Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,14,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, 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("197.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.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: | \(211.244930035\) |
Analytic rank: | \(1\) |
Dimension: | \(104\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −162.329 | −1.79350 | −0.896750 | − | 0.442538i | \(-0.854078\pi\) | ||||
−0.896750 | + | 0.442538i | \(0.854078\pi\) | |||||||
\(3\) | −746.765 | −0.591420 | −0.295710 | − | 0.955278i | \(-0.595556\pi\) | ||||
−0.295710 | + | 0.955278i | \(0.595556\pi\) | |||||||
\(4\) | 18158.7 | 2.21664 | ||||||||
\(5\) | 42494.0 | 1.21625 | 0.608125 | − | 0.793841i | \(-0.291922\pi\) | ||||
0.608125 | + | 0.793841i | \(0.291922\pi\) | |||||||
\(6\) | 121222. | 1.06071 | ||||||||
\(7\) | 350398. | 1.12570 | 0.562852 | − | 0.826558i | \(-0.309704\pi\) | ||||
0.562852 | + | 0.826558i | \(0.309704\pi\) | |||||||
\(8\) | −1.61789e6 | −2.18204 | ||||||||
\(9\) | −1.03666e6 | −0.650222 | ||||||||
\(10\) | −6.89802e6 | −2.18134 | ||||||||
\(11\) | −5.98873e6 | −1.01925 | −0.509627 | − | 0.860395i | \(-0.670217\pi\) | ||||
−0.509627 | + | 0.860395i | \(0.670217\pi\) | |||||||
\(12\) | −1.35603e7 | −1.31097 | ||||||||
\(13\) | −9.45844e6 | −0.543485 | −0.271743 | − | 0.962370i | \(-0.587600\pi\) | ||||
−0.271743 | + | 0.962370i | \(0.587600\pi\) | |||||||
\(14\) | −5.68797e7 | −2.01895 | ||||||||
\(15\) | −3.17331e7 | −0.719315 | ||||||||
\(16\) | 1.13874e8 | 1.69686 | ||||||||
\(17\) | −1.86331e7 | −0.187226 | −0.0936131 | − | 0.995609i | \(-0.529842\pi\) | ||||
−0.0936131 | + | 0.995609i | \(0.529842\pi\) | |||||||
\(18\) | 1.68281e8 | 1.16617 | ||||||||
\(19\) | 9.76912e7 | 0.476384 | 0.238192 | − | 0.971218i | \(-0.423445\pi\) | ||||
0.238192 | + | 0.971218i | \(0.423445\pi\) | |||||||
\(20\) | 7.71638e8 | 2.69599 | ||||||||
\(21\) | −2.61665e8 | −0.665763 | ||||||||
\(22\) | 9.72145e8 | 1.82803 | ||||||||
\(23\) | 1.11174e9 | 1.56594 | 0.782968 | − | 0.622062i | \(-0.213705\pi\) | ||||
0.782968 | + | 0.622062i | \(0.213705\pi\) | |||||||
\(24\) | 1.20818e9 | 1.29050 | ||||||||
\(25\) | 5.85041e8 | 0.479266 | ||||||||
\(26\) | 1.53538e9 | 0.974741 | ||||||||
\(27\) | 1.96473e9 | 0.975974 | ||||||||
\(28\) | 6.36277e9 | 2.49528 | ||||||||
\(29\) | −4.96957e9 | −1.55143 | −0.775714 | − | 0.631084i | \(-0.782610\pi\) | ||||
−0.775714 | + | 0.631084i | \(0.782610\pi\) | |||||||
\(30\) | 5.15120e9 | 1.29009 | ||||||||
\(31\) | −2.62498e9 | −0.531221 | −0.265611 | − | 0.964080i | \(-0.585574\pi\) | ||||
−0.265611 | + | 0.964080i | \(0.585574\pi\) | |||||||
\(32\) | −5.23132e9 | −0.861265 | ||||||||
\(33\) | 4.47218e9 | 0.602807 | ||||||||
\(34\) | 3.02469e9 | 0.335790 | ||||||||
\(35\) | 1.48898e10 | 1.36914 | ||||||||
\(36\) | −1.88245e10 | −1.44131 | ||||||||
\(37\) | −2.75230e9 | −0.176354 | −0.0881768 | − | 0.996105i | \(-0.528104\pi\) | ||||
−0.0881768 | + | 0.996105i | \(0.528104\pi\) | |||||||
\(38\) | −1.58581e10 | −0.854394 | ||||||||
\(39\) | 7.06324e9 | 0.321428 | ||||||||
\(40\) | −6.87506e10 | −2.65391 | ||||||||
\(41\) | −1.94142e10 | −0.638298 | −0.319149 | − | 0.947704i | \(-0.603397\pi\) | ||||
−0.319149 | + | 0.947704i | \(0.603397\pi\) | |||||||
\(42\) | 4.24758e10 | 1.19405 | ||||||||
\(43\) | 4.24240e10 | 1.02345 | 0.511725 | − | 0.859149i | \(-0.329007\pi\) | ||||
0.511725 | + | 0.859149i | \(0.329007\pi\) | |||||||
\(44\) | −1.08748e11 | −2.25932 | ||||||||
\(45\) | −4.40521e10 | −0.790833 | ||||||||
\(46\) | −1.80468e11 | −2.80850 | ||||||||
\(47\) | 1.20787e11 | 1.63449 | 0.817246 | − | 0.576290i | \(-0.195500\pi\) | ||||
0.817246 | + | 0.576290i | \(0.195500\pi\) | |||||||
\(48\) | −8.50372e10 | −1.00355 | ||||||||
\(49\) | 2.58895e10 | 0.267208 | ||||||||
\(50\) | −9.49692e10 | −0.859563 | ||||||||
\(51\) | 1.39145e10 | 0.110729 | ||||||||
\(52\) | −1.71753e11 | −1.20471 | ||||||||
\(53\) | 4.20067e10 | 0.260330 | 0.130165 | − | 0.991492i | \(-0.458449\pi\) | ||||
0.130165 | + | 0.991492i | \(0.458449\pi\) | |||||||
\(54\) | −3.18933e11 | −1.75041 | ||||||||
\(55\) | −2.54486e11 | −1.23967 | ||||||||
\(56\) | −5.66904e11 | −2.45633 | ||||||||
\(57\) | −7.29524e10 | −0.281743 | ||||||||
\(58\) | 8.06705e11 | 2.78249 | ||||||||
\(59\) | 6.60516e10 | 0.203866 | 0.101933 | − | 0.994791i | \(-0.467497\pi\) | ||||
0.101933 | + | 0.994791i | \(0.467497\pi\) | |||||||
\(60\) | −5.76232e11 | −1.59446 | ||||||||
\(61\) | −2.71752e11 | −0.675349 | −0.337675 | − | 0.941263i | \(-0.609640\pi\) | ||||
−0.337675 | + | 0.941263i | \(0.609640\pi\) | |||||||
\(62\) | 4.26111e11 | 0.952745 | ||||||||
\(63\) | −3.63245e11 | −0.731957 | ||||||||
\(64\) | −8.36605e10 | −0.152177 | ||||||||
\(65\) | −4.01928e11 | −0.661014 | ||||||||
\(66\) | −7.25964e11 | −1.08113 | ||||||||
\(67\) | 5.91218e10 | 0.0798475 | 0.0399238 | − | 0.999203i | \(-0.487288\pi\) | ||||
0.0399238 | + | 0.999203i | \(0.487288\pi\) | |||||||
\(68\) | −3.38353e11 | −0.415013 | ||||||||
\(69\) | −8.30212e11 | −0.926125 | ||||||||
\(70\) | −2.41705e12 | −2.45555 | ||||||||
\(71\) | 1.68901e10 | 0.0156478 | 0.00782390 | − | 0.999969i | \(-0.497510\pi\) | ||||
0.00782390 | + | 0.999969i | \(0.497510\pi\) | |||||||
\(72\) | 1.67721e12 | 1.41881 | ||||||||
\(73\) | 4.60459e11 | 0.356116 | 0.178058 | − | 0.984020i | \(-0.443018\pi\) | ||||
0.178058 | + | 0.984020i | \(0.443018\pi\) | |||||||
\(74\) | 4.46778e11 | 0.316290 | ||||||||
\(75\) | −4.36888e11 | −0.283447 | ||||||||
\(76\) | 1.77395e12 | 1.05597 | ||||||||
\(77\) | −2.09844e12 | −1.14738 | ||||||||
\(78\) | −1.14657e12 | −0.576481 | ||||||||
\(79\) | 3.32303e11 | 0.153801 | 0.0769003 | − | 0.997039i | \(-0.475498\pi\) | ||||
0.0769003 | + | 0.997039i | \(0.475498\pi\) | |||||||
\(80\) | 4.83897e12 | 2.06380 | ||||||||
\(81\) | 1.85586e11 | 0.0730117 | ||||||||
\(82\) | 3.15148e12 | 1.14479 | ||||||||
\(83\) | 3.09461e12 | 1.03896 | 0.519480 | − | 0.854483i | \(-0.326126\pi\) | ||||
0.519480 | + | 0.854483i | \(0.326126\pi\) | |||||||
\(84\) | −4.75150e12 | −1.47576 | ||||||||
\(85\) | −7.91795e11 | −0.227714 | ||||||||
\(86\) | −6.88665e12 | −1.83556 | ||||||||
\(87\) | 3.71110e12 | 0.917546 | ||||||||
\(88\) | 9.68910e12 | 2.22406 | ||||||||
\(89\) | −1.81559e12 | −0.387242 | −0.193621 | − | 0.981076i | \(-0.562023\pi\) | ||||
−0.193621 | + | 0.981076i | \(0.562023\pi\) | |||||||
\(90\) | 7.15093e12 | 1.41836 | ||||||||
\(91\) | −3.31422e12 | −0.611803 | ||||||||
\(92\) | 2.01878e13 | 3.47112 | ||||||||
\(93\) | 1.96025e12 | 0.314175 | ||||||||
\(94\) | −1.96072e13 | −2.93146 | ||||||||
\(95\) | 4.15129e12 | 0.579402 | ||||||||
\(96\) | 3.90657e12 | 0.509369 | ||||||||
\(97\) | −9.21227e12 | −1.12292 | −0.561462 | − | 0.827502i | \(-0.689761\pi\) | ||||
−0.561462 | + | 0.827502i | \(0.689761\pi\) | |||||||
\(98\) | −4.20262e12 | −0.479237 | ||||||||
\(99\) | 6.20831e12 | 0.662742 | ||||||||
\(100\) | 1.06236e13 | 1.06236 | ||||||||
\(101\) | 9.07216e12 | 0.850398 | 0.425199 | − | 0.905100i | \(-0.360204\pi\) | ||||
0.425199 | + | 0.905100i | \(0.360204\pi\) | |||||||
\(102\) | −2.25873e12 | −0.198593 | ||||||||
\(103\) | −3.75852e12 | −0.310152 | −0.155076 | − | 0.987903i | \(-0.549562\pi\) | ||||
−0.155076 | + | 0.987903i | \(0.549562\pi\) | |||||||
\(104\) | 1.53027e13 | 1.18591 | ||||||||
\(105\) | −1.11192e13 | −0.809735 | ||||||||
\(106\) | −6.81890e12 | −0.466903 | ||||||||
\(107\) | −2.15266e13 | −1.38669 | −0.693346 | − | 0.720605i | \(-0.743864\pi\) | ||||
−0.693346 | + | 0.720605i | \(0.743864\pi\) | |||||||
\(108\) | 3.56770e13 | 2.16338 | ||||||||
\(109\) | −2.52865e13 | −1.44416 | −0.722082 | − | 0.691808i | \(-0.756815\pi\) | ||||
−0.722082 | + | 0.691808i | \(0.756815\pi\) | |||||||
\(110\) | 4.13104e13 | 2.22335 | ||||||||
\(111\) | 2.05532e12 | 0.104299 | ||||||||
\(112\) | 3.99012e13 | 1.91016 | ||||||||
\(113\) | 4.73239e12 | 0.213831 | 0.106915 | − | 0.994268i | \(-0.465903\pi\) | ||||
0.106915 | + | 0.994268i | \(0.465903\pi\) | |||||||
\(114\) | 1.18423e13 | 0.505306 | ||||||||
\(115\) | 4.72425e13 | 1.90457 | ||||||||
\(116\) | −9.02410e13 | −3.43896 | ||||||||
\(117\) | 9.80523e12 | 0.353386 | ||||||||
\(118\) | −1.07221e13 | −0.365634 | ||||||||
\(119\) | −6.52899e12 | −0.210761 | ||||||||
\(120\) | 5.13406e13 | 1.56958 | ||||||||
\(121\) | 1.34221e12 | 0.0388791 | ||||||||
\(122\) | 4.41132e13 | 1.21124 | ||||||||
\(123\) | 1.44978e13 | 0.377502 | ||||||||
\(124\) | −4.76663e13 | −1.17753 | ||||||||
\(125\) | −2.70119e13 | −0.633344 | ||||||||
\(126\) | 5.89652e13 | 1.31277 | ||||||||
\(127\) | −3.35833e13 | −0.710229 | −0.355115 | − | 0.934823i | \(-0.615558\pi\) | ||||
−0.355115 | + | 0.934823i | \(0.615558\pi\) | |||||||
\(128\) | 5.64355e13 | 1.13419 | ||||||||
\(129\) | −3.16808e13 | −0.605289 | ||||||||
\(130\) | 6.52445e13 | 1.18553 | ||||||||
\(131\) | 8.92494e13 | 1.54291 | 0.771457 | − | 0.636281i | \(-0.219528\pi\) | ||||
0.771457 | + | 0.636281i | \(0.219528\pi\) | |||||||
\(132\) | 8.12090e13 | 1.33621 | ||||||||
\(133\) | 3.42308e13 | 0.536267 | ||||||||
\(134\) | −9.59718e12 | −0.143206 | ||||||||
\(135\) | 8.34893e13 | 1.18703 | ||||||||
\(136\) | 3.01463e13 | 0.408536 | ||||||||
\(137\) | 1.03021e13 | 0.133119 | 0.0665597 | − | 0.997782i | \(-0.478798\pi\) | ||||
0.0665597 | + | 0.997782i | \(0.478798\pi\) | |||||||
\(138\) | 1.34767e14 | 1.66101 | ||||||||
\(139\) | 4.06661e13 | 0.478229 | 0.239115 | − | 0.970991i | \(-0.423143\pi\) | ||||
0.239115 | + | 0.970991i | \(0.423143\pi\) | |||||||
\(140\) | 2.70380e14 | 3.03489 | ||||||||
\(141\) | −9.01992e13 | −0.966671 | ||||||||
\(142\) | −2.74176e12 | −0.0280643 | ||||||||
\(143\) | 5.66441e13 | 0.553950 | ||||||||
\(144\) | −1.18049e14 | −1.10333 | ||||||||
\(145\) | −2.11177e14 | −1.88693 | ||||||||
\(146\) | −7.47458e13 | −0.638695 | ||||||||
\(147\) | −1.93334e13 | −0.158032 | ||||||||
\(148\) | −4.99782e13 | −0.390913 | ||||||||
\(149\) | −1.13626e14 | −0.850683 | −0.425341 | − | 0.905033i | \(-0.639846\pi\) | ||||
−0.425341 | + | 0.905033i | \(0.639846\pi\) | |||||||
\(150\) | 7.09197e13 | 0.508362 | ||||||||
\(151\) | 1.75889e14 | 1.20750 | 0.603752 | − | 0.797172i | \(-0.293672\pi\) | ||||
0.603752 | + | 0.797172i | \(0.293672\pi\) | |||||||
\(152\) | −1.58053e14 | −1.03949 | ||||||||
\(153\) | 1.93163e13 | 0.121739 | ||||||||
\(154\) | 3.40637e14 | 2.05782 | ||||||||
\(155\) | −1.11546e14 | −0.646098 | ||||||||
\(156\) | 1.28259e14 | 0.712491 | ||||||||
\(157\) | 1.17561e14 | 0.626492 | 0.313246 | − | 0.949672i | \(-0.398584\pi\) | ||||
0.313246 | + | 0.949672i | \(0.398584\pi\) | |||||||
\(158\) | −5.39424e13 | −0.275841 | ||||||||
\(159\) | −3.13691e13 | −0.153965 | ||||||||
\(160\) | −2.22300e14 | −1.04751 | ||||||||
\(161\) | 3.89552e14 | 1.76278 | ||||||||
\(162\) | −3.01260e13 | −0.130946 | ||||||||
\(163\) | 4.03818e14 | 1.68642 | 0.843211 | − | 0.537583i | \(-0.180663\pi\) | ||||
0.843211 | + | 0.537583i | \(0.180663\pi\) | |||||||
\(164\) | −3.52536e14 | −1.41488 | ||||||||
\(165\) | 1.90041e14 | 0.733165 | ||||||||
\(166\) | −5.02346e14 | −1.86337 | ||||||||
\(167\) | 5.35696e12 | 0.0191100 | 0.00955501 | − | 0.999954i | \(-0.496959\pi\) | ||||
0.00955501 | + | 0.999954i | \(0.496959\pi\) | |||||||
\(168\) | 4.23344e14 | 1.45273 | ||||||||
\(169\) | −2.13413e14 | −0.704624 | ||||||||
\(170\) | 1.28531e14 | 0.408405 | ||||||||
\(171\) | −1.01273e14 | −0.309755 | ||||||||
\(172\) | 7.70366e14 | 2.26862 | ||||||||
\(173\) | −5.00040e13 | −0.141809 | −0.0709047 | − | 0.997483i | \(-0.522589\pi\) | ||||
−0.0709047 | + | 0.997483i | \(0.522589\pi\) | |||||||
\(174\) | −6.02420e14 | −1.64562 | ||||||||
\(175\) | 2.04997e14 | 0.539511 | ||||||||
\(176\) | −6.81961e14 | −1.72953 | ||||||||
\(177\) | −4.93250e13 | −0.120571 | ||||||||
\(178\) | 2.94723e14 | 0.694518 | ||||||||
\(179\) | −2.96394e14 | −0.673481 | −0.336740 | − | 0.941597i | \(-0.609325\pi\) | ||||
−0.336740 | + | 0.941597i | \(0.609325\pi\) | |||||||
\(180\) | −7.99929e14 | −1.75299 | ||||||||
\(181\) | −4.54526e14 | −0.960833 | −0.480417 | − | 0.877040i | \(-0.659515\pi\) | ||||
−0.480417 | + | 0.877040i | \(0.659515\pi\) | |||||||
\(182\) | 5.37993e14 | 1.09727 | ||||||||
\(183\) | 2.02935e14 | 0.399415 | ||||||||
\(184\) | −1.79868e15 | −3.41694 | ||||||||
\(185\) | −1.16956e14 | −0.214490 | ||||||||
\(186\) | −3.18205e14 | −0.563472 | ||||||||
\(187\) | 1.11589e14 | 0.190831 | ||||||||
\(188\) | 2.19333e15 | 3.62308 | ||||||||
\(189\) | 6.88437e14 | 1.09866 | ||||||||
\(190\) | −6.73876e14 | −1.03916 | ||||||||
\(191\) | −3.86368e14 | −0.575816 | −0.287908 | − | 0.957658i | \(-0.592960\pi\) | ||||
−0.287908 | + | 0.957658i | \(0.592960\pi\) | |||||||
\(192\) | 6.24747e13 | 0.0900008 | ||||||||
\(193\) | −1.06327e15 | −1.48088 | −0.740441 | − | 0.672121i | \(-0.765383\pi\) | ||||
−0.740441 | + | 0.672121i | \(0.765383\pi\) | |||||||
\(194\) | 1.49542e15 | 2.01396 | ||||||||
\(195\) | 3.00146e14 | 0.390937 | ||||||||
\(196\) | 4.70120e14 | 0.592303 | ||||||||
\(197\) | −5.84517e13 | −0.0712470 | ||||||||
\(198\) | −1.00779e15 | −1.18863 | ||||||||
\(199\) | −9.48385e14 | −1.08253 | −0.541265 | − | 0.840852i | \(-0.682054\pi\) | ||||
−0.541265 | + | 0.840852i | \(0.682054\pi\) | |||||||
\(200\) | −9.46531e14 | −1.04578 | ||||||||
\(201\) | −4.41501e13 | −0.0472234 | ||||||||
\(202\) | −1.47268e15 | −1.52519 | ||||||||
\(203\) | −1.74133e15 | −1.74645 | ||||||||
\(204\) | 2.52670e14 | 0.245447 | ||||||||
\(205\) | −8.24987e14 | −0.776331 | ||||||||
\(206\) | 6.10117e14 | 0.556258 | ||||||||
\(207\) | −1.15251e15 | −1.01821 | ||||||||
\(208\) | −1.07707e15 | −0.922216 | ||||||||
\(209\) | −5.85046e14 | −0.485556 | ||||||||
\(210\) | 1.80497e15 | 1.45226 | ||||||||
\(211\) | 3.33389e14 | 0.260085 | 0.130043 | − | 0.991508i | \(-0.458489\pi\) | ||||
0.130043 | + | 0.991508i | \(0.458489\pi\) | |||||||
\(212\) | 7.62787e14 | 0.577059 | ||||||||
\(213\) | −1.26130e13 | −0.00925443 | ||||||||
\(214\) | 3.49439e15 | 2.48703 | ||||||||
\(215\) | 1.80277e15 | 1.24477 | ||||||||
\(216\) | −3.17871e15 | −2.12962 | ||||||||
\(217\) | −9.19787e14 | −0.597997 | ||||||||
\(218\) | 4.10473e15 | 2.59011 | ||||||||
\(219\) | −3.43854e14 | −0.210614 | ||||||||
\(220\) | −4.62113e15 | −2.74790 | ||||||||
\(221\) | 1.76240e14 | 0.101755 | ||||||||
\(222\) | −3.33638e14 | −0.187060 | ||||||||
\(223\) | 2.27974e14 | 0.124138 | 0.0620690 | − | 0.998072i | \(-0.480230\pi\) | ||||
0.0620690 | + | 0.998072i | \(0.480230\pi\) | |||||||
\(224\) | −1.83304e15 | −0.969528 | ||||||||
\(225\) | −6.06491e14 | −0.311629 | ||||||||
\(226\) | −7.68204e14 | −0.383506 | ||||||||
\(227\) | 1.70547e15 | 0.827326 | 0.413663 | − | 0.910430i | \(-0.364249\pi\) | ||||
0.413663 | + | 0.910430i | \(0.364249\pi\) | |||||||
\(228\) | −1.32472e15 | −0.624523 | ||||||||
\(229\) | 1.27399e14 | 0.0583761 | 0.0291881 | − | 0.999574i | \(-0.490708\pi\) | ||||
0.0291881 | + | 0.999574i | \(0.490708\pi\) | |||||||
\(230\) | −7.66883e15 | −3.41585 | ||||||||
\(231\) | 1.56704e15 | 0.678582 | ||||||||
\(232\) | 8.04021e15 | 3.38529 | ||||||||
\(233\) | 4.26980e15 | 1.74821 | 0.874105 | − | 0.485737i | \(-0.161449\pi\) | ||||
0.874105 | + | 0.485737i | \(0.161449\pi\) | |||||||
\(234\) | −1.59167e15 | −0.633798 | ||||||||
\(235\) | 5.13271e15 | 1.98795 | ||||||||
\(236\) | 1.19941e15 | 0.451898 | ||||||||
\(237\) | −2.48152e14 | −0.0909607 | ||||||||
\(238\) | 1.05984e15 | 0.378000 | ||||||||
\(239\) | 4.20711e15 | 1.46015 | 0.730075 | − | 0.683367i | \(-0.239485\pi\) | ||||
0.730075 | + | 0.683367i | \(0.239485\pi\) | |||||||
\(240\) | −3.61357e15 | −1.22057 | ||||||||
\(241\) | 1.04381e15 | 0.343172 | 0.171586 | − | 0.985169i | \(-0.445111\pi\) | ||||
0.171586 | + | 0.985169i | \(0.445111\pi\) | |||||||
\(242\) | −2.17880e14 | −0.0697297 | ||||||||
\(243\) | −3.27100e15 | −1.01916 | ||||||||
\(244\) | −4.93466e15 | −1.49701 | ||||||||
\(245\) | 1.10015e15 | 0.324991 | ||||||||
\(246\) | −2.35342e15 | −0.677050 | ||||||||
\(247\) | −9.24006e14 | −0.258908 | ||||||||
\(248\) | 4.24693e15 | 1.15915 | ||||||||
\(249\) | −2.31095e15 | −0.614462 | ||||||||
\(250\) | 4.38481e15 | 1.13590 | ||||||||
\(251\) | −2.28174e15 | −0.575952 | −0.287976 | − | 0.957638i | \(-0.592982\pi\) | ||||
−0.287976 | + | 0.957638i | \(0.592982\pi\) | |||||||
\(252\) | −6.59606e15 | −1.62249 | ||||||||
\(253\) | −6.65794e15 | −1.59609 | ||||||||
\(254\) | 5.45154e15 | 1.27380 | ||||||||
\(255\) | 5.91285e14 | 0.134675 | ||||||||
\(256\) | −8.47578e15 | −1.88200 | ||||||||
\(257\) | 1.65545e15 | 0.358385 | 0.179192 | − | 0.983814i | \(-0.442652\pi\) | ||||
0.179192 | + | 0.983814i | \(0.442652\pi\) | |||||||
\(258\) | 5.14271e15 | 1.08559 | ||||||||
\(259\) | −9.64399e14 | −0.198522 | ||||||||
\(260\) | −7.29849e15 | −1.46523 | ||||||||
\(261\) | 5.15178e15 | 1.00877 | ||||||||
\(262\) | −1.44878e16 | −2.76722 | ||||||||
\(263\) | −7.60655e15 | −1.41734 | −0.708672 | − | 0.705538i | \(-0.750705\pi\) | ||||
−0.708672 | + | 0.705538i | \(0.750705\pi\) | |||||||
\(264\) | −7.23548e15 | −1.31535 | ||||||||
\(265\) | 1.78503e15 | 0.316627 | ||||||||
\(266\) | −5.55665e15 | −0.961794 | ||||||||
\(267\) | 1.35582e15 | 0.229022 | ||||||||
\(268\) | 1.07358e15 | 0.176993 | ||||||||
\(269\) | −1.69749e15 | −0.273160 | −0.136580 | − | 0.990629i | \(-0.543611\pi\) | ||||
−0.136580 | + | 0.990629i | \(0.543611\pi\) | |||||||
\(270\) | −1.35527e16 | −2.12894 | ||||||||
\(271\) | 6.37386e15 | 0.977467 | 0.488733 | − | 0.872433i | \(-0.337459\pi\) | ||||
0.488733 | + | 0.872433i | \(0.337459\pi\) | |||||||
\(272\) | −2.12182e15 | −0.317696 | ||||||||
\(273\) | 2.47494e15 | 0.361833 | ||||||||
\(274\) | −1.67233e15 | −0.238750 | ||||||||
\(275\) | −3.50365e15 | −0.488493 | ||||||||
\(276\) | −1.50756e16 | −2.05289 | ||||||||
\(277\) | −6.40106e15 | −0.851399 | −0.425700 | − | 0.904865i | \(-0.639972\pi\) | ||||
−0.425700 | + | 0.904865i | \(0.639972\pi\) | |||||||
\(278\) | −6.60129e15 | −0.857704 | ||||||||
\(279\) | 2.72123e15 | 0.345412 | ||||||||
\(280\) | −2.40901e16 | −2.98752 | ||||||||
\(281\) | −1.29626e16 | −1.57073 | −0.785366 | − | 0.619032i | \(-0.787525\pi\) | ||||
−0.785366 | + | 0.619032i | \(0.787525\pi\) | |||||||
\(282\) | 1.46420e16 | 1.73372 | ||||||||
\(283\) | 9.27970e15 | 1.07380 | 0.536898 | − | 0.843647i | \(-0.319596\pi\) | ||||
0.536898 | + | 0.843647i | \(0.319596\pi\) | |||||||
\(284\) | 3.06703e14 | 0.0346856 | ||||||||
\(285\) | −3.10004e15 | −0.342670 | ||||||||
\(286\) | −9.19498e15 | −0.993509 | ||||||||
\(287\) | −6.80268e15 | −0.718534 | ||||||||
\(288\) | 5.42313e15 | 0.560014 | ||||||||
\(289\) | −9.55739e15 | −0.964946 | ||||||||
\(290\) | 3.42802e16 | 3.38420 | ||||||||
\(291\) | 6.87941e15 | 0.664120 | ||||||||
\(292\) | 8.36134e15 | 0.789382 | ||||||||
\(293\) | −3.31521e15 | −0.306106 | −0.153053 | − | 0.988218i | \(-0.548910\pi\) | ||||
−0.153053 | + | 0.988218i | \(0.548910\pi\) | |||||||
\(294\) | 3.13837e15 | 0.283430 | ||||||||
\(295\) | 2.80680e15 | 0.247952 | ||||||||
\(296\) | 4.45291e15 | 0.384811 | ||||||||
\(297\) | −1.17662e16 | −0.994766 | ||||||||
\(298\) | 1.84448e16 | 1.52570 | ||||||||
\(299\) | −1.05154e16 | −0.851063 | ||||||||
\(300\) | −7.93333e15 | −0.628301 | ||||||||
\(301\) | 1.48653e16 | 1.15210 | ||||||||
\(302\) | −2.85519e16 | −2.16566 | ||||||||
\(303\) | −6.77478e15 | −0.502942 | ||||||||
\(304\) | 1.11245e16 | 0.808354 | ||||||||
\(305\) | −1.15478e16 | −0.821394 | ||||||||
\(306\) | −3.13559e15 | −0.218338 | ||||||||
\(307\) | −2.77278e16 | −1.89023 | −0.945117 | − | 0.326733i | \(-0.894052\pi\) | ||||
−0.945117 | + | 0.326733i | \(0.894052\pi\) | |||||||
\(308\) | −3.81049e16 | −2.54332 | ||||||||
\(309\) | 2.80673e15 | 0.183430 | ||||||||
\(310\) | 1.81072e16 | 1.15878 | ||||||||
\(311\) | 6.46299e14 | 0.0405033 | 0.0202517 | − | 0.999795i | \(-0.493553\pi\) | ||||
0.0202517 | + | 0.999795i | \(0.493553\pi\) | |||||||
\(312\) | −1.14275e16 | −0.701370 | ||||||||
\(313\) | 9.90931e15 | 0.595669 | 0.297835 | − | 0.954617i | \(-0.403736\pi\) | ||||
0.297835 | + | 0.954617i | \(0.403736\pi\) | |||||||
\(314\) | −1.90836e16 | −1.12361 | ||||||||
\(315\) | −1.54357e16 | −0.890244 | ||||||||
\(316\) | 6.03419e15 | 0.340920 | ||||||||
\(317\) | 1.24515e16 | 0.689188 | 0.344594 | − | 0.938752i | \(-0.388017\pi\) | ||||
0.344594 | + | 0.938752i | \(0.388017\pi\) | |||||||
\(318\) | 5.09212e15 | 0.276135 | ||||||||
\(319\) | 2.97614e16 | 1.58130 | ||||||||
\(320\) | −3.55507e15 | −0.185086 | ||||||||
\(321\) | 1.60753e16 | 0.820117 | ||||||||
\(322\) | −6.32357e16 | −3.16154 | ||||||||
\(323\) | −1.82029e15 | −0.0891916 | ||||||||
\(324\) | 3.37000e15 | 0.161841 | ||||||||
\(325\) | −5.53358e15 | −0.260474 | ||||||||
\(326\) | −6.55514e16 | −3.02460 | ||||||||
\(327\) | 1.88831e16 | 0.854107 | ||||||||
\(328\) | 3.14100e16 | 1.39280 | ||||||||
\(329\) | 4.23233e16 | 1.83995 | ||||||||
\(330\) | −3.08492e16 | −1.31493 | ||||||||
\(331\) | −4.07958e16 | −1.70504 | −0.852518 | − | 0.522698i | \(-0.824925\pi\) | ||||
−0.852518 | + | 0.522698i | \(0.824925\pi\) | |||||||
\(332\) | 5.61942e16 | 2.30300 | ||||||||
\(333\) | 2.85321e15 | 0.114669 | ||||||||
\(334\) | −8.69590e14 | −0.0342738 | ||||||||
\(335\) | 2.51232e15 | 0.0971146 | ||||||||
\(336\) | −2.97968e16 | −1.12970 | ||||||||
\(337\) | 3.12302e16 | 1.16139 | 0.580697 | − | 0.814120i | \(-0.302780\pi\) | ||||
0.580697 | + | 0.814120i | \(0.302780\pi\) | |||||||
\(338\) | 3.46431e16 | 1.26374 | ||||||||
\(339\) | −3.53398e15 | −0.126464 | ||||||||
\(340\) | −1.43780e16 | −0.504760 | ||||||||
\(341\) | 1.57203e16 | 0.541449 | ||||||||
\(342\) | 1.64396e16 | 0.555546 | ||||||||
\(343\) | −2.48781e16 | −0.824907 | ||||||||
\(344\) | −6.86373e16 | −2.23321 | ||||||||
\(345\) | −3.52791e16 | −1.12640 | ||||||||
\(346\) | 8.11710e15 | 0.254335 | ||||||||
\(347\) | 3.05257e16 | 0.938693 | 0.469347 | − | 0.883014i | \(-0.344489\pi\) | ||||
0.469347 | + | 0.883014i | \(0.344489\pi\) | |||||||
\(348\) | 6.73889e16 | 2.03387 | ||||||||
\(349\) | 1.52268e16 | 0.451068 | 0.225534 | − | 0.974235i | \(-0.427587\pi\) | ||||
0.225534 | + | 0.974235i | \(0.427587\pi\) | |||||||
\(350\) | −3.32770e16 | −0.967612 | ||||||||
\(351\) | −1.85833e16 | −0.530428 | ||||||||
\(352\) | 3.13290e16 | 0.877848 | ||||||||
\(353\) | −3.41502e16 | −0.939416 | −0.469708 | − | 0.882822i | \(-0.655641\pi\) | ||||
−0.469708 | + | 0.882822i | \(0.655641\pi\) | |||||||
\(354\) | 8.00688e15 | 0.216243 | ||||||||
\(355\) | 7.17730e14 | 0.0190317 | ||||||||
\(356\) | −3.29687e16 | −0.858376 | ||||||||
\(357\) | 4.87562e15 | 0.124648 | ||||||||
\(358\) | 4.81134e16 | 1.20789 | ||||||||
\(359\) | −3.06264e15 | −0.0755060 | −0.0377530 | − | 0.999287i | \(-0.512020\pi\) | ||||
−0.0377530 | + | 0.999287i | \(0.512020\pi\) | |||||||
\(360\) | 7.12713e16 | 1.72563 | ||||||||
\(361\) | −3.25094e16 | −0.773058 | ||||||||
\(362\) | 7.37828e16 | 1.72325 | ||||||||
\(363\) | −1.00232e15 | −0.0229939 | ||||||||
\(364\) | −6.01819e16 | −1.35615 | ||||||||
\(365\) | 1.95667e16 | 0.433127 | ||||||||
\(366\) | −3.29422e16 | −0.716350 | ||||||||
\(367\) | 3.05179e15 | 0.0651965 | 0.0325983 | − | 0.999469i | \(-0.489622\pi\) | ||||
0.0325983 | + | 0.999469i | \(0.489622\pi\) | |||||||
\(368\) | 1.26599e17 | 2.65717 | ||||||||
\(369\) | 2.01260e16 | 0.415036 | ||||||||
\(370\) | 1.89854e16 | 0.384688 | ||||||||
\(371\) | 1.47190e16 | 0.293055 | ||||||||
\(372\) | 3.55955e16 | 0.696413 | ||||||||
\(373\) | 5.72453e16 | 1.10061 | 0.550304 | − | 0.834965i | \(-0.314512\pi\) | ||||
0.550304 | + | 0.834965i | \(0.314512\pi\) | |||||||
\(374\) | −1.81141e16 | −0.342256 | ||||||||
\(375\) | 2.01715e16 | 0.374572 | ||||||||
\(376\) | −1.95419e17 | −3.56653 | ||||||||
\(377\) | 4.70044e16 | 0.843179 | ||||||||
\(378\) | −1.11753e17 | −1.97044 | ||||||||
\(379\) | −3.63276e16 | −0.629624 | −0.314812 | − | 0.949154i | \(-0.601941\pi\) | ||||
−0.314812 | + | 0.949154i | \(0.601941\pi\) | |||||||
\(380\) | 7.53822e16 | 1.28433 | ||||||||
\(381\) | 2.50788e16 | 0.420044 | ||||||||
\(382\) | 6.27187e16 | 1.03273 | ||||||||
\(383\) | −1.50985e16 | −0.244423 | −0.122212 | − | 0.992504i | \(-0.538999\pi\) | ||||
−0.122212 | + | 0.992504i | \(0.538999\pi\) | |||||||
\(384\) | −4.21441e16 | −0.670785 | ||||||||
\(385\) | −8.91711e16 | −1.39550 | ||||||||
\(386\) | 1.72599e17 | 2.65596 | ||||||||
\(387\) | −4.39795e16 | −0.665470 | ||||||||
\(388\) | −1.67283e17 | −2.48912 | ||||||||
\(389\) | 7.25477e16 | 1.06158 | 0.530788 | − | 0.847505i | \(-0.321896\pi\) | ||||
0.530788 | + | 0.847505i | \(0.321896\pi\) | |||||||
\(390\) | −4.87223e16 | −0.701145 | ||||||||
\(391\) | −2.07152e16 | −0.293184 | ||||||||
\(392\) | −4.18863e16 | −0.583059 | ||||||||
\(393\) | −6.66484e16 | −0.912510 | ||||||||
\(394\) | 9.48841e15 | 0.127782 | ||||||||
\(395\) | 1.41209e16 | 0.187060 | ||||||||
\(396\) | 1.12735e17 | 1.46906 | ||||||||
\(397\) | −3.48870e16 | −0.447224 | −0.223612 | − | 0.974678i | \(-0.571785\pi\) | ||||
−0.223612 | + | 0.974678i | \(0.571785\pi\) | |||||||
\(398\) | 1.53950e17 | 1.94152 | ||||||||
\(399\) | −2.55623e16 | −0.317159 | ||||||||
\(400\) | 6.66210e16 | 0.813244 | ||||||||
\(401\) | 8.74223e16 | 1.04999 | 0.524993 | − | 0.851106i | \(-0.324068\pi\) | ||||
0.524993 | + | 0.851106i | \(0.324068\pi\) | |||||||
\(402\) | 7.16684e15 | 0.0846952 | ||||||||
\(403\) | 2.48282e16 | 0.288711 | ||||||||
\(404\) | 1.64739e17 | 1.88503 | ||||||||
\(405\) | 7.88630e15 | 0.0888005 | ||||||||
\(406\) | 2.82668e17 | 3.13225 | ||||||||
\(407\) | 1.64828e16 | 0.179749 | ||||||||
\(408\) | −2.25122e16 | −0.241616 | ||||||||
\(409\) | 9.48305e16 | 1.00172 | 0.500860 | − | 0.865528i | \(-0.333017\pi\) | ||||
0.500860 | + | 0.865528i | \(0.333017\pi\) | |||||||
\(410\) | 1.33919e17 | 1.39235 | ||||||||
\(411\) | −7.69324e15 | −0.0787295 | ||||||||
\(412\) | −6.82499e16 | −0.687496 | ||||||||
\(413\) | 2.31443e16 | 0.229493 | ||||||||
\(414\) | 1.87085e17 | 1.82615 | ||||||||
\(415\) | 1.31503e17 | 1.26364 | ||||||||
\(416\) | 4.94802e16 | 0.468085 | ||||||||
\(417\) | −3.03680e16 | −0.282834 | ||||||||
\(418\) | 9.49700e16 | 0.870845 | ||||||||
\(419\) | 1.04698e17 | 0.945247 | 0.472623 | − | 0.881264i | \(-0.343307\pi\) | ||||
0.472623 | + | 0.881264i | \(0.343307\pi\) | |||||||
\(420\) | −2.01910e17 | −1.79489 | ||||||||
\(421\) | 1.21829e17 | 1.06639 | 0.533197 | − | 0.845991i | \(-0.320990\pi\) | ||||
0.533197 | + | 0.845991i | \(0.320990\pi\) | |||||||
\(422\) | −5.41188e16 | −0.466463 | ||||||||
\(423\) | −1.25215e17 | −1.06278 | ||||||||
\(424\) | −6.79621e16 | −0.568053 | ||||||||
\(425\) | −1.09011e16 | −0.0897311 | ||||||||
\(426\) | 2.04745e15 | 0.0165978 | ||||||||
\(427\) | −9.52211e16 | −0.760243 | ||||||||
\(428\) | −3.90895e17 | −3.07380 | ||||||||
\(429\) | −4.22998e16 | −0.327617 | ||||||||
\(430\) | −2.92642e17 | −2.23250 | ||||||||
\(431\) | 9.93881e16 | 0.746848 | 0.373424 | − | 0.927661i | \(-0.378184\pi\) | ||||
0.373424 | + | 0.927661i | \(0.378184\pi\) | |||||||
\(432\) | 2.23732e17 | 1.65609 | ||||||||
\(433\) | −1.61579e17 | −1.17818 | −0.589092 | − | 0.808066i | \(-0.700515\pi\) | ||||
−0.589092 | + | 0.808066i | \(0.700515\pi\) | |||||||
\(434\) | 1.49308e17 | 1.07251 | ||||||||
\(435\) | 1.57700e17 | 1.11597 | ||||||||
\(436\) | −4.59170e17 | −3.20119 | ||||||||
\(437\) | 1.08608e17 | 0.745986 | ||||||||
\(438\) | 5.58176e16 | 0.377737 | ||||||||
\(439\) | −1.15662e17 | −0.771208 | −0.385604 | − | 0.922664i | \(-0.626007\pi\) | ||||
−0.385604 | + | 0.922664i | \(0.626007\pi\) | |||||||
\(440\) | 4.11729e17 | 2.70501 | ||||||||
\(441\) | −2.68387e16 | −0.173744 | ||||||||
\(442\) | −2.86089e16 | −0.182497 | ||||||||
\(443\) | −4.96027e16 | −0.311803 | −0.155902 | − | 0.987773i | \(-0.549828\pi\) | ||||
−0.155902 | + | 0.987773i | \(0.549828\pi\) | |||||||
\(444\) | 3.73220e16 | 0.231193 | ||||||||
\(445\) | −7.71516e16 | −0.470983 | ||||||||
\(446\) | −3.70069e16 | −0.222641 | ||||||||
\(447\) | 8.48521e16 | 0.503111 | ||||||||
\(448\) | −2.93144e16 | −0.171307 | ||||||||
\(449\) | −1.63273e17 | −0.940404 | −0.470202 | − | 0.882559i | \(-0.655819\pi\) | ||||
−0.470202 | + | 0.882559i | \(0.655819\pi\) | |||||||
\(450\) | 9.84512e16 | 0.558907 | ||||||||
\(451\) | 1.16266e17 | 0.650588 | ||||||||
\(452\) | 8.59341e16 | 0.473986 | ||||||||
\(453\) | −1.31348e17 | −0.714142 | ||||||||
\(454\) | −2.76848e17 | −1.48381 | ||||||||
\(455\) | −1.40834e17 | −0.744106 | ||||||||
\(456\) | 1.18029e17 | 0.614776 | ||||||||
\(457\) | −1.29183e17 | −0.663361 | −0.331681 | − | 0.943392i | \(-0.607616\pi\) | ||||
−0.331681 | + | 0.943392i | \(0.607616\pi\) | |||||||
\(458\) | −2.06806e16 | −0.104698 | ||||||||
\(459\) | −3.66090e16 | −0.182728 | ||||||||
\(460\) | 8.57863e17 | 4.22175 | ||||||||
\(461\) | −3.53577e17 | −1.71565 | −0.857824 | − | 0.513944i | \(-0.828184\pi\) | ||||
−0.857824 | + | 0.513944i | \(0.828184\pi\) | |||||||
\(462\) | −2.54376e17 | −1.21704 | ||||||||
\(463\) | 4.66410e16 | 0.220035 | 0.110017 | − | 0.993930i | \(-0.464909\pi\) | ||||
0.110017 | + | 0.993930i | \(0.464909\pi\) | |||||||
\(464\) | −5.65905e17 | −2.63255 | ||||||||
\(465\) | 8.32988e16 | 0.382115 | ||||||||
\(466\) | −6.93112e17 | −3.13541 | ||||||||
\(467\) | 5.02655e16 | 0.224238 | 0.112119 | − | 0.993695i | \(-0.464236\pi\) | ||||
0.112119 | + | 0.993695i | \(0.464236\pi\) | |||||||
\(468\) | 1.78050e17 | 0.783331 | ||||||||
\(469\) | 2.07161e16 | 0.0898846 | ||||||||
\(470\) | −8.33188e17 | −3.56539 | ||||||||
\(471\) | −8.77904e16 | −0.370520 | ||||||||
\(472\) | −1.06864e17 | −0.444845 | ||||||||
\(473\) | −2.54066e17 | −1.04316 | ||||||||
\(474\) | 4.02823e16 | 0.163138 | ||||||||
\(475\) | 5.71534e16 | 0.228314 | ||||||||
\(476\) | −1.18558e17 | −0.467182 | ||||||||
\(477\) | −4.35468e16 | −0.169273 | ||||||||
\(478\) | −6.82936e17 | −2.61878 | ||||||||
\(479\) | 4.33037e17 | 1.63811 | 0.819056 | − | 0.573713i | \(-0.194498\pi\) | ||||
0.819056 | + | 0.573713i | \(0.194498\pi\) | |||||||
\(480\) | 1.66006e17 | 0.619520 | ||||||||
\(481\) | 2.60325e16 | 0.0958456 | ||||||||
\(482\) | −1.69441e17 | −0.615479 | ||||||||
\(483\) | −2.90904e17 | −1.04254 | ||||||||
\(484\) | 2.43729e16 | 0.0861811 | ||||||||
\(485\) | −3.91467e17 | −1.36576 | ||||||||
\(486\) | 5.30979e17 | 1.82785 | ||||||||
\(487\) | −1.64726e17 | −0.559532 | −0.279766 | − | 0.960068i | \(-0.590257\pi\) | ||||
−0.279766 | + | 0.960068i | \(0.590257\pi\) | |||||||
\(488\) | 4.39664e17 | 1.47364 | ||||||||
\(489\) | −3.01557e17 | −0.997383 | ||||||||
\(490\) | −1.78586e17 | −0.582872 | ||||||||
\(491\) | −5.52532e17 | −1.77962 | −0.889811 | − | 0.456329i | \(-0.849164\pi\) | ||||
−0.889811 | + | 0.456329i | \(0.849164\pi\) | |||||||
\(492\) | 2.63262e17 | 0.836787 | ||||||||
\(493\) | 9.25984e16 | 0.290468 | ||||||||
\(494\) | 1.49993e17 | 0.464351 | ||||||||
\(495\) | 2.63816e17 | 0.806060 | ||||||||
\(496\) | −2.98917e17 | −0.901405 | ||||||||
\(497\) | 5.91826e15 | 0.0176148 | ||||||||
\(498\) | 3.75134e17 | 1.10204 | ||||||||
\(499\) | −8.42351e16 | −0.244253 | −0.122126 | − | 0.992515i | \(-0.538971\pi\) | ||||
−0.122126 | + | 0.992515i | \(0.538971\pi\) | |||||||
\(500\) | −4.90501e17 | −1.40390 | ||||||||
\(501\) | −4.00039e15 | −0.0113020 | ||||||||
\(502\) | 3.70392e17 | 1.03297 | ||||||||
\(503\) | −4.11970e16 | −0.113416 | −0.0567079 | − | 0.998391i | \(-0.518060\pi\) | ||||
−0.0567079 | + | 0.998391i | \(0.518060\pi\) | |||||||
\(504\) | 5.87690e17 | 1.59716 | ||||||||
\(505\) | 3.85513e17 | 1.03430 | ||||||||
\(506\) | 1.08078e18 | 2.86258 | ||||||||
\(507\) | 1.59369e17 | 0.416729 | ||||||||
\(508\) | −6.09829e17 | −1.57432 | ||||||||
\(509\) | 2.24293e17 | 0.571677 | 0.285839 | − | 0.958278i | \(-0.407728\pi\) | ||||
0.285839 | + | 0.958278i | \(0.407728\pi\) | |||||||
\(510\) | −9.59828e16 | −0.241539 | ||||||||
\(511\) | 1.61344e17 | 0.400881 | ||||||||
\(512\) | 9.13545e17 | 2.24117 | ||||||||
\(513\) | 1.91937e17 | 0.464938 | ||||||||
\(514\) | −2.68727e17 | −0.642763 | ||||||||
\(515\) | −1.59715e17 | −0.377223 | ||||||||
\(516\) | −5.75282e17 | −1.34171 | ||||||||
\(517\) | −7.23359e17 | −1.66596 | ||||||||
\(518\) | 1.56550e17 | 0.356049 | ||||||||
\(519\) | 3.73412e16 | 0.0838689 | ||||||||
\(520\) | 6.50274e17 | 1.44236 | ||||||||
\(521\) | 1.17707e17 | 0.257843 | 0.128922 | − | 0.991655i | \(-0.458848\pi\) | ||||
0.128922 | + | 0.991655i | \(0.458848\pi\) | |||||||
\(522\) | −8.36283e17 | −1.80924 | ||||||||
\(523\) | 5.82336e16 | 0.124426 | 0.0622132 | − | 0.998063i | \(-0.480184\pi\) | ||||
0.0622132 | + | 0.998063i | \(0.480184\pi\) | |||||||
\(524\) | 1.62065e18 | 3.42009 | ||||||||
\(525\) | −1.53085e17 | −0.319077 | ||||||||
\(526\) | 1.23476e18 | 2.54200 | ||||||||
\(527\) | 4.89115e16 | 0.0994585 | ||||||||
\(528\) | 5.09265e17 | 1.02288 | ||||||||
\(529\) | 7.31938e17 | 1.45215 | ||||||||
\(530\) | −2.89763e17 | −0.567871 | ||||||||
\(531\) | −6.84733e16 | −0.132558 | ||||||||
\(532\) | 6.21587e17 | 1.18871 | ||||||||
\(533\) | 1.83628e17 | 0.346906 | ||||||||
\(534\) | −2.20089e17 | −0.410752 | ||||||||
\(535\) | −9.14751e17 | −1.68657 | ||||||||
\(536\) | −9.56525e16 | −0.174231 | ||||||||
\(537\) | 2.21337e17 | 0.398310 | ||||||||
\(538\) | 2.75551e17 | 0.489912 | ||||||||
\(539\) | −1.55045e17 | −0.272353 | ||||||||
\(540\) | 1.51606e18 | 2.63122 | ||||||||
\(541\) | −3.21741e17 | −0.551726 | −0.275863 | − | 0.961197i | \(-0.588964\pi\) | ||||
−0.275863 | + | 0.961197i | \(0.588964\pi\) | |||||||
\(542\) | −1.03466e18 | −1.75309 | ||||||||
\(543\) | 3.39424e17 | 0.568256 | ||||||||
\(544\) | 9.74757e16 | 0.161251 | ||||||||
\(545\) | −1.07453e18 | −1.75646 | ||||||||
\(546\) | −4.01755e17 | −0.648947 | ||||||||
\(547\) | −7.83664e17 | −1.25087 | −0.625435 | − | 0.780276i | \(-0.715078\pi\) | ||||
−0.625435 | + | 0.780276i | \(0.715078\pi\) | |||||||
\(548\) | 1.87073e17 | 0.295078 | ||||||||
\(549\) | 2.81715e17 | 0.439127 | ||||||||
\(550\) | 5.68745e17 | 0.876113 | ||||||||
\(551\) | −4.85483e17 | −0.739075 | ||||||||
\(552\) | 1.34319e18 | 2.02085 | ||||||||
\(553\) | 1.16438e17 | 0.173134 | ||||||||
\(554\) | 1.03908e18 | 1.52698 | ||||||||
\(555\) | 8.73389e16 | 0.126854 | ||||||||
\(556\) | 7.38444e17 | 1.06006 | ||||||||
\(557\) | −1.17598e18 | −1.66856 | −0.834281 | − | 0.551340i | \(-0.814117\pi\) | ||||
−0.834281 | + | 0.551340i | \(0.814117\pi\) | |||||||
\(558\) | −4.41734e17 | −0.619496 | ||||||||
\(559\) | −4.01265e17 | −0.556230 | ||||||||
\(560\) | 1.69556e18 | 2.32323 | ||||||||
\(561\) | −8.33305e16 | −0.112861 | ||||||||
\(562\) | 2.10421e18 | 2.81711 | ||||||||
\(563\) | 9.32560e17 | 1.23416 | 0.617081 | − | 0.786899i | \(-0.288315\pi\) | ||||
0.617081 | + | 0.786899i | \(0.288315\pi\) | |||||||
\(564\) | −1.63790e18 | −2.14276 | ||||||||
\(565\) | 2.01098e17 | 0.260072 | ||||||||
\(566\) | −1.50636e18 | −1.92585 | ||||||||
\(567\) | 6.50289e16 | 0.0821895 | ||||||||
\(568\) | −2.73263e16 | −0.0341442 | ||||||||
\(569\) | −1.17434e18 | −1.45065 | −0.725326 | − | 0.688405i | \(-0.758311\pi\) | ||||
−0.725326 | + | 0.688405i | \(0.758311\pi\) | |||||||
\(570\) | 5.03227e17 | 0.614578 | ||||||||
\(571\) | 2.00298e17 | 0.241847 | 0.120924 | − | 0.992662i | \(-0.461414\pi\) | ||||
0.120924 | + | 0.992662i | \(0.461414\pi\) | |||||||
\(572\) | 1.02858e18 | 1.22791 | ||||||||
\(573\) | 2.88526e17 | 0.340549 | ||||||||
\(574\) | 1.10427e18 | 1.28869 | ||||||||
\(575\) | 6.50416e17 | 0.750499 | ||||||||
\(576\) | 8.67278e16 | 0.0989492 | ||||||||
\(577\) | −8.49702e17 | −0.958570 | −0.479285 | − | 0.877659i | \(-0.659104\pi\) | ||||
−0.479285 | + | 0.877659i | \(0.659104\pi\) | |||||||
\(578\) | 1.55144e18 | 1.73063 | ||||||||
\(579\) | 7.94012e17 | 0.875823 | ||||||||
\(580\) | −3.83471e18 | −4.18264 | ||||||||
\(581\) | 1.08435e18 | 1.16956 | ||||||||
\(582\) | −1.11673e18 | −1.19110 | ||||||||
\(583\) | −2.51567e17 | −0.265343 | ||||||||
\(584\) | −7.44971e17 | −0.777062 | ||||||||
\(585\) | 4.16664e17 | 0.429806 | ||||||||
\(586\) | 5.38155e17 | 0.549000 | ||||||||
\(587\) | −1.87792e18 | −1.89466 | −0.947328 | − | 0.320265i | \(-0.896228\pi\) | ||||
−0.947328 | + | 0.320265i | \(0.896228\pi\) | |||||||
\(588\) | −3.51069e17 | −0.350300 | ||||||||
\(589\) | −2.56438e17 | −0.253065 | ||||||||
\(590\) | −4.55625e17 | −0.444702 | ||||||||
\(591\) | 4.36497e16 | 0.0421369 | ||||||||
\(592\) | −3.13415e17 | −0.299247 | ||||||||
\(593\) | −1.13216e18 | −1.06918 | −0.534590 | − | 0.845111i | \(-0.679534\pi\) | ||||
−0.534590 | + | 0.845111i | \(0.679534\pi\) | |||||||
\(594\) | 1.91000e18 | 1.78411 | ||||||||
\(595\) | −2.77443e17 | −0.256338 | ||||||||
\(596\) | −2.06331e18 | −1.88566 | ||||||||
\(597\) | 7.08221e17 | 0.640230 | ||||||||
\(598\) | 1.70695e18 | 1.52638 | ||||||||
\(599\) | 1.50059e18 | 1.32736 | 0.663681 | − | 0.748016i | \(-0.268993\pi\) | ||||
0.663681 | + | 0.748016i | \(0.268993\pi\) | |||||||
\(600\) | 7.06836e17 | 0.618494 | ||||||||
\(601\) | −1.25912e18 | −1.08989 | −0.544944 | − | 0.838472i | \(-0.683449\pi\) | ||||
−0.544944 | + | 0.838472i | \(0.683449\pi\) | |||||||
\(602\) | −2.41307e18 | −2.06629 | ||||||||
\(603\) | −6.12895e16 | −0.0519186 | ||||||||
\(604\) | 3.19392e18 | 2.67660 | ||||||||
\(605\) | 5.70361e16 | 0.0472868 | ||||||||
\(606\) | 1.09974e18 | 0.902026 | ||||||||
\(607\) | 1.68800e18 | 1.36976 | 0.684881 | − | 0.728655i | \(-0.259854\pi\) | ||||
0.684881 | + | 0.728655i | \(0.259854\pi\) | |||||||
\(608\) | −5.11054e17 | −0.410293 | ||||||||
\(609\) | 1.30036e18 | 1.03288 | ||||||||
\(610\) | 1.87455e18 | 1.47317 | ||||||||
\(611\) | −1.14245e18 | −0.888322 | ||||||||
\(612\) | 3.50759e17 | 0.269851 | ||||||||
\(613\) | −7.16924e17 | −0.545733 | −0.272866 | − | 0.962052i | \(-0.587972\pi\) | ||||
−0.272866 | + | 0.962052i | \(0.587972\pi\) | |||||||
\(614\) | 4.50102e18 | 3.39013 | ||||||||
\(615\) | 6.16071e17 | 0.459137 | ||||||||
\(616\) | 3.39504e18 | 2.50363 | ||||||||
\(617\) | −5.07239e16 | −0.0370134 | −0.0185067 | − | 0.999829i | \(-0.505891\pi\) | ||||
−0.0185067 | + | 0.999829i | \(0.505891\pi\) | |||||||
\(618\) | −4.55614e17 | −0.328982 | ||||||||
\(619\) | −2.35708e17 | −0.168417 | −0.0842083 | − | 0.996448i | \(-0.526836\pi\) | ||||
−0.0842083 | + | 0.996448i | \(0.526836\pi\) | |||||||
\(620\) | −2.02553e18 | −1.43217 | ||||||||
\(621\) | 2.18428e18 | 1.52831 | ||||||||
\(622\) | −1.04913e17 | −0.0726427 | ||||||||
\(623\) | −6.36177e17 | −0.435919 | ||||||||
\(624\) | 8.04319e17 | 0.545417 | ||||||||
\(625\) | −1.86200e18 | −1.24957 | ||||||||
\(626\) | −1.60857e18 | −1.06833 | ||||||||
\(627\) | 4.36892e17 | 0.287168 | ||||||||
\(628\) | 2.13476e18 | 1.38871 | ||||||||
\(629\) | 5.12838e16 | 0.0330180 | ||||||||
\(630\) | 2.50567e18 | 1.59665 | ||||||||
\(631\) | −1.20203e18 | −0.758094 | −0.379047 | − | 0.925377i | \(-0.623748\pi\) | ||||
−0.379047 | + | 0.925377i | \(0.623748\pi\) | |||||||
\(632\) | −5.37629e17 | −0.335600 | ||||||||
\(633\) | −2.48964e17 | −0.153820 | ||||||||
\(634\) | −2.02124e18 | −1.23606 | ||||||||
\(635\) | −1.42709e18 | −0.863817 | ||||||||
\(636\) | −5.69623e17 | −0.341284 | ||||||||
\(637\) | −2.44874e17 | −0.145223 | ||||||||
\(638\) | −4.83114e18 | −2.83606 | ||||||||
\(639\) | −1.75094e16 | −0.0101746 | ||||||||
\(640\) | 2.39817e18 | 1.37947 | ||||||||
\(641\) | −1.79680e18 | −1.02311 | −0.511556 | − | 0.859250i | \(-0.670931\pi\) | ||||
−0.511556 | + | 0.859250i | \(0.670931\pi\) | |||||||
\(642\) | −2.60949e18 | −1.47088 | ||||||||
\(643\) | −2.49075e18 | −1.38982 | −0.694911 | − | 0.719095i | \(-0.744556\pi\) | ||||
−0.694911 | + | 0.719095i | \(0.744556\pi\) | |||||||
\(644\) | 7.07377e18 | 3.90745 | ||||||||
\(645\) | −1.34624e18 | −0.736183 | ||||||||
\(646\) | 2.95486e17 | 0.159965 | ||||||||
\(647\) | 2.38898e18 | 1.28037 | 0.640183 | − | 0.768222i | \(-0.278858\pi\) | ||||
0.640183 | + | 0.768222i | \(0.278858\pi\) | |||||||
\(648\) | −3.00257e17 | −0.159315 | ||||||||
\(649\) | −3.95565e17 | −0.207791 | ||||||||
\(650\) | 8.98260e17 | 0.467160 | ||||||||
\(651\) | 6.86865e17 | 0.353668 | ||||||||
\(652\) | 7.33282e18 | 3.73819 | ||||||||
\(653\) | −3.08142e18 | −1.55530 | −0.777652 | − | 0.628695i | \(-0.783589\pi\) | ||||
−0.777652 | + | 0.628695i | \(0.783589\pi\) | |||||||
\(654\) | −3.06527e18 | −1.53184 | ||||||||
\(655\) | 3.79257e18 | 1.87657 | ||||||||
\(656\) | −2.21077e18 | −1.08310 | ||||||||
\(657\) | −4.77341e17 | −0.231555 | ||||||||
\(658\) | −6.87031e18 | −3.29995 | ||||||||
\(659\) | −2.86499e17 | −0.136260 | −0.0681299 | − | 0.997676i | \(-0.521703\pi\) | ||||
−0.0681299 | + | 0.997676i | \(0.521703\pi\) | |||||||
\(660\) | 3.45090e18 | 1.62516 | ||||||||
\(661\) | −2.61060e18 | −1.21739 | −0.608697 | − | 0.793403i | \(-0.708308\pi\) | ||||
−0.608697 | + | 0.793403i | \(0.708308\pi\) | |||||||
\(662\) | 6.62234e18 | 3.05798 | ||||||||
\(663\) | −1.31610e17 | −0.0601798 | ||||||||
\(664\) | −5.00674e18 | −2.26706 | ||||||||
\(665\) | 1.45460e18 | 0.652235 | ||||||||
\(666\) | −4.63159e17 | −0.205659 | ||||||||
\(667\) | −5.52489e18 | −2.42944 | ||||||||
\(668\) | 9.72755e16 | 0.0423600 | ||||||||
\(669\) | −1.70243e17 | −0.0734176 | ||||||||
\(670\) | −4.07823e17 | −0.174175 | ||||||||
\(671\) | 1.62745e18 | 0.688352 | ||||||||
\(672\) | 1.36885e18 | 0.573398 | ||||||||
\(673\) | −2.04496e18 | −0.848373 | −0.424186 | − | 0.905575i | \(-0.639440\pi\) | ||||
−0.424186 | + | 0.905575i | \(0.639440\pi\) | |||||||
\(674\) | −5.06956e18 | −2.08296 | ||||||||
\(675\) | 1.14945e18 | 0.467751 | ||||||||
\(676\) | −3.87531e18 | −1.56190 | ||||||||
\(677\) | −3.89797e17 | −0.155601 | −0.0778004 | − | 0.996969i | \(-0.524790\pi\) | ||||
−0.0778004 | + | 0.996969i | \(0.524790\pi\) | |||||||
\(678\) | 5.73668e17 | 0.226813 | ||||||||
\(679\) | −3.22796e18 | −1.26408 | ||||||||
\(680\) | 1.28104e18 | 0.496882 | ||||||||
\(681\) | −1.27359e18 | −0.489297 | ||||||||
\(682\) | −2.55186e18 | −0.971089 | ||||||||
\(683\) | −1.91733e18 | −0.722707 | −0.361353 | − | 0.932429i | \(-0.617685\pi\) | ||||
−0.361353 | + | 0.932429i | \(0.617685\pi\) | |||||||
\(684\) | −1.83899e18 | −0.686617 | ||||||||
\(685\) | 4.37777e17 | 0.161907 | ||||||||
\(686\) | 4.03843e18 | 1.47947 | ||||||||
\(687\) | −9.51371e16 | −0.0345248 | ||||||||
\(688\) | 4.83099e18 | 1.73665 | ||||||||
\(689\) | −3.97318e17 | −0.141486 | ||||||||
\(690\) | 5.72682e18 | 2.02020 | ||||||||
\(691\) | −1.63628e18 | −0.571806 | −0.285903 | − | 0.958259i | \(-0.592294\pi\) | ||||
−0.285903 | + | 0.958259i | \(0.592294\pi\) | |||||||
\(692\) | −9.08008e17 | −0.314340 | ||||||||
\(693\) | 2.17538e18 | 0.746051 | ||||||||
\(694\) | −4.95520e18 | −1.68355 | ||||||||
\(695\) | 1.72807e18 | 0.581647 | ||||||||
\(696\) | −6.00415e18 | −2.00213 | ||||||||
\(697\) | 3.61746e17 | 0.119506 | ||||||||
\(698\) | −2.47175e18 | −0.808991 | ||||||||
\(699\) | −3.18854e18 | −1.03393 | ||||||||
\(700\) | 3.72248e18 | 1.19590 | ||||||||
\(701\) | −8.13845e17 | −0.259045 | −0.129522 | − | 0.991576i | \(-0.541344\pi\) | ||||
−0.129522 | + | 0.991576i | \(0.541344\pi\) | |||||||
\(702\) | 3.01661e18 | 0.951322 | ||||||||
\(703\) | −2.68875e17 | −0.0840120 | ||||||||
\(704\) | 5.01020e17 | 0.155108 | ||||||||
\(705\) | −3.83293e18 | −1.17571 | ||||||||
\(706\) | 5.54358e18 | 1.68484 | ||||||||
\(707\) | 3.17886e18 | 0.957295 | ||||||||
\(708\) | −8.95679e17 | −0.267261 | ||||||||
\(709\) | 4.40859e18 | 1.30346 | 0.651732 | − | 0.758450i | \(-0.274043\pi\) | ||||
0.651732 | + | 0.758450i | \(0.274043\pi\) | |||||||
\(710\) | −1.16508e17 | −0.0341333 | ||||||||
\(711\) | −3.44486e17 | −0.100005 | ||||||||
\(712\) | 2.93742e18 | 0.844978 | ||||||||
\(713\) | −2.91831e18 | −0.831858 | ||||||||
\(714\) | −7.91455e17 | −0.223557 | ||||||||
\(715\) | 2.40704e18 | 0.673742 | ||||||||
\(716\) | −5.38214e18 | −1.49287 | ||||||||
\(717\) | −3.14172e18 | −0.863561 | ||||||||
\(718\) | 4.97155e17 | 0.135420 | ||||||||
\(719\) | −6.27952e18 | −1.69508 | −0.847538 | − | 0.530735i | \(-0.821916\pi\) | ||||
−0.847538 | + | 0.530735i | \(0.821916\pi\) | |||||||
\(720\) | −5.01639e18 | −1.34193 | ||||||||
\(721\) | −1.31698e18 | −0.349139 | ||||||||
\(722\) | 5.27722e18 | 1.38648 | ||||||||
\(723\) | −7.79483e17 | −0.202959 | ||||||||
\(724\) | −8.25361e18 | −2.12982 | ||||||||
\(725\) | −2.90740e18 | −0.743546 | ||||||||
\(726\) | 1.62705e17 | 0.0412396 | ||||||||
\(727\) | −3.12809e18 | −0.785789 | −0.392895 | − | 0.919583i | \(-0.628526\pi\) | ||||
−0.392895 | + | 0.919583i | \(0.628526\pi\) | |||||||
\(728\) | 5.36203e18 | 1.33498 | ||||||||
\(729\) | 2.14679e18 | 0.529737 | ||||||||
\(730\) | −3.17625e18 | −0.776813 | ||||||||
\(731\) | −7.90490e17 | −0.191617 | ||||||||
\(732\) | 3.68503e18 | 0.885359 | ||||||||
\(733\) | 3.13690e18 | 0.747007 | 0.373503 | − | 0.927629i | \(-0.378156\pi\) | ||||
0.373503 | + | 0.927629i | \(0.378156\pi\) | |||||||
\(734\) | −4.95393e17 | −0.116930 | ||||||||
\(735\) | −8.21553e17 | −0.192206 | ||||||||
\(736\) | −5.81589e18 | −1.34868 | ||||||||
\(737\) | −3.54065e17 | −0.0813849 | ||||||||
\(738\) | −3.26703e18 | −0.744367 | ||||||||
\(739\) | −6.09806e18 | −1.37722 | −0.688609 | − | 0.725132i | \(-0.741779\pi\) | ||||
−0.688609 | + | 0.725132i | \(0.741779\pi\) | |||||||
\(740\) | −2.12378e18 | −0.475448 | ||||||||
\(741\) | 6.90016e17 | 0.153123 | ||||||||
\(742\) | −2.38933e18 | −0.525594 | ||||||||
\(743\) | 1.84814e17 | 0.0403003 | 0.0201501 | − | 0.999797i | \(-0.493586\pi\) | ||||
0.0201501 | + | 0.999797i | \(0.493586\pi\) | |||||||
\(744\) | −3.17146e18 | −0.685543 | ||||||||
\(745\) | −4.82843e18 | −1.03464 | ||||||||
\(746\) | −9.29258e18 | −1.97394 | ||||||||
\(747\) | −3.20808e18 | −0.675555 | ||||||||
\(748\) | 2.02631e18 | 0.423004 | ||||||||
\(749\) | −7.54286e18 | −1.56100 | ||||||||
\(750\) | −3.27442e18 | −0.671795 | ||||||||
\(751\) | 4.88053e18 | 0.992675 | 0.496338 | − | 0.868130i | \(-0.334678\pi\) | ||||
0.496338 | + | 0.868130i | \(0.334678\pi\) | |||||||
\(752\) | 1.37545e19 | 2.77349 | ||||||||
\(753\) | 1.70392e18 | 0.340629 | ||||||||
\(754\) | −7.63018e18 | −1.51224 | ||||||||
\(755\) | 7.47424e18 | 1.46863 | ||||||||
\(756\) | 1.25011e19 | 2.43533 | ||||||||
\(757\) | 7.33696e18 | 1.41708 | 0.708538 | − | 0.705673i | \(-0.249355\pi\) | ||||
0.708538 | + | 0.705673i | \(0.249355\pi\) | |||||||
\(758\) | 5.89702e18 | 1.12923 | ||||||||
\(759\) | 4.97192e18 | 0.943957 | ||||||||
\(760\) | −6.71633e18 | −1.26428 | ||||||||
\(761\) | 5.30890e18 | 0.990841 | 0.495421 | − | 0.868653i | \(-0.335014\pi\) | ||||
0.495421 | + | 0.868653i | \(0.335014\pi\) | |||||||
\(762\) | −4.07102e18 | −0.753348 | ||||||||
\(763\) | −8.86033e18 | −1.62570 | ||||||||
\(764\) | −7.01594e18 | −1.27638 | ||||||||
\(765\) | 8.20826e17 | 0.148065 | ||||||||
\(766\) | 2.45093e18 | 0.438373 | ||||||||
\(767\) | −6.24745e17 | −0.110798 | ||||||||
\(768\) | 6.32942e18 | 1.11305 | ||||||||
\(769\) | −8.97182e18 | −1.56444 | −0.782221 | − | 0.623001i | \(-0.785913\pi\) | ||||
−0.782221 | + | 0.623001i | \(0.785913\pi\) | |||||||
\(770\) | 1.44751e19 | 2.50283 | ||||||||
\(771\) | −1.23623e18 | −0.211956 | ||||||||
\(772\) | −1.93076e19 | −3.28258 | ||||||||
\(773\) | 4.11811e18 | 0.694274 | 0.347137 | − | 0.937814i | \(-0.387154\pi\) | ||||
0.347137 | + | 0.937814i | \(0.387154\pi\) | |||||||
\(774\) | 7.13914e18 | 1.19352 | ||||||||
\(775\) | −1.53572e18 | −0.254596 | ||||||||
\(776\) | 1.49044e19 | 2.45027 | ||||||||
\(777\) | 7.20180e17 | 0.117410 | ||||||||
\(778\) | −1.17766e19 | −1.90394 | ||||||||
\(779\) | −1.89659e18 | −0.304075 | ||||||||
\(780\) | 5.45026e18 | 0.866567 | ||||||||
\(781\) | −1.01150e17 | −0.0159491 | ||||||||
\(782\) | 3.36268e18 | 0.525826 | ||||||||
\(783\) | −9.76386e18 | −1.51415 | ||||||||
\(784\) | 2.94814e18 | 0.453413 | ||||||||
\(785\) | 4.99564e18 | 0.761971 | ||||||||
\(786\) | 1.08190e19 | 1.63659 | ||||||||
\(787\) | 5.69642e18 | 0.854606 | 0.427303 | − | 0.904108i | \(-0.359464\pi\) | ||||
0.427303 | + | 0.904108i | \(0.359464\pi\) | |||||||
\(788\) | −1.06141e18 | −0.157929 | ||||||||
\(789\) | 5.68030e18 | 0.838245 | ||||||||
\(790\) | −2.29223e18 | −0.335492 | ||||||||
\(791\) | 1.65822e18 | 0.240710 | ||||||||
\(792\) | −1.00443e19 | −1.44613 | ||||||||
\(793\) | 2.57035e18 | 0.367042 | ||||||||
\(794\) | 5.66317e18 | 0.802096 | ||||||||
\(795\) | −1.33300e18 | −0.187260 | ||||||||
\(796\) | −1.72215e19 | −2.39958 | ||||||||
\(797\) | −1.05222e19 | −1.45421 | −0.727104 | − | 0.686527i | \(-0.759134\pi\) | ||||
−0.727104 | + | 0.686527i | \(0.759134\pi\) | |||||||
\(798\) | 4.14951e18 | 0.568824 | ||||||||
\(799\) | −2.25063e18 | −0.306020 | ||||||||
\(800\) | −3.06054e18 | −0.412775 | ||||||||
\(801\) | 1.88215e18 | 0.251793 | ||||||||
\(802\) | −1.41912e19 | −1.88315 | ||||||||
\(803\) | −2.75756e18 | −0.362973 | ||||||||
\(804\) | −8.01709e17 | −0.104677 | ||||||||
\(805\) | 1.65537e19 | 2.14398 | ||||||||
\(806\) | −4.03034e18 | −0.517803 | ||||||||
\(807\) | 1.26762e18 | 0.161552 | ||||||||
\(808\) | −1.46777e19 | −1.85561 | ||||||||
\(809\) | 9.07498e18 | 1.13810 | 0.569050 | − | 0.822303i | \(-0.307311\pi\) | ||||
0.569050 | + | 0.822303i | \(0.307311\pi\) | |||||||
\(810\) | −1.28018e18 | −0.159264 | ||||||||
\(811\) | 3.35438e18 | 0.413977 | 0.206989 | − | 0.978343i | \(-0.433634\pi\) | ||||
0.206989 | + | 0.978343i | \(0.433634\pi\) | |||||||
\(812\) | −3.16202e19 | −3.87125 | ||||||||
\(813\) | −4.75978e18 | −0.578093 | ||||||||
\(814\) | −2.67563e18 | −0.322380 | ||||||||
\(815\) | 1.71599e19 | 2.05111 | ||||||||
\(816\) | 1.58450e18 | 0.187892 | ||||||||
\(817\) | 4.14445e18 | 0.487555 | ||||||||
\(818\) | −1.53937e19 | −1.79658 | ||||||||
\(819\) | 3.43573e18 | 0.397808 | ||||||||
\(820\) | −1.49807e19 | −1.72085 | ||||||||
\(821\) | −9.95459e18 | −1.13447 | −0.567235 | − | 0.823556i | \(-0.691987\pi\) | ||||
−0.567235 | + | 0.823556i | \(0.691987\pi\) | |||||||
\(822\) | 1.24884e18 | 0.141201 | ||||||||
\(823\) | −9.71689e18 | −1.09000 | −0.545002 | − | 0.838435i | \(-0.683471\pi\) | ||||
−0.545002 | + | 0.838435i | \(0.683471\pi\) | |||||||
\(824\) | 6.08086e18 | 0.676766 | ||||||||
\(825\) | 2.61641e18 | 0.288905 | ||||||||
\(826\) | −3.75699e18 | −0.411595 | ||||||||
\(827\) | 1.41193e19 | 1.53472 | 0.767359 | − | 0.641218i | \(-0.221570\pi\) | ||||
0.767359 | + | 0.641218i | \(0.221570\pi\) | |||||||
\(828\) | −2.09280e19 | −2.25700 | ||||||||
\(829\) | −9.41989e18 | −1.00796 | −0.503978 | − | 0.863717i | \(-0.668131\pi\) | ||||
−0.503978 | + | 0.863717i | \(0.668131\pi\) | |||||||
\(830\) | −2.13467e19 | −2.26633 | ||||||||
\(831\) | 4.78009e18 | 0.503534 | ||||||||
\(832\) | 7.91298e17 | 0.0827062 | ||||||||
\(833\) | −4.82401e17 | −0.0500283 | ||||||||
\(834\) | 4.92961e18 | 0.507263 | ||||||||
\(835\) | 2.27639e17 | 0.0232426 | ||||||||
\(836\) | −1.06237e19 | −1.07630 | ||||||||
\(837\) | −5.15738e18 | −0.518458 | ||||||||
\(838\) | −1.69955e19 | −1.69530 | ||||||||
\(839\) | −2.59679e18 | −0.257030 | −0.128515 | − | 0.991708i | \(-0.541021\pi\) | ||||
−0.128515 | + | 0.991708i | \(0.541021\pi\) | |||||||
\(840\) | 1.79896e19 | 1.76688 | ||||||||
\(841\) | 1.44360e19 | 1.40693 | ||||||||
\(842\) | −1.97764e19 | −1.91258 | ||||||||
\(843\) | 9.68004e18 | 0.928962 | ||||||||
\(844\) | 6.05392e18 | 0.576515 | ||||||||
\(845\) | −9.06878e18 | −0.856999 | ||||||||
\(846\) | 2.03261e19 | 1.90610 | ||||||||
\(847\) | 4.70308e17 | 0.0437664 | ||||||||
\(848\) | 4.78347e18 | 0.441743 | ||||||||
\(849\) | −6.92976e18 | −0.635065 | ||||||||
\(850\) | 1.76957e18 | 0.160933 | ||||||||
\(851\) | −3.05985e18 | −0.276158 | ||||||||
\(852\) | −2.29035e17 | −0.0205137 | ||||||||
\(853\) | −4.17360e18 | −0.370973 | −0.185486 | − | 0.982647i | \(-0.559386\pi\) | ||||
−0.185486 | + | 0.982647i | \(0.559386\pi\) | |||||||
\(854\) | 1.54572e19 | 1.36349 | ||||||||
\(855\) | −4.30350e18 | −0.376740 | ||||||||
\(856\) | 3.48276e19 | 3.02582 | ||||||||
\(857\) | 3.62207e18 | 0.312307 | 0.156153 | − | 0.987733i | \(-0.450091\pi\) | ||||
0.156153 | + | 0.987733i | \(0.450091\pi\) | |||||||
\(858\) | 6.86649e18 | 0.587581 | ||||||||
\(859\) | −2.02485e19 | −1.71964 | −0.859818 | − | 0.510601i | \(-0.829423\pi\) | ||||
−0.859818 | + | 0.510601i | \(0.829423\pi\) | |||||||
\(860\) | 3.27360e19 | 2.75921 | ||||||||
\(861\) | 5.08000e18 | 0.424956 | ||||||||
\(862\) | −1.61336e19 | −1.33947 | ||||||||
\(863\) | 3.99628e18 | 0.329295 | 0.164648 | − | 0.986352i | \(-0.447351\pi\) | ||||
0.164648 | + | 0.986352i | \(0.447351\pi\) | |||||||
\(864\) | −1.02781e19 | −0.840572 | ||||||||
\(865\) | −2.12487e18 | −0.172476 | ||||||||
\(866\) | 2.62289e19 | 2.11307 | ||||||||
\(867\) | 7.13712e18 | 0.570688 | ||||||||
\(868\) | −1.67022e19 | −1.32555 | ||||||||
\(869\) | −1.99007e18 | −0.156762 | ||||||||
\(870\) | −2.55992e19 | −2.00148 | ||||||||
\(871\) | −5.59200e17 | −0.0433960 | ||||||||
\(872\) | 4.09107e19 | 3.15123 | ||||||||
\(873\) | 9.55004e18 | 0.730151 | ||||||||
\(874\) | −1.76302e19 | −1.33793 | ||||||||
\(875\) | −9.46489e18 | −0.712957 | ||||||||
\(876\) | −6.24396e18 | −0.466856 | ||||||||
\(877\) | 2.54327e19 | 1.88754 | 0.943769 | − | 0.330604i | \(-0.107253\pi\) | ||||
0.943769 | + | 0.330604i | \(0.107253\pi\) | |||||||
\(878\) | 1.87753e19 | 1.38316 | ||||||||
\(879\) | 2.47568e18 | 0.181037 | ||||||||
\(880\) | −2.89793e19 | −2.10354 | ||||||||
\(881\) | 2.06368e19 | 1.48696 | 0.743479 | − | 0.668759i | \(-0.233174\pi\) | ||||
0.743479 | + | 0.668759i | \(0.233174\pi\) | |||||||
\(882\) | 4.35670e18 | 0.311611 | ||||||||
\(883\) | −1.35300e19 | −0.960624 | −0.480312 | − | 0.877098i | \(-0.659477\pi\) | ||||
−0.480312 | + | 0.877098i | \(0.659477\pi\) | |||||||
\(884\) | 3.20029e18 | 0.225554 | ||||||||
\(885\) | −2.09602e18 | −0.146644 | ||||||||
\(886\) | 8.05195e18 | 0.559219 | ||||||||
\(887\) | 3.36990e18 | 0.232335 | 0.116167 | − | 0.993230i | \(-0.462939\pi\) | ||||
0.116167 | + | 0.993230i | \(0.462939\pi\) | |||||||
\(888\) | −3.32528e18 | −0.227585 | ||||||||
\(889\) | −1.17675e19 | −0.799508 | ||||||||
\(890\) | 1.25240e19 | 0.844708 | ||||||||
\(891\) | −1.11142e18 | −0.0744175 | ||||||||
\(892\) | 4.13972e18 | 0.275169 | ||||||||
\(893\) | 1.17998e19 | 0.778645 | ||||||||
\(894\) | −1.37740e19 | −0.902329 | ||||||||
\(895\) | −1.25950e19 | −0.819122 | ||||||||
\(896\) | 1.97749e19 | 1.27677 | ||||||||
\(897\) | 7.85251e18 | 0.503336 | ||||||||
\(898\) | 2.65040e19 | 1.68661 | ||||||||
\(899\) | 1.30450e19 | 0.824152 | ||||||||
\(900\) | −1.10131e19 | −0.690770 | ||||||||
\(901\) | −7.82714e17 | −0.0487407 | ||||||||
\(902\) | −1.88734e19 | −1.16683 | ||||||||
\(903\) | −1.11009e19 | −0.681376 | ||||||||
\(904\) | −7.65647e18 | −0.466589 | ||||||||
\(905\) | −1.93146e19 | −1.16861 | ||||||||
\(906\) | 2.13216e19 | 1.28081 | ||||||||
\(907\) | 3.09059e19 | 1.84329 | 0.921647 | − | 0.388030i | \(-0.126844\pi\) | ||||
0.921647 | + | 0.388030i | \(0.126844\pi\) | |||||||
\(908\) | 3.09692e19 | 1.83388 | ||||||||
\(909\) | −9.40479e18 | −0.552948 | ||||||||
\(910\) | 2.28615e19 | 1.33455 | ||||||||
\(911\) | 1.84380e19 | 1.06867 | 0.534335 | − | 0.845273i | \(-0.320562\pi\) | ||||
0.534335 | + | 0.845273i | \(0.320562\pi\) | |||||||
\(912\) | −8.30738e18 | −0.478077 | ||||||||
\(913\) | −1.85328e19 | −1.05896 | ||||||||
\(914\) | 2.09702e19 | 1.18974 | ||||||||
\(915\) | 8.62352e18 | 0.485789 | ||||||||
\(916\) | 2.31340e18 | 0.129399 | ||||||||
\(917\) | 3.12728e19 | 1.73686 | ||||||||
\(918\) | 5.94270e18 | 0.327723 | ||||||||
\(919\) | −2.32400e19 | −1.27258 | −0.636290 | − | 0.771450i | \(-0.719532\pi\) | ||||
−0.636290 | + | 0.771450i | \(0.719532\pi\) | |||||||
\(920\) | −7.64331e19 | −4.15586 | ||||||||
\(921\) | 2.07061e19 | 1.11792 | ||||||||
\(922\) | 5.73958e19 | 3.07701 | ||||||||
\(923\) | −1.59754e17 | −0.00850435 | ||||||||
\(924\) | 2.84555e19 | 1.50417 | ||||||||
\(925\) | −1.61021e18 | −0.0845202 | ||||||||
\(926\) | −7.57119e18 | −0.394633 | ||||||||
\(927\) | 3.89632e18 | 0.201668 | ||||||||
\(928\) | 2.59974e19 | 1.33619 | ||||||||
\(929\) | 1.90343e19 | 0.971482 | 0.485741 | − | 0.874103i | \(-0.338550\pi\) | ||||
0.485741 | + | 0.874103i | \(0.338550\pi\) | |||||||
\(930\) | −1.35218e19 | −0.685324 | ||||||||
\(931\) | 2.52917e18 | 0.127293 | ||||||||
\(932\) | 7.75340e19 | 3.87515 | ||||||||
\(933\) | −4.82633e17 | −0.0239545 | ||||||||
\(934\) | −8.15954e18 | −0.402171 | ||||||||
\(935\) | 4.74185e18 | 0.232099 | ||||||||
\(936\) | −1.58638e19 | −0.771105 | ||||||||
\(937\) | −1.97128e19 | −0.951571 | −0.475785 | − | 0.879561i | \(-0.657836\pi\) | ||||
−0.475785 | + | 0.879561i | \(0.657836\pi\) | |||||||
\(938\) | −3.36283e18 | −0.161208 | ||||||||
\(939\) | −7.39993e18 | −0.352291 | ||||||||
\(940\) | 9.32034e19 | 4.40657 | ||||||||
\(941\) | 3.14602e19 | 1.47717 | 0.738583 | − | 0.674163i | \(-0.235496\pi\) | ||||
0.738583 | + | 0.674163i | \(0.235496\pi\) | |||||||
\(942\) | 1.42509e19 | 0.664527 | ||||||||
\(943\) | −2.15836e19 | −0.999534 | ||||||||
\(944\) | 7.52156e18 | 0.345931 | ||||||||
\(945\) | 2.92545e19 | 1.33624 | ||||||||
\(946\) | 4.12423e19 | 1.87090 | ||||||||
\(947\) | −2.53364e19 | −1.14149 | −0.570743 | − | 0.821129i | \(-0.693345\pi\) | ||||
−0.570743 | + | 0.821129i | \(0.693345\pi\) | |||||||
\(948\) | −4.50613e18 | −0.201627 | ||||||||
\(949\) | −4.35522e18 | −0.193544 | ||||||||
\(950\) | −9.27765e18 | −0.409482 | ||||||||
\(951\) | −9.29837e18 | −0.407599 | ||||||||
\(952\) | 1.05632e19 | 0.459890 | ||||||||
\(953\) | 2.67678e18 | 0.115747 | 0.0578734 | − | 0.998324i | \(-0.481568\pi\) | ||||
0.0578734 | + | 0.998324i | \(0.481568\pi\) | |||||||
\(954\) | 7.06891e18 | 0.303591 | ||||||||
\(955\) | −1.64183e19 | −0.700337 | ||||||||
\(956\) | 7.63957e19 | 3.23663 | ||||||||
\(957\) | −2.22248e19 | −0.935212 | ||||||||
\(958\) | −7.02944e19 | −2.93795 | ||||||||
\(959\) | 3.60983e18 | 0.149853 | ||||||||
\(960\) | 2.65480e18 | 0.109464 | ||||||||
\(961\) | −1.75270e19 | −0.717804 | ||||||||
\(962\) | −4.22582e18 | −0.171899 | ||||||||
\(963\) | 2.23158e19 | 0.901658 | ||||||||
\(964\) | 1.89543e19 | 0.760689 | ||||||||
\(965\) | −4.51826e19 | −1.80112 | ||||||||
\(966\) | 4.72222e19 | 1.86980 | ||||||||
\(967\) | 4.11667e19 | 1.61910 | 0.809551 | − | 0.587049i | \(-0.199710\pi\) | ||||
0.809551 | + | 0.587049i | \(0.199710\pi\) | |||||||
\(968\) | −2.17155e18 | −0.0848360 | ||||||||
\(969\) | 1.35933e18 | 0.0527497 | ||||||||
\(970\) | 6.35464e19 | 2.44949 | ||||||||
\(971\) | −4.24821e19 | −1.62660 | −0.813301 | − | 0.581843i | \(-0.802332\pi\) | ||||
−0.813301 | + | 0.581843i | \(0.802332\pi\) | |||||||
\(972\) | −5.93972e19 | −2.25910 | ||||||||
\(973\) | 1.42493e19 | 0.538344 | ||||||||
\(974\) | 2.67399e19 | 1.00352 | ||||||||
\(975\) | 4.13228e18 | 0.154049 | ||||||||
\(976\) | −3.09455e19 | −1.14597 | ||||||||
\(977\) | 3.96415e19 | 1.45826 | 0.729131 | − | 0.684374i | \(-0.239925\pi\) | ||||
0.729131 | + | 0.684374i | \(0.239925\pi\) | |||||||
\(978\) | 4.89515e19 | 1.78881 | ||||||||
\(979\) | 1.08731e19 | 0.394698 | ||||||||
\(980\) | 1.99773e19 | 0.720389 | ||||||||
\(981\) | 2.62136e19 | 0.939027 | ||||||||
\(982\) | 8.96920e19 | 3.19175 | ||||||||
\(983\) | 5.12783e19 | 1.81274 | 0.906371 | − | 0.422482i | \(-0.138841\pi\) | ||||
0.906371 | + | 0.422482i | \(0.138841\pi\) | |||||||
\(984\) | −2.34559e19 | −0.823727 | ||||||||
\(985\) | −2.48385e18 | −0.0866543 | ||||||||
\(986\) | −1.50314e19 | −0.520955 | ||||||||
\(987\) | −3.16056e19 | −1.08818 | ||||||||
\(988\) | −1.67788e19 | −0.573905 | ||||||||
\(989\) | 4.71646e19 | 1.60266 | ||||||||
\(990\) | −4.28250e19 | −1.44567 | ||||||||
\(991\) | −3.75390e19 | −1.25894 | −0.629469 | − | 0.777026i | \(-0.716727\pi\) | ||||
−0.629469 | + | 0.777026i | \(0.716727\pi\) | |||||||
\(992\) | 1.37321e19 | 0.457522 | ||||||||
\(993\) | 3.04649e19 | 1.00839 | ||||||||
\(994\) | −9.60705e17 | −0.0315921 | ||||||||
\(995\) | −4.03007e19 | −1.31663 | ||||||||
\(996\) | −4.19639e19 | −1.36204 | ||||||||
\(997\) | −3.80050e19 | −1.22553 | −0.612763 | − | 0.790266i | \(-0.709942\pi\) | ||||
−0.612763 | + | 0.790266i | \(0.709942\pi\) | |||||||
\(998\) | 1.36738e19 | 0.438067 | ||||||||
\(999\) | −5.40752e18 | −0.172117 |
(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 | 197.14.a.a.1.8 | ✓ | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.14.a.a.1.8 | ✓ | 104 | 1.1 | even | 1 | trivial |