Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,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, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
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: | \(135.996742959\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −41.9561 | −0.927107 | −0.463554 | − | 0.886069i | \(-0.653426\pi\) | ||||
−0.463554 | + | 0.886069i | \(0.653426\pi\) | |||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | −287.686 | −0.140472 | ||||||||
\(5\) | −4799.69 | −0.686876 | −0.343438 | − | 0.939175i | \(-0.611591\pi\) | ||||
−0.343438 | + | 0.939175i | \(0.611591\pi\) | |||||||
\(6\) | 10195.3 | 0.535266 | ||||||||
\(7\) | −40967.8 | −0.921305 | −0.460653 | − | 0.887580i | \(-0.652385\pi\) | ||||
−0.460653 | + | 0.887580i | \(0.652385\pi\) | |||||||
\(8\) | 97996.3 | 1.05734 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 201376. | 0.636808 | ||||||||
\(11\) | 261833. | 0.490189 | 0.245095 | − | 0.969499i | \(-0.421181\pi\) | ||||
0.245095 | + | 0.969499i | \(0.421181\pi\) | |||||||
\(12\) | 69907.8 | 0.0811014 | ||||||||
\(13\) | −320404. | −0.239337 | −0.119668 | − | 0.992814i | \(-0.538183\pi\) | ||||
−0.119668 | + | 0.992814i | \(0.538183\pi\) | |||||||
\(14\) | 1.71885e6 | 0.854149 | ||||||||
\(15\) | 1.16632e6 | 0.396568 | ||||||||
\(16\) | −3.52236e6 | −0.839796 | ||||||||
\(17\) | 8.00961e6 | 1.36818 | 0.684088 | − | 0.729399i | \(-0.260200\pi\) | ||||
0.684088 | + | 0.729399i | \(0.260200\pi\) | |||||||
\(18\) | −2.47747e6 | −0.309036 | ||||||||
\(19\) | 4.69006e6 | 0.434543 | 0.217272 | − | 0.976111i | \(-0.430284\pi\) | ||||
0.217272 | + | 0.976111i | \(0.430284\pi\) | |||||||
\(20\) | 1.38080e6 | 0.0964867 | ||||||||
\(21\) | 9.95518e6 | 0.531916 | ||||||||
\(22\) | −1.09855e7 | −0.454458 | ||||||||
\(23\) | 2.01048e7 | 0.651324 | 0.325662 | − | 0.945486i | \(-0.394413\pi\) | ||||
0.325662 | + | 0.945486i | \(0.394413\pi\) | |||||||
\(24\) | −2.38131e7 | −0.610455 | ||||||||
\(25\) | −2.57911e7 | −0.528202 | ||||||||
\(26\) | 1.34429e7 | 0.221891 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | 1.17859e7 | 0.129417 | ||||||||
\(29\) | 9.30191e7 | 0.842138 | 0.421069 | − | 0.907029i | \(-0.361655\pi\) | ||||
0.421069 | + | 0.907029i | \(0.361655\pi\) | |||||||
\(30\) | −4.89344e7 | −0.367661 | ||||||||
\(31\) | 4.66282e7 | 0.292523 | 0.146261 | − | 0.989246i | \(-0.453276\pi\) | ||||
0.146261 | + | 0.989246i | \(0.453276\pi\) | |||||||
\(32\) | −5.29119e7 | −0.278759 | ||||||||
\(33\) | −6.36253e7 | −0.283011 | ||||||||
\(34\) | −3.36052e8 | −1.26845 | ||||||||
\(35\) | 1.96633e8 | 0.632822 | ||||||||
\(36\) | −1.69876e7 | −0.0468239 | ||||||||
\(37\) | −4.29096e8 | −1.01729 | −0.508645 | − | 0.860976i | \(-0.669854\pi\) | ||||
−0.508645 | + | 0.860976i | \(0.669854\pi\) | |||||||
\(38\) | −1.96776e8 | −0.402868 | ||||||||
\(39\) | 7.78581e7 | 0.138181 | ||||||||
\(40\) | −4.70352e8 | −0.726261 | ||||||||
\(41\) | 1.99434e7 | 0.0268836 | 0.0134418 | − | 0.999910i | \(-0.495721\pi\) | ||||
0.0134418 | + | 0.999910i | \(0.495721\pi\) | |||||||
\(42\) | −4.17680e8 | −0.493143 | ||||||||
\(43\) | 1.68610e8 | 0.174907 | 0.0874536 | − | 0.996169i | \(-0.472127\pi\) | ||||
0.0874536 | + | 0.996169i | \(0.472127\pi\) | |||||||
\(44\) | −7.53256e7 | −0.0688578 | ||||||||
\(45\) | −2.83417e8 | −0.228959 | ||||||||
\(46\) | −8.43519e8 | −0.603847 | ||||||||
\(47\) | −5.76398e8 | −0.366593 | −0.183296 | − | 0.983058i | \(-0.558677\pi\) | ||||
−0.183296 | + | 0.983058i | \(0.558677\pi\) | |||||||
\(48\) | 8.55933e8 | 0.484856 | ||||||||
\(49\) | −2.98964e8 | −0.151196 | ||||||||
\(50\) | 1.08209e9 | 0.489700 | ||||||||
\(51\) | −1.94633e9 | −0.789917 | ||||||||
\(52\) | 9.21758e7 | 0.0336201 | ||||||||
\(53\) | 4.39963e9 | 1.44510 | 0.722551 | − | 0.691317i | \(-0.242969\pi\) | ||||
0.722551 | + | 0.691317i | \(0.242969\pi\) | |||||||
\(54\) | 6.02024e8 | 0.178422 | ||||||||
\(55\) | −1.25672e9 | −0.336699 | ||||||||
\(56\) | −4.01469e9 | −0.974133 | ||||||||
\(57\) | −1.13968e9 | −0.250884 | ||||||||
\(58\) | −3.90272e9 | −0.780752 | ||||||||
\(59\) | −7.14924e8 | −0.130189 | ||||||||
\(60\) | −3.35536e8 | −0.0557066 | ||||||||
\(61\) | −2.27729e9 | −0.345227 | −0.172613 | − | 0.984990i | \(-0.555221\pi\) | ||||
−0.172613 | + | 0.984990i | \(0.555221\pi\) | |||||||
\(62\) | −1.95634e9 | −0.271200 | ||||||||
\(63\) | −2.41911e9 | −0.307102 | ||||||||
\(64\) | 9.43377e9 | 1.09824 | ||||||||
\(65\) | 1.53784e9 | 0.164395 | ||||||||
\(66\) | 2.66947e9 | 0.262382 | ||||||||
\(67\) | 1.03436e10 | 0.935970 | 0.467985 | − | 0.883736i | \(-0.344980\pi\) | ||||
0.467985 | + | 0.883736i | \(0.344980\pi\) | |||||||
\(68\) | −2.30425e9 | −0.192190 | ||||||||
\(69\) | −4.88547e9 | −0.376042 | ||||||||
\(70\) | −8.24995e9 | −0.586694 | ||||||||
\(71\) | −2.02693e10 | −1.33327 | −0.666635 | − | 0.745384i | \(-0.732266\pi\) | ||||
−0.666635 | + | 0.745384i | \(0.732266\pi\) | |||||||
\(72\) | 5.78658e9 | 0.352447 | ||||||||
\(73\) | −3.07148e10 | −1.73409 | −0.867046 | − | 0.498227i | \(-0.833985\pi\) | ||||
−0.867046 | + | 0.498227i | \(0.833985\pi\) | |||||||
\(74\) | 1.80032e10 | 0.943138 | ||||||||
\(75\) | 6.26724e9 | 0.304957 | ||||||||
\(76\) | −1.34926e9 | −0.0610411 | ||||||||
\(77\) | −1.07267e10 | −0.451614 | ||||||||
\(78\) | −3.26662e9 | −0.128109 | ||||||||
\(79\) | −2.51513e10 | −0.919626 | −0.459813 | − | 0.888016i | \(-0.652083\pi\) | ||||
−0.459813 | + | 0.888016i | \(0.652083\pi\) | |||||||
\(80\) | 1.69062e10 | 0.576835 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −8.36747e8 | −0.0249240 | ||||||||
\(83\) | −1.75237e10 | −0.488312 | −0.244156 | − | 0.969736i | \(-0.578511\pi\) | ||||
−0.244156 | + | 0.969736i | \(0.578511\pi\) | |||||||
\(84\) | −2.86397e9 | −0.0747192 | ||||||||
\(85\) | −3.84436e10 | −0.939767 | ||||||||
\(86\) | −7.07423e9 | −0.162158 | ||||||||
\(87\) | −2.26036e10 | −0.486208 | ||||||||
\(88\) | 2.56586e10 | 0.518297 | ||||||||
\(89\) | −1.52045e10 | −0.288621 | −0.144310 | − | 0.989532i | \(-0.546096\pi\) | ||||
−0.144310 | + | 0.989532i | \(0.546096\pi\) | |||||||
\(90\) | 1.18911e10 | 0.212269 | ||||||||
\(91\) | 1.31262e10 | 0.220502 | ||||||||
\(92\) | −5.78388e9 | −0.0914926 | ||||||||
\(93\) | −1.13307e10 | −0.168888 | ||||||||
\(94\) | 2.41834e10 | 0.339871 | ||||||||
\(95\) | −2.25108e10 | −0.298477 | ||||||||
\(96\) | 1.28576e10 | 0.160942 | ||||||||
\(97\) | 1.56615e10 | 0.185178 | 0.0925889 | − | 0.995704i | \(-0.470486\pi\) | ||||
0.0925889 | + | 0.995704i | \(0.470486\pi\) | |||||||
\(98\) | 1.25434e10 | 0.140175 | ||||||||
\(99\) | 1.54610e10 | 0.163396 | ||||||||
\(100\) | 7.41975e9 | 0.0741975 | ||||||||
\(101\) | 1.14234e11 | 1.08151 | 0.540753 | − | 0.841182i | \(-0.318139\pi\) | ||||
0.540753 | + | 0.841182i | \(0.318139\pi\) | |||||||
\(102\) | 8.16606e10 | 0.732338 | ||||||||
\(103\) | −2.14743e11 | −1.82522 | −0.912610 | − | 0.408831i | \(-0.865937\pi\) | ||||
−0.912610 | + | 0.408831i | \(0.865937\pi\) | |||||||
\(104\) | −3.13984e10 | −0.253060 | ||||||||
\(105\) | −4.77818e10 | −0.365360 | ||||||||
\(106\) | −1.84591e11 | −1.33977 | ||||||||
\(107\) | −7.73008e10 | −0.532811 | −0.266406 | − | 0.963861i | \(-0.585836\pi\) | ||||
−0.266406 | + | 0.963861i | \(0.585836\pi\) | |||||||
\(108\) | 4.12798e9 | 0.0270338 | ||||||||
\(109\) | 1.16831e11 | 0.727300 | 0.363650 | − | 0.931536i | \(-0.381530\pi\) | ||||
0.363650 | + | 0.931536i | \(0.381530\pi\) | |||||||
\(110\) | 5.27269e10 | 0.312156 | ||||||||
\(111\) | 1.04270e11 | 0.587333 | ||||||||
\(112\) | 1.44303e11 | 0.773709 | ||||||||
\(113\) | 3.30169e10 | 0.168580 | 0.0842899 | − | 0.996441i | \(-0.473138\pi\) | ||||
0.0842899 | + | 0.996441i | \(0.473138\pi\) | |||||||
\(114\) | 4.78167e10 | 0.232596 | ||||||||
\(115\) | −9.64968e10 | −0.447378 | ||||||||
\(116\) | −2.67603e10 | −0.118297 | ||||||||
\(117\) | −1.89195e10 | −0.0797789 | ||||||||
\(118\) | 2.99954e10 | 0.120699 | ||||||||
\(119\) | −3.28136e11 | −1.26051 | ||||||||
\(120\) | 1.14295e11 | 0.419307 | ||||||||
\(121\) | −2.16755e11 | −0.759714 | ||||||||
\(122\) | 9.55462e10 | 0.320062 | ||||||||
\(123\) | −4.84624e9 | −0.0155213 | ||||||||
\(124\) | −1.34143e10 | −0.0410912 | ||||||||
\(125\) | 3.58149e11 | 1.04968 | ||||||||
\(126\) | 1.01496e11 | 0.284716 | ||||||||
\(127\) | 3.12876e11 | 0.840333 | 0.420166 | − | 0.907447i | \(-0.361972\pi\) | ||||
0.420166 | + | 0.907447i | \(0.361972\pi\) | |||||||
\(128\) | −2.87440e11 | −0.739423 | ||||||||
\(129\) | −4.09723e10 | −0.100983 | ||||||||
\(130\) | −6.45217e10 | −0.152411 | ||||||||
\(131\) | −2.09307e11 | −0.474014 | −0.237007 | − | 0.971508i | \(-0.576166\pi\) | ||||
−0.237007 | + | 0.971508i | \(0.576166\pi\) | |||||||
\(132\) | 1.83041e10 | 0.0397551 | ||||||||
\(133\) | −1.92141e11 | −0.400347 | ||||||||
\(134\) | −4.33979e11 | −0.867745 | ||||||||
\(135\) | 6.88703e10 | 0.132189 | ||||||||
\(136\) | 7.84912e11 | 1.44663 | ||||||||
\(137\) | −6.26380e11 | −1.10886 | −0.554428 | − | 0.832232i | \(-0.687063\pi\) | ||||
−0.554428 | + | 0.832232i | \(0.687063\pi\) | |||||||
\(138\) | 2.04975e11 | 0.348631 | ||||||||
\(139\) | 8.36338e11 | 1.36710 | 0.683550 | − | 0.729903i | \(-0.260435\pi\) | ||||
0.683550 | + | 0.729903i | \(0.260435\pi\) | |||||||
\(140\) | −5.65686e10 | −0.0888937 | ||||||||
\(141\) | 1.40065e11 | 0.211653 | ||||||||
\(142\) | 8.50422e11 | 1.23609 | ||||||||
\(143\) | −8.38922e10 | −0.117320 | ||||||||
\(144\) | −2.07992e11 | −0.279932 | ||||||||
\(145\) | −4.46463e11 | −0.578444 | ||||||||
\(146\) | 1.28867e12 | 1.60769 | ||||||||
\(147\) | 7.26483e10 | 0.0872932 | ||||||||
\(148\) | 1.23445e11 | 0.142901 | ||||||||
\(149\) | −7.28067e11 | −0.812170 | −0.406085 | − | 0.913835i | \(-0.633106\pi\) | ||||
−0.406085 | + | 0.913835i | \(0.633106\pi\) | |||||||
\(150\) | −2.62949e11 | −0.282728 | ||||||||
\(151\) | 1.11462e12 | 1.15546 | 0.577730 | − | 0.816228i | \(-0.303939\pi\) | ||||
0.577730 | + | 0.816228i | \(0.303939\pi\) | |||||||
\(152\) | 4.59608e11 | 0.459460 | ||||||||
\(153\) | 4.72959e11 | 0.456059 | ||||||||
\(154\) | 4.50051e11 | 0.418695 | ||||||||
\(155\) | −2.23801e11 | −0.200927 | ||||||||
\(156\) | −2.23987e10 | −0.0194106 | ||||||||
\(157\) | 1.18440e12 | 0.990944 | 0.495472 | − | 0.868624i | \(-0.334995\pi\) | ||||
0.495472 | + | 0.868624i | \(0.334995\pi\) | |||||||
\(158\) | 1.05525e12 | 0.852592 | ||||||||
\(159\) | −1.06911e12 | −0.834330 | ||||||||
\(160\) | 2.53961e11 | 0.191473 | ||||||||
\(161\) | −8.23650e11 | −0.600068 | ||||||||
\(162\) | −1.46292e11 | −0.103012 | ||||||||
\(163\) | 1.05240e12 | 0.716387 | 0.358194 | − | 0.933647i | \(-0.383393\pi\) | ||||
0.358194 | + | 0.933647i | \(0.383393\pi\) | |||||||
\(164\) | −5.73744e9 | −0.00377639 | ||||||||
\(165\) | 3.05382e11 | 0.194393 | ||||||||
\(166\) | 7.35228e11 | 0.452717 | ||||||||
\(167\) | 4.67477e11 | 0.278496 | 0.139248 | − | 0.990258i | \(-0.455531\pi\) | ||||
0.139248 | + | 0.990258i | \(0.455531\pi\) | |||||||
\(168\) | 9.75571e11 | 0.562416 | ||||||||
\(169\) | −1.68950e12 | −0.942718 | ||||||||
\(170\) | 1.61294e12 | 0.871265 | ||||||||
\(171\) | 2.76943e11 | 0.144848 | ||||||||
\(172\) | −4.85069e10 | −0.0245695 | ||||||||
\(173\) | 2.74846e12 | 1.34845 | 0.674227 | − | 0.738524i | \(-0.264477\pi\) | ||||
0.674227 | + | 0.738524i | \(0.264477\pi\) | |||||||
\(174\) | 9.48360e11 | 0.450767 | ||||||||
\(175\) | 1.05661e12 | 0.486635 | ||||||||
\(176\) | −9.22268e11 | −0.411659 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | 6.37922e11 | 0.267583 | ||||||||
\(179\) | 1.23655e12 | 0.502946 | 0.251473 | − | 0.967864i | \(-0.419085\pi\) | ||||
0.251473 | + | 0.967864i | \(0.419085\pi\) | |||||||
\(180\) | 8.15351e10 | 0.0321622 | ||||||||
\(181\) | −2.36395e12 | −0.904497 | −0.452248 | − | 0.891892i | \(-0.649378\pi\) | ||||
−0.452248 | + | 0.891892i | \(0.649378\pi\) | |||||||
\(182\) | −5.50726e11 | −0.204429 | ||||||||
\(183\) | 5.53381e11 | 0.199317 | ||||||||
\(184\) | 1.97020e12 | 0.688671 | ||||||||
\(185\) | 2.05953e12 | 0.698752 | ||||||||
\(186\) | 4.75390e11 | 0.156577 | ||||||||
\(187\) | 2.09718e12 | 0.670666 | ||||||||
\(188\) | 1.65822e11 | 0.0514960 | ||||||||
\(189\) | 5.87843e11 | 0.177305 | ||||||||
\(190\) | 9.44466e11 | 0.276721 | ||||||||
\(191\) | 1.66476e12 | 0.473879 | 0.236939 | − | 0.971524i | \(-0.423856\pi\) | ||||
0.236939 | + | 0.971524i | \(0.423856\pi\) | |||||||
\(192\) | −2.29241e12 | −0.634066 | ||||||||
\(193\) | 2.43187e12 | 0.653696 | 0.326848 | − | 0.945077i | \(-0.394014\pi\) | ||||
0.326848 | + | 0.945077i | \(0.394014\pi\) | |||||||
\(194\) | −6.57096e11 | −0.171680 | ||||||||
\(195\) | −3.73695e11 | −0.0949132 | ||||||||
\(196\) | 8.60079e10 | 0.0212388 | ||||||||
\(197\) | 4.03087e12 | 0.967910 | 0.483955 | − | 0.875093i | \(-0.339200\pi\) | ||||
0.483955 | + | 0.875093i | \(0.339200\pi\) | |||||||
\(198\) | −6.48681e11 | −0.151486 | ||||||||
\(199\) | 2.52695e12 | 0.573991 | 0.286996 | − | 0.957932i | \(-0.407343\pi\) | ||||
0.286996 | + | 0.957932i | \(0.407343\pi\) | |||||||
\(200\) | −2.52743e12 | −0.558489 | ||||||||
\(201\) | −2.51350e12 | −0.540382 | ||||||||
\(202\) | −4.79282e12 | −1.00267 | ||||||||
\(203\) | −3.81079e12 | −0.775866 | ||||||||
\(204\) | 5.59934e11 | 0.110961 | ||||||||
\(205\) | −9.57221e10 | −0.0184657 | ||||||||
\(206\) | 9.00980e12 | 1.69218 | ||||||||
\(207\) | 1.18717e12 | 0.217108 | ||||||||
\(208\) | 1.12858e12 | 0.200994 | ||||||||
\(209\) | 1.22801e12 | 0.213009 | ||||||||
\(210\) | 2.00474e12 | 0.338728 | ||||||||
\(211\) | −3.90004e12 | −0.641971 | −0.320985 | − | 0.947084i | \(-0.604014\pi\) | ||||
−0.320985 | + | 0.947084i | \(0.604014\pi\) | |||||||
\(212\) | −1.26571e12 | −0.202996 | ||||||||
\(213\) | 4.92545e12 | 0.769764 | ||||||||
\(214\) | 3.24324e12 | 0.493973 | ||||||||
\(215\) | −8.09277e11 | −0.120139 | ||||||||
\(216\) | −1.40614e12 | −0.203485 | ||||||||
\(217\) | −1.91026e12 | −0.269503 | ||||||||
\(218\) | −4.90179e12 | −0.674285 | ||||||||
\(219\) | 7.46370e12 | 1.00118 | ||||||||
\(220\) | 3.61540e11 | 0.0472967 | ||||||||
\(221\) | −2.56631e12 | −0.327455 | ||||||||
\(222\) | −4.37478e12 | −0.544521 | ||||||||
\(223\) | −4.30330e12 | −0.522546 | −0.261273 | − | 0.965265i | \(-0.584142\pi\) | ||||
−0.261273 | + | 0.965265i | \(0.584142\pi\) | |||||||
\(224\) | 2.16769e12 | 0.256822 | ||||||||
\(225\) | −1.52294e12 | −0.176067 | ||||||||
\(226\) | −1.38526e12 | −0.156291 | ||||||||
\(227\) | 6.55576e12 | 0.721907 | 0.360953 | − | 0.932584i | \(-0.382451\pi\) | ||||
0.360953 | + | 0.932584i | \(0.382451\pi\) | |||||||
\(228\) | 3.27871e11 | 0.0352421 | ||||||||
\(229\) | 1.14174e13 | 1.19805 | 0.599023 | − | 0.800731i | \(-0.295556\pi\) | ||||
0.599023 | + | 0.800731i | \(0.295556\pi\) | |||||||
\(230\) | 4.04863e12 | 0.414768 | ||||||||
\(231\) | 2.60659e12 | 0.260740 | ||||||||
\(232\) | 9.11552e12 | 0.890426 | ||||||||
\(233\) | 1.28113e13 | 1.22218 | 0.611090 | − | 0.791561i | \(-0.290731\pi\) | ||||
0.611090 | + | 0.791561i | \(0.290731\pi\) | |||||||
\(234\) | 7.93790e11 | 0.0739636 | ||||||||
\(235\) | 2.76653e12 | 0.251804 | ||||||||
\(236\) | 2.05674e11 | 0.0182879 | ||||||||
\(237\) | 6.11176e12 | 0.530946 | ||||||||
\(238\) | 1.37673e13 | 1.16863 | ||||||||
\(239\) | −2.88344e12 | −0.239179 | −0.119589 | − | 0.992823i | \(-0.538158\pi\) | ||||
−0.119589 | + | 0.992823i | \(0.538158\pi\) | |||||||
\(240\) | −4.10821e12 | −0.333036 | ||||||||
\(241\) | 9.71704e12 | 0.769911 | 0.384955 | − | 0.922935i | \(-0.374217\pi\) | ||||
0.384955 | + | 0.922935i | \(0.374217\pi\) | |||||||
\(242\) | 9.09421e12 | 0.704337 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | 6.55145e11 | 0.0484946 | ||||||||
\(245\) | 1.43494e12 | 0.103853 | ||||||||
\(246\) | 2.03329e11 | 0.0143899 | ||||||||
\(247\) | −1.50271e12 | −0.104002 | ||||||||
\(248\) | 4.56939e12 | 0.309296 | ||||||||
\(249\) | 4.25827e12 | 0.281927 | ||||||||
\(250\) | −1.50265e13 | −0.973170 | ||||||||
\(251\) | 6.06579e12 | 0.384310 | 0.192155 | − | 0.981365i | \(-0.438452\pi\) | ||||
0.192155 | + | 0.981365i | \(0.438452\pi\) | |||||||
\(252\) | 6.95944e11 | 0.0431392 | ||||||||
\(253\) | 5.26409e12 | 0.319272 | ||||||||
\(254\) | −1.31270e13 | −0.779079 | ||||||||
\(255\) | 9.34180e12 | 0.542575 | ||||||||
\(256\) | −7.26048e12 | −0.412711 | ||||||||
\(257\) | 6.71155e12 | 0.373414 | 0.186707 | − | 0.982416i | \(-0.440219\pi\) | ||||
0.186707 | + | 0.982416i | \(0.440219\pi\) | |||||||
\(258\) | 1.71904e12 | 0.0936218 | ||||||||
\(259\) | 1.75791e13 | 0.937235 | ||||||||
\(260\) | −4.42415e11 | −0.0230928 | ||||||||
\(261\) | 5.49268e12 | 0.280713 | ||||||||
\(262\) | 8.78169e12 | 0.439462 | ||||||||
\(263\) | −3.03108e13 | −1.48539 | −0.742696 | − | 0.669629i | \(-0.766453\pi\) | ||||
−0.742696 | + | 0.669629i | \(0.766453\pi\) | |||||||
\(264\) | −6.23504e12 | −0.299239 | ||||||||
\(265\) | −2.11168e13 | −0.992606 | ||||||||
\(266\) | 8.06150e12 | 0.371165 | ||||||||
\(267\) | 3.69470e12 | 0.166635 | ||||||||
\(268\) | −2.97572e12 | −0.131477 | ||||||||
\(269\) | −3.36364e13 | −1.45604 | −0.728018 | − | 0.685558i | \(-0.759558\pi\) | ||||
−0.728018 | + | 0.685558i | \(0.759558\pi\) | |||||||
\(270\) | −2.88953e12 | −0.122554 | ||||||||
\(271\) | 8.58630e12 | 0.356841 | 0.178420 | − | 0.983954i | \(-0.442901\pi\) | ||||
0.178420 | + | 0.983954i | \(0.442901\pi\) | |||||||
\(272\) | −2.82127e13 | −1.14899 | ||||||||
\(273\) | −3.18968e12 | −0.127307 | ||||||||
\(274\) | 2.62805e13 | 1.02803 | ||||||||
\(275\) | −6.75295e12 | −0.258919 | ||||||||
\(276\) | 1.40548e12 | 0.0528233 | ||||||||
\(277\) | −4.36554e13 | −1.60842 | −0.804210 | − | 0.594345i | \(-0.797411\pi\) | ||||
−0.804210 | + | 0.594345i | \(0.797411\pi\) | |||||||
\(278\) | −3.50895e13 | −1.26745 | ||||||||
\(279\) | 2.75335e12 | 0.0975075 | ||||||||
\(280\) | 1.92693e13 | 0.669108 | ||||||||
\(281\) | −4.91273e13 | −1.67278 | −0.836390 | − | 0.548136i | \(-0.815338\pi\) | ||||
−0.836390 | + | 0.548136i | \(0.815338\pi\) | |||||||
\(282\) | −5.87657e12 | −0.196225 | ||||||||
\(283\) | −5.03326e13 | −1.64825 | −0.824127 | − | 0.566405i | \(-0.808334\pi\) | ||||
−0.824127 | + | 0.566405i | \(0.808334\pi\) | |||||||
\(284\) | 5.83121e12 | 0.187287 | ||||||||
\(285\) | 5.47013e12 | 0.172326 | ||||||||
\(286\) | 3.51979e12 | 0.108769 | ||||||||
\(287\) | −8.17037e11 | −0.0247680 | ||||||||
\(288\) | −3.12440e12 | −0.0929196 | ||||||||
\(289\) | 2.98819e13 | 0.871907 | ||||||||
\(290\) | 1.87318e13 | 0.536280 | ||||||||
\(291\) | −3.80575e12 | −0.106912 | ||||||||
\(292\) | 8.83624e12 | 0.243591 | ||||||||
\(293\) | −3.72144e13 | −1.00679 | −0.503396 | − | 0.864056i | \(-0.667916\pi\) | ||||
−0.503396 | + | 0.864056i | \(0.667916\pi\) | |||||||
\(294\) | −3.04804e12 | −0.0809302 | ||||||||
\(295\) | 3.43141e12 | 0.0894236 | ||||||||
\(296\) | −4.20498e13 | −1.07562 | ||||||||
\(297\) | −3.75701e12 | −0.0943370 | ||||||||
\(298\) | 3.05469e13 | 0.752969 | ||||||||
\(299\) | −6.44166e12 | −0.155886 | ||||||||
\(300\) | −1.80300e12 | −0.0428379 | ||||||||
\(301\) | −6.90760e12 | −0.161143 | ||||||||
\(302\) | −4.67653e13 | −1.07124 | ||||||||
\(303\) | −2.77589e13 | −0.624407 | ||||||||
\(304\) | −1.65201e13 | −0.364928 | ||||||||
\(305\) | 1.09303e13 | 0.237128 | ||||||||
\(306\) | −1.98435e13 | −0.422816 | ||||||||
\(307\) | 4.67400e13 | 0.978199 | 0.489100 | − | 0.872228i | \(-0.337325\pi\) | ||||
0.489100 | + | 0.872228i | \(0.337325\pi\) | |||||||
\(308\) | 3.08593e12 | 0.0634391 | ||||||||
\(309\) | 5.21827e13 | 1.05379 | ||||||||
\(310\) | 9.38981e12 | 0.186281 | ||||||||
\(311\) | −1.49199e13 | −0.290792 | −0.145396 | − | 0.989374i | \(-0.546446\pi\) | ||||
−0.145396 | + | 0.989374i | \(0.546446\pi\) | |||||||
\(312\) | 7.62981e12 | 0.146104 | ||||||||
\(313\) | 2.38159e13 | 0.448097 | 0.224049 | − | 0.974578i | \(-0.428073\pi\) | ||||
0.224049 | + | 0.974578i | \(0.428073\pi\) | |||||||
\(314\) | −4.96927e13 | −0.918712 | ||||||||
\(315\) | 1.16110e13 | 0.210941 | ||||||||
\(316\) | 7.23568e12 | 0.129181 | ||||||||
\(317\) | −5.45968e13 | −0.957947 | −0.478973 | − | 0.877829i | \(-0.658991\pi\) | ||||
−0.478973 | + | 0.877829i | \(0.658991\pi\) | |||||||
\(318\) | 4.48557e13 | 0.773514 | ||||||||
\(319\) | 2.43554e13 | 0.412807 | ||||||||
\(320\) | −4.52792e13 | −0.754351 | ||||||||
\(321\) | 1.87841e13 | 0.307619 | ||||||||
\(322\) | 3.45571e13 | 0.556328 | ||||||||
\(323\) | 3.75655e13 | 0.594532 | ||||||||
\(324\) | −1.00310e12 | −0.0156080 | ||||||||
\(325\) | 8.26357e12 | 0.126418 | ||||||||
\(326\) | −4.41545e13 | −0.664168 | ||||||||
\(327\) | −2.83900e13 | −0.419907 | ||||||||
\(328\) | 1.95438e12 | 0.0284251 | ||||||||
\(329\) | 2.36138e13 | 0.337744 | ||||||||
\(330\) | −1.28126e13 | −0.180224 | ||||||||
\(331\) | 4.03726e13 | 0.558512 | 0.279256 | − | 0.960217i | \(-0.409912\pi\) | ||||
0.279256 | + | 0.960217i | \(0.409912\pi\) | |||||||
\(332\) | 5.04134e12 | 0.0685940 | ||||||||
\(333\) | −2.53377e13 | −0.339097 | ||||||||
\(334\) | −1.96135e13 | −0.258196 | ||||||||
\(335\) | −4.96463e13 | −0.642895 | ||||||||
\(336\) | −3.50657e13 | −0.446701 | ||||||||
\(337\) | −2.58730e12 | −0.0324251 | −0.0162126 | − | 0.999869i | \(-0.505161\pi\) | ||||
−0.0162126 | + | 0.999869i | \(0.505161\pi\) | |||||||
\(338\) | 7.08849e13 | 0.874001 | ||||||||
\(339\) | −8.02311e12 | −0.0973295 | ||||||||
\(340\) | 1.10597e13 | 0.132011 | ||||||||
\(341\) | 1.22088e13 | 0.143391 | ||||||||
\(342\) | −1.16195e13 | −0.134289 | ||||||||
\(343\) | 9.32547e13 | 1.06060 | ||||||||
\(344\) | 1.65232e13 | 0.184936 | ||||||||
\(345\) | 2.34487e13 | 0.258294 | ||||||||
\(346\) | −1.15315e14 | −1.25016 | ||||||||
\(347\) | −1.16111e14 | −1.23897 | −0.619486 | − | 0.785008i | \(-0.712659\pi\) | ||||
−0.619486 | + | 0.785008i | \(0.712659\pi\) | |||||||
\(348\) | 6.50276e12 | 0.0682986 | ||||||||
\(349\) | −8.24104e12 | −0.0852005 | −0.0426002 | − | 0.999092i | \(-0.513564\pi\) | ||||
−0.0426002 | + | 0.999092i | \(0.513564\pi\) | |||||||
\(350\) | −4.43310e13 | −0.451163 | ||||||||
\(351\) | 4.59745e12 | 0.0460604 | ||||||||
\(352\) | −1.38541e13 | −0.136645 | ||||||||
\(353\) | 1.18877e14 | 1.15435 | 0.577174 | − | 0.816621i | \(-0.304156\pi\) | ||||
0.577174 | + | 0.816621i | \(0.304156\pi\) | |||||||
\(354\) | −7.28889e12 | −0.0696857 | ||||||||
\(355\) | 9.72865e13 | 0.915791 | ||||||||
\(356\) | 4.37413e12 | 0.0405431 | ||||||||
\(357\) | 7.97371e13 | 0.727755 | ||||||||
\(358\) | −5.18810e13 | −0.466285 | ||||||||
\(359\) | 1.53675e14 | 1.36014 | 0.680070 | − | 0.733147i | \(-0.261949\pi\) | ||||
0.680070 | + | 0.733147i | \(0.261949\pi\) | |||||||
\(360\) | −2.77738e13 | −0.242087 | ||||||||
\(361\) | −9.44936e13 | −0.811172 | ||||||||
\(362\) | 9.91823e13 | 0.838565 | ||||||||
\(363\) | 5.26716e13 | 0.438621 | ||||||||
\(364\) | −3.77624e12 | −0.0309743 | ||||||||
\(365\) | 1.47422e14 | 1.19111 | ||||||||
\(366\) | −2.32177e13 | −0.184788 | ||||||||
\(367\) | 2.07126e13 | 0.162394 | 0.0811972 | − | 0.996698i | \(-0.474126\pi\) | ||||
0.0811972 | + | 0.996698i | \(0.474126\pi\) | |||||||
\(368\) | −7.08164e13 | −0.546979 | ||||||||
\(369\) | 1.17764e12 | 0.00896121 | ||||||||
\(370\) | −8.64097e13 | −0.647818 | ||||||||
\(371\) | −1.80243e14 | −1.33138 | ||||||||
\(372\) | 3.25967e12 | 0.0237240 | ||||||||
\(373\) | 7.14846e13 | 0.512642 | 0.256321 | − | 0.966592i | \(-0.417490\pi\) | ||||
0.256321 | + | 0.966592i | \(0.417490\pi\) | |||||||
\(374\) | −8.79893e13 | −0.621779 | ||||||||
\(375\) | −8.70302e13 | −0.606036 | ||||||||
\(376\) | −5.64848e13 | −0.387613 | ||||||||
\(377\) | −2.98037e13 | −0.201554 | ||||||||
\(378\) | −2.46636e13 | −0.164381 | ||||||||
\(379\) | −1.47308e14 | −0.967633 | −0.483816 | − | 0.875170i | \(-0.660750\pi\) | ||||
−0.483816 | + | 0.875170i | \(0.660750\pi\) | |||||||
\(380\) | 6.47605e12 | 0.0419277 | ||||||||
\(381\) | −7.60288e13 | −0.485166 | ||||||||
\(382\) | −6.98467e13 | −0.439336 | ||||||||
\(383\) | −2.62373e14 | −1.62677 | −0.813386 | − | 0.581725i | \(-0.802378\pi\) | ||||
−0.813386 | + | 0.581725i | \(0.802378\pi\) | |||||||
\(384\) | 6.98480e13 | 0.426906 | ||||||||
\(385\) | 5.14849e13 | 0.310203 | ||||||||
\(386\) | −1.02032e14 | −0.606046 | ||||||||
\(387\) | 9.95627e12 | 0.0583024 | ||||||||
\(388\) | −4.50560e12 | −0.0260123 | ||||||||
\(389\) | −8.11217e13 | −0.461758 | −0.230879 | − | 0.972982i | \(-0.574160\pi\) | ||||
−0.230879 | + | 0.972982i | \(0.574160\pi\) | |||||||
\(390\) | 1.56788e13 | 0.0879948 | ||||||||
\(391\) | 1.61032e14 | 0.891126 | ||||||||
\(392\) | −2.92974e13 | −0.159866 | ||||||||
\(393\) | 5.08615e13 | 0.273672 | ||||||||
\(394\) | −1.69120e14 | −0.897357 | ||||||||
\(395\) | 1.20718e14 | 0.631668 | ||||||||
\(396\) | −4.44790e12 | −0.0229526 | ||||||||
\(397\) | −1.00735e14 | −0.512663 | −0.256331 | − | 0.966589i | \(-0.582514\pi\) | ||||
−0.256331 | + | 0.966589i | \(0.582514\pi\) | |||||||
\(398\) | −1.06021e14 | −0.532152 | ||||||||
\(399\) | 4.66904e13 | 0.231141 | ||||||||
\(400\) | 9.08455e13 | 0.443582 | ||||||||
\(401\) | −1.25734e14 | −0.605564 | −0.302782 | − | 0.953060i | \(-0.597915\pi\) | ||||
−0.302782 | + | 0.953060i | \(0.597915\pi\) | |||||||
\(402\) | 1.05457e14 | 0.500993 | ||||||||
\(403\) | −1.49399e13 | −0.0700114 | ||||||||
\(404\) | −3.28636e13 | −0.151921 | ||||||||
\(405\) | −1.67355e13 | −0.0763195 | ||||||||
\(406\) | 1.59886e14 | 0.719311 | ||||||||
\(407\) | −1.12351e14 | −0.498665 | ||||||||
\(408\) | −1.90734e14 | −0.835211 | ||||||||
\(409\) | −1.64182e14 | −0.709329 | −0.354664 | − | 0.934994i | \(-0.615405\pi\) | ||||
−0.354664 | + | 0.934994i | \(0.615405\pi\) | |||||||
\(410\) | 4.01612e12 | 0.0171197 | ||||||||
\(411\) | 1.52210e14 | 0.640198 | ||||||||
\(412\) | 6.17788e13 | 0.256392 | ||||||||
\(413\) | 2.92889e13 | 0.119944 | ||||||||
\(414\) | −4.98090e13 | −0.201282 | ||||||||
\(415\) | 8.41085e13 | 0.335409 | ||||||||
\(416\) | 1.69532e13 | 0.0667172 | ||||||||
\(417\) | −2.03230e14 | −0.789296 | ||||||||
\(418\) | −5.15225e13 | −0.197482 | ||||||||
\(419\) | 4.55120e13 | 0.172167 | 0.0860834 | − | 0.996288i | \(-0.472565\pi\) | ||||
0.0860834 | + | 0.996288i | \(0.472565\pi\) | |||||||
\(420\) | 1.37462e13 | 0.0513228 | ||||||||
\(421\) | 1.11206e14 | 0.409804 | 0.204902 | − | 0.978782i | \(-0.434312\pi\) | ||||
0.204902 | + | 0.978782i | \(0.434312\pi\) | |||||||
\(422\) | 1.63630e14 | 0.595176 | ||||||||
\(423\) | −3.40357e13 | −0.122198 | ||||||||
\(424\) | 4.31147e14 | 1.52796 | ||||||||
\(425\) | −2.06577e14 | −0.722673 | ||||||||
\(426\) | −2.06652e14 | −0.713654 | ||||||||
\(427\) | 9.32956e13 | 0.318059 | ||||||||
\(428\) | 2.22384e13 | 0.0748450 | ||||||||
\(429\) | 2.03858e13 | 0.0677349 | ||||||||
\(430\) | 3.39541e13 | 0.111382 | ||||||||
\(431\) | 5.12340e14 | 1.65933 | 0.829667 | − | 0.558259i | \(-0.188531\pi\) | ||||
0.829667 | + | 0.558259i | \(0.188531\pi\) | |||||||
\(432\) | 5.05420e13 | 0.161619 | ||||||||
\(433\) | 5.37809e14 | 1.69803 | 0.849014 | − | 0.528370i | \(-0.177197\pi\) | ||||
0.849014 | + | 0.528370i | \(0.177197\pi\) | |||||||
\(434\) | 8.01469e13 | 0.249858 | ||||||||
\(435\) | 1.08490e14 | 0.333965 | ||||||||
\(436\) | −3.36108e13 | −0.102165 | ||||||||
\(437\) | 9.42927e13 | 0.283028 | ||||||||
\(438\) | −3.13148e14 | −0.928201 | ||||||||
\(439\) | −5.56321e13 | −0.162844 | −0.0814219 | − | 0.996680i | \(-0.525946\pi\) | ||||
−0.0814219 | + | 0.996680i | \(0.525946\pi\) | |||||||
\(440\) | −1.23153e14 | −0.356005 | ||||||||
\(441\) | −1.76535e13 | −0.0503987 | ||||||||
\(442\) | 1.07672e14 | 0.303586 | ||||||||
\(443\) | −9.33511e13 | −0.259955 | −0.129978 | − | 0.991517i | \(-0.541491\pi\) | ||||
−0.129978 | + | 0.991517i | \(0.541491\pi\) | |||||||
\(444\) | −2.99971e13 | −0.0825037 | ||||||||
\(445\) | 7.29770e13 | 0.198247 | ||||||||
\(446\) | 1.80550e14 | 0.484456 | ||||||||
\(447\) | 1.76920e14 | 0.468907 | ||||||||
\(448\) | −3.86481e14 | −1.01181 | ||||||||
\(449\) | 1.14106e14 | 0.295089 | 0.147544 | − | 0.989055i | \(-0.452863\pi\) | ||||
0.147544 | + | 0.989055i | \(0.452863\pi\) | |||||||
\(450\) | 6.38966e13 | 0.163233 | ||||||||
\(451\) | 5.22183e12 | 0.0131781 | ||||||||
\(452\) | −9.49852e12 | −0.0236807 | ||||||||
\(453\) | −2.70854e14 | −0.667106 | ||||||||
\(454\) | −2.75054e14 | −0.669285 | ||||||||
\(455\) | −6.30019e13 | −0.151458 | ||||||||
\(456\) | −1.11685e14 | −0.265269 | ||||||||
\(457\) | −4.34785e13 | −0.102032 | −0.0510159 | − | 0.998698i | \(-0.516246\pi\) | ||||
−0.0510159 | + | 0.998698i | \(0.516246\pi\) | |||||||
\(458\) | −4.79031e14 | −1.11072 | ||||||||
\(459\) | −1.14929e14 | −0.263306 | ||||||||
\(460\) | 2.77608e13 | 0.0628441 | ||||||||
\(461\) | −3.79992e14 | −0.850000 | −0.425000 | − | 0.905193i | \(-0.639726\pi\) | ||||
−0.425000 | + | 0.905193i | \(0.639726\pi\) | |||||||
\(462\) | −1.09362e14 | −0.241734 | ||||||||
\(463\) | 4.53675e14 | 0.990945 | 0.495472 | − | 0.868624i | \(-0.334995\pi\) | ||||
0.495472 | + | 0.868624i | \(0.334995\pi\) | |||||||
\(464\) | −3.27647e14 | −0.707224 | ||||||||
\(465\) | 5.43836e13 | 0.116005 | ||||||||
\(466\) | −5.37512e14 | −1.13309 | ||||||||
\(467\) | 2.87881e14 | 0.599750 | 0.299875 | − | 0.953978i | \(-0.403055\pi\) | ||||
0.299875 | + | 0.953978i | \(0.403055\pi\) | |||||||
\(468\) | 5.44289e12 | 0.0112067 | ||||||||
\(469\) | −4.23756e14 | −0.862314 | ||||||||
\(470\) | −1.16073e14 | −0.233449 | ||||||||
\(471\) | −2.87808e14 | −0.572122 | ||||||||
\(472\) | −7.00599e13 | −0.137654 | ||||||||
\(473\) | 4.41477e13 | 0.0857377 | ||||||||
\(474\) | −2.56426e14 | −0.492244 | ||||||||
\(475\) | −1.20962e14 | −0.229527 | ||||||||
\(476\) | 9.44003e13 | 0.177066 | ||||||||
\(477\) | 2.59794e14 | 0.481701 | ||||||||
\(478\) | 1.20978e14 | 0.221744 | ||||||||
\(479\) | 1.77660e14 | 0.321917 | 0.160959 | − | 0.986961i | \(-0.448541\pi\) | ||||
0.160959 | + | 0.986961i | \(0.448541\pi\) | |||||||
\(480\) | −6.17125e13 | −0.110547 | ||||||||
\(481\) | 1.37484e14 | 0.243475 | ||||||||
\(482\) | −4.07689e14 | −0.713790 | ||||||||
\(483\) | 2.00147e14 | 0.346449 | ||||||||
\(484\) | 6.23575e13 | 0.106718 | ||||||||
\(485\) | −7.51704e13 | −0.127194 | ||||||||
\(486\) | 3.55489e13 | 0.0594740 | ||||||||
\(487\) | 2.41589e14 | 0.399639 | 0.199820 | − | 0.979833i | \(-0.435964\pi\) | ||||
0.199820 | + | 0.979833i | \(0.435964\pi\) | |||||||
\(488\) | −2.23166e14 | −0.365022 | ||||||||
\(489\) | −2.55732e14 | −0.413606 | ||||||||
\(490\) | −6.02043e13 | −0.0962829 | ||||||||
\(491\) | −1.18877e14 | −0.187997 | −0.0939986 | − | 0.995572i | \(-0.529965\pi\) | ||||
−0.0939986 | + | 0.995572i | \(0.529965\pi\) | |||||||
\(492\) | 1.39420e12 | 0.00218030 | ||||||||
\(493\) | 7.45046e14 | 1.15219 | ||||||||
\(494\) | 6.30479e13 | 0.0964212 | ||||||||
\(495\) | −7.42078e13 | −0.112233 | ||||||||
\(496\) | −1.64241e14 | −0.245659 | ||||||||
\(497\) | 8.30390e14 | 1.22835 | ||||||||
\(498\) | −1.78660e14 | −0.261377 | ||||||||
\(499\) | 1.20282e15 | 1.74040 | 0.870200 | − | 0.492698i | \(-0.163989\pi\) | ||||
0.870200 | + | 0.492698i | \(0.163989\pi\) | |||||||
\(500\) | −1.03035e14 | −0.147451 | ||||||||
\(501\) | −1.13597e14 | −0.160790 | ||||||||
\(502\) | −2.54497e14 | −0.356297 | ||||||||
\(503\) | −7.53438e14 | −1.04333 | −0.521667 | − | 0.853149i | \(-0.674690\pi\) | ||||
−0.521667 | + | 0.853149i | \(0.674690\pi\) | |||||||
\(504\) | −2.37064e14 | −0.324711 | ||||||||
\(505\) | −5.48289e14 | −0.742860 | ||||||||
\(506\) | −2.20861e14 | −0.295999 | ||||||||
\(507\) | 4.10549e14 | 0.544278 | ||||||||
\(508\) | −9.00100e13 | −0.118043 | ||||||||
\(509\) | −1.40721e14 | −0.182562 | −0.0912811 | − | 0.995825i | \(-0.529096\pi\) | ||||
−0.0912811 | + | 0.995825i | \(0.529096\pi\) | |||||||
\(510\) | −3.91945e14 | −0.503025 | ||||||||
\(511\) | 1.25832e15 | 1.59763 | ||||||||
\(512\) | 8.93299e14 | 1.12205 | ||||||||
\(513\) | −6.72972e13 | −0.0836279 | ||||||||
\(514\) | −2.81590e14 | −0.346195 | ||||||||
\(515\) | 1.03070e15 | 1.25370 | ||||||||
\(516\) | 1.17872e13 | 0.0141852 | ||||||||
\(517\) | −1.50920e14 | −0.179700 | ||||||||
\(518\) | −7.37552e14 | −0.868918 | ||||||||
\(519\) | −6.67877e14 | −0.778531 | ||||||||
\(520\) | 1.50703e14 | 0.173821 | ||||||||
\(521\) | −2.48690e14 | −0.283825 | −0.141913 | − | 0.989879i | \(-0.545325\pi\) | ||||
−0.141913 | + | 0.989879i | \(0.545325\pi\) | |||||||
\(522\) | −2.30452e14 | −0.260251 | ||||||||
\(523\) | −2.98483e14 | −0.333550 | −0.166775 | − | 0.985995i | \(-0.553335\pi\) | ||||
−0.166775 | + | 0.985995i | \(0.553335\pi\) | |||||||
\(524\) | 6.02147e13 | 0.0665856 | ||||||||
\(525\) | −2.56755e14 | −0.280959 | ||||||||
\(526\) | 1.27172e15 | 1.37712 | ||||||||
\(527\) | 3.73474e14 | 0.400223 | ||||||||
\(528\) | 2.24111e14 | 0.237671 | ||||||||
\(529\) | −5.48606e14 | −0.575777 | ||||||||
\(530\) | 8.85980e14 | 0.920252 | ||||||||
\(531\) | −4.22156e13 | −0.0433963 | ||||||||
\(532\) | 5.52764e13 | 0.0562375 | ||||||||
\(533\) | −6.38994e12 | −0.00643424 | ||||||||
\(534\) | −1.55015e14 | −0.154489 | ||||||||
\(535\) | 3.71020e14 | 0.365975 | ||||||||
\(536\) | 1.01364e15 | 0.989638 | ||||||||
\(537\) | −3.00483e14 | −0.290376 | ||||||||
\(538\) | 1.41125e15 | 1.34990 | ||||||||
\(539\) | −7.82786e13 | −0.0741148 | ||||||||
\(540\) | −1.98130e13 | −0.0185689 | ||||||||
\(541\) | 1.12984e15 | 1.04817 | 0.524085 | − | 0.851666i | \(-0.324407\pi\) | ||||
0.524085 | + | 0.851666i | \(0.324407\pi\) | |||||||
\(542\) | −3.60247e14 | −0.330830 | ||||||||
\(543\) | 5.74441e14 | 0.522211 | ||||||||
\(544\) | −4.23804e14 | −0.381391 | ||||||||
\(545\) | −5.60754e14 | −0.499565 | ||||||||
\(546\) | 1.33826e14 | 0.118027 | ||||||||
\(547\) | 1.49689e15 | 1.30695 | 0.653475 | − | 0.756948i | \(-0.273311\pi\) | ||||
0.653475 | + | 0.756948i | \(0.273311\pi\) | |||||||
\(548\) | 1.80201e14 | 0.155763 | ||||||||
\(549\) | −1.34472e14 | −0.115076 | ||||||||
\(550\) | 2.83327e14 | 0.240046 | ||||||||
\(551\) | 4.36265e14 | 0.365945 | ||||||||
\(552\) | −4.78758e14 | −0.397604 | ||||||||
\(553\) | 1.03039e15 | 0.847256 | ||||||||
\(554\) | 1.83161e15 | 1.49118 | ||||||||
\(555\) | −5.00465e14 | −0.403425 | ||||||||
\(556\) | −2.40603e14 | −0.192039 | ||||||||
\(557\) | 2.00238e15 | 1.58250 | 0.791250 | − | 0.611493i | \(-0.209431\pi\) | ||||
0.791250 | + | 0.611493i | \(0.209431\pi\) | |||||||
\(558\) | −1.15520e14 | −0.0904000 | ||||||||
\(559\) | −5.40234e13 | −0.0418617 | ||||||||
\(560\) | −6.92611e14 | −0.531442 | ||||||||
\(561\) | −5.09614e14 | −0.387209 | ||||||||
\(562\) | 2.06119e15 | 1.55085 | ||||||||
\(563\) | 9.06475e14 | 0.675398 | 0.337699 | − | 0.941254i | \(-0.390351\pi\) | ||||
0.337699 | + | 0.941254i | \(0.390351\pi\) | |||||||
\(564\) | −4.02947e13 | −0.0297312 | ||||||||
\(565\) | −1.58471e14 | −0.115793 | ||||||||
\(566\) | 2.11176e15 | 1.52811 | ||||||||
\(567\) | −1.42846e14 | −0.102367 | ||||||||
\(568\) | −1.98632e15 | −1.40972 | ||||||||
\(569\) | 1.54826e14 | 0.108824 | 0.0544122 | − | 0.998519i | \(-0.482672\pi\) | ||||
0.0544122 | + | 0.998519i | \(0.482672\pi\) | |||||||
\(570\) | −2.29505e14 | −0.159765 | ||||||||
\(571\) | −5.86212e13 | −0.0404163 | −0.0202081 | − | 0.999796i | \(-0.506433\pi\) | ||||
−0.0202081 | + | 0.999796i | \(0.506433\pi\) | |||||||
\(572\) | 2.41346e13 | 0.0164802 | ||||||||
\(573\) | −4.04536e14 | −0.273594 | ||||||||
\(574\) | 3.42797e13 | 0.0229626 | ||||||||
\(575\) | −5.18525e14 | −0.344030 | ||||||||
\(576\) | 5.57055e14 | 0.366078 | ||||||||
\(577\) | 1.96260e15 | 1.27751 | 0.638754 | − | 0.769411i | \(-0.279450\pi\) | ||||
0.638754 | + | 0.769411i | \(0.279450\pi\) | |||||||
\(578\) | −1.25373e15 | −0.808351 | ||||||||
\(579\) | −5.90945e14 | −0.377411 | ||||||||
\(580\) | 1.28441e14 | 0.0812551 | ||||||||
\(581\) | 7.17909e14 | 0.449884 | ||||||||
\(582\) | 1.59674e14 | 0.0991194 | ||||||||
\(583\) | 1.15197e15 | 0.708374 | ||||||||
\(584\) | −3.00994e15 | −1.83353 | ||||||||
\(585\) | 9.08079e13 | 0.0547982 | ||||||||
\(586\) | 1.56137e15 | 0.933404 | ||||||||
\(587\) | 1.27919e15 | 0.757575 | 0.378787 | − | 0.925484i | \(-0.376341\pi\) | ||||
0.378787 | + | 0.925484i | \(0.376341\pi\) | |||||||
\(588\) | −2.08999e13 | −0.0122622 | ||||||||
\(589\) | 2.18689e14 | 0.127114 | ||||||||
\(590\) | −1.43969e14 | −0.0829053 | ||||||||
\(591\) | −9.79502e14 | −0.558823 | ||||||||
\(592\) | 1.51143e15 | 0.854316 | ||||||||
\(593\) | 1.19686e15 | 0.670259 | 0.335130 | − | 0.942172i | \(-0.391220\pi\) | ||||
0.335130 | + | 0.942172i | \(0.391220\pi\) | |||||||
\(594\) | 1.57630e14 | 0.0874605 | ||||||||
\(595\) | 1.57495e15 | 0.865813 | ||||||||
\(596\) | 2.09455e14 | 0.114087 | ||||||||
\(597\) | −6.14050e14 | −0.331394 | ||||||||
\(598\) | 2.70267e14 | 0.144523 | ||||||||
\(599\) | −1.51517e15 | −0.802812 | −0.401406 | − | 0.915900i | \(-0.631478\pi\) | ||||
−0.401406 | + | 0.915900i | \(0.631478\pi\) | |||||||
\(600\) | 6.14166e14 | 0.322444 | ||||||||
\(601\) | 1.56048e15 | 0.811797 | 0.405899 | − | 0.913918i | \(-0.366959\pi\) | ||||
0.405899 | + | 0.913918i | \(0.366959\pi\) | |||||||
\(602\) | 2.89816e14 | 0.149397 | ||||||||
\(603\) | 6.10781e14 | 0.311990 | ||||||||
\(604\) | −3.20662e14 | −0.162310 | ||||||||
\(605\) | 1.04036e15 | 0.521829 | ||||||||
\(606\) | 1.16466e15 | 0.578893 | ||||||||
\(607\) | −1.37734e15 | −0.678426 | −0.339213 | − | 0.940710i | \(-0.610161\pi\) | ||||
−0.339213 | + | 0.940710i | \(0.610161\pi\) | |||||||
\(608\) | −2.48160e14 | −0.121133 | ||||||||
\(609\) | 9.26022e14 | 0.447947 | ||||||||
\(610\) | −4.58592e14 | −0.219843 | ||||||||
\(611\) | 1.84680e14 | 0.0877392 | ||||||||
\(612\) | −1.36064e14 | −0.0640634 | ||||||||
\(613\) | −9.68578e14 | −0.451962 | −0.225981 | − | 0.974132i | \(-0.572559\pi\) | ||||
−0.225981 | + | 0.974132i | \(0.572559\pi\) | |||||||
\(614\) | −1.96103e15 | −0.906896 | ||||||||
\(615\) | 2.32605e13 | 0.0106612 | ||||||||
\(616\) | −1.05118e15 | −0.477510 | ||||||||
\(617\) | 3.92444e15 | 1.76689 | 0.883445 | − | 0.468534i | \(-0.155218\pi\) | ||||
0.883445 | + | 0.468534i | \(0.155218\pi\) | |||||||
\(618\) | −2.18938e15 | −0.976978 | ||||||||
\(619\) | −1.85431e15 | −0.820132 | −0.410066 | − | 0.912056i | \(-0.634494\pi\) | ||||
−0.410066 | + | 0.912056i | \(0.634494\pi\) | |||||||
\(620\) | 6.43845e13 | 0.0282245 | ||||||||
\(621\) | −2.88482e14 | −0.125347 | ||||||||
\(622\) | 6.25979e14 | 0.269596 | ||||||||
\(623\) | 6.22896e14 | 0.265908 | ||||||||
\(624\) | −2.74244e14 | −0.116044 | ||||||||
\(625\) | −4.59673e14 | −0.192801 | ||||||||
\(626\) | −9.99221e14 | −0.415435 | ||||||||
\(627\) | −2.98406e14 | −0.122981 | ||||||||
\(628\) | −3.40735e14 | −0.139200 | ||||||||
\(629\) | −3.43689e15 | −1.39183 | ||||||||
\(630\) | −4.87151e14 | −0.195565 | ||||||||
\(631\) | −1.90250e14 | −0.0757119 | −0.0378560 | − | 0.999283i | \(-0.512053\pi\) | ||||
−0.0378560 | + | 0.999283i | \(0.512053\pi\) | |||||||
\(632\) | −2.46473e15 | −0.972357 | ||||||||
\(633\) | 9.47709e14 | 0.370642 | ||||||||
\(634\) | 2.29067e15 | 0.888120 | ||||||||
\(635\) | −1.50171e15 | −0.577204 | ||||||||
\(636\) | 3.07568e14 | 0.117200 | ||||||||
\(637\) | 9.57893e13 | 0.0361868 | ||||||||
\(638\) | −1.02186e15 | −0.382716 | ||||||||
\(639\) | −1.19688e15 | −0.444424 | ||||||||
\(640\) | 1.37963e15 | 0.507892 | ||||||||
\(641\) | 7.34660e14 | 0.268144 | 0.134072 | − | 0.990972i | \(-0.457195\pi\) | ||||
0.134072 | + | 0.990972i | \(0.457195\pi\) | |||||||
\(642\) | −7.88107e14 | −0.285196 | ||||||||
\(643\) | −1.60145e15 | −0.574584 | −0.287292 | − | 0.957843i | \(-0.592755\pi\) | ||||
−0.287292 | + | 0.957843i | \(0.592755\pi\) | |||||||
\(644\) | 2.36953e14 | 0.0842927 | ||||||||
\(645\) | 1.96654e14 | 0.0693626 | ||||||||
\(646\) | −1.57610e15 | −0.551195 | ||||||||
\(647\) | 3.09071e15 | 1.07173 | 0.535865 | − | 0.844304i | \(-0.319986\pi\) | ||||
0.535865 | + | 0.844304i | \(0.319986\pi\) | |||||||
\(648\) | 3.41692e14 | 0.117482 | ||||||||
\(649\) | −1.87190e14 | −0.0638172 | ||||||||
\(650\) | −3.46707e14 | −0.117203 | ||||||||
\(651\) | 4.64192e14 | 0.155597 | ||||||||
\(652\) | −3.02760e14 | −0.100632 | ||||||||
\(653\) | 3.29713e14 | 0.108671 | 0.0543356 | − | 0.998523i | \(-0.482696\pi\) | ||||
0.0543356 | + | 0.998523i | \(0.482696\pi\) | |||||||
\(654\) | 1.19113e15 | 0.389299 | ||||||||
\(655\) | 1.00461e15 | 0.325589 | ||||||||
\(656\) | −7.02478e13 | −0.0225768 | ||||||||
\(657\) | −1.81368e15 | −0.578031 | ||||||||
\(658\) | −9.90741e14 | −0.313125 | ||||||||
\(659\) | −4.91143e15 | −1.53935 | −0.769676 | − | 0.638435i | \(-0.779582\pi\) | ||||
−0.769676 | + | 0.638435i | \(0.779582\pi\) | |||||||
\(660\) | −8.78542e13 | −0.0273068 | ||||||||
\(661\) | 5.93341e15 | 1.82893 | 0.914464 | − | 0.404668i | \(-0.132613\pi\) | ||||
0.914464 | + | 0.404668i | \(0.132613\pi\) | |||||||
\(662\) | −1.69387e15 | −0.517800 | ||||||||
\(663\) | 6.23613e14 | 0.189056 | ||||||||
\(664\) | −1.71726e15 | −0.516312 | ||||||||
\(665\) | 9.22219e14 | 0.274989 | ||||||||
\(666\) | 1.06307e15 | 0.314379 | ||||||||
\(667\) | 1.87013e15 | 0.548504 | ||||||||
\(668\) | −1.34487e14 | −0.0391209 | ||||||||
\(669\) | 1.04570e15 | 0.301692 | ||||||||
\(670\) | 2.08296e15 | 0.596033 | ||||||||
\(671\) | −5.96269e14 | −0.169226 | ||||||||
\(672\) | −5.26748e14 | −0.148276 | ||||||||
\(673\) | −3.55768e15 | −0.993307 | −0.496653 | − | 0.867949i | \(-0.665438\pi\) | ||||
−0.496653 | + | 0.867949i | \(0.665438\pi\) | |||||||
\(674\) | 1.08553e14 | 0.0300616 | ||||||||
\(675\) | 3.70074e14 | 0.101652 | ||||||||
\(676\) | 4.86046e14 | 0.132425 | ||||||||
\(677\) | −5.94589e15 | −1.60686 | −0.803432 | − | 0.595397i | \(-0.796995\pi\) | ||||
−0.803432 | + | 0.595397i | \(0.796995\pi\) | |||||||
\(678\) | 3.36619e14 | 0.0902349 | ||||||||
\(679\) | −6.41618e14 | −0.170605 | ||||||||
\(680\) | −3.76733e15 | −0.993653 | ||||||||
\(681\) | −1.59305e15 | −0.416793 | ||||||||
\(682\) | −5.12233e14 | −0.132939 | ||||||||
\(683\) | −2.82331e15 | −0.726849 | −0.363424 | − | 0.931624i | \(-0.618392\pi\) | ||||
−0.363424 | + | 0.931624i | \(0.618392\pi\) | |||||||
\(684\) | −7.96727e13 | −0.0203470 | ||||||||
\(685\) | 3.00643e15 | 0.761646 | ||||||||
\(686\) | −3.91260e15 | −0.983293 | ||||||||
\(687\) | −2.77444e15 | −0.691693 | ||||||||
\(688\) | −5.93906e14 | −0.146886 | ||||||||
\(689\) | −1.40966e15 | −0.345866 | ||||||||
\(690\) | −9.83817e14 | −0.239466 | ||||||||
\(691\) | −3.19635e15 | −0.771835 | −0.385918 | − | 0.922533i | \(-0.626115\pi\) | ||||
−0.385918 | + | 0.922533i | \(0.626115\pi\) | |||||||
\(692\) | −7.90695e14 | −0.189420 | ||||||||
\(693\) | −6.33402e14 | −0.150538 | ||||||||
\(694\) | 4.87156e15 | 1.14866 | ||||||||
\(695\) | −4.01416e15 | −0.939028 | ||||||||
\(696\) | −2.21507e15 | −0.514088 | ||||||||
\(697\) | 1.59739e14 | 0.0367815 | ||||||||
\(698\) | 3.45762e14 | 0.0789900 | ||||||||
\(699\) | −3.11314e15 | −0.705626 | ||||||||
\(700\) | −3.03971e14 | −0.0683585 | ||||||||
\(701\) | 3.84612e15 | 0.858172 | 0.429086 | − | 0.903264i | \(-0.358836\pi\) | ||||
0.429086 | + | 0.903264i | \(0.358836\pi\) | |||||||
\(702\) | −1.92891e14 | −0.0427029 | ||||||||
\(703\) | −2.01248e15 | −0.442057 | ||||||||
\(704\) | 2.47007e15 | 0.538343 | ||||||||
\(705\) | −6.72267e14 | −0.145379 | ||||||||
\(706\) | −4.98761e15 | −1.07020 | ||||||||
\(707\) | −4.67993e15 | −0.996397 | ||||||||
\(708\) | −4.99788e13 | −0.0105585 | ||||||||
\(709\) | −4.86982e15 | −1.02084 | −0.510421 | − | 0.859924i | \(-0.670511\pi\) | ||||
−0.510421 | + | 0.859924i | \(0.670511\pi\) | |||||||
\(710\) | −4.08176e15 | −0.849037 | ||||||||
\(711\) | −1.48516e15 | −0.306542 | ||||||||
\(712\) | −1.48999e15 | −0.305170 | ||||||||
\(713\) | 9.37451e14 | 0.190527 | ||||||||
\(714\) | −3.34546e15 | −0.674707 | ||||||||
\(715\) | 4.02656e14 | 0.0805845 | ||||||||
\(716\) | −3.55740e14 | −0.0706497 | ||||||||
\(717\) | 7.00676e14 | 0.138090 | ||||||||
\(718\) | −6.44760e15 | −1.26100 | ||||||||
\(719\) | 3.04461e15 | 0.590913 | 0.295456 | − | 0.955356i | \(-0.404528\pi\) | ||||
0.295456 | + | 0.955356i | \(0.404528\pi\) | |||||||
\(720\) | 9.98296e14 | 0.192278 | ||||||||
\(721\) | 8.79757e15 | 1.68159 | ||||||||
\(722\) | 3.96458e15 | 0.752044 | ||||||||
\(723\) | −2.36124e15 | −0.444508 | ||||||||
\(724\) | 6.80077e14 | 0.127056 | ||||||||
\(725\) | −2.39907e15 | −0.444819 | ||||||||
\(726\) | −2.20989e15 | −0.406649 | ||||||||
\(727\) | −2.20618e15 | −0.402903 | −0.201452 | − | 0.979498i | \(-0.564566\pi\) | ||||
−0.201452 | + | 0.979498i | \(0.564566\pi\) | |||||||
\(728\) | 1.28632e15 | 0.233146 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −6.18524e15 | −1.10428 | ||||||||
\(731\) | 1.35050e15 | 0.239304 | ||||||||
\(732\) | −1.59200e14 | −0.0279984 | ||||||||
\(733\) | −5.07430e15 | −0.885737 | −0.442868 | − | 0.896587i | \(-0.646039\pi\) | ||||
−0.442868 | + | 0.896587i | \(0.646039\pi\) | |||||||
\(734\) | −8.69020e14 | −0.150557 | ||||||||
\(735\) | −3.48689e14 | −0.0599596 | ||||||||
\(736\) | −1.06378e15 | −0.181562 | ||||||||
\(737\) | 2.70830e15 | 0.458803 | ||||||||
\(738\) | −4.94091e13 | −0.00830800 | ||||||||
\(739\) | −5.59265e14 | −0.0933411 | −0.0466706 | − | 0.998910i | \(-0.514861\pi\) | ||||
−0.0466706 | + | 0.998910i | \(0.514861\pi\) | |||||||
\(740\) | −5.92498e14 | −0.0981550 | ||||||||
\(741\) | 3.65159e14 | 0.0600457 | ||||||||
\(742\) | 7.56230e15 | 1.23433 | ||||||||
\(743\) | 9.49565e14 | 0.153846 | 0.0769230 | − | 0.997037i | \(-0.475490\pi\) | ||||
0.0769230 | + | 0.997037i | \(0.475490\pi\) | |||||||
\(744\) | −1.11036e15 | −0.178572 | ||||||||
\(745\) | 3.49450e15 | 0.557860 | ||||||||
\(746\) | −2.99921e15 | −0.475274 | ||||||||
\(747\) | −1.03476e15 | −0.162771 | ||||||||
\(748\) | −6.03329e14 | −0.0942096 | ||||||||
\(749\) | 3.16685e15 | 0.490882 | ||||||||
\(750\) | 3.65145e15 | 0.561860 | ||||||||
\(751\) | 8.88342e15 | 1.35694 | 0.678470 | − | 0.734628i | \(-0.262643\pi\) | ||||
0.678470 | + | 0.734628i | \(0.262643\pi\) | |||||||
\(752\) | 2.03028e15 | 0.307863 | ||||||||
\(753\) | −1.47399e15 | −0.221882 | ||||||||
\(754\) | 1.25045e15 | 0.186863 | ||||||||
\(755\) | −5.34985e15 | −0.793658 | ||||||||
\(756\) | −1.69115e14 | −0.0249064 | ||||||||
\(757\) | −1.55458e15 | −0.227292 | −0.113646 | − | 0.993521i | \(-0.536253\pi\) | ||||
−0.113646 | + | 0.993521i | \(0.536253\pi\) | |||||||
\(758\) | 6.18047e15 | 0.897099 | ||||||||
\(759\) | −1.27918e15 | −0.184332 | ||||||||
\(760\) | −2.20598e15 | −0.315592 | ||||||||
\(761\) | −1.08463e16 | −1.54052 | −0.770261 | − | 0.637729i | \(-0.779874\pi\) | ||||
−0.770261 | + | 0.637729i | \(0.779874\pi\) | |||||||
\(762\) | 3.18987e15 | 0.449801 | ||||||||
\(763\) | −4.78633e15 | −0.670066 | ||||||||
\(764\) | −4.78927e14 | −0.0665666 | ||||||||
\(765\) | −2.27006e15 | −0.313256 | ||||||||
\(766\) | 1.10082e16 | 1.50819 | ||||||||
\(767\) | 2.29065e14 | 0.0311590 | ||||||||
\(768\) | 1.76430e15 | 0.238279 | ||||||||
\(769\) | −1.24330e15 | −0.166718 | −0.0833590 | − | 0.996520i | \(-0.526565\pi\) | ||||
−0.0833590 | + | 0.996520i | \(0.526565\pi\) | |||||||
\(770\) | −2.16010e15 | −0.287591 | ||||||||
\(771\) | −1.63091e15 | −0.215591 | ||||||||
\(772\) | −6.99616e14 | −0.0918258 | ||||||||
\(773\) | 5.01623e15 | 0.653718 | 0.326859 | − | 0.945073i | \(-0.394010\pi\) | ||||
0.326859 | + | 0.945073i | \(0.394010\pi\) | |||||||
\(774\) | −4.17726e14 | −0.0540526 | ||||||||
\(775\) | −1.20259e15 | −0.154511 | ||||||||
\(776\) | 1.53477e15 | 0.195796 | ||||||||
\(777\) | −4.27173e15 | −0.541113 | ||||||||
\(778\) | 3.40355e15 | 0.428099 | ||||||||
\(779\) | 9.35356e13 | 0.0116821 | ||||||||
\(780\) | 1.07507e14 | 0.0133326 | ||||||||
\(781\) | −5.30717e15 | −0.653555 | ||||||||
\(782\) | −6.75626e15 | −0.826169 | ||||||||
\(783\) | −1.33472e15 | −0.162069 | ||||||||
\(784\) | 1.05306e15 | 0.126974 | ||||||||
\(785\) | −5.68474e15 | −0.680655 | ||||||||
\(786\) | −2.13395e15 | −0.253723 | ||||||||
\(787\) | 1.08821e16 | 1.28485 | 0.642423 | − | 0.766350i | \(-0.277929\pi\) | ||||
0.642423 | + | 0.766350i | \(0.277929\pi\) | |||||||
\(788\) | −1.15963e15 | −0.135964 | ||||||||
\(789\) | 7.36553e15 | 0.857591 | ||||||||
\(790\) | −5.06487e15 | −0.585625 | ||||||||
\(791\) | −1.35263e15 | −0.155313 | ||||||||
\(792\) | 1.51512e15 | 0.172766 | ||||||||
\(793\) | 7.29652e14 | 0.0826254 | ||||||||
\(794\) | 4.22644e15 | 0.475293 | ||||||||
\(795\) | 5.13139e15 | 0.573081 | ||||||||
\(796\) | −7.26970e14 | −0.0806296 | ||||||||
\(797\) | −5.27896e15 | −0.581470 | −0.290735 | − | 0.956804i | \(-0.593900\pi\) | ||||
−0.290735 | + | 0.956804i | \(0.593900\pi\) | |||||||
\(798\) | −1.95894e15 | −0.214292 | ||||||||
\(799\) | −4.61672e15 | −0.501564 | ||||||||
\(800\) | 1.36466e15 | 0.147241 | ||||||||
\(801\) | −8.97812e14 | −0.0962069 | ||||||||
\(802\) | 5.27532e15 | 0.561422 | ||||||||
\(803\) | −8.04214e15 | −0.850034 | ||||||||
\(804\) | 7.23101e14 | 0.0759085 | ||||||||
\(805\) | 3.95327e15 | 0.412172 | ||||||||
\(806\) | 6.26818e14 | 0.0649081 | ||||||||
\(807\) | 8.17364e15 | 0.840642 | ||||||||
\(808\) | 1.11945e16 | 1.14352 | ||||||||
\(809\) | −8.64287e14 | −0.0876882 | −0.0438441 | − | 0.999038i | \(-0.513960\pi\) | ||||
−0.0438441 | + | 0.999038i | \(0.513960\pi\) | |||||||
\(810\) | 7.02155e14 | 0.0707564 | ||||||||
\(811\) | −2.23191e15 | −0.223389 | −0.111694 | − | 0.993743i | \(-0.535628\pi\) | ||||
−0.111694 | + | 0.993743i | \(0.535628\pi\) | |||||||
\(812\) | 1.09631e15 | 0.108987 | ||||||||
\(813\) | −2.08647e15 | −0.206022 | ||||||||
\(814\) | 4.71382e15 | 0.462316 | ||||||||
\(815\) | −5.05118e15 | −0.492069 | ||||||||
\(816\) | 6.85569e15 | 0.663369 | ||||||||
\(817\) | 7.90792e14 | 0.0760048 | ||||||||
\(818\) | 6.88844e15 | 0.657624 | ||||||||
\(819\) | 7.75092e14 | 0.0735007 | ||||||||
\(820\) | 2.75379e13 | 0.00259391 | ||||||||
\(821\) | −9.98068e15 | −0.933841 | −0.466920 | − | 0.884299i | \(-0.654637\pi\) | ||||
−0.466920 | + | 0.884299i | \(0.654637\pi\) | |||||||
\(822\) | −6.38615e15 | −0.593532 | ||||||||
\(823\) | 1.41483e16 | 1.30619 | 0.653095 | − | 0.757276i | \(-0.273470\pi\) | ||||
0.653095 | + | 0.757276i | \(0.273470\pi\) | |||||||
\(824\) | −2.10441e16 | −1.92988 | ||||||||
\(825\) | 1.64097e15 | 0.149487 | ||||||||
\(826\) | −1.22885e15 | −0.111201 | ||||||||
\(827\) | 1.34308e16 | 1.20732 | 0.603660 | − | 0.797242i | \(-0.293708\pi\) | ||||
0.603660 | + | 0.797242i | \(0.293708\pi\) | |||||||
\(828\) | −3.41532e14 | −0.0304975 | ||||||||
\(829\) | 1.75970e16 | 1.56095 | 0.780475 | − | 0.625187i | \(-0.214977\pi\) | ||||
0.780475 | + | 0.625187i | \(0.214977\pi\) | |||||||
\(830\) | −3.52886e15 | −0.310961 | ||||||||
\(831\) | 1.06083e16 | 0.928622 | ||||||||
\(832\) | −3.02262e15 | −0.262848 | ||||||||
\(833\) | −2.39459e15 | −0.206863 | ||||||||
\(834\) | 8.52674e15 | 0.731762 | ||||||||
\(835\) | −2.24374e15 | −0.191292 | ||||||||
\(836\) | −3.53282e14 | −0.0299217 | ||||||||
\(837\) | −6.69064e14 | −0.0562960 | ||||||||
\(838\) | −1.90951e15 | −0.159617 | ||||||||
\(839\) | 1.83671e16 | 1.52528 | 0.762640 | − | 0.646823i | \(-0.223903\pi\) | ||||
0.762640 | + | 0.646823i | \(0.223903\pi\) | |||||||
\(840\) | −4.68244e15 | −0.386310 | ||||||||
\(841\) | −3.54796e15 | −0.290804 | ||||||||
\(842\) | −4.66576e15 | −0.379932 | ||||||||
\(843\) | 1.19379e16 | 0.965779 | ||||||||
\(844\) | 1.12199e15 | 0.0901788 | ||||||||
\(845\) | 8.10908e15 | 0.647530 | ||||||||
\(846\) | 1.42801e15 | 0.113290 | ||||||||
\(847\) | 8.87999e15 | 0.699929 | ||||||||
\(848\) | −1.54971e16 | −1.21359 | ||||||||
\(849\) | 1.22308e16 | 0.951620 | ||||||||
\(850\) | 8.66715e15 | 0.669996 | ||||||||
\(851\) | −8.62690e15 | −0.662586 | ||||||||
\(852\) | −1.41698e15 | −0.108130 | ||||||||
\(853\) | 1.35599e16 | 1.02810 | 0.514052 | − | 0.857759i | \(-0.328144\pi\) | ||||
0.514052 | + | 0.857759i | \(0.328144\pi\) | |||||||
\(854\) | −3.91432e15 | −0.294875 | ||||||||
\(855\) | −1.32924e15 | −0.0994924 | ||||||||
\(856\) | −7.57519e15 | −0.563363 | ||||||||
\(857\) | −1.56281e15 | −0.115481 | −0.0577406 | − | 0.998332i | \(-0.518390\pi\) | ||||
−0.0577406 | + | 0.998332i | \(0.518390\pi\) | |||||||
\(858\) | −8.55309e14 | −0.0627976 | ||||||||
\(859\) | −1.35473e16 | −0.988301 | −0.494150 | − | 0.869376i | \(-0.664521\pi\) | ||||
−0.494150 | + | 0.869376i | \(0.664521\pi\) | |||||||
\(860\) | 2.32818e14 | 0.0168762 | ||||||||
\(861\) | 1.98540e14 | 0.0142998 | ||||||||
\(862\) | −2.14958e16 | −1.53838 | ||||||||
\(863\) | 7.25297e15 | 0.515771 | 0.257885 | − | 0.966176i | \(-0.416974\pi\) | ||||
0.257885 | + | 0.966176i | \(0.416974\pi\) | |||||||
\(864\) | 7.59228e14 | 0.0536472 | ||||||||
\(865\) | −1.31918e16 | −0.926221 | ||||||||
\(866\) | −2.25644e16 | −1.57425 | ||||||||
\(867\) | −7.26130e15 | −0.503396 | ||||||||
\(868\) | 5.49555e14 | 0.0378575 | ||||||||
\(869\) | −6.58542e15 | −0.450791 | ||||||||
\(870\) | −4.55184e15 | −0.309621 | ||||||||
\(871\) | −3.31414e15 | −0.224012 | ||||||||
\(872\) | 1.14490e16 | 0.769003 | ||||||||
\(873\) | 9.24796e14 | 0.0617260 | ||||||||
\(874\) | −3.95615e15 | −0.262398 | ||||||||
\(875\) | −1.46726e16 | −0.967080 | ||||||||
\(876\) | −2.14721e15 | −0.140637 | ||||||||
\(877\) | 1.26953e16 | 0.826312 | 0.413156 | − | 0.910660i | \(-0.364426\pi\) | ||||
0.413156 | + | 0.910660i | \(0.364426\pi\) | |||||||
\(878\) | 2.33411e15 | 0.150974 | ||||||||
\(879\) | 9.04311e15 | 0.581271 | ||||||||
\(880\) | 4.42660e15 | 0.282759 | ||||||||
\(881\) | 7.00994e15 | 0.444987 | 0.222493 | − | 0.974934i | \(-0.428580\pi\) | ||||
0.222493 | + | 0.974934i | \(0.428580\pi\) | |||||||
\(882\) | 7.40674e14 | 0.0467251 | ||||||||
\(883\) | −8.35461e15 | −0.523772 | −0.261886 | − | 0.965099i | \(-0.584344\pi\) | ||||
−0.261886 | + | 0.965099i | \(0.584344\pi\) | |||||||
\(884\) | 7.38292e14 | 0.0459982 | ||||||||
\(885\) | −8.33834e14 | −0.0516287 | ||||||||
\(886\) | 3.91665e15 | 0.241007 | ||||||||
\(887\) | 2.16567e16 | 1.32438 | 0.662191 | − | 0.749335i | \(-0.269627\pi\) | ||||
0.662191 | + | 0.749335i | \(0.269627\pi\) | |||||||
\(888\) | 1.02181e16 | 0.621011 | ||||||||
\(889\) | −1.28178e16 | −0.774203 | ||||||||
\(890\) | −3.06183e15 | −0.183796 | ||||||||
\(891\) | 9.12954e14 | 0.0544655 | ||||||||
\(892\) | 1.23800e15 | 0.0734030 | ||||||||
\(893\) | −2.70334e15 | −0.159301 | ||||||||
\(894\) | −7.42288e15 | −0.434727 | ||||||||
\(895\) | −5.93507e15 | −0.345461 | ||||||||
\(896\) | 1.17758e16 | 0.681235 | ||||||||
\(897\) | 1.56532e15 | 0.0900006 | ||||||||
\(898\) | −4.78743e15 | −0.273579 | ||||||||
\(899\) | 4.33731e15 | 0.246344 | ||||||||
\(900\) | 4.38129e14 | 0.0247325 | ||||||||
\(901\) | 3.52393e16 | 1.97716 | ||||||||
\(902\) | −2.19088e14 | −0.0122175 | ||||||||
\(903\) | 1.67855e15 | 0.0930359 | ||||||||
\(904\) | 3.23554e15 | 0.178246 | ||||||||
\(905\) | 1.13462e16 | 0.621277 | ||||||||
\(906\) | 1.13640e16 | 0.618478 | ||||||||
\(907\) | 3.43091e15 | 0.185596 | 0.0927981 | − | 0.995685i | \(-0.470419\pi\) | ||||
0.0927981 | + | 0.995685i | \(0.470419\pi\) | |||||||
\(908\) | −1.88600e15 | −0.101408 | ||||||||
\(909\) | 6.74542e15 | 0.360502 | ||||||||
\(910\) | 2.64331e15 | 0.140417 | ||||||||
\(911\) | 2.56366e16 | 1.35366 | 0.676830 | − | 0.736139i | \(-0.263353\pi\) | ||||
0.676830 | + | 0.736139i | \(0.263353\pi\) | |||||||
\(912\) | 4.01437e15 | 0.210691 | ||||||||
\(913\) | −4.58829e15 | −0.239365 | ||||||||
\(914\) | 1.82419e15 | 0.0945944 | ||||||||
\(915\) | −2.65606e15 | −0.136906 | ||||||||
\(916\) | −3.28464e15 | −0.168292 | ||||||||
\(917\) | 8.57484e15 | 0.436712 | ||||||||
\(918\) | 4.82198e15 | 0.244113 | ||||||||
\(919\) | 8.39129e15 | 0.422273 | 0.211137 | − | 0.977457i | \(-0.432284\pi\) | ||||
0.211137 | + | 0.977457i | \(0.432284\pi\) | |||||||
\(920\) | −9.45633e15 | −0.473031 | ||||||||
\(921\) | −1.13578e16 | −0.564764 | ||||||||
\(922\) | 1.59430e16 | 0.788041 | ||||||||
\(923\) | 6.49437e15 | 0.319101 | ||||||||
\(924\) | −7.49880e14 | −0.0366266 | ||||||||
\(925\) | 1.10669e16 | 0.537335 | ||||||||
\(926\) | −1.90344e16 | −0.918712 | ||||||||
\(927\) | −1.26804e16 | −0.608407 | ||||||||
\(928\) | −4.92182e15 | −0.234753 | ||||||||
\(929\) | 3.81194e16 | 1.80742 | 0.903712 | − | 0.428141i | \(-0.140831\pi\) | ||||
0.903712 | + | 0.428141i | \(0.140831\pi\) | |||||||
\(930\) | −2.28172e15 | −0.107549 | ||||||||
\(931\) | −1.40216e15 | −0.0657013 | ||||||||
\(932\) | −3.68563e15 | −0.171682 | ||||||||
\(933\) | 3.62553e15 | 0.167889 | ||||||||
\(934\) | −1.20784e16 | −0.556033 | ||||||||
\(935\) | −1.00658e16 | −0.460664 | ||||||||
\(936\) | −1.85404e15 | −0.0843534 | ||||||||
\(937\) | 1.21249e16 | 0.548416 | 0.274208 | − | 0.961670i | \(-0.411584\pi\) | ||||
0.274208 | + | 0.961670i | \(0.411584\pi\) | |||||||
\(938\) | 1.77792e16 | 0.799458 | ||||||||
\(939\) | −5.78726e15 | −0.258709 | ||||||||
\(940\) | −7.95893e14 | −0.0353713 | ||||||||
\(941\) | 1.82977e16 | 0.808449 | 0.404224 | − | 0.914660i | \(-0.367541\pi\) | ||||
0.404224 | + | 0.914660i | \(0.367541\pi\) | |||||||
\(942\) | 1.20753e16 | 0.530418 | ||||||||
\(943\) | 4.00958e14 | 0.0175099 | ||||||||
\(944\) | 2.51822e15 | 0.109332 | ||||||||
\(945\) | −2.82147e15 | −0.121787 | ||||||||
\(946\) | −1.85226e15 | −0.0794880 | ||||||||
\(947\) | 2.31106e16 | 0.986022 | 0.493011 | − | 0.870023i | \(-0.335896\pi\) | ||||
0.493011 | + | 0.870023i | \(0.335896\pi\) | |||||||
\(948\) | −1.75827e15 | −0.0745830 | ||||||||
\(949\) | 9.84115e15 | 0.415032 | ||||||||
\(950\) | 5.07508e15 | 0.212796 | ||||||||
\(951\) | 1.32670e16 | 0.553071 | ||||||||
\(952\) | −3.21561e16 | −1.33279 | ||||||||
\(953\) | 1.47887e16 | 0.609424 | 0.304712 | − | 0.952445i | \(-0.401440\pi\) | ||||
0.304712 | + | 0.952445i | \(0.401440\pi\) | |||||||
\(954\) | −1.08999e16 | −0.446588 | ||||||||
\(955\) | −7.99031e15 | −0.325496 | ||||||||
\(956\) | 8.29526e14 | 0.0335978 | ||||||||
\(957\) | −5.91837e15 | −0.238334 | ||||||||
\(958\) | −7.45392e15 | −0.298452 | ||||||||
\(959\) | 2.56614e16 | 1.02159 | ||||||||
\(960\) | 1.10028e16 | 0.435525 | ||||||||
\(961\) | −2.32343e16 | −0.914431 | ||||||||
\(962\) | −5.76829e15 | −0.225727 | ||||||||
\(963\) | −4.56454e15 | −0.177604 | ||||||||
\(964\) | −2.79546e15 | −0.108151 | ||||||||
\(965\) | −1.16722e16 | −0.449008 | ||||||||
\(966\) | −8.39739e15 | −0.321196 | ||||||||
\(967\) | 1.32924e16 | 0.505542 | 0.252771 | − | 0.967526i | \(-0.418658\pi\) | ||||
0.252771 | + | 0.967526i | \(0.418658\pi\) | |||||||
\(968\) | −2.12412e16 | −0.803276 | ||||||||
\(969\) | −9.12842e15 | −0.343253 | ||||||||
\(970\) | 3.15386e15 | 0.117923 | ||||||||
\(971\) | 1.37842e16 | 0.512479 | 0.256239 | − | 0.966613i | \(-0.417516\pi\) | ||||
0.256239 | + | 0.966613i | \(0.417516\pi\) | |||||||
\(972\) | 2.43753e14 | 0.00901127 | ||||||||
\(973\) | −3.42630e16 | −1.25952 | ||||||||
\(974\) | −1.01361e16 | −0.370508 | ||||||||
\(975\) | −2.00805e15 | −0.0729875 | ||||||||
\(976\) | 8.02143e15 | 0.289920 | ||||||||
\(977\) | 4.44842e15 | 0.159877 | 0.0799384 | − | 0.996800i | \(-0.474528\pi\) | ||||
0.0799384 | + | 0.996800i | \(0.474528\pi\) | |||||||
\(978\) | 1.07295e16 | 0.383457 | ||||||||
\(979\) | −3.98104e15 | −0.141479 | ||||||||
\(980\) | −4.12811e14 | −0.0145884 | ||||||||
\(981\) | 6.89877e15 | 0.242433 | ||||||||
\(982\) | 4.98763e15 | 0.174294 | ||||||||
\(983\) | 4.39070e16 | 1.52577 | 0.762885 | − | 0.646534i | \(-0.223782\pi\) | ||||
0.762885 | + | 0.646534i | \(0.223782\pi\) | |||||||
\(984\) | −4.74914e14 | −0.0164113 | ||||||||
\(985\) | −1.93469e16 | −0.664834 | ||||||||
\(986\) | −3.12592e16 | −1.06821 | ||||||||
\(987\) | −5.73815e15 | −0.194997 | ||||||||
\(988\) | 4.32310e14 | 0.0146094 | ||||||||
\(989\) | 3.38988e15 | 0.113921 | ||||||||
\(990\) | 3.11347e15 | 0.104052 | ||||||||
\(991\) | −5.42054e15 | −0.180151 | −0.0900756 | − | 0.995935i | \(-0.528711\pi\) | ||||
−0.0900756 | + | 0.995935i | \(0.528711\pi\) | |||||||
\(992\) | −2.46719e15 | −0.0815433 | ||||||||
\(993\) | −9.81053e15 | −0.322457 | ||||||||
\(994\) | −3.48399e16 | −1.13881 | ||||||||
\(995\) | −1.21286e16 | −0.394261 | ||||||||
\(996\) | −1.22505e15 | −0.0396028 | ||||||||
\(997\) | −2.96023e15 | −0.0951705 | −0.0475852 | − | 0.998867i | \(-0.515153\pi\) | ||||
−0.0475852 | + | 0.998867i | \(0.515153\pi\) | |||||||
\(998\) | −5.04658e16 | −1.61354 | ||||||||
\(999\) | 6.15706e15 | 0.195778 |
(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 | 177.12.a.c.1.8 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.c.1.8 | ✓ | 27 | 1.1 | even | 1 | trivial |