −1.32240e12 | −1.32240 | ||||||||
\(11\) | − | 3.36073e12i | − | 1.07083i | −0.844589 | − | 0.535416i | \(-0.820155\pi\) | ||
0.844589 | − | 0.535416i | \(-0.179845\pi\) | |||||||
\(12\) | −2.26121e12 | + | 3.84202e12i | −0.253610 | + | 0.430908i | ||||
\(13\) | 3.10150e13 | 1.33123 | 0.665613 | − | 0.746297i | \(-0.268170\pi\) | ||||
0.665613 | + | 0.746297i | \(0.268170\pi\) | |||||||
\(14\) | − | 5.26941e12i | − | 0.0929450i | ||||||
\(15\) | −2.09116e14 | − | 1.23075e14i | −1.61173 | − | 0.948580i | ||||
\(16\) | 7.03687e13 | 0.250000 | ||||||||
\(17\) | 1.14524e14i | 0.196566i | 0.995159 | + | 0.0982830i | \(0.0313350\pi\) | ||||
−0.995159 | + | 0.0982830i | \(0.968665\pi\) | |||||||
\(18\) | −7.15148e14 | + | 3.97105e14i | −0.618196 | + | 0.343269i | ||||
\(19\) | 9.25261e14 | 0.418043 | 0.209022 | − | 0.977911i | \(-0.432972\pi\) | ||||
0.209022 | + | 0.977911i | \(0.432972\pi\) | |||||||
\(20\) | 3.83008e15i | 0.935078i | ||||||||
\(21\) | 4.90420e14 | − | 8.33273e14i | 0.0666710 | − | 0.113281i | ||||
\(22\) | −9.73371e15 | −0.757192 | ||||||||
\(23\) | 2.51730e16i | 1.14869i | 0.818615 | + | 0.574343i | \(0.194742\pi\) | ||||
−0.818615 | + | 0.574343i | \(0.805258\pi\) | |||||||
\(24\) | 1.11277e16 | + | 6.54917e15i | 0.304698 | + | 0.179329i | ||||
\(25\) | −1.48862e17 | −2.49749 | ||||||||
\(26\) | − | 8.98290e16i | − | 0.941318i | ||||||
\(27\) | −1.50047e17 | − | 3.76256e15i | −0.999686 | − | 0.0250679i | ||||
\(28\) | −1.52619e16 | −0.0657220 | ||||||||
\(29\) | 5.38831e17i | 1.52292i | 0.648213 | + | 0.761459i | \(0.275517\pi\) | ||||
−0.648213 | + | 0.761459i | \(0.724483\pi\) | |||||||
\(30\) | −3.56463e17 | + | 6.05666e17i | −0.670748 | + | 1.13967i | ||||
\(31\) | 4.67868e17 | 0.593995 | 0.296998 | − | 0.954878i | \(-0.404015\pi\) | ||||
0.296998 | + | 0.954878i | \(0.404015\pi\) | |||||||
\(32\) | − | 2.03810e17i | − | 0.176777i | ||||||
\(33\) | −1.53923e18 | − | 9.05909e17i | −0.922860 | − | 0.543147i | ||||
\(34\) | 3.31696e17 | 0.138993 | ||||||||
\(35\) | − | 8.30683e17i | − | 0.245821i | ||||||
\(36\) | 1.15014e18 | + | 2.07129e18i | 0.242728 | + | 0.437130i | ||||
\(37\) | 3.11155e18 | 0.472668 | 0.236334 | − | 0.971672i | \(-0.424054\pi\) | ||||
0.236334 | + | 0.971672i | \(0.424054\pi\) | |||||||
\(38\) | − | 2.67984e18i | − | 0.295601i | ||||||
\(39\) | 8.36032e18 | − | 1.42050e19i | 0.675224 | − | 1.14727i | ||||
\(40\) | 1.10931e19 | 0.661200 | ||||||||
\(41\) | − | 1.15365e19i | − | 0.511291i | −0.966771 | − | 0.255646i | \(-0.917712\pi\) | ||
0.966771 | − | 0.255646i | \(-0.0822881\pi\) | |||||||
\(42\) | −2.41342e18 | − | 1.42041e18i | −0.0801015 | − | 0.0471435i | ||||
\(43\) | 5.41569e19 | 1.35529 | 0.677645 | − | 0.735390i | \(-0.263001\pi\) | ||||
0.677645 | + | 0.735390i | \(0.263001\pi\) | |||||||
\(44\) | 2.81918e19i | 0.535416i | ||||||||
\(45\) | −1.12738e20 | + | 6.26006e19i | −1.63500 | + | 0.907879i | ||||
\(46\) | 7.29088e19 | 0.812243 | ||||||||
\(47\) | − | 1.41317e20i | − | 1.21624i | −0.793844 | − | 0.608122i | \(-0.791923\pi\) | ||
0.793844 | − | 0.608122i | \(-0.208077\pi\) | |||||||
\(48\) | 1.89684e19 | − | 3.22292e19i | 0.126805 | − | 0.215454i | ||||
\(49\) | −1.88271e20 | −0.982722 | ||||||||
\(50\) | 4.31150e20i | 1.76599i | ||||||||
\(51\) | 5.24524e19 | + | 3.08707e19i | 0.169404 | + | 0.0997022i | ||||
\(52\) | −2.60173e20 | −0.665613 | ||||||||
\(53\) | − | 5.85803e20i | − | 1.19245i | −0.802816 | − | 0.596226i | \(-0.796666\pi\) | ||
0.802816 | − | 0.596226i | \(-0.203334\pi\) | |||||||
\(54\) | −1.08975e19 | + | 4.34584e20i | −0.0177257 | + | 0.706885i | ||||
\(55\) | −1.53445e21 | −2.00262 | ||||||||
\(56\) | 4.42030e19i | 0.0464725i | ||||||||
\(57\) | 2.49411e20 | − | 4.23774e20i | 0.212040 | − | 0.360277i | ||||
\(58\) | 1.56062e21 | 1.07687 | ||||||||
\(59\) | 1.22231e21i | 0.686998i | 0.939153 | + | 0.343499i | \(0.111612\pi\) | ||||
−0.939153 | + | 0.343499i | \(0.888388\pi\) | |||||||
\(60\) | 1.75420e21 | + | 1.03243e21i | 0.805866 | + | 0.474290i | ||||
\(61\) | 3.16259e21 | 1.19148 | 0.595738 | − | 0.803179i | \(-0.296860\pi\) | ||||
0.595738 | + | 0.803179i | \(0.296860\pi\) | |||||||
\(62\) | − | 1.35509e21i | − | 0.420018i | ||||||
\(63\) | −2.49447e20 | − | 4.49230e20i | −0.0638103 | − | 0.114916i | ||||
\(64\) | −5.90296e20 | −0.125000 | ||||||||
\(65\) | − | 1.41609e22i | − | 2.48960i | ||||||
\(66\) | −2.62379e21 | + | 4.45808e21i | −0.384063 | + | 0.652561i | ||||
\(67\) | −2.88702e21 | −0.352820 | −0.176410 | − | 0.984317i | \(-0.556448\pi\) | ||||
−0.176410 | + | 0.984317i | \(0.556448\pi\) | |||||||
\(68\) | − | 9.60695e20i | − | 0.0982830i | ||||||
\(69\) | 1.15294e22 | + | 6.78557e21i | 0.989956 | + | 0.582636i | ||||
\(70\) | −2.40592e21 | −0.173822 | ||||||||
\(71\) | 5.86562e21i | 0.357449i | 0.983899 | + | 0.178724i | \(0.0571970\pi\) | ||||
−0.983899 | + | 0.178724i | \(0.942803\pi\) | |||||||
\(72\) | 5.99910e21 | − | 3.33116e21i | 0.309098 | − | 0.171635i | ||||
\(73\) | −4.89426e21 | −0.213704 | −0.106852 | − | 0.994275i | \(-0.534077\pi\) | ||||
−0.106852 | + | 0.994275i | \(0.534077\pi\) | |||||||
\(74\) | − | 9.01201e21i | − | 0.334227i | ||||||
\(75\) | −4.01268e22 | + | 6.81794e22i | −1.26677 | + | 2.15238i | ||||
\(76\) | −7.76165e21 | −0.209022 | ||||||||
\(77\) | − | 6.11435e21i | − | 0.140754i | ||||||
\(78\) | −4.11421e22 | − | 2.42141e22i | −0.811244 | − | 0.477455i | ||||
\(79\) | 4.71039e22 | 0.797135 | 0.398567 | − | 0.917139i | \(-0.369507\pi\) | ||||
0.398567 | + | 0.917139i | \(0.369507\pi\) | |||||||
\(80\) | − | 3.21290e22i | − | 0.467539i | ||||||
\(81\) | −4.21697e22 | + | 6.77082e22i | −0.528664 | + | 0.848831i | ||||
\(82\) | −3.34133e22 | −0.361538 | ||||||||
\(83\) | − | 1.25799e23i | − | 1.17690i | −0.808534 | − | 0.588449i | \(-0.799739\pi\) | ||
0.808534 | − | 0.588449i | \(-0.200261\pi\) | |||||||
\(84\) | −4.11394e21 | + | 6.99000e21i | −0.0333355 | + | 0.0566403i | ||||
\(85\) | 5.22894e22 | 0.367609 | ||||||||
\(86\) | − | 1.56855e23i | − | 0.958334i | ||||||
\(87\) | 2.46787e23 | + | 1.45246e23i | 1.31248 | + | 0.772454i | ||||
\(88\) | 8.16522e22 | 0.378596 | ||||||||
\(89\) | − | 4.49583e22i | − | 0.182024i | −0.995850 | − | 0.0910122i | \(-0.970990\pi\) | ||
0.995850 | − | 0.0910122i | \(-0.0290102\pi\) | |||||||
\(90\) | 1.81311e23 | + | 3.26523e23i | 0.641968 | + | 1.15612i | ||||
\(91\) | 5.64273e22 | 0.174982 | ||||||||
\(92\) | − | 2.11166e23i | − | 0.574343i | ||||||
\(93\) | 1.26117e23 | − | 2.14286e23i | 0.301286 | − | 0.511915i | ||||
\(94\) | −4.09298e23 | −0.860014 | ||||||||
\(95\) | − | 4.22457e23i | − | 0.781806i | ||||||
\(96\) | −9.33458e22 | − | 5.49384e22i | −0.152349 | − | 0.0896646i | ||||
\(97\) | −2.08004e23 | −0.299786 | −0.149893 | − | 0.988702i | \(-0.547893\pi\) | ||||
−0.149893 | + | 0.988702i | \(0.547893\pi\) | |||||||
\(98\) | 5.45292e23i | 0.694890i | ||||||||
\(99\) | −8.29821e23 | + | 4.60780e23i | −0.936186 | + | 0.519842i | ||||
\(100\) | 1.24874e24 | 1.24874 | ||||||||
\(101\) | 4.79708e23i | 0.425717i | 0.977083 | + | 0.212858i | \(0.0682773\pi\) | ||||
−0.977083 | + | 0.212858i | \(0.931723\pi\) | |||||||
\(102\) | 8.94112e22 | − | 1.51918e23i | 0.0705001 | − | 0.119787i | ||||
\(103\) | −2.07015e24 | −1.45196 | −0.725982 | − | 0.687714i | \(-0.758614\pi\) | ||||
−0.725982 | + | 0.687714i | \(0.758614\pi\) | |||||||
\(104\) | 7.53541e23i | 0.470659i | ||||||||
\(105\) | −3.80457e23 | − | 2.23917e23i | −0.211853 | − | 0.124685i | ||||
\(106\) | −1.69667e24 | −0.843192 | ||||||||
\(107\) | − | 2.26189e24i | − | 1.00430i | −0.864779 | − | 0.502152i | \(-0.832542\pi\) | ||
0.864779 | − | 0.502152i | \(-0.167458\pi\) | |||||||
\(108\) | 1.25869e24 | + | 3.15627e22i | 0.499843 | + | 0.0125340i | ||||
\(109\) | 4.92671e23 | 0.175162 | 0.0875808 | − | 0.996157i | \(-0.472086\pi\) | ||||
0.0875808 | + | 0.996157i | \(0.472086\pi\) | |||||||
\(110\) | 4.44423e24i | 1.41607i | ||||||||
\(111\) | 8.38741e23 | − | 1.42511e24i | 0.239747 | − | 0.407353i | ||||
\(112\) | 1.28026e23 | 0.0328610 | ||||||||
\(113\) | 3.60667e24i | 0.832080i | 0.909346 | + | 0.416040i | \(0.136582\pi\) | ||||
−0.909346 | + | 0.416040i | \(0.863418\pi\) | |||||||
\(114\) | −1.22738e24 | − | 7.22371e23i | −0.254754 | − | 0.149935i | ||||
\(115\) | 1.14935e25 | 2.14822 | ||||||||
\(116\) | − | 4.52004e24i | − | 0.761459i | ||||||
\(117\) | −4.25238e24 | − | 7.65813e24i | −0.646252 | − | 1.16384i | ||||
\(118\) | 3.54017e24 | 0.485781 | ||||||||
\(119\) | 2.08359e23i | 0.0258374i | ||||||||
\(120\) | 2.99023e24 | − | 5.08069e24i | 0.335374 | − | 0.569833i | ||||
\(121\) | −1.44476e24 | −0.146680 | ||||||||
\(122\) | − | 9.15984e24i | − | 0.842500i | ||||||
\(123\) | −5.28378e24 | − | 3.10975e24i | −0.440640 | − | 0.259337i | ||||
\(124\) | −3.92476e24 | −0.296998 | ||||||||
\(125\) | 4.07531e25i | 2.80053i | ||||||||
\(126\) | −1.30111e24 | + | 7.22475e23i | −0.0812581 | + | 0.0451207i | ||||
\(127\) | 1.55723e24 | 0.0884519 | 0.0442259 | − | 0.999022i | \(-0.485918\pi\) | ||||
0.0442259 | + | 0.999022i | \(0.485918\pi\) | |||||||
\(128\) | 1.70968e24i | 0.0883883i | ||||||||
\(129\) | 1.45984e25 | − | 2.48041e25i | 0.687429 | − | 1.16801i | ||||
\(130\) | −4.10143e25 | −1.76041 | ||||||||
\(131\) | 3.80638e24i | 0.149024i | 0.997220 | + | 0.0745121i | \(0.0237399\pi\) | ||||
−0.997220 | + | 0.0745121i | \(0.976260\pi\) | |||||||
\(132\) | 1.29120e25 | + | 7.59931e24i | 0.461430 | + | 0.271573i | ||||
\(133\) | 1.68338e24 | 0.0549493 | ||||||||
\(134\) | 8.36171e24i | 0.249481i | ||||||||
\(135\) | −1.71792e24 | + | 6.85089e25i | −0.0468810 | + | 1.86957i | ||||
\(136\) | −2.78247e24 | −0.0694966 | ||||||||
\(137\) | − | 2.25473e25i | − | 0.515760i | −0.966177 | − | 0.257880i | \(-0.916976\pi\) | ||
0.966177 | − | 0.257880i | \(-0.0830239\pi\) | |||||||
\(138\) | 1.96531e25 | − | 3.33926e25i | 0.411986 | − | 0.700005i | ||||
\(139\) | −7.62088e25 | −1.46497 | −0.732483 | − | 0.680785i | \(-0.761639\pi\) | ||||
−0.732483 | + | 0.680785i | \(0.761639\pi\) | |||||||
\(140\) | 6.96828e24i | 0.122910i | ||||||||
\(141\) | −6.47239e25 | − | 3.80931e25i | −1.04818 | − | 0.616903i | ||||
\(142\) | 1.69886e25 | 0.252754 | ||||||||
\(143\) | − | 1.04233e26i | − | 1.42552i | ||||||
\(144\) | −9.64806e24 | − | 1.73752e25i | −0.121364 | − | 0.218565i | ||||
\(145\) | 2.46020e26 | 2.84810 | ||||||||
\(146\) | 1.41753e25i | 0.151112i | ||||||||
\(147\) | −5.07499e25 | + | 8.62291e25i | −0.498456 | + | 0.846927i | ||||
\(148\) | −2.61016e25 | −0.236334 | ||||||||
\(149\) | − | 2.27765e25i | − | 0.190218i | −0.995467 | − | 0.0951089i | \(-0.969680\pi\) | ||
0.995467 | − | 0.0951089i | \(-0.0303199\pi\) | |||||||
\(150\) | 1.97469e26 | + | 1.16220e26i | 1.52196 | + | 0.895745i | ||||
\(151\) | 1.16110e26 | 0.826314 | 0.413157 | − | 0.910660i | \(-0.364426\pi\) | ||||
0.413157 | + | 0.910660i | \(0.364426\pi\) | |||||||
\(152\) | 2.24802e25i | 0.147801i | ||||||||
\(153\) | 2.82779e25 | − | 1.57020e25i | 0.171850 | − | 0.0954242i | ||||
\(154\) | −1.77091e25 | −0.0995284 | ||||||||
\(155\) | − | 2.13620e26i | − | 1.11086i | ||||||
\(156\) | −7.01315e25 | + | 1.19160e26i | −0.337612 | + | 0.573636i | ||||
\(157\) | −3.85801e26 | −1.72015 | −0.860077 | − | 0.510164i | \(-0.829585\pi\) | ||||
−0.860077 | + | 0.510164i | \(0.829585\pi\) | |||||||
\(158\) | − | 1.36427e26i | − | 0.563660i | ||||||
\(159\) | −2.68301e26 | − | 1.57908e26i | −1.02768 | − | 0.604836i | ||||
\(160\) | −9.30557e25 | −0.330600 | ||||||||
\(161\) | 4.57986e25i | 0.150988i | ||||||||
\(162\) | 1.96104e26 | + | 1.22136e26i | 0.600214 | + | 0.373822i | ||||
\(163\) | 3.94400e26 | 1.12121 | 0.560604 | − | 0.828084i | \(-0.310569\pi\) | ||||
0.560604 | + | 0.828084i | \(0.310569\pi\) | |||||||
\(164\) | 9.67753e25i | 0.255646i | ||||||||
\(165\) | −4.13621e26 | + | 7.02783e26i | −1.01577 | + | 1.72589i | ||||
\(166\) | −3.64352e26 | −0.832193 | ||||||||
\(167\) | − | 2.99402e26i | − | 0.636292i | −0.948042 | − | 0.318146i | \(-0.896940\pi\) | ||
0.948042 | − | 0.318146i | \(-0.103060\pi\) | |||||||
\(168\) | 2.02452e25 | + | 1.19153e25i | 0.0400508 | + | 0.0235718i | ||||
\(169\) | 4.19130e26 | 0.772161 | ||||||||
\(170\) | − | 1.51446e26i | − | 0.259939i | ||||||
\(171\) | −1.26860e26 | − | 2.28463e26i | −0.202942 | − | 0.365479i | ||||
\(172\) | −4.54301e26 | −0.677645 | ||||||||
\(173\) | 1.10874e27i | 1.54268i | 0.636424 | + | 0.771339i | \(0.280413\pi\) | ||||
−0.636424 | + | 0.771339i | \(0.719587\pi\) | |||||||
\(174\) | 4.20677e26 | − | 7.14772e26i | 0.546208 | − | 0.928061i | ||||
\(175\) | −2.70832e26 | −0.328280 | ||||||||
\(176\) | − | 2.36490e26i | − | 0.267708i | ||||||
\(177\) | 5.59822e26 | + | 3.29481e26i | 0.592067 | + | 0.348459i | ||||
\(178\) | −1.30213e26 | −0.128711 | ||||||||
\(179\) | 2.47530e26i | 0.228766i | 0.993437 | + | 0.114383i | \(0.0364891\pi\) | ||||
−0.993437 | + | 0.114383i | \(0.963511\pi\) | |||||||
\(180\) | 9.45713e26 | − | 5.25132e26i | 0.817502 | − | 0.453940i | ||||
\(181\) | 9.06907e26 | 0.733533 | 0.366767 | − | 0.930313i | \(-0.380465\pi\) | ||||
0.366767 | + | 0.930313i | \(0.380465\pi\) | |||||||
\(182\) | − | 1.63431e26i | − | 0.123731i | ||||||
\(183\) | 8.52500e26 | − | 1.44848e27i | 0.604340 | − | 1.02683i | ||||
\(184\) | −6.11603e26 | −0.406121 | ||||||||
\(185\) | − | 1.42068e27i | − | 0.883963i | ||||||
\(186\) | −6.20638e26 | − | 3.65275e26i | −0.361979 | − | 0.213041i | ||||
\(187\) | 3.84883e26 | 0.210489 | ||||||||
\(188\) | 1.18545e27i | 0.608122i | ||||||||
\(189\) | −2.72990e26 | − | 6.84543e24i | −0.131403 | − | 0.00329503i | ||||
\(190\) | −1.22357e27 | −0.552821 | ||||||||
\(191\) | 2.37087e27i | 1.00579i | 0.864348 | + | 0.502895i | \(0.167732\pi\) | ||||
−0.864348 | + | 0.502895i | \(0.832268\pi\) | |||||||
\(192\) | −1.59119e26 | + | 2.70358e26i | −0.0634025 | + | 0.107727i | ||||
\(193\) | 5.09004e27 | 1.90561 | 0.952804 | − | 0.303585i | \(-0.0981835\pi\) | ||||
0.952804 | + | 0.303585i | \(0.0981835\pi\) | |||||||
\(194\) | 6.02444e26i | 0.211980i | ||||||||
\(195\) | −6.48575e27 | − | 3.81717e27i | −2.14558 | − | 1.26277i | ||||
\(196\) | 1.57933e27 | 0.491361 | ||||||||
\(197\) | 4.72370e27i | 1.38257i | 0.722582 | + | 0.691285i | \(0.242955\pi\) | ||||
−0.722582 | + | 0.691285i | \(0.757045\pi\) | |||||||
\(198\) | 1.33456e27 | + | 2.40342e27i | 0.367584 | + | 0.661983i | ||||
\(199\) | −7.31715e27 | −1.89716 | −0.948582 | − | 0.316530i | \(-0.897482\pi\) | ||||
−0.948582 | + | 0.316530i | \(0.897482\pi\) | |||||||
\(200\) | − | 3.61675e27i | − | 0.882995i | ||||||
\(201\) | −7.78219e26 | + | 1.32227e27i | −0.178957 | + | 0.304066i | ||||
\(202\) | 1.38938e27 | 0.301027 | ||||||||
\(203\) | 9.80325e26i | 0.200179i | ||||||||
\(204\) | −4.40003e26 | − | 2.58962e26i | −0.0847020 | − | 0.0498511i | ||||
\(205\) | −5.26736e27 | −0.956195 | ||||||||
\(206\) | 5.99580e27i | 1.02669i | ||||||||
\(207\) | 6.21564e27 | − | 3.45140e27i | 1.00425 | − | 0.557636i | ||||
\(208\) | 2.18249e27 | 0.332806 | ||||||||
\(209\) | − | 3.10955e27i | − | 0.447654i | ||||||
\(210\) | −6.48532e26 | + | 1.10192e27i | −0.0881658 | + | 0.149802i | ||||
\(211\) | 5.52494e27 | 0.709476 | 0.354738 | − | 0.934966i | \(-0.384570\pi\) | ||||
0.354738 | + | 0.934966i | \(0.384570\pi\) | |||||||
\(212\) | 4.91407e27i | 0.596226i | ||||||||
\(213\) | 2.68648e27 | + | 1.58112e27i | 0.308055 | + | 0.181305i | ||||
\(214\) | −6.55112e27 | −0.710150 | ||||||||
\(215\) | − | 2.47270e28i | − | 2.53460i | ||||||
\(216\) | 9.14152e25 | − | 3.64555e27i | 0.00886285 | − | 0.353442i | ||||
\(217\) | 8.51218e26 | 0.0780771 | ||||||||
\(218\) | − | 1.42693e27i | − | 0.123858i | ||||||
\(219\) | −1.31928e27 | + | 2.24160e27i | −0.108395 | + | 0.184174i | ||||
\(220\) | 1.28719e28 | 1.00131 | ||||||||
\(221\) | 3.55195e27i | 0.261674i | ||||||||
\(222\) | −4.12755e27 | − | 2.42925e27i | −0.288042 | − | 0.169526i | ||||
\(223\) | −2.65651e27 | −0.175652 | −0.0878261 | − | 0.996136i | \(-0.527992\pi\) | ||||
−0.0878261 | + | 0.996136i | \(0.527992\pi\) | |||||||
\(224\) | − | 3.70802e26i | − | 0.0232362i | ||||||
\(225\) | 2.04100e28 | + | 3.67565e28i | 1.21242 | + | 2.18345i | ||||
\(226\) | 1.04460e28 | 0.588369 | ||||||||
\(227\) | − | 3.79716e27i | − | 0.202837i | −0.994844 | − | 0.101419i | \(-0.967662\pi\) | ||
0.994844 | − | 0.101419i | \(-0.0323382\pi\) | |||||||
\(228\) | −2.09221e27 | + | 3.55487e27i | −0.106020 | + | 0.180138i | ||||
\(229\) | 1.19916e28 | 0.576570 | 0.288285 | − | 0.957545i | \(-0.406915\pi\) | ||||
0.288285 | + | 0.957545i | \(0.406915\pi\) | |||||||
\(230\) | − | 3.32888e28i | − | 1.51902i | ||||||
\(231\) | −2.80040e27 | − | 1.64817e27i | −0.121304 | − | 0.0713934i | ||||
\(232\) | −1.30914e28 | −0.538433 | ||||||||
\(233\) | 2.52886e28i | 0.987766i | 0.869528 | + | 0.493883i | \(0.164423\pi\) | ||||
−0.869528 | + | 0.493883i | \(0.835577\pi\) | |||||||
\(234\) | −2.21803e28 | + | 1.23162e28i | −0.822958 | + | 0.456969i | ||||
\(235\) | −6.45227e28 | −2.27457 | ||||||||
\(236\) | − | 1.02534e28i | − | 0.343499i | ||||||
\(237\) | 1.26972e28 | − | 2.15738e28i | 0.404323 | − | 0.686984i | ||||
\(238\) | 6.03473e26 | 0.0182698 | ||||||||
\(239\) | − | 2.31937e28i | − | 0.667720i | −0.942623 | − | 0.333860i | \(-0.891649\pi\) | ||
0.942623 | − | 0.333860i | \(-0.108351\pi\) | |||||||
\(240\) | −1.47153e28 | − | 8.66062e27i | −0.402933 | − | 0.237145i | ||||
\(241\) | −9.28349e27 | −0.241828 | −0.120914 | − | 0.992663i | \(-0.538583\pi\) | ||||
−0.120914 | + | 0.992663i | \(0.538583\pi\) | |||||||
\(242\) | 4.18446e27i | 0.103718i | ||||||||
\(243\) | 1.96435e28 | + | 3.75652e28i | 0.463388 | + | 0.886156i | ||||
\(244\) | −2.65297e28 | −0.595738 | ||||||||
\(245\) | 8.59611e28i | 1.83785i | ||||||||
\(246\) | −9.00681e27 | + | 1.53035e28i | −0.183379 | + | 0.311579i | ||||
\(247\) | 2.86970e28 | 0.556510 | ||||||||
\(248\) | 1.13673e28i | 0.210009i | ||||||||
\(249\) | −5.76164e28 | − | 3.39100e28i | −1.01427 | − | 0.596946i | ||||
\(250\) | 1.18034e29 | 1.98028 | ||||||||
\(251\) | − | 1.06381e29i | − | 1.70129i | −0.525742 | − | 0.850644i | \(-0.676212\pi\) | ||
0.525742 | − | 0.850644i | \(-0.323788\pi\) | |||||||
\(252\) | 2.09251e27 | + | 3.76841e27i | 0.0319052 | + | 0.0574582i | ||||
\(253\) | 8.45996e28 | 1.23005 | ||||||||
\(254\) | − | 4.51021e27i | − | 0.0625449i | ||||||
\(255\) | 1.40950e28 | − | 2.39488e28i | 0.186459 | − | 0.316812i | ||||
\(256\) | 4.95176e27 | 0.0625000 | ||||||||
\(257\) | 7.43493e28i | 0.895528i | 0.894152 | + | 0.447764i | \(0.147780\pi\) | ||||
−0.894152 | + | 0.447764i | \(0.852220\pi\) | |||||||
\(258\) | −7.18403e28 | − | 4.22814e28i | −0.825908 | − | 0.486086i | ||||
\(259\) | 5.66101e27 | 0.0621294 | ||||||||
\(260\) | 1.18790e29i | 1.24480i | ||||||||
\(261\) | 1.33047e29 | − | 7.38776e28i | 1.33143 | − | 0.739310i | ||||
\(262\) | 1.10245e28 | 0.105376 | ||||||||
\(263\) | − | 1.08384e29i | − | 0.989685i | −0.868983 | − | 0.494843i | \(-0.835226\pi\) | ||
0.868983 | − | 0.494843i | \(-0.164774\pi\) | |||||||
\(264\) | 2.20100e28 | − | 3.73971e28i | 0.192031 | − | 0.326280i | ||||
\(265\) | −2.67467e29 | −2.23007 | ||||||||
\(266\) | − | 4.87558e27i | − | 0.0388550i | ||||||
\(267\) | −2.05911e28 | − | 1.21188e28i | −0.156872 | − | 0.0923264i | ||||
\(268\) | 2.42181e28 | 0.176410 | ||||||||
\(269\) | − | 1.29861e29i | − | 0.904591i | −0.891868 | − | 0.452296i | \(-0.850605\pi\) | ||
0.891868 | − | 0.452296i | \(-0.149395\pi\) | |||||||
\(270\) | 1.98423e29 | + | 4.97561e27i | 1.32198 | + | 0.0331498i | ||||
\(271\) | −4.00692e28 | −0.255375 | −0.127688 | − | 0.991814i | \(-0.540756\pi\) | ||||
−0.127688 | + | 0.991814i | \(0.540756\pi\) | |||||||
\(272\) | 8.05889e27i | 0.0491415i | ||||||||
\(273\) | 1.52104e28 | − | 2.58440e28i | 0.0887541 | − | 0.150802i | ||||
\(274\) | −6.53040e28 | −0.364697 | ||||||||
\(275\) | 5.00284e29i | 2.67439i | ||||||||
\(276\) | −9.67152e28 | − | 5.69215e28i | −0.494978 | − | 0.291318i | ||||
\(277\) | 1.01057e29 | 0.495232 | 0.247616 | − | 0.968858i | \(-0.420353\pi\) | ||||
0.247616 | + | 0.968858i | \(0.420353\pi\) | |||||||
\(278\) | 2.20724e29i | 1.03589i | ||||||||
\(279\) | −6.41481e28 | − | 1.15525e29i | −0.288359 | − | 0.519307i | ||||
\(280\) | 2.01823e28 | 0.0869108 | ||||||||
\(281\) | 5.95802e28i | 0.245825i | 0.992418 | + | 0.122912i | \(0.0392234\pi\) | ||||
−0.992418 | + | 0.122912i | \(0.960777\pi\) | |||||||
\(282\) | −1.10329e29 | + | 1.87460e29i | −0.436216 | + | 0.741174i | ||||
\(283\) | −1.57986e29 | −0.598663 | −0.299332 | − | 0.954149i | \(-0.596764\pi\) | ||||
−0.299332 | + | 0.954149i | \(0.596764\pi\) | |||||||
\(284\) | − | 4.92044e28i | − | 0.178724i | ||||||
\(285\) | −1.93487e29 | − | 1.13876e29i | −0.673774 | − | 0.396548i | ||||
\(286\) | −3.01891e29 | −1.00799 | ||||||||
\(287\) | − | 2.09890e28i | − | 0.0672062i | ||||||
\(288\) | −5.03241e28 | + | 2.79438e28i | −0.154549 | + | 0.0858174i | ||||
\(289\) | 3.26333e29 | 0.961362 | ||||||||
\(290\) | − | 7.12550e29i | − | 2.01391i | ||||||
\(291\) | −5.60690e28 | + | 9.52668e28i | −0.152057 | + | 0.258360i | ||||
\(292\) | 4.10561e28 | 0.106852 | ||||||||
\(293\) | − | 3.62941e29i | − | 0.906618i | −0.891354 | − | 0.453309i | \(-0.850244\pi\) | ||
0.891354 | − | 0.453309i | \(-0.149756\pi\) | |||||||
\(294\) | 2.49746e29 | + | 1.46987e29i | 0.598868 | + | 0.352462i | ||||
\(295\) | 5.58082e29 | 1.28479 | ||||||||
\(296\) | 7.55982e28i | 0.167113i | ||||||||
\(297\) | −1.26449e28 | + | 5.04269e29i | −0.0268435 | + | 1.07049i | ||||
\(298\) | −6.59677e28 | −0.134504 | ||||||||
\(299\) | 7.80741e29i | 1.52916i | ||||||||
\(300\) | 3.36608e29 | − | 5.71930e29i | 0.633387 | − | 1.07619i | ||||
\(301\) | 9.85305e28 | 0.178145 | ||||||||
\(302\) | − | 3.36290e29i | − | 0.584292i | ||||||
\(303\) | 2.19709e29 | + | 1.29309e29i | 0.366890 | + | 0.215932i | ||||
\(304\) | 6.51095e28 | 0.104511 | ||||||||
\(305\) | − | 1.44398e30i | − | 2.22825i | ||||||
\(306\) | −4.54779e28 | − | 8.19015e28i | −0.0674751 | − | 0.121516i | ||||
\(307\) | 1.61139e29 | 0.229901 | 0.114950 | − | 0.993371i | \(-0.463329\pi\) | ||||
0.114950 | + | 0.993371i | \(0.463329\pi\) | |||||||
\(308\) | 5.12909e28i | 0.0703772i | ||||||||
\(309\) | −5.58025e29 | + | 9.48140e29i | −0.736465 | + | 1.25133i | ||||
\(310\) | −6.18709e29 | −0.785500 | ||||||||
\(311\) | − | 7.23373e29i | − | 0.883563i | −0.897123 | − | 0.441781i | \(-0.854347\pi\) | ||
0.897123 | − | 0.441781i | \(-0.145653\pi\) | |||||||
\(312\) | 3.45125e29 | + | 2.03122e29i | 0.405622 | + | 0.238728i | ||||
\(313\) | 5.06999e29 | 0.573423 | 0.286711 | − | 0.958017i | \(-0.407438\pi\) | ||||
0.286711 | + | 0.958017i | \(0.407438\pi\) | |||||||
\(314\) | 1.11740e30i | 1.21633i | ||||||||
\(315\) | −2.05110e29 | + | 1.13893e29i | −0.214912 | + | 0.119335i | ||||
\(316\) | −3.95136e29 | −0.398567 | ||||||||
\(317\) | 3.48880e29i | 0.338817i | 0.985546 | + | 0.169409i | \(0.0541857\pi\) | ||||
−0.985546 | + | 0.169409i | \(0.945814\pi\) | |||||||
\(318\) | −4.57349e29 | + | 7.77082e29i | −0.427683 | + | 0.726677i | ||||
\(319\) | 1.81086e30 | 1.63079 | ||||||||
\(320\) | 2.69518e29i | 0.233770i | ||||||||
\(321\) | −1.03595e30 | − | 6.09708e29i | −0.865526 | − | 0.509403i | ||||
\(322\) | 1.32647e29 | 0.106764 | ||||||||
\(323\) | 1.05964e29i | 0.0821731i | ||||||||
\(324\) | 3.53745e29 | − | 5.67978e29i | 0.264332 | − | 0.424416i | ||||
\(325\) | −4.61695e30 | −3.32472 | ||||||||
\(326\) | − | 1.14231e30i | − | 0.792813i | ||||||
\(327\) | 1.32803e29 | − | 2.25646e29i | 0.0888454 | − | 0.150957i | ||||
\(328\) | 2.80291e29 | 0.180769 | ||||||||
\(329\) | − | 2.57106e29i | − | 0.159868i | ||||||
\(330\) | 2.03548e30 | + | 1.19797e30i | 1.22039 | + | 0.718258i | ||||
\(331\) | −1.05153e30 | −0.607976 | −0.303988 | − | 0.952676i | \(-0.598318\pi\) | ||||
−0.303988 | + | 0.952676i | \(0.598318\pi\) | |||||||
\(332\) | 1.05528e30i | 0.588449i | ||||||||
\(333\) | −4.26616e29 | − | 7.68295e29i | −0.229460 | − | 0.413235i | ||||
\(334\) | −8.67160e29 | −0.449927 | ||||||||
\(335\) | 1.31816e30i | 0.659828i | ||||||||
\(336\) | 3.45103e28 | − | 5.86364e28i | 0.0166678 | − | 0.0283202i | ||||
\(337\) | 2.48164e30 | 1.15659 | 0.578295 | − | 0.815828i | \(-0.303718\pi\) | ||||
0.578295 | + | 0.815828i | \(0.303718\pi\) | |||||||
\(338\) | − | 1.21393e30i | − | 0.546000i | ||||||
\(339\) | 1.65187e30 | + | 9.72204e29i | 0.717100 | + | 0.422047i | ||||
\(340\) | −4.38635e29 | −0.183805 | ||||||||
\(341\) | − | 1.57238e30i | − | 0.636069i | ||||||
\(342\) | −6.61699e29 | + | 3.67426e29i | −0.258433 | + | 0.143501i | ||||
\(343\) | −6.91086e29 | −0.260617 | ||||||||
\(344\) | 1.31580e30i | 0.479167i | ||||||||
\(345\) | 3.09816e30 | − | 5.26409e30i | 1.08962 | − | 1.85137i | ||||
\(346\) | 3.21125e30 | 1.09084 | ||||||||
\(347\) | 3.73656e30i | 1.22608i | 0.790052 | + | 0.613040i | \(0.210053\pi\) | ||||
−0.790052 | + | 0.613040i | \(0.789947\pi\) | |||||||
\(348\) | −2.07020e30 | − | 1.21841e30i | −0.656238 | − | 0.386227i | ||||
\(349\) | 5.31023e30 | 1.62633 | 0.813164 | − | 0.582035i | \(-0.197743\pi\) | ||||
0.813164 | + | 0.582035i | \(0.197743\pi\) | |||||||
\(350\) | 7.84414e29i | 0.232129i | ||||||||
\(351\) | −4.65372e30 | − | 1.16696e29i | −1.33081 | − | 0.0333711i | ||||
\(352\) | −6.84949e29 | −0.189298 | ||||||||
\(353\) | − | 1.35177e28i | − | 0.00361082i | −0.999998 | − | 0.00180541i | \(-0.999425\pi\) | ||
0.999998 | − | 0.00180541i | \(-0.000574680\pi\) | |||||||
\(354\) | 9.54280e29 | − | 1.62142e30i | 0.246398 | − | 0.418654i | ||||
\(355\) | 2.67813e30 | 0.668485 | ||||||||
\(356\) | 3.77137e29i | 0.0910122i | ||||||||
\(357\) | 9.54296e28 | + | 5.61648e28i | 0.0222671 | + | 0.0131053i | ||||
\(358\) | 7.16923e29 | 0.161762 | ||||||||
\(359\) | 1.08720e30i | 0.237234i | 0.992940 | + | 0.118617i | \(0.0378460\pi\) | ||||
−0.992940 | + | 0.118617i | \(0.962154\pi\) | |||||||
\(360\) | −1.52094e30 | − | 2.73908e30i | −0.320984 | − | 0.578062i | ||||
\(361\) | −4.04265e30 | −0.825240 | ||||||||
\(362\) | − | 2.62668e30i | − | 0.518686i | ||||||
\(363\) | −3.89444e29 | + | 6.61705e29i | −0.0743988 | + | 0.126411i | ||||
\(364\) | −4.73346e29 | −0.0874908 | ||||||||
\(365\) | 2.23463e30i | 0.399660i | ||||||||
\(366\) | −4.19525e30 | − | 2.46910e30i | −0.726081 | − | 0.427333i | ||||
\(367\) | −4.97294e30 | −0.832952 | −0.416476 | − | 0.909147i | \(-0.636735\pi\) | ||||
−0.416476 | + | 0.909147i | \(0.636735\pi\) | |||||||
\(368\) | 1.77139e30i | 0.287171i | ||||||||
\(369\) | −2.84856e30 | + | 1.58174e30i | −0.447002 | + | 0.248210i | ||||
\(370\) | −4.11472e30 | −0.625056 | ||||||||
\(371\) | − | 1.06578e30i | − | 0.156741i | ||||||
\(372\) | −1.05795e30 | + | 1.79756e30i | −0.150643 | + | 0.255958i | ||||
\(373\) | −4.16953e30 | −0.574885 | −0.287443 | − | 0.957798i | \(-0.592805\pi\) | ||||
−0.287443 | + | 0.957798i | \(0.592805\pi\) | |||||||
\(374\) | − | 1.11474e30i | − | 0.148838i | ||||||
\(375\) | 1.86651e31 | + | 1.09853e31i | 2.41355 | + | 1.42049i | ||||
\(376\) | 3.43344e30 | 0.430007 | ||||||||
\(377\) | 1.67118e31i | 2.02735i | ||||||||
\(378\) | −1.98265e28 | + | 7.90662e29i | −0.00232994 | + | 0.0929158i | ||||
\(379\) | −5.25196e30 | −0.597931 | −0.298966 | − | 0.954264i | \(-0.596642\pi\) | ||||
−0.298966 | + | 0.954264i | \(0.596642\pi\) | |||||||
\(380\) | 3.54383e30i | 0.390903i | ||||||||
\(381\) | 4.19762e29 | − | 7.13217e29i | 0.0448645 | − | 0.0762293i | ||||
\(382\) | 6.86677e30 | 0.711200 | ||||||||
\(383\) | − | 1.79845e31i | − | 1.80515i | −0.430532 | − | 0.902575i | \(-0.641674\pi\) | ||
0.430532 | − | 0.902575i | \(-0.358326\pi\) | |||||||
\(384\) | 7.83041e29 | + | 4.60857e29i | 0.0761746 | + | 0.0448323i | ||||
\(385\) | −2.79170e30 | −0.263233 | ||||||||
\(386\) | − | 1.47423e31i | − | 1.34747i | ||||||
\(387\) | −7.42530e30 | − | 1.33723e31i | −0.657934 | − | 1.18488i | ||||
\(388\) | 1.74486e30 | 0.149893 | ||||||||
\(389\) | − | 5.39514e30i | − | 0.449374i | −0.974431 | − | 0.224687i | \(-0.927864\pi\) | ||
0.974431 | − | 0.224687i | \(-0.0721359\pi\) | |||||||
\(390\) | −1.10557e31 | + | 1.87847e31i | −0.892916 | + | 1.51715i | ||||
\(391\) | −2.88291e30 | −0.225793 | ||||||||
\(392\) | − | 4.57424e30i | − | 0.347445i | ||||||
\(393\) | 1.74334e30 | + | 1.02604e30i | 0.128432 | + | 0.0755880i | ||||
\(394\) | 1.36813e31 | 0.977625 | ||||||||
\(395\) | − | 2.15068e31i | − | 1.49077i | ||||||
\(396\) | 6.96104e30 | − | 3.86530e30i | 0.468093 | − | 0.259921i | ||||
\(397\) | 1.06217e31 | 0.692958 | 0.346479 | − | 0.938058i | \(-0.387377\pi\) | ||||
0.346479 | + | 0.938058i | \(0.387377\pi\) | |||||||
\(398\) | 2.11927e31i | 1.34150i | ||||||||
\(399\) | 4.53767e29 | − | 7.70995e29i | 0.0278714 | − | 0.0473562i | ||||
\(400\) | −1.04752e31 | −0.624372 | ||||||||
\(401\) | − | 3.13328e30i | − | 0.181245i | −0.995885 | − | 0.0906226i | \(-0.971114\pi\) | ||
0.995885 | − | 0.0906226i | \(-0.0288857\pi\) | |||||||
\(402\) | 3.82971e30 | + | 2.25396e30i | 0.215007 | + | 0.126542i | ||||
\(403\) | 1.45109e31 | 0.790742 | ||||||||
\(404\) | − | 4.02408e30i | − | 0.212858i | ||||||
\(405\) | 3.09143e31 | + | 1.92539e31i | 1.58745 | + | 0.988685i | ||||
\(406\) | 2.83932e30 | 0.141548 | ||||||||
\(407\) | − | 1.04571e31i | − | 0.506148i | ||||||
\(408\) | −7.50035e29 | + | 1.27438e30i | −0.0352500 | + | 0.0598933i | ||||
\(409\) | −2.02665e31 | −0.924909 | −0.462454 | − | 0.886643i | \(-0.653031\pi\) | ||||
−0.462454 | + | 0.886643i | \(0.653031\pi\) | |||||||
\(410\) | 1.52559e31i | 0.676132i | ||||||||
\(411\) | −1.03268e31 | − | 6.07779e30i | −0.444491 | − | 0.261604i | ||||
\(412\) | 1.73657e31 | 0.725982 | ||||||||
\(413\) | 2.22381e30i | 0.0903018i | ||||||||
\(414\) | −9.99632e30 | − | 1.80024e31i | −0.394309 | − | 0.710112i | ||||
\(415\) | −5.74373e31 | −2.20098 | ||||||||
\(416\) | − | 6.32116e30i | − | 0.235330i | ||||||
\(417\) | −2.05426e31 | + | 3.49040e31i | −0.743060 | + | 1.26253i | ||||
\(418\) | −9.00622e30 | −0.316539 | ||||||||
\(419\) | 1.73826e31i | 0.593674i | 0.954928 | + | 0.296837i | \(0.0959317\pi\) | ||||
−0.954928 | + | 0.296837i | \(0.904068\pi\) | |||||||
\(420\) | 3.19150e30 | + | 1.87835e30i | 0.105926 | + | 0.0623426i | ||||
\(421\) | 3.94616e31 | 1.27289 | 0.636443 | − | 0.771324i | \(-0.280405\pi\) | ||||
0.636443 | + | 0.771324i | \(0.280405\pi\) | |||||||
\(422\) | − | 1.60019e31i | − | 0.501675i | ||||||
\(423\) | −3.48936e31 | + | 1.93756e31i | −1.06331 | + | 0.590433i | ||||
\(424\) | 1.42327e31 | 0.421596 | ||||||||
\(425\) | − | 1.70482e31i | − | 0.490921i | ||||||
\(426\) | 4.57941e30 | − | 7.78088e30i | 0.128202 | − | 0.217828i | ||||
\(427\) | 5.75388e30 | 0.156612 | ||||||||
\(428\) | 1.89741e31i | 0.502152i | ||||||||
\(429\) | −4.77392e31 | − | 2.80968e31i | −1.22854 | − | 0.723051i | ||||
\(430\) | −7.16171e31 | −1.79224 | ||||||||
\(431\) | 5.04053e31i | 1.22673i | 0.789799 | + | 0.613365i | \(0.210185\pi\) | ||||
−0.789799 | + | 0.613365i | \(0.789815\pi\) | |||||||
\(432\) | −1.05587e31 | − | 2.64767e29i | −0.249921 | − | 0.00626698i | ||||
\(433\) | 7.89926e31 | 1.81858 | 0.909289 | − | 0.416166i | \(-0.136627\pi\) | ||||
0.909289 | + | 0.416166i | \(0.136627\pi\) | |||||||
\(434\) | − | 2.46539e30i | − | 0.0552089i | ||||||
\(435\) | 6.63165e31 | − | 1.12678e32i | 1.44461 | − | 2.45454i | ||||
\(436\) | −4.13282e30 | −0.0875808 | ||||||||
\(437\) | 2.32916e31i | 0.480200i | ||||||||
\(438\) | 6.49236e30 | + | 3.82106e30i | 0.130231 | + | 0.0766468i | ||||
\(439\) | 2.86248e31 | 0.558687 | 0.279344 | − | 0.960191i | \(-0.409883\pi\) | ||||
0.279344 | + | 0.960191i | \(0.409883\pi\) | |||||||
\(440\) | − | 3.72809e31i | − | 0.708034i | ||||||
\(441\) | 2.58133e31 | + | 4.64874e31i | 0.477069 | + | 0.859156i | ||||
\(442\) | 1.02876e31 | 0.185031 | ||||||||
\(443\) | 4.49140e31i | 0.786206i | 0.919494 | + | 0.393103i | \(0.128599\pi\) | ||||
−0.919494 | + | 0.393103i | \(0.871401\pi\) | |||||||
\(444\) | −7.03587e30 | + | 1.19546e31i | −0.119873 | + | 0.203677i | ||||
\(445\) | −2.05271e31 | −0.340414 | ||||||||
\(446\) | 7.69408e30i | 0.124205i | ||||||||
\(447\) | −1.04317e31 | − | 6.13956e30i | −0.163933 | − | 0.0964822i | ||||
\(448\) | −1.07396e30 | −0.0164305 | ||||||||
\(449\) | 5.39778e31i | 0.804006i | 0.915638 | + | 0.402003i | \(0.131686\pi\) | ||||
−0.915638 | + | 0.402003i | \(0.868314\pi\) | |||||||
\(450\) | 1.06458e32 | − | 5.91137e31i | 1.54394 | − | 0.857311i | ||||
\(451\) | −3.87711e31 | −0.547507 | ||||||||
\(452\) | − | 3.02549e31i | − | 0.416040i | ||||||
\(453\) | 3.12982e31 | − | 5.31788e31i | 0.419123 | − | 0.712132i | ||||
\(454\) | −1.09977e31 | −0.143428 | ||||||||
\(455\) | − | 2.57636e31i | − | 0.327243i | ||||||
\(456\) | 1.02960e31 | + | 6.05969e30i | 0.127377 | + | 0.0749674i | ||||
\(457\) | −2.97204e31 | −0.358146 | −0.179073 | − | 0.983836i | \(-0.557310\pi\) | ||||
−0.179073 | + | 0.983836i | \(0.557310\pi\) | |||||||
\(458\) | − | 3.47315e31i | − | 0.407697i | ||||||
\(459\) | 4.30903e29 | − | 1.71840e31i | 0.00492750 | − | 0.196504i | ||||
\(460\) | −9.64146e31 | −1.07411 | ||||||||
\(461\) | 2.21817e31i | 0.240759i | 0.992728 | + | 0.120380i | \(0.0384112\pi\) | ||||
−0.992728 | + | 0.120380i | \(0.961589\pi\) | |||||||
\(462\) | −4.77361e30 | + | 8.11084e30i | −0.0504828 | + | 0.0857752i | ||||
\(463\) | 1.34906e32 | 1.39014 | 0.695072 | − | 0.718940i | \(-0.255372\pi\) | ||||
0.695072 | + | 0.718940i | \(0.255372\pi\) | |||||||
\(464\) | 3.79169e31i | 0.380730i | ||||||||
\(465\) | −9.78389e31 | − | 5.75828e31i | −0.957361 | − | 0.563452i | ||||
\(466\) | 7.32437e31 | 0.698456 | ||||||||
\(467\) | − | 2.20131e31i | − | 0.204587i | −0.994754 | − | 0.102294i | \(-0.967382\pi\) | ||
0.994754 | − | 0.102294i | \(-0.0326181\pi\) | |||||||
\(468\) | 3.56716e31 | + | 6.42411e31i | 0.323126 | + | 0.581919i | ||||
\(469\) | −5.25252e30 | −0.0463760 | ||||||||
\(470\) | 1.86878e32i | 1.60836i | ||||||||
\(471\) | −1.03995e32 | + | 1.76699e32i | −0.872496 | + | 1.48246i | ||||
\(472\) | −2.96971e31 | −0.242891 | ||||||||
\(473\) | − | 1.82006e32i | − | 1.45129i | ||||||
\(474\) | −6.24844e31 | − | 3.67750e31i | −0.485771 | − | 0.285899i | ||||
\(475\) | −1.37736e32 | −1.04406 | ||||||||
\(476\) | − | 1.74784e30i | − | 0.0129187i | ||||||
\(477\) | −1.44645e32 | + | 8.03178e31i | −1.04251 | + | 0.578884i | ||||
\(478\) | −6.71760e31 | −0.472150 | ||||||||
\(479\) | − | 1.84865e32i | − | 1.26715i | −0.773681 | − | 0.633575i | \(-0.781587\pi\) | ||
0.773681 | − | 0.633575i | \(-0.218413\pi\) | |||||||
\(480\) | −2.50838e31 | + | 4.26199e31i | −0.167687 | + | 0.284917i | ||||
\(481\) | 9.65047e31 | 0.629228 | ||||||||
\(482\) | 2.68879e31i | 0.170998i | ||||||||
\(483\) | 2.09760e31 | + | 1.23454e31i | 0.130124 | + | 0.0765840i | ||||
\(484\) | 1.21195e31 | 0.0733398 | ||||||||
\(485\) | 9.49707e31i | 0.560646i | ||||||||
\(486\) | 1.08800e32 | − | 5.68938e31i | 0.626607 | − | 0.327665i | ||||
\(487\) | −8.47310e31 | −0.476096 | −0.238048 | − | 0.971253i | \(-0.576508\pi\) | ||||
−0.238048 | + | 0.971253i | \(0.576508\pi\) | |||||||
\(488\) | 7.68383e31i | 0.421250i | ||||||||
\(489\) | 1.06314e32 | − | 1.80637e32i | 0.568699 | − | 0.966275i | ||||
\(490\) | 2.48970e32 | 1.29955 | ||||||||
\(491\) | 8.67400e31i | 0.441816i | 0.975295 | + | 0.220908i | \(0.0709021\pi\) | ||||
−0.975295 | + | 0.220908i | \(0.929098\pi\) | |||||||
\(492\) | 4.43236e31 | + | 2.60865e31i | 0.220320 | + | 0.129669i | ||||
\(493\) | −6.17090e31 | −0.299354 | ||||||||
\(494\) | − | 8.31153e31i | − | 0.393512i | ||||||
\(495\) | 2.10383e32 | + | 3.78881e32i | 0.972186 | + | 1.75081i | ||||
\(496\) | 3.29233e31 | 0.148499 | ||||||||
\(497\) | 1.06716e31i | 0.0469845i | ||||||||
\(498\) | −9.82137e31 | + | 1.66875e32i | −0.422105 | + | 0.717198i | ||||
\(499\) | 2.49415e32 | 1.04645 | 0.523223 | − | 0.852196i | \(-0.324730\pi\) | ||||
0.523223 | + | 0.852196i | \(0.324730\pi\) | |||||||
\(500\) | − | 3.41862e32i | − | 1.40027i | ||||||
\(501\) | −1.37127e32 | − | 8.07059e31i | −0.548367 | − | 0.322740i | ||||
\(502\) | −3.08111e32 | −1.20299 | ||||||||
\(503\) | − | 4.71984e32i | − | 1.79933i | −0.436579 | − | 0.899666i | \(-0.643810\pi\) | ||
0.436579 | − | 0.899666i | \(-0.356190\pi\) | |||||||
\(504\) | 1.09145e31 | − | 6.06056e30i | 0.0406291 | − | 0.0225604i | ||||
\(505\) | 2.19026e32 | 0.796157 | ||||||||
\(506\) | − | 2.45027e32i | − | 0.869775i | ||||||
\(507\) | 1.12979e32 | − | 1.91963e32i | 0.391655 | − | 0.665461i | ||||
\(508\) | −1.30630e31 | −0.0442259 | ||||||||
\(509\) | − | 1.88162e32i | − | 0.622183i | −0.950380 | − | 0.311091i | \(-0.899306\pi\) | ||
0.950380 | − | 0.311091i | \(-0.100694\pi\) | |||||||
\(510\) | −6.93631e31 | − | 4.08235e31i | −0.224020 | − | 0.131846i | ||||
\(511\) | −8.90440e30 | −0.0280901 | ||||||||
\(512\) | − | 1.43418e31i | − | 0.0441942i | ||||||
\(513\) | −1.38833e32 | − | 3.48135e30i | −0.417912 | − | 0.0104795i | ||||
\(514\) | 2.15338e32 | 0.633234 | ||||||||
\(515\) | 9.45193e32i | 2.71540i | ||||||||
\(516\) | −1.22460e32 | + | 2.08072e32i | −0.343715 | + | 0.584005i | ||||
\(517\) | −4.74928e32 | −1.30239 | ||||||||
\(518\) | − | 1.63960e31i | − | 0.0439321i | ||||||
\(519\) | 5.07807e32 | + | 2.98868e32i | 1.32951 | + | 0.782477i | ||||
\(520\) | 3.44053e32 | 0.880207 | ||||||||
\(521\) | 6.65852e31i | 0.166466i | 0.996530 | + | 0.0832329i | \(0.0265245\pi\) | ||||
−0.996530 | + | 0.0832329i | \(0.973475\pi\) | |||||||
\(522\) | −2.13972e32 | − | 3.85344e32i | −0.522771 | − | 0.941462i | ||||
\(523\) | −7.70218e30 | −0.0183905 | −0.00919525 | − | 0.999958i | \(-0.502927\pi\) | ||||
−0.00919525 | + | 0.999958i | \(0.502927\pi\) | |||||||
\(524\) | − | 3.19303e31i | − | 0.0745121i | ||||||
\(525\) | −7.30049e31 | + | 1.24043e32i | −0.166510 | + | 0.282917i | ||||
\(526\) | −3.13914e32 | −0.699813 | ||||||||
\(527\) | 5.35820e31i | 0.116759i | ||||||||
\(528\) | −1.08314e32 | − | 6.37477e31i | −0.230715 | − | 0.135787i | ||||
\(529\) | −1.53429e32 | −0.319477 | ||||||||
\(530\) | 7.74666e32i | 1.57690i | ||||||||
\(531\) | 3.01808e32 | − | 1.67587e32i | 0.600616 | − | 0.333508i | ||||
\(532\) | −1.41212e31 | −0.0274746 | ||||||||
\(533\) | − | 3.57805e32i | − | 0.680644i | ||||||
\(534\) | −3.50999e31 | + | 5.96382e31i | −0.0652846 | + | 0.110925i | ||||
\(535\) | −1.03273e33 | −1.87821 | ||||||||
\(536\) | − | 7.01431e31i | − | 0.124741i | ||||||
\(537\) | 1.13370e32 | + | 6.67235e31i | 0.197154 | + | 0.116035i | ||||
\(538\) | −3.76118e32 | −0.639643 | ||||||||
\(539\) | 6.32728e32i | 1.05233i | ||||||||
\(540\) | 1.44109e31 | − | 5.74694e32i | 0.0234405 | − | 0.934785i | ||||
\(541\) | 6.06284e32 | 0.964514 | 0.482257 | − | 0.876030i | \(-0.339817\pi\) | ||||
0.482257 | + | 0.876030i | \(0.339817\pi\) | |||||||
\(542\) | 1.16053e32i | 0.180578i | ||||||||
\(543\) | 2.44463e32 | − | 4.15368e32i | 0.372062 | − | 0.632171i | ||||
\(544\) | 2.33410e31 | 0.0347483 | ||||||||
\(545\) | − | 2.24944e32i | − | 0.327580i | ||||||
\(546\) | −7.48521e31 | − | 4.40540e31i | −0.106633 | − | 0.0627586i | ||||
\(547\) | −8.04943e32 | −1.12180 | −0.560902 | − | 0.827882i | \(-0.689546\pi\) | ||||
−0.560902 | + | 0.827882i | \(0.689546\pi\) | |||||||
\(548\) | 1.89140e32i | 0.257880i | ||||||||
\(549\) | −4.33614e32 | − | 7.80898e32i | −0.578409 | − | 1.04166i | ||||
\(550\) | 1.44898e33 | 1.89108 | ||||||||
\(551\) | 4.98559e32i | 0.636646i | ||||||||
\(552\) | −1.64862e32 | + | 2.80117e32i | −0.205993 | + | 0.350002i | ||||
\(553\) | 8.56987e31 | 0.104779 | ||||||||
\(554\) | − | 2.92692e32i | − | 0.350182i | ||||||
\(555\) | −6.50676e32 | − | 3.82954e32i | −0.761814 | − | 0.448364i | ||||
\(556\) | 6.39286e32 | 0.732483 | ||||||||
\(557\) | − | 9.36098e32i | − | 1.04968i | −0.851200 | − | 0.524842i | \(-0.824124\pi\) | ||
0.851200 | − | 0.524842i | \(-0.175876\pi\) | |||||||
\(558\) | −3.34595e32 | + | 1.85793e32i | −0.367205 | + | 0.203900i | ||||
\(559\) | 1.67967e33 | 1.80420 | ||||||||
\(560\) | − | 5.84541e31i | − | 0.0614552i | ||||||
\(561\) | 1.03748e32 | − | 1.76278e32i | 0.106764 | − | 0.181403i | ||||
\(562\) | 1.72563e32 | 0.173824 | ||||||||
\(563\) | 3.63395e32i | 0.358326i | 0.983819 | + | 0.179163i | \(0.0573389\pi\) | ||||
−0.983819 | + | 0.179163i | \(0.942661\pi\) | |||||||
\(564\) | 5.42943e32 | + | 3.19548e32i | 0.524089 | + | 0.308451i | ||||
\(565\) | 1.64674e33 | 1.55612 | ||||||||
\(566\) | 4.57577e32i | 0.423319i | ||||||||
\(567\) | −7.67216e31 | + | 1.23185e32i | −0.0694898 | + | 0.111574i | ||||
\(568\) | −1.42511e32 | −0.126377 | ||||||||
\(569\) | 1.56580e33i | 1.35953i | 0.733431 | + | 0.679764i | \(0.237918\pi\) | ||||
−0.733431 | + | 0.679764i | \(0.762082\pi\) | |||||||
\(570\) | −3.29821e32 | + | 5.60399e32i | −0.280401 | + | 0.476430i | ||||
\(571\) | −1.35659e33 | −1.12932 | −0.564659 | − | 0.825324i | \(-0.690992\pi\) | ||||
−0.564659 | + | 0.825324i | \(0.690992\pi\) | |||||||
\(572\) | 8.74369e32i | 0.712759i | ||||||||
\(573\) | 1.08587e33 | + | 6.39085e32i | 0.866806 | + | 0.510156i | ||||
\(574\) | −6.07907e31 | −0.0475220 | ||||||||
\(575\) | − | 3.74730e33i | − | 2.86883i | ||||||
\(576\) | 8.09338e31 | + | 1.45754e32i | 0.0606820 | + | 0.109283i | ||||
\(577\) | −1.34896e33 | −0.990578 | −0.495289 | − | 0.868728i | \(-0.664938\pi\) | ||||
−0.495289 | + | 0.868728i | \(0.664938\pi\) | |||||||
\(578\) | − | 9.45161e32i | − | 0.679785i | ||||||
\(579\) | 1.37206e33 | − | 2.33126e33i | 0.966562 | − | 1.64229i | ||||
\(580\) | −2.06377e33 | −1.42405 | ||||||||
\(581\) | − | 2.28872e32i | − | 0.154696i | ||||||
\(582\) | 2.75922e32 | + | 1.62393e32i | 0.182688 | + | 0.107521i | ||||
\(583\) | −1.96872e33 | −1.27692 | ||||||||
\(584\) | − | 1.18911e32i | − | 0.0755558i | ||||||
\(585\) | −3.49656e33 | + | 1.94156e33i | −2.17656 | + | 1.20859i | ||||
\(586\) | −1.05119e33 | −0.641075 | ||||||||
\(587\) | 3.28919e33i | 1.96531i | 0.185437 | + | 0.982656i | \(0.440630\pi\) | ||||
−0.185437 | + | 0.982656i | \(0.559370\pi\) | |||||||
\(588\) | 4.25721e32 | − | 7.23342e32i | 0.249228 | − | 0.423463i | ||||
\(589\) | 4.32900e32 | 0.248316 | ||||||||
\(590\) | − | 1.61638e33i | − | 0.908487i | ||||||
\(591\) | 2.16348e33 | + | 1.27331e33i | 1.19152 | + | 0.701267i | ||||
\(592\) | 2.18956e32 | 0.118167 | ||||||||
\(593\) | 1.50339e33i | 0.795088i | 0.917583 | + | 0.397544i | \(0.130137\pi\) | ||||
−0.917583 | + | 0.397544i | \(0.869863\pi\) | |||||||
\(594\) | 1.46052e33 | + | 3.66237e31i | 0.756954 | + | 0.0189812i | ||||
\(595\) | 9.51330e31 | 0.0483201 | ||||||||
\(596\) | 1.91063e32i | 0.0951089i | ||||||||
\(597\) | −1.97239e33 | + | 3.35129e33i | −0.962279 | + | 1.63501i | ||||
\(598\) | 2.26127e33 | 1.08128 | ||||||||
\(599\) | − | 2.92781e33i | − | 1.37221i | −0.727501 | − | 0.686107i | \(-0.759318\pi\) | ||
0.727501 | − | 0.686107i | \(-0.240682\pi\) | |||||||
\(600\) | −1.65649e33 | − | 9.74921e32i | −0.760980 | − | 0.447872i | ||||
\(601\) | 1.78506e33 | 0.803821 | 0.401910 | − | 0.915679i | \(-0.368346\pi\) | ||||
0.401910 | + | 0.915679i | \(0.368346\pi\) | |||||||
\(602\) | − | 2.85375e32i | − | 0.125967i | ||||||
\(603\) | 3.95832e32 | + | 7.12856e32i | 0.171279 | + | 0.308456i | ||||
\(604\) | −9.73999e32 | −0.413157 | ||||||||
\(605\) | 6.59648e32i | 0.274314i | ||||||||
\(606\) | 3.74518e32 | − | 6.36344e32i | 0.152687 | − | 0.259430i | ||||
\(607\) | 2.30435e32 | 0.0921050 | 0.0460525 | − | 0.998939i | \(-0.485336\pi\) | ||||
0.0460525 | + | 0.998939i | \(0.485336\pi\) | |||||||
\(608\) | − | 1.88577e32i | − | 0.0739003i | ||||||
\(609\) | 4.48993e32 | + | 2.64254e32i | 0.172517 | + | 0.101534i | ||||
\(610\) | −4.18221e33 | −1.57561 | ||||||||
\(611\) | − | 4.38295e33i | − | 1.61909i | ||||||
\(612\) | −2.37212e32 | + | 1.31718e32i | −0.0859250 | + | 0.0477121i | ||||
\(613\) | 4.46344e33 | 1.58542 | 0.792710 | − | 0.609599i | \(-0.208670\pi\) | ||||
0.792710 | + | 0.609599i | \(0.208670\pi\) | |||||||
\(614\) | − | 4.66709e32i | − | 0.162564i | ||||||
\(615\) | −1.41986e33 | + | 2.41248e33i | −0.485001 | + | 0.824065i | ||||
\(616\) | 1.48554e32 | 0.0497642 | ||||||||
\(617\) | − | 3.92178e32i | − | 0.128843i | −0.997923 | − | 0.0644216i | \(-0.979480\pi\) | ||
0.997923 | − | 0.0644216i | \(-0.0205203\pi\) | |||||||
\(618\) | 2.74611e33 | + | 1.61621e33i | 0.884822 | + | 0.520759i | ||||
\(619\) | −2.74576e32 | −0.0867710 | −0.0433855 | − | 0.999058i | \(-0.513814\pi\) | ||||
−0.0433855 | + | 0.999058i | \(0.513814\pi\) | |||||||
\(620\) | 1.79197e33i | 0.555432i | ||||||||
\(621\) | 9.47150e31 | − | 3.77715e33i | 0.0287952 | − | 1.14832i | ||||
\(622\) | −2.09511e33 | −0.624773 | ||||||||
\(623\) | − | 8.17950e31i | − | 0.0239260i | ||||||
\(624\) | 5.88305e32 | − | 9.99589e32i | 0.168806 | − | 0.286818i | ||||
\(625\) | 9.73426e33 | 2.73995 | ||||||||
\(626\) | − | 1.46843e33i | − | 0.405471i | ||||||
\(627\) | −1.42419e33 | − | 8.38202e32i | −0.385796 | − | 0.227059i | ||||
\(628\) | 3.23633e33 | 0.860077 | ||||||||
\(629\) | 3.56346e32i | 0.0929105i | ||||||||
\(630\) | 3.29868e32 | + | 5.94062e32i | 0.0843828 | + | 0.151965i | ||||
\(631\) | −7.59300e33 | −1.90573 | −0.952864 | − | 0.303397i | \(-0.901879\pi\) | ||||
−0.952864 | + | 0.303397i | \(0.901879\pi\) | |||||||
\(632\) | 1.14444e33i | 0.281830i | ||||||||
\(633\) | 1.48929e33 | − | 2.53045e33i | 0.359860 | − | 0.611439i | ||||
\(634\) | 1.01047e33 | 0.239580 | ||||||||
\(635\) | − | 7.11000e32i | − | 0.165419i | ||||||
\(636\) | 2.25067e33 | + | 1.32462e33i | 0.513838 | + | 0.302418i | ||||
\(637\) | −5.83923e33 | −1.30823 | ||||||||
\(638\) | − | 5.24482e33i | − | 1.15314i | ||||||
\(639\) | 1.44832e33 | − | 8.04219e32i | 0.312503 | − | 0.173526i | ||||
\(640\) | 7.80607e32 | 0.165300 | ||||||||
\(641\) | 5.38294e33i | 1.11872i | 0.828924 | + | 0.559362i | \(0.188954\pi\) | ||||
−0.828924 | + | 0.559362i | \(0.811046\pi\) | |||||||
\(642\) | −1.76590e33 | + | 3.00044e33i | −0.360202 | + | 0.612020i | ||||
\(643\) | −5.58872e32 | −0.111887 | −0.0559436 | − | 0.998434i | \(-0.517817\pi\) | ||||
−0.0559436 | + | 0.998434i | \(0.517817\pi\) | |||||||
\(644\) | − | 3.84187e32i | − | 0.0754939i | ||||||
\(645\) | −1.13251e34 | − | 6.66535e33i | −2.18436 | − | 1.28560i | ||||
\(646\) | 3.06906e32 | 0.0581052 | ||||||||
\(647\) | 9.97296e33i | 1.85342i | 0.375783 | + | 0.926708i | \(0.377374\pi\) | ||||
−0.375783 | + | 0.926708i | \(0.622626\pi\) | |||||||
\(648\) | −1.64504e33 | − | 1.02455e33i | −0.300107 | − | 0.186911i | ||||
\(649\) | 4.10784e33 | 0.735659 | ||||||||
\(650\) | 1.33721e34i | 2.35093i | ||||||||
\(651\) | 2.29452e32 | − | 3.89862e32i | 0.0396023 | − | 0.0672882i | ||||
\(652\) | −3.30847e33 | −0.560604 | ||||||||
\(653\) | 6.38820e32i | 0.106272i | 0.998587 | + | 0.0531362i | \(0.0169217\pi\) | ||||
−0.998587 | + | 0.0531362i | \(0.983078\pi\) | |||||||
\(654\) | −6.53539e32 | − | 3.84639e32i | −0.106743 | − | 0.0628232i | ||||
\(655\) | 1.73792e33 | 0.278699 | ||||||||
\(656\) | − | 8.11810e32i | − | 0.127823i | ||||||
\(657\) | 6.71039e32 | + | 1.20848e33i | 0.103744 | + | 0.186833i | ||||
\(658\) | −7.44658e32 | −0.113044 | ||||||||
\(659\) | − | 6.90599e33i | − | 1.02944i | −0.857359 | − | 0.514720i | \(-0.827896\pi\) | ||
0.857359 | − | 0.514720i | \(-0.172104\pi\) | |||||||
\(660\) | 3.46970e33 | − | 5.89537e33i | 0.507885 | − | 0.862947i | ||||
\(661\) | −1.70554e33 | −0.245156 | −0.122578 | − | 0.992459i | \(-0.539116\pi\) | ||||
−0.122578 | + | 0.992459i | \(0.539116\pi\) | |||||||
\(662\) | 3.04556e33i | 0.429904i | ||||||||
\(663\) | 1.62681e33 | + | 9.57455e32i | 0.225515 | + | 0.132726i | ||||
\(664\) | 3.05641e33 | 0.416096 | ||||||||
\(665\) | − | 7.68599e32i | − | 0.102764i | ||||||
\(666\) | −2.22522e33 | + | 1.23561e33i | −0.292201 | + | 0.162252i | ||||
\(667\) | −1.35640e34 | −1.74935 | ||||||||
\(668\) | 2.51156e33i | 0.318146i | ||||||||
\(669\) | −7.16083e32 | + | 1.21670e33i | −0.0890943 | + | 0.151380i | ||||
\(670\) | 3.81780e33 | 0.466569 | ||||||||
\(671\) | − | 1.06286e34i | − | 1.27587i | ||||||
\(672\) | −1.69829e32 | − | 9.99524e31i | −0.0200254 | − | 0.0117859i | ||||
\(673\) | 5.28039e33 | 0.611625 | 0.305813 | − | 0.952092i | \(-0.401072\pi\) | ||||
0.305813 | + | 0.952092i | \(0.401072\pi\) | |||||||
\(674\) | − | 7.18758e33i | − | 0.817832i | ||||||
\(675\) | 2.23363e34 | + | 5.60102e32i | 2.49670 | + | 0.0626068i | ||||
\(676\) | −3.51591e33 | −0.386080 | ||||||||
\(677\) | 1.06855e34i | 1.15274i | 0.817188 | + | 0.576371i | \(0.195532\pi\) | ||||
−0.817188 | + | 0.576371i | \(0.804468\pi\) | |||||||
\(678\) | 2.81580e33 | − | 4.78433e33i | 0.298432 | − | 0.507066i | ||||
\(679\) | −3.78433e32 | −0.0394050 | ||||||||
\(680\) | 1.27042e33i | 0.129970i | ||||||||
\(681\) | −1.73912e33 | − | 1.02355e33i | −0.174809 | − | 0.102883i | ||||
\(682\) | −4.55409e33 | −0.449769 | ||||||||
\(683\) | 6.35426e32i | 0.0616618i | 0.999525 | + | 0.0308309i | \(0.00981534\pi\) | ||||
−0.999525 | + | 0.0308309i | \(0.990185\pi\) | |||||||
\(684\) | 1.06418e33 | + | 1.91649e33i | 0.101471 | + | 0.182739i | ||||
\(685\) | −1.02947e34 | −0.964552 | ||||||||
\(686\) | 2.00160e33i | 0.184284i | ||||||||
\(687\) | 3.23243e33 | − | 5.49222e33i | 0.292448 | − | 0.496898i | ||||
\(688\) | 3.81095e33 | 0.338822 | ||||||||
\(689\) | − | 1.81687e34i | − | 1.58742i | ||||||
\(690\) | −1.52464e34 | − | 8.97324e33i | −1.30912 | − | 0.770478i | ||||
\(691\) | 2.02979e34 | 1.71283 | 0.856417 | − | 0.516284i | \(-0.172685\pi\) | ||||
0.856417 | + | 0.516284i | \(0.172685\pi\) | |||||||
\(692\) | − | 9.30076e33i | − | 0.771339i | ||||||
\(693\) | −1.50974e33 | + | 8.38322e32i | −0.123056 | + | 0.0683301i | ||||
\(694\) | 1.08222e34 | 0.866969 | ||||||||
\(695\) | 3.47955e34i | 2.73972i | ||||||||
\(696\) | −3.52889e33 | + | 5.99594e33i | −0.273104 | + | 0.464031i | ||||
\(697\) | 1.32121e33 | 0.100503 | ||||||||
\(698\) | − | 1.53801e34i | − | 1.14999i | ||||||
\(699\) | 1.15823e34 | + | 6.81673e33i | 0.851274 | + | 0.501014i | ||||
\(700\) | 2.27191e33 | 0.164140 | ||||||||
\(701\) | − | 1.31882e34i | − | 0.936633i | −0.883561 | − | 0.468317i | \(-0.844861\pi\) | ||
0.883561 | − | 0.468317i | \(-0.155139\pi\) | |||||||
\(702\) | −3.37987e32 | + | 1.34786e34i | −0.0235969 | + | 0.941023i | ||||
\(703\) | 2.87900e33 | 0.197596 | ||||||||
\(704\) | 1.98382e33i | 0.133854i | ||||||||
\(705\) | −1.73926e34 | + | 2.95517e34i | −1.15370 | + | 1.96026i | ||||
\(706\) | −3.91514e31 | −0.00255324 | ||||||||
\(707\) | 8.72759e32i | 0.0559579i | ||||||||
\(708\) | −4.69613e33 | − | 2.76389e33i | −0.296033 | − | 0.174230i | ||||
\(709\) | 1.70214e34 | 1.05497 | 0.527487 | − | 0.849563i | \(-0.323134\pi\) | ||||
0.527487 | + | 0.849563i | \(0.323134\pi\) | |||||||
\(710\) | − | 7.75670e33i | − | 0.472690i | ||||||
\(711\) | −6.45829e33 | − | 1.16308e34i | −0.386974 | − | 0.696904i | ||||
\(712\) | 1.09231e33 | 0.0643553 | ||||||||
\(713\) | 1.17776e34i | 0.682313i | ||||||||
\(714\) | 1.62671e32 | − | 2.76394e32i | 0.00926682 | − | 0.0157452i | ||||
\(715\) | −4.75908e34 | −2.66594 | ||||||||
\(716\) | − | 2.07643e33i | − | 0.114383i | ||||||
\(717\) | −1.06228e34 | − | 6.25202e33i | −0.575453 | − | 0.338681i | ||||
\(718\) | 3.14887e33 | 0.167750 | ||||||||
\(719\) | 9.84142e33i | 0.515598i | 0.966199 | + | 0.257799i | \(0.0829972\pi\) | ||||
−0.966199 | + | 0.257799i | \(0.917003\pi\) | |||||||
\(720\) | −7.93321e33 | + | 4.40512e33i | −0.408751 | + | 0.226970i | ||||
\(721\) | −3.76634e33 | −0.190852 | ||||||||
\(722\) | 1.17088e34i | 0.583533i | ||||||||
\(723\) | −2.50243e33 | + | 4.25188e33i | −0.122660 | + | 0.208411i | ||||
\(724\) | −7.60768e33 | −0.366767 | ||||||||
\(725\) | − | 8.02114e34i | − | 3.80347i | ||||||
\(726\) | 1.91650e33 | + | 1.12795e33i | 0.0893861 | + | 0.0526079i | ||||
\(727\) | −3.38827e34 | −1.55441 | −0.777205 | − | 0.629247i | \(-0.783363\pi\) | ||||
−0.777205 | + | 0.629247i | \(0.783363\pi\) | |||||||
\(728\) | 1.37096e33i | 0.0618653i | ||||||||
\(729\) | 2.25001e34 | + | 1.12913e33i | 0.998743 | + | 0.0501201i | ||||
\(730\) | 6.47218e33 | 0.282603 | ||||||||
\(731\) | 6.20225e33i | 0.266404i | ||||||||
\(732\) | −7.15129e33 | + | 1.21507e34i | −0.302170 | + | 0.513417i | ||||
\(733\) | 6.94273e33 | 0.288591 | 0.144295 | − | 0.989535i | \(-0.453908\pi\) | ||||
0.144295 | + | 0.989535i | \(0.453908\pi\) | |||||||
\(734\) | 1.44032e34i | 0.588986i | ||||||||
\(735\) | 3.93706e34 | + | 2.31714e34i | 1.58389 | + | 0.932191i | ||||
\(736\) | 5.13050e33 | 0.203061 | ||||||||
\(737\) | 9.70250e33i | 0.377810i | ||||||||
\(738\) | 4.58121e33 | + | 8.25032e33i | 0.175511 | + | 0.316078i | ||||
\(739\) | 4.80426e34 | 1.81090 | 0.905448 | − | 0.424458i | \(-0.139535\pi\) | ||||
0.905448 | + | 0.424458i | \(0.139535\pi\) | |||||||
\(740\) | 1.19175e34i | 0.441982i | ||||||||
\(741\) | 7.73548e33 | − | 1.31434e34i | 0.282273 | − | 0.479609i | ||||
\(742\) | −3.08684e33 | −0.110832 | ||||||||
\(743\) | 5.57616e33i | 0.197001i | 0.995137 | + | 0.0985007i | \(0.0314047\pi\) | ||||
−0.995137 | + | 0.0985007i | \(0.968595\pi\) | |||||||
\(744\) | 5.20629e33 | + | 3.06415e33i | 0.180989 | + | 0.106521i | ||||
\(745\) | −1.03993e34 | −0.355737 | ||||||||
\(746\) | 1.20762e34i | 0.406505i | ||||||||
\(747\) | −3.10618e34 | + | 1.72479e34i | −1.02892 | + | 0.571333i | ||||
\(748\) | −3.22863e33 | −0.105245 | ||||||||
\(749\) | − | 4.11517e33i | − | 0.132010i | ||||||
\(750\) | 3.18168e34 | − | 5.40600e34i | 1.00444 | − | 1.70664i | ||||
\(751\) | 2.09656e34 | 0.651371 | 0.325685 | − | 0.945478i | \(-0.394405\pi\) | ||||
0.325685 | + | 0.945478i | \(0.394405\pi\) | |||||||
\(752\) | − | 9.94431e33i | − | 0.304061i | ||||||
\(753\) | −4.87228e34 | − | 2.86757e34i | −1.46620 | − | 0.862927i | ||||
\(754\) | 4.84027e34 | 1.43355 | ||||||||
\(755\) | − | 5.30135e34i | − | 1.54534i | ||||||
\(756\) | 2.29000e33 | + | 5.74237e31i | 0.0657014 | + | 0.00164751i | ||||
\(757\) | −2.59094e34 | −0.731657 | −0.365829 | − | 0.930682i | \(-0.619214\pi\) | ||||
−0.365829 | + | 0.930682i | \(0.619214\pi\) | |||||||
\(758\) | 1.52113e34i | 0.422801i | ||||||||
\(759\) | 2.28044e34 | − | 3.87470e34i | 0.623905 | − | 1.06008i | ||||
\(760\) | 1.02640e34 | 0.276410 | ||||||||
\(761\) | 6.37561e34i | 1.69008i | 0.534707 | + | 0.845038i | \(0.320422\pi\) | ||||
−0.534707 | + | 0.845038i | \(0.679578\pi\) | |||||||
\(762\) | −2.06570e33 | − | 1.21576e33i | −0.0539023 | − | 0.0317240i | ||||
\(763\) | 8.96343e32 | 0.0230239 | ||||||||
\(764\) | − | 1.98883e34i | − | 0.502895i | ||||||
\(765\) | −7.16925e33 | − | 1.29111e34i | −0.178458 | − | 0.321387i | ||||
\(766\) | −5.20887e34 | −1.27643 | ||||||||
\(767\) | 3.79098e34i | 0.914549i | ||||||||
\(768\) | 1.33478e33 | − | 2.26793e33i | 0.0317012 | − | 0.0538635i | ||||
\(769\) | 4.52884e34 | 1.05894 | 0.529470 | − | 0.848329i | \(-0.322391\pi\) | ||||
0.529470 | + | 0.848329i | \(0.322391\pi\) | |||||||
\(770\) | 8.08563e33i | 0.186134i | ||||||||
\(771\) | 3.40523e34 | + | 2.00414e34i | 0.771781 | + | 0.454230i | ||||
\(772\) | −4.26984e34 | −0.952804 | ||||||||
\(773\) | − | 2.41056e34i | − | 0.529619i | −0.964301 | − | 0.264810i | \(-0.914691\pi\) | ||
0.964301 | − | 0.264810i | \(-0.0853091\pi\) | |||||||
\(774\) | −3.87302e34 | + | 2.15060e34i | −0.837834 | + | 0.465229i | ||||
\(775\) | −6.96477e34 | −1.48350 | ||||||||
\(776\) | − | 5.05366e33i | − | 0.105990i | ||||||
\(777\) | 1.52597e33 | − | 2.59277e33i | 0.0315132 | − | 0.0535441i | ||||
\(778\) | −1.56260e34 | −0.317755 | ||||||||
\(779\) | − | 1.06743e34i | − | 0.213742i | ||||||
\(780\) | 5.44064e34 | + | 3.20207e34i | 1.07279 | + | 0.631387i | ||||
\(781\) | 1.97127e34 | 0.382767 | ||||||||
\(782\) | 8.34979e33i | 0.159659i | ||||||||
\(783\) | 2.02739e33 | − | 8.08502e34i | 0.0381764 | − | 1.52244i | ||||
\(784\) | −1.32484e34 | −0.245681 | ||||||||
\(785\) | 1.76149e35i | 3.21696i | ||||||||
\(786\) | 2.97173e33 | − | 5.04926e33i | 0.0534488 | − | 0.0908149i | ||||
\(787\) | −2.11726e33 | −0.0375040 | −0.0187520 | − | 0.999824i | \(-0.505969\pi\) | ||||
−0.0187520 | + | 0.999824i | \(0.505969\pi\) | |||||||
\(788\) | − | 3.96252e34i | − | 0.691285i | ||||||
\(789\) | −4.96405e34 | − | 2.92158e34i | −0.852927 | − | 0.501988i | ||||
\(790\) | −6.22902e34 | −1.05413 | ||||||||
\(791\) | 6.56181e33i | 0.109372i | ||||||||
\(792\) | −1.11951e34 | − | 2.01613e34i | −0.183792 | − | 0.330992i | ||||
\(793\) | 9.80878e34 | 1.58612 | ||||||||
\(794\) | − | 3.07636e34i | − | 0.489995i | ||||||
\(795\) | −7.20976e34 | + | 1.22501e35i | −1.13114 | + | 1.92192i | ||||
\(796\) | 6.13807e34 | 0.948582 | ||||||||
\(797\) | 1.31847e34i | 0.200711i | 0.994952 | + | 0.100355i | \(0.0319979\pi\) | ||||
−0.994952 | + | 0.100355i | \(0.968002\pi\) | |||||||
\(798\) | −2.23304e33 | − | 1.31425e33i | −0.0334859 | − | 0.0197080i | ||||
\(799\) | 1.61842e34 | 0.239072 | ||||||||
\(800\) | 3.03395e34i | 0.441497i | ||||||||
\(801\) | −1.11010e34 | + | 6.16410e33i | −0.159137 | + | 0.0883649i | ||||
\(802\) | −9.07495e33 | −0.128160 | ||||||||
\(803\) | 1.64483e34i | 0.228841i | ||||||||
\(804\) | 6.52817e33 | − | 1.10920e34i | 0.0894785 | − | 0.152033i | ||||
\(805\) | 2.09108e34 | 0.282371 | ||||||||
\(806\) | − | 4.20281e34i | − | 0.559139i | ||||||
\(807\) | −5.94771e34 | − | 3.50051e34i | −0.779592 | − | 0.458826i | ||||
\(808\) | −1.16550e34 | −0.150514 | ||||||||
\(809\) | − | 5.48800e34i | − | 0.698284i | −0.937070 | − | 0.349142i | \(-0.886473\pi\) | ||
0.937070 | − | 0.349142i | \(-0.113527\pi\) | |||||||
\(810\) | 5.57652e34 | − | 8.95374e34i | 0.699106 | − | 1.12249i | ||||
\(811\) | −2.02114e34 | −0.249659 | −0.124829 | − | 0.992178i | \(-0.539838\pi\) | ||||
−0.124829 | + | 0.992178i | \(0.539838\pi\) | |||||||
\(812\) | − | 8.22356e33i | − | 0.100089i | ||||||
\(813\) | −1.08009e34 | + | 1.83519e34i | −0.129531 | + | 0.220087i | ||||
\(814\) | −3.02869e34 | −0.357900 | ||||||||
\(815\) | − | 1.80076e35i | − | 2.09683i | ||||||
\(816\) | 3.69101e33 | + | 2.17233e33i | 0.0423510 | + | 0.0249255i | ||||
\(817\) | 5.01092e34 | 0.566569 | ||||||||
\(818\) | 5.86980e34i | 0.654009i | ||||||||
\(819\) | −7.73659e33 | − | 1.39329e34i | −0.0849459 | − | 0.152980i | ||||
\(820\) | 4.41858e34 | 0.478098 | ||||||||
\(821\) | 4.91287e34i | 0.523862i | 0.965087 | + | 0.261931i | \(0.0843593\pi\) | ||||
−0.965087 | + | 0.261931i | \(0.915641\pi\) | |||||||
\(822\) | −1.76032e34 | + | 2.99095e34i | −0.184982 | + | 0.314302i | ||||
\(823\) | 1.85256e35 | 1.91856 | 0.959279 | − | 0.282461i | \(-0.0911507\pi\) | ||||
0.959279 | + | 0.282461i | \(0.0911507\pi\) | |||||||
\(824\) | − | 5.02964e34i | − | 0.513347i | ||||||
\(825\) | 2.29132e35 | + | 1.34855e35i | 2.30483 | + | 1.35650i | ||||
\(826\) | 6.44083e33 | 0.0638530 | ||||||||
\(827\) | − | 1.63343e35i | − | 1.59600i | −0.602654 | − | 0.798002i | \(-0.705890\pi\) | ||
0.602654 | − | 0.798002i | \(-0.294110\pi\) | |||||||
\(828\) | −5.21406e34 | + | 2.89524e34i | −0.502125 | + | 0.278818i | ||||
\(829\) | −1.13394e35 | −1.07630 | −0.538152 | − | 0.842848i | \(-0.680877\pi\) | ||||
−0.538152 | + | 0.842848i | \(0.680877\pi\) | |||||||
\(830\) | 1.66356e35i | 1.55633i | ||||||||
\(831\) | 2.72406e34 | − | 4.62845e34i | 0.251191 | − | 0.426799i | ||||
\(832\) | −1.83080e34 | −0.166403 | ||||||||
\(833\) | − | 2.15615e34i | − | 0.193170i | ||||||
\(834\) | 1.01093e35 | + | 5.94978e34i | 0.892745 | + | 0.525422i | ||||
\(835\) | −1.36701e35 | −1.18997 | ||||||||
\(836\) | 2.60848e34i | 0.223827i | ||||||||
\(837\) | −7.02024e34 | − | 1.76038e33i | −0.593809 | − | 0.0148902i | ||||
\(838\) | 5.03455e34 | 0.419791 | ||||||||
\(839\) | 2.05511e34i | 0.168924i | 0.996427 | + | 0.0844622i | \(0.0269172\pi\) | ||||
−0.996427 | + | 0.0844622i | \(0.973083\pi\) | |||||||
\(840\) | 5.44028e33 | − | 9.24358e33i | 0.0440829 | − | 0.0749012i | ||||
\(841\) | −1.65154e35 | −1.31928 | ||||||||
\(842\) | − | 1.14293e35i | − | 0.900066i | ||||||
\(843\) | 2.72880e34 | + | 1.60603e34i | 0.211856 | + | 0.124687i | ||||
\(844\) | −4.63465e34 | −0.354738 | ||||||||
\(845\) | − | 1.91367e35i | − | 1.44406i | ||||||
\(846\) | 5.61177e34 | + | 1.01063e35i | 0.417499 | + | 0.751876i | ||||
\(847\) | −2.62852e33 | −0.0192802 | ||||||||
\(848\) | − | 4.12222e34i | − | 0.298113i | ||||||
\(849\) | −4.25864e34 | + | 7.23585e34i | −0.303654 | + | 0.515938i | ||||
\(850\) | −4.93769e34 | −0.347134 | ||||||||
\(851\) | 7.83271e34i | 0.542947i | ||||||||
\(852\) | −2.25358e34 | − | 1.32634e34i | −0.154028 | − | 0.0906525i | ||||
\(853\) | −1.23579e35 | −0.832832 | −0.416416 | − | 0.909174i | \(-0.636714\pi\) | ||||
−0.416416 | + | 0.909174i | \(0.636714\pi\) | |||||||
\(854\) | − | 1.66650e34i | − | 0.110742i | ||||||
\(855\) | −1.04312e35 | + | 5.79219e34i | −0.683503 | + | 0.379533i | ||||
\(856\) | 5.49548e34 | 0.355075 | ||||||||
\(857\) | 1.56805e35i | 0.999055i | 0.866298 | + | 0.499527i | \(0.166493\pi\) | ||||
−0.866298 | + | 0.499527i | \(0.833507\pi\) | |||||||
\(858\) | −8.13769e34 | + | 1.38267e35i | −0.511274 | + | 0.868706i | ||||
\(859\) | −1.59845e35 | −0.990330 | −0.495165 | − | 0.868799i | \(-0.664892\pi\) | ||||
−0.495165 | + | 0.868799i | \(0.664892\pi\) | |||||||
\(860\) | 2.07425e35i | 1.26730i | ||||||||
\(861\) | −9.61307e33 | − | 5.65774e33i | −0.0579194 | − | 0.0340883i | ||||
\(862\) | 1.45989e35 | 0.867430 | ||||||||
\(863\) | 6.37895e34i | 0.373783i | 0.982381 | + | 0.186892i | \(0.0598413\pi\) | ||||
−0.982381 | + | 0.186892i | \(0.940159\pi\) | |||||||
\(864\) | −7.66846e32 | + | 3.05811e34i | −0.00443143 | + | 0.176721i | ||||
\(865\) | 5.06229e35 | 2.88505 | ||||||||
\(866\) | − | 2.28787e35i | − | 1.28593i | ||||||
\(867\) | 8.79655e34 | − | 1.49462e35i | 0.487622 | − | 0.828518i | ||||
\(868\) | −7.14053e33 | −0.0390386 | ||||||||
\(869\) | − | 1.58303e35i | − | 0.853597i | ||||||
\(870\) | −3.26352e35 | − | 1.92073e35i | −1.73562 | − | 1.02149i | ||||
\(871\) | −8.95411e34 | −0.469682 | ||||||||
\(872\) | 1.19699e34i | 0.0619290i | ||||||||
\(873\) | 2.85188e34 | + | 5.13597e34i | 0.145533 | + | 0.262091i | ||||
\(874\) | 6.74597e34 | 0.339553 | ||||||||
\(875\) | 7.41444e34i | 0.368114i | ||||||||
\(876\) | 1.10670e34 | − | 1.88039e34i | 0.0541975 | − | 0.0920869i | ||||
\(877\) | −3.55972e35 | −1.71957 | −0.859787 | − | 0.510652i | \(-0.829404\pi\) | ||||
−0.859787 | + | 0.510652i | \(0.829404\pi\) | |||||||
\(878\) | − | 8.29064e34i | − | 0.395051i | ||||||
\(879\) | −1.66229e35 | − | 9.78333e34i | −0.781338 | − | 0.459854i | ||||
\(880\) | −1.07977e35 | −0.500656 | ||||||||
\(881\) | 1.83672e35i | 0.840101i | 0.907501 | + | 0.420050i | \(0.137988\pi\) | ||||
−0.907501 | + | 0.420050i | \(0.862012\pi\) | |||||||
\(882\) | 1.34642e35 | − | 7.47634e34i | 0.607515 | − | 0.337339i | ||||
\(883\) | 1.85716e35 | 0.826647 | 0.413324 | − | 0.910584i | \(-0.364368\pi\) | ||||
0.413324 | + | 0.910584i | \(0.364368\pi\) | |||||||
\(884\) | − | 2.97960e34i | − | 0.130837i | ||||||
\(885\) | 1.50435e35 | − | 2.55604e35i | 0.651673 | − | 1.10726i | ||||
\(886\) | 1.30085e35 | 0.555932 | ||||||||
\(887\) | 2.36928e35i | 0.998926i | 0.866335 | + | 0.499463i | \(0.166469\pi\) | ||||
−0.866335 | + | 0.499463i | \(0.833531\pi\) | |||||||
\(888\) | 3.46244e34 | + | 2.03781e34i | 0.144021 | + | 0.0847632i | ||||
\(889\) | 2.83315e33 | 0.0116265 | ||||||||
\(890\) | 5.94529e34i | 0.240709i | ||||||||
\(891\) | 2.27549e35 | + | 1.41721e35i | 0.908955 | + | 0.566110i | ||||
\(892\) | 2.22844e34 | 0.0878261 | ||||||||
\(893\) | − | 1.30755e35i | − | 0.508442i | ||||||
\(894\) | −1.77821e34 | + | 3.02135e34i | −0.0682232 | + | 0.115918i | ||||
\(895\) | 1.13018e35 | 0.427828 | ||||||||
\(896\) | 3.11051e33i | 0.0116181i | ||||||||
\(897\) | 3.57583e35 | + | 2.10454e35i | 1.31785 | + | 0.775619i | ||||
\(898\) | 1.56337e35 | 0.568518 | ||||||||
\(899\) | 2.52102e35i | 0.904606i | ||||||||
\(900\) | −1.71212e35 | − | 3.08336e35i | −0.606210 | − | 1.09173i | ||||
\(901\) | 6.70884e34 | 0.234396 | ||||||||
\(902\) | 1.12293e35i | 0.387146i | ||||||||
\(903\) | 2.65596e34 | − | 4.51274e34i | 0.0903585 | − | 0.153528i | ||||
\(904\) | −8.76276e34 | −0.294185 | ||||||||
\(905\) | − | 4.14077e35i | − | 1.37182i | ||||||
\(906\) | −1.54022e35 | − | 9.06494e34i | −0.503553 | − | 0.296365i | ||||
\(907\) | 5.44825e35 | 1.75780 | 0.878901 | − | 0.477004i | \(-0.158277\pi\) | ||||
0.878901 | + | 0.477004i | \(0.158277\pi\) | |||||||
\(908\) | 3.18529e34i | 0.101419i | ||||||||
\(909\) | 1.18448e35 | − | 6.57714e34i | 0.372187 | − | 0.206667i | ||||
\(910\) | −7.46195e34 | −0.231396 | ||||||||
\(911\) | 9.49061e34i | 0.290452i | 0.989399 | + | 0.145226i | \(0.0463908\pi\) | ||||
−0.989399 | + | 0.145226i | \(0.953609\pi\) | |||||||
\(912\) | 1.75507e34 | − | 2.98204e34i | 0.0530099 | − | 0.0900692i | ||||
\(913\) | −4.22775e35 | −1.26026 | ||||||||
\(914\) | 8.60795e34i | 0.253248i | ||||||||
\(915\) | −6.61350e35 | − | 3.89235e35i | −1.92034 | − | 1.13021i | ||||
\(916\) | −1.00593e35 | −0.288285 | ||||||||
\(917\) | 6.92516e33i | 0.0195883i | ||||||||
\(918\) | −4.97702e34 | − | 1.24803e33i | −0.138950 | − | 0.00348427i | ||||
\(919\) | −2.17698e35 | −0.599885 | −0.299943 | − | 0.953957i | \(-0.596968\pi\) | ||||
−0.299943 | + | 0.953957i | \(0.596968\pi\) | |||||||
\(920\) | 2.79247e35i | 0.759511i | ||||||||
\(921\) | 4.34362e34 | − | 7.38025e34i | 0.116610 | − | 0.198132i | ||||
\(922\) | 6.42450e34 | 0.170243 | ||||||||
\(923\) | 1.81922e35i | 0.475845i | ||||||||
\(924\) | 2.34915e34 | + | 1.38258e34i | 0.0606522 | + | 0.0356967i | ||||
\(925\) | −4.63191e35 | −1.18048 | ||||||||
\(926\) | − | 3.90730e35i | − | 0.982981i | ||||||
\(927\) | 2.83833e35 | + | 5.11156e35i | 0.704865 | + | 1.26940i | ||||
\(928\) | 1.09819e35 | 0.269216 | ||||||||
\(929\) | 7.35473e35i | 1.77983i | 0.456127 | + | 0.889915i | \(0.349236\pi\) | ||||
−0.456127 | + | 0.889915i | \(0.650764\pi\) | |||||||
\(930\) | −1.66778e35 | + | 2.83372e35i | −0.398421 | + | 0.676957i | ||||
\(931\) | −1.74200e35 | −0.410820 | ||||||||
\(932\) | − | 2.12136e35i | − | 0.493883i | ||||||
\(933\) | −3.31308e35 | − | 1.94990e35i | −0.761469 | − | 0.448160i | ||||
\(934\) | −6.37567e34 | −0.144665 | ||||||||
\(935\) | − | 1.75730e35i | − | 0.393648i | ||||||
\(936\) | 1.86062e35 | − | 1.03316e35i | 0.411479 | − | 0.228485i | ||||
\(937\) | −6.48186e35 | −1.41522 | −0.707611 | − | 0.706602i | \(-0.750227\pi\) | ||||
−0.707611 | + | 0.706602i | \(0.750227\pi\) | |||||||
\(938\) | 1.52129e34i | 0.0327928i | ||||||||
\(939\) | 1.36665e35 | − | 2.32208e35i | 0.290851 | − | 0.494185i | ||||
\(940\) | 5.41256e35 | 1.13728 | ||||||||
\(941\) | − | 3.85253e35i | − | 0.799229i | −0.916683 | − | 0.399614i | \(-0.869144\pi\) | ||
0.916683 | − | 0.399614i | \(-0.130856\pi\) | |||||||
\(942\) | 5.11774e35 | + | 3.01203e35i | 1.04826 | + | 0.616948i | ||||
\(943\) | 2.90409e35 | 0.587313 | ||||||||
\(944\) | 8.60121e34i | 0.171750i | ||||||||
\(945\) | −3.12550e33 | + | 1.24642e35i | −0.00616222 | + | 0.245744i | ||||
\(946\) | −5.27147e35 | −1.02621 | ||||||||
\(947\) | − | 4.72280e35i | − | 0.907820i | −0.891048 | − | 0.453910i | \(-0.850029\pi\) | ||
0.891048 | − | 0.453910i | \(-0.149971\pi\) | |||||||
\(948\) | −1.06512e35 | + | 1.80974e35i | −0.202161 | + | 0.343492i | ||||
\(949\) | −1.51796e35 | −0.284488 | ||||||||
\(950\) | 3.98926e35i | 0.738260i | ||||||||
\(951\) | 1.59789e35 | + | 9.40432e34i | 0.291998 | + | 0.171855i | ||||
\(952\) | −5.06230e33 | −0.00913491 | ||||||||
\(953\) | 1.06604e36i | 1.89959i | 0.312877 | + | 0.949794i | \(0.398707\pi\) | ||||
−0.312877 | + | 0.949794i | \(0.601293\pi\) | |||||||
\(954\) | 2.32625e35 | + | 4.18936e35i | 0.409333 | + | 0.737169i | ||||
\(955\) | 1.08249e36 | 1.88098 | ||||||||
\(956\) | 1.94563e35i | 0.333860i | ||||||||
\(957\) | 4.88132e35 | − | 8.29384e35i | 0.827168 | − | 1.40544i | ||||
\(958\) | −5.35426e35 | −0.896011 | ||||||||
\(959\) | − | 4.10215e34i | − | 0.0677936i | ||||||
\(960\) | 1.23441e35 | + | 7.26506e34i | 0.201467 | + | 0.118573i | ||||
\(961\) | −4.01512e35 | −0.647170 | ||||||||
\(962\) | − | 2.79508e35i | − | 0.444931i | ||||||
\(963\) | −5.58498e35 | + | 3.10121e35i | −0.878024 | + | 0.487546i | ||||
\(964\) | 7.78755e34 | 0.120914 | ||||||||
\(965\) | − | 2.32402e36i | − | 3.56379i | ||||||
\(966\) | 3.57560e34 | − | 6.07529e34i | 0.0541531 | − | 0.0920114i | ||||
\(967\) | 1.18623e36 | 1.77439 | 0.887197 | − | 0.461391i | \(-0.152649\pi\) | ||||
0.887197 | + | 0.461391i | \(0.152649\pi\) | |||||||
\(968\) | − | 3.51018e34i | − | 0.0518591i | ||||||
\(969\) | 4.85322e34 | + | 2.85635e34i | 0.0708182 | + | 0.0416798i | ||||
\(970\) | 2.75064e35 | 0.396437 | ||||||||
\(971\) | − | 9.47421e35i | − | 1.34869i | −0.738416 | − | 0.674345i | \(-0.764426\pi\) | ||
0.738416 | − | 0.674345i | \(-0.235574\pi\) | |||||||
\(972\) | −1.64782e35 | − | 3.15119e35i | −0.231694 | − | 0.443078i | ||||
\(973\) | −1.38651e35 | −0.192561 | ||||||||
\(974\) | 2.45407e35i | 0.336651i | ||||||||
\(975\) | −1.24453e36 | + | 2.11458e36i | −1.68636 | + | 2.86530i | ||||
\(976\) | 2.22548e35 | 0.297869 | ||||||||
\(977\) | − | 3.91558e35i | − | 0.517679i | −0.965920 | − | 0.258840i | \(-0.916660\pi\) | ||
0.965920 | − | 0.258840i | \(-0.0833401\pi\) | |||||||
\(978\) | −5.23181e35 | − | 3.07917e35i | −0.683260 | − | 0.402131i | ||||
\(979\) | −1.51093e35 | −0.194917 | ||||||||
\(980\) | − | 7.21094e35i | − | 0.918923i | ||||||
\(981\) | −6.75487e34 | − | 1.21649e35i | −0.0850333 | − | 0.153137i | ||||
\(982\) | 2.51226e35 | 0.312411 | ||||||||
\(983\) | − | 8.43619e35i | − | 1.03634i | −0.855276 | − | 0.518172i | \(-0.826613\pi\) | ||
0.855276 | − | 0.518172i | \(-0.173387\pi\) | |||||||
\(984\) | 7.55546e34 | − | 1.28375e35i | 0.0916895 | − | 0.155790i | ||||
\(985\) | 2.15675e36 | 2.58562 | ||||||||
\(986\) | 1.78728e35i | 0.211675i | ||||||||
\(987\) | −1.17756e35 | − | 6.93048e34i | −0.137777 | − | 0.0810882i | ||||
\(988\) | −2.40728e35 | −0.278255 | ||||||||
\(989\) | 1.36329e36i | 1.55680i | ||||||||
\(990\) | 1.09736e36 | − | 6.09336e35i | 1.23801 | − | 0.687439i | ||||
\(991\) | −1.42451e36 | −1.58775 | −0.793876 | − | 0.608079i | \(-0.791940\pi\) | ||||
−0.793876 | + | 0.608079i | \(0.791940\pi\) | |||||||
\(992\) | − | 9.53560e34i | − | 0.105005i | ||||||
\(993\) | −2.83448e35 | + | 4.81606e35i | −0.308377 | + | 0.523964i | ||||
\(994\) | 3.09084e34 | 0.0332230 | ||||||||
\(995\) | 3.34087e36i | 3.54800i | ||||||||
\(996\) | 4.83321e35 | + | 2.84457e35i | 0.507135 | + | 0.298473i | ||||
\(997\) | 8.85938e35 | 0.918463 | 0.459231 | − | 0.888317i | \(-0.348125\pi\) | ||||
0.459231 | + | 0.888317i | \(0.348125\pi\) | |||||||
\(998\) | − | 7.22384e35i | − | 0.739949i | ||||||
\(999\) | −4.66880e35 | − | 1.17074e34i | −0.472519 | − | 0.0118488i |
(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 | 6.25.b.a.5.3 | ✓ | 8 | |
3.2 | odd | 2 | inner | 6.25.b.a.5.7 | yes | 8 | |
4.3 | odd | 2 | 48.25.e.d.17.4 | 8 | |||
12.11 | even | 2 | 48.25.e.d.17.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.25.b.a.5.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
6.25.b.a.5.7 | yes | 8 | 3.2 | odd | 2 | inner | |
48.25.e.d.17.3 | 8 | 12.11 | even | 2 | |||
48.25.e.d.17.4 | 8 | 4.3 | odd | 2 |