Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1040,2,Mod(641,1040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1040, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1040.641");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1040 = 2^{4} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1040.da (of order \(6\), degree \(2\), 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: | \(8.30444181021\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 130) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 881.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1040.881 |
Dual form | 1040.2.da.a.641.1 |
$q$-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 \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(417\) | \(561\) | \(911\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.36603 | − | 2.36603i | −0.788675 | − | 1.36603i | −0.926779 | − | 0.375608i | \(-0.877434\pi\) |
0.138104 | − | 0.990418i | \(-0.455899\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.59808 | + | 1.50000i | 0.981981 | + | 0.566947i | 0.902867 | − | 0.429919i | \(-0.141458\pi\) |
0.0791130 | + | 0.996866i | \(0.474791\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.23205 | + | 3.86603i | −0.744017 | + | 1.28868i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.59808 | − | 1.50000i | 0.783349 | − | 0.452267i | −0.0542666 | − | 0.998526i | \(-0.517282\pi\) |
0.837616 | + | 0.546259i | \(0.183949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.50000 | + | 0.866025i | 0.970725 | + | 0.240192i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.36603 | + | 1.36603i | −0.610905 | + | 0.352706i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.09808 | − | 1.90192i | 0.266323 | − | 0.461284i | −0.701587 | − | 0.712584i | \(-0.747525\pi\) |
0.967909 | + | 0.251300i | \(0.0808580\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.59808 | + | 3.23205i | 1.28429 | + | 0.741483i | 0.977629 | − | 0.210337i | \(-0.0674560\pi\) |
0.306658 | + | 0.951820i | \(0.400789\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 8.19615i | − | 1.78855i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.26795 | + | 2.19615i | 0.264386 | + | 0.457929i | 0.967402 | − | 0.253244i | \(-0.0814975\pi\) |
−0.703017 | + | 0.711173i | \(0.748164\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.73205 | + | 8.19615i | 0.878720 | + | 1.52199i | 0.852747 | + | 0.522325i | \(0.174935\pi\) |
0.0259731 | + | 0.999663i | \(0.491732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.26795i | − | 0.227730i | −0.993496 | − | 0.113865i | \(-0.963677\pi\) | ||
0.993496 | − | 0.113865i | \(-0.0363232\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.09808 | − | 4.09808i | −1.23562 | − | 0.713384i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.50000 | − | 2.59808i | 0.253546 | − | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.69615 | − | 5.59808i | 1.59404 | − | 0.920318i | 0.601433 | − | 0.798923i | \(-0.294597\pi\) |
0.992604 | − | 0.121395i | \(-0.0387368\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.73205 | − | 9.46410i | −0.437478 | − | 1.51547i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.00000 | + | 5.19615i | −1.40556 | + | 0.811503i | −0.994956 | − | 0.100309i | \(-0.968017\pi\) |
−0.410608 | + | 0.911812i | \(0.634683\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | − | 1.73205i | 0.152499 | − | 0.264135i | −0.779647 | − | 0.626219i | \(-0.784601\pi\) |
0.932145 | + | 0.362084i | \(0.117935\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.86603 | + | 2.23205i | 0.576313 | + | 0.332734i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.00000i | − | 0.437595i | −0.975770 | − | 0.218797i | \(-0.929787\pi\) | ||
0.975770 | − | 0.218797i | \(-0.0702134\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 1.73205i | 0.142857 | + | 0.247436i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.00000 | −0.840168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.46410 | −0.887913 | −0.443956 | − | 0.896048i | \(-0.646425\pi\) | ||||
−0.443956 | + | 0.896048i | \(0.646425\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.50000 | − | 2.59808i | −0.202260 | − | 0.350325i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 17.6603i | − | 2.33916i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.00000 | − | 5.19615i | −1.17170 | − | 0.676481i | −0.217620 | − | 0.976034i | \(-0.569829\pi\) |
−0.954080 | + | 0.299552i | \(0.903163\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.09808 | − | 3.63397i | 0.268631 | − | 0.465283i | −0.699877 | − | 0.714263i | \(-0.746762\pi\) |
0.968509 | + | 0.248980i | \(0.0800954\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.5981 | + | 6.69615i | −1.46122 | + | 0.843636i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.866025 | − | 3.50000i | 0.107417 | − | 0.434122i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.46410 | − | 6.00000i | 0.417029 | − | 0.722315i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.19615 | − | 3.00000i | −0.616670 | − | 0.356034i | 0.158901 | − | 0.987294i | \(-0.449205\pi\) |
−0.775571 | + | 0.631260i | \(0.782538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.66025i | − | 0.662483i | −0.943546 | − | 0.331241i | \(-0.892533\pi\) | ||
0.943546 | − | 0.331241i | \(-0.107467\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.36603 | + | 2.36603i | 0.157735 | + | 0.273205i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.00000 | 1.02565 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.19615 | −0.697122 | −0.348561 | − | 0.937286i | \(-0.613330\pi\) | ||||
−0.348561 | + | 0.937286i | \(0.613330\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.23205 | + | 2.13397i | 0.136895 | + | 0.237108i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.19615i | − | 0.241059i | −0.992710 | − | 0.120530i | \(-0.961541\pi\) | ||
0.992710 | − | 0.120530i | \(-0.0384592\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.90192 | − | 1.09808i | −0.206293 | − | 0.119103i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.9282 | − | 22.3923i | 1.38605 | − | 2.40071i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.8923 | + | 8.59808i | −1.57858 | + | 0.911394i | −0.583523 | + | 0.812096i | \(0.698326\pi\) |
−0.995058 | + | 0.0992979i | \(0.968340\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.79423 | + | 7.50000i | 0.817057 | + | 0.786214i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.00000 | + | 1.73205i | −0.311086 | + | 0.179605i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.23205 | − | 5.59808i | 0.331601 | − | 0.574351i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.0981 | + | 7.56218i | 1.32991 | + | 0.767823i | 0.985285 | − | 0.170918i | \(-0.0546734\pi\) |
0.344623 | + | 0.938741i | \(0.388007\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.3923i | 1.34598i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.63397 | − | 6.29423i | −0.361594 | − | 0.626299i | 0.626629 | − | 0.779317i | \(-0.284434\pi\) |
−0.988223 | + | 0.153018i | \(0.951101\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.19615 | −0.117860 | −0.0589302 | − | 0.998262i | \(-0.518769\pi\) | ||||
−0.0589302 | + | 0.998262i | \(0.518769\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.19615 | −0.799863 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.169873 | + | 0.294229i | 0.0164222 | + | 0.0284442i | 0.874120 | − | 0.485710i | \(-0.161439\pi\) |
−0.857697 | + | 0.514155i | \(0.828106\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 15.4641i | − | 1.48119i | −0.671950 | − | 0.740596i | \(-0.734543\pi\) | ||
0.671950 | − | 0.740596i | \(-0.265457\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26.4904 | − | 15.2942i | −2.51436 | − | 1.45166i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.46410 | − | 6.00000i | 0.325875 | − | 0.564433i | −0.655814 | − | 0.754923i | \(-0.727674\pi\) |
0.981689 | + | 0.190490i | \(0.0610077\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.19615 | − | 1.26795i | 0.204792 | − | 0.118237i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.1603 | + | 11.5981i | −1.03177 | + | 1.07224i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.70577 | − | 3.29423i | 0.523047 | − | 0.301981i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | + | 1.73205i | −0.0909091 | + | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 24.5885 | + | 14.1962i | 2.21707 | + | 1.28002i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.5981 | + | 18.3564i | 0.940427 | + | 1.62887i | 0.764658 | + | 0.644436i | \(0.222908\pi\) |
0.175769 | + | 0.984431i | \(0.443759\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.46410 | −0.481087 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.1244 | 1.58353 | 0.791766 | − | 0.610824i | \(-0.209162\pi\) | ||||
0.791766 | + | 0.610824i | \(0.209162\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.69615 | + | 16.7942i | 0.840763 | + | 1.45624i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 4.00000i | − | 0.344265i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.09808 | + | 4.09808i | 0.606430 | + | 0.350122i | 0.771567 | − | 0.636148i | \(-0.219473\pi\) |
−0.165137 | + | 0.986271i | \(0.552807\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.59808 | + | 7.96410i | −0.390004 | + | 0.675506i | −0.992450 | − | 0.122653i | \(-0.960860\pi\) |
0.602446 | + | 0.798160i | \(0.294193\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.09808 | + | 4.09808i | −0.597766 | + | 0.345120i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.3923 | − | 3.00000i | 0.869048 | − | 0.250873i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.19615 | − | 4.73205i | 0.680653 | − | 0.392975i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.73205 | − | 4.73205i | 0.225336 | − | 0.390293i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.19615 | − | 3.00000i | −0.425685 | − | 0.245770i | 0.271821 | − | 0.962348i | \(-0.412374\pi\) |
−0.697507 | + | 0.716578i | \(0.745707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.33975i | 0.515921i | 0.966155 | + | 0.257961i | \(0.0830505\pi\) | ||||
−0.966155 | + | 0.257961i | \(0.916950\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.90192 | + | 8.49038i | 0.396297 | + | 0.686407i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.26795 | −0.101844 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.0000 | −1.03751 | −0.518756 | − | 0.854922i | \(-0.673605\pi\) | ||||
−0.518756 | + | 0.854922i | \(0.673605\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.83013 | + | 15.2942i | 0.700275 | + | 1.21291i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.60770i | 0.599570i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.29423 | − | 3.63397i | −0.493002 | − | 0.284635i | 0.232817 | − | 0.972521i | \(-0.425206\pi\) |
−0.725819 | + | 0.687886i | \(0.758539\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.09808 | + | 7.09808i | −0.319035 | + | 0.552584i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.59808 | − | 1.50000i | 0.201045 | − | 0.116073i | −0.396098 | − | 0.918208i | \(-0.629636\pi\) |
0.597143 | + | 0.802135i | \(0.296303\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | + | 6.06218i | 0.884615 | + | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.9904 | + | 14.4282i | −1.91106 | + | 1.10335i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.50000 | − | 12.9904i | 0.570214 | − | 0.987640i | −0.426329 | − | 0.904568i | \(-0.640193\pi\) |
0.996544 | − | 0.0830722i | \(-0.0264732\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.59808 | − | 1.50000i | −0.196396 | − | 0.113389i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 28.3923i | 2.13410i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.26795 | − | 2.19615i | −0.0947710 | − | 0.164148i | 0.814742 | − | 0.579824i | \(-0.196879\pi\) |
−0.909513 | + | 0.415675i | \(0.863545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.5885 | −1.23301 | −0.616505 | − | 0.787351i | \(-0.711452\pi\) | ||||
−0.616505 | + | 0.787351i | \(0.711452\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.4641 | −0.847451 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.59808 | − | 9.69615i | −0.411579 | − | 0.712875i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.58846i | − | 0.481796i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.3923 | + | 6.00000i | 0.755929 | + | 0.436436i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.63397 | + | 16.6865i | −0.697090 | + | 1.20740i | 0.272381 | + | 0.962189i | \(0.412189\pi\) |
−0.969471 | + | 0.245206i | \(0.921144\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.80385 | + | 2.19615i | −0.273807 | + | 0.158083i | −0.630616 | − | 0.776095i | \(-0.717198\pi\) |
0.356809 | + | 0.934177i | \(0.383865\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.46410 | + | 2.73205i | −0.677738 | + | 0.195646i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.30385 | − | 4.79423i | 0.591625 | − | 0.341575i | −0.174115 | − | 0.984725i | \(-0.555706\pi\) |
0.765740 | + | 0.643151i | \(0.222373\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.19615 | − | 12.4641i | 0.510122 | − | 0.883557i | −0.489810 | − | 0.871829i | \(-0.662934\pi\) |
0.999931 | − | 0.0117273i | \(-0.00373299\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 28.3923i | 1.99275i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.19615 | + | 9.00000i | 0.362915 | + | 0.628587i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.3205 | −0.786830 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.3923 | 1.34139 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.79423 | + | 11.7679i | 0.467734 | + | 0.810139i | 0.999320 | − | 0.0368651i | \(-0.0117372\pi\) |
−0.531586 | + | 0.847004i | \(0.678404\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.3923i | 1.12318i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.73205 | − | 1.00000i | −0.118125 | − | 0.0681994i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.90192 | − | 3.29423i | 0.129111 | − | 0.223627i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.3923 | + | 7.73205i | −0.904968 | + | 0.522484i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.49038 | − | 5.70577i | 0.369323 | − | 0.383812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.401924 | − | 0.232051i | 0.0269148 | − | 0.0155393i | −0.486482 | − | 0.873690i | \(-0.661720\pi\) |
0.513397 | + | 0.858151i | \(0.328387\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.23205 | − | 3.86603i | 0.148803 | − | 0.257735i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.80385 | − | 2.19615i | −0.252470 | − | 0.145764i | 0.368425 | − | 0.929658i | \(-0.379897\pi\) |
−0.620895 | + | 0.783894i | \(0.713231\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4.73205i | − | 0.312703i | −0.987701 | − | 0.156351i | \(-0.950027\pi\) | ||
0.987701 | − | 0.156351i | \(-0.0499732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.2942 | − | 21.2942i | −0.808901 | − | 1.40106i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.26795 | 0.0830661 | 0.0415331 | − | 0.999137i | \(-0.486776\pi\) | ||||
0.0415331 | + | 0.999137i | \(0.486776\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.00000 | −0.195698 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.46410 | + | 14.6603i | 0.549802 | + | 0.952286i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.19615i | 0.530165i | 0.964226 | + | 0.265083i | \(0.0853992\pi\) | ||||
−0.964226 | + | 0.265083i | \(0.914601\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.50000 | − | 4.33013i | −0.483117 | − | 0.278928i | 0.238597 | − | 0.971119i | \(-0.423312\pi\) |
−0.721715 | + | 0.692191i | \(0.756646\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.36603 | − | 16.2224i | 0.600831 | − | 1.04067i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.73205 | − | 1.00000i | 0.110657 | − | 0.0638877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.7942 | + | 16.1603i | 1.06859 | + | 1.02825i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.19615 | + | 3.00000i | −0.329293 | + | 0.190117i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.40192 | − | 5.89230i | 0.214728 | − | 0.371919i | −0.738461 | − | 0.674296i | \(-0.764447\pi\) |
0.953188 | + | 0.302378i | \(0.0977803\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.58846 | + | 3.80385i | 0.414213 | + | 0.239146i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.00000i | 0.375735i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.92820 | − | 12.0000i | −0.432169 | − | 0.748539i | 0.564890 | − | 0.825166i | \(-0.308918\pi\) |
−0.997060 | + | 0.0766265i | \(0.975585\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 33.5885 | 2.08709 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −42.2487 | −2.61513 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.7942 | − | 23.8923i | −0.850589 | − | 1.47326i | −0.880678 | − | 0.473715i | \(-0.842913\pi\) |
0.0300894 | − | 0.999547i | \(-0.490421\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.46410i | 0.397087i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 40.6865 | + | 23.4904i | 2.48998 | + | 1.43759i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.43782 | − | 2.49038i | 0.0876656 | − | 0.151841i | −0.818858 | − | 0.573996i | \(-0.805393\pi\) |
0.906524 | + | 0.422154i | \(0.138726\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.19615 | − | 1.26795i | 0.133407 | − | 0.0770224i | −0.431811 | − | 0.901964i | \(-0.642125\pi\) |
0.565218 | + | 0.824942i | \(0.308792\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.09808 | − | 28.6865i | 0.429595 | − | 1.73619i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.59808 | + | 1.50000i | −0.156670 | + | 0.0904534i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.500000 | − | 0.866025i | 0.0300421 | − | 0.0520344i | −0.850613 | − | 0.525792i | \(-0.823769\pi\) |
0.880656 | + | 0.473757i | \(0.157103\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.90192 | + | 2.83013i | 0.293471 | + | 0.169435i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3923i | 0.619953i | 0.950744 | + | 0.309976i | \(0.100321\pi\) | ||||
−0.950744 | + | 0.309976i | \(0.899679\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.1962 | − | 26.3205i | −0.903317 | − | 1.56459i | −0.823160 | − | 0.567810i | \(-0.807791\pi\) |
−0.0801576 | − | 0.996782i | \(-0.525542\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.6603 | −1.04610 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −31.1769 | −1.84032 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.08846 | + | 10.5455i | 0.358145 | + | 0.620325i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 41.3205i | − | 2.42225i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.696152 | − | 0.401924i | −0.0406697 | − | 0.0234806i | 0.479527 | − | 0.877527i | \(-0.340808\pi\) |
−0.520197 | + | 0.854046i | \(0.674141\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.19615 | + | 9.00000i | −0.302532 | + | 0.524000i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.3923 | − | 6.00000i | 0.603023 | − | 0.348155i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.53590 | + | 8.78461i | 0.146655 | + | 0.508027i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.19615 | − | 3.00000i | 0.299501 | − | 0.172917i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.92820 | + | 17.1962i | −0.570360 | + | 0.987893i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.63397 | − | 2.09808i | −0.208081 | − | 0.120135i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.5359i | 1.17205i | 0.810295 | + | 0.586023i | \(0.199307\pi\) | ||||
−0.810295 | + | 0.586023i | \(0.800693\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.63397 | + | 2.83013i | 0.0929536 | + | 0.161000i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.1244 | −0.857624 | −0.428812 | − | 0.903394i | \(-0.641068\pi\) | ||||
−0.428812 | + | 0.903394i | \(0.641068\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.60770 | 0.316966 | 0.158483 | − | 0.987362i | \(-0.449340\pi\) | ||||
0.158483 | + | 0.987362i | \(0.449340\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.69615 | + | 11.5981i | 0.377285 | + | 0.653478i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 12.8038i | − | 0.719136i | −0.933119 | − | 0.359568i | \(-0.882924\pi\) | ||
0.933119 | − | 0.359568i | \(-0.117076\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.5885 | + | 14.1962i | 1.37669 | + | 0.794832i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.464102 | − | 0.803848i | 0.0259036 | − | 0.0448664i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.2942 | − | 7.09808i | 0.684069 | − | 0.394948i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.50000 | − | 0.866025i | −0.194145 | − | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −36.5885 | + | 21.1244i | −2.02335 | + | 1.16818i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.50000 | − | 7.79423i | 0.248093 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.803848 | − | 0.464102i | −0.0441835 | − | 0.0255093i | 0.477746 | − | 0.878498i | \(-0.341454\pi\) |
−0.521929 | + | 0.852989i | \(0.674787\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 49.9808i | 2.73893i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.19615 | −0.228579 | −0.114289 | − | 0.993447i | \(-0.536459\pi\) | ||||
−0.114289 | + | 0.993447i | \(0.536459\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.9282 | −1.02804 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.90192 | − | 3.29423i | −0.102995 | − | 0.178392i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 15.0000i | − | 0.809924i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.00000 | − | 3.46410i | −0.323029 | − | 0.186501i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.6340 | + | 21.8827i | −0.678227 | + | 1.17472i | 0.297287 | + | 0.954788i | \(0.403918\pi\) |
−0.975514 | + | 0.219936i | \(0.929415\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.4904 | + | 17.0263i | −1.57858 | + | 0.911396i | −0.583527 | + | 0.812094i | \(0.698328\pi\) |
−0.995057 | + | 0.0993018i | \(0.968339\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.0000 | + | 3.46410i | 0.747265 | + | 0.184900i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.4904 | + | 10.0981i | −0.930919 | + | 0.537466i | −0.887102 | − | 0.461573i | \(-0.847285\pi\) |
−0.0438169 | + | 0.999040i | \(0.513952\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.00000 | + | 5.19615i | −0.159223 | + | 0.275783i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.5885 | − | 9.00000i | −0.825029 | − | 0.476331i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 22.3923i | − | 1.18182i | −0.806737 | − | 0.590910i | \(-0.798769\pi\) | ||
0.806737 | − | 0.590910i | \(-0.201231\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.3923 | + | 19.7321i | 0.599595 | + | 1.03853i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.46410 | 0.286791 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.66025 | −0.296271 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.1962 | − | 22.8564i | −0.688834 | − | 1.19309i | −0.972216 | − | 0.234088i | \(-0.924790\pi\) |
0.283382 | − | 0.959007i | \(-0.408544\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 46.3923i | − | 2.41509i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.7942 | − | 9.69615i | −0.871913 | − | 0.503399i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.1962 | + | 17.6603i | −0.527937 | + | 0.914413i | 0.471533 | + | 0.881848i | \(0.343701\pi\) |
−0.999470 | + | 0.0325648i | \(0.989632\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.36603 | − | 1.36603i | 0.122181 | − | 0.0705412i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.46410 | + | 32.7846i | 0.487426 | + | 1.68849i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.2058 | + | 5.89230i | −0.524235 | + | 0.302667i | −0.738666 | − | 0.674072i | \(-0.764544\pi\) |
0.214430 | + | 0.976739i | \(0.431210\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 28.9545 | − | 50.1506i | 1.48338 | − | 2.56929i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.39230 | + | 0.803848i | 0.0711435 | + | 0.0410747i | 0.535150 | − | 0.844757i | \(-0.320255\pi\) |
−0.464006 | + | 0.885832i | \(0.653589\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 9.00000i | − | 0.458682i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.46410 | + | 7.73205i | 0.226923 | + | 0.393042i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.2679 | 0.976924 | 0.488462 | − | 0.872585i | \(-0.337558\pi\) | ||||
0.488462 | + | 0.872585i | \(0.337558\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.56922 | 0.281648 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.7583 | − | 42.8827i | −1.24889 | − | 2.16315i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.19615i | 0.311762i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.696152 | + | 0.401924i | 0.0349389 | + | 0.0201720i | 0.517368 | − | 0.855763i | \(-0.326912\pi\) |
−0.482429 | + | 0.875935i | \(0.660245\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 26.4904 | − | 45.8827i | 1.32618 | − | 2.29701i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.50000 | + | 2.59808i | −0.224719 | + | 0.129742i | −0.608134 | − | 0.793835i | \(-0.708081\pi\) |
0.383414 | + | 0.923576i | \(0.374748\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.09808 | − | 4.43782i | 0.0546991 | − | 0.221064i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.13397 | − | 1.23205i | 0.106038 | − | 0.0612211i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.7942 | − | 29.0885i | 0.832459 | − | 1.44186i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.0885 | + | 9.86603i | 0.844970 | + | 0.487844i | 0.858950 | − | 0.512059i | \(-0.171117\pi\) |
−0.0139806 | + | 0.999902i | \(0.504450\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 22.3923i | − | 1.10453i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.5885 | − | 27.0000i | −0.767058 | − | 1.32858i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.19615 | −0.107805 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.1244 | 1.23034 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.66025 | + | 15.0000i | 0.423081 | + | 0.732798i | 0.996239 | − | 0.0866469i | \(-0.0276152\pi\) |
−0.573158 | + | 0.819445i | \(0.694282\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.1244i | 1.32196i | 0.750403 | + | 0.660980i | \(0.229859\pi\) | ||||
−0.750403 | + | 0.660980i | \(0.770141\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.5981 | + | 6.69615i | 0.563918 | + | 0.325578i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.09808 | + | 1.90192i | −0.0532645 | + | 0.0922569i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.9019 | − | 6.29423i | 0.527581 | − | 0.304599i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21.2942 | − | 20.4904i | −1.02810 | − | 0.989285i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.90192 | − | 1.09808i | 0.0916124 | − | 0.0528925i | −0.453494 | − | 0.891259i | \(-0.649823\pi\) |
0.545106 | + | 0.838367i | \(0.316489\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.19615 | − | 10.7321i | 0.297768 | − | 0.515749i | −0.677857 | − | 0.735194i | \(-0.737091\pi\) |
0.975625 | + | 0.219444i | \(0.0704245\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.3923 | − | 12.9282i | −1.07363 | − | 0.619860i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.3923i | 0.784150i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.2942 | − | 29.9545i | −0.825408 | − | 1.42965i | −0.901607 | − | 0.432557i | \(-0.857612\pi\) |
0.0761982 | − | 0.997093i | \(-0.475722\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.92820 | −0.425153 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.60770 | 0.0763839 | 0.0381920 | − | 0.999270i | \(-0.487840\pi\) | ||||
0.0381920 | + | 0.999270i | \(0.487840\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.59808 | + | 14.8923i | 0.407588 | + | 0.705963i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.3923i | 0.775329i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.5000 | + | 7.79423i | 0.637104 | + | 0.367832i | 0.783498 | − | 0.621394i | \(-0.213433\pi\) |
−0.146394 | + | 0.989226i | \(0.546767\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.5885 | + | 27.0000i | −0.734032 | + | 1.27138i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.0000 | − | 8.66025i | 0.704761 | − | 0.406894i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.50000 | − | 7.79423i | 0.351605 | − | 0.365399i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.8827 | + | 17.8301i | −1.44463 | + | 0.834058i | −0.998154 | − | 0.0607368i | \(-0.980655\pi\) |
−0.446477 | + | 0.894795i | \(0.647322\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.39230 | − | 7.60770i | 0.205015 | − | 0.355097i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.509619 | − | 0.294229i | −0.0237353 | − | 0.0137036i | 0.488085 | − | 0.872796i | \(-0.337695\pi\) |
−0.511821 | + | 0.859092i | \(0.671029\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.928203i | 0.0431373i | 0.999767 | + | 0.0215686i | \(0.00686604\pi\) | ||||
−0.999767 | + | 0.0215686i | \(0.993134\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.73205 | + | 3.00000i | 0.0803219 | + | 0.139122i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.1436 | 0.469390 | 0.234695 | − | 0.972069i | \(-0.424591\pi\) | ||||
0.234695 | + | 0.972069i | \(0.424591\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.7583 | + | 30.7583i | 0.818261 | + | 1.41727i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6.00000i | − | 0.275880i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.59808 | − | 3.23205i | −0.256857 | − | 0.148297i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.4282 | − | 24.9904i | 0.660622 | − | 1.14423i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.50962 | − | 5.49038i | 0.434506 | − | 0.250862i | −0.266759 | − | 0.963763i | \(-0.585953\pi\) |
0.701264 | + | 0.712901i | \(0.252619\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 38.7846 | − | 11.1962i | 1.76843 | − | 0.510501i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.0000 | − | 10.3923i | 0.819028 | − | 0.472866i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.56218 | − | 13.0981i | 0.343381 | − | 0.594753i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.7942 | + | 16.6244i | 1.30479 | + | 0.753321i | 0.981222 | − | 0.192883i | \(-0.0617838\pi\) |
0.323569 | + | 0.946204i | \(0.395117\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.8564i | 0.897938i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.66987 | + | 2.89230i | 0.0753603 | + | 0.130528i | 0.901243 | − | 0.433314i | \(-0.142656\pi\) |
−0.825883 | + | 0.563842i | \(0.809323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.7846 | 0.936092 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.3923 | 0.601939 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.00000 | − | 15.5885i | −0.403705 | − | 0.699238i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.85641i | 0.0831042i | 0.999136 | + | 0.0415521i | \(0.0132302\pi\) | ||||
−0.999136 | + | 0.0415521i | \(0.986770\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.09808 | − | 4.09808i | −0.317119 | − | 0.183089i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.66987 | + | 8.08846i | −0.208219 | + | 0.360646i | −0.951154 | − | 0.308718i | \(-0.900100\pi\) |
0.742934 | + | 0.669364i | \(0.233433\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.29423 | + | 3.63397i | −0.280089 | + | 0.161710i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.36603 | − | 35.4904i | −0.0606673 | − | 1.57618i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.39230 | − | 0.803848i | 0.0617128 | − | 0.0356299i | −0.468826 | − | 0.883290i | \(-0.655323\pi\) |
0.530539 | + | 0.847661i | \(0.321990\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.49038 | − | 14.7058i | 0.375592 | − | 0.650545i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.3923 | + | 12.9282i | 0.988644 | + | 0.570794i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.19615i | 0.0527088i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.50000 | − | 7.79423i | −0.197910 | − | 0.342790i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −40.9808 | −1.79886 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.464102 | −0.0203327 | −0.0101663 | − | 0.999948i | \(-0.503236\pi\) | ||||
−0.0101663 | + | 0.999948i | \(0.503236\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.19615 | + | 15.9282i | 0.402120 | + | 0.696492i | 0.993982 | − | 0.109548i | \(-0.0349402\pi\) |
−0.591862 | + | 0.806039i | \(0.701607\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.19615i | 0.357709i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.41154 | − | 1.39230i | −0.105048 | − | 0.0606498i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.28461 | − | 14.3494i | 0.360200 | − | 0.623885i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40.1769 | − | 23.1962i | 1.74353 | − | 1.00663i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.0000 | + | 10.3923i | −1.55933 | + | 0.450141i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.294229 | − | 0.169873i | 0.0127206 | − | 0.00734425i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.46410 | + | 6.00000i | −0.149487 | + | 0.258919i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.19615 | + | 3.00000i | 0.223814 | + | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 16.0526i | − | 0.690153i | −0.938574 | − | 0.345077i | \(-0.887853\pi\) | ||
0.938574 | − | 0.345077i | \(-0.112147\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.6603 | + | 39.2487i | 0.972445 | + | 1.68432i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.4641 | −0.662409 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.7846 | −1.48728 | −0.743641 | − | 0.668579i | \(-0.766903\pi\) | ||||
−0.743641 | + | 0.668579i | \(0.766903\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.36603 | + | 16.2224i | 0.399732 | + | 0.692357i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 61.1769i | 2.60622i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.0981 | − | 9.29423i | −0.684560 | − | 0.395231i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.2942 | + | 26.4904i | −0.649204 | + | 1.12445i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.8923 | − | 8.59808i | 0.631007 | − | 0.364312i | −0.150135 | − | 0.988666i | \(-0.547971\pi\) |
0.781142 | + | 0.624353i | \(0.214637\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.00000 | − | 5.19615i | 0.211477 | − | 0.219774i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.5885 | + | 9.00000i | −0.658145 | + | 0.379980i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.7321 | − | 18.5885i | 0.452302 | − | 0.783410i | −0.546227 | − | 0.837637i | \(-0.683936\pi\) |
0.998529 | + | 0.0542274i | \(0.0172696\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.00000 | − | 3.46410i | −0.252422 | − | 0.145736i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.39230i | 0.310448i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.6244 | − | 18.4019i | −0.445396 | − | 0.771449i | 0.552684 | − | 0.833391i | \(-0.313604\pi\) |
−0.998080 | + | 0.0619424i | \(0.980270\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.3731 | −1.43847 | −0.719234 | − | 0.694768i | \(-0.755507\pi\) | ||||
−0.719234 | + | 0.694768i | \(0.755507\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 52.6410 | 2.19911 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.26795 | − | 2.19615i | −0.0528771 | − | 0.0915859i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.4449i | 1.35070i | 0.737499 | + | 0.675349i | \(0.236007\pi\) | ||||
−0.737499 | + | 0.675349i | \(0.763993\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.3923 | + | 6.00000i | 0.431889 | + | 0.249351i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.29423 | − | 5.70577i | 0.136668 | − | 0.236715i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.7942 | + | 9.69615i | −0.695546 | + | 0.401574i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.5981 | + | 11.1603i | 0.479521 | + | 0.461420i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.9808 | − | 15.0000i | 1.07234 | − | 0.619116i | 0.143521 | − | 0.989647i | \(-0.454158\pi\) |
0.928820 | + | 0.370531i | \(0.120824\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.09808 | − | 7.09808i | 0.168858 | − | 0.292471i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.6865 | − | 13.0981i | −0.933199 | − | 0.538783i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.7846i | 0.853522i | 0.904365 | + | 0.426761i | \(0.140345\pi\) | ||||
−0.904365 | + | 0.426761i | \(0.859655\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.29423 | − | 5.70577i | −0.135050 | − | 0.233914i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −39.3205 | −1.60928 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.85641 | −0.321004 | −0.160502 | − | 0.987036i | \(-0.551311\pi\) | ||||
−0.160502 | + | 0.987036i | \(0.551311\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.89230 | − | 3.27757i | −0.0771887 | − | 0.133695i | 0.824847 | − | 0.565356i | \(-0.191261\pi\) |
−0.902036 | + | 0.431661i | \(0.857928\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.73205 | + | 1.00000i | 0.0704179 | + | 0.0406558i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.20577 | + | 5.55256i | −0.130118 | + | 0.225371i | −0.923722 | − | 0.383064i | \(-0.874869\pi\) |
0.793604 | + | 0.608435i | \(0.208202\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 67.1769 | − | 38.7846i | 2.72215 | − | 1.57163i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.59808 | − | 10.5000i | 0.105107 | − | 0.424785i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.3038 | − | 13.4545i | 0.941234 | − | 0.543421i | 0.0508868 | − | 0.998704i | \(-0.483795\pi\) |
0.890347 | + | 0.455283i | \(0.150462\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14.1962 | − | 24.5885i | 0.572444 | − | 0.991502i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.5885 | − | 9.00000i | −0.627568 | − | 0.362326i | 0.152242 | − | 0.988343i | \(-0.451351\pi\) |
−0.779809 | + | 0.626017i | \(0.784684\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.6077i | 0.426359i | 0.977013 | + | 0.213180i | \(0.0683820\pi\) | ||||
−0.977013 | + | 0.213180i | \(0.931618\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.07180 | + | 8.78461i | 0.203524 | + | 0.352514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −51.5885 | −2.06685 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −26.4904 | − | 45.8827i | −1.05792 | − | 1.83238i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 24.5885i | − | 0.980406i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.0000 | + | 10.3923i | 0.716569 | + | 0.413711i | 0.813488 | − | 0.581581i | \(-0.197566\pi\) |
−0.0969198 | + | 0.995292i | \(0.530899\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.5622 | − | 32.1506i | 0.737780 | − | 1.27787i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.3564 | − | 10.5981i | 0.728452 | − | 0.420572i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | + | 6.92820i | 0.0792429 | + | 0.274505i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.1962 | − | 13.3923i | 0.917626 | − | 0.529791i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.9641 | + | 39.7750i | −0.907027 | + | 1.57102i | −0.0888552 | + | 0.996045i | \(0.528321\pi\) |
−0.818172 | + | 0.574973i | \(0.805012\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.29423 | − | 3.63397i | −0.248220 | − | 0.143310i | 0.370729 | − | 0.928741i | \(-0.379108\pi\) |
−0.618949 | + | 0.785431i | \(0.712441\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.46410i | 0.215149i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.59808 | − | 9.69615i | −0.220083 | − | 0.381195i | 0.734750 | − | 0.678338i | \(-0.237300\pi\) |
−0.954833 | + | 0.297143i | \(0.903966\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.1769 | −1.22380 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.3923 | −0.407307 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.69615 | + | 16.7942i | 0.379440 | + | 0.657209i | 0.990981 | − | 0.134004i | \(-0.0427834\pi\) |
−0.611541 | + | 0.791213i | \(0.709450\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 18.1244i | − | 0.708177i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21.8827 | + | 12.6340i | 0.853725 | + | 0.492898i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.6603 | − | 25.3923i | 0.571082 | − | 0.989144i | −0.425373 | − | 0.905018i | \(-0.639857\pi\) |
0.996455 | − | 0.0841255i | \(-0.0268097\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.9019 | − | 14.9545i | 1.00747 | − | 0.581662i | 0.0970187 | − | 0.995283i | \(-0.469069\pi\) |
0.910449 | + | 0.413621i | \(0.135736\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21.0000 | − | 5.19615i | −0.815572 | − | 0.201802i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.7942 | − | 9.69615i | 0.651252 | − | 0.376001i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.0000 | + | 20.7846i | −0.464642 | + | 0.804783i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.09808 | − | 0.633975i | −0.0424541 | − | 0.0245109i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 12.5885i | − | 0.485972i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.80385 | − | 3.12436i | −0.0695332 | − | 0.120435i | 0.829163 | − | 0.559007i | \(-0.188818\pi\) |
−0.898696 | + | 0.438572i | \(0.855484\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.85641 | 0.0713475 | 0.0356737 | − | 0.999363i | \(-0.488642\pi\) | ||||
0.0356737 | + | 0.999363i | \(0.488642\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.6865 | + | 39.2942i | 0.870629 | + | 1.50797i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0000i | 0.459841i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.0000 | − | 15.5885i | −1.03313 | − | 0.596476i | −0.115248 | − | 0.993337i | \(-0.536766\pi\) |
−0.917879 | + | 0.396861i | \(0.870099\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.09808 | − | 7.09808i | 0.156579 | − | 0.271204i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.1962 | + | 6.46410i | −0.427160 | + | 0.246621i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.6244 | − | 5.59808i | −0.861919 | − | 0.213270i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.2058 | − | 9.35641i | 0.616497 | − | 0.355934i | −0.159007 | − | 0.987277i | \(-0.550829\pi\) |
0.775504 | + | 0.631343i | \(0.217496\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −20.0885 | + | 34.7942i | −0.763097 | + | 1.32172i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.96410 | + | 4.59808i | 0.302096 | + | 0.174415i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.8231i | 0.864486i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.73205 | − | 3.00000i | −0.0655122 | − | 0.113470i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.9090 | −1.12965 | −0.564823 | − | 0.825212i | \(-0.691056\pi\) | ||||
−0.564823 | + | 0.825212i | \(0.691056\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 72.3731 | 2.72960 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.09808 | + | 7.09808i | 0.154342 | + | 0.267329i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 21.8038i | − | 0.820018i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.4904 | + | 20.4904i | 1.33287 | + | 0.769532i | 0.985738 | − | 0.168284i | \(-0.0538227\pi\) |
0.347131 | + | 0.937817i | \(0.387156\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.8301 | − | 23.9545i | 0.518670 | − | 0.898363i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.78461 | − | 1.60770i | 0.104284 | − | 0.0602087i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.00000 | − | 10.3923i | −0.112194 | − | 0.388650i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.3923 | − | 11.1962i | 0.724219 | − | 0.418128i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.928203 | + | 1.60770i | −0.0346161 | + | 0.0599569i | −0.882814 | − | 0.469722i | \(-0.844354\pi\) |
0.848198 | + | 0.529679i | \(0.177688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.10770 | − | 1.79423i | −0.115737 | − | 0.0668206i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.6603i | 0.879934i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.73205 | − | 8.19615i | −0.175744 | − | 0.304397i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.3731 | 1.42318 | 0.711589 | − | 0.702596i | \(-0.247976\pi\) | ||||
0.711589 | + | 0.702596i | \(0.247976\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.19615 | − | 3.80385i | −0.0812276 | − | 0.140690i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 50.9090i | − | 1.88037i | −0.340670 | − | 0.940183i | \(-0.610654\pi\) | ||
0.340670 | − | 0.940183i | \(-0.389346\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.73205 | − | 2.73205i | −0.174544 | − | 0.100773i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.7942 | + | 25.2846i | −1.61100 | + | 0.930109i | −0.621857 | + | 0.783131i | \(0.713622\pi\) |
−0.989140 | + | 0.146979i | \(0.953045\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.2942 | − | 61.8109i | 0.561848 | − | 2.27068i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.7846 | + | 17.1962i | −1.09269 | + | 0.630866i | −0.934292 | − | 0.356509i | \(-0.883967\pi\) |
−0.158400 | + | 0.987375i | \(0.550633\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.00000 | + | 5.19615i | −0.109911 | + | 0.190372i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.49038 | + | 4.90192i | 0.310647 | + | 0.179352i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.01924i | 0.0372421i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.196152 | + | 0.339746i | 0.00715770 | + | 0.0123975i | 0.869582 | − | 0.493788i | \(-0.164388\pi\) |
−0.862424 | + | 0.506186i | \(0.831055\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.5885 | −0.677401 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.33975 | 0.230727 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.89230 | − | 3.27757i | −0.0687770 | − | 0.119125i | 0.829586 | − | 0.558379i | \(-0.188576\pi\) |
−0.898363 | + | 0.439253i | \(0.855243\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 20.7846i | − | 0.754434i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.2846 | − | 14.5981i | −0.916566 | − | 0.529180i | −0.0340283 | − | 0.999421i | \(-0.510834\pi\) |
−0.882538 | + | 0.470241i | \(0.844167\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.1962 | − | 40.1769i | 0.839757 | − | 1.45450i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.49038 | − | 4.90192i | 0.306970 | − | 0.177229i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.0000 | − | 25.9808i | −0.974913 | − | 0.938111i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.0000 | + | 19.0526i | −1.19001 | + | 0.687053i | −0.958309 | − | 0.285734i | \(-0.907763\pi\) |
−0.231701 | + | 0.972787i | \(0.574429\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.9282 | + | 32.7846i | −0.681683 | + | 1.18071i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.0885 | − | 16.7942i | −1.04624 | − | 0.604046i | −0.124645 | − | 0.992201i | \(-0.539779\pi\) |
−0.921594 | + | 0.388155i | \(0.873113\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.26795i | 0.0455461i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −45.8827 | − | 79.4711i | −1.64603 | − | 2.85101i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −67.1769 | −2.40686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | −0.644091 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.9282 | + | 32.7846i | 0.676439 | + | 1.17163i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.0000i | 0.463990i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.9019 | + | 18.4186i | 1.13718 | + | 0.656552i | 0.945731 | − | 0.324951i | \(-0.105348\pi\) |
0.191450 | + | 0.981502i | \(0.438681\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −37.6865 | + | 65.2750i | −1.34168 | + | 2.32385i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.0000 | − | 10.3923i | 0.640006 | − | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.4904 | − | 10.9019i | 0.372524 | − | 0.387139i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.2942 | − | 8.83013i | 0.542430 | − | 0.313172i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.464102 | + | 0.803848i | −0.0164393 | + | 0.0284737i | −0.874128 | − | 0.485696i | \(-0.838566\pi\) |
0.857689 | + | 0.514169i | \(0.171900\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.70577 | − | 3.29423i | −0.201856 | − | 0.116541i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 76.7654i | − | 2.71237i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.49038 | − | 14.7058i | −0.299619 | − | 0.518955i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.60770 | 0.268136 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.85641 | −0.276559 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.0000 | − | 20.7846i | −0.421898 | − | 0.730748i | 0.574228 | − | 0.818696i | \(-0.305302\pi\) |
−0.996125 | + | 0.0879478i | \(0.971969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22.6077i | − | 0.793864i | −0.917848 | − | 0.396932i | \(-0.870075\pi\) | ||
0.917848 | − | 0.396932i | \(-0.129925\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.00000 | − | 3.46410i | −0.210429 | − | 0.121491i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.63397 | + | 6.29423i | −0.127293 | + | 0.220477i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.1962 | − | 6.46410i | 0.391704 | − | 0.226150i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −46.3923 | + | 13.3923i | −1.62108 | + | 0.467965i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.49038 | + | 4.90192i | −0.296316 | + | 0.171078i | −0.640787 | − | 0.767719i | \(-0.721392\pi\) |
0.344471 | + | 0.938797i | \(0.388058\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.40192 | + | 14.5526i | −0.292873 | + | 0.507270i | −0.974488 | − | 0.224441i | \(-0.927945\pi\) |
0.681615 | + | 0.731711i | \(0.261278\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.09808 | + | 4.09808i | 0.247123 | + | 0.142677i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.4115i | 0.396818i | 0.980119 | + | 0.198409i | \(0.0635775\pi\) | ||||
−0.980119 | + | 0.198409i | \(0.936423\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.0000 | + | 17.3205i | 0.347314 | + | 0.601566i | 0.985771 | − | 0.168091i | \(-0.0537604\pi\) |
−0.638457 | + | 0.769657i | \(0.720427\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.73205 | −0.0947738 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.39230 | 0.152184 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.50000 | − | 2.59808i | −0.0519096 | − | 0.0899101i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 5.07180i | − | 0.175307i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.8827 | + | 16.0981i | 0.962617 | + | 0.555767i | 0.896978 | − | 0.442076i | \(-0.145758\pi\) |
0.0656397 | + | 0.997843i | \(0.479091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.2846 | + | 52.4545i | −1.04430 | + | 1.80878i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.5885 | − | 14.1962i | 0.846871 | − | 0.488941i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.06218 | − | 11.5000i | 0.208545 | − | 0.395612i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.19615 | + | 3.00000i | −0.178542 | + | 0.103081i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −41.5167 | + | 71.9090i | −1.42485 | + | 2.46791i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.5885 | + | 14.1962i | 0.842881 | + | 0.486638i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 13.8564i | − | 0.474434i | −0.971457 | − | 0.237217i | \(-0.923765\pi\) | ||
0.971457 | − | 0.237217i | \(-0.0762353\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.4282 | + | 24.9904i | 0.493434 | + | 0.854653i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.2679 | −0.453225 | −0.226612 | − | 0.973985i | \(-0.572765\pi\) | ||||
−0.226612 | + | 0.973985i | \(0.572765\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.3731 | −1.78695 | −0.893473 | − | 0.449117i | \(-0.851739\pi\) | ||||
−0.893473 | + | 0.449117i | \(0.851739\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 42.5885 | + | 73.7654i | 1.45141 | + | 2.51392i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.1769i | 0.652790i | 0.945234 | + | 0.326395i | \(0.105834\pi\) | ||||
−0.945234 | + | 0.326395i | \(0.894166\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.9904 | − | 7.50000i | −0.441686 | − | 0.255008i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.6340 | − | 28.8109i | 0.564919 | − | 0.978469i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.0981 | + | 9.29423i | −0.546090 | + | 0.315285i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −58.4711 | + | 33.7583i | −1.97895 | + | 1.14255i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.50000 | + | 2.59808i | −0.0507093 | + | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.7846 | + | 10.2679i | 0.600544 | + | 0.346724i | 0.769255 | − | 0.638941i | \(-0.220627\pi\) |
−0.168712 | + | 0.985665i | \(0.553961\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.19615i | 0.0740744i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.16025 | + | 7.20577i | 0.140163 | + | 0.242769i | 0.927558 | − | 0.373680i | \(-0.121904\pi\) |
−0.787395 | + | 0.616449i | \(0.788571\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.5885 | 0.894773 | 0.447386 | − | 0.894341i | \(-0.352355\pi\) | ||||
0.447386 | + | 0.894341i | \(0.352355\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.3923 | 0.954397 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.3827 | + | 45.6962i | 0.885844 | + | 1.53433i | 0.844743 | + | 0.535172i | \(0.179753\pi\) |
0.0411005 | + | 0.999155i | \(0.486914\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 63.5885i | 2.13269i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.40192 | + | 3.69615i | 0.214473 | + | 0.123826i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.69615 | − | 16.7942i | 0.324469 | − | 0.561997i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.19615 | + | 1.26795i | −0.0734093 | + | 0.0423829i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.3205 | − | 18.0000i | 0.578315 | − | 0.601003i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.3923 | − | 6.00000i | 0.346603 | − | 0.200111i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.09808 | + | 12.2942i | −0.236471 | + | 0.409580i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.1962 | − | 8.19615i | −0.472418 | − | 0.272751i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.5885i | 0.551419i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.2942 | − | 23.0263i | −0.441428 | − | 0.764575i | 0.556368 | − | 0.830936i | \(-0.312194\pi\) |
−0.997796 | + | 0.0663609i | \(0.978861\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 32.4449 | 1.07613 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.5359 | 0.481596 | 0.240798 | − | 0.970575i | \(-0.422591\pi\) | ||||
0.240798 | + | 0.970575i | \(0.422591\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.29423 | − | 5.70577i | −0.109023 | − | 0.188833i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.4641i | 0.378992i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 47.0885 | + | 27.1865i | 1.55500 | + | 0.897778i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.39230 | + | 9.33975i | −0.177876 | + | 0.308090i | −0.941153 | − | 0.337982i | \(-0.890256\pi\) |
0.763277 | + | 0.646071i | \(0.223589\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 48.5885 | − | 28.0526i | 1.60104 | − | 0.924363i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.5885 | − | 15.0000i | −0.513100 | − | 0.493731i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.69615 | + | 5.59808i | −0.318808 | + | 0.184064i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.66987 | − | 4.62436i | 0.0876901 | − | 0.151884i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.7846 | + | 22.3923i | 1.27248 | + | 0.734668i | 0.975454 | − | 0.220201i | \(-0.0706714\pi\) |
0.297027 | + | 0.954869i | \(0.404005\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.9282i | 0.423705i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.6603 | + | 35.7846i | 0.676386 | + | 1.17154i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.58846 | −0.215466 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.3923 | −0.992873 | −0.496437 | − | 0.868073i | \(-0.665359\pi\) | ||||
−0.496437 | + | 0.868073i | \(0.665359\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.66025 | − | 13.2679i | −0.249983 | − | 0.432983i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44.7846i | 1.45994i | 0.683481 | + | 0.729968i | \(0.260465\pi\) | ||||
−0.683481 | + | 0.729968i | \(0.739535\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.8231 | − | 13.1769i | −0.743222 | − | 0.429099i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.00000 | − | 10.3923i | 0.195180 | − | 0.338062i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49.6865 | + | 28.6865i | −1.61460 | + | 0.932187i | −0.626309 | + | 0.779575i | \(0.715435\pi\) |
−0.988286 | + | 0.152612i | \(0.951231\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.90192 | − | 19.8109i | 0.159123 | − | 0.643089i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.2942 | + | 17.4904i | −0.982358 | + | 0.567164i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.2942 | + | 21.2942i | −0.398249 | + | 0.689788i | −0.993510 | − | 0.113745i | \(-0.963715\pi\) |
0.595261 | + | 0.803533i | \(0.297049\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.6865 | + | 9.63397i | 0.539964 | + | 0.311748i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 77.5692i | − | 2.50746i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.2942 | + | 21.2942i | 0.397001 | + | 0.687627i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.3923 | 0.948139 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.51666 | −0.0488737 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.19615 | + | 3.80385i | 0.0706966 | + | 0.122450i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 38.5692i | − | 1.24030i | −0.784482 | − | 0.620151i | \(-0.787071\pi\) | ||
0.784482 | − | 0.620151i | \(-0.212929\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −33.5885 | − | 19.3923i | −1.07902 | − | 0.622971i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.3827 | + | 40.5000i | −0.750386 | + | 1.29971i | 0.197250 | + | 0.980353i | \(0.436799\pi\) |
−0.947636 | + | 0.319354i | \(0.896534\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.8923 | + | 13.7942i | −0.765952 | + | 0.442223i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.73205 | + | 9.46410i | 0.0874957 | + | 0.303094i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.80385 | − | 2.19615i | 0.121696 | − | 0.0702611i | −0.437916 | − | 0.899016i | \(-0.644283\pi\) |
0.559612 | + | 0.828755i | \(0.310950\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.7942 | + | 44.6769i | −0.824387 | + | 1.42788i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 59.7846 | + | 34.5167i | 1.90878 | + | 1.10203i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.5692i | 1.23017i | 0.788462 | + | 0.615084i | \(0.210878\pi\) | ||||
−0.788462 | + | 0.615084i | \(0.789122\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.79423 | − | 8.30385i | −0.152757 | − | 0.264583i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.5885 | −0.782659 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.07180 | 0.161274 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.5885 | + | 44.3205i | 0.812844 | + | 1.40789i | 0.910866 | + | 0.412703i | \(0.135415\pi\) |
−0.0980215 | + | 0.995184i | \(0.531251\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.53590i | 0.0804743i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.4641 | − | 7.19615i | −0.395139 | − | 0.228133i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.2846 | − | 36.8660i | 0.674090 | − | 1.16756i | −0.302644 | − | 0.953104i | \(-0.597869\pi\) |
0.976734 | − | 0.214455i | \(-0.0687975\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 38.7846 | − | 22.3923i | 1.22709 | − | 0.708461i |
(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 | 1040.2.da.a.881.1 | 4 | ||
4.3 | odd | 2 | 130.2.l.a.101.2 | ✓ | 4 | ||
12.11 | even | 2 | 1170.2.bs.c.361.1 | 4 | |||
13.4 | even | 6 | inner | 1040.2.da.a.641.1 | 4 | ||
20.3 | even | 4 | 650.2.n.a.49.1 | 4 | |||
20.7 | even | 4 | 650.2.n.b.49.2 | 4 | |||
20.19 | odd | 2 | 650.2.m.a.101.1 | 4 | |||
52.3 | odd | 6 | 1690.2.d.f.1351.3 | 4 | |||
52.7 | even | 12 | 1690.2.e.n.191.2 | 4 | |||
52.11 | even | 12 | 1690.2.a.j.1.1 | 2 | |||
52.15 | even | 12 | 1690.2.a.m.1.1 | 2 | |||
52.19 | even | 12 | 1690.2.e.l.191.2 | 4 | |||
52.23 | odd | 6 | 1690.2.d.f.1351.1 | 4 | |||
52.31 | even | 4 | 1690.2.e.l.991.2 | 4 | |||
52.35 | odd | 6 | 1690.2.l.g.1161.1 | 4 | |||
52.43 | odd | 6 | 130.2.l.a.121.2 | yes | 4 | ||
52.47 | even | 4 | 1690.2.e.n.991.2 | 4 | |||
52.51 | odd | 2 | 1690.2.l.g.361.1 | 4 | |||
156.95 | even | 6 | 1170.2.bs.c.901.1 | 4 | |||
260.43 | even | 12 | 650.2.n.b.199.2 | 4 | |||
260.119 | even | 12 | 8450.2.a.bf.1.2 | 2 | |||
260.147 | even | 12 | 650.2.n.a.199.1 | 4 | |||
260.199 | odd | 6 | 650.2.m.a.251.1 | 4 | |||
260.219 | even | 12 | 8450.2.a.bm.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.l.a.101.2 | ✓ | 4 | 4.3 | odd | 2 | ||
130.2.l.a.121.2 | yes | 4 | 52.43 | odd | 6 | ||
650.2.m.a.101.1 | 4 | 20.19 | odd | 2 | |||
650.2.m.a.251.1 | 4 | 260.199 | odd | 6 | |||
650.2.n.a.49.1 | 4 | 20.3 | even | 4 | |||
650.2.n.a.199.1 | 4 | 260.147 | even | 12 | |||
650.2.n.b.49.2 | 4 | 20.7 | even | 4 | |||
650.2.n.b.199.2 | 4 | 260.43 | even | 12 | |||
1040.2.da.a.641.1 | 4 | 13.4 | even | 6 | inner | ||
1040.2.da.a.881.1 | 4 | 1.1 | even | 1 | trivial | ||
1170.2.bs.c.361.1 | 4 | 12.11 | even | 2 | |||
1170.2.bs.c.901.1 | 4 | 156.95 | even | 6 | |||
1690.2.a.j.1.1 | 2 | 52.11 | even | 12 | |||
1690.2.a.m.1.1 | 2 | 52.15 | even | 12 | |||
1690.2.d.f.1351.1 | 4 | 52.23 | odd | 6 | |||
1690.2.d.f.1351.3 | 4 | 52.3 | odd | 6 | |||
1690.2.e.l.191.2 | 4 | 52.19 | even | 12 | |||
1690.2.e.l.991.2 | 4 | 52.31 | even | 4 | |||
1690.2.e.n.191.2 | 4 | 52.7 | even | 12 | |||
1690.2.e.n.991.2 | 4 | 52.47 | even | 4 | |||
1690.2.l.g.361.1 | 4 | 52.51 | odd | 2 | |||
1690.2.l.g.1161.1 | 4 | 52.35 | odd | 6 | |||
8450.2.a.bf.1.2 | 2 | 260.119 | even | 12 | |||
8450.2.a.bm.1.2 | 2 | 260.219 | even | 12 |