Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,14,Mod(1,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(5.36154644760\) |
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: | \( x^{3} - x^{2} - 4466x - 18720 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(69.3208\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −90.6415 | −1.00146 | −0.500729 | − | 0.865604i | \(-0.666935\pi\) | ||||
−0.500729 | + | 0.865604i | \(0.666935\pi\) | |||||||
\(3\) | −1125.79 | −0.891601 | −0.445801 | − | 0.895132i | \(-0.647081\pi\) | ||||
−0.445801 | + | 0.895132i | \(0.647081\pi\) | |||||||
\(4\) | 23.8902 | 0.00291628 | ||||||||
\(5\) | 15625.0 | 0.447214 | ||||||||
\(6\) | 102044. | 0.892900 | ||||||||
\(7\) | 324482. | 1.04245 | 0.521223 | − | 0.853420i | \(-0.325476\pi\) | ||||
0.521223 | + | 0.853420i | \(0.325476\pi\) | |||||||
\(8\) | 740370. | 0.998537 | ||||||||
\(9\) | −326912. | −0.205047 | ||||||||
\(10\) | −1.41627e6 | −0.447865 | ||||||||
\(11\) | −1.64726e6 | −0.280356 | −0.140178 | − | 0.990126i | \(-0.544768\pi\) | ||||
−0.140178 | + | 0.990126i | \(0.544768\pi\) | |||||||
\(12\) | −26895.4 | −0.00260016 | ||||||||
\(13\) | 6.26700e6 | 0.360104 | 0.180052 | − | 0.983657i | \(-0.442373\pi\) | ||||
0.180052 | + | 0.983657i | \(0.442373\pi\) | |||||||
\(14\) | −2.94116e7 | −1.04397 | ||||||||
\(15\) | −1.75905e7 | −0.398736 | ||||||||
\(16\) | −6.73040e7 | −1.00291 | ||||||||
\(17\) | 1.66481e8 | 1.67281 | 0.836406 | − | 0.548110i | \(-0.184653\pi\) | ||||
0.836406 | + | 0.548110i | \(0.184653\pi\) | |||||||
\(18\) | 2.96318e7 | 0.205346 | ||||||||
\(19\) | 3.12929e8 | 1.52598 | 0.762988 | − | 0.646413i | \(-0.223732\pi\) | ||||
0.762988 | + | 0.646413i | \(0.223732\pi\) | |||||||
\(20\) | 373284. | 0.00130420 | ||||||||
\(21\) | −3.65300e8 | −0.929447 | ||||||||
\(22\) | 1.49311e8 | 0.280765 | ||||||||
\(23\) | −6.32351e8 | −0.890692 | −0.445346 | − | 0.895359i | \(-0.646919\pi\) | ||||
−0.445346 | + | 0.895359i | \(0.646919\pi\) | |||||||
\(24\) | −8.33504e8 | −0.890296 | ||||||||
\(25\) | 2.44141e8 | 0.200000 | ||||||||
\(26\) | −5.68051e8 | −0.360629 | ||||||||
\(27\) | 2.16291e9 | 1.07442 | ||||||||
\(28\) | 7.75194e6 | 0.00304007 | ||||||||
\(29\) | −2.82750e9 | −0.882704 | −0.441352 | − | 0.897334i | \(-0.645501\pi\) | ||||
−0.441352 | + | 0.897334i | \(0.645501\pi\) | |||||||
\(30\) | 1.59443e9 | 0.399317 | ||||||||
\(31\) | 7.61629e9 | 1.54132 | 0.770659 | − | 0.637247i | \(-0.219927\pi\) | ||||
0.770659 | + | 0.637247i | \(0.219927\pi\) | |||||||
\(32\) | 3.54269e7 | 0.00583255 | ||||||||
\(33\) | 1.85448e9 | 0.249966 | ||||||||
\(34\) | −1.50901e10 | −1.67525 | ||||||||
\(35\) | 5.07004e9 | 0.466196 | ||||||||
\(36\) | −7.80998e6 | −0.000597976 0 | ||||||||
\(37\) | 1.99161e10 | 1.27613 | 0.638063 | − | 0.769984i | \(-0.279736\pi\) | ||||
0.638063 | + | 0.769984i | \(0.279736\pi\) | |||||||
\(38\) | −2.83644e10 | −1.52820 | ||||||||
\(39\) | −7.05535e9 | −0.321069 | ||||||||
\(40\) | 1.15683e10 | 0.446559 | ||||||||
\(41\) | −4.69877e10 | −1.54486 | −0.772430 | − | 0.635099i | \(-0.780959\pi\) | ||||
−0.772430 | + | 0.635099i | \(0.780959\pi\) | |||||||
\(42\) | 3.31114e10 | 0.930801 | ||||||||
\(43\) | −7.85897e9 | −0.189592 | −0.0947961 | − | 0.995497i | \(-0.530220\pi\) | ||||
−0.0947961 | + | 0.995497i | \(0.530220\pi\) | |||||||
\(44\) | −3.93534e7 | −0.000817599 0 | ||||||||
\(45\) | −5.10799e9 | −0.0917000 | ||||||||
\(46\) | 5.73173e10 | 0.891990 | ||||||||
\(47\) | 8.31265e10 | 1.12487 | 0.562437 | − | 0.826840i | \(-0.309864\pi\) | ||||
0.562437 | + | 0.826840i | \(0.309864\pi\) | |||||||
\(48\) | 7.57704e10 | 0.894194 | ||||||||
\(49\) | 8.39984e9 | 0.0866955 | ||||||||
\(50\) | −2.21293e10 | −0.200291 | ||||||||
\(51\) | −1.87423e11 | −1.49148 | ||||||||
\(52\) | 1.49720e8 | 0.00105017 | ||||||||
\(53\) | −1.19285e11 | −0.739255 | −0.369628 | − | 0.929180i | \(-0.620515\pi\) | ||||
−0.369628 | + | 0.929180i | \(0.620515\pi\) | |||||||
\(54\) | −1.96050e11 | −1.07599 | ||||||||
\(55\) | −2.57385e10 | −0.125379 | ||||||||
\(56\) | 2.40237e11 | 1.04092 | ||||||||
\(57\) | −3.52294e11 | −1.36056 | ||||||||
\(58\) | 2.56289e11 | 0.883990 | ||||||||
\(59\) | 4.20299e11 | 1.29724 | 0.648620 | − | 0.761112i | \(-0.275346\pi\) | ||||
0.648620 | + | 0.761112i | \(0.275346\pi\) | |||||||
\(60\) | −4.20241e8 | −0.00116283 | ||||||||
\(61\) | 4.15504e11 | 1.03260 | 0.516299 | − | 0.856409i | \(-0.327309\pi\) | ||||
0.516299 | + | 0.856409i | \(0.327309\pi\) | |||||||
\(62\) | −6.90352e11 | −1.54356 | ||||||||
\(63\) | −1.06077e11 | −0.213751 | ||||||||
\(64\) | 5.48143e11 | 0.997067 | ||||||||
\(65\) | 9.79220e10 | 0.161044 | ||||||||
\(66\) | −1.68093e11 | −0.250330 | ||||||||
\(67\) | −1.02968e11 | −0.139065 | −0.0695323 | − | 0.997580i | \(-0.522151\pi\) | ||||
−0.0695323 | + | 0.997580i | \(0.522151\pi\) | |||||||
\(68\) | 3.97727e9 | 0.00487839 | ||||||||
\(69\) | 7.11897e11 | 0.794142 | ||||||||
\(70\) | −4.59556e11 | −0.466876 | ||||||||
\(71\) | −4.00383e11 | −0.370933 | −0.185467 | − | 0.982651i | \(-0.559380\pi\) | ||||
−0.185467 | + | 0.982651i | \(0.559380\pi\) | |||||||
\(72\) | −2.42036e11 | −0.204747 | ||||||||
\(73\) | 5.55011e11 | 0.429243 | 0.214621 | − | 0.976697i | \(-0.431148\pi\) | ||||
0.214621 | + | 0.976697i | \(0.431148\pi\) | |||||||
\(74\) | −1.80523e12 | −1.27798 | ||||||||
\(75\) | −2.74852e11 | −0.178320 | ||||||||
\(76\) | 7.47593e9 | 0.00445017 | ||||||||
\(77\) | −5.34508e11 | −0.292257 | ||||||||
\(78\) | 6.39508e11 | 0.321537 | ||||||||
\(79\) | 1.60313e12 | 0.741980 | 0.370990 | − | 0.928637i | \(-0.379018\pi\) | ||||
0.370990 | + | 0.928637i | \(0.379018\pi\) | |||||||
\(80\) | −1.05163e12 | −0.448514 | ||||||||
\(81\) | −1.91379e12 | −0.752908 | ||||||||
\(82\) | 4.25904e12 | 1.54711 | ||||||||
\(83\) | −2.64201e11 | −0.0887005 | −0.0443503 | − | 0.999016i | \(-0.514122\pi\) | ||||
−0.0443503 | + | 0.999016i | \(0.514122\pi\) | |||||||
\(84\) | −8.72709e9 | −0.00271053 | ||||||||
\(85\) | 2.60127e12 | 0.748104 | ||||||||
\(86\) | 7.12349e11 | 0.189868 | ||||||||
\(87\) | 3.18318e12 | 0.787020 | ||||||||
\(88\) | −1.21958e12 | −0.279946 | ||||||||
\(89\) | −3.69637e12 | −0.788388 | −0.394194 | − | 0.919027i | \(-0.628976\pi\) | ||||
−0.394194 | + | 0.919027i | \(0.628976\pi\) | |||||||
\(90\) | 4.62997e11 | 0.0918336 | ||||||||
\(91\) | 2.03353e12 | 0.375390 | ||||||||
\(92\) | −1.51070e10 | −0.00259751 | ||||||||
\(93\) | −8.57437e12 | −1.37424 | ||||||||
\(94\) | −7.53472e12 | −1.12651 | ||||||||
\(95\) | 4.88952e12 | 0.682437 | ||||||||
\(96\) | −3.98834e10 | −0.00520030 | ||||||||
\(97\) | −1.00920e13 | −1.23016 | −0.615081 | − | 0.788464i | \(-0.710877\pi\) | ||||
−0.615081 | + | 0.788464i | \(0.710877\pi\) | |||||||
\(98\) | −7.61375e11 | −0.0868218 | ||||||||
\(99\) | 5.38510e11 | 0.0574863 | ||||||||
\(100\) | 5.83256e9 | 0.000583256 0 | ||||||||
\(101\) | 2.56737e12 | 0.240658 | 0.120329 | − | 0.992734i | \(-0.461605\pi\) | ||||
0.120329 | + | 0.992734i | \(0.461605\pi\) | |||||||
\(102\) | 1.69884e13 | 1.49365 | ||||||||
\(103\) | 1.21037e13 | 0.998791 | 0.499395 | − | 0.866374i | \(-0.333556\pi\) | ||||
0.499395 | + | 0.866374i | \(0.333556\pi\) | |||||||
\(104\) | 4.63990e12 | 0.359577 | ||||||||
\(105\) | −5.70782e12 | −0.415661 | ||||||||
\(106\) | 1.08122e13 | 0.740332 | ||||||||
\(107\) | 9.37488e12 | 0.603909 | 0.301954 | − | 0.953322i | \(-0.402361\pi\) | ||||
0.301954 | + | 0.953322i | \(0.402361\pi\) | |||||||
\(108\) | 5.16724e10 | 0.00313332 | ||||||||
\(109\) | −2.49908e13 | −1.42727 | −0.713637 | − | 0.700516i | \(-0.752953\pi\) | ||||
−0.713637 | + | 0.700516i | \(0.752953\pi\) | |||||||
\(110\) | 2.33298e12 | 0.125562 | ||||||||
\(111\) | −2.24214e13 | −1.13779 | ||||||||
\(112\) | −2.18390e13 | −1.04548 | ||||||||
\(113\) | 1.35600e13 | 0.612703 | 0.306352 | − | 0.951918i | \(-0.400892\pi\) | ||||
0.306352 | + | 0.951918i | \(0.400892\pi\) | |||||||
\(114\) | 3.19324e13 | 1.36254 | ||||||||
\(115\) | −9.88049e12 | −0.398330 | ||||||||
\(116\) | −6.75494e10 | −0.00257421 | ||||||||
\(117\) | −2.04876e12 | −0.0738384 | ||||||||
\(118\) | −3.80966e13 | −1.29913 | ||||||||
\(119\) | 5.40202e13 | 1.74382 | ||||||||
\(120\) | −1.30235e13 | −0.398153 | ||||||||
\(121\) | −3.18092e13 | −0.921400 | ||||||||
\(122\) | −3.76619e13 | −1.03410 | ||||||||
\(123\) | 5.28985e13 | 1.37740 | ||||||||
\(124\) | 1.81955e11 | 0.00449492 | ||||||||
\(125\) | 3.81470e12 | 0.0894427 | ||||||||
\(126\) | 9.61499e12 | 0.214062 | ||||||||
\(127\) | −1.16836e13 | −0.247088 | −0.123544 | − | 0.992339i | \(-0.539426\pi\) | ||||
−0.123544 | + | 0.992339i | \(0.539426\pi\) | |||||||
\(128\) | −4.99748e13 | −1.00435 | ||||||||
\(129\) | 8.84758e12 | 0.169041 | ||||||||
\(130\) | −8.87580e12 | −0.161278 | ||||||||
\(131\) | 5.12734e13 | 0.886398 | 0.443199 | − | 0.896423i | \(-0.353843\pi\) | ||||
0.443199 | + | 0.896423i | \(0.353843\pi\) | |||||||
\(132\) | 4.43038e10 | 0.000728972 0 | ||||||||
\(133\) | 1.01540e14 | 1.59075 | ||||||||
\(134\) | 9.33319e12 | 0.139267 | ||||||||
\(135\) | 3.37955e13 | 0.480496 | ||||||||
\(136\) | 1.23258e14 | 1.67036 | ||||||||
\(137\) | −7.15579e13 | −0.924642 | −0.462321 | − | 0.886713i | \(-0.652983\pi\) | ||||
−0.462321 | + | 0.886713i | \(0.652983\pi\) | |||||||
\(138\) | −6.45275e13 | −0.795299 | ||||||||
\(139\) | −1.16286e14 | −1.36751 | −0.683754 | − | 0.729712i | \(-0.739654\pi\) | ||||
−0.683754 | + | 0.729712i | \(0.739654\pi\) | |||||||
\(140\) | 1.21124e11 | 0.00135956 | ||||||||
\(141\) | −9.35833e13 | −1.00294 | ||||||||
\(142\) | 3.62913e13 | 0.371474 | ||||||||
\(143\) | −1.03234e13 | −0.100958 | ||||||||
\(144\) | 2.20025e13 | 0.205644 | ||||||||
\(145\) | −4.41796e13 | −0.394757 | ||||||||
\(146\) | −5.03070e13 | −0.429868 | ||||||||
\(147\) | −9.45649e12 | −0.0772978 | ||||||||
\(148\) | 4.75800e11 | 0.00372154 | ||||||||
\(149\) | −1.43657e14 | −1.07552 | −0.537758 | − | 0.843099i | \(-0.680729\pi\) | ||||
−0.537758 | + | 0.843099i | \(0.680729\pi\) | |||||||
\(150\) | 2.49130e13 | 0.178580 | ||||||||
\(151\) | −1.99719e13 | −0.137110 | −0.0685551 | − | 0.997647i | \(-0.521839\pi\) | ||||
−0.0685551 | + | 0.997647i | \(0.521839\pi\) | |||||||
\(152\) | 2.31683e14 | 1.52374 | ||||||||
\(153\) | −5.44246e13 | −0.343006 | ||||||||
\(154\) | 4.84486e13 | 0.292683 | ||||||||
\(155\) | 1.19005e14 | 0.689299 | ||||||||
\(156\) | −1.68554e11 | −0.000936329 0 | ||||||||
\(157\) | 2.46452e14 | 1.31336 | 0.656682 | − | 0.754168i | \(-0.271959\pi\) | ||||
0.656682 | + | 0.754168i | \(0.271959\pi\) | |||||||
\(158\) | −1.45310e14 | −0.743061 | ||||||||
\(159\) | 1.34291e14 | 0.659121 | ||||||||
\(160\) | 5.53545e11 | 0.00260839 | ||||||||
\(161\) | −2.05187e14 | −0.928499 | ||||||||
\(162\) | 1.73469e14 | 0.754005 | ||||||||
\(163\) | 1.33661e14 | 0.558194 | 0.279097 | − | 0.960263i | \(-0.409965\pi\) | ||||
0.279097 | + | 0.960263i | \(0.409965\pi\) | |||||||
\(164\) | −1.12255e12 | −0.00450525 | ||||||||
\(165\) | 2.89762e13 | 0.111788 | ||||||||
\(166\) | 2.39476e13 | 0.0888298 | ||||||||
\(167\) | −1.57170e14 | −0.560676 | −0.280338 | − | 0.959901i | \(-0.590447\pi\) | ||||
−0.280338 | + | 0.959901i | \(0.590447\pi\) | |||||||
\(168\) | −2.70457e14 | −0.928087 | ||||||||
\(169\) | −2.63600e14 | −0.870325 | ||||||||
\(170\) | −2.35783e14 | −0.749194 | ||||||||
\(171\) | −1.02300e14 | −0.312897 | ||||||||
\(172\) | −1.87752e11 | −0.000552904 0 | ||||||||
\(173\) | 3.32272e14 | 0.942309 | 0.471155 | − | 0.882051i | \(-0.343837\pi\) | ||||
0.471155 | + | 0.882051i | \(0.343837\pi\) | |||||||
\(174\) | −2.88528e14 | −0.788167 | ||||||||
\(175\) | 7.92193e13 | 0.208489 | ||||||||
\(176\) | 1.10867e14 | 0.281172 | ||||||||
\(177\) | −4.73170e14 | −1.15662 | ||||||||
\(178\) | 3.35044e14 | 0.789537 | ||||||||
\(179\) | 4.96701e14 | 1.12863 | 0.564313 | − | 0.825561i | \(-0.309141\pi\) | ||||
0.564313 | + | 0.825561i | \(0.309141\pi\) | |||||||
\(180\) | −1.22031e11 | −0.000267423 0 | ||||||||
\(181\) | 5.73895e14 | 1.21317 | 0.606585 | − | 0.795019i | \(-0.292539\pi\) | ||||
0.606585 | + | 0.795019i | \(0.292539\pi\) | |||||||
\(182\) | −1.84323e14 | −0.375937 | ||||||||
\(183\) | −4.67771e14 | −0.920665 | ||||||||
\(184\) | −4.68174e14 | −0.889388 | ||||||||
\(185\) | 3.11189e14 | 0.570701 | ||||||||
\(186\) | 7.77194e14 | 1.37624 | ||||||||
\(187\) | −2.74238e14 | −0.468984 | ||||||||
\(188\) | 1.98591e12 | 0.00328045 | ||||||||
\(189\) | 7.01828e14 | 1.12003 | ||||||||
\(190\) | −4.43193e14 | −0.683431 | ||||||||
\(191\) | −9.21109e14 | −1.37276 | −0.686379 | − | 0.727244i | \(-0.740801\pi\) | ||||
−0.686379 | + | 0.727244i | \(0.740801\pi\) | |||||||
\(192\) | −6.17096e14 | −0.888986 | ||||||||
\(193\) | 8.88779e14 | 1.23786 | 0.618929 | − | 0.785447i | \(-0.287567\pi\) | ||||
0.618929 | + | 0.785447i | \(0.287567\pi\) | |||||||
\(194\) | 9.14757e14 | 1.23195 | ||||||||
\(195\) | −1.10240e14 | −0.143587 | ||||||||
\(196\) | 2.00674e11 | 0.000252829 0 | ||||||||
\(197\) | −4.70943e13 | −0.0574035 | −0.0287017 | − | 0.999588i | \(-0.509137\pi\) | ||||
−0.0287017 | + | 0.999588i | \(0.509137\pi\) | |||||||
\(198\) | −4.88113e13 | −0.0575701 | ||||||||
\(199\) | 4.94174e14 | 0.564072 | 0.282036 | − | 0.959404i | \(-0.408990\pi\) | ||||
0.282036 | + | 0.959404i | \(0.408990\pi\) | |||||||
\(200\) | 1.80754e14 | 0.199707 | ||||||||
\(201\) | 1.15921e14 | 0.123990 | ||||||||
\(202\) | −2.32710e14 | −0.241008 | ||||||||
\(203\) | −9.17473e14 | −0.920172 | ||||||||
\(204\) | −4.47758e12 | −0.00434958 | ||||||||
\(205\) | −7.34183e14 | −0.690883 | ||||||||
\(206\) | −1.09709e15 | −1.00025 | ||||||||
\(207\) | 2.06723e14 | 0.182634 | ||||||||
\(208\) | −4.21795e14 | −0.361151 | ||||||||
\(209\) | −5.15477e14 | −0.427817 | ||||||||
\(210\) | 5.17365e14 | 0.416267 | ||||||||
\(211\) | −1.22476e15 | −0.955466 | −0.477733 | − | 0.878505i | \(-0.658541\pi\) | ||||
−0.477733 | + | 0.878505i | \(0.658541\pi\) | |||||||
\(212\) | −2.84975e12 | −0.00215588 | ||||||||
\(213\) | 4.50748e14 | 0.330725 | ||||||||
\(214\) | −8.49754e14 | −0.604789 | ||||||||
\(215\) | −1.22796e14 | −0.0847882 | ||||||||
\(216\) | 1.60136e15 | 1.07285 | ||||||||
\(217\) | 2.47135e15 | 1.60674 | ||||||||
\(218\) | 2.26520e15 | 1.42935 | ||||||||
\(219\) | −6.24828e14 | −0.382713 | ||||||||
\(220\) | −6.14897e11 | −0.000365641 0 | ||||||||
\(221\) | 1.04334e15 | 0.602387 | ||||||||
\(222\) | 2.03231e15 | 1.13945 | ||||||||
\(223\) | −1.23977e15 | −0.675087 | −0.337544 | − | 0.941310i | \(-0.609596\pi\) | ||||
−0.337544 | + | 0.941310i | \(0.609596\pi\) | |||||||
\(224\) | 1.14954e13 | 0.00608012 | ||||||||
\(225\) | −7.98124e13 | −0.0410095 | ||||||||
\(226\) | −1.22910e15 | −0.613596 | ||||||||
\(227\) | −3.31953e14 | −0.161031 | −0.0805154 | − | 0.996753i | \(-0.525657\pi\) | ||||
−0.0805154 | + | 0.996753i | \(0.525657\pi\) | |||||||
\(228\) | −8.41636e12 | −0.00396778 | ||||||||
\(229\) | −1.92799e15 | −0.883433 | −0.441717 | − | 0.897155i | \(-0.645630\pi\) | ||||
−0.441717 | + | 0.897155i | \(0.645630\pi\) | |||||||
\(230\) | 8.95583e14 | 0.398910 | ||||||||
\(231\) | 6.01746e14 | 0.260576 | ||||||||
\(232\) | −2.09339e15 | −0.881412 | ||||||||
\(233\) | −1.12721e15 | −0.461522 | −0.230761 | − | 0.973010i | \(-0.574122\pi\) | ||||
−0.230761 | + | 0.973010i | \(0.574122\pi\) | |||||||
\(234\) | 1.85703e14 | 0.0739460 | ||||||||
\(235\) | 1.29885e15 | 0.503059 | ||||||||
\(236\) | 1.00410e13 | 0.00378312 | ||||||||
\(237\) | −1.80479e15 | −0.661550 | ||||||||
\(238\) | −4.89648e15 | −1.74636 | ||||||||
\(239\) | −2.13044e15 | −0.739405 | −0.369703 | − | 0.929150i | \(-0.620540\pi\) | ||||
−0.369703 | + | 0.929150i | \(0.620540\pi\) | |||||||
\(240\) | 1.18391e15 | 0.399896 | ||||||||
\(241\) | 3.70709e15 | 1.21877 | 0.609386 | − | 0.792874i | \(-0.291416\pi\) | ||||
0.609386 | + | 0.792874i | \(0.291416\pi\) | |||||||
\(242\) | 2.88324e15 | 0.922743 | ||||||||
\(243\) | −1.29385e15 | −0.403128 | ||||||||
\(244\) | 9.92646e12 | 0.00301134 | ||||||||
\(245\) | 1.31248e14 | 0.0387714 | ||||||||
\(246\) | −4.79480e15 | −1.37941 | ||||||||
\(247\) | 1.96113e15 | 0.549510 | ||||||||
\(248\) | 5.63887e15 | 1.53906 | ||||||||
\(249\) | 2.97435e14 | 0.0790855 | ||||||||
\(250\) | −3.45770e14 | −0.0895730 | ||||||||
\(251\) | 1.69706e15 | 0.428368 | 0.214184 | − | 0.976793i | \(-0.431291\pi\) | ||||
0.214184 | + | 0.976793i | \(0.431291\pi\) | |||||||
\(252\) | −2.53420e12 | −0.000623358 0 | ||||||||
\(253\) | 1.04165e15 | 0.249711 | ||||||||
\(254\) | 1.05902e15 | 0.247448 | ||||||||
\(255\) | −2.92849e15 | −0.667011 | ||||||||
\(256\) | 3.94010e13 | 0.00874877 | ||||||||
\(257\) | −3.42768e14 | −0.0742053 | −0.0371027 | − | 0.999311i | \(-0.511813\pi\) | ||||
−0.0371027 | + | 0.999311i | \(0.511813\pi\) | |||||||
\(258\) | −8.01958e14 | −0.169287 | ||||||||
\(259\) | 6.46243e15 | 1.33029 | ||||||||
\(260\) | 2.33937e12 | 0.000469648 0 | ||||||||
\(261\) | 9.24342e14 | 0.180996 | ||||||||
\(262\) | −4.64750e15 | −0.887690 | ||||||||
\(263\) | 4.63399e15 | 0.863460 | 0.431730 | − | 0.902003i | \(-0.357903\pi\) | ||||
0.431730 | + | 0.902003i | \(0.357903\pi\) | |||||||
\(264\) | 1.37300e15 | 0.249600 | ||||||||
\(265\) | −1.86384e15 | −0.330605 | ||||||||
\(266\) | −9.20374e15 | −1.59307 | ||||||||
\(267\) | 4.16134e15 | 0.702927 | ||||||||
\(268\) | −2.45993e12 | −0.000405552 0 | ||||||||
\(269\) | −5.38103e15 | −0.865915 | −0.432957 | − | 0.901414i | \(-0.642530\pi\) | ||||
−0.432957 | + | 0.901414i | \(0.642530\pi\) | |||||||
\(270\) | −3.06328e15 | −0.481196 | ||||||||
\(271\) | 8.17255e15 | 1.25331 | 0.626653 | − | 0.779298i | \(-0.284424\pi\) | ||||
0.626653 | + | 0.779298i | \(0.284424\pi\) | |||||||
\(272\) | −1.12049e16 | −1.67768 | ||||||||
\(273\) | −2.28934e15 | −0.334698 | ||||||||
\(274\) | 6.48612e15 | 0.925990 | ||||||||
\(275\) | −4.02164e14 | −0.0560713 | ||||||||
\(276\) | 1.70074e13 | 0.00231594 | ||||||||
\(277\) | −7.61841e14 | −0.101332 | −0.0506659 | − | 0.998716i | \(-0.516134\pi\) | ||||
−0.0506659 | + | 0.998716i | \(0.516134\pi\) | |||||||
\(278\) | 1.05403e16 | 1.36950 | ||||||||
\(279\) | −2.48985e15 | −0.316043 | ||||||||
\(280\) | 3.75370e15 | 0.465514 | ||||||||
\(281\) | −9.73851e15 | −1.18005 | −0.590027 | − | 0.807384i | \(-0.700883\pi\) | ||||
−0.590027 | + | 0.807384i | \(0.700883\pi\) | |||||||
\(282\) | 8.48254e15 | 1.00440 | ||||||||
\(283\) | −1.30296e16 | −1.50771 | −0.753857 | − | 0.657038i | \(-0.771809\pi\) | ||||
−0.753857 | + | 0.657038i | \(0.771809\pi\) | |||||||
\(284\) | −9.56522e12 | −0.00108175 | ||||||||
\(285\) | −5.50459e15 | −0.608461 | ||||||||
\(286\) | 9.35730e14 | 0.101105 | ||||||||
\(287\) | −1.52467e16 | −1.61044 | ||||||||
\(288\) | −1.15815e13 | −0.00119595 | ||||||||
\(289\) | 1.78114e16 | 1.79830 | ||||||||
\(290\) | 4.00451e15 | 0.395332 | ||||||||
\(291\) | 1.13615e16 | 1.09681 | ||||||||
\(292\) | 1.32593e13 | 0.00125179 | ||||||||
\(293\) | −4.27472e15 | −0.394701 | −0.197351 | − | 0.980333i | \(-0.563234\pi\) | ||||
−0.197351 | + | 0.980333i | \(0.563234\pi\) | |||||||
\(294\) | 8.57151e14 | 0.0774104 | ||||||||
\(295\) | 6.56718e15 | 0.580144 | ||||||||
\(296\) | 1.47453e16 | 1.27426 | ||||||||
\(297\) | −3.56289e15 | −0.301221 | ||||||||
\(298\) | 1.30213e16 | 1.07708 | ||||||||
\(299\) | −3.96295e15 | −0.320742 | ||||||||
\(300\) | −6.56626e12 | −0.000520032 0 | ||||||||
\(301\) | −2.55010e15 | −0.197640 | ||||||||
\(302\) | 1.81029e15 | 0.137310 | ||||||||
\(303\) | −2.89033e15 | −0.214571 | ||||||||
\(304\) | −2.10614e16 | −1.53041 | ||||||||
\(305\) | 6.49224e15 | 0.461791 | ||||||||
\(306\) | 4.93313e15 | 0.343505 | ||||||||
\(307\) | 1.84450e16 | 1.25742 | 0.628709 | − | 0.777640i | \(-0.283583\pi\) | ||||
0.628709 | + | 0.777640i | \(0.283583\pi\) | |||||||
\(308\) | −1.27695e13 | −0.000852303 0 | ||||||||
\(309\) | −1.36262e16 | −0.890523 | ||||||||
\(310\) | −1.07868e16 | −0.690303 | ||||||||
\(311\) | −2.21772e16 | −1.38984 | −0.694918 | − | 0.719089i | \(-0.744559\pi\) | ||||
−0.694918 | + | 0.719089i | \(0.744559\pi\) | |||||||
\(312\) | −5.22357e15 | −0.320600 | ||||||||
\(313\) | −2.02883e16 | −1.21957 | −0.609785 | − | 0.792567i | \(-0.708744\pi\) | ||||
−0.609785 | + | 0.792567i | \(0.708744\pi\) | |||||||
\(314\) | −2.23388e16 | −1.31528 | ||||||||
\(315\) | −1.65745e15 | −0.0955923 | ||||||||
\(316\) | 3.82990e13 | 0.00216382 | ||||||||
\(317\) | 1.93347e16 | 1.07017 | 0.535085 | − | 0.844798i | \(-0.320280\pi\) | ||||
0.535085 | + | 0.844798i | \(0.320280\pi\) | |||||||
\(318\) | −1.21723e16 | −0.660081 | ||||||||
\(319\) | 4.65763e15 | 0.247472 | ||||||||
\(320\) | 8.56474e15 | 0.445902 | ||||||||
\(321\) | −1.05542e16 | −0.538446 | ||||||||
\(322\) | 1.85985e16 | 0.929852 | ||||||||
\(323\) | 5.20968e16 | 2.55267 | ||||||||
\(324\) | −4.57208e13 | −0.00219569 | ||||||||
\(325\) | 1.53003e15 | 0.0720208 | ||||||||
\(326\) | −1.21152e16 | −0.559008 | ||||||||
\(327\) | 2.81344e16 | 1.27256 | ||||||||
\(328\) | −3.47883e16 | −1.54260 | ||||||||
\(329\) | 2.69731e16 | 1.17262 | ||||||||
\(330\) | −2.62645e15 | −0.111951 | ||||||||
\(331\) | 4.61159e15 | 0.192739 | 0.0963693 | − | 0.995346i | \(-0.469277\pi\) | ||||
0.0963693 | + | 0.995346i | \(0.469277\pi\) | |||||||
\(332\) | −6.31180e12 | −0.000258676 0 | ||||||||
\(333\) | −6.51081e15 | −0.261666 | ||||||||
\(334\) | 1.42461e16 | 0.561493 | ||||||||
\(335\) | −1.60888e15 | −0.0621916 | ||||||||
\(336\) | 2.45862e16 | 0.932150 | ||||||||
\(337\) | −3.91103e16 | −1.45444 | −0.727222 | − | 0.686402i | \(-0.759189\pi\) | ||||
−0.727222 | + | 0.686402i | \(0.759189\pi\) | |||||||
\(338\) | 2.38931e16 | 0.871593 | ||||||||
\(339\) | −1.52658e16 | −0.546287 | ||||||||
\(340\) | 6.21448e13 | 0.00218168 | ||||||||
\(341\) | −1.25460e16 | −0.432119 | ||||||||
\(342\) | 9.27264e15 | 0.313353 | ||||||||
\(343\) | −2.87132e16 | −0.952071 | ||||||||
\(344\) | −5.81854e15 | −0.189315 | ||||||||
\(345\) | 1.11234e16 | 0.355151 | ||||||||
\(346\) | −3.01176e16 | −0.943682 | ||||||||
\(347\) | 5.96375e15 | 0.183391 | 0.0916955 | − | 0.995787i | \(-0.470771\pi\) | ||||
0.0916955 | + | 0.995787i | \(0.470771\pi\) | |||||||
\(348\) | 7.60467e13 | 0.00229517 | ||||||||
\(349\) | 2.76636e15 | 0.0819490 | 0.0409745 | − | 0.999160i | \(-0.486954\pi\) | ||||
0.0409745 | + | 0.999160i | \(0.486954\pi\) | |||||||
\(350\) | −7.18056e15 | −0.208793 | ||||||||
\(351\) | 1.35550e16 | 0.386904 | ||||||||
\(352\) | −5.83574e13 | −0.00163519 | ||||||||
\(353\) | 1.98418e16 | 0.545816 | 0.272908 | − | 0.962040i | \(-0.412015\pi\) | ||||
0.272908 | + | 0.962040i | \(0.412015\pi\) | |||||||
\(354\) | 4.28889e16 | 1.15831 | ||||||||
\(355\) | −6.25598e15 | −0.165887 | ||||||||
\(356\) | −8.83068e13 | −0.00229916 | ||||||||
\(357\) | −6.08156e16 | −1.55479 | ||||||||
\(358\) | −4.50217e16 | −1.13027 | ||||||||
\(359\) | −3.22798e16 | −0.795824 | −0.397912 | − | 0.917424i | \(-0.630265\pi\) | ||||
−0.397912 | + | 0.917424i | \(0.630265\pi\) | |||||||
\(360\) | −3.78181e15 | −0.0915658 | ||||||||
\(361\) | 5.58716e16 | 1.32860 | ||||||||
\(362\) | −5.20187e16 | −1.21494 | ||||||||
\(363\) | 3.58106e16 | 0.821522 | ||||||||
\(364\) | 4.85815e13 | 0.00109474 | ||||||||
\(365\) | 8.67204e15 | 0.191963 | ||||||||
\(366\) | 4.23995e16 | 0.922006 | ||||||||
\(367\) | −4.42436e16 | −0.945194 | −0.472597 | − | 0.881279i | \(-0.656683\pi\) | ||||
−0.472597 | + | 0.881279i | \(0.656683\pi\) | |||||||
\(368\) | 4.25598e16 | 0.893282 | ||||||||
\(369\) | 1.53608e16 | 0.316770 | ||||||||
\(370\) | −2.82067e16 | −0.571532 | ||||||||
\(371\) | −3.87060e16 | −0.770634 | ||||||||
\(372\) | −2.04843e14 | −0.00400768 | ||||||||
\(373\) | 9.26267e16 | 1.78086 | 0.890428 | − | 0.455125i | \(-0.150405\pi\) | ||||
0.890428 | + | 0.455125i | \(0.150405\pi\) | |||||||
\(374\) | 2.48574e16 | 0.469667 | ||||||||
\(375\) | −4.29456e15 | −0.0797472 | ||||||||
\(376\) | 6.15444e16 | 1.12323 | ||||||||
\(377\) | −1.77199e16 | −0.317865 | ||||||||
\(378\) | −6.36147e16 | −1.12166 | ||||||||
\(379\) | −3.71415e16 | −0.643732 | −0.321866 | − | 0.946785i | \(-0.604310\pi\) | ||||
−0.321866 | + | 0.946785i | \(0.604310\pi\) | |||||||
\(380\) | 1.16811e14 | 0.00199018 | ||||||||
\(381\) | 1.31533e16 | 0.220304 | ||||||||
\(382\) | 8.34907e16 | 1.37476 | ||||||||
\(383\) | −1.22127e16 | −0.197706 | −0.0988532 | − | 0.995102i | \(-0.531517\pi\) | ||||
−0.0988532 | + | 0.995102i | \(0.531517\pi\) | |||||||
\(384\) | 5.62613e16 | 0.895482 | ||||||||
\(385\) | −8.35169e15 | −0.130701 | ||||||||
\(386\) | −8.05603e16 | −1.23966 | ||||||||
\(387\) | 2.56919e15 | 0.0388754 | ||||||||
\(388\) | −2.41100e14 | −0.00358750 | ||||||||
\(389\) | 7.53716e16 | 1.10290 | 0.551449 | − | 0.834209i | \(-0.314075\pi\) | ||||
0.551449 | + | 0.834209i | \(0.314075\pi\) | |||||||
\(390\) | 9.99232e15 | 0.143796 | ||||||||
\(391\) | −1.05275e17 | −1.48996 | ||||||||
\(392\) | 6.21899e15 | 0.0865686 | ||||||||
\(393\) | −5.77233e16 | −0.790314 | ||||||||
\(394\) | 4.26870e15 | 0.0574871 | ||||||||
\(395\) | 2.50489e16 | 0.331824 | ||||||||
\(396\) | 1.28651e13 | 0.000167646 0 | ||||||||
\(397\) | 8.59809e16 | 1.10221 | 0.551104 | − | 0.834437i | \(-0.314207\pi\) | ||||
0.551104 | + | 0.834437i | \(0.314207\pi\) | |||||||
\(398\) | −4.47927e16 | −0.564894 | ||||||||
\(399\) | −1.14313e17 | −1.41831 | ||||||||
\(400\) | −1.64316e16 | −0.200582 | ||||||||
\(401\) | −1.13598e17 | −1.36437 | −0.682186 | − | 0.731178i | \(-0.738971\pi\) | ||||
−0.682186 | + | 0.731178i | \(0.738971\pi\) | |||||||
\(402\) | −1.05072e16 | −0.124171 | ||||||||
\(403\) | 4.77313e16 | 0.555035 | ||||||||
\(404\) | 6.13349e13 | 0.000701825 0 | ||||||||
\(405\) | −2.99030e16 | −0.336711 | ||||||||
\(406\) | 8.31612e16 | 0.921513 | ||||||||
\(407\) | −3.28071e16 | −0.357770 | ||||||||
\(408\) | −1.38763e17 | −1.48930 | ||||||||
\(409\) | −3.50572e16 | −0.370318 | −0.185159 | − | 0.982709i | \(-0.559280\pi\) | ||||
−0.185159 | + | 0.982709i | \(0.559280\pi\) | |||||||
\(410\) | 6.65475e16 | 0.691890 | ||||||||
\(411\) | 8.05594e16 | 0.824412 | ||||||||
\(412\) | 2.89159e14 | 0.00291276 | ||||||||
\(413\) | 1.36380e17 | 1.35230 | ||||||||
\(414\) | −1.87377e16 | −0.182900 | ||||||||
\(415\) | −4.12813e15 | −0.0396681 | ||||||||
\(416\) | 2.22020e14 | 0.00210032 | ||||||||
\(417\) | 1.30914e17 | 1.21927 | ||||||||
\(418\) | 4.67236e16 | 0.428440 | ||||||||
\(419\) | −2.82535e15 | −0.0255083 | −0.0127541 | − | 0.999919i | \(-0.504060\pi\) | ||||
−0.0127541 | + | 0.999919i | \(0.504060\pi\) | |||||||
\(420\) | −1.36361e14 | −0.00121219 | ||||||||
\(421\) | 8.17054e16 | 0.715183 | 0.357591 | − | 0.933878i | \(-0.383598\pi\) | ||||
0.357591 | + | 0.933878i | \(0.383598\pi\) | |||||||
\(422\) | 1.11014e17 | 0.956859 | ||||||||
\(423\) | −2.71750e16 | −0.230652 | ||||||||
\(424\) | −8.83154e16 | −0.738173 | ||||||||
\(425\) | 4.06448e16 | 0.334562 | ||||||||
\(426\) | −4.08565e16 | −0.331207 | ||||||||
\(427\) | 1.34824e17 | 1.07643 | ||||||||
\(428\) | 2.23968e14 | 0.00176117 | ||||||||
\(429\) | 1.16220e16 | 0.0900139 | ||||||||
\(430\) | 1.11305e16 | 0.0849118 | ||||||||
\(431\) | 4.31353e16 | 0.324139 | 0.162069 | − | 0.986779i | \(-0.448183\pi\) | ||||
0.162069 | + | 0.986779i | \(0.448183\pi\) | |||||||
\(432\) | −1.45573e17 | −1.07755 | ||||||||
\(433\) | −6.25222e16 | −0.455893 | −0.227947 | − | 0.973674i | \(-0.573201\pi\) | ||||
−0.227947 | + | 0.973674i | \(0.573201\pi\) | |||||||
\(434\) | −2.24007e17 | −1.60908 | ||||||||
\(435\) | 4.97371e16 | 0.351966 | ||||||||
\(436\) | −5.97034e14 | −0.00416233 | ||||||||
\(437\) | −1.97881e17 | −1.35917 | ||||||||
\(438\) | 5.66353e16 | 0.383271 | ||||||||
\(439\) | −7.25265e16 | −0.483590 | −0.241795 | − | 0.970327i | \(-0.577736\pi\) | ||||
−0.241795 | + | 0.970327i | \(0.577736\pi\) | |||||||
\(440\) | −1.90560e16 | −0.125196 | ||||||||
\(441\) | −2.74601e15 | −0.0177767 | ||||||||
\(442\) | −9.45698e16 | −0.603265 | ||||||||
\(443\) | −2.76459e17 | −1.73783 | −0.868914 | − | 0.494962i | \(-0.835182\pi\) | ||||
−0.868914 | + | 0.494962i | \(0.835182\pi\) | |||||||
\(444\) | −5.35652e14 | −0.00331813 | ||||||||
\(445\) | −5.77557e16 | −0.352578 | ||||||||
\(446\) | 1.12375e17 | 0.676071 | ||||||||
\(447\) | 1.61728e17 | 0.958931 | ||||||||
\(448\) | 1.77863e17 | 1.03939 | ||||||||
\(449\) | 2.46120e17 | 1.41757 | 0.708786 | − | 0.705424i | \(-0.249243\pi\) | ||||
0.708786 | + | 0.705424i | \(0.249243\pi\) | |||||||
\(450\) | 7.23432e15 | 0.0410692 | ||||||||
\(451\) | 7.74012e16 | 0.433112 | ||||||||
\(452\) | 3.23951e14 | 0.00178682 | ||||||||
\(453\) | 2.24843e16 | 0.122248 | ||||||||
\(454\) | 3.00888e16 | 0.161265 | ||||||||
\(455\) | 3.17740e16 | 0.167879 | ||||||||
\(456\) | −2.60828e17 | −1.35857 | ||||||||
\(457\) | −3.45983e17 | −1.77664 | −0.888319 | − | 0.459226i | \(-0.848127\pi\) | ||||
−0.888319 | + | 0.459226i | \(0.848127\pi\) | |||||||
\(458\) | 1.74756e17 | 0.884721 | ||||||||
\(459\) | 3.60084e17 | 1.79731 | ||||||||
\(460\) | −2.36047e14 | −0.00116164 | ||||||||
\(461\) | −1.04114e17 | −0.505188 | −0.252594 | − | 0.967572i | \(-0.581284\pi\) | ||||
−0.252594 | + | 0.967572i | \(0.581284\pi\) | |||||||
\(462\) | −5.45432e16 | −0.260956 | ||||||||
\(463\) | −1.70140e17 | −0.802656 | −0.401328 | − | 0.915934i | \(-0.631451\pi\) | ||||
−0.401328 | + | 0.915934i | \(0.631451\pi\) | |||||||
\(464\) | 1.90302e17 | 0.885271 | ||||||||
\(465\) | −1.33975e17 | −0.614579 | ||||||||
\(466\) | 1.02172e17 | 0.462195 | ||||||||
\(467\) | 1.84060e17 | 0.821106 | 0.410553 | − | 0.911837i | \(-0.365336\pi\) | ||||
0.410553 | + | 0.911837i | \(0.365336\pi\) | |||||||
\(468\) | −4.89452e13 | −0.000215334 0 | ||||||||
\(469\) | −3.34114e16 | −0.144968 | ||||||||
\(470\) | −1.17730e17 | −0.503792 | ||||||||
\(471\) | −2.77454e17 | −1.17100 | ||||||||
\(472\) | 3.11177e17 | 1.29534 | ||||||||
\(473\) | 1.29458e16 | 0.0531534 | ||||||||
\(474\) | 1.63589e17 | 0.662514 | ||||||||
\(475\) | 7.63987e16 | 0.305195 | ||||||||
\(476\) | 1.29055e15 | 0.00508546 | ||||||||
\(477\) | 3.89958e16 | 0.151582 | ||||||||
\(478\) | 1.93106e17 | 0.740482 | ||||||||
\(479\) | −2.13215e17 | −0.806562 | −0.403281 | − | 0.915076i | \(-0.632130\pi\) | ||||
−0.403281 | + | 0.915076i | \(0.632130\pi\) | |||||||
\(480\) | −6.23178e14 | −0.00232565 | ||||||||
\(481\) | 1.24814e17 | 0.459538 | ||||||||
\(482\) | −3.36016e17 | −1.22055 | ||||||||
\(483\) | 2.30998e17 | 0.827851 | ||||||||
\(484\) | −7.59928e14 | −0.00268706 | ||||||||
\(485\) | −1.57688e17 | −0.550145 | ||||||||
\(486\) | 1.17276e17 | 0.403715 | ||||||||
\(487\) | −3.74978e17 | −1.27370 | −0.636851 | − | 0.770987i | \(-0.719763\pi\) | ||||
−0.636851 | + | 0.770987i | \(0.719763\pi\) | |||||||
\(488\) | 3.07626e17 | 1.03109 | ||||||||
\(489\) | −1.50475e17 | −0.497687 | ||||||||
\(490\) | −1.18965e16 | −0.0388279 | ||||||||
\(491\) | 4.11003e17 | 1.32378 | 0.661889 | − | 0.749602i | \(-0.269755\pi\) | ||||
0.661889 | + | 0.749602i | \(0.269755\pi\) | |||||||
\(492\) | 1.26375e15 | 0.00401689 | ||||||||
\(493\) | −4.70725e17 | −1.47660 | ||||||||
\(494\) | −1.77760e17 | −0.550311 | ||||||||
\(495\) | 8.41421e15 | 0.0257087 | ||||||||
\(496\) | −5.12607e17 | −1.54580 | ||||||||
\(497\) | −1.29917e17 | −0.386678 | ||||||||
\(498\) | −2.69600e16 | −0.0792007 | ||||||||
\(499\) | 1.73839e17 | 0.504072 | 0.252036 | − | 0.967718i | \(-0.418900\pi\) | ||||
0.252036 | + | 0.967718i | \(0.418900\pi\) | |||||||
\(500\) | 9.11338e13 | 0.000260840 0 | ||||||||
\(501\) | 1.76941e17 | 0.499899 | ||||||||
\(502\) | −1.53824e17 | −0.428992 | ||||||||
\(503\) | −3.28753e17 | −0.905062 | −0.452531 | − | 0.891749i | \(-0.649479\pi\) | ||||
−0.452531 | + | 0.891749i | \(0.649479\pi\) | |||||||
\(504\) | −7.85363e16 | −0.213438 | ||||||||
\(505\) | 4.01152e16 | 0.107625 | ||||||||
\(506\) | −9.44167e16 | −0.250075 | ||||||||
\(507\) | 2.96759e17 | 0.775983 | ||||||||
\(508\) | −2.79123e14 | −0.000720579 0 | ||||||||
\(509\) | 6.89978e16 | 0.175861 | 0.0879305 | − | 0.996127i | \(-0.471975\pi\) | ||||
0.0879305 | + | 0.996127i | \(0.471975\pi\) | |||||||
\(510\) | 2.65443e17 | 0.667983 | ||||||||
\(511\) | 1.80091e17 | 0.447463 | ||||||||
\(512\) | 4.05822e17 | 0.995591 | ||||||||
\(513\) | 6.76839e17 | 1.63954 | ||||||||
\(514\) | 3.10690e16 | 0.0743135 | ||||||||
\(515\) | 1.89120e17 | 0.446673 | ||||||||
\(516\) | 2.11370e14 | 0.000492970 0 | ||||||||
\(517\) | −1.36931e17 | −0.315365 | ||||||||
\(518\) | −5.85765e17 | −1.33223 | ||||||||
\(519\) | −3.74069e17 | −0.840164 | ||||||||
\(520\) | 7.24985e16 | 0.160808 | ||||||||
\(521\) | 8.38335e17 | 1.83642 | 0.918211 | − | 0.396092i | \(-0.129634\pi\) | ||||
0.918211 | + | 0.396092i | \(0.129634\pi\) | |||||||
\(522\) | −8.37838e16 | −0.181260 | ||||||||
\(523\) | −1.91687e17 | −0.409573 | −0.204786 | − | 0.978807i | \(-0.565650\pi\) | ||||
−0.204786 | + | 0.978807i | \(0.565650\pi\) | |||||||
\(524\) | 1.22493e15 | 0.00258499 | ||||||||
\(525\) | −8.91846e16 | −0.185889 | ||||||||
\(526\) | −4.20032e17 | −0.864719 | ||||||||
\(527\) | 1.26797e18 | 2.57834 | ||||||||
\(528\) | −1.24814e17 | −0.250693 | ||||||||
\(529\) | −1.04168e17 | −0.206668 | ||||||||
\(530\) | 1.68941e17 | 0.331087 | ||||||||
\(531\) | −1.37401e17 | −0.265996 | ||||||||
\(532\) | 2.42581e15 | 0.00463907 | ||||||||
\(533\) | −2.94472e17 | −0.556311 | ||||||||
\(534\) | −3.77191e17 | −0.703952 | ||||||||
\(535\) | 1.46483e17 | 0.270076 | ||||||||
\(536\) | −7.62345e16 | −0.138861 | ||||||||
\(537\) | −5.59183e17 | −1.00628 | ||||||||
\(538\) | 4.87744e17 | 0.867177 | ||||||||
\(539\) | −1.38368e16 | −0.0243056 | ||||||||
\(540\) | 8.07381e14 | 0.00140126 | ||||||||
\(541\) | −8.65938e17 | −1.48492 | −0.742462 | − | 0.669888i | \(-0.766342\pi\) | ||||
−0.742462 | + | 0.669888i | \(0.766342\pi\) | |||||||
\(542\) | −7.40773e17 | −1.25513 | ||||||||
\(543\) | −6.46087e17 | −1.08166 | ||||||||
\(544\) | 5.89791e15 | 0.00975675 | ||||||||
\(545\) | −3.90481e17 | −0.638296 | ||||||||
\(546\) | 2.07509e17 | 0.335185 | ||||||||
\(547\) | 1.16237e18 | 1.85536 | 0.927678 | − | 0.373382i | \(-0.121802\pi\) | ||||
0.927678 | + | 0.373382i | \(0.121802\pi\) | |||||||
\(548\) | −1.70953e15 | −0.00269652 | ||||||||
\(549\) | −1.35833e17 | −0.211731 | ||||||||
\(550\) | 3.64528e16 | 0.0561530 | ||||||||
\(551\) | −8.84806e17 | −1.34698 | ||||||||
\(552\) | 5.27067e17 | 0.792980 | ||||||||
\(553\) | 5.20187e17 | 0.773475 | ||||||||
\(554\) | 6.90545e16 | 0.101479 | ||||||||
\(555\) | −3.50335e17 | −0.508837 | ||||||||
\(556\) | −2.77809e15 | −0.00398804 | ||||||||
\(557\) | −1.02746e17 | −0.145783 | −0.0728917 | − | 0.997340i | \(-0.523223\pi\) | ||||
−0.0728917 | + | 0.997340i | \(0.523223\pi\) | |||||||
\(558\) | 2.25684e17 | 0.316504 | ||||||||
\(559\) | −4.92522e16 | −0.0682730 | ||||||||
\(560\) | −3.41234e17 | −0.467552 | ||||||||
\(561\) | 3.08736e17 | 0.418146 | ||||||||
\(562\) | 8.82714e17 | 1.18177 | ||||||||
\(563\) | 7.17343e17 | 0.949341 | 0.474671 | − | 0.880164i | \(-0.342567\pi\) | ||||
0.474671 | + | 0.880164i | \(0.342567\pi\) | |||||||
\(564\) | −2.23572e15 | −0.00292485 | ||||||||
\(565\) | 2.11875e17 | 0.274009 | ||||||||
\(566\) | 1.18102e18 | 1.50991 | ||||||||
\(567\) | −6.20992e17 | −0.784867 | ||||||||
\(568\) | −2.96431e17 | −0.370391 | ||||||||
\(569\) | −1.25353e17 | −0.154848 | −0.0774238 | − | 0.996998i | \(-0.524669\pi\) | ||||
−0.0774238 | + | 0.996998i | \(0.524669\pi\) | |||||||
\(570\) | 4.98944e17 | 0.609348 | ||||||||
\(571\) | −1.00269e17 | −0.121069 | −0.0605344 | − | 0.998166i | \(-0.519280\pi\) | ||||
−0.0605344 | + | 0.998166i | \(0.519280\pi\) | |||||||
\(572\) | −2.46628e14 | −0.000294421 0 | ||||||||
\(573\) | 1.03698e18 | 1.22395 | ||||||||
\(574\) | 1.38198e18 | 1.61278 | ||||||||
\(575\) | −1.54383e17 | −0.178138 | ||||||||
\(576\) | −1.79194e17 | −0.204446 | ||||||||
\(577\) | −1.36098e18 | −1.53535 | −0.767675 | − | 0.640839i | \(-0.778587\pi\) | ||||
−0.767675 | + | 0.640839i | \(0.778587\pi\) | |||||||
\(578\) | −1.61445e18 | −1.80092 | ||||||||
\(579\) | −1.00058e18 | −1.10368 | ||||||||
\(580\) | −1.05546e15 | −0.00115122 | ||||||||
\(581\) | −8.57285e16 | −0.0924656 | ||||||||
\(582\) | −1.02983e18 | −1.09841 | ||||||||
\(583\) | 1.96495e17 | 0.207255 | ||||||||
\(584\) | 4.10913e17 | 0.428614 | ||||||||
\(585\) | −3.20118e16 | −0.0330215 | ||||||||
\(586\) | 3.87468e17 | 0.395276 | ||||||||
\(587\) | −6.87785e16 | −0.0693913 | −0.0346956 | − | 0.999398i | \(-0.511046\pi\) | ||||
−0.0346956 | + | 0.999398i | \(0.511046\pi\) | |||||||
\(588\) | −2.25917e14 | −0.000225422 0 | ||||||||
\(589\) | 2.38336e18 | 2.35201 | ||||||||
\(590\) | −5.95259e17 | −0.580989 | ||||||||
\(591\) | 5.30185e16 | 0.0511810 | ||||||||
\(592\) | −1.34043e18 | −1.27984 | ||||||||
\(593\) | −3.46338e17 | −0.327073 | −0.163536 | − | 0.986537i | \(-0.552290\pi\) | ||||
−0.163536 | + | 0.986537i | \(0.552290\pi\) | |||||||
\(594\) | 3.22946e17 | 0.301660 | ||||||||
\(595\) | 8.44066e17 | 0.779859 | ||||||||
\(596\) | −3.43200e15 | −0.00313651 | ||||||||
\(597\) | −5.56338e17 | −0.502928 | ||||||||
\(598\) | 3.59208e17 | 0.321209 | ||||||||
\(599\) | −1.08982e18 | −0.964004 | −0.482002 | − | 0.876170i | \(-0.660090\pi\) | ||||
−0.482002 | + | 0.876170i | \(0.660090\pi\) | |||||||
\(600\) | −2.03492e17 | −0.178059 | ||||||||
\(601\) | 2.73058e17 | 0.236358 | 0.118179 | − | 0.992992i | \(-0.462294\pi\) | ||||
0.118179 | + | 0.992992i | \(0.462294\pi\) | |||||||
\(602\) | 2.31145e17 | 0.197928 | ||||||||
\(603\) | 3.36615e16 | 0.0285148 | ||||||||
\(604\) | −4.77133e14 | −0.000399852 0 | ||||||||
\(605\) | −4.97019e17 | −0.412063 | ||||||||
\(606\) | 2.61984e17 | 0.214883 | ||||||||
\(607\) | −1.19160e18 | −0.966951 | −0.483476 | − | 0.875358i | \(-0.660626\pi\) | ||||
−0.483476 | + | 0.875358i | \(0.660626\pi\) | |||||||
\(608\) | 1.10861e16 | 0.00890032 | ||||||||
\(609\) | 1.03289e18 | 0.820426 | ||||||||
\(610\) | −5.88467e17 | −0.462464 | ||||||||
\(611\) | 5.20954e17 | 0.405072 | ||||||||
\(612\) | −1.30021e15 | −0.00100030 | ||||||||
\(613\) | 3.63023e17 | 0.276338 | 0.138169 | − | 0.990409i | \(-0.455878\pi\) | ||||
0.138169 | + | 0.990409i | \(0.455878\pi\) | |||||||
\(614\) | −1.67189e18 | −1.25925 | ||||||||
\(615\) | 8.26539e17 | 0.615992 | ||||||||
\(616\) | −3.95734e17 | −0.291829 | ||||||||
\(617\) | 6.06720e17 | 0.442726 | 0.221363 | − | 0.975192i | \(-0.428949\pi\) | ||||
0.221363 | + | 0.975192i | \(0.428949\pi\) | |||||||
\(618\) | 1.23510e18 | 0.891821 | ||||||||
\(619\) | −2.29300e18 | −1.63838 | −0.819190 | − | 0.573523i | \(-0.805576\pi\) | ||||
−0.819190 | + | 0.573523i | \(0.805576\pi\) | |||||||
\(620\) | 2.84304e15 | 0.00201019 | ||||||||
\(621\) | −1.36772e18 | −0.956979 | ||||||||
\(622\) | 2.01017e18 | 1.39186 | ||||||||
\(623\) | −1.19941e18 | −0.821852 | ||||||||
\(624\) | 4.74854e17 | 0.322003 | ||||||||
\(625\) | 5.96046e16 | 0.0400000 | ||||||||
\(626\) | 1.83896e18 | 1.22135 | ||||||||
\(627\) | 5.80320e17 | 0.381442 | ||||||||
\(628\) | 5.88779e15 | 0.00383014 | ||||||||
\(629\) | 3.31566e18 | 2.13472 | ||||||||
\(630\) | 1.50234e17 | 0.0957316 | ||||||||
\(631\) | 3.33398e17 | 0.210268 | 0.105134 | − | 0.994458i | \(-0.466473\pi\) | ||||
0.105134 | + | 0.994458i | \(0.466473\pi\) | |||||||
\(632\) | 1.18691e18 | 0.740894 | ||||||||
\(633\) | 1.37883e18 | 0.851895 | ||||||||
\(634\) | −1.75253e18 | −1.07173 | ||||||||
\(635\) | −1.82556e17 | −0.110501 | ||||||||
\(636\) | 3.20823e15 | 0.00192218 | ||||||||
\(637\) | 5.26418e16 | 0.0312194 | ||||||||
\(638\) | −4.22175e17 | −0.247832 | ||||||||
\(639\) | 1.30890e17 | 0.0760589 | ||||||||
\(640\) | −7.80856e17 | −0.449160 | ||||||||
\(641\) | −8.91188e17 | −0.507449 | −0.253724 | − | 0.967277i | \(-0.581656\pi\) | ||||
−0.253724 | + | 0.967277i | \(0.581656\pi\) | |||||||
\(642\) | 9.56648e17 | 0.539230 | ||||||||
\(643\) | 5.58943e17 | 0.311886 | 0.155943 | − | 0.987766i | \(-0.450158\pi\) | ||||
0.155943 | + | 0.987766i | \(0.450158\pi\) | |||||||
\(644\) | −4.90195e15 | −0.00270776 | ||||||||
\(645\) | 1.38243e17 | 0.0755973 | ||||||||
\(646\) | −4.72213e18 | −2.55639 | ||||||||
\(647\) | 1.62698e18 | 0.871973 | 0.435987 | − | 0.899953i | \(-0.356399\pi\) | ||||
0.435987 | + | 0.899953i | \(0.356399\pi\) | |||||||
\(648\) | −1.41691e18 | −0.751806 | ||||||||
\(649\) | −6.92344e17 | −0.363690 | ||||||||
\(650\) | −1.38684e17 | −0.0721258 | ||||||||
\(651\) | −2.78223e18 | −1.43257 | ||||||||
\(652\) | 3.19319e15 | 0.00162785 | ||||||||
\(653\) | −6.71206e17 | −0.338782 | −0.169391 | − | 0.985549i | \(-0.554180\pi\) | ||||
−0.169391 | + | 0.985549i | \(0.554180\pi\) | |||||||
\(654\) | −2.55015e18 | −1.27441 | ||||||||
\(655\) | 8.01147e17 | 0.396409 | ||||||||
\(656\) | 3.16246e18 | 1.54935 | ||||||||
\(657\) | −1.81439e17 | −0.0880150 | ||||||||
\(658\) | −2.44488e18 | −1.17433 | ||||||||
\(659\) | −1.08505e18 | −0.516053 | −0.258027 | − | 0.966138i | \(-0.583072\pi\) | ||||
−0.258027 | + | 0.966138i | \(0.583072\pi\) | |||||||
\(660\) | 6.92247e14 | 0.000326006 0 | ||||||||
\(661\) | 2.34214e18 | 1.09220 | 0.546100 | − | 0.837720i | \(-0.316112\pi\) | ||||
0.546100 | + | 0.837720i | \(0.316112\pi\) | |||||||
\(662\) | −4.18002e17 | −0.193019 | ||||||||
\(663\) | −1.17458e18 | −0.537089 | ||||||||
\(664\) | −1.95606e17 | −0.0885707 | ||||||||
\(665\) | 1.58656e18 | 0.711404 | ||||||||
\(666\) | 5.90150e17 | 0.262047 | ||||||||
\(667\) | 1.78797e18 | 0.786217 | ||||||||
\(668\) | −3.75481e15 | −0.00163509 | ||||||||
\(669\) | 1.39573e18 | 0.601909 | ||||||||
\(670\) | 1.45831e17 | 0.0622822 | ||||||||
\(671\) | −6.84444e17 | −0.289495 | ||||||||
\(672\) | −1.29415e16 | −0.00542104 | ||||||||
\(673\) | 7.92495e17 | 0.328775 | 0.164387 | − | 0.986396i | \(-0.447435\pi\) | ||||
0.164387 | + | 0.986396i | \(0.447435\pi\) | |||||||
\(674\) | 3.54502e18 | 1.45656 | ||||||||
\(675\) | 5.28055e17 | 0.214884 | ||||||||
\(676\) | −6.29745e15 | −0.00253811 | ||||||||
\(677\) | −2.35105e18 | −0.938503 | −0.469251 | − | 0.883065i | \(-0.655476\pi\) | ||||
−0.469251 | + | 0.883065i | \(0.655476\pi\) | |||||||
\(678\) | 1.38371e18 | 0.547083 | ||||||||
\(679\) | −3.27469e18 | −1.28238 | ||||||||
\(680\) | 1.92590e18 | 0.747010 | ||||||||
\(681\) | 3.73711e17 | 0.143575 | ||||||||
\(682\) | 1.13719e18 | 0.432748 | ||||||||
\(683\) | −3.22912e17 | −0.121717 | −0.0608583 | − | 0.998146i | \(-0.519384\pi\) | ||||
−0.0608583 | + | 0.998146i | \(0.519384\pi\) | |||||||
\(684\) | −2.44397e15 | −0.000912496 0 | ||||||||
\(685\) | −1.11809e18 | −0.413513 | ||||||||
\(686\) | 2.60261e18 | 0.953459 | ||||||||
\(687\) | 2.17052e18 | 0.787670 | ||||||||
\(688\) | 5.28940e17 | 0.190144 | ||||||||
\(689\) | −7.47563e17 | −0.266209 | ||||||||
\(690\) | −1.00824e18 | −0.355669 | ||||||||
\(691\) | 3.36976e18 | 1.17758 | 0.588792 | − | 0.808284i | \(-0.299604\pi\) | ||||
0.588792 | + | 0.808284i | \(0.299604\pi\) | |||||||
\(692\) | 7.93803e15 | 0.00274804 | ||||||||
\(693\) | 1.74737e17 | 0.0599265 | ||||||||
\(694\) | −5.40564e17 | −0.183658 | ||||||||
\(695\) | −1.81696e18 | −0.611568 | ||||||||
\(696\) | 2.35673e18 | 0.785868 | ||||||||
\(697\) | −7.82257e18 | −2.58426 | ||||||||
\(698\) | −2.50747e17 | −0.0820684 | ||||||||
\(699\) | 1.26901e18 | 0.411494 | ||||||||
\(700\) | 1.89256e15 | 0.000608014 0 | ||||||||
\(701\) | −5.38800e18 | −1.71499 | −0.857493 | − | 0.514495i | \(-0.827979\pi\) | ||||
−0.857493 | + | 0.514495i | \(0.827979\pi\) | |||||||
\(702\) | −1.22865e18 | −0.387468 | ||||||||
\(703\) | 6.23233e18 | 1.94734 | ||||||||
\(704\) | −9.02936e17 | −0.279534 | ||||||||
\(705\) | −1.46224e18 | −0.448528 | ||||||||
\(706\) | −1.79849e18 | −0.546611 | ||||||||
\(707\) | 8.33067e17 | 0.250873 | ||||||||
\(708\) | −1.13041e16 | −0.00337303 | ||||||||
\(709\) | −1.40376e18 | −0.415044 | −0.207522 | − | 0.978230i | \(-0.566540\pi\) | ||||
−0.207522 | + | 0.978230i | \(0.566540\pi\) | |||||||
\(710\) | 5.67052e17 | 0.166128 | ||||||||
\(711\) | −5.24082e17 | −0.152141 | ||||||||
\(712\) | −2.73668e18 | −0.787234 | ||||||||
\(713\) | −4.81617e18 | −1.37284 | ||||||||
\(714\) | 5.51242e18 | 1.55706 | ||||||||
\(715\) | −1.61303e17 | −0.0451496 | ||||||||
\(716\) | 1.18663e16 | 0.00329139 | ||||||||
\(717\) | 2.39843e18 | 0.659254 | ||||||||
\(718\) | 2.92589e18 | 0.796984 | ||||||||
\(719\) | −1.38614e18 | −0.374170 | −0.187085 | − | 0.982344i | \(-0.559904\pi\) | ||||
−0.187085 | + | 0.982344i | \(0.559904\pi\) | |||||||
\(720\) | 3.43788e17 | 0.0919666 | ||||||||
\(721\) | 3.92742e18 | 1.04119 | ||||||||
\(722\) | −5.06429e18 | −1.33054 | ||||||||
\(723\) | −4.17342e18 | −1.08666 | ||||||||
\(724\) | 1.37104e16 | 0.00353794 | ||||||||
\(725\) | −6.90307e17 | −0.176541 | ||||||||
\(726\) | −3.24593e18 | −0.822719 | ||||||||
\(727\) | 4.20824e18 | 1.05712 | 0.528562 | − | 0.848894i | \(-0.322731\pi\) | ||||
0.528562 | + | 0.848894i | \(0.322731\pi\) | |||||||
\(728\) | 1.50557e18 | 0.374840 | ||||||||
\(729\) | 4.50781e18 | 1.11234 | ||||||||
\(730\) | −7.86047e17 | −0.192243 | ||||||||
\(731\) | −1.30837e18 | −0.317152 | ||||||||
\(732\) | −1.11751e16 | −0.00268492 | ||||||||
\(733\) | 7.61043e17 | 0.181231 | 0.0906156 | − | 0.995886i | \(-0.471117\pi\) | ||||
0.0906156 | + | 0.995886i | \(0.471117\pi\) | |||||||
\(734\) | 4.01031e18 | 0.946571 | ||||||||
\(735\) | −1.47758e17 | −0.0345686 | ||||||||
\(736\) | −2.24022e16 | −0.00519500 | ||||||||
\(737\) | 1.69616e17 | 0.0389877 | ||||||||
\(738\) | −1.39233e18 | −0.317231 | ||||||||
\(739\) | 6.25215e18 | 1.41202 | 0.706010 | − | 0.708202i | \(-0.250493\pi\) | ||||
0.706010 | + | 0.708202i | \(0.250493\pi\) | |||||||
\(740\) | 7.43437e15 | 0.00166432 | ||||||||
\(741\) | −2.20783e18 | −0.489944 | ||||||||
\(742\) | 3.50838e18 | 0.771757 | ||||||||
\(743\) | 5.60504e18 | 1.22223 | 0.611113 | − | 0.791543i | \(-0.290722\pi\) | ||||
0.611113 | + | 0.791543i | \(0.290722\pi\) | |||||||
\(744\) | −6.34821e18 | −1.37223 | ||||||||
\(745\) | −2.24464e18 | −0.480985 | ||||||||
\(746\) | −8.39583e18 | −1.78345 | ||||||||
\(747\) | 8.63703e16 | 0.0181878 | ||||||||
\(748\) | −6.55160e15 | −0.00136769 | ||||||||
\(749\) | 3.04199e18 | 0.629543 | ||||||||
\(750\) | 3.89266e17 | 0.0798634 | ||||||||
\(751\) | 4.79388e18 | 0.975053 | 0.487526 | − | 0.873108i | \(-0.337899\pi\) | ||||
0.487526 | + | 0.873108i | \(0.337899\pi\) | |||||||
\(752\) | −5.59475e18 | −1.12814 | ||||||||
\(753\) | −1.91053e18 | −0.381933 | ||||||||
\(754\) | 1.60616e18 | 0.318329 | ||||||||
\(755\) | −3.12061e17 | −0.0613175 | ||||||||
\(756\) | 1.67668e16 | 0.00326632 | ||||||||
\(757\) | 2.47656e18 | 0.478328 | 0.239164 | − | 0.970979i | \(-0.423127\pi\) | ||||
0.239164 | + | 0.970979i | \(0.423127\pi\) | |||||||
\(758\) | 3.36656e18 | 0.644669 | ||||||||
\(759\) | −1.17268e18 | −0.222643 | ||||||||
\(760\) | 3.62005e18 | 0.681438 | ||||||||
\(761\) | 1.02209e19 | 1.90761 | 0.953804 | − | 0.300430i | \(-0.0971301\pi\) | ||||
0.953804 | + | 0.300430i | \(0.0971301\pi\) | |||||||
\(762\) | −1.19224e18 | −0.220625 | ||||||||
\(763\) | −8.10906e18 | −1.48786 | ||||||||
\(764\) | −2.20055e16 | −0.00400335 | ||||||||
\(765\) | −8.50385e17 | −0.153397 | ||||||||
\(766\) | 1.10698e18 | 0.197994 | ||||||||
\(767\) | 2.63402e18 | 0.467142 | ||||||||
\(768\) | −4.43574e16 | −0.00780042 | ||||||||
\(769\) | −9.71765e18 | −1.69449 | −0.847247 | − | 0.531199i | \(-0.821742\pi\) | ||||
−0.847247 | + | 0.531199i | \(0.821742\pi\) | |||||||
\(770\) | 7.57010e17 | 0.130892 | ||||||||
\(771\) | 3.85886e17 | 0.0661616 | ||||||||
\(772\) | 2.12331e16 | 0.00360995 | ||||||||
\(773\) | 6.33996e18 | 1.06886 | 0.534429 | − | 0.845213i | \(-0.320527\pi\) | ||||
0.534429 | + | 0.845213i | \(0.320527\pi\) | |||||||
\(774\) | −2.32875e17 | −0.0389320 | ||||||||
\(775\) | 1.85945e18 | 0.308264 | ||||||||
\(776\) | −7.47184e18 | −1.22836 | ||||||||
\(777\) | −7.27536e18 | −1.18609 | ||||||||
\(778\) | −6.83180e18 | −1.10450 | ||||||||
\(779\) | −1.47038e19 | −2.35742 | ||||||||
\(780\) | −2.63365e15 | −0.000418739 0 | ||||||||
\(781\) | 6.59536e17 | 0.103994 | ||||||||
\(782\) | 9.54225e18 | 1.49213 | ||||||||
\(783\) | −6.11563e18 | −0.948396 | ||||||||
\(784\) | −5.65343e17 | −0.0869476 | ||||||||
\(785\) | 3.85082e18 | 0.587354 | ||||||||
\(786\) | 5.23213e18 | 0.791465 | ||||||||
\(787\) | 6.11756e17 | 0.0917789 | 0.0458894 | − | 0.998947i | \(-0.485388\pi\) | ||||
0.0458894 | + | 0.998947i | \(0.485388\pi\) | |||||||
\(788\) | −1.12509e15 | −0.000167405 0 | ||||||||
\(789\) | −5.21691e18 | −0.769862 | ||||||||
\(790\) | −2.27047e18 | −0.332307 | ||||||||
\(791\) | 4.39999e18 | 0.638711 | ||||||||
\(792\) | 3.98696e17 | 0.0574022 | ||||||||
\(793\) | 2.60396e18 | 0.371843 | ||||||||
\(794\) | −7.79344e18 | −1.10381 | ||||||||
\(795\) | 2.09829e18 | 0.294768 | ||||||||
\(796\) | 1.18059e16 | 0.00164499 | ||||||||
\(797\) | 1.19147e18 | 0.164665 | 0.0823327 | − | 0.996605i | \(-0.473763\pi\) | ||||
0.0823327 | + | 0.996605i | \(0.473763\pi\) | |||||||
\(798\) | 1.03615e19 | 1.42038 | ||||||||
\(799\) | 1.38390e19 | 1.88170 | ||||||||
\(800\) | 8.64914e15 | 0.00116651 | ||||||||
\(801\) | 1.20839e18 | 0.161657 | ||||||||
\(802\) | 1.02967e19 | 1.36636 | ||||||||
\(803\) | −9.14249e17 | −0.120341 | ||||||||
\(804\) | 2.76937e15 | 0.000361590 0 | ||||||||
\(805\) | −3.20605e18 | −0.415237 | ||||||||
\(806\) | −4.32644e18 | −0.555844 | ||||||||
\(807\) | 6.05792e18 | 0.772051 | ||||||||
\(808\) | 1.90080e18 | 0.240305 | ||||||||
\(809\) | 7.74613e18 | 0.971447 | 0.485724 | − | 0.874112i | \(-0.338556\pi\) | ||||
0.485724 | + | 0.874112i | \(0.338556\pi\) | |||||||
\(810\) | 2.71045e18 | 0.337201 | ||||||||
\(811\) | −4.31453e18 | −0.532474 | −0.266237 | − | 0.963908i | \(-0.585780\pi\) | ||||
−0.266237 | + | 0.963908i | \(0.585780\pi\) | |||||||
\(812\) | −2.19186e16 | −0.00268348 | ||||||||
\(813\) | −9.20061e18 | −1.11745 | ||||||||
\(814\) | 2.97368e18 | 0.358291 | ||||||||
\(815\) | 2.08845e18 | 0.249632 | ||||||||
\(816\) | 1.26143e19 | 1.49582 | ||||||||
\(817\) | −2.45930e18 | −0.289313 | ||||||||
\(818\) | 3.17764e18 | 0.370858 | ||||||||
\(819\) | −6.64786e17 | −0.0769726 | ||||||||
\(820\) | −1.75398e16 | −0.00201481 | ||||||||
\(821\) | −1.32454e19 | −1.50950 | −0.754752 | − | 0.656011i | \(-0.772243\pi\) | ||||
−0.754752 | + | 0.656011i | \(0.772243\pi\) | |||||||
\(822\) | −7.30203e18 | −0.825613 | ||||||||
\(823\) | −1.59982e19 | −1.79461 | −0.897307 | − | 0.441407i | \(-0.854480\pi\) | ||||
−0.897307 | + | 0.441407i | \(0.854480\pi\) | |||||||
\(824\) | 8.96118e18 | 0.997329 | ||||||||
\(825\) | 4.52754e17 | 0.0499932 | ||||||||
\(826\) | −1.23617e19 | −1.35427 | ||||||||
\(827\) | −7.72194e18 | −0.839345 | −0.419672 | − | 0.907676i | \(-0.637855\pi\) | ||||
−0.419672 | + | 0.907676i | \(0.637855\pi\) | |||||||
\(828\) | 4.93865e15 | 0.000532612 0 | ||||||||
\(829\) | −8.75341e18 | −0.936640 | −0.468320 | − | 0.883559i | \(-0.655141\pi\) | ||||
−0.468320 | + | 0.883559i | \(0.655141\pi\) | |||||||
\(830\) | 3.74180e17 | 0.0397259 | ||||||||
\(831\) | 8.57676e17 | 0.0903476 | ||||||||
\(832\) | 3.43522e18 | 0.359048 | ||||||||
\(833\) | 1.39842e18 | 0.145025 | ||||||||
\(834\) | −1.18662e19 | −1.22105 | ||||||||
\(835\) | −2.45578e18 | −0.250742 | ||||||||
\(836\) | −1.23148e16 | −0.00124764 | ||||||||
\(837\) | 1.64734e19 | 1.65603 | ||||||||
\(838\) | 2.56094e17 | 0.0255454 | ||||||||
\(839\) | 1.14368e19 | 1.13201 | 0.566007 | − | 0.824400i | \(-0.308487\pi\) | ||||
0.566007 | + | 0.824400i | \(0.308487\pi\) | |||||||
\(840\) | −4.22590e18 | −0.415053 | ||||||||
\(841\) | −2.26589e18 | −0.220834 | ||||||||
\(842\) | −7.40590e18 | −0.716225 | ||||||||
\(843\) | 1.09636e19 | 1.05214 | ||||||||
\(844\) | −2.92598e16 | −0.00278641 | ||||||||
\(845\) | −4.11875e18 | −0.389221 | ||||||||
\(846\) | 2.46319e18 | 0.230988 | ||||||||
\(847\) | −1.03215e19 | −0.960511 | ||||||||
\(848\) | 8.02839e18 | 0.741405 | ||||||||
\(849\) | 1.46686e19 | 1.34428 | ||||||||
\(850\) | −3.68411e18 | −0.335050 | ||||||||
\(851\) | −1.25940e19 | −1.13663 | ||||||||
\(852\) | 1.07685e16 | 0.000964487 0 | ||||||||
\(853\) | −9.31629e17 | −0.0828084 | −0.0414042 | − | 0.999142i | \(-0.513183\pi\) | ||||
−0.0414042 | + | 0.999142i | \(0.513183\pi\) | |||||||
\(854\) | −1.22206e19 | −1.07800 | ||||||||
\(855\) | −1.59844e18 | −0.139932 | ||||||||
\(856\) | 6.94088e18 | 0.603025 | ||||||||
\(857\) | 9.56376e18 | 0.824619 | 0.412309 | − | 0.911044i | \(-0.364722\pi\) | ||||
0.412309 | + | 0.911044i | \(0.364722\pi\) | |||||||
\(858\) | −1.05344e18 | −0.0901450 | ||||||||
\(859\) | 7.17114e18 | 0.609022 | 0.304511 | − | 0.952509i | \(-0.401507\pi\) | ||||
0.304511 | + | 0.952509i | \(0.401507\pi\) | |||||||
\(860\) | −2.93363e15 | −0.000247266 0 | ||||||||
\(861\) | 1.71646e19 | 1.43587 | ||||||||
\(862\) | −3.90985e18 | −0.324611 | ||||||||
\(863\) | 1.34010e19 | 1.10425 | 0.552125 | − | 0.833761i | \(-0.313817\pi\) | ||||
0.552125 | + | 0.833761i | \(0.313817\pi\) | |||||||
\(864\) | 7.66253e16 | 0.00626661 | ||||||||
\(865\) | 5.19174e18 | 0.421414 | ||||||||
\(866\) | 5.66711e18 | 0.456557 | ||||||||
\(867\) | −2.00520e19 | −1.60337 | ||||||||
\(868\) | 5.90411e16 | 0.00468572 | ||||||||
\(869\) | −2.64078e18 | −0.208019 | ||||||||
\(870\) | −4.50825e18 | −0.352479 | ||||||||
\(871\) | −6.45302e17 | −0.0500778 | ||||||||
\(872\) | −1.85024e19 | −1.42518 | ||||||||
\(873\) | 3.29920e18 | 0.252241 | ||||||||
\(874\) | 1.79362e19 | 1.36115 | ||||||||
\(875\) | 1.23780e18 | 0.0932393 | ||||||||
\(876\) | −1.49272e16 | −0.00111610 | ||||||||
\(877\) | −8.23622e18 | −0.611266 | −0.305633 | − | 0.952149i | \(-0.598868\pi\) | ||||
−0.305633 | + | 0.952149i | \(0.598868\pi\) | |||||||
\(878\) | 6.57391e18 | 0.484295 | ||||||||
\(879\) | 4.81246e18 | 0.351916 | ||||||||
\(880\) | 1.73230e18 | 0.125744 | ||||||||
\(881\) | 7.58214e18 | 0.546322 | 0.273161 | − | 0.961968i | \(-0.411931\pi\) | ||||
0.273161 | + | 0.961968i | \(0.411931\pi\) | |||||||
\(882\) | 2.48902e17 | 0.0178026 | ||||||||
\(883\) | −1.22388e19 | −0.868946 | −0.434473 | − | 0.900685i | \(-0.643065\pi\) | ||||
−0.434473 | + | 0.900685i | \(0.643065\pi\) | |||||||
\(884\) | 2.49255e16 | 0.00175673 | ||||||||
\(885\) | −7.39328e18 | −0.517257 | ||||||||
\(886\) | 2.50587e19 | 1.74036 | ||||||||
\(887\) | 2.48370e18 | 0.171236 | 0.0856182 | − | 0.996328i | \(-0.472713\pi\) | ||||
0.0856182 | + | 0.996328i | \(0.472713\pi\) | |||||||
\(888\) | −1.66002e19 | −1.13613 | ||||||||
\(889\) | −3.79112e18 | −0.257576 | ||||||||
\(890\) | 5.23507e18 | 0.353091 | ||||||||
\(891\) | 3.15252e18 | 0.211083 | ||||||||
\(892\) | −2.96184e16 | −0.00196875 | ||||||||
\(893\) | 2.60127e19 | 1.71653 | ||||||||
\(894\) | −1.46593e19 | −0.960329 | ||||||||
\(895\) | 7.76095e18 | 0.504737 | ||||||||
\(896\) | −1.62159e19 | −1.04698 | ||||||||
\(897\) | 4.46146e18 | 0.285974 | ||||||||
\(898\) | −2.23087e19 | −1.41964 | ||||||||
\(899\) | −2.15350e19 | −1.36053 | ||||||||
\(900\) | −1.90673e15 | −0.000119595 0 | ||||||||
\(901\) | −1.98588e19 | −1.23664 | ||||||||
\(902\) | −7.01576e18 | −0.433743 | ||||||||
\(903\) | 2.87088e18 | 0.176216 | ||||||||
\(904\) | 1.00394e19 | 0.611807 | ||||||||
\(905\) | 8.96710e18 | 0.542546 | ||||||||
\(906\) | −2.03801e18 | −0.122426 | ||||||||
\(907\) | −6.93837e18 | −0.413819 | −0.206909 | − | 0.978360i | \(-0.566341\pi\) | ||||
−0.206909 | + | 0.978360i | \(0.566341\pi\) | |||||||
\(908\) | −7.93042e15 | −0.000469611 0 | ||||||||
\(909\) | −8.39303e17 | −0.0493462 | ||||||||
\(910\) | −2.88004e18 | −0.168124 | ||||||||
\(911\) | −4.63486e18 | −0.268638 | −0.134319 | − | 0.990938i | \(-0.542885\pi\) | ||||
−0.134319 | + | 0.990938i | \(0.542885\pi\) | |||||||
\(912\) | 2.37108e19 | 1.36452 | ||||||||
\(913\) | 4.35208e17 | 0.0248678 | ||||||||
\(914\) | 3.13604e19 | 1.77923 | ||||||||
\(915\) | −7.30893e18 | −0.411734 | ||||||||
\(916\) | −4.60600e16 | −0.00257634 | ||||||||
\(917\) | 1.66373e19 | 0.924023 | ||||||||
\(918\) | −3.26386e19 | −1.79992 | ||||||||
\(919\) | −4.92534e18 | −0.269703 | −0.134851 | − | 0.990866i | \(-0.543056\pi\) | ||||
−0.134851 | + | 0.990866i | \(0.543056\pi\) | |||||||
\(920\) | −7.31522e18 | −0.397747 | ||||||||
\(921\) | −2.07653e19 | −1.12112 | ||||||||
\(922\) | 9.43705e18 | 0.505924 | ||||||||
\(923\) | −2.50920e18 | −0.133575 | ||||||||
\(924\) | 1.43758e16 | 0.000759914 0 | ||||||||
\(925\) | 4.86233e18 | 0.255225 | ||||||||
\(926\) | 1.54217e19 | 0.803826 | ||||||||
\(927\) | −3.95683e18 | −0.204799 | ||||||||
\(928\) | −1.00169e17 | −0.00514841 | ||||||||
\(929\) | −1.91203e19 | −0.975870 | −0.487935 | − | 0.872880i | \(-0.662250\pi\) | ||||
−0.487935 | + | 0.872880i | \(0.662250\pi\) | |||||||
\(930\) | 1.21437e19 | 0.615475 | ||||||||
\(931\) | 2.62855e18 | 0.132295 | ||||||||
\(932\) | −2.69293e16 | −0.00134593 | ||||||||
\(933\) | 2.49669e19 | 1.23918 | ||||||||
\(934\) | −1.66835e19 | −0.822303 | ||||||||
\(935\) | −4.28497e18 | −0.209736 | ||||||||
\(936\) | −1.51684e18 | −0.0737304 | ||||||||
\(937\) | 4.30002e18 | 0.207569 | 0.103785 | − | 0.994600i | \(-0.466905\pi\) | ||||
0.103785 | + | 0.994600i | \(0.466905\pi\) | |||||||
\(938\) | 3.02846e18 | 0.145179 | ||||||||
\(939\) | 2.28404e19 | 1.08737 | ||||||||
\(940\) | 3.10298e16 | 0.00146706 | ||||||||
\(941\) | 5.18107e18 | 0.243269 | 0.121635 | − | 0.992575i | \(-0.461186\pi\) | ||||
0.121635 | + | 0.992575i | \(0.461186\pi\) | |||||||
\(942\) | 2.51489e19 | 1.17270 | ||||||||
\(943\) | 2.97128e19 | 1.37600 | ||||||||
\(944\) | −2.82878e19 | −1.30101 | ||||||||
\(945\) | 1.09661e19 | 0.500892 | ||||||||
\(946\) | −1.17343e18 | −0.0532309 | ||||||||
\(947\) | 1.94885e19 | 0.878020 | 0.439010 | − | 0.898482i | \(-0.355329\pi\) | ||||
0.439010 | + | 0.898482i | \(0.355329\pi\) | |||||||
\(948\) | −4.31168e16 | −0.00192927 | ||||||||
\(949\) | 3.47825e18 | 0.154572 | ||||||||
\(950\) | −6.92490e18 | −0.305640 | ||||||||
\(951\) | −2.17669e19 | −0.954165 | ||||||||
\(952\) | 3.99950e19 | 1.74127 | ||||||||
\(953\) | −2.96510e19 | −1.28214 | −0.641070 | − | 0.767483i | \(-0.721509\pi\) | ||||
−0.641070 | + | 0.767483i | \(0.721509\pi\) | |||||||
\(954\) | −3.53464e18 | −0.151803 | ||||||||
\(955\) | −1.43923e19 | −0.613916 | ||||||||
\(956\) | −5.08965e16 | −0.00215631 | ||||||||
\(957\) | −5.24353e18 | −0.220646 | ||||||||
\(958\) | 1.93262e19 | 0.807737 | ||||||||
\(959\) | −2.32193e19 | −0.963890 | ||||||||
\(960\) | −9.64213e18 | −0.397567 | ||||||||
\(961\) | 3.35903e19 | 1.37566 | ||||||||
\(962\) | −1.13134e19 | −0.460208 | ||||||||
\(963\) | −3.06476e18 | −0.123830 | ||||||||
\(964\) | 8.85631e16 | 0.00355428 | ||||||||
\(965\) | 1.38872e19 | 0.553587 | ||||||||
\(966\) | −2.09380e19 | −0.829057 | ||||||||
\(967\) | 1.25349e18 | 0.0493004 | 0.0246502 | − | 0.999696i | \(-0.492153\pi\) | ||||
0.0246502 | + | 0.999696i | \(0.492153\pi\) | |||||||
\(968\) | −2.35506e19 | −0.920052 | ||||||||
\(969\) | −5.86502e19 | −2.27596 | ||||||||
\(970\) | 1.42931e19 | 0.550947 | ||||||||
\(971\) | −2.17263e19 | −0.831879 | −0.415940 | − | 0.909392i | \(-0.636547\pi\) | ||||
−0.415940 | + | 0.909392i | \(0.636547\pi\) | |||||||
\(972\) | −3.09103e16 | −0.00117563 | ||||||||
\(973\) | −3.77327e19 | −1.42555 | ||||||||
\(974\) | 3.39886e19 | 1.27556 | ||||||||
\(975\) | −1.72250e18 | −0.0642139 | ||||||||
\(976\) | −2.79651e19 | −1.03560 | ||||||||
\(977\) | −2.56555e19 | −0.943768 | −0.471884 | − | 0.881661i | \(-0.656426\pi\) | ||||
−0.471884 | + | 0.881661i | \(0.656426\pi\) | |||||||
\(978\) | 1.36393e19 | 0.498412 | ||||||||
\(979\) | 6.08889e18 | 0.221030 | ||||||||
\(980\) | 3.13553e15 | 0.000113068 0 | ||||||||
\(981\) | 8.16977e18 | 0.292659 | ||||||||
\(982\) | −3.72539e19 | −1.32571 | ||||||||
\(983\) | 1.02856e19 | 0.363608 | 0.181804 | − | 0.983335i | \(-0.441806\pi\) | ||||
0.181804 | + | 0.983335i | \(0.441806\pi\) | |||||||
\(984\) | 3.91645e19 | 1.37538 | ||||||||
\(985\) | −7.35849e17 | −0.0256716 | ||||||||
\(986\) | 4.26672e19 | 1.47875 | ||||||||
\(987\) | −3.03661e19 | −1.04551 | ||||||||
\(988\) | 4.68517e16 | 0.00160253 | ||||||||
\(989\) | 4.96963e18 | 0.168868 | ||||||||
\(990\) | −7.62677e17 | −0.0257461 | ||||||||
\(991\) | 3.91892e19 | 1.31428 | 0.657140 | − | 0.753769i | \(-0.271766\pi\) | ||||
0.657140 | + | 0.753769i | \(0.271766\pi\) | |||||||
\(992\) | 2.69821e17 | 0.00898981 | ||||||||
\(993\) | −5.19170e18 | −0.171846 | ||||||||
\(994\) | 1.17759e19 | 0.387242 | ||||||||
\(995\) | 7.72147e18 | 0.252261 | ||||||||
\(996\) | 7.10578e15 | 0.000230636 0 | ||||||||
\(997\) | 1.60895e19 | 0.518829 | 0.259414 | − | 0.965766i | \(-0.416470\pi\) | ||||
0.259414 | + | 0.965766i | \(0.416470\pi\) | |||||||
\(998\) | −1.57570e19 | −0.504807 | ||||||||
\(999\) | 4.30768e19 | 1.37110 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5.14.a.b.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 45.14.a.e.1.3 | 3 | |||
4.3 | odd | 2 | 80.14.a.g.1.3 | 3 | |||
5.2 | odd | 4 | 25.14.b.b.24.2 | 6 | |||
5.3 | odd | 4 | 25.14.b.b.24.5 | 6 | |||
5.4 | even | 2 | 25.14.a.b.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.14.a.b.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
25.14.a.b.1.3 | 3 | 5.4 | even | 2 | |||
25.14.b.b.24.2 | 6 | 5.2 | odd | 4 | |||
25.14.b.b.24.5 | 6 | 5.3 | odd | 4 | |||
45.14.a.e.1.3 | 3 | 3.2 | odd | 2 | |||
80.14.a.g.1.3 | 3 | 4.3 | odd | 2 |