Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,26,Mod(49,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.49");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(197.998389976\) |
Analytic rank: | \(0\) |
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: |
\( x^{4} + 53353x^{2} + 711608976 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{2}\cdot 5^{4} \) |
Twist minimal: | no (minimal twist has level 2) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(-162.829i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.49 |
Dual form | 50.26.b.e.49.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).
\(n\) | \(27\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4096.00i | − 0.707107i | ||||||||
\(3\) | 1.75788e6i | 1.90974i | 0.297031 | + | 0.954868i | \(0.404004\pi\) | ||||
−0.297031 | + | 0.954868i | \(0.595996\pi\) | |||||||
\(4\) | −1.67772e7 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 7.20027e9 | 1.35039 | ||||||||
\(7\) | 3.04153e10i | 0.830552i | 0.909696 | + | 0.415276i | \(0.136315\pi\) | ||||
−0.909696 | + | 0.415276i | \(0.863685\pi\) | |||||||
\(8\) | 6.87195e10i | 0.353553i | ||||||||
\(9\) | −2.24285e12 | −2.64709 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.58704e12 | 0.248539 | 0.124270 | − | 0.992248i | \(-0.460341\pi\) | ||||
0.124270 | + | 0.992248i | \(0.460341\pi\) | |||||||
\(12\) | − 2.94923e13i | − 0.954868i | ||||||||
\(13\) | − 9.57327e13i | − 1.13964i | −0.821769 | − | 0.569821i | \(-0.807012\pi\) | ||||
0.821769 | − | 0.569821i | \(-0.192988\pi\) | |||||||
\(14\) | 1.24581e14 | 0.587289 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | 1.64685e15i | 0.685555i | 0.939417 | + | 0.342777i | \(0.111368\pi\) | ||||
−0.939417 | + | 0.342777i | \(0.888632\pi\) | |||||||
\(18\) | 9.18671e15i | 1.87178i | ||||||||
\(19\) | −4.95030e15 | −0.513111 | −0.256555 | − | 0.966530i | \(-0.582588\pi\) | ||||
−0.256555 | + | 0.966530i | \(0.582588\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.34664e16 | −1.58613 | ||||||||
\(22\) | − 1.05965e16i | − 0.175744i | ||||||||
\(23\) | − 1.07650e16i | − 0.102427i | −0.998688 | − | 0.0512136i | \(-0.983691\pi\) | ||||
0.998688 | − | 0.0512136i | \(-0.0163089\pi\) | |||||||
\(24\) | −1.20801e17 | −0.675194 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.92121e17 | −0.805849 | ||||||||
\(27\) | − 2.45323e18i | − 3.14551i | ||||||||
\(28\) | − 5.10284e17i | − 0.415276i | ||||||||
\(29\) | 1.36741e18 | 0.717668 | 0.358834 | − | 0.933401i | \(-0.383174\pi\) | ||||
0.358834 | + | 0.933401i | \(0.383174\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.42000e18 | −1.00786 | −0.503931 | − | 0.863744i | \(-0.668113\pi\) | ||||
−0.503931 | + | 0.863744i | \(0.668113\pi\) | |||||||
\(32\) | − 1.15292e18i | − 0.176777i | ||||||||
\(33\) | 4.54771e18i | 0.474645i | ||||||||
\(34\) | 6.74549e18 | 0.484760 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.76288e19 | 1.32355 | ||||||||
\(37\) | − 1.01944e19i | − 0.254590i | −0.991865 | − | 0.127295i | \(-0.959371\pi\) | ||||
0.991865 | − | 0.127295i | \(-0.0406294\pi\) | |||||||
\(38\) | 2.02764e19i | 0.362824i | ||||||||
\(39\) | 1.68287e20 | 2.17642 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.58687e20 | 1.09835 | 0.549177 | − | 0.835706i | \(-0.314941\pi\) | ||||
0.549177 | + | 0.835706i | \(0.314941\pi\) | |||||||
\(42\) | 2.18999e20i | 1.12157i | ||||||||
\(43\) | 1.83575e20i | 0.700582i | 0.936641 | + | 0.350291i | \(0.113917\pi\) | ||||
−0.936641 | + | 0.350291i | \(0.886083\pi\) | |||||||
\(44\) | −4.34034e19 | −0.124270 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.40934e19 | −0.0724270 | ||||||||
\(47\) | − 1.40203e21i | − 1.76009i | −0.474890 | − | 0.880045i | \(-0.657512\pi\) | ||||
0.474890 | − | 0.880045i | \(-0.342488\pi\) | |||||||
\(48\) | 4.94799e20i | 0.477434i | ||||||||
\(49\) | 4.15978e20 | 0.310184 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.89496e21 | −1.30923 | ||||||||
\(52\) | 1.60613e21i | 0.569821i | ||||||||
\(53\) | − 1.99903e21i | − 0.558946i | −0.960154 | − | 0.279473i | \(-0.909840\pi\) | ||||
0.960154 | − | 0.279473i | \(-0.0901598\pi\) | |||||||
\(54\) | −1.00484e22 | −2.22421 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.09012e21 | −0.293644 | ||||||||
\(57\) | − 8.70202e21i | − 0.979906i | ||||||||
\(58\) | − 5.60091e21i | − 0.507468i | ||||||||
\(59\) | 4.16691e21 | 0.304905 | 0.152452 | − | 0.988311i | \(-0.451283\pi\) | ||||
0.152452 | + | 0.988311i | \(0.451283\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.42128e22 | 1.65031 | 0.825156 | − | 0.564904i | \(-0.191087\pi\) | ||||
0.825156 | + | 0.564904i | \(0.191087\pi\) | |||||||
\(62\) | 1.81043e22i | 0.712666i | ||||||||
\(63\) | − 6.82170e22i | − 2.19855i | ||||||||
\(64\) | −4.72237e21 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.86274e22 | 0.335624 | ||||||||
\(67\) | − 8.67051e22i | − 1.29452i | −0.762268 | − | 0.647261i | \(-0.775914\pi\) | ||||
0.762268 | − | 0.647261i | \(-0.224086\pi\) | |||||||
\(68\) | − 2.76295e22i | − 0.342777i | ||||||||
\(69\) | 1.89236e22 | 0.195609 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.13159e22 | −0.371127 | −0.185564 | − | 0.982632i | \(-0.559411\pi\) | ||||
−0.185564 | + | 0.982632i | \(0.559411\pi\) | |||||||
\(72\) | − 1.54128e23i | − 0.935888i | ||||||||
\(73\) | 3.49147e22i | 0.178432i | 0.996012 | + | 0.0892159i | \(0.0284361\pi\) | ||||
−0.996012 | + | 0.0892159i | \(0.971564\pi\) | |||||||
\(74\) | −4.17563e22 | −0.180022 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.30522e22 | 0.256555 | ||||||||
\(77\) | 7.86857e22i | 0.206425i | ||||||||
\(78\) | − 6.89302e23i | − 1.53896i | ||||||||
\(79\) | −2.91588e23 | −0.555176 | −0.277588 | − | 0.960700i | \(-0.589535\pi\) | ||||
−0.277588 | + | 0.960700i | \(0.589535\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.41214e24 | 3.36000 | ||||||||
\(82\) | − 6.49981e23i | − 0.776654i | ||||||||
\(83\) | − 1.64916e24i | − 1.69351i | −0.531986 | − | 0.846753i | \(-0.678554\pi\) | ||||
0.531986 | − | 0.846753i | \(-0.321446\pi\) | |||||||
\(84\) | 8.97018e23 | 0.793067 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.51925e23 | 0.495386 | ||||||||
\(87\) | 2.40374e24i | 1.37056i | ||||||||
\(88\) | 1.77780e23i | 0.0878720i | ||||||||
\(89\) | −8.74435e23 | −0.375277 | −0.187639 | − | 0.982238i | \(-0.560083\pi\) | ||||
−0.187639 | + | 0.982238i | \(0.560083\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.91174e24 | 0.946532 | ||||||||
\(92\) | 1.80607e23i | 0.0512136i | ||||||||
\(93\) | − 7.76982e24i | − 1.92475i | ||||||||
\(94\) | −5.74273e24 | −1.24457 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.02670e24 | 0.337597 | ||||||||
\(97\) | − 1.00608e25i | − 1.47227i | −0.676835 | − | 0.736134i | \(-0.736649\pi\) | ||||
0.676835 | − | 0.736134i | \(-0.263351\pi\) | |||||||
\(98\) | − 1.70384e24i | − 0.219333i | ||||||||
\(99\) | −5.80235e24 | −0.657907 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.42151e25 | −1.25526 | −0.627628 | − | 0.778513i | \(-0.715974\pi\) | ||||
−0.627628 | + | 0.778513i | \(0.715974\pi\) | |||||||
\(102\) | 1.18578e25i | 0.925764i | ||||||||
\(103\) | 1.03211e25i | 0.713283i | 0.934241 | + | 0.356642i | \(0.116078\pi\) | ||||
−0.934241 | + | 0.356642i | \(0.883922\pi\) | |||||||
\(104\) | 6.57870e24 | 0.402924 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.18801e24 | −0.395235 | ||||||||
\(107\) | 1.74396e25i | 0.748582i | 0.927311 | + | 0.374291i | \(0.122114\pi\) | ||||
−0.927311 | + | 0.374291i | \(0.877886\pi\) | |||||||
\(108\) | 4.11583e25i | 1.57275i | ||||||||
\(109\) | 1.65117e25 | 0.562292 | 0.281146 | − | 0.959665i | \(-0.409286\pi\) | ||||
0.281146 | + | 0.959665i | \(0.409286\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.79205e25 | 0.486199 | ||||||||
\(112\) | 8.56115e24i | 0.207638i | ||||||||
\(113\) | 6.96039e25i | 1.51061i | 0.655372 | + | 0.755306i | \(0.272512\pi\) | ||||
−0.655372 | + | 0.755306i | \(0.727488\pi\) | |||||||
\(114\) | −3.56435e25 | −0.692898 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.29413e25 | −0.358834 | ||||||||
\(117\) | 2.14714e26i | 3.01674i | ||||||||
\(118\) | − 1.70677e25i | − 0.215600i | ||||||||
\(119\) | −5.00894e25 | −0.569389 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.01654e26 | −0.938228 | ||||||||
\(122\) | − 1.40136e26i | − 1.16695i | ||||||||
\(123\) | 2.78952e26i | 2.09757i | ||||||||
\(124\) | 7.41552e25 | 0.503931 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.79417e26 | −1.55461 | ||||||||
\(127\) | 6.18922e25i | 0.311953i | 0.987761 | + | 0.155977i | \(0.0498524\pi\) | ||||
−0.987761 | + | 0.155977i | \(0.950148\pi\) | |||||||
\(128\) | 1.93428e25i | 0.0883883i | ||||||||
\(129\) | −3.22703e26 | −1.33793 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.39682e26 | −0.477805 | −0.238902 | − | 0.971044i | \(-0.576788\pi\) | ||||
−0.238902 | + | 0.971044i | \(0.576788\pi\) | |||||||
\(132\) | − 7.62979e25i | − 0.237322i | ||||||||
\(133\) | − 1.50565e26i | − 0.426165i | ||||||||
\(134\) | −3.55144e26 | −0.915366 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.13171e26 | −0.242380 | ||||||||
\(137\) | 6.92418e26i | 1.35320i | 0.736352 | + | 0.676599i | \(0.236547\pi\) | ||||
−0.736352 | + | 0.676599i | \(0.763453\pi\) | |||||||
\(138\) | − 7.75109e25i | − 0.138317i | ||||||||
\(139\) | 8.06682e26 | 1.31528 | 0.657639 | − | 0.753333i | \(-0.271555\pi\) | ||||
0.657639 | + | 0.753333i | \(0.271555\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.46460e27 | 3.36131 | ||||||||
\(142\) | 2.10190e26i | 0.262427i | ||||||||
\(143\) | − 2.47665e26i | − 0.283246i | ||||||||
\(144\) | −6.31306e26 | −0.661773 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.43010e26 | 0.126170 | ||||||||
\(147\) | 7.31239e26i | 0.592369i | ||||||||
\(148\) | 1.71034e26i | 0.127295i | ||||||||
\(149\) | 4.24039e26 | 0.290120 | 0.145060 | − | 0.989423i | \(-0.453663\pi\) | ||||
0.145060 | + | 0.989423i | \(0.453663\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.51382e27 | 1.45587 | 0.727934 | − | 0.685647i | \(-0.240481\pi\) | ||||
0.727934 | + | 0.685647i | \(0.240481\pi\) | |||||||
\(152\) | − 3.40182e26i | − 0.181412i | ||||||||
\(153\) | − 3.69363e27i | − 1.81473i | ||||||||
\(154\) | 3.22297e26 | 0.145964 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.82338e27 | −1.08821 | ||||||||
\(157\) | − 4.75882e27i | − 1.69338i | −0.532088 | − | 0.846689i | \(-0.678593\pi\) | ||||
0.532088 | − | 0.846689i | \(-0.321407\pi\) | |||||||
\(158\) | 1.19434e27i | 0.392569i | ||||||||
\(159\) | 3.51404e27 | 1.06744 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.27420e26 | 0.0850712 | ||||||||
\(162\) | − 9.88012e27i | − 2.37588i | ||||||||
\(163\) | 7.59899e26i | 0.169204i | 0.996415 | + | 0.0846020i | \(0.0269619\pi\) | ||||
−0.996415 | + | 0.0846020i | \(0.973038\pi\) | |||||||
\(164\) | −2.66232e27 | −0.549177 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.75496e27 | −1.19749 | ||||||||
\(167\) | 1.00207e28i | 1.64794i | 0.566634 | + | 0.823970i | \(0.308245\pi\) | ||||
−0.566634 | + | 0.823970i | \(0.691755\pi\) | |||||||
\(168\) | − 3.67419e27i | − 0.560783i | ||||||||
\(169\) | −2.10835e27 | −0.298785 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.11028e28 | 1.35825 | ||||||||
\(172\) | − 3.07989e27i | − 0.350291i | ||||||||
\(173\) | − 7.89989e27i | − 0.835689i | −0.908518 | − | 0.417845i | \(-0.862786\pi\) | ||||
0.908518 | − | 0.417845i | \(-0.137214\pi\) | |||||||
\(174\) | 9.84571e27 | 0.969129 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.28188e26 | 0.0621349 | ||||||||
\(177\) | 7.32493e27i | 0.582288i | ||||||||
\(178\) | 3.58168e27i | 0.265361i | ||||||||
\(179\) | 8.08087e27 | 0.558207 | 0.279103 | − | 0.960261i | \(-0.409963\pi\) | ||||
0.279103 | + | 0.960261i | \(0.409963\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.80674e27 | 0.108621 | 0.0543104 | − | 0.998524i | \(-0.482704\pi\) | ||||
0.0543104 | + | 0.998524i | \(0.482704\pi\) | |||||||
\(182\) | − 1.19265e28i | − 0.669299i | ||||||||
\(183\) | 6.01420e28i | 3.15166i | ||||||||
\(184\) | 7.39765e26 | 0.0362135 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.18252e28 | −1.36100 | ||||||||
\(187\) | 4.26047e27i | 0.170387i | ||||||||
\(188\) | 2.35222e28i | 0.880045i | ||||||||
\(189\) | 7.46157e28 | 2.61251 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.93091e28 | −1.51360 | −0.756798 | − | 0.653649i | \(-0.773237\pi\) | ||||
−0.756798 | + | 0.653649i | \(0.773237\pi\) | |||||||
\(192\) | − 8.30135e27i | − 0.238717i | ||||||||
\(193\) | 1.42443e28i | 0.383861i | 0.981408 | + | 0.191931i | \(0.0614749\pi\) | ||||
−0.981408 | + | 0.191931i | \(0.938525\pi\) | |||||||
\(194\) | −4.12092e28 | −1.04105 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.97895e27 | −0.155092 | ||||||||
\(197\) | − 3.59073e28i | − 0.748781i | −0.927271 | − | 0.374390i | \(-0.877852\pi\) | ||||
0.927271 | − | 0.374390i | \(-0.122148\pi\) | |||||||
\(198\) | 2.37664e28i | 0.465210i | ||||||||
\(199\) | 8.11996e28 | 1.49242 | 0.746209 | − | 0.665712i | \(-0.231872\pi\) | ||||
0.746209 | + | 0.665712i | \(0.231872\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.52417e29 | 2.47220 | ||||||||
\(202\) | 5.82250e28i | 0.887601i | ||||||||
\(203\) | 4.15902e28i | 0.596060i | ||||||||
\(204\) | 4.85694e28 | 0.654614 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.22753e28 | 0.504367 | ||||||||
\(207\) | 2.41443e28i | 0.271134i | ||||||||
\(208\) | − 2.69464e28i | − 0.284911i | ||||||||
\(209\) | −1.28066e28 | −0.127528 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.03285e29 | −0.913075 | −0.456537 | − | 0.889704i | \(-0.650911\pi\) | ||||
−0.456537 | + | 0.889704i | \(0.650911\pi\) | |||||||
\(212\) | 3.35381e28i | 0.279473i | ||||||||
\(213\) | − 9.02072e28i | − 0.708755i | ||||||||
\(214\) | 7.14326e28 | 0.529327 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.68585e29 | 1.11211 | ||||||||
\(217\) | − 1.34436e29i | − 0.837081i | ||||||||
\(218\) | − 6.76321e28i | − 0.397600i | ||||||||
\(219\) | −6.13758e28 | −0.340757 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.57657e29 | 0.781287 | ||||||||
\(222\) | − 7.34025e28i | − 0.343795i | ||||||||
\(223\) | 1.15542e29i | 0.511597i | 0.966730 | + | 0.255799i | \(0.0823384\pi\) | ||||
−0.966730 | + | 0.255799i | \(0.917662\pi\) | |||||||
\(224\) | 3.50665e28 | 0.146822 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.85098e29 | 1.06816 | ||||||||
\(227\) | 9.01151e28i | 0.319502i | 0.987157 | + | 0.159751i | \(0.0510692\pi\) | ||||
−0.987157 | + | 0.159751i | \(0.948931\pi\) | |||||||
\(228\) | 1.45996e29i | 0.489953i | ||||||||
\(229\) | −3.69415e29 | −1.17374 | −0.586869 | − | 0.809682i | \(-0.699640\pi\) | ||||
−0.586869 | + | 0.809682i | \(0.699640\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.38320e29 | −0.394217 | ||||||||
\(232\) | 9.39676e28i | 0.253734i | ||||||||
\(233\) | 4.10753e28i | 0.105107i | 0.998618 | + | 0.0525536i | \(0.0167360\pi\) | ||||
−0.998618 | + | 0.0525536i | \(0.983264\pi\) | |||||||
\(234\) | 8.79469e29 | 2.13316 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.99092e28 | −0.152452 | ||||||||
\(237\) | − 5.12576e29i | − 1.06024i | ||||||||
\(238\) | 2.05166e29i | 0.402618i | ||||||||
\(239\) | 6.49097e29 | 1.20875 | 0.604374 | − | 0.796701i | \(-0.293423\pi\) | ||||
0.604374 | + | 0.796701i | \(0.293423\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.68781e29 | 0.283212 | 0.141606 | − | 0.989923i | \(-0.454773\pi\) | ||||
0.141606 | + | 0.989923i | \(0.454773\pi\) | |||||||
\(242\) | 4.16376e29i | 0.663427i | ||||||||
\(243\) | 2.16165e30i | 3.27121i | ||||||||
\(244\) | −5.73996e29 | −0.825156 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.14259e30 | 1.48320 | ||||||||
\(247\) | 4.73905e29i | 0.584763i | ||||||||
\(248\) | − 3.03740e29i | − 0.356333i | ||||||||
\(249\) | 2.89903e30 | 3.23415 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.65029e29 | 0.267530 | 0.133765 | − | 0.991013i | \(-0.457293\pi\) | ||||
0.133765 | + | 0.991013i | \(0.457293\pi\) | |||||||
\(252\) | 1.14449e30i | 1.09927i | ||||||||
\(253\) | − 2.78495e28i | − 0.0254572i | ||||||||
\(254\) | 2.53510e29 | 0.220584 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | − 1.11592e30i | − 0.838433i | −0.907886 | − | 0.419217i | \(-0.862305\pi\) | ||||
0.907886 | − | 0.419217i | \(-0.137695\pi\) | |||||||
\(258\) | 1.32179e30i | 0.946057i | ||||||||
\(259\) | 3.10066e29 | 0.211450 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.06689e30 | −1.89973 | ||||||||
\(262\) | 5.72139e29i | 0.337859i | ||||||||
\(263\) | 1.53721e30i | 0.865541i | 0.901504 | + | 0.432770i | \(0.142464\pi\) | ||||
−0.901504 | + | 0.432770i | \(0.857536\pi\) | |||||||
\(264\) | −3.12516e29 | −0.167812 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.16713e29 | −0.301344 | ||||||||
\(267\) | − 1.53715e30i | − 0.716681i | ||||||||
\(268\) | 1.45467e30i | 0.647261i | ||||||||
\(269\) | −2.34612e30 | −0.996431 | −0.498216 | − | 0.867053i | \(-0.666011\pi\) | ||||
−0.498216 | + | 0.867053i | \(0.666011\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.54578e30 | −0.598454 | −0.299227 | − | 0.954182i | \(-0.596729\pi\) | ||||
−0.299227 | + | 0.954182i | \(0.596729\pi\) | |||||||
\(272\) | 4.63547e29i | 0.171389i | ||||||||
\(273\) | 5.11849e30i | 1.80763i | ||||||||
\(274\) | 2.83614e30 | 0.956855 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.17485e29 | −0.0978045 | ||||||||
\(277\) | 1.21614e30i | 0.358085i | 0.983841 | + | 0.179042i | \(0.0572999\pi\) | ||||
−0.983841 | + | 0.179042i | \(0.942700\pi\) | |||||||
\(278\) | − 3.30417e30i | − 0.930042i | ||||||||
\(279\) | 9.91339e30 | 2.66790 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.09885e30 | 1.25500 | 0.627499 | − | 0.778617i | \(-0.284079\pi\) | ||||
0.627499 | + | 0.778617i | \(0.284079\pi\) | |||||||
\(282\) | − 1.00950e31i | − 2.37680i | ||||||||
\(283\) | − 1.56288e30i | − 0.352042i | −0.984386 | − | 0.176021i | \(-0.943677\pi\) | ||||
0.984386 | − | 0.176021i | \(-0.0563227\pi\) | |||||||
\(284\) | 8.60939e29 | 0.185564 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.01444e30 | −0.200285 | ||||||||
\(287\) | 4.82651e30i | 0.912240i | ||||||||
\(288\) | 2.58583e30i | 0.467944i | ||||||||
\(289\) | 3.05852e30 | 0.530015 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.76857e31 | 2.81164 | ||||||||
\(292\) | − 5.85771e29i | − 0.0892159i | ||||||||
\(293\) | − 4.17112e30i | − 0.608706i | −0.952559 | − | 0.304353i | \(-0.901560\pi\) | ||||
0.952559 | − | 0.304353i | \(-0.0984403\pi\) | |||||||
\(294\) | 2.99515e30 | 0.418868 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.00555e29 | 0.0900110 | ||||||||
\(297\) | − 6.34661e30i | − 0.781783i | ||||||||
\(298\) | − 1.73686e30i | − 0.205146i | ||||||||
\(299\) | −1.03056e30 | −0.116730 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.58350e30 | −0.581870 | ||||||||
\(302\) | − 1.02966e31i | − 1.02945i | ||||||||
\(303\) | − 2.49884e31i | − 2.39721i | ||||||||
\(304\) | −1.39338e30 | −0.128278 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.51291e31 | −1.28320 | ||||||||
\(307\) | − 7.69994e30i | − 0.626986i | −0.949591 | − | 0.313493i | \(-0.898501\pi\) | ||||
0.949591 | − | 0.313493i | \(-0.101499\pi\) | |||||||
\(308\) | − 1.32013e30i | − 0.103212i | ||||||||
\(309\) | −1.81433e31 | −1.36218 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.54260e31 | 1.06843 | 0.534217 | − | 0.845347i | \(-0.320606\pi\) | ||||
0.534217 | + | 0.845347i | \(0.320606\pi\) | |||||||
\(312\) | 1.15646e31i | 0.769479i | ||||||||
\(313\) | 1.62517e31i | 1.03895i | 0.854485 | + | 0.519476i | \(0.173873\pi\) | ||||
−0.854485 | + | 0.519476i | \(0.826127\pi\) | |||||||
\(314\) | −1.94921e31 | −1.19740 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.89203e30 | 0.277588 | ||||||||
\(317\) | 2.29098e31i | 1.24963i | 0.780773 | + | 0.624814i | \(0.214825\pi\) | ||||
−0.780773 | + | 0.624814i | \(0.785175\pi\) | |||||||
\(318\) | − 1.43935e31i | − 0.754794i | ||||||||
\(319\) | 3.53755e30 | 0.178369 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.06567e31 | −1.42959 | ||||||||
\(322\) | − 1.34111e30i | − 0.0601544i | ||||||||
\(323\) | − 8.15239e30i | − 0.351765i | ||||||||
\(324\) | −4.04690e31 | −1.68000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.11255e30 | 0.119645 | ||||||||
\(327\) | 2.90256e31i | 1.07383i | ||||||||
\(328\) | 1.09049e31i | 0.388327i | ||||||||
\(329\) | 4.26433e31 | 1.46185 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.45199e31 | 1.09703 | 0.548517 | − | 0.836140i | \(-0.315193\pi\) | ||||
0.548517 | + | 0.836140i | \(0.315193\pi\) | |||||||
\(332\) | 2.76683e31i | 0.846753i | ||||||||
\(333\) | 2.28645e31i | 0.673922i | ||||||||
\(334\) | 4.10447e31 | 1.16527 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.50495e31 | −0.396534 | ||||||||
\(337\) | 5.27735e31i | 1.33981i | 0.742448 | + | 0.669904i | \(0.233665\pi\) | ||||
−0.742448 | + | 0.669904i | \(0.766335\pi\) | |||||||
\(338\) | 8.63579e30i | 0.211273i | ||||||||
\(339\) | −1.22355e32 | −2.88487 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.14347e31 | −0.250493 | ||||||||
\(342\) | − 4.54770e31i | − 0.960429i | ||||||||
\(343\) | 5.34411e31i | 1.08818i | ||||||||
\(344\) | −1.26152e31 | −0.247693 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.23580e31 | −0.590922 | ||||||||
\(347\) | − 4.40093e30i | − 0.0775222i | −0.999249 | − | 0.0387611i | \(-0.987659\pi\) | ||||
0.999249 | − | 0.0387611i | \(-0.0123411\pi\) | |||||||
\(348\) | − 4.03280e31i | − 0.685278i | ||||||||
\(349\) | −2.98069e31 | −0.488651 | −0.244326 | − | 0.969693i | \(-0.578567\pi\) | ||||
−0.244326 | + | 0.969693i | \(0.578567\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.34854e32 | −3.58476 | ||||||||
\(352\) | − 2.98266e30i | − 0.0439360i | ||||||||
\(353\) | 4.46084e31i | 0.634209i | 0.948391 | + | 0.317105i | \(0.102711\pi\) | ||||
−0.948391 | + | 0.317105i | \(0.897289\pi\) | |||||||
\(354\) | 3.00029e31 | 0.411740 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.46706e31 | 0.187639 | ||||||||
\(357\) | − 8.80511e31i | − 1.08738i | ||||||||
\(358\) | − 3.30992e31i | − 0.394712i | ||||||||
\(359\) | −4.38054e31 | −0.504483 | −0.252242 | − | 0.967664i | \(-0.581168\pi\) | ||||
−0.252242 | + | 0.967664i | \(0.581168\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.85711e31 | −0.736717 | ||||||||
\(362\) | − 7.40039e30i | − 0.0768065i | ||||||||
\(363\) | − 1.78696e32i | − 1.79177i | ||||||||
\(364\) | −4.88509e31 | −0.473266 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.46342e32 | 2.22856 | ||||||||
\(367\) | 7.76735e31i | 0.679121i | 0.940584 | + | 0.339560i | \(0.110278\pi\) | ||||
−0.940584 | + | 0.339560i | \(0.889722\pi\) | |||||||
\(368\) | − 3.03008e30i | − 0.0256068i | ||||||||
\(369\) | −3.55911e32 | −2.90744 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.08010e31 | 0.464234 | ||||||||
\(372\) | 1.30356e32i | 0.962374i | ||||||||
\(373\) | − 2.37205e32i | − 1.69342i | −0.532058 | − | 0.846708i | \(-0.678581\pi\) | ||||
0.532058 | − | 0.846708i | \(-0.321419\pi\) | |||||||
\(374\) | 1.74509e31 | 0.120482 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.63470e31 | 0.622286 | ||||||||
\(377\) | − 1.30906e32i | − 0.817884i | ||||||||
\(378\) | − 3.05626e32i | − 1.84732i | ||||||||
\(379\) | 1.38944e32 | 0.812551 | 0.406276 | − | 0.913751i | \(-0.366827\pi\) | ||||
0.406276 | + | 0.913751i | \(0.366827\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.08799e32 | −0.595748 | ||||||||
\(382\) | 2.01970e32i | 1.07027i | ||||||||
\(383\) | − 3.79085e31i | − 0.194425i | −0.995264 | − | 0.0972125i | \(-0.969007\pi\) | ||||
0.995264 | − | 0.0972125i | \(-0.0309926\pi\) | |||||||
\(384\) | −3.40023e31 | −0.168798 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.83446e31 | 0.271431 | ||||||||
\(387\) | − 4.11732e32i | − 1.85450i | ||||||||
\(388\) | 1.68793e32i | 0.736134i | ||||||||
\(389\) | 2.20209e32 | 0.929963 | 0.464982 | − | 0.885320i | \(-0.346061\pi\) | ||||
0.464982 | + | 0.885320i | \(0.346061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.77283e31 | 0.0702195 | ||||||||
\(392\) | 2.85858e31i | 0.109667i | ||||||||
\(393\) | − 2.45545e32i | − 0.912481i | ||||||||
\(394\) | −1.47076e32 | −0.529468 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.73473e31 | 0.328953 | ||||||||
\(397\) | − 2.18941e32i | − 0.716877i | −0.933553 | − | 0.358439i | \(-0.883309\pi\) | ||||
0.933553 | − | 0.358439i | \(-0.116691\pi\) | |||||||
\(398\) | − 3.32594e32i | − 1.05530i | ||||||||
\(399\) | 2.64675e32 | 0.813863 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.99036e32 | 0.863810 | 0.431905 | − | 0.901919i | \(-0.357842\pi\) | ||||
0.431905 | + | 0.901919i | \(0.357842\pi\) | |||||||
\(402\) | − 6.24300e32i | − 1.74811i | ||||||||
\(403\) | 4.23138e32i | 1.14860i | ||||||||
\(404\) | 2.38490e32 | 0.627628 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.70353e32 | 0.421478 | ||||||||
\(407\) | − 2.63734e31i | − 0.0632755i | ||||||||
\(408\) | − 1.98940e32i | − 0.462882i | ||||||||
\(409\) | −7.12330e31 | −0.160746 | −0.0803730 | − | 0.996765i | \(-0.525611\pi\) | ||||
−0.0803730 | + | 0.996765i | \(0.525611\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.21719e33 | −2.58425 | ||||||||
\(412\) | − 1.73160e32i | − 0.356642i | ||||||||
\(413\) | 1.26738e32i | 0.253239i | ||||||||
\(414\) | 9.88949e31 | 0.191721 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.10372e32 | −0.201462 | ||||||||
\(417\) | 1.41805e33i | 2.51183i | ||||||||
\(418\) | 5.24560e31i | 0.0901761i | ||||||||
\(419\) | −2.94461e32 | −0.491307 | −0.245654 | − | 0.969358i | \(-0.579003\pi\) | ||||
−0.245654 | + | 0.969358i | \(0.579003\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.01892e33 | 1.60182 | 0.800908 | − | 0.598787i | \(-0.204350\pi\) | ||||
0.800908 | + | 0.598787i | \(0.204350\pi\) | |||||||
\(422\) | 4.23055e32i | 0.645641i | ||||||||
\(423\) | 3.14455e33i | 4.65912i | ||||||||
\(424\) | 1.37372e32 | 0.197617 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.69489e32 | −0.501166 | ||||||||
\(427\) | 1.04059e33i | 1.37067i | ||||||||
\(428\) | − 2.92588e32i | − 0.374291i | ||||||||
\(429\) | 4.35365e32 | 0.540925 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.79497e32 | −0.796565 | −0.398283 | − | 0.917263i | \(-0.630394\pi\) | ||||
−0.398283 | + | 0.917263i | \(0.630394\pi\) | |||||||
\(432\) | − 6.90523e32i | − 0.786377i | ||||||||
\(433\) | − 7.24164e32i | − 0.801195i | −0.916254 | − | 0.400597i | \(-0.868803\pi\) | ||||
0.916254 | − | 0.400597i | \(-0.131197\pi\) | |||||||
\(434\) | −5.50648e32 | −0.591906 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.77021e32 | −0.281146 | ||||||||
\(437\) | 5.32899e31i | 0.0525566i | ||||||||
\(438\) | 2.51395e32i | 0.240952i | ||||||||
\(439\) | 9.13459e32 | 0.850908 | 0.425454 | − | 0.904980i | \(-0.360114\pi\) | ||||
0.425454 | + | 0.904980i | \(0.360114\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.32976e32 | −0.821085 | ||||||||
\(442\) | − 6.45764e32i | − 0.552453i | ||||||||
\(443\) | − 3.52555e32i | − 0.293211i | −0.989195 | − | 0.146605i | \(-0.953165\pi\) | ||||
0.989195 | − | 0.146605i | \(-0.0468347\pi\) | |||||||
\(444\) | −3.00657e32 | −0.243099 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.73259e32 | 0.361754 | ||||||||
\(447\) | 7.45409e32i | 0.554052i | ||||||||
\(448\) | − 1.43632e32i | − 0.103819i | ||||||||
\(449\) | −3.70918e32 | −0.260735 | −0.130367 | − | 0.991466i | \(-0.541616\pi\) | ||||
−0.130367 | + | 0.991466i | \(0.541616\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.10530e32 | 0.272984 | ||||||||
\(452\) | − 1.16776e33i | − 0.755306i | ||||||||
\(453\) | 4.41899e33i | 2.78032i | ||||||||
\(454\) | 3.69111e32 | 0.225922 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.97998e32 | 0.346449 | ||||||||
\(457\) | − 1.76958e33i | − 0.997512i | −0.866742 | − | 0.498756i | \(-0.833790\pi\) | ||||
0.866742 | − | 0.498756i | \(-0.166210\pi\) | |||||||
\(458\) | 1.51313e33i | 0.829959i | ||||||||
\(459\) | 4.04009e33 | 2.15642 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.01018e32 | 0.354379 | 0.177189 | − | 0.984177i | \(-0.443299\pi\) | ||||
0.177189 | + | 0.984177i | \(0.443299\pi\) | |||||||
\(462\) | 5.66559e32i | 0.278753i | ||||||||
\(463\) | − 9.20521e32i | − 0.440830i | −0.975406 | − | 0.220415i | \(-0.929259\pi\) | ||||
0.975406 | − | 0.220415i | \(-0.0707412\pi\) | |||||||
\(464\) | 3.84891e32 | 0.179417 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.68245e32 | 0.0743219 | ||||||||
\(467\) | 1.84600e33i | 0.793908i | 0.917838 | + | 0.396954i | \(0.129933\pi\) | ||||
−0.917838 | + | 0.396954i | \(0.870067\pi\) | |||||||
\(468\) | − 3.60231e33i | − 1.50837i | ||||||||
\(469\) | 2.63716e33 | 1.07517 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.36543e33 | 3.23390 | ||||||||
\(472\) | 2.86348e32i | 0.107800i | ||||||||
\(473\) | 4.74918e32i | 0.174122i | ||||||||
\(474\) | −2.09951e33 | −0.749703 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.40360e32 | 0.284694 | ||||||||
\(477\) | 4.48351e33i | 1.47958i | ||||||||
\(478\) | − 2.65870e33i | − 0.854714i | ||||||||
\(479\) | 3.88481e32 | 0.121668 | 0.0608339 | − | 0.998148i | \(-0.480624\pi\) | ||||
0.0608339 | + | 0.998148i | \(0.480624\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.75939e32 | −0.290141 | ||||||||
\(482\) | − 6.91328e32i | − 0.200261i | ||||||||
\(483\) | 5.75566e32i | 0.162463i | ||||||||
\(484\) | 1.70548e33 | 0.469114 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.85414e33 | 2.31309 | ||||||||
\(487\) | − 4.26102e33i | − 1.08493i | −0.840078 | − | 0.542465i | \(-0.817491\pi\) | ||||
0.840078 | − | 0.542465i | \(-0.182509\pi\) | |||||||
\(488\) | 2.35109e33i | 0.583474i | ||||||||
\(489\) | −1.33581e33 | −0.323135 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.52548e33 | −1.04027 | −0.520134 | − | 0.854084i | \(-0.674118\pi\) | ||||
−0.520134 | + | 0.854084i | \(0.674118\pi\) | |||||||
\(492\) | − 4.68004e33i | − 1.04878i | ||||||||
\(493\) | 2.25191e33i | 0.492000i | ||||||||
\(494\) | 1.94112e33 | 0.413490 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.24412e33 | −0.251965 | ||||||||
\(497\) | − 1.56079e33i | − 0.308241i | ||||||||
\(498\) | − 1.18744e34i | − 2.28689i | ||||||||
\(499\) | −4.45020e33 | −0.835840 | −0.417920 | − | 0.908484i | \(-0.637241\pi\) | ||||
−0.417920 | + | 0.908484i | \(0.637241\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.76151e34 | −3.14713 | ||||||||
\(502\) | − 1.08556e33i | − 0.189172i | ||||||||
\(503\) | 2.29032e33i | 0.389311i | 0.980872 | + | 0.194656i | \(0.0623590\pi\) | ||||
−0.980872 | + | 0.194656i | \(0.937641\pi\) | |||||||
\(504\) | 4.68784e33 | 0.777304 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.14072e32 | −0.0180010 | ||||||||
\(507\) | − 3.70622e33i | − 0.570600i | ||||||||
\(508\) | − 1.03838e33i | − 0.155977i | ||||||||
\(509\) | −5.35889e33 | −0.785421 | −0.392711 | − | 0.919662i | \(-0.628463\pi\) | ||||
−0.392711 | + | 0.919662i | \(0.628463\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.06194e33 | −0.148197 | ||||||||
\(512\) | − 3.24519e32i | − 0.0441942i | ||||||||
\(513\) | 1.21442e34i | 1.61400i | ||||||||
\(514\) | −4.57080e33 | −0.592862 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.41407e33 | 0.668963 | ||||||||
\(517\) | − 3.62712e33i | − 0.437452i | ||||||||
\(518\) | − 1.27003e33i | − 0.149518i | ||||||||
\(519\) | 1.38871e34 | 1.59595 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.14090e34 | −1.24961 | −0.624807 | − | 0.780779i | \(-0.714822\pi\) | ||||
−0.624807 | + | 0.780779i | \(0.714822\pi\) | |||||||
\(522\) | 1.25620e34i | 1.34331i | ||||||||
\(523\) | 1.37717e34i | 1.43786i | 0.695085 | + | 0.718928i | \(0.255367\pi\) | ||||
−0.695085 | + | 0.718928i | \(0.744633\pi\) | |||||||
\(524\) | 2.34348e33 | 0.238902 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.29643e33 | 0.612030 | ||||||||
\(527\) | − 7.27906e33i | − 0.690944i | ||||||||
\(528\) | 1.28007e33i | 0.118661i | ||||||||
\(529\) | 1.09299e34 | 0.989509 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.34576e33 | −0.807111 | ||||||||
\(532\) | 2.52606e33i | 0.213083i | ||||||||
\(533\) | − 1.51915e34i | − 1.25173i | ||||||||
\(534\) | −6.29617e33 | −0.506770 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.95833e33 | 0.457683 | ||||||||
\(537\) | 1.42052e34i | 1.06603i | ||||||||
\(538\) | 9.60972e33i | 0.704583i | ||||||||
\(539\) | 1.07615e33 | 0.0770929 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.58682e34 | −1.08533 | −0.542667 | − | 0.839948i | \(-0.682585\pi\) | ||||
−0.542667 | + | 0.839948i | \(0.682585\pi\) | |||||||
\(542\) | 6.33151e33i | 0.423171i | ||||||||
\(543\) | 3.17603e33i | 0.207437i | ||||||||
\(544\) | 1.89869e33 | 0.121190 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.09653e34 | 1.27818 | ||||||||
\(547\) | 8.29322e33i | 0.494176i | 0.968993 | + | 0.247088i | \(0.0794737\pi\) | ||||
−0.968993 | + | 0.247088i | \(0.920526\pi\) | |||||||
\(548\) | − 1.16168e34i | − 0.676599i | ||||||||
\(549\) | −7.67343e34 | −4.36853 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.76908e33 | −0.368243 | ||||||||
\(552\) | 1.30042e33i | 0.0691583i | ||||||||
\(553\) | − 8.86874e33i | − 0.461103i | ||||||||
\(554\) | 4.98130e33 | 0.253204 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.35339e34 | −0.657639 | ||||||||
\(557\) | − 3.56496e34i | − 1.69381i | −0.531744 | − | 0.846905i | \(-0.678463\pi\) | ||||
0.531744 | − | 0.846905i | \(-0.321537\pi\) | |||||||
\(558\) | − 4.06052e34i | − 1.88649i | ||||||||
\(559\) | 1.75742e34 | 0.798413 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.48939e33 | −0.325395 | ||||||||
\(562\) | − 2.08849e34i | − 0.887417i | ||||||||
\(563\) | 1.62059e34i | 0.673471i | 0.941599 | + | 0.336735i | \(0.109323\pi\) | ||||
−0.941599 | + | 0.336735i | \(0.890677\pi\) | |||||||
\(564\) | −4.13492e34 | −1.68065 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.40155e33 | −0.248931 | ||||||||
\(567\) | 7.33659e34i | 2.79065i | ||||||||
\(568\) | − 3.52641e33i | − 0.131213i | ||||||||
\(569\) | −4.19926e34 | −1.52851 | −0.764257 | − | 0.644912i | \(-0.776894\pi\) | ||||
−0.764257 | + | 0.644912i | \(0.776894\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.27922e34 | 0.794026 | 0.397013 | − | 0.917813i | \(-0.370047\pi\) | ||||
0.397013 | + | 0.917813i | \(0.370047\pi\) | |||||||
\(572\) | 4.15513e33i | 0.141623i | ||||||||
\(573\) | − 8.66794e34i | − 2.89057i | ||||||||
\(574\) | 1.97694e34 | 0.645051 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.05916e34 | 0.330886 | ||||||||
\(577\) | 1.30064e34i | 0.397613i | 0.980039 | + | 0.198807i | \(0.0637066\pi\) | ||||
−0.980039 | + | 0.198807i | \(0.936293\pi\) | |||||||
\(578\) | − 1.25277e34i | − 0.374777i | ||||||||
\(579\) | −2.50397e34 | −0.733074 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.01597e34 | 1.40655 | ||||||||
\(582\) | − 7.24407e34i | − 1.98813i | ||||||||
\(583\) | − 5.17157e33i | − 0.138920i | ||||||||
\(584\) | −2.39932e33 | −0.0630851 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.70849e34 | −0.430420 | ||||||||
\(587\) | − 3.13619e34i | − 0.773440i | −0.922197 | − | 0.386720i | \(-0.873608\pi\) | ||||
0.922197 | − | 0.386720i | \(-0.126392\pi\) | |||||||
\(588\) | − 1.22681e34i | − 0.296185i | ||||||||
\(589\) | 2.18803e34 | 0.517145 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.31206e34 | 1.42997 | ||||||||
\(592\) | − 2.86947e33i | − 0.0636474i | ||||||||
\(593\) | − 6.43753e34i | − 1.39809i | −0.715077 | − | 0.699046i | \(-0.753608\pi\) | ||||
0.715077 | − | 0.699046i | \(-0.246392\pi\) | |||||||
\(594\) | −2.59957e34 | −0.552804 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.11419e33 | −0.145060 | ||||||||
\(597\) | 1.42739e35i | 2.85012i | ||||||||
\(598\) | 4.22118e33i | 0.0825409i | ||||||||
\(599\) | 9.82124e34 | 1.88075 | 0.940375 | − | 0.340140i | \(-0.110474\pi\) | ||||
0.940375 | + | 0.340140i | \(0.110474\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.10144e34 | 0.202316 | 0.101158 | − | 0.994870i | \(-0.467745\pi\) | ||||
0.101158 | + | 0.994870i | \(0.467745\pi\) | |||||||
\(602\) | 2.28700e34i | 0.411444i | ||||||||
\(603\) | 1.94467e35i | 3.42672i | ||||||||
\(604\) | −4.21749e34 | −0.727934 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.02353e35 | −1.69508 | ||||||||
\(607\) | − 9.06735e34i | − 1.47103i | −0.677508 | − | 0.735516i | \(-0.736940\pi\) | ||||
0.677508 | − | 0.735516i | \(-0.263060\pi\) | |||||||
\(608\) | 5.70730e33i | 0.0907060i | ||||||||
\(609\) | −7.31105e34 | −1.13832 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.34220e35 | −2.00587 | ||||||||
\(612\) | 6.19689e34i | 0.907363i | ||||||||
\(613\) | 2.62922e34i | 0.377199i | 0.982054 | + | 0.188599i | \(0.0603948\pi\) | ||||
−0.982054 | + | 0.188599i | \(0.939605\pi\) | |||||||
\(614\) | −3.15390e34 | −0.443346 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.40724e33 | −0.0729822 | ||||||||
\(617\) | − 6.11422e34i | − 0.808679i | −0.914609 | − | 0.404340i | \(-0.867501\pi\) | ||||
0.914609 | − | 0.404340i | \(-0.132499\pi\) | |||||||
\(618\) | 7.43150e34i | 0.963208i | ||||||||
\(619\) | 4.66687e34 | 0.592779 | 0.296389 | − | 0.955067i | \(-0.404217\pi\) | ||||
0.296389 | + | 0.955067i | \(0.404217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.64090e34 | −0.322186 | ||||||||
\(622\) | − 6.31848e34i | − 0.755497i | ||||||||
\(623\) | − 2.65962e34i | − 0.311687i | ||||||||
\(624\) | 4.73685e34 | 0.544104 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.65672e34 | 0.734651 | ||||||||
\(627\) | − 2.25125e34i | − 0.243545i | ||||||||
\(628\) | 7.98398e34i | 0.846689i | ||||||||
\(629\) | 1.67886e34 | 0.174535 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.88083e33 | −0.0787417 | −0.0393709 | − | 0.999225i | \(-0.512535\pi\) | ||||
−0.0393709 | + | 0.999225i | \(0.512535\pi\) | |||||||
\(632\) | − 2.00378e34i | − 0.196284i | ||||||||
\(633\) | − 1.81562e35i | − 1.74373i | ||||||||
\(634\) | 9.38386e34 | 0.883621 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.89559e34 | −0.533720 | ||||||||
\(637\) | − 3.98227e34i | − 0.353499i | ||||||||
\(638\) | − 1.44898e34i | − 0.126126i | ||||||||
\(639\) | 1.15094e35 | 0.982408 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.14908e34 | 0.258499 | 0.129250 | − | 0.991612i | \(-0.458743\pi\) | ||||
0.129250 | + | 0.991612i | \(0.458743\pi\) | |||||||
\(642\) | 1.25570e35i | 1.01088i | ||||||||
\(643\) | 8.32480e34i | 0.657259i | 0.944459 | + | 0.328630i | \(0.106587\pi\) | ||||
−0.944459 | + | 0.328630i | \(0.893413\pi\) | |||||||
\(644\) | −5.49320e33 | −0.0425356 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.33922e34 | −0.248736 | ||||||||
\(647\) | 1.33124e35i | 0.972641i | 0.873780 | + | 0.486321i | \(0.161661\pi\) | ||||
−0.873780 | + | 0.486321i | \(0.838339\pi\) | |||||||
\(648\) | 1.65761e35i | 1.18794i | ||||||||
\(649\) | 1.07800e34 | 0.0757809 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.36321e35 | 1.59860 | ||||||||
\(652\) | − 1.27490e34i | − 0.0846020i | ||||||||
\(653\) | 2.06756e35i | 1.34599i | 0.739645 | + | 0.672997i | \(0.234993\pi\) | ||||
−0.739645 | + | 0.672997i | \(0.765007\pi\) | |||||||
\(654\) | 1.18889e35 | 0.759311 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.46664e34 | 0.274589 | ||||||||
\(657\) | − 7.83084e34i | − 0.472325i | ||||||||
\(658\) | − 1.74667e35i | − 1.03368i | ||||||||
\(659\) | 2.57849e35 | 1.49726 | 0.748632 | − | 0.662986i | \(-0.230711\pi\) | ||||
0.748632 | + | 0.662986i | \(0.230711\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.31671e34 | −0.185434 | −0.0927170 | − | 0.995692i | \(-0.529555\pi\) | ||||
−0.0927170 | + | 0.995692i | \(0.529555\pi\) | |||||||
\(662\) | − 1.41394e35i | − 0.775720i | ||||||||
\(663\) | 2.77142e35i | 1.49205i | ||||||||
\(664\) | 1.13329e35 | 0.598745 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.36532e34 | 0.476535 | ||||||||
\(667\) | − 1.47201e34i | − 0.0735087i | ||||||||
\(668\) | − 1.68119e35i | − 0.823970i | ||||||||
\(669\) | −2.03109e35 | −0.977016 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.85101e34 | 0.410168 | ||||||||
\(672\) | 6.16426e34i | 0.280392i | ||||||||
\(673\) | − 2.87165e35i | − 1.28216i | −0.767472 | − | 0.641082i | \(-0.778486\pi\) | ||||
0.767472 | − | 0.641082i | \(-0.221514\pi\) | |||||||
\(674\) | 2.16160e35 | 0.947387 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.53722e34 | 0.149392 | ||||||||
\(677\) | − 3.20244e35i | − 1.32777i | −0.747835 | − | 0.663885i | \(-0.768907\pi\) | ||||
0.747835 | − | 0.663885i | \(-0.231093\pi\) | |||||||
\(678\) | 5.01167e35i | 2.03991i | ||||||||
\(679\) | 3.06003e35 | 1.22280 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.58411e35 | −0.610165 | ||||||||
\(682\) | 4.68366e34i | 0.177125i | ||||||||
\(683\) | − 4.34050e35i | − 1.61169i | −0.592129 | − | 0.805843i | \(-0.701712\pi\) | ||||
0.592129 | − | 0.805843i | \(-0.298288\pi\) | |||||||
\(684\) | −1.86274e35 | −0.679126 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.18895e35 | 0.769456 | ||||||||
\(687\) | − 6.49388e35i | − 2.24153i | ||||||||
\(688\) | 5.16719e34i | 0.175145i | ||||||||
\(689\) | −1.91372e35 | −0.636999 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.59659e35 | 1.15456 | 0.577279 | − | 0.816547i | \(-0.304114\pi\) | ||||
0.577279 | + | 0.816547i | \(0.304114\pi\) | |||||||
\(692\) | 1.32538e35i | 0.417845i | ||||||||
\(693\) | − 1.76480e35i | − 0.546425i | ||||||||
\(694\) | −1.80262e34 | −0.0548165 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.65184e35 | −0.484565 | ||||||||
\(697\) | 2.61333e35i | 0.752982i | ||||||||
\(698\) | 1.22089e35i | 0.345529i | ||||||||
\(699\) | −7.22055e34 | −0.200727 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.01671e34 | −0.107745 | −0.0538723 | − | 0.998548i | \(-0.517156\pi\) | ||||
−0.0538723 | + | 0.998548i | \(0.517156\pi\) | |||||||
\(702\) | 9.61963e35i | 2.53481i | ||||||||
\(703\) | 5.04654e34i | 0.130633i | ||||||||
\(704\) | −1.22170e34 | −0.0310674 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.82716e35 | 0.448454 | ||||||||
\(707\) | − 4.32357e35i | − 1.04256i | ||||||||
\(708\) | − 1.22892e35i | − 0.291144i | ||||||||
\(709\) | 2.37128e34 | 0.0551957 | 0.0275979 | − | 0.999619i | \(-0.491214\pi\) | ||||
0.0275979 | + | 0.999619i | \(0.491214\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.53988e35 | 1.46960 | ||||||||
\(712\) | − 6.00907e34i | − 0.132681i | ||||||||
\(713\) | 4.75812e34i | 0.103232i | ||||||||
\(714\) | −3.60657e35 | −0.768895 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.35574e35 | −0.279103 | ||||||||
\(717\) | 1.14103e36i | 2.30839i | ||||||||
\(718\) | 1.79427e35i | 0.356724i | ||||||||
\(719\) | 8.41947e35 | 1.64503 | 0.822514 | − | 0.568744i | \(-0.192571\pi\) | ||||
0.822514 | + | 0.568744i | \(0.192571\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.13920e35 | −0.592419 | ||||||||
\(722\) | 2.80867e35i | 0.520938i | ||||||||
\(723\) | 2.96697e35i | 0.540859i | ||||||||
\(724\) | −3.03120e34 | −0.0543104 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.31938e35 | −1.26697 | ||||||||
\(727\) | − 8.07486e35i | − 1.37390i | −0.726705 | − | 0.686950i | \(-0.758949\pi\) | ||||
0.726705 | − | 0.686950i | \(-0.241051\pi\) | |||||||
\(728\) | 2.00093e35i | 0.334650i | ||||||||
\(729\) | −1.75615e36 | −2.88714 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.02321e35 | −0.480287 | ||||||||
\(732\) | − 1.00902e36i | − 1.57583i | ||||||||
\(733\) | − 9.32041e35i | − 1.43099i | −0.698620 | − | 0.715493i | \(-0.746202\pi\) | ||||
0.698620 | − | 0.715493i | \(-0.253798\pi\) | |||||||
\(734\) | 3.18151e35 | 0.480211 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.24112e34 | −0.0181068 | ||||||||
\(737\) | − 2.24310e35i | − 0.321740i | ||||||||
\(738\) | 1.45781e36i | 2.05587i | ||||||||
\(739\) | 9.24490e34 | 0.128188 | 0.0640939 | − | 0.997944i | \(-0.479584\pi\) | ||||
0.0640939 | + | 0.997944i | \(0.479584\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.33068e35 | −1.11674 | ||||||||
\(742\) | − 2.49041e35i | − 0.328263i | ||||||||
\(743\) | 3.86129e35i | 0.500463i | 0.968186 | + | 0.250232i | \(0.0805068\pi\) | ||||
−0.968186 | + | 0.250232i | \(0.919493\pi\) | |||||||
\(744\) | 5.33938e35 | 0.680501 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.71592e35 | −1.19743 | ||||||||
\(747\) | 3.69882e36i | 4.48287i | ||||||||
\(748\) | − 7.14788e34i | − 0.0851937i | ||||||||
\(749\) | −5.30431e35 | −0.621736 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.31819e35 | 0.602927 | 0.301463 | − | 0.953478i | \(-0.402525\pi\) | ||||
0.301463 | + | 0.953478i | \(0.402525\pi\) | |||||||
\(752\) | − 3.94637e35i | − 0.440023i | ||||||||
\(753\) | 4.65889e35i | 0.510911i | ||||||||
\(754\) | −5.36190e35 | −0.578332 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.25184e36 | −1.30625 | ||||||||
\(757\) | − 1.46803e36i | − 1.50674i | −0.657599 | − | 0.753368i | \(-0.728428\pi\) | ||||
0.657599 | − | 0.753368i | \(-0.271572\pi\) | |||||||
\(758\) | − 5.69116e35i | − 0.574560i | ||||||||
\(759\) | 4.89561e34 | 0.0486166 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.26153e36 | 1.21225 | 0.606123 | − | 0.795371i | \(-0.292724\pi\) | ||||
0.606123 | + | 0.795371i | \(0.292724\pi\) | |||||||
\(762\) | 4.45641e35i | 0.421257i | ||||||||
\(763\) | 5.02210e35i | 0.467012i | ||||||||
\(764\) | 8.27269e35 | 0.756798 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.55273e35 | −0.137479 | ||||||||
\(767\) | − 3.98910e35i | − 0.347482i | ||||||||
\(768\) | 1.39274e35i | 0.119358i | ||||||||
\(769\) | 9.78483e35 | 0.825039 | 0.412519 | − | 0.910949i | \(-0.364649\pi\) | ||||
0.412519 | + | 0.910949i | \(0.364649\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.96165e36 | 1.60119 | ||||||||
\(772\) | − 2.38980e35i | − 0.191931i | ||||||||
\(773\) | − 1.97217e36i | − 1.55848i | −0.626728 | − | 0.779238i | \(-0.715606\pi\) | ||||
0.626728 | − | 0.779238i | \(-0.284394\pi\) | |||||||
\(774\) | −1.68646e36 | −1.31133 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.91375e35 | 0.520526 | ||||||||
\(777\) | 5.45059e35i | 0.403813i | ||||||||
\(778\) | − 9.01978e35i | − 0.657583i | ||||||||
\(779\) | −7.85547e35 | −0.563578 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.32757e35 | −0.0922398 | ||||||||
\(782\) | − 7.26151e34i | − 0.0496527i | ||||||||
\(783\) | − 3.35457e36i | − 2.25743i | ||||||||
\(784\) | 1.17087e35 | 0.0775459 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.00575e36 | −0.645222 | ||||||||
\(787\) | 2.25189e35i | 0.142188i | 0.997470 | + | 0.0710940i | \(0.0226490\pi\) | ||||
−0.997470 | + | 0.0710940i | \(0.977351\pi\) | |||||||
\(788\) | 6.02424e35i | 0.374390i | ||||||||
\(789\) | −2.70224e36 | −1.65295 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.11702e36 | −1.25464 | ||||||||
\(792\) | − 3.98735e35i | − 0.232605i | ||||||||
\(793\) | − 3.27529e36i | − 1.88077i | ||||||||
\(794\) | −8.96781e35 | −0.506909 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.36230e36 | −0.746209 | ||||||||
\(797\) | − 3.69113e36i | − 1.99035i | −0.0980978 | − | 0.995177i | \(-0.531276\pi\) | ||||
0.0980978 | − | 0.995177i | \(-0.468724\pi\) | |||||||
\(798\) | − 1.08411e36i | − 0.575488i | ||||||||
\(799\) | 2.30893e36 | 1.20664 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.96123e36 | 0.993393 | ||||||||
\(802\) | − 1.22485e36i | − 0.610806i | ||||||||
\(803\) | 9.03258e34i | 0.0443473i | ||||||||
\(804\) | −2.55713e36 | −1.23610 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.73317e36 | 0.812184 | ||||||||
\(807\) | − 4.12420e36i | − 1.90292i | ||||||||
\(808\) | − 9.76854e35i | − 0.443800i | ||||||||
\(809\) | 2.93815e36 | 1.31437 | 0.657185 | − | 0.753730i | \(-0.271747\pi\) | ||||
0.657185 | + | 0.753730i | \(0.271747\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.44583e36 | −1.06088 | −0.530439 | − | 0.847723i | \(-0.677973\pi\) | ||||
−0.530439 | + | 0.847723i | \(0.677973\pi\) | |||||||
\(812\) | − 6.97767e35i | − 0.298030i | ||||||||
\(813\) | − 2.71729e36i | − 1.14289i | ||||||||
\(814\) | −1.08025e35 | −0.0447426 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.14859e35 | −0.327307 | ||||||||
\(817\) | − 9.08753e35i | − 0.359476i | ||||||||
\(818\) | 2.91771e35i | 0.113665i | ||||||||
\(819\) | −6.53060e36 | −2.50556 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.33815e36 | 1.24227 | 0.621136 | − | 0.783703i | \(-0.286672\pi\) | ||||
0.621136 | + | 0.783703i | \(0.286672\pi\) | |||||||
\(822\) | 4.98560e36i | 1.82734i | ||||||||
\(823\) | 2.54036e36i | 0.917058i | 0.888679 | + | 0.458529i | \(0.151623\pi\) | ||||
−0.888679 | + | 0.458529i | \(0.848377\pi\) | |||||||
\(824\) | −7.09263e35 | −0.252184 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.19119e35 | 0.179067 | ||||||||
\(827\) | 3.63276e36i | 1.23429i | 0.786849 | + | 0.617146i | \(0.211711\pi\) | ||||
−0.786849 | + | 0.617146i | \(0.788289\pi\) | |||||||
\(828\) | − 4.05074e35i | − 0.135567i | ||||||||
\(829\) | −1.07727e36 | −0.355135 | −0.177567 | − | 0.984109i | \(-0.556823\pi\) | ||||
−0.177567 | + | 0.984109i | \(0.556823\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.13782e36 | −0.683847 | ||||||||
\(832\) | 4.52085e35i | 0.142455i | ||||||||
\(833\) | 6.85052e35i | 0.212648i | ||||||||
\(834\) | 5.80833e36 | 1.77613 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.14860e35 | 0.0637641 | ||||||||
\(837\) | 1.08433e37i | 3.17024i | ||||||||
\(838\) | 1.20611e36i | 0.347407i | ||||||||
\(839\) | 2.96808e36 | 0.842269 | 0.421134 | − | 0.906998i | \(-0.361632\pi\) | ||||
0.421134 | + | 0.906998i | \(0.361632\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.76056e36 | −0.484953 | ||||||||
\(842\) | − 4.17349e36i | − 1.13266i | ||||||||
\(843\) | 8.96316e36i | 2.39671i | ||||||||
\(844\) | 1.73283e36 | 0.456537 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.28801e37 | 3.29450 | ||||||||
\(847\) | − 3.09185e36i | − 0.779247i | ||||||||
\(848\) | − 5.62676e35i | − 0.139737i | ||||||||
\(849\) | 2.74735e36 | 0.672308 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.09743e35 | −0.0260769 | ||||||||
\(852\) | 1.51343e36i | 0.354378i | ||||||||
\(853\) | 6.13786e36i | 1.41630i | 0.706064 | + | 0.708148i | \(0.250469\pi\) | ||||
−0.706064 | + | 0.708148i | \(0.749531\pi\) | |||||||
\(854\) | 4.26227e36 | 0.969210 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.19844e36 | −0.264664 | ||||||||
\(857\) | − 3.16481e36i | − 0.688791i | −0.938825 | − | 0.344395i | \(-0.888084\pi\) | ||||
0.938825 | − | 0.344395i | \(-0.111916\pi\) | |||||||
\(858\) | − 1.78325e36i | − 0.382492i | ||||||||
\(859\) | −5.65370e36 | −1.19514 | −0.597569 | − | 0.801818i | \(-0.703866\pi\) | ||||
−0.597569 | + | 0.801818i | \(0.703866\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.48442e36 | −1.74214 | ||||||||
\(862\) | 2.78322e36i | 0.563257i | ||||||||
\(863\) | − 8.00828e36i | − 1.59736i | −0.601753 | − | 0.798682i | \(-0.705531\pi\) | ||||
0.601753 | − | 0.798682i | \(-0.294469\pi\) | |||||||
\(864\) | −2.82838e36 | −0.556053 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.96617e36 | −0.566530 | ||||||||
\(867\) | 5.37651e36i | 1.01219i | ||||||||
\(868\) | 2.25545e36i | 0.418540i | ||||||||
\(869\) | −7.54351e35 | −0.137983 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.30052e36 | −1.47529 | ||||||||
\(872\) | 1.13468e36i | 0.198800i | ||||||||
\(873\) | 2.25649e37i | 3.89723i | ||||||||
\(874\) | 2.18275e35 | 0.0371631 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.02971e36 | 0.170379 | ||||||||
\(877\) | − 3.29560e36i | − 0.537575i | −0.963199 | − | 0.268788i | \(-0.913377\pi\) | ||||
0.963199 | − | 0.268788i | \(-0.0866230\pi\) | |||||||
\(878\) | − 3.74153e36i | − 0.601683i | ||||||||
\(879\) | 7.33233e36 | 1.16247 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.05386e36 | −1.24109 | −0.620547 | − | 0.784169i | \(-0.713090\pi\) | ||||
−0.620547 | + | 0.784169i | \(0.713090\pi\) | |||||||
\(882\) | 3.82147e36i | 0.580595i | ||||||||
\(883\) | − 4.91849e35i | − 0.0736754i | −0.999321 | − | 0.0368377i | \(-0.988272\pi\) | ||||
0.999321 | − | 0.0368377i | \(-0.0117285\pi\) | |||||||
\(884\) | −2.64505e36 | −0.390644 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.44406e36 | −0.207331 | ||||||||
\(887\) | − 7.79484e36i | − 1.10347i | −0.834018 | − | 0.551737i | \(-0.813965\pi\) | ||||
0.834018 | − | 0.551737i | \(-0.186035\pi\) | |||||||
\(888\) | 1.23149e36i | 0.171897i | ||||||||
\(889\) | −1.88247e36 | −0.259093 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.24031e36 | 0.835093 | ||||||||
\(892\) | − 1.93847e36i | − 0.255799i | ||||||||
\(893\) | 6.94048e36i | 0.903121i | ||||||||
\(894\) | 3.05319e36 | 0.391774 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.88318e35 | −0.0734111 | ||||||||
\(897\) | − 1.81160e36i | − 0.222924i | ||||||||
\(898\) | 1.51928e36i | 0.184367i | ||||||||
\(899\) | −6.04394e36 | −0.723309 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.29209e36 | 0.383188 | ||||||||
\(902\) | − 1.68153e36i | − 0.193029i | ||||||||
\(903\) | − 9.81513e36i | − 1.11122i | ||||||||
\(904\) | −4.78314e36 | −0.534082 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.81002e37 | 1.96599 | ||||||||
\(907\) | 1.31417e37i | 1.40786i | 0.710268 | + | 0.703932i | \(0.248574\pi\) | ||||
−0.710268 | + | 0.703932i | \(0.751426\pi\) | |||||||
\(908\) | − 1.51188e36i | − 0.159751i | ||||||||
\(909\) | 3.18823e37 | 3.32278 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.44767e37 | 1.46788 | 0.733940 | − | 0.679214i | \(-0.237679\pi\) | ||||
0.733940 | + | 0.679214i | \(0.237679\pi\) | |||||||
\(912\) | − 2.44940e36i | − 0.244977i | ||||||||
\(913\) | − 4.26645e36i | − 0.420903i | ||||||||
\(914\) | −7.24821e36 | −0.705347 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.19776e36 | 0.586869 | ||||||||
\(917\) | − 4.24848e36i | − 0.396842i | ||||||||
\(918\) | − 1.65482e37i | − 1.52482i | ||||||||
\(919\) | 1.03191e37 | 0.937990 | 0.468995 | − | 0.883201i | \(-0.344616\pi\) | ||||
0.468995 | + | 0.883201i | \(0.344616\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.35356e37 | 1.19738 | ||||||||
\(922\) | − 2.87137e36i | − 0.250584i | ||||||||
\(923\) | 4.91262e36i | 0.422953i | ||||||||
\(924\) | 2.32062e36 | 0.197108 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.77045e36 | −0.311714 | ||||||||
\(927\) | − 2.31487e37i | − 1.88813i | ||||||||
\(928\) | − 1.57651e36i | − 0.126867i | ||||||||
\(929\) | 2.17912e37 | 1.73015 | 0.865075 | − | 0.501642i | \(-0.167271\pi\) | ||||
0.865075 | + | 0.501642i | \(0.167271\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.05921e36 | −0.159159 | ||||||||
\(932\) | − 6.89130e35i | − 0.0525536i | ||||||||
\(933\) | 2.71170e37i | 2.04043i | ||||||||
\(934\) | 7.56121e36 | 0.561378 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.47550e37 | −1.06658 | ||||||||
\(937\) | 2.08020e37i | 1.48375i | 0.670540 | + | 0.741873i | \(0.266062\pi\) | ||||
−0.670540 | + | 0.741873i | \(0.733938\pi\) | |||||||
\(938\) | − 1.08018e37i | − 0.760258i | ||||||||
\(939\) | −2.85686e37 | −1.98413 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.39454e37 | 1.61939 | 0.809695 | − | 0.586851i | \(-0.199632\pi\) | ||||
0.809695 | + | 0.586851i | \(0.199632\pi\) | |||||||
\(942\) | − 3.42648e37i | − 2.28672i | ||||||||
\(943\) | − 1.70826e36i | − 0.112501i | ||||||||
\(944\) | 1.17288e36 | 0.0762262 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.94526e36 | 0.123123 | ||||||||
\(947\) | 8.06134e36i | 0.503539i | 0.967787 | + | 0.251769i | \(0.0810124\pi\) | ||||
−0.967787 | + | 0.251769i | \(0.918988\pi\) | |||||||
\(948\) | 8.59960e36i | 0.530120i | ||||||||
\(949\) | 3.34248e36 | 0.203348 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.02727e37 | −2.38646 | ||||||||
\(952\) | − 3.44212e36i | − 0.201309i | ||||||||
\(953\) | − 1.92589e37i | − 1.11166i | −0.831297 | − | 0.555829i | \(-0.812401\pi\) | ||||
0.831297 | − | 0.555829i | \(-0.187599\pi\) | |||||||
\(954\) | 1.83645e37 | 1.04622 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.08900e37 | −0.604374 | ||||||||
\(957\) | 6.21858e36i | 0.340637i | ||||||||
\(958\) | − 1.59122e36i | − 0.0860321i | ||||||||
\(959\) | −2.10601e37 | −1.12390 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.03575e35 | 0.0157842 | ||||||||
\(962\) | 3.99745e36i | 0.205161i | ||||||||
\(963\) | − 3.91144e37i | − 1.98157i | ||||||||
\(964\) | −2.83168e36 | −0.141606 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.35752e36 | 0.114879 | ||||||||
\(967\) | − 2.29324e37i | − 1.10311i | −0.834139 | − | 0.551554i | \(-0.814035\pi\) | ||||
0.834139 | − | 0.551554i | \(-0.185965\pi\) | |||||||
\(968\) | − 6.98563e36i | − 0.331714i | ||||||||
\(969\) | 1.43309e37 | 0.671779 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.10199e37 | 0.960265 | 0.480132 | − | 0.877196i | \(-0.340589\pi\) | ||||
0.480132 | + | 0.877196i | \(0.340589\pi\) | |||||||
\(972\) | − 3.62665e37i | − 1.63560i | ||||||||
\(973\) | 2.45355e37i | 1.09241i | ||||||||
\(974\) | −1.74531e37 | −0.767161 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.63006e36 | 0.412578 | ||||||||
\(977\) | 3.52592e37i | 1.49139i | 0.666289 | + | 0.745694i | \(0.267882\pi\) | ||||
−0.666289 | + | 0.745694i | \(0.732118\pi\) | |||||||
\(978\) | 5.47148e36i | 0.228491i | ||||||||
\(979\) | −2.26220e36 | −0.0932712 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.70334e37 | −1.48844 | ||||||||
\(982\) | 1.85363e37i | 0.735581i | ||||||||
\(983\) | 7.31962e36i | 0.286794i | 0.989665 | + | 0.143397i | \(0.0458025\pi\) | ||||
−0.989665 | + | 0.143397i | \(0.954197\pi\) | |||||||
\(984\) | −1.91694e37 | −0.741602 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.22384e36 | 0.347897 | ||||||||
\(987\) | 7.49617e37i | 2.79174i | ||||||||
\(988\) | − 7.95081e36i | − 0.292381i | ||||||||
\(989\) | 1.97619e36 | 0.0717587 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.16985e37 | 0.414200 | 0.207100 | − | 0.978320i | \(-0.433597\pi\) | ||||
0.207100 | + | 0.978320i | \(0.433597\pi\) | |||||||
\(992\) | 5.09591e36i | 0.178166i | ||||||||
\(993\) | 6.06819e37i | 2.09504i | ||||||||
\(994\) | −6.39300e36 | −0.217959 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.86376e37 | −1.61708 | ||||||||
\(997\) | − 2.33411e37i | − 0.766358i | −0.923674 | − | 0.383179i | \(-0.874829\pi\) | ||||
0.923674 | − | 0.383179i | \(-0.125171\pi\) | |||||||
\(998\) | 1.82280e37i | 0.591028i | ||||||||
\(999\) | −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 | 50.26.b.e.49.2 | 4 | ||
5.2 | odd | 4 | 2.26.a.b.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 50.26.a.c.1.1 | 2 | |||
5.4 | even | 2 | inner | 50.26.b.e.49.3 | 4 | ||
15.2 | even | 4 | 18.26.a.e.1.2 | 2 | |||
20.7 | even | 4 | 16.26.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.26.a.b.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
16.26.a.c.1.1 | 2 | 20.7 | even | 4 | |||
18.26.a.e.1.2 | 2 | 15.2 | even | 4 | |||
50.26.a.c.1.1 | 2 | 5.3 | odd | 4 | |||
50.26.b.e.49.2 | 4 | 1.1 | even | 1 | trivial | ||
50.26.b.e.49.3 | 4 | 5.4 | even | 2 | inner |