Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,28,Mod(1,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 28, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.1");
S:= CuspForms(chi, 28);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 28 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.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: | \(23.0927787419\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 19275662x^{2} - 30468026939x + 4134032404260 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{4}\cdot 5^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2324.55\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7959.76 | −0.687061 | −0.343530 | − | 0.939142i | \(-0.611623\pi\) | ||||
−0.343530 | + | 0.939142i | \(0.611623\pi\) | |||||||
\(3\) | 829899. | 0.300530 | 0.150265 | − | 0.988646i | \(-0.451987\pi\) | ||||
0.150265 | + | 0.988646i | \(0.451987\pi\) | |||||||
\(4\) | −7.08599e7 | −0.527947 | ||||||||
\(5\) | 1.22070e9 | 0.447214 | ||||||||
\(6\) | −6.60580e9 | −0.206483 | ||||||||
\(7\) | −2.73788e10 | −0.106805 | −0.0534025 | − | 0.998573i | \(-0.517007\pi\) | ||||
−0.0534025 | + | 0.998573i | \(0.517007\pi\) | |||||||
\(8\) | 1.63237e12 | 1.04979 | ||||||||
\(9\) | −6.93687e12 | −0.909682 | ||||||||
\(10\) | −9.71651e12 | −0.307263 | ||||||||
\(11\) | 6.42529e13 | 0.561166 | 0.280583 | − | 0.959830i | \(-0.409472\pi\) | ||||
0.280583 | + | 0.959830i | \(0.409472\pi\) | |||||||
\(12\) | −5.88066e13 | −0.158664 | ||||||||
\(13\) | 1.71367e15 | 1.56925 | 0.784623 | − | 0.619973i | \(-0.212857\pi\) | ||||
0.784623 | + | 0.619973i | \(0.212857\pi\) | |||||||
\(14\) | 2.17929e14 | 0.0733815 | ||||||||
\(15\) | 1.01306e15 | 0.134401 | ||||||||
\(16\) | −3.48262e15 | −0.193324 | ||||||||
\(17\) | 1.17307e15 | 0.0287252 | 0.0143626 | − | 0.999897i | \(-0.495428\pi\) | ||||
0.0143626 | + | 0.999897i | \(0.495428\pi\) | |||||||
\(18\) | 5.52158e16 | 0.625007 | ||||||||
\(19\) | −2.79305e17 | −1.52372 | −0.761860 | − | 0.647742i | \(-0.775713\pi\) | ||||
−0.761860 | + | 0.647742i | \(0.775713\pi\) | |||||||
\(20\) | −8.64989e16 | −0.236105 | ||||||||
\(21\) | −2.27217e16 | −0.0320981 | ||||||||
\(22\) | −5.11438e17 | −0.385555 | ||||||||
\(23\) | −3.09362e18 | −1.27980 | −0.639899 | − | 0.768459i | \(-0.721024\pi\) | ||||
−0.639899 | + | 0.768459i | \(0.721024\pi\) | |||||||
\(24\) | 1.35470e18 | 0.315495 | ||||||||
\(25\) | 1.49012e18 | 0.200000 | ||||||||
\(26\) | −1.36404e19 | −1.07817 | ||||||||
\(27\) | −1.20854e19 | −0.573917 | ||||||||
\(28\) | 1.94006e18 | 0.0563874 | ||||||||
\(29\) | −7.42209e19 | −1.34324 | −0.671619 | − | 0.740896i | \(-0.734401\pi\) | ||||
−0.671619 | + | 0.740896i | \(0.734401\pi\) | |||||||
\(30\) | −8.06372e18 | −0.0923418 | ||||||||
\(31\) | −1.27785e20 | −0.939937 | −0.469968 | − | 0.882683i | \(-0.655735\pi\) | ||||
−0.469968 | + | 0.882683i | \(0.655735\pi\) | |||||||
\(32\) | −1.91372e20 | −0.916967 | ||||||||
\(33\) | 5.33234e19 | 0.168647 | ||||||||
\(34\) | −9.33735e18 | −0.0197360 | ||||||||
\(35\) | −3.34214e19 | −0.0477646 | ||||||||
\(36\) | 4.91545e20 | 0.480264 | ||||||||
\(37\) | 8.47020e20 | 0.571703 | 0.285851 | − | 0.958274i | \(-0.407724\pi\) | ||||
0.285851 | + | 0.958274i | \(0.407724\pi\) | |||||||
\(38\) | 2.22320e21 | 1.04689 | ||||||||
\(39\) | 1.42217e21 | 0.471606 | ||||||||
\(40\) | 1.99264e21 | 0.469482 | ||||||||
\(41\) | −1.17207e21 | −0.197866 | −0.0989328 | − | 0.995094i | \(-0.531543\pi\) | ||||
−0.0989328 | + | 0.995094i | \(0.531543\pi\) | |||||||
\(42\) | 1.80859e20 | 0.0220534 | ||||||||
\(43\) | 3.56147e21 | 0.316086 | 0.158043 | − | 0.987432i | \(-0.449481\pi\) | ||||
0.158043 | + | 0.987432i | \(0.449481\pi\) | |||||||
\(44\) | −4.55295e21 | −0.296266 | ||||||||
\(45\) | −8.46785e21 | −0.406822 | ||||||||
\(46\) | 2.46245e22 | 0.879299 | ||||||||
\(47\) | 9.14938e21 | 0.244383 | 0.122191 | − | 0.992507i | \(-0.461008\pi\) | ||||
0.122191 | + | 0.992507i | \(0.461008\pi\) | |||||||
\(48\) | −2.89022e21 | −0.0580998 | ||||||||
\(49\) | −6.49628e22 | −0.988593 | ||||||||
\(50\) | −1.18610e22 | −0.137412 | ||||||||
\(51\) | 9.73528e20 | 0.00863279 | ||||||||
\(52\) | −1.21430e23 | −0.828479 | ||||||||
\(53\) | −2.22609e23 | −1.17441 | −0.587204 | − | 0.809439i | \(-0.699772\pi\) | ||||
−0.587204 | + | 0.809439i | \(0.699772\pi\) | |||||||
\(54\) | 9.61967e22 | 0.394316 | ||||||||
\(55\) | 7.84337e22 | 0.250961 | ||||||||
\(56\) | −4.46924e22 | −0.112123 | ||||||||
\(57\) | −2.31795e23 | −0.457924 | ||||||||
\(58\) | 5.90781e23 | 0.922887 | ||||||||
\(59\) | −6.15031e23 | −0.762773 | −0.381386 | − | 0.924416i | \(-0.624553\pi\) | ||||
−0.381386 | + | 0.924416i | \(0.624553\pi\) | |||||||
\(60\) | −7.17853e22 | −0.0709568 | ||||||||
\(61\) | 1.92253e24 | 1.52027 | 0.760134 | − | 0.649767i | \(-0.225133\pi\) | ||||
0.760134 | + | 0.649767i | \(0.225133\pi\) | |||||||
\(62\) | 1.01714e24 | 0.645794 | ||||||||
\(63\) | 1.89923e23 | 0.0971585 | ||||||||
\(64\) | 1.99071e24 | 0.823337 | ||||||||
\(65\) | 2.09188e24 | 0.701788 | ||||||||
\(66\) | −4.24442e23 | −0.115871 | ||||||||
\(67\) | −5.40282e24 | −1.20396 | −0.601978 | − | 0.798513i | \(-0.705620\pi\) | ||||
−0.601978 | + | 0.798513i | \(0.705620\pi\) | |||||||
\(68\) | −8.31235e22 | −0.0151654 | ||||||||
\(69\) | −2.56739e24 | −0.384618 | ||||||||
\(70\) | 2.66027e23 | 0.0328172 | ||||||||
\(71\) | 1.94780e24 | 0.198407 | 0.0992034 | − | 0.995067i | \(-0.468371\pi\) | ||||
0.0992034 | + | 0.995067i | \(0.468371\pi\) | |||||||
\(72\) | −1.13235e25 | −0.954977 | ||||||||
\(73\) | −1.12164e25 | −0.785227 | −0.392614 | − | 0.919703i | \(-0.628429\pi\) | ||||
−0.392614 | + | 0.919703i | \(0.628429\pi\) | |||||||
\(74\) | −6.74208e24 | −0.392795 | ||||||||
\(75\) | 1.23665e24 | 0.0601061 | ||||||||
\(76\) | 1.97915e25 | 0.804443 | ||||||||
\(77\) | −1.75917e24 | −0.0599353 | ||||||||
\(78\) | −1.13201e25 | −0.324022 | ||||||||
\(79\) | −1.22236e25 | −0.294600 | −0.147300 | − | 0.989092i | \(-0.547058\pi\) | ||||
−0.147300 | + | 0.989092i | \(0.547058\pi\) | |||||||
\(80\) | −4.25125e24 | −0.0864573 | ||||||||
\(81\) | 4.28681e25 | 0.737202 | ||||||||
\(82\) | 9.32937e24 | 0.135946 | ||||||||
\(83\) | 4.79523e25 | 0.593274 | 0.296637 | − | 0.954990i | \(-0.404135\pi\) | ||||
0.296637 | + | 0.954990i | \(0.404135\pi\) | |||||||
\(84\) | 1.61006e24 | 0.0169461 | ||||||||
\(85\) | 1.43197e24 | 0.0128463 | ||||||||
\(86\) | −2.83485e25 | −0.217171 | ||||||||
\(87\) | −6.15958e25 | −0.403684 | ||||||||
\(88\) | 1.04884e26 | 0.589108 | ||||||||
\(89\) | 1.66993e26 | 0.805255 | 0.402627 | − | 0.915364i | \(-0.368097\pi\) | ||||
0.402627 | + | 0.915364i | \(0.368097\pi\) | |||||||
\(90\) | 6.74021e25 | 0.279511 | ||||||||
\(91\) | −4.69182e25 | −0.167603 | ||||||||
\(92\) | 2.19214e26 | 0.675666 | ||||||||
\(93\) | −1.06049e26 | −0.282480 | ||||||||
\(94\) | −7.28269e25 | −0.167906 | ||||||||
\(95\) | −3.40948e26 | −0.681428 | ||||||||
\(96\) | −1.58819e26 | −0.275576 | ||||||||
\(97\) | −5.46723e26 | −0.824800 | −0.412400 | − | 0.911003i | \(-0.635309\pi\) | ||||
−0.412400 | + | 0.911003i | \(0.635309\pi\) | |||||||
\(98\) | 5.17088e26 | 0.679223 | ||||||||
\(99\) | −4.45714e26 | −0.510482 | ||||||||
\(100\) | −1.05589e26 | −0.105589 | ||||||||
\(101\) | −1.97130e27 | −1.72351 | −0.861754 | − | 0.507326i | \(-0.830634\pi\) | ||||
−0.861754 | + | 0.507326i | \(0.830634\pi\) | |||||||
\(102\) | −7.74906e24 | −0.00593125 | ||||||||
\(103\) | −1.51530e27 | −1.01671 | −0.508354 | − | 0.861148i | \(-0.669746\pi\) | ||||
−0.508354 | + | 0.861148i | \(0.669746\pi\) | |||||||
\(104\) | 2.79734e27 | 1.64738 | ||||||||
\(105\) | −2.77364e25 | −0.0143547 | ||||||||
\(106\) | 1.77192e27 | 0.806890 | ||||||||
\(107\) | 8.61493e26 | 0.345597 | 0.172799 | − | 0.984957i | \(-0.444719\pi\) | ||||
0.172799 | + | 0.984957i | \(0.444719\pi\) | |||||||
\(108\) | 8.56368e26 | 0.302998 | ||||||||
\(109\) | 2.11934e27 | 0.662131 | 0.331065 | − | 0.943608i | \(-0.392592\pi\) | ||||
0.331065 | + | 0.943608i | \(0.392592\pi\) | |||||||
\(110\) | −6.24314e26 | −0.172426 | ||||||||
\(111\) | 7.02941e26 | 0.171814 | ||||||||
\(112\) | 9.53502e25 | 0.0206480 | ||||||||
\(113\) | 3.78513e27 | 0.726978 | 0.363489 | − | 0.931598i | \(-0.381585\pi\) | ||||
0.363489 | + | 0.931598i | \(0.381585\pi\) | |||||||
\(114\) | 1.84503e27 | 0.314622 | ||||||||
\(115\) | −3.77639e27 | −0.572343 | ||||||||
\(116\) | 5.25928e27 | 0.709159 | ||||||||
\(117\) | −1.18875e28 | −1.42751 | ||||||||
\(118\) | 4.89550e27 | 0.524071 | ||||||||
\(119\) | −3.21173e25 | −0.00306799 | ||||||||
\(120\) | 1.65369e27 | 0.141093 | ||||||||
\(121\) | −8.98156e27 | −0.685093 | ||||||||
\(122\) | −1.53029e28 | −1.04452 | ||||||||
\(123\) | −9.72697e26 | −0.0594646 | ||||||||
\(124\) | 9.05486e27 | 0.496237 | ||||||||
\(125\) | 1.81899e27 | 0.0894427 | ||||||||
\(126\) | −1.51174e27 | −0.0667538 | ||||||||
\(127\) | −4.38836e28 | −1.74161 | −0.870807 | − | 0.491624i | \(-0.836403\pi\) | ||||
−0.870807 | + | 0.491624i | \(0.836403\pi\) | |||||||
\(128\) | 9.83997e27 | 0.351285 | ||||||||
\(129\) | 2.95566e27 | 0.0949935 | ||||||||
\(130\) | −1.66509e28 | −0.482171 | ||||||||
\(131\) | 6.40410e28 | 1.67223 | 0.836114 | − | 0.548556i | \(-0.184822\pi\) | ||||
0.836114 | + | 0.548556i | \(0.184822\pi\) | |||||||
\(132\) | −3.77849e27 | −0.0890369 | ||||||||
\(133\) | 7.64704e27 | 0.162741 | ||||||||
\(134\) | 4.30052e28 | 0.827191 | ||||||||
\(135\) | −1.47527e28 | −0.256664 | ||||||||
\(136\) | 1.91488e27 | 0.0301555 | ||||||||
\(137\) | −1.22682e29 | −1.75005 | −0.875027 | − | 0.484074i | \(-0.839157\pi\) | ||||
−0.875027 | + | 0.484074i | \(0.839157\pi\) | |||||||
\(138\) | 2.04358e28 | 0.264256 | ||||||||
\(139\) | 1.28776e29 | 1.51055 | 0.755273 | − | 0.655410i | \(-0.227504\pi\) | ||||
0.755273 | + | 0.655410i | \(0.227504\pi\) | |||||||
\(140\) | 2.36824e27 | 0.0252172 | ||||||||
\(141\) | 7.59306e27 | 0.0734444 | ||||||||
\(142\) | −1.55040e28 | −0.136318 | ||||||||
\(143\) | 1.10108e29 | 0.880607 | ||||||||
\(144\) | 2.41585e28 | 0.175864 | ||||||||
\(145\) | −9.06017e28 | −0.600715 | ||||||||
\(146\) | 8.92800e28 | 0.539499 | ||||||||
\(147\) | −5.39125e28 | −0.297102 | ||||||||
\(148\) | −6.00197e28 | −0.301829 | ||||||||
\(149\) | 3.62979e29 | 1.66674 | 0.833369 | − | 0.552717i | \(-0.186409\pi\) | ||||
0.833369 | + | 0.552717i | \(0.186409\pi\) | |||||||
\(150\) | −9.84341e27 | −0.0412965 | ||||||||
\(151\) | −3.99824e29 | −1.53349 | −0.766744 | − | 0.641953i | \(-0.778124\pi\) | ||||
−0.766744 | + | 0.641953i | \(0.778124\pi\) | |||||||
\(152\) | −4.55929e29 | −1.59959 | ||||||||
\(153\) | −8.13742e27 | −0.0261308 | ||||||||
\(154\) | 1.40026e28 | 0.0411792 | ||||||||
\(155\) | −1.55988e29 | −0.420353 | ||||||||
\(156\) | −1.00775e29 | −0.248983 | ||||||||
\(157\) | 4.28378e28 | 0.0970917 | 0.0485458 | − | 0.998821i | \(-0.484541\pi\) | ||||
0.0485458 | + | 0.998821i | \(0.484541\pi\) | |||||||
\(158\) | 9.72969e28 | 0.202408 | ||||||||
\(159\) | −1.84743e29 | −0.352945 | ||||||||
\(160\) | −2.33608e29 | −0.410080 | ||||||||
\(161\) | 8.46998e28 | 0.136689 | ||||||||
\(162\) | −3.41220e29 | −0.506503 | ||||||||
\(163\) | 1.17374e30 | 1.60339 | 0.801696 | − | 0.597732i | \(-0.203931\pi\) | ||||
0.801696 | + | 0.597732i | \(0.203931\pi\) | |||||||
\(164\) | 8.30525e28 | 0.104463 | ||||||||
\(165\) | 6.50920e28 | 0.0754214 | ||||||||
\(166\) | −3.81689e29 | −0.407616 | ||||||||
\(167\) | 6.93075e29 | 0.682508 | 0.341254 | − | 0.939971i | \(-0.389148\pi\) | ||||
0.341254 | + | 0.939971i | \(0.389148\pi\) | |||||||
\(168\) | −3.70902e28 | −0.0336964 | ||||||||
\(169\) | 1.74412e30 | 1.46253 | ||||||||
\(170\) | −1.13981e28 | −0.00882619 | ||||||||
\(171\) | 1.93750e30 | 1.38610 | ||||||||
\(172\) | −2.52366e29 | −0.166877 | ||||||||
\(173\) | −1.66313e30 | −1.01696 | −0.508479 | − | 0.861074i | \(-0.669792\pi\) | ||||
−0.508479 | + | 0.861074i | \(0.669792\pi\) | |||||||
\(174\) | 4.90288e29 | 0.277355 | ||||||||
\(175\) | −4.07977e28 | −0.0213610 | ||||||||
\(176\) | −2.23769e29 | −0.108487 | ||||||||
\(177\) | −5.10414e29 | −0.229236 | ||||||||
\(178\) | −1.32923e30 | −0.553259 | ||||||||
\(179\) | −3.59477e30 | −1.38725 | −0.693625 | − | 0.720336i | \(-0.743987\pi\) | ||||
−0.693625 | + | 0.720336i | \(0.743987\pi\) | |||||||
\(180\) | 6.00031e29 | 0.214781 | ||||||||
\(181\) | −1.98619e29 | −0.0659722 | −0.0329861 | − | 0.999456i | \(-0.510502\pi\) | ||||
−0.0329861 | + | 0.999456i | \(0.510502\pi\) | |||||||
\(182\) | 3.73458e29 | 0.115154 | ||||||||
\(183\) | 1.59550e30 | 0.456887 | ||||||||
\(184\) | −5.04993e30 | −1.34352 | ||||||||
\(185\) | 1.03396e30 | 0.255673 | ||||||||
\(186\) | 8.44125e29 | 0.194081 | ||||||||
\(187\) | 7.53730e28 | 0.0161196 | ||||||||
\(188\) | −6.48324e29 | −0.129021 | ||||||||
\(189\) | 3.30884e29 | 0.0612972 | ||||||||
\(190\) | 2.71387e30 | 0.468182 | ||||||||
\(191\) | −3.73765e30 | −0.600688 | −0.300344 | − | 0.953831i | \(-0.597101\pi\) | ||||
−0.300344 | + | 0.953831i | \(0.597101\pi\) | |||||||
\(192\) | 1.65209e30 | 0.247438 | ||||||||
\(193\) | −7.33944e30 | −1.02480 | −0.512400 | − | 0.858747i | \(-0.671244\pi\) | ||||
−0.512400 | + | 0.858747i | \(0.671244\pi\) | |||||||
\(194\) | 4.35178e30 | 0.566688 | ||||||||
\(195\) | 1.73605e30 | 0.210909 | ||||||||
\(196\) | 4.60325e30 | 0.521925 | ||||||||
\(197\) | 8.12445e30 | 0.860003 | 0.430002 | − | 0.902828i | \(-0.358513\pi\) | ||||
0.430002 | + | 0.902828i | \(0.358513\pi\) | |||||||
\(198\) | 3.54777e30 | 0.350732 | ||||||||
\(199\) | −1.52784e31 | −1.41111 | −0.705557 | − | 0.708653i | \(-0.749303\pi\) | ||||
−0.705557 | + | 0.708653i | \(0.749303\pi\) | |||||||
\(200\) | 2.43242e30 | 0.209959 | ||||||||
\(201\) | −4.48379e30 | −0.361825 | ||||||||
\(202\) | 1.56911e31 | 1.18416 | ||||||||
\(203\) | 2.03208e30 | 0.143465 | ||||||||
\(204\) | −6.89841e28 | −0.00455766 | ||||||||
\(205\) | −1.43074e30 | −0.0884881 | ||||||||
\(206\) | 1.20614e31 | 0.698540 | ||||||||
\(207\) | 2.14600e31 | 1.16421 | ||||||||
\(208\) | −5.96805e30 | −0.303373 | ||||||||
\(209\) | −1.79461e31 | −0.855059 | ||||||||
\(210\) | 2.20775e29 | 0.00986257 | ||||||||
\(211\) | −2.23121e31 | −0.934818 | −0.467409 | − | 0.884041i | \(-0.654812\pi\) | ||||
−0.467409 | + | 0.884041i | \(0.654812\pi\) | |||||||
\(212\) | 1.57741e31 | 0.620026 | ||||||||
\(213\) | 1.61648e30 | 0.0596273 | ||||||||
\(214\) | −6.85728e30 | −0.237447 | ||||||||
\(215\) | 4.34750e30 | 0.141358 | ||||||||
\(216\) | −1.97278e31 | −0.602494 | ||||||||
\(217\) | 3.49862e30 | 0.100390 | ||||||||
\(218\) | −1.68695e31 | −0.454924 | ||||||||
\(219\) | −9.30849e30 | −0.235985 | ||||||||
\(220\) | −5.55780e30 | −0.132494 | ||||||||
\(221\) | 2.01025e30 | 0.0450769 | ||||||||
\(222\) | −5.59524e30 | −0.118047 | ||||||||
\(223\) | −5.43506e31 | −1.07917 | −0.539583 | − | 0.841932i | \(-0.681418\pi\) | ||||
−0.539583 | + | 0.841932i | \(0.681418\pi\) | |||||||
\(224\) | 5.23955e30 | 0.0979367 | ||||||||
\(225\) | −1.03367e31 | −0.181936 | ||||||||
\(226\) | −3.01287e31 | −0.499478 | ||||||||
\(227\) | 5.55710e31 | 0.867959 | 0.433979 | − | 0.900923i | \(-0.357109\pi\) | ||||
0.433979 | + | 0.900923i | \(0.357109\pi\) | |||||||
\(228\) | 1.64250e31 | 0.241760 | ||||||||
\(229\) | −1.14629e31 | −0.159043 | −0.0795217 | − | 0.996833i | \(-0.525339\pi\) | ||||
−0.0795217 | + | 0.996833i | \(0.525339\pi\) | |||||||
\(230\) | 3.00592e31 | 0.393235 | ||||||||
\(231\) | −1.45993e30 | −0.0180124 | ||||||||
\(232\) | −1.21156e32 | −1.41012 | ||||||||
\(233\) | 1.27501e32 | 1.40026 | 0.700128 | − | 0.714018i | \(-0.253126\pi\) | ||||
0.700128 | + | 0.714018i | \(0.253126\pi\) | |||||||
\(234\) | 9.46215e31 | 0.980789 | ||||||||
\(235\) | 1.11687e31 | 0.109291 | ||||||||
\(236\) | 4.35811e31 | 0.402704 | ||||||||
\(237\) | −1.01443e31 | −0.0885363 | ||||||||
\(238\) | 2.55646e29 | 0.00210790 | ||||||||
\(239\) | 9.40042e31 | 0.732446 | 0.366223 | − | 0.930527i | \(-0.380651\pi\) | ||||
0.366223 | + | 0.930527i | \(0.380651\pi\) | |||||||
\(240\) | −3.52811e30 | −0.0259830 | ||||||||
\(241\) | 1.81502e32 | 1.26372 | 0.631862 | − | 0.775081i | \(-0.282291\pi\) | ||||
0.631862 | + | 0.775081i | \(0.282291\pi\) | |||||||
\(242\) | 7.14911e31 | 0.470700 | ||||||||
\(243\) | 1.27734e32 | 0.795469 | ||||||||
\(244\) | −1.36230e32 | −0.802621 | ||||||||
\(245\) | −7.93002e31 | −0.442112 | ||||||||
\(246\) | 7.74244e30 | 0.0408558 | ||||||||
\(247\) | −4.78635e32 | −2.39109 | ||||||||
\(248\) | −2.08593e32 | −0.986739 | ||||||||
\(249\) | 3.97956e31 | 0.178297 | ||||||||
\(250\) | −1.44787e31 | −0.0614526 | ||||||||
\(251\) | 8.28027e31 | 0.333004 | 0.166502 | − | 0.986041i | \(-0.446753\pi\) | ||||
0.166502 | + | 0.986041i | \(0.446753\pi\) | |||||||
\(252\) | −1.34579e31 | −0.0512946 | ||||||||
\(253\) | −1.98774e32 | −0.718179 | ||||||||
\(254\) | 3.49303e32 | 1.19660 | ||||||||
\(255\) | 1.18839e30 | 0.00386070 | ||||||||
\(256\) | −3.45512e32 | −1.06469 | ||||||||
\(257\) | −2.07555e32 | −0.606786 | −0.303393 | − | 0.952866i | \(-0.598119\pi\) | ||||
−0.303393 | + | 0.952866i | \(0.598119\pi\) | |||||||
\(258\) | −2.35264e31 | −0.0652663 | ||||||||
\(259\) | −2.31904e31 | −0.0610607 | ||||||||
\(260\) | −1.48230e32 | −0.370507 | ||||||||
\(261\) | 5.14860e32 | 1.22192 | ||||||||
\(262\) | −5.09751e32 | −1.14892 | ||||||||
\(263\) | 9.03345e32 | 1.93397 | 0.966987 | − | 0.254824i | \(-0.0820176\pi\) | ||||
0.966987 | + | 0.254824i | \(0.0820176\pi\) | |||||||
\(264\) | 8.70435e31 | 0.177045 | ||||||||
\(265\) | −2.71740e32 | −0.525212 | ||||||||
\(266\) | −6.08687e31 | −0.111813 | ||||||||
\(267\) | 1.38587e32 | 0.242003 | ||||||||
\(268\) | 3.82843e32 | 0.635625 | ||||||||
\(269\) | −8.06210e31 | −0.127290 | −0.0636448 | − | 0.997973i | \(-0.520272\pi\) | ||||
−0.0636448 | + | 0.997973i | \(0.520272\pi\) | |||||||
\(270\) | 1.17428e32 | 0.176344 | ||||||||
\(271\) | −6.60901e32 | −0.944171 | −0.472086 | − | 0.881553i | \(-0.656499\pi\) | ||||
−0.472086 | + | 0.881553i | \(0.656499\pi\) | |||||||
\(272\) | −4.08535e30 | −0.00555328 | ||||||||
\(273\) | −3.89374e31 | −0.0503699 | ||||||||
\(274\) | 9.76516e32 | 1.20239 | ||||||||
\(275\) | 9.57443e31 | 0.112233 | ||||||||
\(276\) | 1.81925e32 | 0.203058 | ||||||||
\(277\) | 7.48899e32 | 0.796061 | 0.398030 | − | 0.917372i | \(-0.369694\pi\) | ||||
0.398030 | + | 0.917372i | \(0.369694\pi\) | |||||||
\(278\) | −1.02502e33 | −1.03784 | ||||||||
\(279\) | 8.86431e32 | 0.855043 | ||||||||
\(280\) | −5.45561e31 | −0.0501430 | ||||||||
\(281\) | −2.28413e32 | −0.200071 | −0.100036 | − | 0.994984i | \(-0.531896\pi\) | ||||
−0.100036 | + | 0.994984i | \(0.531896\pi\) | |||||||
\(282\) | −6.04390e31 | −0.0504608 | ||||||||
\(283\) | −1.63098e32 | −0.129817 | −0.0649084 | − | 0.997891i | \(-0.520676\pi\) | ||||
−0.0649084 | + | 0.997891i | \(0.520676\pi\) | |||||||
\(284\) | −1.38021e32 | −0.104748 | ||||||||
\(285\) | −2.82953e32 | −0.204790 | ||||||||
\(286\) | −8.76434e32 | −0.605031 | ||||||||
\(287\) | 3.20898e31 | 0.0211330 | ||||||||
\(288\) | 1.32752e33 | 0.834148 | ||||||||
\(289\) | −1.66634e33 | −0.999175 | ||||||||
\(290\) | 7.21168e32 | 0.412727 | ||||||||
\(291\) | −4.53725e32 | −0.247877 | ||||||||
\(292\) | 7.94794e32 | 0.414559 | ||||||||
\(293\) | −4.06308e32 | −0.202368 | −0.101184 | − | 0.994868i | \(-0.532263\pi\) | ||||
−0.101184 | + | 0.994868i | \(0.532263\pi\) | |||||||
\(294\) | 4.29131e32 | 0.204127 | ||||||||
\(295\) | −7.50771e32 | −0.341122 | ||||||||
\(296\) | 1.38265e33 | 0.600169 | ||||||||
\(297\) | −7.76520e32 | −0.322063 | ||||||||
\(298\) | −2.88923e33 | −1.14515 | ||||||||
\(299\) | −5.30143e33 | −2.00832 | ||||||||
\(300\) | −8.76286e31 | −0.0317328 | ||||||||
\(301\) | −9.75090e31 | −0.0337596 | ||||||||
\(302\) | 3.18251e33 | 1.05360 | ||||||||
\(303\) | −1.63598e33 | −0.517967 | ||||||||
\(304\) | 9.72713e32 | 0.294572 | ||||||||
\(305\) | 2.34684e33 | 0.679884 | ||||||||
\(306\) | 6.47719e31 | 0.0179534 | ||||||||
\(307\) | 1.37932e32 | 0.0365844 | 0.0182922 | − | 0.999833i | \(-0.494177\pi\) | ||||
0.0182922 | + | 0.999833i | \(0.494177\pi\) | |||||||
\(308\) | 1.24655e32 | 0.0316427 | ||||||||
\(309\) | −1.25755e33 | −0.305552 | ||||||||
\(310\) | 1.24163e33 | 0.288808 | ||||||||
\(311\) | 4.42328e33 | 0.985097 | 0.492549 | − | 0.870285i | \(-0.336065\pi\) | ||||
0.492549 | + | 0.870285i | \(0.336065\pi\) | |||||||
\(312\) | 2.32151e33 | 0.495089 | ||||||||
\(313\) | 2.96295e33 | 0.605167 | 0.302584 | − | 0.953123i | \(-0.402151\pi\) | ||||
0.302584 | + | 0.953123i | \(0.402151\pi\) | |||||||
\(314\) | −3.40979e32 | −0.0667079 | ||||||||
\(315\) | 2.31840e32 | 0.0434506 | ||||||||
\(316\) | 8.66162e32 | 0.155533 | ||||||||
\(317\) | 5.27424e33 | 0.907527 | 0.453764 | − | 0.891122i | \(-0.350081\pi\) | ||||
0.453764 | + | 0.891122i | \(0.350081\pi\) | |||||||
\(318\) | 1.47051e33 | 0.242495 | ||||||||
\(319\) | −4.76891e33 | −0.753780 | ||||||||
\(320\) | 2.43006e33 | 0.368207 | ||||||||
\(321\) | 7.14952e32 | 0.103863 | ||||||||
\(322\) | −6.74190e32 | −0.0939135 | ||||||||
\(323\) | −3.27644e32 | −0.0437691 | ||||||||
\(324\) | −3.03763e33 | −0.389204 | ||||||||
\(325\) | 2.55356e33 | 0.313849 | ||||||||
\(326\) | −9.34271e33 | −1.10163 | ||||||||
\(327\) | 1.75884e33 | 0.198990 | ||||||||
\(328\) | −1.91325e33 | −0.207718 | ||||||||
\(329\) | −2.50499e32 | −0.0261013 | ||||||||
\(330\) | −5.18117e32 | −0.0518191 | ||||||||
\(331\) | 9.41253e32 | 0.0903709 | 0.0451855 | − | 0.998979i | \(-0.485612\pi\) | ||||
0.0451855 | + | 0.998979i | \(0.485612\pi\) | |||||||
\(332\) | −3.39790e33 | −0.313218 | ||||||||
\(333\) | −5.87566e33 | −0.520067 | ||||||||
\(334\) | −5.51671e33 | −0.468925 | ||||||||
\(335\) | −6.59524e33 | −0.538425 | ||||||||
\(336\) | 7.91310e31 | 0.00620535 | ||||||||
\(337\) | 7.47402e33 | 0.563055 | 0.281527 | − | 0.959553i | \(-0.409159\pi\) | ||||
0.281527 | + | 0.959553i | \(0.409159\pi\) | |||||||
\(338\) | −1.38828e34 | −1.00485 | ||||||||
\(339\) | 3.14127e33 | 0.218479 | ||||||||
\(340\) | −1.01469e32 | −0.00678217 | ||||||||
\(341\) | −8.21059e33 | −0.527461 | ||||||||
\(342\) | −1.54220e34 | −0.952334 | ||||||||
\(343\) | 3.57773e33 | 0.212392 | ||||||||
\(344\) | 5.81364e33 | 0.331825 | ||||||||
\(345\) | −3.13403e33 | −0.172006 | ||||||||
\(346\) | 1.32381e34 | 0.698713 | ||||||||
\(347\) | 2.12986e34 | 1.08119 | 0.540596 | − | 0.841282i | \(-0.318199\pi\) | ||||
0.540596 | + | 0.841282i | \(0.318199\pi\) | |||||||
\(348\) | 4.36467e33 | 0.213124 | ||||||||
\(349\) | 3.74540e34 | 1.75936 | 0.879680 | − | 0.475565i | \(-0.157756\pi\) | ||||
0.879680 | + | 0.475565i | \(0.157756\pi\) | |||||||
\(350\) | 3.24740e32 | 0.0146763 | ||||||||
\(351\) | −2.07103e34 | −0.900617 | ||||||||
\(352\) | −1.22962e34 | −0.514571 | ||||||||
\(353\) | 2.00261e34 | 0.806563 | 0.403282 | − | 0.915076i | \(-0.367869\pi\) | ||||
0.403282 | + | 0.915076i | \(0.367869\pi\) | |||||||
\(354\) | 4.06277e33 | 0.157499 | ||||||||
\(355\) | 2.37769e33 | 0.0887302 | ||||||||
\(356\) | −1.18331e34 | −0.425132 | ||||||||
\(357\) | −2.66541e31 | −0.000922025 0 | ||||||||
\(358\) | 2.86135e34 | 0.953125 | ||||||||
\(359\) | −9.41455e33 | −0.302012 | −0.151006 | − | 0.988533i | \(-0.548251\pi\) | ||||
−0.151006 | + | 0.988533i | \(0.548251\pi\) | |||||||
\(360\) | −1.38227e34 | −0.427079 | ||||||||
\(361\) | 4.44106e34 | 1.32172 | ||||||||
\(362\) | 1.58096e33 | 0.0453269 | ||||||||
\(363\) | −7.45379e33 | −0.205891 | ||||||||
\(364\) | 3.32462e33 | 0.0884857 | ||||||||
\(365\) | −1.36919e34 | −0.351164 | ||||||||
\(366\) | −1.26998e34 | −0.313909 | ||||||||
\(367\) | −7.58151e34 | −1.80619 | −0.903096 | − | 0.429439i | \(-0.858711\pi\) | ||||
−0.903096 | + | 0.429439i | \(0.858711\pi\) | |||||||
\(368\) | 1.07739e34 | 0.247416 | ||||||||
\(369\) | 8.13047e33 | 0.179995 | ||||||||
\(370\) | −8.23008e33 | −0.175663 | ||||||||
\(371\) | 6.09479e33 | 0.125433 | ||||||||
\(372\) | 7.51462e33 | 0.149134 | ||||||||
\(373\) | 3.75622e34 | 0.718922 | 0.359461 | − | 0.933160i | \(-0.382961\pi\) | ||||
0.359461 | + | 0.933160i | \(0.382961\pi\) | |||||||
\(374\) | −5.99952e32 | −0.0110751 | ||||||||
\(375\) | 1.50958e33 | 0.0268803 | ||||||||
\(376\) | 1.49352e34 | 0.256551 | ||||||||
\(377\) | −1.27190e35 | −2.10787 | ||||||||
\(378\) | −2.63375e33 | −0.0421149 | ||||||||
\(379\) | 9.15706e34 | 1.41295 | 0.706475 | − | 0.707738i | \(-0.250284\pi\) | ||||
0.706475 | + | 0.707738i | \(0.250284\pi\) | |||||||
\(380\) | 2.41596e34 | 0.359758 | ||||||||
\(381\) | −3.64190e34 | −0.523408 | ||||||||
\(382\) | 2.97508e34 | 0.412709 | ||||||||
\(383\) | −1.31082e35 | −1.75534 | −0.877670 | − | 0.479266i | \(-0.840903\pi\) | ||||
−0.877670 | + | 0.479266i | \(0.840903\pi\) | |||||||
\(384\) | 8.16618e33 | 0.105572 | ||||||||
\(385\) | −2.14742e33 | −0.0268039 | ||||||||
\(386\) | 5.84202e34 | 0.704100 | ||||||||
\(387\) | −2.47055e34 | −0.287538 | ||||||||
\(388\) | 3.87407e34 | 0.435451 | ||||||||
\(389\) | −7.23296e34 | −0.785229 | −0.392614 | − | 0.919703i | \(-0.628429\pi\) | ||||
−0.392614 | + | 0.919703i | \(0.628429\pi\) | |||||||
\(390\) | −1.38185e34 | −0.144907 | ||||||||
\(391\) | −3.62903e33 | −0.0367624 | ||||||||
\(392\) | −1.06043e35 | −1.03782 | ||||||||
\(393\) | 5.31475e34 | 0.502555 | ||||||||
\(394\) | −6.46687e34 | −0.590875 | ||||||||
\(395\) | −1.49214e34 | −0.131749 | ||||||||
\(396\) | 3.15832e34 | 0.269508 | ||||||||
\(397\) | 1.87264e35 | 1.54448 | 0.772239 | − | 0.635332i | \(-0.219137\pi\) | ||||
0.772239 | + | 0.635332i | \(0.219137\pi\) | |||||||
\(398\) | 1.21613e35 | 0.969522 | ||||||||
\(399\) | 6.34627e33 | 0.0489085 | ||||||||
\(400\) | −5.18951e33 | −0.0386649 | ||||||||
\(401\) | 1.46014e35 | 1.05183 | 0.525916 | − | 0.850537i | \(-0.323723\pi\) | ||||
0.525916 | + | 0.850537i | \(0.323723\pi\) | |||||||
\(402\) | 3.56899e34 | 0.248596 | ||||||||
\(403\) | −2.18982e35 | −1.47499 | ||||||||
\(404\) | 1.39686e35 | 0.909922 | ||||||||
\(405\) | 5.23292e34 | 0.329687 | ||||||||
\(406\) | −1.61749e34 | −0.0985689 | ||||||||
\(407\) | 5.44235e34 | 0.320820 | ||||||||
\(408\) | 1.58916e33 | 0.00906264 | ||||||||
\(409\) | 1.50577e35 | 0.830795 | 0.415398 | − | 0.909640i | \(-0.363642\pi\) | ||||
0.415398 | + | 0.909640i | \(0.363642\pi\) | |||||||
\(410\) | 1.13884e34 | 0.0607967 | ||||||||
\(411\) | −1.01813e35 | −0.525944 | ||||||||
\(412\) | 1.07374e35 | 0.536768 | ||||||||
\(413\) | 1.68388e34 | 0.0814679 | ||||||||
\(414\) | −1.70817e35 | −0.799882 | ||||||||
\(415\) | 5.85356e34 | 0.265320 | ||||||||
\(416\) | −3.27948e35 | −1.43895 | ||||||||
\(417\) | 1.06871e35 | 0.453965 | ||||||||
\(418\) | 1.42847e35 | 0.587478 | ||||||||
\(419\) | −3.49644e35 | −1.39231 | −0.696157 | − | 0.717890i | \(-0.745108\pi\) | ||||
−0.696157 | + | 0.717890i | \(0.745108\pi\) | |||||||
\(420\) | 1.96540e33 | 0.00757854 | ||||||||
\(421\) | −1.36815e35 | −0.510888 | −0.255444 | − | 0.966824i | \(-0.582222\pi\) | ||||
−0.255444 | + | 0.966824i | \(0.582222\pi\) | |||||||
\(422\) | 1.77599e35 | 0.642277 | ||||||||
\(423\) | −6.34680e34 | −0.222310 | ||||||||
\(424\) | −3.63381e35 | −1.23289 | ||||||||
\(425\) | 1.74801e33 | 0.00574504 | ||||||||
\(426\) | −1.28668e34 | −0.0409676 | ||||||||
\(427\) | −5.26366e34 | −0.162372 | ||||||||
\(428\) | −6.10453e34 | −0.182457 | ||||||||
\(429\) | 9.13785e34 | 0.264649 | ||||||||
\(430\) | −3.46051e34 | −0.0971216 | ||||||||
\(431\) | −4.89720e34 | −0.133200 | −0.0666001 | − | 0.997780i | \(-0.521215\pi\) | ||||
−0.0666001 | + | 0.997780i | \(0.521215\pi\) | |||||||
\(432\) | 4.20888e34 | 0.110952 | ||||||||
\(433\) | −4.40990e35 | −1.12679 | −0.563393 | − | 0.826189i | \(-0.690504\pi\) | ||||
−0.563393 | + | 0.826189i | \(0.690504\pi\) | |||||||
\(434\) | −2.78482e34 | −0.0689740 | ||||||||
\(435\) | −7.51902e34 | −0.180533 | ||||||||
\(436\) | −1.50176e35 | −0.349570 | ||||||||
\(437\) | 8.64064e35 | 1.95005 | ||||||||
\(438\) | 7.40934e34 | 0.162136 | ||||||||
\(439\) | −3.19792e35 | −0.678573 | −0.339287 | − | 0.940683i | \(-0.610186\pi\) | ||||
−0.339287 | + | 0.940683i | \(0.610186\pi\) | |||||||
\(440\) | 1.28033e35 | 0.263457 | ||||||||
\(441\) | 4.50638e35 | 0.899305 | ||||||||
\(442\) | −1.60011e34 | −0.0309706 | ||||||||
\(443\) | 2.30373e35 | 0.432496 | 0.216248 | − | 0.976338i | \(-0.430618\pi\) | ||||
0.216248 | + | 0.976338i | \(0.430618\pi\) | |||||||
\(444\) | −4.98103e34 | −0.0907087 | ||||||||
\(445\) | 2.03849e35 | 0.360121 | ||||||||
\(446\) | 4.32618e35 | 0.741453 | ||||||||
\(447\) | 3.01236e35 | 0.500905 | ||||||||
\(448\) | −5.45032e34 | −0.0879365 | ||||||||
\(449\) | 8.08913e35 | 1.26642 | 0.633208 | − | 0.773982i | \(-0.281738\pi\) | ||||
0.633208 | + | 0.773982i | \(0.281738\pi\) | |||||||
\(450\) | 8.22780e34 | 0.125001 | ||||||||
\(451\) | −7.53086e34 | −0.111035 | ||||||||
\(452\) | −2.68214e35 | −0.383806 | ||||||||
\(453\) | −3.31814e35 | −0.460859 | ||||||||
\(454\) | −4.42332e35 | −0.596340 | ||||||||
\(455\) | −5.72732e34 | −0.0749545 | ||||||||
\(456\) | −3.78375e35 | −0.480725 | ||||||||
\(457\) | −4.51820e35 | −0.557309 | −0.278655 | − | 0.960391i | \(-0.589888\pi\) | ||||
−0.278655 | + | 0.960391i | \(0.589888\pi\) | |||||||
\(458\) | 9.12420e34 | 0.109273 | ||||||||
\(459\) | −1.41770e34 | −0.0164859 | ||||||||
\(460\) | 2.67595e35 | 0.302167 | ||||||||
\(461\) | 1.24872e36 | 1.36932 | 0.684658 | − | 0.728865i | \(-0.259952\pi\) | ||||
0.684658 | + | 0.728865i | \(0.259952\pi\) | |||||||
\(462\) | 1.16207e34 | 0.0123756 | ||||||||
\(463\) | −3.60640e35 | −0.373018 | −0.186509 | − | 0.982453i | \(-0.559717\pi\) | ||||
−0.186509 | + | 0.982453i | \(0.559717\pi\) | |||||||
\(464\) | 2.58483e35 | 0.259681 | ||||||||
\(465\) | −1.29454e35 | −0.126329 | ||||||||
\(466\) | −1.01487e36 | −0.962061 | ||||||||
\(467\) | −1.86337e36 | −1.71602 | −0.858009 | − | 0.513634i | \(-0.828299\pi\) | ||||
−0.858009 | + | 0.513634i | \(0.828299\pi\) | |||||||
\(468\) | 8.42345e35 | 0.753652 | ||||||||
\(469\) | 1.47923e35 | 0.128588 | ||||||||
\(470\) | −8.89000e34 | −0.0750898 | ||||||||
\(471\) | 3.55511e34 | 0.0291790 | ||||||||
\(472\) | −1.00396e36 | −0.800753 | ||||||||
\(473\) | 2.28835e35 | 0.177377 | ||||||||
\(474\) | 8.07466e34 | 0.0608298 | ||||||||
\(475\) | −4.16197e35 | −0.304744 | ||||||||
\(476\) | 2.27583e33 | 0.00161974 | ||||||||
\(477\) | 1.54421e36 | 1.06834 | ||||||||
\(478\) | −7.48251e35 | −0.503235 | ||||||||
\(479\) | −9.56809e35 | −0.625599 | −0.312799 | − | 0.949819i | \(-0.601267\pi\) | ||||
−0.312799 | + | 0.949819i | \(0.601267\pi\) | |||||||
\(480\) | −1.93871e35 | −0.123242 | ||||||||
\(481\) | 1.45151e36 | 0.897142 | ||||||||
\(482\) | −1.44472e36 | −0.868255 | ||||||||
\(483\) | 7.02923e34 | 0.0410791 | ||||||||
\(484\) | 6.36432e35 | 0.361693 | ||||||||
\(485\) | −6.67386e35 | −0.368862 | ||||||||
\(486\) | −1.01674e36 | −0.546536 | ||||||||
\(487\) | −1.57059e36 | −0.821150 | −0.410575 | − | 0.911827i | \(-0.634672\pi\) | ||||
−0.410575 | + | 0.911827i | \(0.634672\pi\) | |||||||
\(488\) | 3.13828e36 | 1.59597 | ||||||||
\(489\) | 9.74087e35 | 0.481868 | ||||||||
\(490\) | 6.31211e35 | 0.303758 | ||||||||
\(491\) | −1.55981e36 | −0.730249 | −0.365124 | − | 0.930959i | \(-0.618974\pi\) | ||||
−0.365124 | + | 0.930959i | \(0.618974\pi\) | |||||||
\(492\) | 6.89252e34 | 0.0313942 | ||||||||
\(493\) | −8.70662e34 | −0.0385848 | ||||||||
\(494\) | 3.80982e36 | 1.64282 | ||||||||
\(495\) | −5.44084e35 | −0.228295 | ||||||||
\(496\) | 4.45029e35 | 0.181713 | ||||||||
\(497\) | −5.33285e34 | −0.0211908 | ||||||||
\(498\) | −3.16764e35 | −0.122501 | ||||||||
\(499\) | 1.75600e36 | 0.660948 | 0.330474 | − | 0.943815i | \(-0.392791\pi\) | ||||
0.330474 | + | 0.943815i | \(0.392791\pi\) | |||||||
\(500\) | −1.28893e35 | −0.0472210 | ||||||||
\(501\) | 5.75182e35 | 0.205114 | ||||||||
\(502\) | −6.59090e35 | −0.228794 | ||||||||
\(503\) | −2.95639e36 | −0.999066 | −0.499533 | − | 0.866295i | \(-0.666495\pi\) | ||||
−0.499533 | + | 0.866295i | \(0.666495\pi\) | |||||||
\(504\) | 3.10025e35 | 0.101996 | ||||||||
\(505\) | −2.40637e36 | −0.770777 | ||||||||
\(506\) | 1.58219e36 | 0.493433 | ||||||||
\(507\) | 1.44744e36 | 0.439535 | ||||||||
\(508\) | 3.10959e36 | 0.919481 | ||||||||
\(509\) | −1.51597e36 | −0.436517 | −0.218258 | − | 0.975891i | \(-0.570038\pi\) | ||||
−0.218258 | + | 0.975891i | \(0.570038\pi\) | |||||||
\(510\) | −9.45930e33 | −0.00265254 | ||||||||
\(511\) | 3.07092e35 | 0.0838662 | ||||||||
\(512\) | 1.42949e36 | 0.380223 | ||||||||
\(513\) | 3.37550e36 | 0.874489 | ||||||||
\(514\) | 1.65209e36 | 0.416899 | ||||||||
\(515\) | −1.84973e36 | −0.454686 | ||||||||
\(516\) | −2.09438e35 | −0.0501516 | ||||||||
\(517\) | 5.87874e35 | 0.137139 | ||||||||
\(518\) | 1.84590e35 | 0.0419524 | ||||||||
\(519\) | −1.38023e36 | −0.305627 | ||||||||
\(520\) | 3.41472e36 | 0.736732 | ||||||||
\(521\) | −3.10378e36 | −0.652501 | −0.326250 | − | 0.945283i | \(-0.605785\pi\) | ||||
−0.326250 | + | 0.945283i | \(0.605785\pi\) | |||||||
\(522\) | −4.09817e36 | −0.839533 | ||||||||
\(523\) | −7.80473e36 | −1.55806 | −0.779032 | − | 0.626984i | \(-0.784289\pi\) | ||||
−0.779032 | + | 0.626984i | \(0.784289\pi\) | |||||||
\(524\) | −4.53793e36 | −0.882848 | ||||||||
\(525\) | −3.38579e34 | −0.00641963 | ||||||||
\(526\) | −7.19041e36 | −1.32876 | ||||||||
\(527\) | −1.49901e35 | −0.0269999 | ||||||||
\(528\) | −1.85705e35 | −0.0326037 | ||||||||
\(529\) | 3.72728e36 | 0.637883 | ||||||||
\(530\) | 2.16299e36 | 0.360852 | ||||||||
\(531\) | 4.26639e36 | 0.693880 | ||||||||
\(532\) | −5.41869e35 | −0.0859186 | ||||||||
\(533\) | −2.00853e36 | −0.310500 | ||||||||
\(534\) | −1.10312e36 | −0.166271 | ||||||||
\(535\) | 1.05163e36 | 0.154556 | ||||||||
\(536\) | −8.81940e36 | −1.26390 | ||||||||
\(537\) | −2.98329e36 | −0.416911 | ||||||||
\(538\) | 6.41724e35 | 0.0874556 | ||||||||
\(539\) | −4.17404e36 | −0.554765 | ||||||||
\(540\) | 1.04537e36 | 0.135505 | ||||||||
\(541\) | 1.44148e37 | 1.82241 | 0.911205 | − | 0.411952i | \(-0.135153\pi\) | ||||
0.911205 | + | 0.411952i | \(0.135153\pi\) | |||||||
\(542\) | 5.26061e36 | 0.648703 | ||||||||
\(543\) | −1.64834e35 | −0.0198267 | ||||||||
\(544\) | −2.24493e35 | −0.0263401 | ||||||||
\(545\) | 2.58709e36 | 0.296114 | ||||||||
\(546\) | 3.09932e35 | 0.0346072 | ||||||||
\(547\) | 1.71311e37 | 1.86619 | 0.933096 | − | 0.359626i | \(-0.117096\pi\) | ||||
0.933096 | + | 0.359626i | \(0.117096\pi\) | |||||||
\(548\) | 8.69320e36 | 0.923936 | ||||||||
\(549\) | −1.33363e37 | −1.38296 | ||||||||
\(550\) | −7.62102e35 | −0.0771110 | ||||||||
\(551\) | 2.07303e37 | 2.04672 | ||||||||
\(552\) | −4.19093e36 | −0.403769 | ||||||||
\(553\) | 3.34668e35 | 0.0314648 | ||||||||
\(554\) | −5.96106e36 | −0.546942 | ||||||||
\(555\) | 8.58082e35 | 0.0768376 | ||||||||
\(556\) | −9.12503e36 | −0.797489 | ||||||||
\(557\) | 1.10383e37 | 0.941578 | 0.470789 | − | 0.882246i | \(-0.343969\pi\) | ||||
0.470789 | + | 0.882246i | \(0.343969\pi\) | |||||||
\(558\) | −7.05578e36 | −0.587467 | ||||||||
\(559\) | 6.10318e36 | 0.496017 | ||||||||
\(560\) | 1.16394e35 | 0.00923407 | ||||||||
\(561\) | 6.25520e34 | 0.00484443 | ||||||||
\(562\) | 1.81811e36 | 0.137461 | ||||||||
\(563\) | −1.63003e37 | −1.20319 | −0.601593 | − | 0.798803i | \(-0.705467\pi\) | ||||
−0.601593 | + | 0.798803i | \(0.705467\pi\) | |||||||
\(564\) | −5.38043e35 | −0.0387748 | ||||||||
\(565\) | 4.62052e36 | 0.325115 | ||||||||
\(566\) | 1.29822e36 | 0.0891920 | ||||||||
\(567\) | −1.17368e36 | −0.0787368 | ||||||||
\(568\) | 3.17953e36 | 0.208286 | ||||||||
\(569\) | −1.16009e37 | −0.742120 | −0.371060 | − | 0.928609i | \(-0.621006\pi\) | ||||
−0.371060 | + | 0.928609i | \(0.621006\pi\) | |||||||
\(570\) | 2.25224e36 | 0.140703 | ||||||||
\(571\) | −1.57490e37 | −0.960872 | −0.480436 | − | 0.877030i | \(-0.659522\pi\) | ||||
−0.480436 | + | 0.877030i | \(0.659522\pi\) | |||||||
\(572\) | −7.80224e36 | −0.464914 | ||||||||
\(573\) | −3.10188e36 | −0.180525 | ||||||||
\(574\) | −2.55427e35 | −0.0145197 | ||||||||
\(575\) | −4.60986e36 | −0.255960 | ||||||||
\(576\) | −1.38093e37 | −0.748974 | ||||||||
\(577\) | 1.14306e37 | 0.605611 | 0.302805 | − | 0.953052i | \(-0.402077\pi\) | ||||
0.302805 | + | 0.953052i | \(0.402077\pi\) | |||||||
\(578\) | 1.32636e37 | 0.686494 | ||||||||
\(579\) | −6.09099e36 | −0.307984 | ||||||||
\(580\) | 6.42002e36 | 0.317146 | ||||||||
\(581\) | −1.31288e36 | −0.0633647 | ||||||||
\(582\) | 3.61154e36 | 0.170307 | ||||||||
\(583\) | −1.43033e37 | −0.659038 | ||||||||
\(584\) | −1.83093e37 | −0.824326 | ||||||||
\(585\) | −1.45111e37 | −0.638404 | ||||||||
\(586\) | 3.23411e36 | 0.139039 | ||||||||
\(587\) | 1.18730e37 | 0.498824 | 0.249412 | − | 0.968397i | \(-0.419763\pi\) | ||||
0.249412 | + | 0.968397i | \(0.419763\pi\) | |||||||
\(588\) | 3.82024e36 | 0.156854 | ||||||||
\(589\) | 3.56911e37 | 1.43220 | ||||||||
\(590\) | 5.97596e36 | 0.234372 | ||||||||
\(591\) | 6.74248e36 | 0.258457 | ||||||||
\(592\) | −2.94985e36 | −0.110524 | ||||||||
\(593\) | −3.28233e37 | −1.20211 | −0.601054 | − | 0.799209i | \(-0.705252\pi\) | ||||
−0.601054 | + | 0.799209i | \(0.705252\pi\) | |||||||
\(594\) | 6.18092e36 | 0.221277 | ||||||||
\(595\) | −3.92056e34 | −0.00137205 | ||||||||
\(596\) | −2.57207e37 | −0.879950 | ||||||||
\(597\) | −1.26796e37 | −0.424083 | ||||||||
\(598\) | 4.21982e37 | 1.37984 | ||||||||
\(599\) | 1.12882e37 | 0.360881 | 0.180441 | − | 0.983586i | \(-0.442248\pi\) | ||||
0.180441 | + | 0.983586i | \(0.442248\pi\) | |||||||
\(600\) | 2.01866e36 | 0.0630989 | ||||||||
\(601\) | −7.84746e36 | −0.239841 | −0.119921 | − | 0.992783i | \(-0.538264\pi\) | ||||
−0.119921 | + | 0.992783i | \(0.538264\pi\) | |||||||
\(602\) | 7.76149e35 | 0.0231949 | ||||||||
\(603\) | 3.74786e37 | 1.09522 | ||||||||
\(604\) | 2.83315e37 | 0.809600 | ||||||||
\(605\) | −1.09638e37 | −0.306383 | ||||||||
\(606\) | 1.30220e37 | 0.355875 | ||||||||
\(607\) | −2.64580e37 | −0.707148 | −0.353574 | − | 0.935407i | \(-0.615034\pi\) | ||||
−0.353574 | + | 0.935407i | \(0.615034\pi\) | |||||||
\(608\) | 5.34511e37 | 1.39720 | ||||||||
\(609\) | 1.68642e36 | 0.0431155 | ||||||||
\(610\) | −1.86803e37 | −0.467122 | ||||||||
\(611\) | 1.56790e37 | 0.383496 | ||||||||
\(612\) | 5.76617e35 | 0.0137957 | ||||||||
\(613\) | −7.75347e37 | −1.81459 | −0.907297 | − | 0.420490i | \(-0.861858\pi\) | ||||
−0.907297 | + | 0.420490i | \(0.861858\pi\) | |||||||
\(614\) | −1.09790e36 | −0.0251357 | ||||||||
\(615\) | −1.18737e36 | −0.0265934 | ||||||||
\(616\) | −2.87161e36 | −0.0629197 | ||||||||
\(617\) | −2.09704e37 | −0.449528 | −0.224764 | − | 0.974413i | \(-0.572161\pi\) | ||||
−0.224764 | + | 0.974413i | \(0.572161\pi\) | |||||||
\(618\) | 1.00098e37 | 0.209933 | ||||||||
\(619\) | 6.54119e37 | 1.34225 | 0.671124 | − | 0.741345i | \(-0.265812\pi\) | ||||
0.671124 | + | 0.741345i | \(0.265812\pi\) | |||||||
\(620\) | 1.10533e37 | 0.221924 | ||||||||
\(621\) | 3.73876e37 | 0.734498 | ||||||||
\(622\) | −3.52083e37 | −0.676822 | ||||||||
\(623\) | −4.57208e36 | −0.0860052 | ||||||||
\(624\) | −4.95288e36 | −0.0911729 | ||||||||
\(625\) | 2.22045e36 | 0.0400000 | ||||||||
\(626\) | −2.35844e37 | −0.415787 | ||||||||
\(627\) | −1.48935e37 | −0.256971 | ||||||||
\(628\) | −3.03548e36 | −0.0512593 | ||||||||
\(629\) | 9.93612e35 | 0.0164223 | ||||||||
\(630\) | −1.84539e36 | −0.0298532 | ||||||||
\(631\) | 6.54067e37 | 1.03568 | 0.517841 | − | 0.855477i | \(-0.326736\pi\) | ||||
0.517841 | + | 0.855477i | \(0.326736\pi\) | |||||||
\(632\) | −1.99534e37 | −0.309269 | ||||||||
\(633\) | −1.85168e37 | −0.280941 | ||||||||
\(634\) | −4.19817e37 | −0.623527 | ||||||||
\(635\) | −5.35689e37 | −0.778874 | ||||||||
\(636\) | 1.30909e37 | 0.186337 | ||||||||
\(637\) | −1.11324e38 | −1.55134 | ||||||||
\(638\) | 3.79594e37 | 0.517893 | ||||||||
\(639\) | −1.35116e37 | −0.180487 | ||||||||
\(640\) | 1.20117e37 | 0.157099 | ||||||||
\(641\) | −1.66460e37 | −0.213170 | −0.106585 | − | 0.994304i | \(-0.533992\pi\) | ||||
−0.106585 | + | 0.994304i | \(0.533992\pi\) | |||||||
\(642\) | −5.69085e36 | −0.0713599 | ||||||||
\(643\) | −4.51668e37 | −0.554588 | −0.277294 | − | 0.960785i | \(-0.589438\pi\) | ||||
−0.277294 | + | 0.960785i | \(0.589438\pi\) | |||||||
\(644\) | −6.00182e36 | −0.0721645 | ||||||||
\(645\) | 3.60799e36 | 0.0424824 | ||||||||
\(646\) | 2.60797e36 | 0.0300721 | ||||||||
\(647\) | 5.82402e36 | 0.0657681 | 0.0328840 | − | 0.999459i | \(-0.489531\pi\) | ||||
0.0328840 | + | 0.999459i | \(0.489531\pi\) | |||||||
\(648\) | 6.99766e37 | 0.773909 | ||||||||
\(649\) | −3.95175e37 | −0.428042 | ||||||||
\(650\) | −2.03257e37 | −0.215633 | ||||||||
\(651\) | 2.90350e36 | 0.0301702 | ||||||||
\(652\) | −8.31712e37 | −0.846507 | ||||||||
\(653\) | 7.78394e37 | 0.776017 | 0.388009 | − | 0.921656i | \(-0.373163\pi\) | ||||
0.388009 | + | 0.921656i | \(0.373163\pi\) | |||||||
\(654\) | −1.40000e37 | −0.136718 | ||||||||
\(655\) | 7.81750e37 | 0.747843 | ||||||||
\(656\) | 4.08186e36 | 0.0382522 | ||||||||
\(657\) | 7.78067e37 | 0.714307 | ||||||||
\(658\) | 1.99392e36 | 0.0179332 | ||||||||
\(659\) | 1.70605e38 | 1.50328 | 0.751638 | − | 0.659576i | \(-0.229264\pi\) | ||||
0.751638 | + | 0.659576i | \(0.229264\pi\) | |||||||
\(660\) | −4.61241e36 | −0.0398185 | ||||||||
\(661\) | −1.16463e38 | −0.985072 | −0.492536 | − | 0.870292i | \(-0.663930\pi\) | ||||
−0.492536 | + | 0.870292i | \(0.663930\pi\) | |||||||
\(662\) | −7.49216e36 | −0.0620903 | ||||||||
\(663\) | 1.66830e36 | 0.0135470 | ||||||||
\(664\) | 7.82759e37 | 0.622815 | ||||||||
\(665\) | 9.33477e36 | 0.0727799 | ||||||||
\(666\) | 4.67689e37 | 0.357318 | ||||||||
\(667\) | 2.29611e38 | 1.71907 | ||||||||
\(668\) | −4.91112e37 | −0.360328 | ||||||||
\(669\) | −4.51055e37 | −0.324322 | ||||||||
\(670\) | 5.24965e37 | 0.369931 | ||||||||
\(671\) | 1.23528e38 | 0.853123 | ||||||||
\(672\) | 4.34829e36 | 0.0294329 | ||||||||
\(673\) | −1.98332e38 | −1.31580 | −0.657898 | − | 0.753107i | \(-0.728554\pi\) | ||||
−0.657898 | + | 0.753107i | \(0.728554\pi\) | |||||||
\(674\) | −5.94914e37 | −0.386853 | ||||||||
\(675\) | −1.80086e37 | −0.114783 | ||||||||
\(676\) | −1.23588e38 | −0.772140 | ||||||||
\(677\) | 1.56476e38 | 0.958299 | 0.479149 | − | 0.877733i | \(-0.340945\pi\) | ||||
0.479149 | + | 0.877733i | \(0.340945\pi\) | |||||||
\(678\) | −2.50038e37 | −0.150108 | ||||||||
\(679\) | 1.49686e37 | 0.0880927 | ||||||||
\(680\) | 2.33750e36 | 0.0134860 | ||||||||
\(681\) | 4.61183e37 | 0.260848 | ||||||||
\(682\) | 6.53543e37 | 0.362398 | ||||||||
\(683\) | 1.36864e38 | 0.744061 | 0.372030 | − | 0.928221i | \(-0.378662\pi\) | ||||
0.372030 | + | 0.928221i | \(0.378662\pi\) | |||||||
\(684\) | −1.37291e38 | −0.731787 | ||||||||
\(685\) | −1.49758e38 | −0.782648 | ||||||||
\(686\) | −2.84779e37 | −0.145926 | ||||||||
\(687\) | −9.51306e36 | −0.0477974 | ||||||||
\(688\) | −1.24033e37 | −0.0611072 | ||||||||
\(689\) | −3.81478e38 | −1.84294 | ||||||||
\(690\) | 2.49461e37 | 0.118179 | ||||||||
\(691\) | −3.59443e38 | −1.66984 | −0.834922 | − | 0.550368i | \(-0.814487\pi\) | ||||
−0.834922 | + | 0.550368i | \(0.814487\pi\) | |||||||
\(692\) | 1.17849e38 | 0.536901 | ||||||||
\(693\) | 1.22031e37 | 0.0545221 | ||||||||
\(694\) | −1.69532e38 | −0.742845 | ||||||||
\(695\) | 1.57197e38 | 0.675537 | ||||||||
\(696\) | −1.00547e38 | −0.423785 | ||||||||
\(697\) | −1.37491e36 | −0.00568372 | ||||||||
\(698\) | −2.98125e38 | −1.20879 | ||||||||
\(699\) | 1.05813e38 | 0.420819 | ||||||||
\(700\) | 2.89092e36 | 0.0112775 | ||||||||
\(701\) | 2.57026e38 | 0.983519 | 0.491760 | − | 0.870731i | \(-0.336354\pi\) | ||||
0.491760 | + | 0.870731i | \(0.336354\pi\) | |||||||
\(702\) | 1.64849e38 | 0.618779 | ||||||||
\(703\) | −2.36577e38 | −0.871114 | ||||||||
\(704\) | 1.27909e38 | 0.462029 | ||||||||
\(705\) | 9.26887e36 | 0.0328453 | ||||||||
\(706\) | −1.59403e38 | −0.554158 | ||||||||
\(707\) | 5.39718e37 | 0.184079 | ||||||||
\(708\) | 3.61679e37 | 0.121025 | ||||||||
\(709\) | 1.31686e38 | 0.432330 | 0.216165 | − | 0.976357i | \(-0.430645\pi\) | ||||
0.216165 | + | 0.976357i | \(0.430645\pi\) | |||||||
\(710\) | −1.89258e37 | −0.0609631 | ||||||||
\(711\) | 8.47934e37 | 0.267992 | ||||||||
\(712\) | 2.72594e38 | 0.845351 | ||||||||
\(713\) | 3.95320e38 | 1.20293 | ||||||||
\(714\) | 2.12160e35 | 0.000633487 0 | ||||||||
\(715\) | 1.34409e38 | 0.393820 | ||||||||
\(716\) | 2.54725e38 | 0.732395 | ||||||||
\(717\) | 7.80140e37 | 0.220122 | ||||||||
\(718\) | 7.49376e37 | 0.207501 | ||||||||
\(719\) | −4.19294e38 | −1.13941 | −0.569703 | − | 0.821851i | \(-0.692942\pi\) | ||||
−0.569703 | + | 0.821851i | \(0.692942\pi\) | |||||||
\(720\) | 2.94903e37 | 0.0786486 | ||||||||
\(721\) | 4.14872e37 | 0.108589 | ||||||||
\(722\) | −3.53498e38 | −0.908102 | ||||||||
\(723\) | 1.50629e38 | 0.379787 | ||||||||
\(724\) | 1.40742e37 | 0.0348299 | ||||||||
\(725\) | −1.10598e38 | −0.268648 | ||||||||
\(726\) | 5.93304e37 | 0.141460 | ||||||||
\(727\) | −5.58729e36 | −0.0130764 | −0.00653818 | − | 0.999979i | \(-0.502081\pi\) | ||||
−0.00653818 | + | 0.999979i | \(0.502081\pi\) | |||||||
\(728\) | −7.65878e37 | −0.175949 | ||||||||
\(729\) | −2.20888e38 | −0.498139 | ||||||||
\(730\) | 1.08984e38 | 0.241271 | ||||||||
\(731\) | 4.17785e36 | 0.00907964 | ||||||||
\(732\) | −1.13057e38 | −0.241212 | ||||||||
\(733\) | 3.94722e37 | 0.0826776 | 0.0413388 | − | 0.999145i | \(-0.486838\pi\) | ||||
0.0413388 | + | 0.999145i | \(0.486838\pi\) | |||||||
\(734\) | 6.03470e38 | 1.24096 | ||||||||
\(735\) | −6.58112e37 | −0.132868 | ||||||||
\(736\) | 5.92033e38 | 1.17353 | ||||||||
\(737\) | −3.47147e38 | −0.675619 | ||||||||
\(738\) | −6.47166e37 | −0.123667 | ||||||||
\(739\) | −7.95586e37 | −0.149275 | −0.0746376 | − | 0.997211i | \(-0.523780\pi\) | ||||
−0.0746376 | + | 0.997211i | \(0.523780\pi\) | |||||||
\(740\) | −7.32663e37 | −0.134982 | ||||||||
\(741\) | −3.97219e38 | −0.718595 | ||||||||
\(742\) | −4.85131e37 | −0.0861799 | ||||||||
\(743\) | 4.62071e37 | 0.0806045 | 0.0403023 | − | 0.999188i | \(-0.487168\pi\) | ||||
0.0403023 | + | 0.999188i | \(0.487168\pi\) | |||||||
\(744\) | −1.73111e38 | −0.296545 | ||||||||
\(745\) | 4.43090e38 | 0.745388 | ||||||||
\(746\) | −2.98986e38 | −0.493943 | ||||||||
\(747\) | −3.32639e38 | −0.539691 | ||||||||
\(748\) | −5.34092e36 | −0.00851030 | ||||||||
\(749\) | −2.35867e37 | −0.0369115 | ||||||||
\(750\) | −1.20159e37 | −0.0184684 | ||||||||
\(751\) | 3.67388e38 | 0.554607 | 0.277303 | − | 0.960782i | \(-0.410559\pi\) | ||||
0.277303 | + | 0.960782i | \(0.410559\pi\) | |||||||
\(752\) | −3.18638e37 | −0.0472451 | ||||||||
\(753\) | 6.87179e37 | 0.100078 | ||||||||
\(754\) | 1.01240e39 | 1.44824 | ||||||||
\(755\) | −4.88067e38 | −0.685796 | ||||||||
\(756\) | −2.34464e37 | −0.0323617 | ||||||||
\(757\) | −1.04932e39 | −1.42271 | −0.711354 | − | 0.702834i | \(-0.751918\pi\) | ||||
−0.711354 | + | 0.702834i | \(0.751918\pi\) | |||||||
\(758\) | −7.28880e38 | −0.970782 | ||||||||
\(759\) | −1.64962e38 | −0.215835 | ||||||||
\(760\) | −5.56554e38 | −0.715358 | ||||||||
\(761\) | −5.58189e38 | −0.704836 | −0.352418 | − | 0.935843i | \(-0.614641\pi\) | ||||
−0.352418 | + | 0.935843i | \(0.614641\pi\) | |||||||
\(762\) | 2.89886e38 | 0.359613 | ||||||||
\(763\) | −5.80252e37 | −0.0707188 | ||||||||
\(764\) | 2.64850e38 | 0.317131 | ||||||||
\(765\) | −9.93337e36 | −0.0116860 | ||||||||
\(766\) | 1.04339e39 | 1.20602 | ||||||||
\(767\) | −1.05396e39 | −1.19698 | ||||||||
\(768\) | −2.86740e38 | −0.319972 | ||||||||
\(769\) | 6.88068e38 | 0.754442 | 0.377221 | − | 0.926123i | \(-0.376880\pi\) | ||||
0.377221 | + | 0.926123i | \(0.376880\pi\) | |||||||
\(770\) | 1.70930e37 | 0.0184159 | ||||||||
\(771\) | −1.72249e38 | −0.182358 | ||||||||
\(772\) | 5.20072e38 | 0.541041 | ||||||||
\(773\) | 8.57010e38 | 0.876118 | 0.438059 | − | 0.898946i | \(-0.355666\pi\) | ||||
0.438059 | + | 0.898946i | \(0.355666\pi\) | |||||||
\(774\) | 1.96650e38 | 0.197556 | ||||||||
\(775\) | −1.90415e38 | −0.187987 | ||||||||
\(776\) | −8.92453e38 | −0.865869 | ||||||||
\(777\) | −1.92457e37 | −0.0183506 | ||||||||
\(778\) | 5.75726e38 | 0.539500 | ||||||||
\(779\) | 3.27364e38 | 0.301491 | ||||||||
\(780\) | −1.23016e38 | −0.111349 | ||||||||
\(781\) | 1.25152e38 | 0.111339 | ||||||||
\(782\) | 2.88862e37 | 0.0252580 | ||||||||
\(783\) | 8.96987e38 | 0.770908 | ||||||||
\(784\) | 2.26241e38 | 0.191119 | ||||||||
\(785\) | 5.22923e37 | 0.0434207 | ||||||||
\(786\) | −4.23042e38 | −0.345286 | ||||||||
\(787\) | 2.50661e38 | 0.201107 | 0.100553 | − | 0.994932i | \(-0.467939\pi\) | ||||
0.100553 | + | 0.994932i | \(0.467939\pi\) | |||||||
\(788\) | −5.75698e38 | −0.454036 | ||||||||
\(789\) | 7.49685e38 | 0.581218 | ||||||||
\(790\) | 1.18771e38 | 0.0905197 | ||||||||
\(791\) | −1.03632e38 | −0.0776449 | ||||||||
\(792\) | −7.27569e38 | −0.535901 | ||||||||
\(793\) | 3.29457e39 | 2.38567 | ||||||||
\(794\) | −1.49058e39 | −1.06115 | ||||||||
\(795\) | −2.25517e38 | −0.157842 | ||||||||
\(796\) | 1.08263e39 | 0.744994 | ||||||||
\(797\) | 2.39896e39 | 1.62306 | 0.811531 | − | 0.584309i | \(-0.198634\pi\) | ||||
0.811531 | + | 0.584309i | \(0.198634\pi\) | |||||||
\(798\) | −5.05148e37 | −0.0336031 | ||||||||
\(799\) | 1.07328e37 | 0.00701994 | ||||||||
\(800\) | −2.85167e38 | −0.183393 | ||||||||
\(801\) | −1.15841e39 | −0.732525 | ||||||||
\(802\) | −1.16224e39 | −0.722673 | ||||||||
\(803\) | −7.20687e38 | −0.440643 | ||||||||
\(804\) | 3.17721e38 | 0.191025 | ||||||||
\(805\) | 1.03393e38 | 0.0611291 | ||||||||
\(806\) | 1.74304e39 | 1.01341 | ||||||||
\(807\) | −6.69073e37 | −0.0382544 | ||||||||
\(808\) | −3.21788e39 | −1.80933 | ||||||||
\(809\) | 1.25830e39 | 0.695791 | 0.347896 | − | 0.937533i | \(-0.386896\pi\) | ||||
0.347896 | + | 0.937533i | \(0.386896\pi\) | |||||||
\(810\) | −4.16528e38 | −0.226515 | ||||||||
\(811\) | −3.51523e39 | −1.88006 | −0.940030 | − | 0.341092i | \(-0.889203\pi\) | ||||
−0.940030 | + | 0.341092i | \(0.889203\pi\) | |||||||
\(812\) | −1.43993e38 | −0.0757417 | ||||||||
\(813\) | −5.48481e38 | −0.283752 | ||||||||
\(814\) | −4.33198e38 | −0.220423 | ||||||||
\(815\) | 1.43279e39 | 0.717059 | ||||||||
\(816\) | −3.39043e36 | −0.00166893 | ||||||||
\(817\) | −9.94737e38 | −0.481627 | ||||||||
\(818\) | −1.19856e39 | −0.570807 | ||||||||
\(819\) | 3.25465e38 | 0.152466 | ||||||||
\(820\) | 1.01382e38 | 0.0467171 | ||||||||
\(821\) | 1.79305e39 | 0.812755 | 0.406377 | − | 0.913705i | \(-0.366792\pi\) | ||||
0.406377 | + | 0.913705i | \(0.366792\pi\) | |||||||
\(822\) | 8.10410e38 | 0.361356 | ||||||||
\(823\) | 3.11454e37 | 0.0136614 | 0.00683071 | − | 0.999977i | \(-0.497826\pi\) | ||||
0.00683071 | + | 0.999977i | \(0.497826\pi\) | |||||||
\(824\) | −2.47353e39 | −1.06733 | ||||||||
\(825\) | 7.94581e37 | 0.0337295 | ||||||||
\(826\) | −1.34033e38 | −0.0559734 | ||||||||
\(827\) | −1.45069e39 | −0.596005 | −0.298003 | − | 0.954565i | \(-0.596320\pi\) | ||||
−0.298003 | + | 0.954565i | \(0.596320\pi\) | |||||||
\(828\) | −1.52066e39 | −0.614641 | ||||||||
\(829\) | −4.64859e39 | −1.84857 | −0.924283 | − | 0.381707i | \(-0.875336\pi\) | ||||
−0.924283 | + | 0.381707i | \(0.875336\pi\) | |||||||
\(830\) | −4.65929e38 | −0.182291 | ||||||||
\(831\) | 6.21510e38 | 0.239240 | ||||||||
\(832\) | 3.41141e39 | 1.29202 | ||||||||
\(833\) | −7.62058e37 | −0.0283975 | ||||||||
\(834\) | −8.50666e38 | −0.311902 | ||||||||
\(835\) | 8.46039e38 | 0.305227 | ||||||||
\(836\) | 1.27166e39 | 0.451426 | ||||||||
\(837\) | 1.54434e39 | 0.539446 | ||||||||
\(838\) | 2.78309e39 | 0.956604 | ||||||||
\(839\) | 6.25511e38 | 0.211567 | 0.105784 | − | 0.994389i | \(-0.466265\pi\) | ||||
0.105784 | + | 0.994389i | \(0.466265\pi\) | |||||||
\(840\) | −4.52761e37 | −0.0150695 | ||||||||
\(841\) | 2.45560e39 | 0.804290 | ||||||||
\(842\) | 1.08902e39 | 0.351011 | ||||||||
\(843\) | −1.89559e38 | −0.0601275 | ||||||||
\(844\) | 1.58103e39 | 0.493535 | ||||||||
\(845\) | 2.12905e39 | 0.654064 | ||||||||
\(846\) | 5.05190e38 | 0.152741 | ||||||||
\(847\) | 2.45905e38 | 0.0731713 | ||||||||
\(848\) | 7.75265e38 | 0.227042 | ||||||||
\(849\) | −1.35355e38 | −0.0390139 | ||||||||
\(850\) | −1.39137e37 | −0.00394719 | ||||||||
\(851\) | −2.62036e39 | −0.731664 | ||||||||
\(852\) | −1.14543e38 | −0.0314801 | ||||||||
\(853\) | −1.68444e39 | −0.455662 | −0.227831 | − | 0.973701i | \(-0.573163\pi\) | ||||
−0.227831 | + | 0.973701i | \(0.573163\pi\) | |||||||
\(854\) | 4.18975e38 | 0.111560 | ||||||||
\(855\) | 2.36511e39 | 0.619882 | ||||||||
\(856\) | 1.40627e39 | 0.362806 | ||||||||
\(857\) | 4.47378e39 | 1.13614 | 0.568072 | − | 0.822979i | \(-0.307689\pi\) | ||||
0.568072 | + | 0.822979i | \(0.307689\pi\) | |||||||
\(858\) | −7.27351e38 | −0.181830 | ||||||||
\(859\) | −2.74806e39 | −0.676267 | −0.338134 | − | 0.941098i | \(-0.609796\pi\) | ||||
−0.338134 | + | 0.941098i | \(0.609796\pi\) | |||||||
\(860\) | −3.08064e38 | −0.0746296 | ||||||||
\(861\) | 2.66313e37 | 0.00635111 | ||||||||
\(862\) | 3.89806e38 | 0.0915166 | ||||||||
\(863\) | −4.77950e39 | −1.10468 | −0.552341 | − | 0.833618i | \(-0.686265\pi\) | ||||
−0.552341 | + | 0.833618i | \(0.686265\pi\) | |||||||
\(864\) | 2.31280e39 | 0.526263 | ||||||||
\(865\) | −2.03019e39 | −0.454798 | ||||||||
\(866\) | 3.51017e39 | 0.774171 | ||||||||
\(867\) | −1.38289e39 | −0.300282 | ||||||||
\(868\) | −2.47912e38 | −0.0530006 | ||||||||
\(869\) | −7.85401e38 | −0.165320 | ||||||||
\(870\) | 5.98496e38 | 0.124037 | ||||||||
\(871\) | −9.25863e39 | −1.88930 | ||||||||
\(872\) | 3.45955e39 | 0.695100 | ||||||||
\(873\) | 3.79254e39 | 0.750305 | ||||||||
\(874\) | −6.87774e39 | −1.33980 | ||||||||
\(875\) | −4.98018e37 | −0.00955293 | ||||||||
\(876\) | 6.59599e38 | 0.124587 | ||||||||
\(877\) | −2.09448e39 | −0.389566 | −0.194783 | − | 0.980846i | \(-0.562400\pi\) | ||||
−0.194783 | + | 0.980846i | \(0.562400\pi\) | |||||||
\(878\) | 2.54547e39 | 0.466221 | ||||||||
\(879\) | −3.37194e38 | −0.0608178 | ||||||||
\(880\) | −2.73155e38 | −0.0485169 | ||||||||
\(881\) | −3.84071e39 | −0.671796 | −0.335898 | − | 0.941898i | \(-0.609040\pi\) | ||||
−0.335898 | + | 0.941898i | \(0.609040\pi\) | |||||||
\(882\) | −3.58697e39 | −0.617877 | ||||||||
\(883\) | 5.26228e39 | 0.892697 | 0.446349 | − | 0.894859i | \(-0.352724\pi\) | ||||
0.446349 | + | 0.894859i | \(0.352724\pi\) | |||||||
\(884\) | −1.42446e38 | −0.0237982 | ||||||||
\(885\) | −6.23064e38 | −0.102518 | ||||||||
\(886\) | −1.83372e39 | −0.297151 | ||||||||
\(887\) | 1.78125e38 | 0.0284287 | 0.0142143 | − | 0.999899i | \(-0.495475\pi\) | ||||
0.0142143 | + | 0.999899i | \(0.495475\pi\) | |||||||
\(888\) | 1.14746e39 | 0.180369 | ||||||||
\(889\) | 1.20148e39 | 0.186013 | ||||||||
\(890\) | −1.62259e39 | −0.247425 | ||||||||
\(891\) | 2.75440e39 | 0.413693 | ||||||||
\(892\) | 3.85127e39 | 0.569743 | ||||||||
\(893\) | −2.55547e39 | −0.372371 | ||||||||
\(894\) | −2.39777e39 | −0.344152 | ||||||||
\(895\) | −4.38814e39 | −0.620397 | ||||||||
\(896\) | −2.69407e38 | −0.0375190 | ||||||||
\(897\) | −4.39966e39 | −0.603560 | ||||||||
\(898\) | −6.43876e39 | −0.870105 | ||||||||
\(899\) | 9.48435e39 | 1.26256 | ||||||||
\(900\) | 7.32460e38 | 0.0960528 | ||||||||
\(901\) | −2.61136e38 | −0.0337351 | ||||||||
\(902\) | 5.99439e38 | 0.0762881 | ||||||||
\(903\) | −8.09227e37 | −0.0101458 | ||||||||
\(904\) | 6.17873e39 | 0.763177 | ||||||||
\(905\) | −2.42455e38 | −0.0295037 | ||||||||
\(906\) | 2.64116e39 | 0.316639 | ||||||||
\(907\) | −4.51361e39 | −0.533121 | −0.266561 | − | 0.963818i | \(-0.585887\pi\) | ||||
−0.266561 | + | 0.963818i | \(0.585887\pi\) | |||||||
\(908\) | −3.93775e39 | −0.458236 | ||||||||
\(909\) | 1.36746e40 | 1.56784 | ||||||||
\(910\) | 4.55881e38 | 0.0514983 | ||||||||
\(911\) | −3.61144e38 | −0.0401960 | −0.0200980 | − | 0.999798i | \(-0.506398\pi\) | ||||
−0.0200980 | + | 0.999798i | \(0.506398\pi\) | |||||||
\(912\) | 8.07254e38 | 0.0885278 | ||||||||
\(913\) | 3.08108e39 | 0.332925 | ||||||||
\(914\) | 3.59638e39 | 0.382905 | ||||||||
\(915\) | 1.94764e39 | 0.204326 | ||||||||
\(916\) | 8.12260e38 | 0.0839666 | ||||||||
\(917\) | −1.75337e39 | −0.178602 | ||||||||
\(918\) | 1.12845e38 | 0.0113268 | ||||||||
\(919\) | −1.21557e40 | −1.20233 | −0.601163 | − | 0.799126i | \(-0.705296\pi\) | ||||
−0.601163 | + | 0.799126i | \(0.705296\pi\) | |||||||
\(920\) | −6.16447e39 | −0.600842 | ||||||||
\(921\) | 1.14469e38 | 0.0109947 | ||||||||
\(922\) | −9.93954e39 | −0.940803 | ||||||||
\(923\) | 3.33788e39 | 0.311349 | ||||||||
\(924\) | 1.03451e38 | 0.00950959 | ||||||||
\(925\) | 1.26216e39 | 0.114341 | ||||||||
\(926\) | 2.87061e39 | 0.256286 | ||||||||
\(927\) | 1.05114e40 | 0.924881 | ||||||||
\(928\) | 1.42038e40 | 1.23171 | ||||||||
\(929\) | 7.00396e39 | 0.598593 | 0.299296 | − | 0.954160i | \(-0.403248\pi\) | ||||
0.299296 | + | 0.954160i | \(0.403248\pi\) | |||||||
\(930\) | 1.03043e39 | 0.0867955 | ||||||||
\(931\) | 1.81444e40 | 1.50634 | ||||||||
\(932\) | −9.03468e39 | −0.739261 | ||||||||
\(933\) | 3.67088e39 | 0.296052 | ||||||||
\(934\) | 1.48320e40 | 1.17901 | ||||||||
\(935\) | 9.20081e37 | 0.00720890 | ||||||||
\(936\) | −1.94047e40 | −1.49859 | ||||||||
\(937\) | −1.68667e40 | −1.28394 | −0.641971 | − | 0.766729i | \(-0.721883\pi\) | ||||
−0.641971 | + | 0.766729i | \(0.721883\pi\) | |||||||
\(938\) | −1.17743e39 | −0.0883481 | ||||||||
\(939\) | 2.45895e39 | 0.181871 | ||||||||
\(940\) | −7.91411e38 | −0.0577000 | ||||||||
\(941\) | 8.43439e39 | 0.606169 | 0.303085 | − | 0.952964i | \(-0.401983\pi\) | ||||
0.303085 | + | 0.952964i | \(0.401983\pi\) | |||||||
\(942\) | −2.82978e38 | −0.0200477 | ||||||||
\(943\) | 3.62593e39 | 0.253228 | ||||||||
\(944\) | 2.14192e39 | 0.147463 | ||||||||
\(945\) | 4.03911e38 | 0.0274129 | ||||||||
\(946\) | −1.82147e39 | −0.121869 | ||||||||
\(947\) | −2.44897e40 | −1.61532 | −0.807659 | − | 0.589649i | \(-0.799266\pi\) | ||||
−0.807659 | + | 0.589649i | \(0.799266\pi\) | |||||||
\(948\) | 7.18827e38 | 0.0467425 | ||||||||
\(949\) | −1.92212e40 | −1.23221 | ||||||||
\(950\) | 3.31283e39 | 0.209378 | ||||||||
\(951\) | 4.37709e39 | 0.272740 | ||||||||
\(952\) | −5.24272e37 | −0.00322076 | ||||||||
\(953\) | −1.31618e40 | −0.797191 | −0.398596 | − | 0.917127i | \(-0.630502\pi\) | ||||
−0.398596 | + | 0.917127i | \(0.630502\pi\) | |||||||
\(954\) | −1.22916e40 | −0.734013 | ||||||||
\(955\) | −4.56257e39 | −0.268636 | ||||||||
\(956\) | −6.66113e39 | −0.386693 | ||||||||
\(957\) | −3.95771e39 | −0.226534 | ||||||||
\(958\) | 7.61597e39 | 0.429824 | ||||||||
\(959\) | 3.35888e39 | 0.186915 | ||||||||
\(960\) | 2.01671e39 | 0.110657 | ||||||||
\(961\) | −2.15358e39 | −0.116519 | ||||||||
\(962\) | −1.15537e40 | −0.616391 | ||||||||
\(963\) | −5.97606e39 | −0.314384 | ||||||||
\(964\) | −1.28612e40 | −0.667179 | ||||||||
\(965\) | −8.95928e39 | −0.458305 | ||||||||
\(966\) | −5.59510e38 | −0.0282239 | ||||||||
\(967\) | 3.47387e40 | 1.72805 | 0.864025 | − | 0.503449i | \(-0.167936\pi\) | ||||
0.864025 | + | 0.503449i | \(0.167936\pi\) | |||||||
\(968\) | −1.46612e40 | −0.719205 | ||||||||
\(969\) | −2.71911e38 | −0.0131539 | ||||||||
\(970\) | 5.31223e39 | 0.253430 | ||||||||
\(971\) | 3.09835e40 | 1.45771 | 0.728854 | − | 0.684669i | \(-0.240053\pi\) | ||||
0.728854 | + | 0.684669i | \(0.240053\pi\) | |||||||
\(972\) | −9.05124e39 | −0.419966 | ||||||||
\(973\) | −3.52573e39 | −0.161334 | ||||||||
\(974\) | 1.25015e40 | 0.564180 | ||||||||
\(975\) | 2.11920e39 | 0.0943212 | ||||||||
\(976\) | −6.69544e39 | −0.293905 | ||||||||
\(977\) | 3.13699e40 | 1.35812 | 0.679058 | − | 0.734084i | \(-0.262388\pi\) | ||||
0.679058 | + | 0.734084i | \(0.262388\pi\) | |||||||
\(978\) | −7.75350e39 | −0.331073 | ||||||||
\(979\) | 1.07298e40 | 0.451882 | ||||||||
\(980\) | 5.61921e39 | 0.233412 | ||||||||
\(981\) | −1.47016e40 | −0.602328 | ||||||||
\(982\) | 1.24157e40 | 0.501725 | ||||||||
\(983\) | 7.16907e39 | 0.285752 | 0.142876 | − | 0.989741i | \(-0.454365\pi\) | ||||
0.142876 | + | 0.989741i | \(0.454365\pi\) | |||||||
\(984\) | −1.58780e39 | −0.0624255 | ||||||||
\(985\) | 9.91754e39 | 0.384605 | ||||||||
\(986\) | 6.93026e38 | 0.0265101 | ||||||||
\(987\) | −2.07889e38 | −0.00784423 | ||||||||
\(988\) | 3.39160e40 | 1.26237 | ||||||||
\(989\) | −1.10179e40 | −0.404527 | ||||||||
\(990\) | 4.33078e39 | 0.156852 | ||||||||
\(991\) | −1.14112e40 | −0.407698 | −0.203849 | − | 0.979002i | \(-0.565345\pi\) | ||||
−0.203849 | + | 0.979002i | \(0.565345\pi\) | |||||||
\(992\) | 2.44546e40 | 0.861891 | ||||||||
\(993\) | 7.81145e38 | 0.0271592 | ||||||||
\(994\) | 4.24482e38 | 0.0145594 | ||||||||
\(995\) | −1.86504e40 | −0.631070 | ||||||||
\(996\) | −2.81991e39 | −0.0941314 | ||||||||
\(997\) | 1.49086e40 | 0.490968 | 0.245484 | − | 0.969401i | \(-0.421053\pi\) | ||||
0.245484 | + | 0.969401i | \(0.421053\pi\) | |||||||
\(998\) | −1.39773e40 | −0.454111 | ||||||||
\(999\) | −1.02366e40 | −0.328110 |
(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 | 5.28.a.a.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 45.28.a.b.1.3 | 4 | |||
5.2 | odd | 4 | 25.28.b.b.24.3 | 8 | |||
5.3 | odd | 4 | 25.28.b.b.24.6 | 8 | |||
5.4 | even | 2 | 25.28.a.b.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.28.a.a.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
25.28.a.b.1.3 | 4 | 5.4 | even | 2 | |||
25.28.b.b.24.3 | 8 | 5.2 | odd | 4 | |||
25.28.b.b.24.6 | 8 | 5.3 | odd | 4 | |||
45.28.a.b.1.3 | 4 | 3.2 | odd | 2 |