Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,26,Mod(1,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(197.998389976\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2 x^{5} - 27590779188 x^{4} + 26487255863952 x^{3} + \cdots - 30\!\cdots\!08 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{4}\cdot 5^{18} \) |
Twist minimal: | no (minimal twist has level 10) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(10012.7\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4096.00 | 0.707107 | ||||||||
\(3\) | −233693. | −0.253881 | −0.126940 | − | 0.991910i | \(-0.540516\pi\) | ||||
−0.126940 | + | 0.991910i | \(0.540516\pi\) | |||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −9.57206e8 | −0.179521 | ||||||||
\(7\) | 6.39090e10 | 1.74517 | 0.872583 | − | 0.488466i | \(-0.162443\pi\) | ||||
0.872583 | + | 0.488466i | \(0.162443\pi\) | |||||||
\(8\) | 6.87195e10 | 0.353553 | ||||||||
\(9\) | −7.92676e11 | −0.935545 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.04007e12 | 0.580274 | 0.290137 | − | 0.956985i | \(-0.406299\pi\) | ||||
0.290137 | + | 0.956985i | \(0.406299\pi\) | |||||||
\(12\) | −3.92071e12 | −0.126940 | ||||||||
\(13\) | −1.13809e14 | −1.35483 | −0.677415 | − | 0.735601i | \(-0.736900\pi\) | ||||
−0.677415 | + | 0.735601i | \(0.736900\pi\) | |||||||
\(14\) | 2.61771e14 | 1.23402 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | −9.52541e14 | −0.396526 | −0.198263 | − | 0.980149i | \(-0.563530\pi\) | ||||
−0.198263 | + | 0.980149i | \(0.563530\pi\) | |||||||
\(18\) | −3.24680e15 | −0.661530 | ||||||||
\(19\) | 8.44950e15 | 0.875812 | 0.437906 | − | 0.899021i | \(-0.355720\pi\) | ||||
0.437906 | + | 0.899021i | \(0.355720\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.49351e16 | −0.443064 | ||||||||
\(22\) | 2.47401e16 | 0.410316 | ||||||||
\(23\) | 1.51928e16 | 0.144557 | 0.0722786 | − | 0.997384i | \(-0.476973\pi\) | ||||
0.0722786 | + | 0.997384i | \(0.476973\pi\) | |||||||
\(24\) | −1.60592e16 | −0.0897604 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.66162e17 | −0.958010 | ||||||||
\(27\) | 3.83248e17 | 0.491397 | ||||||||
\(28\) | 1.07222e18 | 0.872583 | ||||||||
\(29\) | −1.63360e18 | −0.857376 | −0.428688 | − | 0.903452i | \(-0.641024\pi\) | ||||
−0.428688 | + | 0.903452i | \(0.641024\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.82464e18 | −1.78420 | −0.892099 | − | 0.451840i | \(-0.850768\pi\) | ||||
−0.892099 | + | 0.451840i | \(0.850768\pi\) | |||||||
\(32\) | 1.15292e18 | 0.176777 | ||||||||
\(33\) | −1.41152e18 | −0.147320 | ||||||||
\(34\) | −3.90161e18 | −0.280386 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.32989e19 | −0.467772 | ||||||||
\(37\) | −3.53342e19 | −0.882417 | −0.441208 | − | 0.897405i | \(-0.645450\pi\) | ||||
−0.441208 | + | 0.897405i | \(0.645450\pi\) | |||||||
\(38\) | 3.46091e19 | 0.619293 | ||||||||
\(39\) | 2.65964e19 | 0.343965 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.35937e20 | −1.63304 | −0.816522 | − | 0.577315i | \(-0.804101\pi\) | ||||
−0.816522 | + | 0.577315i | \(0.804101\pi\) | |||||||
\(42\) | −6.11741e19 | −0.313293 | ||||||||
\(43\) | −3.29832e19 | −0.125874 | −0.0629372 | − | 0.998017i | \(-0.520047\pi\) | ||||
−0.0629372 | + | 0.998017i | \(0.520047\pi\) | |||||||
\(44\) | 1.01335e20 | 0.290137 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.22296e19 | 0.102217 | ||||||||
\(47\) | −1.82685e20 | −0.229340 | −0.114670 | − | 0.993404i | \(-0.536581\pi\) | ||||
−0.114670 | + | 0.993404i | \(0.536581\pi\) | |||||||
\(48\) | −6.57787e19 | −0.0634702 | ||||||||
\(49\) | 2.74329e21 | 2.04560 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.22602e20 | 0.100670 | ||||||||
\(52\) | −1.90940e21 | −0.677415 | ||||||||
\(53\) | 5.40172e21 | 1.51037 | 0.755186 | − | 0.655511i | \(-0.227547\pi\) | ||||
0.755186 | + | 0.655511i | \(0.227547\pi\) | |||||||
\(54\) | 1.56978e21 | 0.347470 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.39179e21 | 0.617009 | ||||||||
\(57\) | −1.97459e21 | −0.222352 | ||||||||
\(58\) | −6.69124e21 | −0.606257 | ||||||||
\(59\) | −1.13226e22 | −0.828509 | −0.414254 | − | 0.910161i | \(-0.635958\pi\) | ||||
−0.414254 | + | 0.910161i | \(0.635958\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.83642e22 | −1.36820 | −0.684098 | − | 0.729390i | \(-0.739804\pi\) | ||||
−0.684098 | + | 0.729390i | \(0.739804\pi\) | |||||||
\(62\) | −3.20497e22 | −1.26162 | ||||||||
\(63\) | −5.06592e22 | −1.63268 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.78158e21 | −0.104171 | ||||||||
\(67\) | 1.16196e23 | 1.73483 | 0.867415 | − | 0.497586i | \(-0.165780\pi\) | ||||
0.867415 | + | 0.497586i | \(0.165780\pi\) | |||||||
\(68\) | −1.59810e22 | −0.198263 | ||||||||
\(69\) | −3.55044e21 | −0.0367003 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.14601e23 | 0.828816 | 0.414408 | − | 0.910091i | \(-0.363989\pi\) | ||||
0.414408 | + | 0.910091i | \(0.363989\pi\) | |||||||
\(72\) | −5.44723e22 | −0.330765 | ||||||||
\(73\) | 8.85118e21 | 0.0452340 | 0.0226170 | − | 0.999744i | \(-0.492800\pi\) | ||||
0.0226170 | + | 0.999744i | \(0.492800\pi\) | |||||||
\(74\) | −1.44729e23 | −0.623963 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.41759e23 | 0.437906 | ||||||||
\(77\) | 3.86015e23 | 1.01267 | ||||||||
\(78\) | 1.08939e23 | 0.243220 | ||||||||
\(79\) | 2.17397e23 | 0.413918 | 0.206959 | − | 0.978350i | \(-0.433643\pi\) | ||||
0.206959 | + | 0.978350i | \(0.433643\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.82063e23 | 0.810788 | ||||||||
\(82\) | −9.66398e23 | −1.15474 | ||||||||
\(83\) | −6.46451e22 | −0.0663834 | −0.0331917 | − | 0.999449i | \(-0.510567\pi\) | ||||
−0.0331917 | + | 0.999449i | \(0.510567\pi\) | |||||||
\(84\) | −2.50569e23 | −0.221532 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.35099e23 | −0.0890067 | ||||||||
\(87\) | 3.81761e23 | 0.217671 | ||||||||
\(88\) | 4.15070e23 | 0.205158 | ||||||||
\(89\) | 3.57337e24 | 1.53357 | 0.766783 | − | 0.641906i | \(-0.221856\pi\) | ||||
0.766783 | + | 0.641906i | \(0.221856\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.27343e24 | −2.36440 | ||||||||
\(92\) | 2.54893e23 | 0.0722786 | ||||||||
\(93\) | 1.82856e24 | 0.452973 | ||||||||
\(94\) | −7.48277e23 | −0.162168 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.69429e23 | −0.0448802 | ||||||||
\(97\) | −2.49389e24 | −0.364948 | −0.182474 | − | 0.983211i | \(-0.558411\pi\) | ||||
−0.182474 | + | 0.983211i | \(0.558411\pi\) | |||||||
\(98\) | 1.12365e25 | 1.44646 | ||||||||
\(99\) | −4.78782e24 | −0.542872 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.34804e25 | −1.19038 | −0.595192 | − | 0.803584i | \(-0.702924\pi\) | ||||
−0.595192 | + | 0.803584i | \(0.702924\pi\) | |||||||
\(102\) | 9.11777e23 | 0.0711847 | ||||||||
\(103\) | −1.98475e25 | −1.37164 | −0.685822 | − | 0.727769i | \(-0.740557\pi\) | ||||
−0.685822 | + | 0.727769i | \(0.740557\pi\) | |||||||
\(104\) | −7.82090e24 | −0.479005 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.21255e25 | 1.06799 | ||||||||
\(107\) | −6.60004e24 | −0.283302 | −0.141651 | − | 0.989917i | \(-0.545241\pi\) | ||||
−0.141651 | + | 0.989917i | \(0.545241\pi\) | |||||||
\(108\) | 6.42983e24 | 0.245699 | ||||||||
\(109\) | −6.35443e24 | −0.216394 | −0.108197 | − | 0.994129i | \(-0.534508\pi\) | ||||
−0.108197 | + | 0.994129i | \(0.534508\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.25735e24 | 0.224029 | ||||||||
\(112\) | 1.79888e25 | 0.436291 | ||||||||
\(113\) | −5.12661e25 | −1.11263 | −0.556313 | − | 0.830973i | \(-0.687785\pi\) | ||||
−0.556313 | + | 0.830973i | \(0.687785\pi\) | |||||||
\(114\) | −8.08791e24 | −0.157226 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.74073e25 | −0.428688 | ||||||||
\(117\) | 9.02138e25 | 1.26750 | ||||||||
\(118\) | −4.63775e25 | −0.585844 | ||||||||
\(119\) | −6.08759e25 | −0.692004 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.18647e25 | −0.663282 | ||||||||
\(122\) | −1.16180e26 | −0.967460 | ||||||||
\(123\) | 5.51368e25 | 0.414598 | ||||||||
\(124\) | −1.31276e26 | −0.892099 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.07500e26 | −1.15448 | ||||||||
\(127\) | −1.52068e26 | −0.766462 | −0.383231 | − | 0.923653i | \(-0.625189\pi\) | ||||
−0.383231 | + | 0.923653i | \(0.625189\pi\) | |||||||
\(128\) | 1.93428e25 | 0.0883883 | ||||||||
\(129\) | 7.70794e24 | 0.0319571 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.54456e26 | −1.55454 | −0.777268 | − | 0.629170i | \(-0.783395\pi\) | ||||
−0.777268 | + | 0.629170i | \(0.783395\pi\) | |||||||
\(132\) | −2.36814e25 | −0.0736602 | ||||||||
\(133\) | 5.39999e26 | 1.52844 | ||||||||
\(134\) | 4.75940e26 | 1.22671 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.54581e25 | −0.140193 | ||||||||
\(137\) | −5.90117e25 | −0.115327 | −0.0576635 | − | 0.998336i | \(-0.518365\pi\) | ||||
−0.0576635 | + | 0.998336i | \(0.518365\pi\) | |||||||
\(138\) | −1.45426e25 | −0.0259510 | ||||||||
\(139\) | −1.48479e26 | −0.242091 | −0.121046 | − | 0.992647i | \(-0.538625\pi\) | ||||
−0.121046 | + | 0.992647i | \(0.538625\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.26921e25 | 0.0582249 | ||||||||
\(142\) | 4.69405e26 | 0.586062 | ||||||||
\(143\) | −6.87414e26 | −0.786173 | ||||||||
\(144\) | −2.23119e26 | −0.233886 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.62544e25 | 0.0319853 | ||||||||
\(147\) | −6.41088e26 | −0.519339 | ||||||||
\(148\) | −5.92809e26 | −0.441208 | ||||||||
\(149\) | −5.34888e26 | −0.365961 | −0.182981 | − | 0.983117i | \(-0.558575\pi\) | ||||
−0.182981 | + | 0.983117i | \(0.558575\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.12275e27 | 1.22938 | 0.614691 | − | 0.788768i | \(-0.289281\pi\) | ||||
0.614691 | + | 0.788768i | \(0.289281\pi\) | |||||||
\(152\) | 5.80645e26 | 0.309646 | ||||||||
\(153\) | 7.55056e26 | 0.370968 | ||||||||
\(154\) | 1.58112e27 | 0.716069 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.46213e26 | 0.171983 | ||||||||
\(157\) | −1.66162e26 | −0.0591271 | −0.0295636 | − | 0.999563i | \(-0.509412\pi\) | ||||
−0.0295636 | + | 0.999563i | \(0.509412\pi\) | |||||||
\(158\) | 8.90456e26 | 0.292684 | ||||||||
\(159\) | −1.26234e27 | −0.383454 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.70956e26 | 0.252276 | ||||||||
\(162\) | 2.38413e27 | 0.573314 | ||||||||
\(163\) | −2.97944e27 | −0.663421 | −0.331710 | − | 0.943381i | \(-0.607626\pi\) | ||||
−0.331710 | + | 0.943381i | \(0.607626\pi\) | |||||||
\(164\) | −3.95837e27 | −0.816522 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.64786e26 | −0.0469401 | ||||||||
\(167\) | −8.95870e27 | −1.47329 | −0.736647 | − | 0.676278i | \(-0.763592\pi\) | ||||
−0.736647 | + | 0.676278i | \(0.763592\pi\) | |||||||
\(168\) | −1.02633e27 | −0.156647 | ||||||||
\(169\) | 5.89610e27 | 0.835567 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.69772e27 | −0.819361 | ||||||||
\(172\) | −5.53367e26 | −0.0629372 | ||||||||
\(173\) | −1.40879e28 | −1.49028 | −0.745142 | − | 0.666905i | \(-0.767619\pi\) | ||||
−0.745142 | + | 0.666905i | \(0.767619\pi\) | |||||||
\(174\) | 1.56369e27 | 0.153917 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.70013e27 | 0.145068 | ||||||||
\(177\) | 2.64602e27 | 0.210342 | ||||||||
\(178\) | 1.46365e28 | 1.08440 | ||||||||
\(179\) | 9.19738e27 | 0.635333 | 0.317667 | − | 0.948202i | \(-0.397101\pi\) | ||||
0.317667 | + | 0.948202i | \(0.397101\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.77373e28 | 1.66756 | 0.833782 | − | 0.552094i | \(-0.186171\pi\) | ||||
0.833782 | + | 0.552094i | \(0.186171\pi\) | |||||||
\(182\) | −2.97920e28 | −1.67189 | ||||||||
\(183\) | 6.62852e27 | 0.347358 | ||||||||
\(184\) | 1.04404e27 | 0.0511087 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.48979e27 | 0.320301 | ||||||||
\(187\) | −5.75341e27 | −0.230094 | ||||||||
\(188\) | −3.06494e27 | −0.114670 | ||||||||
\(189\) | 2.44930e28 | 0.857570 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.68120e28 | −0.516064 | −0.258032 | − | 0.966136i | \(-0.583074\pi\) | ||||
−0.258032 | + | 0.966136i | \(0.583074\pi\) | |||||||
\(192\) | −1.10358e27 | −0.0317351 | ||||||||
\(193\) | 2.97967e28 | 0.802975 | 0.401487 | − | 0.915865i | \(-0.368493\pi\) | ||||
0.401487 | + | 0.915865i | \(0.368493\pi\) | |||||||
\(194\) | −1.02150e28 | −0.258057 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.60248e28 | 1.02280 | ||||||||
\(197\) | 8.93281e27 | 0.186277 | 0.0931387 | − | 0.995653i | \(-0.470310\pi\) | ||||
0.0931387 | + | 0.995653i | \(0.470310\pi\) | |||||||
\(198\) | −1.96109e28 | −0.383869 | ||||||||
\(199\) | −9.58646e28 | −1.76196 | −0.880978 | − | 0.473157i | \(-0.843114\pi\) | ||||
−0.880978 | + | 0.473157i | \(0.843114\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.71542e28 | −0.440440 | ||||||||
\(202\) | −5.52159e28 | −0.841728 | ||||||||
\(203\) | −1.04402e29 | −1.49626 | ||||||||
\(204\) | 3.73464e27 | 0.0503352 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.12956e28 | −0.969899 | ||||||||
\(207\) | −1.20430e28 | −0.135240 | ||||||||
\(208\) | −3.20344e28 | −0.338708 | ||||||||
\(209\) | 5.10355e28 | 0.508211 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.69613e27 | 0.0503558 | 0.0251779 | − | 0.999683i | \(-0.491985\pi\) | ||||
0.0251779 | + | 0.999683i | \(0.491985\pi\) | |||||||
\(212\) | 9.06259e28 | 0.755186 | ||||||||
\(213\) | −2.67814e28 | −0.210420 | ||||||||
\(214\) | −2.70338e28 | −0.200325 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.63366e28 | 0.173735 | ||||||||
\(217\) | −5.00065e29 | −3.11372 | ||||||||
\(218\) | −2.60278e28 | −0.153014 | ||||||||
\(219\) | −2.06846e27 | −0.0114840 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.08408e29 | 0.537226 | ||||||||
\(222\) | 3.38221e28 | 0.158412 | ||||||||
\(223\) | −5.84548e28 | −0.258827 | −0.129413 | − | 0.991591i | \(-0.541309\pi\) | ||||
−0.129413 | + | 0.991591i | \(0.541309\pi\) | |||||||
\(224\) | 7.36821e28 | 0.308505 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.09986e29 | −0.786746 | ||||||||
\(227\) | −5.52270e29 | −1.95807 | −0.979035 | − | 0.203691i | \(-0.934706\pi\) | ||||
−0.979035 | + | 0.203691i | \(0.934706\pi\) | |||||||
\(228\) | −3.31281e28 | −0.111176 | ||||||||
\(229\) | −5.80273e28 | −0.184369 | −0.0921847 | − | 0.995742i | \(-0.529385\pi\) | ||||
−0.0921847 | + | 0.995742i | \(0.529385\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.02088e28 | −0.257098 | ||||||||
\(232\) | −1.12260e29 | −0.303128 | ||||||||
\(233\) | 1.93762e29 | 0.495816 | 0.247908 | − | 0.968784i | \(-0.420257\pi\) | ||||
0.247908 | + | 0.968784i | \(0.420257\pi\) | |||||||
\(234\) | 3.69516e29 | 0.896261 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.89962e29 | −0.414254 | ||||||||
\(237\) | −5.08040e28 | −0.105086 | ||||||||
\(238\) | −2.49348e29 | −0.489321 | ||||||||
\(239\) | 7.15964e28 | 0.133327 | 0.0666634 | − | 0.997776i | \(-0.478765\pi\) | ||||
0.0666634 | + | 0.997776i | \(0.478765\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.42045e29 | −1.41293 | −0.706467 | − | 0.707746i | \(-0.749712\pi\) | ||||
−0.706467 | + | 0.707746i | \(0.749712\pi\) | |||||||
\(242\) | −2.94358e29 | −0.469011 | ||||||||
\(243\) | −4.60746e29 | −0.697241 | ||||||||
\(244\) | −4.75873e29 | −0.684098 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.25840e29 | 0.293165 | ||||||||
\(247\) | −9.61630e29 | −1.18658 | ||||||||
\(248\) | −5.37705e29 | −0.630809 | ||||||||
\(249\) | 1.51071e28 | 0.0168535 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.23321e28 | −0.0326372 | −0.0163186 | − | 0.999867i | \(-0.505195\pi\) | ||||
−0.0163186 | + | 0.999867i | \(0.505195\pi\) | |||||||
\(252\) | −8.49920e29 | −0.816340 | ||||||||
\(253\) | 9.17654e28 | 0.0838827 | ||||||||
\(254\) | −6.22869e29 | −0.541970 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | 2.39756e29 | 0.180138 | 0.0900689 | − | 0.995936i | \(-0.471291\pi\) | ||||
0.0900689 | + | 0.995936i | \(0.471291\pi\) | |||||||
\(258\) | 3.15717e28 | 0.0225971 | ||||||||
\(259\) | −2.25817e30 | −1.53996 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.29492e30 | 0.802114 | ||||||||
\(262\) | −1.86145e30 | −1.09922 | ||||||||
\(263\) | −2.50236e30 | −1.40898 | −0.704488 | − | 0.709716i | \(-0.748823\pi\) | ||||
−0.704488 | + | 0.709716i | \(0.748823\pi\) | |||||||
\(264\) | −9.69989e28 | −0.0520856 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.21184e30 | 1.08077 | ||||||||
\(267\) | −8.35070e29 | −0.389343 | ||||||||
\(268\) | 1.94945e30 | 0.867415 | ||||||||
\(269\) | 3.20998e30 | 1.36332 | 0.681662 | − | 0.731667i | \(-0.261257\pi\) | ||||
0.681662 | + | 0.731667i | \(0.261257\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.88885e30 | 0.731277 | 0.365638 | − | 0.930757i | \(-0.380851\pi\) | ||||
0.365638 | + | 0.930757i | \(0.380851\pi\) | |||||||
\(272\) | −2.68116e29 | −0.0991316 | ||||||||
\(273\) | 1.69975e30 | 0.600277 | ||||||||
\(274\) | −2.41712e29 | −0.0815485 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.95666e28 | −0.0183501 | ||||||||
\(277\) | −2.14925e29 | −0.0632835 | −0.0316417 | − | 0.999499i | \(-0.510074\pi\) | ||||
−0.0316417 | + | 0.999499i | \(0.510074\pi\) | |||||||
\(278\) | −6.08169e29 | −0.171184 | ||||||||
\(279\) | 6.20241e30 | 1.66920 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.34905e30 | −0.332048 | −0.166024 | − | 0.986122i | \(-0.553093\pi\) | ||||
−0.166024 | + | 0.986122i | \(0.553093\pi\) | |||||||
\(282\) | 1.74867e29 | 0.0411712 | ||||||||
\(283\) | −7.01801e30 | −1.58082 | −0.790412 | − | 0.612576i | \(-0.790133\pi\) | ||||
−0.790412 | + | 0.612576i | \(0.790133\pi\) | |||||||
\(284\) | 1.92268e30 | 0.414408 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.81565e30 | −0.555908 | ||||||||
\(287\) | −1.50785e31 | −2.84993 | ||||||||
\(288\) | −9.13894e29 | −0.165382 | ||||||||
\(289\) | −4.86329e30 | −0.842767 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.82805e29 | 0.0926533 | ||||||||
\(292\) | 1.48498e29 | 0.0226170 | ||||||||
\(293\) | 4.23132e30 | 0.617491 | 0.308746 | − | 0.951145i | \(-0.400091\pi\) | ||||
0.308746 | + | 0.951145i | \(0.400091\pi\) | |||||||
\(294\) | −2.62590e30 | −0.367228 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.42815e30 | −0.311981 | ||||||||
\(297\) | 2.31484e30 | 0.285145 | ||||||||
\(298\) | −2.19090e30 | −0.258774 | ||||||||
\(299\) | −1.72908e30 | −0.195850 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.10793e30 | −0.219672 | ||||||||
\(302\) | 8.69478e30 | 0.869304 | ||||||||
\(303\) | 3.15028e30 | 0.302215 | ||||||||
\(304\) | 2.37832e30 | 0.218953 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.09271e30 | 0.262314 | ||||||||
\(307\) | 3.15394e30 | 0.256817 | 0.128409 | − | 0.991721i | \(-0.459013\pi\) | ||||
0.128409 | + | 0.991721i | \(0.459013\pi\) | |||||||
\(308\) | 6.47625e30 | 0.506337 | ||||||||
\(309\) | 4.63823e30 | 0.348234 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.98559e31 | 1.37526 | 0.687628 | − | 0.726063i | \(-0.258652\pi\) | ||||
0.687628 | + | 0.726063i | \(0.258652\pi\) | |||||||
\(312\) | 1.82769e30 | 0.121610 | ||||||||
\(313\) | 5.47200e29 | 0.0349818 | 0.0174909 | − | 0.999847i | \(-0.494432\pi\) | ||||
0.0174909 | + | 0.999847i | \(0.494432\pi\) | |||||||
\(314\) | −6.80601e29 | −0.0418092 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.64731e30 | 0.206959 | ||||||||
\(317\) | 2.18550e31 | 1.19209 | 0.596046 | − | 0.802950i | \(-0.296737\pi\) | ||||
0.596046 | + | 0.802950i | \(0.296737\pi\) | |||||||
\(318\) | −5.17056e30 | −0.271143 | ||||||||
\(319\) | −9.86707e30 | −0.497513 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.54238e30 | 0.0719249 | ||||||||
\(322\) | 3.97704e30 | 0.178386 | ||||||||
\(323\) | −8.04849e30 | −0.347282 | ||||||||
\(324\) | 9.76540e30 | 0.405394 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.22038e31 | −0.469109 | ||||||||
\(327\) | 1.48499e30 | 0.0549383 | ||||||||
\(328\) | −1.62135e31 | −0.577368 | ||||||||
\(329\) | −1.16752e31 | −0.400236 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.93057e31 | −0.931325 | −0.465663 | − | 0.884962i | \(-0.654184\pi\) | ||||
−0.465663 | + | 0.884962i | \(0.654184\pi\) | |||||||
\(332\) | −1.08456e30 | −0.0331917 | ||||||||
\(333\) | 2.80086e31 | 0.825540 | ||||||||
\(334\) | −3.66949e31 | −1.04178 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.20385e30 | −0.110766 | ||||||||
\(337\) | 4.60143e31 | 1.16821 | 0.584103 | − | 0.811680i | \(-0.301447\pi\) | ||||
0.584103 | + | 0.811680i | \(0.301447\pi\) | |||||||
\(338\) | 2.41504e31 | 0.590835 | ||||||||
\(339\) | 1.19805e31 | 0.282474 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.72613e31 | −1.03532 | ||||||||
\(342\) | −2.74338e31 | −0.579376 | ||||||||
\(343\) | 8.96148e31 | 1.82475 | ||||||||
\(344\) | −2.26659e30 | −0.0445033 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.77039e31 | −1.05379 | ||||||||
\(347\) | 7.38077e31 | 1.30012 | 0.650060 | − | 0.759883i | \(-0.274744\pi\) | ||||
0.650060 | + | 0.759883i | \(0.274744\pi\) | |||||||
\(348\) | 6.40489e30 | 0.108836 | ||||||||
\(349\) | 3.56553e31 | 0.584530 | 0.292265 | − | 0.956337i | \(-0.405591\pi\) | ||||
0.292265 | + | 0.956337i | \(0.405591\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.36171e31 | −0.665760 | ||||||||
\(352\) | 6.96372e30 | 0.102579 | ||||||||
\(353\) | −8.69355e31 | −1.23599 | −0.617993 | − | 0.786184i | \(-0.712054\pi\) | ||||
−0.617993 | + | 0.786184i | \(0.712054\pi\) | |||||||
\(354\) | 1.08381e31 | 0.148735 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.99512e31 | 0.766783 | ||||||||
\(357\) | 1.42263e31 | 0.175686 | ||||||||
\(358\) | 3.76725e31 | 0.449248 | ||||||||
\(359\) | 2.26294e30 | 0.0260611 | 0.0130305 | − | 0.999915i | \(-0.495852\pi\) | ||||
0.0130305 | + | 0.999915i | \(0.495852\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.16825e31 | −0.232954 | ||||||||
\(362\) | 1.13612e32 | 1.17915 | ||||||||
\(363\) | 1.67943e31 | 0.168395 | ||||||||
\(364\) | −1.22028e32 | −1.18220 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.71504e31 | 0.245619 | ||||||||
\(367\) | 3.34192e31 | 0.292193 | 0.146096 | − | 0.989270i | \(-0.453329\pi\) | ||||
0.146096 | + | 0.989270i | \(0.453329\pi\) | |||||||
\(368\) | 4.27639e30 | 0.0361393 | ||||||||
\(369\) | 1.87022e32 | 1.52779 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.45219e32 | 2.63585 | ||||||||
\(372\) | 3.06782e31 | 0.226487 | ||||||||
\(373\) | −1.79027e32 | −1.27808 | −0.639041 | − | 0.769172i | \(-0.720669\pi\) | ||||
−0.639041 | + | 0.769172i | \(0.720669\pi\) | |||||||
\(374\) | −2.35660e31 | −0.162701 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.25540e31 | −0.0810839 | ||||||||
\(377\) | 1.85919e32 | 1.16160 | ||||||||
\(378\) | 1.00323e32 | 0.606393 | ||||||||
\(379\) | −9.45760e31 | −0.553084 | −0.276542 | − | 0.961002i | \(-0.589188\pi\) | ||||
−0.276542 | + | 0.961002i | \(0.589188\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.55371e31 | 0.194590 | ||||||||
\(382\) | −6.88621e31 | −0.364912 | ||||||||
\(383\) | 2.01782e32 | 1.03490 | 0.517449 | − | 0.855714i | \(-0.326882\pi\) | ||||
0.517449 | + | 0.855714i | \(0.326882\pi\) | |||||||
\(384\) | −4.52028e30 | −0.0224401 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.22047e32 | 0.567789 | ||||||||
\(387\) | 2.61450e31 | 0.117761 | ||||||||
\(388\) | −4.18406e31 | −0.182474 | ||||||||
\(389\) | 1.16247e32 | 0.490921 | 0.245460 | − | 0.969407i | \(-0.421061\pi\) | ||||
0.245460 | + | 0.969407i | \(0.421061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.44717e31 | −0.0573207 | ||||||||
\(392\) | 1.88518e32 | 0.723230 | ||||||||
\(393\) | 1.06203e32 | 0.394667 | ||||||||
\(394\) | 3.65888e31 | 0.131718 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.03262e31 | −0.271436 | ||||||||
\(397\) | 2.03760e32 | 0.667172 | 0.333586 | − | 0.942720i | \(-0.391741\pi\) | ||||
0.333586 | + | 0.942720i | \(0.391741\pi\) | |||||||
\(398\) | −3.92662e32 | −1.24589 | ||||||||
\(399\) | −1.26194e32 | −0.388041 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.67418e32 | −0.483613 | −0.241806 | − | 0.970324i | \(-0.577740\pi\) | ||||
−0.241806 | + | 0.970324i | \(0.577740\pi\) | |||||||
\(402\) | −1.11224e32 | −0.311438 | ||||||||
\(403\) | 8.90515e32 | 2.41729 | ||||||||
\(404\) | −2.26164e32 | −0.595192 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.27630e32 | −1.05802 | ||||||||
\(407\) | −2.13421e32 | −0.512043 | ||||||||
\(408\) | 1.52971e31 | 0.0355924 | ||||||||
\(409\) | 7.52295e32 | 1.69765 | 0.848823 | − | 0.528678i | \(-0.177312\pi\) | ||||
0.848823 | + | 0.528678i | \(0.177312\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.37906e31 | 0.0292793 | ||||||||
\(412\) | −3.32987e32 | −0.685822 | ||||||||
\(413\) | −7.23618e32 | −1.44589 | ||||||||
\(414\) | −4.93280e31 | −0.0956288 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.31213e32 | −0.239503 | ||||||||
\(417\) | 3.46984e31 | 0.0614623 | ||||||||
\(418\) | 2.09041e32 | 0.359359 | ||||||||
\(419\) | −6.25496e31 | −0.104364 | −0.0521818 | − | 0.998638i | \(-0.516618\pi\) | ||||
−0.0521818 | + | 0.998638i | \(0.516618\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.02159e32 | 1.26106 | 0.630528 | − | 0.776167i | \(-0.282838\pi\) | ||||
0.630528 | + | 0.776167i | \(0.282838\pi\) | |||||||
\(422\) | 2.33314e31 | 0.0356069 | ||||||||
\(423\) | 1.44810e32 | 0.214558 | ||||||||
\(424\) | 3.71204e32 | 0.533997 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.09697e32 | −0.148790 | ||||||||
\(427\) | −1.81273e33 | −2.38773 | ||||||||
\(428\) | −1.10730e32 | −0.141651 | ||||||||
\(429\) | 1.60644e32 | 0.199594 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.32299e33 | 1.55092 | 0.775460 | − | 0.631397i | \(-0.217518\pi\) | ||||
0.775460 | + | 0.631397i | \(0.217518\pi\) | |||||||
\(432\) | 1.07875e32 | 0.122849 | ||||||||
\(433\) | −1.44206e33 | −1.59546 | −0.797730 | − | 0.603015i | \(-0.793966\pi\) | ||||
−0.797730 | + | 0.603015i | \(0.793966\pi\) | |||||||
\(434\) | −2.04827e33 | −2.20173 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.06610e32 | −0.108197 | ||||||||
\(437\) | 1.28371e32 | 0.126605 | ||||||||
\(438\) | −8.47240e30 | −0.00812045 | ||||||||
\(439\) | 9.88019e32 | 0.920362 | 0.460181 | − | 0.887825i | \(-0.347785\pi\) | ||||
0.460181 | + | 0.887825i | \(0.347785\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.17454e33 | −1.91375 | ||||||||
\(442\) | 4.44038e32 | 0.379876 | ||||||||
\(443\) | −6.78172e32 | −0.564018 | −0.282009 | − | 0.959412i | \(-0.591001\pi\) | ||||
−0.282009 | + | 0.959412i | \(0.591001\pi\) | |||||||
\(444\) | 1.38535e32 | 0.112014 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.39431e32 | −0.183018 | ||||||||
\(447\) | 1.25000e32 | 0.0929104 | ||||||||
\(448\) | 3.01802e32 | 0.218146 | ||||||||
\(449\) | −1.40094e33 | −0.984784 | −0.492392 | − | 0.870374i | \(-0.663877\pi\) | ||||
−0.492392 | + | 0.870374i | \(0.663877\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.42507e33 | −0.947613 | ||||||||
\(452\) | −8.60102e32 | −0.556313 | ||||||||
\(453\) | −4.96071e32 | −0.312116 | ||||||||
\(454\) | −2.26210e33 | −1.38456 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.35693e32 | −0.0786132 | ||||||||
\(457\) | −2.87797e33 | −1.62231 | −0.811156 | − | 0.584830i | \(-0.801161\pi\) | ||||
−0.811156 | + | 0.584830i | \(0.801161\pi\) | |||||||
\(458\) | −2.37680e32 | −0.130369 | ||||||||
\(459\) | −3.65059e32 | −0.194852 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.62750e32 | −0.233930 | −0.116965 | − | 0.993136i | \(-0.537316\pi\) | ||||
−0.116965 | + | 0.993136i | \(0.537316\pi\) | |||||||
\(462\) | −3.69495e32 | −0.181796 | ||||||||
\(463\) | −2.53220e32 | −0.121265 | −0.0606325 | − | 0.998160i | \(-0.519312\pi\) | ||||
−0.0606325 | + | 0.998160i | \(0.519312\pi\) | |||||||
\(464\) | −4.59818e32 | −0.214344 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.93650e32 | 0.350595 | ||||||||
\(467\) | 1.56052e33 | 0.671134 | 0.335567 | − | 0.942016i | \(-0.391072\pi\) | ||||
0.335567 | + | 0.942016i | \(0.391072\pi\) | |||||||
\(468\) | 1.51354e33 | 0.633752 | ||||||||
\(469\) | 7.42598e33 | 3.02757 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.88309e31 | 0.0150112 | ||||||||
\(472\) | −7.78085e32 | −0.292922 | ||||||||
\(473\) | −1.99221e32 | −0.0730416 | ||||||||
\(474\) | −2.08093e32 | −0.0743068 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.02133e33 | −0.346002 | ||||||||
\(477\) | −4.28182e33 | −1.41302 | ||||||||
\(478\) | 2.93259e32 | 0.0942763 | ||||||||
\(479\) | 7.23567e32 | 0.226613 | 0.113306 | − | 0.993560i | \(-0.463856\pi\) | ||||
0.113306 | + | 0.993560i | \(0.463856\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.02135e33 | 1.19553 | ||||||||
\(482\) | −3.44901e33 | −0.999096 | ||||||||
\(483\) | −2.26905e32 | −0.0640480 | ||||||||
\(484\) | −1.20569e33 | −0.331641 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.88721e33 | −0.493024 | ||||||||
\(487\) | −3.11091e33 | −0.792091 | −0.396046 | − | 0.918231i | \(-0.629618\pi\) | ||||
−0.396046 | + | 0.918231i | \(0.629618\pi\) | |||||||
\(488\) | −1.94918e33 | −0.483730 | ||||||||
\(489\) | 6.96273e32 | 0.168430 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.51132e33 | 0.807146 | 0.403573 | − | 0.914948i | \(-0.367768\pi\) | ||||
0.403573 | + | 0.914948i | \(0.367768\pi\) | |||||||
\(492\) | 9.25042e32 | 0.207299 | ||||||||
\(493\) | 1.55607e33 | 0.339972 | ||||||||
\(494\) | −3.93883e33 | −0.839037 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.20244e33 | −0.446050 | ||||||||
\(497\) | 7.32402e33 | 1.44642 | ||||||||
\(498\) | 6.18787e31 | 0.0119172 | ||||||||
\(499\) | 8.78119e33 | 1.64929 | 0.824644 | − | 0.565652i | \(-0.191376\pi\) | ||||
0.824644 | + | 0.565652i | \(0.191376\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.09358e33 | 0.374041 | ||||||||
\(502\) | −1.32432e32 | −0.0230780 | ||||||||
\(503\) | 1.68186e33 | 0.285883 | 0.142942 | − | 0.989731i | \(-0.454344\pi\) | ||||
0.142942 | + | 0.989731i | \(0.454344\pi\) | |||||||
\(504\) | −3.48127e33 | −0.577240 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.75871e32 | 0.0593140 | ||||||||
\(507\) | −1.37788e33 | −0.212134 | ||||||||
\(508\) | −2.55127e33 | −0.383231 | ||||||||
\(509\) | −5.67785e33 | −0.832169 | −0.416084 | − | 0.909326i | \(-0.636598\pi\) | ||||
−0.416084 | + | 0.909326i | \(0.636598\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.65670e32 | 0.0789409 | ||||||||
\(512\) | 3.24519e32 | 0.0441942 | ||||||||
\(513\) | 3.23825e33 | 0.430372 | ||||||||
\(514\) | 9.82039e32 | 0.127377 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.29318e32 | 0.0159785 | ||||||||
\(517\) | −1.10343e33 | −0.133080 | ||||||||
\(518\) | −9.24948e33 | −1.08892 | ||||||||
\(519\) | 3.29224e33 | 0.378355 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.57848e33 | 0.939591 | 0.469796 | − | 0.882775i | \(-0.344328\pi\) | ||||
0.469796 | + | 0.882775i | \(0.344328\pi\) | |||||||
\(522\) | 5.30399e33 | 0.567180 | ||||||||
\(523\) | −1.65708e34 | −1.73010 | −0.865052 | − | 0.501683i | \(-0.832714\pi\) | ||||
−0.865052 | + | 0.501683i | \(0.832714\pi\) | |||||||
\(524\) | −7.62451e33 | −0.777268 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.02497e34 | −0.996296 | ||||||||
\(527\) | 7.45329e33 | 0.707482 | ||||||||
\(528\) | −3.97307e32 | −0.0368301 | ||||||||
\(529\) | −1.08149e34 | −0.979103 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.97518e33 | 0.775107 | ||||||||
\(532\) | 9.05968e33 | 0.764218 | ||||||||
\(533\) | 2.68518e34 | 2.21250 | ||||||||
\(534\) | −3.42045e33 | −0.275307 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.98494e33 | 0.613355 | ||||||||
\(537\) | −2.14936e33 | −0.161299 | ||||||||
\(538\) | 1.31481e34 | 0.964016 | ||||||||
\(539\) | 1.65697e34 | 1.18701 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.23198e33 | −0.289453 | −0.144727 | − | 0.989472i | \(-0.546230\pi\) | ||||
−0.144727 | + | 0.989472i | \(0.546230\pi\) | |||||||
\(542\) | 7.73674e33 | 0.517091 | ||||||||
\(543\) | −6.48202e33 | −0.423362 | ||||||||
\(544\) | −1.09820e33 | −0.0700966 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.96217e33 | 0.424460 | ||||||||
\(547\) | 5.57179e33 | 0.332011 | 0.166006 | − | 0.986125i | \(-0.446913\pi\) | ||||
0.166006 | + | 0.986125i | \(0.446913\pi\) | |||||||
\(548\) | −9.90052e32 | −0.0576635 | ||||||||
\(549\) | 2.24837e34 | 1.28001 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.38031e34 | −0.750900 | ||||||||
\(552\) | −2.43985e32 | −0.0129755 | ||||||||
\(553\) | 1.38936e34 | 0.722355 | ||||||||
\(554\) | −8.80334e32 | −0.0447482 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.49106e33 | −0.121046 | ||||||||
\(557\) | 1.51207e34 | 0.718427 | 0.359213 | − | 0.933255i | \(-0.383045\pi\) | ||||
0.359213 | + | 0.933255i | \(0.383045\pi\) | |||||||
\(558\) | 2.54051e34 | 1.18030 | ||||||||
\(559\) | 3.75379e33 | 0.170539 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.34453e33 | 0.0584164 | ||||||||
\(562\) | −5.52573e33 | −0.234793 | ||||||||
\(563\) | −1.21471e34 | −0.504799 | −0.252400 | − | 0.967623i | \(-0.581220\pi\) | ||||
−0.252400 | + | 0.967623i | \(0.581220\pi\) | |||||||
\(564\) | 7.16255e32 | 0.0291125 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.87458e34 | −1.11781 | ||||||||
\(567\) | 3.71991e34 | 1.41496 | ||||||||
\(568\) | 7.87531e33 | 0.293031 | ||||||||
\(569\) | 2.58692e34 | 0.941628 | 0.470814 | − | 0.882232i | \(-0.343960\pi\) | ||||
0.470814 | + | 0.882232i | \(0.343960\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.34607e34 | −1.16569 | −0.582846 | − | 0.812583i | \(-0.698061\pi\) | ||||
−0.582846 | + | 0.812583i | \(0.698061\pi\) | |||||||
\(572\) | −1.15329e34 | −0.393086 | ||||||||
\(573\) | 3.92885e33 | 0.131019 | ||||||||
\(574\) | −6.17615e34 | −2.01521 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.74331e33 | −0.116943 | ||||||||
\(577\) | 1.34968e34 | 0.412603 | 0.206302 | − | 0.978488i | \(-0.433857\pi\) | ||||
0.206302 | + | 0.978488i | \(0.433857\pi\) | |||||||
\(578\) | −1.99201e34 | −0.595926 | ||||||||
\(579\) | −6.96328e33 | −0.203860 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.13140e33 | −0.115850 | ||||||||
\(582\) | 2.38717e33 | 0.0655158 | ||||||||
\(583\) | 3.26268e34 | 0.876429 | ||||||||
\(584\) | 6.08248e32 | 0.0159926 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.73315e34 | 0.436632 | ||||||||
\(587\) | 4.17737e34 | 1.03021 | 0.515107 | − | 0.857126i | \(-0.327752\pi\) | ||||
0.515107 | + | 0.857126i | \(0.327752\pi\) | |||||||
\(588\) | −1.07557e34 | −0.259670 | ||||||||
\(589\) | −6.61143e34 | −1.56262 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.08753e33 | −0.0472923 | ||||||||
\(592\) | −9.94569e33 | −0.220604 | ||||||||
\(593\) | 2.55607e33 | 0.0555123 | 0.0277562 | − | 0.999615i | \(-0.491164\pi\) | ||||
0.0277562 | + | 0.999615i | \(0.491164\pi\) | |||||||
\(594\) | 9.48160e33 | 0.201628 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.97394e33 | −0.182981 | ||||||||
\(597\) | 2.24029e34 | 0.447327 | ||||||||
\(598\) | −7.08230e33 | −0.138487 | ||||||||
\(599\) | 4.70324e34 | 0.900662 | 0.450331 | − | 0.892862i | \(-0.351306\pi\) | ||||
0.450331 | + | 0.892862i | \(0.351306\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.96787e34 | 1.09620 | 0.548099 | − | 0.836414i | \(-0.315352\pi\) | ||||
0.548099 | + | 0.836414i | \(0.315352\pi\) | |||||||
\(602\) | −8.63406e33 | −0.155331 | ||||||||
\(603\) | −9.21060e34 | −1.62301 | ||||||||
\(604\) | 3.56138e34 | 0.614691 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.29036e34 | 0.213699 | ||||||||
\(607\) | 2.92667e34 | 0.474804 | 0.237402 | − | 0.971411i | \(-0.423704\pi\) | ||||
0.237402 | + | 0.971411i | \(0.423704\pi\) | |||||||
\(608\) | 9.74161e33 | 0.154823 | ||||||||
\(609\) | 2.43980e34 | 0.379872 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.07912e34 | 0.310717 | ||||||||
\(612\) | 1.26677e34 | 0.185484 | ||||||||
\(613\) | −8.48844e34 | −1.21779 | −0.608895 | − | 0.793251i | \(-0.708387\pi\) | ||||
−0.608895 | + | 0.793251i | \(0.708387\pi\) | |||||||
\(614\) | 1.29186e34 | 0.181597 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.65267e34 | 0.358034 | ||||||||
\(617\) | −1.30414e35 | −1.72488 | −0.862442 | − | 0.506156i | \(-0.831066\pi\) | ||||
−0.862442 | + | 0.506156i | \(0.831066\pi\) | |||||||
\(618\) | 1.89982e34 | 0.246239 | ||||||||
\(619\) | −8.02670e34 | −1.01954 | −0.509770 | − | 0.860311i | \(-0.670269\pi\) | ||||
−0.509770 | + | 0.860311i | \(0.670269\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.82260e33 | 0.0710350 | ||||||||
\(622\) | 8.13296e34 | 0.972453 | ||||||||
\(623\) | 2.28370e35 | 2.67633 | ||||||||
\(624\) | 7.48621e33 | 0.0859913 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.24133e33 | 0.0247359 | ||||||||
\(627\) | −1.19266e34 | −0.129025 | ||||||||
\(628\) | −2.78774e33 | −0.0295636 | ||||||||
\(629\) | 3.36573e34 | 0.349901 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.51125e34 | −0.350828 | −0.175414 | − | 0.984495i | \(-0.556126\pi\) | ||||
−0.175414 | + | 0.984495i | \(0.556126\pi\) | |||||||
\(632\) | 1.49394e34 | 0.146342 | ||||||||
\(633\) | −1.33115e33 | −0.0127844 | ||||||||
\(634\) | 8.95181e34 | 0.842937 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.11786e34 | −0.191727 | ||||||||
\(637\) | −3.12212e35 | −2.77145 | ||||||||
\(638\) | −4.04155e34 | −0.351795 | ||||||||
\(639\) | −9.08413e34 | −0.775394 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.10476e35 | −0.906862 | −0.453431 | − | 0.891291i | \(-0.649800\pi\) | ||||
−0.453431 | + | 0.891291i | \(0.649800\pi\) | |||||||
\(642\) | 6.31760e33 | 0.0508586 | ||||||||
\(643\) | −5.33371e34 | −0.421107 | −0.210553 | − | 0.977582i | \(-0.567527\pi\) | ||||
−0.210553 | + | 0.977582i | \(0.567527\pi\) | |||||||
\(644\) | 1.62899e34 | 0.126138 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.29666e34 | −0.245566 | ||||||||
\(647\) | −2.39579e34 | −0.175043 | −0.0875216 | − | 0.996163i | \(-0.527895\pi\) | ||||
−0.0875216 | + | 0.996163i | \(0.527895\pi\) | |||||||
\(648\) | 3.99991e34 | 0.286657 | ||||||||
\(649\) | −6.83894e34 | −0.480762 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.16862e35 | 0.790514 | ||||||||
\(652\) | −4.99866e34 | −0.331710 | ||||||||
\(653\) | −6.46858e34 | −0.421109 | −0.210554 | − | 0.977582i | \(-0.567527\pi\) | ||||
−0.210554 | + | 0.977582i | \(0.567527\pi\) | |||||||
\(654\) | 6.08250e33 | 0.0388472 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.64104e34 | −0.408261 | ||||||||
\(657\) | −7.01612e33 | −0.0423185 | ||||||||
\(658\) | −4.78217e34 | −0.283010 | ||||||||
\(659\) | 1.74748e35 | 1.01471 | 0.507357 | − | 0.861736i | \(-0.330623\pi\) | ||||
0.507357 | + | 0.861736i | \(0.330623\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.05707e35 | 1.15009 | 0.575044 | − | 0.818123i | \(-0.304985\pi\) | ||||
0.575044 | + | 0.818123i | \(0.304985\pi\) | |||||||
\(662\) | −1.20036e35 | −0.658547 | ||||||||
\(663\) | −2.53341e34 | −0.136391 | ||||||||
\(664\) | −4.44238e33 | −0.0234701 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.14723e35 | 0.583745 | ||||||||
\(667\) | −2.48190e34 | −0.123940 | ||||||||
\(668\) | −1.50302e35 | −0.736647 | ||||||||
\(669\) | 1.36605e34 | 0.0657112 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.71322e35 | −0.793928 | ||||||||
\(672\) | −1.72190e34 | −0.0783234 | ||||||||
\(673\) | −1.94000e35 | −0.866190 | −0.433095 | − | 0.901348i | \(-0.642579\pi\) | ||||
−0.433095 | + | 0.901348i | \(0.642579\pi\) | |||||||
\(674\) | 1.88475e35 | 0.826046 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.89201e34 | 0.417783 | ||||||||
\(677\) | 1.50061e35 | 0.622172 | 0.311086 | − | 0.950382i | \(-0.399307\pi\) | ||||
0.311086 | + | 0.950382i | \(0.399307\pi\) | |||||||
\(678\) | 4.90722e34 | 0.199740 | ||||||||
\(679\) | −1.59382e35 | −0.636895 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.29062e35 | 0.497116 | ||||||||
\(682\) | −1.93582e35 | −0.732084 | ||||||||
\(683\) | 2.23175e35 | 0.828679 | 0.414339 | − | 0.910122i | \(-0.364013\pi\) | ||||
0.414339 | + | 0.910122i | \(0.364013\pi\) | |||||||
\(684\) | −1.12369e35 | −0.409681 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.67062e35 | 1.29029 | ||||||||
\(687\) | 1.35606e34 | 0.0468078 | ||||||||
\(688\) | −9.28395e33 | −0.0314686 | ||||||||
\(689\) | −6.14765e35 | −2.04630 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.24403e34 | 0.136240 | 0.0681198 | − | 0.997677i | \(-0.478300\pi\) | ||||
0.0681198 | + | 0.997677i | \(0.478300\pi\) | |||||||
\(692\) | −2.36355e35 | −0.745142 | ||||||||
\(693\) | −3.05985e35 | −0.947402 | ||||||||
\(694\) | 3.02316e35 | 0.919324 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.62344e34 | 0.0769584 | ||||||||
\(697\) | 2.24740e35 | 0.647545 | ||||||||
\(698\) | 1.46044e35 | 0.413325 | ||||||||
\(699\) | −4.52808e34 | −0.125878 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.67347e35 | −1.79010 | −0.895048 | − | 0.445969i | \(-0.852859\pi\) | ||||
−0.895048 | + | 0.445969i | \(0.852859\pi\) | |||||||
\(702\) | −1.78656e35 | −0.470764 | ||||||||
\(703\) | −2.98556e35 | −0.772831 | ||||||||
\(704\) | 2.85234e34 | 0.0725342 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.56088e35 | −0.873974 | ||||||||
\(707\) | −8.61522e35 | −2.07742 | ||||||||
\(708\) | 4.43928e34 | 0.105171 | ||||||||
\(709\) | 5.82085e35 | 1.35490 | 0.677452 | − | 0.735567i | \(-0.263084\pi\) | ||||
0.677452 | + | 0.735567i | \(0.263084\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.72325e35 | −0.387238 | ||||||||
\(712\) | 2.45560e35 | 0.542198 | ||||||||
\(713\) | −1.18878e35 | −0.257919 | ||||||||
\(714\) | 5.82708e34 | 0.124229 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.54307e35 | 0.317667 | ||||||||
\(717\) | −1.67316e34 | −0.0338491 | ||||||||
\(718\) | 9.26900e33 | 0.0184280 | ||||||||
\(719\) | −4.08106e35 | −0.797374 | −0.398687 | − | 0.917087i | \(-0.630534\pi\) | ||||
−0.398687 | + | 0.917087i | \(0.630534\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.26844e36 | −2.39375 | ||||||||
\(722\) | −8.88115e34 | −0.164723 | ||||||||
\(723\) | 1.96780e35 | 0.358717 | ||||||||
\(724\) | 4.65355e35 | 0.833782 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.87893e34 | 0.119073 | ||||||||
\(727\) | −7.44759e34 | −0.126717 | −0.0633586 | − | 0.997991i | \(-0.520181\pi\) | ||||
−0.0633586 | + | 0.997991i | \(0.520181\pi\) | |||||||
\(728\) | −4.99826e35 | −0.835943 | ||||||||
\(729\) | −3.85503e35 | −0.633772 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.14179e34 | 0.0499125 | ||||||||
\(732\) | 1.11208e35 | 0.173679 | ||||||||
\(733\) | 1.00546e36 | 1.54371 | 0.771853 | − | 0.635802i | \(-0.219330\pi\) | ||||
0.771853 | + | 0.635802i | \(0.219330\pi\) | |||||||
\(734\) | 1.36885e35 | 0.206612 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.75161e34 | 0.0255543 | ||||||||
\(737\) | 7.01833e35 | 1.00668 | ||||||||
\(738\) | 7.66041e35 | 1.08031 | ||||||||
\(739\) | −7.42029e35 | −1.02888 | −0.514441 | − | 0.857526i | \(-0.672001\pi\) | ||||
−0.514441 | + | 0.857526i | \(0.672001\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.24726e35 | 0.301249 | ||||||||
\(742\) | 1.41402e36 | 1.86383 | ||||||||
\(743\) | 4.93877e35 | 0.640115 | 0.320058 | − | 0.947398i | \(-0.396298\pi\) | ||||
0.320058 | + | 0.947398i | \(0.396298\pi\) | |||||||
\(744\) | 1.25658e35 | 0.160150 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.33296e35 | −0.903741 | ||||||||
\(747\) | 5.12426e34 | 0.0621046 | ||||||||
\(748\) | −9.65262e34 | −0.115047 | ||||||||
\(749\) | −4.21802e35 | −0.494409 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.60017e36 | 1.81413 | 0.907063 | − | 0.420995i | \(-0.138319\pi\) | ||||
0.907063 | + | 0.420995i | \(0.138319\pi\) | |||||||
\(752\) | −5.14212e34 | −0.0573349 | ||||||||
\(753\) | 7.55579e33 | 0.00828595 | ||||||||
\(754\) | 7.61524e35 | 0.821375 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.10924e35 | 0.428785 | ||||||||
\(757\) | −9.77978e34 | −0.100376 | −0.0501881 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501881 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(758\) | −3.87383e35 | −0.391089 | ||||||||
\(759\) | −2.14449e34 | −0.0212962 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.42035e36 | 1.36485 | 0.682427 | − | 0.730954i | \(-0.260924\pi\) | ||||
0.682427 | + | 0.730954i | \(0.260924\pi\) | |||||||
\(762\) | 1.45560e35 | 0.137596 | ||||||||
\(763\) | −4.06106e35 | −0.377644 | ||||||||
\(764\) | −2.82059e35 | −0.258032 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.26499e35 | 0.731784 | ||||||||
\(767\) | 1.28862e36 | 1.12249 | ||||||||
\(768\) | −1.85151e34 | −0.0158675 | ||||||||
\(769\) | 4.43106e35 | 0.373619 | 0.186809 | − | 0.982396i | \(-0.440185\pi\) | ||||
0.186809 | + | 0.982396i | \(0.440185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.60292e34 | −0.0457335 | ||||||||
\(772\) | 4.99906e35 | 0.401487 | ||||||||
\(773\) | −1.04683e36 | −0.827241 | −0.413621 | − | 0.910449i | \(-0.635736\pi\) | ||||
−0.413621 | + | 0.910449i | \(0.635736\pi\) | |||||||
\(774\) | 1.07090e35 | 0.0832697 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.71379e35 | −0.129029 | ||||||||
\(777\) | 5.27719e35 | 0.390967 | ||||||||
\(778\) | 4.76147e35 | 0.347133 | ||||||||
\(779\) | −1.99355e36 | −1.43024 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.92196e35 | 0.480940 | ||||||||
\(782\) | −5.92763e34 | −0.0405319 | ||||||||
\(783\) | −6.26075e35 | −0.421313 | ||||||||
\(784\) | 7.72169e35 | 0.511401 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.35008e35 | 0.279071 | ||||||||
\(787\) | 1.02940e36 | 0.649977 | 0.324989 | − | 0.945718i | \(-0.394640\pi\) | ||||
0.324989 | + | 0.945718i | \(0.394640\pi\) | |||||||
\(788\) | 1.49868e35 | 0.0931387 | ||||||||
\(789\) | 5.84784e35 | 0.357712 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.27636e36 | −1.94172 | ||||||||
\(792\) | −3.29016e35 | −0.191934 | ||||||||
\(793\) | 3.22811e36 | 1.85367 | ||||||||
\(794\) | 8.34601e35 | 0.471762 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.60834e36 | −0.880978 | ||||||||
\(797\) | 2.74499e36 | 1.48017 | 0.740086 | − | 0.672512i | \(-0.234785\pi\) | ||||
0.740086 | + | 0.672512i | \(0.234785\pi\) | |||||||
\(798\) | −5.16890e35 | −0.274386 | ||||||||
\(799\) | 1.74015e35 | 0.0909393 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.83252e36 | −1.43472 | ||||||||
\(802\) | −6.85745e35 | −0.341966 | ||||||||
\(803\) | 5.34617e34 | 0.0262481 | ||||||||
\(804\) | −4.55572e35 | −0.220220 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.64755e36 | 1.70928 | ||||||||
\(807\) | −7.50150e35 | −0.346122 | ||||||||
\(808\) | −9.26369e35 | −0.420864 | ||||||||
\(809\) | 2.35511e36 | 1.05355 | 0.526776 | − | 0.850004i | \(-0.323401\pi\) | ||||
0.526776 | + | 0.850004i | \(0.323401\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.33343e36 | 1.44587 | 0.722936 | − | 0.690915i | \(-0.242792\pi\) | ||||
0.722936 | + | 0.690915i | \(0.242792\pi\) | |||||||
\(812\) | −1.75157e36 | −0.748132 | ||||||||
\(813\) | −4.41411e35 | −0.185657 | ||||||||
\(814\) | −8.74172e35 | −0.362069 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.26569e34 | 0.0251676 | ||||||||
\(817\) | −2.78692e35 | −0.110242 | ||||||||
\(818\) | 3.08140e36 | 1.20042 | ||||||||
\(819\) | 5.76547e36 | 2.21201 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.82523e36 | 0.679249 | 0.339625 | − | 0.940561i | \(-0.389700\pi\) | ||||
0.339625 | + | 0.940561i | \(0.389700\pi\) | |||||||
\(822\) | 5.64864e34 | 0.0207036 | ||||||||
\(823\) | 1.63571e36 | 0.590483 | 0.295241 | − | 0.955423i | \(-0.404600\pi\) | ||||
0.295241 | + | 0.955423i | \(0.404600\pi\) | |||||||
\(824\) | −1.36391e36 | −0.484950 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.96394e36 | −1.02240 | ||||||||
\(827\) | 3.73907e36 | 1.27041 | 0.635206 | − | 0.772342i | \(-0.280915\pi\) | ||||
0.635206 | + | 0.772342i | \(0.280915\pi\) | |||||||
\(828\) | −2.02047e35 | −0.0676198 | ||||||||
\(829\) | −3.08664e36 | −1.01755 | −0.508773 | − | 0.860901i | \(-0.669901\pi\) | ||||
−0.508773 | + | 0.860901i | \(0.669901\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.02265e34 | 0.0160665 | ||||||||
\(832\) | −5.37448e35 | −0.169354 | ||||||||
\(833\) | −2.61310e36 | −0.811135 | ||||||||
\(834\) | 1.42125e35 | 0.0434604 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.56234e35 | 0.254105 | ||||||||
\(837\) | −2.99878e36 | −0.876750 | ||||||||
\(838\) | −2.56203e35 | −0.0737963 | ||||||||
\(839\) | −3.69450e36 | −1.04841 | −0.524205 | − | 0.851592i | \(-0.675637\pi\) | ||||
−0.524205 | + | 0.851592i | \(0.675637\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.61704e35 | −0.264906 | ||||||||
\(842\) | 3.28564e36 | 0.891701 | ||||||||
\(843\) | 3.15264e35 | 0.0843005 | ||||||||
\(844\) | 9.55652e34 | 0.0251779 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.93142e35 | 0.151715 | ||||||||
\(847\) | −4.59280e36 | −1.15754 | ||||||||
\(848\) | 1.52045e36 | 0.377593 | ||||||||
\(849\) | 1.64006e36 | 0.401341 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.36825e35 | −0.127560 | ||||||||
\(852\) | −4.49317e35 | −0.105210 | ||||||||
\(853\) | −7.36060e35 | −0.169844 | −0.0849220 | − | 0.996388i | \(-0.527064\pi\) | ||||
−0.0849220 | + | 0.996388i | \(0.527064\pi\) | |||||||
\(854\) | −7.42494e36 | −1.68838 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.53551e35 | −0.100162 | ||||||||
\(857\) | 5.06811e35 | 0.110303 | 0.0551513 | − | 0.998478i | \(-0.482436\pi\) | ||||
0.0551513 | + | 0.998478i | \(0.482436\pi\) | |||||||
\(858\) | 6.57997e35 | 0.141134 | ||||||||
\(859\) | 7.80778e33 | 0.00165049 | 0.000825245 | − | 1.00000i | \(-0.499737\pi\) | ||||
0.000825245 | 1.00000i | \(0.499737\pi\) | ||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.52374e36 | 0.723543 | ||||||||
\(862\) | 5.41895e36 | 1.09667 | ||||||||
\(863\) | −8.60176e36 | −1.71574 | −0.857871 | − | 0.513864i | \(-0.828213\pi\) | ||||
−0.857871 | + | 0.513864i | \(0.828213\pi\) | |||||||
\(864\) | 4.41855e35 | 0.0868676 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.90669e36 | −1.12816 | ||||||||
\(867\) | 1.13652e36 | 0.213962 | ||||||||
\(868\) | −8.38970e36 | −1.55686 | ||||||||
\(869\) | 1.31309e36 | 0.240186 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.32242e37 | −2.35040 | ||||||||
\(872\) | −4.36673e35 | −0.0765069 | ||||||||
\(873\) | 1.97685e36 | 0.341425 | ||||||||
\(874\) | 5.25809e35 | 0.0895231 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.47029e34 | −0.00574202 | ||||||||
\(877\) | −7.33903e36 | −1.19714 | −0.598568 | − | 0.801072i | \(-0.704263\pi\) | ||||
−0.598568 | + | 0.801072i | \(0.704263\pi\) | |||||||
\(878\) | 4.04692e36 | 0.650794 | ||||||||
\(879\) | −9.88829e35 | −0.156769 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.73442e36 | 1.19187 | 0.595935 | − | 0.803032i | \(-0.296781\pi\) | ||||
0.595935 | + | 0.803032i | \(0.296781\pi\) | |||||||
\(882\) | −8.90693e36 | −1.35323 | ||||||||
\(883\) | 1.11931e37 | 1.67664 | 0.838320 | − | 0.545178i | \(-0.183538\pi\) | ||||
0.838320 | + | 0.545178i | \(0.183538\pi\) | |||||||
\(884\) | 1.81878e36 | 0.268613 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.77779e36 | −0.398821 | ||||||||
\(887\) | −9.94167e36 | −1.40739 | −0.703695 | − | 0.710502i | \(-0.748468\pi\) | ||||
−0.703695 | + | 0.710502i | \(0.748468\pi\) | |||||||
\(888\) | 5.67441e35 | 0.0792060 | ||||||||
\(889\) | −9.71850e36 | −1.33760 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.51570e36 | 0.470479 | ||||||||
\(892\) | −9.80709e35 | −0.129413 | ||||||||
\(893\) | −1.54360e36 | −0.200858 | ||||||||
\(894\) | 5.11998e35 | 0.0656976 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.23618e36 | 0.154252 | ||||||||
\(897\) | 4.04073e35 | 0.0497226 | ||||||||
\(898\) | −5.73826e36 | −0.696347 | ||||||||
\(899\) | 1.27824e37 | 1.52973 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.14536e36 | −0.598902 | ||||||||
\(902\) | −5.83711e36 | −0.670063 | ||||||||
\(903\) | 4.92607e35 | 0.0557704 | ||||||||
\(904\) | −3.52298e36 | −0.393373 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.03191e36 | −0.220700 | ||||||||
\(907\) | 2.49643e36 | 0.267441 | 0.133721 | − | 0.991019i | \(-0.457308\pi\) | ||||
0.133721 | + | 0.991019i | \(0.457308\pi\) | |||||||
\(908\) | −9.26555e36 | −0.979035 | ||||||||
\(909\) | 1.06856e37 | 1.11366 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.34594e36 | 0.947640 | 0.473820 | − | 0.880622i | \(-0.342875\pi\) | ||||
0.473820 | + | 0.880622i | \(0.342875\pi\) | |||||||
\(912\) | −5.55797e35 | −0.0555879 | ||||||||
\(913\) | −3.90461e35 | −0.0385205 | ||||||||
\(914\) | −1.17882e37 | −1.14715 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.73537e35 | −0.0921847 | ||||||||
\(917\) | −2.90438e37 | −2.71292 | ||||||||
\(918\) | −1.49528e36 | −0.137781 | ||||||||
\(919\) | 2.08298e37 | 1.89340 | 0.946698 | − | 0.322122i | \(-0.104396\pi\) | ||||
0.946698 | + | 0.322122i | \(0.104396\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.37054e35 | −0.0652010 | ||||||||
\(922\) | −1.89543e36 | −0.165413 | ||||||||
\(923\) | −1.30426e37 | −1.12291 | ||||||||
\(924\) | −1.51345e36 | −0.128549 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.03719e36 | −0.0857474 | ||||||||
\(927\) | 1.57327e37 | 1.28323 | ||||||||
\(928\) | −1.88342e36 | −0.151564 | ||||||||
\(929\) | −2.93833e36 | −0.233294 | −0.116647 | − | 0.993173i | \(-0.537215\pi\) | ||||
−0.116647 | + | 0.993173i | \(0.537215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.31795e37 | 1.79156 | ||||||||
\(932\) | 3.25079e36 | 0.247908 | ||||||||
\(933\) | −4.64017e36 | −0.349151 | ||||||||
\(934\) | 6.39190e36 | 0.474563 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.19944e36 | 0.448131 | ||||||||
\(937\) | 1.33465e37 | 0.951968 | 0.475984 | − | 0.879454i | \(-0.342092\pi\) | ||||
0.475984 | + | 0.879454i | \(0.342092\pi\) | |||||||
\(938\) | 3.04168e37 | 2.14081 | ||||||||
\(939\) | −1.27877e35 | −0.00888120 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.37070e37 | −0.926983 | −0.463492 | − | 0.886101i | \(-0.653404\pi\) | ||||
−0.463492 | + | 0.886101i | \(0.653404\pi\) | |||||||
\(942\) | 1.59051e35 | 0.0106145 | ||||||||
\(943\) | −3.58454e36 | −0.236068 | ||||||||
\(944\) | −3.18704e36 | −0.207127 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.16009e35 | −0.0516482 | ||||||||
\(947\) | −3.73876e36 | −0.233535 | −0.116768 | − | 0.993159i | \(-0.537253\pi\) | ||||
−0.116768 | + | 0.993159i | \(0.537253\pi\) | |||||||
\(948\) | −8.52350e35 | −0.0525429 | ||||||||
\(949\) | −1.00734e36 | −0.0612845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.10736e36 | −0.302649 | ||||||||
\(952\) | −4.18336e36 | −0.244660 | ||||||||
\(953\) | 4.80715e36 | 0.277477 | 0.138738 | − | 0.990329i | \(-0.455695\pi\) | ||||
0.138738 | + | 0.990329i | \(0.455695\pi\) | |||||||
\(954\) | −1.75383e37 | −0.999156 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.20119e36 | 0.0666634 | ||||||||
\(957\) | 2.30586e36 | 0.126309 | ||||||||
\(958\) | 2.96373e36 | 0.160240 | ||||||||
\(959\) | −3.77138e36 | −0.201265 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.19922e37 | 2.18336 | ||||||||
\(962\) | 1.64715e37 | 0.845364 | ||||||||
\(963\) | 5.23170e36 | 0.265042 | ||||||||
\(964\) | −1.41272e37 | −0.706467 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −9.29405e35 | −0.0452888 | ||||||||
\(967\) | −1.46042e37 | −0.702498 | −0.351249 | − | 0.936282i | \(-0.614243\pi\) | ||||
−0.351249 | + | 0.936282i | \(0.614243\pi\) | |||||||
\(968\) | −4.93850e36 | −0.234506 | ||||||||
\(969\) | 1.88087e36 | 0.0881683 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.16381e37 | −1.44534 | −0.722670 | − | 0.691193i | \(-0.757085\pi\) | ||||
−0.722670 | + | 0.691193i | \(0.757085\pi\) | |||||||
\(972\) | −7.73003e36 | −0.348620 | ||||||||
\(973\) | −9.48913e36 | −0.422490 | ||||||||
\(974\) | −1.27423e37 | −0.560093 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.98382e36 | −0.342049 | ||||||||
\(977\) | 3.15815e37 | 1.33583 | 0.667914 | − | 0.744239i | \(-0.267188\pi\) | ||||
0.667914 | + | 0.744239i | \(0.267188\pi\) | |||||||
\(978\) | 2.85193e36 | 0.119098 | ||||||||
\(979\) | 2.15834e37 | 0.889889 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.03701e36 | 0.202446 | ||||||||
\(982\) | 1.43824e37 | 0.570738 | ||||||||
\(983\) | −1.30026e37 | −0.509461 | −0.254731 | − | 0.967012i | \(-0.581987\pi\) | ||||
−0.254731 | + | 0.967012i | \(0.581987\pi\) | |||||||
\(984\) | 3.78897e36 | 0.146583 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.37368e36 | 0.240397 | ||||||||
\(987\) | 2.72841e36 | 0.101612 | ||||||||
\(988\) | −1.61335e37 | −0.593288 | ||||||||
\(989\) | −5.01107e35 | −0.0181960 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.69845e37 | 0.601355 | 0.300677 | − | 0.953726i | \(-0.402787\pi\) | ||||
0.300677 | + | 0.953726i | \(0.402787\pi\) | |||||||
\(992\) | −9.02119e36 | −0.315405 | ||||||||
\(993\) | 6.84852e36 | 0.236446 | ||||||||
\(994\) | 2.99992e37 | 1.02277 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.53455e35 | 0.00842673 | ||||||||
\(997\) | −1.43944e37 | −0.472612 | −0.236306 | − | 0.971679i | \(-0.575937\pi\) | ||||
−0.236306 | + | 0.971679i | \(0.575937\pi\) | |||||||
\(998\) | 3.59677e37 | 1.16622 | ||||||||
\(999\) | −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 | 50.26.a.l.1.3 | 6 | ||
5.2 | odd | 4 | 10.26.b.a.9.10 | yes | 12 | ||
5.3 | odd | 4 | 10.26.b.a.9.3 | ✓ | 12 | ||
5.4 | even | 2 | 50.26.a.k.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.26.b.a.9.3 | ✓ | 12 | 5.3 | odd | 4 | ||
10.26.b.a.9.10 | yes | 12 | 5.2 | odd | 4 | ||
50.26.a.k.1.4 | 6 | 5.4 | even | 2 | |||
50.26.a.l.1.3 | 6 | 1.1 | even | 1 | trivial |