Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,8,Mod(1,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.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: | \(21.5545667584\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 757x^{6} - 1170x^{5} + 170343x^{4} + 424132x^{3} - 9973075x^{2} - 5161010x + 130545120 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(19.5036\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.5036 | −1.45872 | −0.729362 | − | 0.684128i | \(-0.760183\pi\) | ||||
−0.729362 | + | 0.684128i | \(0.760183\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 144.368 | 1.12788 | ||||||||
\(5\) | −425.514 | −1.52236 | −0.761182 | − | 0.648538i | \(-0.775381\pi\) | ||||
−0.761182 | + | 0.648538i | \(0.775381\pi\) | |||||||
\(6\) | −445.597 | −0.842195 | ||||||||
\(7\) | −1501.62 | −1.65469 | −0.827347 | − | 0.561692i | \(-0.810151\pi\) | ||||
−0.827347 | + | 0.561692i | \(0.810151\pi\) | |||||||
\(8\) | −270.137 | −0.186539 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 7022.50 | 2.22071 | ||||||||
\(11\) | −566.851 | −0.128409 | −0.0642043 | − | 0.997937i | \(-0.520451\pi\) | ||||
−0.0642043 | + | 0.997937i | \(0.520451\pi\) | |||||||
\(12\) | 3897.95 | 0.651181 | ||||||||
\(13\) | −10492.6 | −1.32459 | −0.662297 | − | 0.749241i | \(-0.730418\pi\) | ||||
−0.662297 | + | 0.749241i | \(0.730418\pi\) | |||||||
\(14\) | 24782.1 | 2.41374 | ||||||||
\(15\) | −11488.9 | −0.878937 | ||||||||
\(16\) | −14020.9 | −0.855769 | ||||||||
\(17\) | 8189.40 | 0.404279 | 0.202139 | − | 0.979357i | \(-0.435211\pi\) | ||||
0.202139 | + | 0.979357i | \(0.435211\pi\) | |||||||
\(18\) | −12031.1 | −0.486242 | ||||||||
\(19\) | −48781.8 | −1.63162 | −0.815812 | − | 0.578317i | \(-0.803710\pi\) | ||||
−0.815812 | + | 0.578317i | \(0.803710\pi\) | |||||||
\(20\) | −61430.7 | −1.71704 | ||||||||
\(21\) | −40543.8 | −0.955338 | ||||||||
\(22\) | 9355.07 | 0.187313 | ||||||||
\(23\) | 12167.0 | 0.208514 | ||||||||
\(24\) | −7293.70 | −0.107698 | ||||||||
\(25\) | 102937. | 1.31759 | ||||||||
\(26\) | 173166. | 1.93222 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | −216787. | −1.86629 | ||||||||
\(29\) | −78559.1 | −0.598141 | −0.299071 | − | 0.954231i | \(-0.596677\pi\) | ||||
−0.299071 | + | 0.954231i | \(0.596677\pi\) | |||||||
\(30\) | 189608. | 1.28213 | ||||||||
\(31\) | 182771. | 1.10190 | 0.550950 | − | 0.834538i | \(-0.314265\pi\) | ||||
0.550950 | + | 0.834538i | \(0.314265\pi\) | |||||||
\(32\) | 265973. | 1.43487 | ||||||||
\(33\) | −15305.0 | −0.0741368 | ||||||||
\(34\) | −135154. | −0.589731 | ||||||||
\(35\) | 638961. | 2.51905 | ||||||||
\(36\) | 105245. | 0.375959 | ||||||||
\(37\) | −397244. | −1.28929 | −0.644646 | − | 0.764481i | \(-0.722995\pi\) | ||||
−0.644646 | + | 0.764481i | \(0.722995\pi\) | |||||||
\(38\) | 805075. | 2.38009 | ||||||||
\(39\) | −283301. | −0.764755 | ||||||||
\(40\) | 114947. | 0.283980 | ||||||||
\(41\) | 567191. | 1.28524 | 0.642622 | − | 0.766183i | \(-0.277846\pi\) | ||||
0.642622 | + | 0.766183i | \(0.277846\pi\) | |||||||
\(42\) | 669118. | 1.39357 | ||||||||
\(43\) | 751273. | 1.44098 | 0.720491 | − | 0.693464i | \(-0.243917\pi\) | ||||
0.720491 | + | 0.693464i | \(0.243917\pi\) | |||||||
\(44\) | −81835.3 | −0.144829 | ||||||||
\(45\) | −310199. | −0.507455 | ||||||||
\(46\) | −200799. | −0.304165 | ||||||||
\(47\) | −748990. | −1.05229 | −0.526143 | − | 0.850396i | \(-0.676362\pi\) | ||||
−0.526143 | + | 0.850396i | \(0.676362\pi\) | |||||||
\(48\) | −378565. | −0.494079 | ||||||||
\(49\) | 1.43133e6 | 1.73801 | ||||||||
\(50\) | −1.69883e6 | −1.92200 | ||||||||
\(51\) | 221114. | 0.233410 | ||||||||
\(52\) | −1.51480e6 | −1.49398 | ||||||||
\(53\) | 377925. | 0.348691 | 0.174345 | − | 0.984685i | \(-0.444219\pi\) | ||||
0.174345 | + | 0.984685i | \(0.444219\pi\) | |||||||
\(54\) | −324840. | −0.280732 | ||||||||
\(55\) | 241203. | 0.195485 | ||||||||
\(56\) | 405644. | 0.308665 | ||||||||
\(57\) | −1.31711e6 | −0.942019 | ||||||||
\(58\) | 1.29651e6 | 0.872523 | ||||||||
\(59\) | 2.10007e6 | 1.33122 | 0.665612 | − | 0.746298i | \(-0.268171\pi\) | ||||
0.665612 | + | 0.746298i | \(0.268171\pi\) | |||||||
\(60\) | −1.65863e6 | −0.991334 | ||||||||
\(61\) | 792539. | 0.447060 | 0.223530 | − | 0.974697i | \(-0.428242\pi\) | ||||
0.223530 | + | 0.974697i | \(0.428242\pi\) | |||||||
\(62\) | −3.01638e6 | −1.60737 | ||||||||
\(63\) | −1.09468e6 | −0.551564 | ||||||||
\(64\) | −2.59483e6 | −1.23731 | ||||||||
\(65\) | 4.46476e6 | 2.01651 | ||||||||
\(66\) | 252587. | 0.108145 | ||||||||
\(67\) | −241805. | −0.0982209 | −0.0491105 | − | 0.998793i | \(-0.515639\pi\) | ||||
−0.0491105 | + | 0.998793i | \(0.515639\pi\) | |||||||
\(68\) | 1.18229e6 | 0.455977 | ||||||||
\(69\) | 328509. | 0.120386 | ||||||||
\(70\) | −1.05451e7 | −3.67459 | ||||||||
\(71\) | −4.72270e6 | −1.56598 | −0.782990 | − | 0.622034i | \(-0.786307\pi\) | ||||
−0.782990 | + | 0.622034i | \(0.786307\pi\) | |||||||
\(72\) | −196930. | −0.0621796 | ||||||||
\(73\) | −2.33919e6 | −0.703779 | −0.351889 | − | 0.936042i | \(-0.614461\pi\) | ||||
−0.351889 | + | 0.936042i | \(0.614461\pi\) | |||||||
\(74\) | 6.55596e6 | 1.88072 | ||||||||
\(75\) | 2.77930e6 | 0.760712 | ||||||||
\(76\) | −7.04255e6 | −1.84027 | ||||||||
\(77\) | 851196. | 0.212477 | ||||||||
\(78\) | 4.67549e6 | 1.11557 | ||||||||
\(79\) | 794806. | 0.181370 | 0.0906851 | − | 0.995880i | \(-0.471094\pi\) | ||||
0.0906851 | + | 0.995880i | \(0.471094\pi\) | |||||||
\(80\) | 5.96609e6 | 1.30279 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −9.36068e6 | −1.87482 | ||||||||
\(83\) | 5.22492e6 | 1.00301 | 0.501506 | − | 0.865154i | \(-0.332780\pi\) | ||||
0.501506 | + | 0.865154i | \(0.332780\pi\) | |||||||
\(84\) | −5.85324e6 | −1.07750 | ||||||||
\(85\) | −3.48470e6 | −0.615459 | ||||||||
\(86\) | −1.23987e7 | −2.10200 | ||||||||
\(87\) | −2.12110e6 | −0.345337 | ||||||||
\(88\) | 153127. | 0.0239532 | ||||||||
\(89\) | −5.72503e6 | −0.860821 | −0.430411 | − | 0.902633i | \(-0.641631\pi\) | ||||
−0.430411 | + | 0.902633i | \(0.641631\pi\) | |||||||
\(90\) | 5.11940e6 | 0.740237 | ||||||||
\(91\) | 1.57560e7 | 2.19180 | ||||||||
\(92\) | 1.75653e6 | 0.235179 | ||||||||
\(93\) | 4.93483e6 | 0.636182 | ||||||||
\(94\) | 1.23610e7 | 1.53499 | ||||||||
\(95\) | 2.07573e7 | 2.48393 | ||||||||
\(96\) | 7.18127e6 | 0.828423 | ||||||||
\(97\) | −7.01309e6 | −0.780204 | −0.390102 | − | 0.920772i | \(-0.627560\pi\) | ||||
−0.390102 | + | 0.920772i | \(0.627560\pi\) | |||||||
\(98\) | −2.36220e7 | −2.53528 | ||||||||
\(99\) | −413234. | −0.0428029 | ||||||||
\(100\) | 1.48608e7 | 1.48608 | ||||||||
\(101\) | 1.91067e7 | 1.84527 | 0.922637 | − | 0.385670i | \(-0.126030\pi\) | ||||
0.922637 | + | 0.385670i | \(0.126030\pi\) | |||||||
\(102\) | −3.64917e6 | −0.340482 | ||||||||
\(103\) | −1.99719e7 | −1.80090 | −0.900448 | − | 0.434964i | \(-0.856761\pi\) | ||||
−0.900448 | + | 0.434964i | \(0.856761\pi\) | |||||||
\(104\) | 2.83445e6 | 0.247088 | ||||||||
\(105\) | 1.72519e7 | 1.45437 | ||||||||
\(106\) | −6.23712e6 | −0.508644 | ||||||||
\(107\) | −1.88125e7 | −1.48458 | −0.742288 | − | 0.670081i | \(-0.766259\pi\) | ||||
−0.742288 | + | 0.670081i | \(0.766259\pi\) | |||||||
\(108\) | 2.84160e6 | 0.217060 | ||||||||
\(109\) | −1.74721e6 | −0.129227 | −0.0646133 | − | 0.997910i | \(-0.520581\pi\) | ||||
−0.0646133 | + | 0.997910i | \(0.520581\pi\) | |||||||
\(110\) | −3.98071e6 | −0.285158 | ||||||||
\(111\) | −1.07256e7 | −0.744374 | ||||||||
\(112\) | 2.10541e7 | 1.41604 | ||||||||
\(113\) | −3.56073e6 | −0.232148 | −0.116074 | − | 0.993241i | \(-0.537031\pi\) | ||||
−0.116074 | + | 0.993241i | \(0.537031\pi\) | |||||||
\(114\) | 2.17370e7 | 1.37415 | ||||||||
\(115\) | −5.17722e6 | −0.317435 | ||||||||
\(116\) | −1.13415e7 | −0.674630 | ||||||||
\(117\) | −7.64913e6 | −0.441531 | ||||||||
\(118\) | −3.46586e7 | −1.94189 | ||||||||
\(119\) | −1.22974e7 | −0.668957 | ||||||||
\(120\) | 3.10357e6 | 0.163956 | ||||||||
\(121\) | −1.91659e7 | −0.983511 | ||||||||
\(122\) | −1.30797e7 | −0.652138 | ||||||||
\(123\) | 1.53142e7 | 0.742036 | ||||||||
\(124\) | 2.63864e7 | 1.24281 | ||||||||
\(125\) | −1.05578e7 | −0.483490 | ||||||||
\(126\) | 1.80662e7 | 0.804581 | ||||||||
\(127\) | −4.10534e6 | −0.177843 | −0.0889213 | − | 0.996039i | \(-0.528342\pi\) | ||||
−0.0889213 | + | 0.996039i | \(0.528342\pi\) | |||||||
\(128\) | 8.77948e6 | 0.370027 | ||||||||
\(129\) | 2.02844e7 | 0.831951 | ||||||||
\(130\) | −7.36846e7 | −2.94154 | ||||||||
\(131\) | −2.59973e6 | −0.101037 | −0.0505183 | − | 0.998723i | \(-0.516087\pi\) | ||||
−0.0505183 | + | 0.998723i | \(0.516087\pi\) | |||||||
\(132\) | −2.20955e6 | −0.0836173 | ||||||||
\(133\) | 7.32518e7 | 2.69984 | ||||||||
\(134\) | 3.99065e6 | 0.143277 | ||||||||
\(135\) | −8.37539e6 | −0.292979 | ||||||||
\(136\) | −2.21226e6 | −0.0754137 | ||||||||
\(137\) | −9.66370e6 | −0.321086 | −0.160543 | − | 0.987029i | \(-0.551325\pi\) | ||||
−0.160543 | + | 0.987029i | \(0.551325\pi\) | |||||||
\(138\) | −5.42158e6 | −0.175610 | ||||||||
\(139\) | 2.95184e7 | 0.932268 | 0.466134 | − | 0.884714i | \(-0.345646\pi\) | ||||
0.466134 | + | 0.884714i | \(0.345646\pi\) | |||||||
\(140\) | 9.22457e7 | 2.84118 | ||||||||
\(141\) | −2.02227e7 | −0.607537 | ||||||||
\(142\) | 7.79415e7 | 2.28434 | ||||||||
\(143\) | 5.94776e6 | 0.170089 | ||||||||
\(144\) | −1.02213e7 | −0.285256 | ||||||||
\(145\) | 3.34280e7 | 0.910588 | ||||||||
\(146\) | 3.86051e7 | 1.02662 | ||||||||
\(147\) | 3.86458e7 | 1.00344 | ||||||||
\(148\) | −5.73495e7 | −1.45417 | ||||||||
\(149\) | 3.91998e7 | 0.970805 | 0.485403 | − | 0.874291i | \(-0.338673\pi\) | ||||
0.485403 | + | 0.874291i | \(0.338673\pi\) | |||||||
\(150\) | −4.58683e7 | −1.10967 | ||||||||
\(151\) | −6.10718e7 | −1.44351 | −0.721757 | − | 0.692146i | \(-0.756665\pi\) | ||||
−0.721757 | + | 0.692146i | \(0.756665\pi\) | |||||||
\(152\) | 1.31778e7 | 0.304361 | ||||||||
\(153\) | 5.97007e6 | 0.134760 | ||||||||
\(154\) | −1.40478e7 | −0.309945 | ||||||||
\(155\) | −7.77717e7 | −1.67749 | ||||||||
\(156\) | −4.08997e7 | −0.862550 | ||||||||
\(157\) | 5.82798e7 | 1.20190 | 0.600951 | − | 0.799286i | \(-0.294789\pi\) | ||||
0.600951 | + | 0.799286i | \(0.294789\pi\) | |||||||
\(158\) | −1.31171e7 | −0.264569 | ||||||||
\(159\) | 1.02040e7 | 0.201317 | ||||||||
\(160\) | −1.13175e8 | −2.18440 | ||||||||
\(161\) | −1.82702e7 | −0.345027 | ||||||||
\(162\) | −8.77068e6 | −0.162081 | ||||||||
\(163\) | 1.17687e7 | 0.212850 | 0.106425 | − | 0.994321i | \(-0.466060\pi\) | ||||
0.106425 | + | 0.994321i | \(0.466060\pi\) | |||||||
\(164\) | 8.18844e7 | 1.44960 | ||||||||
\(165\) | 6.51247e6 | 0.112863 | ||||||||
\(166\) | −8.62298e7 | −1.46312 | ||||||||
\(167\) | 2.36080e7 | 0.392239 | 0.196120 | − | 0.980580i | \(-0.437166\pi\) | ||||
0.196120 | + | 0.980580i | \(0.437166\pi\) | |||||||
\(168\) | 1.09524e7 | 0.178208 | ||||||||
\(169\) | 4.73469e7 | 0.754550 | ||||||||
\(170\) | 5.75101e7 | 0.897786 | ||||||||
\(171\) | −3.55619e7 | −0.543875 | ||||||||
\(172\) | 1.08460e8 | 1.62525 | ||||||||
\(173\) | −2.90114e7 | −0.425997 | −0.212999 | − | 0.977052i | \(-0.568323\pi\) | ||||
−0.212999 | + | 0.977052i | \(0.568323\pi\) | |||||||
\(174\) | 3.50057e7 | 0.503752 | ||||||||
\(175\) | −1.54572e8 | −2.18021 | ||||||||
\(176\) | 7.94777e6 | 0.109888 | ||||||||
\(177\) | 5.67018e7 | 0.768582 | ||||||||
\(178\) | 9.44836e7 | 1.25570 | ||||||||
\(179\) | −6.83488e7 | −0.890728 | −0.445364 | − | 0.895350i | \(-0.646926\pi\) | ||||
−0.445364 | + | 0.895350i | \(0.646926\pi\) | |||||||
\(180\) | −4.47830e7 | −0.572347 | ||||||||
\(181\) | −5.06098e7 | −0.634395 | −0.317197 | − | 0.948360i | \(-0.602742\pi\) | ||||
−0.317197 | + | 0.948360i | \(0.602742\pi\) | |||||||
\(182\) | −2.60030e8 | −3.19723 | ||||||||
\(183\) | 2.13986e7 | 0.258110 | ||||||||
\(184\) | −3.28676e6 | −0.0388960 | ||||||||
\(185\) | 1.69033e8 | 1.96277 | ||||||||
\(186\) | −8.14423e7 | −0.928015 | ||||||||
\(187\) | −4.64217e6 | −0.0519129 | ||||||||
\(188\) | −1.08130e8 | −1.18685 | ||||||||
\(189\) | −2.95564e7 | −0.318446 | ||||||||
\(190\) | −3.42570e8 | −3.62336 | ||||||||
\(191\) | −1.11632e8 | −1.15923 | −0.579616 | − | 0.814890i | \(-0.696797\pi\) | ||||
−0.579616 | + | 0.814890i | \(0.696797\pi\) | |||||||
\(192\) | −7.00604e7 | −0.714362 | ||||||||
\(193\) | 1.30760e8 | 1.30926 | 0.654630 | − | 0.755950i | \(-0.272825\pi\) | ||||
0.654630 | + | 0.755950i | \(0.272825\pi\) | |||||||
\(194\) | 1.15741e8 | 1.13810 | ||||||||
\(195\) | 1.20549e8 | 1.16424 | ||||||||
\(196\) | 2.06638e8 | 1.96026 | ||||||||
\(197\) | 1.10071e7 | 0.102575 | 0.0512877 | − | 0.998684i | \(-0.483667\pi\) | ||||
0.0512877 | + | 0.998684i | \(0.483667\pi\) | |||||||
\(198\) | 6.81985e6 | 0.0624376 | ||||||||
\(199\) | 1.33730e8 | 1.20294 | 0.601469 | − | 0.798896i | \(-0.294582\pi\) | ||||
0.601469 | + | 0.798896i | \(0.294582\pi\) | |||||||
\(200\) | −2.78071e7 | −0.245782 | ||||||||
\(201\) | −6.52874e6 | −0.0567079 | ||||||||
\(202\) | −3.15329e8 | −2.69175 | ||||||||
\(203\) | 1.17966e8 | 0.989740 | ||||||||
\(204\) | 3.19218e7 | 0.263259 | ||||||||
\(205\) | −2.41347e8 | −1.95661 | ||||||||
\(206\) | 3.29608e8 | 2.62701 | ||||||||
\(207\) | 8.86974e6 | 0.0695048 | ||||||||
\(208\) | 1.47116e8 | 1.13355 | ||||||||
\(209\) | 2.76520e7 | 0.209515 | ||||||||
\(210\) | −2.84719e8 | −2.12153 | ||||||||
\(211\) | 2.22573e8 | 1.63111 | 0.815555 | − | 0.578679i | \(-0.196432\pi\) | ||||
0.815555 | + | 0.578679i | \(0.196432\pi\) | |||||||
\(212\) | 5.45605e7 | 0.393281 | ||||||||
\(213\) | −1.27513e8 | −0.904119 | ||||||||
\(214\) | 3.10473e8 | 2.16559 | ||||||||
\(215\) | −3.19677e8 | −2.19370 | ||||||||
\(216\) | −5.31711e6 | −0.0358994 | ||||||||
\(217\) | −2.74454e8 | −1.82331 | ||||||||
\(218\) | 2.88352e7 | 0.188506 | ||||||||
\(219\) | −6.31582e7 | −0.406327 | ||||||||
\(220\) | 3.48221e7 | 0.220483 | ||||||||
\(221\) | −8.59284e7 | −0.535505 | ||||||||
\(222\) | 1.77011e8 | 1.08584 | ||||||||
\(223\) | −2.43448e7 | −0.147007 | −0.0735036 | − | 0.997295i | \(-0.523418\pi\) | ||||
−0.0735036 | + | 0.997295i | \(0.523418\pi\) | |||||||
\(224\) | −3.99391e8 | −2.37427 | ||||||||
\(225\) | 7.50410e7 | 0.439197 | ||||||||
\(226\) | 5.87648e7 | 0.338640 | ||||||||
\(227\) | −2.94104e8 | −1.66882 | −0.834411 | − | 0.551143i | \(-0.814192\pi\) | ||||
−0.834411 | + | 0.551143i | \(0.814192\pi\) | |||||||
\(228\) | −1.90149e8 | −1.06248 | ||||||||
\(229\) | 5.37734e7 | 0.295899 | 0.147949 | − | 0.988995i | \(-0.452733\pi\) | ||||
0.147949 | + | 0.988995i | \(0.452733\pi\) | |||||||
\(230\) | 8.54428e7 | 0.463050 | ||||||||
\(231\) | 2.29823e7 | 0.122674 | ||||||||
\(232\) | 2.12217e7 | 0.111577 | ||||||||
\(233\) | 2.87694e8 | 1.49000 | 0.744999 | − | 0.667065i | \(-0.232450\pi\) | ||||
0.744999 | + | 0.667065i | \(0.232450\pi\) | |||||||
\(234\) | 1.26238e8 | 0.644073 | ||||||||
\(235\) | 3.18705e8 | 1.60196 | ||||||||
\(236\) | 3.03183e8 | 1.50146 | ||||||||
\(237\) | 2.14598e7 | 0.104714 | ||||||||
\(238\) | 2.02951e8 | 0.975825 | ||||||||
\(239\) | 2.96078e8 | 1.40286 | 0.701428 | − | 0.712740i | \(-0.252546\pi\) | ||||
0.701428 | + | 0.712740i | \(0.252546\pi\) | |||||||
\(240\) | 1.61085e8 | 0.752167 | ||||||||
\(241\) | −1.39493e8 | −0.641937 | −0.320968 | − | 0.947090i | \(-0.604008\pi\) | ||||
−0.320968 | + | 0.947090i | \(0.604008\pi\) | |||||||
\(242\) | 3.16305e8 | 1.43467 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 1.14418e8 | 0.504230 | ||||||||
\(245\) | −6.09049e8 | −2.64588 | ||||||||
\(246\) | −2.52738e8 | −1.08243 | ||||||||
\(247\) | 5.11850e8 | 2.16124 | ||||||||
\(248\) | −4.93733e7 | −0.205547 | ||||||||
\(249\) | 1.41073e8 | 0.579089 | ||||||||
\(250\) | 1.74241e8 | 0.705280 | ||||||||
\(251\) | 2.67558e8 | 1.06797 | 0.533986 | − | 0.845493i | \(-0.320694\pi\) | ||||
0.533986 | + | 0.845493i | \(0.320694\pi\) | |||||||
\(252\) | −1.58038e8 | −0.622097 | ||||||||
\(253\) | −6.89687e6 | −0.0267751 | ||||||||
\(254\) | 6.77528e7 | 0.259423 | ||||||||
\(255\) | −9.40870e7 | −0.355336 | ||||||||
\(256\) | 1.87246e8 | 0.697544 | ||||||||
\(257\) | −2.10540e8 | −0.773691 | −0.386846 | − | 0.922144i | \(-0.626435\pi\) | ||||
−0.386846 | + | 0.922144i | \(0.626435\pi\) | |||||||
\(258\) | −3.34765e8 | −1.21359 | ||||||||
\(259\) | 5.96511e8 | 2.13338 | ||||||||
\(260\) | 6.44570e8 | 2.27438 | ||||||||
\(261\) | −5.72696e7 | −0.199380 | ||||||||
\(262\) | 4.29049e7 | 0.147385 | ||||||||
\(263\) | 2.37688e8 | 0.805680 | 0.402840 | − | 0.915271i | \(-0.368023\pi\) | ||||
0.402840 | + | 0.915271i | \(0.368023\pi\) | |||||||
\(264\) | 4.13444e6 | 0.0138294 | ||||||||
\(265\) | −1.60812e8 | −0.530834 | ||||||||
\(266\) | −1.20892e9 | −3.93832 | ||||||||
\(267\) | −1.54576e8 | −0.496995 | ||||||||
\(268\) | −3.49090e7 | −0.110781 | ||||||||
\(269\) | 1.97716e8 | 0.619310 | 0.309655 | − | 0.950849i | \(-0.399786\pi\) | ||||
0.309655 | + | 0.950849i | \(0.399786\pi\) | |||||||
\(270\) | 1.38224e8 | 0.427376 | ||||||||
\(271\) | 4.72382e8 | 1.44179 | 0.720893 | − | 0.693046i | \(-0.243732\pi\) | ||||
0.720893 | + | 0.693046i | \(0.243732\pi\) | |||||||
\(272\) | −1.14823e8 | −0.345969 | ||||||||
\(273\) | 4.25411e8 | 1.26543 | ||||||||
\(274\) | 1.59486e8 | 0.468376 | ||||||||
\(275\) | −5.83499e7 | −0.169190 | ||||||||
\(276\) | 4.74263e7 | 0.135781 | ||||||||
\(277\) | 1.22279e8 | 0.345680 | 0.172840 | − | 0.984950i | \(-0.444706\pi\) | ||||
0.172840 | + | 0.984950i | \(0.444706\pi\) | |||||||
\(278\) | −4.87159e8 | −1.35992 | ||||||||
\(279\) | 1.33240e8 | 0.367300 | ||||||||
\(280\) | −1.72607e8 | −0.469900 | ||||||||
\(281\) | 3.64898e8 | 0.981069 | 0.490534 | − | 0.871422i | \(-0.336802\pi\) | ||||
0.490534 | + | 0.871422i | \(0.336802\pi\) | |||||||
\(282\) | 3.33748e8 | 0.886230 | ||||||||
\(283\) | −7.69088e7 | −0.201708 | −0.100854 | − | 0.994901i | \(-0.532158\pi\) | ||||
−0.100854 | + | 0.994901i | \(0.532158\pi\) | |||||||
\(284\) | −6.81809e8 | −1.76624 | ||||||||
\(285\) | 5.60448e8 | 1.43410 | ||||||||
\(286\) | −9.81594e7 | −0.248114 | ||||||||
\(287\) | −8.51706e8 | −2.12669 | ||||||||
\(288\) | 1.93894e8 | 0.478290 | ||||||||
\(289\) | −3.43272e8 | −0.836559 | ||||||||
\(290\) | −5.51682e8 | −1.32830 | ||||||||
\(291\) | −1.89353e8 | −0.450451 | ||||||||
\(292\) | −3.37706e8 | −0.793777 | ||||||||
\(293\) | −2.84862e8 | −0.661603 | −0.330802 | − | 0.943700i | \(-0.607319\pi\) | ||||
−0.330802 | + | 0.943700i | \(0.607319\pi\) | |||||||
\(294\) | −6.37794e8 | −1.46374 | ||||||||
\(295\) | −8.93607e8 | −2.02661 | ||||||||
\(296\) | 1.07310e8 | 0.240503 | ||||||||
\(297\) | −1.11573e7 | −0.0247123 | ||||||||
\(298\) | −6.46938e8 | −1.41614 | ||||||||
\(299\) | −1.27664e8 | −0.276197 | ||||||||
\(300\) | 4.01242e8 | 0.857990 | ||||||||
\(301\) | −1.12813e9 | −2.38438 | ||||||||
\(302\) | 1.00790e9 | 2.10569 | ||||||||
\(303\) | 5.15881e8 | 1.06537 | ||||||||
\(304\) | 6.83966e8 | 1.39629 | ||||||||
\(305\) | −3.37236e8 | −0.680589 | ||||||||
\(306\) | −9.85276e7 | −0.196577 | ||||||||
\(307\) | −6.24159e8 | −1.23115 | −0.615575 | − | 0.788078i | \(-0.711076\pi\) | ||||
−0.615575 | + | 0.788078i | \(0.711076\pi\) | |||||||
\(308\) | 1.22886e8 | 0.239648 | ||||||||
\(309\) | −5.39241e8 | −1.03975 | ||||||||
\(310\) | 1.28351e9 | 2.44700 | ||||||||
\(311\) | −4.84237e8 | −0.912845 | −0.456422 | − | 0.889763i | \(-0.650869\pi\) | ||||
−0.456422 | + | 0.889763i | \(0.650869\pi\) | |||||||
\(312\) | 7.65301e7 | 0.142656 | ||||||||
\(313\) | −4.94156e8 | −0.910874 | −0.455437 | − | 0.890268i | \(-0.650517\pi\) | ||||
−0.455437 | + | 0.890268i | \(0.650517\pi\) | |||||||
\(314\) | −9.61826e8 | −1.75325 | ||||||||
\(315\) | 4.65802e8 | 0.839682 | ||||||||
\(316\) | 1.14745e8 | 0.204564 | ||||||||
\(317\) | 8.96816e8 | 1.58123 | 0.790616 | − | 0.612312i | \(-0.209760\pi\) | ||||
0.790616 | + | 0.612312i | \(0.209760\pi\) | |||||||
\(318\) | −1.68402e8 | −0.293666 | ||||||||
\(319\) | 4.45313e7 | 0.0768065 | ||||||||
\(320\) | 1.10414e9 | 1.88364 | ||||||||
\(321\) | −5.07937e8 | −0.857121 | ||||||||
\(322\) | 3.01524e8 | 0.503300 | ||||||||
\(323\) | −3.99494e8 | −0.659631 | ||||||||
\(324\) | 7.67233e7 | 0.125320 | ||||||||
\(325\) | −1.08008e9 | −1.74527 | ||||||||
\(326\) | −1.94226e8 | −0.310489 | ||||||||
\(327\) | −4.71746e7 | −0.0746090 | ||||||||
\(328\) | −1.53219e8 | −0.239748 | ||||||||
\(329\) | 1.12470e9 | 1.74121 | ||||||||
\(330\) | −1.07479e8 | −0.164636 | ||||||||
\(331\) | 8.34881e8 | 1.26540 | 0.632699 | − | 0.774398i | \(-0.281947\pi\) | ||||
0.632699 | + | 0.774398i | \(0.281947\pi\) | |||||||
\(332\) | 7.54313e8 | 1.13127 | ||||||||
\(333\) | −2.89591e8 | −0.429764 | ||||||||
\(334\) | −3.89616e8 | −0.572169 | ||||||||
\(335\) | 1.02891e8 | 0.149528 | ||||||||
\(336\) | 5.68461e8 | 0.817548 | ||||||||
\(337\) | −1.13042e9 | −1.60892 | −0.804460 | − | 0.594007i | \(-0.797545\pi\) | ||||
−0.804460 | + | 0.594007i | \(0.797545\pi\) | |||||||
\(338\) | −7.81394e8 | −1.10068 | ||||||||
\(339\) | −9.61397e7 | −0.134031 | ||||||||
\(340\) | −5.03081e8 | −0.694163 | ||||||||
\(341\) | −1.03604e8 | −0.141494 | ||||||||
\(342\) | 5.86899e8 | 0.793364 | ||||||||
\(343\) | −9.12660e8 | −1.22118 | ||||||||
\(344\) | −2.02947e8 | −0.268799 | ||||||||
\(345\) | −1.39785e8 | −0.183271 | ||||||||
\(346\) | 4.78792e8 | 0.621413 | ||||||||
\(347\) | 5.09953e8 | 0.655204 | 0.327602 | − | 0.944816i | \(-0.393759\pi\) | ||||
0.327602 | + | 0.944816i | \(0.393759\pi\) | |||||||
\(348\) | −3.06219e8 | −0.389498 | ||||||||
\(349\) | −6.69343e8 | −0.842868 | −0.421434 | − | 0.906859i | \(-0.638473\pi\) | ||||
−0.421434 | + | 0.906859i | \(0.638473\pi\) | |||||||
\(350\) | 2.55100e9 | 3.18033 | ||||||||
\(351\) | −2.06527e8 | −0.254918 | ||||||||
\(352\) | −1.50767e8 | −0.184250 | ||||||||
\(353\) | −5.36062e8 | −0.648639 | −0.324320 | − | 0.945948i | \(-0.605135\pi\) | ||||
−0.324320 | + | 0.945948i | \(0.605135\pi\) | |||||||
\(354\) | −9.35783e8 | −1.12115 | ||||||||
\(355\) | 2.00957e9 | 2.38399 | ||||||||
\(356\) | −8.26514e8 | −0.970901 | ||||||||
\(357\) | −3.32029e8 | −0.386223 | ||||||||
\(358\) | 1.12800e9 | 1.29933 | ||||||||
\(359\) | 6.72522e8 | 0.767142 | 0.383571 | − | 0.923511i | \(-0.374694\pi\) | ||||
0.383571 | + | 0.923511i | \(0.374694\pi\) | |||||||
\(360\) | 8.37964e7 | 0.0946600 | ||||||||
\(361\) | 1.48579e9 | 1.66220 | ||||||||
\(362\) | 8.35243e8 | 0.925408 | ||||||||
\(363\) | −5.17478e8 | −0.567830 | ||||||||
\(364\) | 2.27466e9 | 2.47208 | ||||||||
\(365\) | 9.95359e8 | 1.07141 | ||||||||
\(366\) | −3.53153e8 | −0.376512 | ||||||||
\(367\) | −1.82244e9 | −1.92452 | −0.962261 | − | 0.272128i | \(-0.912272\pi\) | ||||
−0.962261 | + | 0.272128i | \(0.912272\pi\) | |||||||
\(368\) | −1.70593e8 | −0.178440 | ||||||||
\(369\) | 4.13482e8 | 0.428415 | ||||||||
\(370\) | −2.78965e9 | −2.86315 | ||||||||
\(371\) | −5.67501e8 | −0.576976 | ||||||||
\(372\) | 7.12433e8 | 0.717536 | ||||||||
\(373\) | −8.88447e8 | −0.886442 | −0.443221 | − | 0.896412i | \(-0.646164\pi\) | ||||
−0.443221 | + | 0.896412i | \(0.646164\pi\) | |||||||
\(374\) | 7.66124e7 | 0.0757266 | ||||||||
\(375\) | −2.85060e8 | −0.279143 | ||||||||
\(376\) | 2.02330e8 | 0.196292 | ||||||||
\(377\) | 8.24292e8 | 0.792294 | ||||||||
\(378\) | 4.87787e8 | 0.464525 | ||||||||
\(379\) | 1.36718e9 | 1.29000 | 0.645000 | − | 0.764183i | \(-0.276858\pi\) | ||||
0.645000 | + | 0.764183i | \(0.276858\pi\) | |||||||
\(380\) | 2.99670e9 | 2.80157 | ||||||||
\(381\) | −1.10844e8 | −0.102678 | ||||||||
\(382\) | 1.84232e9 | 1.69100 | ||||||||
\(383\) | −5.13649e7 | −0.0467165 | −0.0233583 | − | 0.999727i | \(-0.507436\pi\) | ||||
−0.0233583 | + | 0.999727i | \(0.507436\pi\) | |||||||
\(384\) | 2.37046e8 | 0.213635 | ||||||||
\(385\) | −3.62195e8 | −0.323467 | ||||||||
\(386\) | −2.15802e9 | −1.90985 | ||||||||
\(387\) | 5.47678e8 | 0.480327 | ||||||||
\(388\) | −1.01247e9 | −0.879975 | ||||||||
\(389\) | 1.19577e9 | 1.02997 | 0.514985 | − | 0.857199i | \(-0.327798\pi\) | ||||
0.514985 | + | 0.857199i | \(0.327798\pi\) | |||||||
\(390\) | −1.98948e9 | −1.69830 | ||||||||
\(391\) | 9.96404e7 | 0.0842979 | ||||||||
\(392\) | −3.86654e8 | −0.324206 | ||||||||
\(393\) | −7.01927e7 | −0.0583335 | ||||||||
\(394\) | −1.81657e8 | −0.149629 | ||||||||
\(395\) | −3.38201e8 | −0.276112 | ||||||||
\(396\) | −5.96580e7 | −0.0482764 | ||||||||
\(397\) | −3.11811e8 | −0.250106 | −0.125053 | − | 0.992150i | \(-0.539910\pi\) | ||||
−0.125053 | + | 0.992150i | \(0.539910\pi\) | |||||||
\(398\) | −2.20703e9 | −1.75476 | ||||||||
\(399\) | 1.97780e9 | 1.55875 | ||||||||
\(400\) | −1.44327e9 | −1.12755 | ||||||||
\(401\) | 2.16496e8 | 0.167665 | 0.0838327 | − | 0.996480i | \(-0.473284\pi\) | ||||
0.0838327 | + | 0.996480i | \(0.473284\pi\) | |||||||
\(402\) | 1.07748e8 | 0.0827212 | ||||||||
\(403\) | −1.91775e9 | −1.45957 | ||||||||
\(404\) | 2.75840e9 | 2.08124 | ||||||||
\(405\) | −2.26135e8 | −0.169152 | ||||||||
\(406\) | −1.94686e9 | −1.44376 | ||||||||
\(407\) | 2.25178e8 | 0.165556 | ||||||||
\(408\) | −5.97310e7 | −0.0435401 | ||||||||
\(409\) | −1.11135e9 | −0.803195 | −0.401598 | − | 0.915816i | \(-0.631545\pi\) | ||||
−0.401598 | + | 0.915816i | \(0.631545\pi\) | |||||||
\(410\) | 3.98310e9 | 2.85416 | ||||||||
\(411\) | −2.60920e8 | −0.185379 | ||||||||
\(412\) | −2.88331e9 | −2.03119 | ||||||||
\(413\) | −3.15351e9 | −2.20277 | ||||||||
\(414\) | −1.46383e8 | −0.101388 | ||||||||
\(415\) | −2.22327e9 | −1.52695 | ||||||||
\(416\) | −2.79076e9 | −1.90062 | ||||||||
\(417\) | 7.96996e8 | 0.538245 | ||||||||
\(418\) | −4.56357e8 | −0.305624 | ||||||||
\(419\) | 1.46901e9 | 0.975606 | 0.487803 | − | 0.872954i | \(-0.337798\pi\) | ||||
0.487803 | + | 0.872954i | \(0.337798\pi\) | |||||||
\(420\) | 2.49063e9 | 1.64035 | ||||||||
\(421\) | 3.62126e8 | 0.236522 | 0.118261 | − | 0.992983i | \(-0.462268\pi\) | ||||
0.118261 | + | 0.992983i | \(0.462268\pi\) | |||||||
\(422\) | −3.67325e9 | −2.37934 | ||||||||
\(423\) | −5.46014e8 | −0.350762 | ||||||||
\(424\) | −1.02092e8 | −0.0650444 | ||||||||
\(425\) | 8.42991e8 | 0.532674 | ||||||||
\(426\) | 2.10442e9 | 1.31886 | ||||||||
\(427\) | −1.19009e9 | −0.739748 | ||||||||
\(428\) | −2.71593e9 | −1.67442 | ||||||||
\(429\) | 1.60590e8 | 0.0982012 | ||||||||
\(430\) | 5.27582e9 | 3.20000 | ||||||||
\(431\) | 1.70696e9 | 1.02696 | 0.513480 | − | 0.858102i | \(-0.328356\pi\) | ||||
0.513480 | + | 0.858102i | \(0.328356\pi\) | |||||||
\(432\) | −2.75974e8 | −0.164693 | ||||||||
\(433\) | 1.34325e9 | 0.795151 | 0.397576 | − | 0.917569i | \(-0.369852\pi\) | ||||
0.397576 | + | 0.917569i | \(0.369852\pi\) | |||||||
\(434\) | 4.52947e9 | 2.65970 | ||||||||
\(435\) | 9.02556e8 | 0.525728 | ||||||||
\(436\) | −2.52241e8 | −0.145752 | ||||||||
\(437\) | −5.93528e8 | −0.340217 | ||||||||
\(438\) | 1.04234e9 | 0.592719 | ||||||||
\(439\) | 1.17304e9 | 0.661739 | 0.330870 | − | 0.943677i | \(-0.392658\pi\) | ||||
0.330870 | + | 0.943677i | \(0.392658\pi\) | |||||||
\(440\) | −6.51578e7 | −0.0364655 | ||||||||
\(441\) | 1.04344e9 | 0.579337 | ||||||||
\(442\) | 1.41813e9 | 0.781155 | ||||||||
\(443\) | 2.77494e9 | 1.51649 | 0.758247 | − | 0.651967i | \(-0.226056\pi\) | ||||
0.758247 | + | 0.651967i | \(0.226056\pi\) | |||||||
\(444\) | −1.54844e9 | −0.839563 | ||||||||
\(445\) | 2.43608e9 | 1.31048 | ||||||||
\(446\) | 4.01776e8 | 0.214443 | ||||||||
\(447\) | 1.05839e9 | 0.560495 | ||||||||
\(448\) | 3.89646e9 | 2.04737 | ||||||||
\(449\) | −7.73041e8 | −0.403033 | −0.201516 | − | 0.979485i | \(-0.564587\pi\) | ||||
−0.201516 | + | 0.979485i | \(0.564587\pi\) | |||||||
\(450\) | −1.23845e9 | −0.640668 | ||||||||
\(451\) | −3.21513e8 | −0.165037 | ||||||||
\(452\) | −5.14057e8 | −0.261834 | ||||||||
\(453\) | −1.64894e9 | −0.833414 | ||||||||
\(454\) | 4.85376e9 | 2.43435 | ||||||||
\(455\) | −6.70438e9 | −3.33671 | ||||||||
\(456\) | 3.55800e8 | 0.175723 | ||||||||
\(457\) | −4.61578e8 | −0.226224 | −0.113112 | − | 0.993582i | \(-0.536082\pi\) | ||||
−0.113112 | + | 0.993582i | \(0.536082\pi\) | |||||||
\(458\) | −8.87454e8 | −0.431635 | ||||||||
\(459\) | 1.61192e8 | 0.0778035 | ||||||||
\(460\) | −7.47428e8 | −0.358028 | ||||||||
\(461\) | −1.15391e9 | −0.548555 | −0.274277 | − | 0.961651i | \(-0.588439\pi\) | ||||
−0.274277 | + | 0.961651i | \(0.588439\pi\) | |||||||
\(462\) | −3.79290e8 | −0.178947 | ||||||||
\(463\) | 3.46111e9 | 1.62062 | 0.810312 | − | 0.585999i | \(-0.199298\pi\) | ||||
0.810312 | + | 0.585999i | \(0.199298\pi\) | |||||||
\(464\) | 1.10147e9 | 0.511871 | ||||||||
\(465\) | −2.09984e9 | −0.968501 | ||||||||
\(466\) | −4.74799e9 | −2.17350 | ||||||||
\(467\) | 1.74439e9 | 0.792566 | 0.396283 | − | 0.918129i | \(-0.370300\pi\) | ||||
0.396283 | + | 0.918129i | \(0.370300\pi\) | |||||||
\(468\) | −1.10429e9 | −0.497994 | ||||||||
\(469\) | 3.63100e8 | 0.162525 | ||||||||
\(470\) | −5.25978e9 | −2.33682 | ||||||||
\(471\) | 1.57355e9 | 0.693919 | ||||||||
\(472\) | −5.67306e8 | −0.248325 | ||||||||
\(473\) | −4.25860e8 | −0.185035 | ||||||||
\(474\) | −3.54163e8 | −0.152749 | ||||||||
\(475\) | −5.02145e9 | −2.14982 | ||||||||
\(476\) | −1.77535e9 | −0.754502 | ||||||||
\(477\) | 2.75508e8 | 0.116230 | ||||||||
\(478\) | −4.88635e9 | −2.04638 | ||||||||
\(479\) | −8.46941e8 | −0.352110 | −0.176055 | − | 0.984380i | \(-0.556334\pi\) | ||||
−0.176055 | + | 0.984380i | \(0.556334\pi\) | |||||||
\(480\) | −3.05573e9 | −1.26116 | ||||||||
\(481\) | 4.16814e9 | 1.70779 | ||||||||
\(482\) | 2.30213e9 | 0.936409 | ||||||||
\(483\) | −4.93296e8 | −0.199202 | ||||||||
\(484\) | −2.76694e9 | −1.10928 | ||||||||
\(485\) | 2.98417e9 | 1.18775 | ||||||||
\(486\) | −2.36808e8 | −0.0935772 | ||||||||
\(487\) | −9.15119e8 | −0.359026 | −0.179513 | − | 0.983756i | \(-0.557452\pi\) | ||||
−0.179513 | + | 0.983756i | \(0.557452\pi\) | |||||||
\(488\) | −2.14094e8 | −0.0833941 | ||||||||
\(489\) | 3.17756e8 | 0.122889 | ||||||||
\(490\) | 1.00515e10 | 3.85962 | ||||||||
\(491\) | 2.09615e9 | 0.799167 | 0.399583 | − | 0.916697i | \(-0.369155\pi\) | ||||
0.399583 | + | 0.916697i | \(0.369155\pi\) | |||||||
\(492\) | 2.21088e9 | 0.836926 | ||||||||
\(493\) | −6.43352e8 | −0.241816 | ||||||||
\(494\) | −8.44736e9 | −3.15266 | ||||||||
\(495\) | 1.75837e8 | 0.0651616 | ||||||||
\(496\) | −2.56262e9 | −0.942972 | ||||||||
\(497\) | 7.09172e9 | 2.59122 | ||||||||
\(498\) | −2.32821e9 | −0.844731 | ||||||||
\(499\) | 3.46322e9 | 1.24775 | 0.623875 | − | 0.781524i | \(-0.285557\pi\) | ||||
0.623875 | + | 0.781524i | \(0.285557\pi\) | |||||||
\(500\) | −1.52421e9 | −0.545318 | ||||||||
\(501\) | 6.37415e8 | 0.226459 | ||||||||
\(502\) | −4.41566e9 | −1.55788 | ||||||||
\(503\) | 3.31882e9 | 1.16277 | 0.581387 | − | 0.813627i | \(-0.302510\pi\) | ||||
0.581387 | + | 0.813627i | \(0.302510\pi\) | |||||||
\(504\) | 2.95714e8 | 0.102888 | ||||||||
\(505\) | −8.13016e9 | −2.80918 | ||||||||
\(506\) | 1.13823e8 | 0.0390574 | ||||||||
\(507\) | 1.27837e9 | 0.435640 | ||||||||
\(508\) | −5.92681e8 | −0.200585 | ||||||||
\(509\) | −2.58709e9 | −0.869560 | −0.434780 | − | 0.900537i | \(-0.643174\pi\) | ||||
−0.434780 | + | 0.900537i | \(0.643174\pi\) | |||||||
\(510\) | 1.55277e9 | 0.518337 | ||||||||
\(511\) | 3.51259e9 | 1.16454 | ||||||||
\(512\) | −4.21400e9 | −1.38755 | ||||||||
\(513\) | −9.60172e8 | −0.314006 | ||||||||
\(514\) | 3.47466e9 | 1.12860 | ||||||||
\(515\) | 8.49831e9 | 2.74162 | ||||||||
\(516\) | 2.92842e9 | 0.938339 | ||||||||
\(517\) | 4.24566e8 | 0.135123 | ||||||||
\(518\) | −9.84457e9 | −3.11202 | ||||||||
\(519\) | −7.83307e8 | −0.245950 | ||||||||
\(520\) | −1.20610e9 | −0.376158 | ||||||||
\(521\) | −3.99114e9 | −1.23642 | −0.618208 | − | 0.786015i | \(-0.712141\pi\) | ||||
−0.618208 | + | 0.786015i | \(0.712141\pi\) | |||||||
\(522\) | 9.45154e8 | 0.290841 | ||||||||
\(523\) | −3.15844e9 | −0.965422 | −0.482711 | − | 0.875780i | \(-0.660348\pi\) | ||||
−0.482711 | + | 0.875780i | \(0.660348\pi\) | |||||||
\(524\) | −3.75319e8 | −0.113957 | ||||||||
\(525\) | −4.17345e9 | −1.25875 | ||||||||
\(526\) | −3.92271e9 | −1.17526 | ||||||||
\(527\) | 1.49679e9 | 0.445475 | ||||||||
\(528\) | 2.14590e8 | 0.0634440 | ||||||||
\(529\) | 1.48036e8 | 0.0434783 | ||||||||
\(530\) | 2.65398e9 | 0.774341 | ||||||||
\(531\) | 1.53095e9 | 0.443741 | ||||||||
\(532\) | 1.05752e10 | 3.04509 | ||||||||
\(533\) | −5.95133e9 | −1.70243 | ||||||||
\(534\) | 2.55106e9 | 0.724980 | ||||||||
\(535\) | 8.00496e9 | 2.26007 | ||||||||
\(536\) | 6.53206e7 | 0.0183220 | ||||||||
\(537\) | −1.84542e9 | −0.514262 | ||||||||
\(538\) | −3.26302e9 | −0.903402 | ||||||||
\(539\) | −8.11348e8 | −0.223176 | ||||||||
\(540\) | −1.20914e9 | −0.330445 | ||||||||
\(541\) | 1.45168e9 | 0.394168 | 0.197084 | − | 0.980387i | \(-0.436853\pi\) | ||||
0.197084 | + | 0.980387i | \(0.436853\pi\) | |||||||
\(542\) | −7.79600e9 | −2.10317 | ||||||||
\(543\) | −1.36646e9 | −0.366268 | ||||||||
\(544\) | 2.17816e9 | 0.580088 | ||||||||
\(545\) | 7.43460e8 | 0.196730 | ||||||||
\(546\) | −7.02081e9 | −1.84592 | ||||||||
\(547\) | 5.34408e9 | 1.39610 | 0.698051 | − | 0.716048i | \(-0.254051\pi\) | ||||
0.698051 | + | 0.716048i | \(0.254051\pi\) | |||||||
\(548\) | −1.39513e9 | −0.362146 | ||||||||
\(549\) | 5.77761e8 | 0.149020 | ||||||||
\(550\) | 9.62982e8 | 0.246802 | ||||||||
\(551\) | 3.83226e9 | 0.975942 | ||||||||
\(552\) | −8.87425e7 | −0.0224566 | ||||||||
\(553\) | −1.19350e9 | −0.300112 | ||||||||
\(554\) | −2.01805e9 | −0.504252 | ||||||||
\(555\) | 4.56389e9 | 1.13321 | ||||||||
\(556\) | 4.26152e9 | 1.05148 | ||||||||
\(557\) | 5.00428e9 | 1.22701 | 0.613506 | − | 0.789690i | \(-0.289759\pi\) | ||||
0.613506 | + | 0.789690i | \(0.289759\pi\) | |||||||
\(558\) | −2.19894e9 | −0.535790 | ||||||||
\(559\) | −7.88284e9 | −1.90872 | ||||||||
\(560\) | −8.95882e9 | −2.15572 | ||||||||
\(561\) | −1.25339e8 | −0.0299719 | ||||||||
\(562\) | −6.02213e9 | −1.43111 | ||||||||
\(563\) | 5.16557e9 | 1.21994 | 0.609971 | − | 0.792424i | \(-0.291181\pi\) | ||||
0.609971 | + | 0.792424i | \(0.291181\pi\) | |||||||
\(564\) | −2.91952e9 | −0.685228 | ||||||||
\(565\) | 1.51514e9 | 0.353413 | ||||||||
\(566\) | 1.26927e9 | 0.294237 | ||||||||
\(567\) | −7.98023e8 | −0.183855 | ||||||||
\(568\) | 1.27578e9 | 0.292116 | ||||||||
\(569\) | 2.72876e9 | 0.620974 | 0.310487 | − | 0.950578i | \(-0.399508\pi\) | ||||
0.310487 | + | 0.950578i | \(0.399508\pi\) | |||||||
\(570\) | −9.24940e9 | −2.09195 | ||||||||
\(571\) | 8.49748e8 | 0.191013 | 0.0955066 | − | 0.995429i | \(-0.469553\pi\) | ||||
0.0955066 | + | 0.995429i | \(0.469553\pi\) | |||||||
\(572\) | 8.58668e8 | 0.191840 | ||||||||
\(573\) | −3.01405e9 | −0.669283 | ||||||||
\(574\) | 1.40562e10 | 3.10225 | ||||||||
\(575\) | 1.25243e9 | 0.274737 | ||||||||
\(576\) | −1.89163e9 | −0.412437 | ||||||||
\(577\) | −6.81404e9 | −1.47669 | −0.738345 | − | 0.674423i | \(-0.764392\pi\) | ||||
−0.738345 | + | 0.674423i | \(0.764392\pi\) | |||||||
\(578\) | 5.66523e9 | 1.22031 | ||||||||
\(579\) | 3.53053e9 | 0.755901 | ||||||||
\(580\) | 4.82594e9 | 1.02703 | ||||||||
\(581\) | −7.84585e9 | −1.65968 | ||||||||
\(582\) | 3.12501e9 | 0.657084 | ||||||||
\(583\) | −2.14227e8 | −0.0447749 | ||||||||
\(584\) | 6.31903e8 | 0.131282 | ||||||||
\(585\) | 3.25481e9 | 0.672172 | ||||||||
\(586\) | 4.70124e9 | 0.965097 | ||||||||
\(587\) | −2.05329e9 | −0.419004 | −0.209502 | − | 0.977808i | \(-0.567184\pi\) | ||||
−0.209502 | + | 0.977808i | \(0.567184\pi\) | |||||||
\(588\) | 5.57923e9 | 1.13176 | ||||||||
\(589\) | −8.91592e9 | −1.79789 | ||||||||
\(590\) | 1.47477e10 | 2.95626 | ||||||||
\(591\) | 2.97193e8 | 0.0592219 | ||||||||
\(592\) | 5.56973e9 | 1.10334 | ||||||||
\(593\) | −3.64815e9 | −0.718424 | −0.359212 | − | 0.933256i | \(-0.616954\pi\) | ||||
−0.359212 | + | 0.933256i | \(0.616954\pi\) | |||||||
\(594\) | 1.84136e8 | 0.0360484 | ||||||||
\(595\) | 5.23270e9 | 1.01840 | ||||||||
\(596\) | 5.65921e9 | 1.09495 | ||||||||
\(597\) | 3.61071e9 | 0.694517 | ||||||||
\(598\) | 2.10691e9 | 0.402895 | ||||||||
\(599\) | −2.96538e9 | −0.563750 | −0.281875 | − | 0.959451i | \(-0.590956\pi\) | ||||
−0.281875 | + | 0.959451i | \(0.590956\pi\) | |||||||
\(600\) | −7.50791e8 | −0.141902 | ||||||||
\(601\) | 6.94942e9 | 1.30583 | 0.652917 | − | 0.757429i | \(-0.273545\pi\) | ||||
0.652917 | + | 0.757429i | \(0.273545\pi\) | |||||||
\(602\) | 1.86182e10 | 3.47816 | ||||||||
\(603\) | −1.76276e8 | −0.0327403 | ||||||||
\(604\) | −8.81683e9 | −1.62811 | ||||||||
\(605\) | 8.15533e9 | 1.49726 | ||||||||
\(606\) | −8.51388e9 | −1.55408 | ||||||||
\(607\) | −5.47955e9 | −0.994454 | −0.497227 | − | 0.867620i | \(-0.665648\pi\) | ||||
−0.497227 | + | 0.867620i | \(0.665648\pi\) | |||||||
\(608\) | −1.29746e10 | −2.34117 | ||||||||
\(609\) | 3.18509e9 | 0.571427 | ||||||||
\(610\) | 5.56561e9 | 0.992792 | ||||||||
\(611\) | 7.85888e9 | 1.39385 | ||||||||
\(612\) | 8.61890e8 | 0.151992 | ||||||||
\(613\) | −5.21036e9 | −0.913600 | −0.456800 | − | 0.889570i | \(-0.651004\pi\) | ||||
−0.456800 | + | 0.889570i | \(0.651004\pi\) | |||||||
\(614\) | 1.03009e10 | 1.79591 | ||||||||
\(615\) | −6.51638e9 | −1.12965 | ||||||||
\(616\) | −2.29940e8 | −0.0396352 | ||||||||
\(617\) | −2.60433e8 | −0.0446372 | −0.0223186 | − | 0.999751i | \(-0.507105\pi\) | ||||
−0.0223186 | + | 0.999751i | \(0.507105\pi\) | |||||||
\(618\) | 8.89940e9 | 1.51671 | ||||||||
\(619\) | 2.85535e9 | 0.483885 | 0.241943 | − | 0.970291i | \(-0.422215\pi\) | ||||
0.241943 | + | 0.970291i | \(0.422215\pi\) | |||||||
\(620\) | −1.12278e10 | −1.89201 | ||||||||
\(621\) | 2.39483e8 | 0.0401286 | ||||||||
\(622\) | 7.99165e9 | 1.33159 | ||||||||
\(623\) | 8.59684e9 | 1.42440 | ||||||||
\(624\) | 3.97214e9 | 0.654454 | ||||||||
\(625\) | −3.54946e9 | −0.581543 | ||||||||
\(626\) | 8.15534e9 | 1.32871 | ||||||||
\(627\) | 7.46604e8 | 0.120963 | ||||||||
\(628\) | 8.41376e9 | 1.35560 | ||||||||
\(629\) | −3.25319e9 | −0.521234 | ||||||||
\(630\) | −7.68741e9 | −1.22486 | ||||||||
\(631\) | −1.01242e10 | −1.60420 | −0.802099 | − | 0.597191i | \(-0.796283\pi\) | ||||
−0.802099 | + | 0.597191i | \(0.796283\pi\) | |||||||
\(632\) | −2.14706e8 | −0.0338326 | ||||||||
\(633\) | 6.00946e9 | 0.941722 | ||||||||
\(634\) | −1.48007e10 | −2.30658 | ||||||||
\(635\) | 1.74688e9 | 0.270741 | ||||||||
\(636\) | 1.47313e9 | 0.227061 | ||||||||
\(637\) | −1.50184e10 | −2.30216 | ||||||||
\(638\) | −7.34926e8 | −0.112040 | ||||||||
\(639\) | −3.44285e9 | −0.521994 | ||||||||
\(640\) | −3.73579e9 | −0.563316 | ||||||||
\(641\) | −1.66619e9 | −0.249874 | −0.124937 | − | 0.992165i | \(-0.539873\pi\) | ||||
−0.124937 | + | 0.992165i | \(0.539873\pi\) | |||||||
\(642\) | 8.38278e9 | 1.25030 | ||||||||
\(643\) | −8.04387e9 | −1.19324 | −0.596619 | − | 0.802525i | \(-0.703489\pi\) | ||||
−0.596619 | + | 0.802525i | \(0.703489\pi\) | |||||||
\(644\) | −2.63764e9 | −0.389149 | ||||||||
\(645\) | −8.63128e9 | −1.26653 | ||||||||
\(646\) | 6.59308e9 | 0.962220 | ||||||||
\(647\) | −1.15798e9 | −0.168088 | −0.0840439 | − | 0.996462i | \(-0.526784\pi\) | ||||
−0.0840439 | + | 0.996462i | \(0.526784\pi\) | |||||||
\(648\) | −1.43562e8 | −0.0207265 | ||||||||
\(649\) | −1.19042e9 | −0.170941 | ||||||||
\(650\) | 1.78252e10 | 2.54588 | ||||||||
\(651\) | −7.41024e9 | −1.05269 | ||||||||
\(652\) | 1.69903e9 | 0.240069 | ||||||||
\(653\) | 5.67105e9 | 0.797017 | 0.398508 | − | 0.917165i | \(-0.369528\pi\) | ||||
0.398508 | + | 0.917165i | \(0.369528\pi\) | |||||||
\(654\) | 7.78550e8 | 0.108834 | ||||||||
\(655\) | 1.10622e9 | 0.153815 | ||||||||
\(656\) | −7.95254e9 | −1.09987 | ||||||||
\(657\) | −1.70527e9 | −0.234593 | ||||||||
\(658\) | −1.85616e10 | −2.53995 | ||||||||
\(659\) | 2.21730e9 | 0.301804 | 0.150902 | − | 0.988549i | \(-0.451782\pi\) | ||||
0.150902 | + | 0.988549i | \(0.451782\pi\) | |||||||
\(660\) | 9.40195e8 | 0.127296 | ||||||||
\(661\) | 2.38616e9 | 0.321362 | 0.160681 | − | 0.987006i | \(-0.448631\pi\) | ||||
0.160681 | + | 0.987006i | \(0.448631\pi\) | |||||||
\(662\) | −1.37785e10 | −1.84587 | ||||||||
\(663\) | −2.32007e9 | −0.309174 | ||||||||
\(664\) | −1.41144e9 | −0.187101 | ||||||||
\(665\) | −3.11697e10 | −4.11014 | ||||||||
\(666\) | 4.77929e9 | 0.626908 | ||||||||
\(667\) | −9.55829e8 | −0.124721 | ||||||||
\(668\) | 3.40824e9 | 0.442398 | ||||||||
\(669\) | −6.57309e8 | −0.0848747 | ||||||||
\(670\) | −1.69808e9 | −0.218120 | ||||||||
\(671\) | −4.49251e8 | −0.0574064 | ||||||||
\(672\) | −1.07836e10 | −1.37079 | ||||||||
\(673\) | −7.59718e9 | −0.960727 | −0.480363 | − | 0.877070i | \(-0.659495\pi\) | ||||
−0.480363 | + | 0.877070i | \(0.659495\pi\) | |||||||
\(674\) | 1.86559e10 | 2.34697 | ||||||||
\(675\) | 2.02611e9 | 0.253571 | ||||||||
\(676\) | 6.83539e9 | 0.851040 | ||||||||
\(677\) | −7.61664e9 | −0.943416 | −0.471708 | − | 0.881755i | \(-0.656362\pi\) | ||||
−0.471708 | + | 0.881755i | \(0.656362\pi\) | |||||||
\(678\) | 1.58665e9 | 0.195514 | ||||||||
\(679\) | 1.05310e10 | 1.29100 | ||||||||
\(680\) | 9.41347e8 | 0.114807 | ||||||||
\(681\) | −7.94080e9 | −0.963494 | ||||||||
\(682\) | 1.70984e9 | 0.206400 | ||||||||
\(683\) | −3.27264e9 | −0.393030 | −0.196515 | − | 0.980501i | \(-0.562962\pi\) | ||||
−0.196515 | + | 0.980501i | \(0.562962\pi\) | |||||||
\(684\) | −5.13402e9 | −0.613424 | ||||||||
\(685\) | 4.11204e9 | 0.488810 | ||||||||
\(686\) | 1.50622e10 | 1.78136 | ||||||||
\(687\) | 1.45188e9 | 0.170837 | ||||||||
\(688\) | −1.05335e10 | −1.23315 | ||||||||
\(689\) | −3.96543e9 | −0.461874 | ||||||||
\(690\) | 2.30695e9 | 0.267342 | ||||||||
\(691\) | 6.63679e9 | 0.765218 | 0.382609 | − | 0.923910i | \(-0.375026\pi\) | ||||
0.382609 | + | 0.923910i | \(0.375026\pi\) | |||||||
\(692\) | −4.18832e9 | −0.480473 | ||||||||
\(693\) | 6.20522e8 | 0.0708257 | ||||||||
\(694\) | −8.41605e9 | −0.955763 | ||||||||
\(695\) | −1.25605e10 | −1.41925 | ||||||||
\(696\) | 5.72987e8 | 0.0644187 | ||||||||
\(697\) | 4.64495e9 | 0.519597 | ||||||||
\(698\) | 1.10466e10 | 1.22951 | ||||||||
\(699\) | 7.76775e9 | 0.860251 | ||||||||
\(700\) | −2.23153e10 | −2.45901 | ||||||||
\(701\) | −1.22424e10 | −1.34231 | −0.671155 | − | 0.741317i | \(-0.734201\pi\) | ||||
−0.671155 | + | 0.741317i | \(0.734201\pi\) | |||||||
\(702\) | 3.40843e9 | 0.371856 | ||||||||
\(703\) | 1.93783e10 | 2.10364 | ||||||||
\(704\) | 1.47088e9 | 0.158882 | ||||||||
\(705\) | 8.60505e9 | 0.924893 | ||||||||
\(706\) | 8.84694e9 | 0.946186 | ||||||||
\(707\) | −2.86910e10 | −3.05336 | ||||||||
\(708\) | 8.18595e9 | 0.866867 | ||||||||
\(709\) | 1.58035e10 | 1.66530 | 0.832648 | − | 0.553802i | \(-0.186824\pi\) | ||||
0.832648 | + | 0.553802i | \(0.186824\pi\) | |||||||
\(710\) | −3.31652e10 | −3.47759 | ||||||||
\(711\) | 5.79413e8 | 0.0604568 | ||||||||
\(712\) | 1.54654e9 | 0.160577 | ||||||||
\(713\) | 2.22378e9 | 0.229762 | ||||||||
\(714\) | 5.47968e9 | 0.563393 | ||||||||
\(715\) | −2.53085e9 | −0.258938 | ||||||||
\(716\) | −9.86740e9 | −1.00463 | ||||||||
\(717\) | 7.99410e9 | 0.809940 | ||||||||
\(718\) | −1.10990e10 | −1.11905 | ||||||||
\(719\) | 4.98945e9 | 0.500612 | 0.250306 | − | 0.968167i | \(-0.419469\pi\) | ||||
0.250306 | + | 0.968167i | \(0.419469\pi\) | |||||||
\(720\) | 4.34928e9 | 0.434264 | ||||||||
\(721\) | 2.99902e10 | 2.97993 | ||||||||
\(722\) | −2.45209e10 | −2.42469 | ||||||||
\(723\) | −3.76631e9 | −0.370622 | ||||||||
\(724\) | −7.30646e9 | −0.715520 | ||||||||
\(725\) | −8.08663e9 | −0.788106 | ||||||||
\(726\) | 8.54024e9 | 0.828308 | ||||||||
\(727\) | −6.01676e9 | −0.580754 | −0.290377 | − | 0.956912i | \(-0.593781\pi\) | ||||
−0.290377 | + | 0.956912i | \(0.593781\pi\) | |||||||
\(728\) | −4.25627e9 | −0.408855 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −1.64270e10 | −1.56289 | ||||||||
\(731\) | 6.15248e9 | 0.582558 | ||||||||
\(732\) | 3.08927e9 | 0.291117 | ||||||||
\(733\) | 4.02201e9 | 0.377207 | 0.188603 | − | 0.982053i | \(-0.439604\pi\) | ||||
0.188603 | + | 0.982053i | \(0.439604\pi\) | |||||||
\(734\) | 3.00769e10 | 2.80735 | ||||||||
\(735\) | −1.64443e10 | −1.52760 | ||||||||
\(736\) | 3.23609e9 | 0.299191 | ||||||||
\(737\) | 1.37068e8 | 0.0126124 | ||||||||
\(738\) | −6.82394e9 | −0.624939 | ||||||||
\(739\) | −6.62949e9 | −0.604261 | −0.302130 | − | 0.953267i | \(-0.597698\pi\) | ||||
−0.302130 | + | 0.953267i | \(0.597698\pi\) | |||||||
\(740\) | 2.44030e10 | 2.21377 | ||||||||
\(741\) | 1.38199e10 | 1.24779 | ||||||||
\(742\) | 9.36580e9 | 0.841650 | ||||||||
\(743\) | −1.07995e10 | −0.965923 | −0.482961 | − | 0.875642i | \(-0.660439\pi\) | ||||
−0.482961 | + | 0.875642i | \(0.660439\pi\) | |||||||
\(744\) | −1.33308e9 | −0.118673 | ||||||||
\(745\) | −1.66801e10 | −1.47792 | ||||||||
\(746\) | 1.46626e10 | 1.29308 | ||||||||
\(747\) | 3.80896e9 | 0.334337 | ||||||||
\(748\) | −6.70182e8 | −0.0585514 | ||||||||
\(749\) | 2.82492e10 | 2.45652 | ||||||||
\(750\) | 4.70452e9 | 0.407193 | ||||||||
\(751\) | −4.44278e9 | −0.382750 | −0.191375 | − | 0.981517i | \(-0.561295\pi\) | ||||
−0.191375 | + | 0.981517i | \(0.561295\pi\) | |||||||
\(752\) | 1.05015e10 | 0.900513 | ||||||||
\(753\) | 7.22406e9 | 0.616594 | ||||||||
\(754\) | −1.36038e10 | −1.15574 | ||||||||
\(755\) | 2.59869e10 | 2.19756 | ||||||||
\(756\) | −4.26701e9 | −0.359168 | ||||||||
\(757\) | 8.62219e9 | 0.722407 | 0.361204 | − | 0.932487i | \(-0.382366\pi\) | ||||
0.361204 | + | 0.932487i | \(0.382366\pi\) | |||||||
\(758\) | −2.25634e10 | −1.88175 | ||||||||
\(759\) | −1.86216e8 | −0.0154586 | ||||||||
\(760\) | −5.60732e9 | −0.463349 | ||||||||
\(761\) | 1.61329e10 | 1.32699 | 0.663495 | − | 0.748181i | \(-0.269073\pi\) | ||||
0.663495 | + | 0.748181i | \(0.269073\pi\) | |||||||
\(762\) | 1.82933e9 | 0.149778 | ||||||||
\(763\) | 2.62364e9 | 0.213830 | ||||||||
\(764\) | −1.61161e10 | −1.30747 | ||||||||
\(765\) | −2.54035e9 | −0.205153 | ||||||||
\(766\) | 8.47705e8 | 0.0681465 | ||||||||
\(767\) | −2.20352e10 | −1.76333 | ||||||||
\(768\) | 5.05563e9 | 0.402727 | ||||||||
\(769\) | 9.08946e9 | 0.720769 | 0.360384 | − | 0.932804i | \(-0.382646\pi\) | ||||
0.360384 | + | 0.932804i | \(0.382646\pi\) | |||||||
\(770\) | 5.97752e9 | 0.471850 | ||||||||
\(771\) | −5.68457e9 | −0.446691 | ||||||||
\(772\) | 1.88777e10 | 1.47669 | ||||||||
\(773\) | −3.76432e9 | −0.293129 | −0.146564 | − | 0.989201i | \(-0.546822\pi\) | ||||
−0.146564 | + | 0.989201i | \(0.546822\pi\) | |||||||
\(774\) | −9.03866e9 | −0.700665 | ||||||||
\(775\) | 1.88139e10 | 1.45185 | ||||||||
\(776\) | 1.89450e9 | 0.145538 | ||||||||
\(777\) | 1.61058e10 | 1.23171 | ||||||||
\(778\) | −1.97345e10 | −1.50244 | ||||||||
\(779\) | −2.76686e10 | −2.09704 | ||||||||
\(780\) | 1.74034e10 | 1.31312 | ||||||||
\(781\) | 2.67707e9 | 0.201086 | ||||||||
\(782\) | −1.64442e9 | −0.122968 | ||||||||
\(783\) | −1.54628e9 | −0.115112 | ||||||||
\(784\) | −2.00685e10 | −1.48734 | ||||||||
\(785\) | −2.47989e10 | −1.82973 | ||||||||
\(786\) | 1.15843e9 | 0.0850926 | ||||||||
\(787\) | −9.80851e9 | −0.717284 | −0.358642 | − | 0.933475i | \(-0.616760\pi\) | ||||
−0.358642 | + | 0.933475i | \(0.616760\pi\) | |||||||
\(788\) | 1.58908e9 | 0.115692 | ||||||||
\(789\) | 6.41758e9 | 0.465159 | ||||||||
\(790\) | 5.58152e9 | 0.402771 | ||||||||
\(791\) | 5.34687e9 | 0.384133 | ||||||||
\(792\) | 1.11630e8 | 0.00798440 | ||||||||
\(793\) | −8.31582e9 | −0.592174 | ||||||||
\(794\) | 5.14599e9 | 0.364836 | ||||||||
\(795\) | −4.34194e9 | −0.306477 | ||||||||
\(796\) | 1.93064e10 | 1.35677 | ||||||||
\(797\) | 1.37110e10 | 0.959325 | 0.479662 | − | 0.877453i | \(-0.340759\pi\) | ||||
0.479662 | + | 0.877453i | \(0.340759\pi\) | |||||||
\(798\) | −3.26408e10 | −2.27379 | ||||||||
\(799\) | −6.13378e9 | −0.425417 | ||||||||
\(800\) | 2.73784e10 | 1.89057 | ||||||||
\(801\) | −4.17355e9 | −0.286940 | ||||||||
\(802\) | −3.57295e9 | −0.244578 | ||||||||
\(803\) | 1.32597e9 | 0.0903713 | ||||||||
\(804\) | −9.42544e8 | −0.0639596 | ||||||||
\(805\) | 7.77423e9 | 0.525257 | ||||||||
\(806\) | 3.16498e10 | 2.12911 | ||||||||
\(807\) | 5.33832e9 | 0.357559 | ||||||||
\(808\) | −5.16143e9 | −0.344215 | ||||||||
\(809\) | −4.75415e9 | −0.315685 | −0.157842 | − | 0.987464i | \(-0.550454\pi\) | ||||
−0.157842 | + | 0.987464i | \(0.550454\pi\) | |||||||
\(810\) | 3.73205e9 | 0.246746 | ||||||||
\(811\) | 9.06766e9 | 0.596929 | 0.298464 | − | 0.954421i | \(-0.403526\pi\) | ||||
0.298464 | + | 0.954421i | \(0.403526\pi\) | |||||||
\(812\) | 1.70306e10 | 1.11631 | ||||||||
\(813\) | 1.27543e10 | 0.832416 | ||||||||
\(814\) | −3.71625e9 | −0.241501 | ||||||||
\(815\) | −5.00776e9 | −0.324035 | ||||||||
\(816\) | −3.10022e9 | −0.199745 | ||||||||
\(817\) | −3.66485e10 | −2.35114 | ||||||||
\(818\) | 1.83413e10 | 1.17164 | ||||||||
\(819\) | 1.14861e10 | 0.730599 | ||||||||
\(820\) | −3.48429e10 | −2.20682 | ||||||||
\(821\) | 4.16986e9 | 0.262979 | 0.131489 | − | 0.991318i | \(-0.458024\pi\) | ||||
0.131489 | + | 0.991318i | \(0.458024\pi\) | |||||||
\(822\) | 4.30611e9 | 0.270417 | ||||||||
\(823\) | 1.16734e10 | 0.729959 | 0.364979 | − | 0.931016i | \(-0.381076\pi\) | ||||
0.364979 | + | 0.931016i | \(0.381076\pi\) | |||||||
\(824\) | 5.39514e9 | 0.335937 | ||||||||
\(825\) | −1.57545e9 | −0.0976820 | ||||||||
\(826\) | 5.20442e10 | 3.21323 | ||||||||
\(827\) | 1.43823e10 | 0.884220 | 0.442110 | − | 0.896961i | \(-0.354230\pi\) | ||||
0.442110 | + | 0.896961i | \(0.354230\pi\) | |||||||
\(828\) | 1.28051e9 | 0.0783929 | ||||||||
\(829\) | −2.98191e10 | −1.81783 | −0.908916 | − | 0.416980i | \(-0.863089\pi\) | ||||
−0.908916 | + | 0.416980i | \(0.863089\pi\) | |||||||
\(830\) | 3.66920e10 | 2.22740 | ||||||||
\(831\) | 3.30155e9 | 0.199578 | ||||||||
\(832\) | 2.72266e10 | 1.63894 | ||||||||
\(833\) | 1.17217e10 | 0.702640 | ||||||||
\(834\) | −1.31533e10 | −0.785152 | ||||||||
\(835\) | −1.00455e10 | −0.597131 | ||||||||
\(836\) | 3.99208e9 | 0.236307 | ||||||||
\(837\) | 3.59749e9 | 0.212061 | ||||||||
\(838\) | −2.42439e10 | −1.42314 | ||||||||
\(839\) | −4.47833e9 | −0.261788 | −0.130894 | − | 0.991396i | \(-0.541785\pi\) | ||||
−0.130894 | + | 0.991396i | \(0.541785\pi\) | |||||||
\(840\) | −4.66039e9 | −0.271297 | ||||||||
\(841\) | −1.10783e10 | −0.642227 | ||||||||
\(842\) | −5.97638e9 | −0.345021 | ||||||||
\(843\) | 9.85225e9 | 0.566420 | ||||||||
\(844\) | 3.21325e10 | 1.83969 | ||||||||
\(845\) | −2.01468e10 | −1.14870 | ||||||||
\(846\) | 9.01118e9 | 0.511665 | ||||||||
\(847\) | 2.87799e10 | 1.62741 | ||||||||
\(848\) | −5.29886e9 | −0.298399 | ||||||||
\(849\) | −2.07654e9 | −0.116456 | ||||||||
\(850\) | −1.39124e10 | −0.777025 | ||||||||
\(851\) | −4.83327e9 | −0.268836 | ||||||||
\(852\) | −1.84088e10 | −1.01974 | ||||||||
\(853\) | −9.39831e9 | −0.518476 | −0.259238 | − | 0.965814i | \(-0.583471\pi\) | ||||
−0.259238 | + | 0.965814i | \(0.583471\pi\) | |||||||
\(854\) | 1.96408e10 | 1.07909 | ||||||||
\(855\) | 1.51321e10 | 0.827975 | ||||||||
\(856\) | 5.08194e9 | 0.276931 | ||||||||
\(857\) | −1.07879e10 | −0.585470 | −0.292735 | − | 0.956194i | \(-0.594565\pi\) | ||||
−0.292735 | + | 0.956194i | \(0.594565\pi\) | |||||||
\(858\) | −2.65030e9 | −0.143248 | ||||||||
\(859\) | −1.88319e10 | −1.01372 | −0.506860 | − | 0.862028i | \(-0.669194\pi\) | ||||
−0.506860 | + | 0.862028i | \(0.669194\pi\) | |||||||
\(860\) | −4.61513e10 | −2.47422 | ||||||||
\(861\) | −2.29961e10 | −1.22784 | ||||||||
\(862\) | −2.81710e10 | −1.49805 | ||||||||
\(863\) | 2.24758e10 | 1.19036 | 0.595179 | − | 0.803593i | \(-0.297081\pi\) | ||||
0.595179 | + | 0.803593i | \(0.297081\pi\) | |||||||
\(864\) | 5.23515e9 | 0.276141 | ||||||||
\(865\) | 1.23447e10 | 0.648523 | ||||||||
\(866\) | −2.21685e10 | −1.15991 | ||||||||
\(867\) | −9.26835e9 | −0.482987 | ||||||||
\(868\) | −3.96224e10 | −2.05647 | ||||||||
\(869\) | −4.50536e8 | −0.0232895 | ||||||||
\(870\) | −1.48954e10 | −0.766893 | ||||||||
\(871\) | 2.53717e9 | 0.130103 | ||||||||
\(872\) | 4.71985e8 | 0.0241058 | ||||||||
\(873\) | −5.11254e9 | −0.260068 | ||||||||
\(874\) | 9.79534e9 | 0.496283 | ||||||||
\(875\) | 1.58538e10 | 0.800028 | ||||||||
\(876\) | −9.11805e9 | −0.458287 | ||||||||
\(877\) | 3.68411e10 | 1.84431 | 0.922155 | − | 0.386821i | \(-0.126427\pi\) | ||||
0.922155 | + | 0.386821i | \(0.126427\pi\) | |||||||
\(878\) | −1.93594e10 | −0.965295 | ||||||||
\(879\) | −7.69127e9 | −0.381977 | ||||||||
\(880\) | −3.38189e9 | −0.167290 | ||||||||
\(881\) | −2.17761e10 | −1.07291 | −0.536457 | − | 0.843927i | \(-0.680238\pi\) | ||||
−0.536457 | + | 0.843927i | \(0.680238\pi\) | |||||||
\(882\) | −1.72204e10 | −0.845093 | ||||||||
\(883\) | 6.13071e9 | 0.299673 | 0.149837 | − | 0.988711i | \(-0.452125\pi\) | ||||
0.149837 | + | 0.988711i | \(0.452125\pi\) | |||||||
\(884\) | −1.24053e10 | −0.603985 | ||||||||
\(885\) | −2.41274e10 | −1.17006 | ||||||||
\(886\) | −4.57965e10 | −2.21215 | ||||||||
\(887\) | 8.18008e9 | 0.393572 | 0.196786 | − | 0.980446i | \(-0.436950\pi\) | ||||
0.196786 | + | 0.980446i | \(0.436950\pi\) | |||||||
\(888\) | 2.89738e9 | 0.138855 | ||||||||
\(889\) | 6.16467e9 | 0.294275 | ||||||||
\(890\) | −4.02041e10 | −1.91163 | ||||||||
\(891\) | −3.01248e8 | −0.0142676 | ||||||||
\(892\) | −3.51462e9 | −0.165806 | ||||||||
\(893\) | 3.65371e10 | 1.71693 | ||||||||
\(894\) | −1.74673e10 | −0.817607 | ||||||||
\(895\) | 2.90833e10 | 1.35601 | ||||||||
\(896\) | −1.31835e10 | −0.612282 | ||||||||
\(897\) | −3.44693e9 | −0.159462 | ||||||||
\(898\) | 1.27580e10 | 0.587914 | ||||||||
\(899\) | −1.43584e10 | −0.659092 | ||||||||
\(900\) | 1.08335e10 | 0.495361 | ||||||||
\(901\) | 3.09498e9 | 0.140968 | ||||||||
\(902\) | 5.30611e9 | 0.240743 | ||||||||
\(903\) | −3.04595e10 | −1.37662 | ||||||||
\(904\) | 9.61885e8 | 0.0433046 | ||||||||
\(905\) | 2.15352e10 | 0.965780 | ||||||||
\(906\) | 2.72134e10 | 1.21572 | ||||||||
\(907\) | −4.94515e9 | −0.220067 | −0.110033 | − | 0.993928i | \(-0.535096\pi\) | ||||
−0.110033 | + | 0.993928i | \(0.535096\pi\) | |||||||
\(908\) | −4.24593e10 | −1.88223 | ||||||||
\(909\) | 1.39288e10 | 0.615091 | ||||||||
\(910\) | 1.10646e11 | 4.86735 | ||||||||
\(911\) | 2.27032e10 | 0.994883 | 0.497442 | − | 0.867497i | \(-0.334273\pi\) | ||||
0.497442 | + | 0.867497i | \(0.334273\pi\) | |||||||
\(912\) | 1.84671e10 | 0.806151 | ||||||||
\(913\) | −2.96175e9 | −0.128795 | ||||||||
\(914\) | 7.61770e9 | 0.329998 | ||||||||
\(915\) | −9.10538e9 | −0.392938 | ||||||||
\(916\) | 7.76318e9 | 0.333738 | ||||||||
\(917\) | 3.90381e9 | 0.167185 | ||||||||
\(918\) | −2.66025e9 | −0.113494 | ||||||||
\(919\) | 4.49844e10 | 1.91187 | 0.955933 | − | 0.293586i | \(-0.0948486\pi\) | ||||
0.955933 | + | 0.293586i | \(0.0948486\pi\) | |||||||
\(920\) | 1.39856e9 | 0.0592139 | ||||||||
\(921\) | −1.68523e10 | −0.710805 | ||||||||
\(922\) | 1.90437e10 | 0.800190 | ||||||||
\(923\) | 4.95536e10 | 2.07429 | ||||||||
\(924\) | 3.31792e9 | 0.138361 | ||||||||
\(925\) | −4.08911e10 | −1.69876 | ||||||||
\(926\) | −5.71208e10 | −2.36404 | ||||||||
\(927\) | −1.45595e10 | −0.600299 | ||||||||
\(928\) | −2.08946e10 | −0.858255 | ||||||||
\(929\) | −3.90782e10 | −1.59911 | −0.799557 | − | 0.600590i | \(-0.794932\pi\) | ||||
−0.799557 | + | 0.600590i | \(0.794932\pi\) | |||||||
\(930\) | 3.46548e10 | 1.41278 | ||||||||
\(931\) | −6.98226e10 | −2.83578 | ||||||||
\(932\) | 4.15340e10 | 1.68054 | ||||||||
\(933\) | −1.30744e10 | −0.527031 | ||||||||
\(934\) | −2.87887e10 | −1.15614 | ||||||||
\(935\) | 1.97531e9 | 0.0790303 | ||||||||
\(936\) | 2.06631e9 | 0.0823628 | ||||||||
\(937\) | 3.64378e10 | 1.44699 | 0.723493 | − | 0.690332i | \(-0.242536\pi\) | ||||
0.723493 | + | 0.690332i | \(0.242536\pi\) | |||||||
\(938\) | −5.99245e9 | −0.237080 | ||||||||
\(939\) | −1.33422e10 | −0.525894 | ||||||||
\(940\) | 4.60110e10 | 1.80682 | ||||||||
\(941\) | −2.02949e10 | −0.794004 | −0.397002 | − | 0.917818i | \(-0.629949\pi\) | ||||
−0.397002 | + | 0.917818i | \(0.629949\pi\) | |||||||
\(942\) | −2.59693e10 | −1.01224 | ||||||||
\(943\) | 6.90101e9 | 0.267992 | ||||||||
\(944\) | −2.94449e10 | −1.13922 | ||||||||
\(945\) | 1.25767e10 | 0.484790 | ||||||||
\(946\) | 7.02822e9 | 0.269914 | ||||||||
\(947\) | −3.16533e10 | −1.21114 | −0.605570 | − | 0.795792i | \(-0.707055\pi\) | ||||
−0.605570 | + | 0.795792i | \(0.707055\pi\) | |||||||
\(948\) | 3.09811e9 | 0.118105 | ||||||||
\(949\) | 2.45443e10 | 0.932222 | ||||||||
\(950\) | 8.28719e10 | 3.13599 | ||||||||
\(951\) | 2.42140e10 | 0.912925 | ||||||||
\(952\) | 3.32198e9 | 0.124787 | ||||||||
\(953\) | 2.71017e10 | 1.01431 | 0.507155 | − | 0.861855i | \(-0.330697\pi\) | ||||
0.507155 | + | 0.861855i | \(0.330697\pi\) | |||||||
\(954\) | −4.54686e9 | −0.169548 | ||||||||
\(955\) | 4.75007e10 | 1.76477 | ||||||||
\(956\) | 4.27443e10 | 1.58225 | ||||||||
\(957\) | 1.20235e9 | 0.0443443 | ||||||||
\(958\) | 1.39776e10 | 0.513632 | ||||||||
\(959\) | 1.45112e10 | 0.531299 | ||||||||
\(960\) | 2.98117e10 | 1.08752 | ||||||||
\(961\) | 5.89276e9 | 0.214184 | ||||||||
\(962\) | −6.87893e10 | −2.49120 | ||||||||
\(963\) | −1.37143e10 | −0.494859 | ||||||||
\(964\) | −2.01383e10 | −0.724026 | ||||||||
\(965\) | −5.56403e10 | −1.99317 | ||||||||
\(966\) | 8.14116e9 | 0.290580 | ||||||||
\(967\) | 2.22263e10 | 0.790450 | 0.395225 | − | 0.918584i | \(-0.370667\pi\) | ||||
0.395225 | + | 0.918584i | \(0.370667\pi\) | |||||||
\(968\) | 5.17741e9 | 0.183463 | ||||||||
\(969\) | −1.07863e10 | −0.380838 | ||||||||
\(970\) | −4.92494e10 | −1.73261 | ||||||||
\(971\) | 3.09159e10 | 1.08371 | 0.541857 | − | 0.840471i | \(-0.317721\pi\) | ||||
0.541857 | + | 0.840471i | \(0.317721\pi\) | |||||||
\(972\) | 2.07153e9 | 0.0723534 | ||||||||
\(973\) | −4.43255e10 | −1.54262 | ||||||||
\(974\) | 1.51028e10 | 0.523721 | ||||||||
\(975\) | −2.91621e10 | −1.00763 | ||||||||
\(976\) | −1.11121e10 | −0.382581 | ||||||||
\(977\) | 1.86861e9 | 0.0641044 | 0.0320522 | − | 0.999486i | \(-0.489796\pi\) | ||||
0.0320522 | + | 0.999486i | \(0.489796\pi\) | |||||||
\(978\) | −5.24411e9 | −0.179261 | ||||||||
\(979\) | 3.24524e9 | 0.110537 | ||||||||
\(980\) | −8.79274e10 | −2.98423 | ||||||||
\(981\) | −1.27371e9 | −0.0430755 | ||||||||
\(982\) | −3.45940e10 | −1.16576 | ||||||||
\(983\) | 6.94471e9 | 0.233194 | 0.116597 | − | 0.993179i | \(-0.462801\pi\) | ||||
0.116597 | + | 0.993179i | \(0.462801\pi\) | |||||||
\(984\) | −4.13692e9 | −0.138419 | ||||||||
\(985\) | −4.68369e9 | −0.156157 | ||||||||
\(986\) | 1.06176e10 | 0.352743 | ||||||||
\(987\) | 3.03669e10 | 1.00529 | ||||||||
\(988\) | 7.38949e10 | 2.43762 | ||||||||
\(989\) | 9.14074e9 | 0.300465 | ||||||||
\(990\) | −2.90194e9 | −0.0950528 | ||||||||
\(991\) | 1.61609e10 | 0.527483 | 0.263742 | − | 0.964593i | \(-0.415043\pi\) | ||||
0.263742 | + | 0.964593i | \(0.415043\pi\) | |||||||
\(992\) | 4.86123e10 | 1.58108 | ||||||||
\(993\) | 2.25418e10 | 0.730577 | ||||||||
\(994\) | −1.17039e11 | −3.77987 | ||||||||
\(995\) | −5.69040e10 | −1.83131 | ||||||||
\(996\) | 2.03664e10 | 0.653142 | ||||||||
\(997\) | 1.20763e10 | 0.385922 | 0.192961 | − | 0.981206i | \(-0.438191\pi\) | ||||
0.192961 | + | 0.981206i | \(0.438191\pi\) | |||||||
\(998\) | −5.71555e10 | −1.82012 | ||||||||
\(999\) | −7.81896e9 | −0.248125 |
(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 | 69.8.a.d.1.1 | ✓ | 8 | |
3.2 | odd | 2 | 207.8.a.e.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.8.a.d.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
207.8.a.e.1.8 | 8 | 3.2 | odd | 2 |