Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(189.798744245\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −150.711 | −1.66513 | −0.832566 | − | 0.553926i | \(-0.813129\pi\) | ||||
−0.832566 | + | 0.553926i | \(0.813129\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 14521.7 | 1.77267 | ||||||||
\(5\) | 40403.2 | 1.15641 | 0.578204 | − | 0.815893i | \(-0.303754\pi\) | ||||
0.578204 | + | 0.815893i | \(0.303754\pi\) | |||||||
\(6\) | −109868. | −0.961365 | ||||||||
\(7\) | −111720. | −0.358915 | −0.179458 | − | 0.983766i | \(-0.557434\pi\) | ||||
−0.179458 | + | 0.983766i | \(0.557434\pi\) | |||||||
\(8\) | −953949. | −1.28659 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −6.08919e6 | −1.92557 | ||||||||
\(11\) | 1.14493e7 | 1.94862 | 0.974311 | − | 0.225207i | \(-0.0723059\pi\) | ||||
0.974311 | + | 0.225207i | \(0.0723059\pi\) | |||||||
\(12\) | 1.05863e7 | 1.02345 | ||||||||
\(13\) | −2.30492e7 | −1.32441 | −0.662207 | − | 0.749321i | \(-0.730380\pi\) | ||||
−0.662207 | + | 0.749321i | \(0.730380\pi\) | |||||||
\(14\) | 1.68373e7 | 0.597641 | ||||||||
\(15\) | 2.94539e7 | 0.667652 | ||||||||
\(16\) | 2.48086e7 | 0.369678 | ||||||||
\(17\) | −3.16046e7 | −0.317565 | −0.158783 | − | 0.987314i | \(-0.550757\pi\) | ||||
−0.158783 | + | 0.987314i | \(0.550757\pi\) | |||||||
\(18\) | −8.00938e7 | −0.555044 | ||||||||
\(19\) | −1.79039e8 | −0.873071 | −0.436536 | − | 0.899687i | \(-0.643795\pi\) | ||||
−0.436536 | + | 0.899687i | \(0.643795\pi\) | |||||||
\(20\) | 5.86722e8 | 2.04992 | ||||||||
\(21\) | −8.14436e7 | −0.207220 | ||||||||
\(22\) | −1.72553e9 | −3.24471 | ||||||||
\(23\) | 2.82674e8 | 0.398158 | 0.199079 | − | 0.979983i | \(-0.436205\pi\) | ||||
0.199079 | + | 0.979983i | \(0.436205\pi\) | |||||||
\(24\) | −6.95429e8 | −0.742813 | ||||||||
\(25\) | 4.11716e8 | 0.337278 | ||||||||
\(26\) | 3.47376e9 | 2.20533 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | −1.62236e9 | −0.636237 | ||||||||
\(29\) | 4.89072e9 | 1.52681 | 0.763407 | − | 0.645918i | \(-0.223525\pi\) | ||||
0.763407 | + | 0.645918i | \(0.223525\pi\) | |||||||
\(30\) | −4.43902e9 | −1.11173 | ||||||||
\(31\) | 6.10633e9 | 1.23575 | 0.617873 | − | 0.786278i | \(-0.287995\pi\) | ||||
0.617873 | + | 0.786278i | \(0.287995\pi\) | |||||||
\(32\) | 4.07583e9 | 0.671028 | ||||||||
\(33\) | 8.34656e9 | 1.12504 | ||||||||
\(34\) | 4.76315e9 | 0.528788 | ||||||||
\(35\) | −4.51383e9 | −0.415052 | ||||||||
\(36\) | 7.71741e9 | 0.590889 | ||||||||
\(37\) | −2.53180e10 | −1.62225 | −0.811126 | − | 0.584872i | \(-0.801145\pi\) | ||||
−0.811126 | + | 0.584872i | \(0.801145\pi\) | |||||||
\(38\) | 2.69831e10 | 1.45378 | ||||||||
\(39\) | −1.68029e10 | −0.764651 | ||||||||
\(40\) | −3.85426e10 | −1.48782 | ||||||||
\(41\) | −8.94314e8 | −0.0294032 | −0.0147016 | − | 0.999892i | \(-0.504680\pi\) | ||||
−0.0147016 | + | 0.999892i | \(0.504680\pi\) | |||||||
\(42\) | 1.22744e10 | 0.345048 | ||||||||
\(43\) | −5.19863e10 | −1.25413 | −0.627067 | − | 0.778965i | \(-0.715745\pi\) | ||||
−0.627067 | + | 0.778965i | \(0.715745\pi\) | |||||||
\(44\) | 1.66263e11 | 3.45425 | ||||||||
\(45\) | 2.14719e10 | 0.385469 | ||||||||
\(46\) | −4.26020e10 | −0.662985 | ||||||||
\(47\) | −8.00138e10 | −1.08275 | −0.541376 | − | 0.840781i | \(-0.682096\pi\) | ||||
−0.541376 | + | 0.840781i | \(0.682096\pi\) | |||||||
\(48\) | 1.80855e10 | 0.213433 | ||||||||
\(49\) | −8.44078e10 | −0.871180 | ||||||||
\(50\) | −6.20499e10 | −0.561612 | ||||||||
\(51\) | −2.30398e10 | −0.183346 | ||||||||
\(52\) | −3.34713e11 | −2.34774 | ||||||||
\(53\) | −3.21867e11 | −1.99473 | −0.997363 | − | 0.0725690i | \(-0.976880\pi\) | ||||
−0.997363 | + | 0.0725690i | \(0.976880\pi\) | |||||||
\(54\) | −5.83884e10 | −0.320455 | ||||||||
\(55\) | 4.62590e11 | 2.25340 | ||||||||
\(56\) | 1.06575e11 | 0.461777 | ||||||||
\(57\) | −1.30520e11 | −0.504068 | ||||||||
\(58\) | −7.37084e11 | −2.54235 | ||||||||
\(59\) | 4.21805e10 | 0.130189 | ||||||||
\(60\) | 4.27721e11 | 1.18352 | ||||||||
\(61\) | 9.93954e10 | 0.247014 | 0.123507 | − | 0.992344i | \(-0.460586\pi\) | ||||
0.123507 | + | 0.992344i | \(0.460586\pi\) | |||||||
\(62\) | −9.20288e11 | −2.05768 | ||||||||
\(63\) | −5.93724e10 | −0.119638 | ||||||||
\(64\) | −8.17503e11 | −1.48703 | ||||||||
\(65\) | −9.31261e11 | −1.53156 | ||||||||
\(66\) | −1.25791e12 | −1.87334 | ||||||||
\(67\) | −3.29871e11 | −0.445511 | −0.222755 | − | 0.974874i | \(-0.571505\pi\) | ||||
−0.222755 | + | 0.974874i | \(0.571505\pi\) | |||||||
\(68\) | −4.58952e11 | −0.562937 | ||||||||
\(69\) | 2.06069e11 | 0.229877 | ||||||||
\(70\) | 6.80282e11 | 0.691117 | ||||||||
\(71\) | 1.94331e12 | 1.80038 | 0.900188 | − | 0.435502i | \(-0.143429\pi\) | ||||
0.900188 | + | 0.435502i | \(0.143429\pi\) | |||||||
\(72\) | −5.06968e11 | −0.428863 | ||||||||
\(73\) | −4.35977e11 | −0.337182 | −0.168591 | − | 0.985686i | \(-0.553922\pi\) | ||||
−0.168591 | + | 0.985686i | \(0.553922\pi\) | |||||||
\(74\) | 3.81569e12 | 2.70126 | ||||||||
\(75\) | 3.00141e11 | 0.194727 | ||||||||
\(76\) | −2.59995e12 | −1.54766 | ||||||||
\(77\) | −1.27911e12 | −0.699390 | ||||||||
\(78\) | 2.53237e12 | 1.27325 | ||||||||
\(79\) | −3.67817e12 | −1.70238 | −0.851189 | − | 0.524859i | \(-0.824118\pi\) | ||||
−0.851189 | + | 0.524859i | \(0.824118\pi\) | |||||||
\(80\) | 1.00235e12 | 0.427498 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 1.34783e11 | 0.0489603 | ||||||||
\(83\) | −3.03973e12 | −1.02053 | −0.510267 | − | 0.860016i | \(-0.670454\pi\) | ||||
−0.510267 | + | 0.860016i | \(0.670454\pi\) | |||||||
\(84\) | −1.18270e12 | −0.367331 | ||||||||
\(85\) | −1.27693e12 | −0.367235 | ||||||||
\(86\) | 7.83488e12 | 2.08830 | ||||||||
\(87\) | 3.56534e12 | 0.881506 | ||||||||
\(88\) | −1.09221e13 | −2.50708 | ||||||||
\(89\) | −6.66725e11 | −0.142204 | −0.0711020 | − | 0.997469i | \(-0.522652\pi\) | ||||
−0.0711020 | + | 0.997469i | \(0.522652\pi\) | |||||||
\(90\) | −3.23605e12 | −0.641857 | ||||||||
\(91\) | 2.57505e12 | 0.475353 | ||||||||
\(92\) | 4.10490e12 | 0.705801 | ||||||||
\(93\) | 4.45151e12 | 0.713458 | ||||||||
\(94\) | 1.20589e13 | 1.80293 | ||||||||
\(95\) | −7.23376e12 | −1.00963 | ||||||||
\(96\) | 2.97128e12 | 0.387418 | ||||||||
\(97\) | 1.40882e12 | 0.171727 | 0.0858636 | − | 0.996307i | \(-0.472635\pi\) | ||||
0.0858636 | + | 0.996307i | \(0.472635\pi\) | |||||||
\(98\) | 1.27211e13 | 1.45063 | ||||||||
\(99\) | 6.08464e12 | 0.649541 | ||||||||
\(100\) | 5.97880e12 | 0.597880 | ||||||||
\(101\) | −1.36581e13 | −1.28027 | −0.640136 | − | 0.768262i | \(-0.721122\pi\) | ||||
−0.640136 | + | 0.768262i | \(0.721122\pi\) | |||||||
\(102\) | 3.47234e12 | 0.305296 | ||||||||
\(103\) | −3.36418e12 | −0.277611 | −0.138806 | − | 0.990320i | \(-0.544326\pi\) | ||||
−0.138806 | + | 0.990320i | \(0.544326\pi\) | |||||||
\(104\) | 2.19878e13 | 1.70398 | ||||||||
\(105\) | −3.29058e12 | −0.239630 | ||||||||
\(106\) | 4.85088e13 | 3.32148 | ||||||||
\(107\) | −6.30309e12 | −0.406030 | −0.203015 | − | 0.979176i | \(-0.565074\pi\) | ||||
−0.203015 | + | 0.979176i | \(0.565074\pi\) | |||||||
\(108\) | 5.62599e12 | 0.341150 | ||||||||
\(109\) | −1.06086e12 | −0.0605881 | −0.0302940 | − | 0.999541i | \(-0.509644\pi\) | ||||
−0.0302940 | + | 0.999541i | \(0.509644\pi\) | |||||||
\(110\) | −6.97171e13 | −3.75221 | ||||||||
\(111\) | −1.84568e13 | −0.936607 | ||||||||
\(112\) | −2.77161e12 | −0.132683 | ||||||||
\(113\) | 4.33645e13 | 1.95941 | 0.979703 | − | 0.200456i | \(-0.0642425\pi\) | ||||
0.979703 | + | 0.200456i | \(0.0642425\pi\) | |||||||
\(114\) | 1.96707e13 | 0.839340 | ||||||||
\(115\) | 1.14209e13 | 0.460433 | ||||||||
\(116\) | 7.10215e13 | 2.70653 | ||||||||
\(117\) | −1.22493e13 | −0.441471 | ||||||||
\(118\) | −6.35705e12 | −0.216782 | ||||||||
\(119\) | 3.53086e12 | 0.113979 | ||||||||
\(120\) | −2.80976e13 | −0.858995 | ||||||||
\(121\) | 9.65644e13 | 2.79713 | ||||||||
\(122\) | −1.49799e13 | −0.411312 | ||||||||
\(123\) | −6.51955e11 | −0.0169760 | ||||||||
\(124\) | 8.86741e13 | 2.19056 | ||||||||
\(125\) | −3.26857e13 | −0.766377 | ||||||||
\(126\) | 8.94804e12 | 0.199214 | ||||||||
\(127\) | −6.17167e13 | −1.30521 | −0.652603 | − | 0.757700i | \(-0.726323\pi\) | ||||
−0.652603 | + | 0.757700i | \(0.726323\pi\) | |||||||
\(128\) | 8.98171e13 | 1.80507 | ||||||||
\(129\) | −3.78980e13 | −0.724075 | ||||||||
\(130\) | 1.40351e14 | 2.55025 | ||||||||
\(131\) | −4.55967e13 | −0.788262 | −0.394131 | − | 0.919054i | \(-0.628954\pi\) | ||||
−0.394131 | + | 0.919054i | \(0.628954\pi\) | |||||||
\(132\) | 1.21206e14 | 1.99431 | ||||||||
\(133\) | 2.00022e13 | 0.313359 | ||||||||
\(134\) | 4.97151e13 | 0.741834 | ||||||||
\(135\) | 1.56530e13 | 0.222551 | ||||||||
\(136\) | 3.01492e13 | 0.408576 | ||||||||
\(137\) | −6.74061e13 | −0.870995 | −0.435497 | − | 0.900190i | \(-0.643427\pi\) | ||||
−0.435497 | + | 0.900190i | \(0.643427\pi\) | |||||||
\(138\) | −3.10569e13 | −0.382775 | ||||||||
\(139\) | 1.49487e14 | 1.75795 | 0.878976 | − | 0.476865i | \(-0.158227\pi\) | ||||
0.878976 | + | 0.476865i | \(0.158227\pi\) | |||||||
\(140\) | −6.55483e13 | −0.735749 | ||||||||
\(141\) | −5.83301e13 | −0.625127 | ||||||||
\(142\) | −2.92878e14 | −2.99786 | ||||||||
\(143\) | −2.63898e14 | −2.58078 | ||||||||
\(144\) | 1.31843e13 | 0.123226 | ||||||||
\(145\) | 1.97601e14 | 1.76562 | ||||||||
\(146\) | 6.57063e13 | 0.561453 | ||||||||
\(147\) | −6.15333e13 | −0.502976 | ||||||||
\(148\) | −3.67660e14 | −2.87571 | ||||||||
\(149\) | −2.71532e13 | −0.203287 | −0.101644 | − | 0.994821i | \(-0.532410\pi\) | ||||
−0.101644 | + | 0.994821i | \(0.532410\pi\) | |||||||
\(150\) | −4.52344e13 | −0.324247 | ||||||||
\(151\) | −8.33497e13 | −0.572208 | −0.286104 | − | 0.958199i | \(-0.592360\pi\) | ||||
−0.286104 | + | 0.958199i | \(0.592360\pi\) | |||||||
\(152\) | 1.70794e14 | 1.12328 | ||||||||
\(153\) | −1.67960e13 | −0.105855 | ||||||||
\(154\) | 1.92776e14 | 1.16458 | ||||||||
\(155\) | 2.46715e14 | 1.42903 | ||||||||
\(156\) | −2.44006e14 | −1.35547 | ||||||||
\(157\) | −3.06635e14 | −1.63408 | −0.817042 | − | 0.576579i | \(-0.804387\pi\) | ||||
−0.817042 | + | 0.576579i | \(0.804387\pi\) | |||||||
\(158\) | 5.54339e14 | 2.83468 | ||||||||
\(159\) | −2.34641e14 | −1.15166 | ||||||||
\(160\) | 1.64676e14 | 0.775982 | ||||||||
\(161\) | −3.15802e13 | −0.142905 | ||||||||
\(162\) | −4.25651e13 | −0.185015 | ||||||||
\(163\) | 3.46201e14 | 1.44580 | 0.722902 | − | 0.690951i | \(-0.242808\pi\) | ||||
0.722902 | + | 0.690951i | \(0.242808\pi\) | |||||||
\(164\) | −1.29869e13 | −0.0521221 | ||||||||
\(165\) | 3.37228e14 | 1.30100 | ||||||||
\(166\) | 4.58120e14 | 1.69933 | ||||||||
\(167\) | 4.52597e14 | 1.61456 | 0.807280 | − | 0.590168i | \(-0.200939\pi\) | ||||
0.807280 | + | 0.590168i | \(0.200939\pi\) | |||||||
\(168\) | 7.76930e13 | 0.266607 | ||||||||
\(169\) | 2.28390e14 | 0.754074 | ||||||||
\(170\) | 1.92447e14 | 0.611494 | ||||||||
\(171\) | −9.51488e13 | −0.291024 | ||||||||
\(172\) | −7.54928e14 | −2.22316 | ||||||||
\(173\) | 2.74297e13 | 0.0777895 | 0.0388947 | − | 0.999243i | \(-0.487616\pi\) | ||||
0.0388947 | + | 0.999243i | \(0.487616\pi\) | |||||||
\(174\) | −5.37334e14 | −1.46782 | ||||||||
\(175\) | −4.59967e13 | −0.121054 | ||||||||
\(176\) | 2.84042e14 | 0.720362 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | 1.00483e14 | 0.236789 | ||||||||
\(179\) | 4.68788e14 | 1.06520 | 0.532600 | − | 0.846367i | \(-0.321215\pi\) | ||||
0.532600 | + | 0.846367i | \(0.321215\pi\) | |||||||
\(180\) | 3.11808e14 | 0.683308 | ||||||||
\(181\) | −1.71757e14 | −0.363080 | −0.181540 | − | 0.983384i | \(-0.558108\pi\) | ||||
−0.181540 | + | 0.983384i | \(0.558108\pi\) | |||||||
\(182\) | −3.88087e14 | −0.791525 | ||||||||
\(183\) | 7.24593e13 | 0.142614 | ||||||||
\(184\) | −2.69657e14 | −0.512266 | ||||||||
\(185\) | −1.02293e15 | −1.87598 | ||||||||
\(186\) | −6.70890e14 | −1.18800 | ||||||||
\(187\) | −3.61852e14 | −0.618814 | ||||||||
\(188\) | −1.16193e15 | −1.91936 | ||||||||
\(189\) | −4.32824e13 | −0.0690733 | ||||||||
\(190\) | 1.09020e15 | 1.68116 | ||||||||
\(191\) | 8.15534e14 | 1.21542 | 0.607708 | − | 0.794160i | \(-0.292089\pi\) | ||||
0.607708 | + | 0.794160i | \(0.292089\pi\) | |||||||
\(192\) | −5.95959e14 | −0.858536 | ||||||||
\(193\) | −8.65127e14 | −1.20492 | −0.602459 | − | 0.798150i | \(-0.705812\pi\) | ||||
−0.602459 | + | 0.798150i | \(0.705812\pi\) | |||||||
\(194\) | −2.12324e14 | −0.285949 | ||||||||
\(195\) | −6.78889e14 | −0.884248 | ||||||||
\(196\) | −1.22574e15 | −1.54431 | ||||||||
\(197\) | 3.32229e14 | 0.404955 | 0.202477 | − | 0.979287i | \(-0.435101\pi\) | ||||
0.202477 | + | 0.979287i | \(0.435101\pi\) | |||||||
\(198\) | −9.17020e14 | −1.08157 | ||||||||
\(199\) | 1.08216e15 | 1.23522 | 0.617611 | − | 0.786484i | \(-0.288101\pi\) | ||||
0.617611 | + | 0.786484i | \(0.288101\pi\) | |||||||
\(200\) | −3.92756e14 | −0.433938 | ||||||||
\(201\) | −2.40476e14 | −0.257216 | ||||||||
\(202\) | 2.05842e15 | 2.13182 | ||||||||
\(203\) | −5.46389e14 | −0.547997 | ||||||||
\(204\) | −3.34576e14 | −0.325012 | ||||||||
\(205\) | −3.61331e13 | −0.0340021 | ||||||||
\(206\) | 5.07018e14 | 0.462260 | ||||||||
\(207\) | 1.50225e14 | 0.132719 | ||||||||
\(208\) | −5.71819e14 | −0.489606 | ||||||||
\(209\) | −2.04988e15 | −1.70129 | ||||||||
\(210\) | 4.95925e14 | 0.399016 | ||||||||
\(211\) | −8.38734e14 | −0.654317 | −0.327159 | − | 0.944969i | \(-0.606091\pi\) | ||||
−0.327159 | + | 0.944969i | \(0.606091\pi\) | |||||||
\(212\) | −4.67405e15 | −3.53598 | ||||||||
\(213\) | 1.41667e15 | 1.03945 | ||||||||
\(214\) | 9.49942e14 | 0.676094 | ||||||||
\(215\) | −2.10041e15 | −1.45029 | ||||||||
\(216\) | −3.69579e14 | −0.247604 | ||||||||
\(217\) | −6.82196e14 | −0.443528 | ||||||||
\(218\) | 1.59883e14 | 0.100887 | ||||||||
\(219\) | −3.17827e14 | −0.194672 | ||||||||
\(220\) | 6.71758e15 | 3.99452 | ||||||||
\(221\) | 7.28461e14 | 0.420588 | ||||||||
\(222\) | 2.78164e15 | 1.55957 | ||||||||
\(223\) | 3.09576e14 | 0.168572 | 0.0842861 | − | 0.996442i | \(-0.473139\pi\) | ||||
0.0842861 | + | 0.996442i | \(0.473139\pi\) | |||||||
\(224\) | −4.55350e14 | −0.240842 | ||||||||
\(225\) | 2.18803e14 | 0.112426 | ||||||||
\(226\) | −6.53549e15 | −3.26267 | ||||||||
\(227\) | −1.37548e14 | −0.0667248 | −0.0333624 | − | 0.999443i | \(-0.510622\pi\) | ||||
−0.0333624 | + | 0.999443i | \(0.510622\pi\) | |||||||
\(228\) | −1.89536e15 | −0.893544 | ||||||||
\(229\) | 1.02345e15 | 0.468962 | 0.234481 | − | 0.972121i | \(-0.424661\pi\) | ||||
0.234481 | + | 0.972121i | \(0.424661\pi\) | |||||||
\(230\) | −1.72126e15 | −0.766681 | ||||||||
\(231\) | −9.32474e14 | −0.403793 | ||||||||
\(232\) | −4.66550e15 | −1.96438 | ||||||||
\(233\) | 2.48929e14 | 0.101921 | 0.0509603 | − | 0.998701i | \(-0.483772\pi\) | ||||
0.0509603 | + | 0.998701i | \(0.483772\pi\) | |||||||
\(234\) | 1.84610e15 | 0.735108 | ||||||||
\(235\) | −3.23281e15 | −1.25210 | ||||||||
\(236\) | 6.12532e14 | 0.230781 | ||||||||
\(237\) | −2.68139e15 | −0.982868 | ||||||||
\(238\) | −5.32137e14 | −0.189790 | ||||||||
\(239\) | 3.22328e15 | 1.11870 | 0.559348 | − | 0.828933i | \(-0.311052\pi\) | ||||
0.559348 | + | 0.828933i | \(0.311052\pi\) | |||||||
\(240\) | 7.30712e14 | 0.246816 | ||||||||
\(241\) | −3.46004e15 | −1.13755 | −0.568774 | − | 0.822494i | \(-0.692582\pi\) | ||||
−0.568774 | + | 0.822494i | \(0.692582\pi\) | |||||||
\(242\) | −1.45533e16 | −4.65759 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | 1.44339e15 | 0.437874 | ||||||||
\(245\) | −3.41034e15 | −1.00744 | ||||||||
\(246\) | 9.82565e13 | 0.0282672 | ||||||||
\(247\) | 4.12671e15 | 1.15631 | ||||||||
\(248\) | −5.82512e15 | −1.58990 | ||||||||
\(249\) | −2.21596e15 | −0.589206 | ||||||||
\(250\) | 4.92608e15 | 1.27612 | ||||||||
\(251\) | −6.28189e15 | −1.58566 | −0.792832 | − | 0.609440i | \(-0.791394\pi\) | ||||
−0.792832 | + | 0.609440i | \(0.791394\pi\) | |||||||
\(252\) | −8.62186e14 | −0.212079 | ||||||||
\(253\) | 3.23643e15 | 0.775859 | ||||||||
\(254\) | 9.30136e15 | 2.17334 | ||||||||
\(255\) | −9.30881e14 | −0.212023 | ||||||||
\(256\) | −6.83941e15 | −1.51865 | ||||||||
\(257\) | 1.92923e15 | 0.417655 | 0.208828 | − | 0.977952i | \(-0.433035\pi\) | ||||
0.208828 | + | 0.977952i | \(0.433035\pi\) | |||||||
\(258\) | 5.71163e15 | 1.20568 | ||||||||
\(259\) | 2.82851e15 | 0.582251 | ||||||||
\(260\) | −1.35235e16 | −2.71495 | ||||||||
\(261\) | 2.59913e15 | 0.508938 | ||||||||
\(262\) | 6.87191e15 | 1.31256 | ||||||||
\(263\) | −6.59134e15 | −1.22818 | −0.614089 | − | 0.789237i | \(-0.710476\pi\) | ||||
−0.614089 | + | 0.789237i | \(0.710476\pi\) | |||||||
\(264\) | −7.96219e15 | −1.44746 | ||||||||
\(265\) | −1.30045e16 | −2.30672 | ||||||||
\(266\) | −3.01454e15 | −0.521783 | ||||||||
\(267\) | −4.86043e14 | −0.0821015 | ||||||||
\(268\) | −4.79028e15 | −0.789741 | ||||||||
\(269\) | −1.00825e16 | −1.62248 | −0.811238 | − | 0.584716i | \(-0.801206\pi\) | ||||
−0.811238 | + | 0.584716i | \(0.801206\pi\) | |||||||
\(270\) | −2.35908e15 | −0.370576 | ||||||||
\(271\) | −6.94649e15 | −1.06528 | −0.532642 | − | 0.846341i | \(-0.678801\pi\) | ||||
−0.532642 | + | 0.846341i | \(0.678801\pi\) | |||||||
\(272\) | −7.84068e14 | −0.117397 | ||||||||
\(273\) | 1.87721e15 | 0.274445 | ||||||||
\(274\) | 1.01588e16 | 1.45032 | ||||||||
\(275\) | 4.71387e15 | 0.657226 | ||||||||
\(276\) | 2.99247e15 | 0.407494 | ||||||||
\(277\) | −5.61042e15 | −0.746237 | −0.373119 | − | 0.927784i | \(-0.621712\pi\) | ||||
−0.373119 | + | 0.927784i | \(0.621712\pi\) | |||||||
\(278\) | −2.25293e16 | −2.92722 | ||||||||
\(279\) | 3.24515e15 | 0.411915 | ||||||||
\(280\) | 4.30596e15 | 0.534002 | ||||||||
\(281\) | −2.01691e15 | −0.244397 | −0.122199 | − | 0.992506i | \(-0.538994\pi\) | ||||
−0.122199 | + | 0.992506i | \(0.538994\pi\) | |||||||
\(282\) | 8.79096e15 | 1.04092 | ||||||||
\(283\) | 9.97297e15 | 1.15402 | 0.577009 | − | 0.816738i | \(-0.304220\pi\) | ||||
0.577009 | + | 0.816738i | \(0.304220\pi\) | |||||||
\(284\) | 2.82201e16 | 3.19146 | ||||||||
\(285\) | −5.27341e15 | −0.582908 | ||||||||
\(286\) | 3.97722e16 | 4.29734 | ||||||||
\(287\) | 9.99124e13 | 0.0105533 | ||||||||
\(288\) | 2.16606e15 | 0.223676 | ||||||||
\(289\) | −8.90573e15 | −0.899152 | ||||||||
\(290\) | −2.97805e16 | −2.93999 | ||||||||
\(291\) | 1.02703e15 | 0.0991468 | ||||||||
\(292\) | −6.33111e15 | −0.597712 | ||||||||
\(293\) | −5.67845e15 | −0.524312 | −0.262156 | − | 0.965025i | \(-0.584434\pi\) | ||||
−0.262156 | + | 0.965025i | \(0.584434\pi\) | |||||||
\(294\) | 9.27371e15 | 0.837521 | ||||||||
\(295\) | 1.70423e15 | 0.150551 | ||||||||
\(296\) | 2.41521e16 | 2.08717 | ||||||||
\(297\) | 4.43570e15 | 0.375012 | ||||||||
\(298\) | 4.09227e15 | 0.338500 | ||||||||
\(299\) | −6.51541e15 | −0.527326 | ||||||||
\(300\) | 4.35855e15 | 0.345186 | ||||||||
\(301\) | 5.80789e15 | 0.450128 | ||||||||
\(302\) | 1.25617e16 | 0.952802 | ||||||||
\(303\) | −9.95677e15 | −0.739165 | ||||||||
\(304\) | −4.44172e15 | −0.322755 | ||||||||
\(305\) | 4.01589e15 | 0.285649 | ||||||||
\(306\) | 2.53133e15 | 0.176263 | ||||||||
\(307\) | −3.03492e15 | −0.206894 | −0.103447 | − | 0.994635i | \(-0.532987\pi\) | ||||
−0.103447 | + | 0.994635i | \(0.532987\pi\) | |||||||
\(308\) | −1.85749e16 | −1.23978 | ||||||||
\(309\) | −2.45249e15 | −0.160279 | ||||||||
\(310\) | −3.71826e16 | −2.37952 | ||||||||
\(311\) | 2.74950e16 | 1.72310 | 0.861552 | − | 0.507670i | \(-0.169493\pi\) | ||||
0.861552 | + | 0.507670i | \(0.169493\pi\) | |||||||
\(312\) | 1.60291e16 | 0.983793 | ||||||||
\(313\) | −2.22356e16 | −1.33663 | −0.668315 | − | 0.743879i | \(-0.732984\pi\) | ||||
−0.668315 | + | 0.743879i | \(0.732984\pi\) | |||||||
\(314\) | 4.62132e16 | 2.72097 | ||||||||
\(315\) | −2.39883e15 | −0.138351 | ||||||||
\(316\) | −5.34132e16 | −3.01775 | ||||||||
\(317\) | 8.61319e15 | 0.476737 | 0.238368 | − | 0.971175i | \(-0.423387\pi\) | ||||
0.238368 | + | 0.971175i | \(0.423387\pi\) | |||||||
\(318\) | 3.53629e16 | 1.91766 | ||||||||
\(319\) | 5.59955e16 | 2.97518 | ||||||||
\(320\) | −3.30297e16 | −1.71961 | ||||||||
\(321\) | −4.59495e15 | −0.234422 | ||||||||
\(322\) | 4.75948e15 | 0.237956 | ||||||||
\(323\) | 5.65847e15 | 0.277257 | ||||||||
\(324\) | 4.10135e15 | 0.196963 | ||||||||
\(325\) | −9.48972e15 | −0.446695 | ||||||||
\(326\) | −5.21762e16 | −2.40745 | ||||||||
\(327\) | −7.73369e14 | −0.0349805 | ||||||||
\(328\) | 8.53130e14 | 0.0378299 | ||||||||
\(329\) | 8.93911e15 | 0.388616 | ||||||||
\(330\) | −5.08238e16 | −2.16634 | ||||||||
\(331\) | 1.78462e16 | 0.745870 | 0.372935 | − | 0.927858i | \(-0.378351\pi\) | ||||
0.372935 | + | 0.927858i | \(0.378351\pi\) | |||||||
\(332\) | −4.41420e16 | −1.80907 | ||||||||
\(333\) | −1.34550e16 | −0.540750 | ||||||||
\(334\) | −6.82111e16 | −2.68846 | ||||||||
\(335\) | −1.33278e16 | −0.515192 | ||||||||
\(336\) | −2.02050e15 | −0.0766045 | ||||||||
\(337\) | −4.78621e16 | −1.77991 | −0.889953 | − | 0.456052i | \(-0.849263\pi\) | ||||
−0.889953 | + | 0.456052i | \(0.849263\pi\) | |||||||
\(338\) | −3.44208e16 | −1.25563 | ||||||||
\(339\) | 3.16127e16 | 1.13126 | ||||||||
\(340\) | −1.85431e16 | −0.650984 | ||||||||
\(341\) | 6.99133e16 | 2.40800 | ||||||||
\(342\) | 1.43399e16 | 0.484593 | ||||||||
\(343\) | 2.02544e16 | 0.671595 | ||||||||
\(344\) | 4.95923e16 | 1.61356 | ||||||||
\(345\) | 8.32587e15 | 0.265831 | ||||||||
\(346\) | −4.13394e15 | −0.129530 | ||||||||
\(347\) | 3.10821e16 | 0.955805 | 0.477903 | − | 0.878413i | \(-0.341397\pi\) | ||||
0.477903 | + | 0.878413i | \(0.341397\pi\) | |||||||
\(348\) | 5.17747e16 | 1.56262 | ||||||||
\(349\) | 3.35603e16 | 0.994170 | 0.497085 | − | 0.867702i | \(-0.334404\pi\) | ||||
0.497085 | + | 0.867702i | \(0.334404\pi\) | |||||||
\(350\) | 6.93219e15 | 0.201571 | ||||||||
\(351\) | −8.92973e15 | −0.254884 | ||||||||
\(352\) | 4.66655e16 | 1.30758 | ||||||||
\(353\) | 2.96364e16 | 0.815247 | 0.407624 | − | 0.913150i | \(-0.366358\pi\) | ||||
0.407624 | + | 0.913150i | \(0.366358\pi\) | |||||||
\(354\) | −4.63429e15 | −0.125159 | ||||||||
\(355\) | 7.85160e16 | 2.08197 | ||||||||
\(356\) | −9.68197e15 | −0.252080 | ||||||||
\(357\) | 2.57399e15 | 0.0658058 | ||||||||
\(358\) | −7.06512e16 | −1.77370 | ||||||||
\(359\) | −4.54894e16 | −1.12149 | −0.560747 | − | 0.827987i | \(-0.689486\pi\) | ||||
−0.560747 | + | 0.827987i | \(0.689486\pi\) | |||||||
\(360\) | −2.04831e16 | −0.495941 | ||||||||
\(361\) | −9.99796e15 | −0.237747 | ||||||||
\(362\) | 2.58855e16 | 0.604577 | ||||||||
\(363\) | 7.03955e16 | 1.61492 | ||||||||
\(364\) | 3.73940e16 | 0.842641 | ||||||||
\(365\) | −1.76149e16 | −0.389920 | ||||||||
\(366\) | −1.09204e16 | −0.237471 | ||||||||
\(367\) | 4.75684e16 | 1.01622 | 0.508111 | − | 0.861291i | \(-0.330344\pi\) | ||||
0.508111 | + | 0.861291i | \(0.330344\pi\) | |||||||
\(368\) | 7.01276e15 | 0.147190 | ||||||||
\(369\) | −4.75275e14 | −0.00980107 | ||||||||
\(370\) | 1.54166e17 | 3.12376 | ||||||||
\(371\) | 3.59588e16 | 0.715938 | ||||||||
\(372\) | 6.46434e16 | 1.26472 | ||||||||
\(373\) | 6.36227e16 | 1.22322 | 0.611610 | − | 0.791160i | \(-0.290522\pi\) | ||||
0.611610 | + | 0.791160i | \(0.290522\pi\) | |||||||
\(374\) | 5.45349e16 | 1.03041 | ||||||||
\(375\) | −2.38279e16 | −0.442468 | ||||||||
\(376\) | 7.63291e16 | 1.39306 | ||||||||
\(377\) | −1.12727e17 | −2.02213 | ||||||||
\(378\) | 6.52312e15 | 0.115016 | ||||||||
\(379\) | −5.95563e16 | −1.03222 | −0.516110 | − | 0.856522i | \(-0.672621\pi\) | ||||
−0.516110 | + | 0.856522i | \(0.672621\pi\) | |||||||
\(380\) | −1.05046e17 | −1.78973 | ||||||||
\(381\) | −4.49915e16 | −0.753560 | ||||||||
\(382\) | −1.22910e17 | −2.02383 | ||||||||
\(383\) | 4.03567e16 | 0.653317 | 0.326659 | − | 0.945142i | \(-0.394077\pi\) | ||||
0.326659 | + | 0.945142i | \(0.394077\pi\) | |||||||
\(384\) | 6.54767e16 | 1.04216 | ||||||||
\(385\) | −5.16803e16 | −0.808780 | ||||||||
\(386\) | 1.30384e17 | 2.00635 | ||||||||
\(387\) | −2.76276e16 | −0.418045 | ||||||||
\(388\) | 2.04584e16 | 0.304415 | ||||||||
\(389\) | −1.12817e17 | −1.65082 | −0.825412 | − | 0.564531i | \(-0.809057\pi\) | ||||
−0.825412 | + | 0.564531i | \(0.809057\pi\) | |||||||
\(390\) | 1.02316e17 | 1.47239 | ||||||||
\(391\) | −8.93382e15 | −0.126441 | ||||||||
\(392\) | 8.05207e16 | 1.12085 | ||||||||
\(393\) | −3.32400e16 | −0.455103 | ||||||||
\(394\) | −5.00704e16 | −0.674304 | ||||||||
\(395\) | −1.48610e17 | −1.96864 | ||||||||
\(396\) | 8.83592e16 | 1.15142 | ||||||||
\(397\) | −6.92426e16 | −0.887637 | −0.443818 | − | 0.896117i | \(-0.646376\pi\) | ||||
−0.443818 | + | 0.896117i | \(0.646376\pi\) | |||||||
\(398\) | −1.63092e17 | −2.05681 | ||||||||
\(399\) | 1.45816e16 | 0.180918 | ||||||||
\(400\) | 1.02141e16 | 0.124684 | ||||||||
\(401\) | 6.44868e16 | 0.774519 | 0.387260 | − | 0.921971i | \(-0.373422\pi\) | ||||
0.387260 | + | 0.921971i | \(0.373422\pi\) | |||||||
\(402\) | 3.62423e16 | 0.428298 | ||||||||
\(403\) | −1.40746e17 | −1.63664 | ||||||||
\(404\) | −1.98339e17 | −2.26949 | ||||||||
\(405\) | 1.14111e16 | 0.128490 | ||||||||
\(406\) | 8.23467e16 | 0.912487 | ||||||||
\(407\) | −2.89874e17 | −3.16115 | ||||||||
\(408\) | 2.19788e16 | 0.235892 | ||||||||
\(409\) | −1.89160e16 | −0.199815 | −0.0999077 | − | 0.994997i | \(-0.531855\pi\) | ||||
−0.0999077 | + | 0.994997i | \(0.531855\pi\) | |||||||
\(410\) | 5.44565e15 | 0.0566180 | ||||||||
\(411\) | −4.91390e16 | −0.502869 | ||||||||
\(412\) | −4.88535e16 | −0.492112 | ||||||||
\(413\) | −4.71239e15 | −0.0467268 | ||||||||
\(414\) | −2.26404e16 | −0.220995 | ||||||||
\(415\) | −1.22815e17 | −1.18015 | ||||||||
\(416\) | −9.39445e16 | −0.888720 | ||||||||
\(417\) | 1.08976e17 | 1.01495 | ||||||||
\(418\) | 3.08938e17 | 2.83287 | ||||||||
\(419\) | 3.70729e16 | 0.334708 | 0.167354 | − | 0.985897i | \(-0.446478\pi\) | ||||
0.167354 | + | 0.985897i | \(0.446478\pi\) | |||||||
\(420\) | −4.77847e16 | −0.424785 | ||||||||
\(421\) | −1.28568e16 | −0.112538 | −0.0562689 | − | 0.998416i | \(-0.517920\pi\) | ||||
−0.0562689 | + | 0.998416i | \(0.517920\pi\) | |||||||
\(422\) | 1.26406e17 | 1.08953 | ||||||||
\(423\) | −4.25226e16 | −0.360917 | ||||||||
\(424\) | 3.07045e17 | 2.56640 | ||||||||
\(425\) | −1.30121e16 | −0.107108 | ||||||||
\(426\) | −2.13508e17 | −1.73082 | ||||||||
\(427\) | −1.11044e16 | −0.0886573 | ||||||||
\(428\) | −9.15314e16 | −0.719756 | ||||||||
\(429\) | −1.92381e17 | −1.49002 | ||||||||
\(430\) | 3.16554e17 | 2.41492 | ||||||||
\(431\) | −1.54117e17 | −1.15810 | −0.579052 | − | 0.815291i | \(-0.696577\pi\) | ||||
−0.579052 | + | 0.815291i | \(0.696577\pi\) | |||||||
\(432\) | 9.61137e15 | 0.0711445 | ||||||||
\(433\) | −1.90601e17 | −1.38981 | −0.694903 | − | 0.719104i | \(-0.744553\pi\) | ||||
−0.694903 | + | 0.719104i | \(0.744553\pi\) | |||||||
\(434\) | 1.02814e17 | 0.738533 | ||||||||
\(435\) | 1.44051e17 | 1.01938 | ||||||||
\(436\) | −1.54055e16 | −0.107402 | ||||||||
\(437\) | −5.06098e16 | −0.347620 | ||||||||
\(438\) | 4.78999e16 | 0.324155 | ||||||||
\(439\) | −9.76834e16 | −0.651331 | −0.325665 | − | 0.945485i | \(-0.605588\pi\) | ||||
−0.325665 | + | 0.945485i | \(0.605588\pi\) | |||||||
\(440\) | −4.41287e17 | −2.89920 | ||||||||
\(441\) | −4.48577e16 | −0.290393 | ||||||||
\(442\) | −1.09787e17 | −0.700334 | ||||||||
\(443\) | 9.51248e16 | 0.597956 | 0.298978 | − | 0.954260i | \(-0.403354\pi\) | ||||
0.298978 | + | 0.954260i | \(0.403354\pi\) | |||||||
\(444\) | −2.68024e17 | −1.66029 | ||||||||
\(445\) | −2.69378e16 | −0.164446 | ||||||||
\(446\) | −4.66564e16 | −0.280695 | ||||||||
\(447\) | −1.97947e16 | −0.117368 | ||||||||
\(448\) | 9.13310e16 | 0.533717 | ||||||||
\(449\) | −3.18756e17 | −1.83593 | −0.917967 | − | 0.396656i | \(-0.870171\pi\) | ||||
−0.917967 | + | 0.396656i | \(0.870171\pi\) | |||||||
\(450\) | −3.29759e16 | −0.187204 | ||||||||
\(451\) | −1.02393e16 | −0.0572958 | ||||||||
\(452\) | 6.29725e17 | 3.47337 | ||||||||
\(453\) | −6.07620e16 | −0.330365 | ||||||||
\(454\) | 2.07300e16 | 0.111106 | ||||||||
\(455\) | 1.04040e17 | 0.549701 | ||||||||
\(456\) | 1.24509e17 | 0.648529 | ||||||||
\(457\) | 2.06050e17 | 1.05808 | 0.529039 | − | 0.848598i | \(-0.322553\pi\) | ||||
0.529039 | + | 0.848598i | \(0.322553\pi\) | |||||||
\(458\) | −1.54245e17 | −0.780884 | ||||||||
\(459\) | −1.22443e16 | −0.0611154 | ||||||||
\(460\) | 1.65851e17 | 0.816193 | ||||||||
\(461\) | 7.19050e16 | 0.348901 | 0.174451 | − | 0.984666i | \(-0.444185\pi\) | ||||
0.174451 | + | 0.984666i | \(0.444185\pi\) | |||||||
\(462\) | 1.40534e17 | 0.672369 | ||||||||
\(463\) | 3.53434e17 | 1.66737 | 0.833685 | − | 0.552240i | \(-0.186227\pi\) | ||||
0.833685 | + | 0.552240i | \(0.186227\pi\) | |||||||
\(464\) | 1.21332e17 | 0.564429 | ||||||||
\(465\) | 1.79855e17 | 0.825048 | ||||||||
\(466\) | −3.75162e16 | −0.169711 | ||||||||
\(467\) | 2.16580e17 | 0.966181 | 0.483091 | − | 0.875570i | \(-0.339514\pi\) | ||||
0.483091 | + | 0.875570i | \(0.339514\pi\) | |||||||
\(468\) | −1.77880e17 | −0.782581 | ||||||||
\(469\) | 3.68531e16 | 0.159901 | ||||||||
\(470\) | 4.87219e17 | 2.08492 | ||||||||
\(471\) | −2.23537e17 | −0.943438 | ||||||||
\(472\) | −4.02381e16 | −0.167500 | ||||||||
\(473\) | −5.95208e17 | −2.44383 | ||||||||
\(474\) | 4.04113e17 | 1.63661 | ||||||||
\(475\) | −7.37133e16 | −0.294467 | ||||||||
\(476\) | 5.12739e16 | 0.202047 | ||||||||
\(477\) | −1.71053e17 | −0.664909 | ||||||||
\(478\) | −4.85783e17 | −1.86278 | ||||||||
\(479\) | 2.37808e17 | 0.899592 | 0.449796 | − | 0.893131i | \(-0.351497\pi\) | ||||
0.449796 | + | 0.893131i | \(0.351497\pi\) | |||||||
\(480\) | 1.20049e17 | 0.448013 | ||||||||
\(481\) | 5.83559e17 | 2.14853 | ||||||||
\(482\) | 5.21464e17 | 1.89417 | ||||||||
\(483\) | −2.30220e16 | −0.0825062 | ||||||||
\(484\) | 1.40228e18 | 4.95837 | ||||||||
\(485\) | 5.69209e16 | 0.198587 | ||||||||
\(486\) | −3.10300e16 | −0.106818 | ||||||||
\(487\) | −1.27813e17 | −0.434148 | −0.217074 | − | 0.976155i | \(-0.569651\pi\) | ||||
−0.217074 | + | 0.976155i | \(0.569651\pi\) | |||||||
\(488\) | −9.48182e16 | −0.317806 | ||||||||
\(489\) | 2.52381e17 | 0.834735 | ||||||||
\(490\) | 5.13975e17 | 1.67752 | ||||||||
\(491\) | 1.02449e17 | 0.329973 | 0.164986 | − | 0.986296i | \(-0.447242\pi\) | ||||
0.164986 | + | 0.986296i | \(0.447242\pi\) | |||||||
\(492\) | −9.46748e15 | −0.0300927 | ||||||||
\(493\) | −1.54570e17 | −0.484863 | ||||||||
\(494\) | −6.21939e17 | −1.92541 | ||||||||
\(495\) | 2.45839e17 | 0.751133 | ||||||||
\(496\) | 1.51490e17 | 0.456827 | ||||||||
\(497\) | −2.17106e17 | −0.646182 | ||||||||
\(498\) | 3.33969e17 | 0.981106 | ||||||||
\(499\) | 7.06516e15 | 0.0204865 | 0.0102433 | − | 0.999948i | \(-0.496739\pi\) | ||||
0.0102433 | + | 0.999948i | \(0.496739\pi\) | |||||||
\(500\) | −4.74651e17 | −1.35853 | ||||||||
\(501\) | 3.29943e17 | 0.932167 | ||||||||
\(502\) | 9.46747e17 | 2.64034 | ||||||||
\(503\) | −5.30401e17 | −1.46020 | −0.730100 | − | 0.683341i | \(-0.760526\pi\) | ||||
−0.730100 | + | 0.683341i | \(0.760526\pi\) | |||||||
\(504\) | 5.66382e16 | 0.153926 | ||||||||
\(505\) | −5.51832e17 | −1.48051 | ||||||||
\(506\) | −4.87764e17 | −1.29191 | ||||||||
\(507\) | 1.66496e17 | 0.435365 | ||||||||
\(508\) | −8.96230e17 | −2.31369 | ||||||||
\(509\) | 2.76867e17 | 0.705678 | 0.352839 | − | 0.935684i | \(-0.385216\pi\) | ||||
0.352839 | + | 0.935684i | \(0.385216\pi\) | |||||||
\(510\) | 1.40294e17 | 0.353046 | ||||||||
\(511\) | 4.87071e16 | 0.121020 | ||||||||
\(512\) | 2.94989e17 | 0.723688 | ||||||||
\(513\) | −6.93634e16 | −0.168023 | ||||||||
\(514\) | −2.90755e17 | −0.695451 | ||||||||
\(515\) | −1.35924e17 | −0.321032 | ||||||||
\(516\) | −5.50343e17 | −1.28354 | ||||||||
\(517\) | −9.16104e17 | −2.10987 | ||||||||
\(518\) | −4.26287e17 | −0.969524 | ||||||||
\(519\) | 1.99962e16 | 0.0449118 | ||||||||
\(520\) | 8.88376e17 | 1.97049 | ||||||||
\(521\) | 8.57153e17 | 1.87764 | 0.938822 | − | 0.344403i | \(-0.111919\pi\) | ||||
0.938822 | + | 0.344403i | \(0.111919\pi\) | |||||||
\(522\) | −3.91716e17 | −0.847449 | ||||||||
\(523\) | −4.76424e17 | −1.01796 | −0.508982 | − | 0.860777i | \(-0.669978\pi\) | ||||
−0.508982 | + | 0.860777i | \(0.669978\pi\) | |||||||
\(524\) | −6.62141e17 | −1.39732 | ||||||||
\(525\) | −3.35316e16 | −0.0698906 | ||||||||
\(526\) | 9.93384e17 | 2.04508 | ||||||||
\(527\) | −1.92988e17 | −0.392430 | ||||||||
\(528\) | 2.07067e17 | 0.415901 | ||||||||
\(529\) | −4.24132e17 | −0.841470 | ||||||||
\(530\) | 1.95991e18 | 3.84099 | ||||||||
\(531\) | 2.24165e16 | 0.0433963 | ||||||||
\(532\) | 2.90465e17 | 0.555480 | ||||||||
\(533\) | 2.06132e16 | 0.0389421 | ||||||||
\(534\) | 7.32518e16 | 0.136710 | ||||||||
\(535\) | −2.54665e17 | −0.469537 | ||||||||
\(536\) | 3.14680e17 | 0.573190 | ||||||||
\(537\) | 3.41746e17 | 0.614994 | ||||||||
\(538\) | 1.51954e18 | 2.70164 | ||||||||
\(539\) | −9.66412e17 | −1.69760 | ||||||||
\(540\) | 2.27308e17 | 0.394508 | ||||||||
\(541\) | 1.29060e17 | 0.221314 | 0.110657 | − | 0.993859i | \(-0.464704\pi\) | ||||
0.110657 | + | 0.993859i | \(0.464704\pi\) | |||||||
\(542\) | 1.04691e18 | 1.77384 | ||||||||
\(543\) | −1.25211e17 | −0.209624 | ||||||||
\(544\) | −1.28815e17 | −0.213095 | ||||||||
\(545\) | −4.28623e16 | −0.0700645 | ||||||||
\(546\) | −2.82915e17 | −0.456987 | ||||||||
\(547\) | 8.79234e16 | 0.140342 | 0.0701708 | − | 0.997535i | \(-0.477646\pi\) | ||||
0.0701708 | + | 0.997535i | \(0.477646\pi\) | |||||||
\(548\) | −9.78849e17 | −1.54398 | ||||||||
\(549\) | 5.28228e16 | 0.0823382 | ||||||||
\(550\) | −7.10430e17 | −1.09437 | ||||||||
\(551\) | −8.75631e17 | −1.33302 | ||||||||
\(552\) | −1.96580e17 | −0.295757 | ||||||||
\(553\) | 4.10924e17 | 0.611009 | ||||||||
\(554\) | 8.45549e17 | 1.24258 | ||||||||
\(555\) | −7.45715e17 | −1.08310 | ||||||||
\(556\) | 2.17080e18 | 3.11626 | ||||||||
\(557\) | 4.44967e17 | 0.631348 | 0.315674 | − | 0.948868i | \(-0.397769\pi\) | ||||
0.315674 | + | 0.948868i | \(0.397769\pi\) | |||||||
\(558\) | −4.89079e17 | −0.685893 | ||||||||
\(559\) | 1.19824e18 | 1.66099 | ||||||||
\(560\) | −1.11982e17 | −0.153435 | ||||||||
\(561\) | −2.63790e17 | −0.357273 | ||||||||
\(562\) | 3.03970e17 | 0.406954 | ||||||||
\(563\) | −6.06771e16 | −0.0803008 | −0.0401504 | − | 0.999194i | \(-0.512784\pi\) | ||||
−0.0401504 | + | 0.999194i | \(0.512784\pi\) | |||||||
\(564\) | −8.47050e17 | −1.10814 | ||||||||
\(565\) | 1.75206e18 | 2.26587 | ||||||||
\(566\) | −1.50303e18 | −1.92159 | ||||||||
\(567\) | −3.15529e16 | −0.0398795 | ||||||||
\(568\) | −1.85382e18 | −2.31635 | ||||||||
\(569\) | −8.63262e17 | −1.06638 | −0.533191 | − | 0.845995i | \(-0.679007\pi\) | ||||
−0.533191 | + | 0.845995i | \(0.679007\pi\) | |||||||
\(570\) | 7.94758e17 | 0.970618 | ||||||||
\(571\) | −6.10409e17 | −0.737032 | −0.368516 | − | 0.929621i | \(-0.620134\pi\) | ||||
−0.368516 | + | 0.929621i | \(0.620134\pi\) | |||||||
\(572\) | −3.83224e18 | −4.57486 | ||||||||
\(573\) | 5.94524e17 | 0.701721 | ||||||||
\(574\) | −1.50578e16 | −0.0175726 | ||||||||
\(575\) | 1.16381e17 | 0.134290 | ||||||||
\(576\) | −4.34454e17 | −0.495676 | ||||||||
\(577\) | 1.33145e18 | 1.50204 | 0.751020 | − | 0.660280i | \(-0.229562\pi\) | ||||
0.751020 | + | 0.660280i | \(0.229562\pi\) | |||||||
\(578\) | 1.34219e18 | 1.49721 | ||||||||
\(579\) | −6.30678e17 | −0.695660 | ||||||||
\(580\) | 2.86950e18 | 3.12985 | ||||||||
\(581\) | 3.39598e17 | 0.366285 | ||||||||
\(582\) | −1.54784e17 | −0.165093 | ||||||||
\(583\) | −3.68516e18 | −3.88697 | ||||||||
\(584\) | 4.15900e17 | 0.433816 | ||||||||
\(585\) | −4.94910e17 | −0.510521 | ||||||||
\(586\) | 8.55802e17 | 0.873049 | ||||||||
\(587\) | −2.90660e14 | −0.000293250 0 | −0.000146625 | − | 1.00000i | \(-0.500047\pi\) | ||||
−0.000146625 | 1.00000i | \(0.500047\pi\) | ||||||||
\(588\) | −8.93566e17 | −0.891608 | ||||||||
\(589\) | −1.09327e18 | −1.07889 | ||||||||
\(590\) | −2.56845e17 | −0.250688 | ||||||||
\(591\) | 2.42195e17 | 0.233801 | ||||||||
\(592\) | −6.28105e17 | −0.599710 | ||||||||
\(593\) | −1.26913e18 | −1.19853 | −0.599267 | − | 0.800549i | \(-0.704541\pi\) | ||||
−0.599267 | + | 0.800549i | \(0.704541\pi\) | |||||||
\(594\) | −6.68508e17 | −0.624445 | ||||||||
\(595\) | 1.42658e17 | 0.131806 | ||||||||
\(596\) | −3.94310e17 | −0.360360 | ||||||||
\(597\) | 7.88892e17 | 0.713156 | ||||||||
\(598\) | 9.81941e17 | 0.878068 | ||||||||
\(599\) | −6.45916e17 | −0.571349 | −0.285674 | − | 0.958327i | \(-0.592218\pi\) | ||||
−0.285674 | + | 0.958327i | \(0.592218\pi\) | |||||||
\(600\) | −2.86319e17 | −0.250534 | ||||||||
\(601\) | 4.89938e17 | 0.424089 | 0.212045 | − | 0.977260i | \(-0.431988\pi\) | ||||
0.212045 | + | 0.977260i | \(0.431988\pi\) | |||||||
\(602\) | −8.75310e17 | −0.749522 | ||||||||
\(603\) | −1.75307e17 | −0.148504 | ||||||||
\(604\) | −1.21038e18 | −1.01433 | ||||||||
\(605\) | 3.90151e18 | 3.23462 | ||||||||
\(606\) | 1.50059e18 | 1.23081 | ||||||||
\(607\) | −8.34286e17 | −0.676999 | −0.338500 | − | 0.940966i | \(-0.609919\pi\) | ||||
−0.338500 | + | 0.940966i | \(0.609919\pi\) | |||||||
\(608\) | −7.29733e17 | −0.585855 | ||||||||
\(609\) | −3.98318e17 | −0.316386 | ||||||||
\(610\) | −6.05238e17 | −0.475644 | ||||||||
\(611\) | 1.84425e18 | 1.43401 | ||||||||
\(612\) | −2.43906e17 | −0.187646 | ||||||||
\(613\) | 1.38696e18 | 1.05577 | 0.527887 | − | 0.849315i | \(-0.322985\pi\) | ||||
0.527887 | + | 0.849315i | \(0.322985\pi\) | |||||||
\(614\) | 4.57395e17 | 0.344506 | ||||||||
\(615\) | −2.63411e16 | −0.0196311 | ||||||||
\(616\) | 1.22021e18 | 0.899829 | ||||||||
\(617\) | 1.97534e18 | 1.44141 | 0.720707 | − | 0.693240i | \(-0.243818\pi\) | ||||
0.720707 | + | 0.693240i | \(0.243818\pi\) | |||||||
\(618\) | 3.69616e17 | 0.266886 | ||||||||
\(619\) | −1.11041e18 | −0.793405 | −0.396702 | − | 0.917947i | \(-0.629846\pi\) | ||||
−0.396702 | + | 0.917947i | \(0.629846\pi\) | |||||||
\(620\) | 3.58272e18 | 2.53318 | ||||||||
\(621\) | 1.09514e17 | 0.0766255 | ||||||||
\(622\) | −4.14379e18 | −2.86919 | ||||||||
\(623\) | 7.44863e16 | 0.0510392 | ||||||||
\(624\) | −4.16856e17 | −0.282674 | ||||||||
\(625\) | −1.82319e18 | −1.22352 | ||||||||
\(626\) | 3.35114e18 | 2.22566 | ||||||||
\(627\) | −1.49436e18 | −0.982238 | ||||||||
\(628\) | −4.45286e18 | −2.89668 | ||||||||
\(629\) | 8.00166e17 | 0.515170 | ||||||||
\(630\) | 3.61530e17 | 0.230372 | ||||||||
\(631\) | −2.78757e18 | −1.75806 | −0.879032 | − | 0.476762i | \(-0.841810\pi\) | ||||
−0.879032 | + | 0.476762i | \(0.841810\pi\) | |||||||
\(632\) | 3.50879e18 | 2.19026 | ||||||||
\(633\) | −6.11437e17 | −0.377770 | ||||||||
\(634\) | −1.29810e18 | −0.793830 | ||||||||
\(635\) | −2.49355e18 | −1.50935 | ||||||||
\(636\) | −3.40738e18 | −2.04150 | ||||||||
\(637\) | 1.94553e18 | 1.15380 | ||||||||
\(638\) | −8.43911e18 | −4.95407 | ||||||||
\(639\) | 1.03276e18 | 0.600125 | ||||||||
\(640\) | 3.62890e18 | 2.08740 | ||||||||
\(641\) | −1.24946e18 | −0.711454 | −0.355727 | − | 0.934590i | \(-0.615767\pi\) | ||||
−0.355727 | + | 0.934590i | \(0.615767\pi\) | |||||||
\(642\) | 6.92507e17 | 0.390343 | ||||||||
\(643\) | −1.24735e18 | −0.696011 | −0.348005 | − | 0.937493i | \(-0.613141\pi\) | ||||
−0.348005 | + | 0.937493i | \(0.613141\pi\) | |||||||
\(644\) | −4.58598e17 | −0.253323 | ||||||||
\(645\) | −1.53120e18 | −0.837325 | ||||||||
\(646\) | −8.52791e17 | −0.461669 | ||||||||
\(647\) | 1.84305e17 | 0.0987778 | 0.0493889 | − | 0.998780i | \(-0.484273\pi\) | ||||
0.0493889 | + | 0.998780i | \(0.484273\pi\) | |||||||
\(648\) | −2.69423e17 | −0.142954 | ||||||||
\(649\) | 4.82939e17 | 0.253689 | ||||||||
\(650\) | 1.43020e18 | 0.743807 | ||||||||
\(651\) | −4.97321e17 | −0.256071 | ||||||||
\(652\) | 5.02742e18 | 2.56293 | ||||||||
\(653\) | −2.71262e18 | −1.36916 | −0.684578 | − | 0.728940i | \(-0.740014\pi\) | ||||
−0.684578 | + | 0.728940i | \(0.740014\pi\) | |||||||
\(654\) | 1.16555e17 | 0.0582472 | ||||||||
\(655\) | −1.84225e18 | −0.911551 | ||||||||
\(656\) | −2.21867e16 | −0.0108697 | ||||||||
\(657\) | −2.31696e17 | −0.112394 | ||||||||
\(658\) | −1.34722e18 | −0.647097 | ||||||||
\(659\) | 2.55377e18 | 1.21458 | 0.607290 | − | 0.794480i | \(-0.292257\pi\) | ||||
0.607290 | + | 0.794480i | \(0.292257\pi\) | |||||||
\(660\) | 4.89711e18 | 2.30624 | ||||||||
\(661\) | −1.99227e18 | −0.929051 | −0.464526 | − | 0.885560i | \(-0.653775\pi\) | ||||
−0.464526 | + | 0.885560i | \(0.653775\pi\) | |||||||
\(662\) | −2.68961e18 | −1.24197 | ||||||||
\(663\) | 5.31048e17 | 0.242827 | ||||||||
\(664\) | 2.89975e18 | 1.31301 | ||||||||
\(665\) | 8.08152e17 | 0.362370 | ||||||||
\(666\) | 2.02781e18 | 0.900421 | ||||||||
\(667\) | 1.38248e18 | 0.607913 | ||||||||
\(668\) | 6.57246e18 | 2.86208 | ||||||||
\(669\) | 2.25681e17 | 0.0973252 | ||||||||
\(670\) | 2.00865e18 | 0.857862 | ||||||||
\(671\) | 1.13801e18 | 0.481338 | ||||||||
\(672\) | −3.31950e17 | −0.139050 | ||||||||
\(673\) | −1.71370e18 | −0.710945 | −0.355472 | − | 0.934687i | \(-0.615680\pi\) | ||||
−0.355472 | + | 0.934687i | \(0.615680\pi\) | |||||||
\(674\) | 7.21332e18 | 2.96378 | ||||||||
\(675\) | 1.59507e17 | 0.0649091 | ||||||||
\(676\) | 3.31661e18 | 1.33672 | ||||||||
\(677\) | −4.47301e18 | −1.78556 | −0.892778 | − | 0.450497i | \(-0.851247\pi\) | ||||
−0.892778 | + | 0.450497i | \(0.851247\pi\) | |||||||
\(678\) | −4.76437e18 | −1.88370 | ||||||||
\(679\) | −1.57393e17 | −0.0616355 | ||||||||
\(680\) | 1.21812e18 | 0.472480 | ||||||||
\(681\) | −1.00273e17 | −0.0385236 | ||||||||
\(682\) | −1.05367e19 | −4.00964 | ||||||||
\(683\) | 2.92426e18 | 1.10225 | 0.551126 | − | 0.834422i | \(-0.314198\pi\) | ||||
0.551126 | + | 0.834422i | \(0.314198\pi\) | |||||||
\(684\) | −1.38172e18 | −0.515888 | ||||||||
\(685\) | −2.72342e18 | −1.00722 | ||||||||
\(686\) | −3.05255e18 | −1.11829 | ||||||||
\(687\) | 7.46098e17 | 0.270756 | ||||||||
\(688\) | −1.28971e18 | −0.463625 | ||||||||
\(689\) | 7.41878e18 | 2.64185 | ||||||||
\(690\) | −1.25480e18 | −0.442644 | ||||||||
\(691\) | −1.01726e18 | −0.355488 | −0.177744 | − | 0.984077i | \(-0.556880\pi\) | ||||
−0.177744 | + | 0.984077i | \(0.556880\pi\) | |||||||
\(692\) | 3.98325e17 | 0.137895 | ||||||||
\(693\) | −6.79774e17 | −0.233130 | ||||||||
\(694\) | −4.68441e18 | −1.59154 | ||||||||
\(695\) | 6.03975e18 | 2.03291 | ||||||||
\(696\) | −3.40115e18 | −1.13414 | ||||||||
\(697\) | 2.82645e16 | 0.00933744 | ||||||||
\(698\) | −5.05789e18 | −1.65542 | ||||||||
\(699\) | 1.81469e17 | 0.0588439 | ||||||||
\(700\) | −6.67949e17 | −0.214588 | ||||||||
\(701\) | 1.04531e18 | 0.332719 | 0.166359 | − | 0.986065i | \(-0.446799\pi\) | ||||
0.166359 | + | 0.986065i | \(0.446799\pi\) | |||||||
\(702\) | 1.34580e18 | 0.424415 | ||||||||
\(703\) | 4.53291e18 | 1.41634 | ||||||||
\(704\) | −9.35985e18 | −2.89766 | ||||||||
\(705\) | −2.35672e18 | −0.722901 | ||||||||
\(706\) | −4.46651e18 | −1.35749 | ||||||||
\(707\) | 1.52588e18 | 0.459509 | ||||||||
\(708\) | 4.46536e17 | 0.133242 | ||||||||
\(709\) | −2.81009e16 | −0.00830846 | −0.00415423 | − | 0.999991i | \(-0.501322\pi\) | ||||
−0.00415423 | + | 0.999991i | \(0.501322\pi\) | |||||||
\(710\) | −1.18332e19 | −3.46675 | ||||||||
\(711\) | −1.95473e18 | −0.567459 | ||||||||
\(712\) | 6.36022e17 | 0.182958 | ||||||||
\(713\) | 1.72610e18 | 0.492022 | ||||||||
\(714\) | −3.87928e17 | −0.109575 | ||||||||
\(715\) | −1.06623e19 | −2.98444 | ||||||||
\(716\) | 6.80758e18 | 1.88824 | ||||||||
\(717\) | 2.34977e18 | 0.645879 | ||||||||
\(718\) | 6.85574e18 | 1.86743 | ||||||||
\(719\) | −3.07806e18 | −0.830882 | −0.415441 | − | 0.909620i | \(-0.636373\pi\) | ||||
−0.415441 | + | 0.909620i | \(0.636373\pi\) | |||||||
\(720\) | 5.32689e17 | 0.142499 | ||||||||
\(721\) | 3.75845e17 | 0.0996390 | ||||||||
\(722\) | 1.50680e18 | 0.395880 | ||||||||
\(723\) | −2.52237e18 | −0.656764 | ||||||||
\(724\) | −2.49419e18 | −0.643620 | ||||||||
\(725\) | 2.01359e18 | 0.514960 | ||||||||
\(726\) | −1.06093e19 | −2.68906 | ||||||||
\(727\) | −4.87636e18 | −1.22496 | −0.612480 | − | 0.790486i | \(-0.709828\pi\) | ||||
−0.612480 | + | 0.790486i | \(0.709828\pi\) | |||||||
\(728\) | −2.45646e18 | −0.611584 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | 2.65475e18 | 0.649269 | ||||||||
\(731\) | 1.64301e18 | 0.398269 | ||||||||
\(732\) | 1.05223e18 | 0.252807 | ||||||||
\(733\) | 1.13200e18 | 0.269570 | 0.134785 | − | 0.990875i | \(-0.456966\pi\) | ||||
0.134785 | + | 0.990875i | \(0.456966\pi\) | |||||||
\(734\) | −7.16906e18 | −1.69215 | ||||||||
\(735\) | −2.48614e18 | −0.581645 | ||||||||
\(736\) | 1.15213e18 | 0.267175 | ||||||||
\(737\) | −3.77680e18 | −0.868132 | ||||||||
\(738\) | 7.16290e16 | 0.0163201 | ||||||||
\(739\) | −2.49969e18 | −0.564544 | −0.282272 | − | 0.959334i | \(-0.591088\pi\) | ||||
−0.282272 | + | 0.959334i | \(0.591088\pi\) | |||||||
\(740\) | −1.48546e19 | −3.32549 | ||||||||
\(741\) | 3.00837e18 | 0.667595 | ||||||||
\(742\) | −5.41938e18 | −1.19213 | ||||||||
\(743\) | 5.47842e18 | 1.19461 | 0.597307 | − | 0.802013i | \(-0.296237\pi\) | ||||
0.597307 | + | 0.802013i | \(0.296237\pi\) | |||||||
\(744\) | −4.24652e18 | −0.917928 | ||||||||
\(745\) | −1.09708e18 | −0.235083 | ||||||||
\(746\) | −9.58861e18 | −2.03682 | ||||||||
\(747\) | −1.61544e18 | −0.340178 | ||||||||
\(748\) | −5.25470e18 | −1.09695 | ||||||||
\(749\) | 7.04178e17 | 0.145731 | ||||||||
\(750\) | 3.59111e18 | 0.736768 | ||||||||
\(751\) | −2.91220e18 | −0.592327 | −0.296163 | − | 0.955137i | \(-0.595707\pi\) | ||||
−0.296163 | + | 0.955137i | \(0.595707\pi\) | |||||||
\(752\) | −1.98503e18 | −0.400269 | ||||||||
\(753\) | −4.57950e18 | −0.915484 | ||||||||
\(754\) | 1.69892e19 | 3.36712 | ||||||||
\(755\) | −3.36760e18 | −0.661706 | ||||||||
\(756\) | −6.28534e17 | −0.122444 | ||||||||
\(757\) | 7.98882e17 | 0.154298 | 0.0771488 | − | 0.997020i | \(-0.475418\pi\) | ||||
0.0771488 | + | 0.997020i | \(0.475418\pi\) | |||||||
\(758\) | 8.97576e18 | 1.71878 | ||||||||
\(759\) | 2.35936e18 | 0.447942 | ||||||||
\(760\) | 6.90063e18 | 1.29897 | ||||||||
\(761\) | −7.16912e18 | −1.33803 | −0.669014 | − | 0.743250i | \(-0.733284\pi\) | ||||
−0.669014 | + | 0.743250i | \(0.733284\pi\) | |||||||
\(762\) | 6.78069e18 | 1.25478 | ||||||||
\(763\) | 1.18519e17 | 0.0217460 | ||||||||
\(764\) | 1.18429e19 | 2.15453 | ||||||||
\(765\) | −6.78612e17 | −0.122412 | ||||||||
\(766\) | −6.08219e18 | −1.08786 | ||||||||
\(767\) | −9.72227e17 | −0.172424 | ||||||||
\(768\) | −4.98593e18 | −0.876795 | ||||||||
\(769\) | 2.08585e18 | 0.363715 | 0.181858 | − | 0.983325i | \(-0.441789\pi\) | ||||
0.181858 | + | 0.983325i | \(0.441789\pi\) | |||||||
\(770\) | 7.78877e18 | 1.34673 | ||||||||
\(771\) | 1.40641e18 | 0.241133 | ||||||||
\(772\) | −1.25631e19 | −2.13592 | ||||||||
\(773\) | 7.68583e18 | 1.29576 | 0.647879 | − | 0.761743i | \(-0.275656\pi\) | ||||
0.647879 | + | 0.761743i | \(0.275656\pi\) | |||||||
\(774\) | 4.16378e18 | 0.696100 | ||||||||
\(775\) | 2.51407e18 | 0.416789 | ||||||||
\(776\) | −1.34394e18 | −0.220943 | ||||||||
\(777\) | 2.06199e18 | 0.336163 | ||||||||
\(778\) | 1.70027e19 | 2.74884 | ||||||||
\(779\) | 1.60117e17 | 0.0256711 | ||||||||
\(780\) | −9.85861e18 | −1.56748 | ||||||||
\(781\) | 2.22496e19 | 3.50825 | ||||||||
\(782\) | 1.34642e18 | 0.210541 | ||||||||
\(783\) | 1.89477e18 | 0.293835 | ||||||||
\(784\) | −2.09404e18 | −0.322056 | ||||||||
\(785\) | −1.23890e19 | −1.88967 | ||||||||
\(786\) | 5.00962e18 | 0.757807 | ||||||||
\(787\) | 4.09465e18 | 0.614301 | 0.307151 | − | 0.951661i | \(-0.400624\pi\) | ||||
0.307151 | + | 0.951661i | \(0.400624\pi\) | |||||||
\(788\) | 4.82452e18 | 0.717850 | ||||||||
\(789\) | −4.80508e18 | −0.709088 | ||||||||
\(790\) | 2.23971e19 | 3.27805 | ||||||||
\(791\) | −4.84466e18 | −0.703260 | ||||||||
\(792\) | −5.80444e18 | −0.835693 | ||||||||
\(793\) | −2.29098e18 | −0.327150 | ||||||||
\(794\) | 1.04356e19 | 1.47803 | ||||||||
\(795\) | −9.48025e18 | −1.33178 | ||||||||
\(796\) | 1.57147e19 | 2.18964 | ||||||||
\(797\) | 1.43283e17 | 0.0198022 | 0.00990112 | − | 0.999951i | \(-0.496848\pi\) | ||||
0.00990112 | + | 0.999951i | \(0.496848\pi\) | |||||||
\(798\) | −2.19760e18 | −0.301252 | ||||||||
\(799\) | 2.52881e18 | 0.343844 | ||||||||
\(800\) | 1.67808e18 | 0.226323 | ||||||||
\(801\) | −3.54325e17 | −0.0474013 | ||||||||
\(802\) | −9.71884e18 | −1.28968 | ||||||||
\(803\) | −4.99164e18 | −0.657041 | ||||||||
\(804\) | −3.49211e18 | −0.455957 | ||||||||
\(805\) | −1.27594e18 | −0.165256 | ||||||||
\(806\) | 2.12119e19 | 2.72522 | ||||||||
\(807\) | −7.35014e18 | −0.936737 | ||||||||
\(808\) | 1.30291e19 | 1.64718 | ||||||||
\(809\) | −3.32883e18 | −0.417472 | −0.208736 | − | 0.977972i | \(-0.566935\pi\) | ||||
−0.208736 | + | 0.977972i | \(0.566935\pi\) | |||||||
\(810\) | −1.71977e18 | −0.213952 | ||||||||
\(811\) | 8.14268e17 | 0.100492 | 0.0502460 | − | 0.998737i | \(-0.483999\pi\) | ||||
0.0502460 | + | 0.998737i | \(0.483999\pi\) | |||||||
\(812\) | −7.93449e18 | −0.971415 | ||||||||
\(813\) | −5.06399e18 | −0.615042 | ||||||||
\(814\) | 4.36871e19 | 5.26374 | ||||||||
\(815\) | 1.39876e19 | 1.67194 | ||||||||
\(816\) | −5.71586e17 | −0.0677790 | ||||||||
\(817\) | 9.30758e18 | 1.09495 | ||||||||
\(818\) | 2.85085e18 | 0.332719 | ||||||||
\(819\) | 1.36848e18 | 0.158451 | ||||||||
\(820\) | −5.24714e17 | −0.0602743 | ||||||||
\(821\) | −5.36875e18 | −0.611846 | −0.305923 | − | 0.952056i | \(-0.598965\pi\) | ||||
−0.305923 | + | 0.952056i | \(0.598965\pi\) | |||||||
\(822\) | 7.40577e18 | 0.837343 | ||||||||
\(823\) | 3.09246e18 | 0.346901 | 0.173450 | − | 0.984843i | \(-0.444508\pi\) | ||||
0.173450 | + | 0.984843i | \(0.444508\pi\) | |||||||
\(824\) | 3.20926e18 | 0.357172 | ||||||||
\(825\) | 3.43641e18 | 0.379450 | ||||||||
\(826\) | 7.10207e17 | 0.0778063 | ||||||||
\(827\) | 4.60428e18 | 0.500467 | 0.250234 | − | 0.968185i | \(-0.419493\pi\) | ||||
0.250234 | + | 0.968185i | \(0.419493\pi\) | |||||||
\(828\) | 2.18151e18 | 0.235267 | ||||||||
\(829\) | −8.37747e18 | −0.896414 | −0.448207 | − | 0.893930i | \(-0.647937\pi\) | ||||
−0.448207 | + | 0.893930i | \(0.647937\pi\) | |||||||
\(830\) | 1.85095e19 | 1.96511 | ||||||||
\(831\) | −4.09000e18 | −0.430840 | ||||||||
\(832\) | 1.88428e19 | 1.96944 | ||||||||
\(833\) | 2.66768e18 | 0.276656 | ||||||||
\(834\) | −1.64238e19 | −1.69003 | ||||||||
\(835\) | 1.82864e19 | 1.86709 | ||||||||
\(836\) | −2.97677e19 | −3.01581 | ||||||||
\(837\) | 2.36572e18 | 0.237819 | ||||||||
\(838\) | −5.58728e18 | −0.557333 | ||||||||
\(839\) | −4.66599e18 | −0.461840 | −0.230920 | − | 0.972973i | \(-0.574173\pi\) | ||||
−0.230920 | + | 0.972973i | \(0.574173\pi\) | |||||||
\(840\) | 3.13905e18 | 0.308306 | ||||||||
\(841\) | 1.36585e19 | 1.33116 | ||||||||
\(842\) | 1.93765e18 | 0.187390 | ||||||||
\(843\) | −1.47033e18 | −0.141103 | ||||||||
\(844\) | −1.21798e19 | −1.15989 | ||||||||
\(845\) | 9.22769e18 | 0.872016 | ||||||||
\(846\) | 6.40861e18 | 0.600975 | ||||||||
\(847\) | −1.07881e19 | −1.00393 | ||||||||
\(848\) | −7.98508e18 | −0.737406 | ||||||||
\(849\) | 7.27029e18 | 0.666273 | ||||||||
\(850\) | 1.96107e18 | 0.178348 | ||||||||
\(851\) | −7.15674e18 | −0.645912 | ||||||||
\(852\) | 2.05725e19 | 1.84259 | ||||||||
\(853\) | −8.23919e18 | −0.732345 | −0.366172 | − | 0.930547i | \(-0.619332\pi\) | ||||
−0.366172 | + | 0.930547i | \(0.619332\pi\) | |||||||
\(854\) | 1.67355e18 | 0.147626 | ||||||||
\(855\) | −3.84431e18 | −0.336542 | ||||||||
\(856\) | 6.01282e18 | 0.522395 | ||||||||
\(857\) | −1.56428e18 | −0.134877 | −0.0674385 | − | 0.997723i | \(-0.521483\pi\) | ||||
−0.0674385 | + | 0.997723i | \(0.521483\pi\) | |||||||
\(858\) | 2.89939e19 | 2.48107 | ||||||||
\(859\) | 7.44884e18 | 0.632606 | 0.316303 | − | 0.948658i | \(-0.397558\pi\) | ||||
0.316303 | + | 0.948658i | \(0.397558\pi\) | |||||||
\(860\) | −3.05015e19 | −2.57088 | ||||||||
\(861\) | 7.28361e16 | 0.00609293 | ||||||||
\(862\) | 2.32270e19 | 1.92840 | ||||||||
\(863\) | 1.96442e18 | 0.161870 | 0.0809348 | − | 0.996719i | \(-0.474209\pi\) | ||||
0.0809348 | + | 0.996719i | \(0.474209\pi\) | |||||||
\(864\) | 1.57906e18 | 0.129139 | ||||||||
\(865\) | 1.10825e18 | 0.0899563 | ||||||||
\(866\) | 2.87256e19 | 2.31421 | ||||||||
\(867\) | −6.49227e18 | −0.519126 | ||||||||
\(868\) | −9.90663e18 | −0.786227 | ||||||||
\(869\) | −4.21126e19 | −3.31729 | ||||||||
\(870\) | −2.17100e19 | −1.69740 | ||||||||
\(871\) | 7.60326e18 | 0.590041 | ||||||||
\(872\) | 1.01201e18 | 0.0779520 | ||||||||
\(873\) | 7.48705e17 | 0.0572424 | ||||||||
\(874\) | 7.62742e18 | 0.578833 | ||||||||
\(875\) | 3.65163e18 | 0.275064 | ||||||||
\(876\) | −4.61538e18 | −0.345089 | ||||||||
\(877\) | 5.27261e17 | 0.0391316 | 0.0195658 | − | 0.999809i | \(-0.493772\pi\) | ||||
0.0195658 | + | 0.999809i | \(0.493772\pi\) | |||||||
\(878\) | 1.47219e19 | 1.08455 | ||||||||
\(879\) | −4.13959e18 | −0.302712 | ||||||||
\(880\) | 1.14762e19 | 0.833031 | ||||||||
\(881\) | −2.94286e17 | −0.0212044 | −0.0106022 | − | 0.999944i | \(-0.503375\pi\) | ||||
−0.0106022 | + | 0.999944i | \(0.503375\pi\) | |||||||
\(882\) | 6.76054e18 | 0.483543 | ||||||||
\(883\) | 8.23829e18 | 0.584915 | 0.292457 | − | 0.956279i | \(-0.405527\pi\) | ||||
0.292457 | + | 0.956279i | \(0.405527\pi\) | |||||||
\(884\) | 1.05785e19 | 0.745562 | ||||||||
\(885\) | 1.24238e18 | 0.0869209 | ||||||||
\(886\) | −1.43363e19 | −0.995676 | ||||||||
\(887\) | −2.09541e19 | −1.44466 | −0.722331 | − | 0.691547i | \(-0.756929\pi\) | ||||
−0.722331 | + | 0.691547i | \(0.756929\pi\) | |||||||
\(888\) | 1.76069e19 | 1.20503 | ||||||||
\(889\) | 6.89497e18 | 0.468458 | ||||||||
\(890\) | 4.05982e18 | 0.273824 | ||||||||
\(891\) | 3.23363e18 | 0.216514 | ||||||||
\(892\) | 4.49557e18 | 0.298822 | ||||||||
\(893\) | 1.43256e19 | 0.945319 | ||||||||
\(894\) | 2.98327e18 | 0.195433 | ||||||||
\(895\) | 1.89405e19 | 1.23181 | ||||||||
\(896\) | −1.00343e19 | −0.647867 | ||||||||
\(897\) | −4.74974e18 | −0.304452 | ||||||||
\(898\) | 4.80399e19 | 3.05707 | ||||||||
\(899\) | 2.98644e19 | 1.88675 | ||||||||
\(900\) | 3.17738e18 | 0.199293 | ||||||||
\(901\) | 1.01725e19 | 0.633456 | ||||||||
\(902\) | 1.54317e18 | 0.0954050 | ||||||||
\(903\) | 4.23395e18 | 0.259881 | ||||||||
\(904\) | −4.13675e19 | −2.52095 | ||||||||
\(905\) | −6.93952e18 | −0.419869 | ||||||||
\(906\) | 9.15747e18 | 0.550101 | ||||||||
\(907\) | 1.33688e19 | 0.797345 | 0.398673 | − | 0.917093i | \(-0.369471\pi\) | ||||
0.398673 | + | 0.917093i | \(0.369471\pi\) | |||||||
\(908\) | −1.99743e18 | −0.118281 | ||||||||
\(909\) | −7.25848e18 | −0.426757 | ||||||||
\(910\) | −1.56799e19 | −0.915325 | ||||||||
\(911\) | 1.62023e19 | 0.939093 | 0.469546 | − | 0.882908i | \(-0.344417\pi\) | ||||
0.469546 | + | 0.882908i | \(0.344417\pi\) | |||||||
\(912\) | −3.23801e18 | −0.186343 | ||||||||
\(913\) | −3.48029e19 | −1.98864 | ||||||||
\(914\) | −3.10539e19 | −1.76184 | ||||||||
\(915\) | 2.92759e18 | 0.164920 | ||||||||
\(916\) | 1.48623e19 | 0.831313 | ||||||||
\(917\) | 5.09405e18 | 0.282919 | ||||||||
\(918\) | 1.84534e18 | 0.101765 | ||||||||
\(919\) | −2.50626e19 | −1.37238 | −0.686191 | − | 0.727422i | \(-0.740718\pi\) | ||||
−0.686191 | + | 0.727422i | \(0.740718\pi\) | |||||||
\(920\) | −1.08950e19 | −0.592388 | ||||||||
\(921\) | −2.21246e18 | −0.119450 | ||||||||
\(922\) | −1.08368e19 | −0.580967 | ||||||||
\(923\) | −4.47918e19 | −2.38444 | ||||||||
\(924\) | −1.35411e19 | −0.715790 | ||||||||
\(925\) | −1.04238e19 | −0.547149 | ||||||||
\(926\) | −5.32663e19 | −2.77639 | ||||||||
\(927\) | −1.78786e18 | −0.0925372 | ||||||||
\(928\) | 1.99337e19 | 1.02454 | ||||||||
\(929\) | 6.96456e18 | 0.355460 | 0.177730 | − | 0.984079i | \(-0.443125\pi\) | ||||
0.177730 | + | 0.984079i | \(0.443125\pi\) | |||||||
\(930\) | −2.71061e19 | −1.37381 | ||||||||
\(931\) | 1.51123e19 | 0.760602 | ||||||||
\(932\) | 3.61487e18 | 0.180671 | ||||||||
\(933\) | 2.00439e19 | 0.994834 | ||||||||
\(934\) | −3.26409e19 | −1.60882 | ||||||||
\(935\) | −1.46200e19 | −0.715601 | ||||||||
\(936\) | 1.16852e19 | 0.567993 | ||||||||
\(937\) | −3.69180e19 | −1.78209 | −0.891047 | − | 0.453911i | \(-0.850028\pi\) | ||||
−0.891047 | + | 0.453911i | \(0.850028\pi\) | |||||||
\(938\) | −5.55414e18 | −0.266256 | ||||||||
\(939\) | −1.62098e19 | −0.771703 | ||||||||
\(940\) | −4.69459e19 | −2.21956 | ||||||||
\(941\) | 1.49546e19 | 0.702169 | 0.351085 | − | 0.936344i | \(-0.385813\pi\) | ||||
0.351085 | + | 0.936344i | \(0.385813\pi\) | |||||||
\(942\) | 3.36894e19 | 1.57095 | ||||||||
\(943\) | −2.52799e17 | −0.0117071 | ||||||||
\(944\) | 1.04644e18 | 0.0481279 | ||||||||
\(945\) | −1.74875e18 | −0.0798768 | ||||||||
\(946\) | 8.97042e19 | 4.06930 | ||||||||
\(947\) | −1.48585e19 | −0.669424 | −0.334712 | − | 0.942320i | \(-0.608639\pi\) | ||||
−0.334712 | + | 0.942320i | \(0.608639\pi\) | |||||||
\(948\) | −3.89382e19 | −1.74230 | ||||||||
\(949\) | 1.00489e19 | 0.446569 | ||||||||
\(950\) | 1.11094e19 | 0.490327 | ||||||||
\(951\) | 6.27902e18 | 0.275244 | ||||||||
\(952\) | −3.36826e18 | −0.146644 | ||||||||
\(953\) | 3.06528e19 | 1.32546 | 0.662729 | − | 0.748859i | \(-0.269398\pi\) | ||||
0.662729 | + | 0.748859i | \(0.269398\pi\) | |||||||
\(954\) | 2.57796e19 | 1.10716 | ||||||||
\(955\) | 3.29502e19 | 1.40552 | ||||||||
\(956\) | 4.68075e19 | 1.98307 | ||||||||
\(957\) | 4.08207e19 | 1.71772 | ||||||||
\(958\) | −3.58402e19 | −1.49794 | ||||||||
\(959\) | 7.53058e18 | 0.312613 | ||||||||
\(960\) | −2.40787e19 | −0.992818 | ||||||||
\(961\) | 1.28697e19 | 0.527067 | ||||||||
\(962\) | −8.79486e19 | −3.57759 | ||||||||
\(963\) | −3.34972e18 | −0.135343 | ||||||||
\(964\) | −5.02455e19 | −2.01649 | ||||||||
\(965\) | −3.49539e19 | −1.39338 | ||||||||
\(966\) | 3.46966e18 | 0.137384 | ||||||||
\(967\) | −3.54748e19 | −1.39524 | −0.697618 | − | 0.716470i | \(-0.745757\pi\) | ||||
−0.697618 | + | 0.716470i | \(0.745757\pi\) | |||||||
\(968\) | −9.21175e19 | −3.59876 | ||||||||
\(969\) | 4.12502e18 | 0.160074 | ||||||||
\(970\) | −8.57857e18 | −0.330673 | ||||||||
\(971\) | −2.77192e19 | −1.06134 | −0.530672 | − | 0.847577i | \(-0.678060\pi\) | ||||
−0.530672 | + | 0.847577i | \(0.678060\pi\) | |||||||
\(972\) | 2.98988e18 | 0.113717 | ||||||||
\(973\) | −1.67006e19 | −0.630956 | ||||||||
\(974\) | 1.92628e19 | 0.722914 | ||||||||
\(975\) | −6.91800e18 | −0.257900 | ||||||||
\(976\) | 2.46586e18 | 0.0913157 | ||||||||
\(977\) | 7.89659e18 | 0.290486 | 0.145243 | − | 0.989396i | \(-0.453604\pi\) | ||||
0.145243 | + | 0.989396i | \(0.453604\pi\) | |||||||
\(978\) | −3.80365e19 | −1.38994 | ||||||||
\(979\) | −7.63356e18 | −0.277102 | ||||||||
\(980\) | −4.95239e19 | −1.78585 | ||||||||
\(981\) | −5.63786e17 | −0.0201960 | ||||||||
\(982\) | −1.54402e19 | −0.549448 | ||||||||
\(983\) | −1.08534e19 | −0.383678 | −0.191839 | − | 0.981426i | \(-0.561445\pi\) | ||||
−0.191839 | + | 0.981426i | \(0.561445\pi\) | |||||||
\(984\) | 6.21932e17 | 0.0218411 | ||||||||
\(985\) | 1.34231e19 | 0.468293 | ||||||||
\(986\) | 2.32953e19 | 0.807361 | ||||||||
\(987\) | 6.51661e18 | 0.224368 | ||||||||
\(988\) | 5.99267e19 | 2.04975 | ||||||||
\(989\) | −1.46952e19 | −0.499343 | ||||||||
\(990\) | −3.70505e19 | −1.25074 | ||||||||
\(991\) | −2.68278e19 | −0.899717 | −0.449859 | − | 0.893100i | \(-0.648526\pi\) | ||||
−0.449859 | + | 0.893100i | \(0.648526\pi\) | |||||||
\(992\) | 2.48883e19 | 0.829220 | ||||||||
\(993\) | 1.30099e19 | 0.430628 | ||||||||
\(994\) | 3.27202e19 | 1.07598 | ||||||||
\(995\) | 4.37226e19 | 1.42842 | ||||||||
\(996\) | −3.21795e19 | −1.04446 | ||||||||
\(997\) | −5.47883e18 | −0.176673 | −0.0883364 | − | 0.996091i | \(-0.528155\pi\) | ||||
−0.0883364 | + | 0.996091i | \(0.528155\pi\) | |||||||
\(998\) | −1.06480e18 | −0.0341128 | ||||||||
\(999\) | −9.80871e18 | −0.312202 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.14.a.a.1.5 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.a.1.5 | ✓ | 30 | 1.1 | even | 1 | trivial |