Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(135.996742959\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 45.0643 | 0.995789 | 0.497895 | − | 0.867238i | \(-0.334107\pi\) | ||||
0.497895 | + | 0.867238i | \(0.334107\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | −17.2112 | −0.00840391 | ||||||||
\(5\) | −12444.4 | −1.78089 | −0.890447 | − | 0.455086i | \(-0.849608\pi\) | ||||
−0.890447 | + | 0.455086i | \(0.849608\pi\) | |||||||
\(6\) | 10950.6 | 0.574919 | ||||||||
\(7\) | −11322.2 | −0.254618 | −0.127309 | − | 0.991863i | \(-0.540634\pi\) | ||||
−0.127309 | + | 0.991863i | \(0.540634\pi\) | |||||||
\(8\) | −93067.2 | −1.00416 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −560797. | −1.77340 | ||||||||
\(11\) | −624551. | −1.16925 | −0.584626 | − | 0.811303i | \(-0.698759\pi\) | ||||
−0.584626 | + | 0.811303i | \(0.698759\pi\) | |||||||
\(12\) | −4182.32 | −0.00485200 | ||||||||
\(13\) | −2.19482e6 | −1.63950 | −0.819750 | − | 0.572722i | \(-0.805888\pi\) | ||||
−0.819750 | + | 0.572722i | \(0.805888\pi\) | |||||||
\(14\) | −510225. | −0.253546 | ||||||||
\(15\) | −3.02398e6 | −1.02820 | ||||||||
\(16\) | −4.15876e6 | −0.991525 | ||||||||
\(17\) | −2.69636e6 | −0.460584 | −0.230292 | − | 0.973122i | \(-0.573968\pi\) | ||||
−0.230292 | + | 0.973122i | \(0.573968\pi\) | |||||||
\(18\) | 2.66100e6 | 0.331930 | ||||||||
\(19\) | −1.40825e7 | −1.30477 | −0.652386 | − | 0.757887i | \(-0.726232\pi\) | ||||
−0.652386 | + | 0.757887i | \(0.726232\pi\) | |||||||
\(20\) | 214183. | 0.0149665 | ||||||||
\(21\) | −2.75128e6 | −0.147004 | ||||||||
\(22\) | −2.81450e7 | −1.16433 | ||||||||
\(23\) | 2.01395e7 | 0.652447 | 0.326224 | − | 0.945293i | \(-0.394224\pi\) | ||||
0.326224 | + | 0.945293i | \(0.394224\pi\) | |||||||
\(24\) | −2.26153e7 | −0.579751 | ||||||||
\(25\) | 1.06034e8 | 2.17159 | ||||||||
\(26\) | −9.89082e7 | −1.63260 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | 194868. | 0.00213979 | ||||||||
\(29\) | −3.17284e6 | −0.0287249 | −0.0143625 | − | 0.999897i | \(-0.504572\pi\) | ||||
−0.0143625 | + | 0.999897i | \(0.504572\pi\) | |||||||
\(30\) | −1.36274e8 | −1.02387 | ||||||||
\(31\) | 1.00377e8 | 0.629718 | 0.314859 | − | 0.949138i | \(-0.398043\pi\) | ||||
0.314859 | + | 0.949138i | \(0.398043\pi\) | |||||||
\(32\) | 3.19025e6 | 0.0168074 | ||||||||
\(33\) | −1.51766e8 | −0.675068 | ||||||||
\(34\) | −1.21510e8 | −0.458645 | ||||||||
\(35\) | 1.40897e8 | 0.453449 | ||||||||
\(36\) | −1.01630e6 | −0.00280130 | ||||||||
\(37\) | 7.58547e8 | 1.79834 | 0.899172 | − | 0.437595i | \(-0.144170\pi\) | ||||
0.899172 | + | 0.437595i | \(0.144170\pi\) | |||||||
\(38\) | −6.34617e8 | −1.29928 | ||||||||
\(39\) | −5.33342e8 | −0.946566 | ||||||||
\(40\) | 1.15816e9 | 1.78830 | ||||||||
\(41\) | −7.54684e6 | −0.0101731 | −0.00508656 | − | 0.999987i | \(-0.501619\pi\) | ||||
−0.00508656 | + | 0.999987i | \(0.501619\pi\) | |||||||
\(42\) | −1.23985e8 | −0.146385 | ||||||||
\(43\) | −1.42501e9 | −1.47823 | −0.739116 | − | 0.673579i | \(-0.764756\pi\) | ||||
−0.739116 | + | 0.673579i | \(0.764756\pi\) | |||||||
\(44\) | 1.07493e7 | 0.00982629 | ||||||||
\(45\) | −7.34828e8 | −0.593631 | ||||||||
\(46\) | 9.07572e8 | 0.649700 | ||||||||
\(47\) | −1.00068e9 | −0.636440 | −0.318220 | − | 0.948017i | \(-0.603085\pi\) | ||||
−0.318220 | + | 0.948017i | \(0.603085\pi\) | |||||||
\(48\) | −1.01058e9 | −0.572457 | ||||||||
\(49\) | −1.84914e9 | −0.935169 | ||||||||
\(50\) | 4.77836e9 | 2.16244 | ||||||||
\(51\) | −6.55216e8 | −0.265918 | ||||||||
\(52\) | 3.77756e7 | 0.0137782 | ||||||||
\(53\) | −3.23368e9 | −1.06213 | −0.531067 | − | 0.847330i | \(-0.678209\pi\) | ||||
−0.531067 | + | 0.847330i | \(0.678209\pi\) | |||||||
\(54\) | 6.46623e8 | 0.191640 | ||||||||
\(55\) | 7.77215e9 | 2.08232 | ||||||||
\(56\) | 1.05372e9 | 0.255677 | ||||||||
\(57\) | −3.42204e9 | −0.753310 | ||||||||
\(58\) | −1.42982e8 | −0.0286040 | ||||||||
\(59\) | 7.14924e8 | 0.130189 | ||||||||
\(60\) | 5.20464e7 | 0.00864090 | ||||||||
\(61\) | −9.23337e9 | −1.39974 | −0.699868 | − | 0.714272i | \(-0.746758\pi\) | ||||
−0.699868 | + | 0.714272i | \(0.746758\pi\) | |||||||
\(62\) | 4.52343e9 | 0.627067 | ||||||||
\(63\) | −6.68562e8 | −0.0848728 | ||||||||
\(64\) | 8.66091e9 | 1.00826 | ||||||||
\(65\) | 2.73132e10 | 2.91978 | ||||||||
\(66\) | −6.83922e9 | −0.672226 | ||||||||
\(67\) | −1.91218e9 | −0.173028 | −0.0865141 | − | 0.996251i | \(-0.527573\pi\) | ||||
−0.0865141 | + | 0.996251i | \(0.527573\pi\) | |||||||
\(68\) | 4.64076e7 | 0.00387071 | ||||||||
\(69\) | 4.89390e9 | 0.376691 | ||||||||
\(70\) | 6.34943e9 | 0.451539 | ||||||||
\(71\) | −1.76446e10 | −1.16062 | −0.580311 | − | 0.814395i | \(-0.697069\pi\) | ||||
−0.580311 | + | 0.814395i | \(0.697069\pi\) | |||||||
\(72\) | −5.49553e9 | −0.334719 | ||||||||
\(73\) | 1.51898e10 | 0.857584 | 0.428792 | − | 0.903403i | \(-0.358939\pi\) | ||||
0.428792 | + | 0.903403i | \(0.358939\pi\) | |||||||
\(74\) | 3.41834e10 | 1.79077 | ||||||||
\(75\) | 2.57664e10 | 1.25377 | ||||||||
\(76\) | 2.42377e8 | 0.0109652 | ||||||||
\(77\) | 7.07127e9 | 0.297713 | ||||||||
\(78\) | −2.40347e10 | −0.942580 | ||||||||
\(79\) | 7.55668e9 | 0.276301 | 0.138150 | − | 0.990411i | \(-0.455884\pi\) | ||||
0.138150 | + | 0.990411i | \(0.455884\pi\) | |||||||
\(80\) | 5.17532e10 | 1.76580 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −3.40093e8 | −0.0101303 | ||||||||
\(83\) | 5.47937e10 | 1.52687 | 0.763433 | − | 0.645886i | \(-0.223512\pi\) | ||||
0.763433 | + | 0.645886i | \(0.223512\pi\) | |||||||
\(84\) | 4.73529e7 | 0.00123541 | ||||||||
\(85\) | 3.35545e10 | 0.820252 | ||||||||
\(86\) | −6.42172e10 | −1.47201 | ||||||||
\(87\) | −7.70999e8 | −0.0165843 | ||||||||
\(88\) | 5.81253e10 | 1.17411 | ||||||||
\(89\) | −3.81766e10 | −0.724690 | −0.362345 | − | 0.932044i | \(-0.618024\pi\) | ||||
−0.362345 | + | 0.932044i | \(0.618024\pi\) | |||||||
\(90\) | −3.31145e10 | −0.591132 | ||||||||
\(91\) | 2.48501e10 | 0.417447 | ||||||||
\(92\) | −3.46625e8 | −0.00548311 | ||||||||
\(93\) | 2.43917e10 | 0.363568 | ||||||||
\(94\) | −4.50949e10 | −0.633760 | ||||||||
\(95\) | 1.75248e11 | 2.32366 | ||||||||
\(96\) | 7.75231e8 | 0.00970374 | ||||||||
\(97\) | −5.92325e10 | −0.700351 | −0.350175 | − | 0.936684i | \(-0.613878\pi\) | ||||
−0.350175 | + | 0.936684i | \(0.613878\pi\) | |||||||
\(98\) | −8.33300e10 | −0.931232 | ||||||||
\(99\) | −3.68791e10 | −0.389751 | ||||||||
\(100\) | −1.82498e9 | −0.0182498 | ||||||||
\(101\) | 1.10713e10 | 0.104817 | 0.0524085 | − | 0.998626i | \(-0.483310\pi\) | ||||
0.0524085 | + | 0.998626i | \(0.483310\pi\) | |||||||
\(102\) | −2.95268e10 | −0.264799 | ||||||||
\(103\) | 1.09862e10 | 0.0933777 | 0.0466888 | − | 0.998909i | \(-0.485133\pi\) | ||||
0.0466888 | + | 0.998909i | \(0.485133\pi\) | |||||||
\(104\) | 2.04266e11 | 1.64632 | ||||||||
\(105\) | 3.42380e10 | 0.261799 | ||||||||
\(106\) | −1.45723e11 | −1.05766 | ||||||||
\(107\) | −4.85869e10 | −0.334895 | −0.167447 | − | 0.985881i | \(-0.553552\pi\) | ||||
−0.167447 | + | 0.985881i | \(0.553552\pi\) | |||||||
\(108\) | −2.46962e8 | −0.00161733 | ||||||||
\(109\) | −2.58166e11 | −1.60714 | −0.803571 | − | 0.595209i | \(-0.797069\pi\) | ||||
−0.803571 | + | 0.595209i | \(0.797069\pi\) | |||||||
\(110\) | 3.50247e11 | 2.07355 | ||||||||
\(111\) | 1.84327e11 | 1.03827 | ||||||||
\(112\) | 4.70861e10 | 0.252461 | ||||||||
\(113\) | 2.98929e11 | 1.52629 | 0.763144 | − | 0.646228i | \(-0.223654\pi\) | ||||
0.763144 | + | 0.646228i | \(0.223654\pi\) | |||||||
\(114\) | −1.54212e11 | −0.750138 | ||||||||
\(115\) | −2.50623e11 | −1.16194 | ||||||||
\(116\) | 5.46083e7 | 0.000241402 0 | ||||||||
\(117\) | −1.29602e11 | −0.546500 | ||||||||
\(118\) | 3.22175e10 | 0.129641 | ||||||||
\(119\) | 3.05286e10 | 0.117273 | ||||||||
\(120\) | 2.81434e11 | 1.03247 | ||||||||
\(121\) | 1.04753e11 | 0.367152 | ||||||||
\(122\) | −4.16095e11 | −1.39384 | ||||||||
\(123\) | −1.83388e9 | −0.00587345 | ||||||||
\(124\) | −1.72761e9 | −0.00529210 | ||||||||
\(125\) | −7.11897e11 | −2.08647 | ||||||||
\(126\) | −3.01283e10 | −0.0845154 | ||||||||
\(127\) | −1.68798e11 | −0.453364 | −0.226682 | − | 0.973969i | \(-0.572788\pi\) | ||||
−0.226682 | + | 0.973969i | \(0.572788\pi\) | |||||||
\(128\) | 3.83764e11 | 0.987209 | ||||||||
\(129\) | −3.46278e11 | −0.853457 | ||||||||
\(130\) | 1.23085e12 | 2.90748 | ||||||||
\(131\) | 1.91861e11 | 0.434505 | 0.217252 | − | 0.976115i | \(-0.430291\pi\) | ||||
0.217252 | + | 0.976115i | \(0.430291\pi\) | |||||||
\(132\) | 2.61208e9 | 0.00567321 | ||||||||
\(133\) | 1.59444e11 | 0.332219 | ||||||||
\(134\) | −8.61709e10 | −0.172300 | ||||||||
\(135\) | −1.78563e11 | −0.342733 | ||||||||
\(136\) | 2.50943e11 | 0.462499 | ||||||||
\(137\) | −3.68526e11 | −0.652386 | −0.326193 | − | 0.945303i | \(-0.605766\pi\) | ||||
−0.326193 | + | 0.945303i | \(0.605766\pi\) | |||||||
\(138\) | 2.20540e11 | 0.375104 | ||||||||
\(139\) | 4.13605e11 | 0.676090 | 0.338045 | − | 0.941130i | \(-0.390234\pi\) | ||||
0.338045 | + | 0.941130i | \(0.390234\pi\) | |||||||
\(140\) | −2.42501e9 | −0.00381074 | ||||||||
\(141\) | −2.43165e11 | −0.367449 | ||||||||
\(142\) | −7.95141e11 | −1.15573 | ||||||||
\(143\) | 1.37078e12 | 1.91699 | ||||||||
\(144\) | −2.45571e11 | −0.330508 | ||||||||
\(145\) | 3.94840e10 | 0.0511560 | ||||||||
\(146\) | 6.84518e11 | 0.853973 | ||||||||
\(147\) | −4.49340e11 | −0.539920 | ||||||||
\(148\) | −1.30555e10 | −0.0151131 | ||||||||
\(149\) | 1.51131e12 | 1.68588 | 0.842942 | − | 0.538004i | \(-0.180821\pi\) | ||||
0.842942 | + | 0.538004i | \(0.180821\pi\) | |||||||
\(150\) | 1.16114e12 | 1.24849 | ||||||||
\(151\) | 5.95905e11 | 0.617737 | 0.308869 | − | 0.951105i | \(-0.400050\pi\) | ||||
0.308869 | + | 0.951105i | \(0.400050\pi\) | |||||||
\(152\) | 1.31062e12 | 1.31020 | ||||||||
\(153\) | −1.59217e11 | −0.153528 | ||||||||
\(154\) | 3.18662e11 | 0.296460 | ||||||||
\(155\) | −1.24913e12 | −1.12146 | ||||||||
\(156\) | 9.17946e9 | 0.00795485 | ||||||||
\(157\) | 7.47869e11 | 0.625716 | 0.312858 | − | 0.949800i | \(-0.398714\pi\) | ||||
0.312858 | + | 0.949800i | \(0.398714\pi\) | |||||||
\(158\) | 3.40536e11 | 0.275137 | ||||||||
\(159\) | −7.85784e11 | −0.613223 | ||||||||
\(160\) | −3.97007e10 | −0.0299322 | ||||||||
\(161\) | −2.28022e11 | −0.166125 | ||||||||
\(162\) | 1.57129e11 | 0.110643 | ||||||||
\(163\) | −2.66878e12 | −1.81669 | −0.908345 | − | 0.418221i | \(-0.862654\pi\) | ||||
−0.908345 | + | 0.418221i | \(0.862654\pi\) | |||||||
\(164\) | 1.29890e8 | 8.54940e−5 0 | ||||||||
\(165\) | 1.88863e12 | 1.20223 | ||||||||
\(166\) | 2.46924e12 | 1.52044 | ||||||||
\(167\) | −1.02807e12 | −0.612468 | −0.306234 | − | 0.951956i | \(-0.599069\pi\) | ||||
−0.306234 | + | 0.951956i | \(0.599069\pi\) | |||||||
\(168\) | 2.56054e11 | 0.147615 | ||||||||
\(169\) | 3.02509e12 | 1.68796 | ||||||||
\(170\) | 1.51211e12 | 0.816798 | ||||||||
\(171\) | −8.31557e11 | −0.434924 | ||||||||
\(172\) | 2.45262e10 | 0.0124229 | ||||||||
\(173\) | −1.72017e11 | −0.0843951 | −0.0421975 | − | 0.999109i | \(-0.513436\pi\) | ||||
−0.0421975 | + | 0.999109i | \(0.513436\pi\) | |||||||
\(174\) | −3.47445e10 | −0.0165145 | ||||||||
\(175\) | −1.20054e12 | −0.552926 | ||||||||
\(176\) | 2.59736e12 | 1.15934 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | −1.72040e12 | −0.721638 | ||||||||
\(179\) | 5.62298e11 | 0.228705 | 0.114352 | − | 0.993440i | \(-0.463521\pi\) | ||||
0.114352 | + | 0.993440i | \(0.463521\pi\) | |||||||
\(180\) | 1.26473e10 | 0.00498882 | ||||||||
\(181\) | −3.52626e12 | −1.34922 | −0.674609 | − | 0.738175i | \(-0.735688\pi\) | ||||
−0.674609 | + | 0.738175i | \(0.735688\pi\) | |||||||
\(182\) | 1.11985e12 | 0.415689 | ||||||||
\(183\) | −2.24371e12 | −0.808138 | ||||||||
\(184\) | −1.87433e12 | −0.655160 | ||||||||
\(185\) | −9.43964e12 | −3.20266 | ||||||||
\(186\) | 1.09919e12 | 0.362037 | ||||||||
\(187\) | 1.68402e12 | 0.538539 | ||||||||
\(188\) | 1.72229e10 | 0.00534858 | ||||||||
\(189\) | −1.62461e11 | −0.0490013 | ||||||||
\(190\) | 7.89741e12 | 2.31388 | ||||||||
\(191\) | −2.61082e12 | −0.743178 | −0.371589 | − | 0.928397i | \(-0.621187\pi\) | ||||
−0.371589 | + | 0.928397i | \(0.621187\pi\) | |||||||
\(192\) | 2.10460e12 | 0.582120 | ||||||||
\(193\) | −6.52555e12 | −1.75409 | −0.877046 | − | 0.480407i | \(-0.840489\pi\) | ||||
−0.877046 | + | 0.480407i | \(0.840489\pi\) | |||||||
\(194\) | −2.66927e12 | −0.697402 | ||||||||
\(195\) | 6.63711e12 | 1.68573 | ||||||||
\(196\) | 3.18258e10 | 0.00785908 | ||||||||
\(197\) | −4.64972e12 | −1.11651 | −0.558255 | − | 0.829670i | \(-0.688529\pi\) | ||||
−0.558255 | + | 0.829670i | \(0.688529\pi\) | |||||||
\(198\) | −1.66193e12 | −0.388110 | ||||||||
\(199\) | 6.85711e12 | 1.55758 | 0.778788 | − | 0.627288i | \(-0.215835\pi\) | ||||
0.778788 | + | 0.627288i | \(0.215835\pi\) | |||||||
\(200\) | −9.86833e12 | −2.18061 | ||||||||
\(201\) | −4.64659e11 | −0.0998979 | ||||||||
\(202\) | 4.98921e11 | 0.104376 | ||||||||
\(203\) | 3.59234e10 | 0.00731389 | ||||||||
\(204\) | 1.12771e10 | 0.00223475 | ||||||||
\(205\) | 9.39158e10 | 0.0181173 | ||||||||
\(206\) | 4.95085e11 | 0.0929845 | ||||||||
\(207\) | 1.18922e12 | 0.217482 | ||||||||
\(208\) | 9.12775e12 | 1.62561 | ||||||||
\(209\) | 8.79524e12 | 1.52561 | ||||||||
\(210\) | 1.54291e12 | 0.260696 | ||||||||
\(211\) | −1.53005e12 | −0.251856 | −0.125928 | − | 0.992039i | \(-0.540191\pi\) | ||||
−0.125928 | + | 0.992039i | \(0.540191\pi\) | |||||||
\(212\) | 5.56555e10 | 0.00892608 | ||||||||
\(213\) | −4.28764e12 | −0.670085 | ||||||||
\(214\) | −2.18953e12 | −0.333485 | ||||||||
\(215\) | 1.77334e13 | 2.63257 | ||||||||
\(216\) | −1.33541e12 | −0.193250 | ||||||||
\(217\) | −1.13649e12 | −0.160338 | ||||||||
\(218\) | −1.16341e13 | −1.60037 | ||||||||
\(219\) | 3.69112e12 | 0.495126 | ||||||||
\(220\) | −1.33768e11 | −0.0174996 | ||||||||
\(221\) | 5.91804e12 | 0.755128 | ||||||||
\(222\) | 8.30655e12 | 1.03390 | ||||||||
\(223\) | −4.41839e11 | −0.0536521 | −0.0268261 | − | 0.999640i | \(-0.508540\pi\) | ||||
−0.0268261 | + | 0.999640i | \(0.508540\pi\) | |||||||
\(224\) | −3.61205e10 | −0.00427947 | ||||||||
\(225\) | 6.26123e12 | 0.723862 | ||||||||
\(226\) | 1.34710e13 | 1.51986 | ||||||||
\(227\) | 6.18166e12 | 0.680711 | 0.340355 | − | 0.940297i | \(-0.389453\pi\) | ||||
0.340355 | + | 0.940297i | \(0.389453\pi\) | |||||||
\(228\) | 5.88975e10 | 0.00633075 | ||||||||
\(229\) | 8.41904e12 | 0.883421 | 0.441710 | − | 0.897158i | \(-0.354372\pi\) | ||||
0.441710 | + | 0.897158i | \(0.354372\pi\) | |||||||
\(230\) | −1.12942e13 | −1.15705 | ||||||||
\(231\) | 1.71832e12 | 0.171885 | ||||||||
\(232\) | 2.95287e11 | 0.0288443 | ||||||||
\(233\) | 1.26195e13 | 1.20389 | 0.601944 | − | 0.798538i | \(-0.294393\pi\) | ||||
0.601944 | + | 0.798538i | \(0.294393\pi\) | |||||||
\(234\) | −5.84043e12 | −0.544199 | ||||||||
\(235\) | 1.24528e13 | 1.13343 | ||||||||
\(236\) | −1.23047e10 | −0.00109410 | ||||||||
\(237\) | 1.83627e12 | 0.159522 | ||||||||
\(238\) | 1.37575e12 | 0.116779 | ||||||||
\(239\) | −1.13206e13 | −0.939037 | −0.469518 | − | 0.882923i | \(-0.655572\pi\) | ||||
−0.469518 | + | 0.882923i | \(0.655572\pi\) | |||||||
\(240\) | 1.25760e13 | 1.01949 | ||||||||
\(241\) | 4.78681e12 | 0.379273 | 0.189637 | − | 0.981854i | \(-0.439269\pi\) | ||||
0.189637 | + | 0.981854i | \(0.439269\pi\) | |||||||
\(242\) | 4.72061e12 | 0.365606 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | 1.58917e11 | 0.0117633 | ||||||||
\(245\) | 2.30113e13 | 1.66544 | ||||||||
\(246\) | −8.26426e10 | −0.00584872 | ||||||||
\(247\) | 3.09086e13 | 2.13917 | ||||||||
\(248\) | −9.34184e12 | −0.632337 | ||||||||
\(249\) | 1.33149e13 | 0.881537 | ||||||||
\(250\) | −3.20811e13 | −2.07768 | ||||||||
\(251\) | −4.01399e12 | −0.254314 | −0.127157 | − | 0.991883i | \(-0.540585\pi\) | ||||
−0.127157 | + | 0.991883i | \(0.540585\pi\) | |||||||
\(252\) | 1.15068e10 | 0.000713263 0 | ||||||||
\(253\) | −1.25781e13 | −0.762876 | ||||||||
\(254\) | −7.60677e12 | −0.451455 | ||||||||
\(255\) | 8.15375e12 | 0.473573 | ||||||||
\(256\) | −4.43498e11 | −0.0252099 | ||||||||
\(257\) | −1.94695e13 | −1.08323 | −0.541617 | − | 0.840626i | \(-0.682188\pi\) | ||||
−0.541617 | + | 0.840626i | \(0.682188\pi\) | |||||||
\(258\) | −1.56048e13 | −0.849864 | ||||||||
\(259\) | −8.58838e12 | −0.457892 | ||||||||
\(260\) | −4.70093e11 | −0.0245375 | ||||||||
\(261\) | −1.87353e11 | −0.00957497 | ||||||||
\(262\) | 8.64607e12 | 0.432675 | ||||||||
\(263\) | −3.27832e13 | −1.60655 | −0.803276 | − | 0.595607i | \(-0.796911\pi\) | ||||
−0.803276 | + | 0.595607i | \(0.796911\pi\) | |||||||
\(264\) | 1.41244e13 | 0.677875 | ||||||||
\(265\) | 4.02411e13 | 1.89155 | ||||||||
\(266\) | 7.18523e12 | 0.330820 | ||||||||
\(267\) | −9.27691e12 | −0.418400 | ||||||||
\(268\) | 3.29109e10 | 0.00145411 | ||||||||
\(269\) | −1.49518e11 | −0.00647224 | −0.00323612 | − | 0.999995i | \(-0.501030\pi\) | ||||
−0.00323612 | + | 0.999995i | \(0.501030\pi\) | |||||||
\(270\) | −8.04682e12 | −0.341290 | ||||||||
\(271\) | −3.18363e12 | −0.132310 | −0.0661548 | − | 0.997809i | \(-0.521073\pi\) | ||||
−0.0661548 | + | 0.997809i | \(0.521073\pi\) | |||||||
\(272\) | 1.12135e13 | 0.456681 | ||||||||
\(273\) | 6.03858e12 | 0.241013 | ||||||||
\(274\) | −1.66073e13 | −0.649639 | ||||||||
\(275\) | −6.62240e13 | −2.53913 | ||||||||
\(276\) | −8.42298e10 | −0.00316567 | ||||||||
\(277\) | −3.21889e13 | −1.18595 | −0.592977 | − | 0.805219i | \(-0.702048\pi\) | ||||
−0.592977 | + | 0.805219i | \(0.702048\pi\) | |||||||
\(278\) | 1.86388e13 | 0.673243 | ||||||||
\(279\) | 5.92718e12 | 0.209906 | ||||||||
\(280\) | −1.31129e13 | −0.455334 | ||||||||
\(281\) | 4.16532e13 | 1.41828 | 0.709142 | − | 0.705065i | \(-0.249082\pi\) | ||||
0.709142 | + | 0.705065i | \(0.249082\pi\) | |||||||
\(282\) | −1.09581e13 | −0.365901 | ||||||||
\(283\) | 2.20023e13 | 0.720515 | 0.360258 | − | 0.932853i | \(-0.382689\pi\) | ||||
0.360258 | + | 0.932853i | \(0.382689\pi\) | |||||||
\(284\) | 3.03685e11 | 0.00975376 | ||||||||
\(285\) | 4.25852e13 | 1.34157 | ||||||||
\(286\) | 6.17732e13 | 1.90892 | ||||||||
\(287\) | 8.54466e10 | 0.00259026 | ||||||||
\(288\) | 1.88381e11 | 0.00560246 | ||||||||
\(289\) | −2.70015e13 | −0.787862 | ||||||||
\(290\) | 1.77932e12 | 0.0509406 | ||||||||
\(291\) | −1.43935e13 | −0.404348 | ||||||||
\(292\) | −2.61435e11 | −0.00720706 | ||||||||
\(293\) | −4.68622e11 | −0.0126780 | −0.00633900 | − | 0.999980i | \(-0.502018\pi\) | ||||
−0.00633900 | + | 0.999980i | \(0.502018\pi\) | |||||||
\(294\) | −2.02492e13 | −0.537647 | ||||||||
\(295\) | −8.89679e12 | −0.231853 | ||||||||
\(296\) | −7.05958e13 | −1.80582 | ||||||||
\(297\) | −8.96163e12 | −0.225023 | ||||||||
\(298\) | 6.81059e13 | 1.67879 | ||||||||
\(299\) | −4.42026e13 | −1.06969 | ||||||||
\(300\) | −4.43470e11 | −0.0105365 | ||||||||
\(301\) | 1.61342e13 | 0.376385 | ||||||||
\(302\) | 2.68540e13 | 0.615136 | ||||||||
\(303\) | 2.69033e12 | 0.0605161 | ||||||||
\(304\) | 5.85657e13 | 1.29371 | ||||||||
\(305\) | 1.14904e14 | 2.49278 | ||||||||
\(306\) | −7.17502e12 | −0.152882 | ||||||||
\(307\) | 5.73318e13 | 1.19987 | 0.599935 | − | 0.800049i | \(-0.295193\pi\) | ||||
0.599935 | + | 0.800049i | \(0.295193\pi\) | |||||||
\(308\) | −1.21705e11 | −0.00250196 | ||||||||
\(309\) | 2.66965e12 | 0.0539116 | ||||||||
\(310\) | −5.62913e13 | −1.11674 | ||||||||
\(311\) | 2.08663e13 | 0.406690 | 0.203345 | − | 0.979107i | \(-0.434819\pi\) | ||||
0.203345 | + | 0.979107i | \(0.434819\pi\) | |||||||
\(312\) | 4.96367e13 | 0.950501 | ||||||||
\(313\) | −5.90856e13 | −1.11170 | −0.555850 | − | 0.831283i | \(-0.687607\pi\) | ||||
−0.555850 | + | 0.831283i | \(0.687607\pi\) | |||||||
\(314\) | 3.37022e13 | 0.623081 | ||||||||
\(315\) | 8.31984e12 | 0.151150 | ||||||||
\(316\) | −1.30060e11 | −0.00232201 | ||||||||
\(317\) | −3.81528e13 | −0.669422 | −0.334711 | − | 0.942321i | \(-0.608639\pi\) | ||||
−0.334711 | + | 0.942321i | \(0.608639\pi\) | |||||||
\(318\) | −3.54108e13 | −0.610641 | ||||||||
\(319\) | 1.98160e12 | 0.0335867 | ||||||||
\(320\) | −1.07780e14 | −1.79561 | ||||||||
\(321\) | −1.18066e13 | −0.193352 | ||||||||
\(322\) | −1.02757e13 | −0.165426 | ||||||||
\(323\) | 3.79715e13 | 0.600957 | ||||||||
\(324\) | −6.00118e10 | −0.000933768 0 | ||||||||
\(325\) | −2.32727e14 | −3.56031 | ||||||||
\(326\) | −1.20267e14 | −1.80904 | ||||||||
\(327\) | −6.27344e13 | −0.927883 | ||||||||
\(328\) | 7.02364e11 | 0.0102154 | ||||||||
\(329\) | 1.13299e13 | 0.162049 | ||||||||
\(330\) | 8.51099e13 | 1.19716 | ||||||||
\(331\) | −9.76917e13 | −1.35146 | −0.675731 | − | 0.737148i | \(-0.736172\pi\) | ||||
−0.675731 | + | 0.737148i | \(0.736172\pi\) | |||||||
\(332\) | −9.43066e11 | −0.0128316 | ||||||||
\(333\) | 4.47914e13 | 0.599448 | ||||||||
\(334\) | −4.63294e13 | −0.609889 | ||||||||
\(335\) | 2.37959e13 | 0.308145 | ||||||||
\(336\) | 1.14419e13 | 0.145758 | ||||||||
\(337\) | −1.51543e14 | −1.89920 | −0.949600 | − | 0.313466i | \(-0.898510\pi\) | ||||
−0.949600 | + | 0.313466i | \(0.898510\pi\) | |||||||
\(338\) | 1.36324e14 | 1.68085 | ||||||||
\(339\) | 7.26398e13 | 0.881203 | ||||||||
\(340\) | −5.77514e11 | −0.00689332 | ||||||||
\(341\) | −6.26908e13 | −0.736300 | ||||||||
\(342\) | −3.74735e13 | −0.433092 | ||||||||
\(343\) | 4.33238e13 | 0.492730 | ||||||||
\(344\) | 1.32622e14 | 1.48438 | ||||||||
\(345\) | −6.09015e13 | −0.670846 | ||||||||
\(346\) | −7.75181e12 | −0.0840397 | ||||||||
\(347\) | 9.52383e13 | 1.01625 | 0.508124 | − | 0.861284i | \(-0.330339\pi\) | ||||
0.508124 | + | 0.861284i | \(0.330339\pi\) | |||||||
\(348\) | 1.32698e10 | 0.000139373 0 | ||||||||
\(349\) | 8.82646e13 | 0.912529 | 0.456265 | − | 0.889844i | \(-0.349187\pi\) | ||||
0.456265 | + | 0.889844i | \(0.349187\pi\) | |||||||
\(350\) | −5.41014e13 | −0.550597 | ||||||||
\(351\) | −3.14933e13 | −0.315522 | ||||||||
\(352\) | −1.99247e12 | −0.0196521 | ||||||||
\(353\) | 1.60371e13 | 0.155727 | 0.0778635 | − | 0.996964i | \(-0.475190\pi\) | ||||
0.0778635 | + | 0.996964i | \(0.475190\pi\) | |||||||
\(354\) | 7.82886e12 | 0.0748481 | ||||||||
\(355\) | 2.19576e14 | 2.06695 | ||||||||
\(356\) | 6.57065e11 | 0.00609023 | ||||||||
\(357\) | 7.41846e12 | 0.0677077 | ||||||||
\(358\) | 2.53395e13 | 0.227742 | ||||||||
\(359\) | −1.81807e14 | −1.60913 | −0.804566 | − | 0.593863i | \(-0.797602\pi\) | ||||
−0.804566 | + | 0.593863i | \(0.797602\pi\) | |||||||
\(360\) | 6.83884e13 | 0.596100 | ||||||||
\(361\) | 8.18261e13 | 0.702429 | ||||||||
\(362\) | −1.58908e14 | −1.34354 | ||||||||
\(363\) | 2.54549e13 | 0.211976 | ||||||||
\(364\) | −4.27701e11 | −0.00350819 | ||||||||
\(365\) | −1.89028e14 | −1.52727 | ||||||||
\(366\) | −1.01111e14 | −0.804735 | ||||||||
\(367\) | −3.54522e13 | −0.277958 | −0.138979 | − | 0.990295i | \(-0.544382\pi\) | ||||
−0.138979 | + | 0.990295i | \(0.544382\pi\) | |||||||
\(368\) | −8.37553e13 | −0.646918 | ||||||||
\(369\) | −4.45634e11 | −0.00339104 | ||||||||
\(370\) | −4.25391e14 | −3.18918 | ||||||||
\(371\) | 3.66122e13 | 0.270439 | ||||||||
\(372\) | −4.19810e11 | −0.00305539 | ||||||||
\(373\) | −1.39186e14 | −0.998150 | −0.499075 | − | 0.866559i | \(-0.666327\pi\) | ||||
−0.499075 | + | 0.866559i | \(0.666327\pi\) | |||||||
\(374\) | 7.58890e13 | 0.536272 | ||||||||
\(375\) | −1.72991e14 | −1.20462 | ||||||||
\(376\) | 9.31306e13 | 0.639086 | ||||||||
\(377\) | 6.96382e12 | 0.0470945 | ||||||||
\(378\) | −7.32117e12 | −0.0487950 | ||||||||
\(379\) | −3.23319e12 | −0.0212381 | −0.0106191 | − | 0.999944i | \(-0.503380\pi\) | ||||
−0.0106191 | + | 0.999944i | \(0.503380\pi\) | |||||||
\(380\) | −3.01623e12 | −0.0195278 | ||||||||
\(381\) | −4.10180e13 | −0.261750 | ||||||||
\(382\) | −1.17655e14 | −0.740049 | ||||||||
\(383\) | 7.59209e13 | 0.470726 | 0.235363 | − | 0.971908i | \(-0.424372\pi\) | ||||
0.235363 | + | 0.971908i | \(0.424372\pi\) | |||||||
\(384\) | 9.32546e13 | 0.569965 | ||||||||
\(385\) | −8.79975e13 | −0.530196 | ||||||||
\(386\) | −2.94069e14 | −1.74670 | ||||||||
\(387\) | −8.41456e13 | −0.492744 | ||||||||
\(388\) | 1.01946e12 | 0.00588568 | ||||||||
\(389\) | −8.62586e12 | −0.0490998 | −0.0245499 | − | 0.999699i | \(-0.507815\pi\) | ||||
−0.0245499 | + | 0.999699i | \(0.507815\pi\) | |||||||
\(390\) | 2.99097e14 | 1.67864 | ||||||||
\(391\) | −5.43033e13 | −0.300507 | ||||||||
\(392\) | 1.72094e14 | 0.939058 | ||||||||
\(393\) | 4.66222e13 | 0.250861 | ||||||||
\(394\) | −2.09536e14 | −1.11181 | ||||||||
\(395\) | −9.40382e13 | −0.492063 | ||||||||
\(396\) | 6.34734e11 | 0.00327543 | ||||||||
\(397\) | −2.23278e13 | −0.113631 | −0.0568156 | − | 0.998385i | \(-0.518095\pi\) | ||||
−0.0568156 | + | 0.998385i | \(0.518095\pi\) | |||||||
\(398\) | 3.09011e14 | 1.55102 | ||||||||
\(399\) | 3.87449e13 | 0.191807 | ||||||||
\(400\) | −4.40972e14 | −2.15318 | ||||||||
\(401\) | −2.96381e14 | −1.42744 | −0.713718 | − | 0.700433i | \(-0.752990\pi\) | ||||
−0.713718 | + | 0.700433i | \(0.752990\pi\) | |||||||
\(402\) | −2.09395e13 | −0.0994772 | ||||||||
\(403\) | −2.20311e14 | −1.03242 | ||||||||
\(404\) | −1.90551e11 | −0.000880872 0 | ||||||||
\(405\) | −4.33909e13 | −0.197877 | ||||||||
\(406\) | 1.61886e12 | 0.00728310 | ||||||||
\(407\) | −4.73751e14 | −2.10272 | ||||||||
\(408\) | 6.09791e13 | 0.267024 | ||||||||
\(409\) | −2.90683e14 | −1.25586 | −0.627930 | − | 0.778270i | \(-0.716098\pi\) | ||||
−0.627930 | + | 0.778270i | \(0.716098\pi\) | |||||||
\(410\) | 4.23225e12 | 0.0180410 | ||||||||
\(411\) | −8.95517e13 | −0.376655 | ||||||||
\(412\) | −1.89086e11 | −0.000784737 0 | ||||||||
\(413\) | −8.09448e12 | −0.0331485 | ||||||||
\(414\) | 5.35912e13 | 0.216567 | ||||||||
\(415\) | −6.81874e14 | −2.71919 | ||||||||
\(416\) | −7.00204e12 | −0.0275557 | ||||||||
\(417\) | 1.00506e14 | 0.390341 | ||||||||
\(418\) | 3.96351e14 | 1.51918 | ||||||||
\(419\) | 3.58199e14 | 1.35503 | 0.677513 | − | 0.735511i | \(-0.263058\pi\) | ||||
0.677513 | + | 0.735511i | \(0.263058\pi\) | |||||||
\(420\) | −5.89278e11 | −0.00220013 | ||||||||
\(421\) | 1.75978e14 | 0.648497 | 0.324248 | − | 0.945972i | \(-0.394889\pi\) | ||||
0.324248 | + | 0.945972i | \(0.394889\pi\) | |||||||
\(422\) | −6.89506e13 | −0.250795 | ||||||||
\(423\) | −5.90892e13 | −0.212147 | ||||||||
\(424\) | 3.00949e14 | 1.06655 | ||||||||
\(425\) | −2.85907e14 | −1.00020 | ||||||||
\(426\) | −1.93219e14 | −0.667264 | ||||||||
\(427\) | 1.04542e14 | 0.356399 | ||||||||
\(428\) | 8.36239e11 | 0.00281443 | ||||||||
\(429\) | 3.33100e14 | 1.10677 | ||||||||
\(430\) | 7.99143e14 | 2.62149 | ||||||||
\(431\) | 1.45826e14 | 0.472291 | 0.236145 | − | 0.971718i | \(-0.424116\pi\) | ||||
0.236145 | + | 0.971718i | \(0.424116\pi\) | |||||||
\(432\) | −5.96736e13 | −0.190819 | ||||||||
\(433\) | 3.15377e14 | 0.995741 | 0.497871 | − | 0.867251i | \(-0.334115\pi\) | ||||
0.497871 | + | 0.867251i | \(0.334115\pi\) | |||||||
\(434\) | −5.12150e13 | −0.159663 | ||||||||
\(435\) | 9.59461e12 | 0.0295350 | ||||||||
\(436\) | 4.44336e12 | 0.0135063 | ||||||||
\(437\) | −2.83614e14 | −0.851295 | ||||||||
\(438\) | 1.66338e14 | 0.493042 | ||||||||
\(439\) | 9.13881e13 | 0.267507 | 0.133753 | − | 0.991015i | \(-0.457297\pi\) | ||||
0.133753 | + | 0.991015i | \(0.457297\pi\) | |||||||
\(440\) | −7.23333e14 | −2.09097 | ||||||||
\(441\) | −1.09190e14 | −0.311723 | ||||||||
\(442\) | 2.66692e14 | 0.751948 | ||||||||
\(443\) | −3.80912e14 | −1.06073 | −0.530364 | − | 0.847770i | \(-0.677945\pi\) | ||||
−0.530364 | + | 0.847770i | \(0.677945\pi\) | |||||||
\(444\) | −3.17249e12 | −0.00872556 | ||||||||
\(445\) | 4.75084e14 | 1.29060 | ||||||||
\(446\) | −1.99111e13 | −0.0534262 | ||||||||
\(447\) | 3.67247e14 | 0.973346 | ||||||||
\(448\) | −9.80601e13 | −0.256722 | ||||||||
\(449\) | 1.65064e14 | 0.426871 | 0.213436 | − | 0.976957i | \(-0.431535\pi\) | ||||
0.213436 | + | 0.976957i | \(0.431535\pi\) | |||||||
\(450\) | 2.82158e14 | 0.720814 | ||||||||
\(451\) | 4.71339e12 | 0.0118950 | ||||||||
\(452\) | −5.14493e12 | −0.0128268 | ||||||||
\(453\) | 1.44805e14 | 0.356651 | ||||||||
\(454\) | 2.78572e14 | 0.677844 | ||||||||
\(455\) | −3.09245e14 | −0.743429 | ||||||||
\(456\) | 3.18480e14 | 0.756442 | ||||||||
\(457\) | 7.84400e14 | 1.84077 | 0.920383 | − | 0.391018i | \(-0.127877\pi\) | ||||
0.920383 | + | 0.391018i | \(0.127877\pi\) | |||||||
\(458\) | 3.79398e14 | 0.879701 | ||||||||
\(459\) | −3.86898e13 | −0.0886395 | ||||||||
\(460\) | 4.31353e12 | 0.00976483 | ||||||||
\(461\) | 4.60652e14 | 1.03043 | 0.515215 | − | 0.857061i | \(-0.327712\pi\) | ||||
0.515215 | + | 0.857061i | \(0.327712\pi\) | |||||||
\(462\) | 7.74348e13 | 0.171161 | ||||||||
\(463\) | 5.74513e14 | 1.25489 | 0.627443 | − | 0.778662i | \(-0.284101\pi\) | ||||
0.627443 | + | 0.778662i | \(0.284101\pi\) | |||||||
\(464\) | 1.31951e13 | 0.0284815 | ||||||||
\(465\) | −3.03539e14 | −0.647476 | ||||||||
\(466\) | 5.68690e14 | 1.19882 | ||||||||
\(467\) | 6.03014e14 | 1.25627 | 0.628137 | − | 0.778102i | \(-0.283818\pi\) | ||||
0.628137 | + | 0.778102i | \(0.283818\pi\) | |||||||
\(468\) | 2.23061e12 | 0.00459273 | ||||||||
\(469\) | 2.16500e13 | 0.0440562 | ||||||||
\(470\) | 5.61178e14 | 1.12866 | ||||||||
\(471\) | 1.81732e14 | 0.361257 | ||||||||
\(472\) | −6.65360e13 | −0.130730 | ||||||||
\(473\) | 8.89994e14 | 1.72843 | ||||||||
\(474\) | 8.27503e13 | 0.158851 | ||||||||
\(475\) | −1.49323e15 | −2.83342 | ||||||||
\(476\) | −5.25434e11 | −0.000985554 0 | ||||||||
\(477\) | −1.90945e14 | −0.354045 | ||||||||
\(478\) | −5.10156e14 | −0.935083 | ||||||||
\(479\) | 7.01199e14 | 1.27056 | 0.635282 | − | 0.772281i | \(-0.280884\pi\) | ||||
0.635282 | + | 0.772281i | \(0.280884\pi\) | |||||||
\(480\) | −9.64726e12 | −0.0172813 | ||||||||
\(481\) | −1.66488e15 | −2.94838 | ||||||||
\(482\) | 2.15714e14 | 0.377676 | ||||||||
\(483\) | −5.54095e13 | −0.0959124 | ||||||||
\(484\) | −1.80292e12 | −0.00308551 | ||||||||
\(485\) | 7.37112e14 | 1.24725 | ||||||||
\(486\) | 3.81824e13 | 0.0638799 | ||||||||
\(487\) | 8.80594e14 | 1.45669 | 0.728343 | − | 0.685212i | \(-0.240291\pi\) | ||||
0.728343 | + | 0.685212i | \(0.240291\pi\) | |||||||
\(488\) | 8.59324e14 | 1.40556 | ||||||||
\(489\) | −6.48513e14 | −1.04887 | ||||||||
\(490\) | 1.03699e15 | 1.65843 | ||||||||
\(491\) | −9.75945e14 | −1.54340 | −0.771698 | − | 0.635989i | \(-0.780592\pi\) | ||||
−0.771698 | + | 0.635989i | \(0.780592\pi\) | |||||||
\(492\) | 3.15633e10 | 4.93600e−5 0 | ||||||||
\(493\) | 8.55512e12 | 0.0132302 | ||||||||
\(494\) | 1.39287e15 | 2.13016 | ||||||||
\(495\) | 4.58938e14 | 0.694105 | ||||||||
\(496\) | −4.17445e14 | −0.624382 | ||||||||
\(497\) | 1.99775e14 | 0.295516 | ||||||||
\(498\) | 6.00025e14 | 0.877825 | ||||||||
\(499\) | −5.44945e14 | −0.788496 | −0.394248 | − | 0.919004i | \(-0.628995\pi\) | ||||
−0.394248 | + | 0.919004i | \(0.628995\pi\) | |||||||
\(500\) | 1.22526e13 | 0.0175345 | ||||||||
\(501\) | −2.49822e14 | −0.353609 | ||||||||
\(502\) | −1.80887e14 | −0.253243 | ||||||||
\(503\) | 4.94822e14 | 0.685212 | 0.342606 | − | 0.939479i | \(-0.388690\pi\) | ||||
0.342606 | + | 0.939479i | \(0.388690\pi\) | |||||||
\(504\) | 6.22212e13 | 0.0852257 | ||||||||
\(505\) | −1.37776e14 | −0.186668 | ||||||||
\(506\) | −5.66825e14 | −0.759663 | ||||||||
\(507\) | 7.35098e14 | 0.974544 | ||||||||
\(508\) | 2.90522e12 | 0.00381003 | ||||||||
\(509\) | 6.49641e14 | 0.842802 | 0.421401 | − | 0.906874i | \(-0.361538\pi\) | ||||
0.421401 | + | 0.906874i | \(0.361538\pi\) | |||||||
\(510\) | 3.67443e14 | 0.471579 | ||||||||
\(511\) | −1.71981e14 | −0.218357 | ||||||||
\(512\) | −8.05934e14 | −1.01231 | ||||||||
\(513\) | −2.02068e14 | −0.251103 | ||||||||
\(514\) | −8.77378e14 | −1.07867 | ||||||||
\(515\) | −1.36717e14 | −0.166296 | ||||||||
\(516\) | 5.95987e12 | 0.00717238 | ||||||||
\(517\) | 6.24976e14 | 0.744159 | ||||||||
\(518\) | −3.87029e14 | −0.455964 | ||||||||
\(519\) | −4.18001e13 | −0.0487255 | ||||||||
\(520\) | −2.54197e15 | −2.93192 | ||||||||
\(521\) | 1.36599e15 | 1.55898 | 0.779489 | − | 0.626416i | \(-0.215479\pi\) | ||||
0.779489 | + | 0.626416i | \(0.215479\pi\) | |||||||
\(522\) | −8.44292e12 | −0.00953465 | ||||||||
\(523\) | −1.68812e15 | −1.88644 | −0.943221 | − | 0.332165i | \(-0.892221\pi\) | ||||
−0.943221 | + | 0.332165i | \(0.892221\pi\) | |||||||
\(524\) | −3.30216e12 | −0.00365154 | ||||||||
\(525\) | −2.91731e14 | −0.319232 | ||||||||
\(526\) | −1.47735e15 | −1.59979 | ||||||||
\(527\) | −2.70654e14 | −0.290038 | ||||||||
\(528\) | 6.31158e14 | 0.669348 | ||||||||
\(529\) | −5.47211e14 | −0.574313 | ||||||||
\(530\) | 1.81344e15 | 1.88358 | ||||||||
\(531\) | 4.22156e13 | 0.0433963 | ||||||||
\(532\) | −2.74422e12 | −0.00279194 | ||||||||
\(533\) | 1.65640e13 | 0.0166788 | ||||||||
\(534\) | −4.18057e14 | −0.416638 | ||||||||
\(535\) | 6.04634e14 | 0.596412 | ||||||||
\(536\) | 1.77961e14 | 0.173748 | ||||||||
\(537\) | 1.36638e14 | 0.132043 | ||||||||
\(538\) | −6.73790e12 | −0.00644499 | ||||||||
\(539\) | 1.15488e15 | 1.09345 | ||||||||
\(540\) | 3.07329e12 | 0.00288030 | ||||||||
\(541\) | 6.54086e14 | 0.606806 | 0.303403 | − | 0.952862i | \(-0.401877\pi\) | ||||
0.303403 | + | 0.952862i | \(0.401877\pi\) | |||||||
\(542\) | −1.43468e14 | −0.131752 | ||||||||
\(543\) | −8.56882e14 | −0.778972 | ||||||||
\(544\) | −8.60207e12 | −0.00774121 | ||||||||
\(545\) | 3.21272e15 | 2.86215 | ||||||||
\(546\) | 2.72124e14 | 0.239998 | ||||||||
\(547\) | −2.23272e15 | −1.94941 | −0.974707 | − | 0.223488i | \(-0.928256\pi\) | ||||
−0.974707 | + | 0.223488i | \(0.928256\pi\) | |||||||
\(548\) | 6.34277e12 | 0.00548259 | ||||||||
\(549\) | −5.45221e14 | −0.466579 | ||||||||
\(550\) | −2.98433e15 | −2.52844 | ||||||||
\(551\) | 4.46814e13 | 0.0374794 | ||||||||
\(552\) | −4.55461e14 | −0.378257 | ||||||||
\(553\) | −8.55579e13 | −0.0703513 | ||||||||
\(554\) | −1.45057e15 | −1.18096 | ||||||||
\(555\) | −2.29383e15 | −1.84906 | ||||||||
\(556\) | −7.11864e12 | −0.00568180 | ||||||||
\(557\) | 1.39841e15 | 1.10518 | 0.552589 | − | 0.833454i | \(-0.313640\pi\) | ||||
0.552589 | + | 0.833454i | \(0.313640\pi\) | |||||||
\(558\) | 2.67104e14 | 0.209022 | ||||||||
\(559\) | 3.12765e15 | 2.42356 | ||||||||
\(560\) | −5.85958e14 | −0.449606 | ||||||||
\(561\) | 4.09216e14 | 0.310926 | ||||||||
\(562\) | 1.87707e15 | 1.41231 | ||||||||
\(563\) | −3.16839e14 | −0.236071 | −0.118035 | − | 0.993009i | \(-0.537660\pi\) | ||||
−0.118035 | + | 0.993009i | \(0.537660\pi\) | |||||||
\(564\) | 4.18517e12 | 0.00308800 | ||||||||
\(565\) | −3.71999e15 | −2.71816 | ||||||||
\(566\) | 9.91519e14 | 0.717481 | ||||||||
\(567\) | −3.94779e13 | −0.0282909 | ||||||||
\(568\) | 1.64213e15 | 1.16545 | ||||||||
\(569\) | 2.70314e15 | 1.89999 | 0.949996 | − | 0.312262i | \(-0.101087\pi\) | ||||
0.949996 | + | 0.312262i | \(0.101087\pi\) | |||||||
\(570\) | 1.91907e15 | 1.33592 | ||||||||
\(571\) | −4.19562e14 | −0.289266 | −0.144633 | − | 0.989485i | \(-0.546200\pi\) | ||||
−0.144633 | + | 0.989485i | \(0.546200\pi\) | |||||||
\(572\) | −2.35928e13 | −0.0161102 | ||||||||
\(573\) | −6.34429e14 | −0.429074 | ||||||||
\(574\) | 3.85059e12 | 0.00257936 | ||||||||
\(575\) | 2.13548e15 | 1.41684 | ||||||||
\(576\) | 5.11418e14 | 0.336087 | ||||||||
\(577\) | 1.04042e15 | 0.677239 | 0.338619 | − | 0.940923i | \(-0.390040\pi\) | ||||
0.338619 | + | 0.940923i | \(0.390040\pi\) | |||||||
\(578\) | −1.21680e15 | −0.784545 | ||||||||
\(579\) | −1.58571e15 | −1.01272 | ||||||||
\(580\) | −6.79567e11 | −0.000429911 0 | ||||||||
\(581\) | −6.20383e14 | −0.388769 | ||||||||
\(582\) | −6.48633e14 | −0.402645 | ||||||||
\(583\) | 2.01960e15 | 1.24190 | ||||||||
\(584\) | −1.41367e15 | −0.861150 | ||||||||
\(585\) | 1.61282e15 | 0.973259 | ||||||||
\(586\) | −2.11181e13 | −0.0126246 | ||||||||
\(587\) | 1.53474e14 | 0.0908918 | 0.0454459 | − | 0.998967i | \(-0.485529\pi\) | ||||
0.0454459 | + | 0.998967i | \(0.485529\pi\) | |||||||
\(588\) | 7.73368e12 | 0.00453744 | ||||||||
\(589\) | −1.41356e15 | −0.821639 | ||||||||
\(590\) | −4.00927e14 | −0.230876 | ||||||||
\(591\) | −1.12988e15 | −0.644617 | ||||||||
\(592\) | −3.15461e15 | −1.78310 | ||||||||
\(593\) | 2.29184e15 | 1.28346 | 0.641731 | − | 0.766930i | \(-0.278217\pi\) | ||||
0.641731 | + | 0.766930i | \(0.278217\pi\) | |||||||
\(594\) | −4.03849e14 | −0.224075 | ||||||||
\(595\) | −3.79910e14 | −0.208851 | ||||||||
\(596\) | −2.60114e13 | −0.0141680 | ||||||||
\(597\) | 1.66628e15 | 0.899266 | ||||||||
\(598\) | −1.99196e15 | −1.06518 | ||||||||
\(599\) | 2.05085e15 | 1.08664 | 0.543322 | − | 0.839524i | \(-0.317166\pi\) | ||||
0.543322 | + | 0.839524i | \(0.317166\pi\) | |||||||
\(600\) | −2.39800e15 | −1.25898 | ||||||||
\(601\) | 2.75368e15 | 1.43253 | 0.716264 | − | 0.697829i | \(-0.245851\pi\) | ||||
0.716264 | + | 0.697829i | \(0.245851\pi\) | |||||||
\(602\) | 7.27077e14 | 0.374800 | ||||||||
\(603\) | −1.12912e14 | −0.0576761 | ||||||||
\(604\) | −1.02562e13 | −0.00519141 | ||||||||
\(605\) | −1.30358e15 | −0.653860 | ||||||||
\(606\) | 1.21238e14 | 0.0602613 | ||||||||
\(607\) | −2.93931e15 | −1.44780 | −0.723899 | − | 0.689906i | \(-0.757652\pi\) | ||||
−0.723899 | + | 0.689906i | \(0.757652\pi\) | |||||||
\(608\) | −4.49266e13 | −0.0219298 | ||||||||
\(609\) | 8.72937e12 | 0.00422268 | ||||||||
\(610\) | 5.17804e15 | 2.48229 | ||||||||
\(611\) | 2.19632e15 | 1.04344 | ||||||||
\(612\) | 2.74032e12 | 0.00129024 | ||||||||
\(613\) | −1.72820e15 | −0.806421 | −0.403210 | − | 0.915107i | \(-0.632106\pi\) | ||||
−0.403210 | + | 0.915107i | \(0.632106\pi\) | |||||||
\(614\) | 2.58361e15 | 1.19482 | ||||||||
\(615\) | 2.28215e13 | 0.0104600 | ||||||||
\(616\) | −6.58104e14 | −0.298951 | ||||||||
\(617\) | 2.86506e14 | 0.128993 | 0.0644964 | − | 0.997918i | \(-0.479456\pi\) | ||||
0.0644964 | + | 0.997918i | \(0.479456\pi\) | |||||||
\(618\) | 1.20306e14 | 0.0536846 | ||||||||
\(619\) | −2.04300e15 | −0.903588 | −0.451794 | − | 0.892122i | \(-0.649216\pi\) | ||||
−0.451794 | + | 0.892122i | \(0.649216\pi\) | |||||||
\(620\) | 2.14991e13 | 0.00942466 | ||||||||
\(621\) | 2.88980e14 | 0.125564 | ||||||||
\(622\) | 9.40326e14 | 0.404978 | ||||||||
\(623\) | 4.32241e14 | 0.184519 | ||||||||
\(624\) | 2.21804e15 | 0.938544 | ||||||||
\(625\) | 3.68165e15 | 1.54420 | ||||||||
\(626\) | −2.66265e15 | −1.10702 | ||||||||
\(627\) | 2.13724e15 | 0.880810 | ||||||||
\(628\) | −1.28717e13 | −0.00525846 | ||||||||
\(629\) | −2.04532e15 | −0.828289 | ||||||||
\(630\) | 3.74927e14 | 0.150513 | ||||||||
\(631\) | −1.86553e15 | −0.742405 | −0.371203 | − | 0.928552i | \(-0.621055\pi\) | ||||
−0.371203 | + | 0.928552i | \(0.621055\pi\) | |||||||
\(632\) | −7.03280e14 | −0.277450 | ||||||||
\(633\) | −3.71802e14 | −0.145409 | ||||||||
\(634\) | −1.71933e15 | −0.666603 | ||||||||
\(635\) | 2.10059e15 | 0.807394 | ||||||||
\(636\) | 1.35243e13 | 0.00515347 | ||||||||
\(637\) | 4.05853e15 | 1.53321 | ||||||||
\(638\) | 8.92994e13 | 0.0334453 | ||||||||
\(639\) | −1.04190e15 | −0.386874 | ||||||||
\(640\) | −4.77570e15 | −1.75812 | ||||||||
\(641\) | −2.20124e15 | −0.803429 | −0.401715 | − | 0.915765i | \(-0.631586\pi\) | ||||
−0.401715 | + | 0.915765i | \(0.631586\pi\) | |||||||
\(642\) | −5.32057e14 | −0.192537 | ||||||||
\(643\) | −2.16711e15 | −0.777534 | −0.388767 | − | 0.921336i | \(-0.627099\pi\) | ||||
−0.388767 | + | 0.921336i | \(0.627099\pi\) | |||||||
\(644\) | 3.92454e12 | 0.00139610 | ||||||||
\(645\) | 4.30922e15 | 1.51992 | ||||||||
\(646\) | 1.71116e15 | 0.598427 | ||||||||
\(647\) | −3.64758e15 | −1.26483 | −0.632413 | − | 0.774631i | \(-0.717936\pi\) | ||||
−0.632413 | + | 0.774631i | \(0.717936\pi\) | |||||||
\(648\) | −3.24505e14 | −0.111573 | ||||||||
\(649\) | −4.46507e14 | −0.152224 | ||||||||
\(650\) | −1.04877e16 | −3.54532 | ||||||||
\(651\) | −2.76167e14 | −0.0925711 | ||||||||
\(652\) | 4.59329e13 | 0.0152673 | ||||||||
\(653\) | −8.51590e14 | −0.280678 | −0.140339 | − | 0.990104i | \(-0.544819\pi\) | ||||
−0.140339 | + | 0.990104i | \(0.544819\pi\) | |||||||
\(654\) | −2.82708e15 | −0.923976 | ||||||||
\(655\) | −2.38759e15 | −0.773807 | ||||||||
\(656\) | 3.13855e13 | 0.0100869 | ||||||||
\(657\) | 8.96943e14 | 0.285861 | ||||||||
\(658\) | 5.10572e14 | 0.161367 | ||||||||
\(659\) | −1.70154e15 | −0.533302 | −0.266651 | − | 0.963793i | \(-0.585917\pi\) | ||||
−0.266651 | + | 0.963793i | \(0.585917\pi\) | |||||||
\(660\) | −3.25057e13 | −0.0101034 | ||||||||
\(661\) | −4.26270e15 | −1.31394 | −0.656972 | − | 0.753915i | \(-0.728163\pi\) | ||||
−0.656972 | + | 0.753915i | \(0.728163\pi\) | |||||||
\(662\) | −4.40241e15 | −1.34577 | ||||||||
\(663\) | 1.43808e15 | 0.435973 | ||||||||
\(664\) | −5.09950e15 | −1.53322 | ||||||||
\(665\) | −1.98418e15 | −0.591647 | ||||||||
\(666\) | 2.01849e15 | 0.596924 | ||||||||
\(667\) | −6.38993e13 | −0.0187415 | ||||||||
\(668\) | 1.76944e13 | 0.00514713 | ||||||||
\(669\) | −1.07367e14 | −0.0309761 | ||||||||
\(670\) | 1.07234e15 | 0.306847 | ||||||||
\(671\) | 5.76671e15 | 1.63665 | ||||||||
\(672\) | −8.77728e12 | −0.00247075 | ||||||||
\(673\) | 6.74193e15 | 1.88236 | 0.941178 | − | 0.337912i | \(-0.109721\pi\) | ||||
0.941178 | + | 0.337912i | \(0.109721\pi\) | |||||||
\(674\) | −6.82916e15 | −1.89120 | ||||||||
\(675\) | 1.52148e15 | 0.417922 | ||||||||
\(676\) | −5.20655e13 | −0.0141855 | ||||||||
\(677\) | 4.63491e15 | 1.25257 | 0.626287 | − | 0.779592i | \(-0.284574\pi\) | ||||
0.626287 | + | 0.779592i | \(0.284574\pi\) | |||||||
\(678\) | 3.27346e15 | 0.877493 | ||||||||
\(679\) | 6.70640e14 | 0.178322 | ||||||||
\(680\) | −3.12283e15 | −0.823662 | ||||||||
\(681\) | 1.50214e15 | 0.393009 | ||||||||
\(682\) | −2.82512e15 | −0.733200 | ||||||||
\(683\) | 7.01051e15 | 1.80483 | 0.902414 | − | 0.430870i | \(-0.141793\pi\) | ||||
0.902414 | + | 0.430870i | \(0.141793\pi\) | |||||||
\(684\) | 1.43121e13 | 0.00365506 | ||||||||
\(685\) | 4.58607e15 | 1.16183 | ||||||||
\(686\) | 1.95236e15 | 0.490655 | ||||||||
\(687\) | 2.04583e15 | 0.510043 | ||||||||
\(688\) | 5.92629e15 | 1.46570 | ||||||||
\(689\) | 7.09735e15 | 1.74137 | ||||||||
\(690\) | −2.74448e15 | −0.668021 | ||||||||
\(691\) | −5.90367e15 | −1.42558 | −0.712792 | − | 0.701376i | \(-0.752570\pi\) | ||||
−0.712792 | + | 0.701376i | \(0.752570\pi\) | |||||||
\(692\) | 2.96062e12 | 0.000709249 0 | ||||||||
\(693\) | 4.17551e14 | 0.0992378 | ||||||||
\(694\) | 4.29184e15 | 1.01197 | ||||||||
\(695\) | −5.14706e15 | −1.20404 | ||||||||
\(696\) | 7.17548e13 | 0.0166533 | ||||||||
\(697\) | 2.03490e13 | 0.00468558 | ||||||||
\(698\) | 3.97758e15 | 0.908687 | ||||||||
\(699\) | 3.06655e15 | 0.695065 | ||||||||
\(700\) | 2.06627e13 | 0.00464674 | ||||||||
\(701\) | 6.10899e15 | 1.36308 | 0.681539 | − | 0.731782i | \(-0.261311\pi\) | ||||
0.681539 | + | 0.731782i | \(0.261311\pi\) | |||||||
\(702\) | −1.41922e15 | −0.314193 | ||||||||
\(703\) | −1.06822e16 | −2.34643 | ||||||||
\(704\) | −5.40918e15 | −1.17891 | ||||||||
\(705\) | 3.02604e15 | 0.654387 | ||||||||
\(706\) | 7.22698e14 | 0.155071 | ||||||||
\(707\) | −1.25351e14 | −0.0266883 | ||||||||
\(708\) | −2.99004e12 | −0.000631676 0 | ||||||||
\(709\) | 2.94639e15 | 0.617642 | 0.308821 | − | 0.951120i | \(-0.400066\pi\) | ||||
0.308821 | + | 0.951120i | \(0.400066\pi\) | |||||||
\(710\) | 9.89503e15 | 2.05824 | ||||||||
\(711\) | 4.46215e14 | 0.0921003 | ||||||||
\(712\) | 3.55299e15 | 0.727703 | ||||||||
\(713\) | 2.02155e15 | 0.410858 | ||||||||
\(714\) | 3.34307e14 | 0.0674226 | ||||||||
\(715\) | −1.70585e16 | −3.41396 | ||||||||
\(716\) | −9.67782e12 | −0.00192201 | ||||||||
\(717\) | −2.75092e15 | −0.542153 | ||||||||
\(718\) | −8.19301e15 | −1.60236 | ||||||||
\(719\) | −7.99512e15 | −1.55173 | −0.775865 | − | 0.630899i | \(-0.782686\pi\) | ||||
−0.775865 | + | 0.630899i | \(0.782686\pi\) | |||||||
\(720\) | 3.05597e15 | 0.588601 | ||||||||
\(721\) | −1.24388e14 | −0.0237757 | ||||||||
\(722\) | 3.68743e15 | 0.699471 | ||||||||
\(723\) | 1.16319e15 | 0.218973 | ||||||||
\(724\) | 6.06912e13 | 0.0113387 | ||||||||
\(725\) | −3.36430e14 | −0.0623786 | ||||||||
\(726\) | 1.14711e15 | 0.211083 | ||||||||
\(727\) | 2.89015e15 | 0.527815 | 0.263907 | − | 0.964548i | \(-0.414989\pi\) | ||||
0.263907 | + | 0.964548i | \(0.414989\pi\) | |||||||
\(728\) | −2.31273e15 | −0.419183 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −8.51840e15 | −1.52084 | ||||||||
\(731\) | 3.84235e15 | 0.680850 | ||||||||
\(732\) | 3.86169e13 | 0.00679152 | ||||||||
\(733\) | 3.30445e15 | 0.576802 | 0.288401 | − | 0.957510i | \(-0.406876\pi\) | ||||
0.288401 | + | 0.957510i | \(0.406876\pi\) | |||||||
\(734\) | −1.59763e15 | −0.276788 | ||||||||
\(735\) | 5.59176e15 | 0.961541 | ||||||||
\(736\) | 6.42500e13 | 0.0109659 | ||||||||
\(737\) | 1.19425e15 | 0.202314 | ||||||||
\(738\) | −2.00822e13 | −0.00337676 | ||||||||
\(739\) | −9.69025e15 | −1.61730 | −0.808650 | − | 0.588290i | \(-0.799801\pi\) | ||||
−0.808650 | + | 0.588290i | \(0.799801\pi\) | |||||||
\(740\) | 1.62468e14 | 0.0269149 | ||||||||
\(741\) | 7.51078e15 | 1.23505 | ||||||||
\(742\) | 1.64990e15 | 0.269300 | ||||||||
\(743\) | −7.43546e15 | −1.20467 | −0.602336 | − | 0.798242i | \(-0.705763\pi\) | ||||
−0.602336 | + | 0.798242i | \(0.705763\pi\) | |||||||
\(744\) | −2.27007e15 | −0.365080 | ||||||||
\(745\) | −1.88073e16 | −3.00238 | ||||||||
\(746\) | −6.27230e15 | −0.993947 | ||||||||
\(747\) | 3.23551e15 | 0.508956 | ||||||||
\(748\) | −2.89840e13 | −0.00452584 | ||||||||
\(749\) | 5.50109e14 | 0.0852704 | ||||||||
\(750\) | −7.79571e15 | −1.19955 | ||||||||
\(751\) | 1.07005e16 | 1.63450 | 0.817250 | − | 0.576283i | \(-0.195497\pi\) | ||||
0.817250 | + | 0.576283i | \(0.195497\pi\) | |||||||
\(752\) | 4.16159e15 | 0.631046 | ||||||||
\(753\) | −9.75399e14 | −0.146828 | ||||||||
\(754\) | 3.13819e14 | 0.0468962 | ||||||||
\(755\) | −7.41567e15 | −1.10012 | ||||||||
\(756\) | 2.79614e12 | 0.000411803 0 | ||||||||
\(757\) | 1.05616e16 | 1.54419 | 0.772094 | − | 0.635508i | \(-0.219209\pi\) | ||||
0.772094 | + | 0.635508i | \(0.219209\pi\) | |||||||
\(758\) | −1.45701e14 | −0.0211487 | ||||||||
\(759\) | −3.05649e15 | −0.440447 | ||||||||
\(760\) | −1.63098e16 | −2.33332 | ||||||||
\(761\) | 2.67131e15 | 0.379410 | 0.189705 | − | 0.981841i | \(-0.439247\pi\) | ||||
0.189705 | + | 0.981841i | \(0.439247\pi\) | |||||||
\(762\) | −1.84845e15 | −0.260648 | ||||||||
\(763\) | 2.92300e15 | 0.409208 | ||||||||
\(764\) | 4.49353e13 | 0.00624560 | ||||||||
\(765\) | 1.98136e15 | 0.273417 | ||||||||
\(766\) | 3.42132e15 | 0.468744 | ||||||||
\(767\) | −1.56913e15 | −0.213445 | ||||||||
\(768\) | −1.07770e14 | −0.0145550 | ||||||||
\(769\) | 5.22731e15 | 0.700944 | 0.350472 | − | 0.936573i | \(-0.386021\pi\) | ||||
0.350472 | + | 0.936573i | \(0.386021\pi\) | |||||||
\(770\) | −3.96555e15 | −0.527964 | ||||||||
\(771\) | −4.73108e15 | −0.625405 | ||||||||
\(772\) | 1.12313e14 | 0.0147412 | ||||||||
\(773\) | −2.43776e15 | −0.317690 | −0.158845 | − | 0.987304i | \(-0.550777\pi\) | ||||
−0.158845 | + | 0.987304i | \(0.550777\pi\) | |||||||
\(774\) | −3.79196e15 | −0.490669 | ||||||||
\(775\) | 1.06435e16 | 1.36749 | ||||||||
\(776\) | 5.51261e15 | 0.703263 | ||||||||
\(777\) | −2.08698e15 | −0.264364 | ||||||||
\(778\) | −3.88718e14 | −0.0488931 | ||||||||
\(779\) | 1.06278e14 | 0.0132736 | ||||||||
\(780\) | −1.14233e14 | −0.0141667 | ||||||||
\(781\) | 1.10200e16 | 1.35706 | ||||||||
\(782\) | −2.44714e15 | −0.299242 | ||||||||
\(783\) | −4.55267e13 | −0.00552811 | ||||||||
\(784\) | 7.69011e15 | 0.927244 | ||||||||
\(785\) | −9.30676e15 | −1.11433 | ||||||||
\(786\) | 2.10100e15 | 0.249805 | ||||||||
\(787\) | 5.96374e15 | 0.704138 | 0.352069 | − | 0.935974i | \(-0.385478\pi\) | ||||
0.352069 | + | 0.935974i | \(0.385478\pi\) | |||||||
\(788\) | 8.00272e13 | 0.00938304 | ||||||||
\(789\) | −7.96631e15 | −0.927543 | ||||||||
\(790\) | −4.23776e15 | −0.489991 | ||||||||
\(791\) | −3.38452e15 | −0.388621 | ||||||||
\(792\) | 3.43224e15 | 0.391371 | ||||||||
\(793\) | 2.02656e16 | 2.29487 | ||||||||
\(794\) | −1.00619e15 | −0.113153 | ||||||||
\(795\) | 9.77859e15 | 1.09209 | ||||||||
\(796\) | −1.18019e14 | −0.0130897 | ||||||||
\(797\) | −1.14517e16 | −1.26139 | −0.630693 | − | 0.776033i | \(-0.717229\pi\) | ||||
−0.630693 | + | 0.776033i | \(0.717229\pi\) | |||||||
\(798\) | 1.74601e15 | 0.190999 | ||||||||
\(799\) | 2.69820e15 | 0.293134 | ||||||||
\(800\) | 3.38276e14 | 0.0364986 | ||||||||
\(801\) | −2.25429e15 | −0.241563 | ||||||||
\(802\) | −1.33562e16 | −1.42143 | ||||||||
\(803\) | −9.48682e15 | −1.00273 | ||||||||
\(804\) | 7.99734e12 | 0.000839532 0 | ||||||||
\(805\) | 2.83760e15 | 0.295851 | ||||||||
\(806\) | −9.92814e15 | −1.02808 | ||||||||
\(807\) | −3.63328e13 | −0.00373675 | ||||||||
\(808\) | −1.03038e15 | −0.105253 | ||||||||
\(809\) | 1.32160e16 | 1.34086 | 0.670429 | − | 0.741974i | \(-0.266110\pi\) | ||||
0.670429 | + | 0.741974i | \(0.266110\pi\) | |||||||
\(810\) | −1.95538e15 | −0.197044 | ||||||||
\(811\) | −2.80378e15 | −0.280627 | −0.140313 | − | 0.990107i | \(-0.544811\pi\) | ||||
−0.140313 | + | 0.990107i | \(0.544811\pi\) | |||||||
\(812\) | −6.18284e11 | −6.14653e−5 0 | ||||||||
\(813\) | −7.73621e14 | −0.0763889 | ||||||||
\(814\) | −2.13493e16 | −2.09386 | ||||||||
\(815\) | 3.32113e16 | 3.23533 | ||||||||
\(816\) | 2.72489e15 | 0.263665 | ||||||||
\(817\) | 2.00677e16 | 1.92875 | ||||||||
\(818\) | −1.30994e16 | −1.25057 | ||||||||
\(819\) | 1.46738e15 | 0.139149 | ||||||||
\(820\) | −1.61640e12 | −0.000152256 0 | ||||||||
\(821\) | −1.80837e16 | −1.69199 | −0.845997 | − | 0.533188i | \(-0.820994\pi\) | ||||
−0.845997 | + | 0.533188i | \(0.820994\pi\) | |||||||
\(822\) | −4.03558e15 | −0.375069 | ||||||||
\(823\) | −3.00103e15 | −0.277058 | −0.138529 | − | 0.990358i | \(-0.544237\pi\) | ||||
−0.138529 | + | 0.990358i | \(0.544237\pi\) | |||||||
\(824\) | −1.02246e15 | −0.0937659 | ||||||||
\(825\) | −1.60924e16 | −1.46597 | ||||||||
\(826\) | −3.64772e14 | −0.0330089 | ||||||||
\(827\) | −1.21648e15 | −0.109351 | −0.0546756 | − | 0.998504i | \(-0.517412\pi\) | ||||
−0.0546756 | + | 0.998504i | \(0.517412\pi\) | |||||||
\(828\) | −2.04679e13 | −0.00182770 | ||||||||
\(829\) | 1.13958e16 | 1.01087 | 0.505433 | − | 0.862866i | \(-0.331333\pi\) | ||||
0.505433 | + | 0.862866i | \(0.331333\pi\) | |||||||
\(830\) | −3.07281e16 | −2.70774 | ||||||||
\(831\) | −7.82191e15 | −0.684711 | ||||||||
\(832\) | −1.90092e16 | −1.65305 | ||||||||
\(833\) | 4.98594e15 | 0.430724 | ||||||||
\(834\) | 4.52923e15 | 0.388697 | ||||||||
\(835\) | 1.27937e16 | 1.09074 | ||||||||
\(836\) | −1.51377e14 | −0.0128211 | ||||||||
\(837\) | 1.44031e15 | 0.121189 | ||||||||
\(838\) | 1.61420e16 | 1.34932 | ||||||||
\(839\) | 8.39530e15 | 0.697181 | 0.348591 | − | 0.937275i | \(-0.386660\pi\) | ||||
0.348591 | + | 0.937275i | \(0.386660\pi\) | |||||||
\(840\) | −3.18644e15 | −0.262887 | ||||||||
\(841\) | −1.21904e16 | −0.999175 | ||||||||
\(842\) | 7.93034e15 | 0.645766 | ||||||||
\(843\) | 1.01217e16 | 0.818847 | ||||||||
\(844\) | 2.63340e13 | 0.00211657 | ||||||||
\(845\) | −3.76454e16 | −3.00608 | ||||||||
\(846\) | −2.66281e15 | −0.211253 | ||||||||
\(847\) | −1.18603e15 | −0.0934838 | ||||||||
\(848\) | 1.34481e16 | 1.05313 | ||||||||
\(849\) | 5.34657e15 | 0.415990 | ||||||||
\(850\) | −1.28842e16 | −0.995986 | ||||||||
\(851\) | 1.52767e16 | 1.17332 | ||||||||
\(852\) | 7.37954e13 | 0.00563134 | ||||||||
\(853\) | 3.40599e15 | 0.258240 | 0.129120 | − | 0.991629i | \(-0.458785\pi\) | ||||
0.129120 | + | 0.991629i | \(0.458785\pi\) | |||||||
\(854\) | 4.71109e15 | 0.354898 | ||||||||
\(855\) | 1.03482e16 | 0.774553 | ||||||||
\(856\) | 4.52185e15 | 0.336287 | ||||||||
\(857\) | −1.41524e16 | −1.04577 | −0.522886 | − | 0.852403i | \(-0.675145\pi\) | ||||
−0.522886 | + | 0.852403i | \(0.675145\pi\) | |||||||
\(858\) | 1.50109e16 | 1.10211 | ||||||||
\(859\) | −2.08355e16 | −1.52000 | −0.759998 | − | 0.649925i | \(-0.774800\pi\) | ||||
−0.759998 | + | 0.649925i | \(0.774800\pi\) | |||||||
\(860\) | −3.05213e14 | −0.0221239 | ||||||||
\(861\) | 2.07635e13 | 0.00149549 | ||||||||
\(862\) | 6.57154e15 | 0.470302 | ||||||||
\(863\) | −1.88043e16 | −1.33720 | −0.668601 | − | 0.743621i | \(-0.733107\pi\) | ||||
−0.668601 | + | 0.743621i | \(0.733107\pi\) | |||||||
\(864\) | 4.57766e13 | 0.00323458 | ||||||||
\(865\) | 2.14064e15 | 0.150299 | ||||||||
\(866\) | 1.42122e16 | 0.991549 | ||||||||
\(867\) | −6.56137e15 | −0.454872 | ||||||||
\(868\) | 1.95603e13 | 0.00134747 | ||||||||
\(869\) | −4.71954e15 | −0.323066 | ||||||||
\(870\) | 4.32374e14 | 0.0294106 | ||||||||
\(871\) | 4.19689e15 | 0.283680 | ||||||||
\(872\) | 2.40268e16 | 1.61382 | ||||||||
\(873\) | −3.49762e15 | −0.233450 | ||||||||
\(874\) | −1.27809e16 | −0.847710 | ||||||||
\(875\) | 8.06021e15 | 0.531254 | ||||||||
\(876\) | −6.35287e13 | −0.00416100 | ||||||||
\(877\) | 1.88287e16 | 1.22552 | 0.612761 | − | 0.790268i | \(-0.290059\pi\) | ||||
0.612761 | + | 0.790268i | \(0.290059\pi\) | |||||||
\(878\) | 4.11834e15 | 0.266380 | ||||||||
\(879\) | −1.13875e14 | −0.00731965 | ||||||||
\(880\) | −3.23225e16 | −2.06467 | ||||||||
\(881\) | −2.24685e16 | −1.42629 | −0.713144 | − | 0.701018i | \(-0.752729\pi\) | ||||
−0.713144 | + | 0.701018i | \(0.752729\pi\) | |||||||
\(882\) | −4.92055e15 | −0.310411 | ||||||||
\(883\) | −3.23036e15 | −0.202520 | −0.101260 | − | 0.994860i | \(-0.532287\pi\) | ||||
−0.101260 | + | 0.994860i | \(0.532287\pi\) | |||||||
\(884\) | −1.01857e14 | −0.00634602 | ||||||||
\(885\) | −2.16192e15 | −0.133860 | ||||||||
\(886\) | −1.71655e16 | −1.05626 | ||||||||
\(887\) | 1.42033e16 | 0.868581 | 0.434290 | − | 0.900773i | \(-0.356999\pi\) | ||||
0.434290 | + | 0.900773i | \(0.356999\pi\) | |||||||
\(888\) | −1.71548e16 | −1.04259 | ||||||||
\(889\) | 1.91116e15 | 0.115435 | ||||||||
\(890\) | 2.14093e16 | 1.28516 | ||||||||
\(891\) | −2.17768e15 | −0.129917 | ||||||||
\(892\) | 7.60457e12 | 0.000450887 0 | ||||||||
\(893\) | 1.40921e16 | 0.830408 | ||||||||
\(894\) | 1.65497e16 | 0.969247 | ||||||||
\(895\) | −6.99745e15 | −0.407299 | ||||||||
\(896\) | −4.34503e15 | −0.251362 | ||||||||
\(897\) | −1.07412e16 | −0.617584 | ||||||||
\(898\) | 7.43848e15 | 0.425074 | ||||||||
\(899\) | −3.18481e14 | −0.0180886 | ||||||||
\(900\) | −1.07763e14 | −0.00608327 | ||||||||
\(901\) | 8.71916e15 | 0.489202 | ||||||||
\(902\) | 2.12406e14 | 0.0118449 | ||||||||
\(903\) | 3.92062e15 | 0.217306 | ||||||||
\(904\) | −2.78205e16 | −1.53263 | ||||||||
\(905\) | 4.38821e16 | 2.40282 | ||||||||
\(906\) | 6.52553e15 | 0.355149 | ||||||||
\(907\) | −2.40970e16 | −1.30354 | −0.651769 | − | 0.758418i | \(-0.725973\pi\) | ||||
−0.651769 | + | 0.758418i | \(0.725973\pi\) | |||||||
\(908\) | −1.06394e14 | −0.00572063 | ||||||||
\(909\) | 6.53750e14 | 0.0349390 | ||||||||
\(910\) | −1.39359e16 | −0.740298 | ||||||||
\(911\) | −1.59187e16 | −0.840536 | −0.420268 | − | 0.907400i | \(-0.638064\pi\) | ||||
−0.420268 | + | 0.907400i | \(0.638064\pi\) | |||||||
\(912\) | 1.42315e16 | 0.746926 | ||||||||
\(913\) | −3.42215e16 | −1.78529 | ||||||||
\(914\) | 3.53484e16 | 1.83302 | ||||||||
\(915\) | 2.79216e16 | 1.43921 | ||||||||
\(916\) | −1.44902e14 | −0.00742419 | ||||||||
\(917\) | −2.17228e15 | −0.110633 | ||||||||
\(918\) | −1.74353e15 | −0.0882662 | ||||||||
\(919\) | 3.25248e16 | 1.63674 | 0.818370 | − | 0.574692i | \(-0.194878\pi\) | ||||
0.818370 | + | 0.574692i | \(0.194878\pi\) | |||||||
\(920\) | 2.33248e16 | 1.16677 | ||||||||
\(921\) | 1.39316e16 | 0.692745 | ||||||||
\(922\) | 2.07590e16 | 1.02609 | ||||||||
\(923\) | 3.87268e16 | 1.90284 | ||||||||
\(924\) | −2.95743e13 | −0.00144450 | ||||||||
\(925\) | 8.04321e16 | 3.90526 | ||||||||
\(926\) | 2.58900e16 | 1.24960 | ||||||||
\(927\) | 6.48724e14 | 0.0311259 | ||||||||
\(928\) | −1.01221e13 | −0.000482790 0 | ||||||||
\(929\) | −1.72874e16 | −0.819677 | −0.409838 | − | 0.912158i | \(-0.634415\pi\) | ||||
−0.409838 | + | 0.912158i | \(0.634415\pi\) | |||||||
\(930\) | −1.36788e16 | −0.644750 | ||||||||
\(931\) | 2.60404e16 | 1.22018 | ||||||||
\(932\) | −2.17197e14 | −0.0101174 | ||||||||
\(933\) | 5.07052e15 | 0.234803 | ||||||||
\(934\) | 2.71744e16 | 1.25099 | ||||||||
\(935\) | −2.09565e16 | −0.959082 | ||||||||
\(936\) | 1.20617e16 | 0.548772 | ||||||||
\(937\) | 1.56294e16 | 0.706925 | 0.353462 | − | 0.935449i | \(-0.385004\pi\) | ||||
0.353462 | + | 0.935449i | \(0.385004\pi\) | |||||||
\(938\) | 9.75640e14 | 0.0438707 | ||||||||
\(939\) | −1.43578e16 | −0.641840 | ||||||||
\(940\) | −2.14328e14 | −0.00952526 | ||||||||
\(941\) | −1.99183e16 | −0.880054 | −0.440027 | − | 0.897985i | \(-0.645031\pi\) | ||||
−0.440027 | + | 0.897985i | \(0.645031\pi\) | |||||||
\(942\) | 8.18963e15 | 0.359736 | ||||||||
\(943\) | −1.51990e14 | −0.00663742 | ||||||||
\(944\) | −2.97320e15 | −0.129086 | ||||||||
\(945\) | 2.02172e15 | 0.0872662 | ||||||||
\(946\) | 4.01069e16 | 1.72115 | ||||||||
\(947\) | 1.45996e16 | 0.622899 | 0.311449 | − | 0.950263i | \(-0.399186\pi\) | ||||
0.311449 | + | 0.950263i | \(0.399186\pi\) | |||||||
\(948\) | −3.16045e13 | −0.00134061 | ||||||||
\(949\) | −3.33390e16 | −1.40601 | ||||||||
\(950\) | −6.72912e16 | −2.82149 | ||||||||
\(951\) | −9.27112e15 | −0.386491 | ||||||||
\(952\) | −2.84122e15 | −0.117761 | ||||||||
\(953\) | 4.55783e15 | 0.187822 | 0.0939112 | − | 0.995581i | \(-0.470063\pi\) | ||||
0.0939112 | + | 0.995581i | \(0.470063\pi\) | |||||||
\(954\) | −8.60482e15 | −0.352554 | ||||||||
\(955\) | 3.24900e16 | 1.32352 | ||||||||
\(956\) | 1.94842e14 | 0.00789158 | ||||||||
\(957\) | 4.81529e14 | 0.0193913 | ||||||||
\(958\) | 3.15990e16 | 1.26521 | ||||||||
\(959\) | 4.17250e15 | 0.166110 | ||||||||
\(960\) | −2.61904e16 | −1.03669 | ||||||||
\(961\) | −1.53329e16 | −0.603455 | ||||||||
\(962\) | −7.50265e16 | −2.93597 | ||||||||
\(963\) | −2.86901e15 | −0.111632 | ||||||||
\(964\) | −8.23867e13 | −0.00318738 | ||||||||
\(965\) | 8.12065e16 | 3.12385 | ||||||||
\(966\) | −2.49699e15 | −0.0955085 | ||||||||
\(967\) | −2.52536e16 | −0.960457 | −0.480228 | − | 0.877144i | \(-0.659446\pi\) | ||||
−0.480228 | + | 0.877144i | \(0.659446\pi\) | |||||||
\(968\) | −9.74906e15 | −0.368679 | ||||||||
\(969\) | 9.22707e15 | 0.346963 | ||||||||
\(970\) | 3.32174e16 | 1.24200 | ||||||||
\(971\) | 7.21331e14 | 0.0268182 | 0.0134091 | − | 0.999910i | \(-0.495732\pi\) | ||||
0.0134091 | + | 0.999910i | \(0.495732\pi\) | |||||||
\(972\) | −1.45829e13 | −0.000539111 0 | ||||||||
\(973\) | −4.68290e15 | −0.172145 | ||||||||
\(974\) | 3.96833e16 | 1.45055 | ||||||||
\(975\) | −5.65526e16 | −2.05555 | ||||||||
\(976\) | 3.83994e16 | 1.38787 | ||||||||
\(977\) | −1.43712e15 | −0.0516503 | −0.0258251 | − | 0.999666i | \(-0.508221\pi\) | ||||
−0.0258251 | + | 0.999666i | \(0.508221\pi\) | |||||||
\(978\) | −2.92248e16 | −1.04445 | ||||||||
\(979\) | 2.38432e16 | 0.847346 | ||||||||
\(980\) | −3.96053e14 | −0.0139962 | ||||||||
\(981\) | −1.52445e16 | −0.535714 | ||||||||
\(982\) | −4.39803e16 | −1.53690 | ||||||||
\(983\) | 3.62501e16 | 1.25969 | 0.629847 | − | 0.776719i | \(-0.283118\pi\) | ||||
0.629847 | + | 0.776719i | \(0.283118\pi\) | |||||||
\(984\) | 1.70674e14 | 0.00589787 | ||||||||
\(985\) | 5.78629e16 | 1.98839 | ||||||||
\(986\) | 3.85530e14 | 0.0131745 | ||||||||
\(987\) | 2.75316e15 | 0.0935592 | ||||||||
\(988\) | −5.31974e14 | −0.0179774 | ||||||||
\(989\) | −2.86990e16 | −0.964468 | ||||||||
\(990\) | 2.06817e16 | 0.691183 | ||||||||
\(991\) | 3.84107e16 | 1.27658 | 0.638289 | − | 0.769797i | \(-0.279643\pi\) | ||||
0.638289 | + | 0.769797i | \(0.279643\pi\) | |||||||
\(992\) | 3.20229e14 | 0.0105839 | ||||||||
\(993\) | −2.37391e16 | −0.780267 | ||||||||
\(994\) | 9.00271e15 | 0.294271 | ||||||||
\(995\) | −8.53324e16 | −2.77388 | ||||||||
\(996\) | −2.29165e14 | −0.00740836 | ||||||||
\(997\) | −3.93768e16 | −1.26595 | −0.632975 | − | 0.774172i | \(-0.718167\pi\) | ||||
−0.632975 | + | 0.774172i | \(0.718167\pi\) | |||||||
\(998\) | −2.45576e16 | −0.785176 | ||||||||
\(999\) | 1.08843e16 | 0.346091 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.12.a.d.1.20 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.d.1.20 | ✓ | 28 | 1.1 | even | 1 | trivial |