Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,50,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 50, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 50);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 50 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(30.4132410198\) |
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: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.42020e8\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.67772e7 | 0.707107 | ||||||||
\(3\) | −1.33407e11 | −0.272714 | −0.136357 | − | 0.990660i | \(-0.543539\pi\) | ||||
−0.136357 | + | 0.990660i | \(0.543539\pi\) | |||||||
\(4\) | 2.81475e14 | 0.500000 | ||||||||
\(5\) | 1.87739e17 | 1.40860 | 0.704302 | − | 0.709900i | \(-0.251260\pi\) | ||||
0.704302 | + | 0.709900i | \(0.251260\pi\) | |||||||
\(6\) | −2.23819e18 | −0.192838 | ||||||||
\(7\) | 8.28497e20 | 1.63452 | 0.817258 | − | 0.576272i | \(-0.195493\pi\) | ||||
0.817258 | + | 0.576272i | \(0.195493\pi\) | |||||||
\(8\) | 4.72237e21 | 0.353553 | ||||||||
\(9\) | −2.21502e23 | −0.925627 | ||||||||
\(10\) | 3.14974e24 | 0.996034 | ||||||||
\(11\) | −3.05508e25 | −0.935195 | −0.467598 | − | 0.883941i | \(-0.654880\pi\) | ||||
−0.467598 | + | 0.883941i | \(0.654880\pi\) | |||||||
\(12\) | −3.75507e25 | −0.136357 | ||||||||
\(13\) | −4.92824e25 | −0.0251814 | −0.0125907 | − | 0.999921i | \(-0.504008\pi\) | ||||
−0.0125907 | + | 0.999921i | \(0.504008\pi\) | |||||||
\(14\) | 1.38999e28 | 1.15578 | ||||||||
\(15\) | −2.50456e28 | −0.384146 | ||||||||
\(16\) | 7.92282e28 | 0.250000 | ||||||||
\(17\) | 2.50818e30 | 1.79209 | 0.896047 | − | 0.443959i | \(-0.146427\pi\) | ||||
0.896047 | + | 0.443959i | \(0.146427\pi\) | |||||||
\(18\) | −3.71619e30 | −0.654517 | ||||||||
\(19\) | 5.26388e30 | 0.246515 | 0.123257 | − | 0.992375i | \(-0.460666\pi\) | ||||
0.123257 | + | 0.992375i | \(0.460666\pi\) | |||||||
\(20\) | 5.28438e31 | 0.704302 | ||||||||
\(21\) | −1.10527e32 | −0.445755 | ||||||||
\(22\) | −5.12558e32 | −0.661283 | ||||||||
\(23\) | −7.99827e32 | −0.347268 | −0.173634 | − | 0.984810i | \(-0.555551\pi\) | ||||
−0.173634 | + | 0.984810i | \(0.555551\pi\) | |||||||
\(24\) | −6.29996e32 | −0.0964189 | ||||||||
\(25\) | 1.74823e34 | 0.984168 | ||||||||
\(26\) | −8.26821e32 | −0.0178059 | ||||||||
\(27\) | 6.14740e34 | 0.525145 | ||||||||
\(28\) | 2.33201e35 | 0.817258 | ||||||||
\(29\) | −2.91459e35 | −0.432341 | −0.216171 | − | 0.976356i | \(-0.569357\pi\) | ||||
−0.216171 | + | 0.976356i | \(0.569357\pi\) | |||||||
\(30\) | −4.20196e35 | −0.271632 | ||||||||
\(31\) | 5.98168e36 | 1.73166 | 0.865828 | − | 0.500342i | \(-0.166792\pi\) | ||||
0.865828 | + | 0.500342i | \(0.166792\pi\) | |||||||
\(32\) | 1.32923e36 | 0.176777 | ||||||||
\(33\) | 4.07569e36 | 0.255041 | ||||||||
\(34\) | 4.20803e37 | 1.26720 | ||||||||
\(35\) | 1.55541e38 | 2.30239 | ||||||||
\(36\) | −6.23473e37 | −0.462814 | ||||||||
\(37\) | 1.31540e38 | 0.499018 | 0.249509 | − | 0.968372i | \(-0.419731\pi\) | ||||
0.249509 | + | 0.968372i | \(0.419731\pi\) | |||||||
\(38\) | 8.83133e37 | 0.174312 | ||||||||
\(39\) | 6.57461e36 | 0.00686731 | ||||||||
\(40\) | 8.86572e38 | 0.498017 | ||||||||
\(41\) | −2.57335e39 | −0.789394 | −0.394697 | − | 0.918811i | \(-0.629150\pi\) | ||||
−0.394697 | + | 0.918811i | \(0.629150\pi\) | |||||||
\(42\) | −1.85434e39 | −0.315196 | ||||||||
\(43\) | 3.01162e39 | 0.287622 | 0.143811 | − | 0.989605i | \(-0.454064\pi\) | ||||
0.143811 | + | 0.989605i | \(0.454064\pi\) | |||||||
\(44\) | −8.59930e39 | −0.467598 | ||||||||
\(45\) | −4.15845e40 | −1.30384 | ||||||||
\(46\) | −1.34189e40 | −0.245555 | ||||||||
\(47\) | −1.35707e41 | −1.46624 | −0.733118 | − | 0.680102i | \(-0.761936\pi\) | ||||
−0.733118 | + | 0.680102i | \(0.761936\pi\) | |||||||
\(48\) | −1.05696e40 | −0.0681784 | ||||||||
\(49\) | 4.29484e41 | 1.67164 | ||||||||
\(50\) | 2.93305e41 | 0.695912 | ||||||||
\(51\) | −3.34609e41 | −0.488729 | ||||||||
\(52\) | −1.38718e40 | −0.0125907 | ||||||||
\(53\) | 3.38284e42 | 1.92541 | 0.962704 | − | 0.270557i | \(-0.0872079\pi\) | ||||
0.962704 | + | 0.270557i | \(0.0872079\pi\) | |||||||
\(54\) | 1.03136e42 | 0.371334 | ||||||||
\(55\) | −5.73558e42 | −1.31732 | ||||||||
\(56\) | 3.91247e42 | 0.577889 | ||||||||
\(57\) | −7.02238e41 | −0.0672280 | ||||||||
\(58\) | −4.88987e42 | −0.305711 | ||||||||
\(59\) | −1.39260e42 | −0.0572732 | −0.0286366 | − | 0.999590i | \(-0.509117\pi\) | ||||
−0.0286366 | + | 0.999590i | \(0.509117\pi\) | |||||||
\(60\) | −7.04972e42 | −0.192073 | ||||||||
\(61\) | −8.43699e43 | −1.53323 | −0.766614 | − | 0.642108i | \(-0.778060\pi\) | ||||
−0.766614 | + | 0.642108i | \(0.778060\pi\) | |||||||
\(62\) | 1.00356e44 | 1.22447 | ||||||||
\(63\) | −1.83514e44 | −1.51295 | ||||||||
\(64\) | 2.23007e43 | 0.125000 | ||||||||
\(65\) | −9.25222e42 | −0.0354706 | ||||||||
\(66\) | 6.83787e43 | 0.180341 | ||||||||
\(67\) | 4.28654e44 | 0.782121 | 0.391060 | − | 0.920365i | \(-0.372108\pi\) | ||||
0.391060 | + | 0.920365i | \(0.372108\pi\) | |||||||
\(68\) | 7.05991e44 | 0.896047 | ||||||||
\(69\) | 1.06702e44 | 0.0947046 | ||||||||
\(70\) | 2.60955e45 | 1.62803 | ||||||||
\(71\) | −1.65460e45 | −0.729228 | −0.364614 | − | 0.931159i | \(-0.618799\pi\) | ||||
−0.364614 | + | 0.931159i | \(0.618799\pi\) | |||||||
\(72\) | −1.04601e45 | −0.327259 | ||||||||
\(73\) | −5.25815e45 | −1.17334 | −0.586669 | − | 0.809827i | \(-0.699561\pi\) | ||||
−0.586669 | + | 0.809827i | \(0.699561\pi\) | |||||||
\(74\) | 2.20688e45 | 0.352859 | ||||||||
\(75\) | −2.33226e45 | −0.268396 | ||||||||
\(76\) | 1.48165e45 | 0.123257 | ||||||||
\(77\) | −2.53113e46 | −1.52859 | ||||||||
\(78\) | 1.10304e44 | 0.00485592 | ||||||||
\(79\) | 1.45663e46 | 0.469338 | 0.234669 | − | 0.972075i | \(-0.424599\pi\) | ||||
0.234669 | + | 0.972075i | \(0.424599\pi\) | |||||||
\(80\) | 1.48742e46 | 0.352151 | ||||||||
\(81\) | 4.48042e46 | 0.782413 | ||||||||
\(82\) | −4.31736e46 | −0.558186 | ||||||||
\(83\) | −9.24216e46 | −0.887892 | −0.443946 | − | 0.896054i | \(-0.646422\pi\) | ||||
−0.443946 | + | 0.896054i | \(0.646422\pi\) | |||||||
\(84\) | −3.11106e46 | −0.222877 | ||||||||
\(85\) | 4.70884e47 | 2.52435 | ||||||||
\(86\) | 5.05265e46 | 0.203380 | ||||||||
\(87\) | 3.88826e46 | 0.117905 | ||||||||
\(88\) | −1.44272e47 | −0.330641 | ||||||||
\(89\) | 8.22598e46 | 0.142933 | 0.0714665 | − | 0.997443i | \(-0.477232\pi\) | ||||
0.0714665 | + | 0.997443i | \(0.477232\pi\) | |||||||
\(90\) | −6.97673e47 | −0.921956 | ||||||||
\(91\) | −4.08303e46 | −0.0411594 | ||||||||
\(92\) | −2.25131e47 | −0.173634 | ||||||||
\(93\) | −7.97996e47 | −0.472246 | ||||||||
\(94\) | −2.27678e48 | −1.03678 | ||||||||
\(95\) | 9.88236e47 | 0.347242 | ||||||||
\(96\) | −1.77328e47 | −0.0482094 | ||||||||
\(97\) | −4.76751e48 | −1.00551 | −0.502753 | − | 0.864430i | \(-0.667679\pi\) | ||||
−0.502753 | + | 0.864430i | \(0.667679\pi\) | |||||||
\(98\) | 7.20555e48 | 1.18203 | ||||||||
\(99\) | 6.76707e48 | 0.865642 | ||||||||
\(100\) | 4.92084e48 | 0.492084 | ||||||||
\(101\) | 1.44113e49 | 1.12935 | 0.564674 | − | 0.825314i | \(-0.309002\pi\) | ||||
0.564674 | + | 0.825314i | \(0.309002\pi\) | |||||||
\(102\) | −5.61380e48 | −0.345583 | ||||||||
\(103\) | −1.10349e49 | −0.534879 | −0.267440 | − | 0.963575i | \(-0.586178\pi\) | ||||
−0.267440 | + | 0.963575i | \(0.586178\pi\) | |||||||
\(104\) | −2.32730e47 | −0.00890297 | ||||||||
\(105\) | −2.07502e49 | −0.627893 | ||||||||
\(106\) | 5.67547e49 | 1.36147 | ||||||||
\(107\) | −7.92403e49 | −1.51023 | −0.755116 | − | 0.655591i | \(-0.772419\pi\) | ||||
−0.755116 | + | 0.655591i | \(0.772419\pi\) | |||||||
\(108\) | 1.73034e49 | 0.262573 | ||||||||
\(109\) | −1.47552e48 | −0.0178647 | −0.00893236 | − | 0.999960i | \(-0.502843\pi\) | ||||
−0.00893236 | + | 0.999960i | \(0.502843\pi\) | |||||||
\(110\) | −9.62271e49 | −0.931486 | ||||||||
\(111\) | −1.75484e49 | −0.136089 | ||||||||
\(112\) | 6.56403e49 | 0.408629 | ||||||||
\(113\) | 2.29547e49 | 0.114935 | 0.0574673 | − | 0.998347i | \(-0.481698\pi\) | ||||
0.0574673 | + | 0.998347i | \(0.481698\pi\) | |||||||
\(114\) | −1.17816e49 | −0.0475374 | ||||||||
\(115\) | −1.50159e50 | −0.489163 | ||||||||
\(116\) | −8.20384e49 | −0.216171 | ||||||||
\(117\) | 1.09161e49 | 0.0233086 | ||||||||
\(118\) | −2.33639e49 | −0.0404982 | ||||||||
\(119\) | 2.07802e51 | 2.92921 | ||||||||
\(120\) | −1.18275e50 | −0.135816 | ||||||||
\(121\) | −1.33836e50 | −0.125410 | ||||||||
\(122\) | −1.41549e51 | −1.08416 | ||||||||
\(123\) | 3.43302e50 | 0.215279 | ||||||||
\(124\) | 1.68369e51 | 0.865828 | ||||||||
\(125\) | −5.27986e49 | −0.0223011 | ||||||||
\(126\) | −3.07885e51 | −1.06982 | ||||||||
\(127\) | −5.51820e51 | −1.57981 | −0.789907 | − | 0.613227i | \(-0.789871\pi\) | ||||
−0.789907 | + | 0.613227i | \(0.789871\pi\) | |||||||
\(128\) | 3.74144e50 | 0.0883883 | ||||||||
\(129\) | −4.01770e50 | −0.0784385 | ||||||||
\(130\) | −1.55227e50 | −0.0250815 | ||||||||
\(131\) | −1.30117e51 | −0.174256 | −0.0871282 | − | 0.996197i | \(-0.527769\pi\) | ||||
−0.0871282 | + | 0.996197i | \(0.527769\pi\) | |||||||
\(132\) | 1.14720e51 | 0.127520 | ||||||||
\(133\) | 4.36111e51 | 0.402932 | ||||||||
\(134\) | 7.19162e51 | 0.553043 | ||||||||
\(135\) | 1.15411e52 | 0.739722 | ||||||||
\(136\) | 1.18446e52 | 0.633601 | ||||||||
\(137\) | −1.00417e52 | −0.448902 | −0.224451 | − | 0.974485i | \(-0.572059\pi\) | ||||
−0.224451 | + | 0.974485i | \(0.572059\pi\) | |||||||
\(138\) | 1.79017e51 | 0.0669663 | ||||||||
\(139\) | −3.07477e52 | −0.963719 | −0.481860 | − | 0.876248i | \(-0.660038\pi\) | ||||
−0.481860 | + | 0.876248i | \(0.660038\pi\) | |||||||
\(140\) | 4.37809e52 | 1.15119 | ||||||||
\(141\) | 1.81042e52 | 0.399863 | ||||||||
\(142\) | −2.77596e52 | −0.515642 | ||||||||
\(143\) | 1.50562e51 | 0.0235495 | ||||||||
\(144\) | −1.75492e52 | −0.231407 | ||||||||
\(145\) | −5.47182e52 | −0.608998 | ||||||||
\(146\) | −8.82172e52 | −0.829675 | ||||||||
\(147\) | −5.72961e52 | −0.455880 | ||||||||
\(148\) | 3.70253e52 | 0.249509 | ||||||||
\(149\) | 1.89224e53 | 1.08122 | 0.540608 | − | 0.841275i | \(-0.318194\pi\) | ||||
0.540608 | + | 0.841275i | \(0.318194\pi\) | |||||||
\(150\) | −3.91289e52 | −0.189785 | ||||||||
\(151\) | 2.34497e52 | 0.0966500 | 0.0483250 | − | 0.998832i | \(-0.484612\pi\) | ||||
0.0483250 | + | 0.998832i | \(0.484612\pi\) | |||||||
\(152\) | 2.48580e52 | 0.0871562 | ||||||||
\(153\) | −5.55568e53 | −1.65881 | ||||||||
\(154\) | −4.24653e53 | −1.08088 | ||||||||
\(155\) | 1.12299e54 | 2.43922 | ||||||||
\(156\) | 1.85059e51 | 0.00343366 | ||||||||
\(157\) | 1.13167e54 | 1.79546 | 0.897732 | − | 0.440542i | \(-0.145214\pi\) | ||||
0.897732 | + | 0.440542i | \(0.145214\pi\) | |||||||
\(158\) | 2.44382e53 | 0.331872 | ||||||||
\(159\) | −4.51294e53 | −0.525085 | ||||||||
\(160\) | 2.49548e53 | 0.249009 | ||||||||
\(161\) | −6.62655e53 | −0.567614 | ||||||||
\(162\) | 7.51690e53 | 0.553249 | ||||||||
\(163\) | −2.02699e54 | −1.28308 | −0.641542 | − | 0.767088i | \(-0.721705\pi\) | ||||
−0.641542 | + | 0.767088i | \(0.721705\pi\) | |||||||
\(164\) | −7.24333e53 | −0.394697 | ||||||||
\(165\) | 7.65165e53 | 0.359252 | ||||||||
\(166\) | −1.55058e54 | −0.627834 | ||||||||
\(167\) | −2.35877e54 | −0.824389 | −0.412194 | − | 0.911096i | \(-0.635238\pi\) | ||||
−0.412194 | + | 0.911096i | \(0.635238\pi\) | |||||||
\(168\) | −5.21950e53 | −0.157598 | ||||||||
\(169\) | −3.82780e54 | −0.999366 | ||||||||
\(170\) | 7.90012e54 | 1.78499 | ||||||||
\(171\) | −1.16596e54 | −0.228181 | ||||||||
\(172\) | 8.47695e53 | 0.143811 | ||||||||
\(173\) | 6.16168e53 | 0.0906921 | 0.0453461 | − | 0.998971i | \(-0.485561\pi\) | ||||
0.0453461 | + | 0.998971i | \(0.485561\pi\) | |||||||
\(174\) | 6.52342e53 | 0.0833717 | ||||||||
\(175\) | 1.44841e55 | 1.60864 | ||||||||
\(176\) | −2.42049e54 | −0.233799 | ||||||||
\(177\) | 1.85782e53 | 0.0156192 | ||||||||
\(178\) | 1.38009e54 | 0.101069 | ||||||||
\(179\) | 3.10481e54 | 0.198215 | 0.0991073 | − | 0.995077i | \(-0.468401\pi\) | ||||
0.0991073 | + | 0.995077i | \(0.468401\pi\) | |||||||
\(180\) | −1.17050e55 | −0.651922 | ||||||||
\(181\) | −8.59693e54 | −0.418041 | −0.209020 | − | 0.977911i | \(-0.567027\pi\) | ||||
−0.209020 | + | 0.977911i | \(0.567027\pi\) | |||||||
\(182\) | −6.85019e53 | −0.0291041 | ||||||||
\(183\) | 1.12555e55 | 0.418132 | ||||||||
\(184\) | −3.77708e54 | −0.122778 | ||||||||
\(185\) | 2.46952e55 | 0.702920 | ||||||||
\(186\) | −1.33882e55 | −0.333929 | ||||||||
\(187\) | −7.66271e55 | −1.67596 | ||||||||
\(188\) | −3.81980e55 | −0.733118 | ||||||||
\(189\) | 5.09310e55 | 0.858358 | ||||||||
\(190\) | 1.65798e55 | 0.245537 | ||||||||
\(191\) | −2.27680e55 | −0.296488 | −0.148244 | − | 0.988951i | \(-0.547362\pi\) | ||||
−0.148244 | + | 0.988951i | \(0.547362\pi\) | |||||||
\(192\) | −2.97507e54 | −0.0340892 | ||||||||
\(193\) | 6.99559e55 | 0.705782 | 0.352891 | − | 0.935664i | \(-0.385199\pi\) | ||||
0.352891 | + | 0.935664i | \(0.385199\pi\) | |||||||
\(194\) | −7.99856e55 | −0.710999 | ||||||||
\(195\) | 1.23431e54 | 0.00967333 | ||||||||
\(196\) | 1.20889e56 | 0.835821 | ||||||||
\(197\) | −1.40903e56 | −0.860000 | −0.430000 | − | 0.902829i | \(-0.641486\pi\) | ||||
−0.430000 | + | 0.902829i | \(0.641486\pi\) | |||||||
\(198\) | 1.13533e56 | 0.612101 | ||||||||
\(199\) | 3.14321e56 | 1.49786 | 0.748932 | − | 0.662647i | \(-0.230567\pi\) | ||||
0.748932 | + | 0.662647i | \(0.230567\pi\) | |||||||
\(200\) | 8.25580e55 | 0.347956 | ||||||||
\(201\) | −5.71853e55 | −0.213295 | ||||||||
\(202\) | 2.41781e56 | 0.798570 | ||||||||
\(203\) | −2.41473e56 | −0.706668 | ||||||||
\(204\) | −9.41840e55 | −0.244364 | ||||||||
\(205\) | −4.83117e56 | −1.11194 | ||||||||
\(206\) | −1.85135e56 | −0.378217 | ||||||||
\(207\) | 1.77163e56 | 0.321440 | ||||||||
\(208\) | −3.90455e54 | −0.00629535 | ||||||||
\(209\) | −1.60816e56 | −0.230539 | ||||||||
\(210\) | −3.48131e56 | −0.443987 | ||||||||
\(211\) | −1.36710e57 | −1.55196 | −0.775978 | − | 0.630760i | \(-0.782743\pi\) | ||||
−0.775978 | + | 0.630760i | \(0.782743\pi\) | |||||||
\(212\) | 9.52185e56 | 0.962704 | ||||||||
\(213\) | 2.20735e56 | 0.198870 | ||||||||
\(214\) | −1.32943e57 | −1.06790 | ||||||||
\(215\) | 5.65398e56 | 0.405146 | ||||||||
\(216\) | 2.90303e56 | 0.185667 | ||||||||
\(217\) | 4.95580e57 | 2.83042 | ||||||||
\(218\) | −2.47551e55 | −0.0126323 | ||||||||
\(219\) | 7.01473e56 | 0.319985 | ||||||||
\(220\) | −1.61442e57 | −0.658660 | ||||||||
\(221\) | −1.23609e56 | −0.0451274 | ||||||||
\(222\) | −2.94413e56 | −0.0962296 | ||||||||
\(223\) | 1.75293e56 | 0.0513210 | 0.0256605 | − | 0.999671i | \(-0.491831\pi\) | ||||
0.0256605 | + | 0.999671i | \(0.491831\pi\) | |||||||
\(224\) | 1.10126e57 | 0.288944 | ||||||||
\(225\) | −3.87237e57 | −0.910973 | ||||||||
\(226\) | 3.85117e56 | 0.0812710 | ||||||||
\(227\) | −4.13704e57 | −0.783531 | −0.391765 | − | 0.920065i | \(-0.628135\pi\) | ||||
−0.391765 | + | 0.920065i | \(0.628135\pi\) | |||||||
\(228\) | −1.97662e56 | −0.0336140 | ||||||||
\(229\) | 6.25222e57 | 0.955136 | 0.477568 | − | 0.878595i | \(-0.341518\pi\) | ||||
0.477568 | + | 0.878595i | \(0.341518\pi\) | |||||||
\(230\) | −2.51924e57 | −0.345890 | ||||||||
\(231\) | 3.37670e57 | 0.416868 | ||||||||
\(232\) | −1.37638e57 | −0.152856 | ||||||||
\(233\) | −5.79416e57 | −0.579123 | −0.289561 | − | 0.957159i | \(-0.593509\pi\) | ||||
−0.289561 | + | 0.957159i | \(0.593509\pi\) | |||||||
\(234\) | 1.83143e56 | 0.0164817 | ||||||||
\(235\) | −2.54774e58 | −2.06535 | ||||||||
\(236\) | −3.91981e56 | −0.0286366 | ||||||||
\(237\) | −1.94324e57 | −0.127995 | ||||||||
\(238\) | 3.48634e58 | 2.07126 | ||||||||
\(239\) | 1.99860e58 | 1.07146 | 0.535732 | − | 0.844388i | \(-0.320036\pi\) | ||||
0.535732 | + | 0.844388i | \(0.320036\pi\) | |||||||
\(240\) | −1.98432e57 | −0.0960365 | ||||||||
\(241\) | −8.71374e57 | −0.380879 | −0.190440 | − | 0.981699i | \(-0.560991\pi\) | ||||
−0.190440 | + | 0.981699i | \(0.560991\pi\) | |||||||
\(242\) | −2.24540e57 | −0.0886782 | ||||||||
\(243\) | −2.06879e58 | −0.738520 | ||||||||
\(244\) | −2.37480e58 | −0.766614 | ||||||||
\(245\) | 8.06309e58 | 2.35468 | ||||||||
\(246\) | 5.75965e57 | 0.152225 | ||||||||
\(247\) | −2.59417e56 | −0.00620759 | ||||||||
\(248\) | 2.82477e58 | 0.612233 | ||||||||
\(249\) | 1.23297e58 | 0.242140 | ||||||||
\(250\) | −8.85813e56 | −0.0157693 | ||||||||
\(251\) | −7.09795e58 | −1.14585 | −0.572924 | − | 0.819609i | \(-0.694191\pi\) | ||||
−0.572924 | + | 0.819609i | \(0.694191\pi\) | |||||||
\(252\) | −5.16545e58 | −0.756476 | ||||||||
\(253\) | 2.44354e58 | 0.324763 | ||||||||
\(254\) | −9.25800e58 | −1.11710 | ||||||||
\(255\) | −6.28191e58 | −0.688426 | ||||||||
\(256\) | 6.27710e57 | 0.0625000 | ||||||||
\(257\) | −3.39451e58 | −0.307196 | −0.153598 | − | 0.988133i | \(-0.549086\pi\) | ||||
−0.153598 | + | 0.988133i | \(0.549086\pi\) | |||||||
\(258\) | −6.74058e57 | −0.0554644 | ||||||||
\(259\) | 1.08981e59 | 0.815653 | ||||||||
\(260\) | −2.60427e57 | −0.0177353 | ||||||||
\(261\) | 6.45587e58 | 0.400187 | ||||||||
\(262\) | −2.18301e58 | −0.123218 | ||||||||
\(263\) | −2.34522e59 | −1.20578 | −0.602890 | − | 0.797825i | \(-0.705984\pi\) | ||||
−0.602890 | + | 0.797825i | \(0.705984\pi\) | |||||||
\(264\) | 1.92469e58 | 0.0901705 | ||||||||
\(265\) | 6.35091e59 | 2.71214 | ||||||||
\(266\) | 7.31673e58 | 0.284916 | ||||||||
\(267\) | −1.09740e58 | −0.0389798 | ||||||||
\(268\) | 1.20655e59 | 0.391060 | ||||||||
\(269\) | −2.15592e59 | −0.637826 | −0.318913 | − | 0.947784i | \(-0.603318\pi\) | ||||
−0.318913 | + | 0.947784i | \(0.603318\pi\) | |||||||
\(270\) | 1.93627e59 | 0.523062 | ||||||||
\(271\) | −3.52922e59 | −0.870825 | −0.435413 | − | 0.900231i | \(-0.643398\pi\) | ||||
−0.435413 | + | 0.900231i | \(0.643398\pi\) | |||||||
\(272\) | 1.98719e59 | 0.448023 | ||||||||
\(273\) | 5.44704e57 | 0.0112247 | ||||||||
\(274\) | −1.68471e59 | −0.317421 | ||||||||
\(275\) | −5.34100e59 | −0.920389 | ||||||||
\(276\) | 3.00340e58 | 0.0473523 | ||||||||
\(277\) | 2.94410e59 | 0.424813 | 0.212406 | − | 0.977181i | \(-0.431870\pi\) | ||||
0.212406 | + | 0.977181i | \(0.431870\pi\) | |||||||
\(278\) | −5.15861e59 | −0.681452 | ||||||||
\(279\) | −1.32495e60 | −1.60287 | ||||||||
\(280\) | 7.34522e59 | 0.814017 | ||||||||
\(281\) | 4.56150e59 | 0.463237 | 0.231618 | − | 0.972807i | \(-0.425598\pi\) | ||||
0.231618 | + | 0.972807i | \(0.425598\pi\) | |||||||
\(282\) | 3.03738e59 | 0.282746 | ||||||||
\(283\) | 5.39564e59 | 0.460548 | 0.230274 | − | 0.973126i | \(-0.426038\pi\) | ||||
0.230274 | + | 0.973126i | \(0.426038\pi\) | |||||||
\(284\) | −4.65728e59 | −0.364614 | ||||||||
\(285\) | −1.31837e59 | −0.0946977 | ||||||||
\(286\) | 2.52601e58 | 0.0166520 | ||||||||
\(287\) | −2.13201e60 | −1.29028 | ||||||||
\(288\) | −2.94427e59 | −0.163629 | ||||||||
\(289\) | 4.33215e60 | 2.21160 | ||||||||
\(290\) | −9.18019e59 | −0.430626 | ||||||||
\(291\) | 6.36018e59 | 0.274215 | ||||||||
\(292\) | −1.48004e60 | −0.586669 | ||||||||
\(293\) | 3.90821e60 | 1.42469 | 0.712346 | − | 0.701828i | \(-0.247632\pi\) | ||||
0.712346 | + | 0.701828i | \(0.247632\pi\) | |||||||
\(294\) | −9.61269e59 | −0.322356 | ||||||||
\(295\) | −2.61445e59 | −0.0806753 | ||||||||
\(296\) | 6.21181e59 | 0.176430 | ||||||||
\(297\) | −1.87808e60 | −0.491113 | ||||||||
\(298\) | 3.17465e60 | 0.764535 | ||||||||
\(299\) | 3.94174e58 | 0.00874468 | ||||||||
\(300\) | −6.56473e59 | −0.134198 | ||||||||
\(301\) | 2.49512e60 | 0.470123 | ||||||||
\(302\) | 3.93421e59 | 0.0683419 | ||||||||
\(303\) | −1.92256e60 | −0.307989 | ||||||||
\(304\) | 4.17048e59 | 0.0616287 | ||||||||
\(305\) | −1.58395e61 | −2.15971 | ||||||||
\(306\) | −9.32088e60 | −1.17296 | ||||||||
\(307\) | 2.34251e59 | 0.0272140 | 0.0136070 | − | 0.999907i | \(-0.495669\pi\) | ||||
0.0136070 | + | 0.999907i | \(0.495669\pi\) | |||||||
\(308\) | −7.12449e60 | −0.764296 | ||||||||
\(309\) | 1.47213e60 | 0.145869 | ||||||||
\(310\) | 1.88407e61 | 1.72479 | ||||||||
\(311\) | −4.35273e60 | −0.368241 | −0.184120 | − | 0.982904i | \(-0.558944\pi\) | ||||
−0.184120 | + | 0.982904i | \(0.558944\pi\) | |||||||
\(312\) | 3.10477e58 | 0.00242796 | ||||||||
\(313\) | 1.93545e61 | 1.39941 | 0.699706 | − | 0.714431i | \(-0.253314\pi\) | ||||
0.699706 | + | 0.714431i | \(0.253314\pi\) | |||||||
\(314\) | 1.89862e61 | 1.26958 | ||||||||
\(315\) | −3.44527e61 | −2.13115 | ||||||||
\(316\) | 4.10005e60 | 0.234669 | ||||||||
\(317\) | 2.36551e61 | 1.25306 | 0.626530 | − | 0.779397i | \(-0.284475\pi\) | ||||
0.626530 | + | 0.779397i | \(0.284475\pi\) | |||||||
\(318\) | −7.57145e60 | −0.371291 | ||||||||
\(319\) | 8.90431e60 | 0.404323 | ||||||||
\(320\) | 4.18672e60 | 0.176076 | ||||||||
\(321\) | 1.05712e61 | 0.411861 | ||||||||
\(322\) | −1.11175e61 | −0.401364 | ||||||||
\(323\) | 1.32028e61 | 0.441778 | ||||||||
\(324\) | 1.26113e61 | 0.391206 | ||||||||
\(325\) | −8.61571e59 | −0.0247827 | ||||||||
\(326\) | −3.40072e61 | −0.907277 | ||||||||
\(327\) | 1.96844e59 | 0.00487196 | ||||||||
\(328\) | −1.21523e61 | −0.279093 | ||||||||
\(329\) | −1.12433e62 | −2.39658 | ||||||||
\(330\) | 1.28373e61 | 0.254029 | ||||||||
\(331\) | 6.39438e61 | 1.17493 | 0.587466 | − | 0.809249i | \(-0.300126\pi\) | ||||
0.587466 | + | 0.809249i | \(0.300126\pi\) | |||||||
\(332\) | −2.60144e61 | −0.443946 | ||||||||
\(333\) | −2.91364e61 | −0.461905 | ||||||||
\(334\) | −3.95736e61 | −0.582931 | ||||||||
\(335\) | 8.04750e61 | 1.10170 | ||||||||
\(336\) | −8.75686e60 | −0.111439 | ||||||||
\(337\) | 9.36305e61 | 1.10786 | 0.553930 | − | 0.832563i | \(-0.313128\pi\) | ||||
0.553930 | + | 0.832563i | \(0.313128\pi\) | |||||||
\(338\) | −6.42198e61 | −0.706658 | ||||||||
\(339\) | −3.06232e60 | −0.0313442 | ||||||||
\(340\) | 1.32542e62 | 1.26218 | ||||||||
\(341\) | −1.82745e62 | −1.61944 | ||||||||
\(342\) | −1.95616e61 | −0.161348 | ||||||||
\(343\) | 1.42966e62 | 1.09781 | ||||||||
\(344\) | 1.42220e61 | 0.101690 | ||||||||
\(345\) | 2.00322e61 | 0.133401 | ||||||||
\(346\) | 1.03376e61 | 0.0641290 | ||||||||
\(347\) | −9.31722e61 | −0.538535 | −0.269268 | − | 0.963065i | \(-0.586782\pi\) | ||||
−0.269268 | + | 0.963065i | \(0.586782\pi\) | |||||||
\(348\) | 1.09445e61 | 0.0589527 | ||||||||
\(349\) | 2.03454e62 | 1.02151 | 0.510755 | − | 0.859726i | \(-0.329366\pi\) | ||||
0.510755 | + | 0.859726i | \(0.329366\pi\) | |||||||
\(350\) | 2.43002e62 | 1.13748 | ||||||||
\(351\) | −3.02959e60 | −0.0132239 | ||||||||
\(352\) | −4.06090e61 | −0.165321 | ||||||||
\(353\) | −2.78134e62 | −1.05627 | −0.528133 | − | 0.849161i | \(-0.677108\pi\) | ||||
−0.528133 | + | 0.849161i | \(0.677108\pi\) | |||||||
\(354\) | 3.11690e60 | 0.0110444 | ||||||||
\(355\) | −3.10633e62 | −1.02719 | ||||||||
\(356\) | 2.31541e61 | 0.0714665 | ||||||||
\(357\) | −2.77222e62 | −0.798835 | ||||||||
\(358\) | 5.20900e61 | 0.140159 | ||||||||
\(359\) | 7.25567e62 | 1.82332 | 0.911662 | − | 0.410942i | \(-0.134800\pi\) | ||||
0.911662 | + | 0.410942i | \(0.134800\pi\) | |||||||
\(360\) | −1.96377e62 | −0.460978 | ||||||||
\(361\) | −4.28251e62 | −0.939230 | ||||||||
\(362\) | −1.44233e62 | −0.295599 | ||||||||
\(363\) | 1.78546e61 | 0.0342010 | ||||||||
\(364\) | −1.14927e61 | −0.0205797 | ||||||||
\(365\) | −9.87160e62 | −1.65277 | ||||||||
\(366\) | 1.88836e62 | 0.295664 | ||||||||
\(367\) | −3.66239e62 | −0.536347 | −0.268174 | − | 0.963371i | \(-0.586420\pi\) | ||||
−0.268174 | + | 0.963371i | \(0.586420\pi\) | |||||||
\(368\) | −6.33688e61 | −0.0868169 | ||||||||
\(369\) | 5.70001e62 | 0.730685 | ||||||||
\(370\) | 4.14317e62 | 0.497039 | ||||||||
\(371\) | 2.80267e63 | 3.14711 | ||||||||
\(372\) | −2.24616e62 | −0.236123 | ||||||||
\(373\) | 1.01303e63 | 0.997140 | 0.498570 | − | 0.866850i | \(-0.333859\pi\) | ||||
0.498570 | + | 0.866850i | \(0.333859\pi\) | |||||||
\(374\) | −1.28559e63 | −1.18508 | ||||||||
\(375\) | 7.04369e60 | 0.00608183 | ||||||||
\(376\) | −6.40857e62 | −0.518392 | ||||||||
\(377\) | 1.43638e61 | 0.0108869 | ||||||||
\(378\) | 8.54481e62 | 0.606951 | ||||||||
\(379\) | −4.10768e62 | −0.273486 | −0.136743 | − | 0.990607i | \(-0.543664\pi\) | ||||
−0.136743 | + | 0.990607i | \(0.543664\pi\) | |||||||
\(380\) | 2.78164e62 | 0.173621 | ||||||||
\(381\) | 7.36165e62 | 0.430837 | ||||||||
\(382\) | −3.81984e62 | −0.209649 | ||||||||
\(383\) | −1.90644e63 | −0.981415 | −0.490708 | − | 0.871324i | \(-0.663262\pi\) | ||||
−0.490708 | + | 0.871324i | \(0.663262\pi\) | |||||||
\(384\) | −4.99134e61 | −0.0241047 | ||||||||
\(385\) | −4.75191e63 | −2.15318 | ||||||||
\(386\) | 1.17367e63 | 0.499063 | ||||||||
\(387\) | −6.67079e62 | −0.266231 | ||||||||
\(388\) | −1.34194e63 | −0.502753 | ||||||||
\(389\) | 3.21862e63 | 1.13215 | 0.566076 | − | 0.824353i | \(-0.308461\pi\) | ||||
0.566076 | + | 0.824353i | \(0.308461\pi\) | |||||||
\(390\) | 2.07083e61 | 0.00684008 | ||||||||
\(391\) | −2.00611e63 | −0.622336 | ||||||||
\(392\) | 2.02818e63 | 0.591015 | ||||||||
\(393\) | 1.73586e62 | 0.0475221 | ||||||||
\(394\) | −2.36396e63 | −0.608112 | ||||||||
\(395\) | 2.73466e63 | 0.661111 | ||||||||
\(396\) | 1.90476e63 | 0.432821 | ||||||||
\(397\) | −1.66988e63 | −0.356713 | −0.178356 | − | 0.983966i | \(-0.557078\pi\) | ||||
−0.178356 | + | 0.983966i | \(0.557078\pi\) | |||||||
\(398\) | 5.27343e63 | 1.05915 | ||||||||
\(399\) | −5.81802e62 | −0.109885 | ||||||||
\(400\) | 1.38509e63 | 0.246042 | ||||||||
\(401\) | −3.21505e63 | −0.537218 | −0.268609 | − | 0.963249i | \(-0.586564\pi\) | ||||
−0.268609 | + | 0.963249i | \(0.586564\pi\) | |||||||
\(402\) | −9.59410e62 | −0.150822 | ||||||||
\(403\) | −2.94791e62 | −0.0436055 | ||||||||
\(404\) | 4.05641e63 | 0.564674 | ||||||||
\(405\) | 8.41150e63 | 1.10211 | ||||||||
\(406\) | −4.05124e63 | −0.499690 | ||||||||
\(407\) | −4.01867e63 | −0.466680 | ||||||||
\(408\) | −1.58014e63 | −0.172792 | ||||||||
\(409\) | 1.21477e64 | 1.25104 | 0.625522 | − | 0.780207i | \(-0.284886\pi\) | ||||
0.625522 | + | 0.780207i | \(0.284886\pi\) | |||||||
\(410\) | −8.10537e63 | −0.786263 | ||||||||
\(411\) | 1.33962e63 | 0.122422 | ||||||||
\(412\) | −3.10604e63 | −0.267440 | ||||||||
\(413\) | −1.15376e63 | −0.0936139 | ||||||||
\(414\) | 2.97231e63 | 0.227293 | ||||||||
\(415\) | −1.73511e64 | −1.25069 | ||||||||
\(416\) | −6.55075e61 | −0.00445148 | ||||||||
\(417\) | 4.10196e63 | 0.262820 | ||||||||
\(418\) | −2.69805e63 | −0.163016 | ||||||||
\(419\) | −9.43742e63 | −0.537786 | −0.268893 | − | 0.963170i | \(-0.586658\pi\) | ||||
−0.268893 | + | 0.963170i | \(0.586658\pi\) | |||||||
\(420\) | −5.84067e63 | −0.313946 | ||||||||
\(421\) | −7.07535e63 | −0.358787 | −0.179394 | − | 0.983777i | \(-0.557414\pi\) | ||||
−0.179394 | + | 0.983777i | \(0.557414\pi\) | |||||||
\(422\) | −2.29361e64 | −1.09740 | ||||||||
\(423\) | 3.00593e64 | 1.35719 | ||||||||
\(424\) | 1.59750e64 | 0.680734 | ||||||||
\(425\) | 4.38489e64 | 1.76372 | ||||||||
\(426\) | 3.70331e63 | 0.140623 | ||||||||
\(427\) | −6.99002e64 | −2.50608 | ||||||||
\(428\) | −2.23042e64 | −0.755116 | ||||||||
\(429\) | −2.00860e62 | −0.00642228 | ||||||||
\(430\) | 9.48580e63 | 0.286482 | ||||||||
\(431\) | 1.47866e64 | 0.421867 | 0.210933 | − | 0.977500i | \(-0.432350\pi\) | ||||
0.210933 | + | 0.977500i | \(0.432350\pi\) | |||||||
\(432\) | 4.87047e63 | 0.131286 | ||||||||
\(433\) | 5.40840e64 | 1.37757 | 0.688787 | − | 0.724963i | \(-0.258143\pi\) | ||||
0.688787 | + | 0.724963i | \(0.258143\pi\) | |||||||
\(434\) | 8.31446e64 | 2.00141 | ||||||||
\(435\) | 7.29978e63 | 0.166082 | ||||||||
\(436\) | −4.15322e62 | −0.00893236 | ||||||||
\(437\) | −4.21020e63 | −0.0856066 | ||||||||
\(438\) | 1.17688e64 | 0.226264 | ||||||||
\(439\) | −3.69191e63 | −0.0671229 | −0.0335614 | − | 0.999437i | \(-0.510685\pi\) | ||||
−0.0335614 | + | 0.999437i | \(0.510685\pi\) | |||||||
\(440\) | −2.70855e64 | −0.465743 | ||||||||
\(441\) | −9.51316e64 | −1.54732 | ||||||||
\(442\) | −2.07382e63 | −0.0319099 | ||||||||
\(443\) | −7.49563e64 | −1.09123 | −0.545616 | − | 0.838036i | \(-0.683704\pi\) | ||||
−0.545616 | + | 0.838036i | \(0.683704\pi\) | |||||||
\(444\) | −4.93942e63 | −0.0680446 | ||||||||
\(445\) | 1.54434e64 | 0.201336 | ||||||||
\(446\) | 2.94092e63 | 0.0362894 | ||||||||
\(447\) | −2.52437e64 | −0.294862 | ||||||||
\(448\) | 1.84761e64 | 0.204314 | ||||||||
\(449\) | −5.65052e64 | −0.591634 | −0.295817 | − | 0.955245i | \(-0.595592\pi\) | ||||
−0.295817 | + | 0.955245i | \(0.595592\pi\) | |||||||
\(450\) | −6.49676e64 | −0.644155 | ||||||||
\(451\) | 7.86179e64 | 0.738238 | ||||||||
\(452\) | 6.46118e63 | 0.0574673 | ||||||||
\(453\) | −3.12835e63 | −0.0263578 | ||||||||
\(454\) | −6.94080e64 | −0.554040 | ||||||||
\(455\) | −7.66544e63 | −0.0579773 | ||||||||
\(456\) | −3.31622e63 | −0.0237687 | ||||||||
\(457\) | 5.93488e64 | 0.403148 | 0.201574 | − | 0.979473i | \(-0.435394\pi\) | ||||
0.201574 | + | 0.979473i | \(0.435394\pi\) | |||||||
\(458\) | 1.04895e65 | 0.675383 | ||||||||
\(459\) | 1.54188e65 | 0.941109 | ||||||||
\(460\) | −4.22659e64 | −0.244581 | ||||||||
\(461\) | 1.06042e65 | 0.581840 | 0.290920 | − | 0.956747i | \(-0.406039\pi\) | ||||
0.290920 | + | 0.956747i | \(0.406039\pi\) | |||||||
\(462\) | 5.66516e64 | 0.294770 | ||||||||
\(463\) | 1.86764e65 | 0.921637 | 0.460818 | − | 0.887495i | \(-0.347556\pi\) | ||||
0.460818 | + | 0.887495i | \(0.347556\pi\) | |||||||
\(464\) | −2.30918e64 | −0.108085 | ||||||||
\(465\) | −1.49815e65 | −0.665209 | ||||||||
\(466\) | −9.72099e64 | −0.409502 | ||||||||
\(467\) | −2.28278e64 | −0.0912432 | −0.0456216 | − | 0.998959i | \(-0.514527\pi\) | ||||
−0.0456216 | + | 0.998959i | \(0.514527\pi\) | |||||||
\(468\) | 3.07262e63 | 0.0116543 | ||||||||
\(469\) | 3.55138e65 | 1.27839 | ||||||||
\(470\) | −4.27440e65 | −1.46042 | ||||||||
\(471\) | −1.50972e65 | −0.489648 | ||||||||
\(472\) | −6.57635e63 | −0.0202491 | ||||||||
\(473\) | −9.20074e64 | −0.268983 | ||||||||
\(474\) | −3.26022e64 | −0.0905060 | ||||||||
\(475\) | 9.20250e64 | 0.242612 | ||||||||
\(476\) | 5.84912e65 | 1.46460 | ||||||||
\(477\) | −7.49306e65 | −1.78221 | ||||||||
\(478\) | 3.35309e65 | 0.757639 | ||||||||
\(479\) | −1.07480e65 | −0.230732 | −0.115366 | − | 0.993323i | \(-0.536804\pi\) | ||||
−0.115366 | + | 0.993323i | \(0.536804\pi\) | |||||||
\(480\) | −3.32914e64 | −0.0679081 | ||||||||
\(481\) | −6.48262e63 | −0.0125660 | ||||||||
\(482\) | −1.46192e65 | −0.269322 | ||||||||
\(483\) | 8.84026e64 | 0.154796 | ||||||||
\(484\) | −3.76715e64 | −0.0627049 | ||||||||
\(485\) | −8.95047e65 | −1.41636 | ||||||||
\(486\) | −3.47085e65 | −0.522212 | ||||||||
\(487\) | 9.52950e64 | 0.136336 | 0.0681680 | − | 0.997674i | \(-0.478285\pi\) | ||||
0.0681680 | + | 0.997674i | \(0.478285\pi\) | |||||||
\(488\) | −3.98426e65 | −0.542078 | ||||||||
\(489\) | 2.70414e65 | 0.349915 | ||||||||
\(490\) | 1.35276e66 | 1.66501 | ||||||||
\(491\) | 7.75386e65 | 0.907865 | 0.453933 | − | 0.891036i | \(-0.350021\pi\) | ||||
0.453933 | + | 0.891036i | \(0.350021\pi\) | |||||||
\(492\) | 9.66309e64 | 0.107639 | ||||||||
\(493\) | −7.31033e65 | −0.774796 | ||||||||
\(494\) | −4.35229e63 | −0.00438943 | ||||||||
\(495\) | 1.27044e66 | 1.21935 | ||||||||
\(496\) | 4.73917e65 | 0.432914 | ||||||||
\(497\) | −1.37083e66 | −1.19193 | ||||||||
\(498\) | 2.06857e65 | 0.171219 | ||||||||
\(499\) | 1.56740e66 | 1.23514 | 0.617569 | − | 0.786517i | \(-0.288118\pi\) | ||||
0.617569 | + | 0.786517i | \(0.288118\pi\) | |||||||
\(500\) | −1.48615e64 | −0.0111506 | ||||||||
\(501\) | 3.14676e65 | 0.224822 | ||||||||
\(502\) | −1.19084e66 | −0.810237 | ||||||||
\(503\) | −5.11802e65 | −0.331655 | −0.165827 | − | 0.986155i | \(-0.553029\pi\) | ||||
−0.165827 | + | 0.986155i | \(0.553029\pi\) | |||||||
\(504\) | −8.66619e65 | −0.534909 | ||||||||
\(505\) | 2.70555e66 | 1.59081 | ||||||||
\(506\) | 4.09958e65 | 0.229642 | ||||||||
\(507\) | 5.10654e65 | 0.272541 | ||||||||
\(508\) | −1.55323e66 | −0.789907 | ||||||||
\(509\) | −1.63079e66 | −0.790335 | −0.395167 | − | 0.918609i | \(-0.629313\pi\) | ||||
−0.395167 | + | 0.918609i | \(0.629313\pi\) | |||||||
\(510\) | −1.05393e66 | −0.486790 | ||||||||
\(511\) | −4.35636e66 | −1.91784 | ||||||||
\(512\) | 1.05312e65 | 0.0441942 | ||||||||
\(513\) | 3.23592e65 | 0.129456 | ||||||||
\(514\) | −5.69504e65 | −0.217220 | ||||||||
\(515\) | −2.07168e66 | −0.753434 | ||||||||
\(516\) | −1.13088e65 | −0.0392193 | ||||||||
\(517\) | 4.14595e66 | 1.37122 | ||||||||
\(518\) | 1.82839e66 | 0.576754 | ||||||||
\(519\) | −8.22010e64 | −0.0247330 | ||||||||
\(520\) | −4.36924e64 | −0.0125408 | ||||||||
\(521\) | 3.56843e65 | 0.0977133 | 0.0488566 | − | 0.998806i | \(-0.484442\pi\) | ||||
0.0488566 | + | 0.998806i | \(0.484442\pi\) | |||||||
\(522\) | 1.08312e66 | 0.282975 | ||||||||
\(523\) | −7.86554e65 | −0.196082 | −0.0980408 | − | 0.995182i | \(-0.531258\pi\) | ||||
−0.0980408 | + | 0.995182i | \(0.531258\pi\) | |||||||
\(524\) | −3.66248e65 | −0.0871282 | ||||||||
\(525\) | −1.93227e66 | −0.438698 | ||||||||
\(526\) | −3.93463e66 | −0.852615 | ||||||||
\(527\) | 1.50031e67 | 3.10329 | ||||||||
\(528\) | 3.22909e65 | 0.0637602 | ||||||||
\(529\) | −4.66501e66 | −0.879405 | ||||||||
\(530\) | 1.06551e67 | 1.91777 | ||||||||
\(531\) | 3.08463e65 | 0.0530136 | ||||||||
\(532\) | 1.22754e66 | 0.201466 | ||||||||
\(533\) | 1.26821e65 | 0.0198780 | ||||||||
\(534\) | −1.84113e65 | −0.0275629 | ||||||||
\(535\) | −1.48765e67 | −2.12732 | ||||||||
\(536\) | 2.02426e66 | 0.276522 | ||||||||
\(537\) | −4.14202e65 | −0.0540558 | ||||||||
\(538\) | −3.61704e66 | −0.451011 | ||||||||
\(539\) | −1.31211e67 | −1.56331 | ||||||||
\(540\) | 3.24852e66 | 0.369861 | ||||||||
\(541\) | 9.49189e66 | 1.03281 | 0.516404 | − | 0.856345i | \(-0.327270\pi\) | ||||
0.516404 | + | 0.856345i | \(0.327270\pi\) | |||||||
\(542\) | −5.92105e66 | −0.615766 | ||||||||
\(543\) | 1.14689e66 | 0.114005 | ||||||||
\(544\) | 3.33395e66 | 0.316800 | ||||||||
\(545\) | −2.77013e65 | −0.0251643 | ||||||||
\(546\) | 9.13862e64 | 0.00793708 | ||||||||
\(547\) | −1.44217e67 | −1.19764 | −0.598819 | − | 0.800884i | \(-0.704363\pi\) | ||||
−0.598819 | + | 0.800884i | \(0.704363\pi\) | |||||||
\(548\) | −2.82647e66 | −0.224451 | ||||||||
\(549\) | 1.86881e67 | 1.41920 | ||||||||
\(550\) | −8.96071e66 | −0.650813 | ||||||||
\(551\) | −1.53421e66 | −0.106578 | ||||||||
\(552\) | 5.03888e65 | 0.0334831 | ||||||||
\(553\) | 1.20681e67 | 0.767140 | ||||||||
\(554\) | 4.93937e66 | 0.300388 | ||||||||
\(555\) | −3.29451e66 | −0.191696 | ||||||||
\(556\) | −8.65472e66 | −0.481860 | ||||||||
\(557\) | 7.89683e65 | 0.0420727 | 0.0210364 | − | 0.999779i | \(-0.493303\pi\) | ||||
0.0210364 | + | 0.999779i | \(0.493303\pi\) | |||||||
\(558\) | −2.22290e67 | −1.13340 | ||||||||
\(559\) | −1.48420e65 | −0.00724273 | ||||||||
\(560\) | 1.23232e67 | 0.575597 | ||||||||
\(561\) | 1.02226e67 | 0.457057 | ||||||||
\(562\) | 7.65293e66 | 0.327558 | ||||||||
\(563\) | 2.05636e67 | 0.842643 | 0.421321 | − | 0.906911i | \(-0.361566\pi\) | ||||
0.421321 | + | 0.906911i | \(0.361566\pi\) | |||||||
\(564\) | 5.09588e66 | 0.199931 | ||||||||
\(565\) | 4.30950e66 | 0.161897 | ||||||||
\(566\) | 9.05238e66 | 0.325657 | ||||||||
\(567\) | 3.71202e67 | 1.27887 | ||||||||
\(568\) | −7.81362e66 | −0.257821 | ||||||||
\(569\) | −2.99189e67 | −0.945573 | −0.472787 | − | 0.881177i | \(-0.656752\pi\) | ||||
−0.472787 | + | 0.881177i | \(0.656752\pi\) | |||||||
\(570\) | −2.21186e66 | −0.0669614 | ||||||||
\(571\) | −1.50438e67 | −0.436289 | −0.218144 | − | 0.975917i | \(-0.570000\pi\) | ||||
−0.218144 | + | 0.975917i | \(0.570000\pi\) | |||||||
\(572\) | 4.23794e65 | 0.0117748 | ||||||||
\(573\) | 3.03741e66 | 0.0808564 | ||||||||
\(574\) | −3.57692e67 | −0.912364 | ||||||||
\(575\) | −1.39828e67 | −0.341770 | ||||||||
\(576\) | −4.93966e66 | −0.115703 | ||||||||
\(577\) | 1.42499e67 | 0.319893 | 0.159947 | − | 0.987126i | \(-0.448868\pi\) | ||||
0.159947 | + | 0.987126i | \(0.448868\pi\) | |||||||
\(578\) | 7.26815e67 | 1.56384 | ||||||||
\(579\) | −9.33259e66 | −0.192476 | ||||||||
\(580\) | −1.54018e67 | −0.304499 | ||||||||
\(581\) | −7.65710e67 | −1.45127 | ||||||||
\(582\) | 1.06706e67 | 0.193899 | ||||||||
\(583\) | −1.03349e68 | −1.80063 | ||||||||
\(584\) | −2.48309e67 | −0.414838 | ||||||||
\(585\) | 2.04939e66 | 0.0328326 | ||||||||
\(586\) | 6.55689e67 | 1.00741 | ||||||||
\(587\) | −4.53396e67 | −0.668104 | −0.334052 | − | 0.942555i | \(-0.608416\pi\) | ||||
−0.334052 | + | 0.942555i | \(0.608416\pi\) | |||||||
\(588\) | −1.61274e67 | −0.227940 | ||||||||
\(589\) | 3.14869e67 | 0.426879 | ||||||||
\(590\) | −4.38631e66 | −0.0570460 | ||||||||
\(591\) | 1.87974e67 | 0.234534 | ||||||||
\(592\) | 1.04217e67 | 0.124755 | ||||||||
\(593\) | 5.39408e67 | 0.619552 | 0.309776 | − | 0.950810i | \(-0.399746\pi\) | ||||
0.309776 | + | 0.950810i | \(0.399746\pi\) | |||||||
\(594\) | −3.15090e67 | −0.347269 | ||||||||
\(595\) | 3.90126e68 | 4.12609 | ||||||||
\(596\) | 5.32618e67 | 0.540608 | ||||||||
\(597\) | −4.19325e67 | −0.408488 | ||||||||
\(598\) | 6.61314e65 | 0.00618342 | ||||||||
\(599\) | −1.84268e68 | −1.65383 | −0.826917 | − | 0.562323i | \(-0.809908\pi\) | ||||
−0.826917 | + | 0.562323i | \(0.809908\pi\) | |||||||
\(600\) | −1.10138e67 | −0.0948924 | ||||||||
\(601\) | −6.15406e67 | −0.509023 | −0.254511 | − | 0.967070i | \(-0.581915\pi\) | ||||
−0.254511 | + | 0.967070i | \(0.581915\pi\) | |||||||
\(602\) | 4.18611e67 | 0.332427 | ||||||||
\(603\) | −9.49476e67 | −0.723952 | ||||||||
\(604\) | 6.60050e66 | 0.0483250 | ||||||||
\(605\) | −2.51262e67 | −0.176653 | ||||||||
\(606\) | −3.22552e67 | −0.217781 | ||||||||
\(607\) | 2.91666e68 | 1.89131 | 0.945654 | − | 0.325175i | \(-0.105423\pi\) | ||||
0.945654 | + | 0.325175i | \(0.105423\pi\) | |||||||
\(608\) | 6.99690e66 | 0.0435781 | ||||||||
\(609\) | 3.22141e67 | 0.192718 | ||||||||
\(610\) | −2.65743e68 | −1.52715 | ||||||||
\(611\) | 6.68795e66 | 0.0369218 | ||||||||
\(612\) | −1.56378e68 | −0.829405 | ||||||||
\(613\) | −1.34057e68 | −0.683139 | −0.341569 | − | 0.939857i | \(-0.610958\pi\) | ||||
−0.341569 | + | 0.939857i | \(0.610958\pi\) | |||||||
\(614\) | 3.93008e66 | 0.0192432 | ||||||||
\(615\) | 6.44511e67 | 0.303243 | ||||||||
\(616\) | −1.19529e68 | −0.540439 | ||||||||
\(617\) | −2.63476e68 | −1.14487 | −0.572433 | − | 0.819951i | \(-0.694000\pi\) | ||||
−0.572433 | + | 0.819951i | \(0.694000\pi\) | |||||||
\(618\) | 2.46982e67 | 0.103145 | ||||||||
\(619\) | 1.18534e68 | 0.475799 | 0.237899 | − | 0.971290i | \(-0.423541\pi\) | ||||
0.237899 | + | 0.971290i | \(0.423541\pi\) | |||||||
\(620\) | 3.16095e68 | 1.21961 | ||||||||
\(621\) | −4.91686e67 | −0.182366 | ||||||||
\(622\) | −7.30267e67 | −0.260386 | ||||||||
\(623\) | 6.81520e67 | 0.233626 | ||||||||
\(624\) | 5.20894e65 | 0.00171683 | ||||||||
\(625\) | −3.20461e68 | −1.01558 | ||||||||
\(626\) | 3.24715e68 | 0.989534 | ||||||||
\(627\) | 2.14539e67 | 0.0628713 | ||||||||
\(628\) | 3.18536e68 | 0.897732 | ||||||||
\(629\) | 3.29927e68 | 0.894288 | ||||||||
\(630\) | −5.78020e68 | −1.50695 | ||||||||
\(631\) | 4.68843e68 | 1.17573 | 0.587866 | − | 0.808959i | \(-0.299968\pi\) | ||||
0.587866 | + | 0.808959i | \(0.299968\pi\) | |||||||
\(632\) | 6.87874e67 | 0.165936 | ||||||||
\(633\) | 1.82380e68 | 0.423240 | ||||||||
\(634\) | 3.96866e68 | 0.886048 | ||||||||
\(635\) | −1.03598e69 | −2.22533 | ||||||||
\(636\) | −1.27028e68 | −0.262543 | ||||||||
\(637\) | −2.11660e67 | −0.0420943 | ||||||||
\(638\) | 1.49390e68 | 0.285900 | ||||||||
\(639\) | 3.66497e68 | 0.674993 | ||||||||
\(640\) | 7.02415e67 | 0.124504 | ||||||||
\(641\) | −2.45988e68 | −0.419654 | −0.209827 | − | 0.977738i | \(-0.567290\pi\) | ||||
−0.209827 | + | 0.977738i | \(0.567290\pi\) | |||||||
\(642\) | 1.77355e68 | 0.291230 | ||||||||
\(643\) | 6.14694e68 | 0.971605 | 0.485803 | − | 0.874069i | \(-0.338527\pi\) | ||||
0.485803 | + | 0.874069i | \(0.338527\pi\) | |||||||
\(644\) | −1.86521e68 | −0.283807 | ||||||||
\(645\) | −7.54279e67 | −0.110489 | ||||||||
\(646\) | 2.21506e68 | 0.312384 | ||||||||
\(647\) | −9.77317e68 | −1.32703 | −0.663515 | − | 0.748163i | \(-0.730936\pi\) | ||||
−0.663515 | + | 0.748163i | \(0.730936\pi\) | |||||||
\(648\) | 2.11582e68 | 0.276625 | ||||||||
\(649\) | 4.25450e67 | 0.0535616 | ||||||||
\(650\) | −1.44548e67 | −0.0175240 | ||||||||
\(651\) | −6.61138e68 | −0.771894 | ||||||||
\(652\) | −5.70547e68 | −0.641542 | ||||||||
\(653\) | 8.35256e67 | 0.0904580 | 0.0452290 | − | 0.998977i | \(-0.485598\pi\) | ||||
0.0452290 | + | 0.998977i | \(0.485598\pi\) | |||||||
\(654\) | 3.30250e66 | 0.00344499 | ||||||||
\(655\) | −2.44281e68 | −0.245459 | ||||||||
\(656\) | −2.03882e68 | −0.197349 | ||||||||
\(657\) | 1.16469e69 | 1.08607 | ||||||||
\(658\) | −1.88631e69 | −1.69464 | ||||||||
\(659\) | −3.35474e68 | −0.290380 | −0.145190 | − | 0.989404i | \(-0.546379\pi\) | ||||
−0.145190 | + | 0.989404i | \(0.546379\pi\) | |||||||
\(660\) | 2.15375e68 | 0.179626 | ||||||||
\(661\) | 2.63520e68 | 0.211776 | 0.105888 | − | 0.994378i | \(-0.466231\pi\) | ||||
0.105888 | + | 0.994378i | \(0.466231\pi\) | |||||||
\(662\) | 1.07280e69 | 0.830802 | ||||||||
\(663\) | 1.64903e67 | 0.0123069 | ||||||||
\(664\) | −4.36449e68 | −0.313917 | ||||||||
\(665\) | 8.18751e68 | 0.567572 | ||||||||
\(666\) | −4.88828e68 | −0.326616 | ||||||||
\(667\) | 2.33117e68 | 0.150138 | ||||||||
\(668\) | −6.63935e68 | −0.412194 | ||||||||
\(669\) | −2.33852e67 | −0.0139959 | ||||||||
\(670\) | 1.35015e69 | 0.779019 | ||||||||
\(671\) | 2.57757e69 | 1.43387 | ||||||||
\(672\) | −1.46916e68 | −0.0787991 | ||||||||
\(673\) | 3.25131e69 | 1.68147 | 0.840735 | − | 0.541447i | \(-0.182123\pi\) | ||||
0.840735 | + | 0.541447i | \(0.182123\pi\) | |||||||
\(674\) | 1.57086e69 | 0.783375 | ||||||||
\(675\) | 1.07471e69 | 0.516831 | ||||||||
\(676\) | −1.07743e69 | −0.499683 | ||||||||
\(677\) | −2.82926e69 | −1.26547 | −0.632733 | − | 0.774370i | \(-0.718067\pi\) | ||||
−0.632733 | + | 0.774370i | \(0.718067\pi\) | |||||||
\(678\) | −5.13772e67 | −0.0221637 | ||||||||
\(679\) | −3.94987e69 | −1.64351 | ||||||||
\(680\) | 2.22369e69 | 0.892493 | ||||||||
\(681\) | 5.51909e68 | 0.213680 | ||||||||
\(682\) | −3.06596e69 | −1.14511 | ||||||||
\(683\) | −2.71804e69 | −0.979374 | −0.489687 | − | 0.871898i | \(-0.662889\pi\) | ||||
−0.489687 | + | 0.871898i | \(0.662889\pi\) | |||||||
\(684\) | −3.28189e68 | −0.114090 | ||||||||
\(685\) | −1.88521e69 | −0.632325 | ||||||||
\(686\) | 2.39857e69 | 0.776268 | ||||||||
\(687\) | −8.34089e68 | −0.260479 | ||||||||
\(688\) | 2.38605e68 | 0.0719056 | ||||||||
\(689\) | −1.66715e68 | −0.0484845 | ||||||||
\(690\) | 3.36084e68 | 0.0943291 | ||||||||
\(691\) | −2.43872e69 | −0.660618 | −0.330309 | − | 0.943873i | \(-0.607153\pi\) | ||||
−0.330309 | + | 0.943873i | \(0.607153\pi\) | |||||||
\(692\) | 1.73436e68 | 0.0453461 | ||||||||
\(693\) | 5.60650e69 | 1.41491 | ||||||||
\(694\) | −1.56317e69 | −0.380802 | ||||||||
\(695\) | −5.77255e69 | −1.35750 | ||||||||
\(696\) | 1.83618e68 | 0.0416858 | ||||||||
\(697\) | −6.45443e69 | −1.41467 | ||||||||
\(698\) | 3.41339e69 | 0.722317 | ||||||||
\(699\) | 7.72980e68 | 0.157935 | ||||||||
\(700\) | 4.07690e69 | 0.804319 | ||||||||
\(701\) | 7.63989e69 | 1.45544 | 0.727722 | − | 0.685872i | \(-0.240579\pi\) | ||||
0.727722 | + | 0.685872i | \(0.240579\pi\) | |||||||
\(702\) | −5.08280e67 | −0.00935070 | ||||||||
\(703\) | 6.92413e68 | 0.123015 | ||||||||
\(704\) | −6.81306e68 | −0.116899 | ||||||||
\(705\) | 3.39886e69 | 0.563248 | ||||||||
\(706\) | −4.66631e69 | −0.746893 | ||||||||
\(707\) | 1.19397e70 | 1.84594 | ||||||||
\(708\) | 5.22929e67 | 0.00780959 | ||||||||
\(709\) | 2.36736e69 | 0.341533 | 0.170766 | − | 0.985312i | \(-0.445376\pi\) | ||||
0.170766 | + | 0.985312i | \(0.445376\pi\) | |||||||
\(710\) | −5.21155e69 | −0.726336 | ||||||||
\(711\) | −3.22646e69 | −0.434432 | ||||||||
\(712\) | 3.88461e68 | 0.0505344 | ||||||||
\(713\) | −4.78431e69 | −0.601348 | ||||||||
\(714\) | −4.65102e69 | −0.564861 | ||||||||
\(715\) | 2.82663e68 | 0.0331720 | ||||||||
\(716\) | 8.73926e68 | 0.0991073 | ||||||||
\(717\) | −2.66627e69 | −0.292203 | ||||||||
\(718\) | 1.21730e70 | 1.28928 | ||||||||
\(719\) | 9.01007e69 | 0.922296 | 0.461148 | − | 0.887323i | \(-0.347438\pi\) | ||||
0.461148 | + | 0.887323i | \(0.347438\pi\) | |||||||
\(720\) | −3.29467e69 | −0.325961 | ||||||||
\(721\) | −9.14237e69 | −0.874269 | ||||||||
\(722\) | −7.18486e69 | −0.664136 | ||||||||
\(723\) | 1.16247e69 | 0.103871 | ||||||||
\(724\) | −2.41982e69 | −0.209020 | ||||||||
\(725\) | −5.09538e69 | −0.425496 | ||||||||
\(726\) | 2.99551e68 | 0.0241838 | ||||||||
\(727\) | 1.12644e70 | 0.879257 | 0.439628 | − | 0.898180i | \(-0.355110\pi\) | ||||
0.439628 | + | 0.898180i | \(0.355110\pi\) | |||||||
\(728\) | −1.92816e68 | −0.0145520 | ||||||||
\(729\) | −7.96172e69 | −0.581008 | ||||||||
\(730\) | −1.65618e70 | −1.16868 | ||||||||
\(731\) | 7.55369e69 | 0.515446 | ||||||||
\(732\) | 3.16815e69 | 0.209066 | ||||||||
\(733\) | 4.32996e69 | 0.276335 | 0.138168 | − | 0.990409i | \(-0.455879\pi\) | ||||
0.138168 | + | 0.990409i | \(0.455879\pi\) | |||||||
\(734\) | −6.14447e69 | −0.379255 | ||||||||
\(735\) | −1.07567e70 | −0.642154 | ||||||||
\(736\) | −1.06315e69 | −0.0613888 | ||||||||
\(737\) | −1.30957e70 | −0.731436 | ||||||||
\(738\) | 9.56304e69 | 0.516672 | ||||||||
\(739\) | −2.10376e70 | −1.09953 | −0.549766 | − | 0.835319i | \(-0.685283\pi\) | ||||
−0.549766 | + | 0.835319i | \(0.685283\pi\) | |||||||
\(740\) | 6.95109e69 | 0.351460 | ||||||||
\(741\) | 3.46080e67 | 0.00169289 | ||||||||
\(742\) | 4.70211e70 | 2.22534 | ||||||||
\(743\) | 3.09494e69 | 0.141718 | 0.0708592 | − | 0.997486i | \(-0.477426\pi\) | ||||
0.0708592 | + | 0.997486i | \(0.477426\pi\) | |||||||
\(744\) | −3.76843e69 | −0.166964 | ||||||||
\(745\) | 3.55247e70 | 1.52301 | ||||||||
\(746\) | 1.69958e70 | 0.705084 | ||||||||
\(747\) | 2.04716e70 | 0.821857 | ||||||||
\(748\) | −2.15686e70 | −0.837979 | ||||||||
\(749\) | −6.56504e70 | −2.46850 | ||||||||
\(750\) | 1.18173e68 | 0.00430050 | ||||||||
\(751\) | 2.36292e70 | 0.832281 | 0.416140 | − | 0.909300i | \(-0.363383\pi\) | ||||
0.416140 | + | 0.909300i | \(0.363383\pi\) | |||||||
\(752\) | −1.07518e70 | −0.366559 | ||||||||
\(753\) | 9.46915e69 | 0.312488 | ||||||||
\(754\) | 2.40985e68 | 0.00769824 | ||||||||
\(755\) | 4.40242e69 | 0.136142 | ||||||||
\(756\) | 1.43358e70 | 0.429179 | ||||||||
\(757\) | 4.84445e70 | 1.40409 | 0.702045 | − | 0.712132i | \(-0.252270\pi\) | ||||
0.702045 | + | 0.712132i | \(0.252270\pi\) | |||||||
\(758\) | −6.89154e69 | −0.193384 | ||||||||
\(759\) | −3.25985e69 | −0.0885673 | ||||||||
\(760\) | 4.66681e69 | 0.122769 | ||||||||
\(761\) | −1.48623e70 | −0.378584 | −0.189292 | − | 0.981921i | \(-0.560619\pi\) | ||||
−0.189292 | + | 0.981921i | \(0.560619\pi\) | |||||||
\(762\) | 1.23508e70 | 0.304648 | ||||||||
\(763\) | −1.22247e69 | −0.0292002 | ||||||||
\(764\) | −6.40862e69 | −0.148244 | ||||||||
\(765\) | −1.04302e71 | −2.33661 | ||||||||
\(766\) | −3.19847e70 | −0.693965 | ||||||||
\(767\) | 6.86305e67 | 0.00144222 | ||||||||
\(768\) | −8.37408e68 | −0.0170446 | ||||||||
\(769\) | −6.67570e70 | −1.31614 | −0.658069 | − | 0.752957i | \(-0.728627\pi\) | ||||
−0.658069 | + | 0.752957i | \(0.728627\pi\) | |||||||
\(770\) | −7.97239e70 | −1.52253 | ||||||||
\(771\) | 4.52850e69 | 0.0837765 | ||||||||
\(772\) | 1.96908e70 | 0.352891 | ||||||||
\(773\) | 8.33587e70 | 1.44728 | 0.723642 | − | 0.690176i | \(-0.242467\pi\) | ||||
0.723642 | + | 0.690176i | \(0.242467\pi\) | |||||||
\(774\) | −1.11917e70 | −0.188254 | ||||||||
\(775\) | 1.04574e71 | 1.70424 | ||||||||
\(776\) | −2.25139e70 | −0.355500 | ||||||||
\(777\) | −1.45388e70 | −0.222440 | ||||||||
\(778\) | 5.39995e70 | 0.800553 | ||||||||
\(779\) | −1.35458e70 | −0.194597 | ||||||||
\(780\) | 3.47427e68 | 0.00483667 | ||||||||
\(781\) | 5.05494e70 | 0.681970 | ||||||||
\(782\) | −3.36570e70 | −0.440058 | ||||||||
\(783\) | −1.79172e70 | −0.227042 | ||||||||
\(784\) | 3.40272e70 | 0.417910 | ||||||||
\(785\) | 2.12458e71 | 2.52910 | ||||||||
\(786\) | 2.91228e69 | 0.0336032 | ||||||||
\(787\) | −1.52479e71 | −1.70541 | −0.852706 | − | 0.522390i | \(-0.825040\pi\) | ||||
−0.852706 | + | 0.522390i | \(0.825040\pi\) | |||||||
\(788\) | −3.96607e70 | −0.430000 | ||||||||
\(789\) | 3.12868e70 | 0.328833 | ||||||||
\(790\) | 4.58800e70 | 0.467476 | ||||||||
\(791\) | 1.90179e70 | 0.187862 | ||||||||
\(792\) | 3.19566e70 | 0.306051 | ||||||||
\(793\) | 4.15795e69 | 0.0386088 | ||||||||
\(794\) | −2.80160e70 | −0.252234 | ||||||||
\(795\) | −8.47254e70 | −0.739638 | ||||||||
\(796\) | 8.84734e70 | 0.748932 | ||||||||
\(797\) | 8.15352e70 | 0.669293 | 0.334647 | − | 0.942344i | \(-0.391383\pi\) | ||||
0.334647 | + | 0.942344i | \(0.391383\pi\) | |||||||
\(798\) | −9.76102e69 | −0.0777006 | ||||||||
\(799\) | −3.40377e71 | −2.62763 | ||||||||
\(800\) | 2.32380e70 | 0.173978 | ||||||||
\(801\) | −1.82207e70 | −0.132303 | ||||||||
\(802\) | −5.39396e70 | −0.379871 | ||||||||
\(803\) | 1.60641e71 | 1.09730 | ||||||||
\(804\) | −1.60962e70 | −0.106648 | ||||||||
\(805\) | −1.24406e71 | −0.799544 | ||||||||
\(806\) | −4.94578e69 | −0.0308337 | ||||||||
\(807\) | 2.87615e70 | 0.173944 | ||||||||
\(808\) | 6.80552e70 | 0.399285 | ||||||||
\(809\) | −2.92840e71 | −1.66683 | −0.833416 | − | 0.552646i | \(-0.813618\pi\) | ||||
−0.833416 | + | 0.552646i | \(0.813618\pi\) | |||||||
\(810\) | 1.41121e71 | 0.779310 | ||||||||
\(811\) | 2.95951e71 | 1.58565 | 0.792827 | − | 0.609446i | \(-0.208608\pi\) | ||||
0.792827 | + | 0.609446i | \(0.208608\pi\) | |||||||
\(812\) | −6.79686e70 | −0.353334 | ||||||||
\(813\) | 4.70822e70 | 0.237486 | ||||||||
\(814\) | −6.74220e70 | −0.329992 | ||||||||
\(815\) | −3.80545e71 | −1.80736 | ||||||||
\(816\) | −2.65104e70 | −0.122182 | ||||||||
\(817\) | 1.58528e70 | 0.0709031 | ||||||||
\(818\) | 2.03804e71 | 0.884621 | ||||||||
\(819\) | 9.04400e69 | 0.0380982 | ||||||||
\(820\) | −1.35985e71 | −0.555972 | ||||||||
\(821\) | 2.31367e71 | 0.918107 | 0.459053 | − | 0.888409i | \(-0.348189\pi\) | ||||
0.459053 | + | 0.888409i | \(0.348189\pi\) | |||||||
\(822\) | 2.24752e70 | 0.0865652 | ||||||||
\(823\) | 1.40957e70 | 0.0526976 | 0.0263488 | − | 0.999653i | \(-0.491612\pi\) | ||||
0.0263488 | + | 0.999653i | \(0.491612\pi\) | |||||||
\(824\) | −5.21108e70 | −0.189108 | ||||||||
\(825\) | 7.12525e70 | 0.251003 | ||||||||
\(826\) | −1.93569e70 | −0.0661950 | ||||||||
\(827\) | 3.13935e71 | 1.04221 | 0.521105 | − | 0.853493i | \(-0.325520\pi\) | ||||
0.521105 | + | 0.853493i | \(0.325520\pi\) | |||||||
\(828\) | 4.98670e70 | 0.160720 | ||||||||
\(829\) | −1.00068e71 | −0.313118 | −0.156559 | − | 0.987669i | \(-0.550040\pi\) | ||||
−0.156559 | + | 0.987669i | \(0.550040\pi\) | |||||||
\(830\) | −2.91104e71 | −0.884371 | ||||||||
\(831\) | −3.92762e70 | −0.115852 | ||||||||
\(832\) | −1.09903e69 | −0.00314767 | ||||||||
\(833\) | 1.07722e72 | 2.99574 | ||||||||
\(834\) | 6.88194e70 | 0.185841 | ||||||||
\(835\) | −4.42833e71 | −1.16124 | ||||||||
\(836\) | −4.52657e70 | −0.115270 | ||||||||
\(837\) | 3.67718e71 | 0.909370 | ||||||||
\(838\) | −1.58334e71 | −0.380272 | ||||||||
\(839\) | 7.28357e70 | 0.169893 | 0.0849466 | − | 0.996386i | \(-0.472928\pi\) | ||||
0.0849466 | + | 0.996386i | \(0.472928\pi\) | |||||||
\(840\) | −9.79903e70 | −0.221994 | ||||||||
\(841\) | −3.69518e71 | −0.813081 | ||||||||
\(842\) | −1.18705e71 | −0.253701 | ||||||||
\(843\) | −6.08535e70 | −0.126331 | ||||||||
\(844\) | −3.84804e71 | −0.775978 | ||||||||
\(845\) | −7.18626e71 | −1.40771 | ||||||||
\(846\) | 5.04311e71 | 0.959676 | ||||||||
\(847\) | −1.10883e71 | −0.204984 | ||||||||
\(848\) | 2.68016e71 | 0.481352 | ||||||||
\(849\) | −7.19814e70 | −0.125598 | ||||||||
\(850\) | 7.35663e71 | 1.24714 | ||||||||
\(851\) | −1.05209e71 | −0.173293 | ||||||||
\(852\) | 6.21313e70 | 0.0994352 | ||||||||
\(853\) | −3.12687e71 | −0.486249 | −0.243125 | − | 0.969995i | \(-0.578172\pi\) | ||||
−0.243125 | + | 0.969995i | \(0.578172\pi\) | |||||||
\(854\) | −1.17273e72 | −1.77207 | ||||||||
\(855\) | −2.18896e71 | −0.321417 | ||||||||
\(856\) | −3.74202e71 | −0.533948 | ||||||||
\(857\) | −1.07117e72 | −1.48535 | −0.742675 | − | 0.669652i | \(-0.766443\pi\) | ||||
−0.742675 | + | 0.669652i | \(0.766443\pi\) | |||||||
\(858\) | −3.36987e69 | −0.00454124 | ||||||||
\(859\) | 6.94017e71 | 0.908945 | 0.454473 | − | 0.890761i | \(-0.349828\pi\) | ||||
0.454473 | + | 0.890761i | \(0.349828\pi\) | |||||||
\(860\) | 1.59145e71 | 0.202573 | ||||||||
\(861\) | 2.84425e71 | 0.351876 | ||||||||
\(862\) | 2.48078e71 | 0.298305 | ||||||||
\(863\) | 1.51616e72 | 1.77207 | 0.886037 | − | 0.463614i | \(-0.153448\pi\) | ||||
0.886037 | + | 0.463614i | \(0.153448\pi\) | |||||||
\(864\) | 8.17130e70 | 0.0928334 | ||||||||
\(865\) | 1.15679e71 | 0.127749 | ||||||||
\(866\) | 9.07379e71 | 0.974092 | ||||||||
\(867\) | −5.77938e71 | −0.603134 | ||||||||
\(868\) | 1.39493e72 | 1.41521 | ||||||||
\(869\) | −4.45012e71 | −0.438922 | ||||||||
\(870\) | 1.22470e71 | 0.117438 | ||||||||
\(871\) | −2.11251e70 | −0.0196949 | ||||||||
\(872\) | −6.96795e69 | −0.00631613 | ||||||||
\(873\) | 1.05601e72 | 0.930723 | ||||||||
\(874\) | −7.06354e70 | −0.0605330 | ||||||||
\(875\) | −4.37435e70 | −0.0364516 | ||||||||
\(876\) | 1.97447e71 | 0.159993 | ||||||||
\(877\) | −1.82968e72 | −1.44173 | −0.720867 | − | 0.693073i | \(-0.756256\pi\) | ||||
−0.720867 | + | 0.693073i | \(0.756256\pi\) | |||||||
\(878\) | −6.19400e70 | −0.0474630 | ||||||||
\(879\) | −5.21382e71 | −0.388533 | ||||||||
\(880\) | −4.54420e71 | −0.329330 | ||||||||
\(881\) | 8.23192e71 | 0.580218 | 0.290109 | − | 0.956994i | \(-0.406308\pi\) | ||||
0.290109 | + | 0.956994i | \(0.406308\pi\) | |||||||
\(882\) | −1.59604e72 | −1.09412 | ||||||||
\(883\) | 2.32646e72 | 1.55116 | 0.775582 | − | 0.631247i | \(-0.217456\pi\) | ||||
0.775582 | + | 0.631247i | \(0.217456\pi\) | |||||||
\(884\) | −3.47929e70 | −0.0225637 | ||||||||
\(885\) | 3.48785e70 | 0.0220013 | ||||||||
\(886\) | −1.25756e72 | −0.771617 | ||||||||
\(887\) | 2.02329e72 | 1.20762 | 0.603809 | − | 0.797129i | \(-0.293649\pi\) | ||||
0.603809 | + | 0.797129i | \(0.293649\pi\) | |||||||
\(888\) | −8.28698e70 | −0.0481148 | ||||||||
\(889\) | −4.57181e72 | −2.58223 | ||||||||
\(890\) | 2.59097e71 | 0.142366 | ||||||||
\(891\) | −1.36881e72 | −0.731709 | ||||||||
\(892\) | 4.93405e70 | 0.0256605 | ||||||||
\(893\) | −7.14344e71 | −0.361449 | ||||||||
\(894\) | −4.23520e71 | −0.208499 | ||||||||
\(895\) | 5.82893e71 | 0.279206 | ||||||||
\(896\) | 3.09978e71 | 0.144472 | ||||||||
\(897\) | −5.25855e69 | −0.00238479 | ||||||||
\(898\) | −9.48000e71 | −0.418349 | ||||||||
\(899\) | −1.74341e72 | −0.748666 | ||||||||
\(900\) | −1.08998e72 | −0.455486 | ||||||||
\(901\) | 8.48479e72 | 3.45051 | ||||||||
\(902\) | 1.31899e72 | 0.522013 | ||||||||
\(903\) | −3.32865e71 | −0.128209 | ||||||||
\(904\) | 1.08401e71 | 0.0406355 | ||||||||
\(905\) | −1.61398e72 | −0.588854 | ||||||||
\(906\) | −5.24850e70 | −0.0186378 | ||||||||
\(907\) | 5.38576e72 | 1.86152 | 0.930762 | − | 0.365627i | \(-0.119145\pi\) | ||||
0.930762 | + | 0.365627i | \(0.119145\pi\) | |||||||
\(908\) | −1.16447e72 | −0.391765 | ||||||||
\(909\) | −3.19212e72 | −1.04536 | ||||||||
\(910\) | −1.28605e71 | −0.0409961 | ||||||||
\(911\) | −4.00433e72 | −1.24260 | −0.621298 | − | 0.783574i | \(-0.713394\pi\) | ||||
−0.621298 | + | 0.783574i | \(0.713394\pi\) | |||||||
\(912\) | −5.56370e70 | −0.0168070 | ||||||||
\(913\) | 2.82356e72 | 0.830352 | ||||||||
\(914\) | 9.95707e71 | 0.285069 | ||||||||
\(915\) | 2.11310e72 | 0.588983 | ||||||||
\(916\) | 1.75984e72 | 0.477568 | ||||||||
\(917\) | −1.07802e72 | −0.284825 | ||||||||
\(918\) | 2.58685e72 | 0.665465 | ||||||||
\(919\) | −6.26307e72 | −1.56876 | −0.784381 | − | 0.620279i | \(-0.787019\pi\) | ||||
−0.784381 | + | 0.620279i | \(0.787019\pi\) | |||||||
\(920\) | −7.09104e71 | −0.172945 | ||||||||
\(921\) | −3.12507e70 | −0.00742162 | ||||||||
\(922\) | 1.77908e72 | 0.411423 | ||||||||
\(923\) | 8.15426e70 | 0.0183630 | ||||||||
\(924\) | 9.50455e71 | 0.208434 | ||||||||
\(925\) | 2.29963e72 | 0.491118 | ||||||||
\(926\) | 3.13339e72 | 0.651695 | ||||||||
\(927\) | 2.44425e72 | 0.495099 | ||||||||
\(928\) | −3.87415e71 | −0.0764278 | ||||||||
\(929\) | −3.00047e72 | −0.576508 | −0.288254 | − | 0.957554i | \(-0.593075\pi\) | ||||
−0.288254 | + | 0.957554i | \(0.593075\pi\) | |||||||
\(930\) | −2.51348e72 | −0.470373 | ||||||||
\(931\) | 2.26075e72 | 0.412084 | ||||||||
\(932\) | −1.63091e72 | −0.289561 | ||||||||
\(933\) | 5.80684e71 | 0.100424 | ||||||||
\(934\) | −3.82987e71 | −0.0645187 | ||||||||
\(935\) | −1.43859e73 | −2.36076 | ||||||||
\(936\) | 5.15501e70 | 0.00824083 | ||||||||
\(937\) | −3.72864e72 | −0.580671 | −0.290336 | − | 0.956925i | \(-0.593767\pi\) | ||||
−0.290336 | + | 0.956925i | \(0.593767\pi\) | |||||||
\(938\) | 5.95823e72 | 0.903957 | ||||||||
\(939\) | −2.58202e72 | −0.381639 | ||||||||
\(940\) | −7.17126e72 | −1.03267 | ||||||||
\(941\) | −2.09160e72 | −0.293449 | −0.146724 | − | 0.989177i | \(-0.546873\pi\) | ||||
−0.146724 | + | 0.989177i | \(0.546873\pi\) | |||||||
\(942\) | −2.53289e72 | −0.346233 | ||||||||
\(943\) | 2.05823e72 | 0.274131 | ||||||||
\(944\) | −1.10333e71 | −0.0143183 | ||||||||
\(945\) | 9.56174e72 | 1.20909 | ||||||||
\(946\) | −1.54363e72 | −0.190200 | ||||||||
\(947\) | 8.20140e72 | 0.984721 | 0.492361 | − | 0.870391i | \(-0.336134\pi\) | ||||
0.492361 | + | 0.870391i | \(0.336134\pi\) | |||||||
\(948\) | −5.46974e71 | −0.0639974 | ||||||||
\(949\) | 2.59134e71 | 0.0295463 | ||||||||
\(950\) | 1.54392e72 | 0.171553 | ||||||||
\(951\) | −3.15574e72 | −0.341727 | ||||||||
\(952\) | 9.81319e72 | 1.03563 | ||||||||
\(953\) | 1.17749e73 | 1.21110 | 0.605549 | − | 0.795808i | \(-0.292953\pi\) | ||||
0.605549 | + | 0.795808i | \(0.292953\pi\) | |||||||
\(954\) | −1.25713e73 | −1.26021 | ||||||||
\(955\) | −4.27444e72 | −0.417635 | ||||||||
\(956\) | 5.62556e72 | 0.535732 | ||||||||
\(957\) | −1.18790e72 | −0.110265 | ||||||||
\(958\) | −1.80321e72 | −0.163152 | ||||||||
\(959\) | −8.31948e72 | −0.733737 | ||||||||
\(960\) | −5.58536e71 | −0.0480182 | ||||||||
\(961\) | 2.38482e73 | 1.99863 | ||||||||
\(962\) | −1.08760e71 | −0.00888549 | ||||||||
\(963\) | 1.75519e73 | 1.39791 | ||||||||
\(964\) | −2.45270e72 | −0.190440 | ||||||||
\(965\) | 1.31334e73 | 0.994168 | ||||||||
\(966\) | 1.48315e72 | 0.109457 | ||||||||
\(967\) | −3.48982e72 | −0.251105 | −0.125552 | − | 0.992087i | \(-0.540070\pi\) | ||||
−0.125552 | + | 0.992087i | \(0.540070\pi\) | |||||||
\(968\) | −6.32023e71 | −0.0443391 | ||||||||
\(969\) | −1.76134e72 | −0.120479 | ||||||||
\(970\) | −1.50164e73 | −1.00152 | ||||||||
\(971\) | −2.02593e73 | −1.31751 | −0.658753 | − | 0.752359i | \(-0.728916\pi\) | ||||
−0.658753 | + | 0.752359i | \(0.728916\pi\) | |||||||
\(972\) | −5.82312e72 | −0.369260 | ||||||||
\(973\) | −2.54744e73 | −1.57521 | ||||||||
\(974\) | 1.59879e72 | 0.0964041 | ||||||||
\(975\) | 1.14939e71 | 0.00675859 | ||||||||
\(976\) | −6.68447e72 | −0.383307 | ||||||||
\(977\) | −1.10677e73 | −0.618926 | −0.309463 | − | 0.950911i | \(-0.600149\pi\) | ||||
−0.309463 | + | 0.950911i | \(0.600149\pi\) | |||||||
\(978\) | 4.53679e72 | 0.247427 | ||||||||
\(979\) | −2.51311e72 | −0.133670 | ||||||||
\(980\) | 2.26956e73 | 1.17734 | ||||||||
\(981\) | 3.26831e71 | 0.0165361 | ||||||||
\(982\) | 1.30088e73 | 0.641958 | ||||||||
\(983\) | −6.73348e72 | −0.324100 | −0.162050 | − | 0.986783i | \(-0.551811\pi\) | ||||
−0.162050 | + | 0.986783i | \(0.551811\pi\) | |||||||
\(984\) | 1.62120e72 | 0.0761125 | ||||||||
\(985\) | −2.64530e73 | −1.21140 | ||||||||
\(986\) | −1.22647e73 | −0.547863 | ||||||||
\(987\) | 1.49993e73 | 0.653582 | ||||||||
\(988\) | −7.30193e70 | −0.00310379 | ||||||||
\(989\) | −2.40877e72 | −0.0998819 | ||||||||
\(990\) | 2.13145e73 | 0.862209 | ||||||||
\(991\) | −2.62295e73 | −1.03511 | −0.517554 | − | 0.855650i | \(-0.673157\pi\) | ||||
−0.517554 | + | 0.855650i | \(0.673157\pi\) | |||||||
\(992\) | 7.95101e72 | 0.306116 | ||||||||
\(993\) | −8.53053e72 | −0.320420 | ||||||||
\(994\) | −2.29987e73 | −0.842824 | ||||||||
\(995\) | 5.90102e73 | 2.10990 | ||||||||
\(996\) | 3.47049e72 | 0.121070 | ||||||||
\(997\) | 2.54966e73 | 0.867864 | 0.433932 | − | 0.900946i | \(-0.357126\pi\) | ||||
0.433932 | + | 0.900946i | \(0.357126\pi\) | |||||||
\(998\) | 2.62966e73 | 0.873375 | ||||||||
\(999\) | 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 | 2.50.a.b.1.2 | ✓ | 3 | |
4.3 | odd | 2 | 16.50.a.b.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.50.a.b.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
16.50.a.b.1.2 | 3 | 4.3 | odd | 2 |