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 | 1.26 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 132.796 | 1.46721 | 0.733603 | − | 0.679579i | \(-0.237837\pi\) | ||||
0.733603 | + | 0.679579i | \(0.237837\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 9442.84 | 1.15269 | ||||||||
\(5\) | 3277.42 | 0.0938053 | 0.0469027 | − | 0.998899i | \(-0.485065\pi\) | ||||
0.0469027 | + | 0.998899i | \(0.485065\pi\) | |||||||
\(6\) | 96808.5 | 0.847091 | ||||||||
\(7\) | −296432. | −0.952331 | −0.476165 | − | 0.879356i | \(-0.657974\pi\) | ||||
−0.476165 | + | 0.879356i | \(0.657974\pi\) | |||||||
\(8\) | 166107. | 0.224029 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | 435229. | 0.137632 | ||||||||
\(11\) | 9.14323e6 | 1.55613 | 0.778067 | − | 0.628181i | \(-0.216200\pi\) | ||||
0.778067 | + | 0.628181i | \(0.216200\pi\) | |||||||
\(12\) | 6.88383e6 | 0.665506 | ||||||||
\(13\) | −3.48492e6 | −0.200244 | −0.100122 | − | 0.994975i | \(-0.531923\pi\) | ||||
−0.100122 | + | 0.994975i | \(0.531923\pi\) | |||||||
\(14\) | −3.93651e7 | −1.39726 | ||||||||
\(15\) | 2.38924e6 | 0.0541585 | ||||||||
\(16\) | −5.52973e7 | −0.823995 | ||||||||
\(17\) | −3.85684e7 | −0.387538 | −0.193769 | − | 0.981047i | \(-0.562071\pi\) | ||||
−0.193769 | + | 0.981047i | \(0.562071\pi\) | |||||||
\(18\) | 7.05734e7 | 0.489068 | ||||||||
\(19\) | 2.85648e7 | 0.139294 | 0.0696471 | − | 0.997572i | \(-0.477813\pi\) | ||||
0.0696471 | + | 0.997572i | \(0.477813\pi\) | |||||||
\(20\) | 3.09482e7 | 0.108129 | ||||||||
\(21\) | −2.16099e8 | −0.549829 | ||||||||
\(22\) | 1.21419e9 | 2.28317 | ||||||||
\(23\) | −7.24424e8 | −1.02038 | −0.510190 | − | 0.860062i | \(-0.670425\pi\) | ||||
−0.510190 | + | 0.860062i | \(0.670425\pi\) | |||||||
\(24\) | 1.21092e8 | 0.129343 | ||||||||
\(25\) | −1.20996e9 | −0.991201 | ||||||||
\(26\) | −4.62784e8 | −0.293800 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | −2.79916e9 | −1.09774 | ||||||||
\(29\) | −3.17470e9 | −0.991096 | −0.495548 | − | 0.868580i | \(-0.665033\pi\) | ||||
−0.495548 | + | 0.868580i | \(0.665033\pi\) | |||||||
\(30\) | 3.17282e8 | 0.0794617 | ||||||||
\(31\) | −4.23680e9 | −0.857407 | −0.428704 | − | 0.903445i | \(-0.641030\pi\) | ||||
−0.428704 | + | 0.903445i | \(0.641030\pi\) | |||||||
\(32\) | −8.70403e9 | −1.43300 | ||||||||
\(33\) | 6.66541e9 | 0.898435 | ||||||||
\(34\) | −5.12174e9 | −0.568597 | ||||||||
\(35\) | −9.71533e8 | −0.0893337 | ||||||||
\(36\) | 5.01831e9 | 0.384230 | ||||||||
\(37\) | 2.66331e10 | 1.70652 | 0.853259 | − | 0.521487i | \(-0.174623\pi\) | ||||
0.853259 | + | 0.521487i | \(0.174623\pi\) | |||||||
\(38\) | 3.79330e9 | 0.204373 | ||||||||
\(39\) | −2.54050e9 | −0.115611 | ||||||||
\(40\) | 5.44404e8 | 0.0210151 | ||||||||
\(41\) | −2.67542e10 | −0.879623 | −0.439812 | − | 0.898090i | \(-0.644955\pi\) | ||||
−0.439812 | + | 0.898090i | \(0.644955\pi\) | |||||||
\(42\) | −2.86971e10 | −0.806711 | ||||||||
\(43\) | 7.18936e10 | 1.73438 | 0.867192 | − | 0.497974i | \(-0.165923\pi\) | ||||
0.867192 | + | 0.497974i | \(0.165923\pi\) | |||||||
\(44\) | 8.63381e10 | 1.79374 | ||||||||
\(45\) | 1.74176e9 | 0.0312684 | ||||||||
\(46\) | −9.62007e10 | −1.49711 | ||||||||
\(47\) | 7.60117e10 | 1.02860 | 0.514298 | − | 0.857612i | \(-0.328053\pi\) | ||||
0.514298 | + | 0.857612i | \(0.328053\pi\) | |||||||
\(48\) | −4.03118e10 | −0.475733 | ||||||||
\(49\) | −9.01705e9 | −0.0930657 | ||||||||
\(50\) | −1.60678e11 | −1.45429 | ||||||||
\(51\) | −2.81164e10 | −0.223745 | ||||||||
\(52\) | −3.29075e10 | −0.230820 | ||||||||
\(53\) | −2.54878e11 | −1.57957 | −0.789787 | − | 0.613381i | \(-0.789809\pi\) | ||||
−0.789787 | + | 0.613381i | \(0.789809\pi\) | |||||||
\(54\) | 5.14480e10 | 0.282364 | ||||||||
\(55\) | 2.99662e10 | 0.145974 | ||||||||
\(56\) | −4.92396e10 | −0.213350 | ||||||||
\(57\) | 2.08237e10 | 0.0804215 | ||||||||
\(58\) | −4.21588e11 | −1.45414 | ||||||||
\(59\) | 4.21805e10 | 0.130189 | ||||||||
\(60\) | 2.25612e10 | 0.0624280 | ||||||||
\(61\) | −4.30773e11 | −1.07054 | −0.535272 | − | 0.844680i | \(-0.679791\pi\) | ||||
−0.535272 | + | 0.844680i | \(0.679791\pi\) | |||||||
\(62\) | −5.62632e11 | −1.25799 | ||||||||
\(63\) | −1.57536e11 | −0.317444 | ||||||||
\(64\) | −7.02867e11 | −1.27851 | ||||||||
\(65\) | −1.14215e10 | −0.0187840 | ||||||||
\(66\) | 8.85142e11 | 1.31819 | ||||||||
\(67\) | −1.20675e12 | −1.62978 | −0.814892 | − | 0.579612i | \(-0.803204\pi\) | ||||
−0.814892 | + | 0.579612i | \(0.803204\pi\) | |||||||
\(68\) | −3.64195e11 | −0.446711 | ||||||||
\(69\) | −5.28105e11 | −0.589116 | ||||||||
\(70\) | −1.29016e11 | −0.131071 | ||||||||
\(71\) | 6.68630e11 | 0.619450 | 0.309725 | − | 0.950826i | \(-0.399763\pi\) | ||||
0.309725 | + | 0.950826i | \(0.399763\pi\) | |||||||
\(72\) | 8.82763e10 | 0.0746763 | ||||||||
\(73\) | −2.42459e11 | −0.187517 | −0.0937583 | − | 0.995595i | \(-0.529888\pi\) | ||||
−0.0937583 | + | 0.995595i | \(0.529888\pi\) | |||||||
\(74\) | 3.53678e12 | 2.50381 | ||||||||
\(75\) | −8.82062e11 | −0.572270 | ||||||||
\(76\) | 2.69733e11 | 0.160563 | ||||||||
\(77\) | −2.71035e12 | −1.48196 | ||||||||
\(78\) | −3.37369e11 | −0.169625 | ||||||||
\(79\) | 4.77381e11 | 0.220947 | 0.110474 | − | 0.993879i | \(-0.464763\pi\) | ||||
0.110474 | + | 0.993879i | \(0.464763\pi\) | |||||||
\(80\) | −1.81233e11 | −0.0772951 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | −3.55286e12 | −1.29059 | ||||||||
\(83\) | −2.06958e12 | −0.694825 | −0.347413 | − | 0.937712i | \(-0.612940\pi\) | ||||
−0.347413 | + | 0.937712i | \(0.612940\pi\) | |||||||
\(84\) | −2.04059e12 | −0.633782 | ||||||||
\(85\) | −1.26405e11 | −0.0363531 | ||||||||
\(86\) | 9.54720e12 | 2.54470 | ||||||||
\(87\) | −2.31436e12 | −0.572210 | ||||||||
\(88\) | 1.51876e12 | 0.348619 | ||||||||
\(89\) | −6.68736e12 | −1.42633 | −0.713165 | − | 0.700997i | \(-0.752739\pi\) | ||||
−0.713165 | + | 0.700997i | \(0.752739\pi\) | |||||||
\(90\) | 2.31299e11 | 0.0458772 | ||||||||
\(91\) | 1.03304e12 | 0.190699 | ||||||||
\(92\) | −6.84062e12 | −1.17618 | ||||||||
\(93\) | −3.08863e12 | −0.495024 | ||||||||
\(94\) | 1.00941e13 | 1.50916 | ||||||||
\(95\) | 9.36190e10 | 0.0130665 | ||||||||
\(96\) | −6.34524e12 | −0.827342 | ||||||||
\(97\) | 3.13450e12 | 0.382078 | 0.191039 | − | 0.981582i | \(-0.438814\pi\) | ||||
0.191039 | + | 0.981582i | \(0.438814\pi\) | |||||||
\(98\) | −1.19743e12 | −0.136547 | ||||||||
\(99\) | 4.85909e12 | 0.518712 | ||||||||
\(100\) | −1.14255e13 | −1.14255 | ||||||||
\(101\) | −7.94215e12 | −0.744474 | −0.372237 | − | 0.928138i | \(-0.621409\pi\) | ||||
−0.372237 | + | 0.928138i | \(0.621409\pi\) | |||||||
\(102\) | −3.73375e12 | −0.328280 | ||||||||
\(103\) | −2.08416e13 | −1.71985 | −0.859923 | − | 0.510423i | \(-0.829489\pi\) | ||||
−0.859923 | + | 0.510423i | \(0.829489\pi\) | |||||||
\(104\) | −5.78870e11 | −0.0448605 | ||||||||
\(105\) | −7.08248e11 | −0.0515768 | ||||||||
\(106\) | −3.38469e13 | −2.31756 | ||||||||
\(107\) | 1.89166e13 | 1.21856 | 0.609281 | − | 0.792954i | \(-0.291458\pi\) | ||||
0.609281 | + | 0.792954i | \(0.291458\pi\) | |||||||
\(108\) | 3.65835e12 | 0.221835 | ||||||||
\(109\) | −1.64082e13 | −0.937109 | −0.468554 | − | 0.883435i | \(-0.655225\pi\) | ||||
−0.468554 | + | 0.883435i | \(0.655225\pi\) | |||||||
\(110\) | 3.97940e12 | 0.214173 | ||||||||
\(111\) | 1.94155e13 | 0.985259 | ||||||||
\(112\) | 1.63919e13 | 0.784716 | ||||||||
\(113\) | 1.39969e13 | 0.632443 | 0.316222 | − | 0.948685i | \(-0.397586\pi\) | ||||
0.316222 | + | 0.948685i | \(0.397586\pi\) | |||||||
\(114\) | 2.76532e12 | 0.117995 | ||||||||
\(115\) | −2.37424e12 | −0.0957170 | ||||||||
\(116\) | −2.99782e13 | −1.14243 | ||||||||
\(117\) | −1.85203e12 | −0.0667481 | ||||||||
\(118\) | 5.60142e12 | 0.191014 | ||||||||
\(119\) | 1.14329e13 | 0.369064 | ||||||||
\(120\) | 3.96871e11 | 0.0121331 | ||||||||
\(121\) | 4.90759e13 | 1.42155 | ||||||||
\(122\) | −5.72051e13 | −1.57071 | ||||||||
\(123\) | −1.95038e13 | −0.507851 | ||||||||
\(124\) | −4.00075e13 | −0.988326 | ||||||||
\(125\) | −7.96632e12 | −0.186785 | ||||||||
\(126\) | −2.09202e13 | −0.465755 | ||||||||
\(127\) | −8.70776e13 | −1.84154 | −0.920772 | − | 0.390101i | \(-0.872440\pi\) | ||||
−0.920772 | + | 0.390101i | \(0.872440\pi\) | |||||||
\(128\) | −2.20347e13 | −0.442835 | ||||||||
\(129\) | 5.24104e13 | 1.00135 | ||||||||
\(130\) | −1.51674e12 | −0.0275600 | ||||||||
\(131\) | 8.26459e13 | 1.42876 | 0.714378 | − | 0.699760i | \(-0.246710\pi\) | ||||
0.714378 | + | 0.699760i | \(0.246710\pi\) | |||||||
\(132\) | 6.29405e13 | 1.03562 | ||||||||
\(133\) | −8.46753e12 | −0.132654 | ||||||||
\(134\) | −1.60252e14 | −2.39123 | ||||||||
\(135\) | 1.26974e12 | 0.0180528 | ||||||||
\(136\) | −6.40650e12 | −0.0868196 | ||||||||
\(137\) | −8.20575e13 | −1.06031 | −0.530157 | − | 0.847899i | \(-0.677867\pi\) | ||||
−0.530157 | + | 0.847899i | \(0.677867\pi\) | |||||||
\(138\) | −7.01303e13 | −0.864355 | ||||||||
\(139\) | −8.14600e13 | −0.957961 | −0.478981 | − | 0.877825i | \(-0.658994\pi\) | ||||
−0.478981 | + | 0.877825i | \(0.658994\pi\) | |||||||
\(140\) | −9.17404e12 | −0.102974 | ||||||||
\(141\) | 5.54125e13 | 0.593860 | ||||||||
\(142\) | 8.87915e13 | 0.908861 | ||||||||
\(143\) | −3.18634e13 | −0.311607 | ||||||||
\(144\) | −2.93873e13 | −0.274665 | ||||||||
\(145\) | −1.04048e13 | −0.0929701 | ||||||||
\(146\) | −3.21977e13 | −0.275125 | ||||||||
\(147\) | −6.57343e12 | −0.0537315 | ||||||||
\(148\) | 2.51492e14 | 1.96709 | ||||||||
\(149\) | −9.57664e13 | −0.716972 | −0.358486 | − | 0.933535i | \(-0.616707\pi\) | ||||
−0.358486 | + | 0.933535i | \(0.616707\pi\) | |||||||
\(150\) | −1.17135e14 | −0.839637 | ||||||||
\(151\) | −1.03063e14 | −0.707544 | −0.353772 | − | 0.935332i | \(-0.615101\pi\) | ||||
−0.353772 | + | 0.935332i | \(0.615101\pi\) | |||||||
\(152\) | 4.74483e12 | 0.0312059 | ||||||||
\(153\) | −2.04968e13 | −0.129179 | ||||||||
\(154\) | −3.59924e14 | −2.17433 | ||||||||
\(155\) | −1.38858e13 | −0.0804294 | ||||||||
\(156\) | −2.39896e13 | −0.133264 | ||||||||
\(157\) | 2.47605e14 | 1.31951 | 0.659753 | − | 0.751482i | \(-0.270661\pi\) | ||||
0.659753 | + | 0.751482i | \(0.270661\pi\) | |||||||
\(158\) | 6.33944e13 | 0.324175 | ||||||||
\(159\) | −1.85806e14 | −0.911967 | ||||||||
\(160\) | −2.85268e13 | −0.134423 | ||||||||
\(161\) | 2.14742e14 | 0.971739 | ||||||||
\(162\) | 3.75056e13 | 0.163023 | ||||||||
\(163\) | 4.49313e14 | 1.87642 | 0.938208 | − | 0.346072i | \(-0.112485\pi\) | ||||
0.938208 | + | 0.346072i | \(0.112485\pi\) | |||||||
\(164\) | −2.52636e14 | −1.01393 | ||||||||
\(165\) | 2.18454e13 | 0.0842779 | ||||||||
\(166\) | −2.74833e14 | −1.01945 | ||||||||
\(167\) | −1.95100e14 | −0.695984 | −0.347992 | − | 0.937498i | \(-0.613136\pi\) | ||||
−0.347992 | + | 0.937498i | \(0.613136\pi\) | |||||||
\(168\) | −3.58956e13 | −0.123177 | ||||||||
\(169\) | −2.90730e14 | −0.959902 | ||||||||
\(170\) | −1.67861e13 | −0.0533374 | ||||||||
\(171\) | 1.51805e13 | 0.0464314 | ||||||||
\(172\) | 6.78880e14 | 1.99921 | ||||||||
\(173\) | −1.26094e14 | −0.357597 | −0.178798 | − | 0.983886i | \(-0.557221\pi\) | ||||
−0.178798 | + | 0.983886i | \(0.557221\pi\) | |||||||
\(174\) | −3.07338e14 | −0.839549 | ||||||||
\(175\) | 3.58671e14 | 0.943951 | ||||||||
\(176\) | −5.05596e14 | −1.28225 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | −8.88057e14 | −2.09272 | ||||||||
\(179\) | −3.09537e13 | −0.0703344 | −0.0351672 | − | 0.999381i | \(-0.511196\pi\) | ||||
−0.0351672 | + | 0.999381i | \(0.511196\pi\) | |||||||
\(180\) | 1.64471e13 | 0.0360428 | ||||||||
\(181\) | −2.55327e14 | −0.539741 | −0.269871 | − | 0.962897i | \(-0.586981\pi\) | ||||
−0.269871 | + | 0.962897i | \(0.586981\pi\) | |||||||
\(182\) | 1.37184e14 | 0.279794 | ||||||||
\(183\) | −3.14034e14 | −0.618079 | ||||||||
\(184\) | −1.20332e14 | −0.228594 | ||||||||
\(185\) | 8.72880e13 | 0.160080 | ||||||||
\(186\) | −4.10158e14 | −0.726302 | ||||||||
\(187\) | −3.52640e14 | −0.603061 | ||||||||
\(188\) | 7.17767e14 | 1.18565 | ||||||||
\(189\) | −1.14844e14 | −0.183276 | ||||||||
\(190\) | 1.24322e13 | 0.0191713 | ||||||||
\(191\) | 8.50898e14 | 1.26812 | 0.634060 | − | 0.773284i | \(-0.281387\pi\) | ||||
0.634060 | + | 0.773284i | \(0.281387\pi\) | |||||||
\(192\) | −5.12390e14 | −0.738147 | ||||||||
\(193\) | −2.10969e14 | −0.293830 | −0.146915 | − | 0.989149i | \(-0.546934\pi\) | ||||
−0.146915 | + | 0.989149i | \(0.546934\pi\) | |||||||
\(194\) | 4.16250e14 | 0.560586 | ||||||||
\(195\) | −8.32630e12 | −0.0108449 | ||||||||
\(196\) | −8.51466e13 | −0.107276 | ||||||||
\(197\) | −6.04601e14 | −0.736950 | −0.368475 | − | 0.929638i | \(-0.620120\pi\) | ||||
−0.368475 | + | 0.929638i | \(0.620120\pi\) | |||||||
\(198\) | 6.45269e14 | 0.761056 | ||||||||
\(199\) | 1.46244e14 | 0.166929 | 0.0834647 | − | 0.996511i | \(-0.473401\pi\) | ||||
0.0834647 | + | 0.996511i | \(0.473401\pi\) | |||||||
\(200\) | −2.00984e14 | −0.222058 | ||||||||
\(201\) | −8.79719e14 | −0.940957 | ||||||||
\(202\) | −1.05469e15 | −1.09230 | ||||||||
\(203\) | 9.41083e14 | 0.943852 | ||||||||
\(204\) | −2.65499e14 | −0.257909 | ||||||||
\(205\) | −8.76848e13 | −0.0825133 | ||||||||
\(206\) | −2.76769e15 | −2.52337 | ||||||||
\(207\) | −3.84988e14 | −0.340126 | ||||||||
\(208\) | 1.92707e14 | 0.165000 | ||||||||
\(209\) | 2.61175e14 | 0.216760 | ||||||||
\(210\) | −9.40526e13 | −0.0756738 | ||||||||
\(211\) | 2.16811e15 | 1.69140 | 0.845700 | − | 0.533659i | \(-0.179183\pi\) | ||||
0.845700 | + | 0.533659i | \(0.179183\pi\) | |||||||
\(212\) | −2.40678e15 | −1.82076 | ||||||||
\(213\) | 4.87431e14 | 0.357640 | ||||||||
\(214\) | 2.51205e15 | 1.78788 | ||||||||
\(215\) | 2.35626e14 | 0.162694 | ||||||||
\(216\) | 6.43534e13 | 0.0431144 | ||||||||
\(217\) | 1.25592e15 | 0.816536 | ||||||||
\(218\) | −2.17895e15 | −1.37493 | ||||||||
\(219\) | −1.76753e14 | −0.108263 | ||||||||
\(220\) | 2.82966e14 | 0.168263 | ||||||||
\(221\) | 1.34408e14 | 0.0776022 | ||||||||
\(222\) | 2.57831e15 | 1.44558 | ||||||||
\(223\) | 1.49124e15 | 0.812020 | 0.406010 | − | 0.913869i | \(-0.366920\pi\) | ||||
0.406010 | + | 0.913869i | \(0.366920\pi\) | |||||||
\(224\) | 2.58015e15 | 1.36469 | ||||||||
\(225\) | −6.43023e14 | −0.330400 | ||||||||
\(226\) | 1.85873e15 | 0.927924 | ||||||||
\(227\) | 3.66877e15 | 1.77972 | 0.889862 | − | 0.456229i | \(-0.150800\pi\) | ||||
0.889862 | + | 0.456229i | \(0.150800\pi\) | |||||||
\(228\) | 1.96635e14 | 0.0927012 | ||||||||
\(229\) | 3.82282e15 | 1.75167 | 0.875836 | − | 0.482609i | \(-0.160311\pi\) | ||||
0.875836 | + | 0.482609i | \(0.160311\pi\) | |||||||
\(230\) | −3.15291e14 | −0.140436 | ||||||||
\(231\) | −1.97584e15 | −0.855607 | ||||||||
\(232\) | −5.27341e14 | −0.222034 | ||||||||
\(233\) | −4.06875e15 | −1.66590 | −0.832948 | − | 0.553351i | \(-0.813349\pi\) | ||||
−0.832948 | + | 0.553351i | \(0.813349\pi\) | |||||||
\(234\) | −2.45942e14 | −0.0979332 | ||||||||
\(235\) | 2.49122e14 | 0.0964877 | ||||||||
\(236\) | 3.98304e14 | 0.150068 | ||||||||
\(237\) | 3.48010e14 | 0.127564 | ||||||||
\(238\) | 1.51825e15 | 0.541493 | ||||||||
\(239\) | −4.72269e14 | −0.163909 | −0.0819546 | − | 0.996636i | \(-0.526116\pi\) | ||||
−0.0819546 | + | 0.996636i | \(0.526116\pi\) | |||||||
\(240\) | −1.32119e14 | −0.0446263 | ||||||||
\(241\) | −2.15926e15 | −0.709894 | −0.354947 | − | 0.934886i | \(-0.615501\pi\) | ||||
−0.354947 | + | 0.934886i | \(0.615501\pi\) | |||||||
\(242\) | 6.51710e15 | 2.08571 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | −4.06772e15 | −1.23401 | ||||||||
\(245\) | −2.95527e13 | −0.00873006 | ||||||||
\(246\) | −2.59003e15 | −0.745121 | ||||||||
\(247\) | −9.95459e13 | −0.0278929 | ||||||||
\(248\) | −7.03764e14 | −0.192084 | ||||||||
\(249\) | −1.50873e15 | −0.401157 | ||||||||
\(250\) | −1.05790e15 | −0.274052 | ||||||||
\(251\) | 5.29839e15 | 1.33741 | 0.668705 | − | 0.743528i | \(-0.266849\pi\) | ||||
0.668705 | + | 0.743528i | \(0.266849\pi\) | |||||||
\(252\) | −1.48759e15 | −0.365914 | ||||||||
\(253\) | −6.62357e15 | −1.58785 | ||||||||
\(254\) | −1.15636e16 | −2.70192 | ||||||||
\(255\) | −9.21492e13 | −0.0209885 | ||||||||
\(256\) | 2.83177e15 | 0.628778 | ||||||||
\(257\) | −7.76202e15 | −1.68039 | −0.840193 | − | 0.542287i | \(-0.817559\pi\) | ||||
−0.840193 | + | 0.542287i | \(0.817559\pi\) | |||||||
\(258\) | 6.95991e15 | 1.46918 | ||||||||
\(259\) | −7.89491e15 | −1.62517 | ||||||||
\(260\) | −1.07852e14 | −0.0216521 | ||||||||
\(261\) | −1.68717e15 | −0.330365 | ||||||||
\(262\) | 1.09751e16 | 2.09628 | ||||||||
\(263\) | 4.72422e15 | 0.880273 | 0.440137 | − | 0.897931i | \(-0.354930\pi\) | ||||
0.440137 | + | 0.897931i | \(0.354930\pi\) | |||||||
\(264\) | 1.10717e15 | 0.201275 | ||||||||
\(265\) | −8.35344e14 | −0.148172 | ||||||||
\(266\) | −1.12446e15 | −0.194631 | ||||||||
\(267\) | −4.87509e15 | −0.823492 | ||||||||
\(268\) | −1.13951e16 | −1.87864 | ||||||||
\(269\) | 8.59423e15 | 1.38298 | 0.691492 | − | 0.722384i | \(-0.256954\pi\) | ||||
0.691492 | + | 0.722384i | \(0.256954\pi\) | |||||||
\(270\) | 1.68617e14 | 0.0264872 | ||||||||
\(271\) | −1.15719e16 | −1.77462 | −0.887308 | − | 0.461177i | \(-0.847427\pi\) | ||||
−0.887308 | + | 0.461177i | \(0.847427\pi\) | |||||||
\(272\) | 2.13273e15 | 0.319329 | ||||||||
\(273\) | 7.53087e14 | 0.110100 | ||||||||
\(274\) | −1.08969e16 | −1.55570 | ||||||||
\(275\) | −1.10630e16 | −1.54244 | ||||||||
\(276\) | −4.98681e15 | −0.679069 | ||||||||
\(277\) | 3.59234e15 | 0.477815 | 0.238907 | − | 0.971042i | \(-0.423211\pi\) | ||||
0.238907 | + | 0.971042i | \(0.423211\pi\) | |||||||
\(278\) | −1.08176e16 | −1.40553 | ||||||||
\(279\) | −2.25161e15 | −0.285802 | ||||||||
\(280\) | −1.61379e14 | −0.0200133 | ||||||||
\(281\) | 1.03686e16 | 1.25641 | 0.628204 | − | 0.778048i | \(-0.283790\pi\) | ||||
0.628204 | + | 0.778048i | \(0.283790\pi\) | |||||||
\(282\) | 7.35858e15 | 0.871314 | ||||||||
\(283\) | 1.07320e15 | 0.124185 | 0.0620924 | − | 0.998070i | \(-0.480223\pi\) | ||||
0.0620924 | + | 0.998070i | \(0.480223\pi\) | |||||||
\(284\) | 6.31377e15 | 0.714035 | ||||||||
\(285\) | 6.82482e13 | 0.00754397 | ||||||||
\(286\) | −4.23134e15 | −0.457192 | ||||||||
\(287\) | 7.93080e15 | 0.837692 | ||||||||
\(288\) | −4.62568e15 | −0.477666 | ||||||||
\(289\) | −8.41706e15 | −0.849815 | ||||||||
\(290\) | −1.38172e15 | −0.136406 | ||||||||
\(291\) | 2.28505e15 | 0.220593 | ||||||||
\(292\) | −2.28950e15 | −0.216149 | ||||||||
\(293\) | 1.79687e14 | 0.0165911 | 0.00829557 | − | 0.999966i | \(-0.497359\pi\) | ||||
0.00829557 | + | 0.999966i | \(0.497359\pi\) | |||||||
\(294\) | −8.72926e14 | −0.0788352 | ||||||||
\(295\) | 1.38243e14 | 0.0122124 | ||||||||
\(296\) | 4.42396e15 | 0.382309 | ||||||||
\(297\) | 3.54227e15 | 0.299478 | ||||||||
\(298\) | −1.27174e16 | −1.05195 | ||||||||
\(299\) | 2.52456e15 | 0.204325 | ||||||||
\(300\) | −8.32917e15 | −0.659650 | ||||||||
\(301\) | −2.13116e16 | −1.65171 | ||||||||
\(302\) | −1.36864e16 | −1.03811 | ||||||||
\(303\) | −5.78983e15 | −0.429822 | ||||||||
\(304\) | −1.57956e15 | −0.114778 | ||||||||
\(305\) | −1.41183e15 | −0.100423 | ||||||||
\(306\) | −2.72190e15 | −0.189532 | ||||||||
\(307\) | −7.84218e15 | −0.534610 | −0.267305 | − | 0.963612i | \(-0.586133\pi\) | ||||
−0.267305 | + | 0.963612i | \(0.586133\pi\) | |||||||
\(308\) | −2.55934e16 | −1.70824 | ||||||||
\(309\) | −1.51935e16 | −0.992954 | ||||||||
\(310\) | −1.84398e15 | −0.118006 | ||||||||
\(311\) | 9.56638e15 | 0.599522 | 0.299761 | − | 0.954014i | \(-0.403093\pi\) | ||||
0.299761 | + | 0.954014i | \(0.403093\pi\) | |||||||
\(312\) | −4.21996e14 | −0.0259002 | ||||||||
\(313\) | 4.96244e15 | 0.298303 | 0.149151 | − | 0.988814i | \(-0.452346\pi\) | ||||
0.149151 | + | 0.988814i | \(0.452346\pi\) | |||||||
\(314\) | 3.28810e16 | 1.93599 | ||||||||
\(315\) | −5.16313e14 | −0.0297779 | ||||||||
\(316\) | 4.50783e15 | 0.254684 | ||||||||
\(317\) | 2.91290e16 | 1.61228 | 0.806139 | − | 0.591726i | \(-0.201553\pi\) | ||||
0.806139 | + | 0.591726i | \(0.201553\pi\) | |||||||
\(318\) | −2.46744e16 | −1.33804 | ||||||||
\(319\) | −2.90270e16 | −1.54228 | ||||||||
\(320\) | −2.30359e15 | −0.119931 | ||||||||
\(321\) | 1.37902e16 | 0.703537 | ||||||||
\(322\) | 2.85170e16 | 1.42574 | ||||||||
\(323\) | −1.10170e15 | −0.0539817 | ||||||||
\(324\) | 2.66694e15 | 0.128077 | ||||||||
\(325\) | 4.21661e15 | 0.198482 | ||||||||
\(326\) | 5.96670e16 | 2.75309 | ||||||||
\(327\) | −1.19616e16 | −0.541040 | ||||||||
\(328\) | −4.44407e15 | −0.197061 | ||||||||
\(329\) | −2.25323e16 | −0.979563 | ||||||||
\(330\) | 2.90098e15 | 0.123653 | ||||||||
\(331\) | −2.34480e15 | −0.0979996 | −0.0489998 | − | 0.998799i | \(-0.515603\pi\) | ||||
−0.0489998 | + | 0.998799i | \(0.515603\pi\) | |||||||
\(332\) | −1.95428e16 | −0.800918 | ||||||||
\(333\) | 1.41539e16 | 0.568839 | ||||||||
\(334\) | −2.59085e16 | −1.02115 | ||||||||
\(335\) | −3.95502e15 | −0.152882 | ||||||||
\(336\) | 1.19497e16 | 0.453056 | ||||||||
\(337\) | −4.95458e15 | −0.184252 | −0.0921260 | − | 0.995747i | \(-0.529366\pi\) | ||||
−0.0921260 | + | 0.995747i | \(0.529366\pi\) | |||||||
\(338\) | −3.86079e16 | −1.40837 | ||||||||
\(339\) | 1.02037e16 | 0.365141 | ||||||||
\(340\) | −1.19362e15 | −0.0419039 | ||||||||
\(341\) | −3.87381e16 | −1.33424 | ||||||||
\(342\) | 2.01591e15 | 0.0681244 | ||||||||
\(343\) | 3.13940e16 | 1.04096 | ||||||||
\(344\) | 1.19421e16 | 0.388552 | ||||||||
\(345\) | −1.73082e15 | −0.0552622 | ||||||||
\(346\) | −1.67448e16 | −0.524668 | ||||||||
\(347\) | 3.72121e16 | 1.14431 | 0.572153 | − | 0.820147i | \(-0.306108\pi\) | ||||
0.572153 | + | 0.820147i | \(0.306108\pi\) | |||||||
\(348\) | −2.18541e16 | −0.659581 | ||||||||
\(349\) | −5.71815e16 | −1.69391 | −0.846954 | − | 0.531666i | \(-0.821566\pi\) | ||||
−0.846954 | + | 0.531666i | \(0.821566\pi\) | |||||||
\(350\) | 4.76302e16 | 1.38497 | ||||||||
\(351\) | −1.35013e15 | −0.0385371 | ||||||||
\(352\) | −7.95829e16 | −2.22994 | ||||||||
\(353\) | 1.22107e16 | 0.335896 | 0.167948 | − | 0.985796i | \(-0.446286\pi\) | ||||
0.167948 | + | 0.985796i | \(0.446286\pi\) | |||||||
\(354\) | 4.08343e15 | 0.110282 | ||||||||
\(355\) | 2.19138e15 | 0.0581077 | ||||||||
\(356\) | −6.31477e16 | −1.64412 | ||||||||
\(357\) | 8.33459e15 | 0.213079 | ||||||||
\(358\) | −4.11053e15 | −0.103195 | ||||||||
\(359\) | −3.01276e13 | −0.000742764 0 | −0.000371382 | − | 1.00000i | \(-0.500118\pi\) | ||||
−0.000371382 | 1.00000i | \(0.500118\pi\) | ||||||||
\(360\) | 2.89319e14 | 0.00700503 | ||||||||
\(361\) | −4.12370e16 | −0.980597 | ||||||||
\(362\) | −3.39064e16 | −0.791911 | ||||||||
\(363\) | 3.57763e16 | 0.820735 | ||||||||
\(364\) | 9.75484e15 | 0.219817 | ||||||||
\(365\) | −7.94641e14 | −0.0175901 | ||||||||
\(366\) | −4.17025e16 | −0.906849 | ||||||||
\(367\) | −1.56082e16 | −0.333445 | −0.166722 | − | 0.986004i | \(-0.553318\pi\) | ||||
−0.166722 | + | 0.986004i | \(0.553318\pi\) | |||||||
\(368\) | 4.00587e16 | 0.840787 | ||||||||
\(369\) | −1.42183e16 | −0.293208 | ||||||||
\(370\) | 1.15915e16 | 0.234871 | ||||||||
\(371\) | 7.55541e16 | 1.50428 | ||||||||
\(372\) | −2.91654e16 | −0.570610 | ||||||||
\(373\) | 5.51883e16 | 1.06106 | 0.530530 | − | 0.847666i | \(-0.321993\pi\) | ||||
0.530530 | + | 0.847666i | \(0.321993\pi\) | |||||||
\(374\) | −4.68292e16 | −0.884813 | ||||||||
\(375\) | −5.80744e15 | −0.107840 | ||||||||
\(376\) | 1.26261e16 | 0.230435 | ||||||||
\(377\) | 1.10636e16 | 0.198461 | ||||||||
\(378\) | −1.52508e16 | −0.268904 | ||||||||
\(379\) | −1.00024e17 | −1.73360 | −0.866801 | − | 0.498655i | \(-0.833827\pi\) | ||||
−0.866801 | + | 0.498655i | \(0.833827\pi\) | |||||||
\(380\) | 8.84029e14 | 0.0150617 | ||||||||
\(381\) | −6.34796e16 | −1.06322 | ||||||||
\(382\) | 1.12996e17 | 1.86059 | ||||||||
\(383\) | −4.18380e16 | −0.677297 | −0.338648 | − | 0.940913i | \(-0.609970\pi\) | ||||
−0.338648 | + | 0.940913i | \(0.609970\pi\) | |||||||
\(384\) | −1.60633e16 | −0.255671 | ||||||||
\(385\) | −8.88295e15 | −0.139015 | ||||||||
\(386\) | −2.80159e16 | −0.431108 | ||||||||
\(387\) | 3.82072e16 | 0.578128 | ||||||||
\(388\) | 2.95986e16 | 0.440418 | ||||||||
\(389\) | 1.99542e16 | 0.291986 | 0.145993 | − | 0.989286i | \(-0.453362\pi\) | ||||
0.145993 | + | 0.989286i | \(0.453362\pi\) | |||||||
\(390\) | −1.10570e15 | −0.0159118 | ||||||||
\(391\) | 2.79399e16 | 0.395435 | ||||||||
\(392\) | −1.49780e15 | −0.0208494 | ||||||||
\(393\) | 6.02489e16 | 0.824893 | ||||||||
\(394\) | −8.02887e16 | −1.08126 | ||||||||
\(395\) | 1.56458e15 | 0.0207260 | ||||||||
\(396\) | 4.58836e16 | 0.597914 | ||||||||
\(397\) | −1.04995e15 | −0.0134595 | −0.00672976 | − | 0.999977i | \(-0.502142\pi\) | ||||
−0.00672976 | + | 0.999977i | \(0.502142\pi\) | |||||||
\(398\) | 1.94206e16 | 0.244920 | ||||||||
\(399\) | −6.17283e15 | −0.0765879 | ||||||||
\(400\) | 6.69077e16 | 0.816744 | ||||||||
\(401\) | 7.08401e16 | 0.850826 | 0.425413 | − | 0.904999i | \(-0.360129\pi\) | ||||
0.425413 | + | 0.904999i | \(0.360129\pi\) | |||||||
\(402\) | −1.16823e17 | −1.38058 | ||||||||
\(403\) | 1.47649e16 | 0.171691 | ||||||||
\(404\) | −7.49965e16 | −0.858148 | ||||||||
\(405\) | 9.25641e14 | 0.0104228 | ||||||||
\(406\) | 1.24972e17 | 1.38482 | ||||||||
\(407\) | 2.43513e17 | 2.65557 | ||||||||
\(408\) | −4.67034e15 | −0.0501253 | ||||||||
\(409\) | 1.41645e17 | 1.49624 | 0.748118 | − | 0.663566i | \(-0.230958\pi\) | ||||
0.748118 | + | 0.663566i | \(0.230958\pi\) | |||||||
\(410\) | −1.16442e16 | −0.121064 | ||||||||
\(411\) | −5.98199e16 | −0.612173 | ||||||||
\(412\) | −1.96804e17 | −1.98245 | ||||||||
\(413\) | −1.25037e16 | −0.123983 | ||||||||
\(414\) | −5.11250e16 | −0.499035 | ||||||||
\(415\) | −6.78290e15 | −0.0651783 | ||||||||
\(416\) | 3.03328e16 | 0.286950 | ||||||||
\(417\) | −5.93843e16 | −0.553079 | ||||||||
\(418\) | 3.46830e16 | 0.318032 | ||||||||
\(419\) | 1.73885e17 | 1.56990 | 0.784949 | − | 0.619560i | \(-0.212689\pi\) | ||||
0.784949 | + | 0.619560i | \(0.212689\pi\) | |||||||
\(420\) | −6.68787e15 | −0.0594521 | ||||||||
\(421\) | −1.68885e17 | −1.47828 | −0.739140 | − | 0.673552i | \(-0.764768\pi\) | ||||
−0.739140 | + | 0.673552i | \(0.764768\pi\) | |||||||
\(422\) | 2.87918e17 | 2.48163 | ||||||||
\(423\) | 4.03957e16 | 0.342865 | ||||||||
\(424\) | −4.23372e16 | −0.353870 | ||||||||
\(425\) | 4.66663e16 | 0.384127 | ||||||||
\(426\) | 6.47290e16 | 0.524731 | ||||||||
\(427\) | 1.27695e17 | 1.01951 | ||||||||
\(428\) | 1.78626e17 | 1.40463 | ||||||||
\(429\) | −2.32284e16 | −0.179907 | ||||||||
\(430\) | 3.12902e16 | 0.238706 | ||||||||
\(431\) | 1.52159e17 | 1.14339 | 0.571696 | − | 0.820465i | \(-0.306286\pi\) | ||||
0.571696 | + | 0.820465i | \(0.306286\pi\) | |||||||
\(432\) | −2.14233e16 | −0.158578 | ||||||||
\(433\) | −5.23343e16 | −0.381606 | −0.190803 | − | 0.981628i | \(-0.561109\pi\) | ||||
−0.190803 | + | 0.981628i | \(0.561109\pi\) | |||||||
\(434\) | 1.66782e17 | 1.19803 | ||||||||
\(435\) | −7.58513e15 | −0.0536763 | ||||||||
\(436\) | −1.54941e17 | −1.08020 | ||||||||
\(437\) | −2.06930e16 | −0.142133 | ||||||||
\(438\) | −2.34721e16 | −0.158844 | ||||||||
\(439\) | 1.72056e17 | 1.14723 | 0.573616 | − | 0.819124i | \(-0.305540\pi\) | ||||
0.573616 | + | 0.819124i | \(0.305540\pi\) | |||||||
\(440\) | 4.97761e15 | 0.0327023 | ||||||||
\(441\) | −4.79203e15 | −0.0310219 | ||||||||
\(442\) | 1.78488e16 | 0.113858 | ||||||||
\(443\) | −2.29805e17 | −1.44456 | −0.722280 | − | 0.691601i | \(-0.756906\pi\) | ||||
−0.722280 | + | 0.691601i | \(0.756906\pi\) | |||||||
\(444\) | 1.83338e17 | 1.13570 | ||||||||
\(445\) | −2.19173e16 | −0.133797 | ||||||||
\(446\) | 1.98031e17 | 1.19140 | ||||||||
\(447\) | −6.98137e16 | −0.413944 | ||||||||
\(448\) | 2.08352e17 | 1.21756 | ||||||||
\(449\) | 1.56059e17 | 0.898852 | 0.449426 | − | 0.893318i | \(-0.351629\pi\) | ||||
0.449426 | + | 0.893318i | \(0.351629\pi\) | |||||||
\(450\) | −8.53911e16 | −0.484765 | ||||||||
\(451\) | −2.44620e17 | −1.36881 | ||||||||
\(452\) | 1.32170e17 | 0.729012 | ||||||||
\(453\) | −7.51330e16 | −0.408501 | ||||||||
\(454\) | 4.87199e17 | 2.61122 | ||||||||
\(455\) | 3.38571e15 | 0.0178886 | ||||||||
\(456\) | 3.45898e15 | 0.0180167 | ||||||||
\(457\) | 3.56412e17 | 1.83019 | 0.915097 | − | 0.403234i | \(-0.132114\pi\) | ||||
0.915097 | + | 0.403234i | \(0.132114\pi\) | |||||||
\(458\) | 5.07656e17 | 2.57006 | ||||||||
\(459\) | −1.49422e16 | −0.0745816 | ||||||||
\(460\) | −2.24196e16 | −0.110332 | ||||||||
\(461\) | −2.42553e17 | −1.17693 | −0.588465 | − | 0.808523i | \(-0.700267\pi\) | ||||
−0.588465 | + | 0.808523i | \(0.700267\pi\) | |||||||
\(462\) | −2.62384e17 | −1.25535 | ||||||||
\(463\) | 8.80260e16 | 0.415274 | 0.207637 | − | 0.978206i | \(-0.433423\pi\) | ||||
0.207637 | + | 0.978206i | \(0.433423\pi\) | |||||||
\(464\) | 1.75553e17 | 0.816658 | ||||||||
\(465\) | −1.01227e16 | −0.0464359 | ||||||||
\(466\) | −5.40315e17 | −2.44421 | ||||||||
\(467\) | −9.09789e16 | −0.405864 | −0.202932 | − | 0.979193i | \(-0.565047\pi\) | ||||
−0.202932 | + | 0.979193i | \(0.565047\pi\) | |||||||
\(468\) | −1.74884e16 | −0.0769400 | ||||||||
\(469\) | 3.57719e17 | 1.55209 | ||||||||
\(470\) | 3.30825e16 | 0.141567 | ||||||||
\(471\) | 1.80504e17 | 0.761817 | ||||||||
\(472\) | 7.00650e15 | 0.0291661 | ||||||||
\(473\) | 6.57339e17 | 2.69893 | ||||||||
\(474\) | 4.62145e16 | 0.187163 | ||||||||
\(475\) | −3.45623e16 | −0.138068 | ||||||||
\(476\) | 1.07959e17 | 0.425417 | ||||||||
\(477\) | −1.35453e17 | −0.526525 | ||||||||
\(478\) | −6.27156e16 | −0.240488 | ||||||||
\(479\) | −1.63047e17 | −0.616782 | −0.308391 | − | 0.951260i | \(-0.599791\pi\) | ||||
−0.308391 | + | 0.951260i | \(0.599791\pi\) | |||||||
\(480\) | −2.07960e16 | −0.0776090 | ||||||||
\(481\) | −9.28142e16 | −0.341721 | ||||||||
\(482\) | −2.86741e17 | −1.04156 | ||||||||
\(483\) | 1.56547e17 | 0.561034 | ||||||||
\(484\) | 4.63416e17 | 1.63861 | ||||||||
\(485\) | 1.02731e16 | 0.0358409 | ||||||||
\(486\) | 2.73416e16 | 0.0941213 | ||||||||
\(487\) | 5.00624e17 | 1.70049 | 0.850244 | − | 0.526389i | \(-0.176454\pi\) | ||||
0.850244 | + | 0.526389i | \(0.176454\pi\) | |||||||
\(488\) | −7.15546e16 | −0.239833 | ||||||||
\(489\) | 3.27549e17 | 1.08335 | ||||||||
\(490\) | −3.92448e15 | −0.0128088 | ||||||||
\(491\) | −2.43281e17 | −0.783571 | −0.391786 | − | 0.920057i | \(-0.628143\pi\) | ||||
−0.391786 | + | 0.920057i | \(0.628143\pi\) | |||||||
\(492\) | −1.84171e17 | −0.585395 | ||||||||
\(493\) | 1.22443e17 | 0.384087 | ||||||||
\(494\) | −1.32193e16 | −0.0409246 | ||||||||
\(495\) | 1.59253e16 | 0.0486579 | ||||||||
\(496\) | 2.34284e17 | 0.706499 | ||||||||
\(497\) | −1.98203e17 | −0.589922 | ||||||||
\(498\) | −2.00353e17 | −0.588580 | ||||||||
\(499\) | −1.64054e17 | −0.475701 | −0.237850 | − | 0.971302i | \(-0.576443\pi\) | ||||
−0.237850 | + | 0.971302i | \(0.576443\pi\) | |||||||
\(500\) | −7.52247e16 | −0.215306 | ||||||||
\(501\) | −1.42228e17 | −0.401827 | ||||||||
\(502\) | 7.03606e17 | 1.96226 | ||||||||
\(503\) | −4.62875e17 | −1.27430 | −0.637150 | − | 0.770740i | \(-0.719887\pi\) | ||||
−0.637150 | + | 0.770740i | \(0.719887\pi\) | |||||||
\(504\) | −2.61679e16 | −0.0711165 | ||||||||
\(505\) | −2.60298e16 | −0.0698356 | ||||||||
\(506\) | −8.79585e17 | −2.32970 | ||||||||
\(507\) | −2.11943e17 | −0.554200 | ||||||||
\(508\) | −8.22260e17 | −2.12273 | ||||||||
\(509\) | 2.93175e17 | 0.747242 | 0.373621 | − | 0.927581i | \(-0.378116\pi\) | ||||
0.373621 | + | 0.927581i | \(0.378116\pi\) | |||||||
\(510\) | −1.22371e16 | −0.0307944 | ||||||||
\(511\) | 7.18726e16 | 0.178578 | ||||||||
\(512\) | 5.56556e17 | 1.36538 | ||||||||
\(513\) | 1.10666e16 | 0.0268072 | ||||||||
\(514\) | −1.03077e18 | −2.46547 | ||||||||
\(515\) | −6.83068e16 | −0.161331 | ||||||||
\(516\) | 4.94903e17 | 1.15424 | ||||||||
\(517\) | 6.94992e17 | 1.60063 | ||||||||
\(518\) | −1.04841e18 | −2.38446 | ||||||||
\(519\) | −9.19222e16 | −0.206458 | ||||||||
\(520\) | −1.89720e15 | −0.00420816 | ||||||||
\(521\) | 3.81809e17 | 0.836374 | 0.418187 | − | 0.908361i | \(-0.362666\pi\) | ||||
0.418187 | + | 0.908361i | \(0.362666\pi\) | |||||||
\(522\) | −2.24049e17 | −0.484714 | ||||||||
\(523\) | 3.63828e17 | 0.777384 | 0.388692 | − | 0.921368i | \(-0.372927\pi\) | ||||
0.388692 | + | 0.921368i | \(0.372927\pi\) | |||||||
\(524\) | 7.80413e17 | 1.64691 | ||||||||
\(525\) | 2.61471e17 | 0.544990 | ||||||||
\(526\) | 6.27358e17 | 1.29154 | ||||||||
\(527\) | 1.63407e17 | 0.332278 | ||||||||
\(528\) | −3.68580e17 | −0.740305 | ||||||||
\(529\) | 2.07533e16 | 0.0411742 | ||||||||
\(530\) | −1.10931e17 | −0.217399 | ||||||||
\(531\) | 2.24165e16 | 0.0433963 | ||||||||
\(532\) | −7.99575e16 | −0.152909 | ||||||||
\(533\) | 9.32361e16 | 0.176140 | ||||||||
\(534\) | −6.47393e17 | −1.20823 | ||||||||
\(535\) | 6.19976e16 | 0.114308 | ||||||||
\(536\) | −2.00450e17 | −0.365119 | ||||||||
\(537\) | −2.25652e16 | −0.0406076 | ||||||||
\(538\) | 1.14128e18 | 2.02912 | ||||||||
\(539\) | −8.24449e16 | −0.144823 | ||||||||
\(540\) | 1.19900e16 | 0.0208093 | ||||||||
\(541\) | −2.11790e17 | −0.363181 | −0.181591 | − | 0.983374i | \(-0.558125\pi\) | ||||
−0.181591 | + | 0.983374i | \(0.558125\pi\) | |||||||
\(542\) | −1.53671e18 | −2.60373 | ||||||||
\(543\) | −1.86133e17 | −0.311620 | ||||||||
\(544\) | 3.35701e17 | 0.555340 | ||||||||
\(545\) | −5.37768e16 | −0.0879058 | ||||||||
\(546\) | 1.00007e17 | 0.161539 | ||||||||
\(547\) | −1.02072e18 | −1.62926 | −0.814629 | − | 0.579983i | \(-0.803059\pi\) | ||||
−0.814629 | + | 0.579983i | \(0.803059\pi\) | |||||||
\(548\) | −7.74856e17 | −1.22221 | ||||||||
\(549\) | −2.28931e17 | −0.356848 | ||||||||
\(550\) | −1.46912e18 | −2.26308 | ||||||||
\(551\) | −9.06847e16 | −0.138054 | ||||||||
\(552\) | −8.77221e16 | −0.131979 | ||||||||
\(553\) | −1.41511e17 | −0.210415 | ||||||||
\(554\) | 4.77050e17 | 0.701052 | ||||||||
\(555\) | 6.36330e16 | 0.0924225 | ||||||||
\(556\) | −7.69214e17 | −1.10423 | ||||||||
\(557\) | −1.35287e17 | −0.191954 | −0.0959771 | − | 0.995384i | \(-0.530598\pi\) | ||||
−0.0959771 | + | 0.995384i | \(0.530598\pi\) | |||||||
\(558\) | −2.99005e17 | −0.419331 | ||||||||
\(559\) | −2.50543e17 | −0.347301 | ||||||||
\(560\) | 5.37232e16 | 0.0736105 | ||||||||
\(561\) | −2.57074e17 | −0.348177 | ||||||||
\(562\) | 1.37692e18 | 1.84341 | ||||||||
\(563\) | 6.57878e17 | 0.870644 | 0.435322 | − | 0.900275i | \(-0.356635\pi\) | ||||
0.435322 | + | 0.900275i | \(0.356635\pi\) | |||||||
\(564\) | 5.23252e17 | 0.684537 | ||||||||
\(565\) | 4.58737e16 | 0.0593265 | ||||||||
\(566\) | 1.42517e17 | 0.182205 | ||||||||
\(567\) | −8.37212e16 | −0.105815 | ||||||||
\(568\) | 1.11064e17 | 0.138775 | ||||||||
\(569\) | −2.58560e17 | −0.319398 | −0.159699 | − | 0.987166i | \(-0.551052\pi\) | ||||
−0.159699 | + | 0.987166i | \(0.551052\pi\) | |||||||
\(570\) | 9.06311e15 | 0.0110685 | ||||||||
\(571\) | 4.96473e17 | 0.599460 | 0.299730 | − | 0.954024i | \(-0.403103\pi\) | ||||
0.299730 | + | 0.954024i | \(0.403103\pi\) | |||||||
\(572\) | −3.00881e17 | −0.359187 | ||||||||
\(573\) | 6.20304e17 | 0.732150 | ||||||||
\(574\) | 1.05318e18 | 1.22907 | ||||||||
\(575\) | 8.76525e17 | 1.01140 | ||||||||
\(576\) | −3.73532e17 | −0.426169 | ||||||||
\(577\) | 2.24527e17 | 0.253295 | 0.126647 | − | 0.991948i | \(-0.459578\pi\) | ||||
0.126647 | + | 0.991948i | \(0.459578\pi\) | |||||||
\(578\) | −1.11775e18 | −1.24685 | ||||||||
\(579\) | −1.53796e17 | −0.169643 | ||||||||
\(580\) | −9.82512e16 | −0.107166 | ||||||||
\(581\) | 6.13491e17 | 0.661703 | ||||||||
\(582\) | 3.03446e17 | 0.323655 | ||||||||
\(583\) | −2.33041e18 | −2.45803 | ||||||||
\(584\) | −4.02742e16 | −0.0420091 | ||||||||
\(585\) | −6.06987e15 | −0.00626133 | ||||||||
\(586\) | 2.38617e16 | 0.0243426 | ||||||||
\(587\) | −1.19786e18 | −1.20853 | −0.604267 | − | 0.796782i | \(-0.706534\pi\) | ||||
−0.604267 | + | 0.796782i | \(0.706534\pi\) | |||||||
\(588\) | −6.20718e16 | −0.0619358 | ||||||||
\(589\) | −1.21023e17 | −0.119432 | ||||||||
\(590\) | 1.83582e16 | 0.0179181 | ||||||||
\(591\) | −4.40754e17 | −0.425478 | ||||||||
\(592\) | −1.47274e18 | −1.40616 | ||||||||
\(593\) | 4.49893e17 | 0.424868 | 0.212434 | − | 0.977175i | \(-0.431861\pi\) | ||||
0.212434 | + | 0.977175i | \(0.431861\pi\) | |||||||
\(594\) | 4.70401e17 | 0.439396 | ||||||||
\(595\) | 3.74705e16 | 0.0346202 | ||||||||
\(596\) | −9.04307e17 | −0.826448 | ||||||||
\(597\) | 1.06612e17 | 0.0963767 | ||||||||
\(598\) | 3.35251e17 | 0.299787 | ||||||||
\(599\) | −1.21623e18 | −1.07582 | −0.537912 | − | 0.843001i | \(-0.680787\pi\) | ||||
−0.537912 | + | 0.843001i | \(0.680787\pi\) | |||||||
\(600\) | −1.46517e17 | −0.128205 | ||||||||
\(601\) | −1.74005e18 | −1.50618 | −0.753090 | − | 0.657918i | \(-0.771437\pi\) | ||||
−0.753090 | + | 0.657918i | \(0.771437\pi\) | |||||||
\(602\) | −2.83010e18 | −2.42339 | ||||||||
\(603\) | −6.41315e17 | −0.543262 | ||||||||
\(604\) | −9.73209e17 | −0.815579 | ||||||||
\(605\) | 1.60843e17 | 0.133349 | ||||||||
\(606\) | −7.68868e17 | −0.630637 | ||||||||
\(607\) | −2.51327e17 | −0.203945 | −0.101973 | − | 0.994787i | \(-0.532515\pi\) | ||||
−0.101973 | + | 0.994787i | \(0.532515\pi\) | |||||||
\(608\) | −2.48629e17 | −0.199608 | ||||||||
\(609\) | 6.86050e17 | 0.544933 | ||||||||
\(610\) | −1.87485e17 | −0.147341 | ||||||||
\(611\) | −2.64894e17 | −0.205970 | ||||||||
\(612\) | −1.93548e17 | −0.148904 | ||||||||
\(613\) | −1.43577e18 | −1.09293 | −0.546463 | − | 0.837483i | \(-0.684026\pi\) | ||||
−0.546463 | + | 0.837483i | \(0.684026\pi\) | |||||||
\(614\) | −1.04141e18 | −0.784383 | ||||||||
\(615\) | −6.39222e16 | −0.0476391 | ||||||||
\(616\) | −4.50208e17 | −0.332001 | ||||||||
\(617\) | −7.11480e17 | −0.519169 | −0.259585 | − | 0.965720i | \(-0.583586\pi\) | ||||
−0.259585 | + | 0.965720i | \(0.583586\pi\) | |||||||
\(618\) | −2.01765e18 | −1.45687 | ||||||||
\(619\) | 2.70201e18 | 1.93063 | 0.965313 | − | 0.261096i | \(-0.0840839\pi\) | ||||
0.965313 | + | 0.261096i | \(0.0840839\pi\) | |||||||
\(620\) | −1.31121e17 | −0.0927102 | ||||||||
\(621\) | −2.80657e17 | −0.196372 | ||||||||
\(622\) | 1.27038e18 | 0.879622 | ||||||||
\(623\) | 1.98235e18 | 1.35834 | ||||||||
\(624\) | 1.40483e17 | 0.0952630 | ||||||||
\(625\) | 1.45089e18 | 0.973679 | ||||||||
\(626\) | 6.58994e17 | 0.437671 | ||||||||
\(627\) | 1.90396e17 | 0.125147 | ||||||||
\(628\) | 2.33809e18 | 1.52098 | ||||||||
\(629\) | −1.02720e18 | −0.661340 | ||||||||
\(630\) | −6.85644e16 | −0.0436903 | ||||||||
\(631\) | 2.58875e18 | 1.63268 | 0.816338 | − | 0.577575i | \(-0.196001\pi\) | ||||
0.816338 | + | 0.577575i | \(0.196001\pi\) | |||||||
\(632\) | 7.92964e16 | 0.0494986 | ||||||||
\(633\) | 1.58056e18 | 0.976530 | ||||||||
\(634\) | 3.86822e18 | 2.36554 | ||||||||
\(635\) | −2.85390e17 | −0.172747 | ||||||||
\(636\) | −1.75454e18 | −1.05122 | ||||||||
\(637\) | 3.14236e16 | 0.0186359 | ||||||||
\(638\) | −3.85468e18 | −2.26284 | ||||||||
\(639\) | 3.55337e17 | 0.206483 | ||||||||
\(640\) | −7.22169e16 | −0.0415402 | ||||||||
\(641\) | 1.47806e18 | 0.841617 | 0.420808 | − | 0.907150i | \(-0.361746\pi\) | ||||
0.420808 | + | 0.907150i | \(0.361746\pi\) | |||||||
\(642\) | 1.83128e18 | 1.03223 | ||||||||
\(643\) | 2.44980e18 | 1.36697 | 0.683487 | − | 0.729963i | \(-0.260463\pi\) | ||||
0.683487 | + | 0.729963i | \(0.260463\pi\) | |||||||
\(644\) | 2.02778e18 | 1.12011 | ||||||||
\(645\) | 1.71771e17 | 0.0939316 | ||||||||
\(646\) | −1.46302e17 | −0.0792023 | ||||||||
\(647\) | −1.72269e18 | −0.923270 | −0.461635 | − | 0.887070i | \(-0.652737\pi\) | ||||
−0.461635 | + | 0.887070i | \(0.652737\pi\) | |||||||
\(648\) | 4.69136e16 | 0.0248921 | ||||||||
\(649\) | 3.85666e17 | 0.202591 | ||||||||
\(650\) | 5.59950e17 | 0.291214 | ||||||||
\(651\) | 9.15569e17 | 0.471427 | ||||||||
\(652\) | 4.24279e18 | 2.16293 | ||||||||
\(653\) | −3.90745e17 | −0.197223 | −0.0986114 | − | 0.995126i | \(-0.531440\pi\) | ||||
−0.0986114 | + | 0.995126i | \(0.531440\pi\) | |||||||
\(654\) | −1.58846e18 | −0.793817 | ||||||||
\(655\) | 2.70866e17 | 0.134025 | ||||||||
\(656\) | 1.47944e18 | 0.724805 | ||||||||
\(657\) | −1.28853e17 | −0.0625056 | ||||||||
\(658\) | −2.99221e18 | −1.43722 | ||||||||
\(659\) | 1.27372e18 | 0.605787 | 0.302893 | − | 0.953024i | \(-0.402047\pi\) | ||||
0.302893 | + | 0.953024i | \(0.402047\pi\) | |||||||
\(660\) | 2.06282e17 | 0.0971464 | ||||||||
\(661\) | −1.99395e18 | −0.929832 | −0.464916 | − | 0.885355i | \(-0.653916\pi\) | ||||
−0.464916 | + | 0.885355i | \(0.653916\pi\) | |||||||
\(662\) | −3.11381e17 | −0.143786 | ||||||||
\(663\) | 9.79832e16 | 0.0448037 | ||||||||
\(664\) | −3.43773e17 | −0.155661 | ||||||||
\(665\) | −2.77517e16 | −0.0124437 | ||||||||
\(666\) | 1.87959e18 | 0.834604 | ||||||||
\(667\) | 2.29983e18 | 1.01129 | ||||||||
\(668\) | −1.84229e18 | −0.802254 | ||||||||
\(669\) | 1.08712e18 | 0.468820 | ||||||||
\(670\) | −5.25212e17 | −0.224310 | ||||||||
\(671\) | −3.93866e18 | −1.66591 | ||||||||
\(672\) | 1.88093e18 | 0.787903 | ||||||||
\(673\) | 1.92835e18 | 0.799995 | 0.399998 | − | 0.916516i | \(-0.369011\pi\) | ||||
0.399998 | + | 0.916516i | \(0.369011\pi\) | |||||||
\(674\) | −6.57949e17 | −0.270335 | ||||||||
\(675\) | −4.68764e17 | −0.190757 | ||||||||
\(676\) | −2.74532e18 | −1.10647 | ||||||||
\(677\) | 4.89704e18 | 1.95482 | 0.977411 | − | 0.211347i | \(-0.0677849\pi\) | ||||
0.977411 | + | 0.211347i | \(0.0677849\pi\) | |||||||
\(678\) | 1.35502e18 | 0.535737 | ||||||||
\(679\) | −9.29166e17 | −0.363864 | ||||||||
\(680\) | −2.09968e16 | −0.00814414 | ||||||||
\(681\) | 2.67454e18 | 1.02752 | ||||||||
\(682\) | −5.14427e18 | −1.95761 | ||||||||
\(683\) | 3.31543e18 | 1.24970 | 0.624850 | − | 0.780745i | \(-0.285160\pi\) | ||||
0.624850 | + | 0.780745i | \(0.285160\pi\) | |||||||
\(684\) | 1.43347e17 | 0.0535210 | ||||||||
\(685\) | −2.68937e17 | −0.0994631 | ||||||||
\(686\) | 4.16900e18 | 1.52730 | ||||||||
\(687\) | 2.78683e18 | 1.01133 | ||||||||
\(688\) | −3.97552e18 | −1.42912 | ||||||||
\(689\) | 8.88230e17 | 0.316301 | ||||||||
\(690\) | −2.29847e17 | −0.0810810 | ||||||||
\(691\) | −5.55368e18 | −1.94077 | −0.970385 | − | 0.241565i | \(-0.922339\pi\) | ||||
−0.970385 | + | 0.241565i | \(0.922339\pi\) | |||||||
\(692\) | −1.19068e18 | −0.412198 | ||||||||
\(693\) | −1.44039e18 | −0.493985 | ||||||||
\(694\) | 4.94163e18 | 1.67893 | ||||||||
\(695\) | −2.66979e17 | −0.0898619 | ||||||||
\(696\) | −3.84432e17 | −0.128191 | ||||||||
\(697\) | 1.03187e18 | 0.340887 | ||||||||
\(698\) | −7.59348e18 | −2.48531 | ||||||||
\(699\) | −2.96612e18 | −0.961806 | ||||||||
\(700\) | 3.38688e18 | 1.08808 | ||||||||
\(701\) | −9.71425e17 | −0.309202 | −0.154601 | − | 0.987977i | \(-0.549409\pi\) | ||||
−0.154601 | + | 0.987977i | \(0.549409\pi\) | |||||||
\(702\) | −1.79292e17 | −0.0565418 | ||||||||
\(703\) | 7.60770e17 | 0.237708 | ||||||||
\(704\) | −6.42647e18 | −1.98953 | ||||||||
\(705\) | 1.81610e17 | 0.0557072 | ||||||||
\(706\) | 1.62154e18 | 0.492829 | ||||||||
\(707\) | 2.35431e18 | 0.708985 | ||||||||
\(708\) | 2.90364e17 | 0.0866416 | ||||||||
\(709\) | 5.57260e18 | 1.64762 | 0.823810 | − | 0.566866i | \(-0.191844\pi\) | ||||
0.823810 | + | 0.566866i | \(0.191844\pi\) | |||||||
\(710\) | 2.91007e17 | 0.0852559 | ||||||||
\(711\) | 2.53700e17 | 0.0736491 | ||||||||
\(712\) | −1.11082e18 | −0.319539 | ||||||||
\(713\) | 3.06924e18 | 0.874881 | ||||||||
\(714\) | 1.10680e18 | 0.312631 | ||||||||
\(715\) | −1.04430e17 | −0.0292304 | ||||||||
\(716\) | −2.92291e17 | −0.0810738 | ||||||||
\(717\) | −3.44284e17 | −0.0946330 | ||||||||
\(718\) | −4.00084e15 | −0.00108979 | ||||||||
\(719\) | −5.92454e18 | −1.59925 | −0.799626 | − | 0.600498i | \(-0.794969\pi\) | ||||
−0.799626 | + | 0.600498i | \(0.794969\pi\) | |||||||
\(720\) | −9.63145e16 | −0.0257650 | ||||||||
\(721\) | 6.17813e18 | 1.63786 | ||||||||
\(722\) | −5.47612e18 | −1.43874 | ||||||||
\(723\) | −1.57410e18 | −0.409858 | ||||||||
\(724\) | −2.41101e18 | −0.622155 | ||||||||
\(725\) | 3.84127e18 | 0.982375 | ||||||||
\(726\) | 4.75097e18 | 1.20419 | ||||||||
\(727\) | 1.86694e18 | 0.468983 | 0.234492 | − | 0.972118i | \(-0.424657\pi\) | ||||
0.234492 | + | 0.972118i | \(0.424657\pi\) | |||||||
\(728\) | 1.71596e17 | 0.0427221 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | −1.05525e17 | −0.0258082 | ||||||||
\(731\) | −2.77282e18 | −0.672139 | ||||||||
\(732\) | −2.96537e18 | −0.712454 | ||||||||
\(733\) | −6.19237e18 | −1.47462 | −0.737312 | − | 0.675552i | \(-0.763905\pi\) | ||||
−0.737312 | + | 0.675552i | \(0.763905\pi\) | |||||||
\(734\) | −2.07271e18 | −0.489232 | ||||||||
\(735\) | −2.15439e16 | −0.00504030 | ||||||||
\(736\) | 6.30541e18 | 1.46220 | ||||||||
\(737\) | −1.10336e19 | −2.53616 | ||||||||
\(738\) | −1.88813e18 | −0.430196 | ||||||||
\(739\) | −4.59785e18 | −1.03840 | −0.519201 | − | 0.854652i | \(-0.673770\pi\) | ||||
−0.519201 | + | 0.854652i | \(0.673770\pi\) | |||||||
\(740\) | 8.24247e17 | 0.184523 | ||||||||
\(741\) | −7.25690e16 | −0.0161040 | ||||||||
\(742\) | 1.00333e19 | 2.20708 | ||||||||
\(743\) | −7.98411e18 | −1.74100 | −0.870501 | − | 0.492167i | \(-0.836205\pi\) | ||||
−0.870501 | + | 0.492167i | \(0.836205\pi\) | |||||||
\(744\) | −5.13044e17 | −0.110900 | ||||||||
\(745\) | −3.13867e17 | −0.0672558 | ||||||||
\(746\) | 7.32881e18 | 1.55679 | ||||||||
\(747\) | −1.09986e18 | −0.231608 | ||||||||
\(748\) | −3.32992e18 | −0.695142 | ||||||||
\(749\) | −5.60748e18 | −1.16047 | ||||||||
\(750\) | −7.71207e17 | −0.158224 | ||||||||
\(751\) | −5.05379e18 | −1.02792 | −0.513958 | − | 0.857816i | \(-0.671821\pi\) | ||||
−0.513958 | + | 0.857816i | \(0.671821\pi\) | |||||||
\(752\) | −4.20325e18 | −0.847557 | ||||||||
\(753\) | 3.86253e18 | 0.772154 | ||||||||
\(754\) | 1.46920e18 | 0.291184 | ||||||||
\(755\) | −3.37782e17 | −0.0663714 | ||||||||
\(756\) | −1.08445e18 | −0.211261 | ||||||||
\(757\) | 2.12068e18 | 0.409592 | 0.204796 | − | 0.978805i | \(-0.434347\pi\) | ||||
0.204796 | + | 0.978805i | \(0.434347\pi\) | |||||||
\(758\) | −1.32828e19 | −2.54355 | ||||||||
\(759\) | −4.82858e18 | −0.916744 | ||||||||
\(760\) | 1.55508e16 | 0.00292728 | ||||||||
\(761\) | 1.52694e18 | 0.284985 | 0.142492 | − | 0.989796i | \(-0.454488\pi\) | ||||
0.142492 | + | 0.989796i | \(0.454488\pi\) | |||||||
\(762\) | −8.42985e18 | −1.55996 | ||||||||
\(763\) | 4.86393e18 | 0.892438 | ||||||||
\(764\) | 8.03489e18 | 1.46175 | ||||||||
\(765\) | −6.71768e16 | −0.0121177 | ||||||||
\(766\) | −5.55593e18 | −0.993733 | ||||||||
\(767\) | −1.46996e17 | −0.0260696 | ||||||||
\(768\) | 2.06436e18 | 0.363025 | ||||||||
\(769\) | 5.81098e18 | 1.01328 | 0.506639 | − | 0.862158i | \(-0.330888\pi\) | ||||
0.506639 | + | 0.862158i | \(0.330888\pi\) | |||||||
\(770\) | −1.17962e18 | −0.203964 | ||||||||
\(771\) | −5.65851e18 | −0.970172 | ||||||||
\(772\) | −1.99214e18 | −0.338695 | ||||||||
\(773\) | −6.26176e17 | −0.105567 | −0.0527837 | − | 0.998606i | \(-0.516809\pi\) | ||||
−0.0527837 | + | 0.998606i | \(0.516809\pi\) | |||||||
\(774\) | 5.07377e18 | 0.848232 | ||||||||
\(775\) | 5.12637e18 | 0.849863 | ||||||||
\(776\) | 5.20663e17 | 0.0855965 | ||||||||
\(777\) | −5.75539e18 | −0.938292 | ||||||||
\(778\) | 2.64984e18 | 0.428403 | ||||||||
\(779\) | −7.64228e17 | −0.122526 | ||||||||
\(780\) | −7.86240e16 | −0.0125009 | ||||||||
\(781\) | 6.11343e18 | 0.963948 | ||||||||
\(782\) | 3.71031e18 | 0.580185 | ||||||||
\(783\) | −1.22994e18 | −0.190737 | ||||||||
\(784\) | 4.98619e17 | 0.0766857 | ||||||||
\(785\) | 8.11506e17 | 0.123777 | ||||||||
\(786\) | 8.00083e18 | 1.21029 | ||||||||
\(787\) | 2.26575e18 | 0.339920 | 0.169960 | − | 0.985451i | \(-0.445636\pi\) | ||||
0.169960 | + | 0.985451i | \(0.445636\pi\) | |||||||
\(788\) | −5.70915e18 | −0.849476 | ||||||||
\(789\) | 3.44395e18 | 0.508226 | ||||||||
\(790\) | 2.07770e17 | 0.0304093 | ||||||||
\(791\) | −4.14913e18 | −0.602295 | ||||||||
\(792\) | 8.07130e17 | 0.116206 | ||||||||
\(793\) | 1.50121e18 | 0.214371 | ||||||||
\(794\) | −1.39429e17 | −0.0197479 | ||||||||
\(795\) | −6.08966e17 | −0.0855474 | ||||||||
\(796\) | 1.38096e18 | 0.192418 | ||||||||
\(797\) | −1.35306e19 | −1.86998 | −0.934991 | − | 0.354671i | \(-0.884593\pi\) | ||||
−0.934991 | + | 0.354671i | \(0.884593\pi\) | |||||||
\(798\) | −8.19728e17 | −0.112370 | ||||||||
\(799\) | −2.93165e18 | −0.398619 | ||||||||
\(800\) | 1.05315e19 | 1.42039 | ||||||||
\(801\) | −3.55394e18 | −0.475443 | ||||||||
\(802\) | 9.40730e18 | 1.24834 | ||||||||
\(803\) | −2.21686e18 | −0.291801 | ||||||||
\(804\) | −8.30705e18 | −1.08463 | ||||||||
\(805\) | 7.03802e17 | 0.0911543 | ||||||||
\(806\) | 1.96072e18 | 0.251906 | ||||||||
\(807\) | 6.26519e18 | 0.798466 | ||||||||
\(808\) | −1.31925e18 | −0.166784 | ||||||||
\(809\) | −1.48044e19 | −1.85663 | −0.928316 | − | 0.371792i | \(-0.878743\pi\) | ||||
−0.928316 | + | 0.371792i | \(0.878743\pi\) | |||||||
\(810\) | 1.22922e17 | 0.0152924 | ||||||||
\(811\) | −3.69728e18 | −0.456296 | −0.228148 | − | 0.973626i | \(-0.573267\pi\) | ||||
−0.228148 | + | 0.973626i | \(0.573267\pi\) | |||||||
\(812\) | 8.88650e18 | 1.08797 | ||||||||
\(813\) | −8.43592e18 | −1.02458 | ||||||||
\(814\) | 3.23376e19 | 3.89627 | ||||||||
\(815\) | 1.47259e18 | 0.176018 | ||||||||
\(816\) | 1.55476e18 | 0.184365 | ||||||||
\(817\) | 2.05363e18 | 0.241589 | ||||||||
\(818\) | 1.88099e19 | 2.19528 | ||||||||
\(819\) | 5.49000e17 | 0.0635663 | ||||||||
\(820\) | −8.27994e17 | −0.0951124 | ||||||||
\(821\) | −5.35507e18 | −0.610288 | −0.305144 | − | 0.952306i | \(-0.598705\pi\) | ||||
−0.305144 | + | 0.952306i | \(0.598705\pi\) | |||||||
\(822\) | −7.94386e18 | −0.898183 | ||||||||
\(823\) | −5.20121e18 | −0.583452 | −0.291726 | − | 0.956502i | \(-0.594230\pi\) | ||||
−0.291726 | + | 0.956502i | \(0.594230\pi\) | |||||||
\(824\) | −3.46195e18 | −0.385295 | ||||||||
\(825\) | −8.06490e18 | −0.890529 | ||||||||
\(826\) | −1.66044e18 | −0.181908 | ||||||||
\(827\) | 1.78558e18 | 0.194086 | 0.0970429 | − | 0.995280i | \(-0.469062\pi\) | ||||
0.0970429 | + | 0.995280i | \(0.469062\pi\) | |||||||
\(828\) | −3.63539e18 | −0.392061 | ||||||||
\(829\) | −1.17882e19 | −1.26137 | −0.630685 | − | 0.776039i | \(-0.717226\pi\) | ||||
−0.630685 | + | 0.776039i | \(0.717226\pi\) | |||||||
\(830\) | −9.00744e17 | −0.0956299 | ||||||||
\(831\) | 2.61882e18 | 0.275866 | ||||||||
\(832\) | 2.44943e18 | 0.256014 | ||||||||
\(833\) | 3.47773e17 | 0.0360665 | ||||||||
\(834\) | −7.88601e18 | −0.811481 | ||||||||
\(835\) | −6.39424e17 | −0.0652870 | ||||||||
\(836\) | 2.46623e18 | 0.249858 | ||||||||
\(837\) | −1.64142e18 | −0.165008 | ||||||||
\(838\) | 2.30913e19 | 2.30336 | ||||||||
\(839\) | 5.72612e18 | 0.566771 | 0.283385 | − | 0.959006i | \(-0.408542\pi\) | ||||
0.283385 | + | 0.959006i | \(0.408542\pi\) | |||||||
\(840\) | −1.17645e17 | −0.0115547 | ||||||||
\(841\) | −1.81903e17 | −0.0177282 | ||||||||
\(842\) | −2.24273e19 | −2.16894 | ||||||||
\(843\) | 7.55874e18 | 0.725388 | ||||||||
\(844\) | 2.04732e19 | 1.94966 | ||||||||
\(845\) | −9.52847e17 | −0.0900439 | ||||||||
\(846\) | 5.36440e18 | 0.503053 | ||||||||
\(847\) | −1.45477e19 | −1.35379 | ||||||||
\(848\) | 1.40941e19 | 1.30156 | ||||||||
\(849\) | 7.82362e17 | 0.0716981 | ||||||||
\(850\) | 6.19711e18 | 0.563594 | ||||||||
\(851\) | −1.92937e19 | −1.74130 | ||||||||
\(852\) | 4.60274e18 | 0.412248 | ||||||||
\(853\) | −2.20710e19 | −1.96180 | −0.980899 | − | 0.194518i | \(-0.937686\pi\) | ||||
−0.980899 | + | 0.194518i | \(0.937686\pi\) | |||||||
\(854\) | 1.69574e19 | 1.49583 | ||||||||
\(855\) | 4.97530e16 | 0.00435551 | ||||||||
\(856\) | 3.14218e18 | 0.272993 | ||||||||
\(857\) | −4.23577e17 | −0.0365222 | −0.0182611 | − | 0.999833i | \(-0.505813\pi\) | ||||
−0.0182611 | + | 0.999833i | \(0.505813\pi\) | |||||||
\(858\) | −3.08464e18 | −0.263960 | ||||||||
\(859\) | 2.07535e19 | 1.76253 | 0.881263 | − | 0.472626i | \(-0.156694\pi\) | ||||
0.881263 | + | 0.472626i | \(0.156694\pi\) | |||||||
\(860\) | 2.22498e18 | 0.187536 | ||||||||
\(861\) | 5.78155e18 | 0.483642 | ||||||||
\(862\) | 2.02061e19 | 1.67759 | ||||||||
\(863\) | 1.59791e19 | 1.31669 | 0.658343 | − | 0.752718i | \(-0.271258\pi\) | ||||
0.658343 | + | 0.752718i | \(0.271258\pi\) | |||||||
\(864\) | −3.37212e18 | −0.275781 | ||||||||
\(865\) | −4.13262e17 | −0.0335445 | ||||||||
\(866\) | −6.94980e18 | −0.559894 | ||||||||
\(867\) | −6.13603e18 | −0.490641 | ||||||||
\(868\) | 1.18595e19 | 0.941213 | ||||||||
\(869\) | 4.36480e18 | 0.343824 | ||||||||
\(870\) | −1.00728e18 | −0.0787542 | ||||||||
\(871\) | 4.20541e18 | 0.326355 | ||||||||
\(872\) | −2.72553e18 | −0.209939 | ||||||||
\(873\) | 1.66580e18 | 0.127359 | ||||||||
\(874\) | −2.74796e18 | −0.208538 | ||||||||
\(875\) | 2.36147e18 | 0.177881 | ||||||||
\(876\) | −1.66905e18 | −0.124794 | ||||||||
\(877\) | 1.05162e19 | 0.780478 | 0.390239 | − | 0.920714i | \(-0.372392\pi\) | ||||
0.390239 | + | 0.920714i | \(0.372392\pi\) | |||||||
\(878\) | 2.28484e19 | 1.68323 | ||||||||
\(879\) | 1.30992e17 | 0.00957890 | ||||||||
\(880\) | −1.65705e18 | −0.120282 | ||||||||
\(881\) | −1.06384e19 | −0.766538 | −0.383269 | − | 0.923637i | \(-0.625202\pi\) | ||||
−0.383269 | + | 0.923637i | \(0.625202\pi\) | |||||||
\(882\) | −6.36363e17 | −0.0455155 | ||||||||
\(883\) | −1.69853e19 | −1.20595 | −0.602973 | − | 0.797762i | \(-0.706017\pi\) | ||||
−0.602973 | + | 0.797762i | \(0.706017\pi\) | |||||||
\(884\) | 1.26919e18 | 0.0894514 | ||||||||
\(885\) | 1.00779e17 | 0.00705084 | ||||||||
\(886\) | −3.05173e19 | −2.11947 | ||||||||
\(887\) | −9.89263e18 | −0.682038 | −0.341019 | − | 0.940056i | \(-0.610772\pi\) | ||||
−0.341019 | + | 0.940056i | \(0.610772\pi\) | |||||||
\(888\) | 3.22507e18 | 0.220726 | ||||||||
\(889\) | 2.58126e19 | 1.75376 | ||||||||
\(890\) | −2.91054e18 | −0.196308 | ||||||||
\(891\) | 2.58232e18 | 0.172904 | ||||||||
\(892\) | 1.40816e19 | 0.936008 | ||||||||
\(893\) | 2.17126e18 | 0.143277 | ||||||||
\(894\) | −9.27100e18 | −0.607341 | ||||||||
\(895\) | −1.01448e17 | −0.00659774 | ||||||||
\(896\) | 6.53178e18 | 0.421725 | ||||||||
\(897\) | 1.84040e18 | 0.117967 | ||||||||
\(898\) | 2.07241e19 | 1.31880 | ||||||||
\(899\) | 1.34506e19 | 0.849773 | ||||||||
\(900\) | −6.07197e18 | −0.380849 | ||||||||
\(901\) | 9.83026e18 | 0.612144 | ||||||||
\(902\) | −3.24846e19 | −2.00833 | ||||||||
\(903\) | −1.55361e19 | −0.953613 | ||||||||
\(904\) | 2.32499e18 | 0.141686 | ||||||||
\(905\) | −8.36814e17 | −0.0506306 | ||||||||
\(906\) | −9.97739e18 | −0.599354 | ||||||||
\(907\) | 2.97940e18 | 0.177697 | 0.0888486 | − | 0.996045i | \(-0.471681\pi\) | ||||
0.0888486 | + | 0.996045i | \(0.471681\pi\) | |||||||
\(908\) | 3.46437e19 | 2.05147 | ||||||||
\(909\) | −4.22079e18 | −0.248158 | ||||||||
\(910\) | 4.49610e17 | 0.0262462 | ||||||||
\(911\) | 6.63263e18 | 0.384429 | 0.192214 | − | 0.981353i | \(-0.438433\pi\) | ||||
0.192214 | + | 0.981353i | \(0.438433\pi\) | |||||||
\(912\) | −1.15150e18 | −0.0662669 | ||||||||
\(913\) | −1.89227e19 | −1.08124 | ||||||||
\(914\) | 4.73302e19 | 2.68527 | ||||||||
\(915\) | −1.02922e18 | −0.0579791 | ||||||||
\(916\) | 3.60983e19 | 2.01914 | ||||||||
\(917\) | −2.44989e19 | −1.36065 | ||||||||
\(918\) | −1.98427e18 | −0.109427 | ||||||||
\(919\) | −7.46279e18 | −0.408649 | −0.204325 | − | 0.978903i | \(-0.565500\pi\) | ||||
−0.204325 | + | 0.978903i | \(0.565500\pi\) | |||||||
\(920\) | −3.94379e17 | −0.0214434 | ||||||||
\(921\) | −5.71695e18 | −0.308657 | ||||||||
\(922\) | −3.22101e19 | −1.72680 | ||||||||
\(923\) | −2.33012e18 | −0.124041 | ||||||||
\(924\) | −1.86576e19 | −0.986251 | ||||||||
\(925\) | −3.22251e19 | −1.69150 | ||||||||
\(926\) | 1.16895e19 | 0.609292 | ||||||||
\(927\) | −1.10761e19 | −0.573282 | ||||||||
\(928\) | 2.76327e19 | 1.42024 | ||||||||
\(929\) | −3.43293e19 | −1.75212 | −0.876059 | − | 0.482204i | \(-0.839836\pi\) | ||||
−0.876059 | + | 0.482204i | \(0.839836\pi\) | |||||||
\(930\) | −1.34426e18 | −0.0681310 | ||||||||
\(931\) | −2.57570e17 | −0.0129635 | ||||||||
\(932\) | −3.84206e19 | −1.92026 | ||||||||
\(933\) | 6.97389e18 | 0.346134 | ||||||||
\(934\) | −1.20817e19 | −0.595486 | ||||||||
\(935\) | −1.15575e18 | −0.0565703 | ||||||||
\(936\) | −3.07635e17 | −0.0149535 | ||||||||
\(937\) | −1.72224e19 | −0.831353 | −0.415676 | − | 0.909513i | \(-0.636455\pi\) | ||||
−0.415676 | + | 0.909513i | \(0.636455\pi\) | |||||||
\(938\) | 4.75037e19 | 2.27724 | ||||||||
\(939\) | 3.61762e18 | 0.172225 | ||||||||
\(940\) | 2.35242e18 | 0.111220 | ||||||||
\(941\) | 8.65054e18 | 0.406173 | 0.203086 | − | 0.979161i | \(-0.434903\pi\) | ||||
0.203086 | + | 0.979161i | \(0.434903\pi\) | |||||||
\(942\) | 2.39702e19 | 1.11774 | ||||||||
\(943\) | 1.93814e19 | 0.897549 | ||||||||
\(944\) | −2.33247e18 | −0.107275 | ||||||||
\(945\) | −3.76392e17 | −0.0171923 | ||||||||
\(946\) | 8.72922e19 | 3.95989 | ||||||||
\(947\) | 1.25519e19 | 0.565502 | 0.282751 | − | 0.959193i | \(-0.408753\pi\) | ||||
0.282751 | + | 0.959193i | \(0.408753\pi\) | |||||||
\(948\) | 3.28621e18 | 0.147042 | ||||||||
\(949\) | 8.44949e17 | 0.0375492 | ||||||||
\(950\) | −4.58975e18 | −0.202575 | ||||||||
\(951\) | 2.12350e19 | 0.930849 | ||||||||
\(952\) | 1.89909e18 | 0.0826810 | ||||||||
\(953\) | 2.13965e18 | 0.0925206 | 0.0462603 | − | 0.998929i | \(-0.485270\pi\) | ||||
0.0462603 | + | 0.998929i | \(0.485270\pi\) | |||||||
\(954\) | −1.79876e19 | −0.772520 | ||||||||
\(955\) | 2.78875e18 | 0.118956 | ||||||||
\(956\) | −4.45956e18 | −0.188937 | ||||||||
\(957\) | −2.11607e19 | −0.890435 | ||||||||
\(958\) | −2.16520e19 | −0.904946 | ||||||||
\(959\) | 2.43245e19 | 1.00977 | ||||||||
\(960\) | −1.67932e18 | −0.0692421 | ||||||||
\(961\) | −6.46705e18 | −0.264852 | ||||||||
\(962\) | −1.23254e19 | −0.501374 | ||||||||
\(963\) | 1.00530e19 | 0.406187 | ||||||||
\(964\) | −2.03895e19 | −0.818288 | ||||||||
\(965\) | −6.91434e17 | −0.0275628 | ||||||||
\(966\) | 2.07889e19 | 0.823152 | ||||||||
\(967\) | −2.35896e19 | −0.927787 | −0.463893 | − | 0.885891i | \(-0.653548\pi\) | ||||
−0.463893 | + | 0.885891i | \(0.653548\pi\) | |||||||
\(968\) | 8.15187e18 | 0.318469 | ||||||||
\(969\) | −8.03139e17 | −0.0311664 | ||||||||
\(970\) | 1.36423e18 | 0.0525860 | ||||||||
\(971\) | 4.95150e18 | 0.189589 | 0.0947943 | − | 0.995497i | \(-0.469781\pi\) | ||||
0.0947943 | + | 0.995497i | \(0.469781\pi\) | |||||||
\(972\) | 1.94420e18 | 0.0739452 | ||||||||
\(973\) | 2.41473e19 | 0.912296 | ||||||||
\(974\) | 6.64810e19 | 2.49496 | ||||||||
\(975\) | 3.07391e18 | 0.114594 | ||||||||
\(976\) | 2.38206e19 | 0.882123 | ||||||||
\(977\) | −3.13735e19 | −1.15411 | −0.577057 | − | 0.816704i | \(-0.695799\pi\) | ||||
−0.577057 | + | 0.816704i | \(0.695799\pi\) | |||||||
\(978\) | 4.34973e19 | 1.58950 | ||||||||
\(979\) | −6.11441e19 | −2.21956 | ||||||||
\(980\) | −2.79061e17 | −0.0100631 | ||||||||
\(981\) | −8.72002e18 | −0.312370 | ||||||||
\(982\) | −3.23068e19 | −1.14966 | ||||||||
\(983\) | 4.03527e19 | 1.42651 | 0.713256 | − | 0.700904i | \(-0.247220\pi\) | ||||
0.713256 | + | 0.700904i | \(0.247220\pi\) | |||||||
\(984\) | −3.23972e18 | −0.113773 | ||||||||
\(985\) | −1.98153e18 | −0.0691299 | ||||||||
\(986\) | 1.62600e19 | 0.563534 | ||||||||
\(987\) | −1.64261e19 | −0.565551 | ||||||||
\(988\) | −9.39997e17 | −0.0321519 | ||||||||
\(989\) | −5.20814e19 | −1.76973 | ||||||||
\(990\) | 2.11482e18 | 0.0713911 | ||||||||
\(991\) | 1.85886e19 | 0.623403 | 0.311701 | − | 0.950180i | \(-0.399101\pi\) | ||||
0.311701 | + | 0.950180i | \(0.399101\pi\) | |||||||
\(992\) | 3.68773e19 | 1.22866 | ||||||||
\(993\) | −1.70936e18 | −0.0565801 | ||||||||
\(994\) | −2.63207e19 | −0.865536 | ||||||||
\(995\) | 4.79303e17 | 0.0156589 | ||||||||
\(996\) | −1.42467e19 | −0.462410 | ||||||||
\(997\) | −1.41749e19 | −0.457090 | −0.228545 | − | 0.973533i | \(-0.573397\pi\) | ||||
−0.228545 | + | 0.973533i | \(0.573397\pi\) | |||||||
\(998\) | −2.17858e19 | −0.697951 | ||||||||
\(999\) | 1.03182e19 | 0.328420 |
(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.1.26 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.a.1.26 | ✓ | 30 | 1.1 | even | 1 | trivial |