Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,16,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(14.2693505100\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{239569}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 59892 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-244.229\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 128.000 | 0.707107 | ||||||||
\(3\) | 3972.58 | 1.04873 | 0.524364 | − | 0.851494i | \(-0.324303\pi\) | ||||
0.524364 | + | 0.851494i | \(0.324303\pi\) | |||||||
\(4\) | 16384.0 | 0.500000 | ||||||||
\(5\) | 78125.0 | 0.447214 | ||||||||
\(6\) | 508490. | 0.741563 | ||||||||
\(7\) | 1.57794e6 | 0.724195 | 0.362097 | − | 0.932140i | \(-0.382061\pi\) | ||||
0.362097 | + | 0.932140i | \(0.382061\pi\) | |||||||
\(8\) | 2.09715e6 | 0.353553 | ||||||||
\(9\) | 1.43247e6 | 0.0998316 | ||||||||
\(10\) | 1.00000e7 | 0.316228 | ||||||||
\(11\) | −2.98824e6 | −0.0462349 | −0.0231175 | − | 0.999733i | \(-0.507359\pi\) | ||||
−0.0231175 | + | 0.999733i | \(0.507359\pi\) | |||||||
\(12\) | 6.50867e7 | 0.524364 | ||||||||
\(13\) | 4.92637e6 | 0.0217747 | 0.0108873 | − | 0.999941i | \(-0.496534\pi\) | ||||
0.0108873 | + | 0.999941i | \(0.496534\pi\) | |||||||
\(14\) | 2.01976e8 | 0.512083 | ||||||||
\(15\) | 3.10358e8 | 0.469006 | ||||||||
\(16\) | 2.68435e8 | 0.250000 | ||||||||
\(17\) | 6.45145e8 | 0.381321 | 0.190660 | − | 0.981656i | \(-0.438937\pi\) | ||||
0.190660 | + | 0.981656i | \(0.438937\pi\) | |||||||
\(18\) | 1.83357e8 | 0.0705916 | ||||||||
\(19\) | 2.41911e9 | 0.620874 | 0.310437 | − | 0.950594i | \(-0.399525\pi\) | ||||
0.310437 | + | 0.950594i | \(0.399525\pi\) | |||||||
\(20\) | 1.28000e9 | 0.223607 | ||||||||
\(21\) | 6.26849e9 | 0.759484 | ||||||||
\(22\) | −3.82495e8 | −0.0326930 | ||||||||
\(23\) | 2.33075e10 | 1.42737 | 0.713685 | − | 0.700467i | \(-0.247025\pi\) | ||||
0.713685 | + | 0.700467i | \(0.247025\pi\) | |||||||
\(24\) | 8.33110e9 | 0.370782 | ||||||||
\(25\) | 6.10352e9 | 0.200000 | ||||||||
\(26\) | 6.30575e8 | 0.0153970 | ||||||||
\(27\) | −5.13115e10 | −0.944032 | ||||||||
\(28\) | 2.58530e10 | 0.362097 | ||||||||
\(29\) | −1.80269e11 | −1.94060 | −0.970300 | − | 0.241904i | \(-0.922228\pi\) | ||||
−0.970300 | + | 0.241904i | \(0.922228\pi\) | |||||||
\(30\) | 3.97258e10 | 0.331637 | ||||||||
\(31\) | −2.85505e11 | −1.86381 | −0.931904 | − | 0.362706i | \(-0.881853\pi\) | ||||
−0.931904 | + | 0.362706i | \(0.881853\pi\) | |||||||
\(32\) | 3.43597e10 | 0.176777 | ||||||||
\(33\) | −1.18710e10 | −0.0484879 | ||||||||
\(34\) | 8.25786e10 | 0.269635 | ||||||||
\(35\) | 1.23277e11 | 0.323870 | ||||||||
\(36\) | 2.34697e10 | 0.0499158 | ||||||||
\(37\) | 1.04185e11 | 0.180422 | 0.0902112 | − | 0.995923i | \(-0.471246\pi\) | ||||
0.0902112 | + | 0.995923i | \(0.471246\pi\) | |||||||
\(38\) | 3.09646e11 | 0.439025 | ||||||||
\(39\) | 1.95704e10 | 0.0228357 | ||||||||
\(40\) | 1.63840e11 | 0.158114 | ||||||||
\(41\) | −1.28393e12 | −1.02958 | −0.514792 | − | 0.857315i | \(-0.672131\pi\) | ||||
−0.514792 | + | 0.857315i | \(0.672131\pi\) | |||||||
\(42\) | 8.02367e11 | 0.537036 | ||||||||
\(43\) | −5.11969e11 | −0.287230 | −0.143615 | − | 0.989634i | \(-0.545873\pi\) | ||||
−0.143615 | + | 0.989634i | \(0.545873\pi\) | |||||||
\(44\) | −4.89593e10 | −0.0231175 | ||||||||
\(45\) | 1.11912e11 | 0.0446460 | ||||||||
\(46\) | 2.98336e12 | 1.00930 | ||||||||
\(47\) | 5.22662e12 | 1.50483 | 0.752414 | − | 0.658690i | \(-0.228889\pi\) | ||||
0.752414 | + | 0.658690i | \(0.228889\pi\) | |||||||
\(48\) | 1.06638e12 | 0.262182 | ||||||||
\(49\) | −2.25766e12 | −0.475542 | ||||||||
\(50\) | 7.81250e11 | 0.141421 | ||||||||
\(51\) | 2.56289e12 | 0.399902 | ||||||||
\(52\) | 8.07136e10 | 0.0108873 | ||||||||
\(53\) | −1.39001e13 | −1.62536 | −0.812680 | − | 0.582710i | \(-0.801992\pi\) | ||||
−0.812680 | + | 0.582710i | \(0.801992\pi\) | |||||||
\(54\) | −6.56788e12 | −0.667532 | ||||||||
\(55\) | −2.33456e11 | −0.0206769 | ||||||||
\(56\) | 3.30918e12 | 0.256042 | ||||||||
\(57\) | 9.61011e12 | 0.651129 | ||||||||
\(58\) | −2.30744e13 | −1.37221 | ||||||||
\(59\) | 9.11699e12 | 0.476938 | 0.238469 | − | 0.971150i | \(-0.423355\pi\) | ||||
0.238469 | + | 0.971150i | \(0.423355\pi\) | |||||||
\(60\) | 5.08490e12 | 0.234503 | ||||||||
\(61\) | −1.50270e13 | −0.612206 | −0.306103 | − | 0.951998i | \(-0.599025\pi\) | ||||
−0.306103 | + | 0.951998i | \(0.599025\pi\) | |||||||
\(62\) | −3.65446e13 | −1.31791 | ||||||||
\(63\) | 2.26036e12 | 0.0722975 | ||||||||
\(64\) | 4.39805e12 | 0.125000 | ||||||||
\(65\) | 3.84872e11 | 0.00973793 | ||||||||
\(66\) | −1.51949e12 | −0.0342861 | ||||||||
\(67\) | 2.18097e13 | 0.439631 | 0.219816 | − | 0.975541i | \(-0.429454\pi\) | ||||
0.219816 | + | 0.975541i | \(0.429454\pi\) | |||||||
\(68\) | 1.05701e13 | 0.190660 | ||||||||
\(69\) | 9.25908e13 | 1.49692 | ||||||||
\(70\) | 1.57794e13 | 0.229011 | ||||||||
\(71\) | −6.45213e13 | −0.841909 | −0.420955 | − | 0.907082i | \(-0.638305\pi\) | ||||
−0.420955 | + | 0.907082i | \(0.638305\pi\) | |||||||
\(72\) | 3.00412e12 | 0.0352958 | ||||||||
\(73\) | 9.76233e13 | 1.03427 | 0.517133 | − | 0.855905i | \(-0.326999\pi\) | ||||
0.517133 | + | 0.855905i | \(0.326999\pi\) | |||||||
\(74\) | 1.33356e13 | 0.127578 | ||||||||
\(75\) | 2.42467e13 | 0.209746 | ||||||||
\(76\) | 3.96347e13 | 0.310437 | ||||||||
\(77\) | −4.71526e12 | −0.0334831 | ||||||||
\(78\) | 2.50501e12 | 0.0161473 | ||||||||
\(79\) | 2.35831e14 | 1.38165 | 0.690823 | − | 0.723024i | \(-0.257248\pi\) | ||||
0.690823 | + | 0.723024i | \(0.257248\pi\) | |||||||
\(80\) | 2.09715e13 | 0.111803 | ||||||||
\(81\) | −2.24394e14 | −1.08987 | ||||||||
\(82\) | −1.64343e14 | −0.728026 | ||||||||
\(83\) | −4.13505e14 | −1.67261 | −0.836305 | − | 0.548264i | \(-0.815289\pi\) | ||||
−0.836305 | + | 0.548264i | \(0.815289\pi\) | |||||||
\(84\) | 1.02703e14 | 0.379742 | ||||||||
\(85\) | 5.04020e13 | 0.170532 | ||||||||
\(86\) | −6.55320e13 | −0.203102 | ||||||||
\(87\) | −7.16133e14 | −2.03516 | ||||||||
\(88\) | −6.26679e12 | −0.0163465 | ||||||||
\(89\) | 5.45429e14 | 1.30711 | 0.653556 | − | 0.756878i | \(-0.273276\pi\) | ||||
0.653556 | + | 0.756878i | \(0.273276\pi\) | |||||||
\(90\) | 1.43247e13 | 0.0315695 | ||||||||
\(91\) | 7.77352e12 | 0.0157691 | ||||||||
\(92\) | 3.81870e14 | 0.713685 | ||||||||
\(93\) | −1.13419e15 | −1.95463 | ||||||||
\(94\) | 6.69007e14 | 1.06407 | ||||||||
\(95\) | 1.88993e14 | 0.277664 | ||||||||
\(96\) | 1.36497e14 | 0.185391 | ||||||||
\(97\) | 4.71267e14 | 0.592214 | 0.296107 | − | 0.955155i | \(-0.404311\pi\) | ||||
0.296107 | + | 0.955155i | \(0.404311\pi\) | |||||||
\(98\) | −2.88981e14 | −0.336259 | ||||||||
\(99\) | −4.28057e12 | −0.00461571 | ||||||||
\(100\) | 1.00000e14 | 0.100000 | ||||||||
\(101\) | 8.62387e14 | 0.800372 | 0.400186 | − | 0.916434i | \(-0.368945\pi\) | ||||
0.400186 | + | 0.916434i | \(0.368945\pi\) | |||||||
\(102\) | 3.28050e14 | 0.282773 | ||||||||
\(103\) | −1.08890e15 | −0.872385 | −0.436192 | − | 0.899853i | \(-0.643673\pi\) | ||||
−0.436192 | + | 0.899853i | \(0.643673\pi\) | |||||||
\(104\) | 1.03313e13 | 0.00769851 | ||||||||
\(105\) | 4.89726e14 | 0.339651 | ||||||||
\(106\) | −1.77922e15 | −1.14930 | ||||||||
\(107\) | 1.24168e15 | 0.747536 | 0.373768 | − | 0.927522i | \(-0.378066\pi\) | ||||
0.373768 | + | 0.927522i | \(0.378066\pi\) | |||||||
\(108\) | −8.40688e14 | −0.472016 | ||||||||
\(109\) | 2.12985e15 | 1.11596 | 0.557982 | − | 0.829853i | \(-0.311576\pi\) | ||||
0.557982 | + | 0.829853i | \(0.311576\pi\) | |||||||
\(110\) | −2.98824e13 | −0.0146208 | ||||||||
\(111\) | 4.13881e14 | 0.189214 | ||||||||
\(112\) | 4.23575e14 | 0.181049 | ||||||||
\(113\) | 6.89269e14 | 0.275613 | 0.137807 | − | 0.990459i | \(-0.455995\pi\) | ||||
0.137807 | + | 0.990459i | \(0.455995\pi\) | |||||||
\(114\) | 1.23009e15 | 0.460418 | ||||||||
\(115\) | 1.82090e15 | 0.638339 | ||||||||
\(116\) | −2.95353e15 | −0.970300 | ||||||||
\(117\) | 7.05689e12 | 0.00217380 | ||||||||
\(118\) | 1.16698e15 | 0.337246 | ||||||||
\(119\) | 1.01800e15 | 0.276151 | ||||||||
\(120\) | 6.50867e14 | 0.165819 | ||||||||
\(121\) | −4.16832e15 | −0.997862 | ||||||||
\(122\) | −1.92345e15 | −0.432895 | ||||||||
\(123\) | −5.10050e15 | −1.07975 | ||||||||
\(124\) | −4.67771e15 | −0.931904 | ||||||||
\(125\) | 4.76837e14 | 0.0894427 | ||||||||
\(126\) | 2.89326e14 | 0.0511221 | ||||||||
\(127\) | −6.43459e15 | −1.07150 | −0.535751 | − | 0.844376i | \(-0.679971\pi\) | ||||
−0.535751 | + | 0.844376i | \(0.679971\pi\) | |||||||
\(128\) | 5.62950e14 | 0.0883883 | ||||||||
\(129\) | −2.03384e15 | −0.301226 | ||||||||
\(130\) | 4.92637e13 | 0.00688576 | ||||||||
\(131\) | 2.77378e15 | 0.366047 | 0.183023 | − | 0.983109i | \(-0.441412\pi\) | ||||
0.183023 | + | 0.983109i | \(0.441412\pi\) | |||||||
\(132\) | −1.94495e14 | −0.0242439 | ||||||||
\(133\) | 3.81721e15 | 0.449634 | ||||||||
\(134\) | 2.79164e15 | 0.310866 | ||||||||
\(135\) | −4.00871e15 | −0.422184 | ||||||||
\(136\) | 1.35297e15 | 0.134817 | ||||||||
\(137\) | 1.42960e16 | 1.34837 | 0.674185 | − | 0.738563i | \(-0.264495\pi\) | ||||
0.674185 | + | 0.738563i | \(0.264495\pi\) | |||||||
\(138\) | 1.18516e16 | 1.05849 | ||||||||
\(139\) | −4.57651e15 | −0.387189 | −0.193595 | − | 0.981082i | \(-0.562015\pi\) | ||||
−0.193595 | + | 0.981082i | \(0.562015\pi\) | |||||||
\(140\) | 2.01976e15 | 0.161935 | ||||||||
\(141\) | 2.07632e16 | 1.57816 | ||||||||
\(142\) | −8.25872e15 | −0.595320 | ||||||||
\(143\) | −1.47212e13 | −0.00100675 | ||||||||
\(144\) | 3.84527e14 | 0.0249579 | ||||||||
\(145\) | −1.40835e16 | −0.867863 | ||||||||
\(146\) | 1.24958e16 | 0.731336 | ||||||||
\(147\) | −8.96875e15 | −0.498714 | ||||||||
\(148\) | 1.70696e15 | 0.0902112 | ||||||||
\(149\) | 1.32935e16 | 0.667947 | 0.333974 | − | 0.942582i | \(-0.391610\pi\) | ||||
0.333974 | + | 0.942582i | \(0.391610\pi\) | |||||||
\(150\) | 3.10358e15 | 0.148313 | ||||||||
\(151\) | −1.93100e16 | −0.877922 | −0.438961 | − | 0.898506i | \(-0.644653\pi\) | ||||
−0.438961 | + | 0.898506i | \(0.644653\pi\) | |||||||
\(152\) | 5.07324e15 | 0.219512 | ||||||||
\(153\) | 9.24154e14 | 0.0380679 | ||||||||
\(154\) | −6.03554e14 | −0.0236761 | ||||||||
\(155\) | −2.23051e16 | −0.833520 | ||||||||
\(156\) | 3.20641e14 | 0.0114179 | ||||||||
\(157\) | 1.06880e16 | 0.362784 | 0.181392 | − | 0.983411i | \(-0.441940\pi\) | ||||
0.181392 | + | 0.983411i | \(0.441940\pi\) | |||||||
\(158\) | 3.01863e16 | 0.976971 | ||||||||
\(159\) | −5.52193e16 | −1.70456 | ||||||||
\(160\) | 2.68435e15 | 0.0790569 | ||||||||
\(161\) | 3.67778e16 | 1.03369 | ||||||||
\(162\) | −2.87224e16 | −0.770651 | ||||||||
\(163\) | −3.29026e16 | −0.842991 | −0.421496 | − | 0.906830i | \(-0.638495\pi\) | ||||
−0.421496 | + | 0.906830i | \(0.638495\pi\) | |||||||
\(164\) | −2.10359e16 | −0.514792 | ||||||||
\(165\) | −9.27423e14 | −0.0216844 | ||||||||
\(166\) | −5.29286e16 | −1.18271 | ||||||||
\(167\) | 3.14439e16 | 0.671681 | 0.335841 | − | 0.941919i | \(-0.390980\pi\) | ||||
0.335841 | + | 0.941919i | \(0.390980\pi\) | |||||||
\(168\) | 1.31460e16 | 0.268518 | ||||||||
\(169\) | −5.11616e16 | −0.999526 | ||||||||
\(170\) | 6.45145e15 | 0.120584 | ||||||||
\(171\) | 3.46531e15 | 0.0619829 | ||||||||
\(172\) | −8.38809e15 | −0.143615 | ||||||||
\(173\) | 1.19867e17 | 1.96496 | 0.982482 | − | 0.186359i | \(-0.0596686\pi\) | ||||
0.982482 | + | 0.186359i | \(0.0596686\pi\) | |||||||
\(174\) | −9.16650e16 | −1.43908 | ||||||||
\(175\) | 9.63099e15 | 0.144839 | ||||||||
\(176\) | −8.02149e14 | −0.0115587 | ||||||||
\(177\) | 3.62180e16 | 0.500178 | ||||||||
\(178\) | 6.98149e16 | 0.924268 | ||||||||
\(179\) | 4.18778e16 | 0.531602 | 0.265801 | − | 0.964028i | \(-0.414364\pi\) | ||||
0.265801 | + | 0.964028i | \(0.414364\pi\) | |||||||
\(180\) | 1.83357e15 | 0.0223230 | ||||||||
\(181\) | 1.25193e17 | 1.46214 | 0.731071 | − | 0.682301i | \(-0.239021\pi\) | ||||
0.731071 | + | 0.682301i | \(0.239021\pi\) | |||||||
\(182\) | 9.95010e14 | 0.0111504 | ||||||||
\(183\) | −5.96959e16 | −0.642038 | ||||||||
\(184\) | 4.88793e16 | 0.504652 | ||||||||
\(185\) | 8.13942e15 | 0.0806874 | ||||||||
\(186\) | −1.45176e17 | −1.38213 | ||||||||
\(187\) | −1.92785e15 | −0.0176303 | ||||||||
\(188\) | 8.56330e16 | 0.752414 | ||||||||
\(189\) | −8.09666e16 | −0.683663 | ||||||||
\(190\) | 2.41911e16 | 0.196338 | ||||||||
\(191\) | 7.75948e16 | 0.605456 | 0.302728 | − | 0.953077i | \(-0.402103\pi\) | ||||
0.302728 | + | 0.953077i | \(0.402103\pi\) | |||||||
\(192\) | 1.74716e16 | 0.131091 | ||||||||
\(193\) | −2.25828e17 | −1.62967 | −0.814834 | − | 0.579695i | \(-0.803172\pi\) | ||||
−0.814834 | + | 0.579695i | \(0.803172\pi\) | |||||||
\(194\) | 6.03221e16 | 0.418759 | ||||||||
\(195\) | 1.52894e15 | 0.0102124 | ||||||||
\(196\) | −3.69896e16 | −0.237771 | ||||||||
\(197\) | 5.36977e16 | 0.332246 | 0.166123 | − | 0.986105i | \(-0.446875\pi\) | ||||
0.166123 | + | 0.986105i | \(0.446875\pi\) | |||||||
\(198\) | −5.47914e14 | −0.00326380 | ||||||||
\(199\) | 1.41350e17 | 0.810771 | 0.405386 | − | 0.914146i | \(-0.367137\pi\) | ||||
0.405386 | + | 0.914146i | \(0.367137\pi\) | |||||||
\(200\) | 1.28000e16 | 0.0707107 | ||||||||
\(201\) | 8.66407e16 | 0.461054 | ||||||||
\(202\) | 1.10386e17 | 0.565949 | ||||||||
\(203\) | −2.84454e17 | −1.40537 | ||||||||
\(204\) | 4.19904e16 | 0.199951 | ||||||||
\(205\) | −1.00307e17 | −0.460444 | ||||||||
\(206\) | −1.39379e17 | −0.616869 | ||||||||
\(207\) | 3.33874e16 | 0.142497 | ||||||||
\(208\) | 1.32241e15 | 0.00544367 | ||||||||
\(209\) | −7.22888e15 | −0.0287061 | ||||||||
\(210\) | 6.26849e16 | 0.240170 | ||||||||
\(211\) | −4.41718e16 | −0.163315 | −0.0816577 | − | 0.996660i | \(-0.526021\pi\) | ||||
−0.0816577 | + | 0.996660i | \(0.526021\pi\) | |||||||
\(212\) | −2.27740e17 | −0.812680 | ||||||||
\(213\) | −2.56316e17 | −0.882934 | ||||||||
\(214\) | 1.58935e17 | 0.528587 | ||||||||
\(215\) | −3.99975e16 | −0.128453 | ||||||||
\(216\) | −1.07608e17 | −0.333766 | ||||||||
\(217\) | −4.50510e17 | −1.34976 | ||||||||
\(218\) | 2.72621e17 | 0.789105 | ||||||||
\(219\) | 3.87816e17 | 1.08466 | ||||||||
\(220\) | −3.82495e15 | −0.0103384 | ||||||||
\(221\) | 3.17822e15 | 0.00830314 | ||||||||
\(222\) | 5.29768e16 | 0.133795 | ||||||||
\(223\) | −5.00066e17 | −1.22107 | −0.610535 | − | 0.791989i | \(-0.709046\pi\) | ||||
−0.610535 | + | 0.791989i | \(0.709046\pi\) | |||||||
\(224\) | 5.42176e16 | 0.128021 | ||||||||
\(225\) | 8.74313e15 | 0.0199663 | ||||||||
\(226\) | 8.82264e16 | 0.194888 | ||||||||
\(227\) | −1.16741e17 | −0.249477 | −0.124738 | − | 0.992190i | \(-0.539809\pi\) | ||||
−0.124738 | + | 0.992190i | \(0.539809\pi\) | |||||||
\(228\) | 1.57452e17 | 0.325564 | ||||||||
\(229\) | 6.72239e17 | 1.34511 | 0.672555 | − | 0.740047i | \(-0.265197\pi\) | ||||
0.672555 | + | 0.740047i | \(0.265197\pi\) | |||||||
\(230\) | 2.33075e17 | 0.451374 | ||||||||
\(231\) | −1.87318e16 | −0.0351147 | ||||||||
\(232\) | −3.78052e17 | −0.686106 | ||||||||
\(233\) | 4.08177e17 | 0.717265 | 0.358632 | − | 0.933479i | \(-0.383243\pi\) | ||||
0.358632 | + | 0.933479i | \(0.383243\pi\) | |||||||
\(234\) | 9.03282e14 | 0.00153711 | ||||||||
\(235\) | 4.08330e17 | 0.672980 | ||||||||
\(236\) | 1.49373e17 | 0.238469 | ||||||||
\(237\) | 9.36855e17 | 1.44897 | ||||||||
\(238\) | 1.30304e17 | 0.195268 | ||||||||
\(239\) | 1.27317e18 | 1.84885 | 0.924424 | − | 0.381366i | \(-0.124546\pi\) | ||||
0.924424 | + | 0.381366i | \(0.124546\pi\) | |||||||
\(240\) | 8.33110e16 | 0.117251 | ||||||||
\(241\) | −4.00654e17 | −0.546565 | −0.273282 | − | 0.961934i | \(-0.588109\pi\) | ||||
−0.273282 | + | 0.961934i | \(0.588109\pi\) | |||||||
\(242\) | −5.33545e17 | −0.705595 | ||||||||
\(243\) | −1.55157e17 | −0.198940 | ||||||||
\(244\) | −2.46202e17 | −0.306103 | ||||||||
\(245\) | −1.76380e17 | −0.212669 | ||||||||
\(246\) | −6.52864e17 | −0.763501 | ||||||||
\(247\) | 1.19174e16 | 0.0135193 | ||||||||
\(248\) | −5.98747e17 | −0.658955 | ||||||||
\(249\) | −1.64268e18 | −1.75411 | ||||||||
\(250\) | 6.10352e16 | 0.0632456 | ||||||||
\(251\) | −3.69701e17 | −0.371790 | −0.185895 | − | 0.982570i | \(-0.559518\pi\) | ||||
−0.185895 | + | 0.982570i | \(0.559518\pi\) | |||||||
\(252\) | 3.70337e16 | 0.0361488 | ||||||||
\(253\) | −6.96483e16 | −0.0659944 | ||||||||
\(254\) | −8.23628e17 | −0.757666 | ||||||||
\(255\) | 2.00226e17 | 0.178842 | ||||||||
\(256\) | 7.20576e16 | 0.0625000 | ||||||||
\(257\) | −5.68963e16 | −0.0479276 | −0.0239638 | − | 0.999713i | \(-0.507629\pi\) | ||||
−0.0239638 | + | 0.999713i | \(0.507629\pi\) | |||||||
\(258\) | −2.60331e17 | −0.212999 | ||||||||
\(259\) | 1.64397e17 | 0.130661 | ||||||||
\(260\) | 6.30575e15 | 0.00486896 | ||||||||
\(261\) | −2.58231e17 | −0.193733 | ||||||||
\(262\) | 3.55043e17 | 0.258834 | ||||||||
\(263\) | 4.31202e16 | 0.0305501 | 0.0152751 | − | 0.999883i | \(-0.495138\pi\) | ||||
0.0152751 | + | 0.999883i | \(0.495138\pi\) | |||||||
\(264\) | −2.48953e16 | −0.0171431 | ||||||||
\(265\) | −1.08595e18 | −0.726883 | ||||||||
\(266\) | 4.88603e17 | 0.317939 | ||||||||
\(267\) | 2.16676e18 | 1.37081 | ||||||||
\(268\) | 3.57330e17 | 0.219816 | ||||||||
\(269\) | −2.57678e18 | −1.54147 | −0.770737 | − | 0.637154i | \(-0.780112\pi\) | ||||
−0.770737 | + | 0.637154i | \(0.780112\pi\) | |||||||
\(270\) | −5.13115e17 | −0.298529 | ||||||||
\(271\) | 1.81142e18 | 1.02506 | 0.512530 | − | 0.858669i | \(-0.328708\pi\) | ||||
0.512530 | + | 0.858669i | \(0.328708\pi\) | |||||||
\(272\) | 1.73180e17 | 0.0953302 | ||||||||
\(273\) | 3.08809e16 | 0.0165375 | ||||||||
\(274\) | 1.82988e18 | 0.953442 | ||||||||
\(275\) | −1.82388e16 | −0.00924699 | ||||||||
\(276\) | 1.51701e18 | 0.748462 | ||||||||
\(277\) | −1.36071e18 | −0.653381 | −0.326690 | − | 0.945131i | \(-0.605933\pi\) | ||||
−0.326690 | + | 0.945131i | \(0.605933\pi\) | |||||||
\(278\) | −5.85793e17 | −0.273784 | ||||||||
\(279\) | −4.08979e17 | −0.186067 | ||||||||
\(280\) | 2.58530e17 | 0.114505 | ||||||||
\(281\) | 2.12909e17 | 0.0918115 | 0.0459057 | − | 0.998946i | \(-0.485383\pi\) | ||||
0.0459057 | + | 0.998946i | \(0.485383\pi\) | |||||||
\(282\) | 2.65768e18 | 1.11593 | ||||||||
\(283\) | 1.23798e18 | 0.506193 | 0.253096 | − | 0.967441i | \(-0.418551\pi\) | ||||
0.253096 | + | 0.967441i | \(0.418551\pi\) | |||||||
\(284\) | −1.05712e18 | −0.420955 | ||||||||
\(285\) | 7.50790e17 | 0.291194 | ||||||||
\(286\) | −1.88431e15 | −0.000711880 0 | ||||||||
\(287\) | −2.02596e18 | −0.745619 | ||||||||
\(288\) | 4.92194e16 | 0.0176479 | ||||||||
\(289\) | −2.44621e18 | −0.854594 | ||||||||
\(290\) | −1.80269e18 | −0.613672 | ||||||||
\(291\) | 1.87214e18 | 0.621072 | ||||||||
\(292\) | 1.59946e18 | 0.517133 | ||||||||
\(293\) | 3.88932e18 | 1.22565 | 0.612825 | − | 0.790219i | \(-0.290033\pi\) | ||||
0.612825 | + | 0.790219i | \(0.290033\pi\) | |||||||
\(294\) | −1.14800e18 | −0.352644 | ||||||||
\(295\) | 7.12265e17 | 0.213293 | ||||||||
\(296\) | 2.18491e17 | 0.0637890 | ||||||||
\(297\) | 1.53331e17 | 0.0436473 | ||||||||
\(298\) | 1.70157e18 | 0.472310 | ||||||||
\(299\) | 1.14821e17 | 0.0310805 | ||||||||
\(300\) | 3.97258e17 | 0.104873 | ||||||||
\(301\) | −8.07856e17 | −0.208011 | ||||||||
\(302\) | −2.47169e18 | −0.620785 | ||||||||
\(303\) | 3.42590e18 | 0.839373 | ||||||||
\(304\) | 6.49375e17 | 0.155219 | ||||||||
\(305\) | −1.17398e18 | −0.273787 | ||||||||
\(306\) | 1.18292e17 | 0.0269180 | ||||||||
\(307\) | −7.12129e18 | −1.58132 | −0.790662 | − | 0.612253i | \(-0.790263\pi\) | ||||
−0.790662 | + | 0.612253i | \(0.790263\pi\) | |||||||
\(308\) | −7.72549e16 | −0.0167415 | ||||||||
\(309\) | −4.32573e18 | −0.914895 | ||||||||
\(310\) | −2.85505e18 | −0.589388 | ||||||||
\(311\) | −8.62738e18 | −1.73851 | −0.869253 | − | 0.494367i | \(-0.835400\pi\) | ||||
−0.869253 | + | 0.494367i | \(0.835400\pi\) | |||||||
\(312\) | 4.10421e16 | 0.00807365 | ||||||||
\(313\) | 8.40829e18 | 1.61482 | 0.807411 | − | 0.589989i | \(-0.200868\pi\) | ||||
0.807411 | + | 0.589989i | \(0.200868\pi\) | |||||||
\(314\) | 1.36806e18 | 0.256527 | ||||||||
\(315\) | 1.76591e17 | 0.0323324 | ||||||||
\(316\) | 3.86385e18 | 0.690823 | ||||||||
\(317\) | −5.66897e18 | −0.989828 | −0.494914 | − | 0.868942i | \(-0.664801\pi\) | ||||
−0.494914 | + | 0.868942i | \(0.664801\pi\) | |||||||
\(318\) | −7.06807e18 | −1.20531 | ||||||||
\(319\) | 5.38687e17 | 0.0897235 | ||||||||
\(320\) | 3.43597e17 | 0.0559017 | ||||||||
\(321\) | 4.93268e18 | 0.783962 | ||||||||
\(322\) | 4.70756e18 | 0.730932 | ||||||||
\(323\) | 1.56068e18 | 0.236752 | ||||||||
\(324\) | −3.67646e18 | −0.544933 | ||||||||
\(325\) | 3.00682e16 | 0.00435493 | ||||||||
\(326\) | −4.21153e18 | −0.596085 | ||||||||
\(327\) | 8.46099e18 | 1.17034 | ||||||||
\(328\) | −2.69259e18 | −0.364013 | ||||||||
\(329\) | 8.24730e18 | 1.08979 | ||||||||
\(330\) | −1.18710e17 | −0.0153332 | ||||||||
\(331\) | −6.94615e18 | −0.877070 | −0.438535 | − | 0.898714i | \(-0.644502\pi\) | ||||
−0.438535 | + | 0.898714i | \(0.644502\pi\) | |||||||
\(332\) | −6.77486e18 | −0.836305 | ||||||||
\(333\) | 1.49242e17 | 0.0180119 | ||||||||
\(334\) | 4.02482e18 | 0.474950 | ||||||||
\(335\) | 1.70388e18 | 0.196609 | ||||||||
\(336\) | 1.68269e18 | 0.189871 | ||||||||
\(337\) | 1.06418e19 | 1.17433 | 0.587166 | − | 0.809466i | \(-0.300244\pi\) | ||||
0.587166 | + | 0.809466i | \(0.300244\pi\) | |||||||
\(338\) | −6.54869e18 | −0.706772 | ||||||||
\(339\) | 2.73817e18 | 0.289044 | ||||||||
\(340\) | 8.25786e17 | 0.0852659 | ||||||||
\(341\) | 8.53157e17 | 0.0861730 | ||||||||
\(342\) | 4.43560e17 | 0.0438285 | ||||||||
\(343\) | −1.10538e19 | −1.06858 | ||||||||
\(344\) | −1.07368e18 | −0.101551 | ||||||||
\(345\) | 7.23366e18 | 0.669445 | ||||||||
\(346\) | 1.53430e19 | 1.38944 | ||||||||
\(347\) | 1.32412e18 | 0.117342 | 0.0586712 | − | 0.998277i | \(-0.481314\pi\) | ||||
0.0586712 | + | 0.998277i | \(0.481314\pi\) | |||||||
\(348\) | −1.17331e19 | −1.01758 | ||||||||
\(349\) | 7.66248e18 | 0.650397 | 0.325198 | − | 0.945646i | \(-0.394569\pi\) | ||||
0.325198 | + | 0.945646i | \(0.394569\pi\) | |||||||
\(350\) | 1.23277e18 | 0.102417 | ||||||||
\(351\) | −2.52780e17 | −0.0205560 | ||||||||
\(352\) | −1.02675e17 | −0.00817326 | ||||||||
\(353\) | 2.74207e18 | 0.213682 | 0.106841 | − | 0.994276i | \(-0.465926\pi\) | ||||
0.106841 | + | 0.994276i | \(0.465926\pi\) | |||||||
\(354\) | 4.63590e18 | 0.353679 | ||||||||
\(355\) | −5.04072e18 | −0.376513 | ||||||||
\(356\) | 8.93630e18 | 0.653556 | ||||||||
\(357\) | 4.04409e18 | 0.289607 | ||||||||
\(358\) | 5.36036e18 | 0.375899 | ||||||||
\(359\) | 2.87954e18 | 0.197749 | 0.0988746 | − | 0.995100i | \(-0.468476\pi\) | ||||
0.0988746 | + | 0.995100i | \(0.468476\pi\) | |||||||
\(360\) | 2.34697e17 | 0.0157848 | ||||||||
\(361\) | −9.32903e18 | −0.614515 | ||||||||
\(362\) | 1.60247e19 | 1.03389 | ||||||||
\(363\) | −1.65590e19 | −1.04649 | ||||||||
\(364\) | 1.27361e17 | 0.00788455 | ||||||||
\(365\) | 7.62682e18 | 0.462538 | ||||||||
\(366\) | −7.64107e18 | −0.453990 | ||||||||
\(367\) | −2.01936e19 | −1.17549 | −0.587744 | − | 0.809047i | \(-0.699984\pi\) | ||||
−0.587744 | + | 0.809047i | \(0.699984\pi\) | |||||||
\(368\) | 6.25656e18 | 0.356843 | ||||||||
\(369\) | −1.83919e18 | −0.102785 | ||||||||
\(370\) | 1.04185e18 | 0.0570546 | ||||||||
\(371\) | −2.19336e19 | −1.17708 | ||||||||
\(372\) | −1.85826e19 | −0.977314 | ||||||||
\(373\) | −3.62151e19 | −1.86670 | −0.933348 | − | 0.358972i | \(-0.883127\pi\) | ||||
−0.933348 | + | 0.358972i | \(0.883127\pi\) | |||||||
\(374\) | −2.46765e17 | −0.0124665 | ||||||||
\(375\) | 1.89427e18 | 0.0938011 | ||||||||
\(376\) | 1.09610e19 | 0.532037 | ||||||||
\(377\) | −8.88071e17 | −0.0422559 | ||||||||
\(378\) | −1.03637e19 | −0.483423 | ||||||||
\(379\) | −1.59928e19 | −0.731359 | −0.365679 | − | 0.930741i | \(-0.619163\pi\) | ||||
−0.365679 | + | 0.930741i | \(0.619163\pi\) | |||||||
\(380\) | 3.09646e18 | 0.138832 | ||||||||
\(381\) | −2.55619e19 | −1.12371 | ||||||||
\(382\) | 9.93214e18 | 0.428122 | ||||||||
\(383\) | 3.56761e19 | 1.50795 | 0.753975 | − | 0.656903i | \(-0.228134\pi\) | ||||
0.753975 | + | 0.656903i | \(0.228134\pi\) | |||||||
\(384\) | 2.23636e18 | 0.0926954 | ||||||||
\(385\) | −3.68380e17 | −0.0149741 | ||||||||
\(386\) | −2.89060e19 | −1.15235 | ||||||||
\(387\) | −7.33382e17 | −0.0286746 | ||||||||
\(388\) | 7.72123e18 | 0.296107 | ||||||||
\(389\) | 4.67525e19 | 1.75866 | 0.879331 | − | 0.476211i | \(-0.157990\pi\) | ||||
0.879331 | + | 0.476211i | \(0.157990\pi\) | |||||||
\(390\) | 1.95704e17 | 0.00722129 | ||||||||
\(391\) | 1.50367e19 | 0.544286 | ||||||||
\(392\) | −4.73467e18 | −0.168129 | ||||||||
\(393\) | 1.10190e19 | 0.383884 | ||||||||
\(394\) | 6.87331e18 | 0.234933 | ||||||||
\(395\) | 1.84243e19 | 0.617891 | ||||||||
\(396\) | −7.01329e16 | −0.00230785 | ||||||||
\(397\) | 1.61556e18 | 0.0521668 | 0.0260834 | − | 0.999660i | \(-0.491696\pi\) | ||||
0.0260834 | + | 0.999660i | \(0.491696\pi\) | |||||||
\(398\) | 1.80928e19 | 0.573302 | ||||||||
\(399\) | 1.51642e19 | 0.471544 | ||||||||
\(400\) | 1.63840e18 | 0.0500000 | ||||||||
\(401\) | 3.22657e19 | 0.966402 | 0.483201 | − | 0.875509i | \(-0.339474\pi\) | ||||
0.483201 | + | 0.875509i | \(0.339474\pi\) | |||||||
\(402\) | 1.10900e19 | 0.326014 | ||||||||
\(403\) | −1.40650e18 | −0.0405838 | ||||||||
\(404\) | 1.41294e19 | 0.400186 | ||||||||
\(405\) | −1.75307e19 | −0.487403 | ||||||||
\(406\) | −3.64101e19 | −0.993749 | ||||||||
\(407\) | −3.11328e17 | −0.00834182 | ||||||||
\(408\) | 5.37477e18 | 0.141387 | ||||||||
\(409\) | −2.09116e19 | −0.540084 | −0.270042 | − | 0.962849i | \(-0.587038\pi\) | ||||
−0.270042 | + | 0.962849i | \(0.587038\pi\) | |||||||
\(410\) | −1.28393e19 | −0.325583 | ||||||||
\(411\) | 5.67918e19 | 1.41407 | ||||||||
\(412\) | −1.78405e19 | −0.436192 | ||||||||
\(413\) | 1.43861e19 | 0.345396 | ||||||||
\(414\) | 4.27358e18 | 0.100760 | ||||||||
\(415\) | −3.23051e19 | −0.748014 | ||||||||
\(416\) | 1.69269e17 | 0.00384925 | ||||||||
\(417\) | −1.81805e19 | −0.406057 | ||||||||
\(418\) | −9.25297e17 | −0.0202983 | ||||||||
\(419\) | −4.31574e19 | −0.929930 | −0.464965 | − | 0.885329i | \(-0.653933\pi\) | ||||
−0.464965 | + | 0.885329i | \(0.653933\pi\) | |||||||
\(420\) | 8.02367e18 | 0.169826 | ||||||||
\(421\) | 3.44152e19 | 0.715541 | 0.357770 | − | 0.933810i | \(-0.383537\pi\) | ||||
0.357770 | + | 0.933810i | \(0.383537\pi\) | |||||||
\(422\) | −5.65399e18 | −0.115481 | ||||||||
\(423\) | 7.48700e18 | 0.150229 | ||||||||
\(424\) | −2.91507e19 | −0.574652 | ||||||||
\(425\) | 3.93765e18 | 0.0762642 | ||||||||
\(426\) | −3.28084e19 | −0.624329 | ||||||||
\(427\) | −2.37117e19 | −0.443357 | ||||||||
\(428\) | 2.03437e19 | 0.373768 | ||||||||
\(429\) | −5.84810e16 | −0.00105581 | ||||||||
\(430\) | −5.11969e18 | −0.0908301 | ||||||||
\(431\) | 7.95134e19 | 1.38631 | 0.693156 | − | 0.720788i | \(-0.256220\pi\) | ||||
0.693156 | + | 0.720788i | \(0.256220\pi\) | |||||||
\(432\) | −1.37738e19 | −0.236008 | ||||||||
\(433\) | −6.99185e19 | −1.17742 | −0.588712 | − | 0.808343i | \(-0.700365\pi\) | ||||
−0.588712 | + | 0.808343i | \(0.700365\pi\) | |||||||
\(434\) | −5.76653e19 | −0.954424 | ||||||||
\(435\) | −5.59479e19 | −0.910153 | ||||||||
\(436\) | 3.48954e19 | 0.557982 | ||||||||
\(437\) | 5.63834e19 | 0.886218 | ||||||||
\(438\) | 4.96405e19 | 0.766973 | ||||||||
\(439\) | −5.37736e19 | −0.816743 | −0.408372 | − | 0.912816i | \(-0.633903\pi\) | ||||
−0.408372 | + | 0.912816i | \(0.633903\pi\) | |||||||
\(440\) | −4.89593e17 | −0.00731038 | ||||||||
\(441\) | −3.23405e18 | −0.0474741 | ||||||||
\(442\) | 4.06812e17 | 0.00587121 | ||||||||
\(443\) | 1.46107e19 | 0.207321 | 0.103660 | − | 0.994613i | \(-0.466945\pi\) | ||||
0.103660 | + | 0.994613i | \(0.466945\pi\) | |||||||
\(444\) | 6.78103e18 | 0.0946071 | ||||||||
\(445\) | 4.26116e19 | 0.584558 | ||||||||
\(446\) | −6.40084e19 | −0.863427 | ||||||||
\(447\) | 5.28094e19 | 0.700495 | ||||||||
\(448\) | 6.93986e18 | 0.0905243 | ||||||||
\(449\) | −7.03318e19 | −0.902203 | −0.451101 | − | 0.892473i | \(-0.648969\pi\) | ||||
−0.451101 | + | 0.892473i | \(0.648969\pi\) | |||||||
\(450\) | 1.11912e18 | 0.0141183 | ||||||||
\(451\) | 3.83668e18 | 0.0476027 | ||||||||
\(452\) | 1.12930e19 | 0.137807 | ||||||||
\(453\) | −7.67107e19 | −0.920702 | ||||||||
\(454\) | −1.49429e19 | −0.176407 | ||||||||
\(455\) | 6.07306e17 | 0.00705216 | ||||||||
\(456\) | 2.01539e19 | 0.230209 | ||||||||
\(457\) | 4.35839e19 | 0.489728 | 0.244864 | − | 0.969557i | \(-0.421257\pi\) | ||||
0.244864 | + | 0.969557i | \(0.421257\pi\) | |||||||
\(458\) | 8.60466e19 | 0.951136 | ||||||||
\(459\) | −3.31034e19 | −0.359979 | ||||||||
\(460\) | 2.98336e19 | 0.319170 | ||||||||
\(461\) | −1.24140e20 | −1.30663 | −0.653317 | − | 0.757084i | \(-0.726623\pi\) | ||||
−0.653317 | + | 0.757084i | \(0.726623\pi\) | |||||||
\(462\) | −2.39767e18 | −0.0248298 | ||||||||
\(463\) | 6.58546e19 | 0.671009 | 0.335505 | − | 0.942039i | \(-0.391093\pi\) | ||||
0.335505 | + | 0.942039i | \(0.391093\pi\) | |||||||
\(464\) | −4.83906e19 | −0.485150 | ||||||||
\(465\) | −8.86087e19 | −0.874136 | ||||||||
\(466\) | 5.22467e19 | 0.507183 | ||||||||
\(467\) | 1.28108e19 | 0.122377 | 0.0611886 | − | 0.998126i | \(-0.480511\pi\) | ||||
0.0611886 | + | 0.998126i | \(0.480511\pi\) | |||||||
\(468\) | 1.15620e17 | 0.00108690 | ||||||||
\(469\) | 3.44144e19 | 0.318379 | ||||||||
\(470\) | 5.22662e19 | 0.475869 | ||||||||
\(471\) | 4.24589e19 | 0.380462 | ||||||||
\(472\) | 1.91197e19 | 0.168623 | ||||||||
\(473\) | 1.52988e18 | 0.0132801 | ||||||||
\(474\) | 1.19917e20 | 1.02458 | ||||||||
\(475\) | 1.47651e19 | 0.124175 | ||||||||
\(476\) | 1.66789e19 | 0.138075 | ||||||||
\(477\) | −1.99116e19 | −0.162262 | ||||||||
\(478\) | 1.62965e20 | 1.30733 | ||||||||
\(479\) | 2.89091e19 | 0.228307 | 0.114153 | − | 0.993463i | \(-0.463584\pi\) | ||||
0.114153 | + | 0.993463i | \(0.463584\pi\) | |||||||
\(480\) | 1.06638e19 | 0.0829093 | ||||||||
\(481\) | 5.13251e17 | 0.00392864 | ||||||||
\(482\) | −5.12837e19 | −0.386480 | ||||||||
\(483\) | 1.46103e20 | 1.08406 | ||||||||
\(484\) | −6.82937e19 | −0.498931 | ||||||||
\(485\) | 3.68177e19 | 0.264846 | ||||||||
\(486\) | −1.98600e19 | −0.140672 | ||||||||
\(487\) | 1.96397e20 | 1.36983 | 0.684916 | − | 0.728622i | \(-0.259839\pi\) | ||||
0.684916 | + | 0.728622i | \(0.259839\pi\) | |||||||
\(488\) | −3.15139e19 | −0.216448 | ||||||||
\(489\) | −1.30708e20 | −0.884069 | ||||||||
\(490\) | −2.25766e19 | −0.150380 | ||||||||
\(491\) | −1.38375e20 | −0.907707 | −0.453854 | − | 0.891076i | \(-0.649951\pi\) | ||||
−0.453854 | + | 0.891076i | \(0.649951\pi\) | |||||||
\(492\) | −8.35666e19 | −0.539877 | ||||||||
\(493\) | −1.16300e20 | −0.739992 | ||||||||
\(494\) | 1.52543e18 | 0.00955962 | ||||||||
\(495\) | −3.34420e17 | −0.00206421 | ||||||||
\(496\) | −7.66397e19 | −0.465952 | ||||||||
\(497\) | −1.01811e20 | −0.609706 | ||||||||
\(498\) | −2.10263e20 | −1.24035 | ||||||||
\(499\) | 1.95546e20 | 1.13630 | 0.568152 | − | 0.822924i | \(-0.307659\pi\) | ||||
0.568152 | + | 0.822924i | \(0.307659\pi\) | |||||||
\(500\) | 7.81250e18 | 0.0447214 | ||||||||
\(501\) | 1.24913e20 | 0.704411 | ||||||||
\(502\) | −4.73218e19 | −0.262895 | ||||||||
\(503\) | −1.06861e20 | −0.584869 | −0.292434 | − | 0.956286i | \(-0.594465\pi\) | ||||
−0.292434 | + | 0.956286i | \(0.594465\pi\) | |||||||
\(504\) | 4.74032e18 | 0.0255610 | ||||||||
\(505\) | 6.73740e19 | 0.357937 | ||||||||
\(506\) | −8.91499e18 | −0.0466651 | ||||||||
\(507\) | −2.03244e20 | −1.04823 | ||||||||
\(508\) | −1.05424e20 | −0.535751 | ||||||||
\(509\) | 1.52058e19 | 0.0761424 | 0.0380712 | − | 0.999275i | \(-0.487879\pi\) | ||||
0.0380712 | + | 0.999275i | \(0.487879\pi\) | |||||||
\(510\) | 2.56289e19 | 0.126460 | ||||||||
\(511\) | 1.54044e20 | 0.749010 | ||||||||
\(512\) | 9.22337e18 | 0.0441942 | ||||||||
\(513\) | −1.24128e20 | −0.586126 | ||||||||
\(514\) | −7.28272e18 | −0.0338899 | ||||||||
\(515\) | −8.50702e19 | −0.390142 | ||||||||
\(516\) | −3.33224e19 | −0.150613 | ||||||||
\(517\) | −1.56184e19 | −0.0695756 | ||||||||
\(518\) | 2.10428e19 | 0.0923913 | ||||||||
\(519\) | 4.76182e20 | 2.06071 | ||||||||
\(520\) | 8.07136e17 | 0.00344288 | ||||||||
\(521\) | −1.96345e20 | −0.825536 | −0.412768 | − | 0.910836i | \(-0.635438\pi\) | ||||
−0.412768 | + | 0.910836i | \(0.635438\pi\) | |||||||
\(522\) | −3.30535e19 | −0.136990 | ||||||||
\(523\) | −4.20870e20 | −1.71943 | −0.859716 | − | 0.510773i | \(-0.829359\pi\) | ||||
−0.859716 | + | 0.510773i | \(0.829359\pi\) | |||||||
\(524\) | 4.54455e19 | 0.183023 | ||||||||
\(525\) | 3.82598e19 | 0.151897 | ||||||||
\(526\) | 5.51939e18 | 0.0216022 | ||||||||
\(527\) | −1.84192e20 | −0.710709 | ||||||||
\(528\) | −3.18660e18 | −0.0121220 | ||||||||
\(529\) | 2.76604e20 | 1.03739 | ||||||||
\(530\) | −1.39001e20 | −0.513984 | ||||||||
\(531\) | 1.30599e19 | 0.0476134 | ||||||||
\(532\) | 6.25412e19 | 0.224817 | ||||||||
\(533\) | −6.32510e18 | −0.0224188 | ||||||||
\(534\) | 2.77345e20 | 0.969306 | ||||||||
\(535\) | 9.70064e19 | 0.334308 | ||||||||
\(536\) | 4.57382e19 | 0.155433 | ||||||||
\(537\) | 1.66363e20 | 0.557506 | ||||||||
\(538\) | −3.29828e20 | −1.08999 | ||||||||
\(539\) | 6.74644e18 | 0.0219866 | ||||||||
\(540\) | −6.56788e19 | −0.211092 | ||||||||
\(541\) | 3.30654e20 | 1.04808 | 0.524040 | − | 0.851694i | \(-0.324424\pi\) | ||||
0.524040 | + | 0.851694i | \(0.324424\pi\) | |||||||
\(542\) | 2.31862e20 | 0.724827 | ||||||||
\(543\) | 4.97338e20 | 1.53339 | ||||||||
\(544\) | 2.21670e19 | 0.0674086 | ||||||||
\(545\) | 1.66394e20 | 0.499074 | ||||||||
\(546\) | 3.95276e18 | 0.0116938 | ||||||||
\(547\) | −3.44218e20 | −1.00445 | −0.502225 | − | 0.864737i | \(-0.667485\pi\) | ||||
−0.502225 | + | 0.864737i | \(0.667485\pi\) | |||||||
\(548\) | 2.34225e20 | 0.674185 | ||||||||
\(549\) | −2.15258e19 | −0.0611175 | ||||||||
\(550\) | −2.33456e18 | −0.00653861 | ||||||||
\(551\) | −4.36091e20 | −1.20487 | ||||||||
\(552\) | 1.94177e20 | 0.529243 | ||||||||
\(553\) | 3.72127e20 | 1.00058 | ||||||||
\(554\) | −1.74170e20 | −0.462010 | ||||||||
\(555\) | 3.23345e19 | 0.0846191 | ||||||||
\(556\) | −7.49816e19 | −0.193595 | ||||||||
\(557\) | 4.03852e20 | 1.02875 | 0.514374 | − | 0.857566i | \(-0.328024\pi\) | ||||
0.514374 | + | 0.857566i | \(0.328024\pi\) | |||||||
\(558\) | −5.23493e19 | −0.131569 | ||||||||
\(559\) | −2.52215e18 | −0.00625434 | ||||||||
\(560\) | 3.30918e19 | 0.0809674 | ||||||||
\(561\) | −7.65853e18 | −0.0184894 | ||||||||
\(562\) | 2.72524e19 | 0.0649205 | ||||||||
\(563\) | −3.78722e20 | −0.890240 | −0.445120 | − | 0.895471i | \(-0.646839\pi\) | ||||
−0.445120 | + | 0.895471i | \(0.646839\pi\) | |||||||
\(564\) | 3.40184e20 | 0.789078 | ||||||||
\(565\) | 5.38491e19 | 0.123258 | ||||||||
\(566\) | 1.58462e20 | 0.357932 | ||||||||
\(567\) | −3.54080e20 | −0.789275 | ||||||||
\(568\) | −1.35311e20 | −0.297660 | ||||||||
\(569\) | −5.32798e20 | −1.15670 | −0.578350 | − | 0.815789i | \(-0.696303\pi\) | ||||
−0.578350 | + | 0.815789i | \(0.696303\pi\) | |||||||
\(570\) | 9.61011e19 | 0.205905 | ||||||||
\(571\) | −6.45129e20 | −1.36419 | −0.682097 | − | 0.731262i | \(-0.738932\pi\) | ||||
−0.682097 | + | 0.731262i | \(0.738932\pi\) | |||||||
\(572\) | −2.41192e17 | −0.000503375 0 | ||||||||
\(573\) | 3.08251e20 | 0.634959 | ||||||||
\(574\) | −2.59323e20 | −0.527232 | ||||||||
\(575\) | 1.42258e20 | 0.285474 | ||||||||
\(576\) | 6.30009e18 | 0.0124789 | ||||||||
\(577\) | 5.38124e18 | 0.0105212 | 0.00526058 | − | 0.999986i | \(-0.498325\pi\) | ||||
0.00526058 | + | 0.999986i | \(0.498325\pi\) | |||||||
\(578\) | −3.13115e20 | −0.604289 | ||||||||
\(579\) | −8.97121e20 | −1.70908 | ||||||||
\(580\) | −2.30744e20 | −0.433931 | ||||||||
\(581\) | −6.52486e20 | −1.21130 | ||||||||
\(582\) | 2.39634e20 | 0.439164 | ||||||||
\(583\) | 4.15369e19 | 0.0751484 | ||||||||
\(584\) | 2.04731e20 | 0.365668 | ||||||||
\(585\) | 5.51320e17 | 0.000972153 0 | ||||||||
\(586\) | 4.97833e20 | 0.866665 | ||||||||
\(587\) | −6.26245e20 | −1.07636 | −0.538181 | − | 0.842829i | \(-0.680888\pi\) | ||||
−0.538181 | + | 0.842829i | \(0.680888\pi\) | |||||||
\(588\) | −1.46944e20 | −0.249357 | ||||||||
\(589\) | −6.90668e20 | −1.15719 | ||||||||
\(590\) | 9.11699e19 | 0.150821 | ||||||||
\(591\) | 2.13318e20 | 0.348435 | ||||||||
\(592\) | 2.79668e19 | 0.0451056 | ||||||||
\(593\) | 6.78491e20 | 1.08052 | 0.540262 | − | 0.841497i | \(-0.318325\pi\) | ||||
0.540262 | + | 0.841497i | \(0.318325\pi\) | |||||||
\(594\) | 1.96264e19 | 0.0308633 | ||||||||
\(595\) | 7.95313e19 | 0.123498 | ||||||||
\(596\) | 2.17801e20 | 0.333974 | ||||||||
\(597\) | 5.61525e20 | 0.850279 | ||||||||
\(598\) | 1.46971e19 | 0.0219772 | ||||||||
\(599\) | 1.26446e21 | 1.86725 | 0.933625 | − | 0.358251i | \(-0.116627\pi\) | ||||
0.933625 | + | 0.358251i | \(0.116627\pi\) | |||||||
\(600\) | 5.08490e19 | 0.0741563 | ||||||||
\(601\) | 9.57115e20 | 1.37850 | 0.689248 | − | 0.724526i | \(-0.257941\pi\) | ||||
0.689248 | + | 0.724526i | \(0.257941\pi\) | |||||||
\(602\) | −1.03406e20 | −0.147086 | ||||||||
\(603\) | 3.12418e19 | 0.0438891 | ||||||||
\(604\) | −3.16376e20 | −0.438961 | ||||||||
\(605\) | −3.25650e20 | −0.446258 | ||||||||
\(606\) | 4.38515e20 | 0.593526 | ||||||||
\(607\) | 1.00033e20 | 0.133730 | 0.0668650 | − | 0.997762i | \(-0.478700\pi\) | ||||
0.0668650 | + | 0.997762i | \(0.478700\pi\) | |||||||
\(608\) | 8.31200e19 | 0.109756 | ||||||||
\(609\) | −1.13002e21 | −1.47385 | ||||||||
\(610\) | −1.50270e20 | −0.193597 | ||||||||
\(611\) | 2.57483e19 | 0.0327672 | ||||||||
\(612\) | 1.51413e19 | 0.0190339 | ||||||||
\(613\) | 7.36761e20 | 0.914898 | 0.457449 | − | 0.889236i | \(-0.348763\pi\) | ||||
0.457449 | + | 0.889236i | \(0.348763\pi\) | |||||||
\(614\) | −9.11525e20 | −1.11816 | ||||||||
\(615\) | −3.98477e20 | −0.482881 | ||||||||
\(616\) | −9.88863e18 | −0.0118381 | ||||||||
\(617\) | 1.36626e21 | 1.61582 | 0.807910 | − | 0.589305i | \(-0.200599\pi\) | ||||
0.807910 | + | 0.589305i | \(0.200599\pi\) | |||||||
\(618\) | −5.53694e20 | −0.646928 | ||||||||
\(619\) | 4.69623e20 | 0.542087 | 0.271044 | − | 0.962567i | \(-0.412631\pi\) | ||||
0.271044 | + | 0.962567i | \(0.412631\pi\) | |||||||
\(620\) | −3.65446e20 | −0.416760 | ||||||||
\(621\) | −1.19594e21 | −1.34748 | ||||||||
\(622\) | −1.10431e21 | −1.22931 | ||||||||
\(623\) | 8.60654e20 | 0.946604 | ||||||||
\(624\) | 5.25338e18 | 0.00570893 | ||||||||
\(625\) | 3.72529e19 | 0.0400000 | ||||||||
\(626\) | 1.07626e21 | 1.14185 | ||||||||
\(627\) | −2.87173e19 | −0.0301049 | ||||||||
\(628\) | 1.75112e20 | 0.181392 | ||||||||
\(629\) | 6.72142e19 | 0.0687988 | ||||||||
\(630\) | 2.26036e19 | 0.0228625 | ||||||||
\(631\) | 1.56542e21 | 1.56463 | 0.782315 | − | 0.622882i | \(-0.214039\pi\) | ||||
0.782315 | + | 0.622882i | \(0.214039\pi\) | |||||||
\(632\) | 4.94572e20 | 0.488486 | ||||||||
\(633\) | −1.75476e20 | −0.171273 | ||||||||
\(634\) | −7.25629e20 | −0.699914 | ||||||||
\(635\) | −5.02702e20 | −0.479190 | ||||||||
\(636\) | −9.04713e20 | −0.852281 | ||||||||
\(637\) | −1.11221e19 | −0.0103548 | ||||||||
\(638\) | 6.89519e19 | 0.0634441 | ||||||||
\(639\) | −9.24250e19 | −0.0840491 | ||||||||
\(640\) | 4.39805e19 | 0.0395285 | ||||||||
\(641\) | 1.07910e21 | 0.958578 | 0.479289 | − | 0.877657i | \(-0.340895\pi\) | ||||
0.479289 | + | 0.877657i | \(0.340895\pi\) | |||||||
\(642\) | 6.31383e20 | 0.554345 | ||||||||
\(643\) | 7.31630e20 | 0.634906 | 0.317453 | − | 0.948274i | \(-0.397172\pi\) | ||||
0.317453 | + | 0.948274i | \(0.397172\pi\) | |||||||
\(644\) | 6.02568e20 | 0.516847 | ||||||||
\(645\) | −1.58893e20 | −0.134713 | ||||||||
\(646\) | 1.99767e20 | 0.167409 | ||||||||
\(647\) | −3.86121e20 | −0.319846 | −0.159923 | − | 0.987129i | \(-0.551125\pi\) | ||||
−0.159923 | + | 0.987129i | \(0.551125\pi\) | |||||||
\(648\) | −4.70587e20 | −0.385326 | ||||||||
\(649\) | −2.72438e19 | −0.0220512 | ||||||||
\(650\) | 3.84872e18 | 0.00307940 | ||||||||
\(651\) | −1.78969e21 | −1.41553 | ||||||||
\(652\) | −5.39076e20 | −0.421496 | ||||||||
\(653\) | −8.04784e20 | −0.622057 | −0.311029 | − | 0.950401i | \(-0.600674\pi\) | ||||
−0.311029 | + | 0.950401i | \(0.600674\pi\) | |||||||
\(654\) | 1.08301e21 | 0.827557 | ||||||||
\(655\) | 2.16701e20 | 0.163701 | ||||||||
\(656\) | −3.44652e20 | −0.257396 | ||||||||
\(657\) | 1.39843e20 | 0.103252 | ||||||||
\(658\) | 1.05565e21 | 0.770597 | ||||||||
\(659\) | 1.07785e21 | 0.777889 | 0.388945 | − | 0.921261i | \(-0.372840\pi\) | ||||
0.388945 | + | 0.921261i | \(0.372840\pi\) | |||||||
\(660\) | −1.51949e19 | −0.0108422 | ||||||||
\(661\) | −8.11863e20 | −0.572759 | −0.286379 | − | 0.958116i | \(-0.592452\pi\) | ||||
−0.286379 | + | 0.958116i | \(0.592452\pi\) | |||||||
\(662\) | −8.89107e20 | −0.620182 | ||||||||
\(663\) | 1.26257e19 | 0.00870774 | ||||||||
\(664\) | −8.67183e20 | −0.591357 | ||||||||
\(665\) | 2.98220e20 | 0.201082 | ||||||||
\(666\) | 1.91029e19 | 0.0127363 | ||||||||
\(667\) | −4.20162e21 | −2.76996 | ||||||||
\(668\) | 5.15177e20 | 0.335841 | ||||||||
\(669\) | −1.98655e21 | −1.28057 | ||||||||
\(670\) | 2.18097e20 | 0.139024 | ||||||||
\(671\) | 4.49042e19 | 0.0283053 | ||||||||
\(672\) | 2.15384e20 | 0.134259 | ||||||||
\(673\) | −5.57984e20 | −0.343961 | −0.171980 | − | 0.985100i | \(-0.555017\pi\) | ||||
−0.171980 | + | 0.985100i | \(0.555017\pi\) | |||||||
\(674\) | 1.36215e21 | 0.830378 | ||||||||
\(675\) | −3.13181e20 | −0.188806 | ||||||||
\(676\) | −8.38232e20 | −0.499763 | ||||||||
\(677\) | −1.86877e20 | −0.110190 | −0.0550948 | − | 0.998481i | \(-0.517546\pi\) | ||||
−0.0550948 | + | 0.998481i | \(0.517546\pi\) | |||||||
\(678\) | 3.50486e20 | 0.204385 | ||||||||
\(679\) | 7.43631e20 | 0.428878 | ||||||||
\(680\) | 1.05701e20 | 0.0602921 | ||||||||
\(681\) | −4.63763e20 | −0.261633 | ||||||||
\(682\) | 1.09204e20 | 0.0609335 | ||||||||
\(683\) | −1.32462e21 | −0.731034 | −0.365517 | − | 0.930805i | \(-0.619108\pi\) | ||||
−0.365517 | + | 0.930805i | \(0.619108\pi\) | |||||||
\(684\) | 5.67757e19 | 0.0309914 | ||||||||
\(685\) | 1.11687e21 | 0.603009 | ||||||||
\(686\) | −1.41489e21 | −0.755600 | ||||||||
\(687\) | 2.67052e21 | 1.41065 | ||||||||
\(688\) | −1.37431e20 | −0.0718075 | ||||||||
\(689\) | −6.84771e19 | −0.0353917 | ||||||||
\(690\) | 9.25908e20 | 0.473369 | ||||||||
\(691\) | 1.97901e21 | 1.00084 | 0.500418 | − | 0.865784i | \(-0.333180\pi\) | ||||
0.500418 | + | 0.865784i | \(0.333180\pi\) | |||||||
\(692\) | 1.96390e21 | 0.982482 | ||||||||
\(693\) | −6.75449e18 | −0.00334267 | ||||||||
\(694\) | 1.69487e20 | 0.0829736 | ||||||||
\(695\) | −3.57540e20 | −0.173156 | ||||||||
\(696\) | −1.50184e21 | −0.719539 | ||||||||
\(697\) | −8.28320e20 | −0.392602 | ||||||||
\(698\) | 9.80797e20 | 0.459900 | ||||||||
\(699\) | 1.62152e21 | 0.752216 | ||||||||
\(700\) | 1.57794e20 | 0.0724195 | ||||||||
\(701\) | 2.58448e21 | 1.17351 | 0.586757 | − | 0.809763i | \(-0.300404\pi\) | ||||
0.586757 | + | 0.809763i | \(0.300404\pi\) | |||||||
\(702\) | −3.23558e19 | −0.0145353 | ||||||||
\(703\) | 2.52034e20 | 0.112020 | ||||||||
\(704\) | −1.31424e19 | −0.00577937 | ||||||||
\(705\) | 1.62212e21 | 0.705773 | ||||||||
\(706\) | 3.50985e20 | 0.151096 | ||||||||
\(707\) | 1.36080e21 | 0.579625 | ||||||||
\(708\) | 5.93395e20 | 0.250089 | ||||||||
\(709\) | −2.35138e21 | −0.980562 | −0.490281 | − | 0.871564i | \(-0.663106\pi\) | ||||
−0.490281 | + | 0.871564i | \(0.663106\pi\) | |||||||
\(710\) | −6.45213e20 | −0.266235 | ||||||||
\(711\) | 3.37821e20 | 0.137932 | ||||||||
\(712\) | 1.14385e21 | 0.462134 | ||||||||
\(713\) | −6.65440e21 | −2.66034 | ||||||||
\(714\) | 5.17643e20 | 0.204783 | ||||||||
\(715\) | −1.15009e18 | −0.000450232 0 | ||||||||
\(716\) | 6.86126e20 | 0.265801 | ||||||||
\(717\) | 5.05776e21 | 1.93894 | ||||||||
\(718\) | 3.68581e20 | 0.139830 | ||||||||
\(719\) | 5.01526e21 | 1.88290 | 0.941450 | − | 0.337153i | \(-0.109464\pi\) | ||||
0.941450 | + | 0.337153i | \(0.109464\pi\) | |||||||
\(720\) | 3.00412e19 | 0.0111615 | ||||||||
\(721\) | −1.71822e21 | −0.631776 | ||||||||
\(722\) | −1.19412e21 | −0.434528 | ||||||||
\(723\) | −1.59163e21 | −0.573198 | ||||||||
\(724\) | 2.05116e21 | 0.731071 | ||||||||
\(725\) | −1.10027e21 | −0.388120 | ||||||||
\(726\) | −2.11955e21 | −0.739978 | ||||||||
\(727\) | −2.68041e21 | −0.926175 | −0.463087 | − | 0.886313i | \(-0.653258\pi\) | ||||
−0.463087 | + | 0.886313i | \(0.653258\pi\) | |||||||
\(728\) | 1.63022e19 | 0.00557522 | ||||||||
\(729\) | 2.60343e21 | 0.881231 | ||||||||
\(730\) | 9.76233e20 | 0.327063 | ||||||||
\(731\) | −3.30294e20 | −0.109527 | ||||||||
\(732\) | −9.78057e20 | −0.321019 | ||||||||
\(733\) | −5.84752e21 | −1.89973 | −0.949865 | − | 0.312661i | \(-0.898780\pi\) | ||||
−0.949865 | + | 0.312661i | \(0.898780\pi\) | |||||||
\(734\) | −2.58478e21 | −0.831195 | ||||||||
\(735\) | −7.00684e20 | −0.223032 | ||||||||
\(736\) | 8.00839e20 | 0.252326 | ||||||||
\(737\) | −6.51726e19 | −0.0203263 | ||||||||
\(738\) | −2.35417e20 | −0.0726799 | ||||||||
\(739\) | −2.19735e20 | −0.0671530 | −0.0335765 | − | 0.999436i | \(-0.510690\pi\) | ||||
−0.0335765 | + | 0.999436i | \(0.510690\pi\) | |||||||
\(740\) | 1.33356e20 | 0.0403437 | ||||||||
\(741\) | 4.73429e19 | 0.0141781 | ||||||||
\(742\) | −2.80750e21 | −0.832319 | ||||||||
\(743\) | 1.85608e21 | 0.544730 | 0.272365 | − | 0.962194i | \(-0.412194\pi\) | ||||
0.272365 | + | 0.962194i | \(0.412194\pi\) | |||||||
\(744\) | −2.37857e21 | −0.691065 | ||||||||
\(745\) | 1.03855e21 | 0.298715 | ||||||||
\(746\) | −4.63554e21 | −1.31995 | ||||||||
\(747\) | −5.92335e20 | −0.166979 | ||||||||
\(748\) | −3.15859e19 | −0.00881517 | ||||||||
\(749\) | 1.95930e21 | 0.541361 | ||||||||
\(750\) | 2.42467e20 | 0.0663274 | ||||||||
\(751\) | 4.78115e21 | 1.29489 | 0.647445 | − | 0.762112i | \(-0.275837\pi\) | ||||
0.647445 | + | 0.762112i | \(0.275837\pi\) | |||||||
\(752\) | 1.40301e21 | 0.376207 | ||||||||
\(753\) | −1.46867e21 | −0.389907 | ||||||||
\(754\) | −1.13673e20 | −0.0298795 | ||||||||
\(755\) | −1.50860e21 | −0.392619 | ||||||||
\(756\) | −1.32656e21 | −0.341832 | ||||||||
\(757\) | 2.41955e21 | 0.617326 | 0.308663 | − | 0.951171i | \(-0.400118\pi\) | ||||
0.308663 | + | 0.951171i | \(0.400118\pi\) | |||||||
\(758\) | −2.04708e21 | −0.517149 | ||||||||
\(759\) | −2.76683e20 | −0.0692102 | ||||||||
\(760\) | 3.96347e20 | 0.0981689 | ||||||||
\(761\) | −3.48193e21 | −0.853955 | −0.426978 | − | 0.904262i | \(-0.640422\pi\) | ||||
−0.426978 | + | 0.904262i | \(0.640422\pi\) | |||||||
\(762\) | −3.27193e21 | −0.794586 | ||||||||
\(763\) | 3.36077e21 | 0.808175 | ||||||||
\(764\) | 1.27131e21 | 0.302728 | ||||||||
\(765\) | 7.21995e19 | 0.0170245 | ||||||||
\(766\) | 4.56654e21 | 1.06628 | ||||||||
\(767\) | 4.49137e19 | 0.0103852 | ||||||||
\(768\) | 2.86254e20 | 0.0655455 | ||||||||
\(769\) | −2.58771e21 | −0.586770 | −0.293385 | − | 0.955994i | \(-0.594782\pi\) | ||||
−0.293385 | + | 0.955994i | \(0.594782\pi\) | |||||||
\(770\) | −4.71526e19 | −0.0105883 | ||||||||
\(771\) | −2.26025e20 | −0.0502630 | ||||||||
\(772\) | −3.69997e21 | −0.814834 | ||||||||
\(773\) | 3.07396e21 | 0.670429 | 0.335214 | − | 0.942142i | \(-0.391191\pi\) | ||||
0.335214 | + | 0.942142i | \(0.391191\pi\) | |||||||
\(774\) | −9.38729e19 | −0.0202760 | ||||||||
\(775\) | −1.74258e21 | −0.372762 | ||||||||
\(776\) | 9.88318e20 | 0.209379 | ||||||||
\(777\) | 6.53080e20 | 0.137028 | ||||||||
\(778\) | 5.98431e21 | 1.24356 | ||||||||
\(779\) | −3.10596e21 | −0.639242 | ||||||||
\(780\) | 2.50501e19 | 0.00510622 | ||||||||
\(781\) | 1.92805e20 | 0.0389256 | ||||||||
\(782\) | 1.92470e21 | 0.384868 | ||||||||
\(783\) | 9.24988e21 | 1.83199 | ||||||||
\(784\) | −6.06037e20 | −0.118885 | ||||||||
\(785\) | 8.34999e20 | 0.162242 | ||||||||
\(786\) | 1.41044e21 | 0.271447 | ||||||||
\(787\) | −5.67154e21 | −1.08116 | −0.540581 | − | 0.841292i | \(-0.681795\pi\) | ||||
−0.540581 | + | 0.841292i | \(0.681795\pi\) | |||||||
\(788\) | 8.79784e20 | 0.166123 | ||||||||
\(789\) | 1.71298e20 | 0.0320388 | ||||||||
\(790\) | 2.35831e21 | 0.436915 | ||||||||
\(791\) | 1.08763e21 | 0.199598 | ||||||||
\(792\) | −8.97702e18 | −0.00163190 | ||||||||
\(793\) | −7.40284e19 | −0.0133306 | ||||||||
\(794\) | 2.06792e20 | 0.0368875 | ||||||||
\(795\) | −4.31401e21 | −0.762303 | ||||||||
\(796\) | 2.31588e21 | 0.405386 | ||||||||
\(797\) | 6.99506e21 | 1.21298 | 0.606491 | − | 0.795091i | \(-0.292577\pi\) | ||||
0.606491 | + | 0.795091i | \(0.292577\pi\) | |||||||
\(798\) | 1.94102e21 | 0.333432 | ||||||||
\(799\) | 3.37193e21 | 0.573823 | ||||||||
\(800\) | 2.09715e20 | 0.0353553 | ||||||||
\(801\) | 7.81313e20 | 0.130491 | ||||||||
\(802\) | 4.13001e21 | 0.683350 | ||||||||
\(803\) | −2.91722e20 | −0.0478192 | ||||||||
\(804\) | 1.41952e21 | 0.230527 | ||||||||
\(805\) | 2.87327e21 | 0.462282 | ||||||||
\(806\) | −1.80032e20 | −0.0286971 | ||||||||
\(807\) | −1.02365e22 | −1.61659 | ||||||||
\(808\) | 1.80856e21 | 0.282974 | ||||||||
\(809\) | −1.02572e22 | −1.59007 | −0.795036 | − | 0.606562i | \(-0.792548\pi\) | ||||
−0.795036 | + | 0.606562i | \(0.792548\pi\) | |||||||
\(810\) | −2.24394e21 | −0.344646 | ||||||||
\(811\) | 5.19989e20 | 0.0791294 | 0.0395647 | − | 0.999217i | \(-0.487403\pi\) | ||||
0.0395647 | + | 0.999217i | \(0.487403\pi\) | |||||||
\(812\) | −4.66049e21 | −0.702686 | ||||||||
\(813\) | 7.19601e21 | 1.07501 | ||||||||
\(814\) | −3.98500e19 | −0.00589856 | ||||||||
\(815\) | −2.57051e21 | −0.376997 | ||||||||
\(816\) | 6.87971e20 | 0.0999755 | ||||||||
\(817\) | −1.23851e21 | −0.178334 | ||||||||
\(818\) | −2.67668e21 | −0.381897 | ||||||||
\(819\) | 1.11354e19 | 0.00157425 | ||||||||
\(820\) | −1.64343e21 | −0.230222 | ||||||||
\(821\) | −1.18946e22 | −1.65111 | −0.825557 | − | 0.564319i | \(-0.809139\pi\) | ||||
−0.825557 | + | 0.564319i | \(0.809139\pi\) | |||||||
\(822\) | 7.26935e21 | 0.999901 | ||||||||
\(823\) | −4.67215e21 | −0.636822 | −0.318411 | − | 0.947953i | \(-0.603149\pi\) | ||||
−0.318411 | + | 0.947953i | \(0.603149\pi\) | |||||||
\(824\) | −2.28358e21 | −0.308435 | ||||||||
\(825\) | −7.24549e19 | −0.00969758 | ||||||||
\(826\) | 1.84142e21 | 0.244232 | ||||||||
\(827\) | −6.43261e19 | −0.00845465 | −0.00422733 | − | 0.999991i | \(-0.501346\pi\) | ||||
−0.00422733 | + | 0.999991i | \(0.501346\pi\) | |||||||
\(828\) | 5.47019e20 | 0.0712483 | ||||||||
\(829\) | −1.59621e21 | −0.206030 | −0.103015 | − | 0.994680i | \(-0.532849\pi\) | ||||
−0.103015 | + | 0.994680i | \(0.532849\pi\) | |||||||
\(830\) | −4.13505e21 | −0.528926 | ||||||||
\(831\) | −5.40551e21 | −0.685219 | ||||||||
\(832\) | 2.16664e19 | 0.00272183 | ||||||||
\(833\) | −1.45652e21 | −0.181334 | ||||||||
\(834\) | −2.32711e21 | −0.287125 | ||||||||
\(835\) | 2.45656e21 | 0.300385 | ||||||||
\(836\) | −1.18438e20 | −0.0143530 | ||||||||
\(837\) | 1.46497e22 | 1.75949 | ||||||||
\(838\) | −5.52415e21 | −0.657560 | ||||||||
\(839\) | −1.03172e22 | −1.21715 | −0.608577 | − | 0.793495i | \(-0.708259\pi\) | ||||
−0.608577 | + | 0.793495i | \(0.708259\pi\) | |||||||
\(840\) | 1.02703e21 | 0.120085 | ||||||||
\(841\) | 2.38677e22 | 2.76593 | ||||||||
\(842\) | 4.40514e21 | 0.505964 | ||||||||
\(843\) | 8.45799e20 | 0.0962853 | ||||||||
\(844\) | −7.23711e20 | −0.0816577 | ||||||||
\(845\) | −3.99700e21 | −0.447002 | ||||||||
\(846\) | 9.58336e20 | 0.106228 | ||||||||
\(847\) | −6.57736e21 | −0.722647 | ||||||||
\(848\) | −3.73129e21 | −0.406340 | ||||||||
\(849\) | 4.91798e21 | 0.530859 | ||||||||
\(850\) | 5.04020e20 | 0.0539269 | ||||||||
\(851\) | 2.42828e21 | 0.257530 | ||||||||
\(852\) | −4.19948e21 | −0.441467 | ||||||||
\(853\) | −2.65492e21 | −0.276652 | −0.138326 | − | 0.990387i | \(-0.544172\pi\) | ||||
−0.138326 | + | 0.990387i | \(0.544172\pi\) | |||||||
\(854\) | −3.03510e21 | −0.313501 | ||||||||
\(855\) | 2.70728e20 | 0.0277196 | ||||||||
\(856\) | 2.60399e21 | 0.264294 | ||||||||
\(857\) | 9.17781e21 | 0.923385 | 0.461693 | − | 0.887040i | \(-0.347242\pi\) | ||||
0.461693 | + | 0.887040i | \(0.347242\pi\) | |||||||
\(858\) | −7.48557e18 | −0.000746569 0 | ||||||||
\(859\) | −1.85419e22 | −1.83318 | −0.916592 | − | 0.399824i | \(-0.869071\pi\) | ||||
−0.916592 | + | 0.399824i | \(0.869071\pi\) | |||||||
\(860\) | −6.55320e20 | −0.0642266 | ||||||||
\(861\) | −8.04829e21 | −0.781952 | ||||||||
\(862\) | 1.01777e22 | 0.980270 | ||||||||
\(863\) | 3.65598e21 | 0.349078 | 0.174539 | − | 0.984650i | \(-0.444156\pi\) | ||||
0.174539 | + | 0.984650i | \(0.444156\pi\) | |||||||
\(864\) | −1.76305e21 | −0.166883 | ||||||||
\(865\) | 9.36462e21 | 0.878758 | ||||||||
\(866\) | −8.94957e21 | −0.832565 | ||||||||
\(867\) | −9.71776e21 | −0.896238 | ||||||||
\(868\) | −7.38116e21 | −0.674880 | ||||||||
\(869\) | −7.04718e20 | −0.0638803 | ||||||||
\(870\) | −7.16133e21 | −0.643575 | ||||||||
\(871\) | 1.07443e20 | 0.00957282 | ||||||||
\(872\) | 4.46662e21 | 0.394553 | ||||||||
\(873\) | 6.75077e20 | 0.0591217 | ||||||||
\(874\) | 7.21707e21 | 0.626651 | ||||||||
\(875\) | 7.52421e20 | 0.0647740 | ||||||||
\(876\) | 6.35398e21 | 0.542332 | ||||||||
\(877\) | −1.66541e21 | −0.140937 | −0.0704683 | − | 0.997514i | \(-0.522449\pi\) | ||||
−0.0704683 | + | 0.997514i | \(0.522449\pi\) | |||||||
\(878\) | −6.88302e21 | −0.577525 | ||||||||
\(879\) | 1.54506e22 | 1.28537 | ||||||||
\(880\) | −6.26679e19 | −0.00516922 | ||||||||
\(881\) | 4.64406e21 | 0.379821 | 0.189910 | − | 0.981801i | \(-0.439180\pi\) | ||||
0.189910 | + | 0.981801i | \(0.439180\pi\) | |||||||
\(882\) | −4.13958e20 | −0.0335693 | ||||||||
\(883\) | 1.60318e22 | 1.28907 | 0.644536 | − | 0.764574i | \(-0.277051\pi\) | ||||
0.644536 | + | 0.764574i | \(0.277051\pi\) | |||||||
\(884\) | 5.20720e19 | 0.00415157 | ||||||||
\(885\) | 2.82953e21 | 0.223686 | ||||||||
\(886\) | 1.87017e21 | 0.146598 | ||||||||
\(887\) | −1.91774e21 | −0.149061 | −0.0745304 | − | 0.997219i | \(-0.523746\pi\) | ||||
−0.0745304 | + | 0.997219i | \(0.523746\pi\) | |||||||
\(888\) | 8.67972e20 | 0.0668973 | ||||||||
\(889\) | −1.01534e22 | −0.775976 | ||||||||
\(890\) | 5.45429e21 | 0.413345 | ||||||||
\(891\) | 6.70542e20 | 0.0503898 | ||||||||
\(892\) | −8.19308e21 | −0.610535 | ||||||||
\(893\) | 1.26438e22 | 0.934310 | ||||||||
\(894\) | 6.75961e21 | 0.495325 | ||||||||
\(895\) | 3.27170e21 | 0.237739 | ||||||||
\(896\) | 8.88302e20 | 0.0640104 | ||||||||
\(897\) | 4.56136e20 | 0.0325950 | ||||||||
\(898\) | −9.00247e21 | −0.637954 | ||||||||
\(899\) | 5.14677e22 | 3.61691 | ||||||||
\(900\) | 1.43247e20 | 0.00998316 | ||||||||
\(901\) | −8.96760e21 | −0.619784 | ||||||||
\(902\) | 4.91095e20 | 0.0336602 | ||||||||
\(903\) | −3.20927e21 | −0.218147 | ||||||||
\(904\) | 1.44550e21 | 0.0974440 | ||||||||
\(905\) | 9.78068e21 | 0.653890 | ||||||||
\(906\) | −9.81896e21 | −0.651035 | ||||||||
\(907\) | −1.43639e22 | −0.944532 | −0.472266 | − | 0.881456i | \(-0.656564\pi\) | ||||
−0.472266 | + | 0.881456i | \(0.656564\pi\) | |||||||
\(908\) | −1.91269e21 | −0.124738 | ||||||||
\(909\) | 1.23535e21 | 0.0799024 | ||||||||
\(910\) | 7.77352e19 | 0.00498663 | ||||||||
\(911\) | −1.53974e22 | −0.979626 | −0.489813 | − | 0.871828i | \(-0.662935\pi\) | ||||
−0.489813 | + | 0.871828i | \(0.662935\pi\) | |||||||
\(912\) | 2.57969e21 | 0.162782 | ||||||||
\(913\) | 1.23565e21 | 0.0773330 | ||||||||
\(914\) | 5.57874e21 | 0.346290 | ||||||||
\(915\) | −4.66374e21 | −0.287128 | ||||||||
\(916\) | 1.10140e22 | 0.672555 | ||||||||
\(917\) | 4.37685e21 | 0.265089 | ||||||||
\(918\) | −4.23724e21 | −0.254544 | ||||||||
\(919\) | −9.59237e21 | −0.571557 | −0.285779 | − | 0.958296i | \(-0.592252\pi\) | ||||
−0.285779 | + | 0.958296i | \(0.592252\pi\) | |||||||
\(920\) | 3.81870e21 | 0.225687 | ||||||||
\(921\) | −2.82899e22 | −1.65838 | ||||||||
\(922\) | −1.58899e22 | −0.923930 | ||||||||
\(923\) | −3.17855e20 | −0.0183323 | ||||||||
\(924\) | −3.06901e20 | −0.0175573 | ||||||||
\(925\) | 6.35892e20 | 0.0360845 | ||||||||
\(926\) | 8.42938e21 | 0.474475 | ||||||||
\(927\) | −1.55982e21 | −0.0870915 | ||||||||
\(928\) | −6.19400e21 | −0.343053 | ||||||||
\(929\) | −2.12844e22 | −1.16935 | −0.584673 | − | 0.811269i | \(-0.698777\pi\) | ||||
−0.584673 | + | 0.811269i | \(0.698777\pi\) | |||||||
\(930\) | −1.13419e22 | −0.618108 | ||||||||
\(931\) | −5.46154e21 | −0.295252 | ||||||||
\(932\) | 6.68758e21 | 0.358632 | ||||||||
\(933\) | −3.42730e22 | −1.82322 | ||||||||
\(934\) | 1.63979e21 | 0.0865337 | ||||||||
\(935\) | −1.50613e20 | −0.00788453 | ||||||||
\(936\) | 1.47994e19 | 0.000768554 0 | ||||||||
\(937\) | −3.01568e22 | −1.55360 | −0.776799 | − | 0.629748i | \(-0.783158\pi\) | ||||
−0.776799 | + | 0.629748i | \(0.783158\pi\) | |||||||
\(938\) | 4.40504e21 | 0.225128 | ||||||||
\(939\) | 3.34026e22 | 1.69351 | ||||||||
\(940\) | 6.69007e21 | 0.336490 | ||||||||
\(941\) | −1.85558e22 | −0.925885 | −0.462943 | − | 0.886388i | \(-0.653206\pi\) | ||||
−0.462943 | + | 0.886388i | \(0.653206\pi\) | |||||||
\(942\) | 5.43473e21 | 0.269027 | ||||||||
\(943\) | −2.99251e22 | −1.46960 | ||||||||
\(944\) | 2.44732e21 | 0.119234 | ||||||||
\(945\) | −6.32551e21 | −0.305744 | ||||||||
\(946\) | 1.95825e20 | 0.00939042 | ||||||||
\(947\) | 1.73295e22 | 0.824444 | 0.412222 | − | 0.911083i | \(-0.364753\pi\) | ||||
0.412222 | + | 0.911083i | \(0.364753\pi\) | |||||||
\(948\) | 1.53494e22 | 0.724486 | ||||||||
\(949\) | 4.80928e20 | 0.0225208 | ||||||||
\(950\) | 1.88993e21 | 0.0878049 | ||||||||
\(951\) | −2.25204e22 | −1.03806 | ||||||||
\(952\) | 2.13490e21 | 0.0976340 | ||||||||
\(953\) | 2.51658e22 | 1.14186 | 0.570931 | − | 0.820998i | \(-0.306583\pi\) | ||||
0.570931 | + | 0.820998i | \(0.306583\pi\) | |||||||
\(954\) | −2.54868e21 | −0.114737 | ||||||||
\(955\) | 6.06209e21 | 0.270768 | ||||||||
\(956\) | 2.08596e22 | 0.924424 | ||||||||
\(957\) | 2.13998e21 | 0.0940956 | ||||||||
\(958\) | 3.70037e21 | 0.161437 | ||||||||
\(959\) | 2.25582e22 | 0.976482 | ||||||||
\(960\) | 1.36497e21 | 0.0586257 | ||||||||
\(961\) | 5.80479e22 | 2.47378 | ||||||||
\(962\) | 6.56962e19 | 0.00277797 | ||||||||
\(963\) | 1.77868e21 | 0.0746277 | ||||||||
\(964\) | −6.56432e21 | −0.273282 | ||||||||
\(965\) | −1.76429e22 | −0.728809 | ||||||||
\(966\) | 1.87012e22 | 0.766549 | ||||||||
\(967\) | −9.74068e21 | −0.396178 | −0.198089 | − | 0.980184i | \(-0.563474\pi\) | ||||
−0.198089 | + | 0.980184i | \(0.563474\pi\) | |||||||
\(968\) | −8.74160e21 | −0.352798 | ||||||||
\(969\) | 6.19992e21 | 0.248289 | ||||||||
\(970\) | 4.71267e21 | 0.187275 | ||||||||
\(971\) | −1.21314e22 | −0.478373 | −0.239187 | − | 0.970974i | \(-0.576881\pi\) | ||||
−0.239187 | + | 0.970974i | \(0.576881\pi\) | |||||||
\(972\) | −2.54209e21 | −0.0994702 | ||||||||
\(973\) | −7.22146e21 | −0.280401 | ||||||||
\(974\) | 2.51388e22 | 0.968618 | ||||||||
\(975\) | 1.19448e20 | 0.00456714 | ||||||||
\(976\) | −4.03377e21 | −0.153052 | ||||||||
\(977\) | 1.82562e22 | 0.687388 | 0.343694 | − | 0.939082i | \(-0.388322\pi\) | ||||
0.343694 | + | 0.939082i | \(0.388322\pi\) | |||||||
\(978\) | −1.67306e22 | −0.625131 | ||||||||
\(979\) | −1.62987e21 | −0.0604343 | ||||||||
\(980\) | −2.88981e21 | −0.106334 | ||||||||
\(981\) | 3.05095e21 | 0.111408 | ||||||||
\(982\) | −1.77120e22 | −0.641846 | ||||||||
\(983\) | 4.33715e21 | 0.155974 | 0.0779872 | − | 0.996954i | \(-0.475151\pi\) | ||||
0.0779872 | + | 0.996954i | \(0.475151\pi\) | |||||||
\(984\) | −1.06965e22 | −0.381751 | ||||||||
\(985\) | 4.19513e21 | 0.148585 | ||||||||
\(986\) | −1.48864e22 | −0.523253 | ||||||||
\(987\) | 3.27630e22 | 1.14289 | ||||||||
\(988\) | 1.95255e20 | 0.00675967 | ||||||||
\(989\) | −1.19327e22 | −0.409984 | ||||||||
\(990\) | −4.28057e19 | −0.00145961 | ||||||||
\(991\) | 5.10575e22 | 1.72786 | 0.863928 | − | 0.503615i | \(-0.167997\pi\) | ||||
0.863928 | + | 0.503615i | \(0.167997\pi\) | |||||||
\(992\) | −9.80988e21 | −0.329478 | ||||||||
\(993\) | −2.75941e22 | −0.919808 | ||||||||
\(994\) | −1.30318e22 | −0.431127 | ||||||||
\(995\) | 1.10430e22 | 0.362588 | ||||||||
\(996\) | −2.69137e22 | −0.877057 | ||||||||
\(997\) | 3.95869e22 | 1.28038 | 0.640188 | − | 0.768219i | \(-0.278857\pi\) | ||||
0.640188 | + | 0.768219i | \(0.278857\pi\) | |||||||
\(998\) | 2.50299e22 | 0.803488 | ||||||||
\(999\) | −5.34587e21 | −0.170325 |
(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 | 10.16.a.d.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 90.16.a.j.1.2 | 2 | |||
4.3 | odd | 2 | 80.16.a.f.1.1 | 2 | |||
5.2 | odd | 4 | 50.16.b.e.49.3 | 4 | |||
5.3 | odd | 4 | 50.16.b.e.49.2 | 4 | |||
5.4 | even | 2 | 50.16.a.f.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.16.a.d.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.16.a.f.1.1 | 2 | 5.4 | even | 2 | |||
50.16.b.e.49.2 | 4 | 5.3 | odd | 4 | |||
50.16.b.e.49.3 | 4 | 5.2 | odd | 4 | |||
80.16.a.f.1.1 | 2 | 4.3 | odd | 2 | |||
90.16.a.j.1.2 | 2 | 3.2 | odd | 2 |