Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(148.845356651\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −31.4159 | −1.38840 | −0.694199 | − | 0.719783i | \(-0.744241\pi\) | ||||
−0.694199 | + | 0.719783i | \(0.744241\pi\) | |||||||
\(3\) | 60.4230 | 0.430682 | 0.215341 | − | 0.976539i | \(-0.430914\pi\) | ||||
0.215341 | + | 0.976539i | \(0.430914\pi\) | |||||||
\(4\) | 474.957 | 0.927651 | ||||||||
\(5\) | −1582.21 | −1.13214 | −0.566068 | − | 0.824359i | \(-0.691536\pi\) | ||||
−0.566068 | + | 0.824359i | \(0.691536\pi\) | |||||||
\(6\) | −1898.24 | −0.597959 | ||||||||
\(7\) | 10488.5 | 1.65110 | 0.825550 | − | 0.564329i | \(-0.190865\pi\) | ||||
0.825550 | + | 0.564329i | \(0.190865\pi\) | |||||||
\(8\) | 1163.73 | 0.100450 | ||||||||
\(9\) | −16032.1 | −0.814513 | ||||||||
\(10\) | 49706.4 | 1.57186 | ||||||||
\(11\) | 78187.1 | 1.61016 | 0.805078 | − | 0.593169i | \(-0.202123\pi\) | ||||
0.805078 | + | 0.593169i | \(0.202123\pi\) | |||||||
\(12\) | 28698.4 | 0.399523 | ||||||||
\(13\) | 111709. | 1.08478 | 0.542391 | − | 0.840126i | \(-0.317519\pi\) | ||||
0.542391 | + | 0.840126i | \(0.317519\pi\) | |||||||
\(14\) | −329506. | −2.29238 | ||||||||
\(15\) | −95601.8 | −0.487591 | ||||||||
\(16\) | −279738. | −1.06711 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 503661. | 1.13087 | ||||||||
\(19\) | −202367. | −0.356245 | −0.178123 | − | 0.984008i | \(-0.557002\pi\) | ||||
−0.178123 | + | 0.984008i | \(0.557002\pi\) | |||||||
\(20\) | −751481. | −1.05023 | ||||||||
\(21\) | 633749. | 0.711099 | ||||||||
\(22\) | −2.45632e6 | −2.23554 | ||||||||
\(23\) | −759075. | −0.565600 | −0.282800 | − | 0.959179i | \(-0.591263\pi\) | ||||
−0.282800 | + | 0.959179i | \(0.591263\pi\) | |||||||
\(24\) | 70316.3 | 0.0432619 | ||||||||
\(25\) | 550256. | 0.281731 | ||||||||
\(26\) | −3.50943e6 | −1.50611 | ||||||||
\(27\) | −2.15801e6 | −0.781478 | ||||||||
\(28\) | 4.98160e6 | 1.53164 | ||||||||
\(29\) | −7.48987e6 | −1.96645 | −0.983226 | − | 0.182389i | \(-0.941617\pi\) | ||||
−0.983226 | + | 0.182389i | \(0.941617\pi\) | |||||||
\(30\) | 3.00341e6 | 0.676970 | ||||||||
\(31\) | 1.06329e6 | 0.206788 | 0.103394 | − | 0.994640i | \(-0.467030\pi\) | ||||
0.103394 | + | 0.994640i | \(0.467030\pi\) | |||||||
\(32\) | 8.19237e6 | 1.38113 | ||||||||
\(33\) | 4.72430e6 | 0.693466 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.65950e7 | −1.86927 | ||||||||
\(36\) | −7.61454e6 | −0.755583 | ||||||||
\(37\) | 1.12518e7 | 0.986991 | 0.493496 | − | 0.869748i | \(-0.335719\pi\) | ||||
0.493496 | + | 0.869748i | \(0.335719\pi\) | |||||||
\(38\) | 6.35754e6 | 0.494610 | ||||||||
\(39\) | 6.74979e6 | 0.467196 | ||||||||
\(40\) | −1.84127e6 | −0.113723 | ||||||||
\(41\) | 1.31299e6 | 0.0725661 | 0.0362831 | − | 0.999342i | \(-0.488448\pi\) | ||||
0.0362831 | + | 0.999342i | \(0.488448\pi\) | |||||||
\(42\) | −1.99098e7 | −0.987289 | ||||||||
\(43\) | 5.13056e6 | 0.228853 | 0.114427 | − | 0.993432i | \(-0.463497\pi\) | ||||
0.114427 | + | 0.993432i | \(0.463497\pi\) | |||||||
\(44\) | 3.71355e7 | 1.49366 | ||||||||
\(45\) | 2.53660e7 | 0.922139 | ||||||||
\(46\) | 2.38470e7 | 0.785279 | ||||||||
\(47\) | −2.33308e7 | −0.697412 | −0.348706 | − | 0.937232i | \(-0.613379\pi\) | ||||
−0.348706 | + | 0.937232i | \(0.613379\pi\) | |||||||
\(48\) | −1.69026e7 | −0.459587 | ||||||||
\(49\) | 6.96556e7 | 1.72613 | ||||||||
\(50\) | −1.72868e7 | −0.391155 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.30569e7 | 1.00630 | ||||||||
\(53\) | −4.46435e7 | −0.777172 | −0.388586 | − | 0.921413i | \(-0.627036\pi\) | ||||
−0.388586 | + | 0.921413i | \(0.627036\pi\) | |||||||
\(54\) | 6.77959e7 | 1.08500 | ||||||||
\(55\) | −1.23708e8 | −1.82292 | ||||||||
\(56\) | 1.22058e7 | 0.165852 | ||||||||
\(57\) | −1.22276e7 | −0.153428 | ||||||||
\(58\) | 2.35301e8 | 2.73022 | ||||||||
\(59\) | −1.89411e7 | −0.203503 | −0.101751 | − | 0.994810i | \(-0.532445\pi\) | ||||
−0.101751 | + | 0.994810i | \(0.532445\pi\) | |||||||
\(60\) | −4.54068e7 | −0.452314 | ||||||||
\(61\) | −1.34977e8 | −1.24818 | −0.624089 | − | 0.781353i | \(-0.714530\pi\) | ||||
−0.624089 | + | 0.781353i | \(0.714530\pi\) | |||||||
\(62\) | −3.34042e7 | −0.287104 | ||||||||
\(63\) | −1.68153e8 | −1.34484 | ||||||||
\(64\) | −1.14145e8 | −0.850446 | ||||||||
\(65\) | −1.76747e8 | −1.22812 | ||||||||
\(66\) | −1.48418e8 | −0.962807 | ||||||||
\(67\) | −3.24318e6 | −0.0196623 | −0.00983115 | − | 0.999952i | \(-0.503129\pi\) | ||||
−0.00983115 | + | 0.999952i | \(0.503129\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.58657e7 | −0.243594 | ||||||||
\(70\) | 5.21347e8 | 2.59529 | ||||||||
\(71\) | −2.42466e8 | −1.13237 | −0.566184 | − | 0.824279i | \(-0.691581\pi\) | ||||
−0.566184 | + | 0.824279i | \(0.691581\pi\) | |||||||
\(72\) | −1.86570e7 | −0.0818176 | ||||||||
\(73\) | −1.13987e8 | −0.469790 | −0.234895 | − | 0.972021i | \(-0.575475\pi\) | ||||
−0.234895 | + | 0.972021i | \(0.575475\pi\) | |||||||
\(74\) | −3.53484e8 | −1.37034 | ||||||||
\(75\) | 3.32481e7 | 0.121336 | ||||||||
\(76\) | −9.61157e7 | −0.330471 | ||||||||
\(77\) | 8.20068e8 | 2.65853 | ||||||||
\(78\) | −2.12051e8 | −0.648655 | ||||||||
\(79\) | −4.26199e7 | −0.123109 | −0.0615546 | − | 0.998104i | \(-0.519606\pi\) | ||||
−0.0615546 | + | 0.998104i | \(0.519606\pi\) | |||||||
\(80\) | 4.42603e8 | 1.20812 | ||||||||
\(81\) | 1.85165e8 | 0.477944 | ||||||||
\(82\) | −4.12487e7 | −0.100751 | ||||||||
\(83\) | 4.37207e8 | 1.01120 | 0.505598 | − | 0.862769i | \(-0.331272\pi\) | ||||
0.505598 | + | 0.862769i | \(0.331272\pi\) | |||||||
\(84\) | 3.01003e8 | 0.659652 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.61181e8 | −0.317739 | ||||||||
\(87\) | −4.52561e8 | −0.846916 | ||||||||
\(88\) | 9.09890e7 | 0.161740 | ||||||||
\(89\) | 5.60941e7 | 0.0947681 | 0.0473840 | − | 0.998877i | \(-0.484912\pi\) | ||||
0.0473840 | + | 0.998877i | \(0.484912\pi\) | |||||||
\(90\) | −7.96896e8 | −1.28030 | ||||||||
\(91\) | 1.17166e9 | 1.79108 | ||||||||
\(92\) | −3.60528e8 | −0.524680 | ||||||||
\(93\) | 6.42473e7 | 0.0890598 | ||||||||
\(94\) | 7.32958e8 | 0.968286 | ||||||||
\(95\) | 3.20187e8 | 0.403318 | ||||||||
\(96\) | 4.95008e8 | 0.594829 | ||||||||
\(97\) | 1.52321e9 | 1.74698 | 0.873490 | − | 0.486842i | \(-0.161851\pi\) | ||||
0.873490 | + | 0.486842i | \(0.161851\pi\) | |||||||
\(98\) | −2.18829e9 | −2.39656 | ||||||||
\(99\) | −1.25350e9 | −1.31149 | ||||||||
\(100\) | 2.61348e8 | 0.261348 | ||||||||
\(101\) | 1.68043e9 | 1.60684 | 0.803422 | − | 0.595411i | \(-0.203011\pi\) | ||||
0.803422 | + | 0.595411i | \(0.203011\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.19381e9 | −1.04513 | −0.522563 | − | 0.852600i | \(-0.675024\pi\) | ||||
−0.522563 | + | 0.852600i | \(0.675024\pi\) | |||||||
\(104\) | 1.29999e8 | 0.108966 | ||||||||
\(105\) | −1.00272e9 | −0.805061 | ||||||||
\(106\) | 1.40251e9 | 1.07902 | ||||||||
\(107\) | −1.74575e9 | −1.28752 | −0.643761 | − | 0.765227i | \(-0.722627\pi\) | ||||
−0.643761 | + | 0.765227i | \(0.722627\pi\) | |||||||
\(108\) | −1.02496e9 | −0.724939 | ||||||||
\(109\) | −6.12631e8 | −0.415700 | −0.207850 | − | 0.978161i | \(-0.566647\pi\) | ||||
−0.207850 | + | 0.978161i | \(0.566647\pi\) | |||||||
\(110\) | 3.88640e9 | 2.53093 | ||||||||
\(111\) | 6.79866e8 | 0.425080 | ||||||||
\(112\) | −2.93404e9 | −1.76191 | ||||||||
\(113\) | −8.81532e8 | −0.508610 | −0.254305 | − | 0.967124i | \(-0.581847\pi\) | ||||
−0.254305 | + | 0.967124i | \(0.581847\pi\) | |||||||
\(114\) | 3.84142e8 | 0.213020 | ||||||||
\(115\) | 1.20101e9 | 0.640336 | ||||||||
\(116\) | −3.55737e9 | −1.82418 | ||||||||
\(117\) | −1.79092e9 | −0.883569 | ||||||||
\(118\) | 5.95050e8 | 0.282543 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.11255e8 | −0.0489783 | ||||||||
\(121\) | 3.75528e9 | 1.59260 | ||||||||
\(122\) | 4.24043e9 | 1.73297 | ||||||||
\(123\) | 7.93348e7 | 0.0312529 | ||||||||
\(124\) | 5.05018e8 | 0.191827 | ||||||||
\(125\) | 2.21963e9 | 0.813178 | ||||||||
\(126\) | 5.28266e9 | 1.86718 | ||||||||
\(127\) | −8.61290e8 | −0.293787 | −0.146894 | − | 0.989152i | \(-0.546927\pi\) | ||||
−0.146894 | + | 0.989152i | \(0.546927\pi\) | |||||||
\(128\) | −6.08535e8 | −0.200374 | ||||||||
\(129\) | 3.10004e8 | 0.0985629 | ||||||||
\(130\) | 5.55265e9 | 1.70512 | ||||||||
\(131\) | 7.81474e8 | 0.231843 | 0.115921 | − | 0.993258i | \(-0.463018\pi\) | ||||
0.115921 | + | 0.993258i | \(0.463018\pi\) | |||||||
\(132\) | 2.24384e9 | 0.643294 | ||||||||
\(133\) | −2.12253e9 | −0.588196 | ||||||||
\(134\) | 1.01887e8 | 0.0272991 | ||||||||
\(135\) | 3.41442e9 | 0.884740 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.19075e9 | 1.50141 | 0.750707 | − | 0.660635i | \(-0.229713\pi\) | ||||
0.750707 | + | 0.660635i | \(0.229713\pi\) | |||||||
\(138\) | 1.44091e9 | 0.338206 | ||||||||
\(139\) | −2.41364e8 | −0.0548410 | −0.0274205 | − | 0.999624i | \(-0.508729\pi\) | ||||
−0.0274205 | + | 0.999624i | \(0.508729\pi\) | |||||||
\(140\) | −7.88193e9 | −1.73403 | ||||||||
\(141\) | −1.40972e9 | −0.300363 | ||||||||
\(142\) | 7.61727e9 | 1.57218 | ||||||||
\(143\) | 8.73419e9 | 1.74667 | ||||||||
\(144\) | 4.48477e9 | 0.869179 | ||||||||
\(145\) | 1.18505e10 | 2.22629 | ||||||||
\(146\) | 3.58101e9 | 0.652256 | ||||||||
\(147\) | 4.20880e9 | 0.743414 | ||||||||
\(148\) | 5.34411e9 | 0.915583 | ||||||||
\(149\) | −1.37424e9 | −0.228415 | −0.114208 | − | 0.993457i | \(-0.536433\pi\) | ||||
−0.114208 | + | 0.993457i | \(0.536433\pi\) | |||||||
\(150\) | −1.04452e9 | −0.168463 | ||||||||
\(151\) | −4.38413e9 | −0.686258 | −0.343129 | − | 0.939288i | \(-0.611487\pi\) | ||||
−0.343129 | + | 0.939288i | \(0.611487\pi\) | |||||||
\(152\) | −2.35501e8 | −0.0357847 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.57631e10 | −3.69110 | ||||||||
\(155\) | −1.68235e9 | −0.234112 | ||||||||
\(156\) | 3.20586e9 | 0.433395 | ||||||||
\(157\) | −8.04346e9 | −1.05656 | −0.528280 | − | 0.849070i | \(-0.677163\pi\) | ||||
−0.528280 | + | 0.849070i | \(0.677163\pi\) | |||||||
\(158\) | 1.33894e9 | 0.170925 | ||||||||
\(159\) | −2.69750e9 | −0.334714 | ||||||||
\(160\) | −1.29620e10 | −1.56363 | ||||||||
\(161\) | −7.96158e9 | −0.933863 | ||||||||
\(162\) | −5.81713e9 | −0.663577 | ||||||||
\(163\) | 5.04472e9 | 0.559749 | 0.279874 | − | 0.960037i | \(-0.409707\pi\) | ||||
0.279874 | + | 0.960037i | \(0.409707\pi\) | |||||||
\(164\) | 6.23614e8 | 0.0673160 | ||||||||
\(165\) | −7.47483e9 | −0.785097 | ||||||||
\(166\) | −1.37352e10 | −1.40394 | ||||||||
\(167\) | −1.88827e10 | −1.87862 | −0.939311 | − | 0.343066i | \(-0.888535\pi\) | ||||
−0.939311 | + | 0.343066i | \(0.888535\pi\) | |||||||
\(168\) | 7.37515e8 | 0.0714297 | ||||||||
\(169\) | 1.87437e9 | 0.176752 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.24436e9 | 0.290166 | ||||||||
\(172\) | 2.43680e9 | 0.212296 | ||||||||
\(173\) | −3.03545e9 | −0.257642 | −0.128821 | − | 0.991668i | \(-0.541119\pi\) | ||||
−0.128821 | + | 0.991668i | \(0.541119\pi\) | |||||||
\(174\) | 1.42176e10 | 1.17586 | ||||||||
\(175\) | 5.77137e9 | 0.465166 | ||||||||
\(176\) | −2.18719e10 | −1.71822 | ||||||||
\(177\) | −1.14448e9 | −0.0876451 | ||||||||
\(178\) | −1.76225e9 | −0.131576 | ||||||||
\(179\) | −9.45985e9 | −0.688724 | −0.344362 | − | 0.938837i | \(-0.611905\pi\) | ||||
−0.344362 | + | 0.938837i | \(0.611905\pi\) | |||||||
\(180\) | 1.20478e10 | 0.855423 | ||||||||
\(181\) | 7.53245e9 | 0.521654 | 0.260827 | − | 0.965386i | \(-0.416005\pi\) | ||||
0.260827 | + | 0.965386i | \(0.416005\pi\) | |||||||
\(182\) | −3.68088e10 | −2.48674 | ||||||||
\(183\) | −8.15574e9 | −0.537568 | ||||||||
\(184\) | −8.83362e8 | −0.0568144 | ||||||||
\(185\) | −1.78026e10 | −1.11741 | ||||||||
\(186\) | −2.01838e9 | −0.123650 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.10811e10 | −0.646955 | ||||||||
\(189\) | −2.26344e10 | −1.29030 | ||||||||
\(190\) | −1.00589e10 | −0.559966 | ||||||||
\(191\) | 7.27813e9 | 0.395703 | 0.197852 | − | 0.980232i | \(-0.436604\pi\) | ||||
0.197852 | + | 0.980232i | \(0.436604\pi\) | |||||||
\(192\) | −6.89698e9 | −0.366272 | ||||||||
\(193\) | 7.60493e9 | 0.394537 | 0.197268 | − | 0.980350i | \(-0.436793\pi\) | ||||
0.197268 | + | 0.980350i | \(0.436793\pi\) | |||||||
\(194\) | −4.78531e10 | −2.42550 | ||||||||
\(195\) | −1.06796e10 | −0.528930 | ||||||||
\(196\) | 3.30834e10 | 1.60125 | ||||||||
\(197\) | −2.18071e10 | −1.03157 | −0.515787 | − | 0.856717i | \(-0.672500\pi\) | ||||
−0.515787 | + | 0.856717i | \(0.672500\pi\) | |||||||
\(198\) | 3.93798e10 | 1.82088 | ||||||||
\(199\) | 1.40181e10 | 0.633652 | 0.316826 | − | 0.948484i | \(-0.397383\pi\) | ||||
0.316826 | + | 0.948484i | \(0.397383\pi\) | |||||||
\(200\) | 6.40351e8 | 0.0282998 | ||||||||
\(201\) | −1.95963e8 | −0.00846821 | ||||||||
\(202\) | −5.27921e10 | −2.23094 | ||||||||
\(203\) | −7.85577e10 | −3.24681 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.07742e9 | −0.0821547 | ||||||||
\(206\) | 3.75047e10 | 1.45105 | ||||||||
\(207\) | 1.21695e10 | 0.460689 | ||||||||
\(208\) | −3.12492e10 | −1.15759 | ||||||||
\(209\) | −1.58225e10 | −0.573610 | ||||||||
\(210\) | 3.15014e10 | 1.11775 | ||||||||
\(211\) | −3.40494e10 | −1.18260 | −0.591301 | − | 0.806451i | \(-0.701385\pi\) | ||||
−0.591301 | + | 0.806451i | \(0.701385\pi\) | |||||||
\(212\) | −2.12038e10 | −0.720944 | ||||||||
\(213\) | −1.46505e10 | −0.487691 | ||||||||
\(214\) | 5.48442e10 | 1.78759 | ||||||||
\(215\) | −8.11761e9 | −0.259093 | ||||||||
\(216\) | −2.51135e9 | −0.0784993 | ||||||||
\(217\) | 1.11524e10 | 0.341427 | ||||||||
\(218\) | 1.92463e10 | 0.577157 | ||||||||
\(219\) | −6.88746e9 | −0.202330 | ||||||||
\(220\) | −5.87561e10 | −1.69103 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.13586e10 | −0.590180 | ||||||||
\(223\) | −1.18689e10 | −0.321396 | −0.160698 | − | 0.987004i | \(-0.551374\pi\) | ||||
−0.160698 | + | 0.987004i | \(0.551374\pi\) | |||||||
\(224\) | 8.59259e10 | 2.28039 | ||||||||
\(225\) | −8.82173e9 | −0.229473 | ||||||||
\(226\) | 2.76941e10 | 0.706154 | ||||||||
\(227\) | −4.22158e10 | −1.05526 | −0.527628 | − | 0.849475i | \(-0.676919\pi\) | ||||
−0.527628 | + | 0.849475i | \(0.676919\pi\) | |||||||
\(228\) | −5.80760e9 | −0.142328 | ||||||||
\(229\) | 3.83719e10 | 0.922047 | 0.461024 | − | 0.887388i | \(-0.347482\pi\) | ||||
0.461024 | + | 0.887388i | \(0.347482\pi\) | |||||||
\(230\) | −3.77309e10 | −0.889042 | ||||||||
\(231\) | 4.95510e10 | 1.14498 | ||||||||
\(232\) | −8.71622e9 | −0.197530 | ||||||||
\(233\) | −1.60290e9 | −0.0356290 | −0.0178145 | − | 0.999841i | \(-0.505671\pi\) | ||||
−0.0178145 | + | 0.999841i | \(0.505671\pi\) | |||||||
\(234\) | 5.62634e10 | 1.22675 | ||||||||
\(235\) | 3.69142e10 | 0.789565 | ||||||||
\(236\) | −8.99620e9 | −0.188780 | ||||||||
\(237\) | −2.57522e9 | −0.0530209 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.18864e10 | −1.02864 | −0.514320 | − | 0.857598i | \(-0.671956\pi\) | ||||
−0.514320 | + | 0.857598i | \(0.671956\pi\) | |||||||
\(240\) | 2.67434e10 | 0.520315 | ||||||||
\(241\) | 4.27612e10 | 0.816532 | 0.408266 | − | 0.912863i | \(-0.366134\pi\) | ||||
0.408266 | + | 0.912863i | \(0.366134\pi\) | |||||||
\(242\) | −1.17975e11 | −2.21117 | ||||||||
\(243\) | 5.36644e10 | 0.987320 | ||||||||
\(244\) | −6.41084e10 | −1.15787 | ||||||||
\(245\) | −1.10210e11 | −1.95421 | ||||||||
\(246\) | −2.49237e9 | −0.0433915 | ||||||||
\(247\) | −2.26062e10 | −0.386448 | ||||||||
\(248\) | 1.23739e9 | 0.0207718 | ||||||||
\(249\) | 2.64174e10 | 0.435504 | ||||||||
\(250\) | −6.97316e10 | −1.12902 | ||||||||
\(251\) | −3.86901e10 | −0.615273 | −0.307637 | − | 0.951504i | \(-0.599538\pi\) | ||||
−0.307637 | + | 0.951504i | \(0.599538\pi\) | |||||||
\(252\) | −7.98653e10 | −1.24754 | ||||||||
\(253\) | −5.93499e10 | −0.910705 | ||||||||
\(254\) | 2.70582e10 | 0.407894 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.75598e10 | 1.12864 | ||||||||
\(257\) | −3.96876e10 | −0.567487 | −0.283743 | − | 0.958900i | \(-0.591576\pi\) | ||||
−0.283743 | + | 0.958900i | \(0.591576\pi\) | |||||||
\(258\) | −9.73905e9 | −0.136845 | ||||||||
\(259\) | 1.18015e11 | 1.62962 | ||||||||
\(260\) | −8.39471e10 | −1.13927 | ||||||||
\(261\) | 1.20078e11 | 1.60170 | ||||||||
\(262\) | −2.45507e10 | −0.321890 | ||||||||
\(263\) | −4.03518e10 | −0.520070 | −0.260035 | − | 0.965599i | \(-0.583734\pi\) | ||||
−0.260035 | + | 0.965599i | \(0.583734\pi\) | |||||||
\(264\) | 5.49783e9 | 0.0696584 | ||||||||
\(265\) | 7.06353e10 | 0.879864 | ||||||||
\(266\) | 6.66812e10 | 0.816650 | ||||||||
\(267\) | 3.38938e9 | 0.0408149 | ||||||||
\(268\) | −1.54037e9 | −0.0182398 | ||||||||
\(269\) | −2.49013e10 | −0.289959 | −0.144980 | − | 0.989435i | \(-0.546312\pi\) | ||||
−0.144980 | + | 0.989435i | \(0.546312\pi\) | |||||||
\(270\) | −1.07267e11 | −1.22837 | ||||||||
\(271\) | −5.46121e10 | −0.615074 | −0.307537 | − | 0.951536i | \(-0.599505\pi\) | ||||
−0.307537 | + | 0.951536i | \(0.599505\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.07954e10 | 0.771388 | ||||||||
\(274\) | −1.94488e11 | −2.08456 | ||||||||
\(275\) | 4.30229e10 | 0.453631 | ||||||||
\(276\) | −2.17842e10 | −0.225970 | ||||||||
\(277\) | −5.60797e10 | −0.572330 | −0.286165 | − | 0.958180i | \(-0.592381\pi\) | ||||
−0.286165 | + | 0.958180i | \(0.592381\pi\) | |||||||
\(278\) | 7.58266e9 | 0.0761412 | ||||||||
\(279\) | −1.70467e10 | −0.168431 | ||||||||
\(280\) | −1.93122e10 | −0.187767 | ||||||||
\(281\) | 1.76224e10 | 0.168611 | 0.0843057 | − | 0.996440i | \(-0.473133\pi\) | ||||
0.0843057 | + | 0.996440i | \(0.473133\pi\) | |||||||
\(282\) | 4.42876e10 | 0.417024 | ||||||||
\(283\) | 1.40836e11 | 1.30520 | 0.652598 | − | 0.757705i | \(-0.273679\pi\) | ||||
0.652598 | + | 0.757705i | \(0.273679\pi\) | |||||||
\(284\) | −1.15161e11 | −1.05044 | ||||||||
\(285\) | 1.93467e10 | 0.173702 | ||||||||
\(286\) | −2.74392e11 | −2.42507 | ||||||||
\(287\) | 1.37713e10 | 0.119814 | ||||||||
\(288\) | −1.31341e11 | −1.12495 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −3.72295e11 | −3.09098 | ||||||||
\(291\) | 9.20372e10 | 0.752393 | ||||||||
\(292\) | −5.41391e10 | −0.435801 | ||||||||
\(293\) | −8.38614e10 | −0.664749 | −0.332375 | − | 0.943147i | \(-0.607850\pi\) | ||||
−0.332375 | + | 0.943147i | \(0.607850\pi\) | |||||||
\(294\) | −1.32223e11 | −1.03215 | ||||||||
\(295\) | 2.99687e10 | 0.230393 | ||||||||
\(296\) | 1.30941e10 | 0.0991429 | ||||||||
\(297\) | −1.68729e11 | −1.25830 | ||||||||
\(298\) | 4.31730e10 | 0.317132 | ||||||||
\(299\) | −8.47955e10 | −0.613553 | ||||||||
\(300\) | 1.57914e10 | 0.112558 | ||||||||
\(301\) | 5.38120e10 | 0.377859 | ||||||||
\(302\) | 1.37731e11 | 0.952799 | ||||||||
\(303\) | 1.01537e11 | 0.692039 | ||||||||
\(304\) | 5.66097e10 | 0.380154 | ||||||||
\(305\) | 2.13562e11 | 1.41311 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.75664e11 | −1.12865 | −0.564325 | − | 0.825553i | \(-0.690863\pi\) | ||||
−0.564325 | + | 0.825553i | \(0.690863\pi\) | |||||||
\(308\) | 3.89497e11 | 2.46619 | ||||||||
\(309\) | −7.21338e10 | −0.450118 | ||||||||
\(310\) | 5.28524e10 | 0.325040 | ||||||||
\(311\) | 2.63974e11 | 1.60007 | 0.800037 | − | 0.599951i | \(-0.204813\pi\) | ||||
0.800037 | + | 0.599951i | \(0.204813\pi\) | |||||||
\(312\) | 7.85496e9 | 0.0469297 | ||||||||
\(313\) | 2.54781e10 | 0.150044 | 0.0750220 | − | 0.997182i | \(-0.476097\pi\) | ||||
0.0750220 | + | 0.997182i | \(0.476097\pi\) | |||||||
\(314\) | 2.52692e11 | 1.46693 | ||||||||
\(315\) | 2.66052e11 | 1.52254 | ||||||||
\(316\) | −2.02426e10 | −0.114202 | ||||||||
\(317\) | −2.50051e11 | −1.39079 | −0.695394 | − | 0.718628i | \(-0.744770\pi\) | ||||
−0.695394 | + | 0.718628i | \(0.744770\pi\) | |||||||
\(318\) | 8.47442e10 | 0.464716 | ||||||||
\(319\) | −5.85612e11 | −3.16630 | ||||||||
\(320\) | 1.80601e11 | 0.962820 | ||||||||
\(321\) | −1.05483e11 | −0.554512 | ||||||||
\(322\) | 2.50120e11 | 1.29657 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 8.79456e10 | 0.443365 | ||||||||
\(325\) | 6.14684e10 | 0.305617 | ||||||||
\(326\) | −1.58484e11 | −0.777154 | ||||||||
\(327\) | −3.70170e10 | −0.179034 | ||||||||
\(328\) | 1.52797e9 | 0.00728924 | ||||||||
\(329\) | −2.44706e11 | −1.15150 | ||||||||
\(330\) | 2.34828e11 | 1.09003 | ||||||||
\(331\) | 3.65757e11 | 1.67482 | 0.837408 | − | 0.546579i | \(-0.184070\pi\) | ||||
0.837408 | + | 0.546579i | \(0.184070\pi\) | |||||||
\(332\) | 2.07654e11 | 0.938037 | ||||||||
\(333\) | −1.80389e11 | −0.803917 | ||||||||
\(334\) | 5.93216e11 | 2.60828 | ||||||||
\(335\) | 5.13138e9 | 0.0222604 | ||||||||
\(336\) | −1.77283e11 | −0.758825 | ||||||||
\(337\) | −4.56163e11 | −1.92657 | −0.963287 | − | 0.268474i | \(-0.913481\pi\) | ||||
−0.963287 | + | 0.268474i | \(0.913481\pi\) | |||||||
\(338\) | −5.88850e10 | −0.245403 | ||||||||
\(339\) | −5.32649e10 | −0.219049 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.31356e10 | 0.332960 | ||||||||
\(342\) | −1.01924e11 | −0.402866 | ||||||||
\(343\) | 3.07334e11 | 1.19891 | ||||||||
\(344\) | 5.97060e9 | 0.0229882 | ||||||||
\(345\) | 7.25690e10 | 0.275781 | ||||||||
\(346\) | 9.53615e10 | 0.357709 | ||||||||
\(347\) | 3.36335e11 | 1.24534 | 0.622671 | − | 0.782483i | \(-0.286047\pi\) | ||||
0.622671 | + | 0.782483i | \(0.286047\pi\) | |||||||
\(348\) | −2.14947e11 | −0.785643 | ||||||||
\(349\) | −3.19659e8 | −0.00115338 | −0.000576690 | − | 1.00000i | \(-0.500184\pi\) | ||||
−0.000576690 | 1.00000i | \(0.500184\pi\) | ||||||||
\(350\) | −1.81313e11 | −0.645835 | ||||||||
\(351\) | −2.41069e11 | −0.847734 | ||||||||
\(352\) | 6.40538e11 | 2.22384 | ||||||||
\(353\) | −5.74697e10 | −0.196994 | −0.0984970 | − | 0.995137i | \(-0.531403\pi\) | ||||
−0.0984970 | + | 0.995137i | \(0.531403\pi\) | |||||||
\(354\) | 3.59548e10 | 0.121686 | ||||||||
\(355\) | 3.83631e11 | 1.28199 | ||||||||
\(356\) | 2.66423e10 | 0.0879117 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.97189e11 | 0.956224 | ||||||||
\(359\) | 1.28501e10 | 0.0408302 | 0.0204151 | − | 0.999792i | \(-0.493501\pi\) | ||||
0.0204151 | + | 0.999792i | \(0.493501\pi\) | |||||||
\(360\) | 2.95193e10 | 0.0926286 | ||||||||
\(361\) | −2.81735e11 | −0.873089 | ||||||||
\(362\) | −2.36638e11 | −0.724264 | ||||||||
\(363\) | 2.26905e11 | 0.685906 | ||||||||
\(364\) | 5.56489e11 | 1.66150 | ||||||||
\(365\) | 1.80352e11 | 0.531866 | ||||||||
\(366\) | 2.56220e11 | 0.746359 | ||||||||
\(367\) | 1.20128e11 | 0.345658 | 0.172829 | − | 0.984952i | \(-0.444709\pi\) | ||||
0.172829 | + | 0.984952i | \(0.444709\pi\) | |||||||
\(368\) | 2.12342e11 | 0.603561 | ||||||||
\(369\) | −2.10499e10 | −0.0591060 | ||||||||
\(370\) | 5.59285e11 | 1.55141 | ||||||||
\(371\) | −4.68245e11 | −1.28319 | ||||||||
\(372\) | 3.05147e10 | 0.0826163 | ||||||||
\(373\) | 2.29521e11 | 0.613949 | 0.306975 | − | 0.951718i | \(-0.400683\pi\) | ||||
0.306975 | + | 0.951718i | \(0.400683\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.34117e11 | 0.350221 | ||||||||
\(376\) | −2.71509e10 | −0.0700549 | ||||||||
\(377\) | −8.36685e11 | −2.13317 | ||||||||
\(378\) | 7.11079e11 | 1.79145 | ||||||||
\(379\) | 1.85213e10 | 0.0461099 | 0.0230549 | − | 0.999734i | \(-0.492661\pi\) | ||||
0.0230549 | + | 0.999734i | \(0.492661\pi\) | |||||||
\(380\) | 1.52075e11 | 0.374138 | ||||||||
\(381\) | −5.20418e10 | −0.126529 | ||||||||
\(382\) | −2.28649e11 | −0.549394 | ||||||||
\(383\) | −7.04308e11 | −1.67251 | −0.836253 | − | 0.548343i | \(-0.815259\pi\) | ||||
−0.836253 | + | 0.548343i | \(0.815259\pi\) | |||||||
\(384\) | −3.67695e10 | −0.0862974 | ||||||||
\(385\) | −1.29752e12 | −3.00981 | ||||||||
\(386\) | −2.38915e11 | −0.547774 | ||||||||
\(387\) | −8.22534e10 | −0.186404 | ||||||||
\(388\) | 7.23461e11 | 1.62059 | ||||||||
\(389\) | −8.72755e11 | −1.93250 | −0.966249 | − | 0.257611i | \(-0.917065\pi\) | ||||
−0.966249 | + | 0.257611i | \(0.917065\pi\) | |||||||
\(390\) | 3.35508e11 | 0.734365 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 8.10605e10 | 0.173389 | ||||||||
\(393\) | 4.72190e10 | 0.0998506 | ||||||||
\(394\) | 6.85090e11 | 1.43224 | ||||||||
\(395\) | 6.74335e10 | 0.139376 | ||||||||
\(396\) | −5.95359e11 | −1.21661 | ||||||||
\(397\) | 4.55747e11 | 0.920802 | 0.460401 | − | 0.887711i | \(-0.347706\pi\) | ||||
0.460401 | + | 0.887711i | \(0.347706\pi\) | |||||||
\(398\) | −4.40392e11 | −0.879762 | ||||||||
\(399\) | −1.28250e11 | −0.253326 | ||||||||
\(400\) | −1.53927e11 | −0.300639 | ||||||||
\(401\) | −8.98679e11 | −1.73562 | −0.867810 | − | 0.496896i | \(-0.834473\pi\) | ||||
−0.867810 | + | 0.496896i | \(0.834473\pi\) | |||||||
\(402\) | 6.15634e9 | 0.0117572 | ||||||||
\(403\) | 1.18779e11 | 0.224320 | ||||||||
\(404\) | 7.98131e11 | 1.49059 | ||||||||
\(405\) | −2.92970e11 | −0.541097 | ||||||||
\(406\) | 2.46796e12 | 4.50787 | ||||||||
\(407\) | 8.79744e11 | 1.58921 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.95210e11 | −0.344943 | −0.172472 | − | 0.985015i | \(-0.555175\pi\) | ||||
−0.172472 | + | 0.985015i | \(0.555175\pi\) | |||||||
\(410\) | 6.52640e10 | 0.114063 | ||||||||
\(411\) | 3.74064e11 | 0.646632 | ||||||||
\(412\) | −5.67010e11 | −0.969513 | ||||||||
\(413\) | −1.98664e11 | −0.336004 | ||||||||
\(414\) | −3.82317e11 | −0.639620 | ||||||||
\(415\) | −6.91752e11 | −1.14481 | ||||||||
\(416\) | 9.15161e11 | 1.49823 | ||||||||
\(417\) | −1.45839e10 | −0.0236191 | ||||||||
\(418\) | 4.97078e11 | 0.796400 | ||||||||
\(419\) | 1.38040e11 | 0.218796 | 0.109398 | − | 0.993998i | \(-0.465108\pi\) | ||||
0.109398 | + | 0.993998i | \(0.465108\pi\) | |||||||
\(420\) | −4.76250e11 | −0.746815 | ||||||||
\(421\) | 7.45047e11 | 1.15588 | 0.577942 | − | 0.816078i | \(-0.303856\pi\) | ||||
0.577942 | + | 0.816078i | \(0.303856\pi\) | |||||||
\(422\) | 1.06969e12 | 1.64192 | ||||||||
\(423\) | 3.74041e11 | 0.568051 | ||||||||
\(424\) | −5.19531e10 | −0.0780666 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.60259e11 | 0.677109 | ||||||||
\(427\) | −1.41571e12 | −2.06087 | ||||||||
\(428\) | −8.29155e11 | −1.19437 | ||||||||
\(429\) | 5.27747e11 | 0.752259 | ||||||||
\(430\) | 2.55022e11 | 0.359724 | ||||||||
\(431\) | −1.02134e11 | −0.142568 | −0.0712841 | − | 0.997456i | \(-0.522710\pi\) | ||||
−0.0712841 | + | 0.997456i | \(0.522710\pi\) | |||||||
\(432\) | 6.03678e11 | 0.833927 | ||||||||
\(433\) | −1.06370e12 | −1.45420 | −0.727102 | − | 0.686530i | \(-0.759133\pi\) | ||||
−0.727102 | + | 0.686530i | \(0.759133\pi\) | |||||||
\(434\) | −3.50361e11 | −0.474037 | ||||||||
\(435\) | 7.16045e11 | 0.958824 | ||||||||
\(436\) | −2.90973e11 | −0.385624 | ||||||||
\(437\) | 1.53612e11 | 0.201492 | ||||||||
\(438\) | 2.16376e11 | 0.280915 | ||||||||
\(439\) | 1.32178e12 | 1.69851 | 0.849254 | − | 0.527985i | \(-0.177052\pi\) | ||||
0.849254 | + | 0.527985i | \(0.177052\pi\) | |||||||
\(440\) | −1.43963e11 | −0.183111 | ||||||||
\(441\) | −1.11672e12 | −1.40595 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.29502e12 | 1.59757 | 0.798784 | − | 0.601618i | \(-0.205477\pi\) | ||||
0.798784 | + | 0.601618i | \(0.205477\pi\) | |||||||
\(444\) | 3.22907e11 | 0.394325 | ||||||||
\(445\) | −8.87525e10 | −0.107290 | ||||||||
\(446\) | 3.72873e11 | 0.446225 | ||||||||
\(447\) | −8.30359e10 | −0.0983744 | ||||||||
\(448\) | −1.19721e12 | −1.40417 | ||||||||
\(449\) | 4.24727e11 | 0.493176 | 0.246588 | − | 0.969120i | \(-0.420691\pi\) | ||||
0.246588 | + | 0.969120i | \(0.420691\pi\) | |||||||
\(450\) | 2.77142e11 | 0.318601 | ||||||||
\(451\) | 1.02659e11 | 0.116843 | ||||||||
\(452\) | −4.18690e11 | −0.471813 | ||||||||
\(453\) | −2.64903e11 | −0.295559 | ||||||||
\(454\) | 1.32624e12 | 1.46512 | ||||||||
\(455\) | −1.85381e12 | −2.02775 | ||||||||
\(456\) | −1.42297e10 | −0.0154118 | ||||||||
\(457\) | −4.27181e11 | −0.458131 | −0.229065 | − | 0.973411i | \(-0.573567\pi\) | ||||
−0.229065 | + | 0.973411i | \(0.573567\pi\) | |||||||
\(458\) | −1.20549e12 | −1.28017 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.70431e11 | 0.594008 | ||||||||
\(461\) | −1.13997e12 | −1.17554 | −0.587771 | − | 0.809027i | \(-0.699994\pi\) | ||||
−0.587771 | + | 0.809027i | \(0.699994\pi\) | |||||||
\(462\) | −1.55669e12 | −1.58969 | ||||||||
\(463\) | 1.72036e12 | 1.73982 | 0.869909 | − | 0.493213i | \(-0.164178\pi\) | ||||
0.869909 | + | 0.493213i | \(0.164178\pi\) | |||||||
\(464\) | 2.09520e12 | 2.09843 | ||||||||
\(465\) | −1.01653e11 | −0.100828 | ||||||||
\(466\) | 5.03564e10 | 0.0494673 | ||||||||
\(467\) | −1.58108e12 | −1.53825 | −0.769125 | − | 0.639099i | \(-0.779307\pi\) | ||||
−0.769125 | + | 0.639099i | \(0.779307\pi\) | |||||||
\(468\) | −8.50612e11 | −0.819643 | ||||||||
\(469\) | −3.40162e10 | −0.0324644 | ||||||||
\(470\) | −1.15969e12 | −1.09623 | ||||||||
\(471\) | −4.86010e11 | −0.455042 | ||||||||
\(472\) | −2.20424e10 | −0.0204418 | ||||||||
\(473\) | 4.01144e11 | 0.368489 | ||||||||
\(474\) | 8.09029e10 | 0.0736142 | ||||||||
\(475\) | −1.11354e11 | −0.100365 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.15727e11 | 0.633016 | ||||||||
\(478\) | 1.63006e12 | 1.42816 | ||||||||
\(479\) | 1.08848e12 | 0.944737 | 0.472369 | − | 0.881401i | \(-0.343399\pi\) | ||||
0.472369 | + | 0.881401i | \(0.343399\pi\) | |||||||
\(480\) | −7.83206e11 | −0.673427 | ||||||||
\(481\) | 1.25692e12 | 1.07067 | ||||||||
\(482\) | −1.34338e12 | −1.13367 | ||||||||
\(483\) | −4.81063e11 | −0.402198 | ||||||||
\(484\) | 1.78360e12 | 1.47738 | ||||||||
\(485\) | −2.41004e12 | −1.97782 | ||||||||
\(486\) | −1.68591e12 | −1.37079 | ||||||||
\(487\) | −2.07370e12 | −1.67057 | −0.835287 | − | 0.549815i | \(-0.814698\pi\) | ||||
−0.835287 | + | 0.549815i | \(0.814698\pi\) | |||||||
\(488\) | −1.57078e11 | −0.125379 | ||||||||
\(489\) | 3.04818e11 | 0.241074 | ||||||||
\(490\) | 3.46233e12 | 2.71323 | ||||||||
\(491\) | −1.27855e11 | −0.0992772 | −0.0496386 | − | 0.998767i | \(-0.515807\pi\) | ||||
−0.0496386 | + | 0.998767i | \(0.515807\pi\) | |||||||
\(492\) | 3.76806e10 | 0.0289918 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 7.10194e11 | 0.536544 | ||||||||
\(495\) | 1.98330e12 | 1.48479 | ||||||||
\(496\) | −2.97443e11 | −0.220666 | ||||||||
\(497\) | −2.54311e12 | −1.86965 | ||||||||
\(498\) | −8.29924e11 | −0.604653 | ||||||||
\(499\) | 1.57050e12 | 1.13393 | 0.566964 | − | 0.823743i | \(-0.308118\pi\) | ||||
0.566964 | + | 0.823743i | \(0.308118\pi\) | |||||||
\(500\) | 1.05423e12 | 0.754345 | ||||||||
\(501\) | −1.14095e12 | −0.809090 | ||||||||
\(502\) | 1.21548e12 | 0.854245 | ||||||||
\(503\) | 1.11074e12 | 0.773670 | 0.386835 | − | 0.922149i | \(-0.373568\pi\) | ||||
0.386835 | + | 0.922149i | \(0.373568\pi\) | |||||||
\(504\) | −1.95685e11 | −0.135089 | ||||||||
\(505\) | −2.65878e12 | −1.81916 | ||||||||
\(506\) | 1.86453e12 | 1.26442 | ||||||||
\(507\) | 1.13255e11 | 0.0761241 | ||||||||
\(508\) | −4.09076e11 | −0.272532 | ||||||||
\(509\) | −2.12203e12 | −1.40127 | −0.700636 | − | 0.713519i | \(-0.747100\pi\) | ||||
−0.700636 | + | 0.713519i | \(0.747100\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.19556e12 | −0.775670 | ||||||||
\(512\) | −2.12504e12 | −1.36663 | ||||||||
\(513\) | 4.36711e11 | 0.278398 | ||||||||
\(514\) | 1.24682e12 | 0.787898 | ||||||||
\(515\) | 1.88886e12 | 1.18323 | ||||||||
\(516\) | 1.47239e11 | 0.0914320 | ||||||||
\(517\) | −1.82417e12 | −1.12294 | ||||||||
\(518\) | −3.70753e12 | −2.26256 | ||||||||
\(519\) | −1.83411e11 | −0.110962 | ||||||||
\(520\) | −2.05686e11 | −0.123364 | ||||||||
\(521\) | 1.64335e12 | 0.977150 | 0.488575 | − | 0.872522i | \(-0.337517\pi\) | ||||
0.488575 | + | 0.872522i | \(0.337517\pi\) | |||||||
\(522\) | −3.77236e12 | −2.22380 | ||||||||
\(523\) | −1.94542e12 | −1.13699 | −0.568493 | − | 0.822688i | \(-0.692473\pi\) | ||||
−0.568493 | + | 0.822688i | \(0.692473\pi\) | |||||||
\(524\) | 3.71167e11 | 0.215069 | ||||||||
\(525\) | 3.48724e11 | 0.200339 | ||||||||
\(526\) | 1.26769e12 | 0.722065 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.32157e12 | −0.740008 | ||||||||
\(529\) | −1.22496e12 | −0.680096 | ||||||||
\(530\) | −2.21907e12 | −1.22160 | ||||||||
\(531\) | 3.03664e11 | 0.165756 | ||||||||
\(532\) | −1.00811e12 | −0.545640 | ||||||||
\(533\) | 1.46673e11 | 0.0787184 | ||||||||
\(534\) | −1.06480e11 | −0.0566674 | ||||||||
\(535\) | 2.76213e12 | 1.45765 | ||||||||
\(536\) | −3.77420e9 | −0.00197507 | ||||||||
\(537\) | −5.71593e11 | −0.296621 | ||||||||
\(538\) | 7.82297e11 | 0.402579 | ||||||||
\(539\) | 5.44617e12 | 2.77934 | ||||||||
\(540\) | 1.62170e12 | 0.820729 | ||||||||
\(541\) | −2.58123e12 | −1.29551 | −0.647753 | − | 0.761850i | \(-0.724291\pi\) | ||||
−0.647753 | + | 0.761850i | \(0.724291\pi\) | |||||||
\(542\) | 1.71569e12 | 0.853967 | ||||||||
\(543\) | 4.55133e11 | 0.224667 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.69309e11 | 0.470628 | ||||||||
\(546\) | −2.22410e12 | −1.07099 | ||||||||
\(547\) | −8.12819e11 | −0.388196 | −0.194098 | − | 0.980982i | \(-0.562178\pi\) | ||||
−0.194098 | + | 0.980982i | \(0.562178\pi\) | |||||||
\(548\) | 2.94034e12 | 1.39279 | ||||||||
\(549\) | 2.16396e12 | 1.01666 | ||||||||
\(550\) | −1.35160e12 | −0.629820 | ||||||||
\(551\) | 1.51570e12 | 0.700539 | ||||||||
\(552\) | −5.33754e10 | −0.0244689 | ||||||||
\(553\) | −4.47020e11 | −0.203266 | ||||||||
\(554\) | 1.76179e12 | 0.794622 | ||||||||
\(555\) | −1.07569e12 | −0.481248 | ||||||||
\(556\) | −1.14637e11 | −0.0508733 | ||||||||
\(557\) | 2.77064e12 | 1.21964 | 0.609819 | − | 0.792540i | \(-0.291242\pi\) | ||||
0.609819 | + | 0.792540i | \(0.291242\pi\) | |||||||
\(558\) | 5.35538e11 | 0.233850 | ||||||||
\(559\) | 5.73129e11 | 0.248256 | ||||||||
\(560\) | 4.64226e12 | 1.99472 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.53623e11 | −0.234100 | ||||||||
\(563\) | −3.89099e12 | −1.63220 | −0.816098 | − | 0.577914i | \(-0.803867\pi\) | ||||
−0.816098 | + | 0.577914i | \(0.803867\pi\) | |||||||
\(564\) | −6.69556e11 | −0.278632 | ||||||||
\(565\) | 1.39477e12 | 0.575816 | ||||||||
\(566\) | −4.42449e12 | −1.81213 | ||||||||
\(567\) | 1.94211e12 | 0.789133 | ||||||||
\(568\) | −2.82165e11 | −0.113746 | ||||||||
\(569\) | 1.29595e12 | 0.518304 | 0.259152 | − | 0.965837i | \(-0.416557\pi\) | ||||
0.259152 | + | 0.965837i | \(0.416557\pi\) | |||||||
\(570\) | −6.07792e11 | −0.241167 | ||||||||
\(571\) | 3.67635e12 | 1.44728 | 0.723642 | − | 0.690175i | \(-0.242467\pi\) | ||||
0.723642 | + | 0.690175i | \(0.242467\pi\) | |||||||
\(572\) | 4.14837e12 | 1.62030 | ||||||||
\(573\) | 4.39767e11 | 0.170422 | ||||||||
\(574\) | −4.32638e11 | −0.166349 | ||||||||
\(575\) | −4.17686e11 | −0.159347 | ||||||||
\(576\) | 1.82998e12 | 0.692699 | ||||||||
\(577\) | −7.12314e11 | −0.267535 | −0.133767 | − | 0.991013i | \(-0.542707\pi\) | ||||
−0.133767 | + | 0.991013i | \(0.542707\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.59513e11 | 0.169920 | ||||||||
\(580\) | 5.62850e12 | 2.06522 | ||||||||
\(581\) | 4.58565e12 | 1.66959 | ||||||||
\(582\) | −2.89143e12 | −1.04462 | ||||||||
\(583\) | −3.49055e12 | −1.25137 | ||||||||
\(584\) | −1.32651e11 | −0.0471903 | ||||||||
\(585\) | 2.83361e12 | 1.00032 | ||||||||
\(586\) | 2.63458e12 | 0.922937 | ||||||||
\(587\) | 2.45642e11 | 0.0853948 | 0.0426974 | − | 0.999088i | \(-0.486405\pi\) | ||||
0.0426974 | + | 0.999088i | \(0.486405\pi\) | |||||||
\(588\) | 1.99900e12 | 0.689628 | ||||||||
\(589\) | −2.15175e11 | −0.0736670 | ||||||||
\(590\) | −9.41493e11 | −0.319877 | ||||||||
\(591\) | −1.31765e12 | −0.444280 | ||||||||
\(592\) | −3.14755e12 | −1.05323 | ||||||||
\(593\) | −7.70573e11 | −0.255899 | −0.127949 | − | 0.991781i | \(-0.540839\pi\) | ||||
−0.127949 | + | 0.991781i | \(0.540839\pi\) | |||||||
\(594\) | 5.30076e12 | 1.74703 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.52706e11 | −0.211890 | ||||||||
\(597\) | 8.47018e11 | 0.272903 | ||||||||
\(598\) | 2.66392e12 | 0.851856 | ||||||||
\(599\) | −4.21472e12 | −1.33767 | −0.668834 | − | 0.743412i | \(-0.733206\pi\) | ||||
−0.668834 | + | 0.743412i | \(0.733206\pi\) | |||||||
\(600\) | 3.86920e10 | 0.0121882 | ||||||||
\(601\) | 1.24558e12 | 0.389437 | 0.194719 | − | 0.980859i | \(-0.437621\pi\) | ||||
0.194719 | + | 0.980859i | \(0.437621\pi\) | |||||||
\(602\) | −1.69055e12 | −0.524619 | ||||||||
\(603\) | 5.19948e10 | 0.0160152 | ||||||||
\(604\) | −2.08227e12 | −0.636608 | ||||||||
\(605\) | −5.94163e12 | −1.80304 | ||||||||
\(606\) | −3.18986e12 | −0.960826 | ||||||||
\(607\) | 3.32695e12 | 0.994711 | 0.497355 | − | 0.867547i | \(-0.334305\pi\) | ||||
0.497355 | + | 0.867547i | \(0.334305\pi\) | |||||||
\(608\) | −1.65787e12 | −0.492021 | ||||||||
\(609\) | −4.74670e12 | −1.39834 | ||||||||
\(610\) | −6.70924e12 | −1.96195 | ||||||||
\(611\) | −2.60626e12 | −0.756541 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.74693e12 | 0.785733 | 0.392867 | − | 0.919595i | \(-0.371483\pi\) | ||||
0.392867 | + | 0.919595i | \(0.371483\pi\) | |||||||
\(614\) | 5.51863e12 | 1.56702 | ||||||||
\(615\) | −1.25524e11 | −0.0353826 | ||||||||
\(616\) | 9.54340e11 | 0.267048 | ||||||||
\(617\) | −2.28297e12 | −0.634187 | −0.317094 | − | 0.948394i | \(-0.602707\pi\) | ||||
−0.317094 | + | 0.948394i | \(0.602707\pi\) | |||||||
\(618\) | 2.26615e12 | 0.624943 | ||||||||
\(619\) | −1.30761e10 | −0.00357989 | −0.00178995 | − | 0.999998i | \(-0.500570\pi\) | ||||
−0.00178995 | + | 0.999998i | \(0.500570\pi\) | |||||||
\(620\) | −7.99043e11 | −0.217174 | ||||||||
\(621\) | 1.63809e12 | 0.442005 | ||||||||
\(622\) | −8.29299e12 | −2.22154 | ||||||||
\(623\) | 5.88344e11 | 0.156472 | ||||||||
\(624\) | −1.88817e12 | −0.498552 | ||||||||
\(625\) | −4.58663e12 | −1.20236 | ||||||||
\(626\) | −8.00418e11 | −0.208321 | ||||||||
\(627\) | −9.56044e11 | −0.247044 | ||||||||
\(628\) | −3.82030e12 | −0.980119 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −8.35827e12 | −2.11390 | ||||||||
\(631\) | 1.82848e12 | 0.459154 | 0.229577 | − | 0.973291i | \(-0.426266\pi\) | ||||
0.229577 | + | 0.973291i | \(0.426266\pi\) | |||||||
\(632\) | −4.95982e10 | −0.0123663 | ||||||||
\(633\) | −2.05737e12 | −0.509325 | ||||||||
\(634\) | 7.85556e12 | 1.93097 | ||||||||
\(635\) | 1.36274e12 | 0.332607 | ||||||||
\(636\) | −1.28120e12 | −0.310498 | ||||||||
\(637\) | 7.78114e12 | 1.87248 | ||||||||
\(638\) | 1.83975e13 | 4.39608 | ||||||||
\(639\) | 3.88722e12 | 0.922328 | ||||||||
\(640\) | 9.62828e11 | 0.226850 | ||||||||
\(641\) | 4.34210e12 | 1.01587 | 0.507936 | − | 0.861395i | \(-0.330409\pi\) | ||||
0.507936 | + | 0.861395i | \(0.330409\pi\) | |||||||
\(642\) | 3.31385e12 | 0.769884 | ||||||||
\(643\) | −7.89392e11 | −0.182114 | −0.0910570 | − | 0.995846i | \(-0.529025\pi\) | ||||
−0.0910570 | + | 0.995846i | \(0.529025\pi\) | |||||||
\(644\) | −3.78141e12 | −0.866298 | ||||||||
\(645\) | −4.90491e11 | −0.111587 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.49662e11 | 0.0560122 | 0.0280061 | − | 0.999608i | \(-0.491084\pi\) | ||||
0.0280061 | + | 0.999608i | \(0.491084\pi\) | |||||||
\(648\) | 2.15483e11 | 0.0480093 | ||||||||
\(649\) | −1.48095e12 | −0.327672 | ||||||||
\(650\) | −1.93108e12 | −0.424318 | ||||||||
\(651\) | 6.73859e11 | 0.147047 | ||||||||
\(652\) | 2.39603e12 | 0.519251 | ||||||||
\(653\) | 2.48710e12 | 0.535284 | 0.267642 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267642 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(654\) | 1.16292e12 | 0.248571 | ||||||||
\(655\) | −1.23645e12 | −0.262477 | ||||||||
\(656\) | −3.67293e11 | −0.0774364 | ||||||||
\(657\) | 1.82745e12 | 0.382650 | ||||||||
\(658\) | 7.68765e12 | 1.59874 | ||||||||
\(659\) | −1.78184e12 | −0.368031 | −0.184015 | − | 0.982923i | \(-0.558910\pi\) | ||||
−0.184015 | + | 0.982923i | \(0.558910\pi\) | |||||||
\(660\) | −3.55022e12 | −0.728296 | ||||||||
\(661\) | −3.14479e11 | −0.0640744 | −0.0320372 | − | 0.999487i | \(-0.510200\pi\) | ||||
−0.0320372 | + | 0.999487i | \(0.510200\pi\) | |||||||
\(662\) | −1.14906e13 | −2.32531 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.08792e11 | 0.101574 | ||||||||
\(665\) | 3.35829e12 | 0.665918 | ||||||||
\(666\) | 5.66708e12 | 1.11616 | ||||||||
\(667\) | 5.68538e12 | 1.11223 | ||||||||
\(668\) | −8.96847e12 | −1.74271 | ||||||||
\(669\) | −7.17157e11 | −0.138419 | ||||||||
\(670\) | −1.61207e11 | −0.0309063 | ||||||||
\(671\) | −1.05535e13 | −2.00976 | ||||||||
\(672\) | 5.19191e12 | 0.982121 | ||||||||
\(673\) | −6.58350e11 | −0.123706 | −0.0618528 | − | 0.998085i | \(-0.519701\pi\) | ||||
−0.0618528 | + | 0.998085i | \(0.519701\pi\) | |||||||
\(674\) | 1.43308e13 | 2.67485 | ||||||||
\(675\) | −1.18746e12 | −0.220167 | ||||||||
\(676\) | 8.90246e11 | 0.163965 | ||||||||
\(677\) | −3.47369e12 | −0.635540 | −0.317770 | − | 0.948168i | \(-0.602934\pi\) | ||||
−0.317770 | + | 0.948168i | \(0.602934\pi\) | |||||||
\(678\) | 1.67336e12 | 0.304128 | ||||||||
\(679\) | 1.59763e13 | 2.88444 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.55080e12 | −0.454480 | ||||||||
\(682\) | −2.61178e12 | −0.462282 | ||||||||
\(683\) | −3.82712e12 | −0.672944 | −0.336472 | − | 0.941693i | \(-0.609234\pi\) | ||||
−0.336472 | + | 0.941693i | \(0.609234\pi\) | |||||||
\(684\) | 1.54093e12 | 0.269173 | ||||||||
\(685\) | −9.79504e12 | −1.69980 | ||||||||
\(686\) | −9.65518e12 | −1.66457 | ||||||||
\(687\) | 2.31854e12 | 0.397109 | ||||||||
\(688\) | −1.43521e12 | −0.244212 | ||||||||
\(689\) | −4.98708e12 | −0.843062 | ||||||||
\(690\) | −2.27982e12 | −0.382895 | ||||||||
\(691\) | −6.65485e11 | −0.111042 | −0.0555210 | − | 0.998458i | \(-0.517682\pi\) | ||||
−0.0555210 | + | 0.998458i | \(0.517682\pi\) | |||||||
\(692\) | −1.44171e12 | −0.239002 | ||||||||
\(693\) | −1.31474e13 | −2.16541 | ||||||||
\(694\) | −1.05662e13 | −1.72903 | ||||||||
\(695\) | 3.81888e11 | 0.0620875 | ||||||||
\(696\) | −5.26660e11 | −0.0850725 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.00424e10 | 0.00160135 | ||||||||
\(699\) | −9.68519e10 | −0.0153448 | ||||||||
\(700\) | 2.74115e12 | 0.431511 | ||||||||
\(701\) | −8.18142e12 | −1.27967 | −0.639835 | − | 0.768513i | \(-0.720997\pi\) | ||||
−0.639835 | + | 0.768513i | \(0.720997\pi\) | |||||||
\(702\) | 7.57340e12 | 1.17699 | ||||||||
\(703\) | −2.27699e12 | −0.351611 | ||||||||
\(704\) | −8.92466e12 | −1.36935 | ||||||||
\(705\) | 2.23047e12 | 0.340052 | ||||||||
\(706\) | 1.80546e12 | 0.273506 | ||||||||
\(707\) | 1.76252e13 | 2.65306 | ||||||||
\(708\) | −5.43578e11 | −0.0813040 | ||||||||
\(709\) | −1.25644e13 | −1.86739 | −0.933695 | − | 0.358069i | \(-0.883435\pi\) | ||||
−0.933695 | + | 0.358069i | \(0.883435\pi\) | |||||||
\(710\) | −1.20521e13 | −1.77992 | ||||||||
\(711\) | 6.83285e11 | 0.100274 | ||||||||
\(712\) | 6.52786e10 | 0.00951943 | ||||||||
\(713\) | −8.07118e11 | −0.116959 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.38193e13 | −1.97747 | ||||||||
\(716\) | −4.49302e12 | −0.638896 | ||||||||
\(717\) | −3.13514e12 | −0.443017 | ||||||||
\(718\) | −4.03698e11 | −0.0566887 | ||||||||
\(719\) | −2.91184e12 | −0.406337 | −0.203169 | − | 0.979144i | \(-0.565124\pi\) | ||||
−0.203169 | + | 0.979144i | \(0.565124\pi\) | |||||||
\(720\) | −7.09584e12 | −0.984028 | ||||||||
\(721\) | −1.25213e13 | −1.72561 | ||||||||
\(722\) | 8.85096e12 | 1.21220 | ||||||||
\(723\) | 2.58376e12 | 0.351666 | ||||||||
\(724\) | 3.57759e12 | 0.483913 | ||||||||
\(725\) | −4.12134e12 | −0.554010 | ||||||||
\(726\) | −7.12843e12 | −0.952311 | ||||||||
\(727\) | 6.75451e12 | 0.896786 | 0.448393 | − | 0.893836i | \(-0.351996\pi\) | ||||
0.448393 | + | 0.893836i | \(0.351996\pi\) | |||||||
\(728\) | 1.36350e12 | 0.179914 | ||||||||
\(729\) | −4.02040e11 | −0.0527225 | ||||||||
\(730\) | −5.66590e12 | −0.738442 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −3.87363e12 | −0.498675 | ||||||||
\(733\) | 7.06417e12 | 0.903843 | 0.451922 | − | 0.892058i | \(-0.350739\pi\) | ||||
0.451922 | + | 0.892058i | \(0.350739\pi\) | |||||||
\(734\) | −3.77392e12 | −0.479911 | ||||||||
\(735\) | −6.65920e12 | −0.841645 | ||||||||
\(736\) | −6.21863e12 | −0.781168 | ||||||||
\(737\) | −2.53575e11 | −0.0316594 | ||||||||
\(738\) | 6.61302e11 | 0.0820627 | ||||||||
\(739\) | −1.12061e13 | −1.38215 | −0.691075 | − | 0.722783i | \(-0.742862\pi\) | ||||
−0.691075 | + | 0.722783i | \(0.742862\pi\) | |||||||
\(740\) | −8.45549e12 | −1.03656 | ||||||||
\(741\) | −1.36594e12 | −0.166436 | ||||||||
\(742\) | 1.47103e13 | 1.78158 | ||||||||
\(743\) | −8.45595e12 | −1.01792 | −0.508959 | − | 0.860791i | \(-0.669970\pi\) | ||||
−0.508959 | + | 0.860791i | \(0.669970\pi\) | |||||||
\(744\) | 7.47667e10 | 0.00894602 | ||||||||
\(745\) | 2.17434e12 | 0.258597 | ||||||||
\(746\) | −7.21060e12 | −0.852406 | ||||||||
\(747\) | −7.00932e12 | −0.823632 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.83103e13 | −2.12583 | ||||||||
\(750\) | −4.21340e12 | −0.486247 | ||||||||
\(751\) | 1.41553e12 | 0.162382 | 0.0811911 | − | 0.996699i | \(-0.474128\pi\) | ||||
0.0811911 | + | 0.996699i | \(0.474128\pi\) | |||||||
\(752\) | 6.52651e12 | 0.744219 | ||||||||
\(753\) | −2.33777e12 | −0.264987 | ||||||||
\(754\) | 2.62852e13 | 2.96169 | ||||||||
\(755\) | 6.93661e12 | 0.776937 | ||||||||
\(756\) | −1.07504e13 | −1.19695 | ||||||||
\(757\) | −9.02103e12 | −0.998446 | −0.499223 | − | 0.866473i | \(-0.666381\pi\) | ||||
−0.499223 | + | 0.866473i | \(0.666381\pi\) | |||||||
\(758\) | −5.81861e11 | −0.0640189 | ||||||||
\(759\) | −3.58610e12 | −0.392225 | ||||||||
\(760\) | 3.72612e11 | 0.0405131 | ||||||||
\(761\) | 1.71746e13 | 1.85633 | 0.928165 | − | 0.372169i | \(-0.121386\pi\) | ||||
0.928165 | + | 0.372169i | \(0.121386\pi\) | |||||||
\(762\) | 1.63494e12 | 0.175673 | ||||||||
\(763\) | −6.42559e12 | −0.686361 | ||||||||
\(764\) | 3.45680e12 | 0.367075 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.21264e13 | 2.32211 | ||||||||
\(767\) | −2.11589e12 | −0.220756 | ||||||||
\(768\) | 4.68640e12 | 0.486087 | ||||||||
\(769\) | −4.58214e12 | −0.472498 | −0.236249 | − | 0.971693i | \(-0.575918\pi\) | ||||
−0.236249 | + | 0.971693i | \(0.575918\pi\) | |||||||
\(770\) | 4.07626e13 | 4.17882 | ||||||||
\(771\) | −2.39805e12 | −0.244407 | ||||||||
\(772\) | 3.61202e12 | 0.365992 | ||||||||
\(773\) | 1.36741e12 | 0.137750 | 0.0688750 | − | 0.997625i | \(-0.478059\pi\) | ||||
0.0688750 | + | 0.997625i | \(0.478059\pi\) | |||||||
\(774\) | 2.58406e12 | 0.258803 | ||||||||
\(775\) | 5.85082e11 | 0.0582584 | ||||||||
\(776\) | 1.77261e12 | 0.175484 | ||||||||
\(777\) | 7.13080e12 | 0.701849 | ||||||||
\(778\) | 2.74183e13 | 2.68308 | ||||||||
\(779\) | −2.65706e11 | −0.0258513 | ||||||||
\(780\) | −5.07234e12 | −0.490662 | ||||||||
\(781\) | −1.89577e13 | −1.82329 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.61632e13 | 1.53674 | ||||||||
\(784\) | −1.94853e13 | −1.84198 | ||||||||
\(785\) | 1.27264e13 | 1.19617 | ||||||||
\(786\) | −1.48343e12 | −0.138632 | ||||||||
\(787\) | −1.11886e13 | −1.03966 | −0.519830 | − | 0.854270i | \(-0.674005\pi\) | ||||
−0.519830 | + | 0.854270i | \(0.674005\pi\) | |||||||
\(788\) | −1.03574e13 | −0.956940 | ||||||||
\(789\) | −2.43818e12 | −0.223985 | ||||||||
\(790\) | −2.11848e12 | −0.193510 | ||||||||
\(791\) | −9.24597e12 | −0.839766 | ||||||||
\(792\) | −1.45874e12 | −0.131739 | ||||||||
\(793\) | −1.50782e13 | −1.35400 | ||||||||
\(794\) | −1.43177e13 | −1.27844 | ||||||||
\(795\) | 4.26800e12 | 0.378942 | ||||||||
\(796\) | 6.65801e12 | 0.587808 | ||||||||
\(797\) | 1.02469e13 | 0.899561 | 0.449781 | − | 0.893139i | \(-0.351502\pi\) | ||||
0.449781 | + | 0.893139i | \(0.351502\pi\) | |||||||
\(798\) | 4.02908e12 | 0.351717 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.50790e12 | 0.389107 | ||||||||
\(801\) | −8.99304e11 | −0.0771898 | ||||||||
\(802\) | 2.82328e13 | 2.40973 | ||||||||
\(803\) | −8.91234e12 | −0.756436 | ||||||||
\(804\) | −9.30739e10 | −0.00785554 | ||||||||
\(805\) | 1.25969e13 | 1.05726 | ||||||||
\(806\) | −3.73155e12 | −0.311445 | ||||||||
\(807\) | −1.50461e12 | −0.124880 | ||||||||
\(808\) | 1.95557e12 | 0.161407 | ||||||||
\(809\) | 8.43291e12 | 0.692165 | 0.346082 | − | 0.938204i | \(-0.387512\pi\) | ||||
0.346082 | + | 0.938204i | \(0.387512\pi\) | |||||||
\(810\) | 9.20390e12 | 0.751259 | ||||||||
\(811\) | 1.23986e13 | 1.00642 | 0.503210 | − | 0.864164i | \(-0.332152\pi\) | ||||
0.503210 | + | 0.864164i | \(0.332152\pi\) | |||||||
\(812\) | −3.73116e13 | −3.01190 | ||||||||
\(813\) | −3.29983e12 | −0.264901 | ||||||||
\(814\) | −2.76379e13 | −2.20646 | ||||||||
\(815\) | −7.98180e12 | −0.633712 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.03826e12 | −0.0815278 | ||||||||
\(818\) | 6.13270e12 | 0.478918 | ||||||||
\(819\) | −1.87841e13 | −1.45886 | ||||||||
\(820\) | −9.86686e11 | −0.0762108 | ||||||||
\(821\) | 1.11578e13 | 0.857109 | 0.428554 | − | 0.903516i | \(-0.359023\pi\) | ||||
0.428554 | + | 0.903516i | \(0.359023\pi\) | |||||||
\(822\) | −1.17515e13 | −0.897783 | ||||||||
\(823\) | −2.14178e13 | −1.62733 | −0.813665 | − | 0.581335i | \(-0.802531\pi\) | ||||
−0.813665 | + | 0.581335i | \(0.802531\pi\) | |||||||
\(824\) | −1.38928e12 | −0.104983 | ||||||||
\(825\) | 2.59957e12 | 0.195371 | ||||||||
\(826\) | 6.24120e12 | 0.466507 | ||||||||
\(827\) | 7.63979e12 | 0.567946 | 0.283973 | − | 0.958832i | \(-0.408347\pi\) | ||||
0.283973 | + | 0.958832i | \(0.408347\pi\) | |||||||
\(828\) | 5.78001e12 | 0.427358 | ||||||||
\(829\) | 2.44316e13 | 1.79662 | 0.898309 | − | 0.439365i | \(-0.144796\pi\) | ||||
0.898309 | + | 0.439365i | \(0.144796\pi\) | |||||||
\(830\) | 2.17320e13 | 1.58945 | ||||||||
\(831\) | −3.38850e12 | −0.246492 | ||||||||
\(832\) | −1.27510e13 | −0.922548 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.58167e11 | 0.0327927 | ||||||||
\(835\) | 2.98763e13 | 2.12686 | ||||||||
\(836\) | −7.51501e12 | −0.532110 | ||||||||
\(837\) | −2.29460e12 | −0.161600 | ||||||||
\(838\) | −4.33663e12 | −0.303777 | ||||||||
\(839\) | 2.37461e12 | 0.165449 | 0.0827244 | − | 0.996572i | \(-0.473638\pi\) | ||||
0.0827244 | + | 0.996572i | \(0.473638\pi\) | |||||||
\(840\) | −1.16690e12 | −0.0808681 | ||||||||
\(841\) | 4.15911e13 | 2.86694 | ||||||||
\(842\) | −2.34063e13 | −1.60483 | ||||||||
\(843\) | 1.06480e12 | 0.0726179 | ||||||||
\(844\) | −1.61720e13 | −1.09704 | ||||||||
\(845\) | −2.96564e12 | −0.200108 | ||||||||
\(846\) | −1.17508e13 | −0.788682 | ||||||||
\(847\) | 3.93873e13 | 2.62955 | ||||||||
\(848\) | 1.24885e13 | 0.829331 | ||||||||
\(849\) | 8.50976e12 | 0.562125 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.54095e12 | −0.558243 | ||||||||
\(852\) | −6.95836e12 | −0.452407 | ||||||||
\(853\) | −7.13731e12 | −0.461598 | −0.230799 | − | 0.973001i | \(-0.574134\pi\) | ||||
−0.230799 | + | 0.973001i | \(0.574134\pi\) | |||||||
\(854\) | 4.44758e13 | 2.86130 | ||||||||
\(855\) | −5.13325e12 | −0.328507 | ||||||||
\(856\) | −2.03158e12 | −0.129331 | ||||||||
\(857\) | 1.20992e12 | 0.0766203 | 0.0383102 | − | 0.999266i | \(-0.487803\pi\) | ||||
0.0383102 | + | 0.999266i | \(0.487803\pi\) | |||||||
\(858\) | −1.65796e13 | −1.04444 | ||||||||
\(859\) | −2.16132e13 | −1.35441 | −0.677203 | − | 0.735796i | \(-0.736808\pi\) | ||||
−0.677203 | + | 0.735796i | \(0.736808\pi\) | |||||||
\(860\) | −3.85552e12 | −0.240347 | ||||||||
\(861\) | 8.32105e11 | 0.0516017 | ||||||||
\(862\) | 3.20863e12 | 0.197941 | ||||||||
\(863\) | −2.21387e13 | −1.35864 | −0.679319 | − | 0.733843i | \(-0.737725\pi\) | ||||
−0.679319 | + | 0.733843i | \(0.737725\pi\) | |||||||
\(864\) | −1.76792e13 | −1.07932 | ||||||||
\(865\) | 4.80272e12 | 0.291685 | ||||||||
\(866\) | 3.34172e13 | 2.01901 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.29689e12 | 0.316725 | ||||||||
\(869\) | −3.33233e12 | −0.198225 | ||||||||
\(870\) | −2.24952e13 | −1.33123 | ||||||||
\(871\) | −3.62292e11 | −0.0213293 | ||||||||
\(872\) | −7.12939e11 | −0.0417569 | ||||||||
\(873\) | −2.44202e13 | −1.42294 | ||||||||
\(874\) | −4.82585e12 | −0.279752 | ||||||||
\(875\) | 2.32807e13 | 1.34264 | ||||||||
\(876\) | −3.27125e12 | −0.187692 | ||||||||
\(877\) | −7.22814e11 | −0.0412599 | −0.0206300 | − | 0.999787i | \(-0.506567\pi\) | ||||
−0.0206300 | + | 0.999787i | \(0.506567\pi\) | |||||||
\(878\) | −4.15247e13 | −2.35820 | ||||||||
\(879\) | −5.06716e12 | −0.286296 | ||||||||
\(880\) | 3.46059e13 | 1.94526 | ||||||||
\(881\) | 3.21071e12 | 0.179560 | 0.0897801 | − | 0.995962i | \(-0.471384\pi\) | ||||
0.0897801 | + | 0.995962i | \(0.471384\pi\) | |||||||
\(882\) | 3.50828e13 | 1.95203 | ||||||||
\(883\) | −2.33032e13 | −1.29001 | −0.645004 | − | 0.764179i | \(-0.723144\pi\) | ||||
−0.645004 | + | 0.764179i | \(0.723144\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.81080e12 | 0.0992261 | ||||||||
\(886\) | −4.06841e13 | −2.21806 | ||||||||
\(887\) | −7.98735e12 | −0.433258 | −0.216629 | − | 0.976254i | \(-0.569506\pi\) | ||||
−0.216629 | + | 0.976254i | \(0.569506\pi\) | |||||||
\(888\) | 7.91183e11 | 0.0426991 | ||||||||
\(889\) | −9.03366e12 | −0.485072 | ||||||||
\(890\) | 2.78824e12 | 0.148962 | ||||||||
\(891\) | 1.44775e13 | 0.769564 | ||||||||
\(892\) | −5.63724e12 | −0.298143 | ||||||||
\(893\) | 4.72139e12 | 0.248450 | ||||||||
\(894\) | 2.60865e12 | 0.136583 | ||||||||
\(895\) | 1.49674e13 | 0.779729 | ||||||||
\(896\) | −6.38263e12 | −0.330837 | ||||||||
\(897\) | −5.12360e12 | −0.264247 | ||||||||
\(898\) | −1.33432e13 | −0.684725 | ||||||||
\(899\) | −7.96392e12 | −0.406638 | ||||||||
\(900\) | −4.18994e12 | −0.212871 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −3.22512e12 | −0.162224 | ||||||||
\(903\) | 3.25149e12 | 0.162737 | ||||||||
\(904\) | −1.02587e12 | −0.0510898 | ||||||||
\(905\) | −1.19179e13 | −0.590583 | ||||||||
\(906\) | 8.32215e12 | 0.410354 | ||||||||
\(907\) | 1.23526e13 | 0.606072 | 0.303036 | − | 0.952979i | \(-0.402000\pi\) | ||||
0.303036 | + | 0.952979i | \(0.402000\pi\) | |||||||
\(908\) | −2.00507e13 | −0.978910 | ||||||||
\(909\) | −2.69407e13 | −1.30879 | ||||||||
\(910\) | 5.82391e13 | 2.81532 | ||||||||
\(911\) | −1.91339e13 | −0.920388 | −0.460194 | − | 0.887818i | \(-0.652220\pi\) | ||||
−0.460194 | + | 0.887818i | \(0.652220\pi\) | |||||||
\(912\) | 3.42053e12 | 0.163726 | ||||||||
\(913\) | 3.41839e13 | 1.62818 | ||||||||
\(914\) | 1.34203e13 | 0.636068 | ||||||||
\(915\) | 1.29041e13 | 0.608600 | ||||||||
\(916\) | 1.82250e13 | 0.855338 | ||||||||
\(917\) | 8.19651e12 | 0.382796 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.87258e13 | 1.32847 | 0.664236 | − | 0.747523i | \(-0.268757\pi\) | ||||
0.664236 | + | 0.747523i | \(0.268757\pi\) | |||||||
\(920\) | 1.39766e12 | 0.0643216 | ||||||||
\(921\) | −1.06141e13 | −0.486089 | ||||||||
\(922\) | 3.58131e13 | 1.63212 | ||||||||
\(923\) | −2.70856e13 | −1.22837 | ||||||||
\(924\) | 2.35346e13 | 1.06214 | ||||||||
\(925\) | 6.19135e12 | 0.278066 | ||||||||
\(926\) | −5.40465e13 | −2.41556 | ||||||||
\(927\) | 1.91393e13 | 0.851269 | ||||||||
\(928\) | −6.13599e13 | −2.71593 | ||||||||
\(929\) | −1.08767e13 | −0.479101 | −0.239550 | − | 0.970884i | \(-0.577000\pi\) | ||||
−0.239550 | + | 0.970884i | \(0.577000\pi\) | |||||||
\(930\) | 3.19350e12 | 0.139989 | ||||||||
\(931\) | −1.40960e13 | −0.614925 | ||||||||
\(932\) | −7.61307e11 | −0.0330513 | ||||||||
\(933\) | 1.59501e13 | 0.689124 | ||||||||
\(934\) | 4.96709e13 | 2.13570 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.08416e12 | −0.0887542 | ||||||||
\(937\) | 2.93915e13 | 1.24564 | 0.622822 | − | 0.782363i | \(-0.285986\pi\) | ||||
0.622822 | + | 0.782363i | \(0.285986\pi\) | |||||||
\(938\) | 1.06865e12 | 0.0450736 | ||||||||
\(939\) | 1.53947e12 | 0.0646213 | ||||||||
\(940\) | 1.75327e13 | 0.732441 | ||||||||
\(941\) | −1.74873e10 | −0.000727058 0 | −0.000363529 | − | 1.00000i | \(-0.500116\pi\) | ||||
−0.000363529 | 1.00000i | \(0.500116\pi\) | ||||||||
\(942\) | 1.52684e13 | 0.631779 | ||||||||
\(943\) | −9.96658e11 | −0.0410434 | ||||||||
\(944\) | 5.29853e12 | 0.217161 | ||||||||
\(945\) | 3.58123e13 | 1.46079 | ||||||||
\(946\) | −1.26023e13 | −0.511610 | ||||||||
\(947\) | −3.36845e13 | −1.36099 | −0.680494 | − | 0.732753i | \(-0.738235\pi\) | ||||
−0.680494 | + | 0.732753i | \(0.738235\pi\) | |||||||
\(948\) | −1.22312e12 | −0.0491849 | ||||||||
\(949\) | −1.27334e13 | −0.509620 | ||||||||
\(950\) | 3.49827e12 | 0.139347 | ||||||||
\(951\) | −1.51088e13 | −0.598988 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.95197e13 | −0.766577 | −0.383288 | − | 0.923629i | \(-0.625208\pi\) | ||||
−0.383288 | + | 0.923629i | \(0.625208\pi\) | |||||||
\(954\) | −2.24852e13 | −0.878879 | ||||||||
\(955\) | −1.15155e13 | −0.447990 | ||||||||
\(956\) | −2.46438e13 | −0.954218 | ||||||||
\(957\) | −3.53844e13 | −1.36367 | ||||||||
\(958\) | −3.41956e13 | −1.31167 | ||||||||
\(959\) | 6.49318e13 | 2.47898 | ||||||||
\(960\) | 1.09125e13 | 0.414669 | ||||||||
\(961\) | −2.53090e13 | −0.957239 | ||||||||
\(962\) | −3.94873e13 | −1.48652 | ||||||||
\(963\) | 2.79879e13 | 1.04870 | ||||||||
\(964\) | 2.03097e13 | 0.757457 | ||||||||
\(965\) | −1.20326e13 | −0.446669 | ||||||||
\(966\) | 1.51130e13 | 0.558411 | ||||||||
\(967\) | −5.04513e12 | −0.185547 | −0.0927733 | − | 0.995687i | \(-0.529573\pi\) | ||||
−0.0927733 | + | 0.995687i | \(0.529573\pi\) | |||||||
\(968\) | 4.37014e12 | 0.159977 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.57135e13 | 2.74600 | ||||||||
\(971\) | 2.97871e13 | 1.07533 | 0.537665 | − | 0.843158i | \(-0.319306\pi\) | ||||
0.537665 | + | 0.843158i | \(0.319306\pi\) | |||||||
\(972\) | 2.54883e13 | 0.915888 | ||||||||
\(973\) | −2.53155e12 | −0.0905480 | ||||||||
\(974\) | 6.51471e13 | 2.31942 | ||||||||
\(975\) | 3.71411e12 | 0.131624 | ||||||||
\(976\) | 3.77582e13 | 1.33195 | ||||||||
\(977\) | 1.68301e13 | 0.590965 | 0.295483 | − | 0.955348i | \(-0.404520\pi\) | ||||
0.295483 | + | 0.955348i | \(0.404520\pi\) | |||||||
\(978\) | −9.57611e12 | −0.334707 | ||||||||
\(979\) | 4.38584e12 | 0.152591 | ||||||||
\(980\) | −5.23448e13 | −1.81283 | ||||||||
\(981\) | 9.82173e12 | 0.338593 | ||||||||
\(982\) | 4.01666e12 | 0.137836 | ||||||||
\(983\) | −4.53002e13 | −1.54742 | −0.773711 | − | 0.633538i | \(-0.781602\pi\) | ||||
−0.773711 | + | 0.633538i | \(0.781602\pi\) | |||||||
\(984\) | 9.23246e10 | 0.00313935 | ||||||||
\(985\) | 3.45034e13 | 1.16788 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.47859e13 | −0.495929 | ||||||||
\(988\) | −1.07370e13 | −0.358489 | ||||||||
\(989\) | −3.89448e12 | −0.129439 | ||||||||
\(990\) | −6.23070e13 | −2.06148 | ||||||||
\(991\) | −5.13942e13 | −1.69271 | −0.846356 | − | 0.532618i | \(-0.821208\pi\) | ||||
−0.846356 | + | 0.532618i | \(0.821208\pi\) | |||||||
\(992\) | 8.71088e12 | 0.285601 | ||||||||
\(993\) | 2.21002e13 | 0.721313 | ||||||||
\(994\) | 7.98939e13 | 2.59582 | ||||||||
\(995\) | −2.21796e13 | −0.717380 | ||||||||
\(996\) | 1.25471e13 | 0.403996 | ||||||||
\(997\) | −3.28523e13 | −1.05302 | −0.526512 | − | 0.850168i | \(-0.676500\pi\) | ||||
−0.526512 | + | 0.850168i | \(0.676500\pi\) | |||||||
\(998\) | −4.93386e13 | −1.57434 | ||||||||
\(999\) | −2.42815e13 | −0.771312 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 289.10.a.f.1.6 | 24 | ||
17.2 | even | 8 | 17.10.c.a.4.3 | ✓ | 24 | ||
17.9 | even | 8 | 17.10.c.a.13.10 | yes | 24 | ||
17.16 | even | 2 | inner | 289.10.a.f.1.5 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.c.a.4.3 | ✓ | 24 | 17.2 | even | 8 | ||
17.10.c.a.13.10 | yes | 24 | 17.9 | even | 8 | ||
289.10.a.f.1.5 | 24 | 17.16 | even | 2 | inner | ||
289.10.a.f.1.6 | 24 | 1.1 | even | 1 | trivial |