Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,50,Mod(1,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 50, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.1");
S:= CuspForms(chi, 50);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 50 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.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: | \(243.305928158\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 104434803447206332x + 4289992005756109702361620 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 2) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.42020e8\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.33407e11 | 0.272714 | 0.136357 | − | 0.990660i | \(-0.456461\pi\) | ||||
0.136357 | + | 0.990660i | \(0.456461\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.87739e17 | 1.40860 | 0.704302 | − | 0.709900i | \(-0.251260\pi\) | ||||
0.704302 | + | 0.709900i | \(0.251260\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.28497e20 | −1.63452 | −0.817258 | − | 0.576272i | \(-0.804507\pi\) | ||||
−0.817258 | + | 0.576272i | \(0.804507\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.21502e23 | −0.925627 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.05508e25 | 0.935195 | 0.467598 | − | 0.883941i | \(-0.345120\pi\) | ||||
0.467598 | + | 0.883941i | \(0.345120\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.92824e25 | −0.0251814 | −0.0125907 | − | 0.999921i | \(-0.504008\pi\) | ||||
−0.0125907 | + | 0.999921i | \(0.504008\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.50456e28 | 0.384146 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.50818e30 | 1.79209 | 0.896047 | − | 0.443959i | \(-0.146427\pi\) | ||||
0.896047 | + | 0.443959i | \(0.146427\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.26388e30 | −0.246515 | −0.123257 | − | 0.992375i | \(-0.539334\pi\) | ||||
−0.123257 | + | 0.992375i | \(0.539334\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.10527e32 | −0.445755 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.99827e32 | 0.347268 | 0.173634 | − | 0.984810i | \(-0.444449\pi\) | ||||
0.173634 | + | 0.984810i | \(0.444449\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.74823e34 | 0.984168 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −6.14740e34 | −0.525145 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.91459e35 | −0.432341 | −0.216171 | − | 0.976356i | \(-0.569357\pi\) | ||||
−0.216171 | + | 0.976356i | \(0.569357\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.98168e36 | −1.73166 | −0.865828 | − | 0.500342i | \(-0.833208\pi\) | ||||
−0.865828 | + | 0.500342i | \(0.833208\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.07569e36 | 0.255041 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.55541e38 | −2.30239 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.31540e38 | 0.499018 | 0.249509 | − | 0.968372i | \(-0.419731\pi\) | ||||
0.249509 | + | 0.968372i | \(0.419731\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.57461e36 | −0.00686731 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.57335e39 | −0.789394 | −0.394697 | − | 0.918811i | \(-0.629150\pi\) | ||||
−0.394697 | + | 0.918811i | \(0.629150\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.01162e39 | −0.287622 | −0.143811 | − | 0.989605i | \(-0.545936\pi\) | ||||
−0.143811 | + | 0.989605i | \(0.545936\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.15845e40 | −1.30384 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.35707e41 | 1.46624 | 0.733118 | − | 0.680102i | \(-0.238064\pi\) | ||||
0.733118 | + | 0.680102i | \(0.238064\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.29484e41 | 1.67164 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.34609e41 | 0.488729 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.38284e42 | 1.92541 | 0.962704 | − | 0.270557i | \(-0.0872079\pi\) | ||||
0.962704 | + | 0.270557i | \(0.0872079\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.73558e42 | 1.31732 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.02238e41 | −0.0672280 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.39260e42 | 0.0572732 | 0.0286366 | − | 0.999590i | \(-0.490883\pi\) | ||||
0.0286366 | + | 0.999590i | \(0.490883\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.43699e43 | −1.53323 | −0.766614 | − | 0.642108i | \(-0.778060\pi\) | ||||
−0.766614 | + | 0.642108i | \(0.778060\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.83514e44 | 1.51295 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.25222e42 | −0.0354706 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.28654e44 | −0.782121 | −0.391060 | − | 0.920365i | \(-0.627892\pi\) | ||||
−0.391060 | + | 0.920365i | \(0.627892\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.06702e44 | 0.0947046 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.65460e45 | 0.729228 | 0.364614 | − | 0.931159i | \(-0.381201\pi\) | ||||
0.364614 | + | 0.931159i | \(0.381201\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.25815e45 | −1.17334 | −0.586669 | − | 0.809827i | \(-0.699561\pi\) | ||||
−0.586669 | + | 0.809827i | \(0.699561\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.33226e45 | 0.268396 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.53113e46 | −1.52859 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.45663e46 | −0.469338 | −0.234669 | − | 0.972075i | \(-0.575401\pi\) | ||||
−0.234669 | + | 0.972075i | \(0.575401\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.48042e46 | 0.782413 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.24216e46 | 0.887892 | 0.443946 | − | 0.896054i | \(-0.353578\pi\) | ||||
0.443946 | + | 0.896054i | \(0.353578\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.70884e47 | 2.52435 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.88826e46 | −0.117905 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.22598e46 | 0.142933 | 0.0714665 | − | 0.997443i | \(-0.477232\pi\) | ||||
0.0714665 | + | 0.997443i | \(0.477232\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.08303e46 | 0.0411594 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.97996e47 | −0.472246 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.88236e47 | −0.347242 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.76751e48 | −1.00551 | −0.502753 | − | 0.864430i | \(-0.667679\pi\) | ||||
−0.502753 | + | 0.864430i | \(0.667679\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.76707e48 | −0.865642 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.44113e49 | 1.12935 | 0.564674 | − | 0.825314i | \(-0.309002\pi\) | ||||
0.564674 | + | 0.825314i | \(0.309002\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.10349e49 | 0.534879 | 0.267440 | − | 0.963575i | \(-0.413822\pi\) | ||||
0.267440 | + | 0.963575i | \(0.413822\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.07502e49 | −0.627893 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.92403e49 | 1.51023 | 0.755116 | − | 0.655591i | \(-0.227581\pi\) | ||||
0.755116 | + | 0.655591i | \(0.227581\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.47552e48 | −0.0178647 | −0.00893236 | − | 0.999960i | \(-0.502843\pi\) | ||||
−0.00893236 | + | 0.999960i | \(0.502843\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.75484e49 | 0.136089 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.29547e49 | 0.114935 | 0.0574673 | − | 0.998347i | \(-0.481698\pi\) | ||||
0.0574673 | + | 0.998347i | \(0.481698\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50159e50 | 0.489163 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.09161e49 | 0.0233086 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.07802e51 | −2.92921 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.33836e50 | −0.125410 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.43302e50 | −0.215279 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.27986e49 | −0.0223011 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.51820e51 | 1.57981 | 0.789907 | − | 0.613227i | \(-0.210129\pi\) | ||||
0.789907 | + | 0.613227i | \(0.210129\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.01770e50 | −0.0784385 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.30117e51 | 0.174256 | 0.0871282 | − | 0.996197i | \(-0.472231\pi\) | ||||
0.0871282 | + | 0.996197i | \(0.472231\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.36111e51 | 0.402932 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.15411e52 | −0.739722 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.00417e52 | −0.448902 | −0.224451 | − | 0.974485i | \(-0.572059\pi\) | ||||
−0.224451 | + | 0.974485i | \(0.572059\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.07477e52 | 0.963719 | 0.481860 | − | 0.876248i | \(-0.339962\pi\) | ||||
0.481860 | + | 0.876248i | \(0.339962\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.81042e52 | 0.399863 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.50562e51 | −0.0235495 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.47182e52 | −0.608998 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.72961e52 | 0.455880 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.89224e53 | 1.08122 | 0.540608 | − | 0.841275i | \(-0.318194\pi\) | ||||
0.540608 | + | 0.841275i | \(0.318194\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.34497e52 | −0.0966500 | −0.0483250 | − | 0.998832i | \(-0.515388\pi\) | ||||
−0.0483250 | + | 0.998832i | \(0.515388\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.55568e53 | −1.65881 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.12299e54 | −2.43922 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.13167e54 | 1.79546 | 0.897732 | − | 0.440542i | \(-0.145214\pi\) | ||||
0.897732 | + | 0.440542i | \(0.145214\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.51294e53 | 0.525085 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.62655e53 | −0.567614 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.02699e54 | 1.28308 | 0.641542 | − | 0.767088i | \(-0.278295\pi\) | ||||
0.641542 | + | 0.767088i | \(0.278295\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.65165e53 | 0.359252 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.35877e54 | 0.824389 | 0.412194 | − | 0.911096i | \(-0.364762\pi\) | ||||
0.412194 | + | 0.911096i | \(0.364762\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.82780e54 | −0.999366 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.16596e54 | 0.228181 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.16168e53 | 0.0906921 | 0.0453461 | − | 0.998971i | \(-0.485561\pi\) | ||||
0.0453461 | + | 0.998971i | \(0.485561\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.44841e55 | −1.60864 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.85782e53 | 0.0156192 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.10481e54 | −0.198215 | −0.0991073 | − | 0.995077i | \(-0.531599\pi\) | ||||
−0.0991073 | + | 0.995077i | \(0.531599\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.59693e54 | −0.418041 | −0.209020 | − | 0.977911i | \(-0.567027\pi\) | ||||
−0.209020 | + | 0.977911i | \(0.567027\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.12555e55 | −0.418132 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.46952e55 | 0.702920 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.66271e55 | 1.67596 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.09310e55 | 0.858358 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.27680e55 | 0.296488 | 0.148244 | − | 0.988951i | \(-0.452638\pi\) | ||||
0.148244 | + | 0.988951i | \(0.452638\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.99559e55 | 0.705782 | 0.352891 | − | 0.935664i | \(-0.385199\pi\) | ||||
0.352891 | + | 0.935664i | \(0.385199\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.23431e54 | −0.00967333 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.40903e56 | −0.860000 | −0.430000 | − | 0.902829i | \(-0.641486\pi\) | ||||
−0.430000 | + | 0.902829i | \(0.641486\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.14321e56 | −1.49786 | −0.748932 | − | 0.662647i | \(-0.769433\pi\) | ||||
−0.748932 | + | 0.662647i | \(0.769433\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.71853e55 | −0.213295 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.41473e56 | 0.706668 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.83117e56 | −1.11194 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.77163e56 | −0.321440 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.60816e56 | −0.230539 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.36710e57 | 1.55196 | 0.775978 | − | 0.630760i | \(-0.217257\pi\) | ||||
0.775978 | + | 0.630760i | \(0.217257\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.20735e56 | 0.198870 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.65398e56 | −0.405146 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.95580e57 | 2.83042 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.01473e56 | −0.319985 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.23609e56 | −0.0451274 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.75293e56 | −0.0513210 | −0.0256605 | − | 0.999671i | \(-0.508169\pi\) | ||||
−0.0256605 | + | 0.999671i | \(0.508169\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.87237e57 | −0.910973 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.13704e57 | 0.783531 | 0.391765 | − | 0.920065i | \(-0.371865\pi\) | ||||
0.391765 | + | 0.920065i | \(0.371865\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.25222e57 | 0.955136 | 0.477568 | − | 0.878595i | \(-0.341518\pi\) | ||||
0.477568 | + | 0.878595i | \(0.341518\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.37670e57 | −0.416868 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.79416e57 | −0.579123 | −0.289561 | − | 0.957159i | \(-0.593509\pi\) | ||||
−0.289561 | + | 0.957159i | \(0.593509\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.54774e58 | 2.06535 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.94324e57 | −0.127995 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.99860e58 | −1.07146 | −0.535732 | − | 0.844388i | \(-0.679964\pi\) | ||||
−0.535732 | + | 0.844388i | \(0.679964\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.71374e57 | −0.380879 | −0.190440 | − | 0.981699i | \(-0.560991\pi\) | ||||
−0.190440 | + | 0.981699i | \(0.560991\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.06879e58 | 0.738520 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.06309e58 | 2.35468 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.59417e56 | 0.00620759 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.23297e58 | 0.242140 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.09795e58 | 1.14585 | 0.572924 | − | 0.819609i | \(-0.305809\pi\) | ||||
0.572924 | + | 0.819609i | \(0.305809\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.44354e58 | 0.324763 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.28191e58 | 0.688426 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.39451e58 | −0.307196 | −0.153598 | − | 0.988133i | \(-0.549086\pi\) | ||||
−0.153598 | + | 0.988133i | \(0.549086\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.08981e59 | −0.815653 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.45587e58 | 0.400187 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.34522e59 | 1.20578 | 0.602890 | − | 0.797825i | \(-0.294016\pi\) | ||||
0.602890 | + | 0.797825i | \(0.294016\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.35091e59 | 2.71214 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.09740e58 | 0.0389798 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.15592e59 | −0.637826 | −0.318913 | − | 0.947784i | \(-0.603318\pi\) | ||||
−0.318913 | + | 0.947784i | \(0.603318\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.52922e59 | 0.870825 | 0.435413 | − | 0.900231i | \(-0.356602\pi\) | ||||
0.435413 | + | 0.900231i | \(0.356602\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.44704e57 | 0.0112247 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.34100e59 | 0.920389 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.94410e59 | 0.424813 | 0.212406 | − | 0.977181i | \(-0.431870\pi\) | ||||
0.212406 | + | 0.977181i | \(0.431870\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.32495e60 | 1.60287 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.56150e59 | 0.463237 | 0.231618 | − | 0.972807i | \(-0.425598\pi\) | ||||
0.231618 | + | 0.972807i | \(0.425598\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.39564e59 | −0.460548 | −0.230274 | − | 0.973126i | \(-0.573962\pi\) | ||||
−0.230274 | + | 0.973126i | \(0.573962\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.31837e59 | −0.0946977 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.13201e60 | 1.29028 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.33215e60 | 2.21160 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.36018e59 | −0.274215 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.90821e60 | 1.42469 | 0.712346 | − | 0.701828i | \(-0.247632\pi\) | ||||
0.712346 | + | 0.701828i | \(0.247632\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.61445e59 | 0.0806753 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.87808e60 | −0.491113 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.94174e58 | −0.00874468 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.49512e60 | 0.470123 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.92256e60 | 0.307989 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.58395e61 | −2.15971 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.34251e59 | −0.0272140 | −0.0136070 | − | 0.999907i | \(-0.504331\pi\) | ||||
−0.0136070 | + | 0.999907i | \(0.504331\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.47213e60 | 0.145869 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.35273e60 | 0.368241 | 0.184120 | − | 0.982904i | \(-0.441056\pi\) | ||||
0.184120 | + | 0.982904i | \(0.441056\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.93545e61 | 1.39941 | 0.699706 | − | 0.714431i | \(-0.253314\pi\) | ||||
0.699706 | + | 0.714431i | \(0.253314\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.44527e61 | 2.13115 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.36551e61 | 1.25306 | 0.626530 | − | 0.779397i | \(-0.284475\pi\) | ||||
0.626530 | + | 0.779397i | \(0.284475\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.90431e60 | −0.404323 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.05712e61 | 0.411861 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.32028e61 | −0.441778 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.61571e59 | −0.0247827 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.96844e59 | −0.00487196 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.12433e62 | −2.39658 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.39438e61 | −1.17493 | −0.587466 | − | 0.809249i | \(-0.699874\pi\) | ||||
−0.587466 | + | 0.809249i | \(0.699874\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.91364e61 | −0.461905 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.04750e61 | −1.10170 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.36305e61 | 1.10786 | 0.553930 | − | 0.832563i | \(-0.313128\pi\) | ||||
0.553930 | + | 0.832563i | \(0.313128\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.06232e60 | 0.0313442 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.82745e62 | −1.61944 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.42966e62 | −1.09781 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.00322e61 | 0.133401 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.31722e61 | 0.538535 | 0.269268 | − | 0.963065i | \(-0.413218\pi\) | ||||
0.269268 | + | 0.963065i | \(0.413218\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.03454e62 | 1.02151 | 0.510755 | − | 0.859726i | \(-0.329366\pi\) | ||||
0.510755 | + | 0.859726i | \(0.329366\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.02959e60 | 0.0132239 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.78134e62 | −1.05627 | −0.528133 | − | 0.849161i | \(-0.677108\pi\) | ||||
−0.528133 | + | 0.849161i | \(0.677108\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.10633e62 | 1.02719 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.77222e62 | −0.798835 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.25567e62 | −1.82332 | −0.911662 | − | 0.410942i | \(-0.865200\pi\) | ||||
−0.911662 | + | 0.410942i | \(0.865200\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.28251e62 | −0.939230 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.78546e61 | −0.0342010 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.87160e62 | −1.65277 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.66239e62 | 0.536347 | 0.268174 | − | 0.963371i | \(-0.413580\pi\) | ||||
0.268174 | + | 0.963371i | \(0.413580\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.70001e62 | 0.730685 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.80267e63 | −3.14711 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.01303e63 | 0.997140 | 0.498570 | − | 0.866850i | \(-0.333859\pi\) | ||||
0.498570 | + | 0.866850i | \(0.333859\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.04369e60 | −0.00608183 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.43638e61 | 0.0108869 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.10768e62 | 0.273486 | 0.136743 | − | 0.990607i | \(-0.456336\pi\) | ||||
0.136743 | + | 0.990607i | \(0.456336\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.36165e62 | 0.430837 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.90644e63 | 0.981415 | 0.490708 | − | 0.871324i | \(-0.336738\pi\) | ||||
0.490708 | + | 0.871324i | \(0.336738\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.75191e63 | −2.15318 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.67079e62 | 0.266231 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.21862e63 | 1.13215 | 0.566076 | − | 0.824353i | \(-0.308461\pi\) | ||||
0.566076 | + | 0.824353i | \(0.308461\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.00611e63 | 0.622336 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.73586e62 | 0.0475221 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.73466e63 | −0.661111 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.66988e63 | −0.356713 | −0.178356 | − | 0.983966i | \(-0.557078\pi\) | ||||
−0.178356 | + | 0.983966i | \(0.557078\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.81802e62 | 0.109885 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.21505e63 | −0.537218 | −0.268609 | − | 0.963249i | \(-0.586564\pi\) | ||||
−0.268609 | + | 0.963249i | \(0.586564\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.94791e62 | 0.0436055 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.41150e63 | 1.10211 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.01867e63 | 0.466680 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.21477e64 | 1.25104 | 0.625522 | − | 0.780207i | \(-0.284886\pi\) | ||||
0.625522 | + | 0.780207i | \(0.284886\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.33962e63 | −0.122422 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.15376e63 | −0.0936139 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.73511e64 | 1.25069 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.10196e63 | 0.262820 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.43742e63 | 0.537786 | 0.268893 | − | 0.963170i | \(-0.413342\pi\) | ||||
0.268893 | + | 0.963170i | \(0.413342\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.07535e63 | −0.358787 | −0.179394 | − | 0.983777i | \(-0.557414\pi\) | ||||
−0.179394 | + | 0.983777i | \(0.557414\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00593e64 | −1.35719 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.38489e64 | 1.76372 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.99002e64 | 2.50608 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.00860e62 | −0.00642228 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.47866e64 | −0.421867 | −0.210933 | − | 0.977500i | \(-0.567650\pi\) | ||||
−0.210933 | + | 0.977500i | \(0.567650\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.40840e64 | 1.37757 | 0.688787 | − | 0.724963i | \(-0.258143\pi\) | ||||
0.688787 | + | 0.724963i | \(0.258143\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.29978e63 | −0.166082 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.21020e63 | −0.0856066 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.69191e63 | 0.0671229 | 0.0335614 | − | 0.999437i | \(-0.489315\pi\) | ||||
0.0335614 | + | 0.999437i | \(0.489315\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.51316e64 | −1.54732 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.49563e64 | 1.09123 | 0.545616 | − | 0.838036i | \(-0.316296\pi\) | ||||
0.545616 | + | 0.838036i | \(0.316296\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.54434e64 | 0.201336 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.52437e64 | 0.294862 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.65052e64 | −0.591634 | −0.295817 | − | 0.955245i | \(-0.595592\pi\) | ||||
−0.295817 | + | 0.955245i | \(0.595592\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.86179e64 | −0.738238 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.12835e63 | −0.0263578 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.66544e63 | 0.0579773 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.93488e64 | 0.403148 | 0.201574 | − | 0.979473i | \(-0.435394\pi\) | ||||
0.201574 | + | 0.979473i | \(0.435394\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.54188e65 | −0.941109 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.06042e65 | 0.581840 | 0.290920 | − | 0.956747i | \(-0.406039\pi\) | ||||
0.290920 | + | 0.956747i | \(0.406039\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.86764e65 | −0.921637 | −0.460818 | − | 0.887495i | \(-0.652444\pi\) | ||||
−0.460818 | + | 0.887495i | \(0.652444\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.49815e65 | −0.665209 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.28278e64 | 0.0912432 | 0.0456216 | − | 0.998959i | \(-0.485473\pi\) | ||||
0.0456216 | + | 0.998959i | \(0.485473\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.55138e65 | 1.27839 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.50972e65 | 0.489648 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.20074e64 | −0.268983 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.20250e64 | −0.242612 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.49306e65 | −1.78221 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.07480e65 | 0.230732 | 0.115366 | − | 0.993323i | \(-0.463196\pi\) | ||||
0.115366 | + | 0.993323i | \(0.463196\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.48262e63 | −0.0125660 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.84026e64 | −0.154796 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.95047e65 | −1.41636 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.52950e64 | −0.136336 | −0.0681680 | − | 0.997674i | \(-0.521715\pi\) | ||||
−0.0681680 | + | 0.997674i | \(0.521715\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.70414e65 | 0.349915 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.75386e65 | −0.907865 | −0.453933 | − | 0.891036i | \(-0.649979\pi\) | ||||
−0.453933 | + | 0.891036i | \(0.649979\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.31033e65 | −0.774796 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.27044e66 | −1.21935 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.37083e66 | −1.19193 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.56740e66 | −1.23514 | −0.617569 | − | 0.786517i | \(-0.711882\pi\) | ||||
−0.617569 | + | 0.786517i | \(0.711882\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.14676e65 | 0.224822 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.11802e65 | 0.331655 | 0.165827 | − | 0.986155i | \(-0.446971\pi\) | ||||
0.165827 | + | 0.986155i | \(0.446971\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.70555e66 | 1.59081 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.10654e65 | −0.272541 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.63079e66 | −0.790335 | −0.395167 | − | 0.918609i | \(-0.629313\pi\) | ||||
−0.395167 | + | 0.918609i | \(0.629313\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.35636e66 | 1.91784 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.23592e65 | 0.129456 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.07168e66 | 0.753434 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.14595e66 | 1.37122 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.22010e64 | 0.0247330 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.56843e65 | 0.0977133 | 0.0488566 | − | 0.998806i | \(-0.484442\pi\) | ||||
0.0488566 | + | 0.998806i | \(0.484442\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.86554e65 | 0.196082 | 0.0980408 | − | 0.995182i | \(-0.468742\pi\) | ||||
0.0980408 | + | 0.995182i | \(0.468742\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.93227e66 | −0.438698 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.50031e67 | −3.10329 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.66501e66 | −0.879405 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.08463e65 | −0.0530136 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.26821e65 | 0.0198780 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.48765e67 | 2.12732 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.14202e65 | −0.0540558 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.31211e67 | 1.56331 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.49189e66 | 1.03281 | 0.516404 | − | 0.856345i | \(-0.327270\pi\) | ||||
0.516404 | + | 0.856345i | \(0.327270\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.14689e66 | −0.114005 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.77013e65 | −0.0251643 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.44217e67 | 1.19764 | 0.598819 | − | 0.800884i | \(-0.295637\pi\) | ||||
0.598819 | + | 0.800884i | \(0.295637\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.86881e67 | 1.41920 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.53421e66 | 0.106578 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.20681e67 | 0.767140 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.29451e66 | 0.191696 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.89683e65 | 0.0420727 | 0.0210364 | − | 0.999779i | \(-0.493303\pi\) | ||||
0.0210364 | + | 0.999779i | \(0.493303\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.48420e65 | 0.00724273 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.02226e67 | 0.457057 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.05636e67 | −0.842643 | −0.421321 | − | 0.906911i | \(-0.638434\pi\) | ||||
−0.421321 | + | 0.906911i | \(0.638434\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.30950e66 | 0.161897 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.71202e67 | −1.27887 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.99189e67 | −0.945573 | −0.472787 | − | 0.881177i | \(-0.656752\pi\) | ||||
−0.472787 | + | 0.881177i | \(0.656752\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.50438e67 | 0.436289 | 0.218144 | − | 0.975917i | \(-0.430000\pi\) | ||||
0.218144 | + | 0.975917i | \(0.430000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.03741e66 | 0.0808564 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.39828e67 | 0.341770 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.42499e67 | 0.319893 | 0.159947 | − | 0.987126i | \(-0.448868\pi\) | ||||
0.159947 | + | 0.987126i | \(0.448868\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.33259e66 | 0.192476 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.65710e67 | −1.45127 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.03349e68 | 1.80063 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.04939e66 | 0.0328326 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.53396e67 | 0.668104 | 0.334052 | − | 0.942555i | \(-0.391584\pi\) | ||||
0.334052 | + | 0.942555i | \(0.391584\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.14869e67 | 0.426879 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.87974e67 | −0.234534 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.39408e67 | 0.619552 | 0.309776 | − | 0.950810i | \(-0.399746\pi\) | ||||
0.309776 | + | 0.950810i | \(0.399746\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.90126e68 | −4.12609 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.19325e67 | −0.408488 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.84268e68 | 1.65383 | 0.826917 | − | 0.562323i | \(-0.190092\pi\) | ||||
0.826917 | + | 0.562323i | \(0.190092\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.15406e67 | −0.509023 | −0.254511 | − | 0.967070i | \(-0.581915\pi\) | ||||
−0.254511 | + | 0.967070i | \(0.581915\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.49476e67 | 0.723952 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.51262e67 | −0.176653 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.91666e68 | −1.89131 | −0.945654 | − | 0.325175i | \(-0.894577\pi\) | ||||
−0.945654 | + | 0.325175i | \(0.894577\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.22141e67 | 0.192718 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.68795e66 | −0.0369218 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.34057e68 | −0.683139 | −0.341569 | − | 0.939857i | \(-0.610958\pi\) | ||||
−0.341569 | + | 0.939857i | \(0.610958\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.44511e67 | −0.303243 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.63476e68 | −1.14487 | −0.572433 | − | 0.819951i | \(-0.694000\pi\) | ||||
−0.572433 | + | 0.819951i | \(0.694000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.18534e68 | −0.475799 | −0.237899 | − | 0.971290i | \(-0.576459\pi\) | ||||
−0.237899 | + | 0.971290i | \(0.576459\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.91686e67 | −0.182366 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.81520e67 | −0.233626 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.20461e68 | −1.01558 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.14539e67 | −0.0628713 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.29927e68 | 0.894288 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.68843e68 | −1.17573 | −0.587866 | − | 0.808959i | \(-0.700032\pi\) | ||||
−0.587866 | + | 0.808959i | \(0.700032\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.82380e68 | 0.423240 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.03598e69 | 2.22533 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.11660e67 | −0.0420943 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.66497e68 | −0.674993 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.45988e68 | −0.419654 | −0.209827 | − | 0.977738i | \(-0.567290\pi\) | ||||
−0.209827 | + | 0.977738i | \(0.567290\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.14694e68 | −0.971605 | −0.485803 | − | 0.874069i | \(-0.661473\pi\) | ||||
−0.485803 | + | 0.874069i | \(0.661473\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.54279e67 | −0.110489 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.77317e68 | 1.32703 | 0.663515 | − | 0.748163i | \(-0.269064\pi\) | ||||
0.663515 | + | 0.748163i | \(0.269064\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.25450e67 | 0.0535616 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.61138e68 | 0.771894 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.35256e67 | 0.0904580 | 0.0452290 | − | 0.998977i | \(-0.485598\pi\) | ||||
0.0452290 | + | 0.998977i | \(0.485598\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.44281e68 | 0.245459 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.16469e69 | 1.08607 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.35474e68 | 0.290380 | 0.145190 | − | 0.989404i | \(-0.453621\pi\) | ||||
0.145190 | + | 0.989404i | \(0.453621\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.63520e68 | 0.211776 | 0.105888 | − | 0.994378i | \(-0.466231\pi\) | ||||
0.105888 | + | 0.994378i | \(0.466231\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.64903e67 | −0.0123069 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.18751e68 | 0.567572 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.33117e68 | −0.150138 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.33852e67 | −0.0139959 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.57757e69 | −1.43387 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.25131e69 | 1.68147 | 0.840735 | − | 0.541447i | \(-0.182123\pi\) | ||||
0.840735 | + | 0.541447i | \(0.182123\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.07471e69 | −0.516831 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.82926e69 | −1.26547 | −0.632733 | − | 0.774370i | \(-0.718067\pi\) | ||||
−0.632733 | + | 0.774370i | \(0.718067\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.94987e69 | 1.64351 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.51909e68 | 0.213680 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.71804e69 | 0.979374 | 0.489687 | − | 0.871898i | \(-0.337111\pi\) | ||||
0.489687 | + | 0.871898i | \(0.337111\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.88521e69 | −0.632325 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.34089e68 | 0.260479 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.66715e68 | −0.0484845 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.43872e69 | 0.660618 | 0.330309 | − | 0.943873i | \(-0.392847\pi\) | ||||
0.330309 | + | 0.943873i | \(0.392847\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.60650e69 | 1.41491 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.77255e69 | 1.35750 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.45443e69 | −1.41467 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.72980e68 | −0.157935 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.63989e69 | 1.45544 | 0.727722 | − | 0.685872i | \(-0.240579\pi\) | ||||
0.727722 | + | 0.685872i | \(0.240579\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.92413e68 | −0.123015 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.39886e69 | 0.563248 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.19397e70 | −1.84594 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.36736e69 | 0.341533 | 0.170766 | − | 0.985312i | \(-0.445376\pi\) | ||||
0.170766 | + | 0.985312i | \(0.445376\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.22646e69 | 0.434432 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.78431e69 | −0.601348 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.82663e68 | −0.0331720 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.66627e69 | −0.292203 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.01007e69 | −0.922296 | −0.461148 | − | 0.887323i | \(-0.652562\pi\) | ||||
−0.461148 | + | 0.887323i | \(0.652562\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.14237e69 | −0.874269 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.16247e69 | −0.103871 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.09538e69 | −0.425496 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.12644e70 | −0.879257 | −0.439628 | − | 0.898180i | \(-0.644890\pi\) | ||||
−0.439628 | + | 0.898180i | \(0.644890\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.96172e69 | −0.581008 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.55369e69 | −0.515446 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.32996e69 | 0.276335 | 0.138168 | − | 0.990409i | \(-0.455879\pi\) | ||||
0.138168 | + | 0.990409i | \(0.455879\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.07567e70 | 0.642154 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.30957e70 | −0.731436 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.10376e70 | 1.09953 | 0.549766 | − | 0.835319i | \(-0.314717\pi\) | ||||
0.549766 | + | 0.835319i | \(0.314717\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.46080e67 | 0.00169289 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.09494e69 | −0.141718 | −0.0708592 | − | 0.997486i | \(-0.522574\pi\) | ||||
−0.0708592 | + | 0.997486i | \(0.522574\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.55247e70 | 1.52301 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.04716e70 | −0.821857 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.56504e70 | −2.46850 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.36292e70 | −0.832281 | −0.416140 | − | 0.909300i | \(-0.636617\pi\) | ||||
−0.416140 | + | 0.909300i | \(0.636617\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.46915e69 | 0.312488 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.40242e69 | −0.136142 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.84445e70 | 1.40409 | 0.702045 | − | 0.712132i | \(-0.252270\pi\) | ||||
0.702045 | + | 0.712132i | \(0.252270\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.25985e69 | 0.0885673 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.48623e70 | −0.378584 | −0.189292 | − | 0.981921i | \(-0.560619\pi\) | ||||
−0.189292 | + | 0.981921i | \(0.560619\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.22247e69 | 0.0292002 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.04302e71 | −2.33661 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.86305e67 | −0.00144222 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.67570e70 | −1.31614 | −0.658069 | − | 0.752957i | \(-0.728627\pi\) | ||||
−0.658069 | + | 0.752957i | \(0.728627\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.52850e69 | −0.0837765 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.33587e70 | 1.44728 | 0.723642 | − | 0.690176i | \(-0.242467\pi\) | ||||
0.723642 | + | 0.690176i | \(0.242467\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.04574e71 | −1.70424 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.45388e70 | −0.222440 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.35458e70 | 0.194597 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.05494e70 | 0.681970 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.79172e70 | 0.227042 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.12458e71 | 2.52910 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.52479e71 | 1.70541 | 0.852706 | − | 0.522390i | \(-0.174960\pi\) | ||||
0.852706 | + | 0.522390i | \(0.174960\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.12868e70 | 0.328833 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.90179e70 | −0.187862 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.15795e69 | 0.0386088 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.47254e70 | 0.739638 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.15352e70 | 0.669293 | 0.334647 | − | 0.942344i | \(-0.391383\pi\) | ||||
0.334647 | + | 0.942344i | \(0.391383\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.40377e71 | 2.62763 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.82207e70 | −0.132303 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.60641e71 | −1.09730 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.24406e71 | −0.799544 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.87615e70 | −0.173944 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.92840e71 | −1.66683 | −0.833416 | − | 0.552646i | \(-0.813618\pi\) | ||||
−0.833416 | + | 0.552646i | \(0.813618\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.95951e71 | −1.58565 | −0.792827 | − | 0.609446i | \(-0.791392\pi\) | ||||
−0.792827 | + | 0.609446i | \(0.791392\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.70822e70 | 0.237486 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.80545e71 | 1.80736 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.58528e70 | 0.0709031 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.04400e69 | −0.0380982 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.31367e71 | 0.918107 | 0.459053 | − | 0.888409i | \(-0.348189\pi\) | ||||
0.459053 | + | 0.888409i | \(0.348189\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.40957e70 | −0.0526976 | −0.0263488 | − | 0.999653i | \(-0.508388\pi\) | ||||
−0.0263488 | + | 0.999653i | \(0.508388\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.12525e70 | 0.251003 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.13935e71 | −1.04221 | −0.521105 | − | 0.853493i | \(-0.674480\pi\) | ||||
−0.521105 | + | 0.853493i | \(0.674480\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.00068e71 | −0.313118 | −0.156559 | − | 0.987669i | \(-0.550040\pi\) | ||||
−0.156559 | + | 0.987669i | \(0.550040\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.92762e70 | 0.115852 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.07722e72 | 2.99574 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.42833e71 | 1.16124 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.67718e71 | 0.909370 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.28357e70 | −0.169893 | −0.0849466 | − | 0.996386i | \(-0.527072\pi\) | ||||
−0.0849466 | + | 0.996386i | \(0.527072\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.69518e71 | −0.813081 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.08535e70 | 0.126331 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.18626e71 | −1.40771 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.10883e71 | 0.204984 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.19814e70 | −0.125598 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.05209e71 | 0.173293 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.12687e71 | −0.486249 | −0.243125 | − | 0.969995i | \(-0.578172\pi\) | ||||
−0.243125 | + | 0.969995i | \(0.578172\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.18896e71 | 0.321417 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.07117e72 | −1.48535 | −0.742675 | − | 0.669652i | \(-0.766443\pi\) | ||||
−0.742675 | + | 0.669652i | \(0.766443\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.94017e71 | −0.908945 | −0.454473 | − | 0.890761i | \(-0.650172\pi\) | ||||
−0.454473 | + | 0.890761i | \(0.650172\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.84425e71 | 0.351876 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.51616e72 | −1.77207 | −0.886037 | − | 0.463614i | \(-0.846552\pi\) | ||||
−0.886037 | + | 0.463614i | \(0.846552\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.15679e71 | 0.127749 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.77938e71 | 0.603134 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.45012e71 | −0.438922 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.11251e70 | 0.0196949 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.05601e72 | 0.930723 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.37435e70 | 0.0364516 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.82968e72 | −1.44173 | −0.720867 | − | 0.693073i | \(-0.756256\pi\) | ||||
−0.720867 | + | 0.693073i | \(0.756256\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.21382e71 | 0.388533 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.23192e71 | 0.580218 | 0.290109 | − | 0.956994i | \(-0.406308\pi\) | ||||
0.290109 | + | 0.956994i | \(0.406308\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.32646e72 | −1.55116 | −0.775582 | − | 0.631247i | \(-0.782544\pi\) | ||||
−0.775582 | + | 0.631247i | \(0.782544\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.48785e70 | 0.0220013 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.02329e72 | −1.20762 | −0.603809 | − | 0.797129i | \(-0.706351\pi\) | ||||
−0.603809 | + | 0.797129i | \(0.706351\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.57181e72 | −2.58223 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.36881e72 | 0.731709 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.14344e71 | −0.361449 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.82893e71 | −0.279206 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.25855e69 | −0.00238479 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.74341e72 | 0.748666 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.48479e72 | 3.45051 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.32865e71 | 0.128209 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.61398e72 | −0.588854 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.38576e72 | −1.86152 | −0.930762 | − | 0.365627i | \(-0.880855\pi\) | ||||
−0.930762 | + | 0.365627i | \(0.880855\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.19212e72 | −1.04536 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.00433e72 | 1.24260 | 0.621298 | − | 0.783574i | \(-0.286606\pi\) | ||||
0.621298 | + | 0.783574i | \(0.286606\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.82356e72 | 0.830352 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.11310e72 | −0.588983 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.07802e72 | −0.284825 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.26307e72 | 1.56876 | 0.784381 | − | 0.620279i | \(-0.212981\pi\) | ||||
0.784381 | + | 0.620279i | \(0.212981\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.12507e70 | −0.00742162 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.15426e70 | −0.0183630 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.29963e72 | 0.491118 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.44425e72 | −0.495099 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.00047e72 | −0.576508 | −0.288254 | − | 0.957554i | \(-0.593075\pi\) | ||||
−0.288254 | + | 0.957554i | \(0.593075\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.26075e72 | −0.412084 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.80684e71 | 0.100424 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.43859e73 | 2.36076 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.72864e72 | −0.580671 | −0.290336 | − | 0.956925i | \(-0.593767\pi\) | ||||
−0.290336 | + | 0.956925i | \(0.593767\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.58202e72 | 0.381639 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.09160e72 | −0.293449 | −0.146724 | − | 0.989177i | \(-0.546873\pi\) | ||||
−0.146724 | + | 0.989177i | \(0.546873\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.05823e72 | −0.274131 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.56174e72 | 1.20909 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.20140e72 | −0.984721 | −0.492361 | − | 0.870391i | \(-0.663866\pi\) | ||||
−0.492361 | + | 0.870391i | \(0.663866\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.59134e71 | 0.0295463 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.15574e72 | 0.341727 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.17749e73 | 1.21110 | 0.605549 | − | 0.795808i | \(-0.292953\pi\) | ||||
0.605549 | + | 0.795808i | \(0.292953\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.27444e72 | 0.417635 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.18790e72 | −0.110265 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.31948e72 | 0.733737 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.38482e73 | 1.99863 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.75519e73 | −1.39791 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.31334e73 | 0.994168 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.48982e72 | 0.251105 | 0.125552 | − | 0.992087i | \(-0.459930\pi\) | ||||
0.125552 | + | 0.992087i | \(0.459930\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.76134e72 | −0.120479 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.02593e73 | 1.31751 | 0.658753 | − | 0.752359i | \(-0.271084\pi\) | ||||
0.658753 | + | 0.752359i | \(0.271084\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.54744e73 | −1.57521 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.14939e71 | −0.00675859 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.10677e73 | −0.618926 | −0.309463 | − | 0.950911i | \(-0.600149\pi\) | ||||
−0.309463 | + | 0.950911i | \(0.600149\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.51311e72 | 0.133670 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.26831e71 | 0.0165361 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.73348e72 | 0.324100 | 0.162050 | − | 0.986783i | \(-0.448189\pi\) | ||||
0.162050 | + | 0.986783i | \(0.448189\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.64530e73 | −1.21140 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.49993e73 | −0.653582 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.40877e72 | −0.0998819 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.62295e73 | 1.03511 | 0.517554 | − | 0.855650i | \(-0.326843\pi\) | ||||
0.517554 | + | 0.855650i | \(0.326843\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.53053e72 | −0.320420 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.90102e73 | −2.10990 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.54966e73 | 0.867864 | 0.433932 | − | 0.900946i | \(-0.357126\pi\) | ||||
0.433932 | + | 0.900946i | \(0.357126\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.08631e72 | −0.262057 |
(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 | 16.50.a.b.1.2 | 3 | ||
4.3 | odd | 2 | 2.50.a.b.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.50.a.b.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
16.50.a.b.1.2 | 3 | 1.1 | even | 1 | trivial |