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 | 1.8 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −108.701 | −1.20098 | −0.600492 | − | 0.799631i | \(-0.705029\pi\) | ||||
−0.600492 | + | 0.799631i | \(0.705029\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 3623.83 | 0.442363 | ||||||||
\(5\) | −15679.8 | −0.448783 | −0.224391 | − | 0.974499i | \(-0.572039\pi\) | ||||
−0.224391 | + | 0.974499i | \(0.572039\pi\) | |||||||
\(6\) | −79242.8 | −0.693388 | ||||||||
\(7\) | −222995. | −0.716405 | −0.358203 | − | 0.933644i | \(-0.616610\pi\) | ||||
−0.358203 | + | 0.933644i | \(0.616610\pi\) | |||||||
\(8\) | 496563. | 0.669714 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | 1.70441e6 | 0.538981 | ||||||||
\(11\) | 5.89635e6 | 1.00353 | 0.501766 | − | 0.865004i | \(-0.332684\pi\) | ||||
0.501766 | + | 0.865004i | \(0.332684\pi\) | |||||||
\(12\) | 2.64177e6 | 0.255398 | ||||||||
\(13\) | 5.02542e6 | 0.288762 | 0.144381 | − | 0.989522i | \(-0.453881\pi\) | ||||
0.144381 | + | 0.989522i | \(0.453881\pi\) | |||||||
\(14\) | 2.42398e7 | 0.860391 | ||||||||
\(15\) | −1.14306e7 | −0.259105 | ||||||||
\(16\) | −8.36631e7 | −1.24668 | ||||||||
\(17\) | 1.53014e8 | 1.53749 | 0.768746 | − | 0.639554i | \(-0.220881\pi\) | ||||
0.768746 | + | 0.639554i | \(0.220881\pi\) | |||||||
\(18\) | −5.77680e7 | −0.400328 | ||||||||
\(19\) | −3.69560e8 | −1.80213 | −0.901065 | − | 0.433683i | \(-0.857214\pi\) | ||||
−0.901065 | + | 0.433683i | \(0.857214\pi\) | |||||||
\(20\) | −5.68211e7 | −0.198525 | ||||||||
\(21\) | −1.62564e8 | −0.413617 | ||||||||
\(22\) | −6.40937e8 | −1.20522 | ||||||||
\(23\) | −5.84237e8 | −0.822921 | −0.411461 | − | 0.911428i | \(-0.634981\pi\) | ||||
−0.411461 | + | 0.911428i | \(0.634981\pi\) | |||||||
\(24\) | 3.61994e8 | 0.386659 | ||||||||
\(25\) | −9.74846e8 | −0.798594 | ||||||||
\(26\) | −5.46266e8 | −0.346799 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | −8.08098e8 | −0.316911 | ||||||||
\(29\) | 4.10315e9 | 1.28095 | 0.640473 | − | 0.767981i | \(-0.278738\pi\) | ||||
0.640473 | + | 0.767981i | \(0.278738\pi\) | |||||||
\(30\) | 1.24251e9 | 0.311181 | ||||||||
\(31\) | −3.52084e9 | −0.712517 | −0.356259 | − | 0.934387i | \(-0.615948\pi\) | ||||
−0.356259 | + | 0.934387i | \(0.615948\pi\) | |||||||
\(32\) | 5.02640e9 | 0.827527 | ||||||||
\(33\) | 4.29844e9 | 0.579389 | ||||||||
\(34\) | −1.66327e10 | −1.84650 | ||||||||
\(35\) | 3.49653e9 | 0.321510 | ||||||||
\(36\) | 1.92585e9 | 0.147454 | ||||||||
\(37\) | 1.57485e10 | 1.00909 | 0.504544 | − | 0.863386i | \(-0.331661\pi\) | ||||
0.504544 | + | 0.863386i | \(0.331661\pi\) | |||||||
\(38\) | 4.01714e10 | 2.16433 | ||||||||
\(39\) | 3.66353e9 | 0.166717 | ||||||||
\(40\) | −7.78601e9 | −0.300556 | ||||||||
\(41\) | −4.03243e10 | −1.32578 | −0.662890 | − | 0.748717i | \(-0.730670\pi\) | ||||
−0.662890 | + | 0.748717i | \(0.730670\pi\) | |||||||
\(42\) | 1.76708e10 | 0.496747 | ||||||||
\(43\) | −2.10059e10 | −0.506754 | −0.253377 | − | 0.967368i | \(-0.581541\pi\) | ||||
−0.253377 | + | 0.967368i | \(0.581541\pi\) | |||||||
\(44\) | 2.13674e10 | 0.443925 | ||||||||
\(45\) | −8.33290e9 | −0.149594 | ||||||||
\(46\) | 6.35070e10 | 0.988315 | ||||||||
\(47\) | 6.19726e10 | 0.838617 | 0.419309 | − | 0.907844i | \(-0.362273\pi\) | ||||
0.419309 | + | 0.907844i | \(0.362273\pi\) | |||||||
\(48\) | −6.09904e10 | −0.719770 | ||||||||
\(49\) | −4.71620e10 | −0.486764 | ||||||||
\(50\) | 1.05966e11 | 0.959099 | ||||||||
\(51\) | 1.11547e11 | 0.887672 | ||||||||
\(52\) | 1.82113e10 | 0.127738 | ||||||||
\(53\) | 2.85355e11 | 1.76845 | 0.884224 | − | 0.467062i | \(-0.154688\pi\) | ||||
0.884224 | + | 0.467062i | \(0.154688\pi\) | |||||||
\(54\) | −4.21129e10 | −0.231129 | ||||||||
\(55\) | −9.24537e10 | −0.450367 | ||||||||
\(56\) | −1.10731e11 | −0.479786 | ||||||||
\(57\) | −2.69409e11 | −1.04046 | ||||||||
\(58\) | −4.46015e11 | −1.53839 | ||||||||
\(59\) | 4.21805e10 | 0.130189 | ||||||||
\(60\) | −4.14226e10 | −0.114618 | ||||||||
\(61\) | −1.72604e11 | −0.428951 | −0.214476 | − | 0.976729i | \(-0.568804\pi\) | ||||
−0.214476 | + | 0.976729i | \(0.568804\pi\) | |||||||
\(62\) | 3.82718e11 | 0.855722 | ||||||||
\(63\) | −1.18509e11 | −0.238802 | ||||||||
\(64\) | 1.38996e11 | 0.252832 | ||||||||
\(65\) | −7.87977e10 | −0.129591 | ||||||||
\(66\) | −4.67243e11 | −0.695837 | ||||||||
\(67\) | 4.13709e10 | 0.0558739 | 0.0279369 | − | 0.999610i | \(-0.491106\pi\) | ||||
0.0279369 | + | 0.999610i | \(0.491106\pi\) | |||||||
\(68\) | 5.54497e11 | 0.680129 | ||||||||
\(69\) | −4.25909e11 | −0.475114 | ||||||||
\(70\) | −3.80075e11 | −0.386129 | ||||||||
\(71\) | −6.91656e11 | −0.640783 | −0.320391 | − | 0.947285i | \(-0.603814\pi\) | ||||
−0.320391 | + | 0.947285i | \(0.603814\pi\) | |||||||
\(72\) | 2.63894e11 | 0.223238 | ||||||||
\(73\) | 1.67509e12 | 1.29551 | 0.647754 | − | 0.761849i | \(-0.275708\pi\) | ||||
0.647754 | + | 0.761849i | \(0.275708\pi\) | |||||||
\(74\) | −1.71188e12 | −1.21190 | ||||||||
\(75\) | −7.10663e11 | −0.461069 | ||||||||
\(76\) | −1.33922e12 | −0.797195 | ||||||||
\(77\) | −1.31486e12 | −0.718935 | ||||||||
\(78\) | −3.98228e11 | −0.200224 | ||||||||
\(79\) | −9.79322e11 | −0.453262 | −0.226631 | − | 0.973981i | \(-0.572771\pi\) | ||||
−0.226631 | + | 0.973981i | \(0.572771\pi\) | |||||||
\(80\) | 1.31182e12 | 0.559487 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 4.38328e12 | 1.59224 | ||||||||
\(83\) | −4.95100e12 | −1.66221 | −0.831104 | − | 0.556117i | \(-0.812291\pi\) | ||||
−0.831104 | + | 0.556117i | \(0.812291\pi\) | |||||||
\(84\) | −5.89104e11 | −0.182969 | ||||||||
\(85\) | −2.39923e12 | −0.690000 | ||||||||
\(86\) | 2.28336e12 | 0.608603 | ||||||||
\(87\) | 2.99120e12 | 0.739554 | ||||||||
\(88\) | 2.92791e12 | 0.672078 | ||||||||
\(89\) | 1.48553e11 | 0.0316845 | 0.0158422 | − | 0.999875i | \(-0.494957\pi\) | ||||
0.0158422 | + | 0.999875i | \(0.494957\pi\) | |||||||
\(90\) | 9.05792e11 | 0.179660 | ||||||||
\(91\) | −1.12065e12 | −0.206871 | ||||||||
\(92\) | −2.11718e12 | −0.364030 | ||||||||
\(93\) | −2.56669e12 | −0.411372 | ||||||||
\(94\) | −6.73647e12 | −1.00717 | ||||||||
\(95\) | 5.79463e12 | 0.808765 | ||||||||
\(96\) | 3.66424e12 | 0.477773 | ||||||||
\(97\) | 7.18251e11 | 0.0875508 | 0.0437754 | − | 0.999041i | \(-0.486061\pi\) | ||||
0.0437754 | + | 0.999041i | \(0.486061\pi\) | |||||||
\(98\) | 5.12655e12 | 0.584595 | ||||||||
\(99\) | 3.13356e12 | 0.334510 | ||||||||
\(100\) | −3.53268e12 | −0.353268 | ||||||||
\(101\) | −4.51100e11 | −0.0422847 | −0.0211424 | − | 0.999776i | \(-0.506730\pi\) | ||||
−0.0211424 | + | 0.999776i | \(0.506730\pi\) | |||||||
\(102\) | −1.21252e13 | −1.06608 | ||||||||
\(103\) | 1.45809e13 | 1.20321 | 0.601605 | − | 0.798794i | \(-0.294528\pi\) | ||||
0.601605 | + | 0.798794i | \(0.294528\pi\) | |||||||
\(104\) | 2.49544e12 | 0.193388 | ||||||||
\(105\) | 2.54897e12 | 0.185624 | ||||||||
\(106\) | −3.10183e13 | −2.12388 | ||||||||
\(107\) | 1.93892e13 | 1.24901 | 0.624503 | − | 0.781023i | \(-0.285302\pi\) | ||||
0.624503 | + | 0.781023i | \(0.285302\pi\) | |||||||
\(108\) | 1.40395e12 | 0.0851327 | ||||||||
\(109\) | 1.35000e13 | 0.771015 | 0.385507 | − | 0.922705i | \(-0.374026\pi\) | ||||
0.385507 | + | 0.922705i | \(0.374026\pi\) | |||||||
\(110\) | 1.00498e13 | 0.540884 | ||||||||
\(111\) | 1.14807e13 | 0.582598 | ||||||||
\(112\) | 1.86565e13 | 0.893127 | ||||||||
\(113\) | 2.23948e13 | 1.01190 | 0.505950 | − | 0.862563i | \(-0.331142\pi\) | ||||
0.505950 | + | 0.862563i | \(0.331142\pi\) | |||||||
\(114\) | 2.92849e13 | 1.24958 | ||||||||
\(115\) | 9.16074e12 | 0.369313 | ||||||||
\(116\) | 1.48691e13 | 0.566642 | ||||||||
\(117\) | 2.67071e12 | 0.0962541 | ||||||||
\(118\) | −4.58505e12 | −0.156355 | ||||||||
\(119\) | −3.41214e13 | −1.10147 | ||||||||
\(120\) | −5.67600e12 | −0.173526 | ||||||||
\(121\) | 2.44235e11 | 0.00707461 | ||||||||
\(122\) | 1.87622e13 | 0.515164 | ||||||||
\(123\) | −2.93964e13 | −0.765440 | ||||||||
\(124\) | −1.27589e13 | −0.315191 | ||||||||
\(125\) | 3.44258e13 | 0.807178 | ||||||||
\(126\) | 1.28820e13 | 0.286797 | ||||||||
\(127\) | −2.82759e13 | −0.597989 | −0.298994 | − | 0.954255i | \(-0.596651\pi\) | ||||
−0.298994 | + | 0.954255i | \(0.596651\pi\) | |||||||
\(128\) | −5.62852e13 | −1.13117 | ||||||||
\(129\) | −1.53133e13 | −0.292574 | ||||||||
\(130\) | 8.56536e12 | 0.155637 | ||||||||
\(131\) | 1.00006e13 | 0.172887 | 0.0864437 | − | 0.996257i | \(-0.472450\pi\) | ||||
0.0864437 | + | 0.996257i | \(0.472450\pi\) | |||||||
\(132\) | 1.55768e13 | 0.256300 | ||||||||
\(133\) | 8.24101e13 | 1.29106 | ||||||||
\(134\) | −4.49704e12 | −0.0671036 | ||||||||
\(135\) | −6.07468e12 | −0.0863683 | ||||||||
\(136\) | 7.59810e13 | 1.02968 | ||||||||
\(137\) | 1.21278e14 | 1.56711 | 0.783553 | − | 0.621325i | \(-0.213405\pi\) | ||||
0.783553 | + | 0.621325i | \(0.213405\pi\) | |||||||
\(138\) | 4.62966e13 | 0.570604 | ||||||||
\(139\) | −2.91391e13 | −0.342673 | −0.171337 | − | 0.985213i | \(-0.554809\pi\) | ||||
−0.171337 | + | 0.985213i | \(0.554809\pi\) | |||||||
\(140\) | 1.26708e13 | 0.142224 | ||||||||
\(141\) | 4.51780e13 | 0.484176 | ||||||||
\(142\) | 7.51835e13 | 0.769570 | ||||||||
\(143\) | 2.96316e13 | 0.289782 | ||||||||
\(144\) | −4.44620e13 | −0.415559 | ||||||||
\(145\) | −6.43367e13 | −0.574866 | ||||||||
\(146\) | −1.82084e14 | −1.55589 | ||||||||
\(147\) | −3.43811e13 | −0.281033 | ||||||||
\(148\) | 5.70701e13 | 0.446383 | ||||||||
\(149\) | −7.22942e11 | −0.00541243 | −0.00270622 | − | 0.999996i | \(-0.500861\pi\) | ||||
−0.00270622 | + | 0.999996i | \(0.500861\pi\) | |||||||
\(150\) | 7.72495e13 | 0.553736 | ||||||||
\(151\) | −1.45349e14 | −0.997844 | −0.498922 | − | 0.866647i | \(-0.666271\pi\) | ||||
−0.498922 | + | 0.866647i | \(0.666271\pi\) | |||||||
\(152\) | −1.83510e14 | −1.20691 | ||||||||
\(153\) | 8.13179e13 | 0.512497 | ||||||||
\(154\) | 1.42926e14 | 0.863429 | ||||||||
\(155\) | 5.52062e13 | 0.319765 | ||||||||
\(156\) | 1.32760e13 | 0.0737493 | ||||||||
\(157\) | 3.36777e14 | 1.79471 | 0.897356 | − | 0.441308i | \(-0.145485\pi\) | ||||
0.897356 | + | 0.441308i | \(0.145485\pi\) | |||||||
\(158\) | 1.06453e14 | 0.544360 | ||||||||
\(159\) | 2.08024e14 | 1.02101 | ||||||||
\(160\) | −7.88130e13 | −0.371380 | ||||||||
\(161\) | 1.30282e14 | 0.589545 | ||||||||
\(162\) | −3.07003e13 | −0.133443 | ||||||||
\(163\) | −1.95831e14 | −0.817827 | −0.408913 | − | 0.912573i | \(-0.634092\pi\) | ||||
−0.408913 | + | 0.912573i | \(0.634092\pi\) | |||||||
\(164\) | −1.46128e14 | −0.586476 | ||||||||
\(165\) | −6.73988e13 | −0.260020 | ||||||||
\(166\) | 5.38177e14 | 1.99629 | ||||||||
\(167\) | −4.48292e14 | −1.59920 | −0.799602 | − | 0.600530i | \(-0.794956\pi\) | ||||
−0.799602 | + | 0.600530i | \(0.794956\pi\) | |||||||
\(168\) | −8.07231e13 | −0.277005 | ||||||||
\(169\) | −2.77620e14 | −0.916616 | ||||||||
\(170\) | 2.60798e14 | 0.828679 | ||||||||
\(171\) | −1.96399e14 | −0.600710 | ||||||||
\(172\) | −7.61220e13 | −0.224169 | ||||||||
\(173\) | 5.90983e13 | 0.167601 | 0.0838003 | − | 0.996483i | \(-0.473294\pi\) | ||||
0.0838003 | + | 0.996483i | \(0.473294\pi\) | |||||||
\(174\) | −3.25145e14 | −0.888193 | ||||||||
\(175\) | 2.17386e14 | 0.572117 | ||||||||
\(176\) | −4.93307e14 | −1.25108 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | −1.61478e13 | −0.0380525 | ||||||||
\(179\) | 2.93637e14 | 0.667215 | 0.333608 | − | 0.942712i | \(-0.391734\pi\) | ||||
0.333608 | + | 0.942712i | \(0.391734\pi\) | |||||||
\(180\) | −3.01970e13 | −0.0661749 | ||||||||
\(181\) | −1.37598e14 | −0.290871 | −0.145435 | − | 0.989368i | \(-0.546458\pi\) | ||||
−0.145435 | + | 0.989368i | \(0.546458\pi\) | |||||||
\(182\) | 1.21815e14 | 0.248448 | ||||||||
\(183\) | −1.25829e14 | −0.247655 | ||||||||
\(184\) | −2.90110e14 | −0.551122 | ||||||||
\(185\) | −2.46934e14 | −0.452861 | ||||||||
\(186\) | 2.79001e14 | 0.494051 | ||||||||
\(187\) | 9.02224e14 | 1.54292 | ||||||||
\(188\) | 2.24578e14 | 0.370973 | ||||||||
\(189\) | −8.63930e13 | −0.137872 | ||||||||
\(190\) | −6.29880e14 | −0.971314 | ||||||||
\(191\) | −6.54949e14 | −0.976091 | −0.488046 | − | 0.872818i | \(-0.662290\pi\) | ||||
−0.488046 | + | 0.872818i | \(0.662290\pi\) | |||||||
\(192\) | 1.01328e14 | 0.145972 | ||||||||
\(193\) | 9.63404e14 | 1.34179 | 0.670897 | − | 0.741550i | \(-0.265909\pi\) | ||||
0.670897 | + | 0.741550i | \(0.265909\pi\) | |||||||
\(194\) | −7.80744e13 | −0.105147 | ||||||||
\(195\) | −5.74435e13 | −0.0748197 | ||||||||
\(196\) | −1.70907e14 | −0.215326 | ||||||||
\(197\) | 1.25137e14 | 0.152530 | 0.0762652 | − | 0.997088i | \(-0.475700\pi\) | ||||
0.0762652 | + | 0.997088i | \(0.475700\pi\) | |||||||
\(198\) | −3.40620e14 | −0.401742 | ||||||||
\(199\) | −1.21862e15 | −1.39099 | −0.695494 | − | 0.718532i | \(-0.744815\pi\) | ||||
−0.695494 | + | 0.718532i | \(0.744815\pi\) | |||||||
\(200\) | −4.84072e14 | −0.534829 | ||||||||
\(201\) | 3.01594e13 | 0.0322588 | ||||||||
\(202\) | 4.90348e13 | 0.0507833 | ||||||||
\(203\) | −9.14984e14 | −0.917676 | ||||||||
\(204\) | 4.04228e14 | 0.392673 | ||||||||
\(205\) | 6.32277e14 | 0.594987 | ||||||||
\(206\) | −1.58495e15 | −1.44504 | ||||||||
\(207\) | −3.10488e14 | −0.274307 | ||||||||
\(208\) | −4.20442e14 | −0.359994 | ||||||||
\(209\) | −2.17905e15 | −1.80849 | ||||||||
\(210\) | −2.77075e14 | −0.222931 | ||||||||
\(211\) | −1.39131e15 | −1.08539 | −0.542697 | − | 0.839929i | \(-0.682597\pi\) | ||||
−0.542697 | + | 0.839929i | \(0.682597\pi\) | |||||||
\(212\) | 1.03408e15 | 0.782295 | ||||||||
\(213\) | −5.04217e14 | −0.369956 | ||||||||
\(214\) | −2.10761e15 | −1.50004 | ||||||||
\(215\) | 3.29369e14 | 0.227422 | ||||||||
\(216\) | 1.92379e14 | 0.128886 | ||||||||
\(217\) | 7.85132e14 | 0.510451 | ||||||||
\(218\) | −1.46746e15 | −0.925976 | ||||||||
\(219\) | 1.22114e15 | 0.747962 | ||||||||
\(220\) | −3.35037e14 | −0.199226 | ||||||||
\(221\) | 7.68959e14 | 0.443970 | ||||||||
\(222\) | −1.24796e15 | −0.699690 | ||||||||
\(223\) | 1.05743e14 | 0.0575796 | 0.0287898 | − | 0.999585i | \(-0.490835\pi\) | ||||
0.0287898 | + | 0.999585i | \(0.490835\pi\) | |||||||
\(224\) | −1.12086e15 | −0.592844 | ||||||||
\(225\) | −5.18073e14 | −0.266198 | ||||||||
\(226\) | −2.43433e15 | −1.21528 | ||||||||
\(227\) | −3.35126e15 | −1.62570 | −0.812850 | − | 0.582473i | \(-0.802085\pi\) | ||||
−0.812850 | + | 0.582473i | \(0.802085\pi\) | |||||||
\(228\) | −9.76294e14 | −0.460261 | ||||||||
\(229\) | 7.61807e13 | 0.0349071 | 0.0174536 | − | 0.999848i | \(-0.494444\pi\) | ||||
0.0174536 | + | 0.999848i | \(0.494444\pi\) | |||||||
\(230\) | −9.95778e14 | −0.443539 | ||||||||
\(231\) | −9.58532e14 | −0.415077 | ||||||||
\(232\) | 2.03747e15 | 0.857867 | ||||||||
\(233\) | 9.95149e14 | 0.407450 | 0.203725 | − | 0.979028i | \(-0.434695\pi\) | ||||
0.203725 | + | 0.979028i | \(0.434695\pi\) | |||||||
\(234\) | −2.90308e14 | −0.115600 | ||||||||
\(235\) | −9.71720e14 | −0.376357 | ||||||||
\(236\) | 1.52855e14 | 0.0575907 | ||||||||
\(237\) | −7.13926e14 | −0.261691 | ||||||||
\(238\) | 3.70902e15 | 1.32284 | ||||||||
\(239\) | −2.71528e15 | −0.942386 | −0.471193 | − | 0.882030i | \(-0.656176\pi\) | ||||
−0.471193 | + | 0.882030i | \(0.656176\pi\) | |||||||
\(240\) | 9.56319e14 | 0.323020 | ||||||||
\(241\) | 3.45190e14 | 0.113487 | 0.0567437 | − | 0.998389i | \(-0.481928\pi\) | ||||
0.0567437 | + | 0.998389i | \(0.481928\pi\) | |||||||
\(242\) | −2.65485e13 | −0.00849650 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | −6.25490e14 | −0.189752 | ||||||||
\(245\) | 7.39492e14 | 0.218451 | ||||||||
\(246\) | 3.19541e15 | 0.919281 | ||||||||
\(247\) | −1.85719e15 | −0.520387 | ||||||||
\(248\) | −1.74832e15 | −0.477183 | ||||||||
\(249\) | −3.60928e15 | −0.959676 | ||||||||
\(250\) | −3.74211e15 | −0.969408 | ||||||||
\(251\) | 1.14308e15 | 0.288534 | 0.144267 | − | 0.989539i | \(-0.453918\pi\) | ||||
0.144267 | + | 0.989539i | \(0.453918\pi\) | |||||||
\(252\) | −4.29457e14 | −0.105637 | ||||||||
\(253\) | −3.44487e15 | −0.825827 | ||||||||
\(254\) | 3.07361e15 | 0.718175 | ||||||||
\(255\) | −1.74904e15 | −0.398372 | ||||||||
\(256\) | 4.97958e15 | 1.10569 | ||||||||
\(257\) | −3.33503e15 | −0.721995 | −0.360997 | − | 0.932567i | \(-0.617564\pi\) | ||||
−0.360997 | + | 0.932567i | \(0.617564\pi\) | |||||||
\(258\) | 1.66457e15 | 0.351377 | ||||||||
\(259\) | −3.51185e15 | −0.722916 | ||||||||
\(260\) | −2.85550e14 | −0.0573264 | ||||||||
\(261\) | 2.18058e15 | 0.426982 | ||||||||
\(262\) | −1.08707e15 | −0.207635 | ||||||||
\(263\) | 7.95745e14 | 0.148273 | 0.0741364 | − | 0.997248i | \(-0.476380\pi\) | ||||
0.0741364 | + | 0.997248i | \(0.476380\pi\) | |||||||
\(264\) | 2.13444e15 | 0.388025 | ||||||||
\(265\) | −4.47432e15 | −0.793649 | ||||||||
\(266\) | −8.95804e15 | −1.55054 | ||||||||
\(267\) | 1.08295e14 | 0.0182930 | ||||||||
\(268\) | 1.49921e14 | 0.0247165 | ||||||||
\(269\) | −8.89539e15 | −1.43145 | −0.715723 | − | 0.698384i | \(-0.753903\pi\) | ||||
−0.715723 | + | 0.698384i | \(0.753903\pi\) | |||||||
\(270\) | 6.60322e14 | 0.103727 | ||||||||
\(271\) | −5.35745e15 | −0.821596 | −0.410798 | − | 0.911726i | \(-0.634750\pi\) | ||||
−0.410798 | + | 0.911726i | \(0.634750\pi\) | |||||||
\(272\) | −1.28016e16 | −1.91676 | ||||||||
\(273\) | −8.16950e14 | −0.119437 | ||||||||
\(274\) | −1.31830e16 | −1.88207 | ||||||||
\(275\) | −5.74804e15 | −0.801414 | ||||||||
\(276\) | −1.54342e15 | −0.210173 | ||||||||
\(277\) | −6.20275e15 | −0.825022 | −0.412511 | − | 0.910953i | \(-0.635348\pi\) | ||||
−0.412511 | + | 0.910953i | \(0.635348\pi\) | |||||||
\(278\) | 3.16744e15 | 0.411545 | ||||||||
\(279\) | −1.87112e15 | −0.237506 | ||||||||
\(280\) | 1.73625e15 | 0.215320 | ||||||||
\(281\) | 1.00835e16 | 1.22186 | 0.610930 | − | 0.791685i | \(-0.290796\pi\) | ||||
0.610930 | + | 0.791685i | \(0.290796\pi\) | |||||||
\(282\) | −4.91088e15 | −0.581488 | ||||||||
\(283\) | −8.89753e15 | −1.02957 | −0.514787 | − | 0.857318i | \(-0.672129\pi\) | ||||
−0.514787 | + | 0.857318i | \(0.672129\pi\) | |||||||
\(284\) | −2.50645e15 | −0.283458 | ||||||||
\(285\) | 4.22429e15 | 0.466941 | ||||||||
\(286\) | −3.22098e15 | −0.348023 | ||||||||
\(287\) | 8.99213e15 | 0.949796 | ||||||||
\(288\) | 2.67123e15 | 0.275842 | ||||||||
\(289\) | 1.35087e16 | 1.36388 | ||||||||
\(290\) | 6.99344e15 | 0.690405 | ||||||||
\(291\) | 5.23605e14 | 0.0505475 | ||||||||
\(292\) | 6.07026e15 | 0.573085 | ||||||||
\(293\) | −3.28434e15 | −0.303255 | −0.151628 | − | 0.988438i | \(-0.548451\pi\) | ||||
−0.151628 | + | 0.988438i | \(0.548451\pi\) | |||||||
\(294\) | 3.73725e15 | 0.337516 | ||||||||
\(295\) | −6.61383e14 | −0.0584265 | ||||||||
\(296\) | 7.82014e15 | 0.675800 | ||||||||
\(297\) | 2.28437e15 | 0.193130 | ||||||||
\(298\) | 7.85842e13 | 0.00650025 | ||||||||
\(299\) | −2.93604e15 | −0.237629 | ||||||||
\(300\) | −2.57532e15 | −0.203959 | ||||||||
\(301\) | 4.68423e15 | 0.363041 | ||||||||
\(302\) | 1.57996e16 | 1.19839 | ||||||||
\(303\) | −3.28852e14 | −0.0244131 | ||||||||
\(304\) | 3.09185e16 | 2.24668 | ||||||||
\(305\) | 2.70641e15 | 0.192506 | ||||||||
\(306\) | −8.83931e15 | −0.615501 | ||||||||
\(307\) | −9.09345e15 | −0.619911 | −0.309955 | − | 0.950751i | \(-0.600314\pi\) | ||||
−0.309955 | + | 0.950751i | \(0.600314\pi\) | |||||||
\(308\) | −4.76483e15 | −0.318030 | ||||||||
\(309\) | 1.06295e16 | 0.694674 | ||||||||
\(310\) | −6.00095e15 | −0.384033 | ||||||||
\(311\) | 1.40180e16 | 0.878503 | 0.439252 | − | 0.898364i | \(-0.355244\pi\) | ||||
0.439252 | + | 0.898364i | \(0.355244\pi\) | |||||||
\(312\) | 1.81917e15 | 0.111653 | ||||||||
\(313\) | −2.17374e15 | −0.130668 | −0.0653340 | − | 0.997863i | \(-0.520811\pi\) | ||||
−0.0653340 | + | 0.997863i | \(0.520811\pi\) | |||||||
\(314\) | −3.66079e16 | −2.15542 | ||||||||
\(315\) | 1.85820e15 | 0.107170 | ||||||||
\(316\) | −3.54890e15 | −0.200506 | ||||||||
\(317\) | 1.68840e16 | 0.934522 | 0.467261 | − | 0.884120i | \(-0.345241\pi\) | ||||
0.467261 | + | 0.884120i | \(0.345241\pi\) | |||||||
\(318\) | −2.26123e16 | −1.22622 | ||||||||
\(319\) | 2.41936e16 | 1.28547 | ||||||||
\(320\) | −2.17943e15 | −0.113467 | ||||||||
\(321\) | 1.41347e16 | 0.721114 | ||||||||
\(322\) | −1.41618e16 | −0.708034 | ||||||||
\(323\) | −5.65478e16 | −2.77076 | ||||||||
\(324\) | 1.02348e15 | 0.0491514 | ||||||||
\(325\) | −4.89901e15 | −0.230604 | ||||||||
\(326\) | 2.12869e16 | 0.982197 | ||||||||
\(327\) | 9.84153e15 | 0.445146 | ||||||||
\(328\) | −2.00235e16 | −0.887893 | ||||||||
\(329\) | −1.38196e16 | −0.600790 | ||||||||
\(330\) | 7.32629e15 | 0.312279 | ||||||||
\(331\) | −2.34060e16 | −0.978241 | −0.489121 | − | 0.872216i | \(-0.662682\pi\) | ||||
−0.489121 | + | 0.872216i | \(0.662682\pi\) | |||||||
\(332\) | −1.79416e16 | −0.735299 | ||||||||
\(333\) | 8.36942e15 | 0.336363 | ||||||||
\(334\) | 4.87296e16 | 1.92062 | ||||||||
\(335\) | −6.48688e14 | −0.0250752 | ||||||||
\(336\) | 1.36006e16 | 0.515647 | ||||||||
\(337\) | 1.19509e16 | 0.444432 | 0.222216 | − | 0.974997i | \(-0.428671\pi\) | ||||
0.222216 | + | 0.974997i | \(0.428671\pi\) | |||||||
\(338\) | 3.01775e16 | 1.10084 | ||||||||
\(339\) | 1.63258e16 | 0.584221 | ||||||||
\(340\) | −8.69441e15 | −0.305230 | ||||||||
\(341\) | −2.07601e16 | −0.715033 | ||||||||
\(342\) | 2.13487e16 | 0.721443 | ||||||||
\(343\) | 3.21227e16 | 1.06513 | ||||||||
\(344\) | −1.04308e16 | −0.339380 | ||||||||
\(345\) | 6.67818e15 | 0.213223 | ||||||||
\(346\) | −6.42403e15 | −0.201286 | ||||||||
\(347\) | 1.62883e16 | 0.500881 | 0.250440 | − | 0.968132i | \(-0.419425\pi\) | ||||
0.250440 | + | 0.968132i | \(0.419425\pi\) | |||||||
\(348\) | 1.08396e16 | 0.327151 | ||||||||
\(349\) | 2.82702e15 | 0.0837460 | 0.0418730 | − | 0.999123i | \(-0.486668\pi\) | ||||
0.0418730 | + | 0.999123i | \(0.486668\pi\) | |||||||
\(350\) | −2.36300e16 | −0.687103 | ||||||||
\(351\) | 1.94695e15 | 0.0555723 | ||||||||
\(352\) | 2.96374e16 | 0.830449 | ||||||||
\(353\) | −5.21024e16 | −1.43325 | −0.716625 | − | 0.697458i | \(-0.754314\pi\) | ||||
−0.716625 | + | 0.697458i | \(0.754314\pi\) | |||||||
\(354\) | −3.34250e15 | −0.0902715 | ||||||||
\(355\) | 1.08450e16 | 0.287572 | ||||||||
\(356\) | 5.38331e14 | 0.0140160 | ||||||||
\(357\) | −2.48745e16 | −0.635932 | ||||||||
\(358\) | −3.19185e16 | −0.801315 | ||||||||
\(359\) | 1.76819e16 | 0.435928 | 0.217964 | − | 0.975957i | \(-0.430059\pi\) | ||||
0.217964 | + | 0.975957i | \(0.430059\pi\) | |||||||
\(360\) | −4.13781e15 | −0.100185 | ||||||||
\(361\) | 9.45214e16 | 2.24767 | ||||||||
\(362\) | 1.49570e16 | 0.349331 | ||||||||
\(363\) | 1.78047e14 | 0.00408453 | ||||||||
\(364\) | −4.06103e15 | −0.0915119 | ||||||||
\(365\) | −2.62652e16 | −0.581402 | ||||||||
\(366\) | 1.36777e16 | 0.297430 | ||||||||
\(367\) | −9.04870e15 | −0.193311 | −0.0966556 | − | 0.995318i | \(-0.530815\pi\) | ||||
−0.0966556 | + | 0.995318i | \(0.530815\pi\) | |||||||
\(368\) | 4.88791e16 | 1.02592 | ||||||||
\(369\) | −2.14300e16 | −0.441927 | ||||||||
\(370\) | 2.68419e16 | 0.543879 | ||||||||
\(371\) | −6.36329e16 | −1.26693 | ||||||||
\(372\) | −9.30127e15 | −0.181976 | ||||||||
\(373\) | 7.31250e14 | 0.0140591 | 0.00702957 | − | 0.999975i | \(-0.497762\pi\) | ||||
0.00702957 | + | 0.999975i | \(0.497762\pi\) | |||||||
\(374\) | −9.80723e16 | −1.85302 | ||||||||
\(375\) | 2.50964e16 | 0.466024 | ||||||||
\(376\) | 3.07733e16 | 0.561633 | ||||||||
\(377\) | 2.06201e16 | 0.369889 | ||||||||
\(378\) | 9.39098e15 | 0.165582 | ||||||||
\(379\) | −5.04940e16 | −0.875154 | −0.437577 | − | 0.899181i | \(-0.644163\pi\) | ||||
−0.437577 | + | 0.899181i | \(0.644163\pi\) | |||||||
\(380\) | 2.09988e16 | 0.357767 | ||||||||
\(381\) | −2.06132e16 | −0.345249 | ||||||||
\(382\) | 7.11934e16 | 1.17227 | ||||||||
\(383\) | 2.01642e16 | 0.326430 | 0.163215 | − | 0.986591i | \(-0.447814\pi\) | ||||
0.163215 | + | 0.986591i | \(0.447814\pi\) | |||||||
\(384\) | −4.10319e16 | −0.653083 | ||||||||
\(385\) | 2.06168e16 | 0.322645 | ||||||||
\(386\) | −1.04723e17 | −1.61147 | ||||||||
\(387\) | −1.11634e16 | −0.168918 | ||||||||
\(388\) | 2.60282e15 | 0.0387292 | ||||||||
\(389\) | −8.84541e16 | −1.29433 | −0.647166 | − | 0.762349i | \(-0.724046\pi\) | ||||
−0.647166 | + | 0.762349i | \(0.724046\pi\) | |||||||
\(390\) | 6.24415e15 | 0.0898572 | ||||||||
\(391\) | −8.93964e16 | −1.26524 | ||||||||
\(392\) | −2.34189e16 | −0.325992 | ||||||||
\(393\) | 7.29045e15 | 0.0998166 | ||||||||
\(394\) | −1.36025e16 | −0.183187 | ||||||||
\(395\) | 1.53556e16 | 0.203416 | ||||||||
\(396\) | 1.13555e16 | 0.147975 | ||||||||
\(397\) | −1.49539e17 | −1.91697 | −0.958484 | − | 0.285145i | \(-0.907958\pi\) | ||||
−0.958484 | + | 0.285145i | \(0.907958\pi\) | |||||||
\(398\) | 1.32465e17 | 1.67056 | ||||||||
\(399\) | 6.00770e16 | 0.745391 | ||||||||
\(400\) | 8.15587e16 | 0.995590 | ||||||||
\(401\) | −1.50861e17 | −1.81192 | −0.905959 | − | 0.423365i | \(-0.860849\pi\) | ||||
−0.905959 | + | 0.423365i | \(0.860849\pi\) | |||||||
\(402\) | −3.27835e15 | −0.0387423 | ||||||||
\(403\) | −1.76937e16 | −0.205748 | ||||||||
\(404\) | −1.63471e15 | −0.0187052 | ||||||||
\(405\) | −4.42844e15 | −0.0498647 | ||||||||
\(406\) | 9.94594e16 | 1.10211 | ||||||||
\(407\) | 9.28590e16 | 1.01265 | ||||||||
\(408\) | 5.53901e16 | 0.594486 | ||||||||
\(409\) | −1.27486e17 | −1.34667 | −0.673336 | − | 0.739336i | \(-0.735139\pi\) | ||||
−0.673336 | + | 0.739336i | \(0.735139\pi\) | |||||||
\(410\) | −6.87290e16 | −0.714570 | ||||||||
\(411\) | 8.84116e16 | 0.904769 | ||||||||
\(412\) | 5.28387e16 | 0.532255 | ||||||||
\(413\) | −9.40607e15 | −0.0932680 | ||||||||
\(414\) | 3.37502e16 | 0.329438 | ||||||||
\(415\) | 7.76308e16 | 0.745970 | ||||||||
\(416\) | 2.52597e16 | 0.238958 | ||||||||
\(417\) | −2.12424e16 | −0.197842 | ||||||||
\(418\) | 2.36865e17 | 2.17197 | ||||||||
\(419\) | −1.56729e17 | −1.41501 | −0.707504 | − | 0.706710i | \(-0.750179\pi\) | ||||
−0.707504 | + | 0.706710i | \(0.750179\pi\) | |||||||
\(420\) | 9.23704e15 | 0.0821131 | ||||||||
\(421\) | −1.86804e17 | −1.63513 | −0.817565 | − | 0.575836i | \(-0.804677\pi\) | ||||
−0.817565 | + | 0.575836i | \(0.804677\pi\) | |||||||
\(422\) | 1.51236e17 | 1.30354 | ||||||||
\(423\) | 3.29348e16 | 0.279539 | ||||||||
\(424\) | 1.41697e17 | 1.18435 | ||||||||
\(425\) | −1.49165e17 | −1.22783 | ||||||||
\(426\) | 5.48088e16 | 0.444312 | ||||||||
\(427\) | 3.84900e16 | 0.307303 | ||||||||
\(428\) | 7.02631e16 | 0.552513 | ||||||||
\(429\) | 2.16015e16 | 0.167306 | ||||||||
\(430\) | −3.58026e16 | −0.273130 | ||||||||
\(431\) | 2.66341e16 | 0.200141 | 0.100070 | − | 0.994980i | \(-0.468093\pi\) | ||||
0.100070 | + | 0.994980i | \(0.468093\pi\) | |||||||
\(432\) | −3.24128e16 | −0.239923 | ||||||||
\(433\) | −3.73070e16 | −0.272031 | −0.136016 | − | 0.990707i | \(-0.543430\pi\) | ||||
−0.136016 | + | 0.990707i | \(0.543430\pi\) | |||||||
\(434\) | −8.53443e16 | −0.613044 | ||||||||
\(435\) | −4.69014e16 | −0.331899 | ||||||||
\(436\) | 4.89219e16 | 0.341068 | ||||||||
\(437\) | 2.15911e17 | 1.48301 | ||||||||
\(438\) | −1.32739e17 | −0.898291 | ||||||||
\(439\) | 1.67544e17 | 1.11715 | 0.558574 | − | 0.829455i | \(-0.311349\pi\) | ||||
0.558574 | + | 0.829455i | \(0.311349\pi\) | |||||||
\(440\) | −4.59091e16 | −0.301617 | ||||||||
\(441\) | −2.50638e16 | −0.162255 | ||||||||
\(442\) | −8.35863e16 | −0.533201 | ||||||||
\(443\) | −1.61581e17 | −1.01570 | −0.507851 | − | 0.861445i | \(-0.669560\pi\) | ||||
−0.507851 | + | 0.861445i | \(0.669560\pi\) | |||||||
\(444\) | 4.16041e16 | 0.257719 | ||||||||
\(445\) | −2.32928e15 | −0.0142194 | ||||||||
\(446\) | −1.14943e16 | −0.0691522 | ||||||||
\(447\) | −5.27025e14 | −0.00312487 | ||||||||
\(448\) | −3.09954e16 | −0.181130 | ||||||||
\(449\) | −6.95012e16 | −0.400305 | −0.200153 | − | 0.979765i | \(-0.564144\pi\) | ||||
−0.200153 | + | 0.979765i | \(0.564144\pi\) | |||||||
\(450\) | 5.63149e16 | 0.319700 | ||||||||
\(451\) | −2.37766e17 | −1.33046 | ||||||||
\(452\) | 8.11551e16 | 0.447627 | ||||||||
\(453\) | −1.05960e17 | −0.576105 | ||||||||
\(454\) | 3.64284e17 | 1.95244 | ||||||||
\(455\) | 1.75715e16 | 0.0928400 | ||||||||
\(456\) | −1.33778e17 | −0.696811 | ||||||||
\(457\) | −8.78228e16 | −0.450974 | −0.225487 | − | 0.974246i | \(-0.572397\pi\) | ||||
−0.225487 | + | 0.974246i | \(0.572397\pi\) | |||||||
\(458\) | −8.28089e15 | −0.0419229 | ||||||||
\(459\) | 5.92807e16 | 0.295891 | ||||||||
\(460\) | 3.31970e16 | 0.163370 | ||||||||
\(461\) | 3.70986e17 | 1.80012 | 0.900059 | − | 0.435768i | \(-0.143523\pi\) | ||||
0.900059 | + | 0.435768i | \(0.143523\pi\) | |||||||
\(462\) | 1.04193e17 | 0.498501 | ||||||||
\(463\) | −1.05637e17 | −0.498358 | −0.249179 | − | 0.968458i | \(-0.580161\pi\) | ||||
−0.249179 | + | 0.968458i | \(0.580161\pi\) | |||||||
\(464\) | −3.43283e17 | −1.59693 | ||||||||
\(465\) | 4.02453e16 | 0.184617 | ||||||||
\(466\) | −1.08173e17 | −0.489341 | ||||||||
\(467\) | 1.34010e17 | 0.597829 | 0.298914 | − | 0.954280i | \(-0.403375\pi\) | ||||
0.298914 | + | 0.954280i | \(0.403375\pi\) | |||||||
\(468\) | 9.67822e15 | 0.0425792 | ||||||||
\(469\) | −9.22552e15 | −0.0400283 | ||||||||
\(470\) | 1.05627e17 | 0.451999 | ||||||||
\(471\) | 2.45510e17 | 1.03618 | ||||||||
\(472\) | 2.09453e16 | 0.0871893 | ||||||||
\(473\) | −1.23858e17 | −0.508543 | ||||||||
\(474\) | 7.76042e16 | 0.314287 | ||||||||
\(475\) | 3.60264e17 | 1.43917 | ||||||||
\(476\) | −1.23650e17 | −0.487248 | ||||||||
\(477\) | 1.51649e17 | 0.589483 | ||||||||
\(478\) | 2.95153e17 | 1.13179 | ||||||||
\(479\) | −2.99679e17 | −1.13364 | −0.566820 | − | 0.823842i | \(-0.691826\pi\) | ||||
−0.566820 | + | 0.823842i | \(0.691826\pi\) | |||||||
\(480\) | −5.74547e16 | −0.214416 | ||||||||
\(481\) | 7.91430e16 | 0.291387 | ||||||||
\(482\) | −3.75224e16 | −0.136296 | ||||||||
\(483\) | 9.49758e16 | 0.340374 | ||||||||
\(484\) | 8.85066e14 | 0.00312954 | ||||||||
\(485\) | −1.12620e16 | −0.0392913 | ||||||||
\(486\) | −2.23805e16 | −0.0770432 | ||||||||
\(487\) | 4.24453e17 | 1.44176 | 0.720878 | − | 0.693062i | \(-0.243739\pi\) | ||||
0.720878 | + | 0.693062i | \(0.243739\pi\) | |||||||
\(488\) | −8.57089e16 | −0.287275 | ||||||||
\(489\) | −1.42761e17 | −0.472173 | ||||||||
\(490\) | −8.03833e16 | −0.262356 | ||||||||
\(491\) | 2.82075e16 | 0.0908519 | 0.0454260 | − | 0.998968i | \(-0.485535\pi\) | ||||
0.0454260 | + | 0.998968i | \(0.485535\pi\) | |||||||
\(492\) | −1.06528e17 | −0.338602 | ||||||||
\(493\) | 6.27839e17 | 1.96944 | ||||||||
\(494\) | 2.01878e17 | 0.624977 | ||||||||
\(495\) | −4.91337e16 | −0.150122 | ||||||||
\(496\) | 2.94565e17 | 0.888280 | ||||||||
\(497\) | 1.54236e17 | 0.459060 | ||||||||
\(498\) | 3.92331e17 | 1.15256 | ||||||||
\(499\) | −9.74998e16 | −0.282716 | −0.141358 | − | 0.989959i | \(-0.545147\pi\) | ||||
−0.141358 | + | 0.989959i | \(0.545147\pi\) | |||||||
\(500\) | 1.24753e17 | 0.357065 | ||||||||
\(501\) | −3.26805e17 | −0.923301 | ||||||||
\(502\) | −1.24253e17 | −0.346525 | ||||||||
\(503\) | −4.98003e16 | −0.137101 | −0.0685504 | − | 0.997648i | \(-0.521837\pi\) | ||||
−0.0685504 | + | 0.997648i | \(0.521837\pi\) | |||||||
\(504\) | −5.88471e16 | −0.159929 | ||||||||
\(505\) | 7.07316e15 | 0.0189767 | ||||||||
\(506\) | 3.74459e17 | 0.991805 | ||||||||
\(507\) | −2.02385e17 | −0.529209 | ||||||||
\(508\) | −1.02467e17 | −0.264528 | ||||||||
\(509\) | −4.57244e17 | −1.16542 | −0.582710 | − | 0.812680i | \(-0.698008\pi\) | ||||
−0.582710 | + | 0.812680i | \(0.698008\pi\) | |||||||
\(510\) | 1.90122e17 | 0.478438 | ||||||||
\(511\) | −3.73538e17 | −0.928109 | ||||||||
\(512\) | −8.01958e16 | −0.196742 | ||||||||
\(513\) | −1.43175e17 | −0.346820 | ||||||||
\(514\) | 3.62520e17 | 0.867104 | ||||||||
\(515\) | −2.28626e17 | −0.539980 | ||||||||
\(516\) | −5.54929e16 | −0.129424 | ||||||||
\(517\) | 3.65412e17 | 0.841578 | ||||||||
\(518\) | 3.81741e17 | 0.868211 | ||||||||
\(519\) | 4.30827e16 | 0.0967643 | ||||||||
\(520\) | −3.91280e16 | −0.0867892 | ||||||||
\(521\) | 4.43418e17 | 0.971332 | 0.485666 | − | 0.874144i | \(-0.338577\pi\) | ||||
0.485666 | + | 0.874144i | \(0.338577\pi\) | |||||||
\(522\) | −2.37031e17 | −0.512798 | ||||||||
\(523\) | −1.27369e17 | −0.272146 | −0.136073 | − | 0.990699i | \(-0.543448\pi\) | ||||
−0.136073 | + | 0.990699i | \(0.543448\pi\) | |||||||
\(524\) | 3.62406e16 | 0.0764789 | ||||||||
\(525\) | 1.58475e17 | 0.330312 | ||||||||
\(526\) | −8.64980e16 | −0.178073 | ||||||||
\(527\) | −5.38738e17 | −1.09549 | ||||||||
\(528\) | −3.59621e17 | −0.722311 | ||||||||
\(529\) | −1.62703e17 | −0.322800 | ||||||||
\(530\) | 4.86361e17 | 0.953160 | ||||||||
\(531\) | 2.24165e16 | 0.0433963 | ||||||||
\(532\) | 2.98641e17 | 0.571115 | ||||||||
\(533\) | −2.02646e17 | −0.382835 | ||||||||
\(534\) | −1.17718e16 | −0.0219696 | ||||||||
\(535\) | −3.04018e17 | −0.560532 | ||||||||
\(536\) | 2.05432e16 | 0.0374195 | ||||||||
\(537\) | 2.14061e17 | 0.385217 | ||||||||
\(538\) | 9.66934e17 | 1.71914 | ||||||||
\(539\) | −2.78084e17 | −0.488482 | ||||||||
\(540\) | −2.20136e16 | −0.0382061 | ||||||||
\(541\) | 2.09010e17 | 0.358413 | 0.179207 | − | 0.983811i | \(-0.442647\pi\) | ||||
0.179207 | + | 0.983811i | \(0.442647\pi\) | |||||||
\(542\) | 5.82359e17 | 0.986723 | ||||||||
\(543\) | −1.00309e17 | −0.167934 | ||||||||
\(544\) | 7.69109e17 | 1.27232 | ||||||||
\(545\) | −2.11678e17 | −0.346018 | ||||||||
\(546\) | 8.88031e16 | 0.143442 | ||||||||
\(547\) | 9.22458e17 | 1.47241 | 0.736206 | − | 0.676758i | \(-0.236616\pi\) | ||||
0.736206 | + | 0.676758i | \(0.236616\pi\) | |||||||
\(548\) | 4.39491e17 | 0.693229 | ||||||||
\(549\) | −9.17291e16 | −0.142984 | ||||||||
\(550\) | 6.24815e17 | 0.962485 | ||||||||
\(551\) | −1.51636e18 | −2.30843 | ||||||||
\(552\) | −2.11491e17 | −0.318190 | ||||||||
\(553\) | 2.18384e17 | 0.324719 | ||||||||
\(554\) | 6.74243e17 | 0.990838 | ||||||||
\(555\) | −1.80015e17 | −0.261460 | ||||||||
\(556\) | −1.05595e17 | −0.151586 | ||||||||
\(557\) | −1.22276e18 | −1.73493 | −0.867466 | − | 0.497497i | \(-0.834253\pi\) | ||||
−0.867466 | + | 0.497497i | \(0.834253\pi\) | |||||||
\(558\) | 2.03392e17 | 0.285241 | ||||||||
\(559\) | −1.05564e17 | −0.146331 | ||||||||
\(560\) | −2.92531e17 | −0.400820 | ||||||||
\(561\) | 6.57721e17 | 0.890806 | ||||||||
\(562\) | −1.09609e18 | −1.46743 | ||||||||
\(563\) | −1.25872e18 | −1.66580 | −0.832902 | − | 0.553421i | \(-0.813322\pi\) | ||||
−0.832902 | + | 0.553421i | \(0.813322\pi\) | |||||||
\(564\) | 1.63718e17 | 0.214181 | ||||||||
\(565\) | −3.51147e17 | −0.454123 | ||||||||
\(566\) | 9.67167e17 | 1.23650 | ||||||||
\(567\) | −6.29805e16 | −0.0796006 | ||||||||
\(568\) | −3.43451e17 | −0.429141 | ||||||||
\(569\) | 9.77509e17 | 1.20751 | 0.603756 | − | 0.797170i | \(-0.293670\pi\) | ||||
0.603756 | + | 0.797170i | \(0.293670\pi\) | |||||||
\(570\) | −4.59183e17 | −0.560788 | ||||||||
\(571\) | −8.17555e17 | −0.987147 | −0.493574 | − | 0.869704i | \(-0.664310\pi\) | ||||
−0.493574 | + | 0.869704i | \(0.664310\pi\) | |||||||
\(572\) | 1.07380e17 | 0.128189 | ||||||||
\(573\) | −4.77458e17 | −0.563547 | ||||||||
\(574\) | −9.77450e17 | −1.14069 | ||||||||
\(575\) | 5.69542e17 | 0.657180 | ||||||||
\(576\) | 7.38680e16 | 0.0842773 | ||||||||
\(577\) | −8.66108e17 | −0.977078 | −0.488539 | − | 0.872542i | \(-0.662470\pi\) | ||||
−0.488539 | + | 0.872542i | \(0.662470\pi\) | |||||||
\(578\) | −1.46840e18 | −1.63800 | ||||||||
\(579\) | 7.02322e17 | 0.774686 | ||||||||
\(580\) | −2.33145e17 | −0.254299 | ||||||||
\(581\) | 1.10405e18 | 1.19081 | ||||||||
\(582\) | −5.69162e16 | −0.0607067 | ||||||||
\(583\) | 1.68255e18 | 1.77469 | ||||||||
\(584\) | 8.31789e17 | 0.867620 | ||||||||
\(585\) | −4.18763e16 | −0.0431972 | ||||||||
\(586\) | 3.57010e17 | 0.364205 | ||||||||
\(587\) | 1.48954e17 | 0.150281 | 0.0751407 | − | 0.997173i | \(-0.476059\pi\) | ||||
0.0751407 | + | 0.997173i | \(0.476059\pi\) | |||||||
\(588\) | −1.24592e17 | −0.124319 | ||||||||
\(589\) | 1.30116e18 | 1.28405 | ||||||||
\(590\) | 7.18928e16 | 0.0701693 | ||||||||
\(591\) | 9.12251e16 | 0.0880635 | ||||||||
\(592\) | −1.31757e18 | −1.25801 | ||||||||
\(593\) | 1.21099e18 | 1.14363 | 0.571813 | − | 0.820384i | \(-0.306240\pi\) | ||||
0.571813 | + | 0.820384i | \(0.306240\pi\) | |||||||
\(594\) | −2.48312e17 | −0.231946 | ||||||||
\(595\) | 5.35017e17 | 0.494319 | ||||||||
\(596\) | −2.61982e15 | −0.00239426 | ||||||||
\(597\) | −8.88375e17 | −0.803088 | ||||||||
\(598\) | 3.19149e17 | 0.285388 | ||||||||
\(599\) | −1.99866e18 | −1.76793 | −0.883963 | − | 0.467556i | \(-0.845134\pi\) | ||||
−0.883963 | + | 0.467556i | \(0.845134\pi\) | |||||||
\(600\) | −3.52889e17 | −0.308784 | ||||||||
\(601\) | 7.84877e17 | 0.679388 | 0.339694 | − | 0.940536i | \(-0.389677\pi\) | ||||
0.339694 | + | 0.940536i | \(0.389677\pi\) | |||||||
\(602\) | −5.09178e17 | −0.436006 | ||||||||
\(603\) | 2.19862e16 | 0.0186246 | ||||||||
\(604\) | −5.26721e17 | −0.441409 | ||||||||
\(605\) | −3.82956e15 | −0.00317496 | ||||||||
\(606\) | 3.57464e16 | 0.0293197 | ||||||||
\(607\) | 1.47836e17 | 0.119965 | 0.0599823 | − | 0.998199i | \(-0.480896\pi\) | ||||
0.0599823 | + | 0.998199i | \(0.480896\pi\) | |||||||
\(608\) | −1.85755e18 | −1.49131 | ||||||||
\(609\) | −6.67023e17 | −0.529820 | ||||||||
\(610\) | −2.94188e17 | −0.231197 | ||||||||
\(611\) | 3.11438e17 | 0.242161 | ||||||||
\(612\) | 2.94682e17 | 0.226710 | ||||||||
\(613\) | −7.80291e17 | −0.593969 | −0.296984 | − | 0.954882i | \(-0.595981\pi\) | ||||
−0.296984 | + | 0.954882i | \(0.595981\pi\) | |||||||
\(614\) | 9.88464e17 | 0.744503 | ||||||||
\(615\) | 4.60930e17 | 0.343516 | ||||||||
\(616\) | −6.52910e17 | −0.481480 | ||||||||
\(617\) | 1.41434e18 | 1.03205 | 0.516024 | − | 0.856574i | \(-0.327411\pi\) | ||||
0.516024 | + | 0.856574i | \(0.327411\pi\) | |||||||
\(618\) | −1.15543e18 | −0.834292 | ||||||||
\(619\) | −2.15988e17 | −0.154326 | −0.0771632 | − | 0.997018i | \(-0.524586\pi\) | ||||
−0.0771632 | + | 0.997018i | \(0.524586\pi\) | |||||||
\(620\) | 2.00058e17 | 0.141452 | ||||||||
\(621\) | −2.26345e17 | −0.158371 | ||||||||
\(622\) | −1.52377e18 | −1.05507 | ||||||||
\(623\) | −3.31266e16 | −0.0226989 | ||||||||
\(624\) | −3.06502e17 | −0.207842 | ||||||||
\(625\) | 6.50207e17 | 0.436347 | ||||||||
\(626\) | 2.36287e17 | 0.156930 | ||||||||
\(627\) | −1.58853e18 | −1.04413 | ||||||||
\(628\) | 1.22042e18 | 0.793913 | ||||||||
\(629\) | 2.40975e18 | 1.55147 | ||||||||
\(630\) | −2.01987e17 | −0.128710 | ||||||||
\(631\) | −1.79839e18 | −1.13421 | −0.567106 | − | 0.823645i | \(-0.691937\pi\) | ||||
−0.567106 | + | 0.823645i | \(0.691937\pi\) | |||||||
\(632\) | −4.86295e17 | −0.303556 | ||||||||
\(633\) | −1.01426e18 | −0.626652 | ||||||||
\(634\) | −1.83530e18 | −1.12235 | ||||||||
\(635\) | 4.43362e17 | 0.268367 | ||||||||
\(636\) | 7.53844e17 | 0.451658 | ||||||||
\(637\) | −2.37009e17 | −0.140559 | ||||||||
\(638\) | −2.62986e18 | −1.54383 | ||||||||
\(639\) | −3.67574e17 | −0.213594 | ||||||||
\(640\) | 8.82541e17 | 0.507651 | ||||||||
\(641\) | 2.38786e18 | 1.35966 | 0.679831 | − | 0.733369i | \(-0.262053\pi\) | ||||
0.679831 | + | 0.733369i | \(0.262053\pi\) | |||||||
\(642\) | −1.53645e18 | −0.866046 | ||||||||
\(643\) | 5.98871e17 | 0.334166 | 0.167083 | − | 0.985943i | \(-0.446565\pi\) | ||||
0.167083 | + | 0.985943i | \(0.446565\pi\) | |||||||
\(644\) | 4.72121e17 | 0.260793 | ||||||||
\(645\) | 2.40110e17 | 0.131302 | ||||||||
\(646\) | 6.14678e18 | 3.32764 | ||||||||
\(647\) | −2.24528e18 | −1.20335 | −0.601677 | − | 0.798740i | \(-0.705500\pi\) | ||||
−0.601677 | + | 0.798740i | \(0.705500\pi\) | |||||||
\(648\) | 1.40244e17 | 0.0744126 | ||||||||
\(649\) | 2.48711e17 | 0.130649 | ||||||||
\(650\) | 5.32526e17 | 0.276952 | ||||||||
\(651\) | 5.72361e17 | 0.294709 | ||||||||
\(652\) | −7.09658e17 | −0.361776 | ||||||||
\(653\) | −1.57701e18 | −0.795972 | −0.397986 | − | 0.917392i | \(-0.630291\pi\) | ||||
−0.397986 | + | 0.917392i | \(0.630291\pi\) | |||||||
\(654\) | −1.06978e18 | −0.534613 | ||||||||
\(655\) | −1.56808e17 | −0.0775889 | ||||||||
\(656\) | 3.37366e18 | 1.65282 | ||||||||
\(657\) | 8.90213e17 | 0.431836 | ||||||||
\(658\) | 1.50220e18 | 0.721539 | ||||||||
\(659\) | −3.46469e17 | −0.164782 | −0.0823908 | − | 0.996600i | \(-0.526256\pi\) | ||||
−0.0823908 | + | 0.996600i | \(0.526256\pi\) | |||||||
\(660\) | −2.44242e17 | −0.115023 | ||||||||
\(661\) | 7.70176e17 | 0.359154 | 0.179577 | − | 0.983744i | \(-0.442527\pi\) | ||||
0.179577 | + | 0.983744i | \(0.442527\pi\) | |||||||
\(662\) | 2.54425e18 | 1.17485 | ||||||||
\(663\) | 5.60571e17 | 0.256326 | ||||||||
\(664\) | −2.45848e18 | −1.11320 | ||||||||
\(665\) | −1.29218e18 | −0.579403 | ||||||||
\(666\) | −9.09762e17 | −0.403966 | ||||||||
\(667\) | −2.39721e18 | −1.05412 | ||||||||
\(668\) | −1.62454e18 | −0.707428 | ||||||||
\(669\) | 7.70864e16 | 0.0332436 | ||||||||
\(670\) | 7.05129e16 | 0.0301149 | ||||||||
\(671\) | −1.01774e18 | −0.430466 | ||||||||
\(672\) | −8.17110e17 | −0.342279 | ||||||||
\(673\) | −9.65115e17 | −0.400388 | −0.200194 | − | 0.979756i | \(-0.564157\pi\) | ||||
−0.200194 | + | 0.979756i | \(0.564157\pi\) | |||||||
\(674\) | −1.29907e18 | −0.533756 | ||||||||
\(675\) | −3.77675e17 | −0.153690 | ||||||||
\(676\) | −1.00605e18 | −0.405477 | ||||||||
\(677\) | −3.92149e18 | −1.56540 | −0.782699 | − | 0.622400i | \(-0.786158\pi\) | ||||
−0.782699 | + | 0.622400i | \(0.786158\pi\) | |||||||
\(678\) | −1.77463e18 | −0.701640 | ||||||||
\(679\) | −1.60167e17 | −0.0627218 | ||||||||
\(680\) | −1.19137e18 | −0.462102 | ||||||||
\(681\) | −2.44307e18 | −0.938598 | ||||||||
\(682\) | 2.25664e18 | 0.858744 | ||||||||
\(683\) | 6.77789e16 | 0.0255482 | 0.0127741 | − | 0.999918i | \(-0.495934\pi\) | ||||
0.0127741 | + | 0.999918i | \(0.495934\pi\) | |||||||
\(684\) | −7.11718e17 | −0.265732 | ||||||||
\(685\) | −1.90162e18 | −0.703290 | ||||||||
\(686\) | −3.49176e18 | −1.27920 | ||||||||
\(687\) | 5.55357e16 | 0.0201536 | ||||||||
\(688\) | 1.75742e18 | 0.631759 | ||||||||
\(689\) | 1.43403e18 | 0.510661 | ||||||||
\(690\) | −7.25922e17 | −0.256077 | ||||||||
\(691\) | −4.59196e18 | −1.60469 | −0.802344 | − | 0.596862i | \(-0.796414\pi\) | ||||
−0.802344 | + | 0.596862i | \(0.796414\pi\) | |||||||
\(692\) | 2.14163e17 | 0.0741402 | ||||||||
\(693\) | −6.98770e17 | −0.239645 | ||||||||
\(694\) | −1.77055e18 | −0.601550 | ||||||||
\(695\) | 4.56896e17 | 0.153786 | ||||||||
\(696\) | 1.48532e18 | 0.495289 | ||||||||
\(697\) | −6.17018e18 | −2.03838 | ||||||||
\(698\) | −3.07299e17 | −0.100578 | ||||||||
\(699\) | 7.25464e17 | 0.235242 | ||||||||
\(700\) | 7.87772e17 | 0.253083 | ||||||||
\(701\) | −3.91029e18 | −1.24463 | −0.622317 | − | 0.782765i | \(-0.713808\pi\) | ||||
−0.622317 | + | 0.782765i | \(0.713808\pi\) | |||||||
\(702\) | −2.11635e17 | −0.0667415 | ||||||||
\(703\) | −5.82003e18 | −1.81851 | ||||||||
\(704\) | 8.19568e17 | 0.253725 | ||||||||
\(705\) | −7.08384e17 | −0.217290 | ||||||||
\(706\) | 5.66357e18 | 1.72131 | ||||||||
\(707\) | 1.00593e17 | 0.0302930 | ||||||||
\(708\) | 1.11431e17 | 0.0332500 | ||||||||
\(709\) | 3.21057e18 | 0.949252 | 0.474626 | − | 0.880188i | \(-0.342583\pi\) | ||||
0.474626 | + | 0.880188i | \(0.342583\pi\) | |||||||
\(710\) | −1.17886e18 | −0.345370 | ||||||||
\(711\) | −5.20452e17 | −0.151087 | ||||||||
\(712\) | 7.37659e16 | 0.0212195 | ||||||||
\(713\) | 2.05701e18 | 0.586346 | ||||||||
\(714\) | 2.70387e18 | 0.763745 | ||||||||
\(715\) | −4.64619e17 | −0.130049 | ||||||||
\(716\) | 1.06409e18 | 0.295151 | ||||||||
\(717\) | −1.97944e18 | −0.544087 | ||||||||
\(718\) | −1.92203e18 | −0.523542 | ||||||||
\(719\) | 6.18425e18 | 1.66936 | 0.834679 | − | 0.550737i | \(-0.185653\pi\) | ||||
0.834679 | + | 0.550737i | \(0.185653\pi\) | |||||||
\(720\) | 6.97157e17 | 0.186496 | ||||||||
\(721\) | −3.25147e18 | −0.861986 | ||||||||
\(722\) | −1.02745e19 | −2.69942 | ||||||||
\(723\) | 2.51644e17 | 0.0655220 | ||||||||
\(724\) | −4.98631e17 | −0.128670 | ||||||||
\(725\) | −3.99994e18 | −1.02296 | ||||||||
\(726\) | −1.93538e16 | −0.00490545 | ||||||||
\(727\) | −3.41497e18 | −0.857855 | −0.428927 | − | 0.903339i | \(-0.641108\pi\) | ||||
−0.428927 | + | 0.903339i | \(0.641108\pi\) | |||||||
\(728\) | −5.56471e17 | −0.138544 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | 2.85504e18 | 0.698254 | ||||||||
\(731\) | −3.21420e18 | −0.779130 | ||||||||
\(732\) | −4.55982e17 | −0.109553 | ||||||||
\(733\) | 7.38761e18 | 1.75925 | 0.879626 | − | 0.475667i | \(-0.157793\pi\) | ||||
0.879626 | + | 0.475667i | \(0.157793\pi\) | |||||||
\(734\) | 9.83600e17 | 0.232164 | ||||||||
\(735\) | 5.39090e17 | 0.126123 | ||||||||
\(736\) | −2.93661e18 | −0.680989 | ||||||||
\(737\) | 2.43937e17 | 0.0560712 | ||||||||
\(738\) | 2.32945e18 | 0.530747 | ||||||||
\(739\) | 1.68606e18 | 0.380790 | 0.190395 | − | 0.981708i | \(-0.439023\pi\) | ||||
0.190395 | + | 0.981708i | \(0.439023\pi\) | |||||||
\(740\) | −8.94849e17 | −0.200329 | ||||||||
\(741\) | −1.35389e18 | −0.300446 | ||||||||
\(742\) | 6.91694e18 | 1.52156 | ||||||||
\(743\) | 4.13569e18 | 0.901821 | 0.450910 | − | 0.892569i | \(-0.351099\pi\) | ||||
0.450910 | + | 0.892569i | \(0.351099\pi\) | |||||||
\(744\) | −1.27452e18 | −0.275502 | ||||||||
\(745\) | 1.13356e16 | 0.00242901 | ||||||||
\(746\) | −7.94874e16 | −0.0168848 | ||||||||
\(747\) | −2.63116e18 | −0.554069 | ||||||||
\(748\) | 3.26951e18 | 0.682531 | ||||||||
\(749\) | −4.32369e18 | −0.894794 | ||||||||
\(750\) | −2.72800e18 | −0.559688 | ||||||||
\(751\) | 2.78525e18 | 0.566507 | 0.283253 | − | 0.959045i | \(-0.408586\pi\) | ||||
0.283253 | + | 0.959045i | \(0.408586\pi\) | |||||||
\(752\) | −5.18482e18 | −1.04549 | ||||||||
\(753\) | 8.33305e17 | 0.166585 | ||||||||
\(754\) | −2.24141e18 | −0.444230 | ||||||||
\(755\) | 2.27905e18 | 0.447815 | ||||||||
\(756\) | −3.13074e17 | −0.0609895 | ||||||||
\(757\) | −6.22247e18 | −1.20182 | −0.600911 | − | 0.799316i | \(-0.705195\pi\) | ||||
−0.600911 | + | 0.799316i | \(0.705195\pi\) | |||||||
\(758\) | 5.48873e18 | 1.05105 | ||||||||
\(759\) | −2.51131e18 | −0.476792 | ||||||||
\(760\) | 2.87740e18 | 0.541641 | ||||||||
\(761\) | −6.95135e18 | −1.29738 | −0.648692 | − | 0.761051i | \(-0.724684\pi\) | ||||
−0.648692 | + | 0.761051i | \(0.724684\pi\) | |||||||
\(762\) | 2.24066e18 | 0.414638 | ||||||||
\(763\) | −3.01045e18 | −0.552359 | ||||||||
\(764\) | −2.37343e18 | −0.431786 | ||||||||
\(765\) | −1.27505e18 | −0.230000 | ||||||||
\(766\) | −2.19186e18 | −0.392037 | ||||||||
\(767\) | 2.11975e17 | 0.0375936 | ||||||||
\(768\) | 3.63012e18 | 0.638370 | ||||||||
\(769\) | 9.83745e18 | 1.71538 | 0.857692 | − | 0.514164i | \(-0.171898\pi\) | ||||
0.857692 | + | 0.514164i | \(0.171898\pi\) | |||||||
\(770\) | −2.24105e18 | −0.387492 | ||||||||
\(771\) | −2.43123e18 | −0.416844 | ||||||||
\(772\) | 3.49122e18 | 0.593560 | ||||||||
\(773\) | 3.78743e18 | 0.638525 | 0.319262 | − | 0.947666i | \(-0.396565\pi\) | ||||
0.319262 | + | 0.947666i | \(0.396565\pi\) | |||||||
\(774\) | 1.21347e18 | 0.202868 | ||||||||
\(775\) | 3.43228e18 | 0.569012 | ||||||||
\(776\) | 3.56657e17 | 0.0586339 | ||||||||
\(777\) | −2.56014e18 | −0.417376 | ||||||||
\(778\) | 9.61502e18 | 1.55447 | ||||||||
\(779\) | 1.49022e19 | 2.38923 | ||||||||
\(780\) | −2.08166e17 | −0.0330974 | ||||||||
\(781\) | −4.07825e18 | −0.643046 | ||||||||
\(782\) | 9.71745e18 | 1.51953 | ||||||||
\(783\) | 1.58964e18 | 0.246518 | ||||||||
\(784\) | 3.94572e18 | 0.606837 | ||||||||
\(785\) | −5.28060e18 | −0.805435 | ||||||||
\(786\) | −7.92477e17 | −0.119878 | ||||||||
\(787\) | 1.63498e18 | 0.245288 | 0.122644 | − | 0.992451i | \(-0.460863\pi\) | ||||
0.122644 | + | 0.992451i | \(0.460863\pi\) | |||||||
\(788\) | 4.53477e17 | 0.0674737 | ||||||||
\(789\) | 5.80098e17 | 0.0856053 | ||||||||
\(790\) | −1.66916e18 | −0.244300 | ||||||||
\(791\) | −4.99394e18 | −0.724931 | ||||||||
\(792\) | 1.55601e18 | 0.224026 | ||||||||
\(793\) | −8.67409e17 | −0.123865 | ||||||||
\(794\) | 1.62549e19 | 2.30225 | ||||||||
\(795\) | −3.26178e18 | −0.458213 | ||||||||
\(796\) | −4.41608e18 | −0.615321 | ||||||||
\(797\) | 7.73550e18 | 1.06908 | 0.534539 | − | 0.845144i | \(-0.320485\pi\) | ||||
0.534539 | + | 0.845144i | \(0.320485\pi\) | |||||||
\(798\) | −6.53041e18 | −0.895203 | ||||||||
\(799\) | 9.48267e18 | 1.28937 | ||||||||
\(800\) | −4.89997e18 | −0.660858 | ||||||||
\(801\) | 7.89471e16 | 0.0105615 | ||||||||
\(802\) | 1.63987e19 | 2.17608 | ||||||||
\(803\) | 9.87694e18 | 1.30008 | ||||||||
\(804\) | 1.09293e17 | 0.0142701 | ||||||||
\(805\) | −2.04280e18 | −0.264578 | ||||||||
\(806\) | 1.92332e18 | 0.247100 | ||||||||
\(807\) | −6.48474e18 | −0.826446 | ||||||||
\(808\) | −2.23999e17 | −0.0283187 | ||||||||
\(809\) | −1.10550e18 | −0.138642 | −0.0693210 | − | 0.997594i | \(-0.522083\pi\) | ||||
−0.0693210 | + | 0.997594i | \(0.522083\pi\) | |||||||
\(810\) | 4.81375e17 | 0.0598868 | ||||||||
\(811\) | −7.65197e18 | −0.944360 | −0.472180 | − | 0.881502i | \(-0.656533\pi\) | ||||
−0.472180 | + | 0.881502i | \(0.656533\pi\) | |||||||
\(812\) | −3.31575e18 | −0.405945 | ||||||||
\(813\) | −3.90558e18 | −0.474348 | ||||||||
\(814\) | −1.00938e19 | −1.21618 | ||||||||
\(815\) | 3.07059e18 | 0.367027 | ||||||||
\(816\) | −9.33238e18 | −1.10664 | ||||||||
\(817\) | 7.76295e18 | 0.913236 | ||||||||
\(818\) | 1.38578e19 | 1.61733 | ||||||||
\(819\) | −5.95557e17 | −0.0689569 | ||||||||
\(820\) | 2.29127e18 | 0.263200 | ||||||||
\(821\) | 4.27254e18 | 0.486918 | 0.243459 | − | 0.969911i | \(-0.421718\pi\) | ||||
0.243459 | + | 0.969911i | \(0.421718\pi\) | |||||||
\(822\) | −9.61040e18 | −1.08661 | ||||||||
\(823\) | 5.01299e18 | 0.562339 | 0.281169 | − | 0.959658i | \(-0.409278\pi\) | ||||
0.281169 | + | 0.959658i | \(0.409278\pi\) | |||||||
\(824\) | 7.24032e18 | 0.805807 | ||||||||
\(825\) | −4.19032e18 | −0.462697 | ||||||||
\(826\) | 1.02245e18 | 0.112013 | ||||||||
\(827\) | 8.17322e18 | 0.888397 | 0.444199 | − | 0.895928i | \(-0.353488\pi\) | ||||
0.444199 | + | 0.895928i | \(0.353488\pi\) | |||||||
\(828\) | −1.12516e18 | −0.121343 | ||||||||
\(829\) | 1.32811e19 | 1.42112 | 0.710559 | − | 0.703637i | \(-0.248442\pi\) | ||||
0.710559 | + | 0.703637i | \(0.248442\pi\) | |||||||
\(830\) | −8.43852e18 | −0.895898 | ||||||||
\(831\) | −4.52180e18 | −0.476327 | ||||||||
\(832\) | 6.98512e17 | 0.0730083 | ||||||||
\(833\) | −7.21645e18 | −0.748395 | ||||||||
\(834\) | 2.30906e18 | 0.237606 | ||||||||
\(835\) | 7.02914e18 | 0.717695 | ||||||||
\(836\) | −7.89653e18 | −0.800010 | ||||||||
\(837\) | −1.36405e18 | −0.137124 | ||||||||
\(838\) | 1.70366e19 | 1.69940 | ||||||||
\(839\) | 6.20921e18 | 0.614587 | 0.307293 | − | 0.951615i | \(-0.400577\pi\) | ||||
0.307293 | + | 0.951615i | \(0.400577\pi\) | |||||||
\(840\) | 1.26572e18 | 0.124315 | ||||||||
\(841\) | 6.57522e18 | 0.640821 | ||||||||
\(842\) | 2.03057e19 | 1.96376 | ||||||||
\(843\) | 7.35089e18 | 0.705441 | ||||||||
\(844\) | −5.04187e18 | −0.480138 | ||||||||
\(845\) | 4.35304e18 | 0.411362 | ||||||||
\(846\) | −3.58003e18 | −0.335722 | ||||||||
\(847\) | −5.44633e16 | −0.00506829 | ||||||||
\(848\) | −2.38737e19 | −2.20469 | ||||||||
\(849\) | −6.48630e18 | −0.594425 | ||||||||
\(850\) | 1.62143e19 | 1.47461 | ||||||||
\(851\) | −9.20089e18 | −0.830401 | ||||||||
\(852\) | −1.82720e18 | −0.163655 | ||||||||
\(853\) | 8.60050e18 | 0.764460 | 0.382230 | − | 0.924067i | \(-0.375156\pi\) | ||||
0.382230 | + | 0.924067i | \(0.375156\pi\) | |||||||
\(854\) | −4.18389e18 | −0.369066 | ||||||||
\(855\) | 3.07950e18 | 0.269588 | ||||||||
\(856\) | 9.62793e18 | 0.836476 | ||||||||
\(857\) | 1.07445e18 | 0.0926426 | 0.0463213 | − | 0.998927i | \(-0.485250\pi\) | ||||
0.0463213 | + | 0.998927i | \(0.485250\pi\) | |||||||
\(858\) | −2.34809e18 | −0.200931 | ||||||||
\(859\) | 4.33075e18 | 0.367797 | 0.183898 | − | 0.982945i | \(-0.441128\pi\) | ||||
0.183898 | + | 0.982945i | \(0.441128\pi\) | |||||||
\(860\) | 1.19358e18 | 0.100603 | ||||||||
\(861\) | 6.55526e18 | 0.548365 | ||||||||
\(862\) | −2.89515e18 | −0.240366 | ||||||||
\(863\) | 3.00588e17 | 0.0247686 | 0.0123843 | − | 0.999923i | \(-0.496058\pi\) | ||||
0.0123843 | + | 0.999923i | \(0.496058\pi\) | |||||||
\(864\) | 1.94733e18 | 0.159258 | ||||||||
\(865\) | −9.26651e17 | −0.0752163 | ||||||||
\(866\) | 4.05530e18 | 0.326705 | ||||||||
\(867\) | 9.84783e18 | 0.787438 | ||||||||
\(868\) | 2.84519e18 | 0.225804 | ||||||||
\(869\) | −5.77442e18 | −0.454863 | ||||||||
\(870\) | 5.09822e18 | 0.398605 | ||||||||
\(871\) | 2.07906e17 | 0.0161343 | ||||||||
\(872\) | 6.70361e18 | 0.516359 | ||||||||
\(873\) | 3.81708e17 | 0.0291836 | ||||||||
\(874\) | −2.34696e19 | −1.78107 | ||||||||
\(875\) | −7.67680e18 | −0.578266 | ||||||||
\(876\) | 4.42522e18 | 0.330871 | ||||||||
\(877\) | 5.68672e18 | 0.422051 | 0.211025 | − | 0.977481i | \(-0.432320\pi\) | ||||
0.211025 | + | 0.977481i | \(0.432320\pi\) | |||||||
\(878\) | −1.82122e19 | −1.34168 | ||||||||
\(879\) | −2.39428e18 | −0.175085 | ||||||||
\(880\) | 7.73497e18 | 0.561463 | ||||||||
\(881\) | −2.30035e19 | −1.65749 | −0.828744 | − | 0.559628i | \(-0.810944\pi\) | ||||
−0.828744 | + | 0.559628i | \(0.810944\pi\) | |||||||
\(882\) | 2.72446e18 | 0.194865 | ||||||||
\(883\) | 1.11208e19 | 0.789571 | 0.394786 | − | 0.918773i | \(-0.370819\pi\) | ||||
0.394786 | + | 0.918773i | \(0.370819\pi\) | |||||||
\(884\) | 2.78658e18 | 0.196396 | ||||||||
\(885\) | −4.82148e17 | −0.0337326 | ||||||||
\(886\) | 1.75640e19 | 1.21984 | ||||||||
\(887\) | −1.02391e19 | −0.705923 | −0.352962 | − | 0.935638i | \(-0.614825\pi\) | ||||
−0.352962 | + | 0.935638i | \(0.614825\pi\) | |||||||
\(888\) | 5.70088e18 | 0.390174 | ||||||||
\(889\) | 6.30541e18 | 0.428402 | ||||||||
\(890\) | 2.53195e17 | 0.0170773 | ||||||||
\(891\) | 1.66530e18 | 0.111503 | ||||||||
\(892\) | 3.83194e17 | 0.0254711 | ||||||||
\(893\) | −2.29026e19 | −1.51130 | ||||||||
\(894\) | 5.72879e16 | 0.00375292 | ||||||||
\(895\) | −4.60417e18 | −0.299435 | ||||||||
\(896\) | 1.25513e19 | 0.810379 | ||||||||
\(897\) | −2.14037e18 | −0.137195 | ||||||||
\(898\) | 7.55483e18 | 0.480760 | ||||||||
\(899\) | −1.44465e19 | −0.912696 | ||||||||
\(900\) | −1.87741e18 | −0.117756 | ||||||||
\(901\) | 4.36633e19 | 2.71898 | ||||||||
\(902\) | 2.58453e19 | 1.59786 | ||||||||
\(903\) | 3.41480e18 | 0.209602 | ||||||||
\(904\) | 1.11204e19 | 0.677684 | ||||||||
\(905\) | 2.15751e18 | 0.130538 | ||||||||
\(906\) | 1.15179e19 | 0.691893 | ||||||||
\(907\) | 1.48848e19 | 0.887761 | 0.443881 | − | 0.896086i | \(-0.353601\pi\) | ||||
0.443881 | + | 0.896086i | \(0.353601\pi\) | |||||||
\(908\) | −1.21444e19 | −0.719149 | ||||||||
\(909\) | −2.39733e17 | −0.0140949 | ||||||||
\(910\) | −1.91004e18 | −0.111499 | ||||||||
\(911\) | 1.33460e19 | 0.773540 | 0.386770 | − | 0.922176i | \(-0.373591\pi\) | ||||
0.386770 | + | 0.922176i | \(0.373591\pi\) | |||||||
\(912\) | 2.25396e19 | 1.29712 | ||||||||
\(913\) | −2.91928e19 | −1.66808 | ||||||||
\(914\) | 9.54639e18 | 0.541613 | ||||||||
\(915\) | 1.97297e18 | 0.111143 | ||||||||
\(916\) | 2.76066e17 | 0.0154416 | ||||||||
\(917\) | −2.23009e18 | −0.123857 | ||||||||
\(918\) | −6.44385e18 | −0.355360 | ||||||||
\(919\) | −2.89001e19 | −1.58252 | −0.791260 | − | 0.611480i | \(-0.790575\pi\) | ||||
−0.791260 | + | 0.611480i | \(0.790575\pi\) | |||||||
\(920\) | 4.54888e18 | 0.247334 | ||||||||
\(921\) | −6.62912e18 | −0.357906 | ||||||||
\(922\) | −4.03264e19 | −2.16191 | ||||||||
\(923\) | −3.47586e18 | −0.185034 | ||||||||
\(924\) | −3.47356e18 | −0.183615 | ||||||||
\(925\) | −1.53524e19 | −0.805852 | ||||||||
\(926\) | 1.14828e19 | 0.598519 | ||||||||
\(927\) | 7.74888e18 | 0.401070 | ||||||||
\(928\) | 2.06241e19 | 1.06002 | ||||||||
\(929\) | 1.62264e19 | 0.828169 | 0.414085 | − | 0.910238i | \(-0.364102\pi\) | ||||
0.414085 | + | 0.910238i | \(0.364102\pi\) | |||||||
\(930\) | −4.37469e18 | −0.221722 | ||||||||
\(931\) | 1.74292e19 | 0.877212 | ||||||||
\(932\) | 3.60626e18 | 0.180241 | ||||||||
\(933\) | 1.02191e19 | 0.507204 | ||||||||
\(934\) | −1.45670e19 | −0.717983 | ||||||||
\(935\) | −1.41467e19 | −0.692436 | ||||||||
\(936\) | 1.32618e18 | 0.0644627 | ||||||||
\(937\) | 2.81456e19 | 1.35864 | 0.679318 | − | 0.733844i | \(-0.262276\pi\) | ||||
0.679318 | + | 0.733844i | \(0.262276\pi\) | |||||||
\(938\) | 1.00282e18 | 0.0480734 | ||||||||
\(939\) | −1.58466e18 | −0.0754412 | ||||||||
\(940\) | −3.52135e18 | −0.166486 | ||||||||
\(941\) | −2.97283e19 | −1.39585 | −0.697923 | − | 0.716172i | \(-0.745892\pi\) | ||||
−0.697923 | + | 0.716172i | \(0.745892\pi\) | |||||||
\(942\) | −2.66871e19 | −1.24443 | ||||||||
\(943\) | 2.35589e19 | 1.09101 | ||||||||
\(944\) | −3.52896e18 | −0.162304 | ||||||||
\(945\) | 1.35463e18 | 0.0618747 | ||||||||
\(946\) | 1.34635e19 | 0.610752 | ||||||||
\(947\) | −1.34786e19 | −0.607253 | −0.303626 | − | 0.952791i | \(-0.598197\pi\) | ||||
−0.303626 | + | 0.952791i | \(0.598197\pi\) | |||||||
\(948\) | −2.58715e18 | −0.115762 | ||||||||
\(949\) | 8.41804e18 | 0.374094 | ||||||||
\(950\) | −3.91609e19 | −1.72842 | ||||||||
\(951\) | 1.23084e19 | 0.539546 | ||||||||
\(952\) | −1.69434e19 | −0.737668 | ||||||||
\(953\) | 8.08120e18 | 0.349440 | 0.174720 | − | 0.984618i | \(-0.444098\pi\) | ||||
0.174720 | + | 0.984618i | \(0.444098\pi\) | |||||||
\(954\) | −1.64844e19 | −0.707960 | ||||||||
\(955\) | 1.02695e19 | 0.438053 | ||||||||
\(956\) | −9.83973e18 | −0.416876 | ||||||||
\(957\) | 1.76371e19 | 0.742166 | ||||||||
\(958\) | 3.25753e19 | 1.36148 | ||||||||
\(959\) | −2.70444e19 | −1.12268 | ||||||||
\(960\) | −1.58880e18 | −0.0655099 | ||||||||
\(961\) | −1.20212e19 | −0.492319 | ||||||||
\(962\) | −8.60290e18 | −0.349951 | ||||||||
\(963\) | 1.03042e19 | 0.416335 | ||||||||
\(964\) | 1.25091e18 | 0.0502026 | ||||||||
\(965\) | −1.51060e19 | −0.602174 | ||||||||
\(966\) | −1.03239e19 | −0.408784 | ||||||||
\(967\) | 1.29236e19 | 0.508290 | 0.254145 | − | 0.967166i | \(-0.418206\pi\) | ||||
0.254145 | + | 0.967166i | \(0.418206\pi\) | |||||||
\(968\) | 1.21278e17 | 0.00473797 | ||||||||
\(969\) | −4.12233e19 | −1.59970 | ||||||||
\(970\) | 1.22419e18 | 0.0471882 | ||||||||
\(971\) | 4.54011e19 | 1.73837 | 0.869184 | − | 0.494489i | \(-0.164645\pi\) | ||||
0.869184 | + | 0.494489i | \(0.164645\pi\) | |||||||
\(972\) | 7.46115e17 | 0.0283776 | ||||||||
\(973\) | 6.49789e18 | 0.245493 | ||||||||
\(974\) | −4.61384e19 | −1.73153 | ||||||||
\(975\) | −3.57138e18 | −0.133139 | ||||||||
\(976\) | 1.44406e19 | 0.534764 | ||||||||
\(977\) | −1.55782e19 | −0.573062 | −0.286531 | − | 0.958071i | \(-0.592502\pi\) | ||||
−0.286531 | + | 0.958071i | \(0.592502\pi\) | |||||||
\(978\) | 1.55182e19 | 0.567072 | ||||||||
\(979\) | 8.75920e17 | 0.0317963 | ||||||||
\(980\) | 2.67980e18 | 0.0966346 | ||||||||
\(981\) | 7.17447e18 | 0.257005 | ||||||||
\(982\) | −3.06617e18 | −0.109112 | ||||||||
\(983\) | −8.04089e18 | −0.284254 | −0.142127 | − | 0.989848i | \(-0.545394\pi\) | ||||
−0.142127 | + | 0.989848i | \(0.545394\pi\) | |||||||
\(984\) | −1.45972e19 | −0.512625 | ||||||||
\(985\) | −1.96213e18 | −0.0684530 | ||||||||
\(986\) | −6.82465e19 | −2.36527 | ||||||||
\(987\) | −1.00745e19 | −0.346866 | ||||||||
\(988\) | −6.73016e18 | −0.230200 | ||||||||
\(989\) | 1.22724e19 | 0.417018 | ||||||||
\(990\) | 5.34086e18 | 0.180295 | ||||||||
\(991\) | −4.02795e18 | −0.135085 | −0.0675423 | − | 0.997716i | \(-0.521516\pi\) | ||||
−0.0675423 | + | 0.997716i | \(0.521516\pi\) | |||||||
\(992\) | −1.76971e19 | −0.589627 | ||||||||
\(993\) | −1.70630e19 | −0.564788 | ||||||||
\(994\) | −1.67656e19 | −0.551324 | ||||||||
\(995\) | 1.91078e19 | 0.624252 | ||||||||
\(996\) | −1.30794e19 | −0.424525 | ||||||||
\(997\) | −6.13845e19 | −1.97943 | −0.989715 | − | 0.143052i | \(-0.954308\pi\) | ||||
−0.989715 | + | 0.143052i | \(0.954308\pi\) | |||||||
\(998\) | 1.05983e19 | 0.339537 | ||||||||
\(999\) | 6.10131e18 | 0.194199 |
(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.1.8 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.a.1.8 | ✓ | 30 | 1.1 | even | 1 | trivial |