Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,34,Mod(24,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(172.457072203\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 20265063301 x^{10} + \cdots + 39\!\cdots\!96 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{47}\cdot 3^{10}\cdot 5^{36}\cdot 7^{2}\cdot 11^{4} \) |
Twist minimal: | no (minimal twist has level 5) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.5 | ||
Root | \(-38204.6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.34.b.c.24.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 76409.2i | − 0.824424i | −0.911088 | − | 0.412212i | \(-0.864756\pi\) | ||||
0.911088 | − | 0.412212i | \(-0.135244\pi\) | |||||||
\(3\) | 7.43191e7i | 0.996780i | 0.866953 | + | 0.498390i | \(0.166075\pi\) | ||||
−0.866953 | + | 0.498390i | \(0.833925\pi\) | |||||||
\(4\) | 2.75157e9 | 0.320325 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 5.67866e12 | 0.821770 | ||||||||
\(7\) | − 1.36987e14i | − 1.55798i | −0.627034 | − | 0.778992i | \(-0.715731\pi\) | ||||
0.627034 | − | 0.778992i | \(-0.284269\pi\) | |||||||
\(8\) | − 8.66595e14i | − 1.08851i | ||||||||
\(9\) | 3.57381e13 | 0.00642880 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.84389e16 | 0.252227 | 0.126113 | − | 0.992016i | \(-0.459750\pi\) | ||||
0.126113 | + | 0.992016i | \(0.459750\pi\) | |||||||
\(12\) | 2.04494e17i | 0.319294i | ||||||||
\(13\) | 2.57012e18i | 1.07124i | 0.844458 | + | 0.535622i | \(0.179923\pi\) | ||||
−0.844458 | + | 0.535622i | \(0.820077\pi\) | |||||||
\(14\) | −1.04671e19 | −1.28444 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.25800e19 | −0.577067 | ||||||||
\(17\) | − 1.44621e20i | − 0.720814i | −0.932795 | − | 0.360407i | \(-0.882638\pi\) | ||||
0.932795 | − | 0.360407i | \(-0.117362\pi\) | |||||||
\(18\) | − 2.73072e18i | − 0.00530005i | ||||||||
\(19\) | 2.79512e20 | 0.222314 | 0.111157 | − | 0.993803i | \(-0.464544\pi\) | ||||
0.111157 | + | 0.993803i | \(0.464544\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.01808e22 | 1.55297 | ||||||||
\(22\) | − 2.93708e21i | − 0.207942i | ||||||||
\(23\) | 3.71118e22i | 1.26184i | 0.775849 | + | 0.630918i | \(0.217322\pi\) | ||||
−0.775849 | + | 0.630918i | \(0.782678\pi\) | |||||||
\(24\) | 6.44045e22 | 1.08500 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.96381e23 | 0.883159 | ||||||||
\(27\) | 4.15800e23i | 1.00319i | ||||||||
\(28\) | − 3.76930e23i | − 0.499061i | ||||||||
\(29\) | 1.90470e24 | 1.41339 | 0.706693 | − | 0.707520i | \(-0.250186\pi\) | ||||
0.706693 | + | 0.707520i | \(0.250186\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.88152e24 | 1.45218 | 0.726092 | − | 0.687597i | \(-0.241334\pi\) | ||||
0.726092 | + | 0.687597i | \(0.241334\pi\) | |||||||
\(32\) | − 4.19049e24i | − 0.612760i | ||||||||
\(33\) | 2.85674e24i | 0.251415i | ||||||||
\(34\) | −1.10503e25 | −0.594256 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9.83358e22 | 0.00205930 | ||||||||
\(37\) | − 1.05655e26i | − 1.40787i | −0.710265 | − | 0.703934i | \(-0.751425\pi\) | ||||
0.710265 | − | 0.703934i | \(-0.248575\pi\) | |||||||
\(38\) | − 2.13573e25i | − 0.183281i | ||||||||
\(39\) | −1.91009e26 | −1.06779 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.64164e25 | −0.0647052 | −0.0323526 | − | 0.999477i | \(-0.510300\pi\) | ||||
−0.0323526 | + | 0.999477i | \(0.510300\pi\) | |||||||
\(42\) | − 7.77905e26i | − 1.28030i | ||||||||
\(43\) | 1.20441e27i | 1.34446i | 0.740344 | + | 0.672228i | \(0.234662\pi\) | ||||
−0.740344 | + | 0.672228i | \(0.765338\pi\) | |||||||
\(44\) | 1.05767e26 | 0.0807946 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.83569e27 | 1.04029 | ||||||||
\(47\) | 3.53827e27i | 0.910282i | 0.890419 | + | 0.455141i | \(0.150411\pi\) | ||||
−0.890419 | + | 0.455141i | \(0.849589\pi\) | |||||||
\(48\) | − 3.16451e27i | − 0.575209i | ||||||||
\(49\) | −1.10345e28 | −1.42731 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.07481e28 | 0.718493 | ||||||||
\(52\) | 7.07187e27i | 0.343146i | ||||||||
\(53\) | − 3.25098e28i | − 1.15203i | −0.817440 | − | 0.576014i | \(-0.804608\pi\) | ||||
0.817440 | − | 0.576014i | \(-0.195392\pi\) | |||||||
\(54\) | 3.17710e28 | 0.827053 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.18713e29 | −1.69588 | ||||||||
\(57\) | 2.07731e28i | 0.221598i | ||||||||
\(58\) | − 1.45537e29i | − 1.16523i | ||||||||
\(59\) | −3.41770e28 | −0.206384 | −0.103192 | − | 0.994661i | \(-0.532906\pi\) | ||||
−0.103192 | + | 0.994661i | \(0.532906\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.01152e28 | −0.209431 | −0.104716 | − | 0.994502i | \(-0.533393\pi\) | ||||
−0.104716 | + | 0.994502i | \(0.533393\pi\) | |||||||
\(62\) | − 4.49402e29i | − 1.19722i | ||||||||
\(63\) | − 4.89566e27i | − 0.0100160i | ||||||||
\(64\) | −6.85952e29 | −1.08224 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.18281e29 | 0.207272 | ||||||||
\(67\) | 2.17962e30i | 1.61490i | 0.589934 | + | 0.807451i | \(0.299154\pi\) | ||||
−0.589934 | + | 0.807451i | \(0.700846\pi\) | |||||||
\(68\) | − 3.97934e29i | − 0.230895i | ||||||||
\(69\) | −2.75812e30 | −1.25777 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.20055e29 | 0.261849 | 0.130924 | − | 0.991392i | \(-0.458205\pi\) | ||||
0.130924 | + | 0.991392i | \(0.458205\pi\) | |||||||
\(72\) | − 3.09704e28i | − 0.00699779i | ||||||||
\(73\) | − 4.72873e30i | − 0.850977i | −0.904964 | − | 0.425488i | \(-0.860102\pi\) | ||||
0.904964 | − | 0.425488i | \(-0.139898\pi\) | |||||||
\(74\) | −8.07302e30 | −1.16068 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.69097e29 | 0.0712126 | ||||||||
\(77\) | − 5.26564e30i | − 0.392965i | ||||||||
\(78\) | 1.45948e31i | 0.880316i | ||||||||
\(79\) | 2.14123e31 | 1.04668 | 0.523342 | − | 0.852122i | \(-0.324685\pi\) | ||||
0.523342 | + | 0.852122i | \(0.324685\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.07032e31 | −0.993530 | ||||||||
\(82\) | 2.01845e30i | 0.0533445i | ||||||||
\(83\) | − 6.60838e31i | − 1.42990i | −0.699174 | − | 0.714951i | \(-0.746449\pi\) | ||||
0.699174 | − | 0.714951i | \(-0.253551\pi\) | |||||||
\(84\) | 2.80131e31 | 0.497454 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.20283e31 | 1.10840 | ||||||||
\(87\) | 1.41556e32i | 1.40884i | ||||||||
\(88\) | − 3.33109e31i | − 0.274551i | ||||||||
\(89\) | 6.08523e31 | 0.416238 | 0.208119 | − | 0.978104i | \(-0.433266\pi\) | ||||
0.208119 | + | 0.978104i | \(0.433266\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.52074e32 | 1.66898 | ||||||||
\(92\) | 1.02116e32i | 0.404198i | ||||||||
\(93\) | 4.37109e32i | 1.44751i | ||||||||
\(94\) | 2.70356e32 | 0.750458 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.11433e32 | 0.610787 | ||||||||
\(97\) | − 6.12049e30i | − 0.0101170i | −0.999987 | − | 0.00505851i | \(-0.998390\pi\) | ||||
0.999987 | − | 0.00505851i | \(-0.00161018\pi\) | |||||||
\(98\) | 8.43141e32i | 1.17671i | ||||||||
\(99\) | 1.37373e30 | 0.00162152 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.27681e33 | 1.08349 | 0.541743 | − | 0.840544i | \(-0.317765\pi\) | ||||
0.541743 | + | 0.840544i | \(0.317765\pi\) | |||||||
\(102\) | − 8.21251e32i | − 0.592343i | ||||||||
\(103\) | − 1.91249e33i | − 1.17432i | −0.809473 | − | 0.587158i | \(-0.800247\pi\) | ||||
0.809473 | − | 0.587158i | \(-0.199753\pi\) | |||||||
\(104\) | 2.22725e33 | 1.16606 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.48405e33 | −0.949759 | ||||||||
\(107\) | 5.25843e33i | 1.72196i | 0.508638 | + | 0.860981i | \(0.330149\pi\) | ||||
−0.508638 | + | 0.860981i | \(0.669851\pi\) | |||||||
\(108\) | 1.14410e33i | 0.321346i | ||||||||
\(109\) | −1.63289e33 | −0.393930 | −0.196965 | − | 0.980411i | \(-0.563109\pi\) | ||||
−0.196965 | + | 0.980411i | \(0.563109\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.85219e33 | 1.40334 | ||||||||
\(112\) | 5.83293e33i | 0.899061i | ||||||||
\(113\) | − 1.10961e34i | − 1.47699i | −0.674259 | − | 0.738495i | \(-0.735537\pi\) | ||||
0.674259 | − | 0.738495i | \(-0.264463\pi\) | |||||||
\(114\) | 1.58725e33 | 0.182691 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.24093e33 | 0.452743 | ||||||||
\(117\) | 9.18512e31i | 0.00688681i | ||||||||
\(118\) | 2.61144e33i | 0.170148i | ||||||||
\(119\) | −1.98112e34 | −1.12302 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.17476e34 | −0.936382 | ||||||||
\(122\) | 4.59335e33i | 0.172660i | ||||||||
\(123\) | − 1.96324e33i | − 0.0644969i | ||||||||
\(124\) | 1.61834e34 | 0.465171 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.74074e32 | −0.00825740 | ||||||||
\(127\) | − 9.92625e34i | − 1.92320i | −0.274458 | − | 0.961599i | \(-0.588498\pi\) | ||||
0.274458 | − | 0.961599i | \(-0.411502\pi\) | |||||||
\(128\) | 1.64170e34i | 0.279466i | ||||||||
\(129\) | −8.95110e34 | −1.34013 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.93400e34 | 0.689241 | 0.344621 | − | 0.938742i | \(-0.388008\pi\) | ||||
0.344621 | + | 0.938742i | \(0.388008\pi\) | |||||||
\(132\) | 7.86052e33i | 0.0805344i | ||||||||
\(133\) | − 3.82896e34i | − 0.346361i | ||||||||
\(134\) | 1.66543e35 | 1.33136 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.25328e35 | −0.784611 | ||||||||
\(137\) | 7.72864e34i | 0.428759i | 0.976750 | + | 0.214380i | \(0.0687730\pi\) | ||||
−0.976750 | + | 0.214380i | \(0.931227\pi\) | |||||||
\(138\) | 2.10746e35i | 1.03694i | ||||||||
\(139\) | 3.33723e35 | 1.45761 | 0.728806 | − | 0.684720i | \(-0.240075\pi\) | ||||
0.728806 | + | 0.684720i | \(0.240075\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.62961e35 | −0.907351 | ||||||||
\(142\) | − 7.03006e34i | − 0.215875i | ||||||||
\(143\) | 9.87926e34i | 0.270196i | ||||||||
\(144\) | −1.52173e33 | −0.00370985 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.61319e35 | −0.701566 | ||||||||
\(147\) | − 8.20077e35i | − 1.42272i | ||||||||
\(148\) | − 2.90717e35i | − 0.450975i | ||||||||
\(149\) | −9.18769e35 | −1.27536 | −0.637680 | − | 0.770301i | \(-0.720106\pi\) | ||||
−0.637680 | + | 0.770301i | \(0.720106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.06733e33 | −0.00118899 | −0.000594497 | − | 1.00000i | \(-0.500189\pi\) | ||||
−0.000594497 | 1.00000i | \(0.500189\pi\) | ||||||||
\(152\) | − 2.42224e35i | − 0.241990i | ||||||||
\(153\) | − 5.16846e33i | − 0.00463397i | ||||||||
\(154\) | −4.02343e35 | −0.323970 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.25575e35 | −0.342041 | ||||||||
\(157\) | − 2.04504e36i | − 1.19773i | −0.800851 | − | 0.598863i | \(-0.795619\pi\) | ||||
0.800851 | − | 0.598863i | \(-0.204381\pi\) | |||||||
\(158\) | − 1.63610e36i | − 0.862912i | ||||||||
\(159\) | 2.41610e36 | 1.14832 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.08385e36 | 1.96592 | ||||||||
\(162\) | 2.34601e36i | 0.819090i | ||||||||
\(163\) | 8.53783e35i | 0.269310i | 0.990893 | + | 0.134655i | \(0.0429926\pi\) | ||||
−0.990893 | + | 0.134655i | \(0.957007\pi\) | |||||||
\(164\) | −7.26865e34 | −0.0207267 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.04941e36 | −1.17885 | ||||||||
\(167\) | − 2.30718e36i | − 0.487819i | −0.969798 | − | 0.243910i | \(-0.921570\pi\) | ||||
0.969798 | − | 0.243910i | \(-0.0784301\pi\) | |||||||
\(168\) | − 8.82261e36i | − 1.69042i | ||||||||
\(169\) | −8.49393e35 | −0.147563 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.98922e33 | 0.00142921 | ||||||||
\(172\) | 3.31403e36i | 0.430663i | ||||||||
\(173\) | 7.44289e36i | 0.878984i | 0.898247 | + | 0.439492i | \(0.144842\pi\) | ||||
−0.898247 | + | 0.439492i | \(0.855158\pi\) | |||||||
\(174\) | 1.08162e37 | 1.16148 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.63673e36 | −0.145552 | ||||||||
\(177\) | − 2.54000e36i | − 0.205719i | ||||||||
\(178\) | − 4.64967e36i | − 0.343157i | ||||||||
\(179\) | 1.14363e37 | 0.769506 | 0.384753 | − | 0.923020i | \(-0.374287\pi\) | ||||
0.384753 | + | 0.923020i | \(0.374287\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.37075e36 | 0.524902 | 0.262451 | − | 0.964945i | \(-0.415469\pi\) | ||||
0.262451 | + | 0.964945i | \(0.415469\pi\) | |||||||
\(182\) | − 2.69017e37i | − 1.37595i | ||||||||
\(183\) | − 4.46770e36i | − 0.208757i | ||||||||
\(184\) | 3.21609e37 | 1.37352 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.33992e37 | 1.19336 | ||||||||
\(187\) | − 5.55906e36i | − 0.181809i | ||||||||
\(188\) | 9.73579e36i | 0.291586i | ||||||||
\(189\) | 5.69594e37 | 1.56295 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.69883e37 | 0.391831 | 0.195915 | − | 0.980621i | \(-0.437232\pi\) | ||||
0.195915 | + | 0.980621i | \(0.437232\pi\) | |||||||
\(192\) | − 5.09793e37i | − 1.07876i | ||||||||
\(193\) | 7.50799e36i | 0.145824i | 0.997338 | + | 0.0729119i | \(0.0232292\pi\) | ||||
−0.997338 | + | 0.0729119i | \(0.976771\pi\) | |||||||
\(194\) | −4.67662e35 | −0.00834072 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.03623e37 | −0.457204 | ||||||||
\(197\) | − 1.41045e38i | − 1.95284i | −0.215886 | − | 0.976418i | \(-0.569264\pi\) | ||||
0.215886 | − | 0.976418i | \(-0.430736\pi\) | |||||||
\(198\) | − 1.04966e35i | − 0.00133682i | ||||||||
\(199\) | −1.95572e37 | −0.229208 | −0.114604 | − | 0.993411i | \(-0.536560\pi\) | ||||
−0.114604 | + | 0.993411i | \(0.536560\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.61987e38 | −1.60970 | ||||||||
\(202\) | − 9.75600e37i | − 0.893252i | ||||||||
\(203\) | − 2.60921e38i | − 2.20203i | ||||||||
\(204\) | 2.95741e37 | 0.230151 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.46132e38 | −0.968134 | ||||||||
\(207\) | 1.32631e36i | 0.00811209i | ||||||||
\(208\) | − 1.09436e38i | − 0.618179i | ||||||||
\(209\) | 1.07441e37 | 0.0560735 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.65891e38 | −1.18589 | −0.592944 | − | 0.805244i | \(-0.702034\pi\) | ||||
−0.592944 | + | 0.805244i | \(0.702034\pi\) | |||||||
\(212\) | − 8.94530e37i | − 0.369023i | ||||||||
\(213\) | 6.83776e37i | 0.261006i | ||||||||
\(214\) | 4.01792e38 | 1.41963 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.60330e38 | 1.09198 | ||||||||
\(217\) | − 8.05694e38i | − 2.26248i | ||||||||
\(218\) | 1.24768e38i | 0.324765i | ||||||||
\(219\) | 3.51435e38 | 0.848237 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.71693e38 | 0.772167 | ||||||||
\(222\) | − 5.99979e38i | − 1.15694i | ||||||||
\(223\) | − 2.18179e38i | − 0.390645i | −0.980739 | − | 0.195323i | \(-0.937425\pi\) | ||||
0.980739 | − | 0.195323i | \(-0.0625754\pi\) | |||||||
\(224\) | −5.74044e38 | −0.954670 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.47847e38 | −1.21767 | ||||||||
\(227\) | 5.43077e38i | 0.725161i | 0.931952 | + | 0.362581i | \(0.118104\pi\) | ||||
−0.931952 | + | 0.362581i | \(0.881896\pi\) | |||||||
\(228\) | 5.71586e37i | 0.0709833i | ||||||||
\(229\) | 1.10600e39 | 1.27782 | 0.638908 | − | 0.769284i | \(-0.279387\pi\) | ||||
0.638908 | + | 0.769284i | \(0.279387\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.91337e38 | 0.391700 | ||||||||
\(232\) | − 1.65061e39i | − 1.53848i | ||||||||
\(233\) | − 5.67177e38i | − 0.492431i | −0.969215 | − | 0.246216i | \(-0.920813\pi\) | ||||
0.969215 | − | 0.246216i | \(-0.0791871\pi\) | |||||||
\(234\) | 7.01827e36 | 0.00567765 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.40404e37 | −0.0661099 | ||||||||
\(237\) | 1.59134e39i | 1.04332i | ||||||||
\(238\) | 1.51376e39i | 0.925842i | ||||||||
\(239\) | 2.69103e39 | 1.53587 | 0.767933 | − | 0.640530i | \(-0.221285\pi\) | ||||
0.767933 | + | 0.640530i | \(0.221285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.85216e39 | 1.91612 | 0.958061 | − | 0.286565i | \(-0.0925134\pi\) | ||||
0.958061 | + | 0.286565i | \(0.0925134\pi\) | |||||||
\(242\) | 1.66172e39i | 0.771976i | ||||||||
\(243\) | 2.96249e37i | 0.0128574i | ||||||||
\(244\) | −1.65411e38 | −0.0670861 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.50009e38 | −0.0531728 | ||||||||
\(247\) | 7.18380e38i | 0.238152i | ||||||||
\(248\) | − 5.09690e39i | − 1.58071i | ||||||||
\(249\) | 4.91128e39 | 1.42530 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.40214e37 | 0.00356594 | 0.00178297 | − | 0.999998i | \(-0.499432\pi\) | ||||
0.00178297 | + | 0.999998i | \(0.499432\pi\) | |||||||
\(252\) | − 1.34708e37i | − 0.00320836i | ||||||||
\(253\) | 1.42654e39i | 0.318269i | ||||||||
\(254\) | −7.58457e39 | −1.58553 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.63787e39 | −0.851843 | ||||||||
\(257\) | 3.74219e39i | 0.644510i | 0.946653 | + | 0.322255i | \(0.104441\pi\) | ||||
−0.946653 | + | 0.322255i | \(0.895559\pi\) | |||||||
\(258\) | 6.83946e39i | 1.10483i | ||||||||
\(259\) | −1.44734e40 | −2.19344 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.80705e37 | 0.00908637 | ||||||||
\(262\) | − 4.53412e39i | − 0.568227i | ||||||||
\(263\) | − 8.59682e39i | − 1.01174i | −0.862610 | − | 0.505869i | \(-0.831172\pi\) | ||||
0.862610 | − | 0.505869i | \(-0.168828\pi\) | |||||||
\(264\) | 2.47564e39 | 0.273667 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.92568e39 | −0.285548 | ||||||||
\(267\) | 4.52248e39i | 0.414898i | ||||||||
\(268\) | 5.99737e39i | 0.517293i | ||||||||
\(269\) | −2.20144e40 | −1.78564 | −0.892820 | − | 0.450414i | \(-0.851276\pi\) | ||||
−0.892820 | + | 0.450414i | \(0.851276\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.26536e39 | 0.306170 | 0.153085 | − | 0.988213i | \(-0.451079\pi\) | ||||
0.153085 | + | 0.988213i | \(0.451079\pi\) | |||||||
\(272\) | 6.15795e39i | 0.415958i | ||||||||
\(273\) | 2.61658e40i | 1.66361i | ||||||||
\(274\) | 5.90539e39 | 0.353480 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.58915e39 | −0.402896 | ||||||||
\(277\) | 2.32580e40i | 1.16321i | 0.813473 | + | 0.581603i | \(0.197574\pi\) | ||||
−0.813473 | + | 0.581603i | \(0.802426\pi\) | |||||||
\(278\) | − 2.54995e40i | − 1.20169i | ||||||||
\(279\) | 2.10194e38 | 0.00933580 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.04347e39 | −0.120147 | −0.0600737 | − | 0.998194i | \(-0.519134\pi\) | ||||
−0.0600737 | + | 0.998194i | \(0.519134\pi\) | |||||||
\(282\) | 2.00926e40i | 0.748042i | ||||||||
\(283\) | 1.78513e40i | 0.626893i | 0.949606 | + | 0.313447i | \(0.101484\pi\) | ||||
−0.949606 | + | 0.313447i | \(0.898516\pi\) | |||||||
\(284\) | 2.53160e39 | 0.0838768 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.54866e39 | 0.222756 | ||||||||
\(287\) | 3.61871e39i | 0.100810i | ||||||||
\(288\) | − 1.49760e38i | − 0.00393931i | ||||||||
\(289\) | 1.93394e40 | 0.480427 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.54869e38 | 0.0100844 | ||||||||
\(292\) | − 1.30114e40i | − 0.272589i | ||||||||
\(293\) | 5.63289e39i | 0.111536i | 0.998444 | + | 0.0557681i | \(0.0177607\pi\) | ||||
−0.998444 | + | 0.0557681i | \(0.982239\pi\) | |||||||
\(294\) | −6.26614e40 | −1.17292 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.15602e40 | −1.53248 | ||||||||
\(297\) | 1.59829e40i | 0.253031i | ||||||||
\(298\) | 7.02024e40i | 1.05144i | ||||||||
\(299\) | −9.53819e40 | −1.35174 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.64990e41 | 2.09464 | ||||||||
\(302\) | 8.15540e37i | 0 0.000980236i | ||||||||
\(303\) | 9.48913e40i | 1.08000i | ||||||||
\(304\) | −1.19016e40 | −0.128290 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.94918e38 | −0.00382035 | ||||||||
\(307\) | 1.51598e41i | 1.38966i | 0.719173 | + | 0.694832i | \(0.244521\pi\) | ||||
−0.719173 | + | 0.694832i | \(0.755479\pi\) | |||||||
\(308\) | − 1.44888e40i | − 0.125877i | ||||||||
\(309\) | 1.42134e41 | 1.17053 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.38324e41 | 1.02412 | 0.512062 | − | 0.858949i | \(-0.328882\pi\) | ||||
0.512062 | + | 0.858949i | \(0.328882\pi\) | |||||||
\(312\) | 1.65527e41i | 1.16230i | ||||||||
\(313\) | − 2.31070e41i | − 1.53908i | −0.638598 | − | 0.769540i | \(-0.720485\pi\) | ||||
0.638598 | − | 0.769540i | \(-0.279515\pi\) | |||||||
\(314\) | −1.56260e41 | −0.987434 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.89174e40 | 0.335279 | ||||||||
\(317\) | 1.18117e41i | 0.638022i | 0.947751 | + | 0.319011i | \(0.103351\pi\) | ||||
−0.947751 | + | 0.319011i | \(0.896649\pi\) | |||||||
\(318\) | − 1.84612e41i | − 0.946701i | ||||||||
\(319\) | 7.32147e40 | 0.356494 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.90801e41 | −1.71642 | ||||||||
\(322\) | − 3.88453e41i | − 1.62075i | ||||||||
\(323\) | − 4.04232e40i | − 0.160247i | ||||||||
\(324\) | −8.44820e40 | −0.318252 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.52369e40 | 0.222026 | ||||||||
\(327\) | − 1.21355e41i | − 0.392662i | ||||||||
\(328\) | 2.28923e40i | 0.0704321i | ||||||||
\(329\) | 4.84698e41 | 1.41820 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.42794e41 | 0.642801 | 0.321400 | − | 0.946943i | \(-0.395847\pi\) | ||||
0.321400 | + | 0.946943i | \(0.395847\pi\) | |||||||
\(332\) | − 1.81834e41i | − 0.458033i | ||||||||
\(333\) | − 3.77591e39i | − 0.00905090i | ||||||||
\(334\) | −1.76290e41 | −0.402170 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.33498e41 | −0.896166 | ||||||||
\(337\) | − 5.79957e41i | − 1.14157i | −0.821100 | − | 0.570785i | \(-0.806639\pi\) | ||||
0.821100 | − | 0.570785i | \(-0.193361\pi\) | |||||||
\(338\) | 6.49015e40i | 0.121655i | ||||||||
\(339\) | 8.24654e41 | 1.47223 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.26079e41 | 0.366280 | ||||||||
\(342\) | − 7.63268e38i | − 0.00117827i | ||||||||
\(343\) | 4.52545e41i | 0.665747i | ||||||||
\(344\) | 1.04374e42 | 1.46345 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.68705e41 | 0.724656 | ||||||||
\(347\) | − 1.00536e42i | − 1.22148i | −0.791832 | − | 0.610739i | \(-0.790872\pi\) | ||||
0.791832 | − | 0.610739i | \(-0.209128\pi\) | |||||||
\(348\) | 3.89501e41i | 0.451285i | ||||||||
\(349\) | −1.46484e42 | −1.61872 | −0.809360 | − | 0.587313i | \(-0.800186\pi\) | ||||
−0.809360 | + | 0.587313i | \(0.800186\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.06866e42 | −1.07466 | ||||||||
\(352\) | − 1.61078e41i | − 0.154554i | ||||||||
\(353\) | − 7.67079e40i | − 0.0702356i | −0.999383 | − | 0.0351178i | \(-0.988819\pi\) | ||||
0.999383 | − | 0.0351178i | \(-0.0111806\pi\) | |||||||
\(354\) | −1.94079e41 | −0.169600 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.67439e41 | 0.133331 | ||||||||
\(357\) | − 1.47235e42i | − 1.11940i | ||||||||
\(358\) | − 8.73842e41i | − 0.634399i | ||||||||
\(359\) | 2.27621e42 | 1.57817 | 0.789084 | − | 0.614285i | \(-0.210555\pi\) | ||||
0.789084 | + | 0.614285i | \(0.210555\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.50264e42 | −0.950577 | ||||||||
\(362\) | − 7.16012e41i | − 0.432742i | ||||||||
\(363\) | − 1.61626e42i | − 0.933367i | ||||||||
\(364\) | 9.68757e41 | 0.534616 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.41373e41 | −0.172104 | ||||||||
\(367\) | − 2.44390e42i | − 1.17786i | −0.808185 | − | 0.588929i | \(-0.799550\pi\) | ||||
0.808185 | − | 0.588929i | \(-0.200450\pi\) | |||||||
\(368\) | − 1.58022e42i | − 0.728165i | ||||||||
\(369\) | −9.44070e38 | −0.000415977 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.45343e42 | −1.79484 | ||||||||
\(372\) | 1.20274e42i | 0.463673i | ||||||||
\(373\) | 2.18298e42i | 0.805108i | 0.915396 | + | 0.402554i | \(0.131877\pi\) | ||||
−0.915396 | + | 0.402554i | \(0.868123\pi\) | |||||||
\(374\) | −4.24763e41 | −0.149887 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.06625e42 | 0.990849 | ||||||||
\(377\) | 4.89532e42i | 1.51408i | ||||||||
\(378\) | − 4.35222e42i | − 1.28853i | ||||||||
\(379\) | −3.29619e42 | −0.934254 | −0.467127 | − | 0.884190i | \(-0.654711\pi\) | ||||
−0.467127 | + | 0.884190i | \(0.654711\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.37710e42 | 1.91701 | ||||||||
\(382\) | − 1.29806e42i | − 0.323035i | ||||||||
\(383\) | 2.10779e42i | 0.502399i | 0.967935 | + | 0.251199i | \(0.0808249\pi\) | ||||
−0.967935 | + | 0.251199i | \(0.919175\pi\) | |||||||
\(384\) | −1.22009e42 | −0.278566 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.73680e41 | 0.120221 | ||||||||
\(387\) | 4.30434e40i | 0.00864323i | ||||||||
\(388\) | − 1.68410e40i | − 0.00324073i | ||||||||
\(389\) | 4.71038e42 | 0.868735 | 0.434368 | − | 0.900736i | \(-0.356972\pi\) | ||||
0.434368 | + | 0.900736i | \(0.356972\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.36714e42 | 0.909550 | ||||||||
\(392\) | 9.56249e42i | 1.55364i | ||||||||
\(393\) | 4.41009e42i | 0.687022i | ||||||||
\(394\) | −1.07772e43 | −1.60997 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.77992e39 | 0.000519412 0 | ||||||||
\(397\) | − 4.19658e42i | − 0.553162i | −0.960991 | − | 0.276581i | \(-0.910799\pi\) | ||||
0.960991 | − | 0.276581i | \(-0.0892014\pi\) | |||||||
\(398\) | 1.49435e42i | 0.188965i | ||||||||
\(399\) | 2.84565e42 | 0.345246 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.75416e42 | 0.642835 | 0.321418 | − | 0.946938i | \(-0.395841\pi\) | ||||
0.321418 | + | 0.946938i | \(0.395841\pi\) | |||||||
\(402\) | 1.23773e43i | 1.32708i | ||||||||
\(403\) | 1.51162e43i | 1.55564i | ||||||||
\(404\) | 3.51323e42 | 0.347068 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.99367e43 | −1.81541 | ||||||||
\(407\) | − 4.06126e42i | − 0.355102i | ||||||||
\(408\) | − 9.31423e42i | − 0.782085i | ||||||||
\(409\) | 1.41308e43 | 1.13954 | 0.569772 | − | 0.821803i | \(-0.307032\pi\) | ||||
0.569772 | + | 0.821803i | \(0.307032\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.74385e42 | −0.427379 | ||||||||
\(412\) | − 5.26235e42i | − 0.376162i | ||||||||
\(413\) | 4.68182e42i | 0.321543i | ||||||||
\(414\) | 1.01342e41 | 0.00668780 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.07701e43 | 0.656415 | ||||||||
\(417\) | 2.48020e43i | 1.45292i | ||||||||
\(418\) | − 8.20950e41i | − 0.0462283i | ||||||||
\(419\) | −2.86224e43 | −1.54944 | −0.774720 | − | 0.632305i | \(-0.782109\pi\) | ||||
−0.774720 | + | 0.632305i | \(0.782109\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.34194e43 | 0.671549 | 0.335774 | − | 0.941942i | \(-0.391002\pi\) | ||||
0.335774 | + | 0.941942i | \(0.391002\pi\) | |||||||
\(422\) | 2.03165e43i | 0.977674i | ||||||||
\(423\) | 1.26451e41i | 0.00585202i | ||||||||
\(424\) | −2.81729e43 | −1.25399 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.22468e42 | 0.215180 | ||||||||
\(427\) | 8.23502e42i | 0.326291i | ||||||||
\(428\) | 1.44689e43i | 0.551587i | ||||||||
\(429\) | −7.34217e42 | −0.269327 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.00130e43 | −1.35933 | −0.679667 | − | 0.733521i | \(-0.737876\pi\) | ||||
−0.679667 | + | 0.733521i | \(0.737876\pi\) | |||||||
\(432\) | − 1.77048e43i | − 0.578907i | ||||||||
\(433\) | − 1.03509e43i | − 0.325783i | −0.986644 | − | 0.162891i | \(-0.947918\pi\) | ||||
0.986644 | − | 0.162891i | \(-0.0520820\pi\) | |||||||
\(434\) | −6.15625e43 | −1.86524 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.49300e42 | −0.126186 | ||||||||
\(437\) | 1.03732e43i | 0.280524i | ||||||||
\(438\) | − 2.68529e43i | − 0.699307i | ||||||||
\(439\) | −3.15434e42 | −0.0791122 | −0.0395561 | − | 0.999217i | \(-0.512594\pi\) | ||||
−0.0395561 | + | 0.999217i | \(0.512594\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.94353e41 | −0.00917591 | ||||||||
\(442\) | − 2.84007e43i | − 0.636593i | ||||||||
\(443\) | − 1.66215e43i | − 0.358929i | −0.983764 | − | 0.179464i | \(-0.942564\pi\) | ||||
0.983764 | − | 0.179464i | \(-0.0574365\pi\) | |||||||
\(444\) | 2.16058e43 | 0.449523 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.66709e43 | −0.322057 | ||||||||
\(447\) | − 6.82821e43i | − 1.27125i | ||||||||
\(448\) | 9.39667e43i | 1.68611i | ||||||||
\(449\) | 2.11347e43 | 0.365537 | 0.182768 | − | 0.983156i | \(-0.441494\pi\) | ||||
0.182768 | + | 0.983156i | \(0.441494\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.01542e42 | −0.0163204 | ||||||||
\(452\) | − 3.05318e43i | − 0.473117i | ||||||||
\(453\) | − 7.93231e40i | − 0.00118517i | ||||||||
\(454\) | 4.14961e43 | 0.597840 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.80018e43 | 0.241211 | ||||||||
\(457\) | 1.42828e44i | 1.84585i | 0.384981 | + | 0.922924i | \(0.374208\pi\) | ||||
−0.384981 | + | 0.922924i | \(0.625792\pi\) | |||||||
\(458\) | − 8.45082e43i | − 1.05346i | ||||||||
\(459\) | 6.01333e43 | 0.723112 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.53458e43 | 0.395615 | 0.197807 | − | 0.980241i | \(-0.436618\pi\) | ||||
0.197807 | + | 0.980241i | \(0.436618\pi\) | |||||||
\(462\) | − 2.99018e43i | − 0.322927i | ||||||||
\(463\) | − 3.07914e43i | − 0.320880i | −0.987046 | − | 0.160440i | \(-0.948709\pi\) | ||||
0.987046 | − | 0.160440i | \(-0.0512914\pi\) | |||||||
\(464\) | −8.11024e43 | −0.815618 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.33375e43 | −0.405972 | ||||||||
\(467\) | 3.68923e43i | 0.333586i | 0.985992 | + | 0.166793i | \(0.0533412\pi\) | ||||
−0.985992 | + | 0.166793i | \(0.946659\pi\) | |||||||
\(468\) | 2.52735e41i | 0.00220602i | ||||||||
\(469\) | 2.98580e44 | 2.51599 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.51985e44 | 1.19387 | ||||||||
\(472\) | 2.96176e43i | 0.224650i | ||||||||
\(473\) | 4.62963e43i | 0.339108i | ||||||||
\(474\) | 1.21593e44 | 0.860134 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.45119e43 | −0.359730 | ||||||||
\(477\) | − 1.16184e42i | − 0.00740615i | ||||||||
\(478\) | − 2.05619e44i | − 1.26620i | ||||||||
\(479\) | 3.09046e43 | 0.183860 | 0.0919300 | − | 0.995765i | \(-0.470696\pi\) | ||||
0.0919300 | + | 0.995765i | \(0.470696\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.71546e44 | 1.50817 | ||||||||
\(482\) | − 2.94340e44i | − 1.57970i | ||||||||
\(483\) | 3.77827e44i | 1.95959i | ||||||||
\(484\) | −5.98401e43 | −0.299946 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.26361e42 | 0.0105999 | ||||||||
\(487\) | − 4.31638e44i | − 1.95385i | −0.213578 | − | 0.976926i | \(-0.568512\pi\) | ||||
0.213578 | − | 0.976926i | \(-0.431488\pi\) | |||||||
\(488\) | 5.20955e43i | 0.227968i | ||||||||
\(489\) | −6.34524e43 | −0.268443 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.93145e44 | −1.15941 | −0.579706 | − | 0.814826i | \(-0.696832\pi\) | ||||
−0.579706 | + | 0.814826i | \(0.696832\pi\) | |||||||
\(492\) | − 5.40199e42i | − 0.0206600i | ||||||||
\(493\) | − 2.75460e44i | − 1.01879i | ||||||||
\(494\) | 5.48908e43 | 0.196338 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.50435e44 | −0.838008 | ||||||||
\(497\) | − 1.26036e44i | − 0.407956i | ||||||||
\(498\) | − 3.75267e44i | − 1.17505i | ||||||||
\(499\) | 9.00632e42 | 0.0272828 | 0.0136414 | − | 0.999907i | \(-0.495658\pi\) | ||||
0.0136414 | + | 0.999907i | \(0.495658\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.71467e44 | 0.486249 | ||||||||
\(502\) | − 1.07136e42i | − 0.00293985i | ||||||||
\(503\) | − 3.10986e44i | − 0.825789i | −0.910779 | − | 0.412895i | \(-0.864518\pi\) | ||||
0.910779 | − | 0.412895i | \(-0.135482\pi\) | |||||||
\(504\) | −4.24256e42 | −0.0109024 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.09001e44 | 0.262389 | ||||||||
\(507\) | − 6.31261e43i | − 0.147088i | ||||||||
\(508\) | − 2.73128e44i | − 0.616048i | ||||||||
\(509\) | −7.95788e43 | −0.173762 | −0.0868808 | − | 0.996219i | \(-0.527690\pi\) | ||||
−0.0868808 | + | 0.996219i | \(0.527690\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.47777e44 | −1.32581 | ||||||||
\(512\) | 4.95397e44i | 0.981745i | ||||||||
\(513\) | 1.16221e44i | 0.223023i | ||||||||
\(514\) | 2.85938e44 | 0.531350 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.46296e44 | −0.429276 | ||||||||
\(517\) | 1.36007e44i | 0.229598i | ||||||||
\(518\) | 1.10590e45i | 1.80832i | ||||||||
\(519\) | −5.53149e44 | −0.876154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.27119e44 | 0.188968 | 0.0944841 | − | 0.995526i | \(-0.469880\pi\) | ||||
0.0944841 | + | 0.995526i | \(0.469880\pi\) | |||||||
\(522\) | − 5.20121e42i | − 0.00749102i | ||||||||
\(523\) | − 1.19591e44i | − 0.166887i | −0.996513 | − | 0.0834434i | \(-0.973408\pi\) | ||||
0.996513 | − | 0.0834434i | \(-0.0265918\pi\) | |||||||
\(524\) | 1.63278e44 | 0.220781 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.56876e44 | −0.834101 | ||||||||
\(527\) | − 8.50590e44i | − 1.04675i | ||||||||
\(528\) | − 1.21640e44i | − 0.145083i | ||||||||
\(529\) | −5.12284e44 | −0.592233 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.22142e42 | −0.00132680 | ||||||||
\(532\) | − 1.05357e44i | − 0.110948i | ||||||||
\(533\) | − 6.78932e43i | − 0.0693151i | ||||||||
\(534\) | 3.45559e44 | 0.342052 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.88885e45 | 1.75783 | ||||||||
\(537\) | 8.49938e44i | 0.767029i | ||||||||
\(538\) | 1.68210e45i | 1.47212i | ||||||||
\(539\) | −4.24156e44 | −0.360007 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.24548e45 | −0.994451 | −0.497225 | − | 0.867621i | \(-0.665648\pi\) | ||||
−0.497225 | + | 0.867621i | \(0.665648\pi\) | |||||||
\(542\) | − 3.25913e44i | − 0.252414i | ||||||||
\(543\) | 6.96426e44i | 0.523212i | ||||||||
\(544\) | −6.06031e44 | −0.441686 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.99931e45 | 1.37152 | ||||||||
\(547\) | 9.41755e44i | 0.626826i | 0.949617 | + | 0.313413i | \(0.101472\pi\) | ||||
−0.949617 | + | 0.313413i | \(0.898528\pi\) | |||||||
\(548\) | 2.12659e44i | 0.137342i | ||||||||
\(549\) | −2.14840e42 | −0.00134639 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.32388e44 | 0.314215 | ||||||||
\(552\) | 2.39017e45i | 1.36910i | ||||||||
\(553\) | − 2.93321e45i | − 1.63072i | ||||||||
\(554\) | 1.77713e45 | 0.958975 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.18263e44 | 0.466910 | ||||||||
\(557\) | 2.81038e45i | 1.38725i | 0.720338 | + | 0.693624i | \(0.243987\pi\) | ||||
−0.720338 | + | 0.693624i | \(0.756013\pi\) | |||||||
\(558\) | − 1.60608e43i | − 0.00769666i | ||||||||
\(559\) | −3.09549e45 | −1.44024 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.13144e44 | 0.181223 | ||||||||
\(562\) | 2.32549e44i | 0.0990524i | ||||||||
\(563\) | 2.48634e45i | 1.02842i | 0.857663 | + | 0.514212i | \(0.171916\pi\) | ||||
−0.857663 | + | 0.514212i | \(0.828084\pi\) | |||||||
\(564\) | −7.23555e44 | −0.290647 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.36400e45 | 0.516826 | ||||||||
\(567\) | 4.20595e45i | 1.54790i | ||||||||
\(568\) | − 7.97315e44i | − 0.285025i | ||||||||
\(569\) | −1.50472e45 | −0.522521 | −0.261261 | − | 0.965268i | \(-0.584138\pi\) | ||||
−0.261261 | + | 0.965268i | \(0.584138\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.28889e45 | −0.750117 | −0.375059 | − | 0.927001i | \(-0.622377\pi\) | ||||
−0.375059 | + | 0.927001i | \(0.622377\pi\) | |||||||
\(572\) | 2.71835e44i | 0.0865507i | ||||||||
\(573\) | 1.26255e45i | 0.390569i | ||||||||
\(574\) | 2.76503e44 | 0.0831099 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.45146e43 | −0.00695751 | ||||||||
\(577\) | − 1.59455e45i | − 0.439781i | −0.975525 | − | 0.219891i | \(-0.929430\pi\) | ||||
0.975525 | − | 0.219891i | \(-0.0705701\pi\) | |||||||
\(578\) | − 1.47771e45i | − 0.396076i | ||||||||
\(579\) | −5.57987e44 | −0.145354 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.05264e45 | −2.22776 | ||||||||
\(582\) | − 3.47562e43i | − 0.00831386i | ||||||||
\(583\) | − 1.24964e45i | − 0.290572i | ||||||||
\(584\) | −4.09790e45 | −0.926295 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.30405e44 | 0.0919531 | ||||||||
\(587\) | − 5.55956e45i | − 1.15481i | −0.816457 | − | 0.577407i | \(-0.804065\pi\) | ||||
0.816457 | − | 0.577407i | \(-0.195935\pi\) | |||||||
\(588\) | − 2.25650e45i | − 0.455732i | ||||||||
\(589\) | 1.64396e45 | 0.322841 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.04824e46 | 1.94655 | ||||||||
\(592\) | 4.49880e45i | 0.812434i | ||||||||
\(593\) | − 1.33454e45i | − 0.234384i | −0.993109 | − | 0.117192i | \(-0.962611\pi\) | ||||
0.993109 | − | 0.117192i | \(-0.0373893\pi\) | |||||||
\(594\) | 1.22124e45 | 0.208605 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.52806e45 | −0.408530 | ||||||||
\(597\) | − 1.45347e45i | − 0.228470i | ||||||||
\(598\) | 7.28806e45i | 1.11440i | ||||||||
\(599\) | −2.61382e45 | −0.388806 | −0.194403 | − | 0.980922i | \(-0.562277\pi\) | ||||
−0.194403 | + | 0.980922i | \(0.562277\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.12433e45 | 0.158295 | 0.0791474 | − | 0.996863i | \(-0.474780\pi\) | ||||
0.0791474 | + | 0.996863i | \(0.474780\pi\) | |||||||
\(602\) | − 1.26067e46i | − 1.72687i | ||||||||
\(603\) | 7.78954e43i | 0.0103819i | ||||||||
\(604\) | −2.93684e42 | −0.000380865 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.25056e45 | 0.890376 | ||||||||
\(607\) | − 1.38809e46i | − 1.65884i | −0.558628 | − | 0.829418i | \(-0.688672\pi\) | ||||
0.558628 | − | 0.829418i | \(-0.311328\pi\) | |||||||
\(608\) | − 1.17129e45i | − 0.136225i | ||||||||
\(609\) | 1.93914e46 | 2.19494 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.09378e45 | −0.975134 | ||||||||
\(612\) | − 1.42214e43i | − 0.00148437i | ||||||||
\(613\) | 1.28344e46i | 1.30400i | 0.758218 | + | 0.652001i | \(0.226070\pi\) | ||||
−0.758218 | + | 0.652001i | \(0.773930\pi\) | |||||||
\(614\) | 1.15835e46 | 1.14567 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.56318e45 | −0.427746 | ||||||||
\(617\) | 1.41494e46i | 1.29131i | 0.763628 | + | 0.645657i | \(0.223416\pi\) | ||||
−0.763628 | + | 0.645657i | \(0.776584\pi\) | |||||||
\(618\) | − 1.08604e46i | − 0.965017i | ||||||||
\(619\) | −3.49373e45 | −0.302269 | −0.151134 | − | 0.988513i | \(-0.548293\pi\) | ||||
−0.151134 | + | 0.988513i | \(0.548293\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.54311e46 | −1.26586 | ||||||||
\(622\) | − 1.05693e46i | − 0.844312i | ||||||||
\(623\) | − 8.33600e45i | − 0.648492i | ||||||||
\(624\) | 8.13317e45 | 0.616189 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.76558e46 | −1.26885 | ||||||||
\(627\) | 7.98494e44i | 0.0558929i | ||||||||
\(628\) | − 5.62707e45i | − 0.383662i | ||||||||
\(629\) | −1.52799e46 | −1.01481 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.21383e46 | 1.39528 | 0.697638 | − | 0.716451i | \(-0.254234\pi\) | ||||
0.697638 | + | 0.716451i | \(0.254234\pi\) | |||||||
\(632\) | − 1.85558e46i | − 1.13932i | ||||||||
\(633\) | − 1.97608e46i | − 1.18207i | ||||||||
\(634\) | 9.02525e45 | 0.526001 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.64807e45 | 0.367835 | ||||||||
\(637\) | − 2.83601e46i | − 1.52900i | ||||||||
\(638\) | − 5.59428e45i | − 0.293902i | ||||||||
\(639\) | 3.28810e43 | 0.00168337 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.90058e45 | −0.238281 | −0.119141 | − | 0.992877i | \(-0.538014\pi\) | ||||
−0.119141 | + | 0.992877i | \(0.538014\pi\) | |||||||
\(642\) | 2.98608e46i | 1.41506i | ||||||||
\(643\) | 2.98051e46i | 1.37661i | 0.725423 | + | 0.688303i | \(0.241644\pi\) | ||||
−0.725423 | + | 0.688303i | \(0.758356\pi\) | |||||||
\(644\) | 1.39886e46 | 0.629734 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.08871e45 | −0.132111 | ||||||||
\(647\) | 3.18321e45i | 0.132723i | 0.997796 | + | 0.0663613i | \(0.0211390\pi\) | ||||
−0.997796 | + | 0.0663613i | \(0.978861\pi\) | |||||||
\(648\) | 2.66073e46i | 1.08146i | ||||||||
\(649\) | −1.31372e45 | −0.0520555 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.98785e46 | 2.25520 | ||||||||
\(652\) | 2.34924e45i | 0.0862666i | ||||||||
\(653\) | − 4.44872e46i | − 1.59282i | −0.604756 | − | 0.796411i | \(-0.706729\pi\) | ||||
0.604756 | − | 0.796411i | \(-0.293271\pi\) | |||||||
\(654\) | −9.27261e45 | −0.323720 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.12481e45 | 0.0373392 | ||||||||
\(657\) | − 1.68996e44i | − 0.00547076i | ||||||||
\(658\) | − 3.70354e46i | − 1.16920i | ||||||||
\(659\) | 3.64438e46 | 1.12206 | 0.561028 | − | 0.827797i | \(-0.310406\pi\) | ||||
0.561028 | + | 0.827797i | \(0.310406\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.16411e46 | −0.633804 | −0.316902 | − | 0.948458i | \(-0.602643\pi\) | ||||
−0.316902 | + | 0.948458i | \(0.602643\pi\) | |||||||
\(662\) | − 1.85517e46i | − 0.529940i | ||||||||
\(663\) | 2.76238e46i | 0.769681i | ||||||||
\(664\) | −5.72679e46 | −1.55646 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.88514e44 | −0.00746178 | ||||||||
\(667\) | 7.06871e46i | 1.78346i | ||||||||
\(668\) | − 6.34836e45i | − 0.156261i | ||||||||
\(669\) | 1.62148e46 | 0.389387 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.31076e45 | −0.0528242 | ||||||||
\(672\) | − 4.26624e46i | − 0.951596i | ||||||||
\(673\) | 5.34875e46i | 1.16414i | 0.813140 | + | 0.582068i | \(0.197756\pi\) | ||||
−0.813140 | + | 0.582068i | \(0.802244\pi\) | |||||||
\(674\) | −4.43140e46 | −0.941137 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.33717e45 | −0.0472682 | ||||||||
\(677\) | 3.90814e46i | 0.771359i | 0.922633 | + | 0.385679i | \(0.126033\pi\) | ||||
−0.922633 | + | 0.385679i | \(0.873967\pi\) | |||||||
\(678\) | − 6.30112e46i | − 1.21375i | ||||||||
\(679\) | −8.38430e44 | −0.0157622 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.03610e46 | −0.722826 | ||||||||
\(682\) | − 1.72745e46i | − 0.301970i | ||||||||
\(683\) | 9.82421e46i | 1.67632i | 0.545427 | + | 0.838158i | \(0.316368\pi\) | ||||
−0.545427 | + | 0.838158i | \(0.683632\pi\) | |||||||
\(684\) | 2.74860e43 | 0.000457811 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.45786e46 | 0.548858 | ||||||||
\(687\) | 8.21966e46i | 1.27370i | ||||||||
\(688\) | − 5.12840e46i | − 0.775841i | ||||||||
\(689\) | 8.35542e46 | 1.23410 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.20065e46 | −1.01387 | −0.506937 | − | 0.861983i | \(-0.669222\pi\) | ||||
−0.506937 | + | 0.861983i | \(0.669222\pi\) | |||||||
\(692\) | 2.04796e46i | 0.281560i | ||||||||
\(693\) | − 1.88184e44i | − 0.00252629i | ||||||||
\(694\) | −7.68188e46 | −1.00702 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.22672e47 | 1.53353 | ||||||||
\(697\) | 3.82035e45i | 0.0466404i | ||||||||
\(698\) | 1.11927e47i | 1.33451i | ||||||||
\(699\) | 4.21520e46 | 0.490846 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.78749e46 | −0.420731 | −0.210366 | − | 0.977623i | \(-0.567465\pi\) | ||||
−0.210366 | + | 0.977623i | \(0.567465\pi\) | |||||||
\(702\) | 8.16552e46i | 0.885975i | ||||||||
\(703\) | − 2.95319e46i | − 0.312988i | ||||||||
\(704\) | −2.63672e46 | −0.272970 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.86119e45 | −0.0579039 | ||||||||
\(707\) | − 1.74907e47i | − 1.68805i | ||||||||
\(708\) | − 6.98899e45i | − 0.0658970i | ||||||||
\(709\) | −8.09313e46 | −0.745510 | −0.372755 | − | 0.927930i | \(-0.621587\pi\) | ||||
−0.372755 | + | 0.927930i | \(0.621587\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.65234e44 | 0.00672892 | ||||||||
\(712\) | − 5.27343e46i | − 0.453078i | ||||||||
\(713\) | 2.18274e47i | 1.83242i | ||||||||
\(714\) | −1.12501e47 | −0.922861 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.14679e46 | 0.246492 | ||||||||
\(717\) | 1.99995e47i | 1.53092i | ||||||||
\(718\) | − 1.73923e47i | − 1.30108i | ||||||||
\(719\) | −1.77184e47 | −1.29538 | −0.647692 | − | 0.761902i | \(-0.724266\pi\) | ||||
−0.647692 | + | 0.761902i | \(0.724266\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.61987e47 | −1.82956 | ||||||||
\(722\) | 1.14816e47i | 0.783678i | ||||||||
\(723\) | 2.86289e47i | 1.90995i | ||||||||
\(724\) | 2.57843e46 | 0.168139 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.23497e47 | −0.769490 | ||||||||
\(727\) | − 1.73206e47i | − 1.05498i | −0.849561 | − | 0.527490i | \(-0.823133\pi\) | ||||
0.849561 | − | 0.527490i | \(-0.176867\pi\) | |||||||
\(728\) | − 3.05106e47i | − 1.81670i | ||||||||
\(729\) | −1.72883e47 | −1.00635 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.74183e47 | 0.969102 | ||||||||
\(732\) | − 1.22932e46i | − 0.0668701i | ||||||||
\(733\) | − 2.26618e47i | − 1.20525i | −0.798024 | − | 0.602626i | \(-0.794121\pi\) | ||||
0.798024 | − | 0.602626i | \(-0.205879\pi\) | |||||||
\(734\) | −1.86736e47 | −0.971054 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.55517e47 | 0.773203 | ||||||||
\(737\) | 8.37821e46i | 0.407322i | ||||||||
\(738\) | 7.21356e43i | 0 0.000342941i | ||||||||
\(739\) | −3.80934e46 | −0.177099 | −0.0885496 | − | 0.996072i | \(-0.528223\pi\) | ||||
−0.0885496 | + | 0.996072i | \(0.528223\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.33893e46 | −0.237385 | ||||||||
\(742\) | 3.40283e47i | 1.47971i | ||||||||
\(743\) | − 1.22091e47i | − 0.519238i | −0.965711 | − | 0.259619i | \(-0.916403\pi\) | ||||
0.965711 | − | 0.259619i | \(-0.0835970\pi\) | |||||||
\(744\) | 3.78797e47 | 1.57563 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.66800e47 | 0.663750 | ||||||||
\(747\) | − 2.36171e45i | − 0.00919255i | ||||||||
\(748\) | − 1.52961e46i | − 0.0582378i | ||||||||
\(749\) | 7.20338e47 | 2.68279 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.36534e46 | −0.0843014 | −0.0421507 | − | 0.999111i | \(-0.513421\pi\) | ||||
−0.0421507 | + | 0.999111i | \(0.513421\pi\) | |||||||
\(752\) | − 1.50660e47i | − 0.525294i | ||||||||
\(753\) | 1.04206e45i | 0.00355446i | ||||||||
\(754\) | 3.74048e47 | 1.24824 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.56728e47 | 0.500652 | ||||||||
\(757\) | 1.36056e47i | 0.425243i | 0.977135 | + | 0.212621i | \(0.0682001\pi\) | ||||
−0.977135 | + | 0.212621i | \(0.931800\pi\) | |||||||
\(758\) | 2.51859e47i | 0.770222i | ||||||||
\(759\) | −1.06019e47 | −0.317245 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.10711e47 | 0.603727 | 0.301863 | − | 0.953351i | \(-0.402391\pi\) | ||||
0.301863 | + | 0.953351i | \(0.402391\pi\) | |||||||
\(762\) | − 5.63678e47i | − 1.58043i | ||||||||
\(763\) | 2.23685e47i | 0.613737i | ||||||||
\(764\) | 4.67444e46 | 0.125513 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.61055e47 | 0.414189 | ||||||||
\(767\) | − 8.78390e46i | − 0.221087i | ||||||||
\(768\) | − 3.44682e47i | − 0.849100i | ||||||||
\(769\) | −3.42055e47 | −0.824728 | −0.412364 | − | 0.911019i | \(-0.635297\pi\) | ||||
−0.412364 | + | 0.911019i | \(0.635297\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.78116e47 | −0.642435 | ||||||||
\(772\) | 2.06588e46i | 0.0467110i | ||||||||
\(773\) | 2.59138e47i | 0.573549i | 0.957998 | + | 0.286774i | \(0.0925830\pi\) | ||||
−0.957998 | + | 0.286774i | \(0.907417\pi\) | |||||||
\(774\) | 3.28892e45 | 0.00712569 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.30399e45 | −0.0110125 | ||||||||
\(777\) | − 1.07565e48i | − 2.18637i | ||||||||
\(778\) | − 3.59916e47i | − 0.716206i | ||||||||
\(779\) | −7.38369e45 | −0.0143849 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.53659e46 | 0.0660454 | ||||||||
\(782\) | − 4.10099e47i | − 0.749855i | ||||||||
\(783\) | 7.91977e47i | 1.41789i | ||||||||
\(784\) | 4.69851e47 | 0.823655 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.36972e47 | 0.566398 | ||||||||
\(787\) | 3.31448e47i | 0.545546i | 0.962078 | + | 0.272773i | \(0.0879409\pi\) | ||||
−0.962078 | + | 0.272773i | \(0.912059\pi\) | |||||||
\(788\) | − 3.88096e47i | − 0.625542i | ||||||||
\(789\) | 6.38908e47 | 1.00848 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.52003e48 | −2.30113 | ||||||||
\(792\) | − 1.19047e45i | − 0.00176503i | ||||||||
\(793\) | − 1.54503e47i | − 0.224352i | ||||||||
\(794\) | −3.20658e47 | −0.456040 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.38129e46 | −0.0734211 | ||||||||
\(797\) | 1.21980e48i | 1.63015i | 0.579354 | + | 0.815076i | \(0.303305\pi\) | ||||
−0.579354 | + | 0.815076i | \(0.696695\pi\) | |||||||
\(798\) | − 2.17434e47i | − 0.284629i | ||||||||
\(799\) | 5.11707e47 | 0.656144 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.17474e45 | 0.00267591 | ||||||||
\(802\) | − 4.39671e47i | − 0.529969i | ||||||||
\(803\) | − 1.81767e47i | − 0.214639i | ||||||||
\(804\) | −4.45719e47 | −0.515628 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.15502e48 | 1.28251 | ||||||||
\(807\) | − 1.63609e48i | − 1.77989i | ||||||||
\(808\) | − 1.10648e48i | − 1.17938i | ||||||||
\(809\) | 2.89096e47 | 0.301920 | 0.150960 | − | 0.988540i | \(-0.451764\pi\) | ||||
0.150960 | + | 0.988540i | \(0.451764\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.79228e47 | −0.881571 | −0.440786 | − | 0.897612i | \(-0.645300\pi\) | ||||
−0.440786 | + | 0.897612i | \(0.645300\pi\) | |||||||
\(812\) | − 7.17941e47i | − 0.705366i | ||||||||
\(813\) | 3.16998e47i | 0.305184i | ||||||||
\(814\) | −3.10318e47 | −0.292755 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.57653e47 | −0.414619 | ||||||||
\(817\) | 3.36648e47i | 0.298891i | ||||||||
\(818\) | − 1.07972e48i | − 0.939467i | ||||||||
\(819\) | 1.25825e46 | 0.0107295 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.16314e47 | −0.504824 | −0.252412 | − | 0.967620i | \(-0.581224\pi\) | ||||
−0.252412 | + | 0.967620i | \(0.581224\pi\) | |||||||
\(822\) | 4.38883e47i | 0.352342i | ||||||||
\(823\) | − 1.89117e47i | − 0.148810i | −0.997228 | − | 0.0744052i | \(-0.976294\pi\) | ||||
0.997228 | − | 0.0744052i | \(-0.0237058\pi\) | |||||||
\(824\) | −1.65735e48 | −1.27825 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.57734e47 | 0.265087 | ||||||||
\(827\) | 9.51973e47i | 0.691486i | 0.938329 | + | 0.345743i | \(0.112373\pi\) | ||||
−0.938329 | + | 0.345743i | \(0.887627\pi\) | |||||||
\(828\) | 3.64942e45i | 0.00259851i | ||||||||
\(829\) | −2.56276e48 | −1.78878 | −0.894392 | − | 0.447284i | \(-0.852391\pi\) | ||||
−0.894392 | + | 0.447284i | \(0.852391\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.72851e48 | −1.15946 | ||||||||
\(832\) | − 1.76298e48i | − 1.15934i | ||||||||
\(833\) | 1.59582e48i | 1.02883i | ||||||||
\(834\) | 1.89510e48 | 1.19782 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.95632e46 | 0.0179617 | ||||||||
\(837\) | 2.44554e48i | 1.45682i | ||||||||
\(838\) | 2.18701e48i | 1.27740i | ||||||||
\(839\) | 5.48536e47 | 0.314147 | 0.157073 | − | 0.987587i | \(-0.449794\pi\) | ||||
0.157073 | + | 0.987587i | \(0.449794\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.81182e48 | 0.997659 | ||||||||
\(842\) | − 1.02536e48i | − 0.553641i | ||||||||
\(843\) | − 2.26188e47i | − 0.119761i | ||||||||
\(844\) | −7.31618e47 | −0.379869 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.66201e45 | 0.00482454 | ||||||||
\(847\) | 2.97915e48i | 1.45887i | ||||||||
\(848\) | 1.38427e48i | 0.664797i | ||||||||
\(849\) | −1.32669e48 | −0.624875 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.92105e48 | 1.77650 | ||||||||
\(852\) | 1.88146e47i | 0.0836067i | ||||||||
\(853\) | 6.63073e47i | 0.289003i | 0.989505 | + | 0.144501i | \(0.0461578\pi\) | ||||
−0.989505 | + | 0.144501i | \(0.953842\pi\) | |||||||
\(854\) | 6.29231e47 | 0.269002 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.55693e48 | 1.87437 | ||||||||
\(857\) | 3.61344e48i | 1.45793i | 0.684550 | + | 0.728966i | \(0.259999\pi\) | ||||
−0.684550 | + | 0.728966i | \(0.740001\pi\) | |||||||
\(858\) | 5.61009e47i | 0.222039i | ||||||||
\(859\) | 2.95644e47 | 0.114784 | 0.0573921 | − | 0.998352i | \(-0.481721\pi\) | ||||
0.0573921 | + | 0.998352i | \(0.481721\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.68939e47 | −0.100485 | ||||||||
\(862\) | 3.05736e48i | 1.12067i | ||||||||
\(863\) | 1.94226e48i | 0.698440i | 0.937041 | + | 0.349220i | \(0.113553\pi\) | ||||
−0.937041 | + | 0.349220i | \(0.886447\pi\) | |||||||
\(864\) | 1.74241e48 | 0.614713 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.90904e47 | −0.268583 | ||||||||
\(867\) | 1.43728e48i | 0.478881i | ||||||||
\(868\) | − 2.21692e48i | − 0.724729i | ||||||||
\(869\) | 8.23064e47 | 0.264002 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.60188e48 | −1.72995 | ||||||||
\(872\) | 1.41505e48i | 0.428796i | ||||||||
\(873\) | − 2.18735e44i | 0 6.50403e-5i | ||||||||
\(874\) | 7.92608e47 | 0.231270 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.66998e47 | 0.271711 | ||||||||
\(877\) | − 3.36176e48i | − 0.926985i | −0.886101 | − | 0.463493i | \(-0.846596\pi\) | ||||
0.886101 | − | 0.463493i | \(-0.153404\pi\) | |||||||
\(878\) | 2.41020e47i | 0.0652220i | ||||||||
\(879\) | −4.18631e47 | −0.111177 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.89868e47 | 0.0741477 | 0.0370738 | − | 0.999313i | \(-0.488196\pi\) | ||||
0.0370738 | + | 0.999313i | \(0.488196\pi\) | |||||||
\(882\) | 3.01322e46i | 0.00756484i | ||||||||
\(883\) | − 2.27915e48i | − 0.561592i | −0.959767 | − | 0.280796i | \(-0.909402\pi\) | ||||
0.959767 | − | 0.280796i | \(-0.0905985\pi\) | |||||||
\(884\) | 1.02274e48 | 0.247344 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.27003e48 | −0.295910 | ||||||||
\(887\) | 3.67815e48i | 0.841180i | 0.907251 | + | 0.420590i | \(0.138177\pi\) | ||||
−0.907251 | + | 0.420590i | \(0.861823\pi\) | |||||||
\(888\) | − 6.80467e48i | − 1.52754i | ||||||||
\(889\) | −1.35977e49 | −2.99631 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.18020e48 | −0.250595 | ||||||||
\(892\) | − 6.00334e47i | − 0.125133i | ||||||||
\(893\) | 9.88988e47i | 0.202368i | ||||||||
\(894\) | −5.21738e48 | −1.04805 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.24892e48 | 0.435403 | ||||||||
\(897\) | − 7.08870e48i | − 1.34738i | ||||||||
\(898\) | − 1.61488e48i | − 0.301357i | ||||||||
\(899\) | 1.12026e49 | 2.05250 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.70159e48 | −0.830397 | ||||||||
\(902\) | 7.75870e46i | 0.0134549i | ||||||||
\(903\) | 1.22619e49i | 2.08790i | ||||||||
\(904\) | −9.61586e48 | −1.60771 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.06102e45 | −0.000977080 0 | ||||||||
\(907\) | 1.60568e48i | 0.254178i | 0.991891 | + | 0.127089i | \(0.0405634\pi\) | ||||
−0.991891 | + | 0.127089i | \(0.959437\pi\) | |||||||
\(908\) | 1.49431e48i | 0.232287i | ||||||||
\(909\) | 4.56307e46 | 0.00696551 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.70098e48 | 1.13369 | 0.566843 | − | 0.823826i | \(-0.308165\pi\) | ||||
0.566843 | + | 0.823826i | \(0.308165\pi\) | |||||||
\(912\) | − 8.84518e47i | − 0.127877i | ||||||||
\(913\) | − 2.54019e48i | − 0.360660i | ||||||||
\(914\) | 1.09134e49 | 1.52176 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.04322e48 | 0.409316 | ||||||||
\(917\) | − 8.12883e48i | − 1.07383i | ||||||||
\(918\) | − 4.59474e48i | − 0.596151i | ||||||||
\(919\) | −5.42603e48 | −0.691474 | −0.345737 | − | 0.938331i | \(-0.612371\pi\) | ||||
−0.345737 | + | 0.938331i | \(0.612371\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.12666e49 | −1.38519 | ||||||||
\(922\) | − 2.70074e48i | − 0.326154i | ||||||||
\(923\) | 2.36465e48i | 0.280504i | ||||||||
\(924\) | 1.07679e48 | 0.125471 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.35275e48 | −0.264542 | ||||||||
\(927\) | − 6.83487e46i | − 0.00754944i | ||||||||
\(928\) | − 7.98165e48i | − 0.866066i | ||||||||
\(929\) | 7.82524e48 | 0.834139 | 0.417070 | − | 0.908875i | \(-0.363057\pi\) | ||||
0.417070 | + | 0.908875i | \(0.363057\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.08429e48 | −0.317311 | ||||||||
\(932\) | − 1.56063e48i | − 0.157738i | ||||||||
\(933\) | 1.02801e49i | 1.02083i | ||||||||
\(934\) | 2.81891e48 | 0.275016 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.95978e46 | 0.00749634 | ||||||||
\(937\) | − 1.34653e49i | − 1.24599i | −0.782227 | − | 0.622994i | \(-0.785916\pi\) | ||||
0.782227 | − | 0.622994i | \(-0.214084\pi\) | |||||||
\(938\) | − 2.28143e49i | − 2.07424i | ||||||||
\(939\) | 1.71729e49 | 1.53413 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.57761e49 | −1.36073 | −0.680365 | − | 0.732874i | \(-0.738179\pi\) | ||||
−0.680365 | + | 0.732874i | \(0.738179\pi\) | |||||||
\(942\) | − 1.16131e49i | − 0.984255i | ||||||||
\(943\) | − 9.80360e47i | − 0.0816474i | ||||||||
\(944\) | 1.45526e48 | 0.119097 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.53747e48 | 0.279569 | ||||||||
\(947\) | − 7.45162e48i | − 0.578730i | −0.957219 | − | 0.289365i | \(-0.906556\pi\) | ||||
0.957219 | − | 0.289365i | \(-0.0934441\pi\) | |||||||
\(948\) | 4.37869e48i | 0.334200i | ||||||||
\(949\) | 1.21534e49 | 0.911604 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.77837e48 | −0.635968 | ||||||||
\(952\) | 1.71683e49i | 1.22241i | ||||||||
\(953\) | 2.12970e49i | 1.49034i | 0.666874 | + | 0.745171i | \(0.267632\pi\) | ||||
−0.666874 | + | 0.745171i | \(0.732368\pi\) | |||||||
\(954\) | −8.87751e46 | −0.00610581 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.40456e48 | 0.491976 | ||||||||
\(957\) | 5.44125e48i | 0.355346i | ||||||||
\(958\) | − 2.36140e48i | − 0.151579i | ||||||||
\(959\) | 1.05873e49 | 0.668000 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.81888e49 | 1.10884 | ||||||||
\(962\) | − 2.07486e49i | − 1.24337i | ||||||||
\(963\) | 1.87926e47i | 0.0110701i | ||||||||
\(964\) | 1.05995e49 | 0.613781 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.88695e49 | 1.61553 | ||||||||
\(967\) | − 7.81881e47i | − 0.0430134i | −0.999769 | − | 0.0215067i | \(-0.993154\pi\) | ||||
0.999769 | − | 0.0215067i | \(-0.00684632\pi\) | |||||||
\(968\) | 1.88464e49i | 1.01926i | ||||||||
\(969\) | 3.00422e48 | 0.159731 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.07870e49 | 1.06825 | 0.534127 | − | 0.845404i | \(-0.320640\pi\) | ||||
0.534127 | + | 0.845404i | \(0.320640\pi\) | |||||||
\(972\) | 8.15149e46i | 0.00411854i | ||||||||
\(973\) | − 4.57159e49i | − 2.27094i | ||||||||
\(974\) | −3.29811e49 | −1.61080 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.55971e48 | 0.120856 | ||||||||
\(977\) | 1.16244e49i | 0.539647i | 0.962910 | + | 0.269824i | \(0.0869654\pi\) | ||||
−0.962910 | + | 0.269824i | \(0.913035\pi\) | |||||||
\(978\) | 4.84834e48i | 0.221311i | ||||||||
\(979\) | 2.33909e48 | 0.104986 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.83563e46 | −0.00253250 | ||||||||
\(982\) | 2.23990e49i | 0.955846i | ||||||||
\(983\) | − 2.37943e49i | − 0.998482i | −0.866463 | − | 0.499241i | \(-0.833612\pi\) | ||||
0.866463 | − | 0.499241i | \(-0.166388\pi\) | |||||||
\(984\) | −1.70133e48 | −0.0702054 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.10476e49 | −0.839913 | ||||||||
\(987\) | 3.60223e49i | 1.41364i | ||||||||
\(988\) | 1.97667e48i | 0.0762861i | ||||||||
\(989\) | −4.46980e49 | −1.69648 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.80696e49 | −1.39754 | −0.698768 | − | 0.715348i | \(-0.746268\pi\) | ||||
−0.698768 | + | 0.715348i | \(0.746268\pi\) | |||||||
\(992\) | − 2.46465e49i | − 0.889840i | ||||||||
\(993\) | 1.80442e49i | 0.640731i | ||||||||
\(994\) | −9.63030e48 | −0.336329 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.35137e49 | 0.456559 | ||||||||
\(997\) | − 6.76901e48i | − 0.224934i | −0.993655 | − | 0.112467i | \(-0.964125\pi\) | ||||
0.993655 | − | 0.112467i | \(-0.0358752\pi\) | |||||||
\(998\) | − 6.88166e47i | − 0.0224926i | ||||||||
\(999\) | 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 | 25.34.b.c.24.5 | 12 | ||
5.2 | odd | 4 | 5.34.a.b.1.4 | ✓ | 6 | ||
5.3 | odd | 4 | 25.34.a.c.1.3 | 6 | |||
5.4 | even | 2 | inner | 25.34.b.c.24.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.34.a.b.1.4 | ✓ | 6 | 5.2 | odd | 4 | ||
25.34.a.c.1.3 | 6 | 5.3 | odd | 4 | |||
25.34.b.c.24.5 | 12 | 1.1 | even | 1 | trivial | ||
25.34.b.c.24.8 | 12 | 5.4 | even | 2 | inner |