Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,18,Mod(1,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.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: | \(7.32888349378\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{9361}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 2340 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-47.8761\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 15636.4 | 1.37596 | 0.687982 | − | 0.725728i | \(-0.258497\pi\) | ||||
0.687982 | + | 0.725728i | \(0.258497\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −366730. | −0.419857 | −0.209928 | − | 0.977717i | \(-0.567323\pi\) | ||||
−0.209928 | + | 0.977717i | \(0.567323\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.37095e7 | 1.55449 | 0.777246 | − | 0.629196i | \(-0.216616\pi\) | ||||
0.777246 | + | 0.629196i | \(0.216616\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.15358e8 | 0.893277 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.33786e9 | 1.88180 | 0.940902 | − | 0.338679i | \(-0.109980\pi\) | ||||
0.940902 | + | 0.338679i | \(0.109980\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.68345e9 | −1.25238 | −0.626191 | − | 0.779670i | \(-0.715387\pi\) | ||||
−0.626191 | + | 0.779670i | \(0.715387\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.73434e9 | −0.577708 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.70006e10 | −0.591082 | −0.295541 | − | 0.955330i | \(-0.595500\pi\) | ||||
−0.295541 | + | 0.955330i | \(0.595500\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.59141e9 | −0.0350051 | −0.0175025 | − | 0.999847i | \(-0.505572\pi\) | ||||
−0.0175025 | + | 0.999847i | \(0.505572\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.70732e11 | 2.13893 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.96178e11 | −0.522353 | −0.261177 | − | 0.965291i | \(-0.584111\pi\) | ||||
−0.261177 | + | 0.965291i | \(0.584111\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.28449e11 | −0.823720 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.15505e11 | −0.146847 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.36209e12 | −0.505618 | −0.252809 | − | 0.967516i | \(-0.581354\pi\) | ||||
−0.252809 | + | 0.967516i | \(0.581354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.25575e12 | −0.475025 | −0.237512 | − | 0.971384i | \(-0.576332\pi\) | ||||
−0.237512 | + | 0.971384i | \(0.576332\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.09194e13 | 2.58929 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.69497e12 | −0.652664 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.28643e12 | 0.0602105 | 0.0301052 | − | 0.999547i | \(-0.490416\pi\) | ||||
0.0301052 | + | 0.999547i | \(0.490416\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.75961e13 | −1.72323 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.74268e13 | 0.732014 | 0.366007 | − | 0.930612i | \(-0.380725\pi\) | ||||
0.366007 | + | 0.930612i | \(0.380725\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.61921e13 | −0.341734 | −0.170867 | − | 0.985294i | \(-0.554657\pi\) | ||||
−0.170867 | + | 0.985294i | \(0.554657\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.23052e13 | −0.375048 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.94586e14 | 1.19201 | 0.596006 | − | 0.802980i | \(-0.296754\pi\) | ||||
0.596006 | + | 0.802980i | \(0.296754\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.29509e14 | 1.41645 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.65829e14 | −0.813308 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.69769e14 | −1.03643 | −0.518214 | − | 0.855251i | \(-0.673403\pi\) | ||||
−0.518214 | + | 0.855251i | \(0.673403\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.90635e14 | −0.790088 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.05205e13 | −0.0481657 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.58789e15 | 1.40792 | 0.703962 | − | 0.710238i | \(-0.251413\pi\) | ||||
0.703962 | + | 0.710238i | \(0.251413\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.16562e15 | −1.44637 | −0.723183 | − | 0.690656i | \(-0.757322\pi\) | ||||
−0.723183 | + | 0.690656i | \(0.757322\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.73508e15 | 1.38859 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.35083e15 | 0.525821 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.54302e15 | 0.464232 | 0.232116 | − | 0.972688i | \(-0.425435\pi\) | ||||
0.232116 | + | 0.972688i | \(0.425435\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.06753e15 | −0.718739 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.51083e15 | −0.829011 | −0.414506 | − | 0.910047i | \(-0.636046\pi\) | ||||
−0.414506 | + | 0.910047i | \(0.636046\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.24410e15 | −0.906203 | −0.453101 | − | 0.891459i | \(-0.649682\pi\) | ||||
−0.453101 | + | 0.891459i | \(0.649682\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.82670e15 | −1.13341 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.17201e16 | 2.92525 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.95599e14 | −0.0590016 | −0.0295008 | − | 0.999565i | \(-0.509392\pi\) | ||||
−0.0295008 | + | 0.999565i | \(0.509392\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.82671e16 | −1.09533 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.62699e16 | 1.28025 | 0.640125 | − | 0.768271i | \(-0.278883\pi\) | ||||
0.640125 | + | 0.768271i | \(0.278883\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.23462e15 | 0.248170 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.12982e16 | −0.695712 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.01291e16 | 0.811280 | 0.405640 | − | 0.914033i | \(-0.367049\pi\) | ||||
0.405640 | + | 0.914033i | \(0.367049\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.73327e16 | −1.94682 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.52719e16 | −0.653617 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.50348e14 | 0.0146971 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.38333e16 | 0.438314 | 0.219157 | − | 0.975690i | \(-0.429669\pi\) | ||||
0.219157 | + | 0.975690i | \(0.429669\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.54333e17 | 1.68097 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.50280e16 | 0.505653 | 0.252826 | − | 0.967512i | \(-0.418640\pi\) | ||||
0.252826 | + | 0.967512i | \(0.418640\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.99690e16 | −0.233107 | −0.116554 | − | 0.993184i | \(-0.537185\pi\) | ||||
−0.116554 | + | 0.993184i | \(0.537185\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.35958e17 | −0.898042 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.83477e17 | 1.03233 | 0.516166 | − | 0.856489i | \(-0.327359\pi\) | ||||
0.516166 | + | 0.856489i | \(0.327359\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.65387e17 | −1.27572 | −0.637859 | − | 0.770153i | \(-0.720180\pi\) | ||||
−0.637859 | + | 0.770153i | \(0.720180\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.01152e16 | 0.0828475 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.05318e17 | −0.372681 | −0.186341 | − | 0.982485i | \(-0.559663\pi\) | ||||
−0.186341 | + | 0.982485i | \(0.559663\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.19444e16 | 0.219313 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.24915e17 | −1.11872 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.03075e17 | −0.918833 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.28444e18 | 2.54119 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.85221e17 | 1.00723 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.10263e17 | 0.765701 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.92218e17 | −1.03875 | −0.519377 | − | 0.854545i | \(-0.673836\pi\) | ||||
−0.519377 | + | 0.854545i | \(0.673836\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.09551e17 | −0.470213 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.17088e17 | −0.722381 | −0.361191 | − | 0.932492i | \(-0.617630\pi\) | ||||
−0.361191 | + | 0.932492i | \(0.617630\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.14411e16 | −0.0544152 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.90322e16 | 0.0616548 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.94843e18 | −1.34141 | −0.670703 | − | 0.741726i | \(-0.734008\pi\) | ||||
−0.670703 | + | 0.741726i | \(0.734008\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.23071e18 | 0.749085 | 0.374543 | − | 0.927210i | \(-0.377800\pi\) | ||||
0.374543 | + | 0.927210i | \(0.377800\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.04264e18 | 1.64016 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.92796e18 | −2.35674 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.99518e17 | 0.212287 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.15235e18 | 1.94898 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.33643e18 | 0.787898 | 0.393949 | − | 0.919132i | \(-0.371109\pi\) | ||||
0.393949 | + | 0.919132i | \(0.371109\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.57631e17 | 0.167897 | 0.0839485 | − | 0.996470i | \(-0.473247\pi\) | ||||
0.0839485 | + | 0.996470i | \(0.473247\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.96115e18 | −0.528000 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.27250e17 | 0.199442 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.14946e18 | −1.11331 | −0.556653 | − | 0.830745i | \(-0.687915\pi\) | ||||
−0.556653 | + | 0.830745i | \(0.687915\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.34551e18 | −1.42609 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.65129e18 | −0.811994 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.04483e19 | 1.64230 | 0.821148 | − | 0.570715i | \(-0.193334\pi\) | ||||
0.821148 | + | 0.570715i | \(0.193334\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.67178e18 | −1.08713 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.10713e19 | 1.41614 | 0.708071 | − | 0.706141i | \(-0.249565\pi\) | ||||
0.708071 | + | 0.706141i | \(0.249565\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.91741e18 | 0.568459 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.98940e17 | −0.0312692 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.38307e18 | −0.131055 | −0.0655274 | − | 0.997851i | \(-0.520873\pi\) | ||||
−0.0655274 | + | 0.997851i | \(0.520873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.49002e19 | −1.28047 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.48290e19 | 1.93725 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.50209e19 | 1.06524 | 0.532618 | − | 0.846356i | \(-0.321208\pi\) | ||||
0.532618 | + | 0.846356i | \(0.321208\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.60783e17 | −0.0232798 | −0.0116399 | − | 0.999932i | \(-0.503705\pi\) | ||||
−0.0116399 | + | 0.999932i | \(0.503705\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.38625e19 | −1.99015 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.71773e17 | −0.0252798 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.27445e19 | −1.11230 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.10952e18 | −0.228273 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.97904e18 | 0.366814 | 0.183407 | − | 0.983037i | \(-0.441287\pi\) | ||||
0.183407 | + | 0.983037i | \(0.441287\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.87785e19 | −1.07605 | −0.538023 | − | 0.842930i | \(-0.680829\pi\) | ||||
−0.538023 | + | 0.842930i | \(0.680829\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.11222e19 | 0.723510 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.29790e19 | 1.66395 | 0.831977 | − | 0.554811i | \(-0.187209\pi\) | ||||
0.831977 | + | 0.554811i | \(0.187209\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.52925e19 | 0.729021 | 0.364510 | − | 0.931199i | \(-0.381236\pi\) | ||||
0.364510 | + | 0.931199i | \(0.381236\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.41273e19 | 0.638767 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.22944e19 | −0.785979 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.37255e19 | −0.307341 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.26307e19 | −0.466606 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.46696e18 | −0.0658727 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.87338e19 | 1.20440 | 0.602198 | − | 0.798346i | \(-0.294292\pi\) | ||||
0.602198 | + | 0.798346i | \(0.294292\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.05333e19 | −1.14069 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.60541e18 | 0.143479 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.34826e19 | −0.738423 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.76354e19 | −1.24690 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.26208e19 | 0.740260 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.40564e18 | −0.0482412 | −0.0241206 | − | 0.999709i | \(-0.507679\pi\) | ||||
−0.0241206 | + | 0.999709i | \(0.507679\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.24965e19 | −0.735810 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.27911e19 | 0.308700 | 0.154350 | − | 0.988016i | \(-0.450672\pi\) | ||||
0.154350 | + | 0.988016i | \(0.450672\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.54497e19 | 0.834013 | 0.417006 | − | 0.908904i | \(-0.363079\pi\) | ||||
0.417006 | + | 0.908904i | \(0.363079\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.95989e20 | 4.02504 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.07634e20 | −1.56593 | −0.782965 | − | 0.622066i | \(-0.786294\pi\) | ||||
−0.782965 | + | 0.622066i | \(0.786294\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.13605e19 | −0.500474 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.24403e19 | −0.0811841 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.76425e20 | −1.67956 | −0.839780 | − | 0.542927i | \(-0.817316\pi\) | ||||
−0.839780 | + | 0.542927i | \(0.817316\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.35403e20 | 1.33250 | 0.666249 | − | 0.745730i | \(-0.267899\pi\) | ||||
0.666249 | + | 0.745730i | \(0.267899\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.57802e20 | −1.36029 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.20841e20 | −0.594705 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.54535e18 | 0.0438397 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.10768e20 | 1.76158 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.91593e20 | −1.56895 | −0.784473 | − | 0.620163i | \(-0.787067\pi\) | ||||
−0.784473 | + | 0.620163i | \(0.787067\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.62460e20 | −0.982967 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.74872e19 | 0.341473 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.14828e20 | 1.35968 | 0.679839 | − | 0.733361i | \(-0.262049\pi\) | ||||
0.679839 | + | 0.733361i | \(0.262049\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.05006e19 | 0.0935968 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.57128e20 | −0.451657 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.82407e19 | 0.264647 | 0.132324 | − | 0.991207i | \(-0.457756\pi\) | ||||
0.132324 | + | 0.991207i | \(0.457756\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.72278e20 | 0.435151 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.71112e20 | 1.11629 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.22922e20 | 1.16290 | 0.581450 | − | 0.813582i | \(-0.302486\pi\) | ||||
0.581450 | + | 0.813582i | \(0.302486\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.47142e20 | 0.933698 | 0.466849 | − | 0.884337i | \(-0.345389\pi\) | ||||
0.466849 | + | 0.884337i | \(0.345389\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.36557e21 | −2.67875 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.40780e20 | −1.55008 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.36272e20 | −0.236226 | −0.118113 | − | 0.993000i | \(-0.537684\pi\) | ||||
−0.118113 | + | 0.993000i | \(0.537684\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.60219e20 | −0.424329 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.26390e20 | 0.193958 | 0.0969790 | − | 0.995286i | \(-0.469082\pi\) | ||||
0.0969790 | + | 0.995286i | \(0.469082\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.81664e19 | −0.141833 | −0.0709167 | − | 0.997482i | \(-0.522592\pi\) | ||||
−0.0709167 | + | 0.997482i | \(0.522592\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.48601e19 | 0.0202227 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.87370e20 | 1.13791 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.38220e20 | −0.650622 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.29033e20 | 0.603104 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.01600e21 | 1.09275 | 0.546374 | − | 0.837541i | \(-0.316008\pi\) | ||||
0.546374 | + | 0.837541i | \(0.316008\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.82327e20 | −0.591126 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.88317e20 | −0.276338 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.22613e20 | 0.654185 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.21000e20 | −0.531223 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.60442e20 | 0.695760 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.94196e20 | 0.607266 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.04896e21 | 0.758720 | 0.379360 | − | 0.925249i | \(-0.376144\pi\) | ||||
0.379360 | + | 0.925249i | \(0.376144\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.68609e20 | −0.320747 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.73873e21 | −1.12660 | −0.563298 | − | 0.826254i | \(-0.690468\pi\) | ||||
−0.563298 | + | 0.826254i | \(0.690468\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.56401e21 | −1.57323 | −0.786616 | − | 0.617443i | \(-0.788169\pi\) | ||||
−0.786616 | + | 0.617443i | \(0.788169\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.00303e21 | −0.583010 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.06492e20 | −0.168817 | −0.0844084 | − | 0.996431i | \(-0.526900\pi\) | ||||
−0.0844084 | + | 0.996431i | \(0.526900\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.82229e21 | −0.951474 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.86892e21 | 1.42045 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.40556e19 | 0.0206909 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.31486e21 | 1.03161 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.14971e21 | −1.75534 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.61354e21 | 1.85297 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.66802e21 | 1.78072 | 0.890359 | − | 0.455259i | \(-0.150453\pi\) | ||||
0.890359 | + | 0.455259i | \(0.150453\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.48400e20 | 0.0537846 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.65871e20 | −0.194911 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.64491e21 | −0.538626 | −0.269313 | − | 0.963053i | \(-0.586797\pi\) | ||||
−0.269313 | + | 0.963053i | \(0.586797\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.64681e21 | −0.512796 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.01789e21 | −0.893904 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.29694e21 | 0.647365 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.12495e21 | 0.301767 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.19804e20 | −0.234906 | −0.117453 | − | 0.993078i | \(-0.537473\pi\) | ||||
−0.117453 | + | 0.993078i | \(0.537473\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.23910e21 | −0.301363 | −0.150681 | − | 0.988582i | \(-0.548147\pi\) | ||||
−0.150681 | + | 0.988582i | \(0.548147\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.93804e20 | 0.183909 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.26089e21 | −0.499109 | −0.249554 | − | 0.968361i | \(-0.580284\pi\) | ||||
−0.249554 | + | 0.968361i | \(0.580284\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.65426e21 | 0.348066 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.30266e21 | −1.26428 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.96795e21 | −1.90679 | −0.953395 | − | 0.301725i | \(-0.902438\pi\) | ||||
−0.953395 | + | 0.301725i | \(0.902438\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.47367e21 | −0.998775 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.00840e22 | 3.49658 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.28990e21 | 0.380475 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.17139e21 | 0.820248 | 0.410124 | − | 0.912030i | \(-0.365485\pi\) | ||||
0.410124 | + | 0.912030i | \(0.365485\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.31748e21 | 0.653892 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.11380e22 | −1.61112 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.06342e22 | 1.46954 | 0.734769 | − | 0.678317i | \(-0.237290\pi\) | ||||
0.734769 | + | 0.678317i | \(0.237290\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.97870e21 | 1.05358 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.01719e21 | 0.633226 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.81105e21 | −0.821827 | −0.410914 | − | 0.911674i | \(-0.634790\pi\) | ||||
−0.410914 | + | 0.911674i | \(0.634790\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.23875e22 | −1.42929 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.65462e21 | −0.734402 | −0.367201 | − | 0.930142i | \(-0.619684\pi\) | ||||
−0.367201 | + | 0.930142i | \(0.619684\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.16327e22 | −1.22819 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.02146e21 | −0.305263 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.61442e22 | 1.56115 | 0.780574 | − | 0.625063i | \(-0.214927\pi\) | ||||
0.780574 | + | 0.625063i | \(0.214927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.33515e21 | 0.308754 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.12127e22 | −0.993971 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.91770e20 | 0.0247722 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.02258e21 | 0.0831725 | 0.0415862 | − | 0.999135i | \(-0.486759\pi\) | ||||
0.0415862 | + | 0.999135i | \(0.486759\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.60719e20 | −0.0748733 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.32825e22 | −0.992095 | −0.496047 | − | 0.868295i | \(-0.665216\pi\) | ||||
−0.496047 | + | 0.868295i | \(0.665216\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.30895e21 | 0.594912 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.69908e21 | 0.459883 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.72107e21 | 0.113304 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.58540e22 | 1.63260 | 0.816300 | − | 0.577628i | \(-0.196022\pi\) | ||||
0.816300 | + | 0.577628i | \(0.196022\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.04665e22 | −1.84573 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.76481e22 | 2.18861 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.63395e21 | −0.537521 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.92440e22 | 1.03071 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.13941e22 | 0.585951 | 0.292975 | − | 0.956120i | \(-0.405355\pi\) | ||||
0.292975 | + | 0.956120i | \(0.405355\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.96045e22 | −1.46204 | −0.731021 | − | 0.682354i | \(-0.760956\pi\) | ||||
−0.731021 | + | 0.682354i | \(0.760956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.24471e22 | 1.06480 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.06840e22 | 0.486887 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.13457e22 | −2.24837 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.70557e22 | −3.24278 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.85742e22 | 0.751369 | 0.375684 | − | 0.926748i | \(-0.377408\pi\) | ||||
0.375684 | + | 0.926748i | \(0.377408\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.71171e21 | 0.0665707 | 0.0332854 | − | 0.999446i | \(-0.489403\pi\) | ||||
0.0332854 | + | 0.999446i | \(0.489403\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.81068e21 | 0.292099 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.08379e20 | 0.0182850 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.04484e22 | 1.05346 | 0.526728 | − | 0.850034i | \(-0.323419\pi\) | ||||
0.526728 | + | 0.850034i | \(0.323419\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.80115e22 | 1.26528 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.23180e22 | −0.714864 | −0.357432 | − | 0.933939i | \(-0.616348\pi\) | ||||
−0.357432 | + | 0.933939i | \(0.616348\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.10492e22 | −0.340621 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.65335e22 | 1.08412 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.77731e22 | −1.65056 | −0.825281 | − | 0.564723i | \(-0.808983\pi\) | ||||
−0.825281 | + | 0.564723i | \(0.808983\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.00720e22 | 1.37751 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.71936e21 | 0.231020 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.20275e22 | 0.817384 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.47877e22 | −1.10121 | −0.550606 | − | 0.834766i | \(-0.685603\pi\) | ||||
−0.550606 | + | 0.834766i | \(0.685603\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.66372e21 | 0.0867989 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.44258e22 | 1.69928 | 0.849641 | − | 0.527361i | \(-0.176818\pi\) | ||||
0.849641 | + | 0.527361i | \(0.176818\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.47065e22 | −0.763787 | −0.381893 | − | 0.924206i | \(-0.624728\pi\) | ||||
−0.381893 | + | 0.924206i | \(0.624728\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.29352e22 | 0.274425 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.07656e22 | −0.629321 | −0.314661 | − | 0.949204i | \(-0.601891\pi\) | ||||
−0.314661 | + | 0.949204i | \(0.601891\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.65842e22 | 0.721646 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.05192e22 | −1.53187 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.50414e22 | −0.643076 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.62857e21 | 0.0288344 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.41916e22 | −0.925817 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.50857e22 | −0.413595 | −0.206797 | − | 0.978384i | \(-0.566304\pi\) | ||||
−0.206797 | + | 0.978384i | \(0.566304\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.73851e21 | −0.0754065 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.27295e22 | −1.11728 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.24077e22 | −0.184029 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.25508e23 | 1.79752 | 0.898761 | − | 0.438439i | \(-0.144468\pi\) | ||||
0.898761 | + | 0.438439i | \(0.144468\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.63374e23 | 2.25974 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.29654e22 | 0.707619 | 0.353809 | − | 0.935318i | \(-0.384886\pi\) | ||||
0.353809 | + | 0.935318i | \(0.384886\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.31563e22 | 0.298862 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.65986e22 | −0.705767 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.06949e23 | −1.28869 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.81497e22 | 0.327807 | 0.163904 | − | 0.986476i | \(-0.447591\pi\) | ||||
0.163904 | + | 0.986476i | \(0.447591\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.73115e23 | 1.94856 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.42160e22 | −0.589929 | −0.294964 | − | 0.955508i | \(-0.595308\pi\) | ||||
−0.294964 | + | 0.955508i | \(0.595308\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.01804e22 | −0.212302 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.68907e22 | 0.782179 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.78224e23 | −1.75333 | −0.876666 | − | 0.481099i | \(-0.840238\pi\) | ||||
−0.876666 | + | 0.481099i | \(0.840238\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.48044e23 | −1.40869 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.58463e20 | 0.00514040 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.09905e22 | 0.0978717 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.60330e23 | 2.24313 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.16263e22 | −0.180327 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.94263e22 | −0.156773 | −0.0783863 | − | 0.996923i | \(-0.524977\pi\) | ||||
−0.0783863 | + | 0.996923i | \(0.524977\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.65768e23 | −1.29490 | −0.647451 | − | 0.762107i | \(-0.724165\pi\) | ||||
−0.647451 | + | 0.762107i | \(0.724165\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.32986e23 | −1.76188 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.83491e22 | 0.280779 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.02564e23 | −0.727147 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.83176e23 | 1.25767 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.37860e23 | −0.916761 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.72864e22 | −0.433431 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.34874e23 | 1.46573 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.40839e23 | 2.66548 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.94676e22 | 0.172650 | 0.0863251 | − | 0.996267i | \(-0.472488\pi\) | ||||
0.0863251 | + | 0.996267i | \(0.472488\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.64137e21 | −0.0320321 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.73253e22 | 0.535618 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00474e22 | 0.427027 | 0.213513 | − | 0.976940i | \(-0.431509\pi\) | ||||
0.213513 | + | 0.976940i | \(0.431509\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.49821e23 | −1.29201 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.52974e21 | 0.0176992 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.88632e22 | −0.0917176 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.37684e21 | −0.0347840 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.60669e23 | −0.734790 | −0.367395 | − | 0.930065i | \(-0.619750\pi\) | ||||
−0.367395 | + | 0.930065i | \(0.619750\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.64772e22 | 0.427981 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.55643e23 | −1.53049 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.05044e22 | −0.377875 | −0.188937 | − | 0.981989i | \(-0.560504\pi\) | ||||
−0.188937 | + | 0.981989i | \(0.560504\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.86234e22 | 0.156473 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.33103e23 | −1.70269 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.23350e23 | 1.61527 | 0.807635 | − | 0.589683i | \(-0.200747\pi\) | ||||
0.807635 | + | 0.589683i | \(0.200747\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.34739e21 | 0.00498985 | 0.00249493 | − | 0.999997i | \(-0.499206\pi\) | ||||
0.00249493 | + | 0.999997i | \(0.499206\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.40400e23 | 0.504723 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.23288e23 | 0.430273 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.74144e22 | −0.160663 | −0.0803315 | − | 0.996768i | \(-0.525598\pi\) | ||||
−0.0803315 | + | 0.996768i | \(0.525598\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.49993e23 | −1.48060 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.22846e23 | 1.99014 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.28487e23 | −1.95036 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.55829e23 | 0.469703 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.06143e23 | 0.310790 | 0.155395 | − | 0.987852i | \(-0.450335\pi\) | ||||
0.155395 | + | 0.987852i | \(0.450335\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.84558e21 | 0.0166283 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.28403e23 | 2.28954 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.00230e23 | −0.806285 | −0.403142 | − | 0.915137i | \(-0.632082\pi\) | ||||
−0.403142 | + | 0.915137i | \(0.632082\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.47820e23 | 0.385778 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.95484e23 | 1.00311 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.55455e23 | 0.383246 | 0.191623 | − | 0.981469i | \(-0.438625\pi\) | ||||
0.191623 | + | 0.981469i | \(0.438625\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.11005e22 | −0.170388 | −0.0851941 | − | 0.996364i | \(-0.527151\pi\) | ||||
−0.0851941 | + | 0.996364i | \(0.527151\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.77999e23 | 0.414688 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.71041e23 | −1.06693 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.07763e23 | −0.457576 | −0.228788 | − | 0.973476i | \(-0.573476\pi\) | ||||
−0.228788 | + | 0.973476i | \(0.573476\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.04970e23 | −1.08148 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.16749e23 | −1.49285 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.47051e23 | 1.10819 | 0.554095 | − | 0.832454i | \(-0.313064\pi\) | ||||
0.554095 | + | 0.832454i | \(0.313064\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.14618e23 | −0.422890 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.79656e23 | −1.11108 | −0.555542 | − | 0.831489i | \(-0.687489\pi\) | ||||
−0.555542 | + | 0.831489i | \(0.687489\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.83066e23 | −1.08729 | −0.543647 | − | 0.839314i | \(-0.682957\pi\) | ||||
−0.543647 | + | 0.839314i | \(0.682957\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.22775e22 | 0.0767062 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.14345e23 | 1.26113 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.92340e23 | 0.502236 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.42109e22 | −0.0906385 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.18701e22 | −0.0355894 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.51360e23 | 1.50694 | 0.753469 | − | 0.657483i | \(-0.228379\pi\) | ||||
0.753469 | + | 0.657483i | \(0.228379\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.07475e24 | 1.65721 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.90530e23 | 0.436128 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.21373e24 | −1.77393 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.20360e23 | −0.740537 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.77138e23 | −1.35414 | −0.677069 | − | 0.735920i | \(-0.736750\pi\) | ||||
−0.677069 | + | 0.735920i | \(0.736750\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.56439e23 | 0.750973 | 0.375486 | − | 0.926828i | \(-0.377476\pi\) | ||||
0.375486 | + | 0.926828i | \(0.377476\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.50194e23 | 0.197422 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.15984e24 | 1.48495 | 0.742477 | − | 0.669871i | \(-0.233651\pi\) | ||||
0.742477 | + | 0.669871i | \(0.233651\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.12439e24 | 2.64944 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.36278e23 | −1.01604 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.87432e23 | −1.16881 | −0.584407 | − | 0.811461i | \(-0.698673\pi\) | ||||
−0.584407 | + | 0.811461i | \(0.698673\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.62977e23 | 0.303297 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.20306e23 | −0.809490 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.97449e23 | −0.544782 | −0.272391 | − | 0.962187i | \(-0.587814\pi\) | ||||
−0.272391 | + | 0.962187i | \(0.587814\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.16033e24 | −1.23843 | −0.619214 | − | 0.785222i | \(-0.712549\pi\) | ||||
−0.619214 | + | 0.785222i | \(0.712549\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.79167e23 | 1.01857 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.25323e22 | 0.0228466 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.67212e23 | 0.264111 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.88886e22 | −0.0663781 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.89730e24 | −2.72178 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.13175e24 | −1.03663 | −0.518315 | − | 0.855190i | \(-0.673441\pi\) | ||||
−0.518315 | + | 0.855190i | \(0.673441\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.35434e23 | 0.120961 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.09418e24 | 0.952983 | 0.476492 | − | 0.879179i | \(-0.341908\pi\) | ||||
0.476492 | + | 0.879179i | \(0.341908\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.02171e23 | 0.681356 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.12736e23 | 0.424760 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.05400e22 | 0.00851660 | 0.00425830 | − | 0.999991i | \(-0.498645\pi\) | ||||
0.00425830 | + | 0.999991i | \(0.498645\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.14548e23 | 0.563198 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.49249e24 | 1.14757 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.73037e24 | 1.29800 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.61636e24 | −1.18297 | −0.591485 | − | 0.806316i | \(-0.701458\pi\) | ||||
−0.591485 | + | 0.806316i | \(0.701458\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.65916e24 | 2.61306 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.51339e23 | −0.314508 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.36277e23 | −0.432681 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.24665e24 | −2.15466 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.86841e23 | 0.121024 | 0.0605118 | − | 0.998167i | \(-0.480727\pi\) | ||||
0.0605118 | + | 0.998167i | \(0.480727\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.33368e21 | −0.00210767 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.11582e24 | −0.688634 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.30469e24 | 0.786033 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.18773e23 | −0.128677 | −0.0643385 | − | 0.997928i | \(-0.520494\pi\) | ||||
−0.0643385 | + | 0.997928i | \(0.520494\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.17786e22 | −0.0527048 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.42529e23 | 0.248131 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.80723e24 | 0.989491 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.32230e24 | −2.31101 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.15548e24 | −0.603345 | −0.301673 | − | 0.953412i | \(-0.597545\pi\) | ||||
−0.301673 | + | 0.953412i | \(0.597545\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.10550e23 | −0.362364 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.68086e24 | 1.83347 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.56003e23 | 0.416488 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.57207e24 | −1.69777 | −0.848883 | − | 0.528581i | \(-0.822724\pi\) | ||||
−0.848883 | + | 0.528581i | \(0.822724\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.67208e24 | −0.776379 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.45280e23 | 0.201993 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.90391e23 | −0.217350 | −0.108675 | − | 0.994077i | \(-0.534661\pi\) | ||||
−0.108675 | + | 0.994077i | \(0.534661\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.88952e24 | −0.818293 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.06435e24 | 0.873594 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.17372e24 | 0.898928 | 0.449464 | − | 0.893298i | \(-0.351615\pi\) | ||||
0.449464 | + | 0.893298i | \(0.351615\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.49255e23 | 0.0603219 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.08963e24 | 1.22040 | 0.610199 | − | 0.792248i | \(-0.291089\pi\) | ||||
0.610199 | + | 0.792248i | \(0.291089\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.56839e23 | −0.330804 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.03044e24 | 1.14362 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.35014e24 | 1.60475 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.58172e24 | 1.65230 | 0.826150 | − | 0.563451i | \(-0.190526\pi\) | ||||
0.826150 | + | 0.563451i | \(0.190526\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.12312e24 | −2.15881 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.04500e23 | −0.0704927 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.43112e23 | 0.115644 | 0.0578218 | − | 0.998327i | \(-0.481584\pi\) | ||||
0.0578218 | + | 0.998327i | \(0.481584\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.10394e24 | −1.35253 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.01271e24 | 0.970930 | 0.485465 | − | 0.874256i | \(-0.338650\pi\) | ||||
0.485465 | + | 0.874256i | \(0.338650\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.29219e24 | −1.98309 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.19212e23 | 0.221684 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.84893e24 | −1.76326 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.62418e23 | −0.0478918 | −0.0239459 | − | 0.999713i | \(-0.507623\pi\) | ||||
−0.0239459 | + | 0.999713i | \(0.507623\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.48643e24 | 1.87087 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.43975e24 | −1.25266 | −0.626329 | − | 0.779559i | \(-0.715443\pi\) | ||||
−0.626329 | + | 0.779559i | \(0.715443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.41762e24 | 0.391288 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.76921e23 | 0.128786 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.69883e22 | −0.0256242 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.03488e24 | −1.56004 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.93537e23 | 0.0742486 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.88846e24 | 0.467429 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.95546e24 | 0.715880 | 0.357940 | − | 0.933745i | \(-0.383479\pi\) | ||||
0.357940 | + | 0.933745i | \(0.383479\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.53613e24 | 0.364145 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.49705e24 | −0.579331 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.97695e24 | 1.81140 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.69382e24 | 0.598752 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.01045e24 | −1.30771 | −0.653855 | − | 0.756620i | \(-0.726849\pi\) | ||||
−0.653855 | + | 0.756620i | \(0.726849\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.30808e24 | −0.704577 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.47563e24 | 0.724698 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.35376e24 | −1.70530 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.70576e24 | 0.340921 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.17663e24 | 1.60011 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.16704e24 | 1.37334 | 0.686668 | − | 0.726971i | \(-0.259072\pi\) | ||||
0.686668 | + | 0.726971i | \(0.259072\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.73123e24 | 1.07540 | 0.537701 | − | 0.843136i | \(-0.319293\pi\) | ||||
0.537701 | + | 0.843136i | \(0.319293\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.99170e24 | 1.28473 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.83171e24 | −0.689529 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.78745e22 | 0.0119624 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.00745e25 | −1.73905 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.45653e24 | 0.415341 | 0.207670 | − | 0.978199i | \(-0.433412\pi\) | ||||
0.207670 | + | 0.978199i | \(0.433412\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.00636e25 | −1.66670 | −0.833348 | − | 0.552749i | \(-0.813579\pi\) | ||||
−0.833348 | + | 0.552749i | \(0.813579\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.31468e25 | −2.13286 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.31323e24 | 0.367639 | 0.183820 | − | 0.982960i | \(-0.441154\pi\) | ||||
0.183820 | + | 0.982960i | \(0.441154\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.49125e24 | 0.854983 | 0.427491 | − | 0.904019i | \(-0.359397\pi\) | ||||
0.427491 | + | 0.904019i | \(0.359397\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.13080e24 | −0.325038 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.60185e24 | −0.837237 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.06016e24 | −0.594577 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.86126e23 | 0.0697561 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.39004e24 | 0.336069 | 0.168035 | − | 0.985781i | \(-0.446258\pi\) | ||||
0.168035 | + | 0.985781i | \(0.446258\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.40186e24 | −0.744351 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.97628e24 | 0.266879 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.80336e24 | −0.238671 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.04533e25 | 3.95026 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.53497e24 | −0.195158 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.52370e23 | −0.0314511 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.04660e24 | −0.860821 | −0.430410 | − | 0.902633i | \(-0.641631\pi\) | ||||
−0.430410 | + | 0.902633i | \(0.641631\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.09630e23 | 0.0131286 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.71395e24 | −0.788208 | −0.394104 | − | 0.919066i | \(-0.628945\pi\) | ||||
−0.394104 | + | 0.919066i | \(0.628945\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.58583e24 | 0.988189 | 0.494095 | − | 0.869408i | \(-0.335500\pi\) | ||||
0.494095 | + | 0.869408i | \(0.335500\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.38753e25 | 1.56572 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.52514e24 | −0.611296 | −0.305648 | − | 0.952145i | \(-0.598873\pi\) | ||||
−0.305648 | + | 0.952145i | \(0.598873\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.07214e23 | 0.0550242 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.41585e24 | −0.895232 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.06440e24 | −0.111030 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.68364e24 | −0.581396 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.90294e24 | 0.391536 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.20981e25 | 1.19028 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.54824e24 | −0.631871 | −0.315935 | − | 0.948781i | \(-0.602318\pi\) | ||||
−0.315935 | + | 0.948781i | \(0.602318\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.58867e25 | 1.50358 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.78483e24 | 0.537026 | 0.268513 | − | 0.963276i | \(-0.413468\pi\) | ||||
0.268513 | + | 0.963276i | \(0.413468\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.75999e25 | −1.60267 | −0.801337 | − | 0.598213i | \(-0.795878\pi\) | ||||
−0.801337 | + | 0.598213i | \(0.795878\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.10552e24 | −0.813368 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.06620e25 | 0.934300 | 0.467150 | − | 0.884178i | \(-0.345281\pi\) | ||||
0.467150 | + | 0.884178i | \(0.345281\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.87831e25 | −1.61474 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.44389e25 | −2.06120 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.04254e23 | −0.0417265 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.50862e24 | −0.447246 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.12991e25 | 0.900136 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.07253e24 | 0.240181 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.98634e24 | 0.612615 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.71023e24 | −0.730943 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.32310e23 | 0.00977417 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.63230e25 | −1.18342 | −0.591709 | − | 0.806152i | \(-0.701547\pi\) | ||||
−0.591709 | + | 0.806152i | \(0.701547\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.34792e24 | 0.451688 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.45971e25 | 1.01944 | 0.509719 | − | 0.860341i | \(-0.329749\pi\) | ||||
0.509719 | + | 0.860341i | \(0.329749\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.51456e25 | 2.40918 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.24184e25 | 0.835577 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.70018e25 | −1.12294 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.83968e24 | 0.119278 | 0.0596390 | − | 0.998220i | \(-0.481005\pi\) | ||||
0.0596390 | + | 0.998220i | \(0.481005\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.64019e25 | 1.04397 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.66154e25 | 1.03824 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.08457e23 | −0.0495966 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.45716e24 | −0.208230 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.16411e24 | −0.423671 | −0.211835 | − | 0.977305i | \(-0.567944\pi\) | ||||
−0.211835 | + | 0.977305i | \(0.567944\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.53894e23 | −0.0495829 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.71875e25 | −1.55016 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.34108e24 | 0.467007 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.68079e25 | −0.924119 | −0.462059 | − | 0.886849i | \(-0.652889\pi\) | ||||
−0.462059 | + | 0.886849i | \(0.652889\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.00920e25 | −2.16471 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.99139e25 | 1.58621 | 0.793105 | − | 0.609085i | \(-0.208463\pi\) | ||||
0.793105 | + | 0.609085i | \(0.208463\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.34232e24 | −0.382370 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.87381e24 | 0.0958420 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.00925e25 | 0.507020 | 0.253510 | − | 0.967333i | \(-0.418415\pi\) | ||||
0.253510 | + | 0.967333i | \(0.418415\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.29998e25 | 1.13491 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.79245e24 | −0.232286 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.95941e24 | 0.474181 | 0.237090 | − | 0.971488i | \(-0.423806\pi\) | ||||
0.237090 | + | 0.971488i | \(0.423806\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.29288e24 | −0.154009 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.84941e25 | −1.30919 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.61963e25 | −2.08521 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.74617e25 | −0.774351 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.11655e25 | 0.922158 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.05539e25 | 0.451785 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.62055e24 | −0.194343 | −0.0971715 | − | 0.995268i | \(-0.530980\pi\) | ||||
−0.0971715 | + | 0.995268i | \(0.530980\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.88872e23 | 0.0284699 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.50646e24 | −0.0611780 | −0.0305890 | − | 0.999532i | \(-0.509738\pi\) | ||||
−0.0305890 | + | 0.999532i | \(0.509738\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.91796e25 | 1.16445 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.61962e25 | 1.41946 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.16292e25 | −0.833560 | −0.416780 | − | 0.909007i | \(-0.636841\pi\) | ||||
−0.416780 | + | 0.909007i | \(0.636841\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.03087e25 | 1.52667 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.06145e25 | −1.13957 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.09543e25 | 0.400754 | 0.200377 | − | 0.979719i | \(-0.435783\pi\) | ||||
0.200377 | + | 0.979719i | \(0.435783\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.94290e25 | −0.698622 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.21393e25 | 2.54962 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.13831e24 | 0.178506 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.10377e25 | −0.718410 | −0.359205 | − | 0.933259i | \(-0.616952\pi\) | ||||
−0.359205 | + | 0.933259i | \(0.616952\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.29913e25 | 2.45020 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.27549e24 | −0.306084 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.15374e25 | −0.698690 | −0.349345 | − | 0.936994i | \(-0.613596\pi\) | ||||
−0.349345 | + | 0.936994i | \(0.613596\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.77233e23 | −0.00884175 |
(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 | 4.18.a.a.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 36.18.a.d.1.2 | 2 | |||
4.3 | odd | 2 | 16.18.a.e.1.1 | 2 | |||
5.2 | odd | 4 | 100.18.c.a.49.2 | 4 | |||
5.3 | odd | 4 | 100.18.c.a.49.3 | 4 | |||
5.4 | even | 2 | 100.18.a.b.1.1 | 2 | |||
8.3 | odd | 2 | 64.18.a.g.1.2 | 2 | |||
8.5 | even | 2 | 64.18.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.18.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
16.18.a.e.1.1 | 2 | 4.3 | odd | 2 | |||
36.18.a.d.1.2 | 2 | 3.2 | odd | 2 | |||
64.18.a.g.1.2 | 2 | 8.3 | odd | 2 | |||
64.18.a.l.1.1 | 2 | 8.5 | even | 2 | |||
100.18.a.b.1.1 | 2 | 5.4 | even | 2 | |||
100.18.c.a.49.2 | 4 | 5.2 | odd | 4 | |||
100.18.c.a.49.3 | 4 | 5.3 | odd | 4 |