Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,12,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(22.2819522362\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 15790 x^{9} + 14666 x^{8} + 87206462 x^{7} - 14008334 x^{6} - 203974096304 x^{5} - 388180519304 x^{4} + 193065378004825 x^{3} + \cdots - 75\!\cdots\!58 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{13}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(81.6399\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 78.6399 | 1.73771 | 0.868856 | − | 0.495065i | \(-0.164856\pi\) | ||||
0.868856 | + | 0.495065i | \(0.164856\pi\) | |||||||
\(3\) | −108.951 | −0.258860 | −0.129430 | − | 0.991589i | \(-0.541315\pi\) | ||||
−0.129430 | + | 0.991589i | \(0.541315\pi\) | |||||||
\(4\) | 4136.23 | 2.01964 | ||||||||
\(5\) | −12464.4 | −1.78377 | −0.891883 | − | 0.452267i | \(-0.850615\pi\) | ||||
−0.891883 | + | 0.452267i | \(0.850615\pi\) | |||||||
\(6\) | −8567.92 | −0.449825 | ||||||||
\(7\) | −230.276 | −0.00517856 | −0.00258928 | − | 0.999997i | \(-0.500824\pi\) | ||||
−0.00258928 | + | 0.999997i | \(0.500824\pi\) | |||||||
\(8\) | 164218. | 1.77184 | ||||||||
\(9\) | −165277. | −0.932991 | ||||||||
\(10\) | −980202. | −3.09967 | ||||||||
\(11\) | −26731.2 | −0.0500448 | −0.0250224 | − | 0.999687i | \(-0.507966\pi\) | ||||
−0.0250224 | + | 0.999687i | \(0.507966\pi\) | |||||||
\(12\) | −450648. | −0.522806 | ||||||||
\(13\) | −1.35410e6 | −1.01149 | −0.505745 | − | 0.862683i | \(-0.668782\pi\) | ||||
−0.505745 | + | 0.862683i | \(0.668782\pi\) | |||||||
\(14\) | −18108.8 | −0.00899884 | ||||||||
\(15\) | 1.35802e6 | 0.461746 | ||||||||
\(16\) | 4.44308e6 | 1.05931 | ||||||||
\(17\) | 3.19725e6 | 0.546144 | 0.273072 | − | 0.961994i | \(-0.411960\pi\) | ||||
0.273072 | + | 0.961994i | \(0.411960\pi\) | |||||||
\(18\) | −1.29973e7 | −1.62127 | ||||||||
\(19\) | −9.37456e6 | −0.868573 | −0.434286 | − | 0.900775i | \(-0.642999\pi\) | ||||
−0.434286 | + | 0.900775i | \(0.642999\pi\) | |||||||
\(20\) | −5.15558e7 | −3.60257 | ||||||||
\(21\) | 25088.8 | 0.00134052 | ||||||||
\(22\) | −2.10214e6 | −0.0869635 | ||||||||
\(23\) | −1.17129e7 | −0.379457 | −0.189728 | − | 0.981837i | \(-0.560761\pi\) | ||||
−0.189728 | + | 0.981837i | \(0.560761\pi\) | |||||||
\(24\) | −1.78918e7 | −0.458661 | ||||||||
\(25\) | 1.06534e8 | 2.18182 | ||||||||
\(26\) | −1.06486e8 | −1.75768 | ||||||||
\(27\) | 3.73075e7 | 0.500375 | ||||||||
\(28\) | −952472. | −0.0104588 | ||||||||
\(29\) | 2.05111e7 | 0.185695 | ||||||||
\(30\) | 1.06794e8 | 0.802382 | ||||||||
\(31\) | 1.69267e8 | 1.06190 | 0.530951 | − | 0.847403i | \(-0.321835\pi\) | ||||
0.530951 | + | 0.847403i | \(0.321835\pi\) | |||||||
\(32\) | 1.30850e7 | 0.0689364 | ||||||||
\(33\) | 2.91240e6 | 0.0129546 | ||||||||
\(34\) | 2.51431e8 | 0.949041 | ||||||||
\(35\) | 2.87026e6 | 0.00923733 | ||||||||
\(36\) | −6.83622e8 | −1.88431 | ||||||||
\(37\) | −6.21479e8 | −1.47339 | −0.736694 | − | 0.676227i | \(-0.763614\pi\) | ||||
−0.736694 | + | 0.676227i | \(0.763614\pi\) | |||||||
\(38\) | −7.37214e8 | −1.50933 | ||||||||
\(39\) | 1.47531e8 | 0.261835 | ||||||||
\(40\) | −2.04688e9 | −3.16055 | ||||||||
\(41\) | −9.80521e8 | −1.32174 | −0.660869 | − | 0.750501i | \(-0.729812\pi\) | ||||
−0.660869 | + | 0.750501i | \(0.729812\pi\) | |||||||
\(42\) | 1.97298e6 | 0.00232944 | ||||||||
\(43\) | 1.55730e9 | 1.61546 | 0.807729 | − | 0.589554i | \(-0.200697\pi\) | ||||
0.807729 | + | 0.589554i | \(0.200697\pi\) | |||||||
\(44\) | −1.10566e8 | −0.101073 | ||||||||
\(45\) | 2.06008e9 | 1.66424 | ||||||||
\(46\) | −9.21103e8 | −0.659386 | ||||||||
\(47\) | 7.66462e8 | 0.487475 | 0.243737 | − | 0.969841i | \(-0.421626\pi\) | ||||
0.243737 | + | 0.969841i | \(0.421626\pi\) | |||||||
\(48\) | −4.84080e8 | −0.274214 | ||||||||
\(49\) | −1.97727e9 | −0.999973 | ||||||||
\(50\) | 8.37783e9 | 3.79137 | ||||||||
\(51\) | −3.48345e8 | −0.141375 | ||||||||
\(52\) | −5.60086e9 | −2.04285 | ||||||||
\(53\) | −1.24890e7 | −0.00410215 | −0.00205108 | − | 0.999998i | \(-0.500653\pi\) | ||||
−0.00205108 | + | 0.999998i | \(0.500653\pi\) | |||||||
\(54\) | 2.93386e9 | 0.869508 | ||||||||
\(55\) | 3.33190e8 | 0.0892682 | ||||||||
\(56\) | −3.78154e7 | −0.00917560 | ||||||||
\(57\) | 1.02137e9 | 0.224839 | ||||||||
\(58\) | 1.61299e9 | 0.322685 | ||||||||
\(59\) | 3.94786e9 | 0.718911 | 0.359456 | − | 0.933162i | \(-0.382962\pi\) | ||||
0.359456 | + | 0.933162i | \(0.382962\pi\) | |||||||
\(60\) | 5.61707e9 | 0.932562 | ||||||||
\(61\) | −6.43946e9 | −0.976193 | −0.488096 | − | 0.872790i | \(-0.662309\pi\) | ||||
−0.488096 | + | 0.872790i | \(0.662309\pi\) | |||||||
\(62\) | 1.33112e10 | 1.84528 | ||||||||
\(63\) | 3.80592e7 | 0.00483155 | ||||||||
\(64\) | −8.07043e9 | −0.939522 | ||||||||
\(65\) | 1.68781e10 | 1.80426 | ||||||||
\(66\) | 2.29031e8 | 0.0225114 | ||||||||
\(67\) | 4.26072e9 | 0.385542 | 0.192771 | − | 0.981244i | \(-0.438253\pi\) | ||||
0.192771 | + | 0.981244i | \(0.438253\pi\) | |||||||
\(68\) | 1.32246e10 | 1.10302 | ||||||||
\(69\) | 1.27614e9 | 0.0982263 | ||||||||
\(70\) | 2.25716e8 | 0.0160518 | ||||||||
\(71\) | 2.70019e10 | 1.77612 | 0.888062 | − | 0.459724i | \(-0.152052\pi\) | ||||
0.888062 | + | 0.459724i | \(0.152052\pi\) | |||||||
\(72\) | −2.71414e10 | −1.65312 | ||||||||
\(73\) | −8.00729e9 | −0.452075 | −0.226037 | − | 0.974119i | \(-0.572577\pi\) | ||||
−0.226037 | + | 0.974119i | \(0.572577\pi\) | |||||||
\(74\) | −4.88730e10 | −2.56032 | ||||||||
\(75\) | −1.16070e10 | −0.564786 | ||||||||
\(76\) | −3.87753e10 | −1.75421 | ||||||||
\(77\) | 6.15555e6 | 0.000259160 0 | ||||||||
\(78\) | 1.16018e10 | 0.454994 | ||||||||
\(79\) | 4.92961e10 | 1.80245 | 0.901225 | − | 0.433351i | \(-0.142669\pi\) | ||||
0.901225 | + | 0.433351i | \(0.142669\pi\) | |||||||
\(80\) | −5.53805e10 | −1.88957 | ||||||||
\(81\) | 2.52136e10 | 0.803464 | ||||||||
\(82\) | −7.71080e10 | −2.29680 | ||||||||
\(83\) | −7.07907e10 | −1.97264 | −0.986318 | − | 0.164856i | \(-0.947284\pi\) | ||||
−0.986318 | + | 0.164856i | \(0.947284\pi\) | |||||||
\(84\) | 1.03773e8 | 0.00270738 | ||||||||
\(85\) | −3.98519e10 | −0.974193 | ||||||||
\(86\) | 1.22466e11 | 2.80720 | ||||||||
\(87\) | −2.23472e9 | −0.0480692 | ||||||||
\(88\) | −4.38975e9 | −0.0886717 | ||||||||
\(89\) | −8.54214e10 | −1.62152 | −0.810758 | − | 0.585381i | \(-0.800945\pi\) | ||||
−0.810758 | + | 0.585381i | \(0.800945\pi\) | |||||||
\(90\) | 1.62004e11 | 2.89196 | ||||||||
\(91\) | 3.11816e8 | 0.00523806 | ||||||||
\(92\) | −4.84473e10 | −0.766367 | ||||||||
\(93\) | −1.84419e10 | −0.274884 | ||||||||
\(94\) | 6.02744e10 | 0.847091 | ||||||||
\(95\) | 1.16849e11 | 1.54933 | ||||||||
\(96\) | −1.42563e9 | −0.0178449 | ||||||||
\(97\) | −4.48857e10 | −0.530718 | −0.265359 | − | 0.964150i | \(-0.585490\pi\) | ||||
−0.265359 | + | 0.964150i | \(0.585490\pi\) | |||||||
\(98\) | −1.55493e11 | −1.73767 | ||||||||
\(99\) | 4.41805e9 | 0.0466914 | ||||||||
\(100\) | 4.40649e11 | 4.40649 | ||||||||
\(101\) | −6.57247e9 | −0.0622245 | −0.0311122 | − | 0.999516i | \(-0.509905\pi\) | ||||
−0.0311122 | + | 0.999516i | \(0.509905\pi\) | |||||||
\(102\) | −2.73938e10 | −0.245669 | ||||||||
\(103\) | −1.46925e11 | −1.24880 | −0.624398 | − | 0.781106i | \(-0.714656\pi\) | ||||
−0.624398 | + | 0.781106i | \(0.714656\pi\) | |||||||
\(104\) | −2.22367e11 | −1.79220 | ||||||||
\(105\) | −3.12718e8 | −0.00239118 | ||||||||
\(106\) | −9.82136e8 | −0.00712836 | ||||||||
\(107\) | −1.16620e11 | −0.803825 | −0.401912 | − | 0.915678i | \(-0.631654\pi\) | ||||
−0.401912 | + | 0.915678i | \(0.631654\pi\) | |||||||
\(108\) | 1.54312e11 | 1.01058 | ||||||||
\(109\) | −2.91271e11 | −1.81322 | −0.906612 | − | 0.421966i | \(-0.861340\pi\) | ||||
−0.906612 | + | 0.421966i | \(0.861340\pi\) | |||||||
\(110\) | 2.62020e10 | 0.155122 | ||||||||
\(111\) | 6.77110e10 | 0.381402 | ||||||||
\(112\) | −1.02313e9 | −0.00548571 | ||||||||
\(113\) | −3.60464e10 | −0.184048 | −0.0920239 | − | 0.995757i | \(-0.529334\pi\) | ||||
−0.0920239 | + | 0.995757i | \(0.529334\pi\) | |||||||
\(114\) | 8.03205e10 | 0.390706 | ||||||||
\(115\) | 1.45995e11 | 0.676862 | ||||||||
\(116\) | 8.48388e10 | 0.375038 | ||||||||
\(117\) | 2.23801e11 | 0.943712 | ||||||||
\(118\) | 3.10459e11 | 1.24926 | ||||||||
\(119\) | −7.36248e8 | −0.00282824 | ||||||||
\(120\) | 2.23011e11 | 0.818143 | ||||||||
\(121\) | −2.84597e11 | −0.997496 | ||||||||
\(122\) | −5.06398e11 | −1.69634 | ||||||||
\(123\) | 1.06829e11 | 0.342146 | ||||||||
\(124\) | 7.00129e11 | 2.14466 | ||||||||
\(125\) | −7.19272e11 | −2.10809 | ||||||||
\(126\) | 2.99297e9 | 0.00839584 | ||||||||
\(127\) | −3.25875e11 | −0.875247 | −0.437624 | − | 0.899158i | \(-0.644180\pi\) | ||||
−0.437624 | + | 0.899158i | \(0.644180\pi\) | |||||||
\(128\) | −6.61456e11 | −1.70155 | ||||||||
\(129\) | −1.69670e11 | −0.418178 | ||||||||
\(130\) | 1.32729e12 | 3.13529 | ||||||||
\(131\) | 1.38770e11 | 0.314271 | 0.157136 | − | 0.987577i | \(-0.449774\pi\) | ||||
0.157136 | + | 0.987577i | \(0.449774\pi\) | |||||||
\(132\) | 1.20464e10 | 0.0261637 | ||||||||
\(133\) | 2.15873e9 | 0.00449795 | ||||||||
\(134\) | 3.35063e11 | 0.669961 | ||||||||
\(135\) | −4.65017e11 | −0.892551 | ||||||||
\(136\) | 5.25046e11 | 0.967683 | ||||||||
\(137\) | 8.88362e11 | 1.57263 | 0.786315 | − | 0.617825i | \(-0.211986\pi\) | ||||
0.786315 | + | 0.617825i | \(0.211986\pi\) | |||||||
\(138\) | 1.00355e11 | 0.170689 | ||||||||
\(139\) | −5.26116e11 | −0.860003 | −0.430001 | − | 0.902828i | \(-0.641487\pi\) | ||||
−0.430001 | + | 0.902828i | \(0.641487\pi\) | |||||||
\(140\) | 1.18720e10 | 0.0186561 | ||||||||
\(141\) | −8.35070e10 | −0.126188 | ||||||||
\(142\) | 2.12342e12 | 3.08639 | ||||||||
\(143\) | 3.61967e10 | 0.0506199 | ||||||||
\(144\) | −7.34337e11 | −0.988330 | ||||||||
\(145\) | −2.55660e11 | −0.331237 | ||||||||
\(146\) | −6.29692e11 | −0.785575 | ||||||||
\(147\) | 2.15427e11 | 0.258854 | ||||||||
\(148\) | −2.57058e12 | −2.97572 | ||||||||
\(149\) | −2.24927e11 | −0.250910 | −0.125455 | − | 0.992099i | \(-0.540039\pi\) | ||||
−0.125455 | + | 0.992099i | \(0.540039\pi\) | |||||||
\(150\) | −9.12775e11 | −0.981436 | ||||||||
\(151\) | 7.38831e11 | 0.765900 | 0.382950 | − | 0.923769i | \(-0.374908\pi\) | ||||
0.382950 | + | 0.923769i | \(0.374908\pi\) | |||||||
\(152\) | −1.53947e12 | −1.53898 | ||||||||
\(153\) | −5.28431e11 | −0.509548 | ||||||||
\(154\) | 4.84072e8 | 0.000450345 0 | ||||||||
\(155\) | −2.10982e12 | −1.89418 | ||||||||
\(156\) | 6.10221e11 | 0.528813 | ||||||||
\(157\) | 1.40898e12 | 1.17884 | 0.589422 | − | 0.807825i | \(-0.299355\pi\) | ||||
0.589422 | + | 0.807825i | \(0.299355\pi\) | |||||||
\(158\) | 3.87664e12 | 3.13214 | ||||||||
\(159\) | 1.36070e9 | 0.00106188 | ||||||||
\(160\) | −1.63097e11 | −0.122966 | ||||||||
\(161\) | 2.69720e9 | 0.00196504 | ||||||||
\(162\) | 1.98279e12 | 1.39619 | ||||||||
\(163\) | −9.72492e11 | −0.661994 | −0.330997 | − | 0.943632i | \(-0.607385\pi\) | ||||
−0.330997 | + | 0.943632i | \(0.607385\pi\) | |||||||
\(164\) | −4.05566e12 | −2.66944 | ||||||||
\(165\) | −3.63015e10 | −0.0231080 | ||||||||
\(166\) | −5.56697e12 | −3.42787 | ||||||||
\(167\) | −3.91628e10 | −0.0233310 | −0.0116655 | − | 0.999932i | \(-0.503713\pi\) | ||||
−0.0116655 | + | 0.999932i | \(0.503713\pi\) | |||||||
\(168\) | 4.12004e9 | 0.00237520 | ||||||||
\(169\) | 4.14236e10 | 0.0231138 | ||||||||
\(170\) | −3.13395e12 | −1.69287 | ||||||||
\(171\) | 1.54940e12 | 0.810371 | ||||||||
\(172\) | 6.44134e12 | 3.26265 | ||||||||
\(173\) | −2.21018e12 | −1.08436 | −0.542181 | − | 0.840262i | \(-0.682401\pi\) | ||||
−0.542181 | + | 0.840262i | \(0.682401\pi\) | |||||||
\(174\) | −1.75738e11 | −0.0835304 | ||||||||
\(175\) | −2.45322e10 | −0.0112987 | ||||||||
\(176\) | −1.18769e11 | −0.0530132 | ||||||||
\(177\) | −4.30124e11 | −0.186098 | ||||||||
\(178\) | −6.71752e12 | −2.81773 | ||||||||
\(179\) | 2.23234e12 | 0.907965 | 0.453983 | − | 0.891010i | \(-0.350003\pi\) | ||||
0.453983 | + | 0.891010i | \(0.350003\pi\) | |||||||
\(180\) | 8.52096e12 | 3.36116 | ||||||||
\(181\) | −7.82120e10 | −0.0299255 | −0.0149627 | − | 0.999888i | \(-0.504763\pi\) | ||||
−0.0149627 | + | 0.999888i | \(0.504763\pi\) | |||||||
\(182\) | 2.45212e10 | 0.00910224 | ||||||||
\(183\) | 7.01588e11 | 0.252698 | ||||||||
\(184\) | −1.92347e12 | −0.672338 | ||||||||
\(185\) | 7.74638e12 | 2.62818 | ||||||||
\(186\) | −1.45027e12 | −0.477670 | ||||||||
\(187\) | −8.54664e10 | −0.0273317 | ||||||||
\(188\) | 3.17026e12 | 0.984525 | ||||||||
\(189\) | −8.59101e9 | −0.00259122 | ||||||||
\(190\) | 9.18896e12 | 2.69229 | ||||||||
\(191\) | 2.06678e12 | 0.588317 | 0.294158 | − | 0.955757i | \(-0.404961\pi\) | ||||
0.294158 | + | 0.955757i | \(0.404961\pi\) | |||||||
\(192\) | 8.79284e11 | 0.243205 | ||||||||
\(193\) | 2.83320e12 | 0.761574 | 0.380787 | − | 0.924663i | \(-0.375653\pi\) | ||||
0.380787 | + | 0.924663i | \(0.375653\pi\) | |||||||
\(194\) | −3.52981e12 | −0.922235 | ||||||||
\(195\) | −1.83889e12 | −0.467052 | ||||||||
\(196\) | −8.17845e12 | −2.01959 | ||||||||
\(197\) | 4.94999e12 | 1.18861 | 0.594305 | − | 0.804239i | \(-0.297427\pi\) | ||||
0.594305 | + | 0.804239i | \(0.297427\pi\) | |||||||
\(198\) | 3.47435e11 | 0.0811362 | ||||||||
\(199\) | −3.92808e12 | −0.892253 | −0.446127 | − | 0.894970i | \(-0.647197\pi\) | ||||
−0.446127 | + | 0.894970i | \(0.647197\pi\) | |||||||
\(200\) | 1.74948e13 | 3.86584 | ||||||||
\(201\) | −4.64211e11 | −0.0998016 | ||||||||
\(202\) | −5.16858e11 | −0.108128 | ||||||||
\(203\) | −4.72322e9 | −0.000961634 0 | ||||||||
\(204\) | −1.44083e12 | −0.285527 | ||||||||
\(205\) | 1.22216e13 | 2.35767 | ||||||||
\(206\) | −1.15542e13 | −2.17005 | ||||||||
\(207\) | 1.93587e12 | 0.354030 | ||||||||
\(208\) | −6.01637e12 | −1.07149 | ||||||||
\(209\) | 2.50594e11 | 0.0434676 | ||||||||
\(210\) | −2.45921e10 | −0.00415518 | ||||||||
\(211\) | −6.85663e12 | −1.12865 | −0.564323 | − | 0.825554i | \(-0.690863\pi\) | ||||
−0.564323 | + | 0.825554i | \(0.690863\pi\) | |||||||
\(212\) | −5.16575e10 | −0.00828488 | ||||||||
\(213\) | −2.94189e12 | −0.459768 | ||||||||
\(214\) | −9.17096e12 | −1.39682 | ||||||||
\(215\) | −1.94109e13 | −2.88160 | ||||||||
\(216\) | 6.12656e12 | 0.886587 | ||||||||
\(217\) | −3.89782e10 | −0.00549911 | ||||||||
\(218\) | −2.29055e13 | −3.15086 | ||||||||
\(219\) | 8.72405e11 | 0.117024 | ||||||||
\(220\) | 1.37815e12 | 0.180290 | ||||||||
\(221\) | −4.32939e12 | −0.552420 | ||||||||
\(222\) | 5.32478e12 | 0.662766 | ||||||||
\(223\) | −4.05692e12 | −0.492629 | −0.246314 | − | 0.969190i | \(-0.579220\pi\) | ||||
−0.246314 | + | 0.969190i | \(0.579220\pi\) | |||||||
\(224\) | −3.01315e9 | −0.000356991 0 | ||||||||
\(225\) | −1.76076e13 | −2.03562 | ||||||||
\(226\) | −2.83469e12 | −0.319822 | ||||||||
\(227\) | 1.11423e13 | 1.22696 | 0.613481 | − | 0.789709i | \(-0.289769\pi\) | ||||
0.613481 | + | 0.789709i | \(0.289769\pi\) | |||||||
\(228\) | 4.22462e12 | 0.454095 | ||||||||
\(229\) | 5.75727e12 | 0.604118 | 0.302059 | − | 0.953289i | \(-0.402326\pi\) | ||||
0.302059 | + | 0.953289i | \(0.402326\pi\) | |||||||
\(230\) | 1.14810e13 | 1.17619 | ||||||||
\(231\) | −6.70656e8 | −6.70863e−5 0 | ||||||||
\(232\) | 3.36830e12 | 0.329023 | ||||||||
\(233\) | 3.46144e12 | 0.330217 | 0.165108 | − | 0.986275i | \(-0.447203\pi\) | ||||
0.165108 | + | 0.986275i | \(0.447203\pi\) | |||||||
\(234\) | 1.75997e13 | 1.63990 | ||||||||
\(235\) | −9.55351e12 | −0.869541 | ||||||||
\(236\) | 1.63292e13 | 1.45194 | ||||||||
\(237\) | −5.37087e12 | −0.466583 | ||||||||
\(238\) | −5.78985e10 | −0.00491466 | ||||||||
\(239\) | 1.86431e13 | 1.54643 | 0.773215 | − | 0.634144i | \(-0.218647\pi\) | ||||
0.773215 | + | 0.634144i | \(0.218647\pi\) | |||||||
\(240\) | 6.03378e12 | 0.489134 | ||||||||
\(241\) | −3.22030e12 | −0.255154 | −0.127577 | − | 0.991829i | \(-0.540720\pi\) | ||||
−0.127577 | + | 0.991829i | \(0.540720\pi\) | |||||||
\(242\) | −2.23807e13 | −1.73336 | ||||||||
\(243\) | −9.35596e12 | −0.708360 | ||||||||
\(244\) | −2.66351e13 | −1.97156 | ||||||||
\(245\) | 2.46456e13 | 1.78372 | ||||||||
\(246\) | 8.40102e12 | 0.594551 | ||||||||
\(247\) | 1.26941e13 | 0.878553 | ||||||||
\(248\) | 2.77967e13 | 1.88152 | ||||||||
\(249\) | 7.71274e12 | 0.510637 | ||||||||
\(250\) | −5.65635e13 | −3.66325 | ||||||||
\(251\) | 1.10256e13 | 0.698547 | 0.349273 | − | 0.937021i | \(-0.386428\pi\) | ||||
0.349273 | + | 0.937021i | \(0.386428\pi\) | |||||||
\(252\) | 1.57421e11 | 0.00975800 | ||||||||
\(253\) | 3.13101e11 | 0.0189899 | ||||||||
\(254\) | −2.56268e13 | −1.52093 | ||||||||
\(255\) | 4.34192e12 | 0.252180 | ||||||||
\(256\) | −3.54885e13 | −2.01729 | ||||||||
\(257\) | −1.84306e13 | −1.02543 | −0.512716 | − | 0.858558i | \(-0.671361\pi\) | ||||
−0.512716 | + | 0.858558i | \(0.671361\pi\) | |||||||
\(258\) | −1.33428e13 | −0.726673 | ||||||||
\(259\) | 1.43111e11 | 0.00763002 | ||||||||
\(260\) | 6.98116e13 | 3.64396 | ||||||||
\(261\) | −3.39001e12 | −0.173252 | ||||||||
\(262\) | 1.09129e13 | 0.546113 | ||||||||
\(263\) | 1.30599e13 | 0.640005 | 0.320003 | − | 0.947417i | \(-0.396316\pi\) | ||||
0.320003 | + | 0.947417i | \(0.396316\pi\) | |||||||
\(264\) | 4.78269e11 | 0.0229536 | ||||||||
\(265\) | 1.55669e11 | 0.00731728 | ||||||||
\(266\) | 1.69762e11 | 0.00781614 | ||||||||
\(267\) | 9.30677e12 | 0.419747 | ||||||||
\(268\) | 1.76233e13 | 0.778657 | ||||||||
\(269\) | −3.11337e13 | −1.34770 | −0.673850 | − | 0.738868i | \(-0.735361\pi\) | ||||
−0.673850 | + | 0.738868i | \(0.735361\pi\) | |||||||
\(270\) | −3.65689e13 | −1.55100 | ||||||||
\(271\) | 2.84357e13 | 1.18177 | 0.590885 | − | 0.806756i | \(-0.298779\pi\) | ||||
0.590885 | + | 0.806756i | \(0.298779\pi\) | |||||||
\(272\) | 1.42056e13 | 0.578538 | ||||||||
\(273\) | −3.39728e10 | −0.00135593 | ||||||||
\(274\) | 6.98607e13 | 2.73278 | ||||||||
\(275\) | −2.84779e12 | −0.109189 | ||||||||
\(276\) | 5.27840e12 | 0.198382 | ||||||||
\(277\) | −2.26144e13 | −0.833193 | −0.416597 | − | 0.909091i | \(-0.636777\pi\) | ||||
−0.416597 | + | 0.909091i | \(0.636777\pi\) | |||||||
\(278\) | −4.13737e13 | −1.49444 | ||||||||
\(279\) | −2.79759e13 | −0.990744 | ||||||||
\(280\) | 4.71347e11 | 0.0163671 | ||||||||
\(281\) | 3.67511e13 | 1.25137 | 0.625684 | − | 0.780076i | \(-0.284820\pi\) | ||||
0.625684 | + | 0.780076i | \(0.284820\pi\) | |||||||
\(282\) | −6.56698e12 | −0.219278 | ||||||||
\(283\) | 1.41159e13 | 0.462255 | 0.231128 | − | 0.972923i | \(-0.425759\pi\) | ||||
0.231128 | + | 0.972923i | \(0.425759\pi\) | |||||||
\(284\) | 1.11686e14 | 3.58713 | ||||||||
\(285\) | −1.27308e13 | −0.401060 | ||||||||
\(286\) | 2.84651e12 | 0.0879628 | ||||||||
\(287\) | 2.25790e11 | 0.00684470 | ||||||||
\(288\) | −2.16264e12 | −0.0643170 | ||||||||
\(289\) | −2.40495e13 | −0.701726 | ||||||||
\(290\) | −2.01051e13 | −0.575594 | ||||||||
\(291\) | 4.89036e12 | 0.137382 | ||||||||
\(292\) | −3.31200e13 | −0.913029 | ||||||||
\(293\) | −3.80422e12 | −0.102918 | −0.0514592 | − | 0.998675i | \(-0.516387\pi\) | ||||
−0.0514592 | + | 0.998675i | \(0.516387\pi\) | |||||||
\(294\) | 1.69411e13 | 0.449813 | ||||||||
\(295\) | −4.92078e13 | −1.28237 | ||||||||
\(296\) | −1.02058e14 | −2.61061 | ||||||||
\(297\) | −9.97276e11 | −0.0250412 | ||||||||
\(298\) | −1.76882e13 | −0.436009 | ||||||||
\(299\) | 1.58605e13 | 0.383817 | ||||||||
\(300\) | −4.80093e13 | −1.14067 | ||||||||
\(301\) | −3.58608e11 | −0.00836574 | ||||||||
\(302\) | 5.81016e13 | 1.33091 | ||||||||
\(303\) | 7.16080e11 | 0.0161075 | ||||||||
\(304\) | −4.16519e13 | −0.920090 | ||||||||
\(305\) | 8.02643e13 | 1.74130 | ||||||||
\(306\) | −4.15557e13 | −0.885447 | ||||||||
\(307\) | 7.16897e13 | 1.50036 | 0.750180 | − | 0.661233i | \(-0.229967\pi\) | ||||
0.750180 | + | 0.661233i | \(0.229967\pi\) | |||||||
\(308\) | 2.54608e10 | 0.000523411 0 | ||||||||
\(309\) | 1.60077e13 | 0.323264 | ||||||||
\(310\) | −1.65916e14 | −3.29154 | ||||||||
\(311\) | 5.89462e13 | 1.14888 | 0.574439 | − | 0.818547i | \(-0.305220\pi\) | ||||
0.574439 | + | 0.818547i | \(0.305220\pi\) | |||||||
\(312\) | 2.42272e13 | 0.463931 | ||||||||
\(313\) | −3.15570e13 | −0.593747 | −0.296874 | − | 0.954917i | \(-0.595944\pi\) | ||||
−0.296874 | + | 0.954917i | \(0.595944\pi\) | |||||||
\(314\) | 1.10802e14 | 2.04849 | ||||||||
\(315\) | −4.74386e11 | −0.00861835 | ||||||||
\(316\) | 2.03900e14 | 3.64030 | ||||||||
\(317\) | 4.00150e13 | 0.702096 | 0.351048 | − | 0.936357i | \(-0.385825\pi\) | ||||
0.351048 | + | 0.936357i | \(0.385825\pi\) | |||||||
\(318\) | 1.07005e11 | 0.00184525 | ||||||||
\(319\) | −5.48288e11 | −0.00929309 | ||||||||
\(320\) | 1.00593e14 | 1.67589 | ||||||||
\(321\) | 1.27059e13 | 0.208078 | ||||||||
\(322\) | 2.12107e11 | 0.00341467 | ||||||||
\(323\) | −2.99728e13 | −0.474366 | ||||||||
\(324\) | 1.04289e14 | 1.62271 | ||||||||
\(325\) | −1.44258e14 | −2.20689 | ||||||||
\(326\) | −7.64766e13 | −1.15035 | ||||||||
\(327\) | 3.17344e13 | 0.469372 | ||||||||
\(328\) | −1.61019e14 | −2.34192 | ||||||||
\(329\) | −1.76497e11 | −0.00252442 | ||||||||
\(330\) | −2.85474e12 | −0.0401551 | ||||||||
\(331\) | −7.96381e13 | −1.10171 | −0.550855 | − | 0.834601i | \(-0.685698\pi\) | ||||
−0.550855 | + | 0.834601i | \(0.685698\pi\) | |||||||
\(332\) | −2.92807e14 | −3.98402 | ||||||||
\(333\) | 1.02716e14 | 1.37466 | ||||||||
\(334\) | −3.07976e12 | −0.0405425 | ||||||||
\(335\) | −5.31075e13 | −0.687717 | ||||||||
\(336\) | 1.11472e11 | 0.00142003 | ||||||||
\(337\) | 1.59262e13 | 0.199594 | 0.0997971 | − | 0.995008i | \(-0.468181\pi\) | ||||
0.0997971 | + | 0.995008i | \(0.468181\pi\) | |||||||
\(338\) | 3.25755e12 | 0.0401651 | ||||||||
\(339\) | 3.92731e12 | 0.0476427 | ||||||||
\(340\) | −1.64837e14 | −1.96752 | ||||||||
\(341\) | −4.52473e12 | −0.0531427 | ||||||||
\(342\) | 1.21844e14 | 1.40819 | ||||||||
\(343\) | 9.10648e11 | 0.0103570 | ||||||||
\(344\) | 2.55736e14 | 2.86234 | ||||||||
\(345\) | −1.59064e13 | −0.175213 | ||||||||
\(346\) | −1.73808e14 | −1.88431 | ||||||||
\(347\) | −1.48839e14 | −1.58820 | −0.794100 | − | 0.607787i | \(-0.792057\pi\) | ||||
−0.794100 | + | 0.607787i | \(0.792057\pi\) | |||||||
\(348\) | −9.24330e12 | −0.0970826 | ||||||||
\(349\) | 1.26082e14 | 1.30351 | 0.651755 | − | 0.758430i | \(-0.274033\pi\) | ||||
0.651755 | + | 0.758430i | \(0.274033\pi\) | |||||||
\(350\) | −1.92921e12 | −0.0196338 | ||||||||
\(351\) | −5.05181e13 | −0.506125 | ||||||||
\(352\) | −3.49778e11 | −0.00344991 | ||||||||
\(353\) | −7.45266e12 | −0.0723687 | −0.0361843 | − | 0.999345i | \(-0.511520\pi\) | ||||
−0.0361843 | + | 0.999345i | \(0.511520\pi\) | |||||||
\(354\) | −3.38249e13 | −0.323384 | ||||||||
\(355\) | −3.36563e14 | −3.16819 | ||||||||
\(356\) | −3.53322e14 | −3.27488 | ||||||||
\(357\) | 8.02153e10 | 0.000732119 0 | ||||||||
\(358\) | 1.75551e14 | 1.57778 | ||||||||
\(359\) | −3.60657e13 | −0.319209 | −0.159604 | − | 0.987181i | \(-0.551022\pi\) | ||||
−0.159604 | + | 0.987181i | \(0.551022\pi\) | |||||||
\(360\) | 3.38302e14 | 2.94877 | ||||||||
\(361\) | −2.86079e13 | −0.245582 | ||||||||
\(362\) | −6.15058e12 | −0.0520019 | ||||||||
\(363\) | 3.10072e13 | 0.258212 | ||||||||
\(364\) | 1.28974e12 | 0.0105790 | ||||||||
\(365\) | 9.98064e13 | 0.806395 | ||||||||
\(366\) | 5.51728e13 | 0.439116 | ||||||||
\(367\) | 4.67133e13 | 0.366250 | 0.183125 | − | 0.983090i | \(-0.441379\pi\) | ||||
0.183125 | + | 0.983090i | \(0.441379\pi\) | |||||||
\(368\) | −5.20415e13 | −0.401964 | ||||||||
\(369\) | 1.62057e14 | 1.23317 | ||||||||
\(370\) | 6.09175e14 | 4.56701 | ||||||||
\(371\) | 2.87592e9 | 2.12432e−5 0 | ||||||||
\(372\) | −7.62800e13 | −0.555168 | ||||||||
\(373\) | −1.54301e14 | −1.10655 | −0.553274 | − | 0.832999i | \(-0.686622\pi\) | ||||
−0.553274 | + | 0.832999i | \(0.686622\pi\) | |||||||
\(374\) | −6.72107e12 | −0.0474946 | ||||||||
\(375\) | 7.83657e13 | 0.545700 | ||||||||
\(376\) | 1.25867e14 | 0.863730 | ||||||||
\(377\) | −2.77741e13 | −0.187829 | ||||||||
\(378\) | −6.75596e11 | −0.00450279 | ||||||||
\(379\) | 8.46962e13 | 0.556350 | 0.278175 | − | 0.960530i | \(-0.410270\pi\) | ||||
0.278175 | + | 0.960530i | \(0.410270\pi\) | |||||||
\(380\) | 4.83313e14 | 3.12909 | ||||||||
\(381\) | 3.55045e13 | 0.226567 | ||||||||
\(382\) | 1.62531e14 | 1.02233 | ||||||||
\(383\) | 3.82978e13 | 0.237455 | 0.118727 | − | 0.992927i | \(-0.462119\pi\) | ||||
0.118727 | + | 0.992927i | \(0.462119\pi\) | |||||||
\(384\) | 7.20665e13 | 0.440465 | ||||||||
\(385\) | −7.67255e10 | −0.000462281 0 | ||||||||
\(386\) | 2.22802e14 | 1.32340 | ||||||||
\(387\) | −2.57385e14 | −1.50721 | ||||||||
\(388\) | −1.85658e14 | −1.07186 | ||||||||
\(389\) | 2.06383e14 | 1.17476 | 0.587381 | − | 0.809310i | \(-0.300159\pi\) | ||||
0.587381 | + | 0.809310i | \(0.300159\pi\) | |||||||
\(390\) | −1.44610e14 | −0.811602 | ||||||||
\(391\) | −3.74491e13 | −0.207238 | ||||||||
\(392\) | −3.24704e14 | −1.77180 | ||||||||
\(393\) | −1.51192e13 | −0.0813525 | ||||||||
\(394\) | 3.89266e14 | 2.06546 | ||||||||
\(395\) | −6.14448e14 | −3.21515 | ||||||||
\(396\) | 1.82741e13 | 0.0942999 | ||||||||
\(397\) | −2.05709e12 | −0.0104690 | −0.00523452 | − | 0.999986i | \(-0.501666\pi\) | ||||
−0.00523452 | + | 0.999986i | \(0.501666\pi\) | |||||||
\(398\) | −3.08903e14 | −1.55048 | ||||||||
\(399\) | −2.35197e11 | −0.00116434 | ||||||||
\(400\) | 4.73340e14 | 2.31123 | ||||||||
\(401\) | −3.68472e14 | −1.77464 | −0.887320 | − | 0.461154i | \(-0.847436\pi\) | ||||
−0.887320 | + | 0.461154i | \(0.847436\pi\) | |||||||
\(402\) | −3.65055e13 | −0.173426 | ||||||||
\(403\) | −2.29205e14 | −1.07410 | ||||||||
\(404\) | −2.71852e13 | −0.125671 | ||||||||
\(405\) | −3.14273e14 | −1.43319 | ||||||||
\(406\) | −3.71433e11 | −0.00167104 | ||||||||
\(407\) | 1.66129e13 | 0.0737354 | ||||||||
\(408\) | −5.72044e13 | −0.250495 | ||||||||
\(409\) | 1.82553e14 | 0.788700 | 0.394350 | − | 0.918960i | \(-0.370970\pi\) | ||||
0.394350 | + | 0.918960i | \(0.370970\pi\) | |||||||
\(410\) | 9.61108e14 | 4.09695 | ||||||||
\(411\) | −9.67882e13 | −0.407092 | ||||||||
\(412\) | −6.07716e14 | −2.52212 | ||||||||
\(413\) | −9.09095e11 | −0.00372292 | ||||||||
\(414\) | 1.52237e14 | 0.615202 | ||||||||
\(415\) | 8.82366e14 | 3.51872 | ||||||||
\(416\) | −1.77184e13 | −0.0697285 | ||||||||
\(417\) | 5.73210e13 | 0.222621 | ||||||||
\(418\) | 1.97066e13 | 0.0755341 | ||||||||
\(419\) | −3.84878e14 | −1.45595 | −0.727974 | − | 0.685604i | \(-0.759538\pi\) | ||||
−0.727974 | + | 0.685604i | \(0.759538\pi\) | |||||||
\(420\) | −1.29347e12 | −0.00482933 | ||||||||
\(421\) | 1.47090e14 | 0.542042 | 0.271021 | − | 0.962573i | \(-0.412639\pi\) | ||||
0.271021 | + | 0.962573i | \(0.412639\pi\) | |||||||
\(422\) | −5.39205e14 | −1.96126 | ||||||||
\(423\) | −1.26678e14 | −0.454810 | ||||||||
\(424\) | −2.05092e12 | −0.00726838 | ||||||||
\(425\) | 3.40616e14 | 1.19159 | ||||||||
\(426\) | −2.31350e14 | −0.798945 | ||||||||
\(427\) | 1.48285e12 | 0.00505527 | ||||||||
\(428\) | −4.82366e14 | −1.62344 | ||||||||
\(429\) | −3.94368e12 | −0.0131035 | ||||||||
\(430\) | −1.52647e15 | −5.00739 | ||||||||
\(431\) | 2.42526e14 | 0.785477 | 0.392738 | − | 0.919650i | \(-0.371528\pi\) | ||||
0.392738 | + | 0.919650i | \(0.371528\pi\) | |||||||
\(432\) | 1.65760e14 | 0.530054 | ||||||||
\(433\) | −7.22429e13 | −0.228093 | −0.114046 | − | 0.993475i | \(-0.536381\pi\) | ||||
−0.114046 | + | 0.993475i | \(0.536381\pi\) | |||||||
\(434\) | −3.06524e12 | −0.00955588 | ||||||||
\(435\) | 2.78545e13 | 0.0857441 | ||||||||
\(436\) | −1.20476e15 | −3.66206 | ||||||||
\(437\) | 1.09804e14 | 0.329586 | ||||||||
\(438\) | 6.86058e13 | 0.203354 | ||||||||
\(439\) | 4.25961e14 | 1.24685 | 0.623426 | − | 0.781882i | \(-0.285740\pi\) | ||||
0.623426 | + | 0.781882i | \(0.285740\pi\) | |||||||
\(440\) | 5.47158e13 | 0.158169 | ||||||||
\(441\) | 3.26797e14 | 0.932966 | ||||||||
\(442\) | −3.40463e14 | −0.959947 | ||||||||
\(443\) | −2.61970e14 | −0.729509 | −0.364754 | − | 0.931104i | \(-0.618847\pi\) | ||||
−0.364754 | + | 0.931104i | \(0.618847\pi\) | |||||||
\(444\) | 2.80068e14 | 0.770295 | ||||||||
\(445\) | 1.06473e15 | 2.89240 | ||||||||
\(446\) | −3.19036e14 | −0.856047 | ||||||||
\(447\) | 2.45061e13 | 0.0649506 | ||||||||
\(448\) | 1.85842e12 | 0.00486537 | ||||||||
\(449\) | 5.02452e14 | 1.29939 | 0.649695 | − | 0.760195i | \(-0.274897\pi\) | ||||
0.649695 | + | 0.760195i | \(0.274897\pi\) | |||||||
\(450\) | −1.38466e15 | −3.53732 | ||||||||
\(451\) | 2.62105e13 | 0.0661462 | ||||||||
\(452\) | −1.49096e14 | −0.371711 | ||||||||
\(453\) | −8.04966e13 | −0.198261 | ||||||||
\(454\) | 8.76226e14 | 2.13211 | ||||||||
\(455\) | −3.88661e12 | −0.00934347 | ||||||||
\(456\) | 1.67727e14 | 0.398380 | ||||||||
\(457\) | −3.12924e14 | −0.734344 | −0.367172 | − | 0.930153i | \(-0.619674\pi\) | ||||
−0.367172 | + | 0.930153i | \(0.619674\pi\) | |||||||
\(458\) | 4.52751e14 | 1.04978 | ||||||||
\(459\) | 1.19281e14 | 0.273277 | ||||||||
\(460\) | 6.03869e14 | 1.36702 | ||||||||
\(461\) | −4.17648e14 | −0.934234 | −0.467117 | − | 0.884196i | \(-0.654707\pi\) | ||||
−0.467117 | + | 0.884196i | \(0.654707\pi\) | |||||||
\(462\) | −5.27403e10 | −0.000116577 0 | ||||||||
\(463\) | −2.26782e14 | −0.495351 | −0.247676 | − | 0.968843i | \(-0.579667\pi\) | ||||
−0.247676 | + | 0.968843i | \(0.579667\pi\) | |||||||
\(464\) | 9.11327e13 | 0.196710 | ||||||||
\(465\) | 2.29868e14 | 0.490329 | ||||||||
\(466\) | 2.72207e14 | 0.573821 | ||||||||
\(467\) | 9.21047e14 | 1.91884 | 0.959421 | − | 0.281979i | \(-0.0909909\pi\) | ||||
0.959421 | + | 0.281979i | \(0.0909909\pi\) | |||||||
\(468\) | 9.25691e14 | 1.90596 | ||||||||
\(469\) | −9.81140e11 | −0.00199655 | ||||||||
\(470\) | −7.51287e14 | −1.51101 | ||||||||
\(471\) | −1.53510e14 | −0.305156 | ||||||||
\(472\) | 6.48309e14 | 1.27380 | ||||||||
\(473\) | −4.16285e13 | −0.0808453 | ||||||||
\(474\) | −4.22365e14 | −0.810787 | ||||||||
\(475\) | −9.98710e14 | −1.89507 | ||||||||
\(476\) | −3.04529e12 | −0.00571203 | ||||||||
\(477\) | 2.06415e12 | 0.00382727 | ||||||||
\(478\) | 1.46609e15 | 2.68725 | ||||||||
\(479\) | 2.79890e14 | 0.507156 | 0.253578 | − | 0.967315i | \(-0.418393\pi\) | ||||
0.253578 | + | 0.967315i | \(0.418393\pi\) | |||||||
\(480\) | 1.77696e13 | 0.0318311 | ||||||||
\(481\) | 8.41544e14 | 1.49032 | ||||||||
\(482\) | −2.53244e14 | −0.443384 | ||||||||
\(483\) | −2.93864e11 | −0.000508671 0 | ||||||||
\(484\) | −1.17716e15 | −2.01458 | ||||||||
\(485\) | 5.59476e14 | 0.946676 | ||||||||
\(486\) | −7.35752e14 | −1.23093 | ||||||||
\(487\) | −3.65476e14 | −0.604574 | −0.302287 | − | 0.953217i | \(-0.597750\pi\) | ||||
−0.302287 | + | 0.953217i | \(0.597750\pi\) | |||||||
\(488\) | −1.05748e15 | −1.72966 | ||||||||
\(489\) | 1.05954e14 | 0.171364 | ||||||||
\(490\) | 1.93813e15 | 3.09959 | ||||||||
\(491\) | 8.51205e14 | 1.34613 | 0.673063 | − | 0.739585i | \(-0.264978\pi\) | ||||
0.673063 | + | 0.739585i | \(0.264978\pi\) | |||||||
\(492\) | 4.41869e14 | 0.691012 | ||||||||
\(493\) | 6.55793e13 | 0.101416 | ||||||||
\(494\) | 9.98261e14 | 1.52667 | ||||||||
\(495\) | −5.50685e13 | −0.0832865 | ||||||||
\(496\) | 7.52069e14 | 1.12489 | ||||||||
\(497\) | −6.21787e12 | −0.00919776 | ||||||||
\(498\) | 6.06529e14 | 0.887340 | ||||||||
\(499\) | −1.13855e15 | −1.64740 | −0.823702 | − | 0.567023i | \(-0.808095\pi\) | ||||
−0.823702 | + | 0.567023i | \(0.808095\pi\) | |||||||
\(500\) | −2.97507e15 | −4.25758 | ||||||||
\(501\) | 4.26684e12 | 0.00603947 | ||||||||
\(502\) | 8.67049e14 | 1.21387 | ||||||||
\(503\) | −1.06306e15 | −1.47208 | −0.736041 | − | 0.676936i | \(-0.763307\pi\) | ||||
−0.736041 | + | 0.676936i | \(0.763307\pi\) | |||||||
\(504\) | 6.25000e12 | 0.00856075 | ||||||||
\(505\) | 8.19222e13 | 0.110994 | ||||||||
\(506\) | 2.46222e13 | 0.0329989 | ||||||||
\(507\) | −4.51316e12 | −0.00598325 | ||||||||
\(508\) | −1.34789e15 | −1.76769 | ||||||||
\(509\) | −5.69558e14 | −0.738908 | −0.369454 | − | 0.929249i | \(-0.620455\pi\) | ||||
−0.369454 | + | 0.929249i | \(0.620455\pi\) | |||||||
\(510\) | 3.41448e14 | 0.438216 | ||||||||
\(511\) | 1.84388e12 | 0.00234109 | ||||||||
\(512\) | −1.43615e15 | −1.80391 | ||||||||
\(513\) | −3.49742e14 | −0.434612 | ||||||||
\(514\) | −1.44938e15 | −1.78190 | ||||||||
\(515\) | 1.83134e15 | 2.22756 | ||||||||
\(516\) | −7.01793e14 | −0.844570 | ||||||||
\(517\) | −2.04885e13 | −0.0243956 | ||||||||
\(518\) | 1.12543e13 | 0.0132588 | ||||||||
\(519\) | 2.40802e14 | 0.280699 | ||||||||
\(520\) | 2.77168e15 | 3.19687 | ||||||||
\(521\) | −5.33971e14 | −0.609411 | −0.304706 | − | 0.952447i | \(-0.598558\pi\) | ||||
−0.304706 | + | 0.952447i | \(0.598558\pi\) | |||||||
\(522\) | −2.66590e14 | −0.301062 | ||||||||
\(523\) | −1.01418e15 | −1.13333 | −0.566663 | − | 0.823949i | \(-0.691766\pi\) | ||||
−0.566663 | + | 0.823949i | \(0.691766\pi\) | |||||||
\(524\) | 5.73986e14 | 0.634716 | ||||||||
\(525\) | 2.67282e12 | 0.00292478 | ||||||||
\(526\) | 1.02703e15 | 1.11214 | ||||||||
\(527\) | 5.41190e14 | 0.579951 | ||||||||
\(528\) | 1.29401e13 | 0.0137230 | ||||||||
\(529\) | −8.15617e14 | −0.856013 | ||||||||
\(530\) | 1.22418e13 | 0.0127153 | ||||||||
\(531\) | −6.52488e14 | −0.670738 | ||||||||
\(532\) | 8.92901e12 | 0.00908425 | ||||||||
\(533\) | 1.32772e15 | 1.33693 | ||||||||
\(534\) | 7.31883e14 | 0.729399 | ||||||||
\(535\) | 1.45360e15 | 1.43383 | ||||||||
\(536\) | 6.99687e14 | 0.683121 | ||||||||
\(537\) | −2.43217e14 | −0.235036 | ||||||||
\(538\) | −2.44835e15 | −2.34191 | ||||||||
\(539\) | 5.28550e13 | 0.0500435 | ||||||||
\(540\) | −1.92342e15 | −1.80263 | ||||||||
\(541\) | −2.04525e15 | −1.89741 | −0.948707 | − | 0.316158i | \(-0.897607\pi\) | ||||
−0.948707 | + | 0.316158i | \(0.897607\pi\) | |||||||
\(542\) | 2.23618e15 | 2.05358 | ||||||||
\(543\) | 8.52130e12 | 0.00774652 | ||||||||
\(544\) | 4.18360e13 | 0.0376492 | ||||||||
\(545\) | 3.63053e15 | 3.23436 | ||||||||
\(546\) | −2.67161e12 | −0.00235621 | ||||||||
\(547\) | −2.04513e15 | −1.78562 | −0.892811 | − | 0.450431i | \(-0.851270\pi\) | ||||
−0.892811 | + | 0.450431i | \(0.851270\pi\) | |||||||
\(548\) | 3.67447e15 | 3.17615 | ||||||||
\(549\) | 1.06429e15 | 0.910779 | ||||||||
\(550\) | −2.23950e14 | −0.189739 | ||||||||
\(551\) | −1.92283e14 | −0.161290 | ||||||||
\(552\) | 2.09565e14 | 0.174042 | ||||||||
\(553\) | −1.13517e13 | −0.00933409 | ||||||||
\(554\) | −1.77839e15 | −1.44785 | ||||||||
\(555\) | −8.43979e14 | −0.680331 | ||||||||
\(556\) | −2.17613e15 | −1.73690 | ||||||||
\(557\) | −3.44808e14 | −0.272504 | −0.136252 | − | 0.990674i | \(-0.543506\pi\) | ||||
−0.136252 | + | 0.990674i | \(0.543506\pi\) | |||||||
\(558\) | −2.20002e15 | −1.72163 | ||||||||
\(559\) | −2.10874e15 | −1.63402 | ||||||||
\(560\) | 1.27528e13 | 0.00978522 | ||||||||
\(561\) | 9.31168e12 | 0.00707510 | ||||||||
\(562\) | 2.89010e15 | 2.17452 | ||||||||
\(563\) | −4.52289e14 | −0.336992 | −0.168496 | − | 0.985702i | \(-0.553891\pi\) | ||||
−0.168496 | + | 0.985702i | \(0.553891\pi\) | |||||||
\(564\) | −3.45404e14 | −0.254855 | ||||||||
\(565\) | 4.49298e14 | 0.328298 | ||||||||
\(566\) | 1.11007e15 | 0.803266 | ||||||||
\(567\) | −5.80606e12 | −0.00416078 | ||||||||
\(568\) | 4.43419e15 | 3.14702 | ||||||||
\(569\) | 3.63369e14 | 0.255405 | 0.127703 | − | 0.991812i | \(-0.459240\pi\) | ||||
0.127703 | + | 0.991812i | \(0.459240\pi\) | |||||||
\(570\) | −1.00115e15 | −0.696927 | ||||||||
\(571\) | −2.17931e15 | −1.50252 | −0.751261 | − | 0.660005i | \(-0.770554\pi\) | ||||
−0.751261 | + | 0.660005i | \(0.770554\pi\) | |||||||
\(572\) | 1.49718e14 | 0.102234 | ||||||||
\(573\) | −2.25179e14 | −0.152292 | ||||||||
\(574\) | 1.77561e13 | 0.0118941 | ||||||||
\(575\) | −1.24783e15 | −0.827906 | ||||||||
\(576\) | 1.33385e15 | 0.876566 | ||||||||
\(577\) | 1.34691e15 | 0.876740 | 0.438370 | − | 0.898795i | \(-0.355556\pi\) | ||||
0.438370 | + | 0.898795i | \(0.355556\pi\) | |||||||
\(578\) | −1.89125e15 | −1.21940 | ||||||||
\(579\) | −3.08681e14 | −0.197141 | ||||||||
\(580\) | −1.05747e15 | −0.668980 | ||||||||
\(581\) | 1.63014e13 | 0.0102154 | ||||||||
\(582\) | 3.84577e14 | 0.238730 | ||||||||
\(583\) | 3.33847e11 | 0.000205292 0 | ||||||||
\(584\) | −1.31494e15 | −0.801006 | ||||||||
\(585\) | −2.78955e15 | −1.68336 | ||||||||
\(586\) | −2.99163e14 | −0.178843 | ||||||||
\(587\) | 2.46936e15 | 1.46243 | 0.731214 | − | 0.682148i | \(-0.238954\pi\) | ||||
0.731214 | + | 0.682148i | \(0.238954\pi\) | |||||||
\(588\) | 8.91054e14 | 0.522792 | ||||||||
\(589\) | −1.58681e15 | −0.922338 | ||||||||
\(590\) | −3.86970e15 | −2.22839 | ||||||||
\(591\) | −5.39308e14 | −0.307684 | ||||||||
\(592\) | −2.76128e15 | −1.56078 | ||||||||
\(593\) | −8.09156e14 | −0.453139 | −0.226569 | − | 0.973995i | \(-0.572751\pi\) | ||||
−0.226569 | + | 0.973995i | \(0.572751\pi\) | |||||||
\(594\) | −7.84257e13 | −0.0435144 | ||||||||
\(595\) | 9.17692e12 | 0.00504491 | ||||||||
\(596\) | −9.30350e14 | −0.506748 | ||||||||
\(597\) | 4.27969e14 | 0.230969 | ||||||||
\(598\) | 1.24726e15 | 0.666963 | ||||||||
\(599\) | 6.45581e14 | 0.342061 | 0.171030 | − | 0.985266i | \(-0.445290\pi\) | ||||
0.171030 | + | 0.985266i | \(0.445290\pi\) | |||||||
\(600\) | −1.90608e15 | −1.00071 | ||||||||
\(601\) | 1.25215e14 | 0.0651397 | 0.0325698 | − | 0.999469i | \(-0.489631\pi\) | ||||
0.0325698 | + | 0.999469i | \(0.489631\pi\) | |||||||
\(602\) | −2.82009e13 | −0.0145372 | ||||||||
\(603\) | −7.04198e14 | −0.359707 | ||||||||
\(604\) | 3.05597e15 | 1.54684 | ||||||||
\(605\) | 3.54734e15 | 1.77930 | ||||||||
\(606\) | 5.63124e13 | 0.0279901 | ||||||||
\(607\) | 6.50089e14 | 0.320210 | 0.160105 | − | 0.987100i | \(-0.448817\pi\) | ||||
0.160105 | + | 0.987100i | \(0.448817\pi\) | |||||||
\(608\) | −1.22666e14 | −0.0598762 | ||||||||
\(609\) | 5.14601e11 | 0.000248929 0 | ||||||||
\(610\) | 6.31197e15 | 3.02587 | ||||||||
\(611\) | −1.03786e15 | −0.493076 | ||||||||
\(612\) | −2.18571e15 | −1.02910 | ||||||||
\(613\) | 2.17950e14 | 0.101701 | 0.0508504 | − | 0.998706i | \(-0.483807\pi\) | ||||
0.0508504 | + | 0.998706i | \(0.483807\pi\) | |||||||
\(614\) | 5.63767e15 | 2.60720 | ||||||||
\(615\) | −1.33156e15 | −0.610308 | ||||||||
\(616\) | 1.01085e12 | 0.000459191 0 | ||||||||
\(617\) | −1.34231e15 | −0.604343 | −0.302172 | − | 0.953254i | \(-0.597712\pi\) | ||||
−0.302172 | + | 0.953254i | \(0.597712\pi\) | |||||||
\(618\) | 1.25884e15 | 0.561739 | ||||||||
\(619\) | −1.52758e15 | −0.675624 | −0.337812 | − | 0.941214i | \(-0.609687\pi\) | ||||
−0.337812 | + | 0.941214i | \(0.609687\pi\) | |||||||
\(620\) | −8.72671e15 | −3.82557 | ||||||||
\(621\) | −4.36980e14 | −0.189871 | ||||||||
\(622\) | 4.63552e15 | 1.99642 | ||||||||
\(623\) | 1.96705e13 | 0.00839711 | ||||||||
\(624\) | 6.55492e14 | 0.277365 | ||||||||
\(625\) | 3.76347e15 | 1.57851 | ||||||||
\(626\) | −2.48164e15 | −1.03176 | ||||||||
\(627\) | −2.73025e13 | −0.0112520 | ||||||||
\(628\) | 5.82786e15 | 2.38084 | ||||||||
\(629\) | −1.98702e15 | −0.804682 | ||||||||
\(630\) | −3.73057e13 | −0.0149762 | ||||||||
\(631\) | −3.33450e15 | −1.32699 | −0.663497 | − | 0.748179i | \(-0.730928\pi\) | ||||
−0.663497 | + | 0.748179i | \(0.730928\pi\) | |||||||
\(632\) | 8.09530e15 | 3.19366 | ||||||||
\(633\) | 7.47039e14 | 0.292162 | ||||||||
\(634\) | 3.14677e15 | 1.22004 | ||||||||
\(635\) | 4.06185e15 | 1.56124 | ||||||||
\(636\) | 5.62815e12 | 0.00214463 | ||||||||
\(637\) | 2.67742e15 | 1.01146 | ||||||||
\(638\) | −4.31173e13 | −0.0161487 | ||||||||
\(639\) | −4.46278e15 | −1.65711 | ||||||||
\(640\) | 8.24467e15 | 3.03517 | ||||||||
\(641\) | 5.75395e14 | 0.210013 | 0.105007 | − | 0.994472i | \(-0.466514\pi\) | ||||
0.105007 | + | 0.994472i | \(0.466514\pi\) | |||||||
\(642\) | 9.99189e14 | 0.361580 | ||||||||
\(643\) | −5.23490e14 | −0.187823 | −0.0939113 | − | 0.995581i | \(-0.529937\pi\) | ||||
−0.0939113 | + | 0.995581i | \(0.529937\pi\) | |||||||
\(644\) | 1.11562e13 | 0.00396867 | ||||||||
\(645\) | 2.11484e15 | 0.745932 | ||||||||
\(646\) | −2.35706e15 | −0.824311 | ||||||||
\(647\) | −4.35727e15 | −1.51092 | −0.755458 | − | 0.655197i | \(-0.772586\pi\) | ||||
−0.755458 | + | 0.655197i | \(0.772586\pi\) | |||||||
\(648\) | 4.14052e15 | 1.42361 | ||||||||
\(649\) | −1.05531e14 | −0.0359778 | ||||||||
\(650\) | −1.13444e16 | −3.83494 | ||||||||
\(651\) | 4.24672e12 | 0.00142350 | ||||||||
\(652\) | −4.02245e15 | −1.33699 | ||||||||
\(653\) | −3.06751e14 | −0.101103 | −0.0505514 | − | 0.998721i | \(-0.516098\pi\) | ||||
−0.0505514 | + | 0.998721i | \(0.516098\pi\) | |||||||
\(654\) | 2.49559e15 | 0.815633 | ||||||||
\(655\) | −1.72970e15 | −0.560586 | ||||||||
\(656\) | −4.35653e15 | −1.40014 | ||||||||
\(657\) | 1.32342e15 | 0.421782 | ||||||||
\(658\) | −1.38797e13 | −0.00438671 | ||||||||
\(659\) | 5.67369e14 | 0.177826 | 0.0889132 | − | 0.996039i | \(-0.471661\pi\) | ||||
0.0889132 | + | 0.996039i | \(0.471661\pi\) | |||||||
\(660\) | −1.50151e14 | −0.0466699 | ||||||||
\(661\) | 5.48457e15 | 1.69057 | 0.845287 | − | 0.534312i | \(-0.179429\pi\) | ||||
0.845287 | + | 0.534312i | \(0.179429\pi\) | |||||||
\(662\) | −6.26273e15 | −1.91445 | ||||||||
\(663\) | 4.71693e14 | 0.143000 | ||||||||
\(664\) | −1.16251e16 | −3.49520 | ||||||||
\(665\) | −2.69074e13 | −0.00802329 | ||||||||
\(666\) | 8.07756e15 | 2.38876 | ||||||||
\(667\) | −2.40246e14 | −0.0704633 | ||||||||
\(668\) | −1.61986e14 | −0.0471202 | ||||||||
\(669\) | 4.42007e14 | 0.127522 | ||||||||
\(670\) | −4.17637e15 | −1.19505 | ||||||||
\(671\) | 1.72135e14 | 0.0488534 | ||||||||
\(672\) | 3.28287e11 | 9.24108e−5 0 | ||||||||
\(673\) | 6.70532e15 | 1.87213 | 0.936066 | − | 0.351825i | \(-0.114439\pi\) | ||||
0.936066 | + | 0.351825i | \(0.114439\pi\) | |||||||
\(674\) | 1.25243e15 | 0.346837 | ||||||||
\(675\) | 3.97452e15 | 1.09173 | ||||||||
\(676\) | 1.71338e14 | 0.0466816 | ||||||||
\(677\) | 6.29656e14 | 0.170163 | 0.0850816 | − | 0.996374i | \(-0.472885\pi\) | ||||
0.0850816 | + | 0.996374i | \(0.472885\pi\) | |||||||
\(678\) | 3.08843e14 | 0.0827893 | ||||||||
\(679\) | 1.03361e13 | 0.00274835 | ||||||||
\(680\) | −6.54440e15 | −1.72612 | ||||||||
\(681\) | −1.21396e15 | −0.317612 | ||||||||
\(682\) | −3.55824e14 | −0.0923467 | ||||||||
\(683\) | 3.10297e15 | 0.798846 | 0.399423 | − | 0.916767i | \(-0.369210\pi\) | ||||
0.399423 | + | 0.916767i | \(0.369210\pi\) | |||||||
\(684\) | 6.40865e15 | 1.63666 | ||||||||
\(685\) | −1.10729e16 | −2.80520 | ||||||||
\(686\) | 7.16132e13 | 0.0179974 | ||||||||
\(687\) | −6.27263e14 | −0.156382 | ||||||||
\(688\) | 6.91921e15 | 1.71128 | ||||||||
\(689\) | 1.69114e13 | 0.00414929 | ||||||||
\(690\) | −1.25087e15 | −0.304469 | ||||||||
\(691\) | 4.40450e15 | 1.06357 | 0.531786 | − | 0.846879i | \(-0.321521\pi\) | ||||
0.531786 | + | 0.846879i | \(0.321521\pi\) | |||||||
\(692\) | −9.14182e15 | −2.19002 | ||||||||
\(693\) | −1.01737e12 | −0.000241794 0 | ||||||||
\(694\) | −1.17047e16 | −2.75983 | ||||||||
\(695\) | 6.55774e15 | 1.53404 | ||||||||
\(696\) | −3.66981e14 | −0.0851711 | ||||||||
\(697\) | −3.13497e15 | −0.721860 | ||||||||
\(698\) | 9.91509e15 | 2.26512 | ||||||||
\(699\) | −3.77128e14 | −0.0854800 | ||||||||
\(700\) | −1.01471e14 | −0.0228193 | ||||||||
\(701\) | 2.42636e15 | 0.541385 | 0.270693 | − | 0.962666i | \(-0.412747\pi\) | ||||
0.270693 | + | 0.962666i | \(0.412747\pi\) | |||||||
\(702\) | −3.97273e15 | −0.879499 | ||||||||
\(703\) | 5.82609e15 | 1.27974 | ||||||||
\(704\) | 2.15733e14 | 0.0470182 | ||||||||
\(705\) | 1.04087e15 | 0.225090 | ||||||||
\(706\) | −5.86076e14 | −0.125756 | ||||||||
\(707\) | 1.51348e12 | 0.000322233 0 | ||||||||
\(708\) | −1.77909e15 | −0.375851 | ||||||||
\(709\) | −6.40975e15 | −1.34365 | −0.671826 | − | 0.740709i | \(-0.734490\pi\) | ||||
−0.671826 | + | 0.740709i | \(0.734490\pi\) | |||||||
\(710\) | −2.64673e16 | −5.50540 | ||||||||
\(711\) | −8.14749e15 | −1.68167 | ||||||||
\(712\) | −1.40277e16 | −2.87308 | ||||||||
\(713\) | −1.98262e15 | −0.402946 | ||||||||
\(714\) | 6.30812e12 | 0.00127221 | ||||||||
\(715\) | −4.51172e14 | −0.0902940 | ||||||||
\(716\) | 9.23348e15 | 1.83377 | ||||||||
\(717\) | −2.03119e15 | −0.400309 | ||||||||
\(718\) | −2.83620e15 | −0.554693 | ||||||||
\(719\) | 8.38597e14 | 0.162759 | 0.0813794 | − | 0.996683i | \(-0.474067\pi\) | ||||
0.0813794 | + | 0.996683i | \(0.474067\pi\) | |||||||
\(720\) | 9.15310e15 | 1.76295 | ||||||||
\(721\) | 3.38333e13 | 0.00646696 | ||||||||
\(722\) | −2.24972e15 | −0.426750 | ||||||||
\(723\) | 3.50856e14 | 0.0660493 | ||||||||
\(724\) | −3.23503e14 | −0.0604388 | ||||||||
\(725\) | 2.18514e15 | 0.405153 | ||||||||
\(726\) | 2.43840e15 | 0.448698 | ||||||||
\(727\) | −8.88989e15 | −1.62352 | −0.811759 | − | 0.583993i | \(-0.801490\pi\) | ||||
−0.811759 | + | 0.583993i | \(0.801490\pi\) | |||||||
\(728\) | 5.12058e13 | 0.00928103 | ||||||||
\(729\) | −3.44716e15 | −0.620098 | ||||||||
\(730\) | 7.84876e15 | 1.40128 | ||||||||
\(731\) | 4.97907e15 | 0.882273 | ||||||||
\(732\) | 2.90193e15 | 0.510359 | ||||||||
\(733\) | 3.14574e15 | 0.549099 | 0.274550 | − | 0.961573i | \(-0.411471\pi\) | ||||
0.274550 | + | 0.961573i | \(0.411471\pi\) | |||||||
\(734\) | 3.67353e15 | 0.636437 | ||||||||
\(735\) | −2.68517e15 | −0.461734 | ||||||||
\(736\) | −1.53263e14 | −0.0261584 | ||||||||
\(737\) | −1.13894e14 | −0.0192944 | ||||||||
\(738\) | 1.27442e16 | 2.14290 | ||||||||
\(739\) | 2.14266e15 | 0.357609 | 0.178804 | − | 0.983885i | \(-0.442777\pi\) | ||||
0.178804 | + | 0.983885i | \(0.442777\pi\) | |||||||
\(740\) | 3.20408e16 | 5.30798 | ||||||||
\(741\) | −1.38304e15 | −0.227423 | ||||||||
\(742\) | 2.26162e11 | 3.69146e−5 0 | ||||||||
\(743\) | 3.63029e15 | 0.588170 | 0.294085 | − | 0.955779i | \(-0.404985\pi\) | ||||
0.294085 | + | 0.955779i | \(0.404985\pi\) | |||||||
\(744\) | −3.02849e15 | −0.487052 | ||||||||
\(745\) | 2.80359e15 | 0.447564 | ||||||||
\(746\) | −1.21342e16 | −1.92286 | ||||||||
\(747\) | 1.17000e16 | 1.84045 | ||||||||
\(748\) | −3.53509e14 | −0.0552003 | ||||||||
\(749\) | 2.68547e13 | 0.00416265 | ||||||||
\(750\) | 6.16267e15 | 0.948269 | ||||||||
\(751\) | −4.09016e15 | −0.624770 | −0.312385 | − | 0.949956i | \(-0.601128\pi\) | ||||
−0.312385 | + | 0.949956i | \(0.601128\pi\) | |||||||
\(752\) | 3.40545e15 | 0.516389 | ||||||||
\(753\) | −1.20125e15 | −0.180826 | ||||||||
\(754\) | −2.18415e15 | −0.326393 | ||||||||
\(755\) | −9.20911e15 | −1.36619 | ||||||||
\(756\) | −3.55344e13 | −0.00523334 | ||||||||
\(757\) | −8.56928e15 | −1.25290 | −0.626451 | − | 0.779461i | \(-0.715493\pi\) | ||||
−0.626451 | + | 0.779461i | \(0.715493\pi\) | |||||||
\(758\) | 6.66050e15 | 0.966777 | ||||||||
\(759\) | −3.41128e13 | −0.00491572 | ||||||||
\(760\) | 1.91886e16 | 2.74517 | ||||||||
\(761\) | 3.52288e15 | 0.500360 | 0.250180 | − | 0.968199i | \(-0.419510\pi\) | ||||
0.250180 | + | 0.968199i | \(0.419510\pi\) | |||||||
\(762\) | 2.79207e15 | 0.393708 | ||||||||
\(763\) | 6.70726e13 | 0.00938988 | ||||||||
\(764\) | 8.54868e15 | 1.18819 | ||||||||
\(765\) | 6.58659e15 | 0.908914 | ||||||||
\(766\) | 3.01174e15 | 0.412628 | ||||||||
\(767\) | −5.34579e15 | −0.727172 | ||||||||
\(768\) | 3.86652e15 | 0.522196 | ||||||||
\(769\) | −3.44010e15 | −0.461292 | −0.230646 | − | 0.973038i | \(-0.574084\pi\) | ||||
−0.230646 | + | 0.973038i | \(0.574084\pi\) | |||||||
\(770\) | −6.03368e12 | −0.000803310 0 | ||||||||
\(771\) | 2.00804e15 | 0.265444 | ||||||||
\(772\) | 1.17188e16 | 1.53811 | ||||||||
\(773\) | −1.09067e16 | −1.42137 | −0.710686 | − | 0.703510i | \(-0.751615\pi\) | ||||
−0.710686 | + | 0.703510i | \(0.751615\pi\) | |||||||
\(774\) | −2.02407e16 | −2.61909 | ||||||||
\(775\) | 1.80328e16 | 2.31688 | ||||||||
\(776\) | −7.37104e15 | −0.940350 | ||||||||
\(777\) | −1.55922e13 | −0.00197511 | ||||||||
\(778\) | 1.62299e16 | 2.04140 | ||||||||
\(779\) | 9.19195e15 | 1.14803 | ||||||||
\(780\) | −7.60607e15 | −0.943278 | ||||||||
\(781\) | −7.21794e14 | −0.0888858 | ||||||||
\(782\) | −2.94500e15 | −0.360120 | ||||||||
\(783\) | 7.65220e14 | 0.0929173 | ||||||||
\(784\) | −8.78519e15 | −1.05928 | ||||||||
\(785\) | −1.75621e16 | −2.10278 | ||||||||
\(786\) | −1.18897e15 | −0.141367 | ||||||||
\(787\) | −8.17365e15 | −0.965061 | −0.482531 | − | 0.875879i | \(-0.660282\pi\) | ||||
−0.482531 | + | 0.875879i | \(0.660282\pi\) | |||||||
\(788\) | 2.04743e16 | 2.40057 | ||||||||
\(789\) | −1.42289e15 | −0.165672 | ||||||||
\(790\) | −4.83201e16 | −5.58700 | ||||||||
\(791\) | 8.30061e12 | 0.000953102 0 | ||||||||
\(792\) | 7.25523e14 | 0.0827299 | ||||||||
\(793\) | 8.71967e15 | 0.987410 | ||||||||
\(794\) | −1.61770e14 | −0.0181922 | ||||||||
\(795\) | −1.69603e13 | −0.00189415 | ||||||||
\(796\) | −1.62474e16 | −1.80203 | ||||||||
\(797\) | 1.09849e16 | 1.20997 | 0.604984 | − | 0.796238i | \(-0.293180\pi\) | ||||
0.604984 | + | 0.796238i | \(0.293180\pi\) | |||||||
\(798\) | −1.84958e13 | −0.00202329 | ||||||||
\(799\) | 2.45057e15 | 0.266232 | ||||||||
\(800\) | 1.39400e15 | 0.150407 | ||||||||
\(801\) | 1.41182e16 | 1.51286 | ||||||||
\(802\) | −2.89766e16 | −3.08381 | ||||||||
\(803\) | 2.14045e14 | 0.0226240 | ||||||||
\(804\) | −1.92008e15 | −0.201564 | ||||||||
\(805\) | −3.36191e13 | −0.00350517 | ||||||||
\(806\) | −1.80246e16 | −1.86648 | ||||||||
\(807\) | 3.39206e15 | 0.348866 | ||||||||
\(808\) | −1.07932e15 | −0.110252 | ||||||||
\(809\) | 7.37110e15 | 0.747851 | 0.373926 | − | 0.927459i | \(-0.378011\pi\) | ||||
0.373926 | + | 0.927459i | \(0.378011\pi\) | |||||||
\(810\) | −2.47144e16 | −2.49047 | ||||||||
\(811\) | −1.58534e16 | −1.58674 | −0.793372 | − | 0.608737i | \(-0.791676\pi\) | ||||
−0.793372 | + | 0.608737i | \(0.791676\pi\) | |||||||
\(812\) | −1.95363e13 | −0.00194216 | ||||||||
\(813\) | −3.09811e15 | −0.305914 | ||||||||
\(814\) | 1.30644e15 | 0.128131 | ||||||||
\(815\) | 1.21216e16 | 1.18084 | ||||||||
\(816\) | −1.54772e15 | −0.149761 | ||||||||
\(817\) | −1.45990e16 | −1.40314 | ||||||||
\(818\) | 1.43560e16 | 1.37053 | ||||||||
\(819\) | −5.15359e13 | −0.00488707 | ||||||||
\(820\) | 5.05515e16 | 4.76165 | ||||||||
\(821\) | −5.60490e15 | −0.524422 | −0.262211 | − | 0.965011i | \(-0.584452\pi\) | ||||
−0.262211 | + | 0.965011i | \(0.584452\pi\) | |||||||
\(822\) | −7.61141e15 | −0.707409 | ||||||||
\(823\) | −8.99004e15 | −0.829971 | −0.414985 | − | 0.909828i | \(-0.636213\pi\) | ||||
−0.414985 | + | 0.909828i | \(0.636213\pi\) | |||||||
\(824\) | −2.41278e16 | −2.21267 | ||||||||
\(825\) | 3.10270e14 | 0.0282646 | ||||||||
\(826\) | −7.14911e13 | −0.00646937 | ||||||||
\(827\) | 1.65577e16 | 1.48840 | 0.744199 | − | 0.667958i | \(-0.232832\pi\) | ||||
0.744199 | + | 0.667958i | \(0.232832\pi\) | |||||||
\(828\) | 8.00721e15 | 0.715014 | ||||||||
\(829\) | −5.71365e14 | −0.0506832 | −0.0253416 | − | 0.999679i | \(-0.508067\pi\) | ||||
−0.0253416 | + | 0.999679i | \(0.508067\pi\) | |||||||
\(830\) | 6.93892e16 | 6.11452 | ||||||||
\(831\) | 2.46387e15 | 0.215681 | ||||||||
\(832\) | 1.09282e16 | 0.950318 | ||||||||
\(833\) | −6.32184e15 | −0.546130 | ||||||||
\(834\) | 4.50772e15 | 0.386851 | ||||||||
\(835\) | 4.88142e14 | 0.0416170 | ||||||||
\(836\) | 1.03651e15 | 0.0877890 | ||||||||
\(837\) | 6.31495e15 | 0.531349 | ||||||||
\(838\) | −3.02668e16 | −2.53002 | ||||||||
\(839\) | 1.42940e16 | 1.18703 | 0.593517 | − | 0.804821i | \(-0.297739\pi\) | ||||
0.593517 | + | 0.804821i | \(0.297739\pi\) | |||||||
\(840\) | −5.13539e13 | −0.00423680 | ||||||||
\(841\) | 4.20707e14 | 0.0344828 | ||||||||
\(842\) | 1.15672e16 | 0.941912 | ||||||||
\(843\) | −4.00408e15 | −0.323930 | ||||||||
\(844\) | −2.83606e16 | −2.27946 | ||||||||
\(845\) | −5.16322e14 | −0.0412296 | ||||||||
\(846\) | −9.96195e15 | −0.790328 | ||||||||
\(847\) | 6.55358e13 | 0.00516559 | ||||||||
\(848\) | −5.54898e13 | −0.00434546 | ||||||||
\(849\) | −1.53794e15 | −0.119660 | ||||||||
\(850\) | 2.67860e16 | 2.07064 | ||||||||
\(851\) | 7.27933e15 | 0.559087 | ||||||||
\(852\) | −1.21683e16 | −0.928567 | ||||||||
\(853\) | 1.62880e16 | 1.23495 | 0.617473 | − | 0.786592i | \(-0.288156\pi\) | ||||
0.617473 | + | 0.786592i | \(0.288156\pi\) | |||||||
\(854\) | 1.16611e14 | 0.00878460 | ||||||||
\(855\) | −1.93123e16 | −1.44551 | ||||||||
\(856\) | −1.91511e16 | −1.42425 | ||||||||
\(857\) | −1.41268e16 | −1.04388 | −0.521940 | − | 0.852982i | \(-0.674791\pi\) | ||||
−0.521940 | + | 0.852982i | \(0.674791\pi\) | |||||||
\(858\) | −3.10131e14 | −0.0227701 | ||||||||
\(859\) | −1.09143e16 | −0.796224 | −0.398112 | − | 0.917337i | \(-0.630335\pi\) | ||||
−0.398112 | + | 0.917337i | \(0.630335\pi\) | |||||||
\(860\) | −8.02877e16 | −5.81980 | ||||||||
\(861\) | −2.46001e13 | −0.00177182 | ||||||||
\(862\) | 1.90722e16 | 1.36493 | ||||||||
\(863\) | 6.50838e15 | 0.462822 | 0.231411 | − | 0.972856i | \(-0.425666\pi\) | ||||
0.231411 | + | 0.972856i | \(0.425666\pi\) | |||||||
\(864\) | 4.88168e14 | 0.0344940 | ||||||||
\(865\) | 2.75487e16 | 1.93425 | ||||||||
\(866\) | −5.68117e15 | −0.396359 | ||||||||
\(867\) | 2.62022e15 | 0.181649 | ||||||||
\(868\) | −1.61223e14 | −0.0111062 | ||||||||
\(869\) | −1.31774e15 | −0.0902033 | ||||||||
\(870\) | 2.19047e15 | 0.148999 | ||||||||
\(871\) | −5.76944e15 | −0.389972 | ||||||||
\(872\) | −4.78319e16 | −3.21275 | ||||||||
\(873\) | 7.41856e15 | 0.495155 | ||||||||
\(874\) | 8.63493e15 | 0.572725 | ||||||||
\(875\) | 1.65631e14 | 0.0109168 | ||||||||
\(876\) | 3.60847e15 | 0.236347 | ||||||||
\(877\) | 5.86025e15 | 0.381433 | 0.190716 | − | 0.981645i | \(-0.438919\pi\) | ||||
0.190716 | + | 0.981645i | \(0.438919\pi\) | |||||||
\(878\) | 3.34975e16 | 2.16667 | ||||||||
\(879\) | 4.14475e14 | 0.0266415 | ||||||||
\(880\) | 1.48039e15 | 0.0945630 | ||||||||
\(881\) | −1.13320e16 | −0.719346 | −0.359673 | − | 0.933078i | \(-0.617112\pi\) | ||||
−0.359673 | + | 0.933078i | \(0.617112\pi\) | |||||||
\(882\) | 2.56993e16 | 1.62123 | ||||||||
\(883\) | 4.59592e15 | 0.288130 | 0.144065 | − | 0.989568i | \(-0.453983\pi\) | ||||
0.144065 | + | 0.989568i | \(0.453983\pi\) | |||||||
\(884\) | −1.79074e16 | −1.11569 | ||||||||
\(885\) | 5.36126e15 | 0.331955 | ||||||||
\(886\) | −2.06013e16 | −1.26768 | ||||||||
\(887\) | 1.85397e16 | 1.13376 | 0.566881 | − | 0.823800i | \(-0.308150\pi\) | ||||
0.566881 | + | 0.823800i | \(0.308150\pi\) | |||||||
\(888\) | 1.11194e16 | 0.675784 | ||||||||
\(889\) | 7.50411e13 | 0.00453252 | ||||||||
\(890\) | 8.37302e16 | 5.02617 | ||||||||
\(891\) | −6.73989e14 | −0.0402092 | ||||||||
\(892\) | −1.67804e16 | −0.994934 | ||||||||
\(893\) | −7.18524e15 | −0.423407 | ||||||||
\(894\) | 1.92716e15 | 0.112865 | ||||||||
\(895\) | −2.78249e16 | −1.61960 | ||||||||
\(896\) | 1.52317e14 | 0.00881159 | ||||||||
\(897\) | −1.72802e15 | −0.0993550 | ||||||||
\(898\) | 3.95127e16 | 2.25796 | ||||||||
\(899\) | 3.47187e15 | 0.197190 | ||||||||
\(900\) | −7.28290e16 | −4.11122 | ||||||||
\(901\) | −3.99306e13 | −0.00224037 | ||||||||
\(902\) | 2.06119e15 | 0.114943 | ||||||||
\(903\) | 3.90708e13 | 0.00216556 | ||||||||
\(904\) | −5.91947e15 | −0.326104 | ||||||||
\(905\) | 9.74868e14 | 0.0533800 | ||||||||
\(906\) | −6.33024e15 | −0.344521 | ||||||||
\(907\) | 1.52365e16 | 0.824226 | 0.412113 | − | 0.911133i | \(-0.364791\pi\) | ||||
0.412113 | + | 0.911133i | \(0.364791\pi\) | |||||||
\(908\) | 4.60869e16 | 2.47802 | ||||||||
\(909\) | 1.08628e15 | 0.0580549 | ||||||||
\(910\) | −3.05642e14 | −0.0162363 | ||||||||
\(911\) | −2.85826e16 | −1.50921 | −0.754607 | − | 0.656177i | \(-0.772172\pi\) | ||||
−0.754607 | + | 0.656177i | \(0.772172\pi\) | |||||||
\(912\) | 4.53804e15 | 0.238175 | ||||||||
\(913\) | 1.89232e15 | 0.0987202 | ||||||||
\(914\) | −2.46083e16 | −1.27608 | ||||||||
\(915\) | −8.74490e15 | −0.450753 | ||||||||
\(916\) | 2.38134e16 | 1.22010 | ||||||||
\(917\) | −3.19554e13 | −0.00162747 | ||||||||
\(918\) | 9.38027e15 | 0.474877 | ||||||||
\(919\) | 3.83197e15 | 0.192836 | 0.0964178 | − | 0.995341i | \(-0.469262\pi\) | ||||
0.0964178 | + | 0.995341i | \(0.469262\pi\) | |||||||
\(920\) | 2.39750e16 | 1.19929 | ||||||||
\(921\) | −7.81069e15 | −0.388384 | ||||||||
\(922\) | −3.28438e16 | −1.62343 | ||||||||
\(923\) | −3.65632e16 | −1.79653 | ||||||||
\(924\) | −2.77398e12 | −0.000135490 0 | ||||||||
\(925\) | −6.62087e16 | −3.21466 | ||||||||
\(926\) | −1.78341e16 | −0.860778 | ||||||||
\(927\) | 2.42833e16 | 1.16512 | ||||||||
\(928\) | 2.68388e14 | 0.0128012 | ||||||||
\(929\) | 1.12285e15 | 0.0532396 | 0.0266198 | − | 0.999646i | \(-0.491526\pi\) | ||||
0.0266198 | + | 0.999646i | \(0.491526\pi\) | |||||||
\(930\) | 1.80768e16 | 0.852050 | ||||||||
\(931\) | 1.85361e16 | 0.868549 | ||||||||
\(932\) | 1.43173e16 | 0.666920 | ||||||||
\(933\) | −6.42227e15 | −0.297399 | ||||||||
\(934\) | 7.24310e16 | 3.33439 | ||||||||
\(935\) | 1.06529e15 | 0.0487533 | ||||||||
\(936\) | 3.67521e16 | 1.67211 | ||||||||
\(937\) | 2.64634e16 | 1.19696 | 0.598478 | − | 0.801139i | \(-0.295772\pi\) | ||||
0.598478 | + | 0.801139i | \(0.295772\pi\) | |||||||
\(938\) | −7.71567e13 | −0.00346943 | ||||||||
\(939\) | 3.43818e15 | 0.153698 | ||||||||
\(940\) | −3.95155e16 | −1.75616 | ||||||||
\(941\) | −5.56710e15 | −0.245972 | −0.122986 | − | 0.992408i | \(-0.539247\pi\) | ||||
−0.122986 | + | 0.992408i | \(0.539247\pi\) | |||||||
\(942\) | −1.20720e16 | −0.530274 | ||||||||
\(943\) | 1.14848e16 | 0.501543 | ||||||||
\(944\) | 1.75407e16 | 0.761552 | ||||||||
\(945\) | 1.07082e14 | 0.00462213 | ||||||||
\(946\) | −3.27366e15 | −0.140486 | ||||||||
\(947\) | −4.76013e15 | −0.203093 | −0.101546 | − | 0.994831i | \(-0.532379\pi\) | ||||
−0.101546 | + | 0.994831i | \(0.532379\pi\) | |||||||
\(948\) | −2.22152e16 | −0.942331 | ||||||||
\(949\) | 1.08427e16 | 0.457269 | ||||||||
\(950\) | −7.85384e16 | −3.29308 | ||||||||
\(951\) | −4.35969e15 | −0.181745 | ||||||||
\(952\) | −1.20905e14 | −0.00501120 | ||||||||
\(953\) | −2.30580e16 | −0.950189 | −0.475095 | − | 0.879935i | \(-0.657586\pi\) | ||||
−0.475095 | + | 0.879935i | \(0.657586\pi\) | |||||||
\(954\) | 1.62324e14 | 0.00665070 | ||||||||
\(955\) | −2.57613e16 | −1.04942 | ||||||||
\(956\) | 7.71122e16 | 3.12323 | ||||||||
\(957\) | 5.97368e13 | 0.00240561 | ||||||||
\(958\) | 2.20105e16 | 0.881291 | ||||||||
\(959\) | −2.04568e14 | −0.00814396 | ||||||||
\(960\) | −1.09598e16 | −0.433821 | ||||||||
\(961\) | 3.24299e15 | 0.127634 | ||||||||
\(962\) | 6.61789e16 | 2.58974 | ||||||||
\(963\) | 1.92745e16 | 0.749962 | ||||||||
\(964\) | −1.33199e16 | −0.515320 | ||||||||
\(965\) | −3.53142e16 | −1.35847 | ||||||||
\(966\) | −2.31094e13 | −0.000883923 0 | ||||||||
\(967\) | 4.58017e16 | 1.74195 | 0.870975 | − | 0.491327i | \(-0.163488\pi\) | ||||
0.870975 | + | 0.491327i | \(0.163488\pi\) | |||||||
\(968\) | −4.67360e16 | −1.76741 | ||||||||
\(969\) | 3.26558e15 | 0.122795 | ||||||||
\(970\) | 4.39971e16 | 1.64505 | ||||||||
\(971\) | 3.23841e16 | 1.20400 | 0.601999 | − | 0.798497i | \(-0.294371\pi\) | ||||
0.601999 | + | 0.798497i | \(0.294371\pi\) | |||||||
\(972\) | −3.86984e16 | −1.43063 | ||||||||
\(973\) | 1.21152e14 | 0.00445357 | ||||||||
\(974\) | −2.87410e16 | −1.05058 | ||||||||
\(975\) | 1.57171e16 | 0.571276 | ||||||||
\(976\) | −2.86111e16 | −1.03409 | ||||||||
\(977\) | −1.53051e16 | −0.550069 | −0.275035 | − | 0.961434i | \(-0.588689\pi\) | ||||
−0.275035 | + | 0.961434i | \(0.588689\pi\) | |||||||
\(978\) | 8.33223e15 | 0.297781 | ||||||||
\(979\) | 2.28342e15 | 0.0811485 | ||||||||
\(980\) | 1.01940e17 | 3.60247 | ||||||||
\(981\) | 4.81403e16 | 1.69172 | ||||||||
\(982\) | 6.69386e16 | 2.33918 | ||||||||
\(983\) | −3.08928e16 | −1.07353 | −0.536764 | − | 0.843732i | \(-0.680354\pi\) | ||||
−0.536764 | + | 0.843732i | \(0.680354\pi\) | |||||||
\(984\) | 1.75433e16 | 0.606229 | ||||||||
\(985\) | −6.16988e16 | −2.12020 | ||||||||
\(986\) | 5.15714e15 | 0.176233 | ||||||||
\(987\) | 1.92296e13 | 0.000653471 0 | ||||||||
\(988\) | 5.25056e16 | 1.77436 | ||||||||
\(989\) | −1.82405e16 | −0.612996 | ||||||||
\(990\) | −4.33058e15 | −0.144728 | ||||||||
\(991\) | −1.59520e16 | −0.530163 | −0.265082 | − | 0.964226i | \(-0.585399\pi\) | ||||
−0.265082 | + | 0.964226i | \(0.585399\pi\) | |||||||
\(992\) | 2.21486e15 | 0.0732036 | ||||||||
\(993\) | 8.67668e15 | 0.285189 | ||||||||
\(994\) | −4.88973e14 | −0.0159830 | ||||||||
\(995\) | 4.89613e16 | 1.59157 | ||||||||
\(996\) | 3.19017e16 | 1.03130 | ||||||||
\(997\) | −1.48585e16 | −0.477697 | −0.238848 | − | 0.971057i | \(-0.576770\pi\) | ||||
−0.238848 | + | 0.971057i | \(0.576770\pi\) | |||||||
\(998\) | −8.95356e16 | −2.86271 | ||||||||
\(999\) | −2.31858e16 | −0.737246 |
(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 | 29.12.a.a.1.11 | ✓ | 11 | |
3.2 | odd | 2 | 261.12.a.a.1.1 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.12.a.a.1.11 | ✓ | 11 | 1.1 | even | 1 | trivial | |
261.12.a.a.1.1 | 11 | 3.2 | odd | 2 |