Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(91.1613430010\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 11.8993 | 0.525879 | 0.262940 | − | 0.964812i | \(-0.415308\pi\) | ||||
0.262940 | + | 0.964812i | \(0.415308\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | −370.407 | −0.723451 | ||||||||
\(5\) | −236.774 | −0.169422 | −0.0847108 | − | 0.996406i | \(-0.526997\pi\) | ||||
−0.0847108 | + | 0.996406i | \(0.526997\pi\) | |||||||
\(6\) | −963.842 | −0.303617 | ||||||||
\(7\) | 4185.56 | 0.658889 | 0.329444 | − | 0.944175i | \(-0.393139\pi\) | ||||
0.329444 | + | 0.944175i | \(0.393139\pi\) | |||||||
\(8\) | −10500.0 | −0.906327 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −2817.44 | −0.0890952 | ||||||||
\(11\) | −25832.4 | −0.531983 | −0.265992 | − | 0.963975i | \(-0.585699\pi\) | ||||
−0.265992 | + | 0.963975i | \(0.585699\pi\) | |||||||
\(12\) | 30003.0 | 0.417685 | ||||||||
\(13\) | 10977.2 | 0.106597 | 0.0532987 | − | 0.998579i | \(-0.483026\pi\) | ||||
0.0532987 | + | 0.998579i | \(0.483026\pi\) | |||||||
\(14\) | 49805.2 | 0.346496 | ||||||||
\(15\) | 19178.7 | 0.0978156 | ||||||||
\(16\) | 64705.7 | 0.246832 | ||||||||
\(17\) | −74869.7 | −0.217413 | −0.108707 | − | 0.994074i | \(-0.534671\pi\) | ||||
−0.108707 | + | 0.994074i | \(0.534671\pi\) | |||||||
\(18\) | 78071.2 | 0.175293 | ||||||||
\(19\) | 575877. | 1.01377 | 0.506884 | − | 0.862014i | \(-0.330797\pi\) | ||||
0.506884 | + | 0.862014i | \(0.330797\pi\) | |||||||
\(20\) | 87702.6 | 0.122568 | ||||||||
\(21\) | −339030. | −0.380410 | ||||||||
\(22\) | −307387. | −0.279759 | ||||||||
\(23\) | 1.18652e6 | 0.884098 | 0.442049 | − | 0.896991i | \(-0.354252\pi\) | ||||
0.442049 | + | 0.896991i | \(0.354252\pi\) | |||||||
\(24\) | 850501. | 0.523268 | ||||||||
\(25\) | −1.89706e6 | −0.971296 | ||||||||
\(26\) | 130621. | 0.0560573 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | −1.55036e6 | −0.476674 | ||||||||
\(29\) | 971729. | 0.255126 | 0.127563 | − | 0.991830i | \(-0.459285\pi\) | ||||
0.127563 | + | 0.991830i | \(0.459285\pi\) | |||||||
\(30\) | 228213. | 0.0514392 | ||||||||
\(31\) | 7.66093e6 | 1.48989 | 0.744944 | − | 0.667127i | \(-0.232476\pi\) | ||||
0.744944 | + | 0.667127i | \(0.232476\pi\) | |||||||
\(32\) | 6.14596e6 | 1.03613 | ||||||||
\(33\) | 2.09243e6 | 0.307141 | ||||||||
\(34\) | −890896. | −0.114333 | ||||||||
\(35\) | −991030. | −0.111630 | ||||||||
\(36\) | −2.43024e6 | −0.241150 | ||||||||
\(37\) | −1.34632e7 | −1.18097 | −0.590487 | − | 0.807047i | \(-0.701064\pi\) | ||||
−0.590487 | + | 0.807047i | \(0.701064\pi\) | |||||||
\(38\) | 6.85252e6 | 0.533119 | ||||||||
\(39\) | −889153. | −0.0615440 | ||||||||
\(40\) | 2.48613e6 | 0.153551 | ||||||||
\(41\) | 3.71716e6 | 0.205439 | 0.102720 | − | 0.994710i | \(-0.467246\pi\) | ||||
0.102720 | + | 0.994710i | \(0.467246\pi\) | |||||||
\(42\) | −4.03422e6 | −0.200050 | ||||||||
\(43\) | 1.42413e7 | 0.635248 | 0.317624 | − | 0.948217i | \(-0.397115\pi\) | ||||
0.317624 | + | 0.948217i | \(0.397115\pi\) | |||||||
\(44\) | 9.56851e6 | 0.384864 | ||||||||
\(45\) | −1.55347e6 | −0.0564738 | ||||||||
\(46\) | 1.41188e7 | 0.464929 | ||||||||
\(47\) | 5.03480e7 | 1.50502 | 0.752510 | − | 0.658581i | \(-0.228843\pi\) | ||||
0.752510 | + | 0.658581i | \(0.228843\pi\) | |||||||
\(48\) | −5.24116e6 | −0.142509 | ||||||||
\(49\) | −2.28347e7 | −0.565866 | ||||||||
\(50\) | −2.25737e7 | −0.510785 | ||||||||
\(51\) | 6.06445e6 | 0.125524 | ||||||||
\(52\) | −4.06603e6 | −0.0771180 | ||||||||
\(53\) | −4.53012e7 | −0.788622 | −0.394311 | − | 0.918977i | \(-0.629017\pi\) | ||||
−0.394311 | + | 0.918977i | \(0.629017\pi\) | |||||||
\(54\) | −6.32377e6 | −0.101206 | ||||||||
\(55\) | 6.11644e6 | 0.0901294 | ||||||||
\(56\) | −4.39484e7 | −0.597169 | ||||||||
\(57\) | −4.66460e7 | −0.585299 | ||||||||
\(58\) | 1.15629e7 | 0.134165 | ||||||||
\(59\) | −1.21174e7 | −0.130189 | ||||||||
\(60\) | −7.10391e6 | −0.0707648 | ||||||||
\(61\) | −1.39439e8 | −1.28944 | −0.644718 | − | 0.764421i | \(-0.723025\pi\) | ||||
−0.644718 | + | 0.764421i | \(0.723025\pi\) | |||||||
\(62\) | 9.11596e7 | 0.783501 | ||||||||
\(63\) | 2.74614e7 | 0.219630 | ||||||||
\(64\) | 4.00032e7 | 0.298047 | ||||||||
\(65\) | −2.59911e6 | −0.0180599 | ||||||||
\(66\) | 2.48984e7 | 0.161519 | ||||||||
\(67\) | −1.76510e8 | −1.07012 | −0.535060 | − | 0.844814i | \(-0.679711\pi\) | ||||
−0.535060 | + | 0.844814i | \(0.679711\pi\) | |||||||
\(68\) | 2.77323e7 | 0.157288 | ||||||||
\(69\) | −9.61083e7 | −0.510434 | ||||||||
\(70\) | −1.17926e7 | −0.0587039 | ||||||||
\(71\) | −4.76874e7 | −0.222711 | −0.111355 | − | 0.993781i | \(-0.535519\pi\) | ||||
−0.111355 | + | 0.993781i | \(0.535519\pi\) | |||||||
\(72\) | −6.88906e7 | −0.302109 | ||||||||
\(73\) | −1.70848e8 | −0.704136 | −0.352068 | − | 0.935974i | \(-0.614521\pi\) | ||||
−0.352068 | + | 0.935974i | \(0.614521\pi\) | |||||||
\(74\) | −1.60202e8 | −0.621049 | ||||||||
\(75\) | 1.53662e8 | 0.560778 | ||||||||
\(76\) | −2.13309e8 | −0.733411 | ||||||||
\(77\) | −1.08123e8 | −0.350518 | ||||||||
\(78\) | −1.05803e7 | −0.0323647 | ||||||||
\(79\) | −7.11694e7 | −0.205576 | −0.102788 | − | 0.994703i | \(-0.532776\pi\) | ||||
−0.102788 | + | 0.994703i | \(0.532776\pi\) | |||||||
\(80\) | −1.53206e7 | −0.0418187 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 4.42315e7 | 0.108036 | ||||||||
\(83\) | −3.04121e8 | −0.703388 | −0.351694 | − | 0.936115i | \(-0.614394\pi\) | ||||
−0.351694 | + | 0.936115i | \(0.614394\pi\) | |||||||
\(84\) | 1.25579e8 | 0.275208 | ||||||||
\(85\) | 1.77272e7 | 0.0368345 | ||||||||
\(86\) | 1.69462e8 | 0.334064 | ||||||||
\(87\) | −7.87100e7 | −0.147297 | ||||||||
\(88\) | 2.71241e8 | 0.482151 | ||||||||
\(89\) | −6.08801e8 | −1.02854 | −0.514269 | − | 0.857629i | \(-0.671937\pi\) | ||||
−0.514269 | + | 0.857629i | \(0.671937\pi\) | |||||||
\(90\) | −1.84852e7 | −0.0296984 | ||||||||
\(91\) | 4.59457e7 | 0.0702358 | ||||||||
\(92\) | −4.39496e8 | −0.639602 | ||||||||
\(93\) | −6.20535e8 | −0.860187 | ||||||||
\(94\) | 5.99106e8 | 0.791459 | ||||||||
\(95\) | −1.36353e8 | −0.171754 | ||||||||
\(96\) | −4.97823e8 | −0.598211 | ||||||||
\(97\) | −5.99259e8 | −0.687293 | −0.343646 | − | 0.939099i | \(-0.611662\pi\) | ||||
−0.343646 | + | 0.939099i | \(0.611662\pi\) | |||||||
\(98\) | −2.71717e8 | −0.297577 | ||||||||
\(99\) | −1.69487e8 | −0.177328 | ||||||||
\(100\) | 7.02685e8 | 0.702685 | ||||||||
\(101\) | −1.03425e9 | −0.988965 | −0.494483 | − | 0.869188i | \(-0.664642\pi\) | ||||
−0.494483 | + | 0.869188i | \(0.664642\pi\) | |||||||
\(102\) | 7.21626e7 | 0.0660102 | ||||||||
\(103\) | 1.11407e8 | 0.0975318 | 0.0487659 | − | 0.998810i | \(-0.484471\pi\) | ||||
0.0487659 | + | 0.998810i | \(0.484471\pi\) | |||||||
\(104\) | −1.15261e8 | −0.0966121 | ||||||||
\(105\) | 8.02734e7 | 0.0644496 | ||||||||
\(106\) | −5.39053e8 | −0.414720 | ||||||||
\(107\) | −4.84503e8 | −0.357330 | −0.178665 | − | 0.983910i | \(-0.557178\pi\) | ||||
−0.178665 | + | 0.983910i | \(0.557178\pi\) | |||||||
\(108\) | 1.96849e8 | 0.139228 | ||||||||
\(109\) | 1.80758e9 | 1.22653 | 0.613264 | − | 0.789878i | \(-0.289856\pi\) | ||||
0.613264 | + | 0.789878i | \(0.289856\pi\) | |||||||
\(110\) | 7.27813e7 | 0.0473972 | ||||||||
\(111\) | 1.09052e9 | 0.681835 | ||||||||
\(112\) | 2.70829e8 | 0.162635 | ||||||||
\(113\) | −5.89242e8 | −0.339970 | −0.169985 | − | 0.985447i | \(-0.554372\pi\) | ||||
−0.169985 | + | 0.985447i | \(0.554372\pi\) | |||||||
\(114\) | −5.55054e8 | −0.307797 | ||||||||
\(115\) | −2.80937e8 | −0.149785 | ||||||||
\(116\) | −3.59935e8 | −0.184571 | ||||||||
\(117\) | 7.20214e7 | 0.0355324 | ||||||||
\(118\) | −1.44188e8 | −0.0684636 | ||||||||
\(119\) | −3.13371e8 | −0.143251 | ||||||||
\(120\) | −2.01376e8 | −0.0886529 | ||||||||
\(121\) | −1.69063e9 | −0.716994 | ||||||||
\(122\) | −1.65922e9 | −0.678087 | ||||||||
\(123\) | −3.01090e8 | −0.118610 | ||||||||
\(124\) | −2.83766e9 | −1.07786 | ||||||||
\(125\) | 9.11624e8 | 0.333980 | ||||||||
\(126\) | 3.26772e8 | 0.115499 | ||||||||
\(127\) | −2.92506e9 | −0.997743 | −0.498871 | − | 0.866676i | \(-0.666252\pi\) | ||||
−0.498871 | + | 0.866676i | \(0.666252\pi\) | |||||||
\(128\) | −2.67072e9 | −0.879394 | ||||||||
\(129\) | −1.15355e9 | −0.366760 | ||||||||
\(130\) | −3.09276e7 | −0.00949732 | ||||||||
\(131\) | 6.59454e9 | 1.95643 | 0.978214 | − | 0.207599i | \(-0.0665650\pi\) | ||||
0.978214 | + | 0.207599i | \(0.0665650\pi\) | |||||||
\(132\) | −7.75049e8 | −0.222201 | ||||||||
\(133\) | 2.41037e9 | 0.667960 | ||||||||
\(134\) | −2.10034e9 | −0.562754 | ||||||||
\(135\) | 1.25831e8 | 0.0326052 | ||||||||
\(136\) | 7.86133e8 | 0.197047 | ||||||||
\(137\) | −3.35904e9 | −0.814652 | −0.407326 | − | 0.913283i | \(-0.633539\pi\) | ||||
−0.407326 | + | 0.913283i | \(0.633539\pi\) | |||||||
\(138\) | −1.14362e9 | −0.268427 | ||||||||
\(139\) | 6.25873e9 | 1.42207 | 0.711033 | − | 0.703159i | \(-0.248228\pi\) | ||||
0.711033 | + | 0.703159i | \(0.248228\pi\) | |||||||
\(140\) | 3.67084e8 | 0.0807588 | ||||||||
\(141\) | −4.07819e9 | −0.868924 | ||||||||
\(142\) | −5.67447e8 | −0.117119 | ||||||||
\(143\) | −2.83568e8 | −0.0567080 | ||||||||
\(144\) | 4.24534e8 | 0.0822775 | ||||||||
\(145\) | −2.30080e8 | −0.0432238 | ||||||||
\(146\) | −2.03297e9 | −0.370290 | ||||||||
\(147\) | 1.84961e9 | 0.326703 | ||||||||
\(148\) | 4.98686e9 | 0.854376 | ||||||||
\(149\) | −1.91528e8 | −0.0318341 | −0.0159171 | − | 0.999873i | \(-0.505067\pi\) | ||||
−0.0159171 | + | 0.999873i | \(0.505067\pi\) | |||||||
\(150\) | 1.82847e9 | 0.294902 | ||||||||
\(151\) | −5.18282e9 | −0.811279 | −0.405639 | − | 0.914033i | \(-0.632951\pi\) | ||||
−0.405639 | + | 0.914033i | \(0.632951\pi\) | |||||||
\(152\) | −6.04672e9 | −0.918805 | ||||||||
\(153\) | −4.91220e8 | −0.0724711 | ||||||||
\(154\) | −1.28659e9 | −0.184330 | ||||||||
\(155\) | −1.81391e9 | −0.252419 | ||||||||
\(156\) | 3.29348e8 | 0.0445241 | ||||||||
\(157\) | 6.75931e9 | 0.887879 | 0.443940 | − | 0.896057i | \(-0.353580\pi\) | ||||
0.443940 | + | 0.896057i | \(0.353580\pi\) | |||||||
\(158\) | −8.46865e8 | −0.108108 | ||||||||
\(159\) | 3.66940e9 | 0.455311 | ||||||||
\(160\) | −1.45520e9 | −0.175543 | ||||||||
\(161\) | 4.96626e9 | 0.582522 | ||||||||
\(162\) | 5.12225e8 | 0.0584310 | ||||||||
\(163\) | −1.32321e10 | −1.46819 | −0.734097 | − | 0.679045i | \(-0.762394\pi\) | ||||
−0.734097 | + | 0.679045i | \(0.762394\pi\) | |||||||
\(164\) | −1.37686e9 | −0.148625 | ||||||||
\(165\) | −4.95432e8 | −0.0520362 | ||||||||
\(166\) | −3.61882e9 | −0.369897 | ||||||||
\(167\) | −1.29087e10 | −1.28427 | −0.642137 | − | 0.766590i | \(-0.721952\pi\) | ||||
−0.642137 | + | 0.766590i | \(0.721952\pi\) | |||||||
\(168\) | 3.55982e9 | 0.344776 | ||||||||
\(169\) | −1.04840e10 | −0.988637 | ||||||||
\(170\) | 2.10941e8 | 0.0193705 | ||||||||
\(171\) | 3.77833e9 | 0.337923 | ||||||||
\(172\) | −5.27509e9 | −0.459571 | ||||||||
\(173\) | 1.16986e10 | 0.992948 | 0.496474 | − | 0.868051i | \(-0.334628\pi\) | ||||
0.496474 | + | 0.868051i | \(0.334628\pi\) | |||||||
\(174\) | −9.36593e8 | −0.0774603 | ||||||||
\(175\) | −7.94027e9 | −0.639976 | ||||||||
\(176\) | −1.67150e9 | −0.131311 | ||||||||
\(177\) | 9.81506e8 | 0.0751646 | ||||||||
\(178\) | −7.24430e9 | −0.540887 | ||||||||
\(179\) | −1.47861e10 | −1.07650 | −0.538252 | − | 0.842784i | \(-0.680915\pi\) | ||||
−0.538252 | + | 0.842784i | \(0.680915\pi\) | |||||||
\(180\) | 5.75417e8 | 0.0408561 | ||||||||
\(181\) | 1.06044e10 | 0.734398 | 0.367199 | − | 0.930142i | \(-0.380317\pi\) | ||||
0.367199 | + | 0.930142i | \(0.380317\pi\) | |||||||
\(182\) | 5.46721e8 | 0.0369355 | ||||||||
\(183\) | 1.12945e10 | 0.744456 | ||||||||
\(184\) | −1.24585e10 | −0.801282 | ||||||||
\(185\) | 3.18773e9 | 0.200082 | ||||||||
\(186\) | −7.38393e9 | −0.452355 | ||||||||
\(187\) | 1.93407e9 | 0.115660 | ||||||||
\(188\) | −1.86493e10 | −1.08881 | ||||||||
\(189\) | −2.22438e9 | −0.126803 | ||||||||
\(190\) | −1.62250e9 | −0.0903219 | ||||||||
\(191\) | 1.74635e10 | 0.949471 | 0.474735 | − | 0.880129i | \(-0.342544\pi\) | ||||
0.474735 | + | 0.880129i | \(0.342544\pi\) | |||||||
\(192\) | −3.24026e9 | −0.172078 | ||||||||
\(193\) | 3.68522e9 | 0.191186 | 0.0955929 | − | 0.995421i | \(-0.469525\pi\) | ||||
0.0955929 | + | 0.995421i | \(0.469525\pi\) | |||||||
\(194\) | −7.13075e9 | −0.361433 | ||||||||
\(195\) | 2.10528e8 | 0.0104269 | ||||||||
\(196\) | 8.45814e9 | 0.409376 | ||||||||
\(197\) | −2.92499e10 | −1.38365 | −0.691826 | − | 0.722064i | \(-0.743194\pi\) | ||||
−0.691826 | + | 0.722064i | \(0.743194\pi\) | |||||||
\(198\) | −2.01677e9 | −0.0932530 | ||||||||
\(199\) | −3.10443e10 | −1.40328 | −0.701639 | − | 0.712533i | \(-0.747548\pi\) | ||||
−0.701639 | + | 0.712533i | \(0.747548\pi\) | |||||||
\(200\) | 1.99192e10 | 0.880312 | ||||||||
\(201\) | 1.42973e10 | 0.617834 | ||||||||
\(202\) | −1.23069e10 | −0.520076 | ||||||||
\(203\) | 4.06723e9 | 0.168099 | ||||||||
\(204\) | −2.24631e9 | −0.0908102 | ||||||||
\(205\) | −8.80125e8 | −0.0348058 | ||||||||
\(206\) | 1.32567e9 | 0.0512900 | ||||||||
\(207\) | 7.78477e9 | 0.294699 | ||||||||
\(208\) | 7.10287e8 | 0.0263117 | ||||||||
\(209\) | −1.48763e10 | −0.539308 | ||||||||
\(210\) | 9.55197e8 | 0.0338927 | ||||||||
\(211\) | −7.45417e9 | −0.258898 | −0.129449 | − | 0.991586i | \(-0.541321\pi\) | ||||
−0.129449 | + | 0.991586i | \(0.541321\pi\) | |||||||
\(212\) | 1.67799e10 | 0.570529 | ||||||||
\(213\) | 3.86268e9 | 0.128582 | ||||||||
\(214\) | −5.76524e9 | −0.187912 | ||||||||
\(215\) | −3.37198e9 | −0.107625 | ||||||||
\(216\) | 5.58014e9 | 0.174423 | ||||||||
\(217\) | 3.20652e10 | 0.981671 | ||||||||
\(218\) | 2.15089e10 | 0.645005 | ||||||||
\(219\) | 1.38387e10 | 0.406533 | ||||||||
\(220\) | −2.26557e9 | −0.0652042 | ||||||||
\(221\) | −8.21859e8 | −0.0231757 | ||||||||
\(222\) | 1.29764e10 | 0.358563 | ||||||||
\(223\) | −1.40269e10 | −0.379831 | −0.189915 | − | 0.981800i | \(-0.560821\pi\) | ||||
−0.189915 | + | 0.981800i | \(0.560821\pi\) | |||||||
\(224\) | 2.57243e10 | 0.682695 | ||||||||
\(225\) | −1.24466e10 | −0.323765 | ||||||||
\(226\) | −7.01156e9 | −0.178783 | ||||||||
\(227\) | −2.64313e9 | −0.0660696 | −0.0330348 | − | 0.999454i | \(-0.510517\pi\) | ||||
−0.0330348 | + | 0.999454i | \(0.510517\pi\) | |||||||
\(228\) | 1.72780e10 | 0.423435 | ||||||||
\(229\) | 7.05707e10 | 1.69576 | 0.847881 | − | 0.530187i | \(-0.177878\pi\) | ||||
0.847881 | + | 0.530187i | \(0.177878\pi\) | |||||||
\(230\) | −3.34295e9 | −0.0787690 | ||||||||
\(231\) | 8.75797e9 | 0.202372 | ||||||||
\(232\) | −1.02032e10 | −0.231227 | ||||||||
\(233\) | −4.79787e9 | −0.106647 | −0.0533233 | − | 0.998577i | \(-0.516981\pi\) | ||||
−0.0533233 | + | 0.998577i | \(0.516981\pi\) | |||||||
\(234\) | 8.57003e8 | 0.0186858 | ||||||||
\(235\) | −1.19211e10 | −0.254983 | ||||||||
\(236\) | 4.48835e9 | 0.0941853 | ||||||||
\(237\) | 5.76472e9 | 0.118689 | ||||||||
\(238\) | −3.72890e9 | −0.0753328 | ||||||||
\(239\) | −6.36448e10 | −1.26175 | −0.630874 | − | 0.775885i | \(-0.717303\pi\) | ||||
−0.630874 | + | 0.775885i | \(0.717303\pi\) | |||||||
\(240\) | 1.24097e9 | 0.0241441 | ||||||||
\(241\) | −3.20440e10 | −0.611885 | −0.305942 | − | 0.952050i | \(-0.598971\pi\) | ||||
−0.305942 | + | 0.952050i | \(0.598971\pi\) | |||||||
\(242\) | −2.01173e10 | −0.377052 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 5.16491e10 | 0.932843 | ||||||||
\(245\) | 5.40666e9 | 0.0958698 | ||||||||
\(246\) | −3.58275e9 | −0.0623748 | ||||||||
\(247\) | 6.32151e9 | 0.108065 | ||||||||
\(248\) | −8.04398e10 | −1.35033 | ||||||||
\(249\) | 2.46338e10 | 0.406101 | ||||||||
\(250\) | 1.08477e10 | 0.175633 | ||||||||
\(251\) | 6.51872e10 | 1.03665 | 0.518323 | − | 0.855185i | \(-0.326557\pi\) | ||||
0.518323 | + | 0.855185i | \(0.326557\pi\) | |||||||
\(252\) | −1.01719e10 | −0.158891 | ||||||||
\(253\) | −3.06507e10 | −0.470326 | ||||||||
\(254\) | −3.48062e10 | −0.524692 | ||||||||
\(255\) | −1.43590e9 | −0.0212664 | ||||||||
\(256\) | −5.22613e10 | −0.760503 | ||||||||
\(257\) | −4.28183e10 | −0.612252 | −0.306126 | − | 0.951991i | \(-0.599033\pi\) | ||||
−0.306126 | + | 0.951991i | \(0.599033\pi\) | |||||||
\(258\) | −1.37264e10 | −0.192872 | ||||||||
\(259\) | −5.63509e10 | −0.778130 | ||||||||
\(260\) | 9.62729e8 | 0.0130654 | ||||||||
\(261\) | 6.37551e9 | 0.0850419 | ||||||||
\(262\) | 7.84704e10 | 1.02884 | ||||||||
\(263\) | 1.34491e11 | 1.73338 | 0.866689 | − | 0.498849i | \(-0.166244\pi\) | ||||
0.866689 | + | 0.498849i | \(0.166244\pi\) | |||||||
\(264\) | −2.19705e10 | −0.278370 | ||||||||
\(265\) | 1.07261e10 | 0.133609 | ||||||||
\(266\) | 2.86816e10 | 0.351266 | ||||||||
\(267\) | 4.93129e10 | 0.593827 | ||||||||
\(268\) | 6.53805e10 | 0.774179 | ||||||||
\(269\) | 1.08095e11 | 1.25869 | 0.629346 | − | 0.777126i | \(-0.283323\pi\) | ||||
0.629346 | + | 0.777126i | \(0.283323\pi\) | |||||||
\(270\) | 1.49730e9 | 0.0171464 | ||||||||
\(271\) | 4.11140e10 | 0.463050 | 0.231525 | − | 0.972829i | \(-0.425628\pi\) | ||||
0.231525 | + | 0.972829i | \(0.425628\pi\) | |||||||
\(272\) | −4.84449e9 | −0.0536646 | ||||||||
\(273\) | −3.72160e9 | −0.0405507 | ||||||||
\(274\) | −3.99701e10 | −0.428408 | ||||||||
\(275\) | 4.90057e10 | 0.516714 | ||||||||
\(276\) | 3.55992e10 | 0.369274 | ||||||||
\(277\) | 1.37905e11 | 1.40741 | 0.703703 | − | 0.710494i | \(-0.251528\pi\) | ||||
0.703703 | + | 0.710494i | \(0.251528\pi\) | |||||||
\(278\) | 7.44745e10 | 0.747835 | ||||||||
\(279\) | 5.02633e10 | 0.496629 | ||||||||
\(280\) | 1.04058e10 | 0.101173 | ||||||||
\(281\) | 3.43222e10 | 0.328395 | 0.164197 | − | 0.986427i | \(-0.447497\pi\) | ||||
0.164197 | + | 0.986427i | \(0.447497\pi\) | |||||||
\(282\) | −4.85276e10 | −0.456949 | ||||||||
\(283\) | 2.76964e10 | 0.256675 | 0.128338 | − | 0.991731i | \(-0.459036\pi\) | ||||
0.128338 | + | 0.991731i | \(0.459036\pi\) | |||||||
\(284\) | 1.76638e10 | 0.161120 | ||||||||
\(285\) | 1.10446e10 | 0.0991622 | ||||||||
\(286\) | −3.37425e9 | −0.0298216 | ||||||||
\(287\) | 1.55584e10 | 0.135362 | ||||||||
\(288\) | 4.03236e10 | 0.345377 | ||||||||
\(289\) | −1.12982e11 | −0.952731 | ||||||||
\(290\) | −2.73779e9 | −0.0227305 | ||||||||
\(291\) | 4.85400e10 | 0.396809 | ||||||||
\(292\) | 6.32832e10 | 0.509408 | ||||||||
\(293\) | 4.86080e10 | 0.385304 | 0.192652 | − | 0.981267i | \(-0.438291\pi\) | ||||
0.192652 | + | 0.981267i | \(0.438291\pi\) | |||||||
\(294\) | 2.20091e10 | 0.171806 | ||||||||
\(295\) | 2.86907e9 | 0.0220568 | ||||||||
\(296\) | 1.41364e11 | 1.07035 | ||||||||
\(297\) | 1.37284e10 | 0.102380 | ||||||||
\(298\) | −2.27904e9 | −0.0167409 | ||||||||
\(299\) | 1.30247e10 | 0.0942425 | ||||||||
\(300\) | −5.69175e10 | −0.405696 | ||||||||
\(301\) | 5.96080e10 | 0.418558 | ||||||||
\(302\) | −6.16719e10 | −0.426635 | ||||||||
\(303\) | 8.37746e10 | 0.570979 | ||||||||
\(304\) | 3.72625e10 | 0.250231 | ||||||||
\(305\) | 3.30155e10 | 0.218458 | ||||||||
\(306\) | −5.84517e9 | −0.0381110 | ||||||||
\(307\) | 7.92006e10 | 0.508869 | 0.254434 | − | 0.967090i | \(-0.418111\pi\) | ||||
0.254434 | + | 0.967090i | \(0.418111\pi\) | |||||||
\(308\) | 4.00495e10 | 0.253583 | ||||||||
\(309\) | −9.02399e9 | −0.0563100 | ||||||||
\(310\) | −2.15842e10 | −0.132742 | ||||||||
\(311\) | 1.37118e11 | 0.831140 | 0.415570 | − | 0.909561i | \(-0.363582\pi\) | ||||
0.415570 | + | 0.909561i | \(0.363582\pi\) | |||||||
\(312\) | 9.33612e9 | 0.0557790 | ||||||||
\(313\) | −1.44336e11 | −0.850010 | −0.425005 | − | 0.905191i | \(-0.639728\pi\) | ||||
−0.425005 | + | 0.905191i | \(0.639728\pi\) | |||||||
\(314\) | 8.04310e10 | 0.466917 | ||||||||
\(315\) | −6.50215e9 | −0.0372100 | ||||||||
\(316\) | 2.63616e10 | 0.148724 | ||||||||
\(317\) | 6.54419e9 | 0.0363990 | 0.0181995 | − | 0.999834i | \(-0.494207\pi\) | ||||
0.0181995 | + | 0.999834i | \(0.494207\pi\) | |||||||
\(318\) | 4.36633e10 | 0.239439 | ||||||||
\(319\) | −2.51021e10 | −0.135723 | ||||||||
\(320\) | −9.47172e9 | −0.0504956 | ||||||||
\(321\) | 3.92447e10 | 0.206305 | ||||||||
\(322\) | 5.90949e10 | 0.306336 | ||||||||
\(323\) | −4.31157e10 | −0.220406 | ||||||||
\(324\) | −1.59448e10 | −0.0803835 | ||||||||
\(325\) | −2.08244e10 | −0.103538 | ||||||||
\(326\) | −1.57452e11 | −0.772092 | ||||||||
\(327\) | −1.46414e11 | −0.708136 | ||||||||
\(328\) | −3.90302e10 | −0.186195 | ||||||||
\(329\) | 2.10735e11 | 0.991641 | ||||||||
\(330\) | −5.89528e9 | −0.0273648 | ||||||||
\(331\) | −2.27735e11 | −1.04281 | −0.521403 | − | 0.853310i | \(-0.674591\pi\) | ||||
−0.521403 | + | 0.853310i | \(0.674591\pi\) | |||||||
\(332\) | 1.12648e11 | 0.508866 | ||||||||
\(333\) | −8.83320e10 | −0.393658 | ||||||||
\(334\) | −1.53604e11 | −0.675373 | ||||||||
\(335\) | 4.17929e10 | 0.181301 | ||||||||
\(336\) | −2.19372e10 | −0.0938974 | ||||||||
\(337\) | 4.60566e10 | 0.194517 | 0.0972585 | − | 0.995259i | \(-0.468993\pi\) | ||||
0.0972585 | + | 0.995259i | \(0.468993\pi\) | |||||||
\(338\) | −1.24752e11 | −0.519904 | ||||||||
\(339\) | 4.77286e10 | 0.196282 | ||||||||
\(340\) | −6.56627e9 | −0.0266479 | ||||||||
\(341\) | −1.97900e11 | −0.792596 | ||||||||
\(342\) | 4.49594e10 | 0.177706 | ||||||||
\(343\) | −2.64478e11 | −1.03173 | ||||||||
\(344\) | −1.49534e11 | −0.575742 | ||||||||
\(345\) | 2.27559e10 | 0.0864786 | ||||||||
\(346\) | 1.39205e11 | 0.522171 | ||||||||
\(347\) | 1.44580e11 | 0.535335 | 0.267668 | − | 0.963511i | \(-0.413747\pi\) | ||||
0.267668 | + | 0.963511i | \(0.413747\pi\) | |||||||
\(348\) | 2.91547e10 | 0.106562 | ||||||||
\(349\) | −4.92873e11 | −1.77836 | −0.889182 | − | 0.457553i | \(-0.848726\pi\) | ||||
−0.889182 | + | 0.457553i | \(0.848726\pi\) | |||||||
\(350\) | −9.44835e10 | −0.336550 | ||||||||
\(351\) | −5.83373e9 | −0.0205147 | ||||||||
\(352\) | −1.58765e11 | −0.551205 | ||||||||
\(353\) | −5.00845e11 | −1.71679 | −0.858395 | − | 0.512989i | \(-0.828538\pi\) | ||||
−0.858395 | + | 0.512989i | \(0.828538\pi\) | |||||||
\(354\) | 1.16792e10 | 0.0395275 | ||||||||
\(355\) | 1.12911e10 | 0.0377320 | ||||||||
\(356\) | 2.25504e11 | 0.744097 | ||||||||
\(357\) | 2.53831e10 | 0.0827061 | ||||||||
\(358\) | −1.75944e11 | −0.566111 | ||||||||
\(359\) | 1.96532e11 | 0.624466 | 0.312233 | − | 0.950006i | \(-0.398923\pi\) | ||||
0.312233 | + | 0.950006i | \(0.398923\pi\) | |||||||
\(360\) | 1.63115e10 | 0.0511838 | ||||||||
\(361\) | 8.94644e9 | 0.0277247 | ||||||||
\(362\) | 1.26185e11 | 0.386205 | ||||||||
\(363\) | 1.36941e11 | 0.413956 | ||||||||
\(364\) | −1.70186e10 | −0.0508122 | ||||||||
\(365\) | 4.04523e10 | 0.119296 | ||||||||
\(366\) | 1.34397e11 | 0.391494 | ||||||||
\(367\) | 4.01737e11 | 1.15596 | 0.577982 | − | 0.816050i | \(-0.303840\pi\) | ||||
0.577982 | + | 0.816050i | \(0.303840\pi\) | |||||||
\(368\) | 7.67747e10 | 0.218224 | ||||||||
\(369\) | 2.43883e10 | 0.0684798 | ||||||||
\(370\) | 3.79317e10 | 0.105219 | ||||||||
\(371\) | −1.89611e11 | −0.519614 | ||||||||
\(372\) | 2.29851e11 | 0.622303 | ||||||||
\(373\) | −2.55522e11 | −0.683500 | −0.341750 | − | 0.939791i | \(-0.611020\pi\) | ||||
−0.341750 | + | 0.939791i | \(0.611020\pi\) | |||||||
\(374\) | 2.30140e10 | 0.0608233 | ||||||||
\(375\) | −7.38415e10 | −0.192823 | ||||||||
\(376\) | −5.28655e11 | −1.36404 | ||||||||
\(377\) | 1.06669e10 | 0.0271957 | ||||||||
\(378\) | −2.64685e10 | −0.0666832 | ||||||||
\(379\) | −4.55440e11 | −1.13385 | −0.566924 | − | 0.823770i | \(-0.691867\pi\) | ||||
−0.566924 | + | 0.823770i | \(0.691867\pi\) | |||||||
\(380\) | 5.05059e10 | 0.124256 | ||||||||
\(381\) | 2.36930e11 | 0.576047 | ||||||||
\(382\) | 2.07803e11 | 0.499307 | ||||||||
\(383\) | −4.42583e11 | −1.05099 | −0.525497 | − | 0.850795i | \(-0.676121\pi\) | ||||
−0.525497 | + | 0.850795i | \(0.676121\pi\) | |||||||
\(384\) | 2.16328e11 | 0.507719 | ||||||||
\(385\) | 2.56007e10 | 0.0593853 | ||||||||
\(386\) | 4.38515e10 | 0.100541 | ||||||||
\(387\) | 9.34375e10 | 0.211749 | ||||||||
\(388\) | 2.21970e11 | 0.497223 | ||||||||
\(389\) | −1.20591e11 | −0.267018 | −0.133509 | − | 0.991048i | \(-0.542625\pi\) | ||||
−0.133509 | + | 0.991048i | \(0.542625\pi\) | |||||||
\(390\) | 2.50513e9 | 0.00548328 | ||||||||
\(391\) | −8.88346e10 | −0.192215 | ||||||||
\(392\) | 2.39765e11 | 0.512859 | ||||||||
\(393\) | −5.34158e11 | −1.12954 | ||||||||
\(394\) | −3.48053e11 | −0.727634 | ||||||||
\(395\) | 1.68510e10 | 0.0348289 | ||||||||
\(396\) | 6.27790e10 | 0.128288 | ||||||||
\(397\) | −4.20019e11 | −0.848617 | −0.424308 | − | 0.905518i | \(-0.639483\pi\) | ||||
−0.424308 | + | 0.905518i | \(0.639483\pi\) | |||||||
\(398\) | −3.69406e11 | −0.737954 | ||||||||
\(399\) | −1.95240e11 | −0.385647 | ||||||||
\(400\) | −1.22751e11 | −0.239747 | ||||||||
\(401\) | 4.58107e11 | 0.884743 | 0.442372 | − | 0.896832i | \(-0.354137\pi\) | ||||
0.442372 | + | 0.896832i | \(0.354137\pi\) | |||||||
\(402\) | 1.70128e11 | 0.324906 | ||||||||
\(403\) | 8.40955e10 | 0.158818 | ||||||||
\(404\) | 3.83095e11 | 0.715468 | ||||||||
\(405\) | −1.01923e10 | −0.0188246 | ||||||||
\(406\) | 4.83971e10 | 0.0884000 | ||||||||
\(407\) | 3.47787e11 | 0.628258 | ||||||||
\(408\) | −6.36768e10 | −0.113765 | ||||||||
\(409\) | −6.42534e11 | −1.13538 | −0.567690 | − | 0.823243i | \(-0.692163\pi\) | ||||
−0.567690 | + | 0.823243i | \(0.692163\pi\) | |||||||
\(410\) | −1.04729e10 | −0.0183037 | ||||||||
\(411\) | 2.72082e11 | 0.470339 | ||||||||
\(412\) | −4.12661e10 | −0.0705595 | ||||||||
\(413\) | −5.07179e10 | −0.0857800 | ||||||||
\(414\) | 9.26332e10 | 0.154976 | ||||||||
\(415\) | 7.20078e10 | 0.119169 | ||||||||
\(416\) | 6.74654e10 | 0.110449 | ||||||||
\(417\) | −5.06957e11 | −0.821030 | ||||||||
\(418\) | −1.77017e11 | −0.283611 | ||||||||
\(419\) | −1.02142e12 | −1.61898 | −0.809488 | − | 0.587136i | \(-0.800255\pi\) | ||||
−0.809488 | + | 0.587136i | \(0.800255\pi\) | |||||||
\(420\) | −2.97338e10 | −0.0466261 | ||||||||
\(421\) | −4.44401e11 | −0.689454 | −0.344727 | − | 0.938703i | \(-0.612028\pi\) | ||||
−0.344727 | + | 0.938703i | \(0.612028\pi\) | |||||||
\(422\) | −8.86993e10 | −0.136149 | ||||||||
\(423\) | 3.30334e11 | 0.501673 | ||||||||
\(424\) | 4.75664e11 | 0.714749 | ||||||||
\(425\) | 1.42033e11 | 0.211173 | ||||||||
\(426\) | 4.59632e10 | 0.0676187 | ||||||||
\(427\) | −5.83629e11 | −0.849594 | ||||||||
\(428\) | 1.79463e11 | 0.258511 | ||||||||
\(429\) | 2.29690e10 | 0.0327404 | ||||||||
\(430\) | −4.01241e10 | −0.0565976 | ||||||||
\(431\) | 1.51261e11 | 0.211144 | 0.105572 | − | 0.994412i | \(-0.466333\pi\) | ||||
0.105572 | + | 0.994412i | \(0.466333\pi\) | |||||||
\(432\) | −3.43872e10 | −0.0475029 | ||||||||
\(433\) | −5.86010e11 | −0.801142 | −0.400571 | − | 0.916266i | \(-0.631188\pi\) | ||||
−0.400571 | + | 0.916266i | \(0.631188\pi\) | |||||||
\(434\) | 3.81554e11 | 0.516240 | ||||||||
\(435\) | 1.86365e10 | 0.0249552 | ||||||||
\(436\) | −6.69539e11 | −0.887332 | ||||||||
\(437\) | 6.83291e11 | 0.896270 | ||||||||
\(438\) | 1.64670e11 | 0.213787 | ||||||||
\(439\) | −1.29798e12 | −1.66793 | −0.833963 | − | 0.551820i | \(-0.813933\pi\) | ||||
−0.833963 | + | 0.551820i | \(0.813933\pi\) | |||||||
\(440\) | −6.42227e10 | −0.0816867 | ||||||||
\(441\) | −1.49819e11 | −0.188622 | ||||||||
\(442\) | −9.77954e9 | −0.0121876 | ||||||||
\(443\) | −4.17677e10 | −0.0515257 | −0.0257628 | − | 0.999668i | \(-0.508201\pi\) | ||||
−0.0257628 | + | 0.999668i | \(0.508201\pi\) | |||||||
\(444\) | −4.03935e11 | −0.493274 | ||||||||
\(445\) | 1.44148e11 | 0.174257 | ||||||||
\(446\) | −1.66910e11 | −0.199745 | ||||||||
\(447\) | 1.55137e10 | 0.0183795 | ||||||||
\(448\) | 1.67436e11 | 0.196380 | ||||||||
\(449\) | 2.60197e11 | 0.302130 | 0.151065 | − | 0.988524i | \(-0.451730\pi\) | ||||
0.151065 | + | 0.988524i | \(0.451730\pi\) | |||||||
\(450\) | −1.48106e11 | −0.170262 | ||||||||
\(451\) | −9.60232e10 | −0.109290 | ||||||||
\(452\) | 2.18259e11 | 0.245952 | ||||||||
\(453\) | 4.19809e11 | 0.468392 | ||||||||
\(454\) | −3.14513e10 | −0.0347446 | ||||||||
\(455\) | −1.08787e10 | −0.0118995 | ||||||||
\(456\) | 4.89784e11 | 0.530472 | ||||||||
\(457\) | −9.53046e11 | −1.02209 | −0.511047 | − | 0.859553i | \(-0.670742\pi\) | ||||
−0.511047 | + | 0.859553i | \(0.670742\pi\) | |||||||
\(458\) | 8.39741e11 | 0.891766 | ||||||||
\(459\) | 3.97888e10 | 0.0418412 | ||||||||
\(460\) | 1.04061e11 | 0.108362 | ||||||||
\(461\) | 4.57852e11 | 0.472140 | 0.236070 | − | 0.971736i | \(-0.424141\pi\) | ||||
0.236070 | + | 0.971736i | \(0.424141\pi\) | |||||||
\(462\) | 1.04214e11 | 0.106423 | ||||||||
\(463\) | −3.51961e11 | −0.355943 | −0.177971 | − | 0.984036i | \(-0.556953\pi\) | ||||
−0.177971 | + | 0.984036i | \(0.556953\pi\) | |||||||
\(464\) | 6.28763e10 | 0.0629733 | ||||||||
\(465\) | 1.46926e11 | 0.145734 | ||||||||
\(466\) | −5.70912e10 | −0.0560832 | ||||||||
\(467\) | 1.19947e11 | 0.116698 | 0.0583492 | − | 0.998296i | \(-0.481416\pi\) | ||||
0.0583492 | + | 0.998296i | \(0.481416\pi\) | |||||||
\(468\) | −2.66772e10 | −0.0257060 | ||||||||
\(469\) | −7.38792e11 | −0.705090 | ||||||||
\(470\) | −1.41853e11 | −0.134090 | ||||||||
\(471\) | −5.47504e11 | −0.512617 | ||||||||
\(472\) | 1.27232e11 | 0.117994 | ||||||||
\(473\) | −3.67889e11 | −0.337941 | ||||||||
\(474\) | 6.85961e10 | 0.0624161 | ||||||||
\(475\) | −1.09247e12 | −0.984669 | ||||||||
\(476\) | 1.16075e11 | 0.103635 | ||||||||
\(477\) | −2.97221e11 | −0.262874 | ||||||||
\(478\) | −7.57328e11 | −0.663527 | ||||||||
\(479\) | 1.99573e12 | 1.73218 | 0.866088 | − | 0.499892i | \(-0.166627\pi\) | ||||
0.866088 | + | 0.499892i | \(0.166627\pi\) | |||||||
\(480\) | 1.17871e11 | 0.101350 | ||||||||
\(481\) | −1.47788e11 | −0.125889 | ||||||||
\(482\) | −3.81300e11 | −0.321777 | ||||||||
\(483\) | −4.02267e11 | −0.336319 | ||||||||
\(484\) | 6.26222e11 | 0.518710 | ||||||||
\(485\) | 1.41889e11 | 0.116442 | ||||||||
\(486\) | −4.14903e10 | −0.0337352 | ||||||||
\(487\) | −6.44151e11 | −0.518929 | −0.259464 | − | 0.965753i | \(-0.583546\pi\) | ||||
−0.259464 | + | 0.965753i | \(0.583546\pi\) | |||||||
\(488\) | 1.46411e12 | 1.16865 | ||||||||
\(489\) | 1.07180e12 | 0.847662 | ||||||||
\(490\) | 6.43354e10 | 0.0504159 | ||||||||
\(491\) | 1.01386e11 | 0.0787244 | 0.0393622 | − | 0.999225i | \(-0.487467\pi\) | ||||
0.0393622 | + | 0.999225i | \(0.487467\pi\) | |||||||
\(492\) | 1.11526e11 | 0.0858088 | ||||||||
\(493\) | −7.27530e10 | −0.0554677 | ||||||||
\(494\) | 7.52215e10 | 0.0568291 | ||||||||
\(495\) | 4.01300e10 | 0.0300431 | ||||||||
\(496\) | 4.95705e11 | 0.367753 | ||||||||
\(497\) | −1.99599e11 | −0.146742 | ||||||||
\(498\) | 2.93124e11 | 0.213560 | ||||||||
\(499\) | −1.90534e12 | −1.37569 | −0.687845 | − | 0.725857i | \(-0.741443\pi\) | ||||
−0.687845 | + | 0.725857i | \(0.741443\pi\) | |||||||
\(500\) | −3.37672e11 | −0.241618 | ||||||||
\(501\) | 1.04560e12 | 0.741476 | ||||||||
\(502\) | 7.75681e11 | 0.545150 | ||||||||
\(503\) | 4.69546e11 | 0.327056 | 0.163528 | − | 0.986539i | \(-0.447713\pi\) | ||||
0.163528 | + | 0.986539i | \(0.447713\pi\) | |||||||
\(504\) | −2.88346e11 | −0.199056 | ||||||||
\(505\) | 2.44884e11 | 0.167552 | ||||||||
\(506\) | −3.64722e11 | −0.247334 | ||||||||
\(507\) | 8.49204e11 | 0.570790 | ||||||||
\(508\) | 1.08346e12 | 0.721818 | ||||||||
\(509\) | −9.05674e11 | −0.598056 | −0.299028 | − | 0.954244i | \(-0.596662\pi\) | ||||
−0.299028 | + | 0.954244i | \(0.596662\pi\) | |||||||
\(510\) | −1.70862e10 | −0.0111836 | ||||||||
\(511\) | −7.15093e11 | −0.463947 | ||||||||
\(512\) | 7.45536e11 | 0.479462 | ||||||||
\(513\) | −3.06045e11 | −0.195100 | ||||||||
\(514\) | −5.09507e11 | −0.321971 | ||||||||
\(515\) | −2.63783e10 | −0.0165240 | ||||||||
\(516\) | 4.27283e11 | 0.265333 | ||||||||
\(517\) | −1.30061e12 | −0.800646 | ||||||||
\(518\) | −6.70536e11 | −0.409202 | ||||||||
\(519\) | −9.47587e11 | −0.573279 | ||||||||
\(520\) | 2.72907e10 | 0.0163682 | ||||||||
\(521\) | −4.04998e11 | −0.240815 | −0.120407 | − | 0.992725i | \(-0.538420\pi\) | ||||
−0.120407 | + | 0.992725i | \(0.538420\pi\) | |||||||
\(522\) | 7.58640e10 | 0.0447217 | ||||||||
\(523\) | 1.73293e12 | 1.01280 | 0.506399 | − | 0.862299i | \(-0.330976\pi\) | ||||
0.506399 | + | 0.862299i | \(0.330976\pi\) | |||||||
\(524\) | −2.44266e12 | −1.41538 | ||||||||
\(525\) | 6.43162e11 | 0.369490 | ||||||||
\(526\) | 1.60035e12 | 0.911547 | ||||||||
\(527\) | −5.73571e11 | −0.323921 | ||||||||
\(528\) | 1.35392e11 | 0.0758123 | ||||||||
\(529\) | −3.93318e11 | −0.218370 | ||||||||
\(530\) | 1.27634e11 | 0.0702624 | ||||||||
\(531\) | −7.95020e10 | −0.0433963 | ||||||||
\(532\) | −8.92816e11 | −0.483236 | ||||||||
\(533\) | 4.08040e10 | 0.0218993 | ||||||||
\(534\) | 5.86789e11 | 0.312281 | ||||||||
\(535\) | 1.14718e11 | 0.0605394 | ||||||||
\(536\) | 1.85336e12 | 0.969879 | ||||||||
\(537\) | 1.19767e12 | 0.621519 | ||||||||
\(538\) | 1.28625e12 | 0.661920 | ||||||||
\(539\) | 5.89876e11 | 0.301031 | ||||||||
\(540\) | −4.66088e10 | −0.0235883 | ||||||||
\(541\) | 2.03592e11 | 0.102182 | 0.0510909 | − | 0.998694i | \(-0.483730\pi\) | ||||
0.0510909 | + | 0.998694i | \(0.483730\pi\) | |||||||
\(542\) | 4.89227e11 | 0.243508 | ||||||||
\(543\) | −8.58955e11 | −0.424005 | ||||||||
\(544\) | −4.60146e11 | −0.225269 | ||||||||
\(545\) | −4.27986e11 | −0.207800 | ||||||||
\(546\) | −4.42844e10 | −0.0213247 | ||||||||
\(547\) | −1.51327e11 | −0.0722727 | −0.0361363 | − | 0.999347i | \(-0.511505\pi\) | ||||
−0.0361363 | + | 0.999347i | \(0.511505\pi\) | |||||||
\(548\) | 1.24421e12 | 0.589361 | ||||||||
\(549\) | −9.14858e11 | −0.429812 | ||||||||
\(550\) | 5.83133e11 | 0.271729 | ||||||||
\(551\) | 5.59596e11 | 0.258638 | ||||||||
\(552\) | 1.00914e12 | 0.462621 | ||||||||
\(553\) | −2.97884e11 | −0.135451 | ||||||||
\(554\) | 1.64097e12 | 0.740126 | ||||||||
\(555\) | −2.58206e11 | −0.115518 | ||||||||
\(556\) | −2.31828e12 | −1.02880 | ||||||||
\(557\) | −2.02940e12 | −0.893344 | −0.446672 | − | 0.894698i | \(-0.647391\pi\) | ||||
−0.446672 | + | 0.894698i | \(0.647391\pi\) | |||||||
\(558\) | 5.98098e11 | 0.261167 | ||||||||
\(559\) | 1.56330e11 | 0.0677157 | ||||||||
\(560\) | −6.41252e10 | −0.0275539 | ||||||||
\(561\) | −1.56659e11 | −0.0667765 | ||||||||
\(562\) | 4.08409e11 | 0.172696 | ||||||||
\(563\) | −3.83974e12 | −1.61070 | −0.805348 | − | 0.592802i | \(-0.798022\pi\) | ||||
−0.805348 | + | 0.592802i | \(0.798022\pi\) | |||||||
\(564\) | 1.51059e12 | 0.628624 | ||||||||
\(565\) | 1.39517e11 | 0.0575982 | ||||||||
\(566\) | 3.29567e11 | 0.134980 | ||||||||
\(567\) | 1.80175e11 | 0.0732099 | ||||||||
\(568\) | 5.00719e11 | 0.201849 | ||||||||
\(569\) | 2.59199e12 | 1.03664 | 0.518319 | − | 0.855187i | \(-0.326558\pi\) | ||||
0.518319 | + | 0.855187i | \(0.326558\pi\) | |||||||
\(570\) | 1.31422e11 | 0.0521474 | ||||||||
\(571\) | 2.26611e11 | 0.0892110 | 0.0446055 | − | 0.999005i | \(-0.485797\pi\) | ||||
0.0446055 | + | 0.999005i | \(0.485797\pi\) | |||||||
\(572\) | 1.05035e11 | 0.0410255 | ||||||||
\(573\) | −1.41455e12 | −0.548177 | ||||||||
\(574\) | 1.85134e11 | 0.0711839 | ||||||||
\(575\) | −2.25091e12 | −0.858722 | ||||||||
\(576\) | 2.62461e11 | 0.0993491 | ||||||||
\(577\) | 4.33956e12 | 1.62988 | 0.814938 | − | 0.579548i | \(-0.196771\pi\) | ||||
0.814938 | + | 0.579548i | \(0.196771\pi\) | |||||||
\(578\) | −1.34441e12 | −0.501022 | ||||||||
\(579\) | −2.98503e11 | −0.110381 | ||||||||
\(580\) | 8.52232e10 | 0.0312703 | ||||||||
\(581\) | −1.27291e12 | −0.463454 | ||||||||
\(582\) | 5.77591e11 | 0.208673 | ||||||||
\(583\) | 1.17024e12 | 0.419534 | ||||||||
\(584\) | 1.79390e12 | 0.638177 | ||||||||
\(585\) | −1.70528e10 | −0.00601996 | ||||||||
\(586\) | 5.78401e11 | 0.202624 | ||||||||
\(587\) | 5.17738e12 | 1.79986 | 0.899931 | − | 0.436033i | \(-0.143617\pi\) | ||||
0.899931 | + | 0.436033i | \(0.143617\pi\) | |||||||
\(588\) | −6.85109e11 | −0.236353 | ||||||||
\(589\) | 4.41175e12 | 1.51040 | ||||||||
\(590\) | 3.41399e10 | 0.0115992 | ||||||||
\(591\) | 2.36924e12 | 0.798852 | ||||||||
\(592\) | −8.71144e11 | −0.291503 | ||||||||
\(593\) | 7.39550e11 | 0.245596 | 0.122798 | − | 0.992432i | \(-0.460813\pi\) | ||||
0.122798 | + | 0.992432i | \(0.460813\pi\) | |||||||
\(594\) | 1.63358e11 | 0.0538396 | ||||||||
\(595\) | 7.41981e10 | 0.0242698 | ||||||||
\(596\) | 7.09432e10 | 0.0230304 | ||||||||
\(597\) | 2.51459e12 | 0.810183 | ||||||||
\(598\) | 1.54985e11 | 0.0495602 | ||||||||
\(599\) | −8.86839e11 | −0.281465 | −0.140732 | − | 0.990048i | \(-0.544946\pi\) | ||||
−0.140732 | + | 0.990048i | \(0.544946\pi\) | |||||||
\(600\) | −1.61345e12 | −0.508248 | ||||||||
\(601\) | 3.84620e12 | 1.20253 | 0.601266 | − | 0.799049i | \(-0.294663\pi\) | ||||
0.601266 | + | 0.799049i | \(0.294663\pi\) | |||||||
\(602\) | 7.09293e11 | 0.220111 | ||||||||
\(603\) | −1.15808e12 | −0.356707 | ||||||||
\(604\) | 1.91975e12 | 0.586921 | ||||||||
\(605\) | 4.00298e11 | 0.121474 | ||||||||
\(606\) | 9.96858e11 | 0.300266 | ||||||||
\(607\) | −6.84903e11 | −0.204776 | −0.102388 | − | 0.994745i | \(-0.532648\pi\) | ||||
−0.102388 | + | 0.994745i | \(0.532648\pi\) | |||||||
\(608\) | 3.53932e12 | 1.05040 | ||||||||
\(609\) | −3.29445e11 | −0.0970522 | ||||||||
\(610\) | 3.92860e11 | 0.114883 | ||||||||
\(611\) | 5.52680e11 | 0.160431 | ||||||||
\(612\) | 1.81951e11 | 0.0524293 | ||||||||
\(613\) | −1.76600e12 | −0.505149 | −0.252574 | − | 0.967578i | \(-0.581277\pi\) | ||||
−0.252574 | + | 0.967578i | \(0.581277\pi\) | |||||||
\(614\) | 9.42431e11 | 0.267604 | ||||||||
\(615\) | 7.12901e10 | 0.0200952 | ||||||||
\(616\) | 1.13529e12 | 0.317684 | ||||||||
\(617\) | −1.34640e12 | −0.374018 | −0.187009 | − | 0.982358i | \(-0.559879\pi\) | ||||
−0.187009 | + | 0.982358i | \(0.559879\pi\) | |||||||
\(618\) | −1.07379e11 | −0.0296123 | ||||||||
\(619\) | 9.78641e11 | 0.267926 | 0.133963 | − | 0.990986i | \(-0.457230\pi\) | ||||
0.133963 | + | 0.990986i | \(0.457230\pi\) | |||||||
\(620\) | 6.71884e11 | 0.182613 | ||||||||
\(621\) | −6.30567e11 | −0.170145 | ||||||||
\(622\) | 1.63161e12 | 0.437079 | ||||||||
\(623\) | −2.54817e12 | −0.677693 | ||||||||
\(624\) | −5.75332e10 | −0.0151911 | ||||||||
\(625\) | 3.48935e12 | 0.914713 | ||||||||
\(626\) | −1.71749e12 | −0.447003 | ||||||||
\(627\) | 1.20498e12 | 0.311369 | ||||||||
\(628\) | −2.50370e12 | −0.642337 | ||||||||
\(629\) | 1.00798e12 | 0.256759 | ||||||||
\(630\) | −7.73709e10 | −0.0195680 | ||||||||
\(631\) | 1.69265e11 | 0.0425046 | 0.0212523 | − | 0.999774i | \(-0.493235\pi\) | ||||
0.0212523 | + | 0.999774i | \(0.493235\pi\) | |||||||
\(632\) | 7.47280e11 | 0.186319 | ||||||||
\(633\) | 6.03788e11 | 0.149475 | ||||||||
\(634\) | 7.78713e10 | 0.0191415 | ||||||||
\(635\) | 6.92578e11 | 0.169039 | ||||||||
\(636\) | −1.35917e12 | −0.329395 | ||||||||
\(637\) | −2.50661e11 | −0.0603198 | ||||||||
\(638\) | −2.98697e11 | −0.0713737 | ||||||||
\(639\) | −3.12877e11 | −0.0742370 | ||||||||
\(640\) | 6.32357e11 | 0.148988 | ||||||||
\(641\) | −5.73879e12 | −1.34264 | −0.671319 | − | 0.741169i | \(-0.734272\pi\) | ||||
−0.671319 | + | 0.741169i | \(0.734272\pi\) | |||||||
\(642\) | 4.66984e11 | 0.108491 | ||||||||
\(643\) | −7.62978e12 | −1.76020 | −0.880101 | − | 0.474787i | \(-0.842525\pi\) | ||||
−0.880101 | + | 0.474787i | \(0.842525\pi\) | |||||||
\(644\) | −1.83954e12 | −0.421426 | ||||||||
\(645\) | 2.73130e11 | 0.0621371 | ||||||||
\(646\) | −5.13046e11 | −0.115907 | ||||||||
\(647\) | 3.78174e12 | 0.848442 | 0.424221 | − | 0.905559i | \(-0.360548\pi\) | ||||
0.424221 | + | 0.905559i | \(0.360548\pi\) | |||||||
\(648\) | −4.51991e11 | −0.100703 | ||||||||
\(649\) | 3.13021e11 | 0.0692583 | ||||||||
\(650\) | −2.47796e11 | −0.0544483 | ||||||||
\(651\) | −2.59729e12 | −0.566768 | ||||||||
\(652\) | 4.90125e12 | 1.06217 | ||||||||
\(653\) | −6.52719e12 | −1.40481 | −0.702404 | − | 0.711779i | \(-0.747890\pi\) | ||||
−0.702404 | + | 0.711779i | \(0.747890\pi\) | |||||||
\(654\) | −1.74222e12 | −0.372394 | ||||||||
\(655\) | −1.56141e12 | −0.331461 | ||||||||
\(656\) | 2.40521e11 | 0.0507091 | ||||||||
\(657\) | −1.12093e12 | −0.234712 | ||||||||
\(658\) | 2.50759e12 | 0.521483 | ||||||||
\(659\) | −8.14077e12 | −1.68144 | −0.840719 | − | 0.541471i | \(-0.817868\pi\) | ||||
−0.840719 | + | 0.541471i | \(0.817868\pi\) | |||||||
\(660\) | 1.83511e11 | 0.0376457 | ||||||||
\(661\) | −6.28394e12 | −1.28034 | −0.640170 | − | 0.768233i | \(-0.721136\pi\) | ||||
−0.640170 | + | 0.768233i | \(0.721136\pi\) | |||||||
\(662\) | −2.70988e12 | −0.548390 | ||||||||
\(663\) | 6.65706e10 | 0.0133805 | ||||||||
\(664\) | 3.19327e12 | 0.637499 | ||||||||
\(665\) | −5.70711e11 | −0.113167 | ||||||||
\(666\) | −1.05109e12 | −0.207016 | ||||||||
\(667\) | 1.15298e12 | 0.225556 | ||||||||
\(668\) | 4.78147e12 | 0.929110 | ||||||||
\(669\) | 1.13618e12 | 0.219295 | ||||||||
\(670\) | 4.97306e11 | 0.0953426 | ||||||||
\(671\) | 3.60204e12 | 0.685958 | ||||||||
\(672\) | −2.08367e12 | −0.394154 | ||||||||
\(673\) | −4.54764e12 | −0.854512 | −0.427256 | − | 0.904131i | \(-0.640520\pi\) | ||||
−0.427256 | + | 0.904131i | \(0.640520\pi\) | |||||||
\(674\) | 5.48041e11 | 0.102292 | ||||||||
\(675\) | 1.00818e12 | 0.186926 | ||||||||
\(676\) | 3.88335e12 | 0.715230 | ||||||||
\(677\) | 9.68222e12 | 1.77144 | 0.885719 | − | 0.464221i | \(-0.153666\pi\) | ||||
0.885719 | + | 0.464221i | \(0.153666\pi\) | |||||||
\(678\) | 5.67936e11 | 0.103220 | ||||||||
\(679\) | −2.50823e12 | −0.452849 | ||||||||
\(680\) | −1.86136e11 | −0.0333841 | ||||||||
\(681\) | 2.14093e11 | 0.0381453 | ||||||||
\(682\) | −2.35487e12 | −0.416810 | ||||||||
\(683\) | 1.20065e12 | 0.211117 | 0.105559 | − | 0.994413i | \(-0.466337\pi\) | ||||
0.105559 | + | 0.994413i | \(0.466337\pi\) | |||||||
\(684\) | −1.39952e12 | −0.244470 | ||||||||
\(685\) | 7.95331e11 | 0.138020 | ||||||||
\(686\) | −3.14710e12 | −0.542566 | ||||||||
\(687\) | −5.71623e12 | −0.979049 | ||||||||
\(688\) | 9.21496e11 | 0.156800 | ||||||||
\(689\) | −4.97281e11 | −0.0840650 | ||||||||
\(690\) | 2.70779e11 | 0.0454773 | ||||||||
\(691\) | −2.62792e12 | −0.438491 | −0.219245 | − | 0.975670i | \(-0.570360\pi\) | ||||
−0.219245 | + | 0.975670i | \(0.570360\pi\) | |||||||
\(692\) | −4.33325e12 | −0.718350 | ||||||||
\(693\) | −7.09396e11 | −0.116839 | ||||||||
\(694\) | 1.72040e12 | 0.281522 | ||||||||
\(695\) | −1.48190e12 | −0.240929 | ||||||||
\(696\) | 8.26456e11 | 0.133499 | ||||||||
\(697\) | −2.78302e11 | −0.0446652 | ||||||||
\(698\) | −5.86484e12 | −0.935205 | ||||||||
\(699\) | 3.88628e11 | 0.0615724 | ||||||||
\(700\) | 2.94113e12 | 0.462991 | ||||||||
\(701\) | −2.63768e12 | −0.412563 | −0.206282 | − | 0.978493i | \(-0.566136\pi\) | ||||
−0.206282 | + | 0.978493i | \(0.566136\pi\) | |||||||
\(702\) | −6.94173e10 | −0.0107882 | ||||||||
\(703\) | −7.75314e12 | −1.19723 | ||||||||
\(704\) | −1.03338e12 | −0.158556 | ||||||||
\(705\) | 9.65609e11 | 0.147214 | ||||||||
\(706\) | −5.95970e12 | −0.902824 | ||||||||
\(707\) | −4.32893e12 | −0.651618 | ||||||||
\(708\) | −3.63557e11 | −0.0543779 | ||||||||
\(709\) | 6.76875e12 | 1.00601 | 0.503003 | − | 0.864285i | \(-0.332229\pi\) | ||||
0.503003 | + | 0.864285i | \(0.332229\pi\) | |||||||
\(710\) | 1.34356e11 | 0.0198425 | ||||||||
\(711\) | −4.66942e11 | −0.0685252 | ||||||||
\(712\) | 6.39242e12 | 0.932193 | ||||||||
\(713\) | 9.08986e12 | 1.31721 | ||||||||
\(714\) | 3.02041e11 | 0.0434934 | ||||||||
\(715\) | 6.71414e10 | 0.00960756 | ||||||||
\(716\) | 5.47688e12 | 0.778797 | ||||||||
\(717\) | 5.15523e12 | 0.728470 | ||||||||
\(718\) | 2.33859e12 | 0.328394 | ||||||||
\(719\) | −5.03693e12 | −0.702887 | −0.351444 | − | 0.936209i | \(-0.614309\pi\) | ||||
−0.351444 | + | 0.936209i | \(0.614309\pi\) | |||||||
\(720\) | −1.00518e11 | −0.0139396 | ||||||||
\(721\) | 4.66302e11 | 0.0642626 | ||||||||
\(722\) | 1.06456e11 | 0.0145799 | ||||||||
\(723\) | 2.59556e12 | 0.353272 | ||||||||
\(724\) | −3.92794e12 | −0.531301 | ||||||||
\(725\) | −1.84343e12 | −0.247803 | ||||||||
\(726\) | 1.62950e12 | 0.217691 | ||||||||
\(727\) | −7.13148e12 | −0.946836 | −0.473418 | − | 0.880838i | \(-0.656980\pi\) | ||||
−0.473418 | + | 0.880838i | \(0.656980\pi\) | |||||||
\(728\) | −4.82430e11 | −0.0636566 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 4.81353e11 | 0.0627352 | ||||||||
\(731\) | −1.06625e12 | −0.138111 | ||||||||
\(732\) | −4.18358e12 | −0.538577 | ||||||||
\(733\) | 6.89412e12 | 0.882086 | 0.441043 | − | 0.897486i | \(-0.354609\pi\) | ||||
0.441043 | + | 0.897486i | \(0.354609\pi\) | |||||||
\(734\) | 4.78038e12 | 0.607897 | ||||||||
\(735\) | −4.37940e11 | −0.0553505 | ||||||||
\(736\) | 7.29232e12 | 0.916042 | ||||||||
\(737\) | 4.55968e12 | 0.569286 | ||||||||
\(738\) | 2.90203e11 | 0.0360121 | ||||||||
\(739\) | 9.41890e12 | 1.16172 | 0.580858 | − | 0.814005i | \(-0.302717\pi\) | ||||
0.580858 | + | 0.814005i | \(0.302717\pi\) | |||||||
\(740\) | −1.18076e12 | −0.144750 | ||||||||
\(741\) | −5.12043e11 | −0.0623913 | ||||||||
\(742\) | −2.25624e12 | −0.273254 | ||||||||
\(743\) | −9.53131e12 | −1.14737 | −0.573684 | − | 0.819076i | \(-0.694486\pi\) | ||||
−0.573684 | + | 0.819076i | \(0.694486\pi\) | |||||||
\(744\) | 6.51563e12 | 0.779611 | ||||||||
\(745\) | 4.53487e10 | 0.00539339 | ||||||||
\(746\) | −3.04053e12 | −0.359439 | ||||||||
\(747\) | −1.99534e12 | −0.234463 | ||||||||
\(748\) | −7.16391e11 | −0.0836745 | ||||||||
\(749\) | −2.02791e12 | −0.235441 | ||||||||
\(750\) | −8.78661e11 | −0.101402 | ||||||||
\(751\) | −2.76101e12 | −0.316729 | −0.158364 | − | 0.987381i | \(-0.550622\pi\) | ||||
−0.158364 | + | 0.987381i | \(0.550622\pi\) | |||||||
\(752\) | 3.25780e12 | 0.371488 | ||||||||
\(753\) | −5.28016e12 | −0.598508 | ||||||||
\(754\) | 1.26928e11 | 0.0143017 | ||||||||
\(755\) | 1.22716e12 | 0.137448 | ||||||||
\(756\) | 8.23925e11 | 0.0917359 | ||||||||
\(757\) | −1.15173e12 | −0.127473 | −0.0637366 | − | 0.997967i | \(-0.520302\pi\) | ||||
−0.0637366 | + | 0.997967i | \(0.520302\pi\) | |||||||
\(758\) | −5.41941e12 | −0.596267 | ||||||||
\(759\) | 2.48271e12 | 0.271543 | ||||||||
\(760\) | 1.43170e12 | 0.155665 | ||||||||
\(761\) | −1.51598e13 | −1.63856 | −0.819278 | − | 0.573396i | \(-0.805626\pi\) | ||||
−0.819278 | + | 0.573396i | \(0.805626\pi\) | |||||||
\(762\) | 2.81930e12 | 0.302931 | ||||||||
\(763\) | 7.56571e12 | 0.808145 | ||||||||
\(764\) | −6.46861e12 | −0.686896 | ||||||||
\(765\) | 1.16308e11 | 0.0122782 | ||||||||
\(766\) | −5.26643e12 | −0.552696 | ||||||||
\(767\) | −1.33015e11 | −0.0138778 | ||||||||
\(768\) | 4.23317e12 | 0.439076 | ||||||||
\(769\) | −1.24406e13 | −1.28284 | −0.641419 | − | 0.767191i | \(-0.721654\pi\) | ||||
−0.641419 | + | 0.767191i | \(0.721654\pi\) | |||||||
\(770\) | 3.04630e11 | 0.0312295 | ||||||||
\(771\) | 3.46828e12 | 0.353484 | ||||||||
\(772\) | −1.36503e12 | −0.138314 | ||||||||
\(773\) | 1.80557e13 | 1.81890 | 0.909448 | − | 0.415818i | \(-0.136505\pi\) | ||||
0.909448 | + | 0.415818i | \(0.136505\pi\) | |||||||
\(774\) | 1.11184e12 | 0.111355 | ||||||||
\(775\) | −1.45333e13 | −1.44712 | ||||||||
\(776\) | 6.29223e12 | 0.622912 | ||||||||
\(777\) | 4.56443e12 | 0.449254 | ||||||||
\(778\) | −1.43494e12 | −0.140419 | ||||||||
\(779\) | 2.14062e12 | 0.208268 | ||||||||
\(780\) | −7.79811e10 | −0.00754334 | ||||||||
\(781\) | 1.23188e12 | 0.118479 | ||||||||
\(782\) | −1.05707e12 | −0.101082 | ||||||||
\(783\) | −5.16416e11 | −0.0490989 | ||||||||
\(784\) | −1.47754e12 | −0.139674 | ||||||||
\(785\) | −1.60043e12 | −0.150426 | ||||||||
\(786\) | −6.35610e12 | −0.594004 | ||||||||
\(787\) | 4.66959e12 | 0.433903 | 0.216951 | − | 0.976182i | \(-0.430389\pi\) | ||||
0.216951 | + | 0.976182i | \(0.430389\pi\) | |||||||
\(788\) | 1.08344e13 | 1.00100 | ||||||||
\(789\) | −1.08938e13 | −1.00077 | ||||||||
\(790\) | 2.00515e11 | 0.0183158 | ||||||||
\(791\) | −2.46630e12 | −0.224002 | ||||||||
\(792\) | 1.77961e12 | 0.160717 | ||||||||
\(793\) | −1.53065e12 | −0.137450 | ||||||||
\(794\) | −4.99793e12 | −0.446270 | ||||||||
\(795\) | −8.68818e11 | −0.0771395 | ||||||||
\(796\) | 1.14990e13 | 1.01520 | ||||||||
\(797\) | −6.81590e12 | −0.598358 | −0.299179 | − | 0.954197i | \(-0.596713\pi\) | ||||
−0.299179 | + | 0.954197i | \(0.596713\pi\) | |||||||
\(798\) | −2.32321e12 | −0.202804 | ||||||||
\(799\) | −3.76954e12 | −0.327211 | ||||||||
\(800\) | −1.16593e13 | −1.00639 | ||||||||
\(801\) | −3.99435e12 | −0.342846 | ||||||||
\(802\) | 5.45115e12 | 0.465268 | ||||||||
\(803\) | 4.41341e12 | 0.374589 | ||||||||
\(804\) | −5.29582e12 | −0.446973 | ||||||||
\(805\) | −1.17588e12 | −0.0986918 | ||||||||
\(806\) | 1.00068e12 | 0.0835192 | ||||||||
\(807\) | −8.75567e12 | −0.726706 | ||||||||
\(808\) | 1.08597e13 | 0.896326 | ||||||||
\(809\) | 1.08706e13 | 0.892244 | 0.446122 | − | 0.894972i | \(-0.352805\pi\) | ||||
0.446122 | + | 0.894972i | \(0.352805\pi\) | |||||||
\(810\) | −1.21282e11 | −0.00989947 | ||||||||
\(811\) | −2.22237e12 | −0.180395 | −0.0901973 | − | 0.995924i | \(-0.528750\pi\) | ||||
−0.0901973 | + | 0.995924i | \(0.528750\pi\) | |||||||
\(812\) | −1.50653e12 | −0.121612 | ||||||||
\(813\) | −3.33023e12 | −0.267342 | ||||||||
\(814\) | 4.13841e12 | 0.330388 | ||||||||
\(815\) | 3.13300e12 | 0.248743 | ||||||||
\(816\) | 3.92404e11 | 0.0309833 | ||||||||
\(817\) | 8.20126e12 | 0.643994 | ||||||||
\(818\) | −7.64569e12 | −0.597072 | ||||||||
\(819\) | 3.01450e11 | 0.0234119 | ||||||||
\(820\) | 3.26004e11 | 0.0251803 | ||||||||
\(821\) | −1.89934e13 | −1.45901 | −0.729505 | − | 0.683975i | \(-0.760250\pi\) | ||||
−0.729505 | + | 0.683975i | \(0.760250\pi\) | |||||||
\(822\) | 3.23758e12 | 0.247342 | ||||||||
\(823\) | 2.41144e13 | 1.83222 | 0.916111 | − | 0.400925i | \(-0.131311\pi\) | ||||
0.916111 | + | 0.400925i | \(0.131311\pi\) | |||||||
\(824\) | −1.16978e12 | −0.0883957 | ||||||||
\(825\) | −3.96946e12 | −0.298325 | ||||||||
\(826\) | −6.03507e11 | −0.0451099 | ||||||||
\(827\) | −1.28933e13 | −0.958497 | −0.479249 | − | 0.877679i | \(-0.659091\pi\) | ||||
−0.479249 | + | 0.877679i | \(0.659091\pi\) | |||||||
\(828\) | −2.88353e12 | −0.213201 | ||||||||
\(829\) | 1.20665e13 | 0.887334 | 0.443667 | − | 0.896192i | \(-0.353677\pi\) | ||||
0.443667 | + | 0.896192i | \(0.353677\pi\) | |||||||
\(830\) | 8.56842e11 | 0.0626685 | ||||||||
\(831\) | −1.11703e13 | −0.812567 | ||||||||
\(832\) | 4.39123e11 | 0.0317711 | ||||||||
\(833\) | 1.70963e12 | 0.123027 | ||||||||
\(834\) | −6.03243e12 | −0.431763 | ||||||||
\(835\) | 3.05644e12 | 0.217584 | ||||||||
\(836\) | 5.51028e12 | 0.390163 | ||||||||
\(837\) | −4.07133e12 | −0.286729 | ||||||||
\(838\) | −1.21541e13 | −0.851386 | ||||||||
\(839\) | 1.09334e13 | 0.761771 | 0.380886 | − | 0.924622i | \(-0.375619\pi\) | ||||
0.380886 | + | 0.924622i | \(0.375619\pi\) | |||||||
\(840\) | −8.42872e11 | −0.0584124 | ||||||||
\(841\) | −1.35629e13 | −0.934911 | ||||||||
\(842\) | −5.28805e12 | −0.362569 | ||||||||
\(843\) | −2.78010e12 | −0.189599 | ||||||||
\(844\) | 2.76108e12 | 0.187300 | ||||||||
\(845\) | 2.48234e12 | 0.167496 | ||||||||
\(846\) | 3.93073e12 | 0.263820 | ||||||||
\(847\) | −7.07624e12 | −0.472419 | ||||||||
\(848\) | −2.93125e12 | −0.194657 | ||||||||
\(849\) | −2.24341e12 | −0.148191 | ||||||||
\(850\) | 1.69009e12 | 0.111051 | ||||||||
\(851\) | −1.59744e13 | −1.04410 | ||||||||
\(852\) | −1.43076e12 | −0.0930229 | ||||||||
\(853\) | 6.39450e12 | 0.413557 | 0.206779 | − | 0.978388i | \(-0.433702\pi\) | ||||
0.206779 | + | 0.978388i | \(0.433702\pi\) | |||||||
\(854\) | −6.94477e12 | −0.446784 | ||||||||
\(855\) | −8.94609e11 | −0.0572513 | ||||||||
\(856\) | 5.08729e12 | 0.323858 | ||||||||
\(857\) | −4.53813e12 | −0.287384 | −0.143692 | − | 0.989622i | \(-0.545898\pi\) | ||||
−0.143692 | + | 0.989622i | \(0.545898\pi\) | |||||||
\(858\) | 2.73314e11 | 0.0172175 | ||||||||
\(859\) | −4.99842e12 | −0.313230 | −0.156615 | − | 0.987660i | \(-0.550058\pi\) | ||||
−0.156615 | + | 0.987660i | \(0.550058\pi\) | |||||||
\(860\) | 1.24900e12 | 0.0778611 | ||||||||
\(861\) | −1.26023e12 | −0.0781511 | ||||||||
\(862\) | 1.79990e12 | 0.111036 | ||||||||
\(863\) | 4.53292e12 | 0.278182 | 0.139091 | − | 0.990280i | \(-0.455582\pi\) | ||||
0.139091 | + | 0.990280i | \(0.455582\pi\) | |||||||
\(864\) | −3.26621e12 | −0.199404 | ||||||||
\(865\) | −2.76992e12 | −0.168227 | ||||||||
\(866\) | −6.97310e12 | −0.421304 | ||||||||
\(867\) | 9.15157e12 | 0.550060 | ||||||||
\(868\) | −1.18772e13 | −0.710191 | ||||||||
\(869\) | 1.83848e12 | 0.109363 | ||||||||
\(870\) | 2.21761e11 | 0.0131234 | ||||||||
\(871\) | −1.93758e12 | −0.114072 | ||||||||
\(872\) | −1.89796e13 | −1.11163 | ||||||||
\(873\) | −3.93174e12 | −0.229098 | ||||||||
\(874\) | 8.13067e12 | 0.471330 | ||||||||
\(875\) | 3.81565e12 | 0.220056 | ||||||||
\(876\) | −5.12594e12 | −0.294107 | ||||||||
\(877\) | 4.25995e12 | 0.243168 | 0.121584 | − | 0.992581i | \(-0.461203\pi\) | ||||
0.121584 | + | 0.992581i | \(0.461203\pi\) | |||||||
\(878\) | −1.54450e13 | −0.877128 | ||||||||
\(879\) | −3.93725e12 | −0.222456 | ||||||||
\(880\) | 3.95768e11 | 0.0222469 | ||||||||
\(881\) | 1.07615e13 | 0.601841 | 0.300920 | − | 0.953649i | \(-0.402706\pi\) | ||||
0.300920 | + | 0.953649i | \(0.402706\pi\) | |||||||
\(882\) | −1.78273e12 | −0.0991923 | ||||||||
\(883\) | −2.51265e13 | −1.39094 | −0.695471 | − | 0.718554i | \(-0.744804\pi\) | ||||
−0.695471 | + | 0.718554i | \(0.744804\pi\) | |||||||
\(884\) | 3.04422e11 | 0.0167665 | ||||||||
\(885\) | −2.32395e11 | −0.0127345 | ||||||||
\(886\) | −4.97006e11 | −0.0270963 | ||||||||
\(887\) | 1.29291e13 | 0.701311 | 0.350655 | − | 0.936505i | \(-0.385959\pi\) | ||||
0.350655 | + | 0.936505i | \(0.385959\pi\) | |||||||
\(888\) | −1.14505e13 | −0.617966 | ||||||||
\(889\) | −1.22430e13 | −0.657401 | ||||||||
\(890\) | 1.71526e12 | 0.0916379 | ||||||||
\(891\) | −1.11200e12 | −0.0591093 | ||||||||
\(892\) | 5.19567e12 | 0.274789 | ||||||||
\(893\) | 2.89943e13 | 1.52574 | ||||||||
\(894\) | 1.84602e11 | 0.00966537 | ||||||||
\(895\) | 3.50096e12 | 0.182383 | ||||||||
\(896\) | −1.11785e13 | −0.579423 | ||||||||
\(897\) | −1.05500e12 | −0.0544110 | ||||||||
\(898\) | 3.09616e12 | 0.158884 | ||||||||
\(899\) | 7.44434e12 | 0.380109 | ||||||||
\(900\) | 4.61032e12 | 0.234228 | ||||||||
\(901\) | 3.39169e12 | 0.171457 | ||||||||
\(902\) | −1.14261e12 | −0.0574735 | ||||||||
\(903\) | −4.82825e12 | −0.241654 | ||||||||
\(904\) | 6.18704e12 | 0.308124 | ||||||||
\(905\) | −2.51084e12 | −0.124423 | ||||||||
\(906\) | 4.99542e12 | 0.246318 | ||||||||
\(907\) | 1.13077e13 | 0.554806 | 0.277403 | − | 0.960754i | \(-0.410526\pi\) | ||||
0.277403 | + | 0.960754i | \(0.410526\pi\) | |||||||
\(908\) | 9.79033e11 | 0.0477981 | ||||||||
\(909\) | −6.78574e12 | −0.329655 | ||||||||
\(910\) | −1.29449e11 | −0.00625768 | ||||||||
\(911\) | −8.95975e12 | −0.430986 | −0.215493 | − | 0.976505i | \(-0.569136\pi\) | ||||
−0.215493 | + | 0.976505i | \(0.569136\pi\) | |||||||
\(912\) | −3.01826e12 | −0.144471 | ||||||||
\(913\) | 7.85618e12 | 0.374191 | ||||||||
\(914\) | −1.13406e13 | −0.537498 | ||||||||
\(915\) | −2.67425e12 | −0.126127 | ||||||||
\(916\) | −2.61399e13 | −1.22680 | ||||||||
\(917\) | 2.76018e13 | 1.28907 | ||||||||
\(918\) | 4.73459e11 | 0.0220034 | ||||||||
\(919\) | 1.85630e13 | 0.858477 | 0.429239 | − | 0.903191i | \(-0.358782\pi\) | ||||
0.429239 | + | 0.903191i | \(0.358782\pi\) | |||||||
\(920\) | 2.94985e12 | 0.135754 | ||||||||
\(921\) | −6.41525e12 | −0.293796 | ||||||||
\(922\) | 5.44811e12 | 0.248289 | ||||||||
\(923\) | −5.23475e11 | −0.0237404 | ||||||||
\(924\) | −3.24401e12 | −0.146406 | ||||||||
\(925\) | 2.55405e13 | 1.14708 | ||||||||
\(926\) | −4.18808e12 | −0.187183 | ||||||||
\(927\) | 7.30944e11 | 0.0325106 | ||||||||
\(928\) | 5.97220e12 | 0.264344 | ||||||||
\(929\) | −3.05904e13 | −1.34746 | −0.673728 | − | 0.738980i | \(-0.735308\pi\) | ||||
−0.673728 | + | 0.738980i | \(0.735308\pi\) | |||||||
\(930\) | 1.74832e12 | 0.0766386 | ||||||||
\(931\) | −1.31500e13 | −0.573656 | ||||||||
\(932\) | 1.77716e12 | 0.0771536 | ||||||||
\(933\) | −1.11066e13 | −0.479859 | ||||||||
\(934\) | 1.42729e12 | 0.0613693 | ||||||||
\(935\) | −4.57936e11 | −0.0195953 | ||||||||
\(936\) | −7.56226e11 | −0.0322040 | ||||||||
\(937\) | 3.38827e13 | 1.43599 | 0.717993 | − | 0.696050i | \(-0.245061\pi\) | ||||
0.717993 | + | 0.696050i | \(0.245061\pi\) | |||||||
\(938\) | −8.79110e12 | −0.370792 | ||||||||
\(939\) | 1.16912e13 | 0.490754 | ||||||||
\(940\) | 4.41566e12 | 0.184468 | ||||||||
\(941\) | 3.41437e13 | 1.41957 | 0.709785 | − | 0.704418i | \(-0.248792\pi\) | ||||
0.709785 | + | 0.704418i | \(0.248792\pi\) | |||||||
\(942\) | −6.51491e12 | −0.269575 | ||||||||
\(943\) | 4.41049e12 | 0.181629 | ||||||||
\(944\) | −7.84062e11 | −0.0321349 | ||||||||
\(945\) | 5.26674e11 | 0.0214832 | ||||||||
\(946\) | −4.37761e12 | −0.177716 | ||||||||
\(947\) | 3.30474e13 | 1.33525 | 0.667624 | − | 0.744499i | \(-0.267311\pi\) | ||||
0.667624 | + | 0.744499i | \(0.267311\pi\) | |||||||
\(948\) | −2.13529e12 | −0.0858657 | ||||||||
\(949\) | −1.87543e12 | −0.0750590 | ||||||||
\(950\) | −1.29997e13 | −0.517817 | ||||||||
\(951\) | −5.30080e11 | −0.0210150 | ||||||||
\(952\) | 3.29040e12 | 0.129832 | ||||||||
\(953\) | −3.77689e12 | −0.148326 | −0.0741628 | − | 0.997246i | \(-0.523628\pi\) | ||||
−0.0741628 | + | 0.997246i | \(0.523628\pi\) | |||||||
\(954\) | −3.53672e12 | −0.138240 | ||||||||
\(955\) | −4.13490e12 | −0.160861 | ||||||||
\(956\) | 2.35745e13 | 0.912813 | ||||||||
\(957\) | 2.03327e12 | 0.0783595 | ||||||||
\(958\) | 2.37478e13 | 0.910915 | ||||||||
\(959\) | −1.40594e13 | −0.536765 | ||||||||
\(960\) | 7.67209e11 | 0.0291537 | ||||||||
\(961\) | 3.22502e13 | 1.21977 | ||||||||
\(962\) | −1.75857e12 | −0.0662022 | ||||||||
\(963\) | −3.17882e12 | −0.119110 | ||||||||
\(964\) | 1.18693e13 | 0.442669 | ||||||||
\(965\) | −8.72563e11 | −0.0323910 | ||||||||
\(966\) | −4.78669e12 | −0.176863 | ||||||||
\(967\) | 4.64428e13 | 1.70804 | 0.854022 | − | 0.520237i | \(-0.174156\pi\) | ||||
0.854022 | + | 0.520237i | \(0.174156\pi\) | |||||||
\(968\) | 1.77517e13 | 0.649831 | ||||||||
\(969\) | 3.49237e12 | 0.127252 | ||||||||
\(970\) | 1.68838e12 | 0.0612345 | ||||||||
\(971\) | −9.18432e12 | −0.331559 | −0.165779 | − | 0.986163i | \(-0.553014\pi\) | ||||
−0.165779 | + | 0.986163i | \(0.553014\pi\) | |||||||
\(972\) | 1.29153e12 | 0.0464094 | ||||||||
\(973\) | 2.61963e13 | 0.936983 | ||||||||
\(974\) | −7.66494e12 | −0.272894 | ||||||||
\(975\) | 1.68678e12 | 0.0597775 | ||||||||
\(976\) | −9.02248e12 | −0.318274 | ||||||||
\(977\) | −3.16019e13 | −1.10965 | −0.554826 | − | 0.831966i | \(-0.687215\pi\) | ||||
−0.554826 | + | 0.831966i | \(0.687215\pi\) | |||||||
\(978\) | 1.27536e13 | 0.445768 | ||||||||
\(979\) | 1.57268e13 | 0.547166 | ||||||||
\(980\) | −2.00267e12 | −0.0693571 | ||||||||
\(981\) | 1.18595e13 | 0.408842 | ||||||||
\(982\) | 1.20642e12 | 0.0413995 | ||||||||
\(983\) | 3.93532e13 | 1.34428 | 0.672139 | − | 0.740425i | \(-0.265376\pi\) | ||||
0.672139 | + | 0.740425i | \(0.265376\pi\) | |||||||
\(984\) | 3.16145e12 | 0.107500 | ||||||||
\(985\) | 6.92562e12 | 0.234420 | ||||||||
\(986\) | −8.65709e11 | −0.0291693 | ||||||||
\(987\) | −1.70695e13 | −0.572524 | ||||||||
\(988\) | −2.34153e12 | −0.0781797 | ||||||||
\(989\) | 1.68977e13 | 0.561621 | ||||||||
\(990\) | 4.77518e11 | 0.0157991 | ||||||||
\(991\) | −3.64226e12 | −0.119961 | −0.0599805 | − | 0.998200i | \(-0.519104\pi\) | ||||
−0.0599805 | + | 0.998200i | \(0.519104\pi\) | |||||||
\(992\) | 4.70837e13 | 1.54372 | ||||||||
\(993\) | 1.84465e13 | 0.602065 | ||||||||
\(994\) | −2.37508e12 | −0.0771684 | ||||||||
\(995\) | 7.35048e12 | 0.237745 | ||||||||
\(996\) | −9.12452e12 | −0.293794 | ||||||||
\(997\) | −4.88557e11 | −0.0156598 | −0.00782991 | − | 0.999969i | \(-0.502492\pi\) | ||||
−0.00782991 | + | 0.999969i | \(0.502492\pi\) | |||||||
\(998\) | −2.26722e13 | −0.723447 | ||||||||
\(999\) | 7.15489e12 | 0.227278 |
(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 | 177.10.a.b.1.13 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.b.1.13 | ✓ | 21 | 1.1 | even | 1 | trivial |