Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.31 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 35.6294 | 1.57461 | 0.787307 | − | 0.616562i | \(-0.211475\pi\) | ||||
0.787307 | + | 0.616562i | \(0.211475\pi\) | |||||||
\(3\) | 0.238037 | 0.00169668 | 0.000848340 | − | 1.00000i | \(-0.499730\pi\) | ||||
0.000848340 | 1.00000i | \(0.499730\pi\) | ||||||||
\(4\) | 757.456 | 1.47941 | ||||||||
\(5\) | −2006.11 | −1.43545 | −0.717726 | − | 0.696325i | \(-0.754817\pi\) | ||||
−0.717726 | + | 0.696325i | \(0.754817\pi\) | |||||||
\(6\) | 8.48114 | 0.00267161 | ||||||||
\(7\) | 3110.91 | 0.489719 | 0.244859 | − | 0.969559i | \(-0.421258\pi\) | ||||
0.244859 | + | 0.969559i | \(0.421258\pi\) | |||||||
\(8\) | 8745.46 | 0.754879 | ||||||||
\(9\) | −19682.9 | −0.999997 | ||||||||
\(10\) | −71476.4 | −2.26028 | ||||||||
\(11\) | −21988.6 | −0.452824 | −0.226412 | − | 0.974032i | \(-0.572700\pi\) | ||||
−0.226412 | + | 0.974032i | \(0.572700\pi\) | |||||||
\(12\) | 180.303 | 0.00251008 | ||||||||
\(13\) | −170282. | −1.65358 | −0.826789 | − | 0.562512i | \(-0.809835\pi\) | ||||
−0.826789 | + | 0.562512i | \(0.809835\pi\) | |||||||
\(14\) | 110840. | 0.771118 | ||||||||
\(15\) | −477.528 | −0.00243550 | ||||||||
\(16\) | −76221.9 | −0.290763 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −701292. | −1.57461 | ||||||||
\(19\) | 578915. | 1.01912 | 0.509558 | − | 0.860436i | \(-0.329809\pi\) | ||||
0.509558 | + | 0.860436i | \(0.329809\pi\) | |||||||
\(20\) | −1.51954e6 | −2.12362 | ||||||||
\(21\) | 740.514 | 0.000830896 0 | ||||||||
\(22\) | −783440. | −0.713023 | ||||||||
\(23\) | 1.14210e6 | 0.850996 | 0.425498 | − | 0.904959i | \(-0.360099\pi\) | ||||
0.425498 | + | 0.904959i | \(0.360099\pi\) | |||||||
\(24\) | 2081.75 | 0.00128079 | ||||||||
\(25\) | 2.07134e6 | 1.06052 | ||||||||
\(26\) | −6.06707e6 | −2.60375 | ||||||||
\(27\) | −9370.57 | −0.00339335 | ||||||||
\(28\) | 2.35638e6 | 0.724493 | ||||||||
\(29\) | 2.04445e6 | 0.536767 | 0.268384 | − | 0.963312i | \(-0.413511\pi\) | ||||
0.268384 | + | 0.963312i | \(0.413511\pi\) | |||||||
\(30\) | −17014.1 | −0.00383497 | ||||||||
\(31\) | 6.36010e6 | 1.23691 | 0.618453 | − | 0.785822i | \(-0.287760\pi\) | ||||
0.618453 | + | 0.785822i | \(0.287760\pi\) | |||||||
\(32\) | −7.19342e6 | −1.21272 | ||||||||
\(33\) | −5234.10 | −0.000768298 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.24082e6 | −0.702968 | ||||||||
\(36\) | −1.49090e7 | −1.47940 | ||||||||
\(37\) | 1.74773e7 | 1.53309 | 0.766544 | − | 0.642192i | \(-0.221975\pi\) | ||||
0.766544 | + | 0.642192i | \(0.221975\pi\) | |||||||
\(38\) | 2.06264e7 | 1.60471 | ||||||||
\(39\) | −40533.6 | −0.00280559 | ||||||||
\(40\) | −1.75443e7 | −1.08359 | ||||||||
\(41\) | 8.92910e6 | 0.493492 | 0.246746 | − | 0.969080i | \(-0.420639\pi\) | ||||
0.246746 | + | 0.969080i | \(0.420639\pi\) | |||||||
\(42\) | 26384.1 | 0.00130834 | ||||||||
\(43\) | 2.23811e7 | 0.998327 | 0.499163 | − | 0.866508i | \(-0.333641\pi\) | ||||
0.499163 | + | 0.866508i | \(0.333641\pi\) | |||||||
\(44\) | −1.66554e7 | −0.669911 | ||||||||
\(45\) | 3.94861e7 | 1.43545 | ||||||||
\(46\) | 4.06922e7 | 1.33999 | ||||||||
\(47\) | 5.29083e7 | 1.58155 | 0.790776 | − | 0.612106i | \(-0.209678\pi\) | ||||
0.790776 | + | 0.612106i | \(0.209678\pi\) | |||||||
\(48\) | −18143.7 | −0.000493332 0 | ||||||||
\(49\) | −3.06758e7 | −0.760176 | ||||||||
\(50\) | 7.38005e7 | 1.66992 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.28981e8 | −2.44631 | ||||||||
\(53\) | −4.96802e7 | −0.864853 | −0.432427 | − | 0.901669i | \(-0.642343\pi\) | ||||
−0.432427 | + | 0.901669i | \(0.642343\pi\) | |||||||
\(54\) | −333868. | −0.00534322 | ||||||||
\(55\) | 4.41114e7 | 0.650008 | ||||||||
\(56\) | 2.72064e7 | 0.369679 | ||||||||
\(57\) | 137804. | 0.00172911 | ||||||||
\(58\) | 7.28426e7 | 0.845201 | ||||||||
\(59\) | −1.25066e8 | −1.34371 | −0.671853 | − | 0.740684i | \(-0.734501\pi\) | ||||
−0.671853 | + | 0.740684i | \(0.734501\pi\) | |||||||
\(60\) | −361707. | −0.00360310 | ||||||||
\(61\) | −7.55780e7 | −0.698893 | −0.349447 | − | 0.936956i | \(-0.613630\pi\) | ||||
−0.349447 | + | 0.936956i | \(0.613630\pi\) | |||||||
\(62\) | 2.26607e8 | 1.94765 | ||||||||
\(63\) | −6.12319e7 | −0.489717 | ||||||||
\(64\) | −2.17272e8 | −1.61880 | ||||||||
\(65\) | 3.41605e8 | 2.37363 | ||||||||
\(66\) | −186488. | −0.00120977 | ||||||||
\(67\) | −5.66451e7 | −0.343420 | −0.171710 | − | 0.985148i | \(-0.554929\pi\) | ||||
−0.171710 | + | 0.985148i | \(0.554929\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 271862. | 0.00144387 | ||||||||
\(70\) | −2.22357e8 | −1.10690 | ||||||||
\(71\) | −9.81048e6 | −0.0458171 | −0.0229085 | − | 0.999738i | \(-0.507293\pi\) | ||||
−0.0229085 | + | 0.999738i | \(0.507293\pi\) | |||||||
\(72\) | −1.72136e8 | −0.754877 | ||||||||
\(73\) | −4.37401e8 | −1.80271 | −0.901357 | − | 0.433078i | \(-0.857428\pi\) | ||||
−0.901357 | + | 0.433078i | \(0.857428\pi\) | |||||||
\(74\) | 6.22707e8 | 2.41402 | ||||||||
\(75\) | 493056. | 0.00179937 | ||||||||
\(76\) | 4.38503e8 | 1.50769 | ||||||||
\(77\) | −6.84045e7 | −0.221757 | ||||||||
\(78\) | −1.44419e6 | −0.00441772 | ||||||||
\(79\) | 1.18121e8 | 0.341196 | 0.170598 | − | 0.985341i | \(-0.445430\pi\) | ||||
0.170598 | + | 0.985341i | \(0.445430\pi\) | |||||||
\(80\) | 1.52909e8 | 0.417377 | ||||||||
\(81\) | 3.87417e8 | 0.999991 | ||||||||
\(82\) | 3.18139e8 | 0.777060 | ||||||||
\(83\) | 7.42977e8 | 1.71840 | 0.859199 | − | 0.511641i | \(-0.170962\pi\) | ||||
0.859199 | + | 0.511641i | \(0.170962\pi\) | |||||||
\(84\) | 560907. | 0.00122923 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.97425e8 | 1.57198 | ||||||||
\(87\) | 486656. | 0.000910722 0 | ||||||||
\(88\) | −1.92300e8 | −0.341828 | ||||||||
\(89\) | −6.40009e8 | −1.08126 | −0.540631 | − | 0.841260i | \(-0.681814\pi\) | ||||
−0.540631 | + | 0.841260i | \(0.681814\pi\) | |||||||
\(90\) | 1.40687e9 | 2.26028 | ||||||||
\(91\) | −5.29734e8 | −0.809788 | ||||||||
\(92\) | 8.65088e8 | 1.25897 | ||||||||
\(93\) | 1.51394e6 | 0.00209863 | ||||||||
\(94\) | 1.88509e9 | 2.49033 | ||||||||
\(95\) | −1.16137e9 | −1.46289 | ||||||||
\(96\) | −1.71230e6 | −0.00205760 | ||||||||
\(97\) | 1.49842e9 | 1.71855 | 0.859274 | − | 0.511516i | \(-0.170916\pi\) | ||||
0.859274 | + | 0.511516i | \(0.170916\pi\) | |||||||
\(98\) | −1.09296e9 | −1.19698 | ||||||||
\(99\) | 4.32800e8 | 0.452823 | ||||||||
\(100\) | 1.56895e9 | 1.56895 | ||||||||
\(101\) | 1.10300e7 | 0.0105470 | 0.00527352 | − | 0.999986i | \(-0.498321\pi\) | ||||
0.00527352 | + | 0.999986i | \(0.498321\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.12633e9 | 1.86150 | 0.930748 | − | 0.365660i | \(-0.119157\pi\) | ||||
0.930748 | + | 0.365660i | \(0.119157\pi\) | |||||||
\(104\) | −1.48920e9 | −1.24825 | ||||||||
\(105\) | −1.48555e6 | −0.00119271 | ||||||||
\(106\) | −1.77008e9 | −1.36181 | ||||||||
\(107\) | 1.24966e9 | 0.921651 | 0.460825 | − | 0.887491i | \(-0.347553\pi\) | ||||
0.460825 | + | 0.887491i | \(0.347553\pi\) | |||||||
\(108\) | −7.09779e6 | −0.00502015 | ||||||||
\(109\) | −2.38971e9 | −1.62153 | −0.810766 | − | 0.585371i | \(-0.800949\pi\) | ||||
−0.810766 | + | 0.585371i | \(0.800949\pi\) | |||||||
\(110\) | 1.57166e9 | 1.02351 | ||||||||
\(111\) | 4.16026e6 | 0.00260116 | ||||||||
\(112\) | −2.37120e8 | −0.142392 | ||||||||
\(113\) | 1.78971e9 | 1.03260 | 0.516298 | − | 0.856409i | \(-0.327310\pi\) | ||||
0.516298 | + | 0.856409i | \(0.327310\pi\) | |||||||
\(114\) | 4.90986e6 | 0.00272268 | ||||||||
\(115\) | −2.29117e9 | −1.22156 | ||||||||
\(116\) | 1.54858e9 | 0.794097 | ||||||||
\(117\) | 3.35166e9 | 1.65357 | ||||||||
\(118\) | −4.45602e9 | −2.11582 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.17620e6 | −0.00183851 | ||||||||
\(121\) | −1.87445e9 | −0.794950 | ||||||||
\(122\) | −2.69280e9 | −1.10049 | ||||||||
\(123\) | 2.12546e6 | 0.000837298 0 | ||||||||
\(124\) | 4.81750e9 | 1.82989 | ||||||||
\(125\) | −2.37144e8 | −0.0868796 | ||||||||
\(126\) | −2.18166e9 | −0.771115 | ||||||||
\(127\) | −1.30529e9 | −0.445235 | −0.222618 | − | 0.974906i | \(-0.571460\pi\) | ||||
−0.222618 | + | 0.974906i | \(0.571460\pi\) | |||||||
\(128\) | −4.05824e9 | −1.33626 | ||||||||
\(129\) | 5.32753e6 | 0.00169384 | ||||||||
\(130\) | 1.21712e10 | 3.73755 | ||||||||
\(131\) | 6.34853e8 | 0.188344 | 0.0941722 | − | 0.995556i | \(-0.469980\pi\) | ||||
0.0941722 | + | 0.995556i | \(0.469980\pi\) | |||||||
\(132\) | −3.96460e6 | −0.00113662 | ||||||||
\(133\) | 1.80096e9 | 0.499080 | ||||||||
\(134\) | −2.01823e9 | −0.540754 | ||||||||
\(135\) | 1.87984e7 | 0.00487100 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.67526e9 | 0.406293 | 0.203147 | − | 0.979148i | \(-0.434883\pi\) | ||||
0.203147 | + | 0.979148i | \(0.434883\pi\) | |||||||
\(138\) | 9.68628e6 | 0.00227353 | ||||||||
\(139\) | −3.13923e8 | −0.0713273 | −0.0356637 | − | 0.999364i | \(-0.511355\pi\) | ||||
−0.0356637 | + | 0.999364i | \(0.511355\pi\) | |||||||
\(140\) | −4.72715e9 | −1.03998 | ||||||||
\(141\) | 1.25942e7 | 0.00268338 | ||||||||
\(142\) | −3.49542e8 | −0.0721442 | ||||||||
\(143\) | 3.74427e9 | 0.748781 | ||||||||
\(144\) | 1.50027e9 | 0.290763 | ||||||||
\(145\) | −4.10139e9 | −0.770504 | ||||||||
\(146\) | −1.55843e10 | −2.83858 | ||||||||
\(147\) | −7.30200e6 | −0.00128977 | ||||||||
\(148\) | 1.32383e10 | 2.26806 | ||||||||
\(149\) | 1.88570e8 | 0.0313426 | 0.0156713 | − | 0.999877i | \(-0.495011\pi\) | ||||
0.0156713 | + | 0.999877i | \(0.495011\pi\) | |||||||
\(150\) | 1.75673e7 | 0.00283331 | ||||||||
\(151\) | 2.87194e9 | 0.449551 | 0.224775 | − | 0.974411i | \(-0.427835\pi\) | ||||
0.224775 | + | 0.974411i | \(0.427835\pi\) | |||||||
\(152\) | 5.06288e9 | 0.769310 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.43721e9 | −0.349181 | ||||||||
\(155\) | −1.27590e10 | −1.77552 | ||||||||
\(156\) | −3.07024e7 | −0.00415061 | ||||||||
\(157\) | −1.23729e9 | −0.162526 | −0.0812630 | − | 0.996693i | \(-0.525895\pi\) | ||||
−0.0812630 | + | 0.996693i | \(0.525895\pi\) | |||||||
\(158\) | 4.20857e9 | 0.537251 | ||||||||
\(159\) | −1.18258e7 | −0.00146738 | ||||||||
\(160\) | 1.44308e10 | 1.74080 | ||||||||
\(161\) | 3.55296e9 | 0.416749 | ||||||||
\(162\) | 1.38035e10 | 1.57460 | ||||||||
\(163\) | 1.52441e10 | 1.69144 | 0.845722 | − | 0.533624i | \(-0.179170\pi\) | ||||
0.845722 | + | 0.533624i | \(0.179170\pi\) | |||||||
\(164\) | 6.76340e9 | 0.730076 | ||||||||
\(165\) | 1.05002e7 | 0.00110285 | ||||||||
\(166\) | 2.64718e10 | 2.70581 | ||||||||
\(167\) | 7.98265e9 | 0.794187 | 0.397094 | − | 0.917778i | \(-0.370019\pi\) | ||||
0.397094 | + | 0.917778i | \(0.370019\pi\) | |||||||
\(168\) | 6.47613e6 | 0.000627226 0 | ||||||||
\(169\) | 1.83916e10 | 1.73432 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.13948e10 | −1.01911 | ||||||||
\(172\) | 1.69527e10 | 1.47693 | ||||||||
\(173\) | 6.70354e9 | 0.568980 | 0.284490 | − | 0.958679i | \(-0.408176\pi\) | ||||
0.284490 | + | 0.958679i | \(0.408176\pi\) | |||||||
\(174\) | 1.73393e7 | 0.00143403 | ||||||||
\(175\) | 6.44375e9 | 0.519359 | ||||||||
\(176\) | 1.67601e9 | 0.131665 | ||||||||
\(177\) | −2.97703e7 | −0.00227984 | ||||||||
\(178\) | −2.28031e10 | −1.70257 | ||||||||
\(179\) | −6.50426e9 | −0.473543 | −0.236771 | − | 0.971565i | \(-0.576089\pi\) | ||||
−0.236771 | + | 0.971565i | \(0.576089\pi\) | |||||||
\(180\) | 2.99090e10 | 2.12361 | ||||||||
\(181\) | −1.61582e9 | −0.111902 | −0.0559510 | − | 0.998434i | \(-0.517819\pi\) | ||||
−0.0559510 | + | 0.998434i | \(0.517819\pi\) | |||||||
\(182\) | −1.88741e10 | −1.27510 | ||||||||
\(183\) | −1.79904e7 | −0.00118580 | ||||||||
\(184\) | 9.98816e9 | 0.642399 | ||||||||
\(185\) | −3.50614e10 | −2.20068 | ||||||||
\(186\) | 5.39409e7 | 0.00330453 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.00757e10 | 2.33976 | ||||||||
\(189\) | −2.91510e7 | −0.00166179 | ||||||||
\(190\) | −4.13788e10 | −2.30349 | ||||||||
\(191\) | −3.04910e10 | −1.65776 | −0.828879 | − | 0.559428i | \(-0.811021\pi\) | ||||
−0.828879 | + | 0.559428i | \(0.811021\pi\) | |||||||
\(192\) | −5.17188e7 | −0.00274658 | ||||||||
\(193\) | 2.89268e10 | 1.50070 | 0.750349 | − | 0.661042i | \(-0.229886\pi\) | ||||
0.750349 | + | 0.661042i | \(0.229886\pi\) | |||||||
\(194\) | 5.33879e10 | 2.70605 | ||||||||
\(195\) | 8.13147e7 | 0.00402729 | ||||||||
\(196\) | −2.32356e10 | −1.12461 | ||||||||
\(197\) | −2.47919e9 | −0.117277 | −0.0586383 | − | 0.998279i | \(-0.518676\pi\) | ||||
−0.0586383 | + | 0.998279i | \(0.518676\pi\) | |||||||
\(198\) | 1.54204e10 | 0.713021 | ||||||||
\(199\) | −2.36696e10 | −1.06992 | −0.534960 | − | 0.844877i | \(-0.679673\pi\) | ||||
−0.534960 | + | 0.844877i | \(0.679673\pi\) | |||||||
\(200\) | 1.81148e10 | 0.800568 | ||||||||
\(201\) | −1.34837e7 | −0.000582674 0 | ||||||||
\(202\) | 3.92994e8 | 0.0166075 | ||||||||
\(203\) | 6.36011e9 | 0.262865 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.79127e10 | −0.708385 | ||||||||
\(206\) | 7.57598e10 | 2.93114 | ||||||||
\(207\) | −2.24798e10 | −0.850994 | ||||||||
\(208\) | 1.29792e10 | 0.480800 | ||||||||
\(209\) | −1.27295e10 | −0.461481 | ||||||||
\(210\) | −5.29293e7 | −0.00187806 | ||||||||
\(211\) | −5.06744e10 | −1.76002 | −0.880009 | − | 0.474956i | \(-0.842464\pi\) | ||||
−0.880009 | + | 0.474956i | \(0.842464\pi\) | |||||||
\(212\) | −3.76306e10 | −1.27947 | ||||||||
\(213\) | −2.33526e6 | −7.77369e−5 0 | ||||||||
\(214\) | 4.45248e10 | 1.45124 | ||||||||
\(215\) | −4.48988e10 | −1.43305 | ||||||||
\(216\) | −8.19499e7 | −0.00256157 | ||||||||
\(217\) | 1.97857e10 | 0.605736 | ||||||||
\(218\) | −8.51439e10 | −2.55328 | ||||||||
\(219\) | −1.04118e8 | −0.00305863 | ||||||||
\(220\) | 3.34124e10 | 0.961626 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.48228e8 | 0.00409582 | ||||||||
\(223\) | 1.86341e10 | 0.504588 | 0.252294 | − | 0.967651i | \(-0.418815\pi\) | ||||
0.252294 | + | 0.967651i | \(0.418815\pi\) | |||||||
\(224\) | −2.23781e10 | −0.593891 | ||||||||
\(225\) | −4.07700e10 | −1.06052 | ||||||||
\(226\) | 6.37665e10 | 1.62594 | ||||||||
\(227\) | −6.75910e10 | −1.68956 | −0.844778 | − | 0.535118i | \(-0.820267\pi\) | ||||
−0.844778 | + | 0.535118i | \(0.820267\pi\) | |||||||
\(228\) | 1.04380e8 | 0.00255806 | ||||||||
\(229\) | −4.65557e9 | −0.111870 | −0.0559349 | − | 0.998434i | \(-0.517814\pi\) | ||||
−0.0559349 | + | 0.998434i | \(0.517814\pi\) | |||||||
\(230\) | −8.16330e10 | −1.92349 | ||||||||
\(231\) | −1.62828e7 | −0.000376250 0 | ||||||||
\(232\) | 1.78797e10 | 0.405194 | ||||||||
\(233\) | 3.07788e10 | 0.684148 | 0.342074 | − | 0.939673i | \(-0.388871\pi\) | ||||
0.342074 | + | 0.939673i | \(0.388871\pi\) | |||||||
\(234\) | 1.19418e11 | 2.60374 | ||||||||
\(235\) | −1.06140e11 | −2.27024 | ||||||||
\(236\) | −9.47318e10 | −1.98789 | ||||||||
\(237\) | 2.81171e7 | 0.000578900 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.55716e10 | 1.49819 | 0.749097 | − | 0.662460i | \(-0.230487\pi\) | ||||
0.749097 | + | 0.662460i | \(0.230487\pi\) | |||||||
\(240\) | 3.63981e7 | 0.000708155 0 | ||||||||
\(241\) | 2.68306e10 | 0.512335 | 0.256167 | − | 0.966632i | \(-0.417540\pi\) | ||||
0.256167 | + | 0.966632i | \(0.417540\pi\) | |||||||
\(242\) | −6.67856e10 | −1.25174 | ||||||||
\(243\) | 2.76661e8 | 0.00509002 | ||||||||
\(244\) | −5.72470e10 | −1.03395 | ||||||||
\(245\) | 6.15390e10 | 1.09120 | ||||||||
\(246\) | 7.57290e7 | 0.00131842 | ||||||||
\(247\) | −9.85791e10 | −1.68519 | ||||||||
\(248\) | 5.56220e10 | 0.933714 | ||||||||
\(249\) | 1.76856e8 | 0.00291557 | ||||||||
\(250\) | −8.44932e9 | −0.136802 | ||||||||
\(251\) | 4.14790e10 | 0.659624 | 0.329812 | − | 0.944047i | \(-0.393015\pi\) | ||||
0.329812 | + | 0.944047i | \(0.393015\pi\) | |||||||
\(252\) | −4.63805e10 | −0.724491 | ||||||||
\(253\) | −2.51131e10 | −0.385352 | ||||||||
\(254\) | −4.65066e10 | −0.701073 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.33495e10 | −0.485299 | ||||||||
\(257\) | 4.82861e10 | 0.690435 | 0.345217 | − | 0.938523i | \(-0.387805\pi\) | ||||
0.345217 | + | 0.938523i | \(0.387805\pi\) | |||||||
\(258\) | 1.89817e8 | 0.00266714 | ||||||||
\(259\) | 5.43704e10 | 0.750782 | ||||||||
\(260\) | 2.58750e11 | 3.51157 | ||||||||
\(261\) | −4.02408e10 | −0.536766 | ||||||||
\(262\) | 2.26195e10 | 0.296569 | ||||||||
\(263\) | −2.55822e10 | −0.329714 | −0.164857 | − | 0.986317i | \(-0.552716\pi\) | ||||
−0.164857 | + | 0.986317i | \(0.552716\pi\) | |||||||
\(264\) | −4.57746e7 | −0.000579972 0 | ||||||||
\(265\) | 9.96638e10 | 1.24146 | ||||||||
\(266\) | 6.41670e10 | 0.785859 | ||||||||
\(267\) | −1.52346e8 | −0.00183455 | ||||||||
\(268\) | −4.29062e10 | −0.508058 | ||||||||
\(269\) | 6.96548e10 | 0.811083 | 0.405542 | − | 0.914077i | \(-0.367083\pi\) | ||||
0.405542 | + | 0.914077i | \(0.367083\pi\) | |||||||
\(270\) | 6.69775e8 | 0.00766994 | ||||||||
\(271\) | −5.29874e10 | −0.596775 | −0.298387 | − | 0.954445i | \(-0.596449\pi\) | ||||
−0.298387 | + | 0.954445i | \(0.596449\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.26097e8 | −0.00137395 | ||||||||
\(274\) | 5.96886e10 | 0.639755 | ||||||||
\(275\) | −4.55457e10 | −0.480231 | ||||||||
\(276\) | 2.05923e8 | 0.00213607 | ||||||||
\(277\) | −1.49045e11 | −1.52110 | −0.760552 | − | 0.649277i | \(-0.775072\pi\) | ||||
−0.760552 | + | 0.649277i | \(0.775072\pi\) | |||||||
\(278\) | −1.11849e10 | −0.112313 | ||||||||
\(279\) | −1.25186e11 | −1.23690 | ||||||||
\(280\) | −5.45788e10 | −0.530656 | ||||||||
\(281\) | −2.16237e10 | −0.206896 | −0.103448 | − | 0.994635i | \(-0.532987\pi\) | ||||
−0.103448 | + | 0.994635i | \(0.532987\pi\) | |||||||
\(282\) | 4.48722e8 | 0.00422529 | ||||||||
\(283\) | 1.51427e11 | 1.40335 | 0.701675 | − | 0.712498i | \(-0.252436\pi\) | ||||
0.701675 | + | 0.712498i | \(0.252436\pi\) | |||||||
\(284\) | −7.43100e9 | −0.0677821 | ||||||||
\(285\) | −2.76448e8 | −0.00248206 | ||||||||
\(286\) | 1.33406e11 | 1.17904 | ||||||||
\(287\) | 2.77777e10 | 0.241673 | ||||||||
\(288\) | 1.41588e11 | 1.21272 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −1.46130e11 | −1.21325 | ||||||||
\(291\) | 3.56681e8 | 0.00291582 | ||||||||
\(292\) | −3.31312e11 | −2.66695 | ||||||||
\(293\) | 4.42128e10 | 0.350464 | 0.175232 | − | 0.984527i | \(-0.443932\pi\) | ||||
0.175232 | + | 0.984527i | \(0.443932\pi\) | |||||||
\(294\) | −2.60166e8 | −0.00203089 | ||||||||
\(295\) | 2.50895e11 | 1.92883 | ||||||||
\(296\) | 1.52847e11 | 1.15730 | ||||||||
\(297\) | 2.06045e8 | 0.00153659 | ||||||||
\(298\) | 6.71865e9 | 0.0493525 | ||||||||
\(299\) | −1.94479e11 | −1.40719 | ||||||||
\(300\) | 3.73468e8 | 0.00266200 | ||||||||
\(301\) | 6.96256e10 | 0.488899 | ||||||||
\(302\) | 1.02325e11 | 0.707868 | ||||||||
\(303\) | 2.62556e6 | 1.78950e−5 0 | ||||||||
\(304\) | −4.41260e10 | −0.296322 | ||||||||
\(305\) | 1.51617e11 | 1.00323 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.29583e11 | 1.47509 | 0.737543 | − | 0.675300i | \(-0.235986\pi\) | ||||
0.737543 | + | 0.675300i | \(0.235986\pi\) | |||||||
\(308\) | −5.18134e10 | −0.328068 | ||||||||
\(309\) | 5.06145e8 | 0.00315836 | ||||||||
\(310\) | −4.54597e11 | −2.79576 | ||||||||
\(311\) | −4.73812e10 | −0.287200 | −0.143600 | − | 0.989636i | \(-0.545868\pi\) | ||||
−0.143600 | + | 0.989636i | \(0.545868\pi\) | |||||||
\(312\) | −3.54485e8 | −0.00211788 | ||||||||
\(313\) | 2.62450e11 | 1.54560 | 0.772801 | − | 0.634648i | \(-0.218855\pi\) | ||||
0.772801 | + | 0.634648i | \(0.218855\pi\) | |||||||
\(314\) | −4.40839e10 | −0.255916 | ||||||||
\(315\) | 1.22838e11 | 0.702966 | ||||||||
\(316\) | 8.94711e10 | 0.504767 | ||||||||
\(317\) | 9.07698e10 | 0.504864 | 0.252432 | − | 0.967615i | \(-0.418770\pi\) | ||||
0.252432 | + | 0.967615i | \(0.418770\pi\) | |||||||
\(318\) | −4.21345e8 | −0.00231055 | ||||||||
\(319\) | −4.49546e10 | −0.243061 | ||||||||
\(320\) | 4.35870e11 | 2.32371 | ||||||||
\(321\) | 2.97467e8 | 0.00156375 | ||||||||
\(322\) | 1.26590e11 | 0.656218 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2.93451e11 | 1.47939 | ||||||||
\(325\) | −3.52712e11 | −1.75366 | ||||||||
\(326\) | 5.43138e11 | 2.66337 | ||||||||
\(327\) | −5.68840e8 | −0.00275122 | ||||||||
\(328\) | 7.80891e10 | 0.372527 | ||||||||
\(329\) | 1.64593e11 | 0.774515 | ||||||||
\(330\) | 3.74115e8 | 0.00173657 | ||||||||
\(331\) | 1.53040e11 | 0.700775 | 0.350387 | − | 0.936605i | \(-0.386050\pi\) | ||||
0.350387 | + | 0.936605i | \(0.386050\pi\) | |||||||
\(332\) | 5.62772e11 | 2.54221 | ||||||||
\(333\) | −3.44005e11 | −1.53308 | ||||||||
\(334\) | 2.84417e11 | 1.25054 | ||||||||
\(335\) | 1.13636e11 | 0.492963 | ||||||||
\(336\) | −5.64434e7 | −0.000241594 0 | ||||||||
\(337\) | 4.73479e10 | 0.199971 | 0.0999854 | − | 0.994989i | \(-0.468120\pi\) | ||||
0.0999854 | + | 0.994989i | \(0.468120\pi\) | |||||||
\(338\) | 6.55282e11 | 2.73088 | ||||||||
\(339\) | 4.26019e8 | 0.00175198 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.39850e11 | −0.560101 | ||||||||
\(342\) | −4.05989e11 | −1.60471 | ||||||||
\(343\) | −2.20966e11 | −0.861991 | ||||||||
\(344\) | 1.95733e11 | 0.753616 | ||||||||
\(345\) | −5.45384e8 | −0.00207260 | ||||||||
\(346\) | 2.38843e11 | 0.895923 | ||||||||
\(347\) | 1.71966e11 | 0.636736 | 0.318368 | − | 0.947967i | \(-0.396865\pi\) | ||||
0.318368 | + | 0.947967i | \(0.396865\pi\) | |||||||
\(348\) | 3.68621e8 | 0.00134733 | ||||||||
\(349\) | −9.37822e10 | −0.338381 | −0.169191 | − | 0.985583i | \(-0.554115\pi\) | ||||
−0.169191 | + | 0.985583i | \(0.554115\pi\) | |||||||
\(350\) | 2.29587e11 | 0.817789 | ||||||||
\(351\) | 1.59564e9 | 0.00561118 | ||||||||
\(352\) | 1.58173e11 | 0.549149 | ||||||||
\(353\) | 3.21525e11 | 1.10212 | 0.551059 | − | 0.834466i | \(-0.314224\pi\) | ||||
0.551059 | + | 0.834466i | \(0.314224\pi\) | |||||||
\(354\) | −1.06070e9 | −0.00358986 | ||||||||
\(355\) | 1.96809e10 | 0.0657683 | ||||||||
\(356\) | −4.84778e11 | −1.59963 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.31743e11 | −0.745647 | ||||||||
\(359\) | −2.50132e10 | −0.0794776 | −0.0397388 | − | 0.999210i | \(-0.512653\pi\) | ||||
−0.0397388 | + | 0.999210i | \(0.512653\pi\) | |||||||
\(360\) | 3.45324e11 | 1.08359 | ||||||||
\(361\) | 1.24551e10 | 0.0385981 | ||||||||
\(362\) | −5.75706e10 | −0.176202 | ||||||||
\(363\) | −4.46190e8 | −0.00134878 | ||||||||
\(364\) | −4.01250e11 | −1.19801 | ||||||||
\(365\) | 8.77472e11 | 2.58771 | ||||||||
\(366\) | −6.40987e8 | −0.00186717 | ||||||||
\(367\) | −5.32399e11 | −1.53193 | −0.765967 | − | 0.642880i | \(-0.777740\pi\) | ||||
−0.765967 | + | 0.642880i | \(0.777740\pi\) | |||||||
\(368\) | −8.70528e10 | −0.247439 | ||||||||
\(369\) | −1.75751e11 | −0.493491 | ||||||||
\(370\) | −1.24922e12 | −3.46521 | ||||||||
\(371\) | −1.54551e11 | −0.423535 | ||||||||
\(372\) | 1.14675e9 | 0.00310473 | ||||||||
\(373\) | −3.56768e11 | −0.954325 | −0.477163 | − | 0.878815i | \(-0.658335\pi\) | ||||
−0.477163 | + | 0.878815i | \(0.658335\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.64493e7 | −0.000147407 0 | ||||||||
\(376\) | 4.62707e11 | 1.19388 | ||||||||
\(377\) | −3.48134e11 | −0.887586 | ||||||||
\(378\) | −1.03863e9 | −0.00261667 | ||||||||
\(379\) | 2.85881e11 | 0.711720 | 0.355860 | − | 0.934539i | \(-0.384188\pi\) | ||||
0.355860 | + | 0.934539i | \(0.384188\pi\) | |||||||
\(380\) | −8.79683e11 | −2.16421 | ||||||||
\(381\) | −3.10707e8 | −0.000755421 0 | ||||||||
\(382\) | −1.08638e12 | −2.61033 | ||||||||
\(383\) | −3.68259e11 | −0.874498 | −0.437249 | − | 0.899340i | \(-0.644047\pi\) | ||||
−0.437249 | + | 0.899340i | \(0.644047\pi\) | |||||||
\(384\) | −9.66012e8 | −0.00226721 | ||||||||
\(385\) | 1.37227e11 | 0.318321 | ||||||||
\(386\) | 1.03065e12 | 2.36302 | ||||||||
\(387\) | −4.40525e11 | −0.998324 | ||||||||
\(388\) | 1.13499e12 | 2.54243 | ||||||||
\(389\) | 3.24891e11 | 0.719391 | 0.359696 | − | 0.933070i | \(-0.382881\pi\) | ||||
0.359696 | + | 0.933070i | \(0.382881\pi\) | |||||||
\(390\) | 2.89720e9 | 0.00634143 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2.68274e11 | −0.573841 | ||||||||
\(393\) | 1.51119e8 | 0.000319560 0 | ||||||||
\(394\) | −8.83321e10 | −0.184665 | ||||||||
\(395\) | −2.36962e11 | −0.489770 | ||||||||
\(396\) | 3.27827e11 | 0.669909 | ||||||||
\(397\) | 1.08653e11 | 0.219525 | 0.109763 | − | 0.993958i | \(-0.464991\pi\) | ||||
0.109763 | + | 0.993958i | \(0.464991\pi\) | |||||||
\(398\) | −8.43333e11 | −1.68471 | ||||||||
\(399\) | 4.28695e8 | 0.000846779 0 | ||||||||
\(400\) | −1.57881e11 | −0.308362 | ||||||||
\(401\) | −1.67993e11 | −0.324446 | −0.162223 | − | 0.986754i | \(-0.551866\pi\) | ||||
−0.162223 | + | 0.986754i | \(0.551866\pi\) | |||||||
\(402\) | −4.80415e8 | −0.000917486 0 | ||||||||
\(403\) | −1.08301e12 | −2.04532 | ||||||||
\(404\) | 8.35477e9 | 0.0156034 | ||||||||
\(405\) | −7.77200e11 | −1.43544 | ||||||||
\(406\) | 2.26607e11 | 0.413911 | ||||||||
\(407\) | −3.84301e11 | −0.694220 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.07465e11 | 0.543302 | 0.271651 | − | 0.962396i | \(-0.412430\pi\) | ||||
0.271651 | + | 0.962396i | \(0.412430\pi\) | |||||||
\(410\) | −6.38220e11 | −1.11543 | ||||||||
\(411\) | 3.98775e8 | 0.000689349 0 | ||||||||
\(412\) | 1.61060e12 | 2.75391 | ||||||||
\(413\) | −3.89069e11 | −0.658038 | ||||||||
\(414\) | −8.00943e11 | −1.33999 | ||||||||
\(415\) | −1.49049e12 | −2.46668 | ||||||||
\(416\) | 1.22491e12 | 2.00533 | ||||||||
\(417\) | −7.47254e7 | −0.000121020 0 | ||||||||
\(418\) | −4.53545e11 | −0.726654 | ||||||||
\(419\) | −4.23303e11 | −0.670947 | −0.335473 | − | 0.942050i | \(-0.608896\pi\) | ||||
−0.335473 | + | 0.942050i | \(0.608896\pi\) | |||||||
\(420\) | −1.12524e9 | −0.00176450 | ||||||||
\(421\) | −1.49913e11 | −0.232578 | −0.116289 | − | 0.993215i | \(-0.537100\pi\) | ||||
−0.116289 | + | 0.993215i | \(0.537100\pi\) | |||||||
\(422\) | −1.80550e12 | −2.77135 | ||||||||
\(423\) | −1.04139e12 | −1.58155 | ||||||||
\(424\) | −4.34476e11 | −0.652860 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.32040e7 | −0.000122406 0 | ||||||||
\(427\) | −2.35116e11 | −0.342261 | ||||||||
\(428\) | 9.46566e11 | 1.36350 | ||||||||
\(429\) | 8.91276e8 | 0.00127044 | ||||||||
\(430\) | −1.59972e12 | −2.25650 | ||||||||
\(431\) | 1.13823e12 | 1.58885 | 0.794427 | − | 0.607360i | \(-0.207771\pi\) | ||||
0.794427 | + | 0.607360i | \(0.207771\pi\) | |||||||
\(432\) | 7.14243e8 | 0.000986663 0 | ||||||||
\(433\) | 9.00628e11 | 1.23126 | 0.615630 | − | 0.788035i | \(-0.288902\pi\) | ||||
0.615630 | + | 0.788035i | \(0.288902\pi\) | |||||||
\(434\) | 7.04954e11 | 0.953800 | ||||||||
\(435\) | −9.76284e8 | −0.00130730 | ||||||||
\(436\) | −1.81010e12 | −2.39890 | ||||||||
\(437\) | 6.61177e11 | 0.867264 | ||||||||
\(438\) | −3.70966e9 | −0.00481615 | ||||||||
\(439\) | −2.15467e11 | −0.276879 | −0.138440 | − | 0.990371i | \(-0.544209\pi\) | ||||
−0.138440 | + | 0.990371i | \(0.544209\pi\) | |||||||
\(440\) | 3.85774e11 | 0.490678 | ||||||||
\(441\) | 6.03791e11 | 0.760173 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.47695e11 | 0.428925 | 0.214462 | − | 0.976732i | \(-0.431200\pi\) | ||||
0.214462 | + | 0.976732i | \(0.431200\pi\) | |||||||
\(444\) | 3.15121e9 | 0.00384817 | ||||||||
\(445\) | 1.28393e12 | 1.55210 | ||||||||
\(446\) | 6.63923e11 | 0.794531 | ||||||||
\(447\) | 4.48868e7 | 5.31783e−5 0 | ||||||||
\(448\) | −6.75913e11 | −0.792757 | ||||||||
\(449\) | 1.08563e12 | 1.26059 | 0.630296 | − | 0.776355i | \(-0.282934\pi\) | ||||
0.630296 | + | 0.776355i | \(0.282934\pi\) | |||||||
\(450\) | −1.45261e12 | −1.66991 | ||||||||
\(451\) | −1.96338e11 | −0.223465 | ||||||||
\(452\) | 1.35563e12 | 1.52763 | ||||||||
\(453\) | 6.83629e8 | 0.000762743 0 | ||||||||
\(454\) | −2.40823e12 | −2.66040 | ||||||||
\(455\) | 1.06270e12 | 1.16241 | ||||||||
\(456\) | 1.20515e9 | 0.00130527 | ||||||||
\(457\) | −8.91105e11 | −0.955666 | −0.477833 | − | 0.878451i | \(-0.658578\pi\) | ||||
−0.477833 | + | 0.878451i | \(0.658578\pi\) | |||||||
\(458\) | −1.65875e11 | −0.176152 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.73546e12 | −1.80719 | ||||||||
\(461\) | 7.21170e11 | 0.743675 | 0.371838 | − | 0.928298i | \(-0.378728\pi\) | ||||
0.371838 | + | 0.928298i | \(0.378728\pi\) | |||||||
\(462\) | −5.80148e8 | −0.000592448 0 | ||||||||
\(463\) | 2.47341e11 | 0.250139 | 0.125069 | − | 0.992148i | \(-0.460085\pi\) | ||||
0.125069 | + | 0.992148i | \(0.460085\pi\) | |||||||
\(464\) | −1.55832e11 | −0.156072 | ||||||||
\(465\) | −3.03713e9 | −0.00301249 | ||||||||
\(466\) | 1.09663e12 | 1.07727 | ||||||||
\(467\) | 3.73549e10 | 0.0363431 | 0.0181715 | − | 0.999835i | \(-0.494215\pi\) | ||||
0.0181715 | + | 0.999835i | \(0.494215\pi\) | |||||||
\(468\) | 2.53873e12 | 2.44631 | ||||||||
\(469\) | −1.76218e11 | −0.168179 | ||||||||
\(470\) | −3.78169e12 | −3.57475 | ||||||||
\(471\) | −2.94521e8 | −0.000275754 0 | ||||||||
\(472\) | −1.09376e12 | −1.01434 | ||||||||
\(473\) | −4.92128e11 | −0.452067 | ||||||||
\(474\) | 1.00180e9 | 0.000911543 0 | ||||||||
\(475\) | 1.19913e12 | 1.08080 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.77853e11 | 0.864851 | ||||||||
\(478\) | 2.69257e12 | 2.35908 | ||||||||
\(479\) | −1.56185e11 | −0.135560 | −0.0677798 | − | 0.997700i | \(-0.521592\pi\) | ||||
−0.0677798 | + | 0.997700i | \(0.521592\pi\) | |||||||
\(480\) | 3.43506e9 | 0.00295358 | ||||||||
\(481\) | −2.97608e12 | −2.53508 | ||||||||
\(482\) | 9.55959e11 | 0.806729 | ||||||||
\(483\) | 8.45739e8 | 0.000707089 0 | ||||||||
\(484\) | −1.41981e12 | −1.17605 | ||||||||
\(485\) | −3.00600e12 | −2.46689 | ||||||||
\(486\) | 9.85726e9 | 0.00801481 | ||||||||
\(487\) | 7.04881e11 | 0.567853 | 0.283926 | − | 0.958846i | \(-0.408363\pi\) | ||||
0.283926 | + | 0.958846i | \(0.408363\pi\) | |||||||
\(488\) | −6.60964e11 | −0.527580 | ||||||||
\(489\) | 3.62867e9 | 0.00286984 | ||||||||
\(490\) | 2.19260e12 | 1.71821 | ||||||||
\(491\) | 2.70124e11 | 0.209747 | 0.104874 | − | 0.994486i | \(-0.466556\pi\) | ||||
0.104874 | + | 0.994486i | \(0.466556\pi\) | |||||||
\(492\) | 1.60994e9 | 0.00123870 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −3.51232e12 | −2.65352 | ||||||||
\(495\) | −8.68242e11 | −0.650006 | ||||||||
\(496\) | −4.84779e11 | −0.359647 | ||||||||
\(497\) | −3.05195e10 | −0.0224375 | ||||||||
\(498\) | 6.30129e9 | 0.00459090 | ||||||||
\(499\) | 1.68888e12 | 1.21940 | 0.609699 | − | 0.792633i | \(-0.291290\pi\) | ||||
0.609699 | + | 0.792633i | \(0.291290\pi\) | |||||||
\(500\) | −1.79626e11 | −0.128530 | ||||||||
\(501\) | 1.90017e9 | 0.00134748 | ||||||||
\(502\) | 1.47787e12 | 1.03865 | ||||||||
\(503\) | 4.85829e11 | 0.338398 | 0.169199 | − | 0.985582i | \(-0.445882\pi\) | ||||
0.169199 | + | 0.985582i | \(0.445882\pi\) | |||||||
\(504\) | −5.35501e11 | −0.369678 | ||||||||
\(505\) | −2.21274e10 | −0.0151398 | ||||||||
\(506\) | −8.94764e11 | −0.606780 | ||||||||
\(507\) | 4.37789e9 | 0.00294259 | ||||||||
\(508\) | −9.88698e11 | −0.658684 | ||||||||
\(509\) | 4.99864e11 | 0.330082 | 0.165041 | − | 0.986287i | \(-0.447224\pi\) | ||||
0.165041 | + | 0.986287i | \(0.447224\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.36072e12 | −0.882823 | ||||||||
\(512\) | 8.89593e11 | 0.572106 | ||||||||
\(513\) | −5.42477e9 | −0.00345822 | ||||||||
\(514\) | 1.72040e12 | 1.08717 | ||||||||
\(515\) | −4.26563e12 | −2.67209 | ||||||||
\(516\) | 4.03537e9 | 0.00250588 | ||||||||
\(517\) | −1.16338e12 | −0.716165 | ||||||||
\(518\) | 1.93719e12 | 1.18219 | ||||||||
\(519\) | 1.59569e9 | 0.000965376 0 | ||||||||
\(520\) | 2.98749e12 | 1.79181 | ||||||||
\(521\) | −2.25253e12 | −1.33937 | −0.669687 | − | 0.742644i | \(-0.733572\pi\) | ||||
−0.669687 | + | 0.742644i | \(0.733572\pi\) | |||||||
\(522\) | −1.43376e12 | −0.845198 | ||||||||
\(523\) | 1.33630e12 | 0.780990 | 0.390495 | − | 0.920605i | \(-0.372304\pi\) | ||||
0.390495 | + | 0.920605i | \(0.372304\pi\) | |||||||
\(524\) | 4.80873e11 | 0.278638 | ||||||||
\(525\) | 1.53385e9 | 0.000881185 0 | ||||||||
\(526\) | −9.11481e11 | −0.519172 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 3.98953e8 | 0.000223393 0 | ||||||||
\(529\) | −4.96768e11 | −0.275806 | ||||||||
\(530\) | 3.55097e12 | 1.95481 | ||||||||
\(531\) | 2.46166e12 | 1.34370 | ||||||||
\(532\) | 1.36414e12 | 0.738343 | ||||||||
\(533\) | −1.52047e12 | −0.816028 | ||||||||
\(534\) | −5.42800e9 | −0.00288871 | ||||||||
\(535\) | −2.50696e12 | −1.32299 | ||||||||
\(536\) | −4.95387e11 | −0.259241 | ||||||||
\(537\) | −1.54826e9 | −0.000803451 0 | ||||||||
\(538\) | 2.48176e12 | 1.27714 | ||||||||
\(539\) | 6.74517e11 | 0.344226 | ||||||||
\(540\) | 1.42389e10 | 0.00720618 | ||||||||
\(541\) | −1.60577e12 | −0.805928 | −0.402964 | − | 0.915216i | \(-0.632020\pi\) | ||||
−0.402964 | + | 0.915216i | \(0.632020\pi\) | |||||||
\(542\) | −1.88791e12 | −0.939689 | ||||||||
\(543\) | −3.84625e8 | −0.000189862 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.79400e12 | 2.32763 | ||||||||
\(546\) | −4.49275e9 | −0.00216344 | ||||||||
\(547\) | −2.50244e12 | −1.19515 | −0.597573 | − | 0.801815i | \(-0.703868\pi\) | ||||
−0.597573 | + | 0.801815i | \(0.703868\pi\) | |||||||
\(548\) | 1.26894e12 | 0.601073 | ||||||||
\(549\) | 1.48760e12 | 0.698891 | ||||||||
\(550\) | −1.62277e12 | −0.756178 | ||||||||
\(551\) | 1.18356e12 | 0.547028 | ||||||||
\(552\) | 2.37756e9 | 0.00108995 | ||||||||
\(553\) | 3.67463e11 | 0.167090 | ||||||||
\(554\) | −5.31040e12 | −2.39515 | ||||||||
\(555\) | −8.34592e9 | −0.00373384 | ||||||||
\(556\) | −2.37783e11 | −0.105522 | ||||||||
\(557\) | 3.78565e10 | 0.0166645 | 0.00833225 | − | 0.999965i | \(-0.497348\pi\) | ||||
0.00833225 | + | 0.999965i | \(0.497348\pi\) | |||||||
\(558\) | −4.46029e12 | −1.94764 | ||||||||
\(559\) | −3.81110e12 | −1.65081 | ||||||||
\(560\) | 4.75687e11 | 0.204397 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.70440e11 | −0.325781 | ||||||||
\(563\) | −3.79841e12 | −1.59336 | −0.796681 | − | 0.604400i | \(-0.793413\pi\) | ||||
−0.796681 | + | 0.604400i | \(0.793413\pi\) | |||||||
\(564\) | 9.53952e9 | 0.00396982 | ||||||||
\(565\) | −3.59035e12 | −1.48224 | ||||||||
\(566\) | 5.39527e12 | 2.20973 | ||||||||
\(567\) | 1.20522e12 | 0.489715 | ||||||||
\(568\) | −8.57971e10 | −0.0345864 | ||||||||
\(569\) | 4.15125e12 | 1.66025 | 0.830126 | − | 0.557575i | \(-0.188268\pi\) | ||||
0.830126 | + | 0.557575i | \(0.188268\pi\) | |||||||
\(570\) | −9.84970e9 | −0.00390828 | ||||||||
\(571\) | −2.49821e12 | −0.983483 | −0.491741 | − | 0.870741i | \(-0.663639\pi\) | ||||
−0.491741 | + | 0.870741i | \(0.663639\pi\) | |||||||
\(572\) | 2.83612e12 | 1.10775 | ||||||||
\(573\) | −7.25800e9 | −0.00281268 | ||||||||
\(574\) | 9.89702e11 | 0.380541 | ||||||||
\(575\) | 2.36567e12 | 0.902502 | ||||||||
\(576\) | 4.27655e12 | 1.61880 | ||||||||
\(577\) | 9.96726e11 | 0.374356 | 0.187178 | − | 0.982326i | \(-0.440066\pi\) | ||||
0.187178 | + | 0.982326i | \(0.440066\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.88567e9 | 0.00254620 | ||||||||
\(580\) | −3.10662e12 | −1.13989 | ||||||||
\(581\) | 2.31134e12 | 0.841532 | ||||||||
\(582\) | 1.27083e10 | 0.00459129 | ||||||||
\(583\) | 1.09240e12 | 0.391627 | ||||||||
\(584\) | −3.82527e12 | −1.36083 | ||||||||
\(585\) | −6.72378e12 | −2.37363 | ||||||||
\(586\) | 1.57528e12 | 0.551845 | ||||||||
\(587\) | −3.55291e12 | −1.23513 | −0.617566 | − | 0.786519i | \(-0.711881\pi\) | ||||
−0.617566 | + | 0.786519i | \(0.711881\pi\) | |||||||
\(588\) | −5.53094e9 | −0.00190810 | ||||||||
\(589\) | 3.68196e12 | 1.26055 | ||||||||
\(590\) | 8.93925e12 | 3.03716 | ||||||||
\(591\) | −5.90140e8 | −0.000198981 0 | ||||||||
\(592\) | −1.33215e12 | −0.445766 | ||||||||
\(593\) | 4.25252e12 | 1.41221 | 0.706107 | − | 0.708105i | \(-0.250450\pi\) | ||||
0.706107 | + | 0.708105i | \(0.250450\pi\) | |||||||
\(594\) | 7.34128e9 | 0.00241954 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.42834e11 | 0.0463684 | ||||||||
\(597\) | −5.63424e9 | −0.00181531 | ||||||||
\(598\) | −6.92917e12 | −2.21578 | ||||||||
\(599\) | −4.95143e12 | −1.57149 | −0.785743 | − | 0.618554i | \(-0.787719\pi\) | ||||
−0.785743 | + | 0.618554i | \(0.787719\pi\) | |||||||
\(600\) | 4.31200e9 | 0.00135831 | ||||||||
\(601\) | −1.76825e12 | −0.552850 | −0.276425 | − | 0.961035i | \(-0.589150\pi\) | ||||
−0.276425 | + | 0.961035i | \(0.589150\pi\) | |||||||
\(602\) | 2.48072e12 | 0.769827 | ||||||||
\(603\) | 1.11494e12 | 0.343419 | ||||||||
\(604\) | 2.17537e12 | 0.665068 | ||||||||
\(605\) | 3.76035e12 | 1.14111 | ||||||||
\(606\) | 9.35473e7 | 2.81776e−5 0 | ||||||||
\(607\) | 2.04371e11 | 0.0611042 | 0.0305521 | − | 0.999533i | \(-0.490273\pi\) | ||||
0.0305521 | + | 0.999533i | \(0.490273\pi\) | |||||||
\(608\) | −4.16438e12 | −1.23590 | ||||||||
\(609\) | 1.51395e9 | 0.000445997 0 | ||||||||
\(610\) | 5.40204e12 | 1.57970 | ||||||||
\(611\) | −9.00935e12 | −2.61522 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.76517e12 | −0.504911 | −0.252455 | − | 0.967609i | \(-0.581238\pi\) | ||||
−0.252455 | + | 0.967609i | \(0.581238\pi\) | |||||||
\(614\) | 8.17992e12 | 2.32269 | ||||||||
\(615\) | −4.26390e9 | −0.00120190 | ||||||||
\(616\) | −5.98229e11 | −0.167399 | ||||||||
\(617\) | 4.51327e12 | 1.25374 | 0.626872 | − | 0.779123i | \(-0.284335\pi\) | ||||
0.626872 | + | 0.779123i | \(0.284335\pi\) | |||||||
\(618\) | 1.80337e10 | 0.00497320 | ||||||||
\(619\) | −2.40683e10 | −0.00658926 | −0.00329463 | − | 0.999995i | \(-0.501049\pi\) | ||||
−0.00329463 | + | 0.999995i | \(0.501049\pi\) | |||||||
\(620\) | −9.66441e12 | −2.62671 | ||||||||
\(621\) | −1.07021e10 | −0.00288773 | ||||||||
\(622\) | −1.68816e12 | −0.452228 | ||||||||
\(623\) | −1.99101e12 | −0.529514 | ||||||||
\(624\) | 3.08955e9 | 0.000815764 0 | ||||||||
\(625\) | −3.56984e12 | −0.935813 | ||||||||
\(626\) | 9.35096e12 | 2.43373 | ||||||||
\(627\) | −3.03010e9 | −0.000782985 0 | ||||||||
\(628\) | −9.37192e11 | −0.240442 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 4.37664e12 | 1.10690 | ||||||||
\(631\) | −5.35424e12 | −1.34451 | −0.672257 | − | 0.740318i | \(-0.734675\pi\) | ||||
−0.672257 | + | 0.740318i | \(0.734675\pi\) | |||||||
\(632\) | 1.03302e12 | 0.257562 | ||||||||
\(633\) | −1.20624e10 | −0.00298619 | ||||||||
\(634\) | 3.23408e12 | 0.794966 | ||||||||
\(635\) | 2.61854e12 | 0.639114 | ||||||||
\(636\) | −8.95749e9 | −0.00217085 | ||||||||
\(637\) | 5.22355e12 | 1.25701 | ||||||||
\(638\) | −1.60171e12 | −0.382727 | ||||||||
\(639\) | 1.93099e11 | 0.0458170 | ||||||||
\(640\) | 8.14125e12 | 1.91814 | ||||||||
\(641\) | −6.68364e12 | −1.56369 | −0.781847 | − | 0.623470i | \(-0.785722\pi\) | ||||
−0.781847 | + | 0.623470i | \(0.785722\pi\) | |||||||
\(642\) | 1.05986e10 | 0.00246229 | ||||||||
\(643\) | 4.42198e12 | 1.02016 | 0.510079 | − | 0.860128i | \(-0.329616\pi\) | ||||
0.510079 | + | 0.860128i | \(0.329616\pi\) | |||||||
\(644\) | 2.69121e12 | 0.616541 | ||||||||
\(645\) | −1.06876e10 | −0.00243143 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.65641e12 | 1.71773 | 0.858867 | − | 0.512198i | \(-0.171169\pi\) | ||||
0.858867 | + | 0.512198i | \(0.171169\pi\) | |||||||
\(648\) | 3.38814e12 | 0.754873 | ||||||||
\(649\) | 2.75002e12 | 0.608463 | ||||||||
\(650\) | −1.25669e13 | −2.76134 | ||||||||
\(651\) | 4.70975e9 | 0.00102774 | ||||||||
\(652\) | 1.15467e13 | 2.50233 | ||||||||
\(653\) | 8.87094e12 | 1.90924 | 0.954620 | − | 0.297826i | \(-0.0962617\pi\) | ||||
0.954620 | + | 0.297826i | \(0.0962617\pi\) | |||||||
\(654\) | −2.02674e10 | −0.00433210 | ||||||||
\(655\) | −1.27358e12 | −0.270359 | ||||||||
\(656\) | −6.80593e11 | −0.143490 | ||||||||
\(657\) | 8.60933e12 | 1.80271 | ||||||||
\(658\) | 5.86436e12 | 1.21956 | ||||||||
\(659\) | 2.06299e12 | 0.426101 | 0.213051 | − | 0.977041i | \(-0.431660\pi\) | ||||
0.213051 | + | 0.977041i | \(0.431660\pi\) | |||||||
\(660\) | 7.95341e9 | 0.00163157 | ||||||||
\(661\) | 1.41824e11 | 0.0288965 | 0.0144482 | − | 0.999896i | \(-0.495401\pi\) | ||||
0.0144482 | + | 0.999896i | \(0.495401\pi\) | |||||||
\(662\) | 5.45272e12 | 1.10345 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.49767e12 | 1.29718 | ||||||||
\(665\) | −3.61291e12 | −0.716406 | ||||||||
\(666\) | −1.22567e13 | −2.41401 | ||||||||
\(667\) | 2.33496e12 | 0.456787 | ||||||||
\(668\) | 6.04650e12 | 1.17493 | ||||||||
\(669\) | 4.43562e9 | 0.000856124 0 | ||||||||
\(670\) | 4.04879e12 | 0.776226 | ||||||||
\(671\) | 1.66185e12 | 0.316476 | ||||||||
\(672\) | −5.32683e9 | −0.00100764 | ||||||||
\(673\) | 9.81683e11 | 0.184460 | 0.0922302 | − | 0.995738i | \(-0.470600\pi\) | ||||
0.0922302 | + | 0.995738i | \(0.470600\pi\) | |||||||
\(674\) | 1.68698e12 | 0.314877 | ||||||||
\(675\) | −1.94096e10 | −0.00359873 | ||||||||
\(676\) | 1.39308e13 | 2.56577 | ||||||||
\(677\) | −2.20727e12 | −0.403837 | −0.201919 | − | 0.979402i | \(-0.564718\pi\) | ||||
−0.201919 | + | 0.979402i | \(0.564718\pi\) | |||||||
\(678\) | 1.51788e10 | 0.00275870 | ||||||||
\(679\) | 4.66146e12 | 0.841605 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.60892e10 | −0.00286663 | ||||||||
\(682\) | −4.98276e12 | −0.881942 | ||||||||
\(683\) | −3.00134e11 | −0.0527742 | −0.0263871 | − | 0.999652i | \(-0.508400\pi\) | ||||
−0.0263871 | + | 0.999652i | \(0.508400\pi\) | |||||||
\(684\) | −8.63103e12 | −1.50768 | ||||||||
\(685\) | −3.36075e12 | −0.583215 | ||||||||
\(686\) | −7.87291e12 | −1.35730 | ||||||||
\(687\) | −1.10820e9 | −0.000189807 0 | ||||||||
\(688\) | −1.70593e12 | −0.290277 | ||||||||
\(689\) | 8.45967e12 | 1.43010 | ||||||||
\(690\) | −1.94317e10 | −0.00326355 | ||||||||
\(691\) | −7.77169e10 | −0.0129677 | −0.00648387 | − | 0.999979i | \(-0.502064\pi\) | ||||
−0.00648387 | + | 0.999979i | \(0.502064\pi\) | |||||||
\(692\) | 5.07764e12 | 0.841752 | ||||||||
\(693\) | 1.34640e12 | 0.221756 | ||||||||
\(694\) | 6.12704e12 | 1.00261 | ||||||||
\(695\) | 6.29762e11 | 0.102387 | ||||||||
\(696\) | 4.25603e9 | 0.000687485 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −3.34141e12 | −0.532819 | ||||||||
\(699\) | 7.32651e9 | 0.00116078 | ||||||||
\(700\) | 4.88086e12 | 0.768342 | ||||||||
\(701\) | 5.48906e12 | 0.858552 | 0.429276 | − | 0.903173i | \(-0.358769\pi\) | ||||
0.429276 | + | 0.903173i | \(0.358769\pi\) | |||||||
\(702\) | 5.68519e10 | 0.00883543 | ||||||||
\(703\) | 1.01179e13 | 1.56240 | ||||||||
\(704\) | 4.77749e12 | 0.733032 | ||||||||
\(705\) | −2.52652e10 | −0.00385187 | ||||||||
\(706\) | 1.14557e13 | 1.73541 | ||||||||
\(707\) | 3.43135e10 | 0.00516509 | ||||||||
\(708\) | −2.25497e10 | −0.00337281 | ||||||||
\(709\) | −2.18350e12 | −0.324523 | −0.162262 | − | 0.986748i | \(-0.551879\pi\) | ||||
−0.162262 | + | 0.986748i | \(0.551879\pi\) | |||||||
\(710\) | 7.01217e11 | 0.103560 | ||||||||
\(711\) | −2.32496e12 | −0.341195 | ||||||||
\(712\) | −5.59717e12 | −0.816222 | ||||||||
\(713\) | 7.26385e12 | 1.05260 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.51139e12 | −1.07484 | ||||||||
\(716\) | −4.92669e12 | −0.700562 | ||||||||
\(717\) | 1.79889e10 | 0.00254196 | ||||||||
\(718\) | −8.91207e11 | −0.125146 | ||||||||
\(719\) | 6.20764e12 | 0.866257 | 0.433128 | − | 0.901332i | \(-0.357410\pi\) | ||||
0.433128 | + | 0.901332i | \(0.357410\pi\) | |||||||
\(720\) | −3.00970e12 | −0.417376 | ||||||||
\(721\) | 6.61482e12 | 0.911610 | ||||||||
\(722\) | 4.43769e11 | 0.0607771 | ||||||||
\(723\) | 6.38669e9 | 0.000869267 0 | ||||||||
\(724\) | −1.22391e12 | −0.165549 | ||||||||
\(725\) | 4.23475e12 | 0.569255 | ||||||||
\(726\) | −1.58975e10 | −0.00212380 | ||||||||
\(727\) | 8.67792e12 | 1.15215 | 0.576077 | − | 0.817395i | \(-0.304583\pi\) | ||||
0.576077 | + | 0.817395i | \(0.304583\pi\) | |||||||
\(728\) | −4.63276e12 | −0.611292 | ||||||||
\(729\) | −7.62547e12 | −0.999983 | ||||||||
\(730\) | 3.12638e13 | 4.07464 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.36269e10 | −0.00175428 | ||||||||
\(733\) | 6.34487e12 | 0.811811 | 0.405905 | − | 0.913915i | \(-0.366956\pi\) | ||||
0.405905 | + | 0.913915i | \(0.366956\pi\) | |||||||
\(734\) | −1.89691e13 | −2.41220 | ||||||||
\(735\) | 1.46486e10 | 0.00185141 | ||||||||
\(736\) | −8.21558e12 | −1.03202 | ||||||||
\(737\) | 1.24554e12 | 0.155509 | ||||||||
\(738\) | −6.26191e12 | −0.777057 | ||||||||
\(739\) | −1.28807e13 | −1.58869 | −0.794344 | − | 0.607468i | \(-0.792185\pi\) | ||||
−0.794344 | + | 0.607468i | \(0.792185\pi\) | |||||||
\(740\) | −2.65574e13 | −3.25569 | ||||||||
\(741\) | −2.34655e10 | −0.00285922 | ||||||||
\(742\) | −5.50656e12 | −0.666903 | ||||||||
\(743\) | 1.97478e12 | 0.237722 | 0.118861 | − | 0.992911i | \(-0.462076\pi\) | ||||
0.118861 | + | 0.992911i | \(0.462076\pi\) | |||||||
\(744\) | 1.32401e10 | 0.00158421 | ||||||||
\(745\) | −3.78292e11 | −0.0449908 | ||||||||
\(746\) | −1.27114e13 | −1.50269 | ||||||||
\(747\) | −1.46240e13 | −1.71839 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.88760e12 | 0.451350 | ||||||||
\(750\) | −2.01125e9 | −0.000232109 0 | ||||||||
\(751\) | 1.19872e13 | 1.37512 | 0.687558 | − | 0.726129i | \(-0.258683\pi\) | ||||
0.687558 | + | 0.726129i | \(0.258683\pi\) | |||||||
\(752\) | −4.03277e12 | −0.459857 | ||||||||
\(753\) | 9.87356e9 | 0.00111917 | ||||||||
\(754\) | −1.24038e13 | −1.39761 | ||||||||
\(755\) | −5.76141e12 | −0.645309 | ||||||||
\(756\) | −2.20806e10 | −0.00245846 | ||||||||
\(757\) | −9.64713e12 | −1.06774 | −0.533871 | − | 0.845566i | \(-0.679263\pi\) | ||||
−0.533871 | + | 0.845566i | \(0.679263\pi\) | |||||||
\(758\) | 1.01858e13 | 1.12068 | ||||||||
\(759\) | −5.97785e9 | −0.000653818 0 | ||||||||
\(760\) | −1.01567e13 | −1.10431 | ||||||||
\(761\) | −4.48077e12 | −0.484308 | −0.242154 | − | 0.970238i | \(-0.577854\pi\) | ||||
−0.242154 | + | 0.970238i | \(0.577854\pi\) | |||||||
\(762\) | −1.10703e10 | −0.00118950 | ||||||||
\(763\) | −7.43417e12 | −0.794094 | ||||||||
\(764\) | −2.30956e13 | −2.45250 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.31209e13 | −1.37700 | ||||||||
\(767\) | 2.12965e13 | 2.22192 | ||||||||
\(768\) | −7.93844e9 | −0.000823397 0 | ||||||||
\(769\) | 1.58699e13 | 1.63646 | 0.818230 | − | 0.574891i | \(-0.194956\pi\) | ||||
0.818230 | + | 0.574891i | \(0.194956\pi\) | |||||||
\(770\) | 4.88931e12 | 0.501233 | ||||||||
\(771\) | 1.14939e10 | 0.00117145 | ||||||||
\(772\) | 2.19108e13 | 2.22014 | ||||||||
\(773\) | −1.21257e12 | −0.122151 | −0.0610755 | − | 0.998133i | \(-0.519453\pi\) | ||||
−0.0610755 | + | 0.998133i | \(0.519453\pi\) | |||||||
\(774\) | −1.56957e13 | −1.57197 | ||||||||
\(775\) | 1.31739e13 | 1.31177 | ||||||||
\(776\) | 1.31044e13 | 1.29730 | ||||||||
\(777\) | 1.29422e10 | 0.00127384 | ||||||||
\(778\) | 1.15757e13 | 1.13276 | ||||||||
\(779\) | 5.16919e12 | 0.502926 | ||||||||
\(780\) | 6.15923e10 | 0.00595800 | ||||||||
\(781\) | 2.15718e11 | 0.0207471 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.91577e10 | −0.00182144 | ||||||||
\(784\) | 2.33817e12 | 0.221031 | ||||||||
\(785\) | 2.48213e12 | 0.233298 | ||||||||
\(786\) | 5.38428e9 | 0.000503183 0 | ||||||||
\(787\) | 1.14356e13 | 1.06261 | 0.531304 | − | 0.847181i | \(-0.321702\pi\) | ||||
0.531304 | + | 0.847181i | \(0.321702\pi\) | |||||||
\(788\) | −1.87788e12 | −0.173500 | ||||||||
\(789\) | −6.08953e9 | −0.000559419 0 | ||||||||
\(790\) | −8.44283e12 | −0.771199 | ||||||||
\(791\) | 5.56764e12 | 0.505682 | ||||||||
\(792\) | 3.78503e12 | 0.341827 | ||||||||
\(793\) | 1.28696e13 | 1.15567 | ||||||||
\(794\) | 3.87124e12 | 0.345667 | ||||||||
\(795\) | 2.37237e10 | 0.00210635 | ||||||||
\(796\) | −1.79286e13 | −1.58285 | ||||||||
\(797\) | 1.15535e13 | 1.01427 | 0.507133 | − | 0.861868i | \(-0.330705\pi\) | ||||
0.507133 | + | 0.861868i | \(0.330705\pi\) | |||||||
\(798\) | 1.52742e10 | 0.00133335 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −1.49000e13 | −1.28612 | ||||||||
\(801\) | 1.25973e13 | 1.08126 | ||||||||
\(802\) | −5.98550e12 | −0.510876 | ||||||||
\(803\) | 9.61781e12 | 0.816313 | ||||||||
\(804\) | −1.02133e10 | −0.000862011 0 | ||||||||
\(805\) | −7.12762e12 | −0.598223 | ||||||||
\(806\) | −3.85872e13 | −3.22059 | ||||||||
\(807\) | 1.65804e10 | 0.00137615 | ||||||||
\(808\) | 9.64627e10 | 0.00796175 | ||||||||
\(809\) | 1.64570e13 | 1.35077 | 0.675387 | − | 0.737464i | \(-0.263977\pi\) | ||||
0.675387 | + | 0.737464i | \(0.263977\pi\) | |||||||
\(810\) | −2.76912e13 | −2.26026 | ||||||||
\(811\) | 4.72555e12 | 0.383582 | 0.191791 | − | 0.981436i | \(-0.438570\pi\) | ||||
0.191791 | + | 0.981436i | \(0.438570\pi\) | |||||||
\(812\) | 4.81751e12 | 0.388884 | ||||||||
\(813\) | −1.26130e10 | −0.00101254 | ||||||||
\(814\) | −1.36924e13 | −1.09313 | ||||||||
\(815\) | −3.05813e13 | −2.42799 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.29567e13 | 1.01741 | ||||||||
\(818\) | 1.09548e13 | 0.855490 | ||||||||
\(819\) | 1.04267e13 | 0.809786 | ||||||||
\(820\) | −1.35681e13 | −1.04799 | ||||||||
\(821\) | −1.56503e13 | −1.20221 | −0.601103 | − | 0.799172i | \(-0.705272\pi\) | ||||
−0.601103 | + | 0.799172i | \(0.705272\pi\) | |||||||
\(822\) | 1.42081e10 | 0.00108546 | ||||||||
\(823\) | 7.85441e12 | 0.596780 | 0.298390 | − | 0.954444i | \(-0.403550\pi\) | ||||
0.298390 | + | 0.954444i | \(0.403550\pi\) | |||||||
\(824\) | 1.85957e13 | 1.40521 | ||||||||
\(825\) | −1.08416e10 | −0.000814798 0 | ||||||||
\(826\) | −1.38623e13 | −1.03616 | ||||||||
\(827\) | −2.59264e13 | −1.92738 | −0.963689 | − | 0.267026i | \(-0.913959\pi\) | ||||
−0.963689 | + | 0.267026i | \(0.913959\pi\) | |||||||
\(828\) | −1.70275e13 | −1.25897 | ||||||||
\(829\) | 8.15862e12 | 0.599959 | 0.299979 | − | 0.953946i | \(-0.403020\pi\) | ||||
0.299979 | + | 0.953946i | \(0.403020\pi\) | |||||||
\(830\) | −5.31053e13 | −3.88407 | ||||||||
\(831\) | −3.54784e10 | −0.00258083 | ||||||||
\(832\) | 3.69975e13 | 2.67681 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.66242e9 | −0.000190559 0 | ||||||||
\(835\) | −1.60140e13 | −1.14002 | ||||||||
\(836\) | −9.64205e12 | −0.682717 | ||||||||
\(837\) | −5.95978e10 | −0.00419726 | ||||||||
\(838\) | −1.50820e13 | −1.05648 | ||||||||
\(839\) | −1.19352e13 | −0.831576 | −0.415788 | − | 0.909462i | \(-0.636494\pi\) | ||||
−0.415788 | + | 0.909462i | \(0.636494\pi\) | |||||||
\(840\) | −1.29918e10 | −0.000900353 0 | ||||||||
\(841\) | −1.03274e13 | −0.711881 | ||||||||
\(842\) | −5.34130e12 | −0.366221 | ||||||||
\(843\) | −5.14725e9 | −0.000351036 0 | ||||||||
\(844\) | −3.83836e13 | −2.60378 | ||||||||
\(845\) | −3.68955e13 | −2.48954 | ||||||||
\(846\) | −3.71041e13 | −2.49032 | ||||||||
\(847\) | −5.83125e12 | −0.389302 | ||||||||
\(848\) | 3.78672e12 | 0.251468 | ||||||||
\(849\) | 3.60454e10 | 0.00238103 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.99608e13 | 1.30465 | ||||||||
\(852\) | −1.76886e9 | −0.000115004 0 | ||||||||
\(853\) | 1.88383e13 | 1.21835 | 0.609174 | − | 0.793037i | \(-0.291501\pi\) | ||||
0.609174 | + | 0.793037i | \(0.291501\pi\) | |||||||
\(854\) | −8.37706e12 | −0.538929 | ||||||||
\(855\) | 2.28591e13 | 1.46289 | ||||||||
\(856\) | 1.09289e13 | 0.695735 | ||||||||
\(857\) | −1.23172e13 | −0.780009 | −0.390005 | − | 0.920813i | \(-0.627527\pi\) | ||||
−0.390005 | + | 0.920813i | \(0.627527\pi\) | |||||||
\(858\) | 3.17556e10 | 0.00200045 | ||||||||
\(859\) | 1.58752e13 | 0.994832 | 0.497416 | − | 0.867512i | \(-0.334282\pi\) | ||||
0.497416 | + | 0.867512i | \(0.334282\pi\) | |||||||
\(860\) | −3.40089e13 | −2.12006 | ||||||||
\(861\) | 6.61213e9 | 0.000410041 0 | ||||||||
\(862\) | 4.05546e13 | 2.50183 | ||||||||
\(863\) | 2.03855e13 | 1.25104 | 0.625521 | − | 0.780207i | \(-0.284886\pi\) | ||||
0.625521 | + | 0.780207i | \(0.284886\pi\) | |||||||
\(864\) | 6.74064e10 | 0.00411518 | ||||||||
\(865\) | −1.34480e13 | −0.816743 | ||||||||
\(866\) | 3.20889e13 | 1.93876 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.49868e13 | 0.896129 | ||||||||
\(869\) | −2.59730e12 | −0.154502 | ||||||||
\(870\) | −3.47844e10 | −0.00205849 | ||||||||
\(871\) | 9.64566e12 | 0.567872 | ||||||||
\(872\) | −2.08991e13 | −1.22406 | ||||||||
\(873\) | −2.94934e13 | −1.71854 | ||||||||
\(874\) | 2.35574e13 | 1.36561 | ||||||||
\(875\) | −7.37736e11 | −0.0425466 | ||||||||
\(876\) | −7.88646e10 | −0.00452495 | ||||||||
\(877\) | 2.26963e13 | 1.29556 | 0.647778 | − | 0.761829i | \(-0.275698\pi\) | ||||
0.647778 | + | 0.761829i | \(0.275698\pi\) | |||||||
\(878\) | −7.67696e12 | −0.435977 | ||||||||
\(879\) | 1.05243e10 | 0.000594625 0 | ||||||||
\(880\) | −3.36225e12 | −0.188999 | ||||||||
\(881\) | 5.12762e12 | 0.286764 | 0.143382 | − | 0.989667i | \(-0.454202\pi\) | ||||
0.143382 | + | 0.989667i | \(0.454202\pi\) | |||||||
\(882\) | 2.15127e13 | 1.19698 | ||||||||
\(883\) | −2.76572e13 | −1.53104 | −0.765518 | − | 0.643415i | \(-0.777517\pi\) | ||||
−0.765518 | + | 0.643415i | \(0.777517\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.97224e10 | 0.00327260 | ||||||||
\(886\) | 1.23882e13 | 0.675391 | ||||||||
\(887\) | −2.27687e13 | −1.23504 | −0.617521 | − | 0.786554i | \(-0.711863\pi\) | ||||
−0.617521 | + | 0.786554i | \(0.711863\pi\) | |||||||
\(888\) | 3.63834e10 | 0.00196356 | ||||||||
\(889\) | −4.06064e12 | −0.218040 | ||||||||
\(890\) | 4.57455e13 | 2.44396 | ||||||||
\(891\) | −8.51875e12 | −0.452820 | ||||||||
\(892\) | 1.41145e13 | 0.746491 | ||||||||
\(893\) | 3.06294e13 | 1.61178 | ||||||||
\(894\) | 1.59929e9 | 8.37353e−5 0 | ||||||||
\(895\) | 1.30482e13 | 0.679748 | ||||||||
\(896\) | −1.26248e13 | −0.654394 | ||||||||
\(897\) | −4.62933e10 | −0.00238755 | ||||||||
\(898\) | 3.86805e13 | 1.98494 | ||||||||
\(899\) | 1.30029e13 | 0.663930 | ||||||||
\(900\) | −3.08815e13 | −1.56894 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −6.99542e12 | −0.351872 | ||||||||
\(903\) | 1.65735e10 | 0.000829505 0 | ||||||||
\(904\) | 1.56519e13 | 0.779485 | ||||||||
\(905\) | 3.24150e12 | 0.160630 | ||||||||
\(906\) | 2.43573e10 | 0.00120103 | ||||||||
\(907\) | 1.29915e13 | 0.637423 | 0.318711 | − | 0.947852i | \(-0.396750\pi\) | ||||
0.318711 | + | 0.947852i | \(0.396750\pi\) | |||||||
\(908\) | −5.11972e13 | −2.49954 | ||||||||
\(909\) | −2.17104e11 | −0.0105470 | ||||||||
\(910\) | 3.78635e13 | 1.83035 | ||||||||
\(911\) | 2.54247e13 | 1.22299 | 0.611496 | − | 0.791248i | \(-0.290568\pi\) | ||||
0.611496 | + | 0.791248i | \(0.290568\pi\) | |||||||
\(912\) | −1.05036e10 | −0.000502763 0 | ||||||||
\(913\) | −1.63370e13 | −0.778133 | ||||||||
\(914\) | −3.17496e13 | −1.50480 | ||||||||
\(915\) | 3.60906e10 | 0.00170216 | ||||||||
\(916\) | −3.52639e12 | −0.165501 | ||||||||
\(917\) | 1.97497e12 | 0.0922357 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.91533e13 | −1.34824 | −0.674121 | − | 0.738621i | \(-0.735477\pi\) | ||||
−0.674121 | + | 0.738621i | \(0.735477\pi\) | |||||||
\(920\) | −2.00373e13 | −0.922134 | ||||||||
\(921\) | 5.46494e10 | 0.00250275 | ||||||||
\(922\) | 2.56949e13 | 1.17100 | ||||||||
\(923\) | 1.67055e12 | 0.0757621 | ||||||||
\(924\) | −1.23335e10 | −0.000556626 0 | ||||||||
\(925\) | 3.62014e13 | 1.62588 | ||||||||
\(926\) | 8.81261e12 | 0.393872 | ||||||||
\(927\) | −4.18523e13 | −1.86149 | ||||||||
\(928\) | −1.47066e13 | −0.650948 | ||||||||
\(929\) | 3.16234e13 | 1.39296 | 0.696480 | − | 0.717576i | \(-0.254749\pi\) | ||||
0.696480 | + | 0.717576i | \(0.254749\pi\) | |||||||
\(930\) | −1.08211e11 | −0.00474350 | ||||||||
\(931\) | −1.77587e13 | −0.774707 | ||||||||
\(932\) | 2.33136e13 | 1.01213 | ||||||||
\(933\) | −1.12785e10 | −0.000487286 0 | ||||||||
\(934\) | 1.33093e12 | 0.0572263 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.93118e13 | 1.24825 | ||||||||
\(937\) | −3.18028e13 | −1.34784 | −0.673918 | − | 0.738806i | \(-0.735390\pi\) | ||||
−0.673918 | + | 0.738806i | \(0.735390\pi\) | |||||||
\(938\) | −6.27855e12 | −0.264817 | ||||||||
\(939\) | 6.24730e10 | 0.00262239 | ||||||||
\(940\) | −8.03961e13 | −3.35861 | ||||||||
\(941\) | 2.16662e13 | 0.900803 | 0.450401 | − | 0.892826i | \(-0.351281\pi\) | ||||
0.450401 | + | 0.892826i | \(0.351281\pi\) | |||||||
\(942\) | −1.04936e10 | −0.000434207 0 | ||||||||
\(943\) | 1.01979e13 | 0.419960 | ||||||||
\(944\) | 9.53275e12 | 0.390701 | ||||||||
\(945\) | 5.84801e10 | 0.00238542 | ||||||||
\(946\) | −1.75342e13 | −0.711830 | ||||||||
\(947\) | −1.15699e13 | −0.467470 | −0.233735 | − | 0.972300i | \(-0.575095\pi\) | ||||
−0.233735 | + | 0.972300i | \(0.575095\pi\) | |||||||
\(948\) | 2.12975e10 | 0.000856428 0 | ||||||||
\(949\) | 7.44817e13 | 2.98093 | ||||||||
\(950\) | 4.27242e13 | 1.70184 | ||||||||
\(951\) | 2.16066e10 | 0.000856593 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.14361e13 | −0.449118 | −0.224559 | − | 0.974461i | \(-0.572094\pi\) | ||||
−0.224559 | + | 0.974461i | \(0.572094\pi\) | |||||||
\(954\) | 3.48404e13 | 1.36180 | ||||||||
\(955\) | 6.11681e13 | 2.37963 | ||||||||
\(956\) | 5.72422e13 | 2.21644 | ||||||||
\(957\) | −1.07009e10 | −0.000412397 0 | ||||||||
\(958\) | −5.56479e12 | −0.213454 | ||||||||
\(959\) | 5.21159e12 | 0.198969 | ||||||||
\(960\) | 1.03753e11 | 0.00394259 | ||||||||
\(961\) | 1.40113e13 | 0.529936 | ||||||||
\(962\) | −1.06036e14 | −3.99177 | ||||||||
\(963\) | −2.45971e13 | −0.921648 | ||||||||
\(964\) | 2.03230e13 | 0.757951 | ||||||||
\(965\) | −5.80303e13 | −2.15418 | ||||||||
\(966\) | 3.01332e10 | 0.00111339 | ||||||||
\(967\) | −1.44349e13 | −0.530879 | −0.265439 | − | 0.964128i | \(-0.585517\pi\) | ||||
−0.265439 | + | 0.964128i | \(0.585517\pi\) | |||||||
\(968\) | −1.63929e13 | −0.600091 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.07102e14 | −3.88440 | ||||||||
\(971\) | −3.20825e13 | −1.15819 | −0.579097 | − | 0.815259i | \(-0.696595\pi\) | ||||
−0.579097 | + | 0.815259i | \(0.696595\pi\) | |||||||
\(972\) | 2.09558e11 | 0.00753020 | ||||||||
\(973\) | −9.76586e11 | −0.0349303 | ||||||||
\(974\) | 2.51145e13 | 0.894148 | ||||||||
\(975\) | −8.39587e10 | −0.00297540 | ||||||||
\(976\) | 5.76069e12 | 0.203213 | ||||||||
\(977\) | 1.42575e12 | 0.0500630 | 0.0250315 | − | 0.999687i | \(-0.492031\pi\) | ||||
0.0250315 | + | 0.999687i | \(0.492031\pi\) | |||||||
\(978\) | 1.29287e11 | 0.00451888 | ||||||||
\(979\) | 1.40729e13 | 0.489622 | ||||||||
\(980\) | 4.66130e13 | 1.61432 | ||||||||
\(981\) | 4.70365e13 | 1.62153 | ||||||||
\(982\) | 9.62436e12 | 0.330271 | ||||||||
\(983\) | 1.41784e13 | 0.484323 | 0.242161 | − | 0.970236i | \(-0.422144\pi\) | ||||
0.242161 | + | 0.970236i | \(0.422144\pi\) | |||||||
\(984\) | 1.85881e10 | 0.000632059 0 | ||||||||
\(985\) | 4.97352e12 | 0.168345 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.91793e10 | 0.00131410 | ||||||||
\(988\) | −7.46693e13 | −2.49308 | ||||||||
\(989\) | 2.55613e13 | 0.849572 | ||||||||
\(990\) | −3.09350e13 | −1.02351 | ||||||||
\(991\) | 2.24466e13 | 0.739296 | 0.369648 | − | 0.929172i | \(-0.379478\pi\) | ||||
0.369648 | + | 0.929172i | \(0.379478\pi\) | |||||||
\(992\) | −4.57509e13 | −1.50002 | ||||||||
\(993\) | 3.64292e10 | 0.00118899 | ||||||||
\(994\) | −1.08739e12 | −0.0353304 | ||||||||
\(995\) | 4.74836e13 | 1.53582 | ||||||||
\(996\) | 1.33961e11 | 0.00431331 | ||||||||
\(997\) | 1.92497e13 | 0.617015 | 0.308508 | − | 0.951222i | \(-0.400170\pi\) | ||||
0.308508 | + | 0.951222i | \(0.400170\pi\) | |||||||
\(998\) | 6.01737e13 | 1.92008 | ||||||||
\(999\) | −1.63773e11 | −0.00520231 |
(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 | 289.10.a.h.1.31 | yes | 36 | |
17.16 | even | 2 | 289.10.a.g.1.31 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.g.1.31 | ✓ | 36 | 17.16 | even | 2 | ||
289.10.a.h.1.31 | yes | 36 | 1.1 | even | 1 | trivial |