Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,26,Mod(9,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.9");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(39.5996779952\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{12} + 1406300109694 x^{10} + \cdots + 56\!\cdots\!01 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{90}\cdot 3^{8}\cdot 5^{29} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 9.3 | ||
Root | \(-116846. i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.9 |
Dual form | 10.26.b.a.9.10 |
$q$-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 \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).
\(n\) | \(7\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4096.00i | − | 0.707107i | ||||||
\(3\) | − | 233693.i | − | 0.253881i | −0.991910 | − | 0.126940i | \(-0.959484\pi\) | ||
0.991910 | − | 0.126940i | \(-0.0405157\pi\) | |||||||
\(4\) | −1.67772e7 | −0.500000 | ||||||||
\(5\) | −3.44896e8 | + | 4.23166e8i | −0.631777 | + | 0.775150i | ||||
\(6\) | −9.57206e8 | −0.179521 | ||||||||
\(7\) | − | 6.39090e10i | − | 1.74517i | −0.488466 | − | 0.872583i | \(-0.662443\pi\) | ||
0.488466 | − | 0.872583i | \(-0.337557\pi\) | |||||||
\(8\) | 6.87195e10i | 0.353553i | ||||||||
\(9\) | 7.92676e11 | 0.935545 | ||||||||
\(10\) | 1.73329e12 | + | 1.41270e12i | 0.548114 | + | 0.446734i | ||||
\(11\) | 6.04007e12 | 0.580274 | 0.290137 | − | 0.956985i | \(-0.406299\pi\) | ||||
0.290137 | + | 0.956985i | \(0.406299\pi\) | |||||||
\(12\) | 3.92071e12i | 0.126940i | ||||||||
\(13\) | − | 1.13809e14i | − | 1.35483i | −0.735601 | − | 0.677415i | \(-0.763100\pi\) | ||
0.735601 | − | 0.677415i | \(-0.236900\pi\) | |||||||
\(14\) | −2.61771e14 | −1.23402 | ||||||||
\(15\) | 9.88909e13 | + | 8.05998e13i | 0.196796 | + | 0.160396i | ||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | 9.52541e14i | 0.396526i | 0.980149 | + | 0.198263i | \(0.0635301\pi\) | ||||
−0.980149 | + | 0.198263i | \(0.936470\pi\) | |||||||
\(18\) | − | 3.24680e15i | − | 0.661530i | ||||||
\(19\) | −8.44950e15 | −0.875812 | −0.437906 | − | 0.899021i | \(-0.644280\pi\) | ||||
−0.437906 | + | 0.899021i | \(0.644280\pi\) | |||||||
\(20\) | 5.78640e15 | − | 7.09955e15i | 0.315888 | − | 0.387575i | ||||
\(21\) | −1.49351e16 | −0.443064 | ||||||||
\(22\) | − | 2.47401e16i | − | 0.410316i | ||||||
\(23\) | 1.51928e16i | 0.144557i | 0.997384 | + | 0.0722786i | \(0.0230271\pi\) | ||||
−0.997384 | + | 0.0722786i | \(0.976973\pi\) | |||||||
\(24\) | 1.60592e16 | 0.0897604 | ||||||||
\(25\) | −6.01162e16 | − | 2.91897e17i | −0.201717 | − | 0.979444i | ||||
\(26\) | −4.66162e17 | −0.958010 | ||||||||
\(27\) | − | 3.83248e17i | − | 0.491397i | ||||||
\(28\) | 1.07222e18i | 0.872583i | ||||||||
\(29\) | 1.63360e18 | 0.857376 | 0.428688 | − | 0.903452i | \(-0.358976\pi\) | ||||
0.428688 | + | 0.903452i | \(0.358976\pi\) | |||||||
\(30\) | 3.30137e17 | − | 4.05057e17i | 0.113417 | − | 0.139156i | ||||
\(31\) | −7.82464e18 | −1.78420 | −0.892099 | − | 0.451840i | \(-0.850768\pi\) | ||||
−0.892099 | + | 0.451840i | \(0.850768\pi\) | |||||||
\(32\) | − | 1.15292e18i | − | 0.176777i | ||||||
\(33\) | − | 1.41152e18i | − | 0.147320i | ||||||
\(34\) | 3.90161e18 | 0.280386 | ||||||||
\(35\) | 2.70441e19 | + | 2.20420e19i | 1.35277 | + | 1.10255i | ||||
\(36\) | −1.32989e19 | −0.467772 | ||||||||
\(37\) | 3.53342e19i | 0.882417i | 0.897405 | + | 0.441208i | \(0.145450\pi\) | ||||
−0.897405 | + | 0.441208i | \(0.854550\pi\) | |||||||
\(38\) | 3.46091e19i | 0.619293i | ||||||||
\(39\) | −2.65964e19 | −0.343965 | ||||||||
\(40\) | −2.90798e19 | − | 2.37011e19i | −0.274057 | − | 0.223367i | ||||
\(41\) | −2.35937e20 | −1.63304 | −0.816522 | − | 0.577315i | \(-0.804101\pi\) | ||||
−0.816522 | + | 0.577315i | \(0.804101\pi\) | |||||||
\(42\) | 6.11741e19i | 0.313293i | ||||||||
\(43\) | − | 3.29832e19i | − | 0.125874i | −0.998017 | − | 0.0629372i | \(-0.979953\pi\) | ||
0.998017 | − | 0.0629372i | \(-0.0200468\pi\) | |||||||
\(44\) | −1.01335e20 | −0.290137 | ||||||||
\(45\) | −2.73391e20 | + | 3.35434e20i | −0.591055 | + | 0.725188i | ||||
\(46\) | 6.22296e19 | 0.102217 | ||||||||
\(47\) | 1.82685e20i | 0.229340i | 0.993404 | + | 0.114670i | \(0.0365810\pi\) | ||||
−0.993404 | + | 0.114670i | \(0.963419\pi\) | |||||||
\(48\) | − | 6.57787e19i | − | 0.0634702i | ||||||
\(49\) | −2.74329e21 | −2.04560 | ||||||||
\(50\) | −1.19561e21 | + | 2.46236e20i | −0.692571 | + | 0.142635i | ||||
\(51\) | 2.22602e20 | 0.100670 | ||||||||
\(52\) | 1.90940e21i | 0.677415i | ||||||||
\(53\) | 5.40172e21i | 1.51037i | 0.655511 | + | 0.755186i | \(0.272453\pi\) | ||||
−0.655511 | + | 0.755186i | \(0.727547\pi\) | |||||||
\(54\) | −1.56978e21 | −0.347470 | ||||||||
\(55\) | −2.08320e21 | + | 2.55595e21i | −0.366604 | + | 0.449800i | ||||
\(56\) | 4.39179e21 | 0.617009 | ||||||||
\(57\) | 1.97459e21i | 0.222352i | ||||||||
\(58\) | − | 6.69124e21i | − | 0.606257i | ||||||
\(59\) | 1.13226e22 | 0.828509 | 0.414254 | − | 0.910161i | \(-0.364042\pi\) | ||||
0.414254 | + | 0.910161i | \(0.364042\pi\) | |||||||
\(60\) | −1.65911e21 | − | 1.35224e21i | −0.0983979 | − | 0.0801979i | ||||
\(61\) | −2.83642e22 | −1.36820 | −0.684098 | − | 0.729390i | \(-0.739804\pi\) | ||||
−0.684098 | + | 0.729390i | \(0.739804\pi\) | |||||||
\(62\) | 3.20497e22i | 1.26162i | ||||||||
\(63\) | − | 5.06592e22i | − | 1.63268i | ||||||
\(64\) | −4.72237e21 | −0.125000 | ||||||||
\(65\) | 4.81602e22 | + | 3.92523e22i | 1.05020 | + | 0.855950i | ||||
\(66\) | −5.78158e21 | −0.104171 | ||||||||
\(67\) | − | 1.16196e23i | − | 1.73483i | −0.497586 | − | 0.867415i | \(-0.665780\pi\) | ||
0.497586 | − | 0.867415i | \(-0.334220\pi\) | |||||||
\(68\) | − | 1.59810e22i | − | 0.198263i | ||||||
\(69\) | 3.55044e21 | 0.0367003 | ||||||||
\(70\) | 9.02840e22 | − | 1.10773e23i | 0.779624 | − | 0.956550i | ||||
\(71\) | 1.14601e23 | 0.828816 | 0.414408 | − | 0.910091i | \(-0.363989\pi\) | ||||
0.414408 | + | 0.910091i | \(0.363989\pi\) | |||||||
\(72\) | 5.44723e22i | 0.330765i | ||||||||
\(73\) | 8.85118e21i | 0.0452340i | 0.999744 | + | 0.0226170i | \(0.00719983\pi\) | ||||
−0.999744 | + | 0.0226170i | \(0.992800\pi\) | |||||||
\(74\) | 1.44729e23 | 0.623963 | ||||||||
\(75\) | −6.82142e22 | + | 1.40487e22i | −0.248662 | + | 0.0512119i | ||||
\(76\) | 1.41759e23 | 0.437906 | ||||||||
\(77\) | − | 3.86015e23i | − | 1.01267i | ||||||
\(78\) | 1.08939e23i | 0.243220i | ||||||||
\(79\) | −2.17397e23 | −0.413918 | −0.206959 | − | 0.978350i | \(-0.566357\pi\) | ||||
−0.206959 | + | 0.978350i | \(0.566357\pi\) | |||||||
\(80\) | −9.70797e22 | + | 1.19111e23i | −0.157944 | + | 0.193788i | ||||
\(81\) | 5.82063e23 | 0.810788 | ||||||||
\(82\) | 9.66398e23i | 1.15474i | ||||||||
\(83\) | − | 6.46451e22i | − | 0.0663834i | −0.999449 | − | 0.0331917i | \(-0.989433\pi\) | ||
0.999449 | − | 0.0331917i | \(-0.0105672\pi\) | |||||||
\(84\) | 2.50569e23 | 0.221532 | ||||||||
\(85\) | −4.03083e23 | − | 3.28528e23i | −0.307368 | − | 0.250516i | ||||
\(86\) | −1.35099e23 | −0.0890067 | ||||||||
\(87\) | − | 3.81761e23i | − | 0.217671i | ||||||
\(88\) | 4.15070e23i | 0.205158i | ||||||||
\(89\) | −3.57337e24 | −1.53357 | −0.766783 | − | 0.641906i | \(-0.778144\pi\) | ||||
−0.766783 | + | 0.641906i | \(0.778144\pi\) | |||||||
\(90\) | 1.37394e24 | + | 1.11981e24i | 0.512785 | + | 0.417939i | ||||
\(91\) | −7.27343e24 | −2.36440 | ||||||||
\(92\) | − | 2.54893e23i | − | 0.0722786i | ||||||
\(93\) | 1.82856e24i | 0.452973i | ||||||||
\(94\) | 7.48277e23 | 0.162168 | ||||||||
\(95\) | 2.91420e24 | − | 3.57554e24i | 0.553317 | − | 0.678886i | ||||
\(96\) | −2.69429e23 | −0.0448802 | ||||||||
\(97\) | 2.49389e24i | 0.364948i | 0.983211 | + | 0.182474i | \(0.0584105\pi\) | ||||
−0.983211 | + | 0.182474i | \(0.941589\pi\) | |||||||
\(98\) | 1.12365e25i | 1.44646i | ||||||||
\(99\) | 4.78782e24 | 0.542872 | ||||||||
\(100\) | 1.00858e24 | + | 4.89722e24i | 0.100858 | + | 0.489722i | ||||
\(101\) | −1.34804e25 | −1.19038 | −0.595192 | − | 0.803584i | \(-0.702924\pi\) | ||||
−0.595192 | + | 0.803584i | \(0.702924\pi\) | |||||||
\(102\) | − | 9.11777e23i | − | 0.0711847i | ||||||
\(103\) | − | 1.98475e25i | − | 1.37164i | −0.727769 | − | 0.685822i | \(-0.759443\pi\) | ||
0.727769 | − | 0.685822i | \(-0.240557\pi\) | |||||||
\(104\) | 7.82090e24 | 0.479005 | ||||||||
\(105\) | 5.15105e24 | − | 6.32002e24i | 0.279917 | − | 0.343441i | ||||
\(106\) | 2.21255e25 | 1.06799 | ||||||||
\(107\) | 6.60004e24i | 0.283302i | 0.989917 | + | 0.141651i | \(0.0452411\pi\) | ||||
−0.989917 | + | 0.141651i | \(0.954759\pi\) | |||||||
\(108\) | 6.42983e24i | 0.245699i | ||||||||
\(109\) | 6.35443e24 | 0.216394 | 0.108197 | − | 0.994129i | \(-0.465492\pi\) | ||||
0.108197 | + | 0.994129i | \(0.465492\pi\) | |||||||
\(110\) | 1.04692e25 | + | 8.53277e24i | 0.318056 | + | 0.259228i | ||||
\(111\) | 8.25735e24 | 0.224029 | ||||||||
\(112\) | − | 1.79888e25i | − | 0.436291i | ||||||
\(113\) | − | 5.12661e25i | − | 1.11263i | −0.830973 | − | 0.556313i | \(-0.812215\pi\) | ||
0.830973 | − | 0.556313i | \(-0.187785\pi\) | |||||||
\(114\) | 8.08791e24 | 0.157226 | ||||||||
\(115\) | −6.42907e24 | − | 5.23994e24i | −0.112054 | − | 0.0913278i | ||||
\(116\) | −2.74073e25 | −0.428688 | ||||||||
\(117\) | − | 9.02138e25i | − | 1.26750i | ||||||
\(118\) | − | 4.63775e25i | − | 0.585844i | ||||||
\(119\) | 6.08759e25 | 0.692004 | ||||||||
\(120\) | −5.53878e24 | + | 6.79573e24i | −0.0567085 | + | 0.0695778i | ||||
\(121\) | −7.18647e25 | −0.663282 | ||||||||
\(122\) | 1.16180e26i | 0.967460i | ||||||||
\(123\) | 5.51368e25i | 0.414598i | ||||||||
\(124\) | 1.31276e26 | 0.892099 | ||||||||
\(125\) | 1.44255e26 | + | 7.52351e25i | 0.886656 | + | 0.462429i | ||||
\(126\) | −2.07500e26 | −1.15448 | ||||||||
\(127\) | 1.52068e26i | 0.766462i | 0.923653 | + | 0.383231i | \(0.125189\pi\) | ||||
−0.923653 | + | 0.383231i | \(0.874811\pi\) | |||||||
\(128\) | 1.93428e25i | 0.0883883i | ||||||||
\(129\) | −7.70794e24 | −0.0319571 | ||||||||
\(130\) | 1.60778e26 | − | 1.97264e26i | 0.605248 | − | 0.742602i | ||||
\(131\) | −4.54456e26 | −1.55454 | −0.777268 | − | 0.629170i | \(-0.783395\pi\) | ||||
−0.777268 | + | 0.629170i | \(0.783395\pi\) | |||||||
\(132\) | 2.36814e25i | 0.0736602i | ||||||||
\(133\) | 5.39999e26i | 1.52844i | ||||||||
\(134\) | −4.75940e26 | −1.22671 | ||||||||
\(135\) | 1.62178e26 | + | 1.32181e26i | 0.380907 | + | 0.310453i | ||||
\(136\) | −6.54581e25 | −0.140193 | ||||||||
\(137\) | 5.90117e25i | 0.115327i | 0.998336 | + | 0.0576635i | \(0.0183651\pi\) | ||||
−0.998336 | + | 0.0576635i | \(0.981635\pi\) | |||||||
\(138\) | − | 1.45426e25i | − | 0.0259510i | ||||||
\(139\) | 1.48479e26 | 0.242091 | 0.121046 | − | 0.992647i | \(-0.461375\pi\) | ||||
0.121046 | + | 0.992647i | \(0.461375\pi\) | |||||||
\(140\) | −4.53725e26 | − | 3.69803e26i | −0.676383 | − | 0.551277i | ||||
\(141\) | 4.26921e25 | 0.0582249 | ||||||||
\(142\) | − | 4.69405e26i | − | 0.586062i | ||||||
\(143\) | − | 6.87414e26i | − | 0.786173i | ||||||
\(144\) | 2.23119e26 | 0.233886 | ||||||||
\(145\) | −5.63424e26 | + | 6.91286e26i | −0.541670 | + | 0.664596i | ||||
\(146\) | 3.62544e25 | 0.0319853 | ||||||||
\(147\) | 6.41088e26i | 0.519339i | ||||||||
\(148\) | − | 5.92809e26i | − | 0.441208i | ||||||
\(149\) | 5.34888e26 | 0.365961 | 0.182981 | − | 0.983117i | \(-0.441425\pi\) | ||||
0.182981 | + | 0.983117i | \(0.441425\pi\) | |||||||
\(150\) | 5.75436e25 | + | 2.79406e26i | 0.0362123 | + | 0.175831i | ||||
\(151\) | 2.12275e27 | 1.22938 | 0.614691 | − | 0.788768i | \(-0.289281\pi\) | ||||
0.614691 | + | 0.788768i | \(0.289281\pi\) | |||||||
\(152\) | − | 5.80645e26i | − | 0.309646i | ||||||
\(153\) | 7.55056e26i | 0.370968i | ||||||||
\(154\) | −1.58112e27 | −0.716069 | ||||||||
\(155\) | 2.69869e27 | − | 3.31112e27i | 1.12721 | − | 1.38302i | ||||
\(156\) | 4.46213e26 | 0.171983 | ||||||||
\(157\) | 1.66162e26i | 0.0591271i | 0.999563 | + | 0.0295636i | \(0.00941174\pi\) | ||||
−0.999563 | + | 0.0295636i | \(0.990588\pi\) | |||||||
\(158\) | 8.90456e26i | 0.292684i | ||||||||
\(159\) | 1.26234e27 | 0.383454 | ||||||||
\(160\) | 4.87878e26 | + | 3.97638e26i | 0.137029 | + | 0.111683i | ||||
\(161\) | 9.70956e26 | 0.252276 | ||||||||
\(162\) | − | 2.38413e27i | − | 0.573314i | ||||||
\(163\) | − | 2.97944e27i | − | 0.663421i | −0.943381 | − | 0.331710i | \(-0.892374\pi\) | ||
0.943381 | − | 0.331710i | \(-0.107626\pi\) | |||||||
\(164\) | 3.95837e27 | 0.816522 | ||||||||
\(165\) | 5.97308e26 | + | 4.86828e26i | 0.114195 | + | 0.0930735i | ||||
\(166\) | −2.64786e26 | −0.0469401 | ||||||||
\(167\) | 8.95870e27i | 1.47329i | 0.676278 | + | 0.736647i | \(0.263592\pi\) | ||||
−0.676278 | + | 0.736647i | \(0.736408\pi\) | |||||||
\(168\) | − | 1.02633e27i | − | 0.156647i | ||||||
\(169\) | −5.89610e27 | −0.835567 | ||||||||
\(170\) | −1.34565e27 | + | 1.65103e27i | −0.177142 | + | 0.217342i | ||||
\(171\) | −6.69772e27 | −0.819361 | ||||||||
\(172\) | 5.53367e26i | 0.0629372i | ||||||||
\(173\) | − | 1.40879e28i | − | 1.49028i | −0.666905 | − | 0.745142i | \(-0.732381\pi\) | ||
0.666905 | − | 0.745142i | \(-0.267619\pi\) | |||||||
\(174\) | −1.56369e27 | −0.153917 | ||||||||
\(175\) | −1.86549e28 | + | 3.84197e27i | −1.70929 | + | 0.352029i | ||||
\(176\) | 1.70013e27 | 0.145068 | ||||||||
\(177\) | − | 2.64602e27i | − | 0.210342i | ||||||
\(178\) | 1.46365e28i | 1.08440i | ||||||||
\(179\) | −9.19738e27 | −0.635333 | −0.317667 | − | 0.948202i | \(-0.602899\pi\) | ||||
−0.317667 | + | 0.948202i | \(0.602899\pi\) | |||||||
\(180\) | 4.58674e27 | − | 5.62765e27i | 0.295528 | − | 0.362594i | ||||
\(181\) | 2.77373e28 | 1.66756 | 0.833782 | − | 0.552094i | \(-0.186171\pi\) | ||||
0.833782 | + | 0.552094i | \(0.186171\pi\) | |||||||
\(182\) | 2.97920e28i | 1.67189i | ||||||||
\(183\) | 6.62852e27i | 0.347358i | ||||||||
\(184\) | −1.04404e27 | −0.0511087 | ||||||||
\(185\) | −1.49522e28 | − | 1.21866e28i | −0.684006 | − | 0.557490i | ||||
\(186\) | 7.48979e27 | 0.320301 | ||||||||
\(187\) | 5.75341e27i | 0.230094i | ||||||||
\(188\) | − | 3.06494e27i | − | 0.114670i | ||||||
\(189\) | −2.44930e28 | −0.857570 | ||||||||
\(190\) | −1.46454e28 | − | 1.19366e28i | −0.480045 | − | 0.391255i | ||||
\(191\) | −1.68120e28 | −0.516064 | −0.258032 | − | 0.966136i | \(-0.583074\pi\) | ||||
−0.258032 | + | 0.966136i | \(0.583074\pi\) | |||||||
\(192\) | 1.10358e27i | 0.0317351i | ||||||||
\(193\) | 2.97967e28i | 0.802975i | 0.915865 | + | 0.401487i | \(0.131507\pi\) | ||||
−0.915865 | + | 0.401487i | \(0.868493\pi\) | |||||||
\(194\) | 1.02150e28 | 0.258057 | ||||||||
\(195\) | 9.17299e27 | − | 1.12547e28i | 0.217309 | − | 0.266625i | ||||
\(196\) | 4.60248e28 | 1.02280 | ||||||||
\(197\) | − | 8.93281e27i | − | 0.186277i | −0.995653 | − | 0.0931387i | \(-0.970310\pi\) | ||
0.995653 | − | 0.0931387i | \(-0.0296900\pi\) | |||||||
\(198\) | − | 1.96109e28i | − | 0.383869i | ||||||
\(199\) | 9.58646e28 | 1.76196 | 0.880978 | − | 0.473157i | \(-0.156886\pi\) | ||||
0.880978 | + | 0.473157i | \(0.156886\pi\) | |||||||
\(200\) | 2.00590e28 | − | 4.13116e27i | 0.346286 | − | 0.0713176i | ||||
\(201\) | −2.71542e28 | −0.440440 | ||||||||
\(202\) | 5.52159e28i | 0.841728i | ||||||||
\(203\) | − | 1.04402e29i | − | 1.49626i | ||||||
\(204\) | −3.73464e27 | −0.0503352 | ||||||||
\(205\) | 8.13738e28 | − | 9.98406e28i | 1.03172 | − | 1.26585i | ||||
\(206\) | −8.12956e28 | −0.969899 | ||||||||
\(207\) | 1.20430e28i | 0.135240i | ||||||||
\(208\) | − | 3.20344e28i | − | 0.338708i | ||||||
\(209\) | −5.10355e28 | −0.508211 | ||||||||
\(210\) | −2.58868e28 | − | 2.10987e28i | −0.242850 | − | 0.197931i | ||||
\(211\) | 5.69613e27 | 0.0503558 | 0.0251779 | − | 0.999683i | \(-0.491985\pi\) | ||||
0.0251779 | + | 0.999683i | \(0.491985\pi\) | |||||||
\(212\) | − | 9.06259e28i | − | 0.755186i | ||||||
\(213\) | − | 2.67814e28i | − | 0.210420i | ||||||
\(214\) | 2.70338e28 | 0.200325 | ||||||||
\(215\) | 1.39574e28 | + | 1.13758e28i | 0.0975716 | + | 0.0795245i | ||||
\(216\) | 2.63366e28 | 0.173735 | ||||||||
\(217\) | 5.00065e29i | 3.11372i | ||||||||
\(218\) | − | 2.60278e28i | − | 0.153014i | ||||||
\(219\) | 2.06846e27 | 0.0114840 | ||||||||
\(220\) | 3.49502e28 | − | 4.28818e28i | 0.183302 | − | 0.224900i | ||||
\(221\) | 1.08408e29 | 0.537226 | ||||||||
\(222\) | − | 3.38221e28i | − | 0.158412i | ||||||
\(223\) | − | 5.84548e28i | − | 0.258827i | −0.991591 | − | 0.129413i | \(-0.958691\pi\) | ||
0.991591 | − | 0.129413i | \(-0.0413094\pi\) | |||||||
\(224\) | −7.36821e28 | −0.308505 | ||||||||
\(225\) | −4.76527e28 | − | 2.31380e29i | −0.188715 | − | 0.916313i | ||||
\(226\) | −2.09986e29 | −0.786746 | ||||||||
\(227\) | 5.52270e29i | 1.95807i | 0.203691 | + | 0.979035i | \(0.434706\pi\) | ||||
−0.203691 | + | 0.979035i | \(0.565294\pi\) | |||||||
\(228\) | − | 3.31281e28i | − | 0.111176i | ||||||
\(229\) | 5.80273e28 | 0.184369 | 0.0921847 | − | 0.995742i | \(-0.470615\pi\) | ||||
0.0921847 | + | 0.995742i | \(0.470615\pi\) | |||||||
\(230\) | −2.14628e28 | + | 2.63335e28i | −0.0645785 | + | 0.0792338i | ||||
\(231\) | −9.02088e28 | −0.257098 | ||||||||
\(232\) | 1.12260e29i | 0.303128i | ||||||||
\(233\) | 1.93762e29i | 0.495816i | 0.968784 | + | 0.247908i | \(0.0797430\pi\) | ||||
−0.968784 | + | 0.247908i | \(0.920257\pi\) | |||||||
\(234\) | −3.69516e29 | −0.896261 | ||||||||
\(235\) | −7.73061e28 | − | 6.30073e28i | −0.177773 | − | 0.144892i | ||||
\(236\) | −1.89962e29 | −0.414254 | ||||||||
\(237\) | 5.08040e28i | 0.105086i | ||||||||
\(238\) | − | 2.49348e29i | − | 0.489321i | ||||||
\(239\) | −7.15964e28 | −0.133327 | −0.0666634 | − | 0.997776i | \(-0.521235\pi\) | ||||
−0.0666634 | + | 0.997776i | \(0.521235\pi\) | |||||||
\(240\) | 2.78353e28 | + | 2.26868e28i | 0.0491989 | + | 0.0400990i | ||||
\(241\) | −8.42045e29 | −1.41293 | −0.706467 | − | 0.707746i | \(-0.749712\pi\) | ||||
−0.706467 | + | 0.707746i | \(0.749712\pi\) | |||||||
\(242\) | 2.94358e29i | 0.469011i | ||||||||
\(243\) | − | 4.60746e29i | − | 0.697241i | ||||||
\(244\) | 4.75873e29 | 0.684098 | ||||||||
\(245\) | 9.46152e29 | − | 1.16087e30i | 1.29236 | − | 1.58565i | ||||
\(246\) | 2.25840e29 | 0.293165 | ||||||||
\(247\) | 9.61630e29i | 1.18658i | ||||||||
\(248\) | − | 5.37705e29i | − | 0.630809i | ||||||
\(249\) | −1.51071e28 | −0.0168535 | ||||||||
\(250\) | 3.08163e29 | − | 5.90868e29i | 0.326987 | − | 0.626961i | ||||
\(251\) | −3.23321e28 | −0.0326372 | −0.0163186 | − | 0.999867i | \(-0.505195\pi\) | ||||
−0.0163186 | + | 0.999867i | \(0.505195\pi\) | |||||||
\(252\) | 8.49920e29i | 0.816340i | ||||||||
\(253\) | 9.17654e28i | 0.0838827i | ||||||||
\(254\) | 6.22869e29 | 0.541970 | ||||||||
\(255\) | −7.67746e28 | + | 9.41976e28i | −0.0636012 | + | 0.0780347i | ||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | − | 2.39756e29i | − | 0.180138i | −0.995936 | − | 0.0900689i | \(-0.971291\pi\) | ||
0.995936 | − | 0.0900689i | \(-0.0287087\pi\) | |||||||
\(258\) | 3.15717e28i | 0.0225971i | ||||||||
\(259\) | 2.25817e30 | 1.53996 | ||||||||
\(260\) | −8.07994e29 | − | 6.58545e29i | −0.525099 | − | 0.427975i | ||||
\(261\) | 1.29492e30 | 0.802114 | ||||||||
\(262\) | 1.86145e30i | 1.09922i | ||||||||
\(263\) | − | 2.50236e30i | − | 1.40898i | −0.709716 | − | 0.704488i | \(-0.751177\pi\) | ||
0.709716 | − | 0.704488i | \(-0.248823\pi\) | |||||||
\(264\) | 9.69989e28 | 0.0520856 | ||||||||
\(265\) | −2.28583e30 | − | 1.86303e30i | −1.17077 | − | 0.954218i | ||||
\(266\) | 2.21184e30 | 1.08077 | ||||||||
\(267\) | 8.35070e29i | 0.389343i | ||||||||
\(268\) | 1.94945e30i | 0.867415i | ||||||||
\(269\) | −3.20998e30 | −1.36332 | −0.681662 | − | 0.731667i | \(-0.738743\pi\) | ||||
−0.681662 | + | 0.731667i | \(0.738743\pi\) | |||||||
\(270\) | 5.41413e29 | − | 6.64280e29i | 0.219524 | − | 0.269342i | ||||
\(271\) | 1.88885e30 | 0.731277 | 0.365638 | − | 0.930757i | \(-0.380851\pi\) | ||||
0.365638 | + | 0.930757i | \(0.380851\pi\) | |||||||
\(272\) | 2.68116e29i | 0.0991316i | ||||||||
\(273\) | 1.69975e30i | 0.600277i | ||||||||
\(274\) | 2.41712e29 | 0.0815485 | ||||||||
\(275\) | −3.63106e29 | − | 1.76308e30i | −0.117051 | − | 0.568346i | ||||
\(276\) | −5.95666e28 | −0.0183501 | ||||||||
\(277\) | 2.14925e29i | 0.0632835i | 0.999499 | + | 0.0316417i | \(0.0100736\pi\) | ||||
−0.999499 | + | 0.0316417i | \(0.989926\pi\) | |||||||
\(278\) | − | 6.08169e29i | − | 0.171184i | ||||||
\(279\) | −6.20241e30 | −1.66920 | ||||||||
\(280\) | −1.51471e30 | + | 1.85846e30i | −0.389812 | + | 0.478275i | ||||
\(281\) | −1.34905e30 | −0.332048 | −0.166024 | − | 0.986122i | \(-0.553093\pi\) | ||||
−0.166024 | + | 0.986122i | \(0.553093\pi\) | |||||||
\(282\) | − | 1.74867e29i | − | 0.0411712i | ||||||
\(283\) | − | 7.01801e30i | − | 1.58082i | −0.612576 | − | 0.790412i | \(-0.709867\pi\) | ||
0.612576 | − | 0.790412i | \(-0.290133\pi\) | |||||||
\(284\) | −1.92268e30 | −0.414408 | ||||||||
\(285\) | −8.35578e29 | − | 6.81028e29i | −0.172356 | − | 0.140477i | ||||
\(286\) | −2.81565e30 | −0.555908 | ||||||||
\(287\) | 1.50785e31i | 2.84993i | ||||||||
\(288\) | − | 9.13894e29i | − | 0.165382i | ||||||
\(289\) | 4.86329e30 | 0.842767 | ||||||||
\(290\) | 2.83151e30 | + | 2.30778e30i | 0.469940 | + | 0.383019i | ||||
\(291\) | 5.82805e29 | 0.0926533 | ||||||||
\(292\) | − | 1.48498e29i | − | 0.0226170i | ||||||
\(293\) | 4.23132e30i | 0.617491i | 0.951145 | + | 0.308746i | \(0.0999092\pi\) | ||||
−0.951145 | + | 0.308746i | \(0.900091\pi\) | |||||||
\(294\) | 2.62590e30 | 0.367228 | ||||||||
\(295\) | −3.90513e30 | + | 4.79136e30i | −0.523433 | + | 0.642219i | ||||
\(296\) | −2.42815e30 | −0.311981 | ||||||||
\(297\) | − | 2.31484e30i | − | 0.285145i | ||||||
\(298\) | − | 2.19090e30i | − | 0.258774i | ||||||
\(299\) | 1.72908e30 | 0.195850 | ||||||||
\(300\) | 1.14445e30 | − | 2.35699e29i | 0.124331 | − | 0.0256060i | ||||
\(301\) | −2.10793e30 | −0.219672 | ||||||||
\(302\) | − | 8.69478e30i | − | 0.869304i | ||||||
\(303\) | 3.15028e30i | 0.302215i | ||||||||
\(304\) | −2.37832e30 | −0.218953 | ||||||||
\(305\) | 9.78272e30 | − | 1.20028e31i | 0.864394 | − | 1.06056i | ||||
\(306\) | 3.09271e30 | 0.262314 | ||||||||
\(307\) | − | 3.15394e30i | − | 0.256817i | −0.991721 | − | 0.128409i | \(-0.959013\pi\) | ||
0.991721 | − | 0.128409i | \(-0.0409869\pi\) | |||||||
\(308\) | 6.47625e30i | 0.506337i | ||||||||
\(309\) | −4.63823e30 | −0.348234 | ||||||||
\(310\) | −1.35624e31 | − | 1.10538e31i | −0.977944 | − | 0.797061i | ||||
\(311\) | 1.98559e31 | 1.37526 | 0.687628 | − | 0.726063i | \(-0.258652\pi\) | ||||
0.687628 | + | 0.726063i | \(0.258652\pi\) | |||||||
\(312\) | − | 1.82769e30i | − | 0.121610i | ||||||
\(313\) | 5.47200e29i | 0.0349818i | 0.999847 | + | 0.0174909i | \(0.00556781\pi\) | ||||
−0.999847 | + | 0.0174909i | \(0.994432\pi\) | |||||||
\(314\) | 6.80601e29 | 0.0418092 | ||||||||
\(315\) | 2.14373e31 | + | 1.74722e31i | 1.26557 | + | 1.03149i | ||||
\(316\) | 3.64731e30 | 0.206959 | ||||||||
\(317\) | − | 2.18550e31i | − | 1.19209i | −0.802950 | − | 0.596046i | \(-0.796737\pi\) | ||
0.802950 | − | 0.596046i | \(-0.203263\pi\) | |||||||
\(318\) | − | 5.17056e30i | − | 0.271143i | ||||||
\(319\) | 9.86707e30 | 0.497513 | ||||||||
\(320\) | 1.62873e30 | − | 1.99835e30i | 0.0789721 | − | 0.0968938i | ||||
\(321\) | 1.54238e30 | 0.0719249 | ||||||||
\(322\) | − | 3.97704e30i | − | 0.178386i | ||||||
\(323\) | − | 8.04849e30i | − | 0.347282i | ||||||
\(324\) | −9.76540e30 | −0.405394 | ||||||||
\(325\) | −3.32205e31 | + | 6.84177e30i | −1.32698 | + | 0.273292i | ||||
\(326\) | −1.22038e31 | −0.469109 | ||||||||
\(327\) | − | 1.48499e30i | − | 0.0549383i | ||||||
\(328\) | − | 1.62135e31i | − | 0.577368i | ||||||
\(329\) | 1.16752e31 | 0.400236 | ||||||||
\(330\) | 1.99405e30 | − | 2.44657e30i | 0.0658129 | − | 0.0807484i | ||||
\(331\) | −2.93057e31 | −0.931325 | −0.465663 | − | 0.884962i | \(-0.654184\pi\) | ||||
−0.465663 | + | 0.884962i | \(0.654184\pi\) | |||||||
\(332\) | 1.08456e30i | 0.0331917i | ||||||||
\(333\) | 2.80086e31i | 0.825540i | ||||||||
\(334\) | 3.66949e31 | 1.04178 | ||||||||
\(335\) | 4.91703e31 | + | 4.00756e31i | 1.34475 | + | 1.09602i | ||||
\(336\) | −4.20385e30 | −0.110766 | ||||||||
\(337\) | − | 4.60143e31i | − | 1.16821i | −0.811680 | − | 0.584103i | \(-0.801447\pi\) | ||
0.811680 | − | 0.584103i | \(-0.198553\pi\) | |||||||
\(338\) | 2.41504e31i | 0.590835i | ||||||||
\(339\) | −1.19805e31 | −0.282474 | ||||||||
\(340\) | 6.76261e30 | + | 5.51178e30i | 0.153684 | + | 0.125258i | ||||
\(341\) | −4.72613e31 | −1.03532 | ||||||||
\(342\) | 2.74338e31i | 0.579376i | ||||||||
\(343\) | 8.96148e31i | 1.82475i | ||||||||
\(344\) | 2.26659e30 | 0.0445033 | ||||||||
\(345\) | −1.22454e30 | + | 1.50243e30i | −0.0231864 | + | 0.0284482i | ||||
\(346\) | −5.77039e31 | −1.05379 | ||||||||
\(347\) | − | 7.38077e31i | − | 1.30012i | −0.759883 | − | 0.650060i | \(-0.774744\pi\) | ||
0.759883 | − | 0.650060i | \(-0.225256\pi\) | |||||||
\(348\) | 6.40489e30i | 0.108836i | ||||||||
\(349\) | −3.56553e31 | −0.584530 | −0.292265 | − | 0.956337i | \(-0.594409\pi\) | ||||
−0.292265 | + | 0.956337i | \(0.594409\pi\) | |||||||
\(350\) | 1.57367e31 | + | 7.64103e31i | 0.248922 | + | 1.20865i | ||||
\(351\) | −4.36171e31 | −0.665760 | ||||||||
\(352\) | − | 6.96372e30i | − | 0.102579i | ||||||
\(353\) | − | 8.69355e31i | − | 1.23599i | −0.786184 | − | 0.617993i | \(-0.787946\pi\) | ||
0.786184 | − | 0.617993i | \(-0.212054\pi\) | |||||||
\(354\) | −1.08381e31 | −0.148735 | ||||||||
\(355\) | −3.95254e31 | + | 4.84952e31i | −0.523627 | + | 0.642457i | ||||
\(356\) | 5.99512e31 | 0.766783 | ||||||||
\(357\) | − | 1.42263e31i | − | 0.175686i | ||||||
\(358\) | 3.76725e31i | 0.449248i | ||||||||
\(359\) | −2.26294e30 | −0.0260611 | −0.0130305 | − | 0.999915i | \(-0.504148\pi\) | ||||
−0.0130305 | + | 0.999915i | \(0.504148\pi\) | |||||||
\(360\) | −2.30508e31 | − | 1.87873e31i | −0.256393 | − | 0.208970i | ||||
\(361\) | −2.16825e31 | −0.232954 | ||||||||
\(362\) | − | 1.13612e32i | − | 1.17915i | ||||||
\(363\) | 1.67943e31i | 0.168395i | ||||||||
\(364\) | 1.22028e32 | 1.18220 | ||||||||
\(365\) | −3.74552e30 | − | 3.05274e30i | −0.0350632 | − | 0.0285778i | ||||
\(366\) | 2.71504e31 | 0.245619 | ||||||||
\(367\) | − | 3.34192e31i | − | 0.292193i | −0.989270 | − | 0.146096i | \(-0.953329\pi\) | ||
0.989270 | − | 0.146096i | \(-0.0466710\pi\) | |||||||
\(368\) | 4.27639e30i | 0.0361393i | ||||||||
\(369\) | −1.87022e32 | −1.52779 | ||||||||
\(370\) | −4.99165e31 | + | 6.12444e31i | −0.394205 | + | 0.483665i | ||||
\(371\) | 3.45219e32 | 2.63585 | ||||||||
\(372\) | − | 3.06782e31i | − | 0.226487i | ||||||
\(373\) | − | 1.79027e32i | − | 1.27808i | −0.769172 | − | 0.639041i | \(-0.779331\pi\) | ||
0.769172 | − | 0.639041i | \(-0.220669\pi\) | |||||||
\(374\) | 2.35660e31 | 0.162701 | ||||||||
\(375\) | 1.75819e31 | − | 3.37113e31i | 0.117402 | − | 0.225105i | ||||
\(376\) | −1.25540e31 | −0.0810839 | ||||||||
\(377\) | − | 1.85919e32i | − | 1.16160i | ||||||
\(378\) | 1.00323e32i | 0.606393i | ||||||||
\(379\) | 9.45760e31 | 0.553084 | 0.276542 | − | 0.961002i | \(-0.410812\pi\) | ||||
0.276542 | + | 0.961002i | \(0.410812\pi\) | |||||||
\(380\) | −4.88922e31 | + | 5.99876e31i | −0.276659 | + | 0.339443i | ||||
\(381\) | 3.55371e31 | 0.194590 | ||||||||
\(382\) | 6.88621e31i | 0.364912i | ||||||||
\(383\) | 2.01782e32i | 1.03490i | 0.855714 | + | 0.517449i | \(0.173118\pi\) | ||||
−0.855714 | + | 0.517449i | \(0.826882\pi\) | |||||||
\(384\) | 4.52028e30 | 0.0224401 | ||||||||
\(385\) | 1.63348e32 | + | 1.33135e32i | 0.784975 | + | 0.639784i | ||||
\(386\) | 1.22047e32 | 0.567789 | ||||||||
\(387\) | − | 2.61450e31i | − | 0.117761i | ||||||
\(388\) | − | 4.18406e31i | − | 0.182474i | ||||||
\(389\) | −1.16247e32 | −0.490921 | −0.245460 | − | 0.969407i | \(-0.578939\pi\) | ||||
−0.245460 | + | 0.969407i | \(0.578939\pi\) | |||||||
\(390\) | −4.60992e31 | − | 3.75726e31i | −0.188532 | − | 0.153661i | ||||
\(391\) | −1.44717e31 | −0.0573207 | ||||||||
\(392\) | − | 1.88518e32i | − | 0.723230i | ||||||
\(393\) | 1.06203e32i | 0.394667i | ||||||||
\(394\) | −3.65888e31 | −0.131718 | ||||||||
\(395\) | 7.49793e31 | − | 9.19949e31i | 0.261504 | − | 0.320849i | ||||
\(396\) | −8.03262e31 | −0.271436 | ||||||||
\(397\) | − | 2.03760e32i | − | 0.667172i | −0.942720 | − | 0.333586i | \(-0.891741\pi\) | ||
0.942720 | − | 0.333586i | \(-0.108259\pi\) | |||||||
\(398\) | − | 3.92662e32i | − | 1.24589i | ||||||
\(399\) | 1.26194e32 | 0.388041 | ||||||||
\(400\) | −1.69212e31 | − | 8.21617e31i | −0.0504291 | − | 0.244861i | ||||
\(401\) | −1.67418e32 | −0.483613 | −0.241806 | − | 0.970324i | \(-0.577740\pi\) | ||||
−0.241806 | + | 0.970324i | \(0.577740\pi\) | |||||||
\(402\) | 1.11224e32i | 0.311438i | ||||||||
\(403\) | 8.90515e32i | 2.41729i | ||||||||
\(404\) | 2.26164e32 | 0.595192 | ||||||||
\(405\) | −2.00752e32 | + | 2.46310e32i | −0.512237 | + | 0.628483i | ||||
\(406\) | −4.27630e32 | −1.05802 | ||||||||
\(407\) | 2.13421e32i | 0.512043i | ||||||||
\(408\) | 1.52971e31i | 0.0355924i | ||||||||
\(409\) | −7.52295e32 | −1.69765 | −0.848823 | − | 0.528678i | \(-0.822688\pi\) | ||||
−0.848823 | + | 0.528678i | \(0.822688\pi\) | |||||||
\(410\) | −4.08947e32 | − | 3.33307e32i | −0.895094 | − | 0.729535i | ||||
\(411\) | 1.37906e31 | 0.0292793 | ||||||||
\(412\) | 3.32987e32i | 0.685822i | ||||||||
\(413\) | − | 7.23618e32i | − | 1.44589i | ||||||
\(414\) | 4.93280e31 | 0.0956288 | ||||||||
\(415\) | 2.73556e31 | + | 2.22959e31i | 0.0514571 | + | 0.0419395i | ||||
\(416\) | −1.31213e32 | −0.239503 | ||||||||
\(417\) | − | 3.46984e31i | − | 0.0614623i | ||||||
\(418\) | 2.09041e32i | 0.359359i | ||||||||
\(419\) | 6.25496e31 | 0.104364 | 0.0521818 | − | 0.998638i | \(-0.483382\pi\) | ||||
0.0521818 | + | 0.998638i | \(0.483382\pi\) | |||||||
\(420\) | −8.64203e31 | + | 1.06032e32i | −0.139959 | + | 0.171721i | ||||
\(421\) | 8.02159e32 | 1.26106 | 0.630528 | − | 0.776167i | \(-0.282838\pi\) | ||||
0.630528 | + | 0.776167i | \(0.282838\pi\) | |||||||
\(422\) | − | 2.33314e31i | − | 0.0356069i | ||||||
\(423\) | 1.44810e32i | 0.214558i | ||||||||
\(424\) | −3.71204e32 | −0.533997 | ||||||||
\(425\) | 2.78044e32 | − | 5.72631e31i | 0.388375 | − | 0.0799859i | ||||
\(426\) | −1.09697e32 | −0.148790 | ||||||||
\(427\) | 1.81273e33i | 2.38773i | ||||||||
\(428\) | − | 1.10730e32i | − | 0.141651i | ||||||
\(429\) | −1.60644e32 | −0.199594 | ||||||||
\(430\) | 4.65953e31 | − | 5.71695e31i | 0.0562323 | − | 0.0689936i | ||||
\(431\) | 1.32299e33 | 1.55092 | 0.775460 | − | 0.631397i | \(-0.217518\pi\) | ||||
0.775460 | + | 0.631397i | \(0.217518\pi\) | |||||||
\(432\) | − | 1.07875e32i | − | 0.122849i | ||||||
\(433\) | − | 1.44206e33i | − | 1.59546i | −0.603015 | − | 0.797730i | \(-0.706034\pi\) | ||
0.603015 | − | 0.797730i | \(-0.293966\pi\) | |||||||
\(434\) | 2.04827e33 | 2.20173 | ||||||||
\(435\) | 1.61549e32 | + | 1.31668e32i | 0.168728 | + | 0.137520i | ||||
\(436\) | −1.06610e32 | −0.108197 | ||||||||
\(437\) | − | 1.28371e32i | − | 0.126605i | ||||||
\(438\) | − | 8.47240e30i | − | 0.00812045i | ||||||
\(439\) | −9.88019e32 | −0.920362 | −0.460181 | − | 0.887825i | \(-0.652215\pi\) | ||||
−0.460181 | + | 0.887825i | \(0.652215\pi\) | |||||||
\(440\) | −1.75644e32 | − | 1.43156e32i | −0.159028 | − | 0.129614i | ||||
\(441\) | −2.17454e33 | −1.91375 | ||||||||
\(442\) | − | 4.44038e32i | − | 0.379876i | ||||||
\(443\) | − | 6.78172e32i | − | 0.564018i | −0.959412 | − | 0.282009i | \(-0.908999\pi\) | ||
0.959412 | − | 0.282009i | \(-0.0910008\pi\) | |||||||
\(444\) | −1.38535e32 | −0.112014 | ||||||||
\(445\) | 1.23244e33 | − | 1.51213e33i | 0.968872 | − | 1.18874i | ||||
\(446\) | −2.39431e32 | −0.183018 | ||||||||
\(447\) | − | 1.25000e32i | − | 0.0929104i | ||||||
\(448\) | 3.01802e32i | 0.218146i | ||||||||
\(449\) | 1.40094e33 | 0.984784 | 0.492392 | − | 0.870374i | \(-0.336123\pi\) | ||||
0.492392 | + | 0.870374i | \(0.336123\pi\) | |||||||
\(450\) | −9.47732e32 | + | 1.95185e32i | −0.647931 | + | 0.133442i | ||||
\(451\) | −1.42507e33 | −0.947613 | ||||||||
\(452\) | 8.60102e32i | 0.556313i | ||||||||
\(453\) | − | 4.96071e32i | − | 0.312116i | ||||||
\(454\) | 2.26210e33 | 1.38456 | ||||||||
\(455\) | 2.50858e33 | − | 3.07787e33i | 1.49378 | − | 1.83277i | ||||
\(456\) | −1.35693e32 | −0.0786132 | ||||||||
\(457\) | 2.87797e33i | 1.62231i | 0.584830 | + | 0.811156i | \(0.301161\pi\) | ||||
−0.584830 | + | 0.811156i | \(0.698839\pi\) | |||||||
\(458\) | − | 2.37680e32i | − | 0.130369i | ||||||
\(459\) | 3.65059e32 | 0.194852 | ||||||||
\(460\) | 1.07862e32 | + | 8.79115e31i | 0.0560268 | + | 0.0456639i | ||||
\(461\) | −4.62750e32 | −0.233930 | −0.116965 | − | 0.993136i | \(-0.537316\pi\) | ||||
−0.116965 | + | 0.993136i | \(0.537316\pi\) | |||||||
\(462\) | 3.69495e32i | 0.181796i | ||||||||
\(463\) | − | 2.53220e32i | − | 0.121265i | −0.998160 | − | 0.0606325i | \(-0.980688\pi\) | ||
0.998160 | − | 0.0606325i | \(-0.0193118\pi\) | |||||||
\(464\) | 4.59818e32 | 0.214344 | ||||||||
\(465\) | −7.73786e32 | − | 6.30664e32i | −0.351123 | − | 0.286178i | ||||
\(466\) | 7.93650e32 | 0.350595 | ||||||||
\(467\) | − | 1.56052e33i | − | 0.671134i | −0.942016 | − | 0.335567i | \(-0.891072\pi\) | ||
0.942016 | − | 0.335567i | \(-0.108928\pi\) | |||||||
\(468\) | 1.51354e33i | 0.633752i | ||||||||
\(469\) | −7.42598e33 | −3.02757 | ||||||||
\(470\) | −2.58078e32 | + | 3.16646e32i | −0.102454 | + | 0.125704i | ||||
\(471\) | 3.88309e31 | 0.0150112 | ||||||||
\(472\) | 7.78085e32i | 0.292922i | ||||||||
\(473\) | − | 1.99221e32i | − | 0.0730416i | ||||||
\(474\) | 2.08093e32 | 0.0743068 | ||||||||
\(475\) | 5.07952e32 | + | 2.46638e33i | 0.176666 | + | 0.857809i | ||||
\(476\) | −1.02133e33 | −0.346002 | ||||||||
\(477\) | 4.28182e33i | 1.41302i | ||||||||
\(478\) | 2.93259e32i | 0.0942763i | ||||||||
\(479\) | −7.23567e32 | −0.226613 | −0.113306 | − | 0.993560i | \(-0.536144\pi\) | ||||
−0.113306 | + | 0.993560i | \(0.536144\pi\) | |||||||
\(480\) | 9.29252e31 | − | 1.14013e32i | 0.0283543 | − | 0.0347889i | ||||
\(481\) | 4.02135e33 | 1.19553 | ||||||||
\(482\) | 3.44901e33i | 0.999096i | ||||||||
\(483\) | − | 2.26905e32i | − | 0.0640480i | ||||||
\(484\) | 1.20569e33 | 0.331641 | ||||||||
\(485\) | −1.05533e33 | − | 8.60134e32i | −0.282890 | − | 0.230566i | ||||
\(486\) | −1.88721e33 | −0.493024 | ||||||||
\(487\) | 3.11091e33i | 0.792091i | 0.918231 | + | 0.396046i | \(0.129618\pi\) | ||||
−0.918231 | + | 0.396046i | \(0.870382\pi\) | |||||||
\(488\) | − | 1.94918e33i | − | 0.483730i | ||||||
\(489\) | −6.96273e32 | −0.168430 | ||||||||
\(490\) | −4.75492e33 | − | 3.87544e33i | −1.12122 | − | 0.913839i | ||||
\(491\) | 3.51132e33 | 0.807146 | 0.403573 | − | 0.914948i | \(-0.367768\pi\) | ||||
0.403573 | + | 0.914948i | \(0.367768\pi\) | |||||||
\(492\) | − | 9.25042e32i | − | 0.207299i | ||||||
\(493\) | 1.55607e33i | 0.339972i | ||||||||
\(494\) | 3.93883e33 | 0.839037 | ||||||||
\(495\) | −1.65130e33 | + | 2.02604e33i | −0.342974 | + | 0.420808i | ||||
\(496\) | −2.20244e33 | −0.446050 | ||||||||
\(497\) | − | 7.32402e33i | − | 1.44642i | ||||||
\(498\) | 6.18787e31i | 0.0119172i | ||||||||
\(499\) | −8.78119e33 | −1.64929 | −0.824644 | − | 0.565652i | \(-0.808624\pi\) | ||||
−0.824644 | + | 0.565652i | \(0.808624\pi\) | |||||||
\(500\) | −2.42019e33 | − | 1.26224e33i | −0.443328 | − | 0.231215i | ||||
\(501\) | 2.09358e33 | 0.374041 | ||||||||
\(502\) | 1.32432e32i | 0.0230780i | ||||||||
\(503\) | 1.68186e33i | 0.285883i | 0.989731 | + | 0.142942i | \(0.0456562\pi\) | ||||
−0.989731 | + | 0.142942i | \(0.954344\pi\) | |||||||
\(504\) | 3.48127e33 | 0.577240 | ||||||||
\(505\) | 4.64936e33 | − | 5.70447e33i | 0.752057 | − | 0.922727i | ||||
\(506\) | 3.75871e32 | 0.0593140 | ||||||||
\(507\) | 1.37788e33i | 0.212134i | ||||||||
\(508\) | − | 2.55127e33i | − | 0.383231i | ||||||
\(509\) | 5.67785e33 | 0.832169 | 0.416084 | − | 0.909326i | \(-0.363402\pi\) | ||||
0.416084 | + | 0.909326i | \(0.363402\pi\) | |||||||
\(510\) | 3.85833e32 | + | 3.14469e32i | 0.0551789 | + | 0.0449728i | ||||
\(511\) | 5.65670e32 | 0.0789409 | ||||||||
\(512\) | − | 3.24519e32i | − | 0.0441942i | ||||||
\(513\) | 3.23825e33i | 0.430372i | ||||||||
\(514\) | −9.82039e32 | −0.127377 | ||||||||
\(515\) | 8.39881e33 | + | 6.84535e33i | 1.06323 | + | 0.866573i | ||||
\(516\) | 1.29318e32 | 0.0159785 | ||||||||
\(517\) | 1.10343e33i | 0.133080i | ||||||||
\(518\) | − | 9.24948e33i | − | 1.08892i | ||||||
\(519\) | −3.29224e33 | −0.378355 | ||||||||
\(520\) | −2.69740e33 | + | 3.30954e33i | −0.302624 | + | 0.371301i | ||||
\(521\) | 8.57848e33 | 0.939591 | 0.469796 | − | 0.882775i | \(-0.344328\pi\) | ||||
0.469796 | + | 0.882775i | \(0.344328\pi\) | |||||||
\(522\) | − | 5.30399e33i | − | 0.567180i | ||||||
\(523\) | − | 1.65708e34i | − | 1.73010i | −0.501683 | − | 0.865052i | \(-0.667286\pi\) | ||
0.501683 | − | 0.865052i | \(-0.332714\pi\) | |||||||
\(524\) | 7.62451e33 | 0.777268 | ||||||||
\(525\) | 8.97840e32 | + | 4.35950e33i | 0.0893733 | + | 0.433956i | ||||
\(526\) | −1.02497e34 | −0.996296 | ||||||||
\(527\) | − | 7.45329e33i | − | 0.707482i | ||||||
\(528\) | − | 3.97307e32i | − | 0.0368301i | ||||||
\(529\) | 1.08149e34 | 0.979103 | ||||||||
\(530\) | −7.63099e33 | + | 9.36275e33i | −0.674734 | + | 0.827856i | ||||
\(531\) | 8.97518e33 | 0.775107 | ||||||||
\(532\) | − | 9.05968e33i | − | 0.764218i | ||||||
\(533\) | 2.68518e34i | 2.21250i | ||||||||
\(534\) | 3.42045e33 | 0.275307 | ||||||||
\(535\) | −2.79292e33 | − | 2.27633e33i | −0.219602 | − | 0.178984i | ||||
\(536\) | 7.98494e33 | 0.613355 | ||||||||
\(537\) | 2.14936e33i | 0.161299i | ||||||||
\(538\) | 1.31481e34i | 0.964016i | ||||||||
\(539\) | −1.65697e34 | −1.18701 | ||||||||
\(540\) | −2.72089e33 | − | 2.21763e33i | −0.190453 | − | 0.155227i | ||||
\(541\) | −4.23198e33 | −0.289453 | −0.144727 | − | 0.989472i | \(-0.546230\pi\) | ||||
−0.144727 | + | 0.989472i | \(0.546230\pi\) | |||||||
\(542\) | − | 7.73674e33i | − | 0.517091i | ||||||
\(543\) | − | 6.48202e33i | − | 0.423362i | ||||||
\(544\) | 1.09820e33 | 0.0700966 | ||||||||
\(545\) | −2.19162e33 | + | 2.68898e33i | −0.136713 | + | 0.167738i | ||||
\(546\) | 6.96217e33 | 0.424460 | ||||||||
\(547\) | − | 5.57179e33i | − | 0.332011i | −0.986125 | − | 0.166006i | \(-0.946913\pi\) | ||
0.986125 | − | 0.166006i | \(-0.0530870\pi\) | |||||||
\(548\) | − | 9.90052e32i | − | 0.0576635i | ||||||
\(549\) | −2.24837e34 | −1.28001 | ||||||||
\(550\) | −7.22156e33 | + | 1.48728e33i | −0.401881 | + | 0.0827675i | ||||
\(551\) | −1.38031e34 | −0.750900 | ||||||||
\(552\) | 2.43985e32i | 0.0129755i | ||||||||
\(553\) | 1.38936e34i | 0.722355i | ||||||||
\(554\) | 8.80334e32 | 0.0447482 | ||||||||
\(555\) | −2.84793e33 | + | 3.49423e33i | −0.141536 | + | 0.173656i | ||||
\(556\) | −2.49106e33 | −0.121046 | ||||||||
\(557\) | − | 1.51207e34i | − | 0.718427i | −0.933255 | − | 0.359213i | \(-0.883045\pi\) | ||
0.933255 | − | 0.359213i | \(-0.116955\pi\) | |||||||
\(558\) | 2.54051e34i | 1.18030i | ||||||||
\(559\) | −3.75379e33 | −0.170539 | ||||||||
\(560\) | 7.61225e33 | + | 6.20427e33i | 0.338191 | + | 0.275639i | ||||
\(561\) | 1.34453e33 | 0.0584164 | ||||||||
\(562\) | 5.52573e33i | 0.234793i | ||||||||
\(563\) | − | 1.21471e34i | − | 0.504799i | −0.967623 | − | 0.252400i | \(-0.918780\pi\) | ||
0.967623 | − | 0.252400i | \(-0.0812198\pi\) | |||||||
\(564\) | −7.16255e32 | −0.0291125 | ||||||||
\(565\) | 2.16941e34 | + | 1.76815e34i | 0.862453 | + | 0.702932i | ||||
\(566\) | −2.87458e34 | −1.11781 | ||||||||
\(567\) | − | 3.71991e34i | − | 1.41496i | ||||||
\(568\) | 7.87531e33i | 0.293031i | ||||||||
\(569\) | −2.58692e34 | −0.941628 | −0.470814 | − | 0.882232i | \(-0.656040\pi\) | ||||
−0.470814 | + | 0.882232i | \(0.656040\pi\) | |||||||
\(570\) | −2.78949e33 | + | 3.42253e33i | −0.0993320 | + | 0.121874i | ||||
\(571\) | −3.34607e34 | −1.16569 | −0.582846 | − | 0.812583i | \(-0.698061\pi\) | ||||
−0.582846 | + | 0.812583i | \(0.698061\pi\) | |||||||
\(572\) | 1.15329e34i | 0.393086i | ||||||||
\(573\) | 3.92885e33i | 0.131019i | ||||||||
\(574\) | 6.17615e34 | 2.01521 | ||||||||
\(575\) | 4.43473e33 | − | 9.13333e32i | 0.141586 | − | 0.0291596i | ||||
\(576\) | −3.74331e33 | −0.116943 | ||||||||
\(577\) | − | 1.34968e34i | − | 0.412603i | −0.978488 | − | 0.206302i | \(-0.933857\pi\) | ||
0.978488 | − | 0.206302i | \(-0.0661428\pi\) | |||||||
\(578\) | − | 1.99201e34i | − | 0.595926i | ||||||
\(579\) | 6.96328e33 | 0.203860 | ||||||||
\(580\) | 9.45268e33 | − | 1.15978e34i | 0.270835 | − | 0.332298i | ||||
\(581\) | −4.13140e33 | −0.115850 | ||||||||
\(582\) | − | 2.38717e33i | − | 0.0655158i | ||||||
\(583\) | 3.26268e34i | 0.876429i | ||||||||
\(584\) | −6.08248e32 | −0.0159926 | ||||||||
\(585\) | 3.81754e34 | + | 3.11144e34i | 0.982507 | + | 0.800780i | ||||
\(586\) | 1.73315e34 | 0.436632 | ||||||||
\(587\) | − | 4.17737e34i | − | 1.03021i | −0.857126 | − | 0.515107i | \(-0.827752\pi\) | ||
0.857126 | − | 0.515107i | \(-0.172248\pi\) | |||||||
\(588\) | − | 1.07557e34i | − | 0.259670i | ||||||
\(589\) | 6.61143e34 | 1.56262 | ||||||||
\(590\) | 1.96254e34 | + | 1.59954e34i | 0.454117 | + | 0.370123i | ||||
\(591\) | −2.08753e33 | −0.0472923 | ||||||||
\(592\) | 9.94569e33i | 0.220604i | ||||||||
\(593\) | 2.55607e33i | 0.0555123i | 0.999615 | + | 0.0277562i | \(0.00883620\pi\) | ||||
−0.999615 | + | 0.0277562i | \(0.991164\pi\) | |||||||
\(594\) | −9.48160e33 | −0.201628 | ||||||||
\(595\) | −2.09959e34 | + | 2.57606e34i | −0.437192 | + | 0.536407i | ||||
\(596\) | −8.97394e33 | −0.182981 | ||||||||
\(597\) | − | 2.24029e34i | − | 0.447327i | ||||||
\(598\) | − | 7.08230e33i | − | 0.138487i | ||||||
\(599\) | −4.70324e34 | −0.900662 | −0.450331 | − | 0.892862i | \(-0.648694\pi\) | ||||
−0.450331 | + | 0.892862i | \(0.648694\pi\) | |||||||
\(600\) | −9.65421e32 | − | 4.68765e33i | −0.0181062 | − | 0.0879153i | ||||
\(601\) | 5.96787e34 | 1.09620 | 0.548099 | − | 0.836414i | \(-0.315352\pi\) | ||||
0.548099 | + | 0.836414i | \(0.315352\pi\) | |||||||
\(602\) | 8.63406e33i | 0.155331i | ||||||||
\(603\) | − | 9.21060e34i | − | 1.62301i | ||||||
\(604\) | −3.56138e34 | −0.614691 | ||||||||
\(605\) | 2.47859e34 | − | 3.04107e34i | 0.419046 | − | 0.514143i | ||||
\(606\) | 1.29036e34 | 0.213699 | ||||||||
\(607\) | − | 2.92667e34i | − | 0.474804i | −0.971411 | − | 0.237402i | \(-0.923704\pi\) | ||
0.971411 | − | 0.237402i | \(-0.0762959\pi\) | |||||||
\(608\) | 9.74161e33i | 0.154823i | ||||||||
\(609\) | −2.43980e34 | −0.379872 | ||||||||
\(610\) | −4.91634e34 | − | 4.00700e34i | −0.749927 | − | 0.611219i | ||||
\(611\) | 2.07912e34 | 0.310717 | ||||||||
\(612\) | − | 1.26677e34i | − | 0.185484i | ||||||
\(613\) | − | 8.48844e34i | − | 1.21779i | −0.793251 | − | 0.608895i | \(-0.791613\pi\) | ||
0.793251 | − | 0.608895i | \(-0.208387\pi\) | |||||||
\(614\) | −1.29186e34 | −0.181597 | ||||||||
\(615\) | −2.33320e34 | − | 1.90165e34i | −0.321376 | − | 0.261933i | ||||
\(616\) | 2.65267e34 | 0.358034 | ||||||||
\(617\) | 1.30414e35i | 1.72488i | 0.506156 | + | 0.862442i | \(0.331066\pi\) | ||||
−0.506156 | + | 0.862442i | \(0.668934\pi\) | |||||||
\(618\) | 1.89982e34i | 0.246239i | ||||||||
\(619\) | 8.02670e34 | 1.01954 | 0.509770 | − | 0.860311i | \(-0.329731\pi\) | ||||
0.509770 | + | 0.860311i | \(0.329731\pi\) | |||||||
\(620\) | −4.52765e34 | + | 5.55514e34i | −0.563607 | + | 0.691511i | ||||
\(621\) | 5.82260e33 | 0.0710350 | ||||||||
\(622\) | − | 8.13296e34i | − | 0.972453i | ||||||
\(623\) | 2.28370e35i | 2.67633i | ||||||||
\(624\) | −7.48621e33 | −0.0859913 | ||||||||
\(625\) | −8.15899e34 | + | 3.50955e34i | −0.918621 | + | 0.395140i | ||||
\(626\) | 2.24133e33 | 0.0247359 | ||||||||
\(627\) | 1.19266e34i | 0.129025i | ||||||||
\(628\) | − | 2.78774e33i | − | 0.0295636i | ||||||
\(629\) | −3.36573e34 | −0.349901 | ||||||||
\(630\) | 7.15660e34 | − | 8.78070e34i | 0.729373 | − | 0.894895i | ||||
\(631\) | −3.51125e34 | −0.350828 | −0.175414 | − | 0.984495i | \(-0.556126\pi\) | ||||
−0.175414 | + | 0.984495i | \(0.556126\pi\) | |||||||
\(632\) | − | 1.49394e34i | − | 0.146342i | ||||||
\(633\) | − | 1.33115e33i | − | 0.0127844i | ||||||
\(634\) | −8.95181e34 | −0.842937 | ||||||||
\(635\) | −6.43499e34 | − | 5.24476e34i | −0.594123 | − | 0.484233i | ||||
\(636\) | −2.11786e34 | −0.191727 | ||||||||
\(637\) | 3.12212e35i | 2.77145i | ||||||||
\(638\) | − | 4.04155e34i | − | 0.351795i | ||||||
\(639\) | 9.08413e34 | 0.775394 | ||||||||
\(640\) | −8.18523e33 | − | 6.67127e33i | −0.0685143 | − | 0.0558417i | ||||
\(641\) | −1.10476e35 | −0.906862 | −0.453431 | − | 0.891291i | \(-0.649800\pi\) | ||||
−0.453431 | + | 0.891291i | \(0.649800\pi\) | |||||||
\(642\) | − | 6.31760e33i | − | 0.0508586i | ||||||
\(643\) | − | 5.33371e34i | − | 0.421107i | −0.977582 | − | 0.210553i | \(-0.932473\pi\) | ||
0.977582 | − | 0.210553i | \(-0.0675266\pi\) | |||||||
\(644\) | −1.62899e34 | −0.126138 | ||||||||
\(645\) | 2.65844e33 | − | 3.26174e33i | 0.0201897 | − | 0.0247715i | ||||
\(646\) | −3.29666e34 | −0.245566 | ||||||||
\(647\) | 2.39579e34i | 0.175043i | 0.996163 | + | 0.0875216i | \(0.0278947\pi\) | ||||
−0.996163 | + | 0.0875216i | \(0.972105\pi\) | |||||||
\(648\) | 3.99991e34i | 0.286657i | ||||||||
\(649\) | 6.83894e34 | 0.480762 | ||||||||
\(650\) | 2.80239e34 | + | 1.36071e35i | 0.193246 | + | 0.938317i | ||||
\(651\) | 1.16862e35 | 0.790514 | ||||||||
\(652\) | 4.99866e34i | 0.331710i | ||||||||
\(653\) | − | 6.46858e34i | − | 0.421109i | −0.977582 | − | 0.210554i | \(-0.932473\pi\) | ||
0.977582 | − | 0.210554i | \(-0.0675269\pi\) | |||||||
\(654\) | −6.08250e33 | −0.0388472 | ||||||||
\(655\) | 1.56740e35 | − | 1.92310e35i | 0.982119 | − | 1.20500i | ||||
\(656\) | −6.64104e34 | −0.408261 | ||||||||
\(657\) | 7.01612e33i | 0.0423185i | ||||||||
\(658\) | − | 4.78217e34i | − | 0.283010i | ||||||
\(659\) | −1.74748e35 | −1.01471 | −0.507357 | − | 0.861736i | \(-0.669377\pi\) | ||||
−0.507357 | + | 0.861736i | \(0.669377\pi\) | |||||||
\(660\) | −1.00212e34 | − | 8.16762e33i | −0.0570977 | − | 0.0465368i | ||||
\(661\) | 2.05707e35 | 1.15009 | 0.575044 | − | 0.818123i | \(-0.304985\pi\) | ||||
0.575044 | + | 0.818123i | \(0.304985\pi\) | |||||||
\(662\) | 1.20036e35i | 0.658547i | ||||||||
\(663\) | − | 2.53341e34i | − | 0.136391i | ||||||
\(664\) | 4.44238e33 | 0.0234701 | ||||||||
\(665\) | −2.28509e35 | − | 1.86244e35i | −1.18477 | − | 0.965631i | ||||
\(666\) | 1.14723e35 | 0.583745 | ||||||||
\(667\) | 2.48190e34i | 0.123940i | ||||||||
\(668\) | − | 1.50302e35i | − | 0.736647i | ||||||
\(669\) | −1.36605e34 | −0.0657112 | ||||||||
\(670\) | 1.64150e35 | − | 2.01402e35i | 0.775007 | − | 0.950885i | ||||
\(671\) | −1.71322e35 | −0.793928 | ||||||||
\(672\) | 1.72190e34i | 0.0783234i | ||||||||
\(673\) | − | 1.94000e35i | − | 0.866190i | −0.901348 | − | 0.433095i | \(-0.857421\pi\) | ||
0.901348 | − | 0.433095i | \(-0.142579\pi\) | |||||||
\(674\) | −1.88475e35 | −0.826046 | ||||||||
\(675\) | −1.11869e35 | + | 2.30394e34i | −0.481296 | + | 0.0991230i | ||||
\(676\) | 9.89201e34 | 0.417783 | ||||||||
\(677\) | − | 1.50061e35i | − | 0.622172i | −0.950382 | − | 0.311086i | \(-0.899307\pi\) | ||
0.950382 | − | 0.311086i | \(-0.100693\pi\) | |||||||
\(678\) | 4.90722e34i | 0.199740i | ||||||||
\(679\) | 1.59382e35 | 0.636895 | ||||||||
\(680\) | 2.25763e34 | − | 2.76997e34i | 0.0885708 | − | 0.108671i | ||||
\(681\) | 1.29062e35 | 0.497116 | ||||||||
\(682\) | 1.93582e35i | 0.732084i | ||||||||
\(683\) | 2.23175e35i | 0.828679i | 0.910122 | + | 0.414339i | \(0.135987\pi\) | ||||
−0.910122 | + | 0.414339i | \(0.864013\pi\) | |||||||
\(684\) | 1.12369e35 | 0.409681 | ||||||||
\(685\) | −2.49718e34 | − | 2.03529e34i | −0.0893958 | − | 0.0728609i | ||||
\(686\) | 3.67062e35 | 1.29029 | ||||||||
\(687\) | − | 1.35606e34i | − | 0.0468078i | ||||||
\(688\) | − | 9.28395e33i | − | 0.0314686i | ||||||
\(689\) | 6.14765e35 | 2.04630 | ||||||||
\(690\) | 6.15395e33 | + | 5.01570e33i | 0.0201159 | + | 0.0163952i | ||||
\(691\) | 4.24403e34 | 0.136240 | 0.0681198 | − | 0.997677i | \(-0.478300\pi\) | ||||
0.0681198 | + | 0.997677i | \(0.478300\pi\) | |||||||
\(692\) | 2.36355e35i | 0.745142i | ||||||||
\(693\) | − | 3.05985e35i | − | 0.947402i | ||||||
\(694\) | −3.02316e35 | −0.919324 | ||||||||
\(695\) | −5.12098e34 | + | 6.28312e34i | −0.152948 | + | 0.187657i | ||||
\(696\) | 2.62344e34 | 0.0769584 | ||||||||
\(697\) | − | 2.24740e35i | − | 0.647545i | ||||||
\(698\) | 1.46044e35i | 0.413325i | ||||||||
\(699\) | 4.52808e34 | 0.125878 | ||||||||
\(700\) | 3.12977e35 | − | 6.44575e34i | 0.854646 | − | 0.176014i | ||||
\(701\) | −6.67347e35 | −1.79010 | −0.895048 | − | 0.445969i | \(-0.852859\pi\) | ||||
−0.895048 | + | 0.445969i | \(0.852859\pi\) | |||||||
\(702\) | 1.78656e35i | 0.470764i | ||||||||
\(703\) | − | 2.98556e35i | − | 0.772831i | ||||||
\(704\) | −2.85234e34 | −0.0725342 | ||||||||
\(705\) | −1.47244e34 | + | 1.80659e34i | −0.0367852 | + | 0.0451331i | ||||
\(706\) | −3.56088e35 | −0.873974 | ||||||||
\(707\) | 8.61522e35i | 2.07742i | ||||||||
\(708\) | 4.43928e34i | 0.105171i | ||||||||
\(709\) | −5.82085e35 | −1.35490 | −0.677452 | − | 0.735567i | \(-0.736916\pi\) | ||||
−0.677452 | + | 0.735567i | \(0.736916\pi\) | |||||||
\(710\) | 1.98636e35 | + | 1.61896e35i | 0.454286 | + | 0.370260i | ||||
\(711\) | −1.72325e35 | −0.387238 | ||||||||
\(712\) | − | 2.45560e35i | − | 0.542198i | ||||||
\(713\) | − | 1.18878e35i | − | 0.257919i | ||||||
\(714\) | −5.82708e34 | −0.124229 | ||||||||
\(715\) | 2.90891e35 | + | 2.37087e35i | 0.609402 | + | 0.496686i | ||||
\(716\) | 1.54307e35 | 0.317667 | ||||||||
\(717\) | 1.67316e34i | 0.0338491i | ||||||||
\(718\) | 9.26900e33i | 0.0184280i | ||||||||
\(719\) | 4.08106e35 | 0.797374 | 0.398687 | − | 0.917087i | \(-0.369466\pi\) | ||||
0.398687 | + | 0.917087i | \(0.369466\pi\) | |||||||
\(720\) | −7.69528e34 | + | 9.44162e34i | −0.147764 | + | 0.181297i | ||||
\(721\) | −1.26844e36 | −2.39375 | ||||||||
\(722\) | 8.88115e34i | 0.164723i | ||||||||
\(723\) | 1.96780e35i | 0.358717i | ||||||||
\(724\) | −4.65355e35 | −0.833782 | ||||||||
\(725\) | −9.82060e34 | − | 4.76844e35i | −0.172947 | − | 0.839752i | ||||
\(726\) | 6.87893e34 | 0.119073 | ||||||||
\(727\) | 7.44759e34i | 0.126717i | 0.997991 | + | 0.0633586i | \(0.0201812\pi\) | ||||
−0.997991 | + | 0.0633586i | \(0.979819\pi\) | |||||||
\(728\) | − | 4.99826e35i | − | 0.835943i | ||||||
\(729\) | 3.85503e35 | 0.633772 | ||||||||
\(730\) | −1.25040e34 | + | 1.53417e34i | −0.0202076 | + | 0.0247934i | ||||
\(731\) | 3.14179e34 | 0.0499125 | ||||||||
\(732\) | − | 1.11208e35i | − | 0.173679i | ||||||
\(733\) | 1.00546e36i | 1.54371i | 0.635802 | + | 0.771853i | \(0.280670\pi\) | ||||
−0.635802 | + | 0.771853i | \(0.719330\pi\) | |||||||
\(734\) | −1.36885e35 | −0.206612 | ||||||||
\(735\) | −2.71287e35 | − | 2.21109e35i | −0.402566 | − | 0.328106i | ||||
\(736\) | 1.75161e34 | 0.0255543 | ||||||||
\(737\) | − | 7.01833e35i | − | 1.00668i | ||||||
\(738\) | 7.66041e35i | 1.08031i | ||||||||
\(739\) | 7.42029e35 | 1.02888 | 0.514441 | − | 0.857526i | \(-0.327999\pi\) | ||||
0.514441 | + | 0.857526i | \(0.327999\pi\) | |||||||
\(740\) | 2.50857e35 | + | 2.04458e35i | 0.342003 | + | 0.278745i | ||||
\(741\) | 2.24726e35 | 0.301249 | ||||||||
\(742\) | − | 1.41402e36i | − | 1.86383i | ||||||
\(743\) | 4.93877e35i | 0.640115i | 0.947398 | + | 0.320058i | \(0.103702\pi\) | ||||
−0.947398 | + | 0.320058i | \(0.896298\pi\) | |||||||
\(744\) | −1.25658e35 | −0.160150 | ||||||||
\(745\) | −1.84481e35 | + | 2.26347e35i | −0.231206 | + | 0.283675i | ||||
\(746\) | −7.33296e35 | −0.903741 | ||||||||
\(747\) | − | 5.12426e34i | − | 0.0621046i | ||||||
\(748\) | − | 9.65262e34i | − | 0.115047i | ||||||
\(749\) | 4.21802e35 | 0.494409 | ||||||||
\(750\) | −1.38082e35 | − | 7.20154e34i | −0.159173 | − | 0.0830156i | ||||
\(751\) | 1.60017e36 | 1.81413 | 0.907063 | − | 0.420995i | \(-0.138319\pi\) | ||||
0.907063 | + | 0.420995i | \(0.138319\pi\) | |||||||
\(752\) | 5.14212e34i | 0.0573349i | ||||||||
\(753\) | 7.55579e33i | 0.00828595i | ||||||||
\(754\) | −7.61524e35 | −0.821375 | ||||||||
\(755\) | −7.32128e35 | + | 8.98276e35i | −0.776695 | + | 0.952956i | ||||
\(756\) | 4.10924e35 | 0.428785 | ||||||||
\(757\) | 9.77978e34i | 0.100376i | 0.998740 | + | 0.0501881i | \(0.0159821\pi\) | ||||
−0.998740 | + | 0.0501881i | \(0.984018\pi\) | |||||||
\(758\) | − | 3.87383e35i | − | 0.391089i | ||||||
\(759\) | 2.14449e34 | 0.0212962 | ||||||||
\(760\) | 2.45709e35 | + | 2.00262e35i | 0.240022 | + | 0.195627i | ||||
\(761\) | 1.42035e36 | 1.36485 | 0.682427 | − | 0.730954i | \(-0.260924\pi\) | ||||
0.682427 | + | 0.730954i | \(0.260924\pi\) | |||||||
\(762\) | − | 1.45560e35i | − | 0.137596i | ||||||
\(763\) | − | 4.06106e35i | − | 0.377644i | ||||||
\(764\) | 2.82059e35 | 0.258032 | ||||||||
\(765\) | −3.19514e35 | − | 2.60416e35i | −0.287556 | − | 0.234369i | ||||
\(766\) | 8.26499e35 | 0.731784 | ||||||||
\(767\) | − | 1.28862e36i | − | 1.12249i | ||||||
\(768\) | − | 1.85151e34i | − | 0.0158675i | ||||||
\(769\) | −4.43106e35 | −0.373619 | −0.186809 | − | 0.982396i | \(-0.559815\pi\) | ||||
−0.186809 | + | 0.982396i | \(0.559815\pi\) | |||||||
\(770\) | 5.45321e35 | − | 6.69075e35i | 0.452395 | − | 0.555061i | ||||
\(771\) | −5.60292e34 | −0.0457335 | ||||||||
\(772\) | − | 4.99906e35i | − | 0.401487i | ||||||
\(773\) | − | 1.04683e36i | − | 0.827241i | −0.910449 | − | 0.413621i | \(-0.864264\pi\) | ||
0.910449 | − | 0.413621i | \(-0.135736\pi\) | |||||||
\(774\) | −1.07090e35 | −0.0832697 | ||||||||
\(775\) | 4.70388e35 | + | 2.28399e36i | 0.359902 | + | 1.74752i | ||||
\(776\) | −1.71379e35 | −0.129029 | ||||||||
\(777\) | − | 5.27719e35i | − | 0.390967i | ||||||
\(778\) | 4.76147e35i | 0.347133i | ||||||||
\(779\) | 1.99355e36 | 1.43024 | ||||||||
\(780\) | −1.53897e35 | + | 1.88822e35i | −0.108655 | + | 0.133312i | ||||
\(781\) | 6.92196e35 | 0.480940 | ||||||||
\(782\) | 5.92763e34i | 0.0405319i | ||||||||
\(783\) | − | 6.26075e35i | − | 0.421313i | ||||||
\(784\) | −7.72169e35 | −0.511401 | ||||||||
\(785\) | −7.03143e34 | − | 5.73088e34i | −0.0458324 | − | 0.0373551i | ||||
\(786\) | 4.35008e35 | 0.279071 | ||||||||
\(787\) | − | 1.02940e36i | − | 0.649977i | −0.945718 | − | 0.324989i | \(-0.894640\pi\) | ||
0.945718 | − | 0.324989i | \(-0.105360\pi\) | |||||||
\(788\) | 1.49868e35i | 0.0931387i | ||||||||
\(789\) | −5.84784e35 | −0.357712 | ||||||||
\(790\) | −3.76811e35 | − | 3.07115e35i | −0.226874 | − | 0.184911i | ||||
\(791\) | −3.27636e36 | −1.94172 | ||||||||
\(792\) | 3.29016e35i | 0.191934i | ||||||||
\(793\) | 3.22811e36i | 1.85367i | ||||||||
\(794\) | −8.34601e35 | −0.471762 | ||||||||
\(795\) | −4.35378e35 | + | 5.34181e35i | −0.242257 | + | 0.297235i | ||||
\(796\) | −1.60834e36 | −0.880978 | ||||||||
\(797\) | − | 2.74499e36i | − | 1.48017i | −0.672512 | − | 0.740086i | \(-0.734785\pi\) | ||
0.672512 | − | 0.740086i | \(-0.265215\pi\) | |||||||
\(798\) | − | 5.16890e35i | − | 0.274386i | ||||||
\(799\) | −1.74015e35 | −0.0909393 | ||||||||
\(800\) | −3.36534e35 | + | 6.93093e34i | −0.173143 | + | 0.0356588i | ||||
\(801\) | −2.83252e36 | −1.43472 | ||||||||
\(802\) | 6.85745e35i | 0.341966i | ||||||||
\(803\) | 5.34617e34i | 0.0262481i | ||||||||
\(804\) | 4.55572e35 | 0.220220 | ||||||||
\(805\) | −3.34879e35 | + | 4.10876e35i | −0.159382 | + | 0.195552i | ||||
\(806\) | 3.64755e36 | 1.70928 | ||||||||
\(807\) | 7.50150e35i | 0.346122i | ||||||||
\(808\) | − | 9.26369e35i | − | 0.420864i | ||||||
\(809\) | −2.35511e36 | −1.05355 | −0.526776 | − | 0.850004i | \(-0.676599\pi\) | ||||
−0.526776 | + | 0.850004i | \(0.676599\pi\) | |||||||
\(810\) | 1.00888e36 | + | 8.22278e35i | 0.444405 | + | 0.362206i | ||||
\(811\) | 3.33343e36 | 1.44587 | 0.722936 | − | 0.690915i | \(-0.242792\pi\) | ||||
0.722936 | + | 0.690915i | \(0.242792\pi\) | |||||||
\(812\) | 1.75157e36i | 0.748132i | ||||||||
\(813\) | − | 4.41411e35i | − | 0.185657i | ||||||
\(814\) | 8.74172e35 | 0.362069 | ||||||||
\(815\) | 1.26080e36 | + | 1.02760e36i | 0.514251 | + | 0.419134i | ||||
\(816\) | 6.26569e34 | 0.0251676 | ||||||||
\(817\) | 2.78692e35i | 0.110242i | ||||||||
\(818\) | 3.08140e36i | 1.20042i | ||||||||
\(819\) | −5.76547e36 | −2.21201 | ||||||||
\(820\) | −1.36523e36 | + | 1.67505e36i | −0.515859 | + | 0.632927i | ||||
\(821\) | 1.82523e36 | 0.679249 | 0.339625 | − | 0.940561i | \(-0.389700\pi\) | ||||
0.339625 | + | 0.940561i | \(0.389700\pi\) | |||||||
\(822\) | − | 5.64864e34i | − | 0.0207036i | ||||||
\(823\) | 1.63571e36i | 0.590483i | 0.955423 | + | 0.295241i | \(0.0954001\pi\) | ||||
−0.955423 | + | 0.295241i | \(0.904600\pi\) | |||||||
\(824\) | 1.36391e36 | 0.484950 | ||||||||
\(825\) | −4.12018e35 | + | 8.48552e34i | −0.144292 | + | 0.0297170i | ||||
\(826\) | −2.96394e36 | −1.02240 | ||||||||
\(827\) | − | 3.73907e36i | − | 1.27041i | −0.772342 | − | 0.635206i | \(-0.780915\pi\) | ||
0.772342 | − | 0.635206i | \(-0.219085\pi\) | |||||||
\(828\) | − | 2.02047e35i | − | 0.0676198i | ||||||
\(829\) | 3.08664e36 | 1.01755 | 0.508773 | − | 0.860901i | \(-0.330099\pi\) | ||||
0.508773 | + | 0.860901i | \(0.330099\pi\) | |||||||
\(830\) | 9.13238e34 | − | 1.12049e35i | 0.0296557 | − | 0.0363857i | ||||
\(831\) | 5.02265e34 | 0.0160665 | ||||||||
\(832\) | 5.37448e35i | 0.169354i | ||||||||
\(833\) | − | 2.61310e36i | − | 0.811135i | ||||||
\(834\) | −1.42125e35 | −0.0434604 | ||||||||
\(835\) | −3.79102e36 | − | 3.08982e36i | −1.14202 | − | 0.930792i | ||||
\(836\) | 8.56234e35 | 0.254105 | ||||||||
\(837\) | 2.99878e36i | 0.876750i | ||||||||
\(838\) | − | 2.56203e35i | − | 0.0737963i | ||||||
\(839\) | 3.69450e36 | 1.04841 | 0.524205 | − | 0.851592i | \(-0.324363\pi\) | ||||
0.524205 | + | 0.851592i | \(0.324363\pi\) | |||||||
\(840\) | 4.34309e35 | + | 3.53978e35i | 0.121425 | + | 0.0989657i | ||||
\(841\) | −9.61704e35 | −0.264906 | ||||||||
\(842\) | − | 3.28564e36i | − | 0.891701i | ||||||
\(843\) | 3.15264e35i | 0.0843005i | ||||||||
\(844\) | −9.55652e34 | −0.0251779 | ||||||||
\(845\) | 2.03354e36 | − | 2.49503e36i | 0.527891 | − | 0.647690i | ||||
\(846\) | 5.93142e35 | 0.151715 | ||||||||
\(847\) | 4.59280e36i | 1.15754i | ||||||||
\(848\) | 1.52045e36i | 0.377593i | ||||||||
\(849\) | −1.64006e36 | −0.401341 | ||||||||
\(850\) | −2.34550e35 | − | 1.13887e36i | −0.0565586 | − | 0.274623i | ||||
\(851\) | −5.36825e35 | −0.127560 | ||||||||
\(852\) | 4.49317e35i | 0.105210i | ||||||||
\(853\) | − | 7.36060e35i | − | 0.169844i | −0.996388 | − | 0.0849220i | \(-0.972936\pi\) | ||
0.996388 | − | 0.0849220i | \(-0.0270641\pi\) | |||||||
\(854\) | 7.42494e36 | 1.68838 | ||||||||
\(855\) | 2.31002e36 | − | 2.83425e36i | 0.517653 | − | 0.635128i | ||||
\(856\) | −4.53551e35 | −0.100162 | ||||||||
\(857\) | − | 5.06811e35i | − | 0.110303i | −0.998478 | − | 0.0551513i | \(-0.982436\pi\) | ||
0.998478 | − | 0.0551513i | \(-0.0175641\pi\) | |||||||
\(858\) | 6.57997e35i | 0.141134i | ||||||||
\(859\) | −7.80778e33 | −0.00165049 | −0.000825245 | − | 1.00000i | \(-0.500263\pi\) | ||||
−0.000825245 | 1.00000i | \(0.500263\pi\) | ||||||||
\(860\) | −2.34166e35 | − | 1.90854e35i | −0.0487858 | − | 0.0397623i | ||||
\(861\) | 3.52374e36 | 0.723543 | ||||||||
\(862\) | − | 5.41895e36i | − | 1.09667i | ||||||
\(863\) | − | 8.60176e36i | − | 1.71574i | −0.513864 | − | 0.857871i | \(-0.671787\pi\) | ||
0.513864 | − | 0.857871i | \(-0.328213\pi\) | |||||||
\(864\) | −4.41855e35 | −0.0868676 | ||||||||
\(865\) | 5.96152e36 | + | 4.85886e36i | 1.15520 | + | 0.941527i | ||||
\(866\) | −5.90669e36 | −1.12816 | ||||||||
\(867\) | − | 1.13652e36i | − | 0.213962i | ||||||
\(868\) | − | 8.38970e36i | − | 1.55686i | ||||||
\(869\) | −1.31309e36 | −0.240186 | ||||||||
\(870\) | 5.39312e35 | − | 6.61703e35i | 0.0972411 | − | 0.119309i | ||||
\(871\) | −1.32242e37 | −2.35040 | ||||||||
\(872\) | 4.36673e35i | 0.0765069i | ||||||||
\(873\) | 1.97685e36i | 0.341425i | ||||||||
\(874\) | −5.25809e35 | −0.0895231 | ||||||||
\(875\) | 4.80820e36 | − | 9.21919e36i | 0.807015 | − | 1.54736i | ||||
\(876\) | −3.47029e34 | −0.00574202 | ||||||||
\(877\) | 7.33903e36i | 1.19714i | 0.801072 | + | 0.598568i | \(0.204263\pi\) | ||||
−0.801072 | + | 0.598568i | \(0.795737\pi\) | |||||||
\(878\) | 4.04692e36i | 0.650794i | ||||||||
\(879\) | 9.88829e35 | 0.156769 | ||||||||
\(880\) | −5.86368e35 | + | 7.19437e35i | −0.0916509 | + | 0.112450i | ||||
\(881\) | 7.73442e36 | 1.19187 | 0.595935 | − | 0.803032i | \(-0.296781\pi\) | ||||
0.595935 | + | 0.803032i | \(0.296781\pi\) | |||||||
\(882\) | 8.90693e36i | 1.35323i | ||||||||
\(883\) | 1.11931e37i | 1.67664i | 0.545178 | + | 0.838320i | \(0.316462\pi\) | ||||
−0.545178 | + | 0.838320i | \(0.683538\pi\) | |||||||
\(884\) | −1.81878e36 | −0.268613 | ||||||||
\(885\) | 1.11971e36 | + | 9.12602e35i | 0.163047 | + | 0.132889i | ||||
\(886\) | −2.77779e36 | −0.398821 | ||||||||
\(887\) | 9.94167e36i | 1.40739i | 0.710502 | + | 0.703695i | \(0.248468\pi\) | ||||
−0.710502 | + | 0.703695i | \(0.751532\pi\) | |||||||
\(888\) | 5.67441e35i | 0.0792060i | ||||||||
\(889\) | 9.71850e36 | 1.33760 | ||||||||
\(890\) | −6.19368e36 | − | 5.04808e36i | −0.840570 | − | 0.685096i | ||||
\(891\) | 3.51570e36 | 0.470479 | ||||||||
\(892\) | 9.80709e35i | 0.129413i | ||||||||
\(893\) | − | 1.54360e36i | − | 0.200858i | ||||||
\(894\) | −5.11998e35 | −0.0656976 | ||||||||
\(895\) | 3.17214e36 | − | 3.89202e36i | 0.401389 | − | 0.492479i | ||||
\(896\) | 1.23618e36 | 0.154252 | ||||||||
\(897\) | − | 4.04073e35i | − | 0.0497226i | ||||||
\(898\) | − | 5.73826e36i | − | 0.696347i | ||||||
\(899\) | −1.27824e37 | −1.52973 | ||||||||
\(900\) | 7.99480e35 | + | 3.88191e36i | 0.0943574 | + | 0.458157i | ||||
\(901\) | −5.14536e36 | −0.598902 | ||||||||
\(902\) | 5.83711e36i | 0.670063i | ||||||||
\(903\) | 4.92607e35i | 0.0557704i | ||||||||
\(904\) | 3.52298e36 | 0.393373 | ||||||||
\(905\) | −9.56651e36 | + | 1.17375e37i | −1.05353 | + | 1.29261i | ||||
\(906\) | −2.03191e36 | −0.220700 | ||||||||
\(907\) | − | 2.49643e36i | − | 0.267441i | −0.991019 | − | 0.133721i | \(-0.957308\pi\) | ||
0.991019 | − | 0.133721i | \(-0.0426924\pi\) | |||||||
\(908\) | − | 9.26555e36i | − | 0.979035i | ||||||
\(909\) | −1.06856e37 | −1.11366 | ||||||||
\(910\) | −1.26070e37 | − | 1.02751e37i | −1.29596 | − | 1.05626i | ||||
\(911\) | 9.34594e36 | 0.947640 | 0.473820 | − | 0.880622i | \(-0.342875\pi\) | ||||
0.473820 | + | 0.880622i | \(0.342875\pi\) | |||||||
\(912\) | 5.55797e35i | 0.0555879i | ||||||||
\(913\) | − | 3.90461e35i | − | 0.0385205i | ||||||
\(914\) | 1.17882e37 | 1.14715 | ||||||||
\(915\) | −2.80497e36 | − | 2.28615e36i | −0.269255 | − | 0.219453i | ||||
\(916\) | −9.73537e35 | −0.0921847 | ||||||||
\(917\) | 2.90438e37i | 2.71292i | ||||||||
\(918\) | − | 1.49528e36i | − | 0.137781i | ||||||
\(919\) | −2.08298e37 | −1.89340 | −0.946698 | − | 0.322122i | \(-0.895604\pi\) | ||||
−0.946698 | + | 0.322122i | \(0.895604\pi\) | |||||||
\(920\) | 3.60086e35 | − | 4.41803e35i | 0.0322893 | − | 0.0396169i | ||||
\(921\) | −7.37054e35 | −0.0652010 | ||||||||
\(922\) | 1.89543e36i | 0.165413i | ||||||||
\(923\) | − | 1.30426e37i | − | 1.12291i | ||||||
\(924\) | 1.51345e36 | 0.128549 | ||||||||
\(925\) | 1.03139e37 | − | 2.12416e36i | 0.864278 | − | 0.177998i | ||||
\(926\) | −1.03719e36 | −0.0857474 | ||||||||
\(927\) | − | 1.57327e37i | − | 1.28323i | ||||||
\(928\) | − | 1.88342e36i | − | 0.151564i | ||||||
\(929\) | 2.93833e36 | 0.233294 | 0.116647 | − | 0.993173i | \(-0.462785\pi\) | ||||
0.116647 | + | 0.993173i | \(0.462785\pi\) | |||||||
\(930\) | −2.58320e36 | + | 3.16943e36i | −0.202358 | + | 0.248281i | ||||
\(931\) | 2.31795e37 | 1.79156 | ||||||||
\(932\) | − | 3.25079e36i | − | 0.247908i | ||||||
\(933\) | − | 4.64017e36i | − | 0.349151i | ||||||
\(934\) | −6.39190e36 | −0.474563 | ||||||||
\(935\) | −2.43465e36 | − | 1.98433e36i | −0.178357 | − | 0.145368i | ||||
\(936\) | 6.19944e36 | 0.448131 | ||||||||
\(937\) | − | 1.33465e37i | − | 0.951968i | −0.879454 | − | 0.475984i | \(-0.842092\pi\) | ||
0.879454 | − | 0.475984i | \(-0.157908\pi\) | |||||||
\(938\) | 3.04168e37i | 2.14081i | ||||||||
\(939\) | 1.27877e35 | 0.00888120 | ||||||||
\(940\) | 1.29698e36 | + | 1.05709e36i | 0.0888864 | + | 0.0724458i | ||||
\(941\) | −1.37070e37 | −0.926983 | −0.463492 | − | 0.886101i | \(-0.653404\pi\) | ||||
−0.463492 | + | 0.886101i | \(0.653404\pi\) | |||||||
\(942\) | − | 1.59051e35i | − | 0.0106145i | ||||||
\(943\) | − | 3.58454e36i | − | 0.236068i | ||||||
\(944\) | 3.18704e36 | 0.207127 | ||||||||
\(945\) | 8.44755e36 | − | 1.03646e37i | 0.541793 | − | 0.664746i | ||||
\(946\) | −8.16009e35 | −0.0516482 | ||||||||
\(947\) | 3.73876e36i | 0.233535i | 0.993159 | + | 0.116768i | \(0.0372533\pi\) | ||||
−0.993159 | + | 0.116768i | \(0.962747\pi\) | |||||||
\(948\) | − | 8.52350e35i | − | 0.0525429i | ||||||
\(949\) | 1.00734e36 | 0.0612845 | ||||||||
\(950\) | 1.01023e37 | − | 2.08057e36i | 0.606562 | − | 0.124922i | ||||
\(951\) | −5.10736e36 | −0.302649 | ||||||||
\(952\) | 4.18336e36i | 0.244660i | ||||||||
\(953\) | 4.80715e36i | 0.277477i | 0.990329 | + | 0.138738i | \(0.0443047\pi\) | ||||
−0.990329 | + | 0.138738i | \(0.955695\pi\) | |||||||
\(954\) | 1.75383e37 | 0.999156 | ||||||||
\(955\) | 5.79841e36 | − | 7.11429e36i | 0.326037 | − | 0.400027i | ||||
\(956\) | 1.20119e36 | 0.0666634 | ||||||||
\(957\) | − | 2.30586e36i | − | 0.126309i | ||||||
\(958\) | 2.96373e36i | 0.160240i | ||||||||
\(959\) | 3.77138e36 | 0.201265 | ||||||||
\(960\) | −4.66999e35 | − | 3.80622e35i | −0.0245995 | − | 0.0200495i | ||||
\(961\) | 4.19922e37 | 2.18336 | ||||||||
\(962\) | − | 1.64715e37i | − | 0.845364i | ||||||
\(963\) | 5.23170e36i | 0.265042i | ||||||||
\(964\) | 1.41272e37 | 0.706467 | ||||||||
\(965\) | −1.26090e37 | − | 1.02768e37i | −0.622426 | − | 0.507301i | ||||
\(966\) | −9.29405e35 | −0.0452888 | ||||||||
\(967\) | 1.46042e37i | 0.702498i | 0.936282 | + | 0.351249i | \(0.114243\pi\) | ||||
−0.936282 | + | 0.351249i | \(0.885757\pi\) | |||||||
\(968\) | − | 4.93850e36i | − | 0.234506i | ||||||
\(969\) | −1.88087e36 | −0.0881683 | ||||||||
\(970\) | −3.52311e36 | + | 4.32264e36i | −0.163035 | + | 0.200033i | ||||
\(971\) | −3.16381e37 | −1.44534 | −0.722670 | − | 0.691193i | \(-0.757085\pi\) | ||||
−0.722670 | + | 0.691193i | \(0.757085\pi\) | |||||||
\(972\) | 7.73003e36i | 0.348620i | ||||||||
\(973\) | − | 9.48913e36i | − | 0.422490i | ||||||
\(974\) | 1.27423e37 | 0.560093 | ||||||||
\(975\) | 1.59887e36 | + | 7.76340e36i | 0.0693835 | + | 0.336895i | ||||
\(976\) | −7.98382e36 | −0.342049 | ||||||||
\(977\) | − | 3.15815e37i | − | 1.33583i | −0.744239 | − | 0.667914i | \(-0.767188\pi\) | ||
0.744239 | − | 0.667914i | \(-0.232812\pi\) | |||||||
\(978\) | 2.85193e36i | 0.119098i | ||||||||
\(979\) | −2.15834e37 | −0.889889 | ||||||||
\(980\) | −1.58738e37 | + | 1.94762e37i | −0.646182 | + | 0.792825i | ||||
\(981\) | 5.03701e36 | 0.202446 | ||||||||
\(982\) | − | 1.43824e37i | − | 0.570738i | ||||||
\(983\) | − | 1.30026e37i | − | 0.509461i | −0.967012 | − | 0.254731i | \(-0.918013\pi\) | ||
0.967012 | − | 0.254731i | \(-0.0819868\pi\) | |||||||
\(984\) | −3.78897e36 | −0.146583 | ||||||||
\(985\) | 3.78006e36 | + | 3.08089e36i | 0.144393 | + | 0.117686i | ||||
\(986\) | 6.37368e36 | 0.240397 | ||||||||
\(987\) | − | 2.72841e36i | − | 0.101612i | ||||||
\(988\) | − | 1.61335e37i | − | 0.593288i | ||||||
\(989\) | 5.01107e35 | 0.0181960 | ||||||||
\(990\) | 8.29867e36 | + | 6.76373e36i | 0.297556 | + | 0.242519i | ||||
\(991\) | 1.69845e37 | 0.601355 | 0.300677 | − | 0.953726i | \(-0.402787\pi\) | ||||
0.300677 | + | 0.953726i | \(0.402787\pi\) | |||||||
\(992\) | 9.02119e36i | 0.315405i | ||||||||
\(993\) | 6.84852e36i | 0.236446i | ||||||||
\(994\) | −2.99992e37 | −1.02277 | ||||||||
\(995\) | −3.30634e37 | + | 4.05667e37i | −1.11316 | + | 1.36578i | ||||
\(996\) | 2.53455e35 | 0.00842673 | ||||||||
\(997\) | 1.43944e37i | 0.472612i | 0.971679 | + | 0.236306i | \(0.0759368\pi\) | ||||
−0.971679 | + | 0.236306i | \(0.924063\pi\) | |||||||
\(998\) | 3.59677e37i | 1.16622i | ||||||||
\(999\) | 1.35418e37 | 0.433617 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 10.26.b.a.9.3 | ✓ | 12 | |
5.2 | odd | 4 | 50.26.a.l.1.3 | 6 | |||
5.3 | odd | 4 | 50.26.a.k.1.4 | 6 | |||
5.4 | even | 2 | inner | 10.26.b.a.9.10 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.26.b.a.9.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
10.26.b.a.9.10 | yes | 12 | 5.4 | even | 2 | inner | |
50.26.a.k.1.4 | 6 | 5.3 | odd | 4 | |||
50.26.a.l.1.3 | 6 | 5.2 | odd | 4 |