Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,34,Mod(1,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.1");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.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: | \(34.4914144405\) |
Analytic rank: | \(0\) |
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: | \( x^{6} - x^{5} - 9680197848 x^{4} + 8052423720422 x^{3} + \cdots - 10\!\cdots\!50 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{5}\cdot 5^{6}\cdot 7\cdot 11^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(25925.6\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 76409.2 | 0.824424 | 0.412212 | − | 0.911088i | \(-0.364756\pi\) | ||||
0.412212 | + | 0.911088i | \(0.364756\pi\) | |||||||
\(3\) | 7.43191e7 | 0.996780 | 0.498390 | − | 0.866953i | \(-0.333925\pi\) | ||||
0.498390 | + | 0.866953i | \(0.333925\pi\) | |||||||
\(4\) | −2.75157e9 | −0.320325 | ||||||||
\(5\) | 1.52588e11 | 0.447214 | ||||||||
\(6\) | 5.67866e12 | 0.821770 | ||||||||
\(7\) | 1.36987e14 | 1.55798 | 0.778992 | − | 0.627034i | \(-0.215731\pi\) | ||||
0.778992 | + | 0.627034i | \(0.215731\pi\) | |||||||
\(8\) | −8.66595e14 | −1.08851 | ||||||||
\(9\) | −3.57381e13 | −0.00642880 | ||||||||
\(10\) | 1.16591e16 | 0.368694 | ||||||||
\(11\) | 3.84389e16 | 0.252227 | 0.126113 | − | 0.992016i | \(-0.459750\pi\) | ||||
0.126113 | + | 0.992016i | \(0.459750\pi\) | |||||||
\(12\) | −2.04494e17 | −0.319294 | ||||||||
\(13\) | 2.57012e18 | 1.07124 | 0.535622 | − | 0.844458i | \(-0.320077\pi\) | ||||
0.535622 | + | 0.844458i | \(0.320077\pi\) | |||||||
\(14\) | 1.04671e19 | 1.28444 | ||||||||
\(15\) | 1.13402e19 | 0.445774 | ||||||||
\(16\) | −4.25800e19 | −0.577067 | ||||||||
\(17\) | 1.44621e20 | 0.720814 | 0.360407 | − | 0.932795i | \(-0.382638\pi\) | ||||
0.360407 | + | 0.932795i | \(0.382638\pi\) | |||||||
\(18\) | −2.73072e18 | −0.00530005 | ||||||||
\(19\) | −2.79512e20 | −0.222314 | −0.111157 | − | 0.993803i | \(-0.535456\pi\) | ||||
−0.111157 | + | 0.993803i | \(0.535456\pi\) | |||||||
\(20\) | −4.19856e20 | −0.143254 | ||||||||
\(21\) | 1.01808e22 | 1.55297 | ||||||||
\(22\) | 2.93708e21 | 0.207942 | ||||||||
\(23\) | 3.71118e22 | 1.26184 | 0.630918 | − | 0.775849i | \(-0.282678\pi\) | ||||
0.630918 | + | 0.775849i | \(0.282678\pi\) | |||||||
\(24\) | −6.44045e22 | −1.08500 | ||||||||
\(25\) | 2.32831e22 | 0.200000 | ||||||||
\(26\) | 1.96381e23 | 0.883159 | ||||||||
\(27\) | −4.15800e23 | −1.00319 | ||||||||
\(28\) | −3.76930e23 | −0.499061 | ||||||||
\(29\) | −1.90470e24 | −1.41339 | −0.706693 | − | 0.707520i | \(-0.749814\pi\) | ||||
−0.706693 | + | 0.707520i | \(0.749814\pi\) | |||||||
\(30\) | 8.66495e23 | 0.367507 | ||||||||
\(31\) | 5.88152e24 | 1.45218 | 0.726092 | − | 0.687597i | \(-0.241334\pi\) | ||||
0.726092 | + | 0.687597i | \(0.241334\pi\) | |||||||
\(32\) | 4.19049e24 | 0.612760 | ||||||||
\(33\) | 2.85674e24 | 0.251415 | ||||||||
\(34\) | 1.10503e25 | 0.594256 | ||||||||
\(35\) | 2.09026e25 | 0.696751 | ||||||||
\(36\) | 9.83358e22 | 0.00205930 | ||||||||
\(37\) | 1.05655e26 | 1.40787 | 0.703934 | − | 0.710265i | \(-0.251425\pi\) | ||||
0.703934 | + | 0.710265i | \(0.251425\pi\) | |||||||
\(38\) | −2.13573e25 | −0.183281 | ||||||||
\(39\) | 1.91009e26 | 1.06779 | ||||||||
\(40\) | −1.32232e26 | −0.486795 | ||||||||
\(41\) | −2.64164e25 | −0.0647052 | −0.0323526 | − | 0.999477i | \(-0.510300\pi\) | ||||
−0.0323526 | + | 0.999477i | \(0.510300\pi\) | |||||||
\(42\) | 7.77905e26 | 1.28030 | ||||||||
\(43\) | 1.20441e27 | 1.34446 | 0.672228 | − | 0.740344i | \(-0.265338\pi\) | ||||
0.672228 | + | 0.740344i | \(0.265338\pi\) | |||||||
\(44\) | −1.05767e26 | −0.0807946 | ||||||||
\(45\) | −5.45320e24 | −0.00287505 | ||||||||
\(46\) | 2.83569e27 | 1.04029 | ||||||||
\(47\) | −3.53827e27 | −0.910282 | −0.455141 | − | 0.890419i | \(-0.650411\pi\) | ||||
−0.455141 | + | 0.890419i | \(0.650411\pi\) | |||||||
\(48\) | −3.16451e27 | −0.575209 | ||||||||
\(49\) | 1.10345e28 | 1.42731 | ||||||||
\(50\) | 1.77904e27 | 0.164885 | ||||||||
\(51\) | 1.07481e28 | 0.718493 | ||||||||
\(52\) | −7.07187e27 | −0.343146 | ||||||||
\(53\) | −3.25098e28 | −1.15203 | −0.576014 | − | 0.817440i | \(-0.695392\pi\) | ||||
−0.576014 | + | 0.817440i | \(0.695392\pi\) | |||||||
\(54\) | −3.17710e28 | −0.827053 | ||||||||
\(55\) | 5.86531e27 | 0.112799 | ||||||||
\(56\) | −1.18713e29 | −1.69588 | ||||||||
\(57\) | −2.07731e28 | −0.221598 | ||||||||
\(58\) | −1.45537e29 | −1.16523 | ||||||||
\(59\) | 3.41770e28 | 0.206384 | 0.103192 | − | 0.994661i | \(-0.467094\pi\) | ||||
0.103192 | + | 0.994661i | \(0.467094\pi\) | |||||||
\(60\) | −3.12033e28 | −0.142792 | ||||||||
\(61\) | −6.01152e28 | −0.209431 | −0.104716 | − | 0.994502i | \(-0.533393\pi\) | ||||
−0.104716 | + | 0.994502i | \(0.533393\pi\) | |||||||
\(62\) | 4.49402e29 | 1.19722 | ||||||||
\(63\) | −4.89566e27 | −0.0100160 | ||||||||
\(64\) | 6.85952e29 | 1.08224 | ||||||||
\(65\) | 3.92169e29 | 0.479075 | ||||||||
\(66\) | 2.18281e29 | 0.207272 | ||||||||
\(67\) | −2.17962e30 | −1.61490 | −0.807451 | − | 0.589934i | \(-0.799154\pi\) | ||||
−0.807451 | + | 0.589934i | \(0.799154\pi\) | |||||||
\(68\) | −3.97934e29 | −0.230895 | ||||||||
\(69\) | 2.75812e30 | 1.25777 | ||||||||
\(70\) | 1.59715e30 | 0.574419 | ||||||||
\(71\) | 9.20055e29 | 0.261849 | 0.130924 | − | 0.991392i | \(-0.458205\pi\) | ||||
0.130924 | + | 0.991392i | \(0.458205\pi\) | |||||||
\(72\) | 3.09704e28 | 0.00699779 | ||||||||
\(73\) | −4.72873e30 | −0.850977 | −0.425488 | − | 0.904964i | \(-0.639898\pi\) | ||||
−0.425488 | + | 0.904964i | \(0.639898\pi\) | |||||||
\(74\) | 8.07302e30 | 1.16068 | ||||||||
\(75\) | 1.73038e30 | 0.199356 | ||||||||
\(76\) | 7.69097e29 | 0.0712126 | ||||||||
\(77\) | 5.26564e30 | 0.392965 | ||||||||
\(78\) | 1.45948e31 | 0.880316 | ||||||||
\(79\) | −2.14123e31 | −1.04668 | −0.523342 | − | 0.852122i | \(-0.675315\pi\) | ||||
−0.523342 | + | 0.852122i | \(0.675315\pi\) | |||||||
\(80\) | −6.49720e30 | −0.258072 | ||||||||
\(81\) | −3.07032e31 | −0.993530 | ||||||||
\(82\) | −2.01845e30 | −0.0533445 | ||||||||
\(83\) | −6.60838e31 | −1.42990 | −0.714951 | − | 0.699174i | \(-0.753551\pi\) | ||||
−0.714951 | + | 0.699174i | \(0.753551\pi\) | |||||||
\(84\) | −2.80131e31 | −0.497454 | ||||||||
\(85\) | 2.20674e31 | 0.322358 | ||||||||
\(86\) | 9.20283e31 | 1.10840 | ||||||||
\(87\) | −1.41556e32 | −1.40884 | ||||||||
\(88\) | −3.33109e31 | −0.274551 | ||||||||
\(89\) | −6.08523e31 | −0.416238 | −0.208119 | − | 0.978104i | \(-0.566734\pi\) | ||||
−0.208119 | + | 0.978104i | \(0.566734\pi\) | |||||||
\(90\) | −4.16674e29 | −0.00237026 | ||||||||
\(91\) | 3.52074e32 | 1.66898 | ||||||||
\(92\) | −1.02116e32 | −0.404198 | ||||||||
\(93\) | 4.37109e32 | 1.44751 | ||||||||
\(94\) | −2.70356e32 | −0.750458 | ||||||||
\(95\) | −4.26502e31 | −0.0994217 | ||||||||
\(96\) | 3.11433e32 | 0.610787 | ||||||||
\(97\) | 6.12049e30 | 0.0101170 | 0.00505851 | − | 0.999987i | \(-0.498390\pi\) | ||||
0.00505851 | + | 0.999987i | \(0.498390\pi\) | |||||||
\(98\) | 8.43141e32 | 1.17671 | ||||||||
\(99\) | −1.37373e30 | −0.00162152 | ||||||||
\(100\) | −6.40650e31 | −0.0640650 | ||||||||
\(101\) | 1.27681e33 | 1.08349 | 0.541743 | − | 0.840544i | \(-0.317765\pi\) | ||||
0.541743 | + | 0.840544i | \(0.317765\pi\) | |||||||
\(102\) | 8.21251e32 | 0.592343 | ||||||||
\(103\) | −1.91249e33 | −1.17432 | −0.587158 | − | 0.809473i | \(-0.699753\pi\) | ||||
−0.587158 | + | 0.809473i | \(0.699753\pi\) | |||||||
\(104\) | −2.22725e33 | −1.16606 | ||||||||
\(105\) | 1.55346e33 | 0.694508 | ||||||||
\(106\) | −2.48405e33 | −0.949759 | ||||||||
\(107\) | −5.25843e33 | −1.72196 | −0.860981 | − | 0.508638i | \(-0.830149\pi\) | ||||
−0.860981 | + | 0.508638i | \(0.830149\pi\) | |||||||
\(108\) | 1.14410e33 | 0.321346 | ||||||||
\(109\) | 1.63289e33 | 0.393930 | 0.196965 | − | 0.980411i | \(-0.436891\pi\) | ||||
0.196965 | + | 0.980411i | \(0.436891\pi\) | |||||||
\(110\) | 4.48163e32 | 0.0929945 | ||||||||
\(111\) | 7.85219e33 | 1.40334 | ||||||||
\(112\) | −5.83293e33 | −0.899061 | ||||||||
\(113\) | −1.10961e34 | −1.47699 | −0.738495 | − | 0.674259i | \(-0.764463\pi\) | ||||
−0.738495 | + | 0.674259i | \(0.764463\pi\) | |||||||
\(114\) | −1.58725e33 | −0.182691 | ||||||||
\(115\) | 5.66282e33 | 0.564311 | ||||||||
\(116\) | 5.24093e33 | 0.452743 | ||||||||
\(117\) | −9.18512e31 | −0.00688681 | ||||||||
\(118\) | 2.61144e33 | 0.170148 | ||||||||
\(119\) | 1.98112e34 | 1.12302 | ||||||||
\(120\) | −9.82735e33 | −0.485228 | ||||||||
\(121\) | −2.17476e34 | −0.936382 | ||||||||
\(122\) | −4.59335e33 | −0.172660 | ||||||||
\(123\) | −1.96324e33 | −0.0644969 | ||||||||
\(124\) | −1.61834e34 | −0.465171 | ||||||||
\(125\) | 3.55271e33 | 0.0894427 | ||||||||
\(126\) | −3.74074e32 | −0.00825740 | ||||||||
\(127\) | 9.92625e34 | 1.92320 | 0.961599 | − | 0.274458i | \(-0.0884985\pi\) | ||||
0.961599 | + | 0.274458i | \(0.0884985\pi\) | |||||||
\(128\) | 1.64170e34 | 0.279466 | ||||||||
\(129\) | 8.95110e34 | 1.34013 | ||||||||
\(130\) | 2.99653e34 | 0.394961 | ||||||||
\(131\) | 5.93400e34 | 0.689241 | 0.344621 | − | 0.938742i | \(-0.388008\pi\) | ||||
0.344621 | + | 0.938742i | \(0.388008\pi\) | |||||||
\(132\) | −7.86052e33 | −0.0805344 | ||||||||
\(133\) | −3.82896e34 | −0.346361 | ||||||||
\(134\) | −1.66543e35 | −1.33136 | ||||||||
\(135\) | −6.34461e34 | −0.448640 | ||||||||
\(136\) | −1.25328e35 | −0.784611 | ||||||||
\(137\) | −7.72864e34 | −0.428759 | −0.214380 | − | 0.976750i | \(-0.568773\pi\) | ||||
−0.214380 | + | 0.976750i | \(0.568773\pi\) | |||||||
\(138\) | 2.10746e35 | 1.03694 | ||||||||
\(139\) | −3.33723e35 | −1.45761 | −0.728806 | − | 0.684720i | \(-0.759925\pi\) | ||||
−0.728806 | + | 0.684720i | \(0.759925\pi\) | |||||||
\(140\) | −5.75150e34 | −0.223187 | ||||||||
\(141\) | −2.62961e35 | −0.907351 | ||||||||
\(142\) | 7.03006e34 | 0.215875 | ||||||||
\(143\) | 9.87926e34 | 0.270196 | ||||||||
\(144\) | 1.52173e33 | 0.00370985 | ||||||||
\(145\) | −2.90635e35 | −0.632085 | ||||||||
\(146\) | −3.61319e35 | −0.701566 | ||||||||
\(147\) | 8.20077e35 | 1.42272 | ||||||||
\(148\) | −2.90717e35 | −0.450975 | ||||||||
\(149\) | 9.18769e35 | 1.27536 | 0.637680 | − | 0.770301i | \(-0.279894\pi\) | ||||
0.637680 | + | 0.770301i | \(0.279894\pi\) | |||||||
\(150\) | 1.32217e35 | 0.164354 | ||||||||
\(151\) | −1.06733e33 | −0.00118899 | −0.000594497 | − | 1.00000i | \(-0.500189\pi\) | ||||
−0.000594497 | 1.00000i | \(0.500189\pi\) | ||||||||
\(152\) | 2.42224e35 | 0.241990 | ||||||||
\(153\) | −5.16846e33 | −0.00463397 | ||||||||
\(154\) | 4.02343e35 | 0.323970 | ||||||||
\(155\) | 8.97449e35 | 0.649437 | ||||||||
\(156\) | −5.25575e35 | −0.342041 | ||||||||
\(157\) | 2.04504e36 | 1.19773 | 0.598863 | − | 0.800851i | \(-0.295619\pi\) | ||||
0.598863 | + | 0.800851i | \(0.295619\pi\) | |||||||
\(158\) | −1.63610e36 | −0.862912 | ||||||||
\(159\) | −2.41610e36 | −1.14832 | ||||||||
\(160\) | 6.39418e35 | 0.274034 | ||||||||
\(161\) | 5.08385e36 | 1.96592 | ||||||||
\(162\) | −2.34601e36 | −0.819090 | ||||||||
\(163\) | 8.53783e35 | 0.269310 | 0.134655 | − | 0.990893i | \(-0.457007\pi\) | ||||
0.134655 | + | 0.990893i | \(0.457007\pi\) | |||||||
\(164\) | 7.26865e34 | 0.0207267 | ||||||||
\(165\) | 4.35904e35 | 0.112436 | ||||||||
\(166\) | −5.04941e36 | −1.17885 | ||||||||
\(167\) | 2.30718e36 | 0.487819 | 0.243910 | − | 0.969798i | \(-0.421570\pi\) | ||||
0.243910 | + | 0.969798i | \(0.421570\pi\) | |||||||
\(168\) | −8.82261e36 | −1.69042 | ||||||||
\(169\) | 8.49393e35 | 0.147563 | ||||||||
\(170\) | 1.68615e36 | 0.265759 | ||||||||
\(171\) | 9.98922e33 | 0.00142921 | ||||||||
\(172\) | −3.31403e36 | −0.430663 | ||||||||
\(173\) | 7.44289e36 | 0.878984 | 0.439492 | − | 0.898247i | \(-0.355158\pi\) | ||||
0.439492 | + | 0.898247i | \(0.355158\pi\) | |||||||
\(174\) | −1.08162e37 | −1.16148 | ||||||||
\(175\) | 3.18949e36 | 0.311597 | ||||||||
\(176\) | −1.63673e36 | −0.145552 | ||||||||
\(177\) | 2.54000e36 | 0.205719 | ||||||||
\(178\) | −4.64967e36 | −0.343157 | ||||||||
\(179\) | −1.14363e37 | −0.769506 | −0.384753 | − | 0.923020i | \(-0.625713\pi\) | ||||
−0.384753 | + | 0.923020i | \(0.625713\pi\) | |||||||
\(180\) | 1.50049e34 | 0.000920949 0 | ||||||||
\(181\) | 9.37075e36 | 0.524902 | 0.262451 | − | 0.964945i | \(-0.415469\pi\) | ||||
0.262451 | + | 0.964945i | \(0.415469\pi\) | |||||||
\(182\) | 2.69017e37 | 1.37595 | ||||||||
\(183\) | −4.46770e36 | −0.208757 | ||||||||
\(184\) | −3.21609e37 | −1.37352 | ||||||||
\(185\) | 1.61217e37 | 0.629618 | ||||||||
\(186\) | 3.33992e37 | 1.19336 | ||||||||
\(187\) | 5.55906e36 | 0.181809 | ||||||||
\(188\) | 9.73579e36 | 0.291586 | ||||||||
\(189\) | −5.69594e37 | −1.56295 | ||||||||
\(190\) | −3.25886e36 | −0.0819656 | ||||||||
\(191\) | 1.69883e37 | 0.391831 | 0.195915 | − | 0.980621i | \(-0.437232\pi\) | ||||
0.195915 | + | 0.980621i | \(0.437232\pi\) | |||||||
\(192\) | 5.09793e37 | 1.07876 | ||||||||
\(193\) | 7.50799e36 | 0.145824 | 0.0729119 | − | 0.997338i | \(-0.476771\pi\) | ||||
0.0729119 | + | 0.997338i | \(0.476771\pi\) | |||||||
\(194\) | 4.67662e35 | 0.00834072 | ||||||||
\(195\) | 2.91457e37 | 0.477532 | ||||||||
\(196\) | −3.03623e37 | −0.457204 | ||||||||
\(197\) | 1.41045e38 | 1.95284 | 0.976418 | − | 0.215886i | \(-0.0692641\pi\) | ||||
0.976418 | + | 0.215886i | \(0.0692641\pi\) | |||||||
\(198\) | −1.04966e35 | −0.00133682 | ||||||||
\(199\) | 1.95572e37 | 0.229208 | 0.114604 | − | 0.993411i | \(-0.463440\pi\) | ||||
0.114604 | + | 0.993411i | \(0.463440\pi\) | |||||||
\(200\) | −2.01770e37 | −0.217702 | ||||||||
\(201\) | −1.61987e38 | −1.60970 | ||||||||
\(202\) | 9.75600e37 | 0.893252 | ||||||||
\(203\) | −2.60921e38 | −2.20203 | ||||||||
\(204\) | −2.95741e37 | −0.230151 | ||||||||
\(205\) | −4.03082e36 | −0.0289371 | ||||||||
\(206\) | −1.46132e38 | −0.968134 | ||||||||
\(207\) | −1.32631e36 | −0.00811209 | ||||||||
\(208\) | −1.09436e38 | −0.618179 | ||||||||
\(209\) | −1.07441e37 | −0.0560735 | ||||||||
\(210\) | 1.18699e38 | 0.572569 | ||||||||
\(211\) | −2.65891e38 | −1.18589 | −0.592944 | − | 0.805244i | \(-0.702034\pi\) | ||||
−0.592944 | + | 0.805244i | \(0.702034\pi\) | |||||||
\(212\) | 8.94530e37 | 0.369023 | ||||||||
\(213\) | 6.83776e37 | 0.261006 | ||||||||
\(214\) | −4.01792e38 | −1.41963 | ||||||||
\(215\) | 1.83779e38 | 0.601259 | ||||||||
\(216\) | 3.60330e38 | 1.09198 | ||||||||
\(217\) | 8.05694e38 | 2.26248 | ||||||||
\(218\) | 1.24768e38 | 0.324765 | ||||||||
\(219\) | −3.51435e38 | −0.848237 | ||||||||
\(220\) | −1.61388e37 | −0.0361324 | ||||||||
\(221\) | 3.71693e38 | 0.772167 | ||||||||
\(222\) | 5.99979e38 | 1.15694 | ||||||||
\(223\) | −2.18179e38 | −0.390645 | −0.195323 | − | 0.980739i | \(-0.562575\pi\) | ||||
−0.195323 | + | 0.980739i | \(0.562575\pi\) | |||||||
\(224\) | 5.74044e38 | 0.954670 | ||||||||
\(225\) | −8.32092e35 | −0.00128576 | ||||||||
\(226\) | −8.47847e38 | −1.21767 | ||||||||
\(227\) | −5.43077e38 | −0.725161 | −0.362581 | − | 0.931952i | \(-0.618104\pi\) | ||||
−0.362581 | + | 0.931952i | \(0.618104\pi\) | |||||||
\(228\) | 5.71586e37 | 0.0709833 | ||||||||
\(229\) | −1.10600e39 | −1.27782 | −0.638908 | − | 0.769284i | \(-0.720613\pi\) | ||||
−0.638908 | + | 0.769284i | \(0.720613\pi\) | |||||||
\(230\) | 4.32691e38 | 0.465231 | ||||||||
\(231\) | 3.91337e38 | 0.391700 | ||||||||
\(232\) | 1.65061e39 | 1.53848 | ||||||||
\(233\) | −5.67177e38 | −0.492431 | −0.246216 | − | 0.969215i | \(-0.579187\pi\) | ||||
−0.246216 | + | 0.969215i | \(0.579187\pi\) | |||||||
\(234\) | −7.01827e36 | −0.00567765 | ||||||||
\(235\) | −5.39897e38 | −0.407091 | ||||||||
\(236\) | −9.40404e37 | −0.0661099 | ||||||||
\(237\) | −1.59134e39 | −1.04332 | ||||||||
\(238\) | 1.51376e39 | 0.925842 | ||||||||
\(239\) | −2.69103e39 | −1.53587 | −0.767933 | − | 0.640530i | \(-0.778715\pi\) | ||||
−0.767933 | + | 0.640530i | \(0.778715\pi\) | |||||||
\(240\) | −4.82866e38 | −0.257241 | ||||||||
\(241\) | 3.85216e39 | 1.91612 | 0.958061 | − | 0.286565i | \(-0.0925134\pi\) | ||||
0.958061 | + | 0.286565i | \(0.0925134\pi\) | |||||||
\(242\) | −1.66172e39 | −0.771976 | ||||||||
\(243\) | 2.96249e37 | 0.0128574 | ||||||||
\(244\) | 1.65411e38 | 0.0670861 | ||||||||
\(245\) | 1.68374e39 | 0.638314 | ||||||||
\(246\) | −1.50009e38 | −0.0531728 | ||||||||
\(247\) | −7.18380e38 | −0.238152 | ||||||||
\(248\) | −5.09690e39 | −1.58071 | ||||||||
\(249\) | −4.91128e39 | −1.42530 | ||||||||
\(250\) | 2.71460e38 | 0.0737387 | ||||||||
\(251\) | 1.40214e37 | 0.00356594 | 0.00178297 | − | 0.999998i | \(-0.499432\pi\) | ||||
0.00178297 | + | 0.999998i | \(0.499432\pi\) | |||||||
\(252\) | 1.34708e37 | 0.00320836 | ||||||||
\(253\) | 1.42654e39 | 0.318269 | ||||||||
\(254\) | 7.58457e39 | 1.58553 | ||||||||
\(255\) | 1.64003e39 | 0.321320 | ||||||||
\(256\) | −4.63787e39 | −0.851843 | ||||||||
\(257\) | −3.74219e39 | −0.644510 | −0.322255 | − | 0.946653i | \(-0.604441\pi\) | ||||
−0.322255 | + | 0.946653i | \(0.604441\pi\) | |||||||
\(258\) | 6.83946e39 | 1.10483 | ||||||||
\(259\) | 1.44734e40 | 2.19344 | ||||||||
\(260\) | −1.07908e39 | −0.153460 | ||||||||
\(261\) | 6.80705e37 | 0.00908637 | ||||||||
\(262\) | 4.53412e39 | 0.568227 | ||||||||
\(263\) | −8.59682e39 | −1.01174 | −0.505869 | − | 0.862610i | \(-0.668828\pi\) | ||||
−0.505869 | + | 0.862610i | \(0.668828\pi\) | |||||||
\(264\) | −2.47564e39 | −0.273667 | ||||||||
\(265\) | −4.96060e39 | −0.515202 | ||||||||
\(266\) | −2.92568e39 | −0.285548 | ||||||||
\(267\) | −4.52248e39 | −0.414898 | ||||||||
\(268\) | 5.99737e39 | 0.517293 | ||||||||
\(269\) | 2.20144e40 | 1.78564 | 0.892820 | − | 0.450414i | \(-0.148724\pi\) | ||||
0.892820 | + | 0.450414i | \(0.148724\pi\) | |||||||
\(270\) | −4.84786e39 | −0.369869 | ||||||||
\(271\) | 4.26536e39 | 0.306170 | 0.153085 | − | 0.988213i | \(-0.451079\pi\) | ||||
0.153085 | + | 0.988213i | \(0.451079\pi\) | |||||||
\(272\) | −6.15795e39 | −0.415958 | ||||||||
\(273\) | 2.61658e40 | 1.66361 | ||||||||
\(274\) | −5.90539e39 | −0.353480 | ||||||||
\(275\) | 8.94975e38 | 0.0504454 | ||||||||
\(276\) | −7.58915e39 | −0.402896 | ||||||||
\(277\) | −2.32580e40 | −1.16321 | −0.581603 | − | 0.813473i | \(-0.697574\pi\) | ||||
−0.581603 | + | 0.813473i | \(0.697574\pi\) | |||||||
\(278\) | −2.54995e40 | −1.20169 | ||||||||
\(279\) | −2.10194e38 | −0.00933580 | ||||||||
\(280\) | −1.81141e40 | −0.758419 | ||||||||
\(281\) | −3.04347e39 | −0.120147 | −0.0600737 | − | 0.998194i | \(-0.519134\pi\) | ||||
−0.0600737 | + | 0.998194i | \(0.519134\pi\) | |||||||
\(282\) | −2.00926e40 | −0.748042 | ||||||||
\(283\) | 1.78513e40 | 0.626893 | 0.313447 | − | 0.949606i | \(-0.398516\pi\) | ||||
0.313447 | + | 0.949606i | \(0.398516\pi\) | |||||||
\(284\) | −2.53160e39 | −0.0838768 | ||||||||
\(285\) | −3.16972e39 | −0.0991016 | ||||||||
\(286\) | 7.54866e39 | 0.222756 | ||||||||
\(287\) | −3.61871e39 | −0.100810 | ||||||||
\(288\) | −1.49760e38 | −0.00393931 | ||||||||
\(289\) | −1.93394e40 | −0.480427 | ||||||||
\(290\) | −2.22072e40 | −0.521106 | ||||||||
\(291\) | 4.54869e38 | 0.0100844 | ||||||||
\(292\) | 1.30114e40 | 0.272589 | ||||||||
\(293\) | 5.63289e39 | 0.111536 | 0.0557681 | − | 0.998444i | \(-0.482239\pi\) | ||||
0.0557681 | + | 0.998444i | \(0.482239\pi\) | |||||||
\(294\) | 6.26614e40 | 1.17292 | ||||||||
\(295\) | 5.21499e39 | 0.0922976 | ||||||||
\(296\) | −9.15602e40 | −1.53248 | ||||||||
\(297\) | −1.59829e40 | −0.253031 | ||||||||
\(298\) | 7.02024e40 | 1.05144 | ||||||||
\(299\) | 9.53819e40 | 1.35174 | ||||||||
\(300\) | −4.76125e39 | −0.0638587 | ||||||||
\(301\) | 1.64990e41 | 2.09464 | ||||||||
\(302\) | −8.15540e37 | −0.000980236 0 | ||||||||
\(303\) | 9.48913e40 | 1.08000 | ||||||||
\(304\) | 1.19016e40 | 0.128290 | ||||||||
\(305\) | −9.17284e39 | −0.0936605 | ||||||||
\(306\) | −3.94918e38 | −0.00382035 | ||||||||
\(307\) | −1.51598e41 | −1.38966 | −0.694832 | − | 0.719173i | \(-0.744521\pi\) | ||||
−0.694832 | + | 0.719173i | \(0.744521\pi\) | |||||||
\(308\) | −1.44888e40 | −0.125877 | ||||||||
\(309\) | −1.42134e41 | −1.17053 | ||||||||
\(310\) | 6.85734e40 | 0.535411 | ||||||||
\(311\) | 1.38324e41 | 1.02412 | 0.512062 | − | 0.858949i | \(-0.328882\pi\) | ||||
0.512062 | + | 0.858949i | \(0.328882\pi\) | |||||||
\(312\) | −1.65527e41 | −1.16230 | ||||||||
\(313\) | −2.31070e41 | −1.53908 | −0.769540 | − | 0.638598i | \(-0.779515\pi\) | ||||
−0.769540 | + | 0.638598i | \(0.779515\pi\) | |||||||
\(314\) | 1.56260e41 | 0.987434 | ||||||||
\(315\) | −7.47019e38 | −0.00447927 | ||||||||
\(316\) | 5.89174e40 | 0.335279 | ||||||||
\(317\) | −1.18117e41 | −0.638022 | −0.319011 | − | 0.947751i | \(-0.603351\pi\) | ||||
−0.319011 | + | 0.947751i | \(0.603351\pi\) | |||||||
\(318\) | −1.84612e41 | −0.946701 | ||||||||
\(319\) | −7.32147e40 | −0.356494 | ||||||||
\(320\) | 1.04668e41 | 0.483993 | ||||||||
\(321\) | −3.90801e41 | −1.71642 | ||||||||
\(322\) | 3.88453e41 | 1.62075 | ||||||||
\(323\) | −4.04232e40 | −0.160247 | ||||||||
\(324\) | 8.44820e40 | 0.318252 | ||||||||
\(325\) | 5.98403e40 | 0.214249 | ||||||||
\(326\) | 6.52369e40 | 0.222026 | ||||||||
\(327\) | 1.21355e41 | 0.392662 | ||||||||
\(328\) | 2.28923e40 | 0.0704321 | ||||||||
\(329\) | −4.84698e41 | −1.41820 | ||||||||
\(330\) | 3.33071e40 | 0.0926951 | ||||||||
\(331\) | 2.42794e41 | 0.642801 | 0.321400 | − | 0.946943i | \(-0.395847\pi\) | ||||
0.321400 | + | 0.946943i | \(0.395847\pi\) | |||||||
\(332\) | 1.81834e41 | 0.458033 | ||||||||
\(333\) | −3.77591e39 | −0.00905090 | ||||||||
\(334\) | 1.76290e41 | 0.402170 | ||||||||
\(335\) | −3.32583e41 | −0.722206 | ||||||||
\(336\) | −4.33498e41 | −0.896166 | ||||||||
\(337\) | 5.79957e41 | 1.14157 | 0.570785 | − | 0.821100i | \(-0.306639\pi\) | ||||
0.570785 | + | 0.821100i | \(0.306639\pi\) | |||||||
\(338\) | 6.49015e40 | 0.121655 | ||||||||
\(339\) | −8.24654e41 | −1.47223 | ||||||||
\(340\) | −6.07199e40 | −0.103259 | ||||||||
\(341\) | 2.26079e41 | 0.366280 | ||||||||
\(342\) | 7.63268e38 | 0.00117827 | ||||||||
\(343\) | 4.52545e41 | 0.665747 | ||||||||
\(344\) | −1.04374e42 | −1.46345 | ||||||||
\(345\) | 4.20855e41 | 0.562494 | ||||||||
\(346\) | 5.68705e41 | 0.724656 | ||||||||
\(347\) | 1.00536e42 | 1.22148 | 0.610739 | − | 0.791832i | \(-0.290872\pi\) | ||||
0.610739 | + | 0.791832i | \(0.290872\pi\) | |||||||
\(348\) | 3.89501e41 | 0.451285 | ||||||||
\(349\) | 1.46484e42 | 1.61872 | 0.809360 | − | 0.587313i | \(-0.199814\pi\) | ||||
0.809360 | + | 0.587313i | \(0.199814\pi\) | |||||||
\(350\) | 2.43706e41 | 0.256888 | ||||||||
\(351\) | −1.06866e42 | −1.07466 | ||||||||
\(352\) | 1.61078e41 | 0.154554 | ||||||||
\(353\) | −7.67079e40 | −0.0702356 | −0.0351178 | − | 0.999383i | \(-0.511181\pi\) | ||||
−0.0351178 | + | 0.999383i | \(0.511181\pi\) | |||||||
\(354\) | 1.94079e41 | 0.169600 | ||||||||
\(355\) | 1.40389e41 | 0.117102 | ||||||||
\(356\) | 1.67439e41 | 0.133331 | ||||||||
\(357\) | 1.47235e42 | 1.11940 | ||||||||
\(358\) | −8.73842e41 | −0.634399 | ||||||||
\(359\) | −2.27621e42 | −1.57817 | −0.789084 | − | 0.614285i | \(-0.789445\pi\) | ||||
−0.789084 | + | 0.614285i | \(0.789445\pi\) | |||||||
\(360\) | 4.72571e39 | 0.00312951 | ||||||||
\(361\) | −1.50264e42 | −0.950577 | ||||||||
\(362\) | 7.16012e41 | 0.432742 | ||||||||
\(363\) | −1.61626e42 | −0.933367 | ||||||||
\(364\) | −9.68757e41 | −0.534616 | ||||||||
\(365\) | −7.21548e41 | −0.380568 | ||||||||
\(366\) | −3.41373e41 | −0.172104 | ||||||||
\(367\) | 2.44390e42 | 1.17786 | 0.588929 | − | 0.808185i | \(-0.299550\pi\) | ||||
0.588929 | + | 0.808185i | \(0.299550\pi\) | |||||||
\(368\) | −1.58022e42 | −0.728165 | ||||||||
\(369\) | 9.44070e38 | 0.000415977 0 | ||||||||
\(370\) | 1.23184e42 | 0.519072 | ||||||||
\(371\) | −4.45343e42 | −1.79484 | ||||||||
\(372\) | −1.20274e42 | −0.463673 | ||||||||
\(373\) | 2.18298e42 | 0.805108 | 0.402554 | − | 0.915396i | \(-0.368123\pi\) | ||||
0.402554 | + | 0.915396i | \(0.368123\pi\) | |||||||
\(374\) | 4.24763e41 | 0.149887 | ||||||||
\(375\) | 2.64034e41 | 0.0891548 | ||||||||
\(376\) | 3.06625e42 | 0.990849 | ||||||||
\(377\) | −4.89532e42 | −1.51408 | ||||||||
\(378\) | −4.35222e42 | −1.28853 | ||||||||
\(379\) | 3.29619e42 | 0.934254 | 0.467127 | − | 0.884190i | \(-0.345289\pi\) | ||||
0.467127 | + | 0.884190i | \(0.345289\pi\) | |||||||
\(380\) | 1.17355e41 | 0.0318472 | ||||||||
\(381\) | 7.37710e42 | 1.91701 | ||||||||
\(382\) | 1.29806e42 | 0.323035 | ||||||||
\(383\) | 2.10779e42 | 0.502399 | 0.251199 | − | 0.967935i | \(-0.419175\pi\) | ||||
0.251199 | + | 0.967935i | \(0.419175\pi\) | |||||||
\(384\) | 1.22009e42 | 0.278566 | ||||||||
\(385\) | 8.03473e41 | 0.175739 | ||||||||
\(386\) | 5.73680e41 | 0.120221 | ||||||||
\(387\) | −4.30434e40 | −0.00864323 | ||||||||
\(388\) | −1.68410e40 | −0.00324073 | ||||||||
\(389\) | −4.71038e42 | −0.868735 | −0.434368 | − | 0.900736i | \(-0.643028\pi\) | ||||
−0.434368 | + | 0.900736i | \(0.643028\pi\) | |||||||
\(390\) | 2.22700e42 | 0.393689 | ||||||||
\(391\) | 5.36714e42 | 0.909550 | ||||||||
\(392\) | −9.56249e42 | −1.55364 | ||||||||
\(393\) | 4.41009e42 | 0.687022 | ||||||||
\(394\) | 1.07772e43 | 1.60997 | ||||||||
\(395\) | −3.26726e42 | −0.468092 | ||||||||
\(396\) | 3.77992e39 | 0.000519412 0 | ||||||||
\(397\) | 4.19658e42 | 0.553162 | 0.276581 | − | 0.960991i | \(-0.410799\pi\) | ||||
0.276581 | + | 0.960991i | \(0.410799\pi\) | |||||||
\(398\) | 1.49435e42 | 0.188965 | ||||||||
\(399\) | −2.84565e42 | −0.345246 | ||||||||
\(400\) | −9.91394e41 | −0.115413 | ||||||||
\(401\) | 5.75416e42 | 0.642835 | 0.321418 | − | 0.946938i | \(-0.395841\pi\) | ||||
0.321418 | + | 0.946938i | \(0.395841\pi\) | |||||||
\(402\) | −1.23773e43 | −1.32708 | ||||||||
\(403\) | 1.51162e43 | 1.55564 | ||||||||
\(404\) | −3.51323e42 | −0.347068 | ||||||||
\(405\) | −4.68494e42 | −0.444320 | ||||||||
\(406\) | −1.99367e43 | −1.81541 | ||||||||
\(407\) | 4.06126e42 | 0.355102 | ||||||||
\(408\) | −9.31423e42 | −0.782085 | ||||||||
\(409\) | −1.41308e43 | −1.13954 | −0.569772 | − | 0.821803i | \(-0.692968\pi\) | ||||
−0.569772 | + | 0.821803i | \(0.692968\pi\) | |||||||
\(410\) | −3.07991e41 | −0.0238564 | ||||||||
\(411\) | −5.74385e42 | −0.427379 | ||||||||
\(412\) | 5.26235e42 | 0.376162 | ||||||||
\(413\) | 4.68182e42 | 0.321543 | ||||||||
\(414\) | −1.01342e41 | −0.00668780 | ||||||||
\(415\) | −1.00836e43 | −0.639472 | ||||||||
\(416\) | 1.07701e43 | 0.656415 | ||||||||
\(417\) | −2.48020e43 | −1.45292 | ||||||||
\(418\) | −8.20950e41 | −0.0462283 | ||||||||
\(419\) | 2.86224e43 | 1.54944 | 0.774720 | − | 0.632305i | \(-0.217891\pi\) | ||||
0.774720 | + | 0.632305i | \(0.217891\pi\) | |||||||
\(420\) | −4.27446e42 | −0.222468 | ||||||||
\(421\) | 1.34194e43 | 0.671549 | 0.335774 | − | 0.941942i | \(-0.391002\pi\) | ||||
0.335774 | + | 0.941942i | \(0.391002\pi\) | |||||||
\(422\) | −2.03165e43 | −0.977674 | ||||||||
\(423\) | 1.26451e41 | 0.00585202 | ||||||||
\(424\) | 2.81729e43 | 1.25399 | ||||||||
\(425\) | 3.36721e42 | 0.144163 | ||||||||
\(426\) | 5.22468e42 | 0.215180 | ||||||||
\(427\) | −8.23502e42 | −0.326291 | ||||||||
\(428\) | 1.44689e43 | 0.551587 | ||||||||
\(429\) | 7.34217e42 | 0.269327 | ||||||||
\(430\) | 1.40424e43 | 0.495692 | ||||||||
\(431\) | −4.00130e43 | −1.35933 | −0.679667 | − | 0.733521i | \(-0.737876\pi\) | ||||
−0.679667 | + | 0.733521i | \(0.737876\pi\) | |||||||
\(432\) | 1.77048e43 | 0.578907 | ||||||||
\(433\) | −1.03509e43 | −0.325783 | −0.162891 | − | 0.986644i | \(-0.552082\pi\) | ||||
−0.162891 | + | 0.986644i | \(0.552082\pi\) | |||||||
\(434\) | 6.15625e43 | 1.86524 | ||||||||
\(435\) | −2.15997e43 | −0.630050 | ||||||||
\(436\) | −4.49300e42 | −0.126186 | ||||||||
\(437\) | −1.03732e43 | −0.280524 | ||||||||
\(438\) | −2.68529e43 | −0.699307 | ||||||||
\(439\) | 3.15434e42 | 0.0791122 | 0.0395561 | − | 0.999217i | \(-0.487406\pi\) | ||||
0.0395561 | + | 0.999217i | \(0.487406\pi\) | |||||||
\(440\) | −5.08285e42 | −0.122783 | ||||||||
\(441\) | −3.94353e41 | −0.00917591 | ||||||||
\(442\) | 2.84007e43 | 0.636593 | ||||||||
\(443\) | −1.66215e43 | −0.358929 | −0.179464 | − | 0.983764i | \(-0.557436\pi\) | ||||
−0.179464 | + | 0.983764i | \(0.557436\pi\) | |||||||
\(444\) | −2.16058e43 | −0.449523 | ||||||||
\(445\) | −9.28532e42 | −0.186147 | ||||||||
\(446\) | −1.66709e43 | −0.322057 | ||||||||
\(447\) | 6.82821e43 | 1.27125 | ||||||||
\(448\) | 9.39667e43 | 1.68611 | ||||||||
\(449\) | −2.11347e43 | −0.365537 | −0.182768 | − | 0.983156i | \(-0.558506\pi\) | ||||
−0.182768 | + | 0.983156i | \(0.558506\pi\) | |||||||
\(450\) | −6.35795e40 | −0.00106001 | ||||||||
\(451\) | −1.01542e42 | −0.0163204 | ||||||||
\(452\) | 3.05318e43 | 0.473117 | ||||||||
\(453\) | −7.93231e40 | −0.00118517 | ||||||||
\(454\) | −4.14961e43 | −0.597840 | ||||||||
\(455\) | 5.37223e43 | 0.746391 | ||||||||
\(456\) | 1.80018e43 | 0.241211 | ||||||||
\(457\) | −1.42828e44 | −1.84585 | −0.922924 | − | 0.384981i | \(-0.874208\pi\) | ||||
−0.922924 | + | 0.384981i | \(0.874208\pi\) | |||||||
\(458\) | −8.45082e43 | −1.05346 | ||||||||
\(459\) | −6.01333e43 | −0.723112 | ||||||||
\(460\) | −1.55816e43 | −0.180763 | ||||||||
\(461\) | 3.53458e43 | 0.395615 | 0.197807 | − | 0.980241i | \(-0.436618\pi\) | ||||
0.197807 | + | 0.980241i | \(0.436618\pi\) | |||||||
\(462\) | 2.99018e43 | 0.322927 | ||||||||
\(463\) | −3.07914e43 | −0.320880 | −0.160440 | − | 0.987046i | \(-0.551291\pi\) | ||||
−0.160440 | + | 0.987046i | \(0.551291\pi\) | |||||||
\(464\) | 8.11024e43 | 0.815618 | ||||||||
\(465\) | 6.66976e43 | 0.647346 | ||||||||
\(466\) | −4.33375e43 | −0.405972 | ||||||||
\(467\) | −3.68923e43 | −0.333586 | −0.166793 | − | 0.985992i | \(-0.553341\pi\) | ||||
−0.166793 | + | 0.985992i | \(0.553341\pi\) | |||||||
\(468\) | 2.52735e41 | 0.00220602 | ||||||||
\(469\) | −2.98580e44 | −2.51599 | ||||||||
\(470\) | −4.12531e43 | −0.335615 | ||||||||
\(471\) | 1.51985e44 | 1.19387 | ||||||||
\(472\) | −2.96176e43 | −0.224650 | ||||||||
\(473\) | 4.62963e43 | 0.339108 | ||||||||
\(474\) | −1.21593e44 | −0.860134 | ||||||||
\(475\) | −6.50790e42 | −0.0444627 | ||||||||
\(476\) | −5.45119e43 | −0.359730 | ||||||||
\(477\) | 1.16184e42 | 0.00740615 | ||||||||
\(478\) | −2.05619e44 | −1.26620 | ||||||||
\(479\) | −3.09046e43 | −0.183860 | −0.0919300 | − | 0.995765i | \(-0.529304\pi\) | ||||
−0.0919300 | + | 0.995765i | \(0.529304\pi\) | |||||||
\(480\) | 4.75209e43 | 0.273152 | ||||||||
\(481\) | 2.71546e44 | 1.50817 | ||||||||
\(482\) | 2.94340e44 | 1.57970 | ||||||||
\(483\) | 3.77827e44 | 1.95959 | ||||||||
\(484\) | 5.98401e43 | 0.299946 | ||||||||
\(485\) | 9.33913e41 | 0.00452447 | ||||||||
\(486\) | 2.26361e42 | 0.0105999 | ||||||||
\(487\) | 4.31638e44 | 1.95385 | 0.976926 | − | 0.213578i | \(-0.0685118\pi\) | ||||
0.976926 | + | 0.213578i | \(0.0685118\pi\) | |||||||
\(488\) | 5.20955e43 | 0.227968 | ||||||||
\(489\) | 6.34524e43 | 0.268443 | ||||||||
\(490\) | 1.28653e44 | 0.526241 | ||||||||
\(491\) | −2.93145e44 | −1.15941 | −0.579706 | − | 0.814826i | \(-0.696832\pi\) | ||||
−0.579706 | + | 0.814826i | \(0.696832\pi\) | |||||||
\(492\) | 5.40199e42 | 0.0206600 | ||||||||
\(493\) | −2.75460e44 | −1.01879 | ||||||||
\(494\) | −5.48908e43 | −0.196338 | ||||||||
\(495\) | −2.09615e41 | −0.000725164 0 | ||||||||
\(496\) | −2.50435e44 | −0.838008 | ||||||||
\(497\) | 1.26036e44 | 0.407956 | ||||||||
\(498\) | −3.75267e44 | −1.17505 | ||||||||
\(499\) | −9.00632e42 | −0.0272828 | −0.0136414 | − | 0.999907i | \(-0.504342\pi\) | ||||
−0.0136414 | + | 0.999907i | \(0.504342\pi\) | |||||||
\(500\) | −9.77554e42 | −0.0286507 | ||||||||
\(501\) | 1.71467e44 | 0.486249 | ||||||||
\(502\) | 1.07136e42 | 0.00293985 | ||||||||
\(503\) | −3.10986e44 | −0.825789 | −0.412895 | − | 0.910779i | \(-0.635482\pi\) | ||||
−0.412895 | + | 0.910779i | \(0.635482\pi\) | |||||||
\(504\) | 4.24256e42 | 0.0109024 | ||||||||
\(505\) | 1.94826e44 | 0.484550 | ||||||||
\(506\) | 1.09001e44 | 0.262389 | ||||||||
\(507\) | 6.31261e43 | 0.147088 | ||||||||
\(508\) | −2.73128e44 | −0.616048 | ||||||||
\(509\) | 7.95788e43 | 0.173762 | 0.0868808 | − | 0.996219i | \(-0.472310\pi\) | ||||
0.0868808 | + | 0.996219i | \(0.472310\pi\) | |||||||
\(510\) | 1.25313e44 | 0.264904 | ||||||||
\(511\) | −6.47777e44 | −1.32581 | ||||||||
\(512\) | −4.95397e44 | −0.981745 | ||||||||
\(513\) | 1.16221e44 | 0.223023 | ||||||||
\(514\) | −2.85938e44 | −0.531350 | ||||||||
\(515\) | −2.91823e44 | −0.525170 | ||||||||
\(516\) | −2.46296e44 | −0.429276 | ||||||||
\(517\) | −1.36007e44 | −0.229598 | ||||||||
\(518\) | 1.10590e45 | 1.80832 | ||||||||
\(519\) | 5.53149e44 | 0.876154 | ||||||||
\(520\) | −3.39852e44 | −0.521477 | ||||||||
\(521\) | 1.27119e44 | 0.188968 | 0.0944841 | − | 0.995526i | \(-0.469880\pi\) | ||||
0.0944841 | + | 0.995526i | \(0.469880\pi\) | |||||||
\(522\) | 5.20121e42 | 0.00749102 | ||||||||
\(523\) | −1.19591e44 | −0.166887 | −0.0834434 | − | 0.996513i | \(-0.526592\pi\) | ||||
−0.0834434 | + | 0.996513i | \(0.526592\pi\) | |||||||
\(524\) | −1.63278e44 | −0.220781 | ||||||||
\(525\) | 2.37040e44 | 0.310594 | ||||||||
\(526\) | −6.56876e44 | −0.834101 | ||||||||
\(527\) | 8.50590e44 | 1.04675 | ||||||||
\(528\) | −1.21640e44 | −0.145083 | ||||||||
\(529\) | 5.12284e44 | 0.592233 | ||||||||
\(530\) | −3.79036e44 | −0.424745 | ||||||||
\(531\) | −1.22142e42 | −0.00132680 | ||||||||
\(532\) | 1.05357e44 | 0.110948 | ||||||||
\(533\) | −6.78932e43 | −0.0693151 | ||||||||
\(534\) | −3.45559e44 | −0.342052 | ||||||||
\(535\) | −8.02372e44 | −0.770085 | ||||||||
\(536\) | 1.88885e45 | 1.75783 | ||||||||
\(537\) | −8.49938e44 | −0.767029 | ||||||||
\(538\) | 1.68210e45 | 1.47212 | ||||||||
\(539\) | 4.24156e44 | 0.360007 | ||||||||
\(540\) | 1.74576e44 | 0.143710 | ||||||||
\(541\) | −1.24548e45 | −0.994451 | −0.497225 | − | 0.867621i | \(-0.665648\pi\) | ||||
−0.497225 | + | 0.867621i | \(0.665648\pi\) | |||||||
\(542\) | 3.25913e44 | 0.252414 | ||||||||
\(543\) | 6.96426e44 | 0.523212 | ||||||||
\(544\) | 6.06031e44 | 0.441686 | ||||||||
\(545\) | 2.49159e44 | 0.176171 | ||||||||
\(546\) | 1.99931e45 | 1.37152 | ||||||||
\(547\) | −9.41755e44 | −0.626826 | −0.313413 | − | 0.949617i | \(-0.601472\pi\) | ||||
−0.313413 | + | 0.949617i | \(0.601472\pi\) | |||||||
\(548\) | 2.12659e44 | 0.137342 | ||||||||
\(549\) | 2.14840e42 | 0.00134639 | ||||||||
\(550\) | 6.83843e43 | 0.0415884 | ||||||||
\(551\) | 5.32388e44 | 0.314215 | ||||||||
\(552\) | −2.39017e45 | −1.36910 | ||||||||
\(553\) | −2.93321e45 | −1.63072 | ||||||||
\(554\) | −1.77713e45 | −0.958975 | ||||||||
\(555\) | 1.19815e45 | 0.627591 | ||||||||
\(556\) | 9.18263e44 | 0.466910 | ||||||||
\(557\) | −2.81038e45 | −1.38725 | −0.693624 | − | 0.720338i | \(-0.743987\pi\) | ||||
−0.693624 | + | 0.720338i | \(0.743987\pi\) | |||||||
\(558\) | −1.60608e43 | −0.00769666 | ||||||||
\(559\) | 3.09549e45 | 1.44024 | ||||||||
\(560\) | −8.90034e44 | −0.402072 | ||||||||
\(561\) | 4.13144e44 | 0.181223 | ||||||||
\(562\) | −2.32549e44 | −0.0990524 | ||||||||
\(563\) | 2.48634e45 | 1.02842 | 0.514212 | − | 0.857663i | \(-0.328084\pi\) | ||||
0.514212 | + | 0.857663i | \(0.328084\pi\) | |||||||
\(564\) | 7.23555e44 | 0.290647 | ||||||||
\(565\) | −1.69314e45 | −0.660530 | ||||||||
\(566\) | 1.36400e45 | 0.516826 | ||||||||
\(567\) | −4.20595e45 | −1.54790 | ||||||||
\(568\) | −7.97315e44 | −0.285025 | ||||||||
\(569\) | 1.50472e45 | 0.522521 | 0.261261 | − | 0.965268i | \(-0.415862\pi\) | ||||
0.261261 | + | 0.965268i | \(0.415862\pi\) | |||||||
\(570\) | −2.42196e44 | −0.0817017 | ||||||||
\(571\) | −2.28889e45 | −0.750117 | −0.375059 | − | 0.927001i | \(-0.622377\pi\) | ||||
−0.375059 | + | 0.927001i | \(0.622377\pi\) | |||||||
\(572\) | −2.71835e44 | −0.0865507 | ||||||||
\(573\) | 1.26255e45 | 0.390569 | ||||||||
\(574\) | −2.76503e44 | −0.0831099 | ||||||||
\(575\) | 8.64077e44 | 0.252367 | ||||||||
\(576\) | −2.45146e43 | −0.00695751 | ||||||||
\(577\) | 1.59455e45 | 0.439781 | 0.219891 | − | 0.975525i | \(-0.429430\pi\) | ||||
0.219891 | + | 0.975525i | \(0.429430\pi\) | |||||||
\(578\) | −1.47771e45 | −0.396076 | ||||||||
\(579\) | 5.57987e44 | 0.145354 | ||||||||
\(580\) | 7.99702e44 | 0.202473 | ||||||||
\(581\) | −9.05264e45 | −2.22776 | ||||||||
\(582\) | 3.47562e43 | 0.00831386 | ||||||||
\(583\) | −1.24964e45 | −0.290572 | ||||||||
\(584\) | 4.09790e45 | 0.926295 | ||||||||
\(585\) | −1.40154e43 | −0.00307987 | ||||||||
\(586\) | 4.30405e44 | 0.0919531 | ||||||||
\(587\) | 5.55956e45 | 1.15481 | 0.577407 | − | 0.816457i | \(-0.304065\pi\) | ||||
0.577407 | + | 0.816457i | \(0.304065\pi\) | |||||||
\(588\) | −2.25650e45 | −0.455732 | ||||||||
\(589\) | −1.64396e45 | −0.322841 | ||||||||
\(590\) | 3.98473e44 | 0.0760924 | ||||||||
\(591\) | 1.04824e46 | 1.94655 | ||||||||
\(592\) | −4.49880e45 | −0.812434 | ||||||||
\(593\) | −1.33454e45 | −0.234384 | −0.117192 | − | 0.993109i | \(-0.537389\pi\) | ||||
−0.117192 | + | 0.993109i | \(0.537389\pi\) | |||||||
\(594\) | −1.22124e45 | −0.208605 | ||||||||
\(595\) | 3.02295e45 | 0.502228 | ||||||||
\(596\) | −2.52806e45 | −0.408530 | ||||||||
\(597\) | 1.45347e45 | 0.228470 | ||||||||
\(598\) | 7.28806e45 | 1.11440 | ||||||||
\(599\) | 2.61382e45 | 0.388806 | 0.194403 | − | 0.980922i | \(-0.437723\pi\) | ||||
0.194403 | + | 0.980922i | \(0.437723\pi\) | |||||||
\(600\) | −1.49954e45 | −0.217001 | ||||||||
\(601\) | 1.12433e45 | 0.158295 | 0.0791474 | − | 0.996863i | \(-0.474780\pi\) | ||||
0.0791474 | + | 0.996863i | \(0.474780\pi\) | |||||||
\(602\) | 1.26067e46 | 1.72687 | ||||||||
\(603\) | 7.78954e43 | 0.0103819 | ||||||||
\(604\) | 2.93684e42 | 0.000380865 0 | ||||||||
\(605\) | −3.31842e45 | −0.418763 | ||||||||
\(606\) | 7.25056e45 | 0.890376 | ||||||||
\(607\) | 1.38809e46 | 1.65884 | 0.829418 | − | 0.558628i | \(-0.188672\pi\) | ||||
0.829418 | + | 0.558628i | \(0.188672\pi\) | |||||||
\(608\) | −1.17129e45 | −0.136225 | ||||||||
\(609\) | −1.93914e46 | −2.19494 | ||||||||
\(610\) | −7.00890e44 | −0.0772160 | ||||||||
\(611\) | −9.09378e45 | −0.975134 | ||||||||
\(612\) | 1.42214e43 | 0.00148437 | ||||||||
\(613\) | 1.28344e46 | 1.30400 | 0.652001 | − | 0.758218i | \(-0.273930\pi\) | ||||
0.652001 | + | 0.758218i | \(0.273930\pi\) | |||||||
\(614\) | −1.15835e46 | −1.14567 | ||||||||
\(615\) | −2.99566e44 | −0.0288439 | ||||||||
\(616\) | −4.56318e45 | −0.427746 | ||||||||
\(617\) | −1.41494e46 | −1.29131 | −0.645657 | − | 0.763628i | \(-0.723416\pi\) | ||||
−0.645657 | + | 0.763628i | \(0.723416\pi\) | |||||||
\(618\) | −1.08604e46 | −0.965017 | ||||||||
\(619\) | 3.49373e45 | 0.302269 | 0.151134 | − | 0.988513i | \(-0.451707\pi\) | ||||
0.151134 | + | 0.988513i | \(0.451707\pi\) | |||||||
\(620\) | −2.46939e45 | −0.208031 | ||||||||
\(621\) | −1.54311e46 | −1.26586 | ||||||||
\(622\) | 1.05693e46 | 0.844312 | ||||||||
\(623\) | −8.33600e45 | −0.648492 | ||||||||
\(624\) | −8.13317e45 | −0.616189 | ||||||||
\(625\) | 5.42101e44 | 0.0400000 | ||||||||
\(626\) | −1.76558e46 | −1.26885 | ||||||||
\(627\) | −7.98494e44 | −0.0558929 | ||||||||
\(628\) | −5.62707e45 | −0.383662 | ||||||||
\(629\) | 1.52799e46 | 1.01481 | ||||||||
\(630\) | −5.70791e43 | −0.00369282 | ||||||||
\(631\) | 2.21383e46 | 1.39528 | 0.697638 | − | 0.716451i | \(-0.254234\pi\) | ||||
0.697638 | + | 0.716451i | \(0.254234\pi\) | |||||||
\(632\) | 1.85558e46 | 1.13932 | ||||||||
\(633\) | −1.97608e46 | −1.18207 | ||||||||
\(634\) | −9.02525e45 | −0.526001 | ||||||||
\(635\) | 1.51463e46 | 0.860080 | ||||||||
\(636\) | 6.64807e45 | 0.367835 | ||||||||
\(637\) | 2.83601e46 | 1.52900 | ||||||||
\(638\) | −5.59428e45 | −0.293902 | ||||||||
\(639\) | −3.28810e43 | −0.00168337 | ||||||||
\(640\) | 2.50503e45 | 0.124981 | ||||||||
\(641\) | −4.90058e45 | −0.238281 | −0.119141 | − | 0.992877i | \(-0.538014\pi\) | ||||
−0.119141 | + | 0.992877i | \(0.538014\pi\) | |||||||
\(642\) | −2.98608e46 | −1.41506 | ||||||||
\(643\) | 2.98051e46 | 1.37661 | 0.688303 | − | 0.725423i | \(-0.258356\pi\) | ||||
0.688303 | + | 0.725423i | \(0.258356\pi\) | |||||||
\(644\) | −1.39886e46 | −0.629734 | ||||||||
\(645\) | 1.36583e46 | 0.599323 | ||||||||
\(646\) | −3.08871e45 | −0.132111 | ||||||||
\(647\) | −3.18321e45 | −0.132723 | −0.0663613 | − | 0.997796i | \(-0.521139\pi\) | ||||
−0.0663613 | + | 0.997796i | \(0.521139\pi\) | |||||||
\(648\) | 2.66073e46 | 1.08146 | ||||||||
\(649\) | 1.31372e45 | 0.0520555 | ||||||||
\(650\) | 4.57235e45 | 0.176632 | ||||||||
\(651\) | 5.98785e46 | 2.25520 | ||||||||
\(652\) | −2.34924e45 | −0.0862666 | ||||||||
\(653\) | −4.44872e46 | −1.59282 | −0.796411 | − | 0.604756i | \(-0.793271\pi\) | ||||
−0.796411 | + | 0.604756i | \(0.793271\pi\) | |||||||
\(654\) | 9.27261e45 | 0.323720 | ||||||||
\(655\) | 9.05457e45 | 0.308238 | ||||||||
\(656\) | 1.12481e45 | 0.0373392 | ||||||||
\(657\) | 1.68996e44 | 0.00547076 | ||||||||
\(658\) | −3.70354e46 | −1.16920 | ||||||||
\(659\) | −3.64438e46 | −1.12206 | −0.561028 | − | 0.827797i | \(-0.689594\pi\) | ||||
−0.561028 | + | 0.827797i | \(0.689594\pi\) | |||||||
\(660\) | −1.19942e45 | −0.0360161 | ||||||||
\(661\) | −2.16411e46 | −0.633804 | −0.316902 | − | 0.948458i | \(-0.602643\pi\) | ||||
−0.316902 | + | 0.948458i | \(0.602643\pi\) | |||||||
\(662\) | 1.85517e46 | 0.529940 | ||||||||
\(663\) | 2.76238e46 | 0.769681 | ||||||||
\(664\) | 5.72679e46 | 1.55646 | ||||||||
\(665\) | −5.84253e45 | −0.154897 | ||||||||
\(666\) | −2.88514e44 | −0.00746178 | ||||||||
\(667\) | −7.06871e46 | −1.78346 | ||||||||
\(668\) | −6.34836e45 | −0.156261 | ||||||||
\(669\) | −1.62148e46 | −0.389387 | ||||||||
\(670\) | −2.54124e46 | −0.595404 | ||||||||
\(671\) | −2.31076e45 | −0.0528242 | ||||||||
\(672\) | 4.26624e46 | 0.951596 | ||||||||
\(673\) | 5.34875e46 | 1.16414 | 0.582068 | − | 0.813140i | \(-0.302244\pi\) | ||||
0.582068 | + | 0.813140i | \(0.302244\pi\) | |||||||
\(674\) | 4.43140e46 | 0.941137 | ||||||||
\(675\) | −9.68110e45 | −0.200638 | ||||||||
\(676\) | −2.33717e45 | −0.0472682 | ||||||||
\(677\) | −3.90814e46 | −0.771359 | −0.385679 | − | 0.922633i | \(-0.626033\pi\) | ||||
−0.385679 | + | 0.922633i | \(0.626033\pi\) | |||||||
\(678\) | −6.30112e46 | −1.21375 | ||||||||
\(679\) | 8.38430e44 | 0.0157622 | ||||||||
\(680\) | −1.91235e46 | −0.350889 | ||||||||
\(681\) | −4.03610e46 | −0.722826 | ||||||||
\(682\) | 1.72745e46 | 0.301970 | ||||||||
\(683\) | 9.82421e46 | 1.67632 | 0.838158 | − | 0.545427i | \(-0.183632\pi\) | ||||
0.838158 | + | 0.545427i | \(0.183632\pi\) | |||||||
\(684\) | −2.74860e43 | −0.000457811 0 | ||||||||
\(685\) | −1.17930e46 | −0.191747 | ||||||||
\(686\) | 3.45786e46 | 0.548858 | ||||||||
\(687\) | −8.21966e46 | −1.27370 | ||||||||
\(688\) | −5.12840e46 | −0.775841 | ||||||||
\(689\) | −8.35542e46 | −1.23410 | ||||||||
\(690\) | 3.21572e46 | 0.463733 | ||||||||
\(691\) | −7.20065e46 | −1.01387 | −0.506937 | − | 0.861983i | \(-0.669222\pi\) | ||||
−0.506937 | + | 0.861983i | \(0.669222\pi\) | |||||||
\(692\) | −2.04796e46 | −0.281560 | ||||||||
\(693\) | −1.88184e44 | −0.00252629 | ||||||||
\(694\) | 7.68188e46 | 1.00702 | ||||||||
\(695\) | −5.09221e46 | −0.651864 | ||||||||
\(696\) | 1.22672e47 | 1.53353 | ||||||||
\(697\) | −3.82035e45 | −0.0466404 | ||||||||
\(698\) | 1.11927e47 | 1.33451 | ||||||||
\(699\) | −4.21520e46 | −0.490846 | ||||||||
\(700\) | −8.77609e45 | −0.0998122 | ||||||||
\(701\) | −3.78749e46 | −0.420731 | −0.210366 | − | 0.977623i | \(-0.567465\pi\) | ||||
−0.210366 | + | 0.977623i | \(0.567465\pi\) | |||||||
\(702\) | −8.16552e46 | −0.885975 | ||||||||
\(703\) | −2.95319e46 | −0.312988 | ||||||||
\(704\) | 2.63672e46 | 0.272970 | ||||||||
\(705\) | −4.01246e46 | −0.405780 | ||||||||
\(706\) | −5.86119e45 | −0.0579039 | ||||||||
\(707\) | 1.74907e47 | 1.68805 | ||||||||
\(708\) | −6.98899e45 | −0.0658970 | ||||||||
\(709\) | 8.09313e46 | 0.745510 | 0.372755 | − | 0.927930i | \(-0.378413\pi\) | ||||
0.372755 | + | 0.927930i | \(0.378413\pi\) | |||||||
\(710\) | 1.07270e46 | 0.0965421 | ||||||||
\(711\) | 7.65234e44 | 0.00672892 | ||||||||
\(712\) | 5.27343e46 | 0.453078 | ||||||||
\(713\) | 2.18274e47 | 1.83242 | ||||||||
\(714\) | 1.12501e47 | 0.922861 | ||||||||
\(715\) | 1.50746e46 | 0.120836 | ||||||||
\(716\) | 3.14679e46 | 0.246492 | ||||||||
\(717\) | −1.99995e47 | −1.53092 | ||||||||
\(718\) | −1.73923e47 | −1.30108 | ||||||||
\(719\) | 1.77184e47 | 1.29538 | 0.647692 | − | 0.761902i | \(-0.275734\pi\) | ||||
0.647692 | + | 0.761902i | \(0.275734\pi\) | |||||||
\(720\) | 2.32197e44 | 0.00165909 | ||||||||
\(721\) | −2.61987e47 | −1.82956 | ||||||||
\(722\) | −1.14816e47 | −0.783678 | ||||||||
\(723\) | 2.86289e47 | 1.90995 | ||||||||
\(724\) | −2.57843e46 | −0.168139 | ||||||||
\(725\) | −4.43474e46 | −0.282677 | ||||||||
\(726\) | −1.23497e47 | −0.769490 | ||||||||
\(727\) | 1.73206e47 | 1.05498 | 0.527490 | − | 0.849561i | \(-0.323133\pi\) | ||||
0.527490 | + | 0.849561i | \(0.323133\pi\) | |||||||
\(728\) | −3.05106e47 | −1.81670 | ||||||||
\(729\) | 1.72883e47 | 1.00635 | ||||||||
\(730\) | −5.51329e46 | −0.313750 | ||||||||
\(731\) | 1.74183e47 | 0.969102 | ||||||||
\(732\) | 1.22932e46 | 0.0668701 | ||||||||
\(733\) | −2.26618e47 | −1.20525 | −0.602626 | − | 0.798024i | \(-0.705879\pi\) | ||||
−0.602626 | + | 0.798024i | \(0.705879\pi\) | |||||||
\(734\) | 1.86736e47 | 0.971054 | ||||||||
\(735\) | 1.25134e47 | 0.636259 | ||||||||
\(736\) | 1.55517e47 | 0.773203 | ||||||||
\(737\) | −8.37821e46 | −0.407322 | ||||||||
\(738\) | 7.21356e43 | 0.000342941 0 | ||||||||
\(739\) | 3.80934e46 | 0.177099 | 0.0885496 | − | 0.996072i | \(-0.471777\pi\) | ||||
0.0885496 | + | 0.996072i | \(0.471777\pi\) | |||||||
\(740\) | −4.43599e46 | −0.201682 | ||||||||
\(741\) | −5.33893e46 | −0.237385 | ||||||||
\(742\) | −3.40283e47 | −1.47971 | ||||||||
\(743\) | −1.22091e47 | −0.519238 | −0.259619 | − | 0.965711i | \(-0.583597\pi\) | ||||
−0.259619 | + | 0.965711i | \(0.583597\pi\) | |||||||
\(744\) | −3.78797e47 | −1.57563 | ||||||||
\(745\) | 1.40193e47 | 0.570359 | ||||||||
\(746\) | 1.66800e47 | 0.663750 | ||||||||
\(747\) | 2.36171e45 | 0.00919255 | ||||||||
\(748\) | −1.52961e46 | −0.0582378 | ||||||||
\(749\) | −7.20338e47 | −2.68279 | ||||||||
\(750\) | 2.01747e46 | 0.0735013 | ||||||||
\(751\) | −2.36534e46 | −0.0843014 | −0.0421507 | − | 0.999111i | \(-0.513421\pi\) | ||||
−0.0421507 | + | 0.999111i | \(0.513421\pi\) | |||||||
\(752\) | 1.50660e47 | 0.525294 | ||||||||
\(753\) | 1.04206e45 | 0.00355446 | ||||||||
\(754\) | −3.74048e47 | −1.24824 | ||||||||
\(755\) | −1.62862e44 | −0.000531735 0 | ||||||||
\(756\) | 1.56728e47 | 0.500652 | ||||||||
\(757\) | −1.36056e47 | −0.425243 | −0.212621 | − | 0.977135i | \(-0.568200\pi\) | ||||
−0.212621 | + | 0.977135i | \(0.568200\pi\) | |||||||
\(758\) | 2.51859e47 | 0.770222 | ||||||||
\(759\) | 1.06019e47 | 0.317245 | ||||||||
\(760\) | 3.69604e46 | 0.108221 | ||||||||
\(761\) | 2.10711e47 | 0.603727 | 0.301863 | − | 0.953351i | \(-0.402391\pi\) | ||||
0.301863 | + | 0.953351i | \(0.402391\pi\) | |||||||
\(762\) | 5.63678e47 | 1.58043 | ||||||||
\(763\) | 2.23685e47 | 0.613737 | ||||||||
\(764\) | −4.67444e46 | −0.125513 | ||||||||
\(765\) | −7.88645e44 | −0.00207237 | ||||||||
\(766\) | 1.61055e47 | 0.414189 | ||||||||
\(767\) | 8.78390e46 | 0.221087 | ||||||||
\(768\) | −3.44682e47 | −0.849100 | ||||||||
\(769\) | 3.42055e47 | 0.824728 | 0.412364 | − | 0.911019i | \(-0.364703\pi\) | ||||
0.412364 | + | 0.911019i | \(0.364703\pi\) | |||||||
\(770\) | 6.13927e46 | 0.144884 | ||||||||
\(771\) | −2.78116e47 | −0.642435 | ||||||||
\(772\) | −2.06588e46 | −0.0467110 | ||||||||
\(773\) | 2.59138e47 | 0.573549 | 0.286774 | − | 0.957998i | \(-0.407417\pi\) | ||||
0.286774 | + | 0.957998i | \(0.407417\pi\) | |||||||
\(774\) | −3.28892e45 | −0.00712569 | ||||||||
\(775\) | 1.36940e47 | 0.290437 | ||||||||
\(776\) | −5.30399e45 | −0.0110125 | ||||||||
\(777\) | 1.07565e48 | 2.18637 | ||||||||
\(778\) | −3.59916e47 | −0.716206 | ||||||||
\(779\) | 7.38369e45 | 0.0143849 | ||||||||
\(780\) | −8.01963e46 | −0.152966 | ||||||||
\(781\) | 3.53659e46 | 0.0660454 | ||||||||
\(782\) | 4.10099e47 | 0.749855 | ||||||||
\(783\) | 7.91977e47 | 1.41789 | ||||||||
\(784\) | −4.69851e47 | −0.823655 | ||||||||
\(785\) | 3.12048e47 | 0.535639 | ||||||||
\(786\) | 3.36972e47 | 0.566398 | ||||||||
\(787\) | −3.31448e47 | −0.545546 | −0.272773 | − | 0.962078i | \(-0.587941\pi\) | ||||
−0.272773 | + | 0.962078i | \(0.587941\pi\) | |||||||
\(788\) | −3.88096e47 | −0.625542 | ||||||||
\(789\) | −6.38908e47 | −1.00848 | ||||||||
\(790\) | −2.49648e47 | −0.385906 | ||||||||
\(791\) | −1.52003e48 | −2.30113 | ||||||||
\(792\) | 1.19047e45 | 0.00176503 | ||||||||
\(793\) | −1.54503e47 | −0.224352 | ||||||||
\(794\) | 3.20658e47 | 0.456040 | ||||||||
\(795\) | −3.68667e47 | −0.513543 | ||||||||
\(796\) | −5.38129e46 | −0.0734211 | ||||||||
\(797\) | −1.21980e48 | −1.63015 | −0.815076 | − | 0.579354i | \(-0.803305\pi\) | ||||
−0.815076 | + | 0.579354i | \(0.803305\pi\) | |||||||
\(798\) | −2.17434e47 | −0.284629 | ||||||||
\(799\) | −5.11707e47 | −0.656144 | ||||||||
\(800\) | 9.75675e46 | 0.122552 | ||||||||
\(801\) | 2.17474e45 | 0.00267591 | ||||||||
\(802\) | 4.39671e47 | 0.529969 | ||||||||
\(803\) | −1.81767e47 | −0.214639 | ||||||||
\(804\) | 4.45719e47 | 0.515628 | ||||||||
\(805\) | 7.75735e47 | 0.879187 | ||||||||
\(806\) | 1.15502e48 | 1.28251 | ||||||||
\(807\) | 1.63609e48 | 1.77989 | ||||||||
\(808\) | −1.10648e48 | −1.17938 | ||||||||
\(809\) | −2.89096e47 | −0.301920 | −0.150960 | − | 0.988540i | \(-0.548236\pi\) | ||||
−0.150960 | + | 0.988540i | \(0.548236\pi\) | |||||||
\(810\) | −3.57972e47 | −0.366308 | ||||||||
\(811\) | −8.79228e47 | −0.881571 | −0.440786 | − | 0.897612i | \(-0.645300\pi\) | ||||
−0.440786 | + | 0.897612i | \(0.645300\pi\) | |||||||
\(812\) | 7.17941e47 | 0.705366 | ||||||||
\(813\) | 3.16998e47 | 0.305184 | ||||||||
\(814\) | 3.10318e47 | 0.292755 | ||||||||
\(815\) | 1.30277e47 | 0.120439 | ||||||||
\(816\) | −4.57653e47 | −0.414619 | ||||||||
\(817\) | −3.36648e47 | −0.298891 | ||||||||
\(818\) | −1.07972e48 | −0.939467 | ||||||||
\(819\) | −1.25825e46 | −0.0107295 | ||||||||
\(820\) | 1.10911e46 | 0.00926926 | ||||||||
\(821\) | −6.16314e47 | −0.504824 | −0.252412 | − | 0.967620i | \(-0.581224\pi\) | ||||
−0.252412 | + | 0.967620i | \(0.581224\pi\) | |||||||
\(822\) | −4.38883e47 | −0.352342 | ||||||||
\(823\) | −1.89117e47 | −0.148810 | −0.0744052 | − | 0.997228i | \(-0.523706\pi\) | ||||
−0.0744052 | + | 0.997228i | \(0.523706\pi\) | |||||||
\(824\) | 1.65735e48 | 1.27825 | ||||||||
\(825\) | 6.65137e46 | 0.0502830 | ||||||||
\(826\) | 3.57734e47 | 0.265087 | ||||||||
\(827\) | −9.51973e47 | −0.691486 | −0.345743 | − | 0.938329i | \(-0.612373\pi\) | ||||
−0.345743 | + | 0.938329i | \(0.612373\pi\) | |||||||
\(828\) | 3.64942e45 | 0.00259851 | ||||||||
\(829\) | 2.56276e48 | 1.78878 | 0.894392 | − | 0.447284i | \(-0.147609\pi\) | ||||
0.894392 | + | 0.447284i | \(0.147609\pi\) | |||||||
\(830\) | −7.70479e47 | −0.527196 | ||||||||
\(831\) | −1.72851e48 | −1.15946 | ||||||||
\(832\) | 1.76298e48 | 1.15934 | ||||||||
\(833\) | 1.59582e48 | 1.02883 | ||||||||
\(834\) | −1.89510e48 | −1.19782 | ||||||||
\(835\) | 3.52047e47 | 0.218159 | ||||||||
\(836\) | 2.95632e46 | 0.0179617 | ||||||||
\(837\) | −2.44554e48 | −1.45682 | ||||||||
\(838\) | 2.18701e48 | 1.27740 | ||||||||
\(839\) | −5.48536e47 | −0.314147 | −0.157073 | − | 0.987587i | \(-0.550206\pi\) | ||||
−0.157073 | + | 0.987587i | \(0.550206\pi\) | |||||||
\(840\) | −1.34622e48 | −0.755978 | ||||||||
\(841\) | 1.81182e48 | 0.997659 | ||||||||
\(842\) | 1.02536e48 | 0.553641 | ||||||||
\(843\) | −2.26188e47 | −0.119761 | ||||||||
\(844\) | 7.31618e47 | 0.379869 | ||||||||
\(845\) | 1.29607e47 | 0.0659923 | ||||||||
\(846\) | 9.66201e45 | 0.00482454 | ||||||||
\(847\) | −2.97915e48 | −1.45887 | ||||||||
\(848\) | 1.38427e48 | 0.664797 | ||||||||
\(849\) | 1.32669e48 | 0.624875 | ||||||||
\(850\) | 2.57286e47 | 0.118851 | ||||||||
\(851\) | 3.92105e48 | 1.77650 | ||||||||
\(852\) | −1.88146e47 | −0.0836067 | ||||||||
\(853\) | 6.63073e47 | 0.289003 | 0.144501 | − | 0.989505i | \(-0.453842\pi\) | ||||
0.144501 | + | 0.989505i | \(0.453842\pi\) | |||||||
\(854\) | −6.29231e47 | −0.269002 | ||||||||
\(855\) | 1.52423e45 | 0.000639162 0 | ||||||||
\(856\) | 4.55693e48 | 1.87437 | ||||||||
\(857\) | −3.61344e48 | −1.45793 | −0.728966 | − | 0.684550i | \(-0.759999\pi\) | ||||
−0.728966 | + | 0.684550i | \(0.759999\pi\) | |||||||
\(858\) | 5.61009e47 | 0.222039 | ||||||||
\(859\) | −2.95644e47 | −0.114784 | −0.0573921 | − | 0.998352i | \(-0.518279\pi\) | ||||
−0.0573921 | + | 0.998352i | \(0.518279\pi\) | |||||||
\(860\) | −5.05681e47 | −0.192598 | ||||||||
\(861\) | −2.68939e47 | −0.100485 | ||||||||
\(862\) | −3.05736e48 | −1.12067 | ||||||||
\(863\) | 1.94226e48 | 0.698440 | 0.349220 | − | 0.937041i | \(-0.386447\pi\) | ||||
0.349220 | + | 0.937041i | \(0.386447\pi\) | |||||||
\(864\) | −1.74241e48 | −0.614713 | ||||||||
\(865\) | 1.13570e48 | 0.393094 | ||||||||
\(866\) | −7.90904e47 | −0.268583 | ||||||||
\(867\) | −1.43728e48 | −0.478881 | ||||||||
\(868\) | −2.21692e48 | −0.724729 | ||||||||
\(869\) | −8.23064e47 | −0.264002 | ||||||||
\(870\) | −1.65042e48 | −0.519429 | ||||||||
\(871\) | −5.60188e48 | −1.72995 | ||||||||
\(872\) | −1.41505e48 | −0.428796 | ||||||||
\(873\) | −2.18735e44 | −6.50403e−5 0 | ||||||||
\(874\) | −7.92608e47 | −0.231270 | ||||||||
\(875\) | 4.86677e47 | 0.139350 | ||||||||
\(876\) | 9.66998e47 | 0.271711 | ||||||||
\(877\) | 3.36176e48 | 0.926985 | 0.463493 | − | 0.886101i | \(-0.346596\pi\) | ||||
0.463493 | + | 0.886101i | \(0.346596\pi\) | |||||||
\(878\) | 2.41020e47 | 0.0652220 | ||||||||
\(879\) | 4.18631e47 | 0.111177 | ||||||||
\(880\) | −2.49745e47 | −0.0650928 | ||||||||
\(881\) | 2.89868e47 | 0.0741477 | 0.0370738 | − | 0.999313i | \(-0.488196\pi\) | ||||
0.0370738 | + | 0.999313i | \(0.488196\pi\) | |||||||
\(882\) | −3.01322e46 | −0.00756484 | ||||||||
\(883\) | −2.27915e48 | −0.561592 | −0.280796 | − | 0.959767i | \(-0.590598\pi\) | ||||
−0.280796 | + | 0.959767i | \(0.590598\pi\) | |||||||
\(884\) | −1.02274e48 | −0.247344 | ||||||||
\(885\) | 3.87573e47 | 0.0920005 | ||||||||
\(886\) | −1.27003e48 | −0.295910 | ||||||||
\(887\) | −3.67815e48 | −0.841180 | −0.420590 | − | 0.907251i | \(-0.638177\pi\) | ||||
−0.420590 | + | 0.907251i | \(0.638177\pi\) | |||||||
\(888\) | −6.80467e48 | −1.52754 | ||||||||
\(889\) | 1.35977e49 | 2.99631 | ||||||||
\(890\) | −7.09484e47 | −0.153464 | ||||||||
\(891\) | −1.18020e48 | −0.250595 | ||||||||
\(892\) | 6.00334e47 | 0.125133 | ||||||||
\(893\) | 9.88988e47 | 0.202368 | ||||||||
\(894\) | 5.21738e48 | 1.04805 | ||||||||
\(895\) | −1.74505e48 | −0.344134 | ||||||||
\(896\) | 2.24892e48 | 0.435403 | ||||||||
\(897\) | 7.08870e48 | 1.34738 | ||||||||
\(898\) | −1.61488e48 | −0.301357 | ||||||||
\(899\) | −1.12026e49 | −2.05250 | ||||||||
\(900\) | 2.28956e45 | 0.000411861 0 | ||||||||
\(901\) | −4.70159e48 | −0.830397 | ||||||||
\(902\) | −7.75870e46 | −0.0134549 | ||||||||
\(903\) | 1.22619e49 | 2.08790 | ||||||||
\(904\) | 9.61586e48 | 1.60771 | ||||||||
\(905\) | 1.42986e48 | 0.234743 | ||||||||
\(906\) | −6.06102e45 | −0.000977080 0 | ||||||||
\(907\) | −1.60568e48 | −0.254178 | −0.127089 | − | 0.991891i | \(-0.540563\pi\) | ||||
−0.127089 | + | 0.991891i | \(0.540563\pi\) | |||||||
\(908\) | 1.49431e48 | 0.232287 | ||||||||
\(909\) | −4.56307e46 | −0.00696551 | ||||||||
\(910\) | 4.10487e48 | 0.615342 | ||||||||
\(911\) | 7.70098e48 | 1.13369 | 0.566843 | − | 0.823826i | \(-0.308165\pi\) | ||||
0.566843 | + | 0.823826i | \(0.308165\pi\) | |||||||
\(912\) | 8.84518e47 | 0.127877 | ||||||||
\(913\) | −2.54019e48 | −0.360660 | ||||||||
\(914\) | −1.09134e49 | −1.52176 | ||||||||
\(915\) | −6.81717e47 | −0.0933590 | ||||||||
\(916\) | 3.04322e48 | 0.409316 | ||||||||
\(917\) | 8.12883e48 | 1.07383 | ||||||||
\(918\) | −4.59474e48 | −0.596151 | ||||||||
\(919\) | 5.42603e48 | 0.691474 | 0.345737 | − | 0.938331i | \(-0.387629\pi\) | ||||
0.345737 | + | 0.938331i | \(0.387629\pi\) | |||||||
\(920\) | −4.90737e48 | −0.614256 | ||||||||
\(921\) | −1.12666e49 | −1.38519 | ||||||||
\(922\) | 2.70074e48 | 0.326154 | ||||||||
\(923\) | 2.36465e48 | 0.280504 | ||||||||
\(924\) | −1.07679e48 | −0.125471 | ||||||||
\(925\) | 2.45997e48 | 0.281574 | ||||||||
\(926\) | −2.35275e48 | −0.264542 | ||||||||
\(927\) | 6.83487e46 | 0.00754944 | ||||||||
\(928\) | −7.98165e48 | −0.866066 | ||||||||
\(929\) | −7.82524e48 | −0.834139 | −0.417070 | − | 0.908875i | \(-0.636943\pi\) | ||||
−0.417070 | + | 0.908875i | \(0.636943\pi\) | |||||||
\(930\) | 5.09631e48 | 0.533688 | ||||||||
\(931\) | −3.08429e48 | −0.317311 | ||||||||
\(932\) | 1.56063e48 | 0.157738 | ||||||||
\(933\) | 1.02801e49 | 1.02083 | ||||||||
\(934\) | −2.81891e48 | −0.275016 | ||||||||
\(935\) | 8.48245e47 | 0.0813073 | ||||||||
\(936\) | 7.95978e46 | 0.00749634 | ||||||||
\(937\) | 1.34653e49 | 1.24599 | 0.622994 | − | 0.782227i | \(-0.285916\pi\) | ||||
0.622994 | + | 0.782227i | \(0.285916\pi\) | |||||||
\(938\) | −2.28143e49 | −2.07424 | ||||||||
\(939\) | −1.71729e49 | −1.53413 | ||||||||
\(940\) | 1.48556e48 | 0.130401 | ||||||||
\(941\) | −1.57761e49 | −1.36073 | −0.680365 | − | 0.732874i | \(-0.738179\pi\) | ||||
−0.680365 | + | 0.732874i | \(0.738179\pi\) | |||||||
\(942\) | 1.16131e49 | 0.984255 | ||||||||
\(943\) | −9.80360e47 | −0.0816474 | ||||||||
\(944\) | −1.45526e48 | −0.119097 | ||||||||
\(945\) | −8.69131e48 | −0.698973 | ||||||||
\(946\) | 3.53747e48 | 0.279569 | ||||||||
\(947\) | 7.45162e48 | 0.578730 | 0.289365 | − | 0.957219i | \(-0.406556\pi\) | ||||
0.289365 | + | 0.957219i | \(0.406556\pi\) | |||||||
\(948\) | 4.37869e48 | 0.334200 | ||||||||
\(949\) | −1.21534e49 | −0.911604 | ||||||||
\(950\) | −4.97263e47 | −0.0366561 | ||||||||
\(951\) | −8.77837e48 | −0.635968 | ||||||||
\(952\) | −1.71683e49 | −1.22241 | ||||||||
\(953\) | 2.12970e49 | 1.49034 | 0.745171 | − | 0.666874i | \(-0.232368\pi\) | ||||
0.745171 | + | 0.666874i | \(0.232368\pi\) | |||||||
\(954\) | 8.87751e46 | 0.00610581 | ||||||||
\(955\) | 2.59220e48 | 0.175232 | ||||||||
\(956\) | 7.40456e48 | 0.491976 | ||||||||
\(957\) | −5.44125e48 | −0.355346 | ||||||||
\(958\) | −2.36140e48 | −0.151579 | ||||||||
\(959\) | −1.05873e49 | −0.668000 | ||||||||
\(960\) | 7.77882e48 | 0.482435 | ||||||||
\(961\) | 1.81888e49 | 1.10884 | ||||||||
\(962\) | 2.07486e49 | 1.24337 | ||||||||
\(963\) | 1.87926e47 | 0.0110701 | ||||||||
\(964\) | −1.05995e49 | −0.613781 | ||||||||
\(965\) | 1.14563e48 | 0.0652144 | ||||||||
\(966\) | 2.88695e49 | 1.61553 | ||||||||
\(967\) | 7.81881e47 | 0.0430134 | 0.0215067 | − | 0.999769i | \(-0.493154\pi\) | ||||
0.0215067 | + | 0.999769i | \(0.493154\pi\) | |||||||
\(968\) | 1.88464e49 | 1.01926 | ||||||||
\(969\) | −3.00422e48 | −0.159731 | ||||||||
\(970\) | 7.13595e46 | 0.00373008 | ||||||||
\(971\) | 2.07870e49 | 1.06825 | 0.534127 | − | 0.845404i | \(-0.320640\pi\) | ||||
0.534127 | + | 0.845404i | \(0.320640\pi\) | |||||||
\(972\) | −8.15149e46 | −0.00411854 | ||||||||
\(973\) | −4.57159e49 | −2.27094 | ||||||||
\(974\) | 3.29811e49 | 1.61080 | ||||||||
\(975\) | 4.44727e48 | 0.213559 | ||||||||
\(976\) | 2.55971e48 | 0.120856 | ||||||||
\(977\) | −1.16244e49 | −0.539647 | −0.269824 | − | 0.962910i | \(-0.586965\pi\) | ||||
−0.269824 | + | 0.962910i | \(0.586965\pi\) | |||||||
\(978\) | 4.84834e48 | 0.221311 | ||||||||
\(979\) | −2.33909e48 | −0.104986 | ||||||||
\(980\) | −4.63292e48 | −0.204468 | ||||||||
\(981\) | −5.83563e46 | −0.00253250 | ||||||||
\(982\) | −2.23990e49 | −0.955846 | ||||||||
\(983\) | −2.37943e49 | −0.998482 | −0.499241 | − | 0.866463i | \(-0.666388\pi\) | ||||
−0.499241 | + | 0.866463i | \(0.666388\pi\) | |||||||
\(984\) | 1.70133e48 | 0.0702054 | ||||||||
\(985\) | 2.15218e49 | 0.873335 | ||||||||
\(986\) | −2.10476e49 | −0.839913 | ||||||||
\(987\) | −3.60223e49 | −1.41364 | ||||||||
\(988\) | 1.97667e48 | 0.0762861 | ||||||||
\(989\) | 4.46980e49 | 1.69648 | ||||||||
\(990\) | −1.60165e46 | −0.000597842 0 | ||||||||
\(991\) | −3.80696e49 | −1.39754 | −0.698768 | − | 0.715348i | \(-0.746268\pi\) | ||||
−0.698768 | + | 0.715348i | \(0.746268\pi\) | |||||||
\(992\) | 2.46465e49 | 0.889840 | ||||||||
\(993\) | 1.80442e49 | 0.640731 | ||||||||
\(994\) | 9.63030e48 | 0.336329 | ||||||||
\(995\) | 2.98419e48 | 0.102505 | ||||||||
\(996\) | 1.35137e49 | 0.456559 | ||||||||
\(997\) | 6.76901e48 | 0.224934 | 0.112467 | − | 0.993655i | \(-0.464125\pi\) | ||||
0.112467 | + | 0.993655i | \(0.464125\pi\) | |||||||
\(998\) | −6.88166e47 | −0.0224926 | ||||||||
\(999\) | −4.39314e49 | −1.41236 |
(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 | 5.34.a.b.1.4 | ✓ | 6 | |
5.2 | odd | 4 | 25.34.b.c.24.8 | 12 | |||
5.3 | odd | 4 | 25.34.b.c.24.5 | 12 | |||
5.4 | even | 2 | 25.34.a.c.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.34.a.b.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial | |
25.34.a.c.1.3 | 6 | 5.4 | even | 2 | |||
25.34.b.c.24.5 | 12 | 5.3 | odd | 4 | |||
25.34.b.c.24.8 | 12 | 5.2 | odd | 4 |