Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,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, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
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: | \(135.996742959\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −86.7335 | −1.91656 | −0.958278 | − | 0.285837i | \(-0.907728\pi\) | ||||
−0.958278 | + | 0.285837i | \(0.907728\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | 5474.69 | 2.67319 | ||||||||
\(5\) | −11727.0 | −1.67823 | −0.839114 | − | 0.543956i | \(-0.816926\pi\) | ||||
−0.839114 | + | 0.543956i | \(0.816926\pi\) | |||||||
\(6\) | −21076.2 | −1.10652 | ||||||||
\(7\) | 24236.6 | 0.545045 | 0.272522 | − | 0.962149i | \(-0.412142\pi\) | ||||
0.272522 | + | 0.962149i | \(0.412142\pi\) | |||||||
\(8\) | −297209. | −3.20676 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 1.01712e6 | 3.21642 | ||||||||
\(11\) | −225721. | −0.422582 | −0.211291 | − | 0.977423i | \(-0.567767\pi\) | ||||
−0.211291 | + | 0.977423i | \(0.567767\pi\) | |||||||
\(12\) | 1.33035e6 | 1.54337 | ||||||||
\(13\) | −1.93565e6 | −1.44590 | −0.722950 | − | 0.690901i | \(-0.757214\pi\) | ||||
−0.722950 | + | 0.690901i | \(0.757214\pi\) | |||||||
\(14\) | −2.10212e6 | −1.04461 | ||||||||
\(15\) | −2.84965e6 | −0.968925 | ||||||||
\(16\) | 1.45658e7 | 3.47275 | ||||||||
\(17\) | −7.58845e6 | −1.29624 | −0.648118 | − | 0.761540i | \(-0.724444\pi\) | ||||
−0.648118 | + | 0.761540i | \(0.724444\pi\) | |||||||
\(18\) | −5.12152e6 | −0.638852 | ||||||||
\(19\) | 2.02438e7 | 1.87563 | 0.937815 | − | 0.347136i | \(-0.112846\pi\) | ||||
0.937815 | + | 0.347136i | \(0.112846\pi\) | |||||||
\(20\) | −6.42015e7 | −4.48622 | ||||||||
\(21\) | 5.88949e6 | 0.314682 | ||||||||
\(22\) | 1.95775e7 | 0.809903 | ||||||||
\(23\) | 4.13605e6 | 0.133993 | 0.0669965 | − | 0.997753i | \(-0.478658\pi\) | ||||
0.0669965 | + | 0.997753i | \(0.478658\pi\) | |||||||
\(24\) | −7.22217e7 | −1.85142 | ||||||||
\(25\) | 8.86937e7 | 1.81645 | ||||||||
\(26\) | 1.67885e8 | 2.77115 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | 1.32688e8 | 1.45701 | ||||||||
\(29\) | 1.28733e8 | 1.16547 | 0.582736 | − | 0.812662i | \(-0.301982\pi\) | ||||
0.582736 | + | 0.812662i | \(0.301982\pi\) | |||||||
\(30\) | 2.47160e8 | 1.85700 | ||||||||
\(31\) | −1.26556e8 | −0.793953 | −0.396976 | − | 0.917829i | \(-0.629941\pi\) | ||||
−0.396976 | + | 0.917829i | \(0.629941\pi\) | |||||||
\(32\) | −6.54656e8 | −3.44896 | ||||||||
\(33\) | −5.48501e7 | −0.243978 | ||||||||
\(34\) | 6.58173e8 | 2.48431 | ||||||||
\(35\) | −2.84222e8 | −0.914709 | ||||||||
\(36\) | 3.23275e8 | 0.891063 | ||||||||
\(37\) | 1.58528e8 | 0.375834 | 0.187917 | − | 0.982185i | \(-0.439826\pi\) | ||||
0.187917 | + | 0.982185i | \(0.439826\pi\) | |||||||
\(38\) | −1.75581e9 | −3.59475 | ||||||||
\(39\) | −4.70363e8 | −0.834790 | ||||||||
\(40\) | 3.48536e9 | 5.38168 | ||||||||
\(41\) | 7.42011e8 | 1.00023 | 0.500114 | − | 0.865959i | \(-0.333291\pi\) | ||||
0.500114 | + | 0.865959i | \(0.333291\pi\) | |||||||
\(42\) | −5.10816e8 | −0.603105 | ||||||||
\(43\) | −1.64490e8 | −0.170633 | −0.0853166 | − | 0.996354i | \(-0.527190\pi\) | ||||
−0.0853166 | + | 0.996354i | \(0.527190\pi\) | |||||||
\(44\) | −1.23575e9 | −1.12964 | ||||||||
\(45\) | −6.92466e8 | −0.559409 | ||||||||
\(46\) | −3.58734e8 | −0.256805 | ||||||||
\(47\) | −1.37797e9 | −0.876401 | −0.438200 | − | 0.898877i | \(-0.644384\pi\) | ||||
−0.438200 | + | 0.898877i | \(0.644384\pi\) | |||||||
\(48\) | 3.53948e9 | 2.00499 | ||||||||
\(49\) | −1.38992e9 | −0.702926 | ||||||||
\(50\) | −7.69271e9 | −3.48132 | ||||||||
\(51\) | −1.84399e9 | −0.748382 | ||||||||
\(52\) | −1.05971e10 | −3.86516 | ||||||||
\(53\) | 4.06680e8 | 0.133578 | 0.0667891 | − | 0.997767i | \(-0.478725\pi\) | ||||
0.0667891 | + | 0.997767i | \(0.478725\pi\) | |||||||
\(54\) | −1.24453e9 | −0.368841 | ||||||||
\(55\) | 2.64702e9 | 0.709189 | ||||||||
\(56\) | −7.20332e9 | −1.74783 | ||||||||
\(57\) | 4.91924e9 | 1.08290 | ||||||||
\(58\) | −1.11655e10 | −2.23369 | ||||||||
\(59\) | −7.14924e8 | −0.130189 | ||||||||
\(60\) | −1.56010e10 | −2.59012 | ||||||||
\(61\) | 1.25207e9 | 0.189808 | 0.0949042 | − | 0.995486i | \(-0.469746\pi\) | ||||
0.0949042 | + | 0.995486i | \(0.469746\pi\) | |||||||
\(62\) | 1.09767e10 | 1.52166 | ||||||||
\(63\) | 1.43115e9 | 0.181682 | ||||||||
\(64\) | 2.69499e10 | 3.13738 | ||||||||
\(65\) | 2.26993e10 | 2.42655 | ||||||||
\(66\) | 4.75734e9 | 0.467598 | ||||||||
\(67\) | −3.89914e9 | −0.352823 | −0.176412 | − | 0.984316i | \(-0.556449\pi\) | ||||
−0.176412 | + | 0.984316i | \(0.556449\pi\) | |||||||
\(68\) | −4.15444e10 | −3.46508 | ||||||||
\(69\) | 1.00506e9 | 0.0773609 | ||||||||
\(70\) | 2.46515e10 | 1.75309 | ||||||||
\(71\) | 2.09101e10 | 1.37542 | 0.687709 | − | 0.725986i | \(-0.258617\pi\) | ||||
0.687709 | + | 0.725986i | \(0.258617\pi\) | |||||||
\(72\) | −1.75499e10 | −1.06892 | ||||||||
\(73\) | 1.32307e10 | 0.746975 | 0.373487 | − | 0.927635i | \(-0.378162\pi\) | ||||
0.373487 | + | 0.927635i | \(0.378162\pi\) | |||||||
\(74\) | −1.37497e10 | −0.720308 | ||||||||
\(75\) | 2.15526e10 | 1.04873 | ||||||||
\(76\) | 1.10829e11 | 5.01391 | ||||||||
\(77\) | −5.47069e9 | −0.230326 | ||||||||
\(78\) | 4.07962e10 | 1.59992 | ||||||||
\(79\) | 3.04105e10 | 1.11192 | 0.555961 | − | 0.831208i | \(-0.312350\pi\) | ||||
0.555961 | + | 0.831208i | \(0.312350\pi\) | |||||||
\(80\) | −1.70812e11 | −5.82807 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −6.43572e10 | −1.91699 | ||||||||
\(83\) | −6.10863e10 | −1.70221 | −0.851107 | − | 0.524993i | \(-0.824068\pi\) | ||||
−0.851107 | + | 0.524993i | \(0.824068\pi\) | |||||||
\(84\) | 3.22431e10 | 0.841204 | ||||||||
\(85\) | 8.89895e10 | 2.17538 | ||||||||
\(86\) | 1.42668e10 | 0.327028 | ||||||||
\(87\) | 3.12822e10 | 0.672885 | ||||||||
\(88\) | 6.70861e10 | 1.35512 | ||||||||
\(89\) | 6.05385e10 | 1.14918 | 0.574588 | − | 0.818443i | \(-0.305162\pi\) | ||||
0.574588 | + | 0.818443i | \(0.305162\pi\) | |||||||
\(90\) | 6.00600e10 | 1.07214 | ||||||||
\(91\) | −4.69135e10 | −0.788080 | ||||||||
\(92\) | 2.26436e10 | 0.358189 | ||||||||
\(93\) | −3.07532e10 | −0.458389 | ||||||||
\(94\) | 1.19516e11 | 1.67967 | ||||||||
\(95\) | −2.37398e11 | −3.14773 | ||||||||
\(96\) | −1.59081e11 | −1.99126 | ||||||||
\(97\) | −1.06180e11 | −1.25544 | −0.627720 | − | 0.778439i | \(-0.716012\pi\) | ||||
−0.627720 | + | 0.778439i | \(0.716012\pi\) | |||||||
\(98\) | 1.20552e11 | 1.34720 | ||||||||
\(99\) | −1.33286e10 | −0.140861 | ||||||||
\(100\) | 4.85571e11 | 4.85571 | ||||||||
\(101\) | 1.20010e11 | 1.13619 | 0.568094 | − | 0.822964i | \(-0.307681\pi\) | ||||
0.568094 | + | 0.822964i | \(0.307681\pi\) | |||||||
\(102\) | 1.59936e11 | 1.43432 | ||||||||
\(103\) | 8.50039e10 | 0.722493 | 0.361247 | − | 0.932470i | \(-0.382351\pi\) | ||||
0.361247 | + | 0.932470i | \(0.382351\pi\) | |||||||
\(104\) | 5.75292e11 | 4.63665 | ||||||||
\(105\) | −6.90659e10 | −0.528107 | ||||||||
\(106\) | −3.52728e10 | −0.256010 | ||||||||
\(107\) | 1.46709e11 | 1.01122 | 0.505612 | − | 0.862761i | \(-0.331267\pi\) | ||||
0.505612 | + | 0.862761i | \(0.331267\pi\) | |||||||
\(108\) | 7.85558e10 | 0.514455 | ||||||||
\(109\) | 2.04883e11 | 1.27544 | 0.637721 | − | 0.770267i | \(-0.279877\pi\) | ||||
0.637721 | + | 0.770267i | \(0.279877\pi\) | |||||||
\(110\) | −2.29585e11 | −1.35920 | ||||||||
\(111\) | 3.85223e10 | 0.216988 | ||||||||
\(112\) | 3.53024e11 | 1.89280 | ||||||||
\(113\) | 2.74469e10 | 0.140140 | 0.0700699 | − | 0.997542i | \(-0.477678\pi\) | ||||
0.0700699 | + | 0.997542i | \(0.477678\pi\) | |||||||
\(114\) | −4.26663e11 | −2.07543 | ||||||||
\(115\) | −4.85033e10 | −0.224871 | ||||||||
\(116\) | 7.04775e11 | 3.11553 | ||||||||
\(117\) | −1.14298e11 | −0.481966 | ||||||||
\(118\) | 6.20079e10 | 0.249514 | ||||||||
\(119\) | −1.83918e11 | −0.706506 | ||||||||
\(120\) | 8.46942e11 | 3.10711 | ||||||||
\(121\) | −2.34362e11 | −0.821424 | ||||||||
\(122\) | −1.08597e11 | −0.363779 | ||||||||
\(123\) | 1.80309e11 | 0.577482 | ||||||||
\(124\) | −6.92857e11 | −2.12239 | ||||||||
\(125\) | −4.67503e11 | −1.37018 | ||||||||
\(126\) | −1.24128e11 | −0.348203 | ||||||||
\(127\) | 3.40084e11 | 0.913411 | 0.456706 | − | 0.889618i | \(-0.349029\pi\) | ||||
0.456706 | + | 0.889618i | \(0.349029\pi\) | |||||||
\(128\) | −9.96721e11 | −2.56400 | ||||||||
\(129\) | −3.99711e10 | −0.0985151 | ||||||||
\(130\) | −1.96879e12 | −4.65062 | ||||||||
\(131\) | −8.54131e11 | −1.93434 | −0.967169 | − | 0.254133i | \(-0.918210\pi\) | ||||
−0.967169 | + | 0.254133i | \(0.918210\pi\) | |||||||
\(132\) | −3.00287e11 | −0.652199 | ||||||||
\(133\) | 4.90640e11 | 1.02230 | ||||||||
\(134\) | 3.38186e11 | 0.676206 | ||||||||
\(135\) | −1.68269e11 | −0.322975 | ||||||||
\(136\) | 2.25535e12 | 4.15672 | ||||||||
\(137\) | 4.87116e11 | 0.862321 | 0.431161 | − | 0.902275i | \(-0.358104\pi\) | ||||
0.431161 | + | 0.902275i | \(0.358104\pi\) | |||||||
\(138\) | −8.71722e10 | −0.148267 | ||||||||
\(139\) | 4.36340e11 | 0.713253 | 0.356627 | − | 0.934247i | \(-0.383927\pi\) | ||||
0.356627 | + | 0.934247i | \(0.383927\pi\) | |||||||
\(140\) | −1.55603e12 | −2.44519 | ||||||||
\(141\) | −3.34848e11 | −0.505990 | ||||||||
\(142\) | −1.81360e12 | −2.63607 | ||||||||
\(143\) | 4.36916e11 | 0.611012 | ||||||||
\(144\) | 8.60094e11 | 1.15758 | ||||||||
\(145\) | −1.50965e12 | −1.95593 | ||||||||
\(146\) | −1.14754e12 | −1.43162 | ||||||||
\(147\) | −3.37749e11 | −0.405835 | ||||||||
\(148\) | 8.67892e11 | 1.00468 | ||||||||
\(149\) | 1.56344e11 | 0.174405 | 0.0872023 | − | 0.996191i | \(-0.472207\pi\) | ||||
0.0872023 | + | 0.996191i | \(0.472207\pi\) | |||||||
\(150\) | −1.86933e12 | −2.00994 | ||||||||
\(151\) | −9.22244e11 | −0.956032 | −0.478016 | − | 0.878351i | \(-0.658644\pi\) | ||||
−0.478016 | + | 0.878351i | \(0.658644\pi\) | |||||||
\(152\) | −6.01663e12 | −6.01470 | ||||||||
\(153\) | −4.48090e11 | −0.432079 | ||||||||
\(154\) | 4.74492e11 | 0.441433 | ||||||||
\(155\) | 1.48412e12 | 1.33243 | ||||||||
\(156\) | −2.57509e12 | −2.23155 | ||||||||
\(157\) | −1.30773e12 | −1.09413 | −0.547067 | − | 0.837089i | \(-0.684256\pi\) | ||||
−0.547067 | + | 0.837089i | \(0.684256\pi\) | |||||||
\(158\) | −2.63761e12 | −2.13106 | ||||||||
\(159\) | 9.88233e10 | 0.0771214 | ||||||||
\(160\) | 7.67713e12 | 5.78814 | ||||||||
\(161\) | 1.00244e11 | 0.0730322 | ||||||||
\(162\) | −3.02421e11 | −0.212951 | ||||||||
\(163\) | −1.36308e12 | −0.927873 | −0.463937 | − | 0.885868i | \(-0.653563\pi\) | ||||
−0.463937 | + | 0.885868i | \(0.653563\pi\) | |||||||
\(164\) | 4.06228e12 | 2.67380 | ||||||||
\(165\) | 6.43225e11 | 0.409451 | ||||||||
\(166\) | 5.29822e12 | 3.26239 | ||||||||
\(167\) | 1.84641e12 | 1.09999 | 0.549995 | − | 0.835168i | \(-0.314630\pi\) | ||||
0.549995 | + | 0.835168i | \(0.314630\pi\) | |||||||
\(168\) | −1.75041e12 | −1.00911 | ||||||||
\(169\) | 1.95458e12 | 1.09063 | ||||||||
\(170\) | −7.71837e12 | −4.16924 | ||||||||
\(171\) | 1.19538e12 | 0.625210 | ||||||||
\(172\) | −9.00533e11 | −0.456135 | ||||||||
\(173\) | 1.76237e12 | 0.864655 | 0.432327 | − | 0.901717i | \(-0.357693\pi\) | ||||
0.432327 | + | 0.901717i | \(0.357693\pi\) | |||||||
\(174\) | −2.71321e12 | −1.28962 | ||||||||
\(175\) | 2.14963e12 | 0.990045 | ||||||||
\(176\) | −3.28779e12 | −1.46752 | ||||||||
\(177\) | −1.73727e11 | −0.0751646 | ||||||||
\(178\) | −5.25071e12 | −2.20246 | ||||||||
\(179\) | 4.00844e12 | 1.63036 | 0.815180 | − | 0.579208i | \(-0.196638\pi\) | ||||
0.815180 | + | 0.579208i | \(0.196638\pi\) | |||||||
\(180\) | −3.79104e12 | −1.49541 | ||||||||
\(181\) | 9.05666e11 | 0.346526 | 0.173263 | − | 0.984876i | \(-0.444569\pi\) | ||||
0.173263 | + | 0.984876i | \(0.444569\pi\) | |||||||
\(182\) | 4.06897e12 | 1.51040 | ||||||||
\(183\) | 3.04254e11 | 0.109586 | ||||||||
\(184\) | −1.22927e12 | −0.429684 | ||||||||
\(185\) | −1.85905e12 | −0.630735 | ||||||||
\(186\) | 2.66733e12 | 0.878528 | ||||||||
\(187\) | 1.71287e12 | 0.547766 | ||||||||
\(188\) | −7.54398e12 | −2.34278 | ||||||||
\(189\) | 3.47768e11 | 0.104894 | ||||||||
\(190\) | 2.05904e13 | 6.03281 | ||||||||
\(191\) | −6.55756e12 | −1.86663 | −0.933316 | − | 0.359055i | \(-0.883099\pi\) | ||||
−0.933316 | + | 0.359055i | \(0.883099\pi\) | |||||||
\(192\) | 6.54882e12 | 1.81137 | ||||||||
\(193\) | −6.69275e12 | −1.79903 | −0.899517 | − | 0.436885i | \(-0.856082\pi\) | ||||
−0.899517 | + | 0.436885i | \(0.856082\pi\) | |||||||
\(194\) | 9.20932e12 | 2.40612 | ||||||||
\(195\) | 5.51593e12 | 1.40097 | ||||||||
\(196\) | −7.60936e12 | −1.87906 | ||||||||
\(197\) | −3.16829e12 | −0.760783 | −0.380391 | − | 0.924826i | \(-0.624211\pi\) | ||||
−0.380391 | + | 0.924826i | \(0.624211\pi\) | |||||||
\(198\) | 1.15603e12 | 0.269968 | ||||||||
\(199\) | 4.98278e12 | 1.13183 | 0.565913 | − | 0.824465i | \(-0.308524\pi\) | ||||
0.565913 | + | 0.824465i | \(0.308524\pi\) | |||||||
\(200\) | −2.63605e13 | −5.82491 | ||||||||
\(201\) | −9.47490e11 | −0.203703 | ||||||||
\(202\) | −1.04089e13 | −2.17757 | ||||||||
\(203\) | 3.12005e12 | 0.635234 | ||||||||
\(204\) | −1.00953e13 | −2.00057 | ||||||||
\(205\) | −8.70154e12 | −1.67861 | ||||||||
\(206\) | −7.37268e12 | −1.38470 | ||||||||
\(207\) | 2.44229e11 | 0.0446643 | ||||||||
\(208\) | −2.81942e13 | −5.02125 | ||||||||
\(209\) | −4.56944e12 | −0.792608 | ||||||||
\(210\) | 5.99032e12 | 1.01215 | ||||||||
\(211\) | 4.55874e12 | 0.750397 | 0.375199 | − | 0.926944i | \(-0.377575\pi\) | ||||
0.375199 | + | 0.926944i | \(0.377575\pi\) | |||||||
\(212\) | 2.22645e12 | 0.357080 | ||||||||
\(213\) | 5.08115e12 | 0.794098 | ||||||||
\(214\) | −1.27246e13 | −1.93807 | ||||||||
\(215\) | 1.92897e12 | 0.286361 | ||||||||
\(216\) | −4.26462e12 | −0.617142 | ||||||||
\(217\) | −3.06729e12 | −0.432740 | ||||||||
\(218\) | −1.77702e13 | −2.44446 | ||||||||
\(219\) | 3.21505e12 | 0.431266 | ||||||||
\(220\) | 1.44916e13 | 1.89580 | ||||||||
\(221\) | 1.46886e13 | 1.87423 | ||||||||
\(222\) | −3.34117e12 | −0.415870 | ||||||||
\(223\) | −8.99847e12 | −1.09268 | −0.546339 | − | 0.837564i | \(-0.683979\pi\) | ||||
−0.546339 | + | 0.837564i | \(0.683979\pi\) | |||||||
\(224\) | −1.58666e13 | −1.87984 | ||||||||
\(225\) | 5.23727e12 | 0.605482 | ||||||||
\(226\) | −2.38056e12 | −0.268586 | ||||||||
\(227\) | −1.33843e12 | −0.147385 | −0.0736925 | − | 0.997281i | \(-0.523478\pi\) | ||||
−0.0736925 | + | 0.997281i | \(0.523478\pi\) | |||||||
\(228\) | 2.69313e13 | 2.89478 | ||||||||
\(229\) | −1.15610e13 | −1.21311 | −0.606555 | − | 0.795042i | \(-0.707449\pi\) | ||||
−0.606555 | + | 0.795042i | \(0.707449\pi\) | |||||||
\(230\) | 4.20686e12 | 0.430978 | ||||||||
\(231\) | −1.32938e12 | −0.132979 | ||||||||
\(232\) | −3.82606e13 | −3.73739 | ||||||||
\(233\) | −5.98856e12 | −0.571301 | −0.285650 | − | 0.958334i | \(-0.592210\pi\) | ||||
−0.285650 | + | 0.958334i | \(0.592210\pi\) | |||||||
\(234\) | 9.91347e12 | 0.923716 | ||||||||
\(235\) | 1.61595e13 | 1.47080 | ||||||||
\(236\) | −3.91399e12 | −0.348020 | ||||||||
\(237\) | 7.38975e12 | 0.641969 | ||||||||
\(238\) | 1.59519e13 | 1.35406 | ||||||||
\(239\) | 1.71328e13 | 1.42115 | 0.710576 | − | 0.703620i | \(-0.248434\pi\) | ||||
0.710576 | + | 0.703620i | \(0.248434\pi\) | |||||||
\(240\) | −4.15074e13 | −3.36484 | ||||||||
\(241\) | 1.29158e13 | 1.02336 | 0.511679 | − | 0.859177i | \(-0.329024\pi\) | ||||
0.511679 | + | 0.859177i | \(0.329024\pi\) | |||||||
\(242\) | 2.03270e13 | 1.57431 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | 6.85471e12 | 0.507394 | ||||||||
\(245\) | 1.62995e13 | 1.17967 | ||||||||
\(246\) | −1.56388e13 | −1.10678 | ||||||||
\(247\) | −3.91849e13 | −2.71197 | ||||||||
\(248\) | 3.76137e13 | 2.54602 | ||||||||
\(249\) | −1.48440e13 | −0.982773 | ||||||||
\(250\) | 4.05481e13 | 2.62604 | ||||||||
\(251\) | −2.60915e13 | −1.65308 | −0.826540 | − | 0.562879i | \(-0.809694\pi\) | ||||
−0.826540 | + | 0.562879i | \(0.809694\pi\) | |||||||
\(252\) | 7.83508e12 | 0.485669 | ||||||||
\(253\) | −9.33591e11 | −0.0566231 | ||||||||
\(254\) | −2.94967e13 | −1.75060 | ||||||||
\(255\) | 2.16245e13 | 1.25596 | ||||||||
\(256\) | 3.12557e13 | 1.77668 | ||||||||
\(257\) | 2.28259e13 | 1.26998 | 0.634989 | − | 0.772521i | \(-0.281005\pi\) | ||||
0.634989 | + | 0.772521i | \(0.281005\pi\) | |||||||
\(258\) | 3.46683e12 | 0.188810 | ||||||||
\(259\) | 3.84218e12 | 0.204846 | ||||||||
\(260\) | 1.24272e14 | 6.48662 | ||||||||
\(261\) | 7.60157e12 | 0.388491 | ||||||||
\(262\) | 7.40818e13 | 3.70727 | ||||||||
\(263\) | −2.36115e13 | −1.15709 | −0.578545 | − | 0.815651i | \(-0.696379\pi\) | ||||
−0.578545 | + | 0.815651i | \(0.696379\pi\) | |||||||
\(264\) | 1.63019e13 | 0.782379 | ||||||||
\(265\) | −4.76912e12 | −0.224175 | ||||||||
\(266\) | −4.25549e13 | −1.95930 | ||||||||
\(267\) | 1.47108e13 | 0.663477 | ||||||||
\(268\) | −2.13466e13 | −0.943163 | ||||||||
\(269\) | −3.13089e13 | −1.35528 | −0.677642 | − | 0.735392i | \(-0.736998\pi\) | ||||
−0.677642 | + | 0.735392i | \(0.736998\pi\) | |||||||
\(270\) | 1.45946e13 | 0.619000 | ||||||||
\(271\) | −4.19841e13 | −1.74483 | −0.872417 | − | 0.488763i | \(-0.837448\pi\) | ||||
−0.872417 | + | 0.488763i | \(0.837448\pi\) | |||||||
\(272\) | −1.10532e14 | −4.50151 | ||||||||
\(273\) | −1.14000e13 | −0.454998 | ||||||||
\(274\) | −4.22492e13 | −1.65269 | ||||||||
\(275\) | −2.00200e13 | −0.767599 | ||||||||
\(276\) | 5.50239e12 | 0.206800 | ||||||||
\(277\) | −3.49366e13 | −1.28719 | −0.643595 | − | 0.765366i | \(-0.722558\pi\) | ||||
−0.643595 | + | 0.765366i | \(0.722558\pi\) | |||||||
\(278\) | −3.78453e13 | −1.36699 | ||||||||
\(279\) | −7.47303e12 | −0.264651 | ||||||||
\(280\) | 8.44732e13 | 2.93325 | ||||||||
\(281\) | −5.31784e13 | −1.81072 | −0.905359 | − | 0.424647i | \(-0.860398\pi\) | ||||
−0.905359 | + | 0.424647i | \(0.860398\pi\) | |||||||
\(282\) | 2.90425e13 | 0.969759 | ||||||||
\(283\) | −1.01159e13 | −0.331267 | −0.165633 | − | 0.986187i | \(-0.552967\pi\) | ||||
−0.165633 | + | 0.986187i | \(0.552967\pi\) | |||||||
\(284\) | 1.14476e14 | 3.67675 | ||||||||
\(285\) | −5.76878e13 | −1.81734 | ||||||||
\(286\) | −3.78952e13 | −1.17104 | ||||||||
\(287\) | 1.79838e13 | 0.545169 | ||||||||
\(288\) | −3.86568e13 | −1.14965 | ||||||||
\(289\) | 2.33127e13 | 0.680228 | ||||||||
\(290\) | 1.30937e14 | 3.74864 | ||||||||
\(291\) | −2.58016e13 | −0.724829 | ||||||||
\(292\) | 7.24338e13 | 1.99680 | ||||||||
\(293\) | −1.50814e13 | −0.408008 | −0.204004 | − | 0.978970i | \(-0.565396\pi\) | ||||
−0.204004 | + | 0.978970i | \(0.565396\pi\) | |||||||
\(294\) | 2.92942e13 | 0.777805 | ||||||||
\(295\) | 8.38390e12 | 0.218487 | ||||||||
\(296\) | −4.71159e13 | −1.20521 | ||||||||
\(297\) | −3.23884e12 | −0.0813260 | ||||||||
\(298\) | −1.35603e13 | −0.334256 | ||||||||
\(299\) | −8.00593e12 | −0.193740 | ||||||||
\(300\) | 1.17994e14 | 2.80344 | ||||||||
\(301\) | −3.98668e12 | −0.0930027 | ||||||||
\(302\) | 7.99894e13 | 1.83229 | ||||||||
\(303\) | 2.91624e13 | 0.655978 | ||||||||
\(304\) | 2.94866e14 | 6.51359 | ||||||||
\(305\) | −1.46830e13 | −0.318542 | ||||||||
\(306\) | 3.88644e13 | 0.828103 | ||||||||
\(307\) | 1.31999e13 | 0.276256 | 0.138128 | − | 0.990414i | \(-0.455892\pi\) | ||||
0.138128 | + | 0.990414i | \(0.455892\pi\) | |||||||
\(308\) | −2.99504e13 | −0.615706 | ||||||||
\(309\) | 2.06559e13 | 0.417132 | ||||||||
\(310\) | −1.28723e14 | −2.55368 | ||||||||
\(311\) | −5.37958e13 | −1.04850 | −0.524248 | − | 0.851566i | \(-0.675653\pi\) | ||||
−0.524248 | + | 0.851566i | \(0.675653\pi\) | |||||||
\(312\) | 1.39796e14 | 2.67697 | ||||||||
\(313\) | 2.38417e13 | 0.448583 | 0.224291 | − | 0.974522i | \(-0.427993\pi\) | ||||
0.224291 | + | 0.974522i | \(0.427993\pi\) | |||||||
\(314\) | 1.13424e14 | 2.09697 | ||||||||
\(315\) | −1.67830e13 | −0.304903 | ||||||||
\(316\) | 1.66488e14 | 2.97238 | ||||||||
\(317\) | 5.46736e13 | 0.959294 | 0.479647 | − | 0.877461i | \(-0.340765\pi\) | ||||
0.479647 | + | 0.877461i | \(0.340765\pi\) | |||||||
\(318\) | −8.57128e12 | −0.147808 | ||||||||
\(319\) | −2.90577e13 | −0.492508 | ||||||||
\(320\) | −3.16041e14 | −5.26524 | ||||||||
\(321\) | 3.56504e13 | 0.583830 | ||||||||
\(322\) | −8.69447e12 | −0.139970 | ||||||||
\(323\) | −1.53619e14 | −2.43126 | ||||||||
\(324\) | 1.90891e13 | 0.297021 | ||||||||
\(325\) | −1.71680e14 | −2.62640 | ||||||||
\(326\) | 1.18224e14 | 1.77832 | ||||||||
\(327\) | 4.97866e13 | 0.736377 | ||||||||
\(328\) | −2.20532e14 | −3.20749 | ||||||||
\(329\) | −3.33974e13 | −0.477677 | ||||||||
\(330\) | −5.57892e13 | −0.784735 | ||||||||
\(331\) | −4.00410e13 | −0.553925 | −0.276962 | − | 0.960881i | \(-0.589328\pi\) | ||||
−0.276962 | + | 0.960881i | \(0.589328\pi\) | |||||||
\(332\) | −3.34428e14 | −4.55034 | ||||||||
\(333\) | 9.36092e12 | 0.125278 | ||||||||
\(334\) | −1.60146e14 | −2.10819 | ||||||||
\(335\) | 4.57251e13 | 0.592118 | ||||||||
\(336\) | 8.57850e13 | 1.09281 | ||||||||
\(337\) | 1.09478e14 | 1.37203 | 0.686013 | − | 0.727589i | \(-0.259359\pi\) | ||||
0.686013 | + | 0.727589i | \(0.259359\pi\) | |||||||
\(338\) | −1.69527e14 | −2.09024 | ||||||||
\(339\) | 6.66959e12 | 0.0809098 | ||||||||
\(340\) | 4.87190e14 | 5.81520 | ||||||||
\(341\) | 2.85664e13 | 0.335511 | ||||||||
\(342\) | −1.03679e14 | −1.19825 | ||||||||
\(343\) | −8.16104e13 | −0.928171 | ||||||||
\(344\) | 4.88879e13 | 0.547180 | ||||||||
\(345\) | −1.17863e13 | −0.129829 | ||||||||
\(346\) | −1.52856e14 | −1.65716 | ||||||||
\(347\) | 6.14955e13 | 0.656193 | 0.328096 | − | 0.944644i | \(-0.393593\pi\) | ||||
0.328096 | + | 0.944644i | \(0.393593\pi\) | |||||||
\(348\) | 1.71260e14 | 1.79875 | ||||||||
\(349\) | −1.61145e14 | −1.66601 | −0.833005 | − | 0.553266i | \(-0.813381\pi\) | ||||
−0.833005 | + | 0.553266i | \(0.813381\pi\) | |||||||
\(350\) | −1.86445e14 | −1.89748 | ||||||||
\(351\) | −2.77744e13 | −0.278263 | ||||||||
\(352\) | 1.47769e14 | 1.45747 | ||||||||
\(353\) | −5.18807e13 | −0.503785 | −0.251892 | − | 0.967755i | \(-0.581053\pi\) | ||||
−0.251892 | + | 0.967755i | \(0.581053\pi\) | |||||||
\(354\) | 1.50679e13 | 0.144057 | ||||||||
\(355\) | −2.45212e14 | −2.30826 | ||||||||
\(356\) | 3.31429e14 | 3.07196 | ||||||||
\(357\) | −4.46921e13 | −0.407902 | ||||||||
\(358\) | −3.47665e14 | −3.12468 | ||||||||
\(359\) | −2.44194e13 | −0.216130 | −0.108065 | − | 0.994144i | \(-0.534466\pi\) | ||||
−0.108065 | + | 0.994144i | \(0.534466\pi\) | |||||||
\(360\) | 2.05807e14 | 1.79389 | ||||||||
\(361\) | 2.93321e14 | 2.51799 | ||||||||
\(362\) | −7.85515e13 | −0.664137 | ||||||||
\(363\) | −5.69499e13 | −0.474249 | ||||||||
\(364\) | −2.56837e14 | −2.10669 | ||||||||
\(365\) | −1.55156e14 | −1.25359 | ||||||||
\(366\) | −2.63890e13 | −0.210028 | ||||||||
\(367\) | 1.30968e14 | 1.02684 | 0.513418 | − | 0.858139i | \(-0.328379\pi\) | ||||
0.513418 | + | 0.858139i | \(0.328379\pi\) | |||||||
\(368\) | 6.02447e13 | 0.465324 | ||||||||
\(369\) | 4.38150e13 | 0.333409 | ||||||||
\(370\) | 1.61242e14 | 1.20884 | ||||||||
\(371\) | 9.85653e12 | 0.0728061 | ||||||||
\(372\) | −1.68364e14 | −1.22536 | ||||||||
\(373\) | 2.23070e14 | 1.59972 | 0.799858 | − | 0.600189i | \(-0.204908\pi\) | ||||
0.799858 | + | 0.600189i | \(0.204908\pi\) | |||||||
\(374\) | −1.48563e14 | −1.04983 | ||||||||
\(375\) | −1.13603e14 | −0.791076 | ||||||||
\(376\) | 4.09546e14 | 2.81041 | ||||||||
\(377\) | −2.49182e14 | −1.68515 | ||||||||
\(378\) | −3.01632e13 | −0.201035 | ||||||||
\(379\) | 9.13403e13 | 0.599994 | 0.299997 | − | 0.953940i | \(-0.403014\pi\) | ||||
0.299997 | + | 0.953940i | \(0.403014\pi\) | |||||||
\(380\) | −1.29968e15 | −8.41449 | ||||||||
\(381\) | 8.26405e13 | 0.527358 | ||||||||
\(382\) | 5.68760e14 | 3.57751 | ||||||||
\(383\) | −1.79938e14 | −1.11565 | −0.557826 | − | 0.829958i | \(-0.688364\pi\) | ||||
−0.557826 | + | 0.829958i | \(0.688364\pi\) | |||||||
\(384\) | −2.42203e14 | −1.48033 | ||||||||
\(385\) | 6.41547e13 | 0.386540 | ||||||||
\(386\) | 5.80485e14 | 3.44795 | ||||||||
\(387\) | −9.71298e12 | −0.0568777 | ||||||||
\(388\) | −5.81300e14 | −3.35603 | ||||||||
\(389\) | −2.49341e14 | −1.41929 | −0.709643 | − | 0.704561i | \(-0.751144\pi\) | ||||
−0.709643 | + | 0.704561i | \(0.751144\pi\) | |||||||
\(390\) | −4.78416e14 | −2.68503 | ||||||||
\(391\) | −3.13862e13 | −0.173687 | ||||||||
\(392\) | 4.13095e14 | 2.25412 | ||||||||
\(393\) | −2.07554e14 | −1.11679 | ||||||||
\(394\) | 2.74797e14 | 1.45808 | ||||||||
\(395\) | −3.56623e14 | −1.86606 | ||||||||
\(396\) | −7.29698e13 | −0.376548 | ||||||||
\(397\) | 2.47278e14 | 1.25845 | 0.629226 | − | 0.777222i | \(-0.283372\pi\) | ||||
0.629226 | + | 0.777222i | \(0.283372\pi\) | |||||||
\(398\) | −4.32174e14 | −2.16921 | ||||||||
\(399\) | 1.19226e14 | 0.590226 | ||||||||
\(400\) | 1.29189e15 | 6.30807 | ||||||||
\(401\) | 3.49823e13 | 0.168483 | 0.0842413 | − | 0.996445i | \(-0.473153\pi\) | ||||
0.0842413 | + | 0.996445i | \(0.473153\pi\) | |||||||
\(402\) | 8.21791e13 | 0.390407 | ||||||||
\(403\) | 2.44969e14 | 1.14798 | ||||||||
\(404\) | 6.57018e14 | 3.03724 | ||||||||
\(405\) | −4.08894e13 | −0.186470 | ||||||||
\(406\) | −2.70613e14 | −1.21746 | ||||||||
\(407\) | −3.57830e13 | −0.158821 | ||||||||
\(408\) | 5.48051e14 | 2.39988 | ||||||||
\(409\) | −2.42776e14 | −1.04888 | −0.524441 | − | 0.851447i | \(-0.675726\pi\) | ||||
−0.524441 | + | 0.851447i | \(0.675726\pi\) | |||||||
\(410\) | 7.54715e14 | 3.21715 | ||||||||
\(411\) | 1.18369e14 | 0.497861 | ||||||||
\(412\) | 4.65370e14 | 1.93136 | ||||||||
\(413\) | −1.73273e13 | −0.0709588 | ||||||||
\(414\) | −2.11829e13 | −0.0856017 | ||||||||
\(415\) | 7.16357e14 | 2.85670 | ||||||||
\(416\) | 1.26718e15 | 4.98685 | ||||||||
\(417\) | 1.06031e14 | 0.411797 | ||||||||
\(418\) | 3.96323e14 | 1.51908 | ||||||||
\(419\) | 1.65501e14 | 0.626069 | 0.313035 | − | 0.949742i | \(-0.398654\pi\) | ||||
0.313035 | + | 0.949742i | \(0.398654\pi\) | |||||||
\(420\) | −3.78114e14 | −1.41173 | ||||||||
\(421\) | −5.33194e14 | −1.96487 | −0.982435 | − | 0.186604i | \(-0.940252\pi\) | ||||
−0.982435 | + | 0.186604i | \(0.940252\pi\) | |||||||
\(422\) | −3.95395e14 | −1.43818 | ||||||||
\(423\) | −8.13680e13 | −0.292134 | ||||||||
\(424\) | −1.20869e14 | −0.428353 | ||||||||
\(425\) | −6.73048e14 | −2.35454 | ||||||||
\(426\) | −4.40706e14 | −1.52193 | ||||||||
\(427\) | 3.03460e13 | 0.103454 | ||||||||
\(428\) | 8.03189e14 | 2.70319 | ||||||||
\(429\) | 1.06171e14 | 0.352768 | ||||||||
\(430\) | −1.67306e14 | −0.548828 | ||||||||
\(431\) | 2.86684e14 | 0.928494 | 0.464247 | − | 0.885706i | \(-0.346325\pi\) | ||||
0.464247 | + | 0.885706i | \(0.346325\pi\) | |||||||
\(432\) | 2.09003e14 | 0.668331 | ||||||||
\(433\) | 3.80518e14 | 1.20141 | 0.600706 | − | 0.799470i | \(-0.294886\pi\) | ||||
0.600706 | + | 0.799470i | \(0.294886\pi\) | |||||||
\(434\) | 2.66037e14 | 0.829370 | ||||||||
\(435\) | −3.66845e14 | −1.12925 | ||||||||
\(436\) | 1.12167e15 | 3.40950 | ||||||||
\(437\) | 8.37293e13 | 0.251321 | ||||||||
\(438\) | −2.78852e14 | −0.826546 | ||||||||
\(439\) | −4.85503e14 | −1.42114 | −0.710570 | − | 0.703626i | \(-0.751563\pi\) | ||||
−0.710570 | + | 0.703626i | \(0.751563\pi\) | |||||||
\(440\) | −7.86717e14 | −2.27420 | ||||||||
\(441\) | −8.20731e13 | −0.234309 | ||||||||
\(442\) | −1.27399e15 | −3.59206 | ||||||||
\(443\) | 6.11464e14 | 1.70275 | 0.851373 | − | 0.524560i | \(-0.175770\pi\) | ||||
0.851373 | + | 0.524560i | \(0.175770\pi\) | |||||||
\(444\) | 2.10898e14 | 0.580050 | ||||||||
\(445\) | −7.09933e14 | −1.92858 | ||||||||
\(446\) | 7.80468e14 | 2.09418 | ||||||||
\(447\) | 3.79917e13 | 0.100693 | ||||||||
\(448\) | 6.53173e14 | 1.71001 | ||||||||
\(449\) | −3.00652e14 | −0.777516 | −0.388758 | − | 0.921340i | \(-0.627096\pi\) | ||||
−0.388758 | + | 0.921340i | \(0.627096\pi\) | |||||||
\(450\) | −4.54247e14 | −1.16044 | ||||||||
\(451\) | −1.67487e14 | −0.422679 | ||||||||
\(452\) | 1.50263e14 | 0.374620 | ||||||||
\(453\) | −2.24105e14 | −0.551965 | ||||||||
\(454\) | 1.16087e14 | 0.282472 | ||||||||
\(455\) | 5.50153e14 | 1.32258 | ||||||||
\(456\) | −1.46204e15 | −3.47259 | ||||||||
\(457\) | 8.18072e12 | 0.0191979 | 0.00959893 | − | 0.999954i | \(-0.496945\pi\) | ||||
0.00959893 | + | 0.999954i | \(0.496945\pi\) | |||||||
\(458\) | 1.00272e15 | 2.32499 | ||||||||
\(459\) | −1.08886e14 | −0.249461 | ||||||||
\(460\) | −2.65541e14 | −0.601122 | ||||||||
\(461\) | −3.92650e14 | −0.878316 | −0.439158 | − | 0.898410i | \(-0.644723\pi\) | ||||
−0.439158 | + | 0.898410i | \(0.644723\pi\) | |||||||
\(462\) | 1.15302e14 | 0.254862 | ||||||||
\(463\) | −4.44783e13 | −0.0971522 | −0.0485761 | − | 0.998819i | \(-0.515468\pi\) | ||||
−0.0485761 | + | 0.998819i | \(0.515468\pi\) | |||||||
\(464\) | 1.87510e15 | 4.04739 | ||||||||
\(465\) | 3.60642e14 | 0.769281 | ||||||||
\(466\) | 5.19408e14 | 1.09493 | ||||||||
\(467\) | −1.85784e14 | −0.387048 | −0.193524 | − | 0.981096i | \(-0.561992\pi\) | ||||
−0.193524 | + | 0.981096i | \(0.561992\pi\) | |||||||
\(468\) | −6.25747e14 | −1.28839 | ||||||||
\(469\) | −9.45017e13 | −0.192304 | ||||||||
\(470\) | −1.40157e15 | −2.81887 | ||||||||
\(471\) | −3.17779e14 | −0.631698 | ||||||||
\(472\) | 2.12482e14 | 0.417485 | ||||||||
\(473\) | 3.71288e13 | 0.0721066 | ||||||||
\(474\) | −6.40939e14 | −1.23037 | ||||||||
\(475\) | 1.79550e15 | 3.40698 | ||||||||
\(476\) | −1.00689e15 | −1.88863 | ||||||||
\(477\) | 2.40141e13 | 0.0445261 | ||||||||
\(478\) | −1.48599e15 | −2.72372 | ||||||||
\(479\) | −4.25471e14 | −0.770948 | −0.385474 | − | 0.922719i | \(-0.625962\pi\) | ||||
−0.385474 | + | 0.922719i | \(0.625962\pi\) | |||||||
\(480\) | 1.86554e15 | 3.34179 | ||||||||
\(481\) | −3.06854e14 | −0.543419 | ||||||||
\(482\) | −1.12023e15 | −1.96132 | ||||||||
\(483\) | 2.43592e13 | 0.0421652 | ||||||||
\(484\) | −1.28306e15 | −2.19582 | ||||||||
\(485\) | 1.24516e15 | 2.10692 | ||||||||
\(486\) | −7.34883e13 | −0.122947 | ||||||||
\(487\) | −4.34881e12 | −0.00719385 | −0.00359692 | − | 0.999994i | \(-0.501145\pi\) | ||||
−0.00359692 | + | 0.999994i | \(0.501145\pi\) | |||||||
\(488\) | −3.72127e14 | −0.608670 | ||||||||
\(489\) | −3.31228e14 | −0.535708 | ||||||||
\(490\) | −1.41371e15 | −2.26090 | ||||||||
\(491\) | −1.49931e14 | −0.237107 | −0.118553 | − | 0.992948i | \(-0.537826\pi\) | ||||
−0.118553 | + | 0.992948i | \(0.537826\pi\) | |||||||
\(492\) | 9.87134e14 | 1.54372 | ||||||||
\(493\) | −9.76886e14 | −1.51073 | ||||||||
\(494\) | 3.39864e15 | 5.19765 | ||||||||
\(495\) | 1.56304e14 | 0.236396 | ||||||||
\(496\) | −1.84339e15 | −2.75720 | ||||||||
\(497\) | 5.06789e14 | 0.749664 | ||||||||
\(498\) | 1.28747e15 | 1.88354 | ||||||||
\(499\) | 6.62725e14 | 0.958916 | 0.479458 | − | 0.877565i | \(-0.340833\pi\) | ||||
0.479458 | + | 0.877565i | \(0.340833\pi\) | |||||||
\(500\) | −2.55943e15 | −3.66276 | ||||||||
\(501\) | 4.48679e14 | 0.635079 | ||||||||
\(502\) | 2.26301e15 | 3.16822 | ||||||||
\(503\) | −1.25716e15 | −1.74087 | −0.870433 | − | 0.492286i | \(-0.836161\pi\) | ||||
−0.870433 | + | 0.492286i | \(0.836161\pi\) | |||||||
\(504\) | −4.25349e14 | −0.582609 | ||||||||
\(505\) | −1.40735e15 | −1.90678 | ||||||||
\(506\) | 8.09735e13 | 0.108521 | ||||||||
\(507\) | 4.74962e14 | 0.629673 | ||||||||
\(508\) | 1.86186e15 | 2.44172 | ||||||||
\(509\) | −7.08145e14 | −0.918702 | −0.459351 | − | 0.888255i | \(-0.651918\pi\) | ||||
−0.459351 | + | 0.888255i | \(0.651918\pi\) | |||||||
\(510\) | −1.87556e15 | −2.40711 | ||||||||
\(511\) | 3.20666e14 | 0.407134 | ||||||||
\(512\) | −6.69628e14 | −0.841102 | ||||||||
\(513\) | 2.90476e14 | 0.360965 | ||||||||
\(514\) | −1.97977e15 | −2.43398 | ||||||||
\(515\) | −9.96838e14 | −1.21251 | ||||||||
\(516\) | −2.18829e14 | −0.263349 | ||||||||
\(517\) | 3.11037e14 | 0.370351 | ||||||||
\(518\) | −3.33245e14 | −0.392600 | ||||||||
\(519\) | 4.28255e14 | 0.499209 | ||||||||
\(520\) | −6.74643e15 | −7.78136 | ||||||||
\(521\) | 1.38595e15 | 1.58176 | 0.790881 | − | 0.611971i | \(-0.209623\pi\) | ||||
0.790881 | + | 0.611971i | \(0.209623\pi\) | |||||||
\(522\) | −6.59310e14 | −0.744564 | ||||||||
\(523\) | −3.11808e14 | −0.348440 | −0.174220 | − | 0.984707i | \(-0.555740\pi\) | ||||
−0.174220 | + | 0.984707i | \(0.555740\pi\) | |||||||
\(524\) | −4.67611e15 | −5.17085 | ||||||||
\(525\) | 5.22361e14 | 0.571603 | ||||||||
\(526\) | 2.04791e15 | 2.21763 | ||||||||
\(527\) | 9.60367e14 | 1.02915 | ||||||||
\(528\) | −7.98934e14 | −0.847275 | ||||||||
\(529\) | −9.35703e14 | −0.982046 | ||||||||
\(530\) | 4.13643e14 | 0.429643 | ||||||||
\(531\) | −4.22156e13 | −0.0433963 | ||||||||
\(532\) | 2.68610e15 | 2.73281 | ||||||||
\(533\) | −1.43627e15 | −1.44623 | ||||||||
\(534\) | −1.27592e15 | −1.27159 | ||||||||
\(535\) | −1.72046e15 | −1.69706 | ||||||||
\(536\) | 1.15886e15 | 1.13142 | ||||||||
\(537\) | 9.74050e14 | 0.941288 | ||||||||
\(538\) | 2.71553e15 | 2.59748 | ||||||||
\(539\) | 3.13732e14 | 0.297044 | ||||||||
\(540\) | −9.21222e14 | −0.863373 | ||||||||
\(541\) | −1.49757e15 | −1.38932 | −0.694660 | − | 0.719338i | \(-0.744445\pi\) | ||||
−0.694660 | + | 0.719338i | \(0.744445\pi\) | |||||||
\(542\) | 3.64143e15 | 3.34407 | ||||||||
\(543\) | 2.20077e14 | 0.200067 | ||||||||
\(544\) | 4.96783e15 | 4.47067 | ||||||||
\(545\) | −2.40266e15 | −2.14048 | ||||||||
\(546\) | 9.88760e14 | 0.872029 | ||||||||
\(547\) | 3.15839e14 | 0.275762 | 0.137881 | − | 0.990449i | \(-0.455971\pi\) | ||||
0.137881 | + | 0.990449i | \(0.455971\pi\) | |||||||
\(548\) | 2.66681e15 | 2.30515 | ||||||||
\(549\) | 7.39337e13 | 0.0632695 | ||||||||
\(550\) | 1.73640e15 | 1.47115 | ||||||||
\(551\) | 2.60605e15 | 2.18599 | ||||||||
\(552\) | −2.98712e14 | −0.248078 | ||||||||
\(553\) | 7.37047e14 | 0.606048 | ||||||||
\(554\) | 3.03018e15 | 2.46697 | ||||||||
\(555\) | −4.51750e14 | −0.364155 | ||||||||
\(556\) | 2.38883e15 | 1.90666 | ||||||||
\(557\) | −8.63856e14 | −0.682712 | −0.341356 | − | 0.939934i | \(-0.610886\pi\) | ||||
−0.341356 | + | 0.939934i | \(0.610886\pi\) | |||||||
\(558\) | 6.48162e14 | 0.507219 | ||||||||
\(559\) | 3.18395e14 | 0.246718 | ||||||||
\(560\) | −4.13991e15 | −3.17656 | ||||||||
\(561\) | 4.16227e14 | 0.316253 | ||||||||
\(562\) | 4.61235e15 | 3.47034 | ||||||||
\(563\) | 2.02055e15 | 1.50548 | 0.752739 | − | 0.658319i | \(-0.228732\pi\) | ||||
0.752739 | + | 0.658319i | \(0.228732\pi\) | |||||||
\(564\) | −1.83319e15 | −1.35261 | ||||||||
\(565\) | −3.21869e14 | −0.235187 | ||||||||
\(566\) | 8.77385e14 | 0.634892 | ||||||||
\(567\) | 8.45077e13 | 0.0605605 | ||||||||
\(568\) | −6.21466e15 | −4.41064 | ||||||||
\(569\) | −8.80440e14 | −0.618846 | −0.309423 | − | 0.950925i | \(-0.600136\pi\) | ||||
−0.309423 | + | 0.950925i | \(0.600136\pi\) | |||||||
\(570\) | 5.00346e15 | 3.48304 | ||||||||
\(571\) | −1.19192e15 | −0.821767 | −0.410883 | − | 0.911688i | \(-0.634780\pi\) | ||||
−0.410883 | + | 0.911688i | \(0.634780\pi\) | |||||||
\(572\) | 2.39198e15 | 1.63335 | ||||||||
\(573\) | −1.59349e15 | −1.07770 | ||||||||
\(574\) | −1.55980e15 | −1.04485 | ||||||||
\(575\) | 3.66841e14 | 0.243391 | ||||||||
\(576\) | 1.59136e15 | 1.04579 | ||||||||
\(577\) | 2.00994e14 | 0.130832 | 0.0654162 | − | 0.997858i | \(-0.479162\pi\) | ||||
0.0654162 | + | 0.997858i | \(0.479162\pi\) | |||||||
\(578\) | −2.02199e15 | −1.30370 | ||||||||
\(579\) | −1.62634e15 | −1.03867 | ||||||||
\(580\) | −8.26487e15 | −5.22856 | ||||||||
\(581\) | −1.48052e15 | −0.927782 | ||||||||
\(582\) | 2.23786e15 | 1.38918 | ||||||||
\(583\) | −9.17960e13 | −0.0564478 | ||||||||
\(584\) | −3.93227e15 | −2.39537 | ||||||||
\(585\) | 1.34037e15 | 0.808849 | ||||||||
\(586\) | 1.30806e15 | 0.781971 | ||||||||
\(587\) | −9.19761e14 | −0.544710 | −0.272355 | − | 0.962197i | \(-0.587803\pi\) | ||||
−0.272355 | + | 0.962197i | \(0.587803\pi\) | |||||||
\(588\) | −1.84907e15 | −1.08487 | ||||||||
\(589\) | −2.56198e15 | −1.48916 | ||||||||
\(590\) | −7.27164e14 | −0.418742 | ||||||||
\(591\) | −7.69894e14 | −0.439238 | ||||||||
\(592\) | 2.30908e15 | 1.30518 | ||||||||
\(593\) | 7.80639e14 | 0.437169 | 0.218585 | − | 0.975818i | \(-0.429856\pi\) | ||||
0.218585 | + | 0.975818i | \(0.429856\pi\) | |||||||
\(594\) | 2.80916e14 | 0.155866 | ||||||||
\(595\) | 2.15680e15 | 1.18568 | ||||||||
\(596\) | 8.55937e14 | 0.466216 | ||||||||
\(597\) | 1.21082e15 | 0.653460 | ||||||||
\(598\) | 6.94382e14 | 0.371315 | ||||||||
\(599\) | −5.49675e14 | −0.291245 | −0.145622 | − | 0.989340i | \(-0.546518\pi\) | ||||
−0.145622 | + | 0.989340i | \(0.546518\pi\) | |||||||
\(600\) | −6.40561e15 | −3.36302 | ||||||||
\(601\) | −1.50512e15 | −0.783000 | −0.391500 | − | 0.920178i | \(-0.628044\pi\) | ||||
−0.391500 | + | 0.920178i | \(0.628044\pi\) | |||||||
\(602\) | 3.45778e14 | 0.178245 | ||||||||
\(603\) | −2.30240e14 | −0.117608 | ||||||||
\(604\) | −5.04900e15 | −2.55565 | ||||||||
\(605\) | 2.74836e15 | 1.37854 | ||||||||
\(606\) | −2.52936e15 | −1.25722 | ||||||||
\(607\) | −2.78314e15 | −1.37087 | −0.685436 | − | 0.728133i | \(-0.740388\pi\) | ||||
−0.685436 | + | 0.728133i | \(0.740388\pi\) | |||||||
\(608\) | −1.32527e16 | −6.46898 | ||||||||
\(609\) | 7.58173e14 | 0.366753 | ||||||||
\(610\) | 1.27351e15 | 0.610503 | ||||||||
\(611\) | 2.66727e15 | 1.26719 | ||||||||
\(612\) | −2.45316e15 | −1.15503 | ||||||||
\(613\) | −1.81488e15 | −0.846868 | −0.423434 | − | 0.905927i | \(-0.639175\pi\) | ||||
−0.423434 | + | 0.905927i | \(0.639175\pi\) | |||||||
\(614\) | −1.14488e15 | −0.529460 | ||||||||
\(615\) | −2.11447e15 | −0.969146 | ||||||||
\(616\) | 1.62594e15 | 0.738601 | ||||||||
\(617\) | 2.32132e15 | 1.04512 | 0.522559 | − | 0.852603i | \(-0.324977\pi\) | ||||
0.522559 | + | 0.852603i | \(0.324977\pi\) | |||||||
\(618\) | −1.79156e15 | −0.799457 | ||||||||
\(619\) | 1.23097e15 | 0.544440 | 0.272220 | − | 0.962235i | \(-0.412242\pi\) | ||||
0.272220 | + | 0.962235i | \(0.412242\pi\) | |||||||
\(620\) | 8.12512e15 | 3.56185 | ||||||||
\(621\) | 5.93477e13 | 0.0257870 | ||||||||
\(622\) | 4.66590e15 | 2.00950 | ||||||||
\(623\) | 1.46725e15 | 0.626352 | ||||||||
\(624\) | −6.85120e15 | −2.89902 | ||||||||
\(625\) | 1.15164e15 | 0.483033 | ||||||||
\(626\) | −2.06787e15 | −0.859735 | ||||||||
\(627\) | −1.11037e15 | −0.457612 | ||||||||
\(628\) | −7.15942e15 | −2.92483 | ||||||||
\(629\) | −1.20298e15 | −0.487170 | ||||||||
\(630\) | 1.45565e15 | 0.584364 | ||||||||
\(631\) | 1.68636e15 | 0.671101 | 0.335551 | − | 0.942022i | \(-0.391078\pi\) | ||||
0.335551 | + | 0.942022i | \(0.391078\pi\) | |||||||
\(632\) | −9.03827e15 | −3.56567 | ||||||||
\(633\) | 1.10777e15 | 0.433242 | ||||||||
\(634\) | −4.74203e15 | −1.83854 | ||||||||
\(635\) | −3.98816e15 | −1.53291 | ||||||||
\(636\) | 5.41027e14 | 0.206160 | ||||||||
\(637\) | 2.69039e15 | 1.01636 | ||||||||
\(638\) | 2.52028e15 | 0.943919 | ||||||||
\(639\) | 1.23472e15 | 0.458473 | ||||||||
\(640\) | 1.16885e16 | 4.30298 | ||||||||
\(641\) | 1.29835e15 | 0.473885 | 0.236943 | − | 0.971524i | \(-0.423855\pi\) | ||||
0.236943 | + | 0.971524i | \(0.423855\pi\) | |||||||
\(642\) | −3.09208e15 | −1.11894 | ||||||||
\(643\) | −2.08702e15 | −0.748800 | −0.374400 | − | 0.927267i | \(-0.622151\pi\) | ||||
−0.374400 | + | 0.927267i | \(0.622151\pi\) | |||||||
\(644\) | 5.48803e14 | 0.195229 | ||||||||
\(645\) | 4.68740e14 | 0.165331 | ||||||||
\(646\) | 1.33239e16 | 4.65964 | ||||||||
\(647\) | −4.43825e15 | −1.53900 | −0.769499 | − | 0.638649i | \(-0.779494\pi\) | ||||
−0.769499 | + | 0.638649i | \(0.779494\pi\) | |||||||
\(648\) | −1.03630e15 | −0.356307 | ||||||||
\(649\) | 1.61373e14 | 0.0550155 | ||||||||
\(650\) | 1.48904e16 | 5.03364 | ||||||||
\(651\) | −7.45352e14 | −0.249842 | ||||||||
\(652\) | −7.46243e15 | −2.48038 | ||||||||
\(653\) | −2.02446e15 | −0.667247 | −0.333624 | − | 0.942706i | \(-0.608271\pi\) | ||||
−0.333624 | + | 0.942706i | \(0.608271\pi\) | |||||||
\(654\) | −4.31817e15 | −1.41131 | ||||||||
\(655\) | 1.00164e16 | 3.24626 | ||||||||
\(656\) | 1.08080e16 | 3.47354 | ||||||||
\(657\) | 7.81257e14 | 0.248992 | ||||||||
\(658\) | 2.89667e15 | 0.915496 | ||||||||
\(659\) | 5.05072e15 | 1.58301 | 0.791504 | − | 0.611164i | \(-0.209298\pi\) | ||||
0.791504 | + | 0.611164i | \(0.209298\pi\) | |||||||
\(660\) | 3.52146e15 | 1.09454 | ||||||||
\(661\) | −5.90345e15 | −1.81969 | −0.909845 | − | 0.414947i | \(-0.863800\pi\) | ||||
−0.909845 | + | 0.414947i | \(0.863800\pi\) | |||||||
\(662\) | 3.47289e15 | 1.06163 | ||||||||
\(663\) | 3.56932e15 | 1.08209 | ||||||||
\(664\) | 1.81554e16 | 5.45859 | ||||||||
\(665\) | −5.75372e15 | −1.71565 | ||||||||
\(666\) | −8.11905e14 | −0.240103 | ||||||||
\(667\) | 5.32447e14 | 0.156165 | ||||||||
\(668\) | 1.01086e16 | 2.94048 | ||||||||
\(669\) | −2.18663e15 | −0.630858 | ||||||||
\(670\) | −3.96589e15 | −1.13483 | ||||||||
\(671\) | −2.82619e14 | −0.0802097 | ||||||||
\(672\) | −3.85559e15 | −1.08533 | ||||||||
\(673\) | −2.41929e15 | −0.675470 | −0.337735 | − | 0.941241i | \(-0.609661\pi\) | ||||
−0.337735 | + | 0.941241i | \(0.609661\pi\) | |||||||
\(674\) | −9.49541e15 | −2.62957 | ||||||||
\(675\) | 1.27266e15 | 0.349575 | ||||||||
\(676\) | 1.07007e16 | 2.91545 | ||||||||
\(677\) | −4.11801e15 | −1.11288 | −0.556442 | − | 0.830887i | \(-0.687834\pi\) | ||||
−0.556442 | + | 0.830887i | \(0.687834\pi\) | |||||||
\(678\) | −5.78477e14 | −0.155068 | ||||||||
\(679\) | −2.57343e15 | −0.684271 | ||||||||
\(680\) | −2.64485e16 | −6.97592 | ||||||||
\(681\) | −3.25238e14 | −0.0850928 | ||||||||
\(682\) | −2.47766e15 | −0.643025 | ||||||||
\(683\) | −1.64718e15 | −0.424059 | −0.212029 | − | 0.977263i | \(-0.568007\pi\) | ||||
−0.212029 | + | 0.977263i | \(0.568007\pi\) | |||||||
\(684\) | 6.54431e15 | 1.67130 | ||||||||
\(685\) | −5.71239e15 | −1.44717 | ||||||||
\(686\) | 7.07835e15 | 1.77889 | ||||||||
\(687\) | −2.80932e15 | −0.700389 | ||||||||
\(688\) | −2.39593e15 | −0.592566 | ||||||||
\(689\) | −7.87190e14 | −0.193141 | ||||||||
\(690\) | 1.02227e15 | 0.248825 | ||||||||
\(691\) | −8.24714e14 | −0.199147 | −0.0995736 | − | 0.995030i | \(-0.531748\pi\) | ||||
−0.0995736 | + | 0.995030i | \(0.531748\pi\) | |||||||
\(692\) | 9.64841e15 | 2.31139 | ||||||||
\(693\) | −3.23039e14 | −0.0767754 | ||||||||
\(694\) | −5.33372e15 | −1.25763 | ||||||||
\(695\) | −5.11695e15 | −1.19700 | ||||||||
\(696\) | −9.29734e15 | −2.15778 | ||||||||
\(697\) | −5.63071e15 | −1.29653 | ||||||||
\(698\) | 1.39767e16 | 3.19300 | ||||||||
\(699\) | −1.45522e15 | −0.329841 | ||||||||
\(700\) | 1.17686e16 | 2.64658 | ||||||||
\(701\) | 6.73359e14 | 0.150244 | 0.0751221 | − | 0.997174i | \(-0.476065\pi\) | ||||
0.0751221 | + | 0.997174i | \(0.476065\pi\) | |||||||
\(702\) | 2.40897e15 | 0.533308 | ||||||||
\(703\) | 3.20921e15 | 0.704926 | ||||||||
\(704\) | −6.08314e15 | −1.32580 | ||||||||
\(705\) | 3.92675e15 | 0.849166 | ||||||||
\(706\) | 4.49979e15 | 0.965532 | ||||||||
\(707\) | 2.90863e15 | 0.619273 | ||||||||
\(708\) | −9.51100e14 | −0.200929 | ||||||||
\(709\) | −2.01792e15 | −0.423008 | −0.211504 | − | 0.977377i | \(-0.567836\pi\) | ||||
−0.211504 | + | 0.977377i | \(0.567836\pi\) | |||||||
\(710\) | 2.12681e16 | 4.42392 | ||||||||
\(711\) | 1.79571e15 | 0.370641 | ||||||||
\(712\) | −1.79926e16 | −3.68513 | ||||||||
\(713\) | −5.23443e14 | −0.106384 | ||||||||
\(714\) | 3.87630e15 | 0.781767 | ||||||||
\(715\) | −5.12370e15 | −1.02542 | ||||||||
\(716\) | 2.19449e16 | 4.35826 | ||||||||
\(717\) | 4.16328e15 | 0.820502 | ||||||||
\(718\) | 2.11798e15 | 0.414226 | ||||||||
\(719\) | 3.13698e15 | 0.608839 | 0.304419 | − | 0.952538i | \(-0.401538\pi\) | ||||
0.304419 | + | 0.952538i | \(0.401538\pi\) | |||||||
\(720\) | −1.00863e16 | −1.94269 | ||||||||
\(721\) | 2.06020e15 | 0.393791 | ||||||||
\(722\) | −2.54407e16 | −4.82586 | ||||||||
\(723\) | 3.13854e15 | 0.590836 | ||||||||
\(724\) | 4.95824e15 | 0.926329 | ||||||||
\(725\) | 1.14178e16 | 2.11702 | ||||||||
\(726\) | 4.93946e15 | 0.908926 | ||||||||
\(727\) | 9.93240e15 | 1.81391 | 0.906953 | − | 0.421231i | \(-0.138402\pi\) | ||||
0.906953 | + | 0.421231i | \(0.138402\pi\) | |||||||
\(728\) | 1.39431e16 | 2.52718 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 1.34572e16 | 2.40258 | ||||||||
\(731\) | 1.24823e15 | 0.221181 | ||||||||
\(732\) | 1.66570e15 | 0.292944 | ||||||||
\(733\) | −5.38590e15 | −0.940127 | −0.470064 | − | 0.882633i | \(-0.655769\pi\) | ||||
−0.470064 | + | 0.882633i | \(0.655769\pi\) | |||||||
\(734\) | −1.13593e16 | −1.96799 | ||||||||
\(735\) | 3.96078e15 | 0.681083 | ||||||||
\(736\) | −2.70769e15 | −0.462137 | ||||||||
\(737\) | 8.80115e14 | 0.149097 | ||||||||
\(738\) | −3.80023e15 | −0.638998 | ||||||||
\(739\) | 8.41325e15 | 1.40417 | 0.702085 | − | 0.712094i | \(-0.252253\pi\) | ||||
0.702085 | + | 0.712094i | \(0.252253\pi\) | |||||||
\(740\) | −1.01777e16 | −1.68608 | ||||||||
\(741\) | −9.52192e15 | −1.56576 | ||||||||
\(742\) | −8.54891e14 | −0.139537 | ||||||||
\(743\) | −9.16171e15 | −1.48436 | −0.742178 | − | 0.670203i | \(-0.766207\pi\) | ||||
−0.742178 | + | 0.670203i | \(0.766207\pi\) | |||||||
\(744\) | 9.14012e15 | 1.46994 | ||||||||
\(745\) | −1.83345e15 | −0.292691 | ||||||||
\(746\) | −1.93476e16 | −3.06595 | ||||||||
\(747\) | −3.60708e15 | −0.567405 | ||||||||
\(748\) | 9.37743e15 | 1.46428 | ||||||||
\(749\) | 3.55573e15 | 0.551162 | ||||||||
\(750\) | 9.85319e15 | 1.51614 | ||||||||
\(751\) | 5.67309e15 | 0.866563 | 0.433281 | − | 0.901259i | \(-0.357356\pi\) | ||||
0.433281 | + | 0.901259i | \(0.357356\pi\) | |||||||
\(752\) | −2.00712e16 | −3.04352 | ||||||||
\(753\) | −6.34024e15 | −0.954406 | ||||||||
\(754\) | 2.16124e16 | 3.22969 | ||||||||
\(755\) | 1.08151e16 | 1.60444 | ||||||||
\(756\) | 1.90392e15 | 0.280401 | ||||||||
\(757\) | 5.88431e13 | 0.00860337 | 0.00430168 | − | 0.999991i | \(-0.498631\pi\) | ||||
0.00430168 | + | 0.999991i | \(0.498631\pi\) | |||||||
\(758\) | −7.92226e15 | −1.14992 | ||||||||
\(759\) | −2.26863e14 | −0.0326914 | ||||||||
\(760\) | 7.05569e16 | 10.0940 | ||||||||
\(761\) | −1.03107e16 | −1.46444 | −0.732222 | − | 0.681066i | \(-0.761517\pi\) | ||||
−0.732222 | + | 0.681066i | \(0.761517\pi\) | |||||||
\(762\) | −7.16770e15 | −1.01071 | ||||||||
\(763\) | 4.96567e15 | 0.695173 | ||||||||
\(764\) | −3.59006e16 | −4.98986 | ||||||||
\(765\) | 5.25474e15 | 0.725126 | ||||||||
\(766\) | 1.56066e16 | 2.13821 | ||||||||
\(767\) | 1.38384e15 | 0.188240 | ||||||||
\(768\) | 7.59513e15 | 1.02577 | ||||||||
\(769\) | 2.13146e15 | 0.285813 | 0.142906 | − | 0.989736i | \(-0.454355\pi\) | ||||
0.142906 | + | 0.989736i | \(0.454355\pi\) | |||||||
\(770\) | −5.56436e15 | −0.740825 | ||||||||
\(771\) | 5.54670e15 | 0.733222 | ||||||||
\(772\) | −3.66407e16 | −4.80916 | ||||||||
\(773\) | −1.93099e15 | −0.251648 | −0.125824 | − | 0.992053i | \(-0.540157\pi\) | ||||
−0.125824 | + | 0.992053i | \(0.540157\pi\) | |||||||
\(774\) | 8.42440e14 | 0.109009 | ||||||||
\(775\) | −1.12248e16 | −1.44217 | ||||||||
\(776\) | 3.15575e16 | 4.02590 | ||||||||
\(777\) | 9.33649e14 | 0.118268 | ||||||||
\(778\) | 2.16262e16 | 2.72014 | ||||||||
\(779\) | 1.50211e16 | 1.87606 | ||||||||
\(780\) | 3.01980e16 | 3.74505 | ||||||||
\(781\) | −4.71983e15 | −0.581227 | ||||||||
\(782\) | 2.72223e15 | 0.332880 | ||||||||
\(783\) | 1.84718e15 | 0.224295 | ||||||||
\(784\) | −2.02452e16 | −2.44109 | ||||||||
\(785\) | 1.53357e16 | 1.83621 | ||||||||
\(786\) | 1.80019e16 | 2.14039 | ||||||||
\(787\) | −3.71511e15 | −0.438642 | −0.219321 | − | 0.975653i | \(-0.570384\pi\) | ||||
−0.219321 | + | 0.975653i | \(0.570384\pi\) | |||||||
\(788\) | −1.73454e16 | −2.03372 | ||||||||
\(789\) | −5.73759e15 | −0.668046 | ||||||||
\(790\) | 3.09312e16 | 3.57641 | ||||||||
\(791\) | 6.65219e14 | 0.0763825 | ||||||||
\(792\) | 3.96137e15 | 0.451707 | ||||||||
\(793\) | −2.42357e15 | −0.274444 | ||||||||
\(794\) | −2.14472e16 | −2.41190 | ||||||||
\(795\) | −1.15890e15 | −0.129427 | ||||||||
\(796\) | 2.72792e16 | 3.02559 | ||||||||
\(797\) | 7.65519e15 | 0.843209 | 0.421604 | − | 0.906780i | \(-0.361467\pi\) | ||||
0.421604 | + | 0.906780i | \(0.361467\pi\) | |||||||
\(798\) | −1.03408e16 | −1.13120 | ||||||||
\(799\) | 1.04567e16 | 1.13602 | ||||||||
\(800\) | −5.80639e16 | −6.26486 | ||||||||
\(801\) | 3.57474e15 | 0.383059 | ||||||||
\(802\) | −3.03414e15 | −0.322906 | ||||||||
\(803\) | −2.98643e15 | −0.315658 | ||||||||
\(804\) | −5.18722e15 | −0.544535 | ||||||||
\(805\) | −1.17555e15 | −0.122565 | ||||||||
\(806\) | −2.12470e16 | −2.20016 | ||||||||
\(807\) | −7.60807e15 | −0.782474 | ||||||||
\(808\) | −3.56680e16 | −3.64348 | ||||||||
\(809\) | 1.66989e16 | 1.69422 | 0.847111 | − | 0.531416i | \(-0.178340\pi\) | ||||
0.847111 | + | 0.531416i | \(0.178340\pi\) | |||||||
\(810\) | 3.54648e15 | 0.357380 | ||||||||
\(811\) | 7.06461e15 | 0.707088 | 0.353544 | − | 0.935418i | \(-0.384976\pi\) | ||||
0.353544 | + | 0.935418i | \(0.384976\pi\) | |||||||
\(812\) | 1.70813e16 | 1.69810 | ||||||||
\(813\) | −1.02021e16 | −1.00738 | ||||||||
\(814\) | 3.10358e15 | 0.304389 | ||||||||
\(815\) | 1.59848e16 | 1.55718 | ||||||||
\(816\) | −2.68592e16 | −2.59895 | ||||||||
\(817\) | −3.32990e15 | −0.320045 | ||||||||
\(818\) | 2.10568e16 | 2.01024 | ||||||||
\(819\) | −2.77020e15 | −0.262693 | ||||||||
\(820\) | −4.76383e16 | −4.48724 | ||||||||
\(821\) | 6.78885e15 | 0.635197 | 0.317599 | − | 0.948225i | \(-0.397124\pi\) | ||||
0.317599 | + | 0.948225i | \(0.397124\pi\) | |||||||
\(822\) | −1.02666e16 | −0.954179 | ||||||||
\(823\) | −1.37578e15 | −0.127014 | −0.0635068 | − | 0.997981i | \(-0.520228\pi\) | ||||
−0.0635068 | + | 0.997981i | \(0.520228\pi\) | |||||||
\(824\) | −2.52639e16 | −2.31686 | ||||||||
\(825\) | −4.86486e15 | −0.443173 | ||||||||
\(826\) | 1.50286e15 | 0.135996 | ||||||||
\(827\) | 1.88493e16 | 1.69439 | 0.847196 | − | 0.531280i | \(-0.178289\pi\) | ||||
0.847196 | + | 0.531280i | \(0.178289\pi\) | |||||||
\(828\) | 1.33708e15 | 0.119396 | ||||||||
\(829\) | 7.56471e15 | 0.671031 | 0.335515 | − | 0.942035i | \(-0.391090\pi\) | ||||
0.335515 | + | 0.942035i | \(0.391090\pi\) | |||||||
\(830\) | −6.21321e16 | −5.47503 | ||||||||
\(831\) | −8.48961e15 | −0.743159 | ||||||||
\(832\) | −5.21655e16 | −4.53634 | ||||||||
\(833\) | 1.05473e16 | 0.911158 | ||||||||
\(834\) | −9.19640e15 | −0.789232 | ||||||||
\(835\) | −2.16529e16 | −1.84603 | ||||||||
\(836\) | −2.50163e16 | −2.11879 | ||||||||
\(837\) | −1.81595e15 | −0.152796 | ||||||||
\(838\) | −1.43544e16 | −1.19990 | ||||||||
\(839\) | 1.36055e16 | 1.12986 | 0.564928 | − | 0.825140i | \(-0.308904\pi\) | ||||
0.564928 | + | 0.825140i | \(0.308904\pi\) | |||||||
\(840\) | 2.05270e16 | 1.69351 | ||||||||
\(841\) | 4.37174e15 | 0.358324 | ||||||||
\(842\) | 4.62458e16 | 3.76579 | ||||||||
\(843\) | −1.29224e16 | −1.04542 | ||||||||
\(844\) | 2.49577e16 | 2.00595 | ||||||||
\(845\) | −2.29212e16 | −1.83032 | ||||||||
\(846\) | 7.05732e15 | 0.559890 | ||||||||
\(847\) | −5.68013e15 | −0.447713 | ||||||||
\(848\) | 5.92361e15 | 0.463884 | ||||||||
\(849\) | −2.45816e15 | −0.191257 | ||||||||
\(850\) | 5.83758e16 | 4.51262 | ||||||||
\(851\) | 6.55679e14 | 0.0503592 | ||||||||
\(852\) | 2.78177e16 | 2.12277 | ||||||||
\(853\) | −7.49852e15 | −0.568533 | −0.284267 | − | 0.958745i | \(-0.591750\pi\) | ||||
−0.284267 | + | 0.958745i | \(0.591750\pi\) | |||||||
\(854\) | −2.63201e15 | −0.198276 | ||||||||
\(855\) | −1.40181e16 | −1.04924 | ||||||||
\(856\) | −4.36033e16 | −3.24275 | ||||||||
\(857\) | 1.40143e16 | 1.03557 | 0.517783 | − | 0.855512i | \(-0.326757\pi\) | ||||
0.517783 | + | 0.855512i | \(0.326757\pi\) | |||||||
\(858\) | −9.20854e15 | −0.676099 | ||||||||
\(859\) | −1.43539e16 | −1.04715 | −0.523575 | − | 0.851980i | \(-0.675402\pi\) | ||||
−0.523575 | + | 0.851980i | \(0.675402\pi\) | |||||||
\(860\) | 1.05605e16 | 0.765498 | ||||||||
\(861\) | 4.37007e15 | 0.314754 | ||||||||
\(862\) | −2.48651e16 | −1.77951 | ||||||||
\(863\) | −2.01996e16 | −1.43643 | −0.718213 | − | 0.695823i | \(-0.755040\pi\) | ||||
−0.718213 | + | 0.695823i | \(0.755040\pi\) | |||||||
\(864\) | −9.39360e15 | −0.663753 | ||||||||
\(865\) | −2.06672e16 | −1.45109 | ||||||||
\(866\) | −3.30037e16 | −2.30257 | ||||||||
\(867\) | 5.66499e15 | 0.392730 | ||||||||
\(868\) | −1.67925e16 | −1.15680 | ||||||||
\(869\) | −6.86428e15 | −0.469879 | ||||||||
\(870\) | 3.18177e16 | 2.16428 | ||||||||
\(871\) | 7.54736e15 | 0.510147 | ||||||||
\(872\) | −6.08931e16 | −4.09004 | ||||||||
\(873\) | −6.26980e15 | −0.418480 | ||||||||
\(874\) | −7.26213e15 | −0.481672 | ||||||||
\(875\) | −1.13307e16 | −0.746811 | ||||||||
\(876\) | 1.76014e16 | 1.15286 | ||||||||
\(877\) | −1.06436e16 | −0.692774 | −0.346387 | − | 0.938092i | \(-0.612592\pi\) | ||||
−0.346387 | + | 0.938092i | \(0.612592\pi\) | |||||||
\(878\) | 4.21094e16 | 2.72370 | ||||||||
\(879\) | −3.66477e15 | −0.235564 | ||||||||
\(880\) | 3.85559e16 | 2.46284 | ||||||||
\(881\) | −6.05995e15 | −0.384682 | −0.192341 | − | 0.981328i | \(-0.561608\pi\) | ||||
−0.192341 | + | 0.981328i | \(0.561608\pi\) | |||||||
\(882\) | 7.11848e15 | 0.449066 | ||||||||
\(883\) | 3.73590e15 | 0.234213 | 0.117107 | − | 0.993119i | \(-0.462638\pi\) | ||||
0.117107 | + | 0.993119i | \(0.462638\pi\) | |||||||
\(884\) | 8.04154e16 | 5.01016 | ||||||||
\(885\) | 2.03729e15 | 0.126143 | ||||||||
\(886\) | −5.30343e16 | −3.26341 | ||||||||
\(887\) | 1.30168e16 | 0.796023 | 0.398011 | − | 0.917380i | \(-0.369700\pi\) | ||||
0.398011 | + | 0.917380i | \(0.369700\pi\) | |||||||
\(888\) | −1.14492e16 | −0.695829 | ||||||||
\(889\) | 8.24248e15 | 0.497850 | ||||||||
\(890\) | 6.15749e16 | 3.69623 | ||||||||
\(891\) | −7.87039e14 | −0.0469536 | ||||||||
\(892\) | −4.92638e16 | −2.92093 | ||||||||
\(893\) | −2.78954e16 | −1.64380 | ||||||||
\(894\) | −3.29515e15 | −0.192983 | ||||||||
\(895\) | −4.70068e16 | −2.73611 | ||||||||
\(896\) | −2.41571e16 | −1.39750 | ||||||||
\(897\) | −1.94544e15 | −0.111856 | ||||||||
\(898\) | 2.60766e16 | 1.49015 | ||||||||
\(899\) | −1.62920e16 | −0.925330 | ||||||||
\(900\) | 2.86725e16 | 1.61857 | ||||||||
\(901\) | −3.08607e15 | −0.173149 | ||||||||
\(902\) | 1.45267e16 | 0.810088 | ||||||||
\(903\) | −9.68763e14 | −0.0536951 | ||||||||
\(904\) | −8.15746e15 | −0.449395 | ||||||||
\(905\) | −1.06207e16 | −0.581549 | ||||||||
\(906\) | 1.94374e16 | 1.05787 | ||||||||
\(907\) | 3.18539e16 | 1.72315 | 0.861575 | − | 0.507631i | \(-0.169479\pi\) | ||||
0.861575 | + | 0.507631i | \(0.169479\pi\) | |||||||
\(908\) | −7.32749e15 | −0.393988 | ||||||||
\(909\) | 7.08647e15 | 0.378729 | ||||||||
\(910\) | −4.77167e16 | −2.53479 | ||||||||
\(911\) | 4.37440e15 | 0.230976 | 0.115488 | − | 0.993309i | \(-0.463157\pi\) | ||||
0.115488 | + | 0.993309i | \(0.463157\pi\) | |||||||
\(912\) | 7.16526e16 | 3.76063 | ||||||||
\(913\) | 1.37884e16 | 0.719325 | ||||||||
\(914\) | −7.09542e14 | −0.0367938 | ||||||||
\(915\) | −3.56797e15 | −0.183910 | ||||||||
\(916\) | −6.32929e16 | −3.24287 | ||||||||
\(917\) | −2.07012e16 | −1.05430 | ||||||||
\(918\) | 9.44406e15 | 0.478106 | ||||||||
\(919\) | 1.89945e16 | 0.955858 | 0.477929 | − | 0.878399i | \(-0.341388\pi\) | ||||
0.477929 | + | 0.878399i | \(0.341388\pi\) | |||||||
\(920\) | 1.44156e16 | 0.721107 | ||||||||
\(921\) | 3.20759e15 | 0.159496 | ||||||||
\(922\) | 3.40559e16 | 1.68334 | ||||||||
\(923\) | −4.04746e16 | −1.98872 | ||||||||
\(924\) | −7.27794e15 | −0.355478 | ||||||||
\(925\) | 1.40604e16 | 0.682683 | ||||||||
\(926\) | 3.85776e15 | 0.186198 | ||||||||
\(927\) | 5.01939e15 | 0.240831 | ||||||||
\(928\) | −8.42760e16 | −4.01967 | ||||||||
\(929\) | 3.75792e16 | 1.78181 | 0.890904 | − | 0.454191i | \(-0.150072\pi\) | ||||
0.890904 | + | 0.454191i | \(0.150072\pi\) | |||||||
\(930\) | −3.12797e16 | −1.47437 | ||||||||
\(931\) | −2.81372e16 | −1.31843 | ||||||||
\(932\) | −3.27855e16 | −1.52719 | ||||||||
\(933\) | −1.30724e16 | −0.605349 | ||||||||
\(934\) | 1.61137e16 | 0.741799 | ||||||||
\(935\) | −2.00868e16 | −0.919277 | ||||||||
\(936\) | 3.39704e16 | 1.54555 | ||||||||
\(937\) | 1.34406e16 | 0.607928 | 0.303964 | − | 0.952684i | \(-0.401690\pi\) | ||||
0.303964 | + | 0.952684i | \(0.401690\pi\) | |||||||
\(938\) | 8.19646e15 | 0.368562 | ||||||||
\(939\) | 5.79353e15 | 0.258989 | ||||||||
\(940\) | 8.84680e16 | 3.93172 | ||||||||
\(941\) | −8.15918e15 | −0.360499 | −0.180249 | − | 0.983621i | \(-0.557690\pi\) | ||||
−0.180249 | + | 0.983621i | \(0.557690\pi\) | |||||||
\(942\) | 2.75620e16 | 1.21069 | ||||||||
\(943\) | 3.06899e15 | 0.134024 | ||||||||
\(944\) | −1.04134e16 | −0.452114 | ||||||||
\(945\) | −4.07827e15 | −0.176036 | ||||||||
\(946\) | −3.22031e15 | −0.138196 | ||||||||
\(947\) | −2.94524e15 | −0.125660 | −0.0628298 | − | 0.998024i | \(-0.520013\pi\) | ||||
−0.0628298 | + | 0.998024i | \(0.520013\pi\) | |||||||
\(948\) | 4.04566e16 | 1.71610 | ||||||||
\(949\) | −2.56099e16 | −1.08005 | ||||||||
\(950\) | −1.55730e17 | −6.52967 | ||||||||
\(951\) | 1.32857e16 | 0.553849 | ||||||||
\(952\) | 5.46621e16 | 2.26560 | ||||||||
\(953\) | −4.33689e16 | −1.78718 | −0.893588 | − | 0.448889i | \(-0.851820\pi\) | ||||
−0.893588 | + | 0.448889i | \(0.851820\pi\) | |||||||
\(954\) | −2.08282e15 | −0.0853367 | ||||||||
\(955\) | 7.69003e16 | 3.13263 | ||||||||
\(956\) | 9.37969e16 | 3.79901 | ||||||||
\(957\) | −7.06103e15 | −0.284349 | ||||||||
\(958\) | 3.69026e16 | 1.47757 | ||||||||
\(959\) | 1.18060e16 | 0.470004 | ||||||||
\(960\) | −7.67979e16 | −3.03989 | ||||||||
\(961\) | −9.39196e15 | −0.369639 | ||||||||
\(962\) | 2.66145e16 | 1.04149 | ||||||||
\(963\) | 8.66305e15 | 0.337075 | ||||||||
\(964\) | 7.07100e16 | 2.73563 | ||||||||
\(965\) | 7.84857e16 | 3.01919 | ||||||||
\(966\) | −2.11276e15 | −0.0808119 | ||||||||
\(967\) | −3.73342e16 | −1.41991 | −0.709957 | − | 0.704246i | \(-0.751285\pi\) | ||||
−0.709957 | + | 0.704246i | \(0.751285\pi\) | |||||||
\(968\) | 6.96544e16 | 2.63411 | ||||||||
\(969\) | −3.73294e16 | −1.40369 | ||||||||
\(970\) | −1.07997e17 | −4.03802 | ||||||||
\(971\) | −2.32292e15 | −0.0863632 | −0.0431816 | − | 0.999067i | \(-0.513749\pi\) | ||||
−0.0431816 | + | 0.999067i | \(0.513749\pi\) | |||||||
\(972\) | 4.63864e15 | 0.171485 | ||||||||
\(973\) | 1.05754e16 | 0.388755 | ||||||||
\(974\) | 3.77187e14 | 0.0137874 | ||||||||
\(975\) | −4.17182e16 | −1.51635 | ||||||||
\(976\) | 1.82374e16 | 0.659157 | ||||||||
\(977\) | −3.64377e16 | −1.30958 | −0.654789 | − | 0.755812i | \(-0.727242\pi\) | ||||
−0.654789 | + | 0.755812i | \(0.727242\pi\) | |||||||
\(978\) | 2.87285e16 | 1.02671 | ||||||||
\(979\) | −1.36648e16 | −0.485621 | ||||||||
\(980\) | 8.92347e16 | 3.15348 | ||||||||
\(981\) | 1.20982e16 | 0.425147 | ||||||||
\(982\) | 1.30041e16 | 0.454429 | ||||||||
\(983\) | 1.95246e16 | 0.678480 | 0.339240 | − | 0.940700i | \(-0.389830\pi\) | ||||
0.339240 | + | 0.940700i | \(0.389830\pi\) | |||||||
\(984\) | −5.35893e16 | −1.85185 | ||||||||
\(985\) | 3.71544e16 | 1.27677 | ||||||||
\(986\) | 8.47287e16 | 2.89539 | ||||||||
\(987\) | −8.11556e15 | −0.275787 | ||||||||
\(988\) | −2.14525e17 | −7.24961 | ||||||||
\(989\) | −6.80339e14 | −0.0228637 | ||||||||
\(990\) | −1.35568e16 | −0.453067 | ||||||||
\(991\) | −5.04520e16 | −1.67677 | −0.838384 | − | 0.545080i | \(-0.816499\pi\) | ||||
−0.838384 | + | 0.545080i | \(0.816499\pi\) | |||||||
\(992\) | 8.28509e16 | 2.73831 | ||||||||
\(993\) | −9.72996e15 | −0.319809 | ||||||||
\(994\) | −4.39555e16 | −1.43677 | ||||||||
\(995\) | −5.84329e16 | −1.89946 | ||||||||
\(996\) | −8.12661e16 | −2.62714 | ||||||||
\(997\) | −4.06996e16 | −1.30848 | −0.654239 | − | 0.756288i | \(-0.727011\pi\) | ||||
−0.654239 | + | 0.756288i | \(0.727011\pi\) | |||||||
\(998\) | −5.74804e16 | −1.83782 | ||||||||
\(999\) | 2.27470e15 | 0.0723293 |
(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 | 177.12.a.b.1.2 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.b.1.2 | ✓ | 27 | 1.1 | even | 1 | trivial |