Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,26,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(7.91993559904\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{106705}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 26676 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7}\cdot 3\cdot 5^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-162.829\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4096.00 | 0.707107 | ||||||||
\(3\) | 1.75788e6 | 1.90974 | 0.954868 | − | 0.297031i | \(-0.0959963\pi\) | ||||
0.954868 | + | 0.297031i | \(0.0959963\pi\) | |||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | −1.37041e8 | −0.251030 | −0.125515 | − | 0.992092i | \(-0.540058\pi\) | ||||
−0.125515 | + | 0.992092i | \(0.540058\pi\) | |||||||
\(6\) | 7.20027e9 | 1.35039 | ||||||||
\(7\) | −3.04153e10 | −0.830552 | −0.415276 | − | 0.909696i | \(-0.636315\pi\) | ||||
−0.415276 | + | 0.909696i | \(0.636315\pi\) | |||||||
\(8\) | 6.87195e10 | 0.353553 | ||||||||
\(9\) | 2.24285e12 | 2.64709 | ||||||||
\(10\) | −5.61320e11 | −0.177505 | ||||||||
\(11\) | 2.58704e12 | 0.248539 | 0.124270 | − | 0.992248i | \(-0.460341\pi\) | ||||
0.124270 | + | 0.992248i | \(0.460341\pi\) | |||||||
\(12\) | 2.94923e13 | 0.954868 | ||||||||
\(13\) | −9.57327e13 | −1.13964 | −0.569821 | − | 0.821769i | \(-0.692988\pi\) | ||||
−0.569821 | + | 0.821769i | \(0.692988\pi\) | |||||||
\(14\) | −1.24581e14 | −0.587289 | ||||||||
\(15\) | −2.40901e14 | −0.479400 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | −1.64685e15 | −0.685555 | −0.342777 | − | 0.939417i | \(-0.611368\pi\) | ||||
−0.342777 | + | 0.939417i | \(0.611368\pi\) | |||||||
\(18\) | 9.18671e15 | 1.87178 | ||||||||
\(19\) | 4.95030e15 | 0.513111 | 0.256555 | − | 0.966530i | \(-0.417412\pi\) | ||||
0.256555 | + | 0.966530i | \(0.417412\pi\) | |||||||
\(20\) | −2.29916e15 | −0.125515 | ||||||||
\(21\) | −5.34664e16 | −1.58613 | ||||||||
\(22\) | 1.05965e16 | 0.175744 | ||||||||
\(23\) | −1.07650e16 | −0.102427 | −0.0512136 | − | 0.998688i | \(-0.516309\pi\) | ||||
−0.0512136 | + | 0.998688i | \(0.516309\pi\) | |||||||
\(24\) | 1.20801e17 | 0.675194 | ||||||||
\(25\) | −2.79243e17 | −0.936984 | ||||||||
\(26\) | −3.92121e17 | −0.805849 | ||||||||
\(27\) | 2.45323e18 | 3.14551 | ||||||||
\(28\) | −5.10284e17 | −0.415276 | ||||||||
\(29\) | −1.36741e18 | −0.717668 | −0.358834 | − | 0.933401i | \(-0.616826\pi\) | ||||
−0.358834 | + | 0.933401i | \(0.616826\pi\) | |||||||
\(30\) | −9.86732e17 | −0.338987 | ||||||||
\(31\) | −4.42000e18 | −1.00786 | −0.503931 | − | 0.863744i | \(-0.668113\pi\) | ||||
−0.503931 | + | 0.863744i | \(0.668113\pi\) | |||||||
\(32\) | 1.15292e18 | 0.176777 | ||||||||
\(33\) | 4.54771e18 | 0.474645 | ||||||||
\(34\) | −6.74549e18 | −0.484760 | ||||||||
\(35\) | 4.16814e18 | 0.208493 | ||||||||
\(36\) | 3.76288e19 | 1.32355 | ||||||||
\(37\) | 1.01944e19 | 0.254590 | 0.127295 | − | 0.991865i | \(-0.459371\pi\) | ||||
0.127295 | + | 0.991865i | \(0.459371\pi\) | |||||||
\(38\) | 2.02764e19 | 0.362824 | ||||||||
\(39\) | −1.68287e20 | −2.17642 | ||||||||
\(40\) | −9.41738e18 | −0.0887524 | ||||||||
\(41\) | 1.58687e20 | 1.09835 | 0.549177 | − | 0.835706i | \(-0.314941\pi\) | ||||
0.549177 | + | 0.835706i | \(0.314941\pi\) | |||||||
\(42\) | −2.18999e20 | −1.12157 | ||||||||
\(43\) | 1.83575e20 | 0.700582 | 0.350291 | − | 0.936641i | \(-0.386083\pi\) | ||||
0.350291 | + | 0.936641i | \(0.386083\pi\) | |||||||
\(44\) | 4.34034e19 | 0.124270 | ||||||||
\(45\) | −3.07362e20 | −0.664499 | ||||||||
\(46\) | −4.40934e19 | −0.0724270 | ||||||||
\(47\) | 1.40203e21 | 1.76009 | 0.880045 | − | 0.474890i | \(-0.157512\pi\) | ||||
0.880045 | + | 0.474890i | \(0.157512\pi\) | |||||||
\(48\) | 4.94799e20 | 0.477434 | ||||||||
\(49\) | −4.15978e20 | −0.310184 | ||||||||
\(50\) | −1.14378e21 | −0.662548 | ||||||||
\(51\) | −2.89496e21 | −1.30923 | ||||||||
\(52\) | −1.60613e21 | −0.569821 | ||||||||
\(53\) | −1.99903e21 | −0.558946 | −0.279473 | − | 0.960154i | \(-0.590160\pi\) | ||||
−0.279473 | + | 0.960154i | \(0.590160\pi\) | |||||||
\(54\) | 1.00484e22 | 2.22421 | ||||||||
\(55\) | −3.54531e20 | −0.0623908 | ||||||||
\(56\) | −2.09012e21 | −0.293644 | ||||||||
\(57\) | 8.70202e21 | 0.979906 | ||||||||
\(58\) | −5.60091e21 | −0.507468 | ||||||||
\(59\) | −4.16691e21 | −0.304905 | −0.152452 | − | 0.988311i | \(-0.548717\pi\) | ||||
−0.152452 | + | 0.988311i | \(0.548717\pi\) | |||||||
\(60\) | −4.04165e21 | −0.239700 | ||||||||
\(61\) | 3.42128e22 | 1.65031 | 0.825156 | − | 0.564904i | \(-0.191087\pi\) | ||||
0.825156 | + | 0.564904i | \(0.191087\pi\) | |||||||
\(62\) | −1.81043e22 | −0.712666 | ||||||||
\(63\) | −6.82170e22 | −2.19855 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | 1.31193e22 | 0.286084 | ||||||||
\(66\) | 1.86274e22 | 0.335624 | ||||||||
\(67\) | 8.67051e22 | 1.29452 | 0.647261 | − | 0.762268i | \(-0.275914\pi\) | ||||
0.647261 | + | 0.762268i | \(0.275914\pi\) | |||||||
\(68\) | −2.76295e22 | −0.342777 | ||||||||
\(69\) | −1.89236e22 | −0.195609 | ||||||||
\(70\) | 1.70727e22 | 0.147427 | ||||||||
\(71\) | −5.13159e22 | −0.371127 | −0.185564 | − | 0.982632i | \(-0.559411\pi\) | ||||
−0.185564 | + | 0.982632i | \(0.559411\pi\) | |||||||
\(72\) | 1.54128e23 | 0.935888 | ||||||||
\(73\) | 3.49147e22 | 0.178432 | 0.0892159 | − | 0.996012i | \(-0.471564\pi\) | ||||
0.0892159 | + | 0.996012i | \(0.471564\pi\) | |||||||
\(74\) | 4.17563e22 | 0.180022 | ||||||||
\(75\) | −4.90875e23 | −1.78939 | ||||||||
\(76\) | 8.30522e22 | 0.256555 | ||||||||
\(77\) | −7.86857e22 | −0.206425 | ||||||||
\(78\) | −6.89302e23 | −1.53896 | ||||||||
\(79\) | 2.91588e23 | 0.555176 | 0.277588 | − | 0.960700i | \(-0.410465\pi\) | ||||
0.277588 | + | 0.960700i | \(0.410465\pi\) | |||||||
\(80\) | −3.85736e22 | −0.0627574 | ||||||||
\(81\) | 2.41214e24 | 3.36000 | ||||||||
\(82\) | 6.49981e23 | 0.776654 | ||||||||
\(83\) | −1.64916e24 | −1.69351 | −0.846753 | − | 0.531986i | \(-0.821446\pi\) | ||||
−0.846753 | + | 0.531986i | \(0.821446\pi\) | |||||||
\(84\) | −8.97018e23 | −0.793067 | ||||||||
\(85\) | 2.25686e23 | 0.172095 | ||||||||
\(86\) | 7.51925e23 | 0.495386 | ||||||||
\(87\) | −2.40374e24 | −1.37056 | ||||||||
\(88\) | 1.77780e23 | 0.0878720 | ||||||||
\(89\) | 8.74435e23 | 0.375277 | 0.187639 | − | 0.982238i | \(-0.439917\pi\) | ||||
0.187639 | + | 0.982238i | \(0.439917\pi\) | |||||||
\(90\) | −1.25896e24 | −0.469871 | ||||||||
\(91\) | 2.91174e24 | 0.946532 | ||||||||
\(92\) | −1.80607e23 | −0.0512136 | ||||||||
\(93\) | −7.76982e24 | −1.92475 | ||||||||
\(94\) | 5.74273e24 | 1.24457 | ||||||||
\(95\) | −6.78393e23 | −0.128806 | ||||||||
\(96\) | 2.02670e24 | 0.337597 | ||||||||
\(97\) | 1.00608e25 | 1.47227 | 0.736134 | − | 0.676835i | \(-0.236649\pi\) | ||||
0.736134 | + | 0.676835i | \(0.236649\pi\) | |||||||
\(98\) | −1.70384e24 | −0.219333 | ||||||||
\(99\) | 5.80235e24 | 0.657907 | ||||||||
\(100\) | −4.68492e24 | −0.468492 | ||||||||
\(101\) | −1.42151e25 | −1.25526 | −0.627628 | − | 0.778513i | \(-0.715974\pi\) | ||||
−0.627628 | + | 0.778513i | \(0.715974\pi\) | |||||||
\(102\) | −1.18578e25 | −0.925764 | ||||||||
\(103\) | 1.03211e25 | 0.713283 | 0.356642 | − | 0.934241i | \(-0.383922\pi\) | ||||
0.356642 | + | 0.934241i | \(0.383922\pi\) | |||||||
\(104\) | −6.57870e24 | −0.402924 | ||||||||
\(105\) | 7.32709e24 | 0.398167 | ||||||||
\(106\) | −8.18801e24 | −0.395235 | ||||||||
\(107\) | −1.74396e25 | −0.748582 | −0.374291 | − | 0.927311i | \(-0.622114\pi\) | ||||
−0.374291 | + | 0.927311i | \(0.622114\pi\) | |||||||
\(108\) | 4.11583e25 | 1.57275 | ||||||||
\(109\) | −1.65117e25 | −0.562292 | −0.281146 | − | 0.959665i | \(-0.590714\pi\) | ||||
−0.281146 | + | 0.959665i | \(0.590714\pi\) | |||||||
\(110\) | −1.45216e24 | −0.0441169 | ||||||||
\(111\) | 1.79205e25 | 0.486199 | ||||||||
\(112\) | −8.56115e24 | −0.207638 | ||||||||
\(113\) | 6.96039e25 | 1.51061 | 0.755306 | − | 0.655372i | \(-0.227488\pi\) | ||||
0.755306 | + | 0.655372i | \(0.227488\pi\) | |||||||
\(114\) | 3.56435e25 | 0.692898 | ||||||||
\(115\) | 1.47524e24 | 0.0257123 | ||||||||
\(116\) | −2.29413e25 | −0.358834 | ||||||||
\(117\) | −2.14714e26 | −3.01674 | ||||||||
\(118\) | −1.70677e25 | −0.215600 | ||||||||
\(119\) | 5.00894e25 | 0.569389 | ||||||||
\(120\) | −1.65546e25 | −0.169494 | ||||||||
\(121\) | −1.01654e26 | −0.938228 | ||||||||
\(122\) | 1.40136e26 | 1.16695 | ||||||||
\(123\) | 2.78952e26 | 2.09757 | ||||||||
\(124\) | −7.41552e25 | −0.503931 | ||||||||
\(125\) | 7.91091e25 | 0.486241 | ||||||||
\(126\) | −2.79417e26 | −1.55461 | ||||||||
\(127\) | −6.18922e25 | −0.311953 | −0.155977 | − | 0.987761i | \(-0.549852\pi\) | ||||
−0.155977 | + | 0.987761i | \(0.549852\pi\) | |||||||
\(128\) | 1.93428e25 | 0.0883883 | ||||||||
\(129\) | 3.22703e26 | 1.33793 | ||||||||
\(130\) | 5.37367e25 | 0.202292 | ||||||||
\(131\) | −1.39682e26 | −0.477805 | −0.238902 | − | 0.971044i | \(-0.576788\pi\) | ||||
−0.238902 | + | 0.971044i | \(0.576788\pi\) | |||||||
\(132\) | 7.62979e25 | 0.237322 | ||||||||
\(133\) | −1.50565e26 | −0.426165 | ||||||||
\(134\) | 3.55144e26 | 0.915366 | ||||||||
\(135\) | −3.36193e26 | −0.789616 | ||||||||
\(136\) | −1.13171e26 | −0.242380 | ||||||||
\(137\) | −6.92418e26 | −1.35320 | −0.676599 | − | 0.736352i | \(-0.736547\pi\) | ||||
−0.676599 | + | 0.736352i | \(0.736547\pi\) | |||||||
\(138\) | −7.75109e25 | −0.138317 | ||||||||
\(139\) | −8.06682e26 | −1.31528 | −0.657639 | − | 0.753333i | \(-0.728445\pi\) | ||||
−0.657639 | + | 0.753333i | \(0.728445\pi\) | |||||||
\(140\) | 6.99298e25 | 0.104247 | ||||||||
\(141\) | 2.46460e27 | 3.36131 | ||||||||
\(142\) | −2.10190e26 | −0.262427 | ||||||||
\(143\) | −2.47665e26 | −0.283246 | ||||||||
\(144\) | 6.31306e26 | 0.661773 | ||||||||
\(145\) | 1.87391e26 | 0.180156 | ||||||||
\(146\) | 1.43010e26 | 0.126170 | ||||||||
\(147\) | −7.31239e26 | −0.592369 | ||||||||
\(148\) | 1.71034e26 | 0.127295 | ||||||||
\(149\) | −4.24039e26 | −0.290120 | −0.145060 | − | 0.989423i | \(-0.546337\pi\) | ||||
−0.145060 | + | 0.989423i | \(0.546337\pi\) | |||||||
\(150\) | −2.01063e27 | −1.26529 | ||||||||
\(151\) | 2.51382e27 | 1.45587 | 0.727934 | − | 0.685647i | \(-0.240481\pi\) | ||||
0.727934 | + | 0.685647i | \(0.240481\pi\) | |||||||
\(152\) | 3.40182e26 | 0.181412 | ||||||||
\(153\) | −3.69363e27 | −1.81473 | ||||||||
\(154\) | −3.22297e26 | −0.145964 | ||||||||
\(155\) | 6.05720e26 | 0.253003 | ||||||||
\(156\) | −2.82338e27 | −1.08821 | ||||||||
\(157\) | 4.75882e27 | 1.69338 | 0.846689 | − | 0.532088i | \(-0.178593\pi\) | ||||
0.846689 | + | 0.532088i | \(0.178593\pi\) | |||||||
\(158\) | 1.19434e27 | 0.392569 | ||||||||
\(159\) | −3.51404e27 | −1.06744 | ||||||||
\(160\) | −1.57997e26 | −0.0443762 | ||||||||
\(161\) | 3.27420e26 | 0.0850712 | ||||||||
\(162\) | 9.88012e27 | 2.37588 | ||||||||
\(163\) | 7.59899e26 | 0.169204 | 0.0846020 | − | 0.996415i | \(-0.473038\pi\) | ||||
0.0846020 | + | 0.996415i | \(0.473038\pi\) | |||||||
\(164\) | 2.66232e27 | 0.549177 | ||||||||
\(165\) | −6.23222e26 | −0.119150 | ||||||||
\(166\) | −6.75496e27 | −1.19749 | ||||||||
\(167\) | −1.00207e28 | −1.64794 | −0.823970 | − | 0.566634i | \(-0.808245\pi\) | ||||
−0.823970 | + | 0.566634i | \(0.808245\pi\) | |||||||
\(168\) | −3.67419e27 | −0.560783 | ||||||||
\(169\) | 2.10835e27 | 0.298785 | ||||||||
\(170\) | 9.24408e26 | 0.121689 | ||||||||
\(171\) | 1.11028e28 | 1.35825 | ||||||||
\(172\) | 3.07989e27 | 0.350291 | ||||||||
\(173\) | −7.89989e27 | −0.835689 | −0.417845 | − | 0.908518i | \(-0.637214\pi\) | ||||
−0.417845 | + | 0.908518i | \(0.637214\pi\) | |||||||
\(174\) | −9.84571e27 | −0.969129 | ||||||||
\(175\) | 8.49326e27 | 0.778214 | ||||||||
\(176\) | 7.28188e26 | 0.0621349 | ||||||||
\(177\) | −7.32493e27 | −0.582288 | ||||||||
\(178\) | 3.58168e27 | 0.265361 | ||||||||
\(179\) | −8.08087e27 | −0.558207 | −0.279103 | − | 0.960261i | \(-0.590037\pi\) | ||||
−0.279103 | + | 0.960261i | \(0.590037\pi\) | |||||||
\(180\) | −5.15668e27 | −0.332249 | ||||||||
\(181\) | 1.80674e27 | 0.108621 | 0.0543104 | − | 0.998524i | \(-0.482704\pi\) | ||||
0.0543104 | + | 0.998524i | \(0.482704\pi\) | |||||||
\(182\) | 1.19265e28 | 0.669299 | ||||||||
\(183\) | 6.01420e28 | 3.15166 | ||||||||
\(184\) | −7.39765e26 | −0.0362135 | ||||||||
\(185\) | −1.39705e27 | −0.0639096 | ||||||||
\(186\) | −3.18252e28 | −1.36100 | ||||||||
\(187\) | −4.26047e27 | −0.170387 | ||||||||
\(188\) | 2.35222e28 | 0.880045 | ||||||||
\(189\) | −7.46157e28 | −2.61251 | ||||||||
\(190\) | −2.77870e27 | −0.0910796 | ||||||||
\(191\) | −4.93091e28 | −1.51360 | −0.756798 | − | 0.653649i | \(-0.773237\pi\) | ||||
−0.756798 | + | 0.653649i | \(0.773237\pi\) | |||||||
\(192\) | 8.30135e27 | 0.238717 | ||||||||
\(193\) | 1.42443e28 | 0.383861 | 0.191931 | − | 0.981408i | \(-0.438525\pi\) | ||||
0.191931 | + | 0.981408i | \(0.438525\pi\) | |||||||
\(194\) | 4.12092e28 | 1.04105 | ||||||||
\(195\) | 2.30621e28 | 0.546345 | ||||||||
\(196\) | −6.97895e27 | −0.155092 | ||||||||
\(197\) | 3.59073e28 | 0.748781 | 0.374390 | − | 0.927271i | \(-0.377852\pi\) | ||||
0.374390 | + | 0.927271i | \(0.377852\pi\) | |||||||
\(198\) | 2.37664e28 | 0.465210 | ||||||||
\(199\) | −8.11996e28 | −1.49242 | −0.746209 | − | 0.665712i | \(-0.768128\pi\) | ||||
−0.746209 | + | 0.665712i | \(0.768128\pi\) | |||||||
\(200\) | −1.91894e28 | −0.331274 | ||||||||
\(201\) | 1.52417e29 | 2.47220 | ||||||||
\(202\) | −5.82250e28 | −0.887601 | ||||||||
\(203\) | 4.15902e28 | 0.596060 | ||||||||
\(204\) | −4.85694e28 | −0.654614 | ||||||||
\(205\) | −2.17466e28 | −0.275720 | ||||||||
\(206\) | 4.22753e28 | 0.504367 | ||||||||
\(207\) | −2.41443e28 | −0.271134 | ||||||||
\(208\) | −2.69464e28 | −0.284911 | ||||||||
\(209\) | 1.28066e28 | 0.127528 | ||||||||
\(210\) | 3.00118e28 | 0.281547 | ||||||||
\(211\) | −1.03285e29 | −0.913075 | −0.456537 | − | 0.889704i | \(-0.650911\pi\) | ||||
−0.456537 | + | 0.889704i | \(0.650911\pi\) | |||||||
\(212\) | −3.35381e28 | −0.279473 | ||||||||
\(213\) | −9.02072e28 | −0.708755 | ||||||||
\(214\) | −7.14326e28 | −0.529327 | ||||||||
\(215\) | −2.51573e28 | −0.175867 | ||||||||
\(216\) | 1.68585e29 | 1.11211 | ||||||||
\(217\) | 1.34436e29 | 0.837081 | ||||||||
\(218\) | −6.76321e28 | −0.397600 | ||||||||
\(219\) | 6.13758e28 | 0.340757 | ||||||||
\(220\) | −5.94804e27 | −0.0311954 | ||||||||
\(221\) | 1.57657e29 | 0.781287 | ||||||||
\(222\) | 7.34025e28 | 0.343795 | ||||||||
\(223\) | 1.15542e29 | 0.511597 | 0.255799 | − | 0.966730i | \(-0.417662\pi\) | ||||
0.255799 | + | 0.966730i | \(0.417662\pi\) | |||||||
\(224\) | −3.50665e28 | −0.146822 | ||||||||
\(225\) | −6.26300e29 | −2.48028 | ||||||||
\(226\) | 2.85098e29 | 1.06816 | ||||||||
\(227\) | −9.01151e28 | −0.319502 | −0.159751 | − | 0.987157i | \(-0.551069\pi\) | ||||
−0.159751 | + | 0.987157i | \(0.551069\pi\) | |||||||
\(228\) | 1.45996e29 | 0.489953 | ||||||||
\(229\) | 3.69415e29 | 1.17374 | 0.586869 | − | 0.809682i | \(-0.300360\pi\) | ||||
0.586869 | + | 0.809682i | \(0.300360\pi\) | |||||||
\(230\) | 6.04260e27 | 0.0181813 | ||||||||
\(231\) | −1.38320e29 | −0.394217 | ||||||||
\(232\) | −9.39676e28 | −0.253734 | ||||||||
\(233\) | 4.10753e28 | 0.105107 | 0.0525536 | − | 0.998618i | \(-0.483264\pi\) | ||||
0.0525536 | + | 0.998618i | \(0.483264\pi\) | |||||||
\(234\) | −8.79469e29 | −2.13316 | ||||||||
\(235\) | −1.92136e29 | −0.441835 | ||||||||
\(236\) | −6.99092e28 | −0.152452 | ||||||||
\(237\) | 5.12576e29 | 1.06024 | ||||||||
\(238\) | 2.05166e29 | 0.402618 | ||||||||
\(239\) | −6.49097e29 | −1.20875 | −0.604374 | − | 0.796701i | \(-0.706577\pi\) | ||||
−0.604374 | + | 0.796701i | \(0.706577\pi\) | |||||||
\(240\) | −6.78077e28 | −0.119850 | ||||||||
\(241\) | 1.68781e29 | 0.283212 | 0.141606 | − | 0.989923i | \(-0.454773\pi\) | ||||
0.141606 | + | 0.989923i | \(0.454773\pi\) | |||||||
\(242\) | −4.16376e29 | −0.663427 | ||||||||
\(243\) | 2.16165e30 | 3.27121 | ||||||||
\(244\) | 5.73996e29 | 0.825156 | ||||||||
\(245\) | 5.70060e28 | 0.0778653 | ||||||||
\(246\) | 1.14259e30 | 1.48320 | ||||||||
\(247\) | −4.73905e29 | −0.584763 | ||||||||
\(248\) | −3.03740e29 | −0.356333 | ||||||||
\(249\) | −2.89903e30 | −3.23415 | ||||||||
\(250\) | 3.24031e29 | 0.343824 | ||||||||
\(251\) | 2.65029e29 | 0.267530 | 0.133765 | − | 0.991013i | \(-0.457293\pi\) | ||||
0.133765 | + | 0.991013i | \(0.457293\pi\) | |||||||
\(252\) | −1.14449e30 | −1.09927 | ||||||||
\(253\) | −2.78495e28 | −0.0254572 | ||||||||
\(254\) | −2.53510e29 | −0.220584 | ||||||||
\(255\) | 3.96728e29 | 0.328655 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | 1.11592e30 | 0.838433 | 0.419217 | − | 0.907886i | \(-0.362305\pi\) | ||||
0.419217 | + | 0.907886i | \(0.362305\pi\) | |||||||
\(258\) | 1.32179e30 | 0.946057 | ||||||||
\(259\) | −3.10066e29 | −0.211450 | ||||||||
\(260\) | 2.20105e29 | 0.143042 | ||||||||
\(261\) | −3.06689e30 | −1.89973 | ||||||||
\(262\) | −5.72139e29 | −0.337859 | ||||||||
\(263\) | 1.53721e30 | 0.865541 | 0.432770 | − | 0.901504i | \(-0.357536\pi\) | ||||
0.432770 | + | 0.901504i | \(0.357536\pi\) | |||||||
\(264\) | 3.12516e29 | 0.167812 | ||||||||
\(265\) | 2.73948e29 | 0.140312 | ||||||||
\(266\) | −6.16713e29 | −0.301344 | ||||||||
\(267\) | 1.53715e30 | 0.716681 | ||||||||
\(268\) | 1.45467e30 | 0.647261 | ||||||||
\(269\) | 2.34612e30 | 0.996431 | 0.498216 | − | 0.867053i | \(-0.333989\pi\) | ||||
0.498216 | + | 0.867053i | \(0.333989\pi\) | |||||||
\(270\) | −1.37705e30 | −0.558343 | ||||||||
\(271\) | −1.54578e30 | −0.598454 | −0.299227 | − | 0.954182i | \(-0.596729\pi\) | ||||
−0.299227 | + | 0.954182i | \(0.596729\pi\) | |||||||
\(272\) | −4.63547e29 | −0.171389 | ||||||||
\(273\) | 5.11849e30 | 1.80763 | ||||||||
\(274\) | −2.83614e30 | −0.956855 | ||||||||
\(275\) | −7.22414e29 | −0.232877 | ||||||||
\(276\) | −3.17485e29 | −0.0978045 | ||||||||
\(277\) | −1.21614e30 | −0.358085 | −0.179042 | − | 0.983841i | \(-0.557300\pi\) | ||||
−0.179042 | + | 0.983841i | \(0.557300\pi\) | |||||||
\(278\) | −3.30417e30 | −0.930042 | ||||||||
\(279\) | −9.91339e30 | −2.66790 | ||||||||
\(280\) | 2.86432e29 | 0.0737135 | ||||||||
\(281\) | 5.09885e30 | 1.25500 | 0.627499 | − | 0.778617i | \(-0.284079\pi\) | ||||
0.627499 | + | 0.778617i | \(0.284079\pi\) | |||||||
\(282\) | 1.00950e31 | 2.37680 | ||||||||
\(283\) | −1.56288e30 | −0.352042 | −0.176021 | − | 0.984386i | \(-0.556323\pi\) | ||||
−0.176021 | + | 0.984386i | \(0.556323\pi\) | |||||||
\(284\) | −8.60939e29 | −0.185564 | ||||||||
\(285\) | −1.19253e30 | −0.245986 | ||||||||
\(286\) | −1.01444e30 | −0.200285 | ||||||||
\(287\) | −4.82651e30 | −0.912240 | ||||||||
\(288\) | 2.58583e30 | 0.467944 | ||||||||
\(289\) | −3.05852e30 | −0.530015 | ||||||||
\(290\) | 7.67553e29 | 0.127389 | ||||||||
\(291\) | 1.76857e31 | 2.81164 | ||||||||
\(292\) | 5.85771e29 | 0.0892159 | ||||||||
\(293\) | −4.17112e30 | −0.608706 | −0.304353 | − | 0.952559i | \(-0.598440\pi\) | ||||
−0.304353 | + | 0.952559i | \(0.598440\pi\) | |||||||
\(294\) | −2.99515e30 | −0.418868 | ||||||||
\(295\) | 5.71038e29 | 0.0765402 | ||||||||
\(296\) | 7.00555e29 | 0.0900110 | ||||||||
\(297\) | 6.34661e30 | 0.781783 | ||||||||
\(298\) | −1.73686e30 | −0.205146 | ||||||||
\(299\) | 1.03056e30 | 0.116730 | ||||||||
\(300\) | −8.23552e30 | −0.894696 | ||||||||
\(301\) | −5.58350e30 | −0.581870 | ||||||||
\(302\) | 1.02966e31 | 1.02945 | ||||||||
\(303\) | −2.49884e31 | −2.39721 | ||||||||
\(304\) | 1.39338e30 | 0.128278 | ||||||||
\(305\) | −4.68856e30 | −0.414278 | ||||||||
\(306\) | −1.51291e31 | −1.28320 | ||||||||
\(307\) | 7.69994e30 | 0.626986 | 0.313493 | − | 0.949591i | \(-0.398501\pi\) | ||||
0.313493 | + | 0.949591i | \(0.398501\pi\) | |||||||
\(308\) | −1.32013e30 | −0.103212 | ||||||||
\(309\) | 1.81433e31 | 1.36218 | ||||||||
\(310\) | 2.48103e30 | 0.178900 | ||||||||
\(311\) | 1.54260e31 | 1.06843 | 0.534217 | − | 0.845347i | \(-0.320606\pi\) | ||||
0.534217 | + | 0.845347i | \(0.320606\pi\) | |||||||
\(312\) | −1.15646e31 | −0.769479 | ||||||||
\(313\) | 1.62517e31 | 1.03895 | 0.519476 | − | 0.854485i | \(-0.326127\pi\) | ||||
0.519476 | + | 0.854485i | \(0.326127\pi\) | |||||||
\(314\) | 1.94921e31 | 1.19740 | ||||||||
\(315\) | 9.34852e30 | 0.551900 | ||||||||
\(316\) | 4.89203e30 | 0.277588 | ||||||||
\(317\) | −2.29098e31 | −1.24963 | −0.624814 | − | 0.780773i | \(-0.714825\pi\) | ||||
−0.624814 | + | 0.780773i | \(0.714825\pi\) | |||||||
\(318\) | −1.43935e31 | −0.754794 | ||||||||
\(319\) | −3.53755e30 | −0.178369 | ||||||||
\(320\) | −6.47157e29 | −0.0313787 | ||||||||
\(321\) | −3.06567e31 | −1.42959 | ||||||||
\(322\) | 1.34111e30 | 0.0601544 | ||||||||
\(323\) | −8.15239e30 | −0.351765 | ||||||||
\(324\) | 4.04690e31 | 1.68000 | ||||||||
\(325\) | 2.67327e31 | 1.06783 | ||||||||
\(326\) | 3.11255e30 | 0.119645 | ||||||||
\(327\) | −2.90256e31 | −1.07383 | ||||||||
\(328\) | 1.09049e31 | 0.388327 | ||||||||
\(329\) | −4.26433e31 | −1.46185 | ||||||||
\(330\) | −2.55272e30 | −0.0842517 | ||||||||
\(331\) | 3.45199e31 | 1.09703 | 0.548517 | − | 0.836140i | \(-0.315193\pi\) | ||||
0.548517 | + | 0.836140i | \(0.315193\pi\) | |||||||
\(332\) | −2.76683e31 | −0.846753 | ||||||||
\(333\) | 2.28645e31 | 0.673922 | ||||||||
\(334\) | −4.10447e31 | −1.16527 | ||||||||
\(335\) | −1.18821e31 | −0.324964 | ||||||||
\(336\) | −1.50495e31 | −0.396534 | ||||||||
\(337\) | −5.27735e31 | −1.33981 | −0.669904 | − | 0.742448i | \(-0.733665\pi\) | ||||
−0.669904 | + | 0.742448i | \(0.733665\pi\) | |||||||
\(338\) | 8.63579e30 | 0.211273 | ||||||||
\(339\) | 1.22355e32 | 2.88487 | ||||||||
\(340\) | 3.78638e30 | 0.0860473 | ||||||||
\(341\) | −1.14347e31 | −0.250493 | ||||||||
\(342\) | 4.54770e31 | 0.960429 | ||||||||
\(343\) | 5.34411e31 | 1.08818 | ||||||||
\(344\) | 1.26152e31 | 0.247693 | ||||||||
\(345\) | 2.59330e30 | 0.0491037 | ||||||||
\(346\) | −3.23580e31 | −0.590922 | ||||||||
\(347\) | 4.40093e30 | 0.0775222 | 0.0387611 | − | 0.999249i | \(-0.487659\pi\) | ||||
0.0387611 | + | 0.999249i | \(0.487659\pi\) | |||||||
\(348\) | −4.03280e31 | −0.685278 | ||||||||
\(349\) | 2.98069e31 | 0.488651 | 0.244326 | − | 0.969693i | \(-0.421433\pi\) | ||||
0.244326 | + | 0.969693i | \(0.421433\pi\) | |||||||
\(350\) | 3.47884e31 | 0.550280 | ||||||||
\(351\) | −2.34854e32 | −3.58476 | ||||||||
\(352\) | 2.98266e30 | 0.0439360 | ||||||||
\(353\) | 4.46084e31 | 0.634209 | 0.317105 | − | 0.948391i | \(-0.397289\pi\) | ||||
0.317105 | + | 0.948391i | \(0.397289\pi\) | |||||||
\(354\) | −3.00029e31 | −0.411740 | ||||||||
\(355\) | 7.03238e30 | 0.0931640 | ||||||||
\(356\) | 1.46706e31 | 0.187639 | ||||||||
\(357\) | 8.80511e31 | 1.08738 | ||||||||
\(358\) | −3.30992e31 | −0.394712 | ||||||||
\(359\) | 4.38054e31 | 0.504483 | 0.252242 | − | 0.967664i | \(-0.418832\pi\) | ||||
0.252242 | + | 0.967664i | \(0.418832\pi\) | |||||||
\(360\) | −2.11218e31 | −0.234936 | ||||||||
\(361\) | −6.85711e31 | −0.736717 | ||||||||
\(362\) | 7.40039e30 | 0.0768065 | ||||||||
\(363\) | −1.78696e32 | −1.79177 | ||||||||
\(364\) | 4.88509e31 | 0.473266 | ||||||||
\(365\) | −4.78474e30 | −0.0447917 | ||||||||
\(366\) | 2.46342e32 | 2.22856 | ||||||||
\(367\) | −7.76735e31 | −0.679121 | −0.339560 | − | 0.940584i | \(-0.610278\pi\) | ||||
−0.339560 | + | 0.940584i | \(0.610278\pi\) | |||||||
\(368\) | −3.03008e30 | −0.0256068 | ||||||||
\(369\) | 3.55911e32 | 2.90744 | ||||||||
\(370\) | −5.72232e30 | −0.0451909 | ||||||||
\(371\) | 6.08010e31 | 0.464234 | ||||||||
\(372\) | −1.30356e32 | −0.962374 | ||||||||
\(373\) | −2.37205e32 | −1.69342 | −0.846708 | − | 0.532058i | \(-0.821419\pi\) | ||||
−0.846708 | + | 0.532058i | \(0.821419\pi\) | |||||||
\(374\) | −1.74509e31 | −0.120482 | ||||||||
\(375\) | 1.39064e32 | 0.928591 | ||||||||
\(376\) | 9.63470e31 | 0.622286 | ||||||||
\(377\) | 1.30906e32 | 0.817884 | ||||||||
\(378\) | −3.05626e32 | −1.84732 | ||||||||
\(379\) | −1.38944e32 | −0.812551 | −0.406276 | − | 0.913751i | \(-0.633173\pi\) | ||||
−0.406276 | + | 0.913751i | \(0.633173\pi\) | |||||||
\(380\) | −1.13815e31 | −0.0644030 | ||||||||
\(381\) | −1.08799e32 | −0.595748 | ||||||||
\(382\) | −2.01970e32 | −1.07027 | ||||||||
\(383\) | −3.79085e31 | −0.194425 | −0.0972125 | − | 0.995264i | \(-0.530993\pi\) | ||||
−0.0972125 | + | 0.995264i | \(0.530993\pi\) | |||||||
\(384\) | 3.40023e31 | 0.168798 | ||||||||
\(385\) | 1.07832e31 | 0.0518188 | ||||||||
\(386\) | 5.83446e31 | 0.271431 | ||||||||
\(387\) | 4.11732e32 | 1.85450 | ||||||||
\(388\) | 1.68793e32 | 0.736134 | ||||||||
\(389\) | −2.20209e32 | −0.929963 | −0.464982 | − | 0.885320i | \(-0.653939\pi\) | ||||
−0.464982 | + | 0.885320i | \(0.653939\pi\) | |||||||
\(390\) | 9.44625e31 | 0.386324 | ||||||||
\(391\) | 1.77283e31 | 0.0702195 | ||||||||
\(392\) | −2.85858e31 | −0.109667 | ||||||||
\(393\) | −2.45545e32 | −0.912481 | ||||||||
\(394\) | 1.47076e32 | 0.529468 | ||||||||
\(395\) | −3.99595e31 | −0.139366 | ||||||||
\(396\) | 9.73473e31 | 0.328953 | ||||||||
\(397\) | 2.18941e32 | 0.716877 | 0.358439 | − | 0.933553i | \(-0.383309\pi\) | ||||
0.358439 | + | 0.933553i | \(0.383309\pi\) | |||||||
\(398\) | −3.32594e32 | −1.05530 | ||||||||
\(399\) | −2.64675e32 | −0.813863 | ||||||||
\(400\) | −7.85999e31 | −0.234246 | ||||||||
\(401\) | 2.99036e32 | 0.863810 | 0.431905 | − | 0.901919i | \(-0.357842\pi\) | ||||
0.431905 | + | 0.901919i | \(0.357842\pi\) | |||||||
\(402\) | 6.24300e32 | 1.74811 | ||||||||
\(403\) | 4.23138e32 | 1.14860 | ||||||||
\(404\) | −2.38490e32 | −0.627628 | ||||||||
\(405\) | −3.30562e32 | −0.843460 | ||||||||
\(406\) | 1.70353e32 | 0.421478 | ||||||||
\(407\) | 2.63734e31 | 0.0632755 | ||||||||
\(408\) | −1.98940e32 | −0.462882 | ||||||||
\(409\) | 7.12330e31 | 0.160746 | 0.0803730 | − | 0.996765i | \(-0.474389\pi\) | ||||
0.0803730 | + | 0.996765i | \(0.474389\pi\) | |||||||
\(410\) | −8.90740e31 | −0.194963 | ||||||||
\(411\) | −1.21719e33 | −2.58425 | ||||||||
\(412\) | 1.73160e32 | 0.356642 | ||||||||
\(413\) | 1.26738e32 | 0.253239 | ||||||||
\(414\) | −9.88949e31 | −0.191721 | ||||||||
\(415\) | 2.26003e32 | 0.425121 | ||||||||
\(416\) | −1.10372e32 | −0.201462 | ||||||||
\(417\) | −1.41805e33 | −2.51183 | ||||||||
\(418\) | 5.24560e31 | 0.0901761 | ||||||||
\(419\) | 2.94461e32 | 0.491307 | 0.245654 | − | 0.969358i | \(-0.420997\pi\) | ||||
0.245654 | + | 0.969358i | \(0.420997\pi\) | |||||||
\(420\) | 1.22928e32 | 0.199083 | ||||||||
\(421\) | 1.01892e33 | 1.60182 | 0.800908 | − | 0.598787i | \(-0.204350\pi\) | ||||
0.800908 | + | 0.598787i | \(0.204350\pi\) | |||||||
\(422\) | −4.23055e32 | −0.645641 | ||||||||
\(423\) | 3.14455e33 | 4.65912 | ||||||||
\(424\) | −1.37372e32 | −0.197617 | ||||||||
\(425\) | 4.59871e32 | 0.642354 | ||||||||
\(426\) | −3.69489e32 | −0.501166 | ||||||||
\(427\) | −1.04059e33 | −1.37067 | ||||||||
\(428\) | −2.92588e32 | −0.374291 | ||||||||
\(429\) | −4.35365e32 | −0.540925 | ||||||||
\(430\) | −1.03044e32 | −0.124357 | ||||||||
\(431\) | −6.79497e32 | −0.796565 | −0.398283 | − | 0.917263i | \(-0.630394\pi\) | ||||
−0.398283 | + | 0.917263i | \(0.630394\pi\) | |||||||
\(432\) | 6.90523e32 | 0.786377 | ||||||||
\(433\) | −7.24164e32 | −0.801195 | −0.400597 | − | 0.916254i | \(-0.631197\pi\) | ||||
−0.400597 | + | 0.916254i | \(0.631197\pi\) | |||||||
\(434\) | 5.50648e32 | 0.591906 | ||||||||
\(435\) | 3.29411e32 | 0.344050 | ||||||||
\(436\) | −2.77021e32 | −0.281146 | ||||||||
\(437\) | −5.32899e31 | −0.0525566 | ||||||||
\(438\) | 2.51395e32 | 0.240952 | ||||||||
\(439\) | −9.13459e32 | −0.850908 | −0.425454 | − | 0.904980i | \(-0.639886\pi\) | ||||
−0.425454 | + | 0.904980i | \(0.639886\pi\) | |||||||
\(440\) | −2.43632e31 | −0.0220585 | ||||||||
\(441\) | −9.32976e32 | −0.821085 | ||||||||
\(442\) | 6.45764e32 | 0.552453 | ||||||||
\(443\) | −3.52555e32 | −0.293211 | −0.146605 | − | 0.989195i | \(-0.546835\pi\) | ||||
−0.146605 | + | 0.989195i | \(0.546835\pi\) | |||||||
\(444\) | 3.00657e32 | 0.243099 | ||||||||
\(445\) | −1.19833e32 | −0.0942058 | ||||||||
\(446\) | 4.73259e32 | 0.361754 | ||||||||
\(447\) | −7.45409e32 | −0.554052 | ||||||||
\(448\) | −1.43632e32 | −0.103819 | ||||||||
\(449\) | 3.70918e32 | 0.260735 | 0.130367 | − | 0.991466i | \(-0.458384\pi\) | ||||
0.130367 | + | 0.991466i | \(0.458384\pi\) | |||||||
\(450\) | −2.56533e33 | −1.75382 | ||||||||
\(451\) | 4.10530e32 | 0.272984 | ||||||||
\(452\) | 1.16776e33 | 0.755306 | ||||||||
\(453\) | 4.41899e33 | 2.78032 | ||||||||
\(454\) | −3.69111e32 | −0.225922 | ||||||||
\(455\) | −3.99028e32 | −0.237608 | ||||||||
\(456\) | 5.97998e32 | 0.346449 | ||||||||
\(457\) | 1.76958e33 | 0.997512 | 0.498756 | − | 0.866742i | \(-0.333790\pi\) | ||||
0.498756 | + | 0.866742i | \(0.333790\pi\) | |||||||
\(458\) | 1.51313e33 | 0.829959 | ||||||||
\(459\) | −4.04009e33 | −2.15642 | ||||||||
\(460\) | 2.47505e31 | 0.0128561 | ||||||||
\(461\) | 7.01018e32 | 0.354379 | 0.177189 | − | 0.984177i | \(-0.443299\pi\) | ||||
0.177189 | + | 0.984177i | \(0.443299\pi\) | |||||||
\(462\) | −5.66559e32 | −0.278753 | ||||||||
\(463\) | −9.20521e32 | −0.440830 | −0.220415 | − | 0.975406i | \(-0.570741\pi\) | ||||
−0.220415 | + | 0.975406i | \(0.570741\pi\) | |||||||
\(464\) | −3.84891e32 | −0.179417 | ||||||||
\(465\) | 1.06478e33 | 0.483169 | ||||||||
\(466\) | 1.68245e32 | 0.0743219 | ||||||||
\(467\) | −1.84600e33 | −0.793908 | −0.396954 | − | 0.917838i | \(-0.629933\pi\) | ||||
−0.396954 | + | 0.917838i | \(0.629933\pi\) | |||||||
\(468\) | −3.60231e33 | −1.50837 | ||||||||
\(469\) | −2.63716e33 | −1.07517 | ||||||||
\(470\) | −7.86988e32 | −0.312425 | ||||||||
\(471\) | 8.36543e33 | 3.23390 | ||||||||
\(472\) | −2.86348e32 | −0.107800 | ||||||||
\(473\) | 4.74918e32 | 0.174122 | ||||||||
\(474\) | 2.09951e33 | 0.749703 | ||||||||
\(475\) | −1.38234e33 | −0.480777 | ||||||||
\(476\) | 8.40360e32 | 0.284694 | ||||||||
\(477\) | −4.48351e33 | −1.47958 | ||||||||
\(478\) | −2.65870e33 | −0.854714 | ||||||||
\(479\) | −3.88481e32 | −0.121668 | −0.0608339 | − | 0.998148i | \(-0.519376\pi\) | ||||
−0.0608339 | + | 0.998148i | \(0.519376\pi\) | |||||||
\(480\) | −2.77740e32 | −0.0847468 | ||||||||
\(481\) | −9.75939e32 | −0.290141 | ||||||||
\(482\) | 6.91328e32 | 0.200261 | ||||||||
\(483\) | 5.75566e32 | 0.162463 | ||||||||
\(484\) | −1.70548e33 | −0.469114 | ||||||||
\(485\) | −1.37875e33 | −0.369583 | ||||||||
\(486\) | 8.85414e33 | 2.31309 | ||||||||
\(487\) | 4.26102e33 | 1.08493 | 0.542465 | − | 0.840078i | \(-0.317491\pi\) | ||||
0.542465 | + | 0.840078i | \(0.317491\pi\) | |||||||
\(488\) | 2.35109e33 | 0.583474 | ||||||||
\(489\) | 1.33581e33 | 0.323135 | ||||||||
\(490\) | 2.33496e32 | 0.0550591 | ||||||||
\(491\) | −4.52548e33 | −1.04027 | −0.520134 | − | 0.854084i | \(-0.674118\pi\) | ||||
−0.520134 | + | 0.854084i | \(0.674118\pi\) | |||||||
\(492\) | 4.68004e33 | 1.04878 | ||||||||
\(493\) | 2.25191e33 | 0.492000 | ||||||||
\(494\) | −1.94112e33 | −0.413490 | ||||||||
\(495\) | −7.95160e32 | −0.165154 | ||||||||
\(496\) | −1.24412e33 | −0.251965 | ||||||||
\(497\) | 1.56079e33 | 0.308241 | ||||||||
\(498\) | −1.18744e34 | −2.28689 | ||||||||
\(499\) | 4.45020e33 | 0.835840 | 0.417920 | − | 0.908484i | \(-0.362759\pi\) | ||||
0.417920 | + | 0.908484i | \(0.362759\pi\) | |||||||
\(500\) | 1.32723e33 | 0.243120 | ||||||||
\(501\) | −1.76151e34 | −3.14713 | ||||||||
\(502\) | 1.08556e33 | 0.189172 | ||||||||
\(503\) | 2.29032e33 | 0.389311 | 0.194656 | − | 0.980872i | \(-0.437641\pi\) | ||||
0.194656 | + | 0.980872i | \(0.437641\pi\) | |||||||
\(504\) | −4.68784e33 | −0.777304 | ||||||||
\(505\) | 1.94805e33 | 0.315107 | ||||||||
\(506\) | −1.14072e32 | −0.0180010 | ||||||||
\(507\) | 3.70622e33 | 0.570600 | ||||||||
\(508\) | −1.03838e33 | −0.155977 | ||||||||
\(509\) | 5.35889e33 | 0.785421 | 0.392711 | − | 0.919662i | \(-0.371537\pi\) | ||||
0.392711 | + | 0.919662i | \(0.371537\pi\) | |||||||
\(510\) | 1.62500e33 | 0.232394 | ||||||||
\(511\) | −1.06194e33 | −0.148197 | ||||||||
\(512\) | 3.24519e32 | 0.0441942 | ||||||||
\(513\) | 1.21442e34 | 1.61400 | ||||||||
\(514\) | 4.57080e33 | 0.592862 | ||||||||
\(515\) | −1.41442e33 | −0.179055 | ||||||||
\(516\) | 5.41407e33 | 0.668963 | ||||||||
\(517\) | 3.62712e33 | 0.437452 | ||||||||
\(518\) | −1.27003e33 | −0.149518 | ||||||||
\(519\) | −1.38871e34 | −1.59595 | ||||||||
\(520\) | 9.01552e32 | 0.101146 | ||||||||
\(521\) | −1.14090e34 | −1.24961 | −0.624807 | − | 0.780779i | \(-0.714822\pi\) | ||||
−0.624807 | + | 0.780779i | \(0.714822\pi\) | |||||||
\(522\) | −1.25620e34 | −1.34331 | ||||||||
\(523\) | 1.37717e34 | 1.43786 | 0.718928 | − | 0.695085i | \(-0.244633\pi\) | ||||
0.718928 | + | 0.695085i | \(0.244633\pi\) | |||||||
\(524\) | −2.34348e33 | −0.238902 | ||||||||
\(525\) | 1.49301e34 | 1.48618 | ||||||||
\(526\) | 6.29643e33 | 0.612030 | ||||||||
\(527\) | 7.27906e33 | 0.690944 | ||||||||
\(528\) | 1.28007e33 | 0.118661 | ||||||||
\(529\) | −1.09299e34 | −0.989509 | ||||||||
\(530\) | 1.12209e33 | 0.0992156 | ||||||||
\(531\) | −9.34576e33 | −0.807111 | ||||||||
\(532\) | −2.52606e33 | −0.213083 | ||||||||
\(533\) | −1.51915e34 | −1.25173 | ||||||||
\(534\) | 6.29617e33 | 0.506770 | ||||||||
\(535\) | 2.38994e33 | 0.187916 | ||||||||
\(536\) | 5.95833e33 | 0.457683 | ||||||||
\(537\) | −1.42052e34 | −1.06603 | ||||||||
\(538\) | 9.60972e33 | 0.704583 | ||||||||
\(539\) | −1.07615e33 | −0.0770929 | ||||||||
\(540\) | −5.64038e33 | −0.394808 | ||||||||
\(541\) | −1.58682e34 | −1.08533 | −0.542667 | − | 0.839948i | \(-0.682585\pi\) | ||||
−0.542667 | + | 0.839948i | \(0.682585\pi\) | |||||||
\(542\) | −6.33151e33 | −0.423171 | ||||||||
\(543\) | 3.17603e33 | 0.207437 | ||||||||
\(544\) | −1.89869e33 | −0.121190 | ||||||||
\(545\) | 2.26278e33 | 0.141152 | ||||||||
\(546\) | 2.09653e34 | 1.27818 | ||||||||
\(547\) | −8.29322e33 | −0.494176 | −0.247088 | − | 0.968993i | \(-0.579474\pi\) | ||||
−0.247088 | + | 0.968993i | \(0.579474\pi\) | |||||||
\(548\) | −1.16168e34 | −0.676599 | ||||||||
\(549\) | 7.67343e34 | 4.36853 | ||||||||
\(550\) | −2.95901e33 | −0.164669 | ||||||||
\(551\) | −6.76908e33 | −0.368243 | ||||||||
\(552\) | −1.30042e33 | −0.0691583 | ||||||||
\(553\) | −8.86874e33 | −0.461103 | ||||||||
\(554\) | −4.98130e33 | −0.253204 | ||||||||
\(555\) | −2.45585e33 | −0.122050 | ||||||||
\(556\) | −1.35339e34 | −0.657639 | ||||||||
\(557\) | 3.56496e34 | 1.69381 | 0.846905 | − | 0.531744i | \(-0.178463\pi\) | ||||
0.846905 | + | 0.531744i | \(0.178463\pi\) | |||||||
\(558\) | −4.06052e34 | −1.88649 | ||||||||
\(559\) | −1.75742e34 | −0.798413 | ||||||||
\(560\) | 1.17323e33 | 0.0521233 | ||||||||
\(561\) | −7.48939e33 | −0.325395 | ||||||||
\(562\) | 2.08849e34 | 0.887417 | ||||||||
\(563\) | 1.62059e34 | 0.673471 | 0.336735 | − | 0.941599i | \(-0.390677\pi\) | ||||
0.336735 | + | 0.941599i | \(0.390677\pi\) | |||||||
\(564\) | 4.13492e34 | 1.68065 | ||||||||
\(565\) | −9.53858e33 | −0.379209 | ||||||||
\(566\) | −6.40155e33 | −0.248931 | ||||||||
\(567\) | −7.33659e34 | −2.79065 | ||||||||
\(568\) | −3.52641e33 | −0.131213 | ||||||||
\(569\) | 4.19926e34 | 1.52851 | 0.764257 | − | 0.644912i | \(-0.223106\pi\) | ||||
0.764257 | + | 0.644912i | \(0.223106\pi\) | |||||||
\(570\) | −4.88462e33 | −0.173938 | ||||||||
\(571\) | 2.27922e34 | 0.794026 | 0.397013 | − | 0.917813i | \(-0.370047\pi\) | ||||
0.397013 | + | 0.917813i | \(0.370047\pi\) | |||||||
\(572\) | −4.15513e33 | −0.141623 | ||||||||
\(573\) | −8.66794e34 | −2.89057 | ||||||||
\(574\) | −1.97694e34 | −0.645051 | ||||||||
\(575\) | 3.00605e33 | 0.0959727 | ||||||||
\(576\) | 1.05916e34 | 0.330886 | ||||||||
\(577\) | −1.30064e34 | −0.397613 | −0.198807 | − | 0.980039i | \(-0.563707\pi\) | ||||
−0.198807 | + | 0.980039i | \(0.563707\pi\) | |||||||
\(578\) | −1.25277e34 | −0.374777 | ||||||||
\(579\) | 2.50397e34 | 0.733074 | ||||||||
\(580\) | 3.14390e33 | 0.0900780 | ||||||||
\(581\) | 5.01597e34 | 1.40655 | ||||||||
\(582\) | 7.24407e34 | 1.98813 | ||||||||
\(583\) | −5.17157e33 | −0.138920 | ||||||||
\(584\) | 2.39932e33 | 0.0630851 | ||||||||
\(585\) | 2.94246e34 | 0.757291 | ||||||||
\(586\) | −1.70849e34 | −0.430420 | ||||||||
\(587\) | 3.13619e34 | 0.773440 | 0.386720 | − | 0.922197i | \(-0.373608\pi\) | ||||
0.386720 | + | 0.922197i | \(0.373608\pi\) | |||||||
\(588\) | −1.22681e34 | −0.296185 | ||||||||
\(589\) | −2.18803e34 | −0.517145 | ||||||||
\(590\) | 2.33897e33 | 0.0541221 | ||||||||
\(591\) | 6.31206e34 | 1.42997 | ||||||||
\(592\) | 2.86947e33 | 0.0636474 | ||||||||
\(593\) | −6.43753e34 | −1.39809 | −0.699046 | − | 0.715077i | \(-0.746392\pi\) | ||||
−0.699046 | + | 0.715077i | \(0.746392\pi\) | |||||||
\(594\) | 2.59957e34 | 0.552804 | ||||||||
\(595\) | −6.86429e33 | −0.142933 | ||||||||
\(596\) | −7.11419e33 | −0.145060 | ||||||||
\(597\) | −1.42739e35 | −2.85012 | ||||||||
\(598\) | 4.22118e33 | 0.0825409 | ||||||||
\(599\) | −9.82124e34 | −1.88075 | −0.940375 | − | 0.340140i | \(-0.889526\pi\) | ||||
−0.940375 | + | 0.340140i | \(0.889526\pi\) | |||||||
\(600\) | −3.37327e34 | −0.632646 | ||||||||
\(601\) | 1.10144e34 | 0.202316 | 0.101158 | − | 0.994870i | \(-0.467745\pi\) | ||||
0.101158 | + | 0.994870i | \(0.467745\pi\) | |||||||
\(602\) | −2.28700e34 | −0.411444 | ||||||||
\(603\) | 1.94467e35 | 3.42672 | ||||||||
\(604\) | 4.21749e34 | 0.727934 | ||||||||
\(605\) | 1.39308e34 | 0.235523 | ||||||||
\(606\) | −1.02353e35 | −1.69508 | ||||||||
\(607\) | 9.06735e34 | 1.47103 | 0.735516 | − | 0.677508i | \(-0.236940\pi\) | ||||
0.735516 | + | 0.677508i | \(0.236940\pi\) | |||||||
\(608\) | 5.70730e33 | 0.0907060 | ||||||||
\(609\) | 7.31105e34 | 1.13832 | ||||||||
\(610\) | −1.92043e34 | −0.292938 | ||||||||
\(611\) | −1.34220e35 | −2.00587 | ||||||||
\(612\) | −6.19689e34 | −0.907363 | ||||||||
\(613\) | 2.62922e34 | 0.377199 | 0.188599 | − | 0.982054i | \(-0.439605\pi\) | ||||
0.188599 | + | 0.982054i | \(0.439605\pi\) | |||||||
\(614\) | 3.15390e34 | 0.443346 | ||||||||
\(615\) | −3.82279e34 | −0.526552 | ||||||||
\(616\) | −5.40724e33 | −0.0729822 | ||||||||
\(617\) | 6.11422e34 | 0.808679 | 0.404340 | − | 0.914609i | \(-0.367501\pi\) | ||||
0.404340 | + | 0.914609i | \(0.367501\pi\) | |||||||
\(618\) | 7.43150e34 | 0.963208 | ||||||||
\(619\) | −4.66687e34 | −0.592779 | −0.296389 | − | 0.955067i | \(-0.595783\pi\) | ||||
−0.296389 | + | 0.955067i | \(0.595783\pi\) | |||||||
\(620\) | 1.01623e34 | 0.126502 | ||||||||
\(621\) | −2.64090e34 | −0.322186 | ||||||||
\(622\) | 6.31848e34 | 0.755497 | ||||||||
\(623\) | −2.65962e34 | −0.311687 | ||||||||
\(624\) | −4.73685e34 | −0.544104 | ||||||||
\(625\) | 7.23797e34 | 0.814923 | ||||||||
\(626\) | 6.65672e34 | 0.734651 | ||||||||
\(627\) | 2.25125e34 | 0.243545 | ||||||||
\(628\) | 7.98398e34 | 0.846689 | ||||||||
\(629\) | −1.67886e34 | −0.174535 | ||||||||
\(630\) | 3.82915e34 | 0.390253 | ||||||||
\(631\) | −7.88083e33 | −0.0787417 | −0.0393709 | − | 0.999225i | \(-0.512535\pi\) | ||||
−0.0393709 | + | 0.999225i | \(0.512535\pi\) | |||||||
\(632\) | 2.00378e34 | 0.196284 | ||||||||
\(633\) | −1.81562e35 | −1.74373 | ||||||||
\(634\) | −9.38386e34 | −0.883621 | ||||||||
\(635\) | 8.48176e33 | 0.0783095 | ||||||||
\(636\) | −5.89559e34 | −0.533720 | ||||||||
\(637\) | 3.98227e34 | 0.353499 | ||||||||
\(638\) | −1.44898e34 | −0.126126 | ||||||||
\(639\) | −1.15094e35 | −0.982408 | ||||||||
\(640\) | −2.65076e33 | −0.0221881 | ||||||||
\(641\) | 3.14908e34 | 0.258499 | 0.129250 | − | 0.991612i | \(-0.458743\pi\) | ||||
0.129250 | + | 0.991612i | \(0.458743\pi\) | |||||||
\(642\) | −1.25570e35 | −1.01088 | ||||||||
\(643\) | 8.32480e34 | 0.657259 | 0.328630 | − | 0.944459i | \(-0.393413\pi\) | ||||
0.328630 | + | 0.944459i | \(0.393413\pi\) | |||||||
\(644\) | 5.49320e33 | 0.0425356 | ||||||||
\(645\) | −4.42236e34 | −0.335859 | ||||||||
\(646\) | −3.33922e34 | −0.248736 | ||||||||
\(647\) | −1.33124e35 | −0.972641 | −0.486321 | − | 0.873780i | \(-0.661661\pi\) | ||||
−0.486321 | + | 0.873780i | \(0.661661\pi\) | |||||||
\(648\) | 1.65761e35 | 1.18794 | ||||||||
\(649\) | −1.07800e34 | −0.0757809 | ||||||||
\(650\) | 1.09497e35 | 0.755068 | ||||||||
\(651\) | 2.36321e35 | 1.59860 | ||||||||
\(652\) | 1.27490e34 | 0.0846020 | ||||||||
\(653\) | 2.06756e35 | 1.34599 | 0.672997 | − | 0.739645i | \(-0.265007\pi\) | ||||
0.672997 | + | 0.739645i | \(0.265007\pi\) | |||||||
\(654\) | −1.18889e35 | −0.759311 | ||||||||
\(655\) | 1.91422e34 | 0.119943 | ||||||||
\(656\) | 4.46664e34 | 0.274589 | ||||||||
\(657\) | 7.83084e34 | 0.472325 | ||||||||
\(658\) | −1.74667e35 | −1.03368 | ||||||||
\(659\) | −2.57849e35 | −1.49726 | −0.748632 | − | 0.662986i | \(-0.769289\pi\) | ||||
−0.748632 | + | 0.662986i | \(0.769289\pi\) | |||||||
\(660\) | −1.04559e34 | −0.0595750 | ||||||||
\(661\) | −3.31671e34 | −0.185434 | −0.0927170 | − | 0.995692i | \(-0.529555\pi\) | ||||
−0.0927170 | + | 0.995692i | \(0.529555\pi\) | |||||||
\(662\) | 1.41394e35 | 0.775720 | ||||||||
\(663\) | 2.77142e35 | 1.49205 | ||||||||
\(664\) | −1.13329e35 | −0.598745 | ||||||||
\(665\) | 2.06335e34 | 0.106980 | ||||||||
\(666\) | 9.36532e34 | 0.476535 | ||||||||
\(667\) | 1.47201e34 | 0.0735087 | ||||||||
\(668\) | −1.68119e35 | −0.823970 | ||||||||
\(669\) | 2.03109e35 | 0.977016 | ||||||||
\(670\) | −4.86693e34 | −0.229784 | ||||||||
\(671\) | 8.85101e34 | 0.410168 | ||||||||
\(672\) | −6.16426e34 | −0.280392 | ||||||||
\(673\) | −2.87165e35 | −1.28216 | −0.641082 | − | 0.767472i | \(-0.721514\pi\) | ||||
−0.641082 | + | 0.767472i | \(0.721514\pi\) | |||||||
\(674\) | −2.16160e35 | −0.947387 | ||||||||
\(675\) | −6.85047e35 | −2.94729 | ||||||||
\(676\) | 3.53722e34 | 0.149392 | ||||||||
\(677\) | 3.20244e35 | 1.32777 | 0.663885 | − | 0.747835i | \(-0.268907\pi\) | ||||
0.663885 | + | 0.747835i | \(0.268907\pi\) | |||||||
\(678\) | 5.01167e35 | 2.03991 | ||||||||
\(679\) | −3.06003e35 | −1.22280 | ||||||||
\(680\) | 1.55090e34 | 0.0608446 | ||||||||
\(681\) | −1.58411e35 | −0.610165 | ||||||||
\(682\) | −4.68366e34 | −0.177125 | ||||||||
\(683\) | −4.34050e35 | −1.61169 | −0.805843 | − | 0.592129i | \(-0.798288\pi\) | ||||
−0.805843 | + | 0.592129i | \(0.798288\pi\) | |||||||
\(684\) | 1.86274e35 | 0.679126 | ||||||||
\(685\) | 9.48896e34 | 0.339693 | ||||||||
\(686\) | 2.18895e35 | 0.769456 | ||||||||
\(687\) | 6.49388e35 | 2.24153 | ||||||||
\(688\) | 5.16719e34 | 0.175145 | ||||||||
\(689\) | 1.91372e35 | 0.636999 | ||||||||
\(690\) | 1.06222e34 | 0.0347216 | ||||||||
\(691\) | 3.59659e35 | 1.15456 | 0.577279 | − | 0.816547i | \(-0.304114\pi\) | ||||
0.577279 | + | 0.816547i | \(0.304114\pi\) | |||||||
\(692\) | −1.32538e35 | −0.417845 | ||||||||
\(693\) | −1.76480e35 | −0.546425 | ||||||||
\(694\) | 1.80262e34 | 0.0548165 | ||||||||
\(695\) | 1.10548e35 | 0.330174 | ||||||||
\(696\) | −1.65184e35 | −0.484565 | ||||||||
\(697\) | −2.61333e35 | −0.752982 | ||||||||
\(698\) | 1.22089e35 | 0.345529 | ||||||||
\(699\) | 7.22055e34 | 0.200727 | ||||||||
\(700\) | 1.42493e35 | 0.389107 | ||||||||
\(701\) | −4.01671e34 | −0.107745 | −0.0538723 | − | 0.998548i | \(-0.517156\pi\) | ||||
−0.0538723 | + | 0.998548i | \(0.517156\pi\) | |||||||
\(702\) | −9.61963e35 | −2.53481 | ||||||||
\(703\) | 5.04654e34 | 0.130633 | ||||||||
\(704\) | 1.22170e34 | 0.0310674 | ||||||||
\(705\) | −3.37752e35 | −0.843788 | ||||||||
\(706\) | 1.82716e35 | 0.448454 | ||||||||
\(707\) | 4.32357e35 | 1.04256 | ||||||||
\(708\) | −1.22892e35 | −0.291144 | ||||||||
\(709\) | −2.37128e34 | −0.0551957 | −0.0275979 | − | 0.999619i | \(-0.508786\pi\) | ||||
−0.0275979 | + | 0.999619i | \(0.508786\pi\) | |||||||
\(710\) | 2.88046e34 | 0.0658769 | ||||||||
\(711\) | 6.53988e35 | 1.46960 | ||||||||
\(712\) | 6.00907e34 | 0.132681 | ||||||||
\(713\) | 4.75812e34 | 0.103232 | ||||||||
\(714\) | 3.60657e35 | 0.768895 | ||||||||
\(715\) | 3.39402e34 | 0.0711032 | ||||||||
\(716\) | −1.35574e35 | −0.279103 | ||||||||
\(717\) | −1.14103e36 | −2.30839 | ||||||||
\(718\) | 1.79427e35 | 0.356724 | ||||||||
\(719\) | −8.41947e35 | −1.64503 | −0.822514 | − | 0.568744i | \(-0.807429\pi\) | ||||
−0.822514 | + | 0.568744i | \(0.807429\pi\) | |||||||
\(720\) | −8.65148e34 | −0.166125 | ||||||||
\(721\) | −3.13920e35 | −0.592419 | ||||||||
\(722\) | −2.80867e35 | −0.520938 | ||||||||
\(723\) | 2.96697e35 | 0.540859 | ||||||||
\(724\) | 3.03120e34 | 0.0543104 | ||||||||
\(725\) | 3.81839e35 | 0.672443 | ||||||||
\(726\) | −7.31938e35 | −1.26697 | ||||||||
\(727\) | 8.07486e35 | 1.37390 | 0.686950 | − | 0.726705i | \(-0.258949\pi\) | ||||
0.686950 | + | 0.726705i | \(0.258949\pi\) | |||||||
\(728\) | 2.00093e35 | 0.334650 | ||||||||
\(729\) | 1.75615e36 | 2.88714 | ||||||||
\(730\) | −1.95983e34 | −0.0316725 | ||||||||
\(731\) | −3.02321e35 | −0.480287 | ||||||||
\(732\) | 1.00902e36 | 1.57583 | ||||||||
\(733\) | −9.32041e35 | −1.43099 | −0.715493 | − | 0.698620i | \(-0.753798\pi\) | ||||
−0.715493 | + | 0.698620i | \(0.753798\pi\) | |||||||
\(734\) | −3.18151e35 | −0.480211 | ||||||||
\(735\) | 1.00210e35 | 0.148702 | ||||||||
\(736\) | −1.24112e34 | −0.0181068 | ||||||||
\(737\) | 2.24310e35 | 0.321740 | ||||||||
\(738\) | 1.45781e36 | 2.05587 | ||||||||
\(739\) | −9.24490e34 | −0.128188 | −0.0640939 | − | 0.997944i | \(-0.520416\pi\) | ||||
−0.0640939 | + | 0.997944i | \(0.520416\pi\) | |||||||
\(740\) | −2.34386e34 | −0.0319548 | ||||||||
\(741\) | −8.33068e35 | −1.11674 | ||||||||
\(742\) | 2.49041e35 | 0.328263 | ||||||||
\(743\) | 3.86129e35 | 0.500463 | 0.250232 | − | 0.968186i | \(-0.419493\pi\) | ||||
0.250232 | + | 0.968186i | \(0.419493\pi\) | |||||||
\(744\) | −5.33938e35 | −0.680501 | ||||||||
\(745\) | 5.81106e34 | 0.0728287 | ||||||||
\(746\) | −9.71592e35 | −1.19743 | ||||||||
\(747\) | −3.69882e36 | −4.48287 | ||||||||
\(748\) | −7.14788e34 | −0.0851937 | ||||||||
\(749\) | 5.30431e35 | 0.621736 | ||||||||
\(750\) | 5.69607e35 | 0.656613 | ||||||||
\(751\) | 5.31819e35 | 0.602927 | 0.301463 | − | 0.953478i | \(-0.402525\pi\) | ||||
0.301463 | + | 0.953478i | \(0.402525\pi\) | |||||||
\(752\) | 3.94637e35 | 0.440023 | ||||||||
\(753\) | 4.65889e35 | 0.510911 | ||||||||
\(754\) | 5.36190e35 | 0.578332 | ||||||||
\(755\) | −3.44496e35 | −0.365466 | ||||||||
\(756\) | −1.25184e36 | −1.30625 | ||||||||
\(757\) | 1.46803e36 | 1.50674 | 0.753368 | − | 0.657599i | \(-0.228428\pi\) | ||||
0.753368 | + | 0.657599i | \(0.228428\pi\) | |||||||
\(758\) | −5.69116e35 | −0.574560 | ||||||||
\(759\) | −4.89561e34 | −0.0486166 | ||||||||
\(760\) | −4.66188e34 | −0.0455398 | ||||||||
\(761\) | 1.26153e36 | 1.21225 | 0.606123 | − | 0.795371i | \(-0.292724\pi\) | ||||
0.606123 | + | 0.795371i | \(0.292724\pi\) | |||||||
\(762\) | −4.45641e35 | −0.421257 | ||||||||
\(763\) | 5.02210e35 | 0.467012 | ||||||||
\(764\) | −8.27269e35 | −0.756798 | ||||||||
\(765\) | 5.06179e35 | 0.455550 | ||||||||
\(766\) | −1.55273e35 | −0.137479 | ||||||||
\(767\) | 3.98910e35 | 0.347482 | ||||||||
\(768\) | 1.39274e35 | 0.119358 | ||||||||
\(769\) | −9.78483e35 | −0.825039 | −0.412519 | − | 0.910949i | \(-0.635351\pi\) | ||||
−0.412519 | + | 0.910949i | \(0.635351\pi\) | |||||||
\(770\) | 4.41678e34 | 0.0366414 | ||||||||
\(771\) | 1.96165e36 | 1.60119 | ||||||||
\(772\) | 2.38980e35 | 0.191931 | ||||||||
\(773\) | −1.97217e36 | −1.55848 | −0.779238 | − | 0.626728i | \(-0.784394\pi\) | ||||
−0.779238 | + | 0.626728i | \(0.784394\pi\) | |||||||
\(774\) | 1.68646e36 | 1.31133 | ||||||||
\(775\) | 1.23425e36 | 0.944350 | ||||||||
\(776\) | 6.91375e35 | 0.520526 | ||||||||
\(777\) | −5.45059e35 | −0.403813 | ||||||||
\(778\) | −9.01978e35 | −0.657583 | ||||||||
\(779\) | 7.85547e35 | 0.563578 | ||||||||
\(780\) | 3.86919e35 | 0.273173 | ||||||||
\(781\) | −1.32757e35 | −0.0922398 | ||||||||
\(782\) | 7.26151e34 | 0.0496527 | ||||||||
\(783\) | −3.35457e36 | −2.25743 | ||||||||
\(784\) | −1.17087e35 | −0.0775459 | ||||||||
\(785\) | −6.52153e35 | −0.425088 | ||||||||
\(786\) | −1.00575e36 | −0.645222 | ||||||||
\(787\) | −2.25189e35 | −0.142188 | −0.0710940 | − | 0.997470i | \(-0.522649\pi\) | ||||
−0.0710940 | + | 0.997470i | \(0.522649\pi\) | |||||||
\(788\) | 6.02424e35 | 0.374390 | ||||||||
\(789\) | 2.70224e36 | 1.65295 | ||||||||
\(790\) | −1.63674e35 | −0.0985465 | ||||||||
\(791\) | −2.11702e36 | −1.25464 | ||||||||
\(792\) | 3.98735e35 | 0.232605 | ||||||||
\(793\) | −3.27529e36 | −1.88077 | ||||||||
\(794\) | 8.96781e35 | 0.506909 | ||||||||
\(795\) | 4.81568e35 | 0.267959 | ||||||||
\(796\) | −1.36230e36 | −0.746209 | ||||||||
\(797\) | 3.69113e36 | 1.99035 | 0.995177 | − | 0.0980978i | \(-0.0312758\pi\) | ||||
0.995177 | + | 0.0980978i | \(0.0312758\pi\) | |||||||
\(798\) | −1.08411e36 | −0.575488 | ||||||||
\(799\) | −2.30893e36 | −1.20664 | ||||||||
\(800\) | −3.21945e35 | −0.165637 | ||||||||
\(801\) | 1.96123e36 | 0.993393 | ||||||||
\(802\) | 1.22485e36 | 0.610806 | ||||||||
\(803\) | 9.03258e34 | 0.0443473 | ||||||||
\(804\) | 2.55713e36 | 1.23610 | ||||||||
\(805\) | −4.48700e34 | −0.0213554 | ||||||||
\(806\) | 1.73317e36 | 0.812184 | ||||||||
\(807\) | 4.12420e36 | 1.90292 | ||||||||
\(808\) | −9.76854e35 | −0.443800 | ||||||||
\(809\) | −2.93815e36 | −1.31437 | −0.657185 | − | 0.753730i | \(-0.728253\pi\) | ||||
−0.657185 | + | 0.753730i | \(0.728253\pi\) | |||||||
\(810\) | −1.35398e36 | −0.596416 | ||||||||
\(811\) | −2.44583e36 | −1.06088 | −0.530439 | − | 0.847723i | \(-0.677973\pi\) | ||||
−0.530439 | + | 0.847723i | \(0.677973\pi\) | |||||||
\(812\) | 6.97767e35 | 0.298030 | ||||||||
\(813\) | −2.71729e36 | −1.14289 | ||||||||
\(814\) | 1.08025e35 | 0.0447426 | ||||||||
\(815\) | −1.04137e35 | −0.0424752 | ||||||||
\(816\) | −8.14859e35 | −0.327307 | ||||||||
\(817\) | 9.08753e35 | 0.359476 | ||||||||
\(818\) | 2.91771e35 | 0.113665 | ||||||||
\(819\) | 6.53060e36 | 2.50556 | ||||||||
\(820\) | −3.64847e35 | −0.137860 | ||||||||
\(821\) | 3.33815e36 | 1.24227 | 0.621136 | − | 0.783703i | \(-0.286672\pi\) | ||||
0.621136 | + | 0.783703i | \(0.286672\pi\) | |||||||
\(822\) | −4.98560e36 | −1.82734 | ||||||||
\(823\) | 2.54036e36 | 0.917058 | 0.458529 | − | 0.888679i | \(-0.348377\pi\) | ||||
0.458529 | + | 0.888679i | \(0.348377\pi\) | |||||||
\(824\) | 7.09263e35 | 0.252184 | ||||||||
\(825\) | −1.26992e36 | −0.444734 | ||||||||
\(826\) | 5.19119e35 | 0.179067 | ||||||||
\(827\) | −3.63276e36 | −1.23429 | −0.617146 | − | 0.786849i | \(-0.711711\pi\) | ||||
−0.617146 | + | 0.786849i | \(0.711711\pi\) | |||||||
\(828\) | −4.05074e35 | −0.135567 | ||||||||
\(829\) | 1.07727e36 | 0.355135 | 0.177567 | − | 0.984109i | \(-0.443177\pi\) | ||||
0.177567 | + | 0.984109i | \(0.443177\pi\) | |||||||
\(830\) | 9.25706e35 | 0.300606 | ||||||||
\(831\) | −2.13782e36 | −0.683847 | ||||||||
\(832\) | −4.52085e35 | −0.142455 | ||||||||
\(833\) | 6.85052e35 | 0.212648 | ||||||||
\(834\) | −5.80833e36 | −1.77613 | ||||||||
\(835\) | 1.37324e36 | 0.413682 | ||||||||
\(836\) | 2.14860e35 | 0.0637641 | ||||||||
\(837\) | −1.08433e37 | −3.17024 | ||||||||
\(838\) | 1.20611e36 | 0.347407 | ||||||||
\(839\) | −2.96808e36 | −0.842269 | −0.421134 | − | 0.906998i | \(-0.638368\pi\) | ||||
−0.421134 | + | 0.906998i | \(0.638368\pi\) | |||||||
\(840\) | 5.03514e35 | 0.140773 | ||||||||
\(841\) | −1.76056e36 | −0.484953 | ||||||||
\(842\) | 4.17349e36 | 1.13266 | ||||||||
\(843\) | 8.96316e36 | 2.39671 | ||||||||
\(844\) | −1.73283e36 | −0.456537 | ||||||||
\(845\) | −2.88930e35 | −0.0750039 | ||||||||
\(846\) | 1.28801e37 | 3.29450 | ||||||||
\(847\) | 3.09185e36 | 0.779247 | ||||||||
\(848\) | −5.62676e35 | −0.139737 | ||||||||
\(849\) | −2.74735e36 | −0.672308 | ||||||||
\(850\) | 1.88363e36 | 0.454213 | ||||||||
\(851\) | −1.09743e35 | −0.0260769 | ||||||||
\(852\) | −1.51343e36 | −0.354378 | ||||||||
\(853\) | 6.13786e36 | 1.41630 | 0.708148 | − | 0.706064i | \(-0.249531\pi\) | ||||
0.708148 | + | 0.706064i | \(0.249531\pi\) | |||||||
\(854\) | −4.26227e36 | −0.969210 | ||||||||
\(855\) | −1.52153e36 | −0.340961 | ||||||||
\(856\) | −1.19844e36 | −0.264664 | ||||||||
\(857\) | 3.16481e36 | 0.688791 | 0.344395 | − | 0.938825i | \(-0.388084\pi\) | ||||
0.344395 | + | 0.938825i | \(0.388084\pi\) | |||||||
\(858\) | −1.78325e36 | −0.382492 | ||||||||
\(859\) | 5.65370e36 | 1.19514 | 0.597569 | − | 0.801818i | \(-0.296134\pi\) | ||||
0.597569 | + | 0.801818i | \(0.296134\pi\) | |||||||
\(860\) | −4.22070e35 | −0.0879334 | ||||||||
\(861\) | −8.48442e36 | −1.74214 | ||||||||
\(862\) | −2.78322e36 | −0.563257 | ||||||||
\(863\) | −8.00828e36 | −1.59736 | −0.798682 | − | 0.601753i | \(-0.794469\pi\) | ||||
−0.798682 | + | 0.601753i | \(0.794469\pi\) | |||||||
\(864\) | 2.82838e36 | 0.556053 | ||||||||
\(865\) | 1.08261e36 | 0.209783 | ||||||||
\(866\) | −2.96617e36 | −0.566530 | ||||||||
\(867\) | −5.37651e36 | −1.01219 | ||||||||
\(868\) | 2.25545e36 | 0.418540 | ||||||||
\(869\) | 7.54351e35 | 0.137983 | ||||||||
\(870\) | 1.34927e36 | 0.243280 | ||||||||
\(871\) | −8.30052e36 | −1.47529 | ||||||||
\(872\) | −1.13468e36 | −0.198800 | ||||||||
\(873\) | 2.25649e37 | 3.89723 | ||||||||
\(874\) | −2.18275e35 | −0.0371631 | ||||||||
\(875\) | −2.40613e36 | −0.403848 | ||||||||
\(876\) | 1.02971e36 | 0.170379 | ||||||||
\(877\) | 3.29560e36 | 0.537575 | 0.268788 | − | 0.963199i | \(-0.413377\pi\) | ||||
0.268788 | + | 0.963199i | \(0.413377\pi\) | |||||||
\(878\) | −3.74153e36 | −0.601683 | ||||||||
\(879\) | −7.33233e36 | −1.16247 | ||||||||
\(880\) | −9.97916e34 | −0.0155977 | ||||||||
\(881\) | −8.05386e36 | −1.24109 | −0.620547 | − | 0.784169i | \(-0.713090\pi\) | ||||
−0.620547 | + | 0.784169i | \(0.713090\pi\) | |||||||
\(882\) | −3.82147e36 | −0.580595 | ||||||||
\(883\) | −4.91849e35 | −0.0736754 | −0.0368377 | − | 0.999321i | \(-0.511728\pi\) | ||||
−0.0368377 | + | 0.999321i | \(0.511728\pi\) | |||||||
\(884\) | 2.64505e36 | 0.390644 | ||||||||
\(885\) | 1.00381e36 | 0.146172 | ||||||||
\(886\) | −1.44406e36 | −0.207331 | ||||||||
\(887\) | 7.79484e36 | 1.10347 | 0.551737 | − | 0.834018i | \(-0.313965\pi\) | ||||
0.551737 | + | 0.834018i | \(0.313965\pi\) | |||||||
\(888\) | 1.23149e36 | 0.171897 | ||||||||
\(889\) | 1.88247e36 | 0.259093 | ||||||||
\(890\) | −4.90837e35 | −0.0666135 | ||||||||
\(891\) | 6.24031e36 | 0.835093 | ||||||||
\(892\) | 1.93847e36 | 0.255799 | ||||||||
\(893\) | 6.94048e36 | 0.903121 | ||||||||
\(894\) | −3.05319e36 | −0.391774 | ||||||||
\(895\) | 1.10741e36 | 0.140127 | ||||||||
\(896\) | −5.88318e35 | −0.0734111 | ||||||||
\(897\) | 1.81160e36 | 0.222924 | ||||||||
\(898\) | 1.51928e36 | 0.184367 | ||||||||
\(899\) | 6.04394e36 | 0.723309 | ||||||||
\(900\) | −1.05076e37 | −1.24014 | ||||||||
\(901\) | 3.29209e36 | 0.383188 | ||||||||
\(902\) | 1.68153e36 | 0.193029 | ||||||||
\(903\) | −9.81513e36 | −1.11122 | ||||||||
\(904\) | 4.78314e36 | 0.534082 | ||||||||
\(905\) | −2.47597e35 | −0.0272670 | ||||||||
\(906\) | 1.81002e37 | 1.96599 | ||||||||
\(907\) | −1.31417e37 | −1.40786 | −0.703932 | − | 0.710268i | \(-0.748574\pi\) | ||||
−0.703932 | + | 0.710268i | \(0.748574\pi\) | |||||||
\(908\) | −1.51188e36 | −0.159751 | ||||||||
\(909\) | −3.18823e37 | −3.32278 | ||||||||
\(910\) | −1.63442e36 | −0.168014 | ||||||||
\(911\) | 1.44767e37 | 1.46788 | 0.733940 | − | 0.679214i | \(-0.237679\pi\) | ||||
0.733940 | + | 0.679214i | \(0.237679\pi\) | |||||||
\(912\) | 2.44940e36 | 0.244977 | ||||||||
\(913\) | −4.26645e36 | −0.420903 | ||||||||
\(914\) | 7.24821e36 | 0.705347 | ||||||||
\(915\) | −8.24192e36 | −0.791161 | ||||||||
\(916\) | 6.19776e36 | 0.586869 | ||||||||
\(917\) | 4.24848e36 | 0.396842 | ||||||||
\(918\) | −1.65482e37 | −1.52482 | ||||||||
\(919\) | −1.03191e37 | −0.937990 | −0.468995 | − | 0.883201i | \(-0.655384\pi\) | ||||
−0.468995 | + | 0.883201i | \(0.655384\pi\) | |||||||
\(920\) | 1.01378e35 | 0.00909067 | ||||||||
\(921\) | 1.35356e37 | 1.19738 | ||||||||
\(922\) | 2.87137e36 | 0.250584 | ||||||||
\(923\) | 4.91262e36 | 0.422953 | ||||||||
\(924\) | −2.32062e36 | −0.197108 | ||||||||
\(925\) | −2.84672e36 | −0.238546 | ||||||||
\(926\) | −3.77045e36 | −0.311714 | ||||||||
\(927\) | 2.31487e37 | 1.88813 | ||||||||
\(928\) | −1.57651e36 | −0.126867 | ||||||||
\(929\) | −2.17912e37 | −1.73015 | −0.865075 | − | 0.501642i | \(-0.832729\pi\) | ||||
−0.865075 | + | 0.501642i | \(0.832729\pi\) | |||||||
\(930\) | 4.36135e36 | 0.341652 | ||||||||
\(931\) | −2.05921e36 | −0.159159 | ||||||||
\(932\) | 6.89130e35 | 0.0525536 | ||||||||
\(933\) | 2.71170e37 | 2.04043 | ||||||||
\(934\) | −7.56121e36 | −0.561378 | ||||||||
\(935\) | 5.83858e35 | 0.0427723 | ||||||||
\(936\) | −1.47550e37 | −1.06658 | ||||||||
\(937\) | −2.08020e37 | −1.48375 | −0.741873 | − | 0.670540i | \(-0.766062\pi\) | ||||
−0.741873 | + | 0.670540i | \(0.766062\pi\) | |||||||
\(938\) | −1.08018e37 | −0.760258 | ||||||||
\(939\) | 2.85686e37 | 1.98413 | ||||||||
\(940\) | −3.22350e36 | −0.220917 | ||||||||
\(941\) | 2.39454e37 | 1.61939 | 0.809695 | − | 0.586851i | \(-0.199632\pi\) | ||||
0.809695 | + | 0.586851i | \(0.199632\pi\) | |||||||
\(942\) | 3.42648e37 | 2.28672 | ||||||||
\(943\) | −1.70826e36 | −0.112501 | ||||||||
\(944\) | −1.17288e36 | −0.0762262 | ||||||||
\(945\) | 1.02254e37 | 0.655817 | ||||||||
\(946\) | 1.94526e36 | 0.123123 | ||||||||
\(947\) | −8.06134e36 | −0.503539 | −0.251769 | − | 0.967787i | \(-0.581012\pi\) | ||||
−0.251769 | + | 0.967787i | \(0.581012\pi\) | |||||||
\(948\) | 8.59960e36 | 0.530120 | ||||||||
\(949\) | −3.34248e36 | −0.203348 | ||||||||
\(950\) | −5.66205e36 | −0.339960 | ||||||||
\(951\) | −4.02727e37 | −2.38646 | ||||||||
\(952\) | 3.44212e36 | 0.201309 | ||||||||
\(953\) | −1.92589e37 | −1.11166 | −0.555829 | − | 0.831297i | \(-0.687599\pi\) | ||||
−0.555829 | + | 0.831297i | \(0.687599\pi\) | |||||||
\(954\) | −1.83645e37 | −1.04622 | ||||||||
\(955\) | 6.75736e36 | 0.379957 | ||||||||
\(956\) | −1.08900e37 | −0.604374 | ||||||||
\(957\) | −6.21858e36 | −0.340637 | ||||||||
\(958\) | −1.59122e36 | −0.0860321 | ||||||||
\(959\) | 2.10601e37 | 1.12390 | ||||||||
\(960\) | −1.13762e36 | −0.0599251 | ||||||||
\(961\) | 3.03575e35 | 0.0157842 | ||||||||
\(962\) | −3.99745e36 | −0.205161 | ||||||||
\(963\) | −3.91144e37 | −1.98157 | ||||||||
\(964\) | 2.83168e36 | 0.141606 | ||||||||
\(965\) | −1.95205e36 | −0.0963606 | ||||||||
\(966\) | 2.35752e36 | 0.114879 | ||||||||
\(967\) | 2.29324e37 | 1.10311 | 0.551554 | − | 0.834139i | \(-0.314035\pi\) | ||||
0.551554 | + | 0.834139i | \(0.314035\pi\) | |||||||
\(968\) | −6.98563e36 | −0.331714 | ||||||||
\(969\) | −1.43309e37 | −0.671779 | ||||||||
\(970\) | −5.64734e36 | −0.261335 | ||||||||
\(971\) | 2.10199e37 | 0.960265 | 0.480132 | − | 0.877196i | \(-0.340589\pi\) | ||||
0.480132 | + | 0.877196i | \(0.340589\pi\) | |||||||
\(972\) | 3.62665e37 | 1.63560 | ||||||||
\(973\) | 2.45355e37 | 1.09241 | ||||||||
\(974\) | 1.74531e37 | 0.767161 | ||||||||
\(975\) | 4.69929e37 | 2.03927 | ||||||||
\(976\) | 9.63006e36 | 0.412578 | ||||||||
\(977\) | −3.52592e37 | −1.49139 | −0.745694 | − | 0.666289i | \(-0.767882\pi\) | ||||
−0.745694 | + | 0.666289i | \(0.767882\pi\) | |||||||
\(978\) | 5.47148e36 | 0.228491 | ||||||||
\(979\) | 2.26220e36 | 0.0932712 | ||||||||
\(980\) | 9.56401e35 | 0.0389327 | ||||||||
\(981\) | −3.70334e37 | −1.48844 | ||||||||
\(982\) | −1.85363e37 | −0.735581 | ||||||||
\(983\) | 7.31962e36 | 0.286794 | 0.143397 | − | 0.989665i | \(-0.454197\pi\) | ||||
0.143397 | + | 0.989665i | \(0.454197\pi\) | |||||||
\(984\) | 1.91694e37 | 0.741602 | ||||||||
\(985\) | −4.92076e36 | −0.187966 | ||||||||
\(986\) | 9.22384e36 | 0.347897 | ||||||||
\(987\) | −7.49617e37 | −2.79174 | ||||||||
\(988\) | −7.95081e36 | −0.292381 | ||||||||
\(989\) | −1.97619e36 | −0.0717587 | ||||||||
\(990\) | −3.25697e36 | −0.116782 | ||||||||
\(991\) | 1.16985e37 | 0.414200 | 0.207100 | − | 0.978320i | \(-0.433597\pi\) | ||||
0.207100 | + | 0.978320i | \(0.433597\pi\) | |||||||
\(992\) | −5.09591e36 | −0.178166 | ||||||||
\(993\) | 6.06819e37 | 2.09504 | ||||||||
\(994\) | 6.39300e36 | 0.217959 | ||||||||
\(995\) | 1.11277e37 | 0.374641 | ||||||||
\(996\) | −4.86376e37 | −1.61708 | ||||||||
\(997\) | 2.33411e37 | 0.766358 | 0.383179 | − | 0.923674i | \(-0.374829\pi\) | ||||
0.383179 | + | 0.923674i | \(0.374829\pi\) | |||||||
\(998\) | 1.82280e37 | 0.591028 | ||||||||
\(999\) | 2.50092e37 | 0.800814 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2.26.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 18.26.a.e.1.2 | 2 | |||
4.3 | odd | 2 | 16.26.a.c.1.1 | 2 | |||
5.2 | odd | 4 | 50.26.b.e.49.3 | 4 | |||
5.3 | odd | 4 | 50.26.b.e.49.2 | 4 | |||
5.4 | even | 2 | 50.26.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.26.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
16.26.a.c.1.1 | 2 | 4.3 | odd | 2 | |||
18.26.a.e.1.2 | 2 | 3.2 | odd | 2 | |||
50.26.a.c.1.1 | 2 | 5.4 | even | 2 | |||
50.26.b.e.49.2 | 4 | 5.3 | odd | 4 | |||
50.26.b.e.49.3 | 4 | 5.2 | odd | 4 |