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 | 1.10 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −36.2963 | −1.60408 | −0.802042 | − | 0.597268i | \(-0.796253\pi\) | ||||
−0.802042 | + | 0.597268i | \(0.796253\pi\) | |||||||
\(3\) | −223.000 | −1.58950 | −0.794749 | − | 0.606938i | \(-0.792397\pi\) | ||||
−0.794749 | + | 0.606938i | \(0.792397\pi\) | |||||||
\(4\) | 805.418 | 1.57308 | ||||||||
\(5\) | 837.898 | 0.599551 | 0.299775 | − | 0.954010i | \(-0.403088\pi\) | ||||
0.299775 | + | 0.954010i | \(0.403088\pi\) | |||||||
\(6\) | 8094.08 | 2.54969 | ||||||||
\(7\) | −7154.81 | −1.12631 | −0.563154 | − | 0.826352i | \(-0.690412\pi\) | ||||
−0.563154 | + | 0.826352i | \(0.690412\pi\) | |||||||
\(8\) | −10650.0 | −0.919272 | ||||||||
\(9\) | 30046.2 | 1.52650 | ||||||||
\(10\) | −30412.5 | −0.961729 | ||||||||
\(11\) | −48642.2 | −1.00172 | −0.500859 | − | 0.865529i | \(-0.666983\pi\) | ||||
−0.500859 | + | 0.865529i | \(0.666983\pi\) | |||||||
\(12\) | −179609. | −2.50041 | ||||||||
\(13\) | −165417. | −1.60633 | −0.803164 | − | 0.595758i | \(-0.796852\pi\) | ||||
−0.803164 | + | 0.595758i | \(0.796852\pi\) | |||||||
\(14\) | 259693. | 1.80669 | ||||||||
\(15\) | −186851. | −0.952985 | ||||||||
\(16\) | −25819.7 | −0.0984943 | ||||||||
\(17\) | 237529. | 0.689759 | 0.344879 | − | 0.938647i | \(-0.387920\pi\) | ||||
0.344879 | + | 0.938647i | \(0.387920\pi\) | |||||||
\(18\) | −1.09056e6 | −2.44864 | ||||||||
\(19\) | 247911. | 0.436420 | 0.218210 | − | 0.975902i | \(-0.429978\pi\) | ||||
0.218210 | + | 0.975902i | \(0.429978\pi\) | |||||||
\(20\) | 674858. | 0.943143 | ||||||||
\(21\) | 1.59552e6 | 1.79026 | ||||||||
\(22\) | 1.76553e6 | 1.60684 | ||||||||
\(23\) | 2.19717e6 | 1.63715 | 0.818574 | − | 0.574402i | \(-0.194765\pi\) | ||||
0.818574 | + | 0.574402i | \(0.194765\pi\) | |||||||
\(24\) | 2.37495e6 | 1.46118 | ||||||||
\(25\) | −1.25105e6 | −0.640539 | ||||||||
\(26\) | 6.00401e6 | 2.57668 | ||||||||
\(27\) | −2.31099e6 | −0.836876 | ||||||||
\(28\) | −5.76261e6 | −1.77177 | ||||||||
\(29\) | −3.47504e6 | −0.912365 | −0.456182 | − | 0.889886i | \(-0.650784\pi\) | ||||
−0.456182 | + | 0.889886i | \(0.650784\pi\) | |||||||
\(30\) | 6.78201e6 | 1.52867 | ||||||||
\(31\) | −8.53092e6 | −1.65908 | −0.829541 | − | 0.558445i | \(-0.811398\pi\) | ||||
−0.829541 | + | 0.558445i | \(0.811398\pi\) | |||||||
\(32\) | 6.38995e6 | 1.07726 | ||||||||
\(33\) | 1.08472e7 | 1.59223 | ||||||||
\(34\) | −8.62143e6 | −1.10643 | ||||||||
\(35\) | −5.99500e6 | −0.675278 | ||||||||
\(36\) | 2.41997e7 | 2.40132 | ||||||||
\(37\) | 9.70151e6 | 0.851004 | 0.425502 | − | 0.904957i | \(-0.360098\pi\) | ||||
0.425502 | + | 0.904957i | \(0.360098\pi\) | |||||||
\(38\) | −8.99823e6 | −0.700053 | ||||||||
\(39\) | 3.68880e7 | 2.55325 | ||||||||
\(40\) | −8.92359e6 | −0.551150 | ||||||||
\(41\) | −4.25913e6 | −0.235393 | −0.117697 | − | 0.993050i | \(-0.537551\pi\) | ||||
−0.117697 | + | 0.993050i | \(0.537551\pi\) | |||||||
\(42\) | −5.79116e7 | −2.87173 | ||||||||
\(43\) | 1.45669e6 | 0.0649767 | 0.0324883 | − | 0.999472i | \(-0.489657\pi\) | ||||
0.0324883 | + | 0.999472i | \(0.489657\pi\) | |||||||
\(44\) | −3.91773e7 | −1.57579 | ||||||||
\(45\) | 2.51756e7 | 0.915216 | ||||||||
\(46\) | −7.97489e7 | −2.62612 | ||||||||
\(47\) | −2.59145e7 | −0.774646 | −0.387323 | − | 0.921944i | \(-0.626600\pi\) | ||||
−0.387323 | + | 0.921944i | \(0.626600\pi\) | |||||||
\(48\) | 5.75780e6 | 0.156556 | ||||||||
\(49\) | 1.08377e7 | 0.268567 | ||||||||
\(50\) | 4.54085e7 | 1.02748 | ||||||||
\(51\) | −5.29691e7 | −1.09637 | ||||||||
\(52\) | −1.33230e8 | −2.52689 | ||||||||
\(53\) | −7.22332e7 | −1.25746 | −0.628732 | − | 0.777622i | \(-0.716426\pi\) | ||||
−0.628732 | + | 0.777622i | \(0.716426\pi\) | |||||||
\(54\) | 8.38802e7 | 1.34242 | ||||||||
\(55\) | −4.07571e7 | −0.600581 | ||||||||
\(56\) | 7.61986e7 | 1.03538 | ||||||||
\(57\) | −5.52842e7 | −0.693688 | ||||||||
\(58\) | 1.26131e8 | 1.46351 | ||||||||
\(59\) | 8.95363e7 | 0.961978 | 0.480989 | − | 0.876727i | \(-0.340278\pi\) | ||||
0.480989 | + | 0.876727i | \(0.340278\pi\) | |||||||
\(60\) | −1.50494e8 | −1.49912 | ||||||||
\(61\) | −1.82830e8 | −1.69068 | −0.845342 | − | 0.534226i | \(-0.820603\pi\) | ||||
−0.845342 | + | 0.534226i | \(0.820603\pi\) | |||||||
\(62\) | 3.09640e8 | 2.66131 | ||||||||
\(63\) | −2.14975e8 | −1.71931 | ||||||||
\(64\) | −2.18712e8 | −1.62953 | ||||||||
\(65\) | −1.38602e8 | −0.963075 | ||||||||
\(66\) | −3.93713e8 | −2.55407 | ||||||||
\(67\) | −1.41642e8 | −0.858727 | −0.429363 | − | 0.903132i | \(-0.641262\pi\) | ||||
−0.429363 | + | 0.903132i | \(0.641262\pi\) | |||||||
\(68\) | 1.91310e8 | 1.08505 | ||||||||
\(69\) | −4.89969e8 | −2.60224 | ||||||||
\(70\) | 2.17596e8 | 1.08320 | ||||||||
\(71\) | 1.72970e8 | 0.807806 | 0.403903 | − | 0.914802i | \(-0.367653\pi\) | ||||
0.403903 | + | 0.914802i | \(0.367653\pi\) | |||||||
\(72\) | −3.19991e8 | −1.40327 | ||||||||
\(73\) | −3.77861e8 | −1.55732 | −0.778662 | − | 0.627444i | \(-0.784101\pi\) | ||||
−0.778662 | + | 0.627444i | \(0.784101\pi\) | |||||||
\(74\) | −3.52129e8 | −1.36508 | ||||||||
\(75\) | 2.78985e8 | 1.01814 | ||||||||
\(76\) | 1.99672e8 | 0.686524 | ||||||||
\(77\) | 3.48025e8 | 1.12824 | ||||||||
\(78\) | −1.33890e9 | −4.09563 | ||||||||
\(79\) | −5.40375e8 | −1.56089 | −0.780447 | − | 0.625222i | \(-0.785008\pi\) | ||||
−0.780447 | + | 0.625222i | \(0.785008\pi\) | |||||||
\(80\) | −2.16343e7 | −0.0590523 | ||||||||
\(81\) | −7.60473e7 | −0.196291 | ||||||||
\(82\) | 1.54591e8 | 0.377590 | ||||||||
\(83\) | 3.32445e8 | 0.768897 | 0.384448 | − | 0.923146i | \(-0.374392\pi\) | ||||
0.384448 | + | 0.923146i | \(0.374392\pi\) | |||||||
\(84\) | 1.28506e9 | 2.81623 | ||||||||
\(85\) | 1.99025e8 | 0.413545 | ||||||||
\(86\) | −5.28722e7 | −0.104228 | ||||||||
\(87\) | 7.74935e8 | 1.45020 | ||||||||
\(88\) | 5.18038e8 | 0.920852 | ||||||||
\(89\) | −4.21712e8 | −0.712460 | −0.356230 | − | 0.934398i | \(-0.615938\pi\) | ||||
−0.356230 | + | 0.934398i | \(0.615938\pi\) | |||||||
\(90\) | −9.13780e8 | −1.46808 | ||||||||
\(91\) | 1.18352e9 | 1.80922 | ||||||||
\(92\) | 1.76964e9 | 2.57537 | ||||||||
\(93\) | 1.90240e9 | 2.63711 | ||||||||
\(94\) | 9.40601e8 | 1.24260 | ||||||||
\(95\) | 2.07724e8 | 0.261656 | ||||||||
\(96\) | −1.42496e9 | −1.71231 | ||||||||
\(97\) | −4.05306e8 | −0.464847 | −0.232424 | − | 0.972615i | \(-0.574666\pi\) | ||||
−0.232424 | + | 0.972615i | \(0.574666\pi\) | |||||||
\(98\) | −3.93367e8 | −0.430805 | ||||||||
\(99\) | −1.46151e9 | −1.52913 | ||||||||
\(100\) | −1.00762e9 | −1.00762 | ||||||||
\(101\) | −1.51903e9 | −1.45252 | −0.726259 | − | 0.687421i | \(-0.758743\pi\) | ||||
−0.726259 | + | 0.687421i | \(0.758743\pi\) | |||||||
\(102\) | 1.92258e9 | 1.75867 | ||||||||
\(103\) | 5.44230e7 | 0.0476448 | 0.0238224 | − | 0.999716i | \(-0.492416\pi\) | ||||
0.0238224 | + | 0.999716i | \(0.492416\pi\) | |||||||
\(104\) | 1.76168e9 | 1.47665 | ||||||||
\(105\) | 1.33689e9 | 1.07335 | ||||||||
\(106\) | 2.62180e9 | 2.01708 | ||||||||
\(107\) | −2.67718e9 | −1.97447 | −0.987235 | − | 0.159268i | \(-0.949087\pi\) | ||||
−0.987235 | + | 0.159268i | \(0.949087\pi\) | |||||||
\(108\) | −1.86131e9 | −1.31647 | ||||||||
\(109\) | −8.58867e8 | −0.582783 | −0.291391 | − | 0.956604i | \(-0.594118\pi\) | ||||
−0.291391 | + | 0.956604i | \(0.594118\pi\) | |||||||
\(110\) | 1.47933e9 | 0.963382 | ||||||||
\(111\) | −2.16344e9 | −1.35267 | ||||||||
\(112\) | 1.84735e8 | 0.110935 | ||||||||
\(113\) | 2.68450e9 | 1.54885 | 0.774426 | − | 0.632664i | \(-0.218039\pi\) | ||||
0.774426 | + | 0.632664i | \(0.218039\pi\) | |||||||
\(114\) | 2.00661e9 | 1.11273 | ||||||||
\(115\) | 1.84100e9 | 0.981553 | ||||||||
\(116\) | −2.79886e9 | −1.43523 | ||||||||
\(117\) | −4.97014e9 | −2.45206 | ||||||||
\(118\) | −3.24983e9 | −1.54309 | ||||||||
\(119\) | −1.69948e9 | −0.776880 | ||||||||
\(120\) | 1.98996e9 | 0.876052 | ||||||||
\(121\) | 8.11187e6 | 0.00344023 | ||||||||
\(122\) | 6.63603e9 | 2.71200 | ||||||||
\(123\) | 9.49788e8 | 0.374157 | ||||||||
\(124\) | −6.87095e9 | −2.60987 | ||||||||
\(125\) | −2.68477e9 | −0.983586 | ||||||||
\(126\) | 7.80277e9 | 2.75792 | ||||||||
\(127\) | 1.96576e9 | 0.670522 | 0.335261 | − | 0.942125i | \(-0.391176\pi\) | ||||
0.335261 | + | 0.942125i | \(0.391176\pi\) | |||||||
\(128\) | 4.66676e9 | 1.53663 | ||||||||
\(129\) | −3.24841e8 | −0.103280 | ||||||||
\(130\) | 5.03074e9 | 1.54485 | ||||||||
\(131\) | −4.30836e9 | −1.27818 | −0.639089 | − | 0.769133i | \(-0.720688\pi\) | ||||
−0.639089 | + | 0.769133i | \(0.720688\pi\) | |||||||
\(132\) | 8.73655e9 | 2.50471 | ||||||||
\(133\) | −1.77375e9 | −0.491542 | ||||||||
\(134\) | 5.14107e9 | 1.37747 | ||||||||
\(135\) | −1.93637e9 | −0.501749 | ||||||||
\(136\) | −2.52968e9 | −0.634076 | ||||||||
\(137\) | −2.01231e9 | −0.488037 | −0.244019 | − | 0.969771i | \(-0.578466\pi\) | ||||
−0.244019 | + | 0.969771i | \(0.578466\pi\) | |||||||
\(138\) | 1.77840e10 | 4.17421 | ||||||||
\(139\) | 7.24917e9 | 1.64711 | 0.823553 | − | 0.567239i | \(-0.191988\pi\) | ||||
0.823553 | + | 0.567239i | \(0.191988\pi\) | |||||||
\(140\) | −4.82848e9 | −1.06227 | ||||||||
\(141\) | 5.77895e9 | 1.23130 | ||||||||
\(142\) | −6.27815e9 | −1.29579 | ||||||||
\(143\) | 8.04622e9 | 1.60909 | ||||||||
\(144\) | −7.75783e8 | −0.150352 | ||||||||
\(145\) | −2.91173e9 | −0.547009 | ||||||||
\(146\) | 1.37149e10 | 2.49808 | ||||||||
\(147\) | −2.41680e9 | −0.426887 | ||||||||
\(148\) | 7.81377e9 | 1.33870 | ||||||||
\(149\) | −4.57307e9 | −0.760098 | −0.380049 | − | 0.924966i | \(-0.624093\pi\) | ||||
−0.380049 | + | 0.924966i | \(0.624093\pi\) | |||||||
\(150\) | −1.01261e10 | −1.63317 | ||||||||
\(151\) | −1.05540e10 | −1.65204 | −0.826018 | − | 0.563644i | \(-0.809399\pi\) | ||||
−0.826018 | + | 0.563644i | \(0.809399\pi\) | |||||||
\(152\) | −2.64025e9 | −0.401188 | ||||||||
\(153\) | 7.13685e9 | 1.05292 | ||||||||
\(154\) | −1.26320e10 | −1.80979 | ||||||||
\(155\) | −7.14803e9 | −0.994704 | ||||||||
\(156\) | 2.97102e10 | 4.01648 | ||||||||
\(157\) | −5.91949e9 | −0.777564 | −0.388782 | − | 0.921330i | \(-0.627104\pi\) | ||||
−0.388782 | + | 0.921330i | \(0.627104\pi\) | |||||||
\(158\) | 1.96136e10 | 2.50380 | ||||||||
\(159\) | 1.61080e10 | 1.99874 | ||||||||
\(160\) | 5.35412e9 | 0.645875 | ||||||||
\(161\) | −1.57203e10 | −1.84393 | ||||||||
\(162\) | 2.76023e9 | 0.314868 | ||||||||
\(163\) | −5.78478e9 | −0.641864 | −0.320932 | − | 0.947102i | \(-0.603996\pi\) | ||||
−0.320932 | + | 0.947102i | \(0.603996\pi\) | |||||||
\(164\) | −3.43038e9 | −0.370293 | ||||||||
\(165\) | 9.08886e9 | 0.954622 | ||||||||
\(166\) | −1.20665e10 | −1.23337 | ||||||||
\(167\) | −4.50440e9 | −0.448139 | −0.224069 | − | 0.974573i | \(-0.571934\pi\) | ||||
−0.224069 | + | 0.974573i | \(0.571934\pi\) | |||||||
\(168\) | −1.69923e10 | −1.64574 | ||||||||
\(169\) | 1.67582e10 | 1.58029 | ||||||||
\(170\) | −7.22387e9 | −0.663361 | ||||||||
\(171\) | 7.44877e9 | 0.666196 | ||||||||
\(172\) | 1.17324e9 | 0.102214 | ||||||||
\(173\) | −1.31715e9 | −0.111796 | −0.0558981 | − | 0.998436i | \(-0.517802\pi\) | ||||
−0.0558981 | + | 0.998436i | \(0.517802\pi\) | |||||||
\(174\) | −2.81272e10 | −2.32624 | ||||||||
\(175\) | 8.95104e9 | 0.721443 | ||||||||
\(176\) | 1.25593e9 | 0.0986636 | ||||||||
\(177\) | −1.99666e10 | −1.52906 | ||||||||
\(178\) | 1.53066e10 | 1.14285 | ||||||||
\(179\) | 1.01850e10 | 0.741522 | 0.370761 | − | 0.928728i | \(-0.379097\pi\) | ||||
0.370761 | + | 0.928728i | \(0.379097\pi\) | |||||||
\(180\) | 2.02769e10 | 1.43971 | ||||||||
\(181\) | 1.63383e10 | 1.13149 | 0.565747 | − | 0.824579i | \(-0.308588\pi\) | ||||
0.565747 | + | 0.824579i | \(0.308588\pi\) | |||||||
\(182\) | −4.29575e10 | −2.90214 | ||||||||
\(183\) | 4.07711e10 | 2.68734 | ||||||||
\(184\) | −2.33998e10 | −1.50498 | ||||||||
\(185\) | 8.12887e9 | 0.510220 | ||||||||
\(186\) | −6.90499e10 | −4.23014 | ||||||||
\(187\) | −1.15539e10 | −0.690944 | ||||||||
\(188\) | −2.08720e10 | −1.21858 | ||||||||
\(189\) | 1.65347e10 | 0.942579 | ||||||||
\(190\) | −7.53960e9 | −0.419717 | ||||||||
\(191\) | −3.27140e10 | −1.77862 | −0.889309 | − | 0.457306i | \(-0.848814\pi\) | ||||
−0.889309 | + | 0.457306i | \(0.848814\pi\) | |||||||
\(192\) | 4.87727e10 | 2.59013 | ||||||||
\(193\) | −1.58246e10 | −0.820965 | −0.410483 | − | 0.911868i | \(-0.634640\pi\) | ||||
−0.410483 | + | 0.911868i | \(0.634640\pi\) | |||||||
\(194\) | 1.47111e10 | 0.745653 | ||||||||
\(195\) | 3.09083e10 | 1.53081 | ||||||||
\(196\) | 8.72885e9 | 0.422479 | ||||||||
\(197\) | 1.50614e9 | 0.0712470 | ||||||||
\(198\) | 5.30473e10 | 2.45285 | ||||||||
\(199\) | −2.39794e10 | −1.08393 | −0.541964 | − | 0.840402i | \(-0.682319\pi\) | ||||
−0.541964 | + | 0.840402i | \(0.682319\pi\) | |||||||
\(200\) | 1.33237e10 | 0.588829 | ||||||||
\(201\) | 3.15862e10 | 1.36494 | ||||||||
\(202\) | 5.51353e10 | 2.32996 | ||||||||
\(203\) | 2.48632e10 | 1.02760 | ||||||||
\(204\) | −4.26623e10 | −1.72468 | ||||||||
\(205\) | −3.56872e9 | −0.141130 | ||||||||
\(206\) | −1.97535e9 | −0.0764262 | ||||||||
\(207\) | 6.60164e10 | 2.49911 | ||||||||
\(208\) | 4.27101e9 | 0.158214 | ||||||||
\(209\) | −1.20589e10 | −0.437170 | ||||||||
\(210\) | −4.85240e10 | −1.72175 | ||||||||
\(211\) | −1.76343e10 | −0.612473 | −0.306237 | − | 0.951955i | \(-0.599070\pi\) | ||||
−0.306237 | + | 0.951955i | \(0.599070\pi\) | |||||||
\(212\) | −5.81779e10 | −1.97809 | ||||||||
\(213\) | −3.85723e10 | −1.28401 | ||||||||
\(214\) | 9.71716e10 | 3.16722 | ||||||||
\(215\) | 1.22055e9 | 0.0389568 | ||||||||
\(216\) | 2.46120e10 | 0.769316 | ||||||||
\(217\) | 6.10371e10 | 1.86864 | ||||||||
\(218\) | 3.11737e10 | 0.934832 | ||||||||
\(219\) | 8.42631e10 | 2.47536 | ||||||||
\(220\) | −3.28265e10 | −0.944764 | ||||||||
\(221\) | −3.92913e10 | −1.10798 | ||||||||
\(222\) | 7.85248e10 | 2.16979 | ||||||||
\(223\) | 2.99192e10 | 0.810173 | 0.405086 | − | 0.914278i | \(-0.367241\pi\) | ||||
0.405086 | + | 0.914278i | \(0.367241\pi\) | |||||||
\(224\) | −4.57188e10 | −1.21333 | ||||||||
\(225\) | −3.75893e10 | −0.977785 | ||||||||
\(226\) | −9.74372e10 | −2.48449 | ||||||||
\(227\) | 1.49180e10 | 0.372901 | 0.186450 | − | 0.982464i | \(-0.440302\pi\) | ||||
0.186450 | + | 0.982464i | \(0.440302\pi\) | |||||||
\(228\) | −4.45269e10 | −1.09123 | ||||||||
\(229\) | 7.56672e9 | 0.181823 | 0.0909113 | − | 0.995859i | \(-0.471022\pi\) | ||||
0.0909113 | + | 0.995859i | \(0.471022\pi\) | |||||||
\(230\) | −6.68214e10 | −1.57449 | ||||||||
\(231\) | −7.76098e10 | −1.79334 | ||||||||
\(232\) | 3.70091e10 | 0.838711 | ||||||||
\(233\) | −5.29276e10 | −1.17647 | −0.588234 | − | 0.808691i | \(-0.700177\pi\) | ||||
−0.588234 | + | 0.808691i | \(0.700177\pi\) | |||||||
\(234\) | 1.80397e11 | 3.93331 | ||||||||
\(235\) | −2.17137e10 | −0.464440 | ||||||||
\(236\) | 7.21142e10 | 1.51327 | ||||||||
\(237\) | 1.20504e11 | 2.48104 | ||||||||
\(238\) | 6.16847e10 | 1.24618 | ||||||||
\(239\) | 1.19650e8 | 0.00237204 | 0.00118602 | − | 0.999999i | \(-0.499622\pi\) | ||||
0.00118602 | + | 0.999999i | \(0.499622\pi\) | |||||||
\(240\) | 4.82445e9 | 0.0938636 | ||||||||
\(241\) | −3.90771e10 | −0.746184 | −0.373092 | − | 0.927794i | \(-0.621702\pi\) | ||||
−0.373092 | + | 0.927794i | \(0.621702\pi\) | |||||||
\(242\) | −2.94431e8 | −0.00551841 | ||||||||
\(243\) | 6.24458e10 | 1.14888 | ||||||||
\(244\) | −1.47254e11 | −2.65959 | ||||||||
\(245\) | 9.08085e9 | 0.161020 | ||||||||
\(246\) | −3.44737e10 | −0.600178 | ||||||||
\(247\) | −4.10086e10 | −0.701033 | ||||||||
\(248\) | 9.08541e10 | 1.52515 | ||||||||
\(249\) | −7.41353e10 | −1.22216 | ||||||||
\(250\) | 9.74472e10 | 1.57775 | ||||||||
\(251\) | −3.84879e10 | −0.612058 | −0.306029 | − | 0.952022i | \(-0.599001\pi\) | ||||
−0.306029 | + | 0.952022i | \(0.599001\pi\) | |||||||
\(252\) | −1.73144e11 | −2.70462 | ||||||||
\(253\) | −1.06875e11 | −1.63996 | ||||||||
\(254\) | −7.13496e10 | −1.07557 | ||||||||
\(255\) | −4.43827e10 | −0.657329 | ||||||||
\(256\) | −5.74054e10 | −0.835359 | ||||||||
\(257\) | −2.78466e10 | −0.398174 | −0.199087 | − | 0.979982i | \(-0.563798\pi\) | ||||
−0.199087 | + | 0.979982i | \(0.563798\pi\) | |||||||
\(258\) | 1.17905e10 | 0.165670 | ||||||||
\(259\) | −6.94125e10 | −0.958492 | ||||||||
\(260\) | −1.11633e11 | −1.51500 | ||||||||
\(261\) | −1.04412e11 | −1.39273 | ||||||||
\(262\) | 1.56377e11 | 2.05030 | ||||||||
\(263\) | 9.68880e10 | 1.24873 | 0.624366 | − | 0.781132i | \(-0.285357\pi\) | ||||
0.624366 | + | 0.781132i | \(0.285357\pi\) | |||||||
\(264\) | −1.15523e11 | −1.46369 | ||||||||
\(265\) | −6.05240e10 | −0.753913 | ||||||||
\(266\) | 6.43806e10 | 0.788475 | ||||||||
\(267\) | 9.40418e10 | 1.13245 | ||||||||
\(268\) | −1.14081e11 | −1.35085 | ||||||||
\(269\) | 4.64112e10 | 0.540428 | 0.270214 | − | 0.962800i | \(-0.412906\pi\) | ||||
0.270214 | + | 0.962800i | \(0.412906\pi\) | |||||||
\(270\) | 7.02831e10 | 0.804848 | ||||||||
\(271\) | −9.49935e10 | −1.06987 | −0.534936 | − | 0.844893i | \(-0.679664\pi\) | ||||
−0.534936 | + | 0.844893i | \(0.679664\pi\) | |||||||
\(272\) | −6.13294e9 | −0.0679373 | ||||||||
\(273\) | −2.63926e11 | −2.87575 | ||||||||
\(274\) | 7.30394e10 | 0.782852 | ||||||||
\(275\) | 6.08539e10 | 0.641640 | ||||||||
\(276\) | −3.94630e11 | −4.09354 | ||||||||
\(277\) | −1.40482e10 | −0.143371 | −0.0716857 | − | 0.997427i | \(-0.522838\pi\) | ||||
−0.0716857 | + | 0.997427i | \(0.522838\pi\) | |||||||
\(278\) | −2.63118e11 | −2.64210 | ||||||||
\(279\) | −2.56321e11 | −2.53259 | ||||||||
\(280\) | 6.38466e10 | 0.620764 | ||||||||
\(281\) | −4.90910e10 | −0.469703 | −0.234852 | − | 0.972031i | \(-0.575460\pi\) | ||||
−0.234852 | + | 0.972031i | \(0.575460\pi\) | |||||||
\(282\) | −2.09754e11 | −1.97510 | ||||||||
\(283\) | 1.99025e11 | 1.84446 | 0.922228 | − | 0.386646i | \(-0.126367\pi\) | ||||
0.922228 | + | 0.386646i | \(0.126367\pi\) | |||||||
\(284\) | 1.39313e11 | 1.27075 | ||||||||
\(285\) | −4.63225e10 | −0.415901 | ||||||||
\(286\) | −2.92048e11 | −2.58111 | ||||||||
\(287\) | 3.04733e10 | 0.265125 | ||||||||
\(288\) | 1.91993e11 | 1.64445 | ||||||||
\(289\) | −6.21677e10 | −0.524233 | ||||||||
\(290\) | 1.05685e11 | 0.877448 | ||||||||
\(291\) | 9.03834e10 | 0.738873 | ||||||||
\(292\) | −3.04336e11 | −2.44980 | ||||||||
\(293\) | 6.27330e10 | 0.497269 | 0.248635 | − | 0.968597i | \(-0.420018\pi\) | ||||
0.248635 | + | 0.968597i | \(0.420018\pi\) | |||||||
\(294\) | 8.77209e10 | 0.684763 | ||||||||
\(295\) | 7.50223e10 | 0.576755 | ||||||||
\(296\) | −1.03321e11 | −0.782304 | ||||||||
\(297\) | 1.12411e11 | 0.838314 | ||||||||
\(298\) | 1.65985e11 | 1.21926 | ||||||||
\(299\) | −3.63448e11 | −2.62979 | ||||||||
\(300\) | 2.24700e11 | 1.60161 | ||||||||
\(301\) | −1.04223e10 | −0.0731837 | ||||||||
\(302\) | 3.83069e11 | 2.65000 | ||||||||
\(303\) | 3.38745e11 | 2.30877 | ||||||||
\(304\) | −6.40098e9 | −0.0429849 | ||||||||
\(305\) | −1.53193e11 | −1.01365 | ||||||||
\(306\) | −2.59041e11 | −1.68897 | ||||||||
\(307\) | 2.83364e11 | 1.82063 | 0.910316 | − | 0.413913i | \(-0.135838\pi\) | ||||
0.910316 | + | 0.413913i | \(0.135838\pi\) | |||||||
\(308\) | 2.80306e11 | 1.77482 | ||||||||
\(309\) | −1.21364e10 | −0.0757313 | ||||||||
\(310\) | 2.59447e11 | 1.59559 | ||||||||
\(311\) | 1.22406e11 | 0.741958 | 0.370979 | − | 0.928641i | \(-0.379022\pi\) | ||||
0.370979 | + | 0.928641i | \(0.379022\pi\) | |||||||
\(312\) | −3.92856e11 | −2.34713 | ||||||||
\(313\) | −3.37873e10 | −0.198978 | −0.0994888 | − | 0.995039i | \(-0.531721\pi\) | ||||
−0.0994888 | + | 0.995039i | \(0.531721\pi\) | |||||||
\(314\) | 2.14856e11 | 1.24728 | ||||||||
\(315\) | −1.80127e11 | −1.03081 | ||||||||
\(316\) | −4.35228e11 | −2.45541 | ||||||||
\(317\) | 1.20564e11 | 0.670583 | 0.335291 | − | 0.942115i | \(-0.391165\pi\) | ||||
0.335291 | + | 0.942115i | \(0.391165\pi\) | |||||||
\(318\) | −5.84661e11 | −3.20614 | ||||||||
\(319\) | 1.69033e11 | 0.913933 | ||||||||
\(320\) | −1.83258e11 | −0.976984 | ||||||||
\(321\) | 5.97012e11 | 3.13842 | ||||||||
\(322\) | 5.70588e11 | 2.95782 | ||||||||
\(323\) | 5.88861e10 | 0.301024 | ||||||||
\(324\) | −6.12498e10 | −0.308782 | ||||||||
\(325\) | 2.06945e11 | 1.02892 | ||||||||
\(326\) | 2.09966e11 | 1.02960 | ||||||||
\(327\) | 1.91528e11 | 0.926332 | ||||||||
\(328\) | 4.53597e10 | 0.216390 | ||||||||
\(329\) | 1.85414e11 | 0.872489 | ||||||||
\(330\) | −3.29892e11 | −1.53129 | ||||||||
\(331\) | 1.71475e11 | 0.785190 | 0.392595 | − | 0.919711i | \(-0.371577\pi\) | ||||
0.392595 | + | 0.919711i | \(0.371577\pi\) | |||||||
\(332\) | 2.67757e11 | 1.20954 | ||||||||
\(333\) | 2.91493e11 | 1.29906 | ||||||||
\(334\) | 1.63493e11 | 0.718852 | ||||||||
\(335\) | −1.18681e11 | −0.514850 | ||||||||
\(336\) | −4.11960e10 | −0.176331 | ||||||||
\(337\) | −4.26686e10 | −0.180208 | −0.0901039 | − | 0.995932i | \(-0.528720\pi\) | ||||
−0.0901039 | + | 0.995932i | \(0.528720\pi\) | |||||||
\(338\) | −6.08259e11 | −2.53491 | ||||||||
\(339\) | −5.98644e11 | −2.46190 | ||||||||
\(340\) | 1.60299e11 | 0.650541 | ||||||||
\(341\) | 4.14962e11 | 1.66193 | ||||||||
\(342\) | −2.70362e11 | −1.06863 | ||||||||
\(343\) | 2.11181e11 | 0.823818 | ||||||||
\(344\) | −1.55137e10 | −0.0597312 | ||||||||
\(345\) | −4.10544e11 | −1.56018 | ||||||||
\(346\) | 4.78075e10 | 0.179330 | ||||||||
\(347\) | −1.40769e11 | −0.521224 | −0.260612 | − | 0.965444i | \(-0.583924\pi\) | ||||
−0.260612 | + | 0.965444i | \(0.583924\pi\) | |||||||
\(348\) | 6.24147e11 | 2.28129 | ||||||||
\(349\) | −1.65686e11 | −0.597821 | −0.298911 | − | 0.954281i | \(-0.596623\pi\) | ||||
−0.298911 | + | 0.954281i | \(0.596623\pi\) | |||||||
\(350\) | −3.24889e11 | −1.15726 | ||||||||
\(351\) | 3.82276e11 | 1.34430 | ||||||||
\(352\) | −3.10821e11 | −1.07912 | ||||||||
\(353\) | −4.59387e11 | −1.57468 | −0.787341 | − | 0.616518i | \(-0.788543\pi\) | ||||
−0.787341 | + | 0.616518i | \(0.788543\pi\) | |||||||
\(354\) | 7.24714e11 | 2.45274 | ||||||||
\(355\) | 1.44931e11 | 0.484321 | ||||||||
\(356\) | −3.39654e11 | −1.12076 | ||||||||
\(357\) | 3.78984e11 | 1.23485 | ||||||||
\(358\) | −3.69679e11 | −1.18946 | ||||||||
\(359\) | 4.69834e11 | 1.49286 | 0.746431 | − | 0.665463i | \(-0.231766\pi\) | ||||
0.746431 | + | 0.665463i | \(0.231766\pi\) | |||||||
\(360\) | −2.68120e11 | −0.841332 | ||||||||
\(361\) | −2.61228e11 | −0.809538 | ||||||||
\(362\) | −5.93017e11 | −1.81501 | ||||||||
\(363\) | −1.80895e9 | −0.00546823 | ||||||||
\(364\) | 9.53232e11 | 2.84605 | ||||||||
\(365\) | −3.16609e11 | −0.933694 | ||||||||
\(366\) | −1.47984e12 | −4.31071 | ||||||||
\(367\) | 2.25109e11 | 0.647732 | 0.323866 | − | 0.946103i | \(-0.395017\pi\) | ||||
0.323866 | + | 0.946103i | \(0.395017\pi\) | |||||||
\(368\) | −5.67302e10 | −0.161250 | ||||||||
\(369\) | −1.27971e11 | −0.359328 | ||||||||
\(370\) | −2.95048e11 | −0.818435 | ||||||||
\(371\) | 5.16815e11 | 1.41629 | ||||||||
\(372\) | 1.53223e12 | 4.14839 | ||||||||
\(373\) | 2.42835e11 | 0.649562 | 0.324781 | − | 0.945789i | \(-0.394709\pi\) | ||||
0.324781 | + | 0.945789i | \(0.394709\pi\) | |||||||
\(374\) | 4.19365e11 | 1.10833 | ||||||||
\(375\) | 5.98705e11 | 1.56341 | ||||||||
\(376\) | 2.75989e11 | 0.712110 | ||||||||
\(377\) | 5.74829e11 | 1.46556 | ||||||||
\(378\) | −6.00147e11 | −1.51197 | ||||||||
\(379\) | −4.12709e10 | −0.102747 | −0.0513734 | − | 0.998680i | \(-0.516360\pi\) | ||||
−0.0513734 | + | 0.998680i | \(0.516360\pi\) | |||||||
\(380\) | 1.67305e11 | 0.411606 | ||||||||
\(381\) | −4.38364e11 | −1.06579 | ||||||||
\(382\) | 1.18739e12 | 2.85305 | ||||||||
\(383\) | −2.40285e11 | −0.570600 | −0.285300 | − | 0.958438i | \(-0.592093\pi\) | ||||
−0.285300 | + | 0.958438i | \(0.592093\pi\) | |||||||
\(384\) | −1.04069e12 | −2.44247 | ||||||||
\(385\) | 2.91610e11 | 0.676439 | ||||||||
\(386\) | 5.74374e11 | 1.31690 | ||||||||
\(387\) | 4.37678e10 | 0.0991871 | ||||||||
\(388\) | −3.26441e11 | −0.731243 | ||||||||
\(389\) | 4.37568e11 | 0.968885 | 0.484443 | − | 0.874823i | \(-0.339022\pi\) | ||||
0.484443 | + | 0.874823i | \(0.339022\pi\) | |||||||
\(390\) | −1.12186e12 | −2.45554 | ||||||||
\(391\) | 5.21892e11 | 1.12924 | ||||||||
\(392\) | −1.15421e11 | −0.246886 | ||||||||
\(393\) | 9.60766e11 | 2.03166 | ||||||||
\(394\) | −5.46672e10 | −0.114286 | ||||||||
\(395\) | −4.52779e11 | −0.935835 | ||||||||
\(396\) | −1.17713e12 | −2.40544 | ||||||||
\(397\) | −3.81340e11 | −0.770469 | −0.385234 | − | 0.922819i | \(-0.625879\pi\) | ||||
−0.385234 | + | 0.922819i | \(0.625879\pi\) | |||||||
\(398\) | 8.70364e11 | 1.73871 | ||||||||
\(399\) | 3.95548e11 | 0.781306 | ||||||||
\(400\) | 3.23018e10 | 0.0630894 | ||||||||
\(401\) | −6.35926e11 | −1.22817 | −0.614083 | − | 0.789241i | \(-0.710474\pi\) | ||||
−0.614083 | + | 0.789241i | \(0.710474\pi\) | |||||||
\(402\) | −1.14646e12 | −2.18948 | ||||||||
\(403\) | 1.41116e12 | 2.66503 | ||||||||
\(404\) | −1.22346e12 | −2.28493 | ||||||||
\(405\) | −6.37198e10 | −0.117687 | ||||||||
\(406\) | −9.02442e11 | −1.64836 | ||||||||
\(407\) | −4.71902e11 | −0.852467 | ||||||||
\(408\) | 5.64120e11 | 1.00786 | ||||||||
\(409\) | −2.14433e11 | −0.378910 | −0.189455 | − | 0.981889i | \(-0.560672\pi\) | ||||
−0.189455 | + | 0.981889i | \(0.560672\pi\) | |||||||
\(410\) | 1.29531e11 | 0.226384 | ||||||||
\(411\) | 4.48746e11 | 0.775734 | ||||||||
\(412\) | 4.38333e10 | 0.0749492 | ||||||||
\(413\) | −6.40615e11 | −1.08348 | ||||||||
\(414\) | −2.39615e12 | −4.00878 | ||||||||
\(415\) | 2.78555e11 | 0.460993 | ||||||||
\(416\) | −1.05700e12 | −1.73044 | ||||||||
\(417\) | −1.61657e12 | −2.61807 | ||||||||
\(418\) | 4.37694e11 | 0.701256 | ||||||||
\(419\) | 8.62883e11 | 1.36769 | 0.683847 | − | 0.729626i | \(-0.260306\pi\) | ||||
0.683847 | + | 0.729626i | \(0.260306\pi\) | |||||||
\(420\) | 1.07675e12 | 1.68847 | ||||||||
\(421\) | −7.11528e11 | −1.10388 | −0.551941 | − | 0.833883i | \(-0.686113\pi\) | ||||
−0.551941 | + | 0.833883i | \(0.686113\pi\) | |||||||
\(422\) | 6.40059e11 | 0.982458 | ||||||||
\(423\) | −7.78633e11 | −1.18250 | ||||||||
\(424\) | 7.69282e11 | 1.15595 | ||||||||
\(425\) | −2.97162e11 | −0.441817 | ||||||||
\(426\) | 1.40003e12 | 2.05965 | ||||||||
\(427\) | 1.30811e12 | 1.90423 | ||||||||
\(428\) | −2.15625e12 | −3.10601 | ||||||||
\(429\) | −1.79431e12 | −2.55764 | ||||||||
\(430\) | −4.43015e10 | −0.0624900 | ||||||||
\(431\) | −1.72211e10 | −0.0240388 | −0.0120194 | − | 0.999928i | \(-0.503826\pi\) | ||||
−0.0120194 | + | 0.999928i | \(0.503826\pi\) | |||||||
\(432\) | 5.96690e10 | 0.0824275 | ||||||||
\(433\) | 1.27905e12 | 1.74861 | 0.874304 | − | 0.485379i | \(-0.161319\pi\) | ||||
0.874304 | + | 0.485379i | \(0.161319\pi\) | |||||||
\(434\) | −2.21542e12 | −2.99745 | ||||||||
\(435\) | 6.49316e11 | 0.869470 | ||||||||
\(436\) | −6.91747e11 | −0.916765 | ||||||||
\(437\) | 5.44701e11 | 0.714483 | ||||||||
\(438\) | −3.05843e12 | −3.97069 | ||||||||
\(439\) | 5.36222e11 | 0.689056 | 0.344528 | − | 0.938776i | \(-0.388039\pi\) | ||||
0.344528 | + | 0.938776i | \(0.388039\pi\) | |||||||
\(440\) | 4.34063e11 | 0.552097 | ||||||||
\(441\) | 3.25630e11 | 0.409969 | ||||||||
\(442\) | 1.42613e12 | 1.77729 | ||||||||
\(443\) | −3.86887e10 | −0.0477274 | −0.0238637 | − | 0.999715i | \(-0.507597\pi\) | ||||
−0.0238637 | + | 0.999715i | \(0.507597\pi\) | |||||||
\(444\) | −1.74247e12 | −2.12786 | ||||||||
\(445\) | −3.53351e11 | −0.427156 | ||||||||
\(446\) | −1.08595e12 | −1.29958 | ||||||||
\(447\) | 1.01980e12 | 1.20817 | ||||||||
\(448\) | 1.56484e12 | 1.83535 | ||||||||
\(449\) | 1.14374e12 | 1.32806 | 0.664031 | − | 0.747705i | \(-0.268844\pi\) | ||||
0.664031 | + | 0.747705i | \(0.268844\pi\) | |||||||
\(450\) | 1.36435e12 | 1.56845 | ||||||||
\(451\) | 2.07173e11 | 0.235798 | ||||||||
\(452\) | 2.16214e12 | 2.43647 | ||||||||
\(453\) | 2.35354e12 | 2.62591 | ||||||||
\(454\) | −5.41467e11 | −0.598164 | ||||||||
\(455\) | 9.91672e11 | 1.08472 | ||||||||
\(456\) | 5.88776e11 | 0.637688 | ||||||||
\(457\) | −1.09433e11 | −0.117361 | −0.0586806 | − | 0.998277i | \(-0.518689\pi\) | ||||
−0.0586806 | + | 0.998277i | \(0.518689\pi\) | |||||||
\(458\) | −2.74643e11 | −0.291658 | ||||||||
\(459\) | −5.48928e11 | −0.577242 | ||||||||
\(460\) | 1.48278e12 | 1.54406 | ||||||||
\(461\) | −8.07098e11 | −0.832286 | −0.416143 | − | 0.909299i | \(-0.636618\pi\) | ||||
−0.416143 | + | 0.909299i | \(0.636618\pi\) | |||||||
\(462\) | 2.81694e12 | 2.87667 | ||||||||
\(463\) | −1.47892e12 | −1.49565 | −0.747825 | − | 0.663896i | \(-0.768902\pi\) | ||||
−0.747825 | + | 0.663896i | \(0.768902\pi\) | |||||||
\(464\) | 8.97244e10 | 0.0898628 | ||||||||
\(465\) | 1.59401e12 | 1.58108 | ||||||||
\(466\) | 1.92107e12 | 1.88715 | ||||||||
\(467\) | 6.69178e11 | 0.651052 | 0.325526 | − | 0.945533i | \(-0.394459\pi\) | ||||
0.325526 | + | 0.945533i | \(0.394459\pi\) | |||||||
\(468\) | −4.00304e12 | −3.85730 | ||||||||
\(469\) | 1.01342e12 | 0.967190 | ||||||||
\(470\) | 7.88127e11 | 0.745000 | ||||||||
\(471\) | 1.32005e12 | 1.23594 | ||||||||
\(472\) | −9.53560e11 | −0.884319 | ||||||||
\(473\) | −7.08563e10 | −0.0650884 | ||||||||
\(474\) | −4.37384e12 | −3.97979 | ||||||||
\(475\) | −3.10149e11 | −0.279544 | ||||||||
\(476\) | −1.36879e12 | −1.22210 | ||||||||
\(477\) | −2.17033e12 | −1.91952 | ||||||||
\(478\) | −4.34285e9 | −0.00380495 | ||||||||
\(479\) | −1.60620e12 | −1.39409 | −0.697044 | − | 0.717028i | \(-0.745502\pi\) | ||||
−0.697044 | + | 0.717028i | \(0.745502\pi\) | |||||||
\(480\) | −1.19397e12 | −1.02662 | ||||||||
\(481\) | −1.60479e12 | −1.36699 | ||||||||
\(482\) | 1.41835e12 | 1.19694 | ||||||||
\(483\) | 3.50563e12 | 2.93092 | ||||||||
\(484\) | 6.53345e9 | 0.00541176 | ||||||||
\(485\) | −3.39605e11 | −0.278699 | ||||||||
\(486\) | −2.26655e12 | −1.84290 | ||||||||
\(487\) | −2.11418e11 | −0.170319 | −0.0851593 | − | 0.996367i | \(-0.527140\pi\) | ||||
−0.0851593 | + | 0.996367i | \(0.527140\pi\) | |||||||
\(488\) | 1.94713e12 | 1.55420 | ||||||||
\(489\) | 1.29001e12 | 1.02024 | ||||||||
\(490\) | −3.29601e11 | −0.258289 | ||||||||
\(491\) | −3.60341e11 | −0.279800 | −0.139900 | − | 0.990166i | \(-0.544678\pi\) | ||||
−0.139900 | + | 0.990166i | \(0.544678\pi\) | |||||||
\(492\) | 7.64976e11 | 0.588579 | ||||||||
\(493\) | −8.25424e11 | −0.629312 | ||||||||
\(494\) | 1.48846e12 | 1.12451 | ||||||||
\(495\) | −1.22460e12 | −0.916789 | ||||||||
\(496\) | 2.20266e11 | 0.163410 | ||||||||
\(497\) | −1.23756e12 | −0.909837 | ||||||||
\(498\) | 2.69083e12 | 1.96045 | ||||||||
\(499\) | 1.52358e11 | 0.110005 | 0.0550026 | − | 0.998486i | \(-0.482483\pi\) | ||||
0.0550026 | + | 0.998486i | \(0.482483\pi\) | |||||||
\(500\) | −2.16236e12 | −1.54726 | ||||||||
\(501\) | 1.00448e12 | 0.712315 | ||||||||
\(502\) | 1.39697e12 | 0.981792 | ||||||||
\(503\) | −2.07644e12 | −1.44632 | −0.723159 | − | 0.690682i | \(-0.757310\pi\) | ||||
−0.723159 | + | 0.690682i | \(0.757310\pi\) | |||||||
\(504\) | 2.28947e12 | 1.58051 | ||||||||
\(505\) | −1.27280e12 | −0.870858 | ||||||||
\(506\) | 3.87916e12 | 2.63063 | ||||||||
\(507\) | −3.73708e12 | −2.51187 | ||||||||
\(508\) | 1.58326e12 | 1.05479 | ||||||||
\(509\) | 1.38430e12 | 0.914115 | 0.457058 | − | 0.889437i | \(-0.348903\pi\) | ||||
0.457058 | + | 0.889437i | \(0.348903\pi\) | |||||||
\(510\) | 1.61093e12 | 1.05441 | ||||||||
\(511\) | 2.70352e12 | 1.75402 | ||||||||
\(512\) | −3.05776e11 | −0.196647 | ||||||||
\(513\) | −5.72919e11 | −0.365229 | ||||||||
\(514\) | 1.01073e12 | 0.638704 | ||||||||
\(515\) | 4.56009e10 | 0.0285655 | ||||||||
\(516\) | −2.61633e11 | −0.162468 | ||||||||
\(517\) | 1.26054e12 | 0.775977 | ||||||||
\(518\) | 2.51941e12 | 1.53750 | ||||||||
\(519\) | 2.93724e11 | 0.177700 | ||||||||
\(520\) | 1.47611e12 | 0.885327 | ||||||||
\(521\) | −1.04843e12 | −0.623403 | −0.311702 | − | 0.950180i | \(-0.600899\pi\) | ||||
−0.311702 | + | 0.950180i | \(0.600899\pi\) | |||||||
\(522\) | 3.78975e12 | 2.23405 | ||||||||
\(523\) | 1.59947e12 | 0.934800 | 0.467400 | − | 0.884046i | \(-0.345191\pi\) | ||||
0.467400 | + | 0.884046i | \(0.345191\pi\) | |||||||
\(524\) | −3.47003e12 | −2.01068 | ||||||||
\(525\) | −1.99609e12 | −1.14673 | ||||||||
\(526\) | −3.51667e12 | −2.00307 | ||||||||
\(527\) | −2.02634e12 | −1.14437 | ||||||||
\(528\) | −2.80072e11 | −0.156826 | ||||||||
\(529\) | 3.02639e12 | 1.68025 | ||||||||
\(530\) | 2.19680e12 | 1.20934 | ||||||||
\(531\) | 2.69022e12 | 1.46846 | ||||||||
\(532\) | −1.42861e12 | −0.773237 | ||||||||
\(533\) | 7.04531e11 | 0.378118 | ||||||||
\(534\) | −3.41337e12 | −1.81655 | ||||||||
\(535\) | −2.24320e12 | −1.18380 | ||||||||
\(536\) | 1.50848e12 | 0.789403 | ||||||||
\(537\) | −2.27127e12 | −1.17865 | ||||||||
\(538\) | −1.68455e12 | −0.866891 | ||||||||
\(539\) | −5.27167e11 | −0.269029 | ||||||||
\(540\) | −1.55959e12 | −0.789293 | ||||||||
\(541\) | 3.48281e12 | 1.74800 | 0.874001 | − | 0.485924i | \(-0.161517\pi\) | ||||
0.874001 | + | 0.485924i | \(0.161517\pi\) | |||||||
\(542\) | 3.44791e12 | 1.71616 | ||||||||
\(543\) | −3.64344e12 | −1.79851 | ||||||||
\(544\) | 1.51780e12 | 0.743053 | ||||||||
\(545\) | −7.19642e11 | −0.349408 | ||||||||
\(546\) | 9.57954e12 | 4.61294 | ||||||||
\(547\) | −2.74309e11 | −0.131008 | −0.0655040 | − | 0.997852i | \(-0.520865\pi\) | ||||
−0.0655040 | + | 0.997852i | \(0.520865\pi\) | |||||||
\(548\) | −1.62075e12 | −0.767723 | ||||||||
\(549\) | −5.49333e12 | −2.58083 | ||||||||
\(550\) | −2.20877e12 | −1.02924 | ||||||||
\(551\) | −8.61499e11 | −0.398174 | ||||||||
\(552\) | 5.21816e12 | 2.39217 | ||||||||
\(553\) | 3.86628e12 | 1.75805 | ||||||||
\(554\) | 5.09898e11 | 0.229980 | ||||||||
\(555\) | −1.81274e12 | −0.810994 | ||||||||
\(556\) | 5.83861e12 | 2.59103 | ||||||||
\(557\) | −2.37068e11 | −0.104358 | −0.0521789 | − | 0.998638i | \(-0.516617\pi\) | ||||
−0.0521789 | + | 0.998638i | \(0.516617\pi\) | |||||||
\(558\) | 9.30350e12 | 4.06249 | ||||||||
\(559\) | −2.40960e11 | −0.104374 | ||||||||
\(560\) | 1.54789e11 | 0.0665111 | ||||||||
\(561\) | 2.57653e12 | 1.09825 | ||||||||
\(562\) | 1.78182e12 | 0.753443 | ||||||||
\(563\) | −2.68204e12 | −1.12507 | −0.562533 | − | 0.826775i | \(-0.690173\pi\) | ||||
−0.562533 | + | 0.826775i | \(0.690173\pi\) | |||||||
\(564\) | 4.65447e12 | 1.93693 | ||||||||
\(565\) | 2.24933e12 | 0.928615 | ||||||||
\(566\) | −7.22386e12 | −2.95866 | ||||||||
\(567\) | 5.44104e11 | 0.221084 | ||||||||
\(568\) | −1.84212e12 | −0.742593 | ||||||||
\(569\) | 3.06021e12 | 1.22390 | 0.611949 | − | 0.790897i | \(-0.290386\pi\) | ||||
0.611949 | + | 0.790897i | \(0.290386\pi\) | |||||||
\(570\) | 1.68133e12 | 0.667140 | ||||||||
\(571\) | −4.43210e12 | −1.74480 | −0.872402 | − | 0.488789i | \(-0.837439\pi\) | ||||
−0.872402 | + | 0.488789i | \(0.837439\pi\) | |||||||
\(572\) | 6.48057e12 | 2.53123 | ||||||||
\(573\) | 7.29522e12 | 2.82711 | ||||||||
\(574\) | −1.10607e12 | −0.425282 | ||||||||
\(575\) | −2.74877e12 | −1.04866 | ||||||||
\(576\) | −6.57144e12 | −2.48748 | ||||||||
\(577\) | −4.06079e12 | −1.52517 | −0.762586 | − | 0.646887i | \(-0.776071\pi\) | ||||
−0.762586 | + | 0.646887i | \(0.776071\pi\) | |||||||
\(578\) | 2.25645e12 | 0.840913 | ||||||||
\(579\) | 3.52889e12 | 1.30492 | ||||||||
\(580\) | −2.34516e12 | −0.860490 | ||||||||
\(581\) | −2.37858e12 | −0.866014 | ||||||||
\(582\) | −3.28058e12 | −1.18521 | ||||||||
\(583\) | 3.51358e12 | 1.25962 | ||||||||
\(584\) | 4.02421e12 | 1.43160 | ||||||||
\(585\) | −4.16446e12 | −1.47014 | ||||||||
\(586\) | −2.27697e12 | −0.797662 | ||||||||
\(587\) | −1.69116e12 | −0.587915 | −0.293957 | − | 0.955819i | \(-0.594972\pi\) | ||||
−0.293957 | + | 0.955819i | \(0.594972\pi\) | |||||||
\(588\) | −1.94654e12 | −0.671529 | ||||||||
\(589\) | −2.11491e12 | −0.724056 | ||||||||
\(590\) | −2.72303e12 | −0.925162 | ||||||||
\(591\) | −3.35869e11 | −0.113247 | ||||||||
\(592\) | −2.50490e11 | −0.0838191 | ||||||||
\(593\) | 2.63198e12 | 0.874050 | 0.437025 | − | 0.899449i | \(-0.356032\pi\) | ||||
0.437025 | + | 0.899449i | \(0.356032\pi\) | |||||||
\(594\) | −4.08012e12 | −1.34473 | ||||||||
\(595\) | −1.42399e12 | −0.465779 | ||||||||
\(596\) | −3.68323e12 | −1.19570 | ||||||||
\(597\) | 5.34742e12 | 1.72290 | ||||||||
\(598\) | 1.31918e13 | 4.21841 | ||||||||
\(599\) | 1.24241e12 | 0.394316 | 0.197158 | − | 0.980372i | \(-0.436829\pi\) | ||||
0.197158 | + | 0.980372i | \(0.436829\pi\) | |||||||
\(600\) | −2.97119e12 | −0.935943 | ||||||||
\(601\) | 5.97867e12 | 1.86926 | 0.934630 | − | 0.355622i | \(-0.115731\pi\) | ||||
0.934630 | + | 0.355622i | \(0.115731\pi\) | |||||||
\(602\) | 3.78291e11 | 0.117393 | ||||||||
\(603\) | −4.25579e12 | −1.31085 | ||||||||
\(604\) | −8.50035e12 | −2.59879 | ||||||||
\(605\) | 6.79692e9 | 0.00206259 | ||||||||
\(606\) | −1.22952e13 | −3.70347 | ||||||||
\(607\) | −4.12922e12 | −1.23458 | −0.617289 | − | 0.786736i | \(-0.711769\pi\) | ||||
−0.617289 | + | 0.786736i | \(0.711769\pi\) | |||||||
\(608\) | 1.58414e12 | 0.470139 | ||||||||
\(609\) | −5.54451e12 | −1.63337 | ||||||||
\(610\) | 5.56032e12 | 1.62598 | ||||||||
\(611\) | 4.28670e12 | 1.24434 | ||||||||
\(612\) | 5.74815e12 | 1.65633 | ||||||||
\(613\) | −4.24710e12 | −1.21484 | −0.607422 | − | 0.794379i | \(-0.707796\pi\) | ||||
−0.607422 | + | 0.794379i | \(0.707796\pi\) | |||||||
\(614\) | −1.02851e13 | −2.92045 | ||||||||
\(615\) | 7.95825e11 | 0.224326 | ||||||||
\(616\) | −3.70646e12 | −1.03716 | ||||||||
\(617\) | 1.22102e12 | 0.339186 | 0.169593 | − | 0.985514i | \(-0.445755\pi\) | ||||
0.169593 | + | 0.985514i | \(0.445755\pi\) | |||||||
\(618\) | 4.40504e11 | 0.121479 | ||||||||
\(619\) | 6.04820e11 | 0.165584 | 0.0827920 | − | 0.996567i | \(-0.473616\pi\) | ||||
0.0827920 | + | 0.996567i | \(0.473616\pi\) | |||||||
\(620\) | −5.75716e12 | −1.56475 | ||||||||
\(621\) | −5.07763e12 | −1.37009 | ||||||||
\(622\) | −4.44286e12 | −1.19016 | ||||||||
\(623\) | 3.01727e12 | 0.802449 | ||||||||
\(624\) | −9.52436e11 | −0.251481 | ||||||||
\(625\) | 1.93897e11 | 0.0508291 | ||||||||
\(626\) | 1.22635e12 | 0.319177 | ||||||||
\(627\) | 2.68914e12 | 0.694880 | ||||||||
\(628\) | −4.76767e12 | −1.22317 | ||||||||
\(629\) | 2.30439e12 | 0.586987 | ||||||||
\(630\) | 6.53792e12 | 1.65351 | ||||||||
\(631\) | 3.22615e12 | 0.810125 | 0.405063 | − | 0.914289i | \(-0.367250\pi\) | ||||
0.405063 | + | 0.914289i | \(0.367250\pi\) | |||||||
\(632\) | 5.75498e12 | 1.43489 | ||||||||
\(633\) | 3.93245e12 | 0.973525 | ||||||||
\(634\) | −4.37603e12 | −1.07567 | ||||||||
\(635\) | 1.64710e12 | 0.402012 | ||||||||
\(636\) | 1.29737e13 | 3.14418 | ||||||||
\(637\) | −1.79273e12 | −0.431407 | ||||||||
\(638\) | −6.13528e12 | −1.46602 | ||||||||
\(639\) | 5.19707e12 | 1.23312 | ||||||||
\(640\) | 3.91026e12 | 0.921289 | ||||||||
\(641\) | −5.23129e12 | −1.22391 | −0.611953 | − | 0.790894i | \(-0.709616\pi\) | ||||
−0.611953 | + | 0.790894i | \(0.709616\pi\) | |||||||
\(642\) | −2.16693e13 | −5.03428 | ||||||||
\(643\) | 5.33218e12 | 1.23014 | 0.615072 | − | 0.788471i | \(-0.289127\pi\) | ||||
0.615072 | + | 0.788471i | \(0.289127\pi\) | |||||||
\(644\) | −1.26614e13 | −2.90065 | ||||||||
\(645\) | −2.72184e11 | −0.0619218 | ||||||||
\(646\) | −2.13734e12 | −0.482868 | ||||||||
\(647\) | 1.58217e12 | 0.354964 | 0.177482 | − | 0.984124i | \(-0.443205\pi\) | ||||
0.177482 | + | 0.984124i | \(0.443205\pi\) | |||||||
\(648\) | 8.09902e11 | 0.180445 | ||||||||
\(649\) | −4.35524e12 | −0.963631 | ||||||||
\(650\) | −7.51133e12 | −1.65047 | ||||||||
\(651\) | −1.36113e13 | −2.97019 | ||||||||
\(652\) | −4.65917e12 | −1.00970 | ||||||||
\(653\) | −7.13212e12 | −1.53500 | −0.767502 | − | 0.641046i | \(-0.778501\pi\) | ||||
−0.767502 | + | 0.641046i | \(0.778501\pi\) | |||||||
\(654\) | −6.95174e12 | −1.48591 | ||||||||
\(655\) | −3.60996e12 | −0.766332 | ||||||||
\(656\) | 1.09969e11 | 0.0231849 | ||||||||
\(657\) | −1.13533e13 | −2.37726 | ||||||||
\(658\) | −6.72982e12 | −1.39955 | ||||||||
\(659\) | −4.48841e12 | −0.927062 | −0.463531 | − | 0.886081i | \(-0.653418\pi\) | ||||
−0.463531 | + | 0.886081i | \(0.653418\pi\) | |||||||
\(660\) | 7.32033e12 | 1.50170 | ||||||||
\(661\) | −2.71638e12 | −0.553458 | −0.276729 | − | 0.960948i | \(-0.589250\pi\) | ||||
−0.276729 | + | 0.960948i | \(0.589250\pi\) | |||||||
\(662\) | −6.22390e12 | −1.25951 | ||||||||
\(663\) | 8.76198e12 | 1.76113 | ||||||||
\(664\) | −3.54053e12 | −0.706825 | ||||||||
\(665\) | −1.48622e12 | −0.294705 | ||||||||
\(666\) | −1.05801e13 | −2.08380 | ||||||||
\(667\) | −7.63524e12 | −1.49368 | ||||||||
\(668\) | −3.62792e12 | −0.704959 | ||||||||
\(669\) | −6.67199e12 | −1.28777 | ||||||||
\(670\) | 4.30769e12 | 0.825862 | ||||||||
\(671\) | 8.89323e12 | 1.69359 | ||||||||
\(672\) | 1.01953e13 | 1.92859 | ||||||||
\(673\) | 4.83949e12 | 0.909351 | 0.454676 | − | 0.890657i | \(-0.349755\pi\) | ||||
0.454676 | + | 0.890657i | \(0.349755\pi\) | |||||||
\(674\) | 1.54871e12 | 0.289068 | ||||||||
\(675\) | 2.89117e12 | 0.536051 | ||||||||
\(676\) | 1.34973e13 | 2.48592 | ||||||||
\(677\) | −1.01283e13 | −1.85305 | −0.926523 | − | 0.376238i | \(-0.877218\pi\) | ||||
−0.926523 | + | 0.376238i | \(0.877218\pi\) | |||||||
\(678\) | 2.17285e13 | 3.94909 | ||||||||
\(679\) | 2.89989e12 | 0.523560 | ||||||||
\(680\) | −2.11962e12 | −0.380160 | ||||||||
\(681\) | −3.32671e12 | −0.592725 | ||||||||
\(682\) | −1.50616e13 | −2.66588 | ||||||||
\(683\) | −2.10573e12 | −0.370262 | −0.185131 | − | 0.982714i | \(-0.559271\pi\) | ||||
−0.185131 | + | 0.982714i | \(0.559271\pi\) | |||||||
\(684\) | 5.99937e12 | 1.04798 | ||||||||
\(685\) | −1.68611e12 | −0.292603 | ||||||||
\(686\) | −7.66508e12 | −1.32147 | ||||||||
\(687\) | −1.68738e12 | −0.289007 | ||||||||
\(688\) | −3.76112e10 | −0.00639984 | ||||||||
\(689\) | 1.19486e13 | 2.01990 | ||||||||
\(690\) | 1.49012e13 | 2.50265 | ||||||||
\(691\) | 6.50389e12 | 1.08523 | 0.542615 | − | 0.839982i | \(-0.317434\pi\) | ||||
0.542615 | + | 0.839982i | \(0.317434\pi\) | |||||||
\(692\) | −1.06085e12 | −0.175865 | ||||||||
\(693\) | 1.04568e13 | 1.72227 | ||||||||
\(694\) | 5.10939e12 | 0.836087 | ||||||||
\(695\) | 6.07406e12 | 0.987524 | ||||||||
\(696\) | −8.25304e12 | −1.33313 | ||||||||
\(697\) | −1.01167e12 | −0.162364 | ||||||||
\(698\) | 6.01378e12 | 0.958955 | ||||||||
\(699\) | 1.18029e13 | 1.86999 | ||||||||
\(700\) | 7.20933e12 | 1.13489 | ||||||||
\(701\) | 4.33793e12 | 0.678503 | 0.339252 | − | 0.940696i | \(-0.389826\pi\) | ||||
0.339252 | + | 0.940696i | \(0.389826\pi\) | |||||||
\(702\) | −1.38752e13 | −2.15636 | ||||||||
\(703\) | 2.40511e12 | 0.371395 | ||||||||
\(704\) | 1.06386e13 | 1.63233 | ||||||||
\(705\) | 4.84217e12 | 0.738226 | ||||||||
\(706\) | 1.66740e13 | 2.52592 | ||||||||
\(707\) | 1.08684e13 | 1.63598 | ||||||||
\(708\) | −1.60815e13 | −2.40534 | ||||||||
\(709\) | −1.14641e13 | −1.70386 | −0.851929 | − | 0.523658i | \(-0.824567\pi\) | ||||
−0.851929 | + | 0.523658i | \(0.824567\pi\) | |||||||
\(710\) | −5.26044e12 | −0.776890 | ||||||||
\(711\) | −1.62362e13 | −2.38271 | ||||||||
\(712\) | 4.49122e12 | 0.654944 | ||||||||
\(713\) | −1.87438e13 | −2.71616 | ||||||||
\(714\) | −1.37557e13 | −1.98080 | ||||||||
\(715\) | 6.74191e12 | 0.964730 | ||||||||
\(716\) | 8.20322e12 | 1.16648 | ||||||||
\(717\) | −2.66820e10 | −0.00377036 | ||||||||
\(718\) | −1.70532e13 | −2.39467 | ||||||||
\(719\) | −3.02789e12 | −0.422533 | −0.211266 | − | 0.977429i | \(-0.567759\pi\) | ||||
−0.211266 | + | 0.977429i | \(0.567759\pi\) | |||||||
\(720\) | −6.50026e11 | −0.0901436 | ||||||||
\(721\) | −3.89386e11 | −0.0536627 | ||||||||
\(722\) | 9.48160e12 | 1.29857 | ||||||||
\(723\) | 8.71421e12 | 1.18606 | ||||||||
\(724\) | 1.31591e13 | 1.77993 | ||||||||
\(725\) | 4.34746e12 | 0.584405 | ||||||||
\(726\) | 6.56581e10 | 0.00877150 | ||||||||
\(727\) | −2.43179e12 | −0.322865 | −0.161433 | − | 0.986884i | \(-0.551611\pi\) | ||||
−0.161433 | + | 0.986884i | \(0.551611\pi\) | |||||||
\(728\) | −1.26045e13 | −1.66316 | ||||||||
\(729\) | −1.24286e13 | −1.62985 | ||||||||
\(730\) | 1.14917e13 | 1.49772 | ||||||||
\(731\) | 3.46006e11 | 0.0448182 | ||||||||
\(732\) | 3.28378e13 | 4.22740 | ||||||||
\(733\) | −3.52706e11 | −0.0451279 | −0.0225639 | − | 0.999745i | \(-0.507183\pi\) | ||||
−0.0225639 | + | 0.999745i | \(0.507183\pi\) | |||||||
\(734\) | −8.17061e12 | −1.03902 | ||||||||
\(735\) | −2.02503e12 | −0.255941 | ||||||||
\(736\) | 1.40398e13 | 1.76364 | ||||||||
\(737\) | 6.88976e12 | 0.860203 | ||||||||
\(738\) | 4.64485e12 | 0.576392 | ||||||||
\(739\) | −6.46135e12 | −0.796936 | −0.398468 | − | 0.917182i | \(-0.630458\pi\) | ||||
−0.398468 | + | 0.917182i | \(0.630458\pi\) | |||||||
\(740\) | 6.54714e12 | 0.802618 | ||||||||
\(741\) | 9.14493e12 | 1.11429 | ||||||||
\(742\) | −1.87584e13 | −2.27185 | ||||||||
\(743\) | −1.26195e13 | −1.51912 | −0.759559 | − | 0.650439i | \(-0.774585\pi\) | ||||
−0.759559 | + | 0.650439i | \(0.774585\pi\) | |||||||
\(744\) | −2.02605e13 | −2.42422 | ||||||||
\(745\) | −3.83176e12 | −0.455717 | ||||||||
\(746\) | −8.81398e12 | −1.04195 | ||||||||
\(747\) | 9.98869e12 | 1.17372 | ||||||||
\(748\) | −9.30575e12 | −1.08691 | ||||||||
\(749\) | 1.91547e13 | 2.22386 | ||||||||
\(750\) | −2.17308e13 | −2.50784 | ||||||||
\(751\) | −8.97948e12 | −1.03008 | −0.515041 | − | 0.857166i | \(-0.672223\pi\) | ||||
−0.515041 | + | 0.857166i | \(0.672223\pi\) | |||||||
\(752\) | 6.69106e11 | 0.0762982 | ||||||||
\(753\) | 8.58282e12 | 0.972865 | ||||||||
\(754\) | −2.08641e13 | −2.35088 | ||||||||
\(755\) | −8.84314e12 | −0.990479 | ||||||||
\(756\) | 1.33173e13 | 1.48275 | ||||||||
\(757\) | −1.60509e13 | −1.77651 | −0.888255 | − | 0.459351i | \(-0.848082\pi\) | ||||
−0.888255 | + | 0.459351i | \(0.848082\pi\) | |||||||
\(758\) | 1.49798e12 | 0.164814 | ||||||||
\(759\) | 2.38331e13 | 2.60671 | ||||||||
\(760\) | −2.21226e12 | −0.240533 | ||||||||
\(761\) | −1.21379e13 | −1.31194 | −0.655969 | − | 0.754788i | \(-0.727740\pi\) | ||||
−0.655969 | + | 0.754788i | \(0.727740\pi\) | |||||||
\(762\) | 1.59110e13 | 1.70962 | ||||||||
\(763\) | 6.14503e12 | 0.656392 | ||||||||
\(764\) | −2.63484e13 | −2.79791 | ||||||||
\(765\) | 5.97995e12 | 0.631278 | ||||||||
\(766\) | 8.72144e12 | 0.915290 | ||||||||
\(767\) | −1.48108e13 | −1.54525 | ||||||||
\(768\) | 1.28014e13 | 1.32780 | ||||||||
\(769\) | 1.17141e13 | 1.20792 | 0.603962 | − | 0.797013i | \(-0.293588\pi\) | ||||
0.603962 | + | 0.797013i | \(0.293588\pi\) | |||||||
\(770\) | −1.05843e13 | −1.08506 | ||||||||
\(771\) | 6.20980e12 | 0.632897 | ||||||||
\(772\) | −1.27454e13 | −1.29145 | ||||||||
\(773\) | 1.06869e13 | 1.07657 | 0.538285 | − | 0.842763i | \(-0.319072\pi\) | ||||
0.538285 | + | 0.842763i | \(0.319072\pi\) | |||||||
\(774\) | −1.58861e12 | −0.159104 | ||||||||
\(775\) | 1.06726e13 | 1.06271 | ||||||||
\(776\) | 4.31650e12 | 0.427321 | ||||||||
\(777\) | 1.54790e13 | 1.52352 | ||||||||
\(778\) | −1.58821e13 | −1.55417 | ||||||||
\(779\) | −1.05588e12 | −0.102730 | ||||||||
\(780\) | 2.48941e13 | 2.40808 | ||||||||
\(781\) | −8.41361e12 | −0.809194 | ||||||||
\(782\) | −1.89427e13 | −1.81139 | ||||||||
\(783\) | 8.03077e12 | 0.763536 | ||||||||
\(784\) | −2.79825e11 | −0.0264524 | ||||||||
\(785\) | −4.95993e12 | −0.466189 | ||||||||
\(786\) | −3.48722e13 | −3.25895 | ||||||||
\(787\) | 1.05523e13 | 0.980534 | 0.490267 | − | 0.871572i | \(-0.336899\pi\) | ||||
0.490267 | + | 0.871572i | \(0.336899\pi\) | |||||||
\(788\) | 1.21307e12 | 0.112077 | ||||||||
\(789\) | −2.16061e13 | −1.98486 | ||||||||
\(790\) | 1.64342e13 | 1.50116 | ||||||||
\(791\) | −1.92071e13 | −1.74448 | ||||||||
\(792\) | 1.55651e13 | 1.40568 | ||||||||
\(793\) | 3.02431e13 | 2.71579 | ||||||||
\(794\) | 1.38412e13 | 1.23590 | ||||||||
\(795\) | 1.34969e13 | 1.19834 | ||||||||
\(796\) | −1.93135e13 | −1.70511 | ||||||||
\(797\) | −1.09660e12 | −0.0962692 | −0.0481346 | − | 0.998841i | \(-0.515328\pi\) | ||||
−0.0481346 | + | 0.998841i | \(0.515328\pi\) | |||||||
\(798\) | −1.43569e13 | −1.25328 | ||||||||
\(799\) | −6.15547e12 | −0.534319 | ||||||||
\(800\) | −7.99416e12 | −0.690030 | ||||||||
\(801\) | −1.26708e13 | −1.08757 | ||||||||
\(802\) | 2.30817e13 | 1.97008 | ||||||||
\(803\) | 1.83800e13 | 1.56000 | ||||||||
\(804\) | 2.54401e13 | 2.14717 | ||||||||
\(805\) | −1.31720e13 | −1.10553 | ||||||||
\(806\) | −5.12197e13 | −4.27493 | ||||||||
\(807\) | −1.03497e13 | −0.859009 | ||||||||
\(808\) | 1.61777e13 | 1.33526 | ||||||||
\(809\) | 6.68419e12 | 0.548631 | 0.274316 | − | 0.961640i | \(-0.411549\pi\) | ||||
0.274316 | + | 0.961640i | \(0.411549\pi\) | |||||||
\(810\) | 2.31279e12 | 0.188779 | ||||||||
\(811\) | −2.62878e12 | −0.213384 | −0.106692 | − | 0.994292i | \(-0.534026\pi\) | ||||
−0.106692 | + | 0.994292i | \(0.534026\pi\) | |||||||
\(812\) | 2.00253e13 | 1.61650 | ||||||||
\(813\) | 2.11836e13 | 1.70056 | ||||||||
\(814\) | 1.71283e13 | 1.36743 | ||||||||
\(815\) | −4.84706e12 | −0.384830 | ||||||||
\(816\) | 1.36765e12 | 0.107986 | ||||||||
\(817\) | 3.61128e11 | 0.0283571 | ||||||||
\(818\) | 7.78310e12 | 0.607803 | ||||||||
\(819\) | 3.55604e13 | 2.76178 | ||||||||
\(820\) | −2.87431e12 | −0.222009 | ||||||||
\(821\) | 3.71457e12 | 0.285341 | 0.142671 | − | 0.989770i | \(-0.454431\pi\) | ||||
0.142671 | + | 0.989770i | \(0.454431\pi\) | |||||||
\(822\) | −1.62878e13 | −1.24434 | ||||||||
\(823\) | −8.98302e12 | −0.682532 | −0.341266 | − | 0.939967i | \(-0.610856\pi\) | ||||
−0.341266 | + | 0.939967i | \(0.610856\pi\) | |||||||
\(824\) | −5.79604e11 | −0.0437985 | ||||||||
\(825\) | −1.35704e13 | −1.01989 | ||||||||
\(826\) | 2.32519e13 | 1.73800 | ||||||||
\(827\) | 1.43496e13 | 1.06676 | 0.533379 | − | 0.845876i | \(-0.320922\pi\) | ||||
0.533379 | + | 0.845876i | \(0.320922\pi\) | |||||||
\(828\) | 5.31708e13 | 3.93131 | ||||||||
\(829\) | −2.23056e13 | −1.64028 | −0.820141 | − | 0.572162i | \(-0.806105\pi\) | ||||
−0.820141 | + | 0.572162i | \(0.806105\pi\) | |||||||
\(830\) | −1.01105e13 | −0.739470 | ||||||||
\(831\) | 3.13276e12 | 0.227888 | ||||||||
\(832\) | 3.61785e13 | 2.61756 | ||||||||
\(833\) | 2.57426e12 | 0.185247 | ||||||||
\(834\) | 5.86754e13 | 4.19961 | ||||||||
\(835\) | −3.77422e12 | −0.268682 | ||||||||
\(836\) | −9.71247e12 | −0.687704 | ||||||||
\(837\) | 1.97149e13 | 1.38845 | ||||||||
\(838\) | −3.13194e13 | −2.19389 | ||||||||
\(839\) | −1.73183e13 | −1.20664 | −0.603320 | − | 0.797500i | \(-0.706156\pi\) | ||||
−0.603320 | + | 0.797500i | \(0.706156\pi\) | |||||||
\(840\) | −1.42378e13 | −0.986703 | ||||||||
\(841\) | −2.43126e12 | −0.167590 | ||||||||
\(842\) | 2.58258e13 | 1.77072 | ||||||||
\(843\) | 1.09473e13 | 0.746592 | ||||||||
\(844\) | −1.42030e13 | −0.963471 | ||||||||
\(845\) | 1.40416e13 | 0.947463 | ||||||||
\(846\) | 2.82615e13 | 1.89683 | ||||||||
\(847\) | −5.80389e10 | −0.00387475 | ||||||||
\(848\) | 1.86504e12 | 0.123853 | ||||||||
\(849\) | −4.43826e13 | −2.93176 | ||||||||
\(850\) | 1.07859e13 | 0.708712 | ||||||||
\(851\) | 2.13158e13 | 1.39322 | ||||||||
\(852\) | −3.10668e13 | −2.01985 | ||||||||
\(853\) | −7.93401e12 | −0.513124 | −0.256562 | − | 0.966528i | \(-0.582590\pi\) | ||||
−0.256562 | + | 0.966528i | \(0.582590\pi\) | |||||||
\(854\) | −4.74795e13 | −3.05454 | ||||||||
\(855\) | 6.24131e12 | 0.399418 | ||||||||
\(856\) | 2.85119e13 | 1.81507 | ||||||||
\(857\) | 1.08137e13 | 0.684795 | 0.342397 | − | 0.939555i | \(-0.388761\pi\) | ||||
0.342397 | + | 0.939555i | \(0.388761\pi\) | |||||||
\(858\) | 6.51268e13 | 4.10267 | ||||||||
\(859\) | 8.64575e12 | 0.541793 | 0.270896 | − | 0.962609i | \(-0.412680\pi\) | ||||
0.270896 | + | 0.962609i | \(0.412680\pi\) | |||||||
\(860\) | 9.83056e11 | 0.0612823 | ||||||||
\(861\) | −6.79555e12 | −0.421415 | ||||||||
\(862\) | 6.25062e11 | 0.0385603 | ||||||||
\(863\) | 2.44385e13 | 1.49978 | 0.749888 | − | 0.661565i | \(-0.230107\pi\) | ||||
0.749888 | + | 0.661565i | \(0.230107\pi\) | |||||||
\(864\) | −1.47671e13 | −0.901537 | ||||||||
\(865\) | −1.10363e12 | −0.0670275 | ||||||||
\(866\) | −4.64248e13 | −2.80491 | ||||||||
\(867\) | 1.38634e13 | 0.833267 | ||||||||
\(868\) | 4.91604e13 | 2.93952 | ||||||||
\(869\) | 2.62850e13 | 1.56358 | ||||||||
\(870\) | −2.35677e13 | −1.39470 | ||||||||
\(871\) | 2.34299e13 | 1.37940 | ||||||||
\(872\) | 9.14691e12 | 0.535736 | ||||||||
\(873\) | −1.21779e13 | −0.709590 | ||||||||
\(874\) | −1.97706e13 | −1.14609 | ||||||||
\(875\) | 1.92090e13 | 1.10782 | ||||||||
\(876\) | 6.78670e13 | 3.89395 | ||||||||
\(877\) | 2.14237e13 | 1.22292 | 0.611458 | − | 0.791277i | \(-0.290583\pi\) | ||||
0.611458 | + | 0.791277i | \(0.290583\pi\) | |||||||
\(878\) | −1.94629e13 | −1.10530 | ||||||||
\(879\) | −1.39895e13 | −0.790409 | ||||||||
\(880\) | 1.05234e12 | 0.0591538 | ||||||||
\(881\) | −8.21905e12 | −0.459653 | −0.229826 | − | 0.973232i | \(-0.573816\pi\) | ||||
−0.229826 | + | 0.973232i | \(0.573816\pi\) | |||||||
\(882\) | −1.18192e13 | −0.657624 | ||||||||
\(883\) | 3.88822e12 | 0.215242 | 0.107621 | − | 0.994192i | \(-0.465677\pi\) | ||||
0.107621 | + | 0.994192i | \(0.465677\pi\) | |||||||
\(884\) | −3.16459e13 | −1.74294 | ||||||||
\(885\) | −1.67300e13 | −0.916750 | ||||||||
\(886\) | 1.40425e12 | 0.0765586 | ||||||||
\(887\) | −5.49999e12 | −0.298336 | −0.149168 | − | 0.988812i | \(-0.547660\pi\) | ||||
−0.149168 | + | 0.988812i | \(0.547660\pi\) | |||||||
\(888\) | 2.30406e13 | 1.24347 | ||||||||
\(889\) | −1.40646e13 | −0.755213 | ||||||||
\(890\) | 1.28253e13 | 0.685194 | ||||||||
\(891\) | 3.69910e12 | 0.196629 | ||||||||
\(892\) | 2.40974e13 | 1.27447 | ||||||||
\(893\) | −6.42450e12 | −0.338071 | ||||||||
\(894\) | −3.70148e13 | −1.93801 | ||||||||
\(895\) | 8.53402e12 | 0.444580 | ||||||||
\(896\) | −3.33897e13 | −1.73072 | ||||||||
\(897\) | 8.10490e13 | 4.18005 | ||||||||
\(898\) | −4.15134e13 | −2.13032 | ||||||||
\(899\) | 2.96453e13 | 1.51369 | ||||||||
\(900\) | −3.02751e13 | −1.53814 | ||||||||
\(901\) | −1.71575e13 | −0.867347 | ||||||||
\(902\) | −7.51962e12 | −0.378239 | ||||||||
\(903\) | 2.32418e12 | 0.116325 | ||||||||
\(904\) | −2.85898e13 | −1.42382 | ||||||||
\(905\) | 1.36898e13 | 0.678388 | ||||||||
\(906\) | −8.54246e13 | −4.21217 | ||||||||
\(907\) | 1.38465e13 | 0.679370 | 0.339685 | − | 0.940539i | \(-0.389680\pi\) | ||||
0.339685 | + | 0.940539i | \(0.389680\pi\) | |||||||
\(908\) | 1.20152e13 | 0.586604 | ||||||||
\(909\) | −4.56412e13 | −2.21727 | ||||||||
\(910\) | −3.59940e13 | −1.73998 | ||||||||
\(911\) | 3.12545e13 | 1.50342 | 0.751710 | − | 0.659494i | \(-0.229229\pi\) | ||||
0.751710 | + | 0.659494i | \(0.229229\pi\) | |||||||
\(912\) | 1.42742e12 | 0.0683243 | ||||||||
\(913\) | −1.61708e13 | −0.770218 | ||||||||
\(914\) | 3.97200e12 | 0.188257 | ||||||||
\(915\) | 3.41620e13 | 1.61120 | ||||||||
\(916\) | 6.09437e12 | 0.286022 | ||||||||
\(917\) | 3.08255e13 | 1.43962 | ||||||||
\(918\) | 1.99240e13 | 0.925944 | ||||||||
\(919\) | 1.04138e12 | 0.0481604 | 0.0240802 | − | 0.999710i | \(-0.492334\pi\) | ||||
0.0240802 | + | 0.999710i | \(0.492334\pi\) | |||||||
\(920\) | −1.96066e13 | −0.902314 | ||||||||
\(921\) | −6.31903e13 | −2.89389 | ||||||||
\(922\) | 2.92947e13 | 1.33506 | ||||||||
\(923\) | −2.86120e13 | −1.29760 | ||||||||
\(924\) | −6.25083e13 | −2.82107 | ||||||||
\(925\) | −1.21371e13 | −0.545101 | ||||||||
\(926\) | 5.36792e13 | 2.39915 | ||||||||
\(927\) | 1.63520e12 | 0.0727299 | ||||||||
\(928\) | −2.22053e13 | −0.982858 | ||||||||
\(929\) | 7.79811e11 | 0.0343494 | 0.0171747 | − | 0.999853i | \(-0.494533\pi\) | ||||
0.0171747 | + | 0.999853i | \(0.494533\pi\) | |||||||
\(930\) | −5.78567e13 | −2.53618 | ||||||||
\(931\) | 2.68677e12 | 0.117208 | ||||||||
\(932\) | −4.26288e13 | −1.85068 | ||||||||
\(933\) | −2.72965e13 | −1.17934 | ||||||||
\(934\) | −2.42887e13 | −1.04434 | ||||||||
\(935\) | −9.68102e12 | −0.414256 | ||||||||
\(936\) | 5.29318e13 | 2.25411 | ||||||||
\(937\) | −1.40171e12 | −0.0594060 | −0.0297030 | − | 0.999559i | \(-0.509456\pi\) | ||||
−0.0297030 | + | 0.999559i | \(0.509456\pi\) | |||||||
\(938\) | −3.67834e13 | −1.55145 | ||||||||
\(939\) | 7.53459e12 | 0.316275 | ||||||||
\(940\) | −1.74886e13 | −0.730602 | ||||||||
\(941\) | −2.41785e13 | −1.00525 | −0.502627 | − | 0.864504i | \(-0.667633\pi\) | ||||
−0.502627 | + | 0.864504i | \(0.667633\pi\) | |||||||
\(942\) | −4.79129e13 | −1.98254 | ||||||||
\(943\) | −9.35802e12 | −0.385373 | ||||||||
\(944\) | −2.31180e12 | −0.0947494 | ||||||||
\(945\) | 1.38544e13 | 0.565124 | ||||||||
\(946\) | 2.57182e12 | 0.104407 | ||||||||
\(947\) | 3.03758e12 | 0.122730 | 0.0613652 | − | 0.998115i | \(-0.480455\pi\) | ||||
0.0613652 | + | 0.998115i | \(0.480455\pi\) | |||||||
\(948\) | 9.70560e13 | 3.90288 | ||||||||
\(949\) | 6.25045e13 | 2.50157 | ||||||||
\(950\) | 1.12573e13 | 0.448411 | ||||||||
\(951\) | −2.68859e13 | −1.06589 | ||||||||
\(952\) | 1.80994e13 | 0.714164 | ||||||||
\(953\) | −2.51073e13 | −0.986011 | −0.493006 | − | 0.870026i | \(-0.664102\pi\) | ||||
−0.493006 | + | 0.870026i | \(0.664102\pi\) | |||||||
\(954\) | 7.87749e13 | 3.07907 | ||||||||
\(955\) | −2.74109e13 | −1.06637 | ||||||||
\(956\) | 9.63684e10 | 0.00373142 | ||||||||
\(957\) | −3.76945e13 | −1.45269 | ||||||||
\(958\) | 5.82991e13 | 2.23623 | ||||||||
\(959\) | 1.43977e13 | 0.549680 | ||||||||
\(960\) | 4.08666e13 | 1.55291 | ||||||||
\(961\) | 4.63369e13 | 1.75256 | ||||||||
\(962\) | 5.82479e13 | 2.19277 | ||||||||
\(963\) | −8.04390e13 | −3.01404 | ||||||||
\(964\) | −3.14734e13 | −1.17381 | ||||||||
\(965\) | −1.32594e13 | −0.492210 | ||||||||
\(966\) | −1.27241e14 | −4.70144 | ||||||||
\(967\) | −8.20610e11 | −0.0301799 | −0.0150899 | − | 0.999886i | \(-0.504803\pi\) | ||||
−0.0150899 | + | 0.999886i | \(0.504803\pi\) | |||||||
\(968\) | −8.63913e10 | −0.00316250 | ||||||||
\(969\) | −1.31316e13 | −0.478477 | ||||||||
\(970\) | 1.23264e13 | 0.447057 | ||||||||
\(971\) | 3.07977e13 | 1.11181 | 0.555907 | − | 0.831245i | \(-0.312371\pi\) | ||||
0.555907 | + | 0.831245i | \(0.312371\pi\) | |||||||
\(972\) | 5.02949e13 | 1.80728 | ||||||||
\(973\) | −5.18664e13 | −1.85515 | ||||||||
\(974\) | 7.67369e12 | 0.273205 | ||||||||
\(975\) | −4.61488e13 | −1.63546 | ||||||||
\(976\) | 4.72061e12 | 0.166523 | ||||||||
\(977\) | 1.54215e13 | 0.541505 | 0.270753 | − | 0.962649i | \(-0.412727\pi\) | ||||
0.270753 | + | 0.962649i | \(0.412727\pi\) | |||||||
\(978\) | −4.68225e13 | −1.63655 | ||||||||
\(979\) | 2.05130e13 | 0.713685 | ||||||||
\(980\) | 7.31389e12 | 0.253297 | ||||||||
\(981\) | −2.58057e13 | −0.889620 | ||||||||
\(982\) | 1.30790e13 | 0.448822 | ||||||||
\(983\) | 8.73130e12 | 0.298255 | 0.149128 | − | 0.988818i | \(-0.452353\pi\) | ||||
0.149128 | + | 0.988818i | \(0.452353\pi\) | |||||||
\(984\) | −1.01152e13 | −0.343952 | ||||||||
\(985\) | 1.26199e12 | 0.0427162 | ||||||||
\(986\) | 2.99598e13 | 1.00947 | ||||||||
\(987\) | −4.13473e13 | −1.38682 | ||||||||
\(988\) | −3.30291e13 | −1.10278 | ||||||||
\(989\) | 3.20058e12 | 0.106376 | ||||||||
\(990\) | 4.44482e13 | 1.47061 | ||||||||
\(991\) | −1.88055e13 | −0.619376 | −0.309688 | − | 0.950838i | \(-0.600225\pi\) | ||||
−0.309688 | + | 0.950838i | \(0.600225\pi\) | |||||||
\(992\) | −5.45121e13 | −1.78727 | ||||||||
\(993\) | −3.82390e13 | −1.24806 | ||||||||
\(994\) | 4.49189e13 | 1.45945 | ||||||||
\(995\) | −2.00923e13 | −0.649870 | ||||||||
\(996\) | −5.97099e13 | −1.92256 | ||||||||
\(997\) | 2.93778e12 | 0.0941655 | 0.0470827 | − | 0.998891i | \(-0.485008\pi\) | ||||
0.0470827 | + | 0.998891i | \(0.485008\pi\) | |||||||
\(998\) | −5.53003e12 | −0.176458 | ||||||||
\(999\) | −2.24201e13 | −0.712185 |
(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.1.10 | ✓ | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.10.a.b.1.10 | ✓ | 76 | 1.1 | even | 1 | trivial |