Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,10,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.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: | \(101.462059724\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −39.0491 | −1.72574 | −0.862871 | − | 0.505424i | \(-0.831336\pi\) | ||||
−0.862871 | + | 0.505424i | \(0.831336\pi\) | |||||||
\(3\) | −79.6019 | −0.567385 | −0.283692 | − | 0.958915i | \(-0.591559\pi\) | ||||
−0.283692 | + | 0.958915i | \(0.591559\pi\) | |||||||
\(4\) | 1012.83 | 1.97819 | ||||||||
\(5\) | −1275.42 | −0.912618 | −0.456309 | − | 0.889822i | \(-0.650829\pi\) | ||||
−0.456309 | + | 0.889822i | \(0.650829\pi\) | |||||||
\(6\) | 3108.38 | 0.979160 | ||||||||
\(7\) | 8453.17 | 1.33069 | 0.665347 | − | 0.746534i | \(-0.268284\pi\) | ||||
0.665347 | + | 0.746534i | \(0.268284\pi\) | |||||||
\(8\) | −19557.0 | −1.68810 | ||||||||
\(9\) | −13346.5 | −0.678074 | ||||||||
\(10\) | 49804.1 | 1.57494 | ||||||||
\(11\) | −89247.0 | −1.83792 | −0.918960 | − | 0.394350i | \(-0.870970\pi\) | ||||
−0.918960 | + | 0.394350i | \(0.870970\pi\) | |||||||
\(12\) | −80623.3 | −1.12239 | ||||||||
\(13\) | −15037.6 | −0.146027 | −0.0730136 | − | 0.997331i | \(-0.523262\pi\) | ||||
−0.0730136 | + | 0.997331i | \(0.523262\pi\) | |||||||
\(14\) | −330088. | −2.29644 | ||||||||
\(15\) | 101526. | 0.517805 | ||||||||
\(16\) | 245114. | 0.935034 | ||||||||
\(17\) | −142485. | −0.413760 | −0.206880 | − | 0.978366i | \(-0.566331\pi\) | ||||
−0.206880 | + | 0.978366i | \(0.566331\pi\) | |||||||
\(18\) | 521170. | 1.17018 | ||||||||
\(19\) | 600806. | 1.05765 | 0.528826 | − | 0.848730i | \(-0.322632\pi\) | ||||
0.528826 | + | 0.848730i | \(0.322632\pi\) | |||||||
\(20\) | −1.29179e6 | −1.80533 | ||||||||
\(21\) | −672888. | −0.755016 | ||||||||
\(22\) | 3.48502e6 | 3.17178 | ||||||||
\(23\) | −2.40992e6 | −1.79567 | −0.897836 | − | 0.440331i | \(-0.854861\pi\) | ||||
−0.897836 | + | 0.440331i | \(0.854861\pi\) | |||||||
\(24\) | 1.55677e6 | 0.957801 | ||||||||
\(25\) | −326424. | −0.167129 | ||||||||
\(26\) | 587205. | 0.252005 | ||||||||
\(27\) | 2.62921e6 | 0.952114 | ||||||||
\(28\) | 8.56163e6 | 2.63236 | ||||||||
\(29\) | −1.26844e6 | −0.333028 | −0.166514 | − | 0.986039i | \(-0.553251\pi\) | ||||
−0.166514 | + | 0.986039i | \(0.553251\pi\) | |||||||
\(30\) | −3.96450e6 | −0.893599 | ||||||||
\(31\) | 3.18354e6 | 0.619132 | 0.309566 | − | 0.950878i | \(-0.399816\pi\) | ||||
0.309566 | + | 0.950878i | \(0.399816\pi\) | |||||||
\(32\) | 441726. | 0.0744695 | ||||||||
\(33\) | 7.10423e6 | 1.04281 | ||||||||
\(34\) | 5.56390e6 | 0.714042 | ||||||||
\(35\) | −1.07814e7 | −1.21441 | ||||||||
\(36\) | −1.35178e7 | −1.34136 | ||||||||
\(37\) | 1.60137e6 | 0.140470 | 0.0702352 | − | 0.997530i | \(-0.477625\pi\) | ||||
0.0702352 | + | 0.997530i | \(0.477625\pi\) | |||||||
\(38\) | −2.34609e7 | −1.82523 | ||||||||
\(39\) | 1.19702e6 | 0.0828536 | ||||||||
\(40\) | 2.49434e7 | 1.54059 | ||||||||
\(41\) | −1.15907e7 | −0.640593 | −0.320297 | − | 0.947317i | \(-0.603783\pi\) | ||||
−0.320297 | + | 0.947317i | \(0.603783\pi\) | |||||||
\(42\) | 2.62757e7 | 1.30296 | ||||||||
\(43\) | −1.10757e7 | −0.494040 | −0.247020 | − | 0.969010i | \(-0.579451\pi\) | ||||
−0.247020 | + | 0.969010i | \(0.579451\pi\) | |||||||
\(44\) | −9.03922e7 | −3.63575 | ||||||||
\(45\) | 1.70225e7 | 0.618822 | ||||||||
\(46\) | 9.41051e7 | 3.09887 | ||||||||
\(47\) | −1.71311e7 | −0.512088 | −0.256044 | − | 0.966665i | \(-0.582419\pi\) | ||||
−0.256044 | + | 0.966665i | \(0.582419\pi\) | |||||||
\(48\) | −1.95115e7 | −0.530524 | ||||||||
\(49\) | 3.11024e7 | 0.770747 | ||||||||
\(50\) | 1.27466e7 | 0.288422 | ||||||||
\(51\) | 1.13421e7 | 0.234761 | ||||||||
\(52\) | −1.52306e7 | −0.288869 | ||||||||
\(53\) | −4.36131e7 | −0.759234 | −0.379617 | − | 0.925144i | \(-0.623944\pi\) | ||||
−0.379617 | + | 0.925144i | \(0.623944\pi\) | |||||||
\(54\) | −1.02668e8 | −1.64310 | ||||||||
\(55\) | 1.13828e8 | 1.67732 | ||||||||
\(56\) | −1.65319e8 | −2.24634 | ||||||||
\(57\) | −4.78253e7 | −0.600096 | ||||||||
\(58\) | 4.95316e7 | 0.574720 | ||||||||
\(59\) | 9.68517e7 | 1.04057 | 0.520287 | − | 0.853991i | \(-0.325825\pi\) | ||||
0.520287 | + | 0.853991i | \(0.325825\pi\) | |||||||
\(60\) | 1.02829e8 | 1.02432 | ||||||||
\(61\) | −1.42632e8 | −1.31897 | −0.659483 | − | 0.751720i | \(-0.729225\pi\) | ||||
−0.659483 | + | 0.751720i | \(0.729225\pi\) | |||||||
\(62\) | −1.24314e8 | −1.06846 | ||||||||
\(63\) | −1.12821e8 | −0.902310 | ||||||||
\(64\) | −1.42747e8 | −1.06355 | ||||||||
\(65\) | 1.91793e7 | 0.133267 | ||||||||
\(66\) | −2.77414e8 | −1.79962 | ||||||||
\(67\) | −2.80649e8 | −1.70148 | −0.850741 | − | 0.525585i | \(-0.823846\pi\) | ||||
−0.850741 | + | 0.525585i | \(0.823846\pi\) | |||||||
\(68\) | −1.44313e8 | −0.818493 | ||||||||
\(69\) | 1.91834e8 | 1.01884 | ||||||||
\(70\) | 4.21002e8 | 2.09577 | ||||||||
\(71\) | −3.55491e8 | −1.66022 | −0.830111 | − | 0.557598i | \(-0.811723\pi\) | ||||
−0.830111 | + | 0.557598i | \(0.811723\pi\) | |||||||
\(72\) | 2.61018e8 | 1.14466 | ||||||||
\(73\) | −2.25622e8 | −0.929883 | −0.464941 | − | 0.885341i | \(-0.653925\pi\) | ||||
−0.464941 | + | 0.885341i | \(0.653925\pi\) | |||||||
\(74\) | −6.25321e7 | −0.242416 | ||||||||
\(75\) | 2.59840e7 | 0.0948266 | ||||||||
\(76\) | 6.08515e8 | 2.09223 | ||||||||
\(77\) | −7.54420e8 | −2.44571 | ||||||||
\(78\) | −4.67426e7 | −0.142984 | ||||||||
\(79\) | −1.66304e8 | −0.480376 | −0.240188 | − | 0.970726i | \(-0.577209\pi\) | ||||
−0.240188 | + | 0.970726i | \(0.577209\pi\) | |||||||
\(80\) | −3.12623e8 | −0.853328 | ||||||||
\(81\) | 5.34094e7 | 0.137859 | ||||||||
\(82\) | 4.52606e8 | 1.10550 | ||||||||
\(83\) | −3.45602e8 | −0.799328 | −0.399664 | − | 0.916662i | \(-0.630873\pi\) | ||||
−0.399664 | + | 0.916662i | \(0.630873\pi\) | |||||||
\(84\) | −6.81522e8 | −1.49356 | ||||||||
\(85\) | 1.81728e8 | 0.377604 | ||||||||
\(86\) | 4.32495e8 | 0.852585 | ||||||||
\(87\) | 1.00971e8 | 0.188955 | ||||||||
\(88\) | 1.74540e9 | 3.10259 | ||||||||
\(89\) | 3.49116e8 | 0.589814 | 0.294907 | − | 0.955526i | \(-0.404711\pi\) | ||||
0.294907 | + | 0.955526i | \(0.404711\pi\) | |||||||
\(90\) | −6.64712e8 | −1.06793 | ||||||||
\(91\) | −1.27115e8 | −0.194318 | ||||||||
\(92\) | −2.44084e9 | −3.55217 | ||||||||
\(93\) | −2.53416e8 | −0.351286 | ||||||||
\(94\) | 6.68953e8 | 0.883731 | ||||||||
\(95\) | −7.66281e8 | −0.965232 | ||||||||
\(96\) | −3.51623e7 | −0.0422529 | ||||||||
\(97\) | −1.34695e9 | −1.54482 | −0.772412 | − | 0.635122i | \(-0.780950\pi\) | ||||
−0.772412 | + | 0.635122i | \(0.780950\pi\) | |||||||
\(98\) | −1.21452e9 | −1.33011 | ||||||||
\(99\) | 1.19114e9 | 1.24625 | ||||||||
\(100\) | −3.30613e8 | −0.330613 | ||||||||
\(101\) | −5.32171e8 | −0.508868 | −0.254434 | − | 0.967090i | \(-0.581889\pi\) | ||||
−0.254434 | + | 0.967090i | \(0.581889\pi\) | |||||||
\(102\) | −4.42897e8 | −0.405137 | ||||||||
\(103\) | 4.01519e8 | 0.351511 | 0.175756 | − | 0.984434i | \(-0.443763\pi\) | ||||
0.175756 | + | 0.984434i | \(0.443763\pi\) | |||||||
\(104\) | 2.94091e8 | 0.246508 | ||||||||
\(105\) | 8.58216e8 | 0.689041 | ||||||||
\(106\) | 1.70305e9 | 1.31024 | ||||||||
\(107\) | −4.67531e8 | −0.344813 | −0.172407 | − | 0.985026i | \(-0.555154\pi\) | ||||
−0.172407 | + | 0.985026i | \(0.555154\pi\) | |||||||
\(108\) | 2.66295e9 | 1.88346 | ||||||||
\(109\) | −1.54398e9 | −1.04766 | −0.523831 | − | 0.851822i | \(-0.675498\pi\) | ||||
−0.523831 | + | 0.851822i | \(0.675498\pi\) | |||||||
\(110\) | −4.44486e9 | −2.89462 | ||||||||
\(111\) | −1.27472e8 | −0.0797007 | ||||||||
\(112\) | 2.07199e9 | 1.24424 | ||||||||
\(113\) | 2.09523e9 | 1.20887 | 0.604433 | − | 0.796656i | \(-0.293400\pi\) | ||||
0.604433 | + | 0.796656i | \(0.293400\pi\) | |||||||
\(114\) | 1.86753e9 | 1.03561 | ||||||||
\(115\) | 3.07366e9 | 1.63876 | ||||||||
\(116\) | −1.28472e9 | −0.658791 | ||||||||
\(117\) | 2.00700e8 | 0.0990173 | ||||||||
\(118\) | −3.78197e9 | −1.79576 | ||||||||
\(119\) | −1.20445e9 | −0.550588 | ||||||||
\(120\) | −1.98554e9 | −0.874106 | ||||||||
\(121\) | 5.60708e9 | 2.37795 | ||||||||
\(122\) | 5.56966e9 | 2.27619 | ||||||||
\(123\) | 9.22642e8 | 0.363463 | ||||||||
\(124\) | 3.22439e9 | 1.22476 | ||||||||
\(125\) | 2.90739e9 | 1.06514 | ||||||||
\(126\) | 4.40554e9 | 1.55715 | ||||||||
\(127\) | −2.22074e9 | −0.757499 | −0.378749 | − | 0.925499i | \(-0.623646\pi\) | ||||
−0.378749 | + | 0.925499i | \(0.623646\pi\) | |||||||
\(128\) | 5.34798e9 | 1.76094 | ||||||||
\(129\) | 8.81644e8 | 0.280311 | ||||||||
\(130\) | −7.48934e8 | −0.229984 | ||||||||
\(131\) | 1.42085e9 | 0.421530 | 0.210765 | − | 0.977537i | \(-0.432405\pi\) | ||||
0.210765 | + | 0.977537i | \(0.432405\pi\) | |||||||
\(132\) | 7.19539e9 | 2.06287 | ||||||||
\(133\) | 5.07871e9 | 1.40741 | ||||||||
\(134\) | 1.09591e10 | 2.93632 | ||||||||
\(135\) | −3.35336e9 | −0.868916 | ||||||||
\(136\) | 2.78657e9 | 0.698466 | ||||||||
\(137\) | −1.19961e9 | −0.290936 | −0.145468 | − | 0.989363i | \(-0.546469\pi\) | ||||
−0.145468 | + | 0.989363i | \(0.546469\pi\) | |||||||
\(138\) | −7.49094e9 | −1.75825 | ||||||||
\(139\) | −2.22400e9 | −0.505322 | −0.252661 | − | 0.967555i | \(-0.581306\pi\) | ||||
−0.252661 | + | 0.967555i | \(0.581306\pi\) | |||||||
\(140\) | −1.09197e10 | −2.40234 | ||||||||
\(141\) | 1.36367e9 | 0.290551 | ||||||||
\(142\) | 1.38816e10 | 2.86511 | ||||||||
\(143\) | 1.34206e9 | 0.268386 | ||||||||
\(144\) | −3.27142e9 | −0.634022 | ||||||||
\(145\) | 1.61780e9 | 0.303927 | ||||||||
\(146\) | 8.81033e9 | 1.60474 | ||||||||
\(147\) | −2.47581e9 | −0.437310 | ||||||||
\(148\) | 1.62192e9 | 0.277876 | ||||||||
\(149\) | 4.96037e9 | 0.824473 | 0.412236 | − | 0.911077i | \(-0.364748\pi\) | ||||
0.412236 | + | 0.911077i | \(0.364748\pi\) | |||||||
\(150\) | −1.01465e9 | −0.163646 | ||||||||
\(151\) | −1.90705e9 | −0.298515 | −0.149257 | − | 0.988798i | \(-0.547688\pi\) | ||||
−0.149257 | + | 0.988798i | \(0.547688\pi\) | |||||||
\(152\) | −1.17500e10 | −1.78542 | ||||||||
\(153\) | 1.90168e9 | 0.280560 | ||||||||
\(154\) | 2.94594e10 | 4.22067 | ||||||||
\(155\) | −4.06036e9 | −0.565030 | ||||||||
\(156\) | 1.21238e9 | 0.163900 | ||||||||
\(157\) | 3.66831e7 | 0.00481857 | 0.00240928 | − | 0.999997i | \(-0.499233\pi\) | ||||
0.00240928 | + | 0.999997i | \(0.499233\pi\) | |||||||
\(158\) | 6.49402e9 | 0.829004 | ||||||||
\(159\) | 3.47169e9 | 0.430778 | ||||||||
\(160\) | −5.63387e8 | −0.0679622 | ||||||||
\(161\) | −2.03714e10 | −2.38949 | ||||||||
\(162\) | −2.08559e9 | −0.237909 | ||||||||
\(163\) | −1.53611e9 | −0.170443 | −0.0852213 | − | 0.996362i | \(-0.527160\pi\) | ||||
−0.0852213 | + | 0.996362i | \(0.527160\pi\) | |||||||
\(164\) | −1.17394e10 | −1.26721 | ||||||||
\(165\) | −9.06089e9 | −0.951685 | ||||||||
\(166\) | 1.34954e10 | 1.37943 | ||||||||
\(167\) | −8.96869e9 | −0.892288 | −0.446144 | − | 0.894961i | \(-0.647203\pi\) | ||||
−0.446144 | + | 0.894961i | \(0.647203\pi\) | |||||||
\(168\) | 1.31597e10 | 1.27454 | ||||||||
\(169\) | −1.03784e10 | −0.978676 | ||||||||
\(170\) | −7.09632e9 | −0.651648 | ||||||||
\(171\) | −8.01868e9 | −0.717167 | ||||||||
\(172\) | −1.12178e10 | −0.977302 | ||||||||
\(173\) | −5.25118e9 | −0.445707 | −0.222854 | − | 0.974852i | \(-0.571537\pi\) | ||||
−0.222854 | + | 0.974852i | \(0.571537\pi\) | |||||||
\(174\) | −3.94281e9 | −0.326087 | ||||||||
\(175\) | −2.75932e9 | −0.222398 | ||||||||
\(176\) | −2.18757e10 | −1.71852 | ||||||||
\(177\) | −7.70958e9 | −0.590406 | ||||||||
\(178\) | −1.36327e10 | −1.01787 | ||||||||
\(179\) | −4.79868e9 | −0.349368 | −0.174684 | − | 0.984625i | \(-0.555890\pi\) | ||||
−0.174684 | + | 0.984625i | \(0.555890\pi\) | |||||||
\(180\) | 1.72409e10 | 1.22415 | ||||||||
\(181\) | −1.53526e10 | −1.06323 | −0.531615 | − | 0.846986i | \(-0.678415\pi\) | ||||
−0.531615 | + | 0.846986i | \(0.678415\pi\) | |||||||
\(182\) | 4.96374e9 | 0.335342 | ||||||||
\(183\) | 1.13538e10 | 0.748361 | ||||||||
\(184\) | 4.71308e10 | 3.03127 | ||||||||
\(185\) | −2.04243e9 | −0.128196 | ||||||||
\(186\) | 9.89566e9 | 0.606229 | ||||||||
\(187\) | 1.27163e10 | 0.760457 | ||||||||
\(188\) | −1.73509e10 | −1.01300 | ||||||||
\(189\) | 2.22252e10 | 1.26697 | ||||||||
\(190\) | 2.99226e10 | 1.66574 | ||||||||
\(191\) | 1.87145e10 | 1.01748 | 0.508742 | − | 0.860919i | \(-0.330111\pi\) | ||||
0.508742 | + | 0.860919i | \(0.330111\pi\) | |||||||
\(192\) | 1.13629e10 | 0.603442 | ||||||||
\(193\) | 1.45956e10 | 0.757206 | 0.378603 | − | 0.925559i | \(-0.376405\pi\) | ||||
0.378603 | + | 0.925559i | \(0.376405\pi\) | |||||||
\(194\) | 5.25972e10 | 2.66597 | ||||||||
\(195\) | −1.52671e9 | −0.0756137 | ||||||||
\(196\) | 3.15015e10 | 1.52468 | ||||||||
\(197\) | 1.50614e9 | 0.0712470 | ||||||||
\(198\) | −4.65129e10 | −2.15070 | ||||||||
\(199\) | −1.01298e10 | −0.457893 | −0.228947 | − | 0.973439i | \(-0.573528\pi\) | ||||
−0.228947 | + | 0.973439i | \(0.573528\pi\) | |||||||
\(200\) | 6.38388e9 | 0.282130 | ||||||||
\(201\) | 2.23402e10 | 0.965395 | ||||||||
\(202\) | 2.07808e10 | 0.878175 | ||||||||
\(203\) | −1.07224e10 | −0.443158 | ||||||||
\(204\) | 1.14876e10 | 0.464401 | ||||||||
\(205\) | 1.47830e10 | 0.584616 | ||||||||
\(206\) | −1.56790e10 | −0.606618 | ||||||||
\(207\) | 3.21640e10 | 1.21760 | ||||||||
\(208\) | −3.68592e9 | −0.136540 | ||||||||
\(209\) | −5.36201e10 | −1.94388 | ||||||||
\(210\) | −3.35126e10 | −1.18911 | ||||||||
\(211\) | 2.35402e10 | 0.817596 | 0.408798 | − | 0.912625i | \(-0.365948\pi\) | ||||
0.408798 | + | 0.912625i | \(0.365948\pi\) | |||||||
\(212\) | −4.41727e10 | −1.50191 | ||||||||
\(213\) | 2.82978e10 | 0.941985 | ||||||||
\(214\) | 1.82567e10 | 0.595059 | ||||||||
\(215\) | 1.41261e10 | 0.450869 | ||||||||
\(216\) | −5.14195e10 | −1.60726 | ||||||||
\(217\) | 2.69110e10 | 0.823875 | ||||||||
\(218\) | 6.02908e10 | 1.80799 | ||||||||
\(219\) | 1.79599e10 | 0.527602 | ||||||||
\(220\) | 1.15288e11 | 3.31805 | ||||||||
\(221\) | 2.14263e9 | 0.0604201 | ||||||||
\(222\) | 4.97768e9 | 0.137543 | ||||||||
\(223\) | −5.35567e10 | −1.45025 | −0.725123 | − | 0.688619i | \(-0.758217\pi\) | ||||
−0.725123 | + | 0.688619i | \(0.758217\pi\) | |||||||
\(224\) | 3.73399e9 | 0.0990961 | ||||||||
\(225\) | 4.35663e9 | 0.113326 | ||||||||
\(226\) | −8.18167e10 | −2.08619 | ||||||||
\(227\) | 1.59083e10 | 0.397655 | 0.198828 | − | 0.980034i | \(-0.436287\pi\) | ||||
0.198828 | + | 0.980034i | \(0.436287\pi\) | |||||||
\(228\) | −4.84389e10 | −1.18710 | ||||||||
\(229\) | −7.41530e10 | −1.78184 | −0.890920 | − | 0.454160i | \(-0.849939\pi\) | ||||
−0.890920 | + | 0.454160i | \(0.849939\pi\) | |||||||
\(230\) | −1.20024e11 | −2.82808 | ||||||||
\(231\) | 6.00533e10 | 1.38766 | ||||||||
\(232\) | 2.48070e10 | 0.562183 | ||||||||
\(233\) | 4.29576e10 | 0.954857 | 0.477428 | − | 0.878671i | \(-0.341569\pi\) | ||||
0.477428 | + | 0.878671i | \(0.341569\pi\) | |||||||
\(234\) | −7.83715e9 | −0.170878 | ||||||||
\(235\) | 2.18493e10 | 0.467340 | ||||||||
\(236\) | 9.80944e10 | 2.05845 | ||||||||
\(237\) | 1.32381e10 | 0.272558 | ||||||||
\(238\) | 4.70326e10 | 0.950172 | ||||||||
\(239\) | −9.42540e10 | −1.86857 | −0.934285 | − | 0.356527i | \(-0.883961\pi\) | ||||
−0.934285 | + | 0.356527i | \(0.883961\pi\) | |||||||
\(240\) | 2.48854e10 | 0.484166 | ||||||||
\(241\) | 2.19180e10 | 0.418528 | 0.209264 | − | 0.977859i | \(-0.432893\pi\) | ||||
0.209264 | + | 0.977859i | \(0.432893\pi\) | |||||||
\(242\) | −2.18952e11 | −4.10373 | ||||||||
\(243\) | −5.60023e10 | −1.03033 | ||||||||
\(244\) | −1.44462e11 | −2.60916 | ||||||||
\(245\) | −3.96687e10 | −0.703397 | ||||||||
\(246\) | −3.60283e10 | −0.627243 | ||||||||
\(247\) | −9.03468e9 | −0.154446 | ||||||||
\(248\) | −6.22605e10 | −1.04515 | ||||||||
\(249\) | 2.75106e10 | 0.453527 | ||||||||
\(250\) | −1.13531e11 | −1.83816 | ||||||||
\(251\) | 5.15861e10 | 0.820354 | 0.410177 | − | 0.912006i | \(-0.365467\pi\) | ||||
0.410177 | + | 0.912006i | \(0.365467\pi\) | |||||||
\(252\) | −1.14268e11 | −1.78494 | ||||||||
\(253\) | 2.15078e11 | 3.30030 | ||||||||
\(254\) | 8.67181e10 | 1.30725 | ||||||||
\(255\) | −1.44659e10 | −0.214247 | ||||||||
\(256\) | −1.35747e11 | −1.97538 | ||||||||
\(257\) | 1.40209e10 | 0.200482 | 0.100241 | − | 0.994963i | \(-0.468039\pi\) | ||||
0.100241 | + | 0.994963i | \(0.468039\pi\) | |||||||
\(258\) | −3.44274e10 | −0.483744 | ||||||||
\(259\) | 1.35367e10 | 0.186923 | ||||||||
\(260\) | 1.94254e10 | 0.263627 | ||||||||
\(261\) | 1.69293e10 | 0.225817 | ||||||||
\(262\) | −5.54830e10 | −0.727452 | ||||||||
\(263\) | 1.36610e11 | 1.76068 | 0.880341 | − | 0.474341i | \(-0.157314\pi\) | ||||
0.880341 | + | 0.474341i | \(0.157314\pi\) | |||||||
\(264\) | −1.38938e11 | −1.76036 | ||||||||
\(265\) | 5.56251e10 | 0.692890 | ||||||||
\(266\) | −1.98319e11 | −2.42883 | ||||||||
\(267\) | −2.77903e10 | −0.334652 | ||||||||
\(268\) | −2.84250e11 | −3.36585 | ||||||||
\(269\) | −1.41052e11 | −1.64246 | −0.821230 | − | 0.570597i | \(-0.806712\pi\) | ||||
−0.821230 | + | 0.570597i | \(0.806712\pi\) | |||||||
\(270\) | 1.30946e11 | 1.49953 | ||||||||
\(271\) | 4.91664e10 | 0.553740 | 0.276870 | − | 0.960907i | \(-0.410703\pi\) | ||||
0.276870 | + | 0.960907i | \(0.410703\pi\) | |||||||
\(272\) | −3.49249e10 | −0.386879 | ||||||||
\(273\) | 1.01186e10 | 0.110253 | ||||||||
\(274\) | 4.68437e10 | 0.502081 | ||||||||
\(275\) | 2.91324e10 | 0.307170 | ||||||||
\(276\) | 1.94295e11 | 2.01545 | ||||||||
\(277\) | 2.96882e10 | 0.302988 | 0.151494 | − | 0.988458i | \(-0.451592\pi\) | ||||
0.151494 | + | 0.988458i | \(0.451592\pi\) | |||||||
\(278\) | 8.68451e10 | 0.872055 | ||||||||
\(279\) | −4.24893e10 | −0.419817 | ||||||||
\(280\) | 2.10851e11 | 2.05005 | ||||||||
\(281\) | 1.85410e11 | 1.77400 | 0.887000 | − | 0.461769i | \(-0.152785\pi\) | ||||
0.887000 | + | 0.461769i | \(0.152785\pi\) | |||||||
\(282\) | −5.32499e10 | −0.501416 | ||||||||
\(283\) | 1.87000e11 | 1.73302 | 0.866509 | − | 0.499162i | \(-0.166359\pi\) | ||||
0.866509 | + | 0.499162i | \(0.166359\pi\) | |||||||
\(284\) | −3.60052e11 | −3.28423 | ||||||||
\(285\) | 6.09974e10 | 0.547658 | ||||||||
\(286\) | −5.24063e10 | −0.463166 | ||||||||
\(287\) | −9.79781e10 | −0.852433 | ||||||||
\(288\) | −5.89552e9 | −0.0504958 | ||||||||
\(289\) | −9.82860e10 | −0.828803 | ||||||||
\(290\) | −6.31736e10 | −0.524499 | ||||||||
\(291\) | 1.07220e11 | 0.876510 | ||||||||
\(292\) | −2.28517e11 | −1.83948 | ||||||||
\(293\) | 1.63221e11 | 1.29381 | 0.646906 | − | 0.762570i | \(-0.276063\pi\) | ||||
0.646906 | + | 0.762570i | \(0.276063\pi\) | |||||||
\(294\) | 9.66782e10 | 0.754685 | ||||||||
\(295\) | −1.23527e11 | −0.949647 | ||||||||
\(296\) | −3.13180e10 | −0.237127 | ||||||||
\(297\) | −2.34650e11 | −1.74991 | ||||||||
\(298\) | −1.93698e11 | −1.42283 | ||||||||
\(299\) | 3.62394e10 | 0.262217 | ||||||||
\(300\) | 2.63174e10 | 0.187585 | ||||||||
\(301\) | −9.36245e10 | −0.657416 | ||||||||
\(302\) | 7.44685e10 | 0.515159 | ||||||||
\(303\) | 4.23619e10 | 0.288724 | ||||||||
\(304\) | 1.47266e11 | 0.988941 | ||||||||
\(305\) | 1.81916e11 | 1.20371 | ||||||||
\(306\) | −7.42588e10 | −0.484174 | ||||||||
\(307\) | −2.46455e11 | −1.58349 | −0.791744 | − | 0.610853i | \(-0.790826\pi\) | ||||
−0.791744 | + | 0.610853i | \(0.790826\pi\) | |||||||
\(308\) | −7.64100e11 | −4.83807 | ||||||||
\(309\) | −3.19617e10 | −0.199442 | ||||||||
\(310\) | 1.58553e11 | 0.975097 | ||||||||
\(311\) | −6.07495e10 | −0.368231 | −0.184116 | − | 0.982905i | \(-0.558942\pi\) | ||||
−0.184116 | + | 0.982905i | \(0.558942\pi\) | |||||||
\(312\) | −2.34102e10 | −0.139865 | ||||||||
\(313\) | −1.06777e10 | −0.0628820 | −0.0314410 | − | 0.999506i | \(-0.510010\pi\) | ||||
−0.0314410 | + | 0.999506i | \(0.510010\pi\) | |||||||
\(314\) | −1.43244e9 | −0.00831560 | ||||||||
\(315\) | 1.43894e11 | 0.823464 | ||||||||
\(316\) | −1.68438e11 | −0.950272 | ||||||||
\(317\) | 4.35923e9 | 0.0242462 | 0.0121231 | − | 0.999927i | \(-0.496141\pi\) | ||||
0.0121231 | + | 0.999927i | \(0.496141\pi\) | |||||||
\(318\) | −1.35566e11 | −0.743412 | ||||||||
\(319\) | 1.13205e11 | 0.612078 | ||||||||
\(320\) | 1.82063e11 | 0.970613 | ||||||||
\(321\) | 3.72164e10 | 0.195642 | ||||||||
\(322\) | 7.95486e11 | 4.12364 | ||||||||
\(323\) | −8.56056e10 | −0.437614 | ||||||||
\(324\) | 5.40947e10 | 0.272711 | ||||||||
\(325\) | 4.90864e9 | 0.0244054 | ||||||||
\(326\) | 5.99837e10 | 0.294140 | ||||||||
\(327\) | 1.22903e11 | 0.594428 | ||||||||
\(328\) | 2.26679e11 | 1.08138 | ||||||||
\(329\) | −1.44812e11 | −0.681432 | ||||||||
\(330\) | 3.53820e11 | 1.64236 | ||||||||
\(331\) | −1.15879e11 | −0.530614 | −0.265307 | − | 0.964164i | \(-0.585473\pi\) | ||||
−0.265307 | + | 0.964164i | \(0.585473\pi\) | |||||||
\(332\) | −3.50037e11 | −1.58122 | ||||||||
\(333\) | −2.13728e10 | −0.0952493 | ||||||||
\(334\) | 3.50219e11 | 1.53986 | ||||||||
\(335\) | 3.57946e11 | 1.55280 | ||||||||
\(336\) | −1.64934e11 | −0.705965 | ||||||||
\(337\) | 3.02194e11 | 1.27630 | 0.638148 | − | 0.769914i | \(-0.279701\pi\) | ||||
0.638148 | + | 0.769914i | \(0.279701\pi\) | |||||||
\(338\) | 4.05266e11 | 1.68894 | ||||||||
\(339\) | −1.66784e11 | −0.685892 | ||||||||
\(340\) | 1.84060e11 | 0.746971 | ||||||||
\(341\) | −2.84122e11 | −1.13791 | ||||||||
\(342\) | 3.13122e11 | 1.23764 | ||||||||
\(343\) | −7.82017e10 | −0.305065 | ||||||||
\(344\) | 2.16607e11 | 0.833987 | ||||||||
\(345\) | −2.44669e11 | −0.929808 | ||||||||
\(346\) | 2.05054e11 | 0.769176 | ||||||||
\(347\) | 2.99477e11 | 1.10887 | 0.554436 | − | 0.832226i | \(-0.312934\pi\) | ||||
0.554436 | + | 0.832226i | \(0.312934\pi\) | |||||||
\(348\) | 1.02266e11 | 0.373788 | ||||||||
\(349\) | 3.11765e11 | 1.12490 | 0.562448 | − | 0.826832i | \(-0.309859\pi\) | ||||
0.562448 | + | 0.826832i | \(0.309859\pi\) | |||||||
\(350\) | 1.07749e11 | 0.383802 | ||||||||
\(351\) | −3.95371e10 | −0.139035 | ||||||||
\(352\) | −3.94228e10 | −0.136869 | ||||||||
\(353\) | 2.58265e11 | 0.885278 | 0.442639 | − | 0.896700i | \(-0.354042\pi\) | ||||
0.442639 | + | 0.896700i | \(0.354042\pi\) | |||||||
\(354\) | 3.01052e11 | 1.01889 | ||||||||
\(355\) | 4.53401e11 | 1.51515 | ||||||||
\(356\) | 3.53596e11 | 1.16676 | ||||||||
\(357\) | 9.58763e10 | 0.312395 | ||||||||
\(358\) | 1.87384e11 | 0.602919 | ||||||||
\(359\) | −2.60364e11 | −0.827286 | −0.413643 | − | 0.910439i | \(-0.635744\pi\) | ||||
−0.413643 | + | 0.910439i | \(0.635744\pi\) | |||||||
\(360\) | −3.32908e11 | −1.04463 | ||||||||
\(361\) | 3.82798e10 | 0.118628 | ||||||||
\(362\) | 5.99503e11 | 1.83486 | ||||||||
\(363\) | −4.46335e11 | −1.34921 | ||||||||
\(364\) | −1.28746e11 | −0.384396 | ||||||||
\(365\) | 2.87763e11 | 0.848627 | ||||||||
\(366\) | −4.43355e11 | −1.29148 | ||||||||
\(367\) | 1.77047e10 | 0.0509439 | 0.0254719 | − | 0.999676i | \(-0.491891\pi\) | ||||
0.0254719 | + | 0.999676i | \(0.491891\pi\) | |||||||
\(368\) | −5.90703e11 | −1.67901 | ||||||||
\(369\) | 1.54696e11 | 0.434370 | ||||||||
\(370\) | 7.97548e10 | 0.221233 | ||||||||
\(371\) | −3.68669e11 | −1.01031 | ||||||||
\(372\) | −2.56668e11 | −0.694909 | ||||||||
\(373\) | −2.31864e11 | −0.620218 | −0.310109 | − | 0.950701i | \(-0.600365\pi\) | ||||
−0.310109 | + | 0.950701i | \(0.600365\pi\) | |||||||
\(374\) | −4.96561e11 | −1.31235 | ||||||||
\(375\) | −2.31434e11 | −0.604346 | ||||||||
\(376\) | 3.35032e11 | 0.864453 | ||||||||
\(377\) | 1.90744e10 | 0.0486311 | ||||||||
\(378\) | −8.67873e11 | −2.18647 | ||||||||
\(379\) | −3.15074e11 | −0.784397 | −0.392199 | − | 0.919881i | \(-0.628285\pi\) | ||||
−0.392199 | + | 0.919881i | \(0.628285\pi\) | |||||||
\(380\) | −7.76113e11 | −1.90941 | ||||||||
\(381\) | 1.76776e11 | 0.429793 | ||||||||
\(382\) | −7.30783e11 | −1.75591 | ||||||||
\(383\) | −5.19998e11 | −1.23483 | −0.617415 | − | 0.786638i | \(-0.711820\pi\) | ||||
−0.617415 | + | 0.786638i | \(0.711820\pi\) | |||||||
\(384\) | −4.25710e11 | −0.999132 | ||||||||
\(385\) | 9.62204e11 | 2.23200 | ||||||||
\(386\) | −5.69945e11 | −1.30674 | ||||||||
\(387\) | 1.47822e11 | 0.334996 | ||||||||
\(388\) | −1.36423e12 | −3.05595 | ||||||||
\(389\) | 7.66921e11 | 1.69816 | 0.849078 | − | 0.528267i | \(-0.177158\pi\) | ||||
0.849078 | + | 0.528267i | \(0.177158\pi\) | |||||||
\(390\) | 5.96166e10 | 0.130490 | ||||||||
\(391\) | 3.43376e11 | 0.742976 | ||||||||
\(392\) | −6.08270e11 | −1.30110 | ||||||||
\(393\) | −1.13103e11 | −0.239170 | ||||||||
\(394\) | −5.88133e10 | −0.122954 | ||||||||
\(395\) | 2.12108e11 | 0.438399 | ||||||||
\(396\) | 1.20642e12 | 2.46531 | ||||||||
\(397\) | 3.62638e11 | 0.732682 | 0.366341 | − | 0.930481i | \(-0.380610\pi\) | ||||
0.366341 | + | 0.930481i | \(0.380610\pi\) | |||||||
\(398\) | 3.95561e11 | 0.790205 | ||||||||
\(399\) | −4.04275e11 | −0.798544 | ||||||||
\(400\) | −8.00110e10 | −0.156272 | ||||||||
\(401\) | 3.57307e11 | 0.690068 | 0.345034 | − | 0.938590i | \(-0.387867\pi\) | ||||
0.345034 | + | 0.938590i | \(0.387867\pi\) | |||||||
\(402\) | −8.72365e11 | −1.66602 | ||||||||
\(403\) | −4.78728e10 | −0.0904100 | ||||||||
\(404\) | −5.39000e11 | −1.00664 | ||||||||
\(405\) | −6.81195e10 | −0.125813 | ||||||||
\(406\) | 4.18699e11 | 0.764776 | ||||||||
\(407\) | −1.42918e11 | −0.258173 | ||||||||
\(408\) | −2.21817e11 | −0.396299 | ||||||||
\(409\) | 9.49530e11 | 1.67785 | 0.838926 | − | 0.544245i | \(-0.183184\pi\) | ||||
0.838926 | + | 0.544245i | \(0.183184\pi\) | |||||||
\(410\) | −5.77264e11 | −1.00890 | ||||||||
\(411\) | 9.54914e10 | 0.165073 | ||||||||
\(412\) | 4.06671e11 | 0.695354 | ||||||||
\(413\) | 8.18704e11 | 1.38469 | ||||||||
\(414\) | −1.25598e12 | −2.10126 | ||||||||
\(415\) | 4.40788e11 | 0.729480 | ||||||||
\(416\) | −6.64251e9 | −0.0108746 | ||||||||
\(417\) | 1.77035e11 | 0.286712 | ||||||||
\(418\) | 2.09382e12 | 3.35464 | ||||||||
\(419\) | −4.72730e11 | −0.749291 | −0.374645 | − | 0.927168i | \(-0.622236\pi\) | ||||
−0.374645 | + | 0.927168i | \(0.622236\pi\) | |||||||
\(420\) | 8.69228e11 | 1.36305 | ||||||||
\(421\) | −5.33072e11 | −0.827021 | −0.413511 | − | 0.910499i | \(-0.635698\pi\) | ||||
−0.413511 | + | 0.910499i | \(0.635698\pi\) | |||||||
\(422\) | −9.19223e11 | −1.41096 | ||||||||
\(423\) | 2.28640e11 | 0.347233 | ||||||||
\(424\) | 8.52942e11 | 1.28166 | ||||||||
\(425\) | 4.65105e10 | 0.0691513 | ||||||||
\(426\) | −1.10500e12 | −1.62562 | ||||||||
\(427\) | −1.20569e12 | −1.75514 | ||||||||
\(428\) | −4.73530e11 | −0.682105 | ||||||||
\(429\) | −1.06831e11 | −0.152278 | ||||||||
\(430\) | −5.51613e11 | −0.778084 | ||||||||
\(431\) | −9.22826e11 | −1.28817 | −0.644084 | − | 0.764955i | \(-0.722761\pi\) | ||||
−0.644084 | + | 0.764955i | \(0.722761\pi\) | |||||||
\(432\) | 6.44456e11 | 0.890259 | ||||||||
\(433\) | 1.08108e12 | 1.47795 | 0.738976 | − | 0.673731i | \(-0.235309\pi\) | ||||
0.738976 | + | 0.673731i | \(0.235309\pi\) | |||||||
\(434\) | −1.05085e12 | −1.42180 | ||||||||
\(435\) | −1.28780e11 | −0.172444 | ||||||||
\(436\) | −1.56379e12 | −2.07247 | ||||||||
\(437\) | −1.44789e12 | −1.89920 | ||||||||
\(438\) | −7.01319e11 | −0.910504 | ||||||||
\(439\) | 4.65455e11 | 0.598119 | 0.299059 | − | 0.954235i | \(-0.403327\pi\) | ||||
0.299059 | + | 0.954235i | \(0.403327\pi\) | |||||||
\(440\) | −2.22613e12 | −2.83148 | ||||||||
\(441\) | −4.15110e11 | −0.522624 | ||||||||
\(442\) | −8.36677e10 | −0.104270 | ||||||||
\(443\) | 8.59536e11 | 1.06034 | 0.530172 | − | 0.847890i | \(-0.322127\pi\) | ||||
0.530172 | + | 0.847890i | \(0.322127\pi\) | |||||||
\(444\) | −1.29108e11 | −0.157663 | ||||||||
\(445\) | −4.45271e11 | −0.538275 | ||||||||
\(446\) | 2.09134e12 | 2.50275 | ||||||||
\(447\) | −3.94855e11 | −0.467793 | ||||||||
\(448\) | −1.20667e12 | −1.41526 | ||||||||
\(449\) | 9.10060e11 | 1.05672 | 0.528362 | − | 0.849019i | \(-0.322807\pi\) | ||||
0.528362 | + | 0.849019i | \(0.322807\pi\) | |||||||
\(450\) | −1.70123e11 | −0.195572 | ||||||||
\(451\) | 1.03444e12 | 1.17736 | ||||||||
\(452\) | 2.12211e12 | 2.39136 | ||||||||
\(453\) | 1.51805e11 | 0.169373 | ||||||||
\(454\) | −6.21204e11 | −0.686250 | ||||||||
\(455\) | 1.62126e11 | 0.177338 | ||||||||
\(456\) | 9.35319e11 | 1.01302 | ||||||||
\(457\) | 4.94571e11 | 0.530403 | 0.265201 | − | 0.964193i | \(-0.414562\pi\) | ||||
0.265201 | + | 0.964193i | \(0.414562\pi\) | |||||||
\(458\) | 2.89561e12 | 3.07500 | ||||||||
\(459\) | −3.74623e11 | −0.393946 | ||||||||
\(460\) | 3.11310e12 | 3.24177 | ||||||||
\(461\) | 1.03892e12 | 1.07134 | 0.535670 | − | 0.844428i | \(-0.320059\pi\) | ||||
0.535670 | + | 0.844428i | \(0.320059\pi\) | |||||||
\(462\) | −2.34503e12 | −2.39474 | ||||||||
\(463\) | −5.14038e11 | −0.519853 | −0.259926 | − | 0.965628i | \(-0.583698\pi\) | ||||
−0.259926 | + | 0.965628i | \(0.583698\pi\) | |||||||
\(464\) | −3.10913e11 | −0.311392 | ||||||||
\(465\) | 3.23212e11 | 0.320590 | ||||||||
\(466\) | −1.67745e12 | −1.64784 | ||||||||
\(467\) | 8.14302e11 | 0.792245 | 0.396123 | − | 0.918198i | \(-0.370355\pi\) | ||||
0.396123 | + | 0.918198i | \(0.370355\pi\) | |||||||
\(468\) | 2.03275e11 | 0.195875 | ||||||||
\(469\) | −2.37238e12 | −2.26415 | ||||||||
\(470\) | −8.53197e11 | −0.806508 | ||||||||
\(471\) | −2.92005e9 | −0.00273398 | ||||||||
\(472\) | −1.89413e12 | −1.75659 | ||||||||
\(473\) | 9.88470e11 | 0.908006 | ||||||||
\(474\) | −5.16936e11 | −0.470365 | ||||||||
\(475\) | −1.96118e11 | −0.176765 | ||||||||
\(476\) | −1.21990e12 | −1.08916 | ||||||||
\(477\) | 5.82084e11 | 0.514817 | ||||||||
\(478\) | 3.68053e12 | 3.22467 | ||||||||
\(479\) | 1.58296e12 | 1.37391 | 0.686956 | − | 0.726699i | \(-0.258946\pi\) | ||||
0.686956 | + | 0.726699i | \(0.258946\pi\) | |||||||
\(480\) | 4.48467e10 | 0.0385607 | ||||||||
\(481\) | −2.40808e10 | −0.0205125 | ||||||||
\(482\) | −8.55878e11 | −0.722271 | ||||||||
\(483\) | 1.62160e12 | 1.35576 | ||||||||
\(484\) | 5.67903e12 | 4.70403 | ||||||||
\(485\) | 1.71793e12 | 1.40983 | ||||||||
\(486\) | 2.18684e12 | 1.77809 | ||||||||
\(487\) | −1.51814e12 | −1.22302 | −0.611508 | − | 0.791238i | \(-0.709437\pi\) | ||||
−0.611508 | + | 0.791238i | \(0.709437\pi\) | |||||||
\(488\) | 2.78946e12 | 2.22654 | ||||||||
\(489\) | 1.22277e11 | 0.0967065 | ||||||||
\(490\) | 1.54903e12 | 1.21388 | ||||||||
\(491\) | −2.12449e12 | −1.64963 | −0.824817 | − | 0.565400i | \(-0.808722\pi\) | ||||
−0.824817 | + | 0.565400i | \(0.808722\pi\) | |||||||
\(492\) | 9.34480e11 | 0.718997 | ||||||||
\(493\) | 1.80734e11 | 0.137793 | ||||||||
\(494\) | 3.52796e11 | 0.266534 | ||||||||
\(495\) | −1.51920e12 | −1.13735 | ||||||||
\(496\) | 7.80329e11 | 0.578909 | ||||||||
\(497\) | −3.00503e12 | −2.20925 | ||||||||
\(498\) | −1.07426e12 | −0.782670 | ||||||||
\(499\) | 1.94053e12 | 1.40109 | 0.700547 | − | 0.713606i | \(-0.252939\pi\) | ||||
0.700547 | + | 0.713606i | \(0.252939\pi\) | |||||||
\(500\) | 2.94469e12 | 2.10705 | ||||||||
\(501\) | 7.13925e11 | 0.506271 | ||||||||
\(502\) | −2.01439e12 | −1.41572 | ||||||||
\(503\) | −3.37063e11 | −0.234777 | −0.117388 | − | 0.993086i | \(-0.537452\pi\) | ||||
−0.117388 | + | 0.993086i | \(0.537452\pi\) | |||||||
\(504\) | 2.20643e12 | 1.52319 | ||||||||
\(505\) | 6.78743e11 | 0.464402 | ||||||||
\(506\) | −8.39860e12 | −5.69547 | ||||||||
\(507\) | 8.26138e11 | 0.555286 | ||||||||
\(508\) | −2.24924e12 | −1.49847 | ||||||||
\(509\) | −1.68624e12 | −1.11350 | −0.556748 | − | 0.830681i | \(-0.687951\pi\) | ||||
−0.556748 | + | 0.830681i | \(0.687951\pi\) | |||||||
\(510\) | 5.64880e11 | 0.369735 | ||||||||
\(511\) | −1.90722e12 | −1.23739 | ||||||||
\(512\) | 2.56264e12 | 1.64806 | ||||||||
\(513\) | 1.57965e12 | 1.00701 | ||||||||
\(514\) | −5.47502e11 | −0.345981 | ||||||||
\(515\) | −5.12107e11 | −0.320795 | ||||||||
\(516\) | 8.92957e11 | 0.554507 | ||||||||
\(517\) | 1.52890e12 | 0.941176 | ||||||||
\(518\) | −5.28595e11 | −0.322581 | ||||||||
\(519\) | 4.18004e11 | 0.252888 | ||||||||
\(520\) | −3.75089e11 | −0.224968 | ||||||||
\(521\) | 1.78643e12 | 1.06223 | 0.531113 | − | 0.847301i | \(-0.321774\pi\) | ||||
0.531113 | + | 0.847301i | \(0.321774\pi\) | |||||||
\(522\) | −6.61075e11 | −0.389703 | ||||||||
\(523\) | −2.70264e11 | −0.157954 | −0.0789769 | − | 0.996876i | \(-0.525165\pi\) | ||||
−0.0789769 | + | 0.996876i | \(0.525165\pi\) | |||||||
\(524\) | 1.43908e12 | 0.833865 | ||||||||
\(525\) | 2.19647e11 | 0.126185 | ||||||||
\(526\) | −5.33449e12 | −3.03848 | ||||||||
\(527\) | −4.53606e11 | −0.256172 | ||||||||
\(528\) | 1.74134e12 | 0.975061 | ||||||||
\(529\) | 4.00655e12 | 2.22444 | ||||||||
\(530\) | −2.17211e12 | −1.19575 | ||||||||
\(531\) | −1.29263e12 | −0.705587 | ||||||||
\(532\) | 5.14388e12 | 2.78412 | ||||||||
\(533\) | 1.74296e11 | 0.0935440 | ||||||||
\(534\) | 1.08519e12 | 0.577522 | ||||||||
\(535\) | 5.96300e11 | 0.314683 | ||||||||
\(536\) | 5.48866e12 | 2.87227 | ||||||||
\(537\) | 3.81984e11 | 0.198226 | ||||||||
\(538\) | 5.50797e12 | 2.83446 | ||||||||
\(539\) | −2.77580e12 | −1.41657 | ||||||||
\(540\) | −3.39638e12 | −1.71888 | ||||||||
\(541\) | 2.30383e12 | 1.15628 | 0.578139 | − | 0.815938i | \(-0.303779\pi\) | ||||
0.578139 | + | 0.815938i | \(0.303779\pi\) | |||||||
\(542\) | −1.91990e12 | −0.955613 | ||||||||
\(543\) | 1.22209e12 | 0.603261 | ||||||||
\(544\) | −6.29392e10 | −0.0308125 | ||||||||
\(545\) | 1.96922e12 | 0.956114 | ||||||||
\(546\) | −3.95123e11 | −0.190268 | ||||||||
\(547\) | 3.70350e12 | 1.76876 | 0.884380 | − | 0.466767i | \(-0.154581\pi\) | ||||
0.884380 | + | 0.466767i | \(0.154581\pi\) | |||||||
\(548\) | −1.21500e12 | −0.575526 | ||||||||
\(549\) | 1.90365e12 | 0.894357 | ||||||||
\(550\) | −1.13759e12 | −0.530097 | ||||||||
\(551\) | −7.62088e11 | −0.352227 | ||||||||
\(552\) | −3.75170e12 | −1.71990 | ||||||||
\(553\) | −1.40580e12 | −0.639233 | ||||||||
\(554\) | −1.15930e12 | −0.522878 | ||||||||
\(555\) | 1.62581e11 | 0.0727363 | ||||||||
\(556\) | −2.25254e12 | −0.999621 | ||||||||
\(557\) | −8.74013e11 | −0.384742 | −0.192371 | − | 0.981322i | \(-0.561618\pi\) | ||||
−0.192371 | + | 0.981322i | \(0.561618\pi\) | |||||||
\(558\) | 1.65917e12 | 0.724496 | ||||||||
\(559\) | 1.66552e11 | 0.0721432 | ||||||||
\(560\) | −2.64266e12 | −1.13552 | ||||||||
\(561\) | −1.01224e12 | −0.431472 | ||||||||
\(562\) | −7.24007e12 | −3.06147 | ||||||||
\(563\) | −1.02727e12 | −0.430921 | −0.215461 | − | 0.976513i | \(-0.569125\pi\) | ||||
−0.215461 | + | 0.976513i | \(0.569125\pi\) | |||||||
\(564\) | 1.38116e12 | 0.574763 | ||||||||
\(565\) | −2.67230e12 | −1.10323 | ||||||||
\(566\) | −7.30218e12 | −2.99074 | ||||||||
\(567\) | 4.51479e11 | 0.183448 | ||||||||
\(568\) | 6.95234e12 | 2.80261 | ||||||||
\(569\) | −1.21328e12 | −0.485238 | −0.242619 | − | 0.970122i | \(-0.578006\pi\) | ||||
−0.242619 | + | 0.970122i | \(0.578006\pi\) | |||||||
\(570\) | −2.38189e12 | −0.945117 | ||||||||
\(571\) | −8.45365e11 | −0.332799 | −0.166399 | − | 0.986058i | \(-0.553214\pi\) | ||||
−0.166399 | + | 0.986058i | \(0.553214\pi\) | |||||||
\(572\) | 1.35928e12 | 0.530918 | ||||||||
\(573\) | −1.48971e12 | −0.577305 | ||||||||
\(574\) | 3.82596e12 | 1.47108 | ||||||||
\(575\) | 7.86656e11 | 0.300109 | ||||||||
\(576\) | 1.90518e12 | 0.721165 | ||||||||
\(577\) | 7.88912e11 | 0.296304 | 0.148152 | − | 0.988965i | \(-0.452668\pi\) | ||||
0.148152 | + | 0.988965i | \(0.452668\pi\) | |||||||
\(578\) | 3.83798e12 | 1.43030 | ||||||||
\(579\) | −1.16184e12 | −0.429627 | ||||||||
\(580\) | 1.63856e12 | 0.601224 | ||||||||
\(581\) | −2.92143e12 | −1.06366 | ||||||||
\(582\) | −4.18684e12 | −1.51263 | ||||||||
\(583\) | 3.89234e12 | 1.39541 | ||||||||
\(584\) | 4.41249e12 | 1.56973 | ||||||||
\(585\) | −2.55977e11 | −0.0903649 | ||||||||
\(586\) | −6.37362e12 | −2.23279 | ||||||||
\(587\) | −3.62250e12 | −1.25932 | −0.629661 | − | 0.776870i | \(-0.716806\pi\) | ||||
−0.629661 | + | 0.776870i | \(0.716806\pi\) | |||||||
\(588\) | −2.50758e12 | −0.865081 | ||||||||
\(589\) | 1.91269e12 | 0.654826 | ||||||||
\(590\) | 4.82361e12 | 1.63885 | ||||||||
\(591\) | −1.19891e11 | −0.0404245 | ||||||||
\(592\) | 3.92518e11 | 0.131344 | ||||||||
\(593\) | −3.87408e12 | −1.28654 | −0.643269 | − | 0.765640i | \(-0.722422\pi\) | ||||
−0.643269 | + | 0.765640i | \(0.722422\pi\) | |||||||
\(594\) | 9.16285e12 | 3.01989 | ||||||||
\(595\) | 1.53618e12 | 0.502476 | ||||||||
\(596\) | 5.02402e12 | 1.63096 | ||||||||
\(597\) | 8.06355e11 | 0.259802 | ||||||||
\(598\) | −1.41511e12 | −0.452519 | ||||||||
\(599\) | 2.34043e12 | 0.742805 | 0.371402 | − | 0.928472i | \(-0.378877\pi\) | ||||
0.371402 | + | 0.928472i | \(0.378877\pi\) | |||||||
\(600\) | −5.08169e11 | −0.160077 | ||||||||
\(601\) | −4.41644e12 | −1.38082 | −0.690410 | − | 0.723418i | \(-0.742570\pi\) | ||||
−0.690410 | + | 0.723418i | \(0.742570\pi\) | |||||||
\(602\) | 3.65595e12 | 1.13453 | ||||||||
\(603\) | 3.74570e12 | 1.15373 | ||||||||
\(604\) | −1.93152e12 | −0.590518 | ||||||||
\(605\) | −7.15140e12 | −2.17016 | ||||||||
\(606\) | −1.65419e12 | −0.498264 | ||||||||
\(607\) | 1.79254e12 | 0.535943 | 0.267972 | − | 0.963427i | \(-0.413647\pi\) | ||||
0.267972 | + | 0.963427i | \(0.413647\pi\) | |||||||
\(608\) | 2.65392e11 | 0.0787628 | ||||||||
\(609\) | 8.53521e11 | 0.251441 | ||||||||
\(610\) | −7.10366e12 | −2.07729 | ||||||||
\(611\) | 2.57610e11 | 0.0747787 | ||||||||
\(612\) | 1.92608e12 | 0.554999 | ||||||||
\(613\) | 8.04928e11 | 0.230242 | 0.115121 | − | 0.993351i | \(-0.463274\pi\) | ||||
0.115121 | + | 0.993351i | \(0.463274\pi\) | |||||||
\(614\) | 9.62384e12 | 2.73269 | ||||||||
\(615\) | −1.17676e12 | −0.331703 | ||||||||
\(616\) | 1.47542e13 | 4.12860 | ||||||||
\(617\) | −6.31640e12 | −1.75463 | −0.877317 | − | 0.479911i | \(-0.840669\pi\) | ||||
−0.877317 | + | 0.479911i | \(0.840669\pi\) | |||||||
\(618\) | 1.24808e12 | 0.344186 | ||||||||
\(619\) | −5.48930e12 | −1.50283 | −0.751413 | − | 0.659832i | \(-0.770628\pi\) | ||||
−0.751413 | + | 0.659832i | \(0.770628\pi\) | |||||||
\(620\) | −4.11246e12 | −1.11773 | ||||||||
\(621\) | −6.33619e12 | −1.70968 | ||||||||
\(622\) | 2.37221e12 | 0.635473 | ||||||||
\(623\) | 2.95114e12 | 0.784862 | ||||||||
\(624\) | 2.93406e11 | 0.0774709 | ||||||||
\(625\) | −3.07060e12 | −0.804939 | ||||||||
\(626\) | 4.16953e11 | 0.108518 | ||||||||
\(627\) | 4.26826e12 | 1.10293 | ||||||||
\(628\) | 3.71538e10 | 0.00953202 | ||||||||
\(629\) | −2.28171e11 | −0.0581209 | ||||||||
\(630\) | −5.61892e12 | −1.42109 | ||||||||
\(631\) | −3.02802e12 | −0.760373 | −0.380186 | − | 0.924910i | \(-0.624140\pi\) | ||||
−0.380186 | + | 0.924910i | \(0.624140\pi\) | |||||||
\(632\) | 3.25241e12 | 0.810920 | ||||||||
\(633\) | −1.87384e12 | −0.463892 | ||||||||
\(634\) | −1.70224e11 | −0.0418427 | ||||||||
\(635\) | 2.83239e12 | 0.691307 | ||||||||
\(636\) | 3.51623e12 | 0.852159 | ||||||||
\(637\) | −4.67706e11 | −0.112550 | ||||||||
\(638\) | −4.42055e12 | −1.05629 | ||||||||
\(639\) | 4.74457e12 | 1.12575 | ||||||||
\(640\) | −6.82093e12 | −1.60707 | ||||||||
\(641\) | −7.28464e12 | −1.70430 | −0.852152 | − | 0.523294i | \(-0.824703\pi\) | ||||
−0.852152 | + | 0.523294i | \(0.824703\pi\) | |||||||
\(642\) | −1.45327e12 | −0.337627 | ||||||||
\(643\) | 4.15435e12 | 0.958415 | 0.479207 | − | 0.877702i | \(-0.340924\pi\) | ||||
0.479207 | + | 0.877702i | \(0.340924\pi\) | |||||||
\(644\) | −2.06328e13 | −4.72685 | ||||||||
\(645\) | −1.12447e12 | −0.255816 | ||||||||
\(646\) | 3.34282e12 | 0.755208 | ||||||||
\(647\) | 4.98496e12 | 1.11839 | 0.559194 | − | 0.829037i | \(-0.311111\pi\) | ||||
0.559194 | + | 0.829037i | \(0.311111\pi\) | |||||||
\(648\) | −1.04453e12 | −0.232719 | ||||||||
\(649\) | −8.64373e12 | −1.91249 | ||||||||
\(650\) | −1.91678e11 | −0.0421174 | ||||||||
\(651\) | −2.14217e12 | −0.467454 | ||||||||
\(652\) | −1.55582e12 | −0.337167 | ||||||||
\(653\) | 2.92509e12 | 0.629550 | 0.314775 | − | 0.949166i | \(-0.398071\pi\) | ||||
0.314775 | + | 0.949166i | \(0.398071\pi\) | |||||||
\(654\) | −4.79926e12 | −1.02583 | ||||||||
\(655\) | −1.81219e12 | −0.384696 | ||||||||
\(656\) | −2.84104e12 | −0.598976 | ||||||||
\(657\) | 3.01127e12 | 0.630530 | ||||||||
\(658\) | 5.65477e12 | 1.17598 | ||||||||
\(659\) | 8.90371e11 | 0.183902 | 0.0919510 | − | 0.995764i | \(-0.470690\pi\) | ||||
0.0919510 | + | 0.995764i | \(0.470690\pi\) | |||||||
\(660\) | −9.17716e12 | −1.88261 | ||||||||
\(661\) | −4.27530e12 | −0.871084 | −0.435542 | − | 0.900168i | \(-0.643443\pi\) | ||||
−0.435542 | + | 0.900168i | \(0.643443\pi\) | |||||||
\(662\) | 4.52497e12 | 0.915703 | ||||||||
\(663\) | −1.70557e11 | −0.0342815 | ||||||||
\(664\) | 6.75894e12 | 1.34934 | ||||||||
\(665\) | −6.47750e12 | −1.28443 | ||||||||
\(666\) | 8.34587e11 | 0.164376 | ||||||||
\(667\) | 3.05684e12 | 0.598008 | ||||||||
\(668\) | −9.08377e12 | −1.76511 | ||||||||
\(669\) | 4.26321e12 | 0.822848 | ||||||||
\(670\) | −1.39775e13 | −2.67974 | ||||||||
\(671\) | 1.27295e13 | 2.42415 | ||||||||
\(672\) | −2.97232e11 | −0.0562257 | ||||||||
\(673\) | 3.41372e12 | 0.641445 | 0.320723 | − | 0.947173i | \(-0.396074\pi\) | ||||
0.320723 | + | 0.947173i | \(0.396074\pi\) | |||||||
\(674\) | −1.18004e13 | −2.20256 | ||||||||
\(675\) | −8.58239e11 | −0.159126 | ||||||||
\(676\) | −1.05115e13 | −1.93600 | ||||||||
\(677\) | 4.27690e11 | 0.0782492 | 0.0391246 | − | 0.999234i | \(-0.487543\pi\) | ||||
0.0391246 | + | 0.999234i | \(0.487543\pi\) | |||||||
\(678\) | 6.51277e12 | 1.18367 | ||||||||
\(679\) | −1.13860e13 | −2.05569 | ||||||||
\(680\) | −3.55406e12 | −0.637433 | ||||||||
\(681\) | −1.26633e12 | −0.225624 | ||||||||
\(682\) | 1.10947e13 | 1.96375 | ||||||||
\(683\) | 8.79939e12 | 1.54725 | 0.773623 | − | 0.633647i | \(-0.218443\pi\) | ||||
0.773623 | + | 0.633647i | \(0.218443\pi\) | |||||||
\(684\) | −8.12156e12 | −1.41869 | ||||||||
\(685\) | 1.53001e12 | 0.265514 | ||||||||
\(686\) | 3.05371e12 | 0.526464 | ||||||||
\(687\) | 5.90272e12 | 1.01099 | ||||||||
\(688\) | −2.71480e12 | −0.461944 | ||||||||
\(689\) | 6.55837e11 | 0.110869 | ||||||||
\(690\) | 9.55411e12 | 1.60461 | ||||||||
\(691\) | −6.74731e12 | −1.12585 | −0.562924 | − | 0.826509i | \(-0.690324\pi\) | ||||
−0.562924 | + | 0.826509i | \(0.690324\pi\) | |||||||
\(692\) | −5.31856e12 | −0.881692 | ||||||||
\(693\) | 1.00689e13 | 1.65837 | ||||||||
\(694\) | −1.16943e13 | −1.91363 | ||||||||
\(695\) | 2.83654e12 | 0.461166 | ||||||||
\(696\) | −1.97468e12 | −0.318974 | ||||||||
\(697\) | 1.65150e12 | 0.265052 | ||||||||
\(698\) | −1.21741e13 | −1.94128 | ||||||||
\(699\) | −3.41951e12 | −0.541772 | ||||||||
\(700\) | −2.79472e12 | −0.439945 | ||||||||
\(701\) | −8.83497e12 | −1.38189 | −0.690946 | − | 0.722907i | \(-0.742806\pi\) | ||||
−0.690946 | + | 0.722907i | \(0.742806\pi\) | |||||||
\(702\) | 1.54389e12 | 0.239938 | ||||||||
\(703\) | 9.62114e11 | 0.148569 | ||||||||
\(704\) | 1.27398e13 | 1.95472 | ||||||||
\(705\) | −1.73925e12 | −0.265162 | ||||||||
\(706\) | −1.00850e13 | −1.52776 | ||||||||
\(707\) | −4.49853e12 | −0.677148 | ||||||||
\(708\) | −7.80850e12 | −1.16793 | ||||||||
\(709\) | 7.92256e12 | 1.17749 | 0.588745 | − | 0.808318i | \(-0.299622\pi\) | ||||
0.588745 | + | 0.808318i | \(0.299622\pi\) | |||||||
\(710\) | −1.77049e13 | −2.61475 | ||||||||
\(711\) | 2.21958e12 | 0.325730 | ||||||||
\(712\) | −6.82767e12 | −0.995663 | ||||||||
\(713\) | −7.67207e12 | −1.11176 | ||||||||
\(714\) | −3.74388e12 | −0.539113 | ||||||||
\(715\) | −1.71169e12 | −0.244934 | ||||||||
\(716\) | −4.86025e12 | −0.691115 | ||||||||
\(717\) | 7.50280e12 | 1.06020 | ||||||||
\(718\) | 1.01670e13 | 1.42768 | ||||||||
\(719\) | −7.51488e12 | −1.04868 | −0.524339 | − | 0.851510i | \(-0.675687\pi\) | ||||
−0.524339 | + | 0.851510i | \(0.675687\pi\) | |||||||
\(720\) | 4.17244e12 | 0.578620 | ||||||||
\(721\) | 3.39411e12 | 0.467754 | ||||||||
\(722\) | −1.49479e12 | −0.204721 | ||||||||
\(723\) | −1.74472e12 | −0.237466 | ||||||||
\(724\) | −1.55495e13 | −2.10327 | ||||||||
\(725\) | 4.14051e11 | 0.0556587 | ||||||||
\(726\) | 1.74290e13 | 2.32840 | ||||||||
\(727\) | −1.01859e13 | −1.35237 | −0.676185 | − | 0.736732i | \(-0.736368\pi\) | ||||
−0.676185 | + | 0.736732i | \(0.736368\pi\) | |||||||
\(728\) | 2.48600e12 | 0.328027 | ||||||||
\(729\) | 3.40663e12 | 0.446737 | ||||||||
\(730\) | −1.12369e13 | −1.46451 | ||||||||
\(731\) | 1.57811e12 | 0.204414 | ||||||||
\(732\) | 1.14995e13 | 1.48040 | ||||||||
\(733\) | 2.12333e12 | 0.271675 | 0.135837 | − | 0.990731i | \(-0.456628\pi\) | ||||
0.135837 | + | 0.990731i | \(0.456628\pi\) | |||||||
\(734\) | −6.91354e11 | −0.0879160 | ||||||||
\(735\) | 3.15771e12 | 0.399097 | ||||||||
\(736\) | −1.06452e12 | −0.133723 | ||||||||
\(737\) | 2.50471e13 | 3.12719 | ||||||||
\(738\) | −6.04072e12 | −0.749610 | ||||||||
\(739\) | 3.80150e12 | 0.468873 | 0.234436 | − | 0.972131i | \(-0.424676\pi\) | ||||
0.234436 | + | 0.972131i | \(0.424676\pi\) | |||||||
\(740\) | −2.06863e12 | −0.253595 | ||||||||
\(741\) | 7.19178e11 | 0.0876303 | ||||||||
\(742\) | 1.43962e13 | 1.74353 | ||||||||
\(743\) | −5.70236e12 | −0.686444 | −0.343222 | − | 0.939254i | \(-0.611518\pi\) | ||||
−0.343222 | + | 0.939254i | \(0.611518\pi\) | |||||||
\(744\) | 4.95606e12 | 0.593005 | ||||||||
\(745\) | −6.32657e12 | −0.752428 | ||||||||
\(746\) | 9.05409e12 | 1.07034 | ||||||||
\(747\) | 4.61259e12 | 0.542004 | ||||||||
\(748\) | 1.28795e13 | 1.50433 | ||||||||
\(749\) | −3.95212e12 | −0.458841 | ||||||||
\(750\) | 9.03727e12 | 1.04295 | ||||||||
\(751\) | 1.51873e13 | 1.74221 | 0.871103 | − | 0.491100i | \(-0.163405\pi\) | ||||
0.871103 | + | 0.491100i | \(0.163405\pi\) | |||||||
\(752\) | −4.19906e12 | −0.478819 | ||||||||
\(753\) | −4.10635e12 | −0.465456 | ||||||||
\(754\) | −7.44836e11 | −0.0839247 | ||||||||
\(755\) | 2.43229e12 | 0.272430 | ||||||||
\(756\) | 2.25104e13 | 2.50631 | ||||||||
\(757\) | −5.88356e12 | −0.651192 | −0.325596 | − | 0.945509i | \(-0.605565\pi\) | ||||
−0.325596 | + | 0.945509i | \(0.605565\pi\) | |||||||
\(758\) | 1.23033e13 | 1.35367 | ||||||||
\(759\) | −1.71206e13 | −1.87254 | ||||||||
\(760\) | 1.49862e13 | 1.62940 | ||||||||
\(761\) | −1.54838e12 | −0.167358 | −0.0836791 | − | 0.996493i | \(-0.526667\pi\) | ||||
−0.0836791 | + | 0.996493i | \(0.526667\pi\) | |||||||
\(762\) | −6.90292e12 | −0.741713 | ||||||||
\(763\) | −1.30515e13 | −1.39412 | ||||||||
\(764\) | 1.89546e13 | 2.01277 | ||||||||
\(765\) | −2.42544e12 | −0.256044 | ||||||||
\(766\) | 2.03054e13 | 2.13100 | ||||||||
\(767\) | −1.45642e12 | −0.151952 | ||||||||
\(768\) | 1.08057e13 | 1.12080 | ||||||||
\(769\) | −1.67793e13 | −1.73024 | −0.865119 | − | 0.501567i | \(-0.832757\pi\) | ||||
−0.865119 | + | 0.501567i | \(0.832757\pi\) | |||||||
\(770\) | −3.75732e13 | −3.85185 | ||||||||
\(771\) | −1.11609e12 | −0.113751 | ||||||||
\(772\) | 1.47829e13 | 1.49789 | ||||||||
\(773\) | 1.30862e13 | 1.31827 | 0.659135 | − | 0.752025i | \(-0.270923\pi\) | ||||
0.659135 | + | 0.752025i | \(0.270923\pi\) | |||||||
\(774\) | −5.77231e12 | −0.578116 | ||||||||
\(775\) | −1.03919e12 | −0.103475 | ||||||||
\(776\) | 2.63423e13 | 2.60781 | ||||||||
\(777\) | −1.07754e12 | −0.106057 | ||||||||
\(778\) | −2.99476e13 | −2.93058 | ||||||||
\(779\) | −6.96376e12 | −0.677525 | ||||||||
\(780\) | −1.54630e12 | −0.149578 | ||||||||
\(781\) | 3.17265e13 | 3.05136 | ||||||||
\(782\) | −1.34085e13 | −1.28219 | ||||||||
\(783\) | −3.33501e12 | −0.317080 | ||||||||
\(784\) | 7.62363e12 | 0.720675 | ||||||||
\(785\) | −4.67865e10 | −0.00439751 | ||||||||
\(786\) | 4.41656e12 | 0.412745 | ||||||||
\(787\) | 1.29789e13 | 1.20601 | 0.603007 | − | 0.797736i | \(-0.293969\pi\) | ||||
0.603007 | + | 0.797736i | \(0.293969\pi\) | |||||||
\(788\) | 1.52546e12 | 0.140940 | ||||||||
\(789\) | −1.08744e13 | −0.998985 | ||||||||
\(790\) | −8.28262e12 | −0.756564 | ||||||||
\(791\) | 1.77113e13 | 1.60863 | ||||||||
\(792\) | −2.32951e13 | −2.10378 | ||||||||
\(793\) | 2.14485e12 | 0.192605 | ||||||||
\(794\) | −1.41607e13 | −1.26442 | ||||||||
\(795\) | −4.42786e12 | −0.393135 | ||||||||
\(796\) | −1.02598e13 | −0.905798 | ||||||||
\(797\) | −1.21803e13 | −1.06929 | −0.534643 | − | 0.845078i | \(-0.679554\pi\) | ||||
−0.534643 | + | 0.845078i | \(0.679554\pi\) | |||||||
\(798\) | 1.57866e13 | 1.37808 | ||||||||
\(799\) | 2.44092e12 | 0.211881 | ||||||||
\(800\) | −1.44190e11 | −0.0124460 | ||||||||
\(801\) | −4.65949e12 | −0.399938 | ||||||||
\(802\) | −1.39525e13 | −1.19088 | ||||||||
\(803\) | 2.01361e13 | 1.70905 | ||||||||
\(804\) | 2.26269e13 | 1.90973 | ||||||||
\(805\) | 2.59822e13 | 2.18069 | ||||||||
\(806\) | 1.86939e12 | 0.156024 | ||||||||
\(807\) | 1.12280e13 | 0.931908 | ||||||||
\(808\) | 1.04077e13 | 0.859019 | ||||||||
\(809\) | −2.09872e13 | −1.72260 | −0.861301 | − | 0.508094i | \(-0.830350\pi\) | ||||
−0.861301 | + | 0.508094i | \(0.830350\pi\) | |||||||
\(810\) | 2.66001e12 | 0.217120 | ||||||||
\(811\) | 1.43158e12 | 0.116204 | 0.0581022 | − | 0.998311i | \(-0.481495\pi\) | ||||
0.0581022 | + | 0.998311i | \(0.481495\pi\) | |||||||
\(812\) | −1.08599e13 | −0.876649 | ||||||||
\(813\) | −3.91374e12 | −0.314184 | ||||||||
\(814\) | 5.58081e12 | 0.445540 | ||||||||
\(815\) | 1.95919e12 | 0.155549 | ||||||||
\(816\) | 2.78009e12 | 0.219509 | ||||||||
\(817\) | −6.65432e12 | −0.522522 | ||||||||
\(818\) | −3.70783e13 | −2.89554 | ||||||||
\(819\) | 1.69655e12 | 0.131762 | ||||||||
\(820\) | 1.49727e13 | 1.15648 | ||||||||
\(821\) | 1.83664e13 | 1.41085 | 0.705424 | − | 0.708786i | \(-0.250757\pi\) | ||||
0.705424 | + | 0.708786i | \(0.250757\pi\) | |||||||
\(822\) | −3.72885e12 | −0.284873 | ||||||||
\(823\) | 1.70966e13 | 1.29900 | 0.649501 | − | 0.760361i | \(-0.274978\pi\) | ||||
0.649501 | + | 0.760361i | \(0.274978\pi\) | |||||||
\(824\) | −7.85252e12 | −0.593385 | ||||||||
\(825\) | −2.31899e12 | −0.174284 | ||||||||
\(826\) | −3.19696e13 | −2.38961 | ||||||||
\(827\) | −1.72326e12 | −0.128108 | −0.0640541 | − | 0.997946i | \(-0.520403\pi\) | ||||
−0.0640541 | + | 0.997946i | \(0.520403\pi\) | |||||||
\(828\) | 3.25767e13 | 2.40864 | ||||||||
\(829\) | −5.63109e12 | −0.414093 | −0.207046 | − | 0.978331i | \(-0.566385\pi\) | ||||
−0.207046 | + | 0.978331i | \(0.566385\pi\) | |||||||
\(830\) | −1.72124e13 | −1.25890 | ||||||||
\(831\) | −2.36324e12 | −0.171911 | ||||||||
\(832\) | 2.14658e12 | 0.155307 | ||||||||
\(833\) | −4.43162e12 | −0.318904 | ||||||||
\(834\) | −6.91304e12 | −0.494791 | ||||||||
\(835\) | 1.14389e13 | 0.814318 | ||||||||
\(836\) | −5.43081e13 | −3.84536 | ||||||||
\(837\) | 8.37021e12 | 0.589484 | ||||||||
\(838\) | 1.84597e13 | 1.29308 | ||||||||
\(839\) | 4.57522e12 | 0.318775 | 0.159387 | − | 0.987216i | \(-0.449048\pi\) | ||||
0.159387 | + | 0.987216i | \(0.449048\pi\) | |||||||
\(840\) | −1.67841e13 | −1.16317 | ||||||||
\(841\) | −1.28982e13 | −0.889093 | ||||||||
\(842\) | 2.08160e13 | 1.42723 | ||||||||
\(843\) | −1.47590e13 | −1.00654 | ||||||||
\(844\) | 2.38422e13 | 1.61736 | ||||||||
\(845\) | 1.32368e13 | 0.893157 | ||||||||
\(846\) | −8.92820e12 | −0.599235 | ||||||||
\(847\) | 4.73976e13 | 3.16433 | ||||||||
\(848\) | −1.06902e13 | −0.709909 | ||||||||
\(849\) | −1.48856e13 | −0.983288 | ||||||||
\(850\) | −1.81619e12 | −0.119337 | ||||||||
\(851\) | −3.85917e12 | −0.252238 | ||||||||
\(852\) | 2.86609e13 | 1.86342 | ||||||||
\(853\) | 2.11280e13 | 1.36643 | 0.683216 | − | 0.730217i | \(-0.260581\pi\) | ||||
0.683216 | + | 0.730217i | \(0.260581\pi\) | |||||||
\(854\) | 4.70813e13 | 3.02892 | ||||||||
\(855\) | 1.02272e13 | 0.654499 | ||||||||
\(856\) | 9.14351e12 | 0.582078 | ||||||||
\(857\) | −2.25888e13 | −1.43047 | −0.715236 | − | 0.698883i | \(-0.753681\pi\) | ||||
−0.715236 | + | 0.698883i | \(0.753681\pi\) | |||||||
\(858\) | 4.17164e12 | 0.262793 | ||||||||
\(859\) | 4.85641e12 | 0.304331 | 0.152165 | − | 0.988355i | \(-0.451375\pi\) | ||||
0.152165 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(860\) | 1.43074e13 | 0.891903 | ||||||||
\(861\) | 7.79924e12 | 0.483658 | ||||||||
\(862\) | 3.60355e13 | 2.22304 | ||||||||
\(863\) | −1.98231e13 | −1.21653 | −0.608265 | − | 0.793734i | \(-0.708134\pi\) | ||||
−0.608265 | + | 0.793734i | \(0.708134\pi\) | |||||||
\(864\) | 1.16139e12 | 0.0709035 | ||||||||
\(865\) | 6.69747e12 | 0.406760 | ||||||||
\(866\) | −4.22150e13 | −2.55057 | ||||||||
\(867\) | 7.82375e12 | 0.470250 | ||||||||
\(868\) | 2.72563e13 | 1.62978 | ||||||||
\(869\) | 1.48421e13 | 0.882892 | ||||||||
\(870\) | 5.02874e12 | 0.297593 | ||||||||
\(871\) | 4.22029e12 | 0.248463 | ||||||||
\(872\) | 3.01955e13 | 1.76855 | ||||||||
\(873\) | 1.79771e13 | 1.04751 | ||||||||
\(874\) | 5.65389e13 | 3.27752 | ||||||||
\(875\) | 2.45766e13 | 1.41738 | ||||||||
\(876\) | 1.81904e13 | 1.04369 | ||||||||
\(877\) | 2.66447e13 | 1.52094 | 0.760470 | − | 0.649373i | \(-0.224968\pi\) | ||||
0.760470 | + | 0.649373i | \(0.224968\pi\) | |||||||
\(878\) | −1.81756e13 | −1.03220 | ||||||||
\(879\) | −1.29927e13 | −0.734089 | ||||||||
\(880\) | 2.79007e13 | 1.56835 | ||||||||
\(881\) | −1.95120e13 | −1.09121 | −0.545606 | − | 0.838042i | \(-0.683701\pi\) | ||||
−0.545606 | + | 0.838042i | \(0.683701\pi\) | |||||||
\(882\) | 1.62097e13 | 0.901914 | ||||||||
\(883\) | −2.04432e13 | −1.13169 | −0.565843 | − | 0.824513i | \(-0.691449\pi\) | ||||
−0.565843 | + | 0.824513i | \(0.691449\pi\) | |||||||
\(884\) | 2.17012e12 | 0.119522 | ||||||||
\(885\) | 9.83297e12 | 0.538815 | ||||||||
\(886\) | −3.35641e13 | −1.82988 | ||||||||
\(887\) | 1.17863e13 | 0.639327 | 0.319663 | − | 0.947531i | \(-0.396430\pi\) | ||||
0.319663 | + | 0.947531i | \(0.396430\pi\) | |||||||
\(888\) | 2.49298e12 | 0.134543 | ||||||||
\(889\) | −1.87723e13 | −1.00800 | ||||||||
\(890\) | 1.73874e13 | 0.928923 | ||||||||
\(891\) | −4.76663e12 | −0.253374 | ||||||||
\(892\) | −5.42439e13 | −2.86886 | ||||||||
\(893\) | −1.02924e13 | −0.541610 | ||||||||
\(894\) | 1.54187e13 | 0.807291 | ||||||||
\(895\) | 6.12034e12 | 0.318839 | ||||||||
\(896\) | 4.52074e13 | 2.34328 | ||||||||
\(897\) | −2.88472e12 | −0.148778 | ||||||||
\(898\) | −3.55370e13 | −1.82363 | ||||||||
\(899\) | −4.03814e12 | −0.206188 | ||||||||
\(900\) | 4.41254e12 | 0.224180 | ||||||||
\(901\) | 6.21420e12 | 0.314140 | ||||||||
\(902\) | −4.03938e13 | −2.03182 | ||||||||
\(903\) | 7.45269e12 | 0.373008 | ||||||||
\(904\) | −4.09764e13 | −2.04068 | ||||||||
\(905\) | 1.95810e13 | 0.970322 | ||||||||
\(906\) | −5.92784e12 | −0.292294 | ||||||||
\(907\) | 1.15261e13 | 0.565521 | 0.282761 | − | 0.959191i | \(-0.408750\pi\) | ||||
0.282761 | + | 0.959191i | \(0.408750\pi\) | |||||||
\(908\) | 1.61124e13 | 0.786636 | ||||||||
\(909\) | 7.10265e12 | 0.345050 | ||||||||
\(910\) | −6.33086e12 | −0.306039 | ||||||||
\(911\) | −2.35555e13 | −1.13308 | −0.566539 | − | 0.824035i | \(-0.691718\pi\) | ||||
−0.566539 | + | 0.824035i | \(0.691718\pi\) | |||||||
\(912\) | −1.17226e13 | −0.561110 | ||||||||
\(913\) | 3.08440e13 | 1.46910 | ||||||||
\(914\) | −1.93125e13 | −0.915338 | ||||||||
\(915\) | −1.44809e13 | −0.682968 | ||||||||
\(916\) | −7.51044e13 | −3.52481 | ||||||||
\(917\) | 1.20107e13 | 0.560928 | ||||||||
\(918\) | 1.46287e13 | 0.679850 | ||||||||
\(919\) | 2.09257e13 | 0.967744 | 0.483872 | − | 0.875139i | \(-0.339230\pi\) | ||||
0.483872 | + | 0.875139i | \(0.339230\pi\) | |||||||
\(920\) | −6.01116e13 | −2.76639 | ||||||||
\(921\) | 1.96183e13 | 0.898447 | ||||||||
\(922\) | −4.05688e13 | −1.84886 | ||||||||
\(923\) | 5.34573e12 | 0.242437 | ||||||||
\(924\) | 6.08238e13 | 2.74505 | ||||||||
\(925\) | −5.22727e11 | −0.0234767 | ||||||||
\(926\) | 2.00727e13 | 0.897132 | ||||||||
\(927\) | −5.35889e12 | −0.238351 | ||||||||
\(928\) | −5.60305e11 | −0.0248004 | ||||||||
\(929\) | −3.80942e13 | −1.67799 | −0.838993 | − | 0.544143i | \(-0.816855\pi\) | ||||
−0.838993 | + | 0.544143i | \(0.816855\pi\) | |||||||
\(930\) | −1.26211e13 | −0.553255 | ||||||||
\(931\) | 1.86865e13 | 0.815183 | ||||||||
\(932\) | 4.35088e13 | 1.88888 | ||||||||
\(933\) | 4.83578e12 | 0.208929 | ||||||||
\(934\) | −3.17978e13 | −1.36721 | ||||||||
\(935\) | −1.62187e13 | −0.694007 | ||||||||
\(936\) | −3.92509e12 | −0.167151 | ||||||||
\(937\) | −4.31602e13 | −1.82917 | −0.914587 | − | 0.404390i | \(-0.867484\pi\) | ||||
−0.914587 | + | 0.404390i | \(0.867484\pi\) | |||||||
\(938\) | 9.26391e13 | 3.90734 | ||||||||
\(939\) | 8.49962e11 | 0.0356783 | ||||||||
\(940\) | 2.21297e13 | 0.924486 | ||||||||
\(941\) | −4.21804e13 | −1.75371 | −0.876853 | − | 0.480758i | \(-0.840362\pi\) | ||||
−0.876853 | + | 0.480758i | \(0.840362\pi\) | |||||||
\(942\) | 1.14025e11 | 0.00471815 | ||||||||
\(943\) | 2.79326e13 | 1.15029 | ||||||||
\(944\) | 2.37397e13 | 0.972972 | ||||||||
\(945\) | −2.83465e13 | −1.15626 | ||||||||
\(946\) | −3.85989e13 | −1.56698 | ||||||||
\(947\) | 3.96137e13 | 1.60055 | 0.800277 | − | 0.599631i | \(-0.204686\pi\) | ||||
0.800277 | + | 0.599631i | \(0.204686\pi\) | |||||||
\(948\) | 1.34080e13 | 0.539170 | ||||||||
\(949\) | 3.39281e12 | 0.135788 | ||||||||
\(950\) | 7.65821e12 | 0.305050 | ||||||||
\(951\) | −3.47003e11 | −0.0137569 | ||||||||
\(952\) | 2.35554e13 | 0.929445 | ||||||||
\(953\) | −4.14491e13 | −1.62778 | −0.813892 | − | 0.581016i | \(-0.802655\pi\) | ||||
−0.813892 | + | 0.581016i | \(0.802655\pi\) | |||||||
\(954\) | −2.27298e13 | −0.888441 | ||||||||
\(955\) | −2.38688e13 | −0.928573 | ||||||||
\(956\) | −9.54634e13 | −3.69638 | ||||||||
\(957\) | −9.01132e12 | −0.347284 | ||||||||
\(958\) | −6.18130e13 | −2.37102 | ||||||||
\(959\) | −1.01405e13 | −0.387148 | ||||||||
\(960\) | −1.44925e13 | −0.550711 | ||||||||
\(961\) | −1.63047e13 | −0.616676 | ||||||||
\(962\) | 9.40334e11 | 0.0353993 | ||||||||
\(963\) | 6.23993e12 | 0.233809 | ||||||||
\(964\) | 2.21992e13 | 0.827926 | ||||||||
\(965\) | −1.86155e13 | −0.691039 | ||||||||
\(966\) | −6.33222e13 | −2.33969 | ||||||||
\(967\) | −1.93142e13 | −0.710326 | −0.355163 | − | 0.934804i | \(-0.615575\pi\) | ||||
−0.355163 | + | 0.934804i | \(0.615575\pi\) | |||||||
\(968\) | −1.09658e14 | −4.01421 | ||||||||
\(969\) | 6.81437e12 | 0.248295 | ||||||||
\(970\) | −6.70836e13 | −2.43301 | ||||||||
\(971\) | −8.57087e12 | −0.309413 | −0.154706 | − | 0.987960i | \(-0.549443\pi\) | ||||
−0.154706 | + | 0.987960i | \(0.549443\pi\) | |||||||
\(972\) | −5.67209e13 | −2.03819 | ||||||||
\(973\) | −1.87998e13 | −0.672429 | ||||||||
\(974\) | 5.92821e13 | 2.11061 | ||||||||
\(975\) | −3.90737e11 | −0.0138473 | ||||||||
\(976\) | −3.49611e13 | −1.23328 | ||||||||
\(977\) | −1.39653e13 | −0.490373 | −0.245186 | − | 0.969476i | \(-0.578849\pi\) | ||||
−0.245186 | + | 0.969476i | \(0.578849\pi\) | |||||||
\(978\) | −4.77482e12 | −0.166891 | ||||||||
\(979\) | −3.11576e13 | −1.08403 | ||||||||
\(980\) | −4.01777e13 | −1.39145 | ||||||||
\(981\) | 2.06067e13 | 0.710392 | ||||||||
\(982\) | 8.29593e13 | 2.84684 | ||||||||
\(983\) | −1.91478e13 | −0.654074 | −0.327037 | − | 0.945011i | \(-0.606050\pi\) | ||||
−0.327037 | + | 0.945011i | \(0.606050\pi\) | |||||||
\(984\) | −1.80441e13 | −0.613561 | ||||||||
\(985\) | −1.92096e12 | −0.0650213 | ||||||||
\(986\) | −7.05749e12 | −0.237796 | ||||||||
\(987\) | 1.15273e13 | 0.386634 | ||||||||
\(988\) | −9.15061e12 | −0.305523 | ||||||||
\(989\) | 2.66914e13 | 0.887133 | ||||||||
\(990\) | 5.93235e13 | 1.96277 | ||||||||
\(991\) | 3.97256e12 | 0.130840 | 0.0654199 | − | 0.997858i | \(-0.479161\pi\) | ||||
0.0654199 | + | 0.997858i | \(0.479161\pi\) | |||||||
\(992\) | 1.40625e12 | 0.0461064 | ||||||||
\(993\) | 9.22419e12 | 0.301062 | ||||||||
\(994\) | 1.17343e14 | 3.81259 | ||||||||
\(995\) | 1.29198e13 | 0.417881 | ||||||||
\(996\) | 2.78636e13 | 0.897160 | ||||||||
\(997\) | 4.96779e13 | 1.59234 | 0.796169 | − | 0.605074i | \(-0.206857\pi\) | ||||
0.796169 | + | 0.605074i | \(0.206857\pi\) | |||||||
\(998\) | −7.57759e13 | −2.41793 | ||||||||
\(999\) | 4.21035e12 | 0.133744 |
(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 | 197.10.a.b.1.6 | ✓ | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.10.a.b.1.6 | ✓ | 76 | 1.1 | even | 1 | trivial |