Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,14,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(2.14461857904\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −64.0000 | −0.707107 | ||||||||
\(3\) | −1836.00 | −1.45407 | −0.727034 | − | 0.686602i | \(-0.759102\pi\) | ||||
−0.727034 | + | 0.686602i | \(0.759102\pi\) | |||||||
\(4\) | 4096.00 | 0.500000 | ||||||||
\(5\) | 3990.00 | 0.114200 | 0.0571002 | − | 0.998368i | \(-0.481815\pi\) | ||||
0.0571002 | + | 0.998368i | \(0.481815\pi\) | |||||||
\(6\) | 117504. | 1.02818 | ||||||||
\(7\) | −433432. | −1.39246 | −0.696232 | − | 0.717817i | \(-0.745141\pi\) | ||||
−0.696232 | + | 0.717817i | \(0.745141\pi\) | |||||||
\(8\) | −262144. | −0.353553 | ||||||||
\(9\) | 1.77657e6 | 1.11431 | ||||||||
\(10\) | −255360. | −0.0807519 | ||||||||
\(11\) | 1.61977e6 | 0.275678 | 0.137839 | − | 0.990455i | \(-0.455984\pi\) | ||||
0.137839 | + | 0.990455i | \(0.455984\pi\) | |||||||
\(12\) | −7.52026e6 | −0.727034 | ||||||||
\(13\) | −1.08785e7 | −0.625080 | −0.312540 | − | 0.949905i | \(-0.601180\pi\) | ||||
−0.312540 | + | 0.949905i | \(0.601180\pi\) | |||||||
\(14\) | 2.77396e7 | 0.984620 | ||||||||
\(15\) | −7.32564e6 | −0.166055 | ||||||||
\(16\) | 1.67772e7 | 0.250000 | ||||||||
\(17\) | 6.05693e7 | 0.608604 | 0.304302 | − | 0.952576i | \(-0.401577\pi\) | ||||
0.304302 | + | 0.952576i | \(0.401577\pi\) | |||||||
\(18\) | −1.13701e8 | −0.787937 | ||||||||
\(19\) | −2.43132e8 | −1.18561 | −0.592807 | − | 0.805345i | \(-0.701980\pi\) | ||||
−0.592807 | + | 0.805345i | \(0.701980\pi\) | |||||||
\(20\) | 1.63430e7 | 0.0571002 | ||||||||
\(21\) | 7.95781e8 | 2.02474 | ||||||||
\(22\) | −1.03665e8 | −0.194933 | ||||||||
\(23\) | −6.06096e8 | −0.853711 | −0.426855 | − | 0.904320i | \(-0.640379\pi\) | ||||
−0.426855 | + | 0.904320i | \(0.640379\pi\) | |||||||
\(24\) | 4.81296e8 | 0.514090 | ||||||||
\(25\) | −1.20478e9 | −0.986958 | ||||||||
\(26\) | 6.96222e8 | 0.441999 | ||||||||
\(27\) | −3.34611e8 | −0.166217 | ||||||||
\(28\) | −1.77534e9 | −0.696232 | ||||||||
\(29\) | 5.25864e9 | 1.64167 | 0.820836 | − | 0.571164i | \(-0.193508\pi\) | ||||
0.820836 | + | 0.571164i | \(0.193508\pi\) | |||||||
\(30\) | 4.68841e8 | 0.117419 | ||||||||
\(31\) | −1.82431e9 | −0.369189 | −0.184594 | − | 0.982815i | \(-0.559097\pi\) | ||||
−0.184594 | + | 0.982815i | \(0.559097\pi\) | |||||||
\(32\) | −1.07374e9 | −0.176777 | ||||||||
\(33\) | −2.97390e9 | −0.400854 | ||||||||
\(34\) | −3.87644e9 | −0.430348 | ||||||||
\(35\) | −1.72939e9 | −0.159020 | ||||||||
\(36\) | 7.27684e9 | 0.557156 | ||||||||
\(37\) | −3.00588e9 | −0.192602 | −0.0963008 | − | 0.995352i | \(-0.530701\pi\) | ||||
−0.0963008 | + | 0.995352i | \(0.530701\pi\) | |||||||
\(38\) | 1.55604e10 | 0.838356 | ||||||||
\(39\) | 1.99729e10 | 0.908909 | ||||||||
\(40\) | −1.04595e9 | −0.0403760 | ||||||||
\(41\) | −4.97049e10 | −1.63420 | −0.817098 | − | 0.576499i | \(-0.804418\pi\) | ||||
−0.817098 | + | 0.576499i | \(0.804418\pi\) | |||||||
\(42\) | −5.09300e10 | −1.43170 | ||||||||
\(43\) | 5.87667e10 | 1.41771 | 0.708853 | − | 0.705356i | \(-0.249213\pi\) | ||||
0.708853 | + | 0.705356i | \(0.249213\pi\) | |||||||
\(44\) | 6.63459e9 | 0.137839 | ||||||||
\(45\) | 7.08853e9 | 0.127255 | ||||||||
\(46\) | 3.87902e10 | 0.603665 | ||||||||
\(47\) | −4.20959e10 | −0.569644 | −0.284822 | − | 0.958580i | \(-0.591934\pi\) | ||||
−0.284822 | + | 0.958580i | \(0.591934\pi\) | |||||||
\(48\) | −3.08030e10 | −0.363517 | ||||||||
\(49\) | 9.09743e10 | 0.938954 | ||||||||
\(50\) | 7.71061e10 | 0.697885 | ||||||||
\(51\) | −1.11205e11 | −0.884951 | ||||||||
\(52\) | −4.45582e10 | −0.312540 | ||||||||
\(53\) | −1.81141e11 | −1.12259 | −0.561297 | − | 0.827614i | \(-0.689698\pi\) | ||||
−0.561297 | + | 0.827614i | \(0.689698\pi\) | |||||||
\(54\) | 2.14151e10 | 0.117533 | ||||||||
\(55\) | 6.46289e9 | 0.0314825 | ||||||||
\(56\) | 1.13622e11 | 0.492310 | ||||||||
\(57\) | 4.46390e11 | 1.72396 | ||||||||
\(58\) | −3.36553e11 | −1.16084 | ||||||||
\(59\) | 2.06731e11 | 0.638068 | 0.319034 | − | 0.947743i | \(-0.396642\pi\) | ||||
0.319034 | + | 0.947743i | \(0.396642\pi\) | |||||||
\(60\) | −3.00058e10 | −0.0830276 | ||||||||
\(61\) | −1.24479e11 | −0.309351 | −0.154676 | − | 0.987965i | \(-0.549433\pi\) | ||||
−0.154676 | + | 0.987965i | \(0.549433\pi\) | |||||||
\(62\) | 1.16756e11 | 0.261056 | ||||||||
\(63\) | −7.70024e11 | −1.55164 | ||||||||
\(64\) | 6.87195e10 | 0.125000 | ||||||||
\(65\) | −4.34051e10 | −0.0713845 | ||||||||
\(66\) | 1.90330e11 | 0.283446 | ||||||||
\(67\) | 9.56651e10 | 0.129201 | 0.0646007 | − | 0.997911i | \(-0.479423\pi\) | ||||
0.0646007 | + | 0.997911i | \(0.479423\pi\) | |||||||
\(68\) | 2.48092e11 | 0.304302 | ||||||||
\(69\) | 1.11279e12 | 1.24135 | ||||||||
\(70\) | 1.10681e11 | 0.112444 | ||||||||
\(71\) | −3.71436e11 | −0.344116 | −0.172058 | − | 0.985087i | \(-0.555042\pi\) | ||||
−0.172058 | + | 0.985087i | \(0.555042\pi\) | |||||||
\(72\) | −4.65718e11 | −0.393969 | ||||||||
\(73\) | −1.80058e12 | −1.39256 | −0.696278 | − | 0.717772i | \(-0.745162\pi\) | ||||
−0.696278 | + | 0.717772i | \(0.745162\pi\) | |||||||
\(74\) | 1.92376e11 | 0.136190 | ||||||||
\(75\) | 2.21198e12 | 1.43510 | ||||||||
\(76\) | −9.95868e11 | −0.592807 | ||||||||
\(77\) | −7.02061e11 | −0.383871 | ||||||||
\(78\) | −1.27826e12 | −0.642696 | ||||||||
\(79\) | 1.55793e12 | 0.721062 | 0.360531 | − | 0.932747i | \(-0.382596\pi\) | ||||
0.360531 | + | 0.932747i | \(0.382596\pi\) | |||||||
\(80\) | 6.69411e10 | 0.0285501 | ||||||||
\(81\) | −2.21809e12 | −0.872621 | ||||||||
\(82\) | 3.18111e12 | 1.15555 | ||||||||
\(83\) | 2.49279e12 | 0.836909 | 0.418455 | − | 0.908238i | \(-0.362572\pi\) | ||||
0.418455 | + | 0.908238i | \(0.362572\pi\) | |||||||
\(84\) | 3.25952e12 | 1.01237 | ||||||||
\(85\) | 2.41671e11 | 0.0695028 | ||||||||
\(86\) | −3.76107e12 | −1.00247 | ||||||||
\(87\) | −9.65486e12 | −2.38710 | ||||||||
\(88\) | −4.24614e11 | −0.0974667 | ||||||||
\(89\) | 2.99424e12 | 0.638632 | 0.319316 | − | 0.947648i | \(-0.396547\pi\) | ||||
0.319316 | + | 0.947648i | \(0.396547\pi\) | |||||||
\(90\) | −4.53666e11 | −0.0899828 | ||||||||
\(91\) | 4.71508e12 | 0.870401 | ||||||||
\(92\) | −2.48257e12 | −0.426855 | ||||||||
\(93\) | 3.34944e12 | 0.536825 | ||||||||
\(94\) | 2.69414e12 | 0.402799 | ||||||||
\(95\) | −9.70096e11 | −0.135398 | ||||||||
\(96\) | 1.97139e12 | 0.257045 | ||||||||
\(97\) | 4.38249e12 | 0.534201 | 0.267101 | − | 0.963669i | \(-0.413934\pi\) | ||||
0.267101 | + | 0.963669i | \(0.413934\pi\) | |||||||
\(98\) | −5.82235e12 | −0.663940 | ||||||||
\(99\) | 2.87764e12 | 0.307191 | ||||||||
\(100\) | −4.93479e12 | −0.493479 | ||||||||
\(101\) | −5.66110e12 | −0.530655 | −0.265327 | − | 0.964158i | \(-0.585480\pi\) | ||||
−0.265327 | + | 0.964158i | \(0.585480\pi\) | |||||||
\(102\) | 7.11713e12 | 0.625755 | ||||||||
\(103\) | −2.16104e13 | −1.78329 | −0.891644 | − | 0.452737i | \(-0.850448\pi\) | ||||
−0.891644 | + | 0.452737i | \(0.850448\pi\) | |||||||
\(104\) | 2.85172e12 | 0.220999 | ||||||||
\(105\) | 3.17517e12 | 0.231226 | ||||||||
\(106\) | 1.15930e13 | 0.793794 | ||||||||
\(107\) | 1.09348e13 | 0.704397 | 0.352198 | − | 0.935925i | \(-0.385434\pi\) | ||||
0.352198 | + | 0.935925i | \(0.385434\pi\) | |||||||
\(108\) | −1.37057e12 | −0.0831086 | ||||||||
\(109\) | −4.20682e12 | −0.240260 | −0.120130 | − | 0.992758i | \(-0.538331\pi\) | ||||
−0.120130 | + | 0.992758i | \(0.538331\pi\) | |||||||
\(110\) | −4.13625e11 | −0.0222615 | ||||||||
\(111\) | 5.51879e12 | 0.280056 | ||||||||
\(112\) | −7.27178e12 | −0.348116 | ||||||||
\(113\) | 2.87650e13 | 1.29974 | 0.649868 | − | 0.760047i | \(-0.274824\pi\) | ||||
0.649868 | + | 0.760047i | \(0.274824\pi\) | |||||||
\(114\) | −2.85690e13 | −1.21903 | ||||||||
\(115\) | −2.41832e12 | −0.0974942 | ||||||||
\(116\) | 2.15394e13 | 0.820836 | ||||||||
\(117\) | −1.93264e13 | −0.696534 | ||||||||
\(118\) | −1.32308e13 | −0.451182 | ||||||||
\(119\) | −2.62527e13 | −0.847458 | ||||||||
\(120\) | 1.92037e12 | 0.0587094 | ||||||||
\(121\) | −3.18991e13 | −0.924002 | ||||||||
\(122\) | 7.96666e12 | 0.218745 | ||||||||
\(123\) | 9.12582e13 | 2.37623 | ||||||||
\(124\) | −7.47239e12 | −0.184594 | ||||||||
\(125\) | −9.67769e12 | −0.226912 | ||||||||
\(126\) | 4.92815e13 | 1.09717 | ||||||||
\(127\) | 4.78013e13 | 1.01092 | 0.505458 | − | 0.862851i | \(-0.331323\pi\) | ||||
0.505458 | + | 0.862851i | \(0.331323\pi\) | |||||||
\(128\) | −4.39805e12 | −0.0883883 | ||||||||
\(129\) | −1.07896e14 | −2.06144 | ||||||||
\(130\) | 2.77793e12 | 0.0504764 | ||||||||
\(131\) | −1.03694e14 | −1.79262 | −0.896312 | − | 0.443425i | \(-0.853763\pi\) | ||||
−0.896312 | + | 0.443425i | \(0.853763\pi\) | |||||||
\(132\) | −1.21811e13 | −0.200427 | ||||||||
\(133\) | 1.05381e14 | 1.65092 | ||||||||
\(134\) | −6.12257e12 | −0.0913592 | ||||||||
\(135\) | −1.33510e12 | −0.0189821 | ||||||||
\(136\) | −1.58779e13 | −0.215174 | ||||||||
\(137\) | 5.05383e13 | 0.653035 | 0.326518 | − | 0.945191i | \(-0.394125\pi\) | ||||
0.326518 | + | 0.945191i | \(0.394125\pi\) | |||||||
\(138\) | −7.12188e13 | −0.877769 | ||||||||
\(139\) | 2.14878e13 | 0.252694 | 0.126347 | − | 0.991986i | \(-0.459675\pi\) | ||||
0.126347 | + | 0.991986i | \(0.459675\pi\) | |||||||
\(140\) | −7.08360e12 | −0.0795100 | ||||||||
\(141\) | 7.72880e13 | 0.828301 | ||||||||
\(142\) | 2.37719e13 | 0.243327 | ||||||||
\(143\) | −1.76206e13 | −0.172321 | ||||||||
\(144\) | 2.98059e13 | 0.278578 | ||||||||
\(145\) | 2.09820e13 | 0.187480 | ||||||||
\(146\) | 1.15237e14 | 0.984686 | ||||||||
\(147\) | −1.67029e14 | −1.36530 | ||||||||
\(148\) | −1.23121e13 | −0.0963008 | ||||||||
\(149\) | −8.79741e13 | −0.658634 | −0.329317 | − | 0.944219i | \(-0.606818\pi\) | ||||
−0.329317 | + | 0.944219i | \(0.606818\pi\) | |||||||
\(150\) | −1.41567e14 | −1.01477 | ||||||||
\(151\) | −2.07435e13 | −0.142407 | −0.0712037 | − | 0.997462i | \(-0.522684\pi\) | ||||
−0.0712037 | + | 0.997462i | \(0.522684\pi\) | |||||||
\(152\) | 6.37355e13 | 0.419178 | ||||||||
\(153\) | 1.07606e14 | 0.678174 | ||||||||
\(154\) | 4.49319e13 | 0.271438 | ||||||||
\(155\) | −7.27901e12 | −0.0421615 | ||||||||
\(156\) | 8.18088e13 | 0.454454 | ||||||||
\(157\) | −2.27523e14 | −1.21249 | −0.606243 | − | 0.795279i | \(-0.707324\pi\) | ||||
−0.606243 | + | 0.795279i | \(0.707324\pi\) | |||||||
\(158\) | −9.97077e13 | −0.509868 | ||||||||
\(159\) | 3.32574e14 | 1.63233 | ||||||||
\(160\) | −4.28423e12 | −0.0201880 | ||||||||
\(161\) | 2.62702e14 | 1.18876 | ||||||||
\(162\) | 1.41957e14 | 0.617036 | ||||||||
\(163\) | −1.41533e14 | −0.591070 | −0.295535 | − | 0.955332i | \(-0.595498\pi\) | ||||
−0.295535 | + | 0.955332i | \(0.595498\pi\) | |||||||
\(164\) | −2.03591e14 | −0.817098 | ||||||||
\(165\) | −1.18659e13 | −0.0457777 | ||||||||
\(166\) | −1.59539e14 | −0.591784 | ||||||||
\(167\) | 5.58000e13 | 0.199057 | 0.0995284 | − | 0.995035i | \(-0.468267\pi\) | ||||
0.0995284 | + | 0.995035i | \(0.468267\pi\) | |||||||
\(168\) | −2.08609e14 | −0.715852 | ||||||||
\(169\) | −1.84534e14 | −0.609275 | ||||||||
\(170\) | −1.54670e13 | −0.0491459 | ||||||||
\(171\) | −4.31941e14 | −1.32114 | ||||||||
\(172\) | 2.40708e14 | 0.708853 | ||||||||
\(173\) | 1.26777e14 | 0.359535 | 0.179767 | − | 0.983709i | \(-0.442465\pi\) | ||||
0.179767 | + | 0.983709i | \(0.442465\pi\) | |||||||
\(174\) | 6.17911e14 | 1.68794 | ||||||||
\(175\) | 5.22192e14 | 1.37430 | ||||||||
\(176\) | 2.71753e13 | 0.0689194 | ||||||||
\(177\) | −3.79557e14 | −0.927793 | ||||||||
\(178\) | −1.91631e14 | −0.451581 | ||||||||
\(179\) | 3.08976e14 | 0.702070 | 0.351035 | − | 0.936362i | \(-0.385830\pi\) | ||||
0.351035 | + | 0.936362i | \(0.385830\pi\) | |||||||
\(180\) | 2.90346e13 | 0.0636275 | ||||||||
\(181\) | −4.74336e14 | −1.00271 | −0.501355 | − | 0.865242i | \(-0.667165\pi\) | ||||
−0.501355 | + | 0.865242i | \(0.667165\pi\) | |||||||
\(182\) | −3.01765e14 | −0.615467 | ||||||||
\(183\) | 2.28543e14 | 0.449818 | ||||||||
\(184\) | 1.58885e14 | 0.301832 | ||||||||
\(185\) | −1.19934e13 | −0.0219952 | ||||||||
\(186\) | −2.14364e14 | −0.379593 | ||||||||
\(187\) | 9.81085e13 | 0.167778 | ||||||||
\(188\) | −1.72425e14 | −0.284822 | ||||||||
\(189\) | 1.45031e14 | 0.231451 | ||||||||
\(190\) | 6.20861e13 | 0.0957406 | ||||||||
\(191\) | −6.58450e14 | −0.981310 | −0.490655 | − | 0.871354i | \(-0.663242\pi\) | ||||
−0.490655 | + | 0.871354i | \(0.663242\pi\) | |||||||
\(192\) | −1.26169e14 | −0.181758 | ||||||||
\(193\) | 2.10092e14 | 0.292609 | 0.146305 | − | 0.989240i | \(-0.453262\pi\) | ||||
0.146305 | + | 0.989240i | \(0.453262\pi\) | |||||||
\(194\) | −2.80480e14 | −0.377737 | ||||||||
\(195\) | 7.96917e13 | 0.103798 | ||||||||
\(196\) | 3.72631e14 | 0.469477 | ||||||||
\(197\) | 1.56559e15 | 1.90831 | 0.954153 | − | 0.299320i | \(-0.0967599\pi\) | ||||
0.954153 | + | 0.299320i | \(0.0967599\pi\) | |||||||
\(198\) | −1.84169e14 | −0.217217 | ||||||||
\(199\) | 3.66804e14 | 0.418686 | 0.209343 | − | 0.977842i | \(-0.432867\pi\) | ||||
0.209343 | + | 0.977842i | \(0.432867\pi\) | |||||||
\(200\) | 3.15827e14 | 0.348942 | ||||||||
\(201\) | −1.75641e14 | −0.187868 | ||||||||
\(202\) | 3.62311e14 | 0.375230 | ||||||||
\(203\) | −2.27926e15 | −2.28597 | ||||||||
\(204\) | −4.55497e14 | −0.442475 | ||||||||
\(205\) | −1.98322e14 | −0.186626 | ||||||||
\(206\) | 1.38307e15 | 1.26097 | ||||||||
\(207\) | −1.07677e15 | −0.951300 | ||||||||
\(208\) | −1.82510e14 | −0.156270 | ||||||||
\(209\) | −3.93818e14 | −0.326847 | ||||||||
\(210\) | −2.03211e14 | −0.163501 | ||||||||
\(211\) | 1.34485e15 | 1.04915 | 0.524574 | − | 0.851365i | \(-0.324224\pi\) | ||||
0.524574 | + | 0.851365i | \(0.324224\pi\) | |||||||
\(212\) | −7.41953e14 | −0.561297 | ||||||||
\(213\) | 6.81957e14 | 0.500368 | ||||||||
\(214\) | −6.99829e14 | −0.498084 | ||||||||
\(215\) | 2.34479e14 | 0.161903 | ||||||||
\(216\) | 8.77163e13 | 0.0587666 | ||||||||
\(217\) | 7.90716e14 | 0.514082 | ||||||||
\(218\) | 2.69237e14 | 0.169890 | ||||||||
\(219\) | 3.30586e15 | 2.02487 | ||||||||
\(220\) | 2.64720e13 | 0.0157413 | ||||||||
\(221\) | −6.58901e14 | −0.380426 | ||||||||
\(222\) | −3.53202e14 | −0.198029 | ||||||||
\(223\) | −2.04083e15 | −1.11128 | −0.555642 | − | 0.831421i | \(-0.687528\pi\) | ||||
−0.555642 | + | 0.831421i | \(0.687528\pi\) | |||||||
\(224\) | 4.65394e14 | 0.246155 | ||||||||
\(225\) | −2.14038e15 | −1.09978 | ||||||||
\(226\) | −1.84096e15 | −0.919052 | ||||||||
\(227\) | 2.91994e14 | 0.141647 | 0.0708233 | − | 0.997489i | \(-0.477437\pi\) | ||||
0.0708233 | + | 0.997489i | \(0.477437\pi\) | |||||||
\(228\) | 1.82841e15 | 0.861981 | ||||||||
\(229\) | −2.81485e15 | −1.28981 | −0.644903 | − | 0.764264i | \(-0.723102\pi\) | ||||
−0.644903 | + | 0.764264i | \(0.723102\pi\) | |||||||
\(230\) | 1.54773e14 | 0.0689388 | ||||||||
\(231\) | 1.28898e15 | 0.558174 | ||||||||
\(232\) | −1.37852e15 | −0.580419 | ||||||||
\(233\) | 4.39377e15 | 1.79897 | 0.899486 | − | 0.436950i | \(-0.143941\pi\) | ||||
0.899486 | + | 0.436950i | \(0.143941\pi\) | |||||||
\(234\) | 1.23689e15 | 0.492524 | ||||||||
\(235\) | −1.67963e14 | −0.0650536 | ||||||||
\(236\) | 8.46768e14 | 0.319034 | ||||||||
\(237\) | −2.86036e15 | −1.04847 | ||||||||
\(238\) | 1.68017e15 | 0.599243 | ||||||||
\(239\) | −4.40953e15 | −1.53040 | −0.765202 | − | 0.643791i | \(-0.777361\pi\) | ||||
−0.765202 | + | 0.643791i | \(0.777361\pi\) | |||||||
\(240\) | −1.22904e14 | −0.0415138 | ||||||||
\(241\) | 1.92940e15 | 0.634324 | 0.317162 | − | 0.948371i | \(-0.397270\pi\) | ||||
0.317162 | + | 0.948371i | \(0.397270\pi\) | |||||||
\(242\) | 2.04154e15 | 0.653368 | ||||||||
\(243\) | 4.60588e15 | 1.43507 | ||||||||
\(244\) | −5.09866e14 | −0.154676 | ||||||||
\(245\) | 3.62987e14 | 0.107229 | ||||||||
\(246\) | −5.84052e15 | −1.68025 | ||||||||
\(247\) | 2.64490e15 | 0.741104 | ||||||||
\(248\) | 4.78233e14 | 0.130528 | ||||||||
\(249\) | −4.57676e15 | −1.21692 | ||||||||
\(250\) | 6.19372e14 | 0.160451 | ||||||||
\(251\) | 3.46331e14 | 0.0874202 | 0.0437101 | − | 0.999044i | \(-0.486082\pi\) | ||||
0.0437101 | + | 0.999044i | \(0.486082\pi\) | |||||||
\(252\) | −3.15402e15 | −0.775819 | ||||||||
\(253\) | −9.81738e14 | −0.235349 | ||||||||
\(254\) | −3.05928e15 | −0.714826 | ||||||||
\(255\) | −4.43709e14 | −0.101062 | ||||||||
\(256\) | 2.81475e14 | 0.0625000 | ||||||||
\(257\) | 4.59506e14 | 0.0994778 | 0.0497389 | − | 0.998762i | \(-0.484161\pi\) | ||||
0.0497389 | + | 0.998762i | \(0.484161\pi\) | |||||||
\(258\) | 6.90532e15 | 1.45766 | ||||||||
\(259\) | 1.30284e15 | 0.268191 | ||||||||
\(260\) | −1.77787e14 | −0.0356922 | ||||||||
\(261\) | 9.34236e15 | 1.82933 | ||||||||
\(262\) | 6.63640e15 | 1.26758 | ||||||||
\(263\) | −8.08966e15 | −1.50736 | −0.753681 | − | 0.657240i | \(-0.771724\pi\) | ||||
−0.753681 | + | 0.657240i | \(0.771724\pi\) | |||||||
\(264\) | 7.79590e14 | 0.141723 | ||||||||
\(265\) | −7.22752e14 | −0.128201 | ||||||||
\(266\) | −6.74439e15 | −1.16738 | ||||||||
\(267\) | −5.49742e15 | −0.928615 | ||||||||
\(268\) | 3.91844e14 | 0.0646007 | ||||||||
\(269\) | 5.06059e15 | 0.814350 | 0.407175 | − | 0.913350i | \(-0.366514\pi\) | ||||
0.407175 | + | 0.913350i | \(0.366514\pi\) | |||||||
\(270\) | 8.54463e13 | 0.0134224 | ||||||||
\(271\) | −4.91453e14 | −0.0753671 | −0.0376835 | − | 0.999290i | \(-0.511998\pi\) | ||||
−0.0376835 | + | 0.999290i | \(0.511998\pi\) | |||||||
\(272\) | 1.01618e15 | 0.152151 | ||||||||
\(273\) | −8.65688e15 | −1.26562 | ||||||||
\(274\) | −3.23445e15 | −0.461766 | ||||||||
\(275\) | −1.95147e15 | −0.272082 | ||||||||
\(276\) | 4.55800e15 | 0.620677 | ||||||||
\(277\) | 3.92917e15 | 0.522615 | 0.261308 | − | 0.965256i | \(-0.415846\pi\) | ||||
0.261308 | + | 0.965256i | \(0.415846\pi\) | |||||||
\(278\) | −1.37522e15 | −0.178682 | ||||||||
\(279\) | −3.24103e15 | −0.411391 | ||||||||
\(280\) | 4.53350e14 | 0.0562220 | ||||||||
\(281\) | 1.14417e16 | 1.38644 | 0.693219 | − | 0.720727i | \(-0.256192\pi\) | ||||
0.693219 | + | 0.720727i | \(0.256192\pi\) | |||||||
\(282\) | −4.94643e15 | −0.585697 | ||||||||
\(283\) | 2.12246e15 | 0.245599 | 0.122800 | − | 0.992431i | \(-0.460813\pi\) | ||||
0.122800 | + | 0.992431i | \(0.460813\pi\) | |||||||
\(284\) | −1.52140e15 | −0.172058 | ||||||||
\(285\) | 1.78110e15 | 0.196877 | ||||||||
\(286\) | 1.12772e15 | 0.121849 | ||||||||
\(287\) | 2.15437e16 | 2.27556 | ||||||||
\(288\) | −1.90758e15 | −0.196984 | ||||||||
\(289\) | −6.23594e15 | −0.629602 | ||||||||
\(290\) | −1.34285e15 | −0.132568 | ||||||||
\(291\) | −8.04626e15 | −0.776765 | ||||||||
\(292\) | −7.37516e15 | −0.696278 | ||||||||
\(293\) | −1.99050e16 | −1.83790 | −0.918951 | − | 0.394372i | \(-0.870962\pi\) | ||||
−0.918951 | + | 0.394372i | \(0.870962\pi\) | |||||||
\(294\) | 1.06898e16 | 0.965414 | ||||||||
\(295\) | 8.24855e14 | 0.0728676 | ||||||||
\(296\) | 7.87972e14 | 0.0680949 | ||||||||
\(297\) | −5.41994e14 | −0.0458223 | ||||||||
\(298\) | 5.63034e15 | 0.465724 | ||||||||
\(299\) | 6.59340e15 | 0.533638 | ||||||||
\(300\) | 9.06028e15 | 0.717552 | ||||||||
\(301\) | −2.54714e16 | −1.97410 | ||||||||
\(302\) | 1.32759e15 | 0.100697 | ||||||||
\(303\) | 1.03938e16 | 0.771608 | ||||||||
\(304\) | −4.07907e15 | −0.296403 | ||||||||
\(305\) | −4.96671e14 | −0.0353281 | ||||||||
\(306\) | −6.88677e15 | −0.479542 | ||||||||
\(307\) | −1.26611e16 | −0.863118 | −0.431559 | − | 0.902085i | \(-0.642036\pi\) | ||||
−0.431559 | + | 0.902085i | \(0.642036\pi\) | |||||||
\(308\) | −2.87564e15 | −0.191935 | ||||||||
\(309\) | 3.96768e16 | 2.59302 | ||||||||
\(310\) | 4.65857e14 | 0.0298127 | ||||||||
\(311\) | 1.08678e15 | 0.0681081 | 0.0340541 | − | 0.999420i | \(-0.489158\pi\) | ||||
0.0340541 | + | 0.999420i | \(0.489158\pi\) | |||||||
\(312\) | −5.23577e15 | −0.321348 | ||||||||
\(313\) | 2.13383e16 | 1.28269 | 0.641346 | − | 0.767252i | \(-0.278376\pi\) | ||||
0.641346 | + | 0.767252i | \(0.278376\pi\) | |||||||
\(314\) | 1.45615e16 | 0.857358 | ||||||||
\(315\) | −3.07239e15 | −0.177198 | ||||||||
\(316\) | 6.38129e15 | 0.360531 | ||||||||
\(317\) | −3.00971e16 | −1.66586 | −0.832932 | − | 0.553375i | \(-0.813340\pi\) | ||||
−0.832932 | + | 0.553375i | \(0.813340\pi\) | |||||||
\(318\) | −2.12848e16 | −1.15423 | ||||||||
\(319\) | 8.51780e15 | 0.452572 | ||||||||
\(320\) | 2.74191e14 | 0.0142751 | ||||||||
\(321\) | −2.00763e16 | −1.02424 | ||||||||
\(322\) | −1.68129e16 | −0.840581 | ||||||||
\(323\) | −1.47263e16 | −0.721569 | ||||||||
\(324\) | −9.08528e15 | −0.436310 | ||||||||
\(325\) | 1.31062e16 | 0.616928 | ||||||||
\(326\) | 9.05813e15 | 0.417950 | ||||||||
\(327\) | 7.72373e15 | 0.349355 | ||||||||
\(328\) | 1.30298e16 | 0.577775 | ||||||||
\(329\) | 1.82457e16 | 0.793208 | ||||||||
\(330\) | 7.59415e14 | 0.0323697 | ||||||||
\(331\) | 1.00468e16 | 0.419900 | 0.209950 | − | 0.977712i | \(-0.432670\pi\) | ||||
0.209950 | + | 0.977712i | \(0.432670\pi\) | |||||||
\(332\) | 1.02105e16 | 0.418455 | ||||||||
\(333\) | −5.34016e15 | −0.214618 | ||||||||
\(334\) | −3.57120e15 | −0.140754 | ||||||||
\(335\) | 3.81704e14 | 0.0147549 | ||||||||
\(336\) | 1.33510e16 | 0.506184 | ||||||||
\(337\) | 4.00487e15 | 0.148934 | 0.0744671 | − | 0.997223i | \(-0.476274\pi\) | ||||
0.0744671 | + | 0.997223i | \(0.476274\pi\) | |||||||
\(338\) | 1.18102e16 | 0.430822 | ||||||||
\(339\) | −5.28126e16 | −1.88990 | ||||||||
\(340\) | 9.89886e14 | 0.0347514 | ||||||||
\(341\) | −2.95497e15 | −0.101777 | ||||||||
\(342\) | 2.76442e16 | 0.934190 | ||||||||
\(343\) | 2.56363e15 | 0.0850048 | ||||||||
\(344\) | −1.54053e16 | −0.501235 | ||||||||
\(345\) | 4.44004e15 | 0.141763 | ||||||||
\(346\) | −8.11373e15 | −0.254229 | ||||||||
\(347\) | 6.06273e13 | 0.00186435 | 0.000932173 | − | 1.00000i | \(-0.499703\pi\) | ||||
0.000932173 | 1.00000i | \(0.499703\pi\) | ||||||||
\(348\) | −3.95463e16 | −1.19355 | ||||||||
\(349\) | 3.07578e16 | 0.911151 | 0.455576 | − | 0.890197i | \(-0.349433\pi\) | ||||
0.455576 | + | 0.890197i | \(0.349433\pi\) | |||||||
\(350\) | −3.34203e16 | −0.971779 | ||||||||
\(351\) | 3.64005e15 | 0.103899 | ||||||||
\(352\) | −1.73922e15 | −0.0487334 | ||||||||
\(353\) | −2.08897e16 | −0.574640 | −0.287320 | − | 0.957835i | \(-0.592764\pi\) | ||||
−0.287320 | + | 0.957835i | \(0.592764\pi\) | |||||||
\(354\) | 2.42917e16 | 0.656049 | ||||||||
\(355\) | −1.48203e15 | −0.0392982 | ||||||||
\(356\) | 1.22644e16 | 0.319316 | ||||||||
\(357\) | 4.81999e16 | 1.23226 | ||||||||
\(358\) | −1.97745e16 | −0.496439 | ||||||||
\(359\) | −2.46366e16 | −0.607390 | −0.303695 | − | 0.952769i | \(-0.598220\pi\) | ||||
−0.303695 | + | 0.952769i | \(0.598220\pi\) | |||||||
\(360\) | −1.85821e15 | −0.0449914 | ||||||||
\(361\) | 1.70601e16 | 0.405680 | ||||||||
\(362\) | 3.03575e16 | 0.709023 | ||||||||
\(363\) | 5.85667e16 | 1.34356 | ||||||||
\(364\) | 1.93129e16 | 0.435201 | ||||||||
\(365\) | −7.18430e15 | −0.159031 | ||||||||
\(366\) | −1.46268e16 | −0.318069 | ||||||||
\(367\) | −5.28651e16 | −1.12938 | −0.564689 | − | 0.825304i | \(-0.691004\pi\) | ||||
−0.564689 | + | 0.825304i | \(0.691004\pi\) | |||||||
\(368\) | −1.01686e16 | −0.213428 | ||||||||
\(369\) | −8.83043e16 | −1.82100 | ||||||||
\(370\) | 7.67580e14 | 0.0155529 | ||||||||
\(371\) | 7.85122e16 | 1.56317 | ||||||||
\(372\) | 1.37193e16 | 0.268413 | ||||||||
\(373\) | −6.44569e15 | −0.123926 | −0.0619630 | − | 0.998078i | \(-0.519736\pi\) | ||||
−0.0619630 | + | 0.998078i | \(0.519736\pi\) | |||||||
\(374\) | −6.27894e15 | −0.118637 | ||||||||
\(375\) | 1.77682e16 | 0.329945 | ||||||||
\(376\) | 1.10352e16 | 0.201400 | ||||||||
\(377\) | −5.72059e16 | −1.02618 | ||||||||
\(378\) | −9.28199e15 | −0.163661 | ||||||||
\(379\) | −6.58787e16 | −1.14180 | −0.570900 | − | 0.821019i | \(-0.693406\pi\) | ||||
−0.570900 | + | 0.821019i | \(0.693406\pi\) | |||||||
\(380\) | −3.97351e15 | −0.0676988 | ||||||||
\(381\) | −8.77632e16 | −1.46994 | ||||||||
\(382\) | 4.21408e16 | 0.693891 | ||||||||
\(383\) | 8.87457e16 | 1.43666 | 0.718332 | − | 0.695700i | \(-0.244906\pi\) | ||||
0.718332 | + | 0.695700i | \(0.244906\pi\) | |||||||
\(384\) | 8.07481e15 | 0.128523 | ||||||||
\(385\) | −2.80122e15 | −0.0438382 | ||||||||
\(386\) | −1.34459e16 | −0.206906 | ||||||||
\(387\) | 1.04403e17 | 1.57977 | ||||||||
\(388\) | 1.79507e16 | 0.267101 | ||||||||
\(389\) | 6.27464e16 | 0.918156 | 0.459078 | − | 0.888396i | \(-0.348180\pi\) | ||||
0.459078 | + | 0.888396i | \(0.348180\pi\) | |||||||
\(390\) | −5.10027e15 | −0.0733961 | ||||||||
\(391\) | −3.67108e16 | −0.519572 | ||||||||
\(392\) | −2.38484e16 | −0.331970 | ||||||||
\(393\) | 1.90382e17 | 2.60659 | ||||||||
\(394\) | −1.00198e17 | −1.34938 | ||||||||
\(395\) | 6.21615e15 | 0.0823456 | ||||||||
\(396\) | 1.17868e16 | 0.153595 | ||||||||
\(397\) | −9.86261e16 | −1.26431 | −0.632155 | − | 0.774842i | \(-0.717829\pi\) | ||||
−0.632155 | + | 0.774842i | \(0.717829\pi\) | |||||||
\(398\) | −2.34754e16 | −0.296056 | ||||||||
\(399\) | −1.93480e17 | −2.40055 | ||||||||
\(400\) | −2.02129e16 | −0.246740 | ||||||||
\(401\) | −3.66088e15 | −0.0439691 | −0.0219845 | − | 0.999758i | \(-0.506998\pi\) | ||||
−0.0219845 | + | 0.999758i | \(0.506998\pi\) | |||||||
\(402\) | 1.12410e16 | 0.132842 | ||||||||
\(403\) | 1.98457e16 | 0.230773 | ||||||||
\(404\) | −2.31879e16 | −0.265327 | ||||||||
\(405\) | −8.85016e15 | −0.0996537 | ||||||||
\(406\) | 1.45873e17 | 1.61642 | ||||||||
\(407\) | −4.86883e15 | −0.0530959 | ||||||||
\(408\) | 2.91518e16 | 0.312877 | ||||||||
\(409\) | 1.41675e17 | 1.49655 | 0.748273 | − | 0.663390i | \(-0.230883\pi\) | ||||
0.748273 | + | 0.663390i | \(0.230883\pi\) | |||||||
\(410\) | 1.26926e16 | 0.131964 | ||||||||
\(411\) | −9.27882e16 | −0.949557 | ||||||||
\(412\) | −8.85163e16 | −0.891644 | ||||||||
\(413\) | −8.96037e16 | −0.888486 | ||||||||
\(414\) | 6.89136e16 | 0.672671 | ||||||||
\(415\) | 9.94624e15 | 0.0955754 | ||||||||
\(416\) | 1.16807e16 | 0.110500 | ||||||||
\(417\) | −3.94515e16 | −0.367434 | ||||||||
\(418\) | 2.52044e16 | 0.231116 | ||||||||
\(419\) | 1.44390e17 | 1.30360 | 0.651801 | − | 0.758390i | \(-0.274014\pi\) | ||||
0.651801 | + | 0.758390i | \(0.274014\pi\) | |||||||
\(420\) | 1.30055e16 | 0.115613 | ||||||||
\(421\) | 1.32169e17 | 1.15690 | 0.578451 | − | 0.815717i | \(-0.303657\pi\) | ||||
0.578451 | + | 0.815717i | \(0.303657\pi\) | |||||||
\(422\) | −8.60702e16 | −0.741860 | ||||||||
\(423\) | −7.47864e16 | −0.634761 | ||||||||
\(424\) | 4.74850e16 | 0.396897 | ||||||||
\(425\) | −7.29729e16 | −0.600666 | ||||||||
\(426\) | −4.36453e16 | −0.353814 | ||||||||
\(427\) | 5.39532e16 | 0.430761 | ||||||||
\(428\) | 4.47890e16 | 0.352198 | ||||||||
\(429\) | 3.23515e16 | 0.250566 | ||||||||
\(430\) | −1.50067e16 | −0.114483 | ||||||||
\(431\) | −1.80535e17 | −1.35662 | −0.678312 | − | 0.734774i | \(-0.737288\pi\) | ||||
−0.678312 | + | 0.734774i | \(0.737288\pi\) | |||||||
\(432\) | −5.61384e15 | −0.0415543 | ||||||||
\(433\) | −1.33563e17 | −0.973900 | −0.486950 | − | 0.873430i | \(-0.661891\pi\) | ||||
−0.486950 | + | 0.873430i | \(0.661891\pi\) | |||||||
\(434\) | −5.06058e16 | −0.363511 | ||||||||
\(435\) | −3.85229e16 | −0.272608 | ||||||||
\(436\) | −1.72311e16 | −0.120130 | ||||||||
\(437\) | 1.47361e17 | 1.01217 | ||||||||
\(438\) | −2.11575e17 | −1.43180 | ||||||||
\(439\) | 2.34588e17 | 1.56418 | 0.782090 | − | 0.623165i | \(-0.214154\pi\) | ||||
0.782090 | + | 0.623165i | \(0.214154\pi\) | |||||||
\(440\) | −1.69421e15 | −0.0111307 | ||||||||
\(441\) | 1.61622e17 | 1.04629 | ||||||||
\(442\) | 4.21697e16 | 0.269002 | ||||||||
\(443\) | −1.26522e17 | −0.795318 | −0.397659 | − | 0.917533i | \(-0.630177\pi\) | ||||
−0.397659 | + | 0.917533i | \(0.630177\pi\) | |||||||
\(444\) | 2.26050e16 | 0.140028 | ||||||||
\(445\) | 1.19470e16 | 0.0729321 | ||||||||
\(446\) | 1.30613e17 | 0.785797 | ||||||||
\(447\) | 1.61520e17 | 0.957698 | ||||||||
\(448\) | −2.97852e16 | −0.174058 | ||||||||
\(449\) | −1.91607e17 | −1.10359 | −0.551797 | − | 0.833978i | \(-0.686058\pi\) | ||||
−0.551797 | + | 0.833978i | \(0.686058\pi\) | |||||||
\(450\) | 1.36985e17 | 0.777661 | ||||||||
\(451\) | −8.05106e16 | −0.450511 | ||||||||
\(452\) | 1.17822e17 | 0.649868 | ||||||||
\(453\) | 3.80851e16 | 0.207070 | ||||||||
\(454\) | −1.86876e16 | −0.100159 | ||||||||
\(455\) | 1.88132e16 | 0.0994002 | ||||||||
\(456\) | −1.17018e17 | −0.609513 | ||||||||
\(457\) | −2.62243e17 | −1.34663 | −0.673316 | − | 0.739355i | \(-0.735131\pi\) | ||||
−0.673316 | + | 0.739355i | \(0.735131\pi\) | |||||||
\(458\) | 1.80150e17 | 0.912031 | ||||||||
\(459\) | −2.02672e16 | −0.101160 | ||||||||
\(460\) | −9.90546e15 | −0.0487471 | ||||||||
\(461\) | −6.94961e16 | −0.337213 | −0.168607 | − | 0.985683i | \(-0.553927\pi\) | ||||
−0.168607 | + | 0.985683i | \(0.553927\pi\) | |||||||
\(462\) | −8.24950e16 | −0.394689 | ||||||||
\(463\) | −2.31198e17 | −1.09071 | −0.545353 | − | 0.838207i | \(-0.683604\pi\) | ||||
−0.545353 | + | 0.838207i | \(0.683604\pi\) | |||||||
\(464\) | 8.82253e16 | 0.410418 | ||||||||
\(465\) | 1.33643e16 | 0.0613057 | ||||||||
\(466\) | −2.81202e17 | −1.27206 | ||||||||
\(467\) | 1.70771e17 | 0.761825 | 0.380913 | − | 0.924611i | \(-0.375610\pi\) | ||||
0.380913 | + | 0.924611i | \(0.375610\pi\) | |||||||
\(468\) | −7.91609e16 | −0.348267 | ||||||||
\(469\) | −4.14643e16 | −0.179908 | ||||||||
\(470\) | 1.07496e16 | 0.0459998 | ||||||||
\(471\) | 4.17732e17 | 1.76304 | ||||||||
\(472\) | −5.41932e16 | −0.225591 | ||||||||
\(473\) | 9.51886e16 | 0.390830 | ||||||||
\(474\) | 1.83063e17 | 0.741382 | ||||||||
\(475\) | 2.92921e17 | 1.17015 | ||||||||
\(476\) | −1.07531e17 | −0.423729 | ||||||||
\(477\) | −3.21810e17 | −1.25092 | ||||||||
\(478\) | 2.82210e17 | 1.08216 | ||||||||
\(479\) | 3.22880e17 | 1.22141 | 0.610703 | − | 0.791859i | \(-0.290887\pi\) | ||||
0.610703 | + | 0.791859i | \(0.290887\pi\) | |||||||
\(480\) | 7.86585e15 | 0.0293547 | ||||||||
\(481\) | 3.26993e16 | 0.120391 | ||||||||
\(482\) | −1.23481e17 | −0.448535 | ||||||||
\(483\) | −4.82320e17 | −1.72854 | ||||||||
\(484\) | −1.30659e17 | −0.462001 | ||||||||
\(485\) | 1.74861e16 | 0.0610060 | ||||||||
\(486\) | −2.94776e17 | −1.01475 | ||||||||
\(487\) | −2.41562e16 | −0.0820521 | −0.0410261 | − | 0.999158i | \(-0.513063\pi\) | ||||
−0.0410261 | + | 0.999158i | \(0.513063\pi\) | |||||||
\(488\) | 3.26314e16 | 0.109372 | ||||||||
\(489\) | 2.59855e17 | 0.859456 | ||||||||
\(490\) | −2.32312e16 | −0.0758223 | ||||||||
\(491\) | −4.61064e17 | −1.48502 | −0.742508 | − | 0.669837i | \(-0.766364\pi\) | ||||
−0.742508 | + | 0.669837i | \(0.766364\pi\) | |||||||
\(492\) | 3.73793e17 | 1.18812 | ||||||||
\(493\) | 3.18512e17 | 0.999128 | ||||||||
\(494\) | −1.69274e17 | −0.524040 | ||||||||
\(495\) | 1.14818e16 | 0.0350813 | ||||||||
\(496\) | −3.06069e16 | −0.0922972 | ||||||||
\(497\) | 1.60992e17 | 0.479169 | ||||||||
\(498\) | 2.92913e17 | 0.860494 | ||||||||
\(499\) | −5.85158e17 | −1.69676 | −0.848379 | − | 0.529390i | \(-0.822421\pi\) | ||||
−0.848379 | + | 0.529390i | \(0.822421\pi\) | |||||||
\(500\) | −3.96398e16 | −0.113456 | ||||||||
\(501\) | −1.02449e17 | −0.289442 | ||||||||
\(502\) | −2.21652e16 | −0.0618154 | ||||||||
\(503\) | −5.03073e17 | −1.38497 | −0.692483 | − | 0.721434i | \(-0.743483\pi\) | ||||
−0.692483 | + | 0.721434i | \(0.743483\pi\) | |||||||
\(504\) | 2.01857e17 | 0.548587 | ||||||||
\(505\) | −2.25878e16 | −0.0606010 | ||||||||
\(506\) | 6.28312e16 | 0.166417 | ||||||||
\(507\) | 3.38805e17 | 0.885926 | ||||||||
\(508\) | 1.95794e17 | 0.505458 | ||||||||
\(509\) | 2.39181e17 | 0.609622 | 0.304811 | − | 0.952413i | \(-0.401407\pi\) | ||||
0.304811 | + | 0.952413i | \(0.401407\pi\) | |||||||
\(510\) | 2.83974e16 | 0.0714615 | ||||||||
\(511\) | 7.80427e17 | 1.93908 | ||||||||
\(512\) | −1.80144e16 | −0.0441942 | ||||||||
\(513\) | 8.13546e16 | 0.197069 | ||||||||
\(514\) | −2.94084e16 | −0.0703415 | ||||||||
\(515\) | −8.62256e16 | −0.203652 | ||||||||
\(516\) | −4.41941e17 | −1.03072 | ||||||||
\(517\) | −6.81857e16 | −0.157038 | ||||||||
\(518\) | −8.33819e16 | −0.189639 | ||||||||
\(519\) | −2.32763e17 | −0.522788 | ||||||||
\(520\) | 1.13784e16 | 0.0252382 | ||||||||
\(521\) | 5.84939e17 | 1.28134 | 0.640671 | − | 0.767815i | \(-0.278656\pi\) | ||||
0.640671 | + | 0.767815i | \(0.278656\pi\) | |||||||
\(522\) | −5.97911e17 | −1.29353 | ||||||||
\(523\) | −1.38091e17 | −0.295055 | −0.147528 | − | 0.989058i | \(-0.547132\pi\) | ||||
−0.147528 | + | 0.989058i | \(0.547132\pi\) | |||||||
\(524\) | −4.24729e17 | −0.896312 | ||||||||
\(525\) | −9.58744e17 | −1.99833 | ||||||||
\(526\) | 5.17738e17 | 1.06587 | ||||||||
\(527\) | −1.10497e17 | −0.224690 | ||||||||
\(528\) | −4.98938e16 | −0.100213 | ||||||||
\(529\) | −1.36683e17 | −0.271178 | ||||||||
\(530\) | 4.62561e16 | 0.0906517 | ||||||||
\(531\) | 3.67272e17 | 0.711006 | ||||||||
\(532\) | 4.31641e17 | 0.825462 | ||||||||
\(533\) | 5.40713e17 | 1.02150 | ||||||||
\(534\) | 3.51835e17 | 0.656630 | ||||||||
\(535\) | 4.36299e16 | 0.0804424 | ||||||||
\(536\) | −2.50780e16 | −0.0456796 | ||||||||
\(537\) | −5.67281e17 | −1.02086 | ||||||||
\(538\) | −3.23878e17 | −0.575833 | ||||||||
\(539\) | 1.47358e17 | 0.258848 | ||||||||
\(540\) | −5.46856e15 | −0.00949104 | ||||||||
\(541\) | 2.87308e16 | 0.0492680 | 0.0246340 | − | 0.999697i | \(-0.492158\pi\) | ||||
0.0246340 | + | 0.999697i | \(0.492158\pi\) | |||||||
\(542\) | 3.14530e16 | 0.0532926 | ||||||||
\(543\) | 8.70880e17 | 1.45801 | ||||||||
\(544\) | −6.50358e16 | −0.107587 | ||||||||
\(545\) | −1.67852e16 | −0.0274378 | ||||||||
\(546\) | 5.54040e17 | 0.894930 | ||||||||
\(547\) | 1.77510e17 | 0.283338 | 0.141669 | − | 0.989914i | \(-0.454753\pi\) | ||||
0.141669 | + | 0.989914i | \(0.454753\pi\) | |||||||
\(548\) | 2.07005e17 | 0.326518 | ||||||||
\(549\) | −2.21146e17 | −0.344714 | ||||||||
\(550\) | 1.24894e17 | 0.192391 | ||||||||
\(551\) | −1.27854e18 | −1.94639 | ||||||||
\(552\) | −2.91712e17 | −0.438885 | ||||||||
\(553\) | −6.75258e17 | −1.00405 | ||||||||
\(554\) | −2.51467e17 | −0.369545 | ||||||||
\(555\) | 2.20200e16 | 0.0319825 | ||||||||
\(556\) | 8.80138e16 | 0.126347 | ||||||||
\(557\) | 6.70558e17 | 0.951432 | 0.475716 | − | 0.879599i | \(-0.342189\pi\) | ||||
0.475716 | + | 0.879599i | \(0.342189\pi\) | |||||||
\(558\) | 2.07426e17 | 0.290898 | ||||||||
\(559\) | −6.39291e17 | −0.886180 | ||||||||
\(560\) | −2.90144e16 | −0.0397550 | ||||||||
\(561\) | −1.80127e17 | −0.243961 | ||||||||
\(562\) | −7.32271e17 | −0.980360 | ||||||||
\(563\) | 3.10511e17 | 0.410934 | 0.205467 | − | 0.978664i | \(-0.434129\pi\) | ||||
0.205467 | + | 0.978664i | \(0.434129\pi\) | |||||||
\(564\) | 3.16572e17 | 0.414150 | ||||||||
\(565\) | 1.14772e17 | 0.148430 | ||||||||
\(566\) | −1.35837e17 | −0.173665 | ||||||||
\(567\) | 9.61389e17 | 1.21509 | ||||||||
\(568\) | 9.73698e16 | 0.121663 | ||||||||
\(569\) | −2.58365e17 | −0.319157 | −0.159578 | − | 0.987185i | \(-0.551013\pi\) | ||||
−0.159578 | + | 0.987185i | \(0.551013\pi\) | |||||||
\(570\) | −1.13990e17 | −0.139213 | ||||||||
\(571\) | 9.91259e17 | 1.19688 | 0.598442 | − | 0.801166i | \(-0.295787\pi\) | ||||
0.598442 | + | 0.801166i | \(0.295787\pi\) | |||||||
\(572\) | −7.21741e16 | −0.0861603 | ||||||||
\(573\) | 1.20891e18 | 1.42689 | ||||||||
\(574\) | −1.37880e18 | −1.60906 | ||||||||
\(575\) | 7.30215e17 | 0.842577 | ||||||||
\(576\) | 1.22085e17 | 0.139289 | ||||||||
\(577\) | −9.99359e17 | −1.12740 | −0.563701 | − | 0.825979i | \(-0.690623\pi\) | ||||
−0.563701 | + | 0.825979i | \(0.690623\pi\) | |||||||
\(578\) | 3.99100e17 | 0.445196 | ||||||||
\(579\) | −3.85730e17 | −0.425473 | ||||||||
\(580\) | 8.59422e16 | 0.0937399 | ||||||||
\(581\) | −1.08046e18 | −1.16536 | ||||||||
\(582\) | 5.14960e17 | 0.549256 | ||||||||
\(583\) | −2.93407e17 | −0.309474 | ||||||||
\(584\) | 4.72010e17 | 0.492343 | ||||||||
\(585\) | −7.71123e16 | −0.0795446 | ||||||||
\(586\) | 1.27392e18 | 1.29959 | ||||||||
\(587\) | 7.79668e17 | 0.786614 | 0.393307 | − | 0.919407i | \(-0.371331\pi\) | ||||
0.393307 | + | 0.919407i | \(0.371331\pi\) | |||||||
\(588\) | −6.84150e17 | −0.682651 | ||||||||
\(589\) | 4.43548e17 | 0.437715 | ||||||||
\(590\) | −5.27907e16 | −0.0515252 | ||||||||
\(591\) | −2.87443e18 | −2.77480 | ||||||||
\(592\) | −5.04302e16 | −0.0481504 | ||||||||
\(593\) | 8.86852e17 | 0.837521 | 0.418761 | − | 0.908097i | \(-0.362465\pi\) | ||||
0.418761 | + | 0.908097i | \(0.362465\pi\) | |||||||
\(594\) | 3.46876e16 | 0.0324013 | ||||||||
\(595\) | −1.04748e17 | −0.0967801 | ||||||||
\(596\) | −3.60342e17 | −0.329317 | ||||||||
\(597\) | −6.73452e17 | −0.608798 | ||||||||
\(598\) | −4.21978e17 | −0.377339 | ||||||||
\(599\) | −1.56613e18 | −1.38533 | −0.692665 | − | 0.721260i | \(-0.743563\pi\) | ||||
−0.692665 | + | 0.721260i | \(0.743563\pi\) | |||||||
\(600\) | −5.79858e17 | −0.507386 | ||||||||
\(601\) | 1.44186e18 | 1.24807 | 0.624036 | − | 0.781396i | \(-0.285492\pi\) | ||||
0.624036 | + | 0.781396i | \(0.285492\pi\) | |||||||
\(602\) | 1.63017e18 | 1.39590 | ||||||||
\(603\) | 1.69956e17 | 0.143971 | ||||||||
\(604\) | −8.49655e16 | −0.0712037 | ||||||||
\(605\) | −1.27277e17 | −0.105521 | ||||||||
\(606\) | −6.65202e17 | −0.545609 | ||||||||
\(607\) | 4.08280e17 | 0.331307 | 0.165654 | − | 0.986184i | \(-0.447027\pi\) | ||||
0.165654 | + | 0.986184i | \(0.447027\pi\) | |||||||
\(608\) | 2.61061e17 | 0.209589 | ||||||||
\(609\) | 4.18473e18 | 3.32395 | ||||||||
\(610\) | 3.17870e16 | 0.0249807 | ||||||||
\(611\) | 4.57939e17 | 0.356073 | ||||||||
\(612\) | 4.40753e17 | 0.339087 | ||||||||
\(613\) | −1.01386e18 | −0.771768 | −0.385884 | − | 0.922547i | \(-0.626104\pi\) | ||||
−0.385884 | + | 0.922547i | \(0.626104\pi\) | |||||||
\(614\) | 8.10307e17 | 0.610317 | ||||||||
\(615\) | 3.64120e17 | 0.271367 | ||||||||
\(616\) | 1.84041e17 | 0.135719 | ||||||||
\(617\) | −2.38764e18 | −1.74227 | −0.871133 | − | 0.491047i | \(-0.836614\pi\) | ||||
−0.871133 | + | 0.491047i | \(0.836614\pi\) | |||||||
\(618\) | −2.53931e18 | −1.83354 | ||||||||
\(619\) | −8.05525e17 | −0.575559 | −0.287780 | − | 0.957697i | \(-0.592917\pi\) | ||||
−0.287780 | + | 0.957697i | \(0.592917\pi\) | |||||||
\(620\) | −2.98148e16 | −0.0210808 | ||||||||
\(621\) | 2.02807e17 | 0.141901 | ||||||||
\(622\) | −6.95539e16 | −0.0481597 | ||||||||
\(623\) | −1.29780e18 | −0.889272 | ||||||||
\(624\) | 3.35089e17 | 0.227227 | ||||||||
\(625\) | 1.43207e18 | 0.961045 | ||||||||
\(626\) | −1.36565e18 | −0.907001 | ||||||||
\(627\) | 7.23050e17 | 0.475258 | ||||||||
\(628\) | −9.31933e17 | −0.606243 | ||||||||
\(629\) | −1.82064e17 | −0.117218 | ||||||||
\(630\) | 1.96633e17 | 0.125298 | ||||||||
\(631\) | 2.64035e18 | 1.66521 | 0.832607 | − | 0.553865i | \(-0.186847\pi\) | ||||
0.832607 | + | 0.553865i | \(0.186847\pi\) | |||||||
\(632\) | −4.08403e17 | −0.254934 | ||||||||
\(633\) | −2.46914e18 | −1.52553 | ||||||||
\(634\) | 1.92622e18 | 1.17794 | ||||||||
\(635\) | 1.90727e17 | 0.115447 | ||||||||
\(636\) | 1.36222e18 | 0.816164 | ||||||||
\(637\) | −9.89661e17 | −0.586921 | ||||||||
\(638\) | −5.45139e17 | −0.320017 | ||||||||
\(639\) | −6.59884e17 | −0.383453 | ||||||||
\(640\) | −1.75482e16 | −0.0100940 | ||||||||
\(641\) | −1.06429e18 | −0.606015 | −0.303007 | − | 0.952988i | \(-0.597991\pi\) | ||||
−0.303007 | + | 0.952988i | \(0.597991\pi\) | |||||||
\(642\) | 1.28489e18 | 0.724247 | ||||||||
\(643\) | 6.81097e17 | 0.380047 | 0.190024 | − | 0.981780i | \(-0.439144\pi\) | ||||
0.190024 | + | 0.981780i | \(0.439144\pi\) | |||||||
\(644\) | 1.07603e18 | 0.594380 | ||||||||
\(645\) | −4.30504e17 | −0.235417 | ||||||||
\(646\) | 9.42484e17 | 0.510226 | ||||||||
\(647\) | 2.04457e18 | 1.09578 | 0.547891 | − | 0.836550i | \(-0.315431\pi\) | ||||
0.547891 | + | 0.836550i | \(0.315431\pi\) | |||||||
\(648\) | 5.81458e17 | 0.308518 | ||||||||
\(649\) | 3.34856e17 | 0.175901 | ||||||||
\(650\) | −8.38796e17 | −0.436234 | ||||||||
\(651\) | −1.45175e18 | −0.747509 | ||||||||
\(652\) | −5.79720e17 | −0.295535 | ||||||||
\(653\) | 2.08196e18 | 1.05084 | 0.525419 | − | 0.850844i | \(-0.323909\pi\) | ||||
0.525419 | + | 0.850844i | \(0.323909\pi\) | |||||||
\(654\) | −4.94318e17 | −0.247031 | ||||||||
\(655\) | −4.13738e17 | −0.204718 | ||||||||
\(656\) | −8.33910e17 | −0.408549 | ||||||||
\(657\) | −3.19885e18 | −1.55174 | ||||||||
\(658\) | −1.16772e18 | −0.560883 | ||||||||
\(659\) | 2.11908e18 | 1.00784 | 0.503920 | − | 0.863750i | \(-0.331891\pi\) | ||||
0.503920 | + | 0.863750i | \(0.331891\pi\) | |||||||
\(660\) | −4.86026e16 | −0.0228888 | ||||||||
\(661\) | −1.46459e18 | −0.682980 | −0.341490 | − | 0.939885i | \(-0.610931\pi\) | ||||
−0.341490 | + | 0.939885i | \(0.610931\pi\) | |||||||
\(662\) | −6.42996e17 | −0.296914 | ||||||||
\(663\) | 1.20974e18 | 0.553165 | ||||||||
\(664\) | −6.53470e17 | −0.295892 | ||||||||
\(665\) | 4.20470e17 | 0.188536 | ||||||||
\(666\) | 3.41770e17 | 0.151758 | ||||||||
\(667\) | −3.18724e18 | −1.40151 | ||||||||
\(668\) | 2.28557e17 | 0.0995284 | ||||||||
\(669\) | 3.74696e18 | 1.61588 | ||||||||
\(670\) | −2.44290e16 | −0.0104333 | ||||||||
\(671\) | −2.01628e17 | −0.0852813 | ||||||||
\(672\) | −8.54464e17 | −0.357926 | ||||||||
\(673\) | 7.25358e17 | 0.300922 | 0.150461 | − | 0.988616i | \(-0.451924\pi\) | ||||
0.150461 | + | 0.988616i | \(0.451924\pi\) | |||||||
\(674\) | −2.56312e17 | −0.105312 | ||||||||
\(675\) | 4.03134e17 | 0.164049 | ||||||||
\(676\) | −7.55852e17 | −0.304637 | ||||||||
\(677\) | 4.22902e17 | 0.168816 | 0.0844079 | − | 0.996431i | \(-0.473100\pi\) | ||||
0.0844079 | + | 0.996431i | \(0.473100\pi\) | |||||||
\(678\) | 3.38001e18 | 1.33636 | ||||||||
\(679\) | −1.89951e18 | −0.743856 | ||||||||
\(680\) | −6.33527e16 | −0.0245730 | ||||||||
\(681\) | −5.36102e17 | −0.205964 | ||||||||
\(682\) | 1.89118e17 | 0.0719672 | ||||||||
\(683\) | 1.37469e18 | 0.518168 | 0.259084 | − | 0.965855i | \(-0.416579\pi\) | ||||
0.259084 | + | 0.965855i | \(0.416579\pi\) | |||||||
\(684\) | −1.76923e18 | −0.660572 | ||||||||
\(685\) | 2.01648e17 | 0.0745769 | ||||||||
\(686\) | −1.64072e17 | −0.0601075 | ||||||||
\(687\) | 5.16806e18 | 1.87546 | ||||||||
\(688\) | 9.85942e17 | 0.354427 | ||||||||
\(689\) | 1.97053e18 | 0.701712 | ||||||||
\(690\) | −2.84163e17 | −0.100242 | ||||||||
\(691\) | −3.23918e18 | −1.13195 | −0.565976 | − | 0.824422i | \(-0.691500\pi\) | ||||
−0.565976 | + | 0.824422i | \(0.691500\pi\) | |||||||
\(692\) | 5.19279e17 | 0.179767 | ||||||||
\(693\) | −1.24726e18 | −0.427752 | ||||||||
\(694\) | −3.88014e15 | −0.00131829 | ||||||||
\(695\) | 8.57361e16 | 0.0288578 | ||||||||
\(696\) | 2.53096e18 | 0.843968 | ||||||||
\(697\) | −3.01059e18 | −0.994577 | ||||||||
\(698\) | −1.96850e18 | −0.644281 | ||||||||
\(699\) | −8.06697e18 | −2.61583 | ||||||||
\(700\) | 2.13890e18 | 0.687152 | ||||||||
\(701\) | −4.32730e18 | −1.37737 | −0.688683 | − | 0.725062i | \(-0.741811\pi\) | ||||
−0.688683 | + | 0.725062i | \(0.741811\pi\) | |||||||
\(702\) | −2.32963e17 | −0.0734677 | ||||||||
\(703\) | 7.30824e17 | 0.228351 | ||||||||
\(704\) | 1.11310e17 | 0.0344597 | ||||||||
\(705\) | 3.08379e17 | 0.0945923 | ||||||||
\(706\) | 1.33694e18 | 0.406332 | ||||||||
\(707\) | 2.45370e18 | 0.738917 | ||||||||
\(708\) | −1.55467e18 | −0.463897 | ||||||||
\(709\) | 3.72211e18 | 1.10050 | 0.550248 | − | 0.835001i | \(-0.314533\pi\) | ||||
0.550248 | + | 0.835001i | \(0.314533\pi\) | |||||||
\(710\) | 9.48500e16 | 0.0277881 | ||||||||
\(711\) | 2.76778e18 | 0.803488 | ||||||||
\(712\) | −7.84921e17 | −0.225791 | ||||||||
\(713\) | 1.10571e18 | 0.315180 | ||||||||
\(714\) | −3.08479e18 | −0.871340 | ||||||||
\(715\) | −7.03063e16 | −0.0196791 | ||||||||
\(716\) | 1.26557e18 | 0.351035 | ||||||||
\(717\) | 8.09590e18 | 2.22531 | ||||||||
\(718\) | 1.57674e18 | 0.429489 | ||||||||
\(719\) | −2.69743e18 | −0.728135 | −0.364068 | − | 0.931373i | \(-0.618612\pi\) | ||||
−0.364068 | + | 0.931373i | \(0.618612\pi\) | |||||||
\(720\) | 1.18926e17 | 0.0318137 | ||||||||
\(721\) | 9.36665e18 | 2.48316 | ||||||||
\(722\) | −1.09184e18 | −0.286859 | ||||||||
\(723\) | −3.54237e18 | −0.922349 | ||||||||
\(724\) | −1.94288e18 | −0.501355 | ||||||||
\(725\) | −6.33552e18 | −1.62026 | ||||||||
\(726\) | −3.74827e18 | −0.950041 | ||||||||
\(727\) | −1.30338e18 | −0.327414 | −0.163707 | − | 0.986509i | \(-0.552345\pi\) | ||||
−0.163707 | + | 0.986509i | \(0.552345\pi\) | |||||||
\(728\) | −1.23603e18 | −0.307733 | ||||||||
\(729\) | −4.92006e18 | −1.21406 | ||||||||
\(730\) | 4.59795e17 | 0.112452 | ||||||||
\(731\) | 3.55946e18 | 0.862821 | ||||||||
\(732\) | 9.36114e17 | 0.224909 | ||||||||
\(733\) | 1.23214e18 | 0.293417 | 0.146708 | − | 0.989180i | \(-0.453132\pi\) | ||||
0.146708 | + | 0.989180i | \(0.453132\pi\) | |||||||
\(734\) | 3.38336e18 | 0.798591 | ||||||||
\(735\) | −6.66445e17 | −0.155918 | ||||||||
\(736\) | 6.50791e17 | 0.150916 | ||||||||
\(737\) | 1.54956e17 | 0.0356179 | ||||||||
\(738\) | 5.65148e18 | 1.28764 | ||||||||
\(739\) | −2.37998e18 | −0.537508 | −0.268754 | − | 0.963209i | \(-0.586612\pi\) | ||||
−0.268754 | + | 0.963209i | \(0.586612\pi\) | |||||||
\(740\) | −4.91251e16 | −0.0109976 | ||||||||
\(741\) | −4.85604e18 | −1.07762 | ||||||||
\(742\) | −5.02478e18 | −1.10533 | ||||||||
\(743\) | −1.71342e18 | −0.373626 | −0.186813 | − | 0.982396i | \(-0.559816\pi\) | ||||
−0.186813 | + | 0.982396i | \(0.559816\pi\) | |||||||
\(744\) | −8.78035e17 | −0.189796 | ||||||||
\(745\) | −3.51017e17 | −0.0752163 | ||||||||
\(746\) | 4.12524e17 | 0.0876289 | ||||||||
\(747\) | 4.42863e18 | 0.932578 | ||||||||
\(748\) | 4.01852e17 | 0.0838892 | ||||||||
\(749\) | −4.73950e18 | −0.980846 | ||||||||
\(750\) | −1.13717e18 | −0.233306 | ||||||||
\(751\) | 8.15576e18 | 1.65884 | 0.829421 | − | 0.558624i | \(-0.188671\pi\) | ||||
0.829421 | + | 0.558624i | \(0.188671\pi\) | |||||||
\(752\) | −7.06252e17 | −0.142411 | ||||||||
\(753\) | −6.35863e17 | −0.127115 | ||||||||
\(754\) | 3.66118e18 | 0.725617 | ||||||||
\(755\) | −8.27667e16 | −0.0162630 | ||||||||
\(756\) | 5.94047e17 | 0.115726 | ||||||||
\(757\) | −4.08819e18 | −0.789601 | −0.394800 | − | 0.918767i | \(-0.629186\pi\) | ||||
−0.394800 | + | 0.918767i | \(0.629186\pi\) | |||||||
\(758\) | 4.21624e18 | 0.807375 | ||||||||
\(759\) | 1.80247e18 | 0.342213 | ||||||||
\(760\) | 2.54305e17 | 0.0478703 | ||||||||
\(761\) | 4.83340e18 | 0.902094 | 0.451047 | − | 0.892500i | \(-0.351051\pi\) | ||||
0.451047 | + | 0.892500i | \(0.351051\pi\) | |||||||
\(762\) | 5.61684e18 | 1.03941 | ||||||||
\(763\) | 1.82337e18 | 0.334554 | ||||||||
\(764\) | −2.69701e18 | −0.490655 | ||||||||
\(765\) | 4.29347e17 | 0.0774478 | ||||||||
\(766\) | −5.67972e18 | −1.01587 | ||||||||
\(767\) | −2.24891e18 | −0.398844 | ||||||||
\(768\) | −5.16788e17 | −0.0908792 | ||||||||
\(769\) | −5.13768e18 | −0.895873 | −0.447936 | − | 0.894065i | \(-0.647841\pi\) | ||||
−0.447936 | + | 0.894065i | \(0.647841\pi\) | |||||||
\(770\) | 1.79278e17 | 0.0309983 | ||||||||
\(771\) | −8.43654e17 | −0.144647 | ||||||||
\(772\) | 8.60539e17 | 0.146305 | ||||||||
\(773\) | −2.81948e18 | −0.475337 | −0.237669 | − | 0.971346i | \(-0.576383\pi\) | ||||
−0.237669 | + | 0.971346i | \(0.576383\pi\) | |||||||
\(774\) | −6.68181e18 | −1.11706 | ||||||||
\(775\) | 2.19790e18 | 0.364374 | ||||||||
\(776\) | −1.14884e18 | −0.188869 | ||||||||
\(777\) | −2.39202e18 | −0.389967 | ||||||||
\(778\) | −4.01577e18 | −0.649235 | ||||||||
\(779\) | 1.20848e19 | 1.93752 | ||||||||
\(780\) | 3.26417e17 | 0.0518989 | ||||||||
\(781\) | −6.01642e17 | −0.0948652 | ||||||||
\(782\) | 2.34949e18 | 0.367393 | ||||||||
\(783\) | −1.75960e18 | −0.272874 | ||||||||
\(784\) | 1.52630e18 | 0.234738 | ||||||||
\(785\) | −9.07816e17 | −0.138467 | ||||||||
\(786\) | −1.21844e19 | −1.84314 | ||||||||
\(787\) | −5.90600e18 | −0.886050 | −0.443025 | − | 0.896509i | \(-0.646095\pi\) | ||||
−0.443025 | + | 0.896509i | \(0.646095\pi\) | |||||||
\(788\) | 6.41266e18 | 0.954153 | ||||||||
\(789\) | 1.48526e19 | 2.19181 | ||||||||
\(790\) | −3.97834e17 | −0.0582271 | ||||||||
\(791\) | −1.24677e19 | −1.80983 | ||||||||
\(792\) | −7.54357e17 | −0.108608 | ||||||||
\(793\) | 1.35414e18 | 0.193370 | ||||||||
\(794\) | 6.31207e18 | 0.894002 | ||||||||
\(795\) | 1.32697e18 | 0.186413 | ||||||||
\(796\) | 1.50243e18 | 0.209343 | ||||||||
\(797\) | 6.00465e18 | 0.829867 | 0.414933 | − | 0.909852i | \(-0.363805\pi\) | ||||
0.414933 | + | 0.909852i | \(0.363805\pi\) | |||||||
\(798\) | 1.23827e19 | 1.69745 | ||||||||
\(799\) | −2.54972e18 | −0.346687 | ||||||||
\(800\) | 1.29363e18 | 0.174471 | ||||||||
\(801\) | 5.31948e18 | 0.711636 | ||||||||
\(802\) | 2.34296e17 | 0.0310908 | ||||||||
\(803\) | −2.91652e18 | −0.383897 | ||||||||
\(804\) | −7.19426e17 | −0.0939338 | ||||||||
\(805\) | 1.04818e18 | 0.135757 | ||||||||
\(806\) | −1.27013e18 | −0.163181 | ||||||||
\(807\) | −9.29124e18 | −1.18412 | ||||||||
\(808\) | 1.48402e18 | 0.187615 | ||||||||
\(809\) | −1.03281e19 | −1.29525 | −0.647624 | − | 0.761960i | \(-0.724237\pi\) | ||||
−0.647624 | + | 0.761960i | \(0.724237\pi\) | |||||||
\(810\) | 5.66410e17 | 0.0704658 | ||||||||
\(811\) | 2.37489e18 | 0.293094 | 0.146547 | − | 0.989204i | \(-0.453184\pi\) | ||||
0.146547 | + | 0.989204i | \(0.453184\pi\) | |||||||
\(812\) | −9.33586e18 | −1.14298 | ||||||||
\(813\) | 9.02308e17 | 0.109589 | ||||||||
\(814\) | 3.11605e17 | 0.0375445 | ||||||||
\(815\) | −5.64718e17 | −0.0675005 | ||||||||
\(816\) | −1.86571e18 | −0.221238 | ||||||||
\(817\) | −1.42880e19 | −1.68085 | ||||||||
\(818\) | −9.06717e18 | −1.05822 | ||||||||
\(819\) | 8.37668e18 | 0.969899 | ||||||||
\(820\) | −8.12329e17 | −0.0933129 | ||||||||
\(821\) | 6.17741e18 | 0.704006 | 0.352003 | − | 0.935999i | \(-0.385501\pi\) | ||||
0.352003 | + | 0.935999i | \(0.385501\pi\) | |||||||
\(822\) | 5.93845e18 | 0.671438 | ||||||||
\(823\) | −3.84246e18 | −0.431033 | −0.215516 | − | 0.976500i | \(-0.569143\pi\) | ||||
−0.215516 | + | 0.976500i | \(0.569143\pi\) | |||||||
\(824\) | 5.66504e18 | 0.630487 | ||||||||
\(825\) | 3.58291e18 | 0.395626 | ||||||||
\(826\) | 5.73463e18 | 0.628254 | ||||||||
\(827\) | 1.35926e19 | 1.47746 | 0.738731 | − | 0.674001i | \(-0.235426\pi\) | ||||
0.738731 | + | 0.674001i | \(0.235426\pi\) | |||||||
\(828\) | −4.41047e18 | −0.475650 | ||||||||
\(829\) | 4.07966e17 | 0.0436536 | 0.0218268 | − | 0.999762i | \(-0.493052\pi\) | ||||
0.0218268 | + | 0.999762i | \(0.493052\pi\) | |||||||
\(830\) | −6.36559e17 | −0.0675820 | ||||||||
\(831\) | −7.21395e18 | −0.759917 | ||||||||
\(832\) | −7.47562e17 | −0.0781350 | ||||||||
\(833\) | 5.51025e18 | 0.571451 | ||||||||
\(834\) | 2.52490e18 | 0.259815 | ||||||||
\(835\) | 2.22642e17 | 0.0227324 | ||||||||
\(836\) | −1.61308e18 | −0.163424 | ||||||||
\(837\) | 6.10435e17 | 0.0613655 | ||||||||
\(838\) | −9.24094e18 | −0.921785 | ||||||||
\(839\) | 4.60930e18 | 0.456229 | 0.228114 | − | 0.973634i | \(-0.426744\pi\) | ||||
0.228114 | + | 0.973634i | \(0.426744\pi\) | |||||||
\(840\) | −8.32351e17 | −0.0817506 | ||||||||
\(841\) | 1.73927e19 | 1.69509 | ||||||||
\(842\) | −8.45883e18 | −0.818054 | ||||||||
\(843\) | −2.10070e19 | −2.01598 | ||||||||
\(844\) | 5.50849e18 | 0.524574 | ||||||||
\(845\) | −7.36291e17 | −0.0695794 | ||||||||
\(846\) | 4.78633e18 | 0.448844 | ||||||||
\(847\) | 1.38261e19 | 1.28664 | ||||||||
\(848\) | −3.03904e18 | −0.280649 | ||||||||
\(849\) | −3.89683e18 | −0.357118 | ||||||||
\(850\) | 4.67026e18 | 0.424735 | ||||||||
\(851\) | 1.82185e18 | 0.164426 | ||||||||
\(852\) | 2.79330e18 | 0.250184 | ||||||||
\(853\) | −5.13496e18 | −0.456424 | −0.228212 | − | 0.973612i | \(-0.573288\pi\) | ||||
−0.228212 | + | 0.973612i | \(0.573288\pi\) | |||||||
\(854\) | −3.45300e18 | −0.304594 | ||||||||
\(855\) | −1.72345e18 | −0.150875 | ||||||||
\(856\) | −2.86650e18 | −0.249042 | ||||||||
\(857\) | 8.29128e18 | 0.714901 | 0.357451 | − | 0.933932i | \(-0.383646\pi\) | ||||
0.357451 | + | 0.933932i | \(0.383646\pi\) | |||||||
\(858\) | −2.07050e18 | −0.177177 | ||||||||
\(859\) | −6.79619e17 | −0.0577179 | −0.0288589 | − | 0.999583i | \(-0.509187\pi\) | ||||
−0.0288589 | + | 0.999583i | \(0.509187\pi\) | |||||||
\(860\) | 9.60426e17 | 0.0809514 | ||||||||
\(861\) | −3.95542e19 | −3.30881 | ||||||||
\(862\) | 1.15543e19 | 0.959279 | ||||||||
\(863\) | −2.11875e19 | −1.74586 | −0.872929 | − | 0.487846i | \(-0.837783\pi\) | ||||
−0.872929 | + | 0.487846i | \(0.837783\pi\) | |||||||
\(864\) | 3.59286e17 | 0.0293833 | ||||||||
\(865\) | 5.05840e17 | 0.0410590 | ||||||||
\(866\) | 8.54802e18 | 0.688651 | ||||||||
\(867\) | 1.14492e19 | 0.915483 | ||||||||
\(868\) | 3.23877e18 | 0.257041 | ||||||||
\(869\) | 2.52349e18 | 0.198781 | ||||||||
\(870\) | 2.46547e18 | 0.192763 | ||||||||
\(871\) | −1.04069e18 | −0.0807613 | ||||||||
\(872\) | 1.10279e18 | 0.0849448 | ||||||||
\(873\) | 7.78582e18 | 0.595267 | ||||||||
\(874\) | −9.43112e18 | −0.715713 | ||||||||
\(875\) | 4.19462e18 | 0.315966 | ||||||||
\(876\) | 1.35408e19 | 1.01244 | ||||||||
\(877\) | 5.29243e18 | 0.392788 | 0.196394 | − | 0.980525i | \(-0.437077\pi\) | ||||
0.196394 | + | 0.980525i | \(0.437077\pi\) | |||||||
\(878\) | −1.50136e19 | −1.10604 | ||||||||
\(879\) | 3.65455e19 | 2.67243 | ||||||||
\(880\) | 1.08429e17 | 0.00787063 | ||||||||
\(881\) | 2.31832e18 | 0.167043 | 0.0835217 | − | 0.996506i | \(-0.473383\pi\) | ||||
0.0835217 | + | 0.996506i | \(0.473383\pi\) | |||||||
\(882\) | −1.03438e19 | −0.739837 | ||||||||
\(883\) | 1.38961e19 | 0.986615 | 0.493307 | − | 0.869855i | \(-0.335788\pi\) | ||||
0.493307 | + | 0.869855i | \(0.335788\pi\) | |||||||
\(884\) | −2.69886e18 | −0.190213 | ||||||||
\(885\) | −1.51443e18 | −0.105954 | ||||||||
\(886\) | 8.09739e18 | 0.562375 | ||||||||
\(887\) | −1.68484e19 | −1.16159 | −0.580797 | − | 0.814048i | \(-0.697259\pi\) | ||||
−0.580797 | + | 0.814048i | \(0.697259\pi\) | |||||||
\(888\) | −1.44672e18 | −0.0990146 | ||||||||
\(889\) | −2.07186e19 | −1.40766 | ||||||||
\(890\) | −7.64608e17 | −0.0515708 | ||||||||
\(891\) | −3.59279e18 | −0.240562 | ||||||||
\(892\) | −8.35924e18 | −0.555642 | ||||||||
\(893\) | 1.02348e19 | 0.675378 | ||||||||
\(894\) | −1.03373e19 | −0.677195 | ||||||||
\(895\) | 1.23282e18 | 0.0801768 | ||||||||
\(896\) | 1.90625e18 | 0.123078 | ||||||||
\(897\) | −1.21055e19 | −0.775945 | ||||||||
\(898\) | 1.22628e19 | 0.780359 | ||||||||
\(899\) | −9.59340e18 | −0.606087 | ||||||||
\(900\) | −8.76702e18 | −0.549890 | ||||||||
\(901\) | −1.09716e19 | −0.683215 | ||||||||
\(902\) | 5.15268e18 | 0.318559 | ||||||||
\(903\) | 4.67654e19 | 2.87048 | ||||||||
\(904\) | −7.54058e18 | −0.459526 | ||||||||
\(905\) | −1.89260e18 | −0.114510 | ||||||||
\(906\) | −2.43745e18 | −0.146420 | ||||||||
\(907\) | −2.54854e19 | −1.52000 | −0.760000 | − | 0.649923i | \(-0.774801\pi\) | ||||
−0.760000 | + | 0.649923i | \(0.774801\pi\) | |||||||
\(908\) | 1.19601e18 | 0.0708233 | ||||||||
\(909\) | −1.00574e19 | −0.591315 | ||||||||
\(910\) | −1.20404e18 | −0.0702866 | ||||||||
\(911\) | −1.75641e19 | −1.01802 | −0.509010 | − | 0.860761i | \(-0.669988\pi\) | ||||
−0.509010 | + | 0.860761i | \(0.669988\pi\) | |||||||
\(912\) | 7.48918e18 | 0.430991 | ||||||||
\(913\) | 4.03775e18 | 0.230717 | ||||||||
\(914\) | 1.67836e19 | 0.952213 | ||||||||
\(915\) | 9.11888e17 | 0.0513694 | ||||||||
\(916\) | −1.15296e19 | −0.644903 | ||||||||
\(917\) | 4.49442e19 | 2.49616 | ||||||||
\(918\) | 1.29710e18 | 0.0715312 | ||||||||
\(919\) | 2.76291e18 | 0.151292 | 0.0756460 | − | 0.997135i | \(-0.475898\pi\) | ||||
0.0756460 | + | 0.997135i | \(0.475898\pi\) | |||||||
\(920\) | 6.33949e17 | 0.0344694 | ||||||||
\(921\) | 2.32457e19 | 1.25503 | ||||||||
\(922\) | 4.44775e18 | 0.238446 | ||||||||
\(923\) | 4.04066e18 | 0.215100 | ||||||||
\(924\) | 5.27968e18 | 0.279087 | ||||||||
\(925\) | 3.62143e18 | 0.190090 | ||||||||
\(926\) | 1.47967e19 | 0.771245 | ||||||||
\(927\) | −3.83925e19 | −1.98714 | ||||||||
\(928\) | −5.64642e18 | −0.290209 | ||||||||
\(929\) | −2.02252e19 | −1.03226 | −0.516131 | − | 0.856510i | \(-0.672628\pi\) | ||||
−0.516131 | + | 0.856510i | \(0.672628\pi\) | |||||||
\(930\) | −8.55313e17 | −0.0433497 | ||||||||
\(931\) | −2.21187e19 | −1.11324 | ||||||||
\(932\) | 1.79969e19 | 0.899486 | ||||||||
\(933\) | −1.99533e18 | −0.0990338 | ||||||||
\(934\) | −1.09294e19 | −0.538692 | ||||||||
\(935\) | 3.91453e17 | 0.0191604 | ||||||||
\(936\) | 5.06630e18 | 0.246262 | ||||||||
\(937\) | 9.12409e18 | 0.440436 | 0.220218 | − | 0.975451i | \(-0.429323\pi\) | ||||
0.220218 | + | 0.975451i | \(0.429323\pi\) | |||||||
\(938\) | 2.65372e18 | 0.127214 | ||||||||
\(939\) | −3.91772e19 | −1.86512 | ||||||||
\(940\) | −6.87975e17 | −0.0325268 | ||||||||
\(941\) | 9.47005e18 | 0.444651 | 0.222326 | − | 0.974972i | \(-0.428635\pi\) | ||||
0.222326 | + | 0.974972i | \(0.428635\pi\) | |||||||
\(942\) | −2.67348e19 | −1.24666 | ||||||||
\(943\) | 3.01260e19 | 1.39513 | ||||||||
\(944\) | 3.46836e18 | 0.159517 | ||||||||
\(945\) | 5.78674e17 | 0.0264318 | ||||||||
\(946\) | −6.09207e18 | −0.276358 | ||||||||
\(947\) | −1.07060e19 | −0.482340 | −0.241170 | − | 0.970483i | \(-0.577531\pi\) | ||||
−0.241170 | + | 0.970483i | \(0.577531\pi\) | |||||||
\(948\) | −1.17160e19 | −0.524236 | ||||||||
\(949\) | 1.95875e19 | 0.870460 | ||||||||
\(950\) | −1.87469e19 | −0.827422 | ||||||||
\(951\) | 5.52583e19 | 2.42228 | ||||||||
\(952\) | 6.88198e18 | 0.299622 | ||||||||
\(953\) | −1.17296e17 | −0.00507199 | −0.00253599 | − | 0.999997i | \(-0.500807\pi\) | ||||
−0.00253599 | + | 0.999997i | \(0.500807\pi\) | |||||||
\(954\) | 2.05958e19 | 0.884534 | ||||||||
\(955\) | −2.62722e18 | −0.112066 | ||||||||
\(956\) | −1.80614e19 | −0.765202 | ||||||||
\(957\) | −1.56387e19 | −0.658070 | ||||||||
\(958\) | −2.06643e19 | −0.863665 | ||||||||
\(959\) | −2.19049e19 | −0.909328 | ||||||||
\(960\) | −5.03414e17 | −0.0207569 | ||||||||
\(961\) | −2.10894e19 | −0.863700 | ||||||||
\(962\) | −2.09276e18 | −0.0851296 | ||||||||
\(963\) | 1.94265e19 | 0.784917 | ||||||||
\(964\) | 7.90281e18 | 0.317162 | ||||||||
\(965\) | 8.38269e17 | 0.0334161 | ||||||||
\(966\) | 3.08685e19 | 1.22226 | ||||||||
\(967\) | 1.48196e19 | 0.582860 | 0.291430 | − | 0.956592i | \(-0.405869\pi\) | ||||
0.291430 | + | 0.956592i | \(0.405869\pi\) | |||||||
\(968\) | 8.36214e18 | 0.326684 | ||||||||
\(969\) | 2.70375e19 | 1.04921 | ||||||||
\(970\) | −1.11911e18 | −0.0431378 | ||||||||
\(971\) | 3.03687e19 | 1.16279 | 0.581395 | − | 0.813622i | \(-0.302507\pi\) | ||||
0.581395 | + | 0.813622i | \(0.302507\pi\) | |||||||
\(972\) | 1.88657e19 | 0.717533 | ||||||||
\(973\) | −9.31348e18 | −0.351867 | ||||||||
\(974\) | 1.54599e18 | 0.0580196 | ||||||||
\(975\) | −2.40630e19 | −0.897055 | ||||||||
\(976\) | −2.08841e18 | −0.0773379 | ||||||||
\(977\) | −3.42204e19 | −1.25884 | −0.629419 | − | 0.777066i | \(-0.716707\pi\) | ||||
−0.629419 | + | 0.777066i | \(0.716707\pi\) | |||||||
\(978\) | −1.66307e19 | −0.607727 | ||||||||
\(979\) | 4.84998e18 | 0.176057 | ||||||||
\(980\) | 1.48680e18 | 0.0536145 | ||||||||
\(981\) | −7.47373e18 | −0.267725 | ||||||||
\(982\) | 2.95081e19 | 1.05007 | ||||||||
\(983\) | −2.19778e19 | −0.776939 | −0.388469 | − | 0.921462i | \(-0.626996\pi\) | ||||
−0.388469 | + | 0.921462i | \(0.626996\pi\) | |||||||
\(984\) | −2.39228e19 | −0.840124 | ||||||||
\(985\) | 6.24671e18 | 0.217929 | ||||||||
\(986\) | −2.03848e19 | −0.706490 | ||||||||
\(987\) | −3.34991e19 | −1.15338 | ||||||||
\(988\) | 1.08335e19 | 0.370552 | ||||||||
\(989\) | −3.56183e19 | −1.21031 | ||||||||
\(990\) | −7.34835e17 | −0.0248062 | ||||||||
\(991\) | 1.72348e19 | 0.578001 | 0.289000 | − | 0.957329i | \(-0.406677\pi\) | ||||
0.289000 | + | 0.957329i | \(0.406677\pi\) | |||||||
\(992\) | 1.95884e18 | 0.0652639 | ||||||||
\(993\) | −1.84459e19 | −0.610564 | ||||||||
\(994\) | −1.03035e19 | −0.338824 | ||||||||
\(995\) | 1.46355e18 | 0.0478142 | ||||||||
\(996\) | −1.87464e19 | −0.608461 | ||||||||
\(997\) | 5.30366e19 | 1.71024 | 0.855119 | − | 0.518431i | \(-0.173484\pi\) | ||||
0.855119 | + | 0.518431i | \(0.173484\pi\) | |||||||
\(998\) | 3.74501e19 | 1.19979 | ||||||||
\(999\) | 1.00580e18 | 0.0320137 |
(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 | 2.14.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 18.14.a.d.1.1 | 1 | |||
4.3 | odd | 2 | 16.14.a.d.1.1 | 1 | |||
5.2 | odd | 4 | 50.14.b.e.49.1 | 2 | |||
5.3 | odd | 4 | 50.14.b.e.49.2 | 2 | |||
5.4 | even | 2 | 50.14.a.e.1.1 | 1 | |||
7.2 | even | 3 | 98.14.c.h.67.1 | 2 | |||
7.3 | odd | 6 | 98.14.c.e.79.1 | 2 | |||
7.4 | even | 3 | 98.14.c.h.79.1 | 2 | |||
7.5 | odd | 6 | 98.14.c.e.67.1 | 2 | |||
7.6 | odd | 2 | 98.14.a.b.1.1 | 1 | |||
8.3 | odd | 2 | 64.14.a.a.1.1 | 1 | |||
8.5 | even | 2 | 64.14.a.i.1.1 | 1 | |||
12.11 | even | 2 | 144.14.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.14.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
16.14.a.d.1.1 | 1 | 4.3 | odd | 2 | |||
18.14.a.d.1.1 | 1 | 3.2 | odd | 2 | |||
50.14.a.e.1.1 | 1 | 5.4 | even | 2 | |||
50.14.b.e.49.1 | 2 | 5.2 | odd | 4 | |||
50.14.b.e.49.2 | 2 | 5.3 | odd | 4 | |||
64.14.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
64.14.a.i.1.1 | 1 | 8.5 | even | 2 | |||
98.14.a.b.1.1 | 1 | 7.6 | odd | 2 | |||
98.14.c.e.67.1 | 2 | 7.5 | odd | 6 | |||
98.14.c.e.79.1 | 2 | 7.3 | odd | 6 | |||
98.14.c.h.67.1 | 2 | 7.2 | even | 3 | |||
98.14.c.h.79.1 | 2 | 7.4 | even | 3 | |||
144.14.a.d.1.1 | 1 | 12.11 | even | 2 |